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LIMDEP Student User Manual

1. Variable Mean Std Dev Minimum Maximum Cases All observations in current sample x 177875E 01 972540 3 14333 3 02263 1000 0 Y 983443 1 42493 162304E 07 11 6616 1000 0 Matrix LastD sta 2 7 Order Statistics for Variables Percentile X Y Min 3 1433 16230E 07 10 1 2680 11610E 01 20 84366 51309E 01 250 68126 83422E 01 30 53522 13160 40 26384 28056 Med 48192E 01 43805 60 25616 71992 70 51574 1 0797 75 65565 1 3230 go 83508 1 6071 90 1 1866 2 5999 ax 3 0226 11 662 Partition of range Minimum to Maximum Range of X X Y inimum 3 1433 16230E 07 1 ortl 1 6018 2 9154 idpoint 60348E 01 5 8308 3 Ortl 1 4811 8 7462 aximum 3 0226 11 662 Matrix LastQntl 13 2 13 4 Describing Sample Data 13 3 Histograms The command for computing and plotting a histogram for a variable is HISTOGRAM Rhs the variable LIMDEP computes two types of histograms for discrete count and for continuous data The default type is for a frequency count of discrete data Data are assumed to be coded 0 1 99 Values less than zero or above 99 are treated as out of range A count of invalid observations is given with the output of the command Continuous variables are assigned to 40 equal width intervals over the range of the variables The histogram is accompanied by a table listing the relative frequencies and c
2. User s Guide by William H Greene Econometric Software Inc 1986 2007 Econometric Software Inc All rights reserved This software product including both the program code and the accompanying documentation is copyrighted by and all rights are reserved by Econometric Software Inc No part of this product either the software or the documentation may be reproduced stored in a retrieval system or transmitted in any form or by any means without prior written permission of Econometric Software Inc LIMDEP and NLOGIT are trademarks of Econometric Software Inc All other brand and product names are trademarks or registered trademarks of their respective companies Econometric Software Inc 15 Gloria Place Plainview NY 11803 USA Tel 1 516 938 5254 Fax 1 516 938 2441 Email sales limdep com Websites www limdep com and www nlogit com Econometric Software Australia 215 Excelsior Avenue Castle Hill NSW 2154 Australia Tel 61 0 418 433 057 Fax 61 0 2 9899 6674 Email hgroup optusnet com au End User License Agreement This is a contract between you and Econometric Software Inc The software product refers to the computer software and documentation as well as any upgrades modified versions copies or supplements supplied by Econometric Software By installing downloading accessing or otherwise using the software product you agree to be bound by the
3. Primary Index Equation for Model Constant 415 387564 44 3490483 366 0000 F 12523697 01598256 964 0000 1081 68110 Cc 25745128 05517398 666 0000 276 017150 Disturbance standard deviation Sigma 170 271654 17 4589668 Matrix Cov Mat has 4 rows and 4 columns 2 1966 83809 41180 49583 14178 46393 02825 516 41180 02825 304 81552 Figure 8 10 Model Output with Covariance Matrix 1 2 3 4 Estimating Models Output Status Trace Begin main iterations for optimization Maximum iterations reached Exit iterations with status ANOVA based fit DECOMP based fit Variable Coeffi Primary ONE 6 99036e 006 0 109852 0 151828 6 98979e 006 6 9901e Constant 62 0 109852 0 000442098 0 000262459 1 63595 0 684 E 0151828 0 000262459 o 000976984 0 655774 0 381 1 63595 0 655774 6 9968e 006 6 99282e 0 684501 0 381283 6 99282e 006 6 99169e 0 644044 0 120749 6 9925e 006 6 99103e 0 175491 0 13336 6 99042e 006 6 99005e 0 128232 0 345531 6 98679e 006 6 98697e 00010142 0 0118859 440 106 446 Ii Figure 8 11 Regression Output with Embedded Covariance Matrix 8 10 Estimating Models 8 3 Model Components and Results The primary components of a model are provided with the model command MODEL COMMAND Lhs dependent variable Rhs independent variables In many cases this is all that is required Ho
4. Cross tabulation of predictions Row is actual column is predicted Model Probit Prediction is number of the most probable cell 4 an _ aa ak ale are mann k 4 sake a e i iz iho it mt nl ab aea id Actual Row Sum 0 1 2 3 4 5 6 7 8 i do ea abe ihe he a S b ae lt d 0 447 0 0 0 0 0 447 1 255 0 0 0 0 0 255 2 642 0 0 0 0 0 642 3 1173 0 0 0 0 O 1173 4 1390 0 0 0 0 O 1390 5 4233 0 0 0 0 O 4233 p ps Shes as a tet ec iiz sod ei pm ole z Pes ake al pen a a a he am pen par a Col Sum 8140 0 0 0 0 O 8140 0 ol 0 aks als ade ahi ae Fo abs ak Even though the model appears to be highly significant the table of predictions has some large gaps in it The estimation criterion for the ordered probability model is unrelated to its ability to predict those cells and you will rarely see a predictions table that closely matches the actual outcomes It often happens that even in a set of results with highly significant coefficients only one or a few of the outcomes are predicted by the model Computation of predictions and ancillary variables is as follows For each observation the predicted probabilities for all J 1 outcomes are computed Then if you request List the listing will contain Predicted Y is the Y with the largest probability Residual is the largest of the J 1 probabilities i e Prob y fitted YJ Varl is the estimate of E y 2o ix Prob
5. NOTE The covariance and correlation matrices are based on the subset of observations for which there were no missing data for any variables Each row in the table of results will list the number of valid cases used for that particular variable Unfortunately if different observations are missing for the various variables used in a covariance or correlation matrix the union of the observations for which all variables are present can contain very few observations For better or worse this union is the set of observations used in computing the matrices If your data contain missing values the scaling in the previous section is automatically adjusted for each variable Moments are scaled by the number of valid observations or sum of weights for that variable 13 2 3 Sample Quantiles You may obtain more detailed statistics about variables by requesting the sample quantiles This feature produces sample order statistics and the deciles and quartiles of the sample of values for each variable The keyword in the command is Quantiles Describing Sample Data For example CALC SAMPLE CREATE CREATE DSTAT 13 3 3 Ran 12345 31 1000 x Rnn 0 1 y Rnn 0 1 2 Rhs x y Quantiles Matrix The CREATE commands produce random samples from the standard normal and the chi squared 1 distributions Descriptive Statisti All results based on The following output results cs nonmissing observations
6. You may not change them with your commands Most of these results apply to the linear regression model but values such as ybar sy and logl are saved by nearly all models Scalars mda and theta will change from model to model depending on the ancillary parameters in the model After you estimate a model you will find these scalars defined automatically with the indicated values These values can thereafter be used on the right hand side of any command The final one exitcode is an indicator of the success or failure of the most recent estimation command Scientific Calculator 10 7 HINT Since it is such a common application there is an exception to the read only setting of these scalars The scalar rho may be set by a loop control For example for scanning in a model of autocorrelation you might EXECUTE rho 0 1 025 In general rho is not a protected name However you cannot delete rho 10 4 2 Work Space for the Calculator Although there are 50 scalars available the 14 protected names leave you a total of 36 to work with If you find yourself running out of room the command CALC Delete name name can be used to clear space Note that there is no comma or semicolon between the Delete specification and the first scalar name You may also delete scalars that are not reserved in the project window by highlighting their names and pressing the Del key 10 4 3 Compound Names for Scalars The names of scal
7. there is no need to distinguish e g variables from previously computed matrices Each result in the following table produces a result that for later purposes may be treated as a single matrix a b transpose of a times b a w b a diag w b Do not create diagonal matrices a lt w gt b a diag w b a c b acb a lt c gt b a c b cisany matrix lt a gt a a G 2 inverse ofa lt a b gt a by lt a w b gt a w b lt a lt w gt b gt a lt w gt b Table 9 1 Matrix Expressions In a matrix expression the symbol 1 can be used where needed to stand for a column of ones Thus 9 14 Using Matrix Algebra l a arow of ones times matrix a a transpose of matrix a times a column of ones Note that in each of these cases the apostrophe is an operator that connotes multiplication after transposition NOTE You should never need to compute a b Always use a b Thus in the earlier example c lt c gt c is better than c Ginv c c or c lt c gt c In any matrix function list you may use the transpose operator for transposition For example two ways to obtain the sum of a matrix and its transpose are sum ata and sum Msum a a The transpose of a matrix may appear in an expression simply by writing it with a following apostrophe For example a c c a could be computed with a c c a though a c c a wo
8. 200 208 216 142 143 148 LOLs 162 IT34 183 192 3929 0746 0580 1179 2315 8312 3568 8002 7533 5460 9441 8 20 Estimating Models LOTT 218 30 210 46 TeS 19753139 223 6107 1972 226 80 219 00 7 8000 205 4731 232 5270 1973 237 90 242 57 4 6662 226 7579 258 3745 1974 225 80 271 46 45 6629 197 8524 345 0734 1975 232 40 282 81 50 4150 E93 s9799 371 6504 1976 241 70 295 84 54 1380 199 1641 392 5119 Be ONL 249 20 310 71 61 5120 201 1378 420 2862 1978 261 30 328 38 67 0848 210 8962 445 8733 x LITI 248 90 388 25 139 3480 168 3394 608 1566 1980 226 80 469 95 243 1545 93 6745 846 2345 98 1 225 60 505 76 280 1606 67 3596 944 1616 1982 228 80 486 73 F257 C9265 80 0424 893 4107 x T983 239 60 482 43 242 8259 97 6831 867 1688 1984 244 70 493 02 248 3244 122 6819 863 3669 1983 245 80 499 99 254 1909 126 6925 873 2893 1986 269 40 439 62 170z 2191 191 3035 687 9347 Using Matrix Algebra 9 1 Chapter 9 Using Matrix Algebra 9 1 Introduction The data manipulation and estimation programs described in the chapters to follow are part of LIMDEP s general package for data analysis The MATRIX CREATE and CALCULATE commands provide most of the additional tools By defining data matrices with the NAMELIST SAMPLE REJECT INCLUDE PERIOD and DRAW commands you can arbitrarily define as many data matrices as you want Simple compact procedures using MATRIX commands will then allow you to obt
9. e Many operations allow you to access particular observations of a variable by using an observation subscript enclosed in parentheses If you will be using this construction you must avoid variable names which are the same as the function names listed in Section 7 3 3 For example if you have a variable named phi then Phi 1 could be the first observation on phi or the standard normal CDF evaluated at 1 0 CREATE will translate it as the latter Function names all have three letters You should examine the list given in Section 7 3 3 Variables may appear on both sides of the equals sign as long as they already exist and transformations may be grouped in a single command In a multiple CREATE command later transformations may make use of variables created in earlier ones For example CREATE sam xl1 x2 bob x2 x3 this sam bob that Log this that 1 that is the same as five consecutive CREATE commands You should write your transformations so that they are as self documenting as possible that is so that they are as easy to understand as possible Essentials of Data Management 7 13 7 3 2 Conditional Transformations Any transformation may be made conditional The essential format is CREATE If logical expression name expression Logical expressions are any desired expressions that provide the condition for the transformation to be carried out They may include any number of levels of parentheses a
10. Batch mode or batching commands provides a middle ground between these whereby you can submit groups of commands from input files or as streams of commands from the editor or in a procedure If the use of this is merely to submit a sequence of commands with a small number of keystrokes for which LIMDEP provides several methods then batching provides nothing more than a convenience But LIMDEP also provides batch like capabilities which make it operate more like a compiler than an interpreter Consider the logic of an iterative program Step 1 Initial setup Step 2 Compute a result based on current information and previous results Step 3 Decide whether to exit the iteration or return to Step 2 and act on the decision In order to carry out such a sequence of commands you must have several capabilities available First results of Steps 1 and 2 must be retrievable Second it must be possible not only to submit the set of commands in Step 2 in a batch mode it must be possible to do so repeatedly Step 3 may call for many repetitions of the same set of commands Here is a trivial example Step 1 CALCULATE i 0 Step 2 CALCULATE List i i 1 Step 3 Ifi lt 10 go to Step 2 If we execute this program it will display the numbers 1 to 10 The problem of retrievability is obviously solved assuming of course that CALC can compute and define something called i in such a way that later on 7 will exist Certainly it can se
11. Figure 6 5 Data Confirmation Cok 52 6 8 Application and Tutorial You can verify that the data have been properly imported by looking at the data editor This is a small spreadsheet editor You might use it to enter a small data set with a few observations by typing them directly into the program s memory The data editor will display the data that have already been placed in memory To open the data editor click the Data Editor button on the desktop toolbar as shown in Figure 6 6 Limdep Data Editor Figure 6 6 Data Editor Rereading the Data Though each one of these methods of reading the data into the program is short and simple it might still seem like a bit of effort just to get the data ready to use The first time you use a data set there has to be some way to get the data ready for this program to use them You could just type them in yourself there is a spreadsheet style editor as shown in Figure 6 6 But if the data already exist somewhere else that would be terribly inefficient and inconvenient We do emphasize however that however you enter your data set into LIMDEP the first time you will only do it once Once the data are in the program and in a project you will save that project in a file Thereafter when you want to use these data again you will simply double click the project in a mini explorer on your desktop in LIMDEP s recently used files or somewhere else and you will be re
12. G Variables commands that 7 data Namelists Run Line Ctrl R Matrices SAMPLE 1 1 i Sala CREATE X Ri E Procedures H 4 Output Insert Command E Az Insert File Path utput Window Paste Insert Text File Find Replace Figure 3 8 The Edit Right Mouse Button Menu You may have noted by this point that operating of LIMDEP uses a mixture of menus and commands submitted from the text editor Though most modem software is largely point and click menu driven much of what you do in econometrics is not very well suited to this style of processing In fact it is possible to operate LIMDEP almost without using your keyboard once your data are entered and ready We will demonstrate use of the menus for model building as we go along But you will almost surely find that using the command editor and the LIMDEP command language is far simpler and more efficient than using the menus and dialog windows Moreover when you do begin to write your own computations such as using matrix algebra where you must compose mathematical expressions then the menus will no longer be useful 3 4 A Short Tutorial Start the Program We assume that you have successfully installed LIMDEP on your computer and created a shortcut to use to invoke the program Now invoke LIMDEP for example by double clicking the shortcut icon or from the Start Programs menu The desktop will appear as shown in Fig
13. Keep may not actually be a residual or a fitted value Individual model Estimating Models descriptions will provide details In general the List specification produces the following 8 19 1 an indicator of whether the observation was used in estimating the model If not the observation is marked with an asterisk the observation number or date if the data are time series the observed dependent variable when this is well defined the fitted value variable retained by Keep the residual variable retained by Res variable 1 a useful additional function of the model which is not kept and variable 2 another computation SLA SE o Although the last two variables are not kept internally they are written to your output window and to the output file if one is open so you can retrieve them later by editing the file with a word processor In all cases the formulas for these variables will be given so if you need to have them at the time they are computed you can use a subsequent CREATE command to obtain the variables We illustrate these computations with a Poisson regression and with the out of sample predictions generated by the regression above The POISSON command would be POISSON Lhs 3 Rhs List The following table results and items listed for the Poisson model are Actual y Prediction Ely exp b x Residual y Ely b x Probability Pr Y y exp A
14. The Linear Regression Model part 3 below 2 Ordinary least squares estimates of Model 4 above Output is the same as in part 1 the usual for a least squares regression The estimates of the dummy variable coefficients and the estimated standard errors are listed in the output file if requested with Output 2 There may be hundreds or thousands of them 3 Test statistics for the various classical models The table contains a b For Models 1 4 the log likelihood function sum of squared residuals based on the least squares estimates and R Chi squared statistics based on the likelihood functions and F statistics based on the sums of squares for testing the restrictions of Model 1 as a restriction on Model 2 no group effects on the mean of y Model 1 as a restriction on Model 3 no fit in the regression of y on xs Model 1 as a restriction on Model 4 no group effects or fit in regression Model 2 as a restriction on Model 4 group effects but no fit in regression Model 3 as a restriction on Model 4 fit in regression but no group effects The statistic degrees of freedom and prob value probability that the statistic would be equaled or exceeded by the chi squared or F random variable are given for each hypothesis Saved Results As always the matrices b and varb are saved by the procedure In addition a matrix alphafe will contain the estimates of the fixed effects a This matrix is limited to 20 000 ce
15. We do note the second explanation for the finding however We have presumed so far that we are actually fitting a demand curve and that we can treat the price as exogenous If the price were determined on a world market this might be reasonable but that is less so in the U S which does maniopulate the price of gasoline We leave for others to resolve this issue and continue with the multiple regression The more complete model is estimated with the command REGRESS Lhs logG Rhs one logpg logi Application and Tutorial 6 21 The results shown below are more in line with expectations and conform fairly closely to the hypothetical exercise done earlier The data from this period do suggest that the income elasticity is close to one and the price elasticity is indeed negative and around 0 17 The fit of the model is extremely good as well Ordinary least squares regression LHS LOGG Mean 12 24504 Standard deviation 2388115 WTS none Number of observs 52 Model size Parameters 3 Degrees of freedom 49 Residuals Sum of squares 1849006 Standard error of e 6142867E O1 Fit R squared 9364292 Adjusted R squared 9338345 Model test F 2 49 prob 360 90 0000 Diagnostic Log likelihood 72 83389 Restricted b 0 1 188266 Chi sq 2 prob 143 29 0000 Autocorrel Durbin Watson Stat 1168578 Rho cor e e 1 9415711 Variable Coef
16. note that w n by Ewx T waxy j 2 Sy Zwi xb Est Var b sy An K Swix where W is your weighting variable Your original weighting variable is not modified scaled during this computation The scale factor is computed separately and carried through the computations NOTE Apart from the scaling your weighting variable is the reciprocal of the individual specific variance not the standard deviation and not the reciprocal of the standard deviation This construction is used to maintain consistency with the other models in LIMDEP T 2 For example consider the common case Var 0 z For this case you would use CREATE swt 1 z 2 REGRESS Lhs Rhs Wts wt 14 4 Correcting for First Order Autocorrelation There are numerous procedures for estimating a linear regression with first order autoregressive disturbances yr B x T E PE amp rt uy The simplest form of the command is REGRESS Lhs Rhs AR1 The default estimator is the iterative Prais Winsten algorithm That is the first observation is not discarded the full GLS transformation is used This is a repeated two step estimator Step 1 OLS regression of y on X Then estimate p with r 1 1 2 x Durbin Watson statistic Step 2 OLS regression of y 1 r yand y y TY t 2 T on the same transformation of x 14 10 The Linear Regression Model After Step 2 r is
17. where P is the probability predicted by the model The three models are M the model fit by maximum likelihood MC the model in which all predicted probabilities are the sample proportion of ones here 0 6291 and MO no model in which all predicted probabilities are 0 5 The normalized entropy is the entropy divided by nlog2 Finally the entropy ratio statistic equals 2 nlog2 1 normalized entropy The percent correct predicted values are discussed below The next set of results examines the success of the prediction rule Predict y 1if P gt P and 0 otherwise where P is a defined threshold probability The default value of P is 0 5 which makes the prediction rule equivalent to Predict y 1 if the model says the predicted event y 1 x is more likely than the complement y 0 x You can change the threshold from 0 5 to some other value with Limit your P Models for Discrete C hoice oO oe DOOWDOOWOCOO ONO KR OO O w Oro W O O n Model 93986 io ooloooroowo09o o OG OA OOGO O or OOO O Information Statistics for Discrete Choice Model M Model MC Constants Only MO No Criterion F log L 17673 09788 18019 55173 18940 LR Statistic vs MC 692 90772 00000 Degrees of Freedom 5 00000 00000 Prob Value for LR 00000 00000 Entropy for probs 17673 09788 18019 55173 18940 ormalized Entropy 93306 95135 1 Entropy Ratio Stat 25
18. 12 4 12 5 12 6 Chapter 13 13 1 13 2 Econometric Model Estimation Introduction 12 1 Econometric Models 12 1 Model Commands 12 1 Command Builders 12 3 Model Groups Supported by LIMDEP 12 3 Common Features of Most Models 12 5 12 6 1 Controlling Output from Model Commands 12 5 12 6 2 Robust Asymptotic Covariance Matrices 12 5 12 6 3 Predictions and Residuals 12 6 Describing Data Introduction 13 1 Summary Statistics 13 1 13 2 1 Weights 13 2 13 2 2 Missing Observations in Descriptive Statistics 13 2 13 2 3 Sample Quantiles 13 2 TOC 4 13 3 13 4 13 5 13 6 Chapter 14 14 1 14 2 14 3 14 4 14 5 14 6 Chapter 15 15 1 15 2 Table of Contents Histograms 13 4 13 3 1 Histograms for Continuous Data 13 4 13 3 2 Histograms for Discrete Data 13 6 Cross Tabulations 13 6 Kernel Density Estimation 13 7 Scatter Plots and Plotting Data 13 10 13 6 1 Printing and Exporting Figures 13 10 13 6 2 Saving a Graph as a Graphics File 13 10 13 6 3 The PLOT Command 13 12 13 6 4 Plotting One Variable Against Another 13 12 13 6 5 Plotting a Simple Linear Regression 13 13 13 6 6 Time Series Plots 13 13 13 6 7 Plotting Several Variables Against One Variable 13 14 13 6 8 Options for Scaling and Labeling the Figure 13 15 The Linear Regression Model Introduction 14 1 Least Squares Regression 14 1 14 2 1 Retrievable Results 14 3 14 2 2 Predictions and Residuals 14 3 14 2 3 Robust Covariance Matrix Estimation 14 5 14 2 4 Restricte
19. 13 4 Cross Tabulations The command for crosstabs based on two variables is CROSSTAB Lhs rows variable Rhs columns variable Use CROSSTAB to analyze a pair discrete of variables that are coded 0 1 up to 49 i e up to 2 500 possible outcomes The table may be anywhere from 2x2 to 50x50 Row and column Describing Sample Data 13 7 sizes need not be the same Observations which do not take these values are tabulated as out of range This command assumes that your data are coded as integers 0 1 If you wish to analyze continuous variables you must use the RECODE command to recode the continuous ranges to these values The categories are automatically labeled NAME 0 NAME 1 etc for the two variables To provide your own labels and to specify the number of categories for the variables add Labels list of labels for Lhs list of labels for Rhs to the command Labels may contain up to eight characters Separate labels in the lists with commas Cross tabulations may be computed with unequally weighted observations The specification is Wts variable as usual This scales the weights to sum to the sample size If the weights are replications that should not be scaled use Wts variable Noscale 13 5 Kernel Density Estimation The command for kernel density estimation KERNEL Rhs the variable The kernel density estimator is a device used to describe the distribution
20. 6 1 Application An Econometrics Problem Set This chapter will illustrate most of the features in LIMDEP that you will use for basic econometric analysis We will use a simulated problem set to motivate the computations This application will use many of the commands and computational tools in the program Of course we have not docomented these yet they appear later in the manual in the succeeding chapters We do anticipate however that you will be able to proceed from this chapter alone to further use of the program 6 2 Assignment The Linear Regression Model The data listed below are a set of yearly time series observations 1953 2004 on the U S Gasoline Market Use these data to perform the following analyses 1 Read the raw data into LIMDEP 2 Obtain descriptive statistics means standard deviations etc for the raw data in your data set 3 The data are in levels We wish to fit a constant elasticity model which will require that the variables be in logarithms Obtain the following variables logG log of per capital gasoline consumption logPg log of the price index of gasoline logl log of per capita income logPnc log of price index for new cars logPuc log of price index for used cars logPpt log of price index for public transportation t time trend year 1952 4 We notice immediately that if we intend to use the logs of the price indexes in our regression model there is at least the p
21. AC as if A were Diag a This result will be crucial when C is a data matrix X which may have tens or hundreds of thousands of rows The second aspect of the computation of matrices that involve your data is that once the data are in place in the data area in fact there is no need to create A or Diag a at all The data are just used in place you need only use variables and namelists by name Invariably when you manipulate data matrices directly in matrix algebra expressions you will be computing sums of squares and or cross products perhaps weighted but in any event of order KxK The simple approach that will allow you to do so is to ensure that when xnames and vnames namelists and variables appear in matrix expressions they appear in one of the following constructions where x and y are namelists of variables and w is a variable Some data summation functions are listed in Table 9 2 9 20 Using Matrix Algebra x x the usual moment matrix Xy cross moments X w x X diag w X weighted sums W is a variable Or X W Y x lt w gt x X diag w X weighted by reciprocals of weights lt x x gt X X inverse of moment matrix lt x y gt X Y inverse of cross moments if it exists lt x w x gt X w X inverse of weighted moments Or lt X w Y gt lt x lt w gt x gt X lt w gt X inverse weighted by reciprocals of weights able 0 2 Sums of Observations in
22. Fit R squared Adjusted R squared Model test Pl i 50 prob Diagnostic Log likelihood Restricted b 0 Chi sq 1 prob Info criter LogAmemiya Prd Crt Akaike Info Criter Autocorrel Durbin Watson Stat 2360328 Rho cor e e 1 8819836 9 672148 3485909 52 2 50 6656577 1153826 8925890 8904408 415 50 0000 39 52900 18 47941 116 02 0000 4 281262 4 281300 Variable Coefficient Standard Error t ratio P T gt t Mean of X s MMi 4 Constant 7 86328655 09017087 87 204 0000 LOGPG 48503996 02379529 20 384 0000 3 72930296 lt Figure 6 16 Regression Results 6 20 Application and Tutorial The regression output shows LIMDEP s standard format The set of diagnostics including R s sum of squares F statistic for the regression and so on are shown above the regression coefficients The coefficients are reported with standard errors t ratios p values and the means of the associated independent variables For the specific application we note the estimated price elasticity is indeed positive which is unexpected for economic data Two explanations seem natural First assuming we are estimating a demand equation then a demand equation should include income as well as price In thie particular market in fact it is well known that demand is strikingly inelastic with respect to price and that income is the primary driver of consumption
23. N t lissi dependent variable set of independent variables stratification indicator number of regressors not including one number of groups number of observations in group i NADY ll The data set for all panel data models will normally consist of multiple observations denoted t 1 7 on each of i 1 N observation units or groups A typical data set would include observations on several persons or countries each observed at several points in time 7 for each individual In the following we use to symbolize time purely for convenience The panel could consist of N cross sections observed at different locations or N time series drawn at different times or most commonly a cross section of N time series each of length T The estimation routines are structured to accommodate large values of N such as in the national longitudinal data sets with T being as large or small as dictated by the study but not directly relevant to the internal capacity of the estimator We define a balanced panel to be one in which T is the same for all i and correspondingly an unbalanced panel is one in which the group sizes may be different across i NOTE Panels are never required to be balanced That is the number of time observations T may vary with i The computation of the panel data estimators is neither simpler nor harder with constant T No distinction is made internally Ther
24. Rank c rank of any matrix The rank is computed as the number of nonzero characteristic roots of C C To find the rank of a data matrix X i e several columns of data in a namelist X you could use c Rank x However this may not be reliable if the variables are of different scales and there are many variables You should use instead MATRIX C Diag X X C Isqr C X X Isqr C Rank C 9 7 Sums of Observations There is no obstacle to computing a matrix X X even if X has 1 000 000 rows so long as the number of columns in X is not more than 225 The essential ingredient is that X X is not treated as the product of a Kxn and an nxK matrix it is accumulated as a sum of KxK matrices By this device the number of rows n is immaterial except perhaps for its relevance to how long the computation will take Matrix operations that involve C AC or C A C are as in all cases limited to 50 000 cells But suppose that C is 5 000x2 and A is a diagonal matrix Then the result is only 2x2 but apparently it cannot be computed because A requires 25 000 000 cells But in fact only 5 000 cells of A are needed those on the principal diagonal LIMDEP allows you to do this computation by providing a vector in this case 5 000x1 instead of a matrix for a quadratic form Thus in e aJe if a is a column or row vector LIMDEP will expand at least in principle the diagonal matrix and compute the quadratic form C
25. W V i DOWN 14 Scalars SAMPLE 1 100 E Strings CREATE X RNN 0 1 5 Procedures CREATE Y X RNW 0 1 24 Output gt REGRESS Lhs Rhs ONE X Tables fe a Pa rae E a ae Ordinary least squares regression L Model was estimated Dec 07 2007 at 11 34 28AM LHS Mean 3415034E 1 Standard deviation 1 340983 WTS none Number of observs 100 Ln 33 33 Idle 11 36 4 Figure 4 6 Command Builder Output 4 8 LIMDEP Commands This page intentionally left blank Program Output Chapter 5 Program Output 5 1 The Output Window LIMDEP will automatically open an output window and use it for the display of results produced by your commands Figure 5 1 below shows an example The output window is split into two parts In the lower part an echo of the commands and the actual statistical results are accumulated The upper part of the window displays the TRACE LIM file as it is being accumulated Note that there are two tabs in the upper window You have two options for display in this window The Trace display is as shown below If you select the Status tab instead this window will display technical information during model estimation such as the iterations line search and function value during maximum likelihood estimation and execution time if you have selected this option from the Project Project Settings Execution tab as well DER RESET L
26. Year 1961 Quarter v Month Cancel Figure 7 18 Dialog Box for DATES Command The SAMPLE and PERIOD commands may be given from the Project Set Sample Range dialog box See Figure 7 19 7 30 Essentials of Data Management at Limdep Untitled 1 Model Run T CREATE Sy Data SAMPLE SQ Variables REJECT px 3 Namelists 3 Matrices 4 Scalars E Strings C Procedures Sy Output 0 970373 E Tables 0 229617 Output Window Observation dates From 1961 4 To fis7qa Namelists 0 of 25 used 2 31595 lanz oo Figure 7 19 Dialog Box for the PERIOD Command NOTE The current data type Data U Data Y Data Q or Data M is displayed at the top of the project window The data editor will also be changed to show the time series data Figure R7 7 shows an example using quarterly data The top of the project window displays the Q which indicates quarterly data The data editor has also automatically adjusted following the setting in Figure 7 19 for quarterly data beginning in 1961 4 7 6 Missing Data Observations that contain missing values for variables in a model are automatically bypassed The full version of LIMDEP uses a SKIP command for this setting The SKIP switch is automatically turned on in the Student version Missing values are handled specifically elsewhere in the program by the CREATE CALCULATE and MATRIX commands The treatment of missing values by CALCULATE
27. a oie at ns a a nan p ato 2 ake Constant 39 6343740 9 30415297 4 260 0000 A 4 38284585 5 12356623 855 23923 23529412 C 1 60558349 4 85887959 4133 0 7411 23529412 D 1 75161158 4 99174267 BSL FT25 T 23529412 E 1 28368407 7 62716506 168 8663 05882353 C67 13630013 4 67310647 029 9767 29411765 C72 5 06717068 4 97659408 1 018 3086 29411765 Gr 7 29195392 5 63651443 1 294 1958 14705882 LOGMTH 1 3330381292 1 36910416 5 335 0000 7 04925451 Estimating Models 8 13 The following are the standard results for a model estimated by maximum likelihood or some other technique Most parts are common while a few are specific to the particular model Poisson Regression Maximum Likelihood Estimates Dependent variable NUM Number of observations 34 Log likelihood function 126 9 DAL Number of parameters 9 Info Criterion AIC 4 80575 Finite Sample AIC 5 02634 Info Criterion BIC 5 20978 Info Criterion HQIC 4 94354 Restricted log likelihood 356 2029 Chi squared 567 0104 Degrees of freedom 8 Prob ChiSqd gt value 0000000 Chi squared 46 55065 RsqP 9403 G squared 47 52893 RsqD 9227 Overdispersion tests g mu i E S Overdispersion tests g mu i 2 498 Variable Coefficient Standard Error b St Er P Z gt z Mean of X Constant 4 80807969 65751784 She t2 0000 A 00373503 15767690 024 9811 23529412 C 83536379 36686744
28. and the indirect part which is of opposite sign the term in parentheses is always negative 0 A a x A ox It is not obvious which part will dominate Most applications have at least some variables that appear in both equations so this is an important consideration Note also that variables which do not appear in the index function still affect the conditional mean function through their affect on the inverse Mills ratio the selection variable We note the risk of conflict in the notation used here for the selection term j and the loglinear term in the conditional mean functions of the generalized linear models in the previous chapter There is no relationship between the two The two uses of lambda are so common in the literature as to have become part of the common parlance and as such the risk of ambiguity is worse if we try to change the notation used here for clarity LIMDEP contains three estimators for this model Heckman s two step or Heckit estimator full information maximum likelihood and two step maximum likelihood which is more or less a limited information maximum likelihood estimator The two step estimator is given here The others are documented in the full manual for the program 16 3 2 Two Step Estimation of the Standard Model Heckman s two step or Heckit estimation method is based on the method of moments It is consistent but not efficient estimator Step 1 Use a probit
29. 0 1 Prob y 1 Bot Bix We are interested in using a likelihood ratio statistic to test the hypothesis that the same parameters Bo and B apply to all 10 subsamples against the alternative that the parameters vary across the groups We also want to examine the set of coefficients The first two commands initialize the log likelihood function and define a place to store the estimates CALC slu 0 i1 1 MATRIX Slopes Init 10 2 0 The following commands define a procedure to compute probit models and sum unrestricted log L PROC CALC 3i12 i1 99 SAMPLE i1 i2 PROBIT Lhs y Rhs one x CALC lu lu logl il i1 100 MATRIX Slopes i b ENDPROC Execute the procedure 10 times resetting the sample each time EXECUTE 31 1 10 The next two commands compute the restricted log likelihood SAMPLE 31 1000 PROBIT Lhs y Rhs one x Computes restricted pooled logL 10 2 Scientific Calculator Now carry out the likelihood ratio test CALC chisq 2 lu logl prob 1 Chi chisq 18 CALC plays several roles in this example It is used to accumulate the unrestricted log likelihood function Ju The counters il and i2 are set and incremented to set the sample to 1 100 101 200 etc The loop index i is also a calculator scalar and once it is defined any other command such as the MATRIX command above can use i like any other number Finally the last CALC command retrieves the log
30. 07 y yee e Name of the weighting variable if one was specified e Number of observations n e Number of parameters in regression K e Degrees of freedom n K 7 a 2 _ n y2 e Sum of squared residuals e e wat y y Sn y x b e Standard error of e s e e n K e R R ee E Q x b e Adjusted R R 1 n 1 n K 1 R e F statistic F K 1 n K R K 1 1 R n K e Prob value for F Probe Prob F K 1 n k gt observed F e Log likelihood logL n 2 1 log2r log e e n e Restricted log likelihood logLo n 2 1 log2n log 1 ME y yy e Chi squared K 1 vA 2 logL logLo e Prob value for chi squared Prob Prob y K 1 gt observed chi squared e Log Amemiya Prediction Criterion log s 1 K n The Linear Regression Model 14 3 e Akaike Information Criterion AIC logh K n 2 1 log2n e Durbin Watson dw E e ey Le 1 dw 2 e Autocorrelation F The R and related statistics are problematic if your regression does not contain a constant term For the linear model LIMDEP will check your specification and issue a warning in the output Finally the main table of regression results contains for each Rhs variable in the regression e Name of the variable e Coefficient b e Standard error of coefficient estimate se s X X e e tratio for the coefficient estimate t b4 seg e Significance level of each ratio based on the distributio
31. 1 000 times The statistic of interest is z computed at the last line Since the model results are not useful we use Silent to suppress them The number of repetitions is specified generically in a scalar named nrep so if a larger or smaller sample is desired it is necessary only to change the fixed value in the first line 11 4 2 Parameters and Character Strings in Procedures Procedures may have parameters Define the procedure as follows PROC name parameter1 up to 15 parameters Then EXECUTE Proc name actuall The actual arguments are substituted for the dummy parameters at execution time This is like a subroutine call but more flexible For execution the passed parameters are simply expanded as character strings then the procedure after creation in this fashion becomes the current procedure For example PROC Dstats x DSTAT Rhs x ENDPROC NAMELIST zbc a list of variables q123 a different list of variables EXEC Proc Dstats zbc EXEC Proc Dstats q123 Any string may be substituted anywhere in the procedure This will allow great flexibility For example even models can be changed with the procedure PROC Modeler model Model Lhs y Rhs one x ENDPROC EXEC Proc Modeler probit EXEC Proc Modeler logit e Your procedures may have up to 15 parameters in the list e The number of parameters in the EXEC command is checked against the numb
32. 123457 CREATE 1 Rnu 1 3 k Rnu 5 2 ll Log l Ik Log k 1k2 1k Ik 112 I 1 Ikl I 1k sly 3 6 11 4 Ik 05 12 15 1k2 2 IkI Rnn 0 4 REGRESS Lhs ly Rhs one ll Ik 112 1k2 Ikl CLS b 2 b 3 1 b 4 b S b 6 0 1 4 8 The Linear Regression Model Ordinary least squares regression Model was estimated Dec 13 2007 at 09 30 11AM LHS LY ean 3 494703 Standard deviation 4 036799 WTS none Number of observs 500 Model size Parameters 6 Degrees of freedom 494 Residuals Sum of squares 8108 399 Standard error of e 4 051390 Fit R squared 2850337E 02 Adjusted R squared 7242271E 02 Model test F 5 494 prob 228 9227 Diagnostic Log likelihood 1405 981 Restricted b 0 1406 695 Chi sq 5 prob 1 43 9213 Info criter LogAmemiya Prd Crt 2 810049 Akaike Info Criter 2 810048 Variable Coefficient Standard Error t ratio P T gt t Mean of X Constant 40853548 76285798 4 468 0000 LL 09422513 2 56561134 037 9707 66349271 LK 05073476 1 16722384 043 9653 16198512 LL2 54115572 2 06524209 262 7934 53150388 LK2 70218471 1 38385662 4507 6121 16242739 LKL 15810258 1 55538131 102 9191 10542795 Linearly restricted regression Ordinary least squares regression Model was estimated Dec 13 2007 at 0
33. 22 The Linear Regression Model NOTE The default command for panel data regressions is simply REGRESS Lhs Rhs Panel Str or Pds This command requests both FE and RE results The full set of results for both models will be presented Adding either Fixed Effects or Random Effects will suppress the display of results for the other model NOTE In computing the random effects model the second step FGLS estimator generally relies on the first step OLS and LSDV fixed effects sums of squares You may be suppressing the FE model perhaps because of the presence of time invariant variables which preclude the FE model but not the RE model In previous versions of LIMDEP and in some other programs this will force the estimator to rely on another device to estimate the variance components typically a group means estimator In the current version of LIMDEP the FE model is computed in the background whether reported or not The sums of squares needed are obtainable even in the presence of time invariant variables Thus you will get the same results for the RE model whether or not you have allowed LIMDEP to report the fixed effects results A crucial element of the computation of the random effects model is the estimation of the variance components You may supply your own values for o and o The specification is Var s2e s2u This overrides all other computations The values are checked for valid
34. But you can go beyond this last row by giving specific ranges on the command For example suppose you begin your session by reading a file of 100 7 26 Essentials of Data Management observations Thereafter SAMPLE All would be equivalent to SAMPLE 1 100 But you could then do the following SAMPLE 31 250 CREATE x Rnn 0 1 Random sample Now since there are 250 rows containing at least some valid data SAMPLE All is equivalent to SAMPLE 1 250 Exclusion and Inclusion The REJECT and INCLUDE Commands These commands are used to delete observations from or add observations to the currently defined sample They have the form VERB logical expression VERB is either REJECT or INCLUDE Logical expression is any desired expression that provides the condition for the observation to be rejected or included It may include any number of levels of parentheses and may involve mathematical expressions of any complexity involving variables named scalars matrix or vector elements and literal numbers The operators are as follows Math and relational operators are gt gt lt lt Concatenation operators are amp for and for or A simple example appears in Figure 7 15 Another might be REJECT 3x gt 0 For a more complex example we compute an expression for observations which are not inside a ball of unit radius REJECT 3x42 y 2 242 gt 1 The
35. F2e2T 0228 23529412 D 29514731 24430603 1 208 2270 23529412 E 13092973 32043868 409 6828 05882353 C67 70947001 17792942 3 987 0001 29411765 C72 86911092 19268330 4 511 0000 29411765 C77 51343007 24440891 2 101 0357 14705882 LOGMTH 80295174 06534072 12 289 0000 7 04925451 Some notes about the results shown above The sample was changed from the initial 40 observations to the 34 observations with a nonmissing value of num before estimation The least squares results are the standard set of results that will appear with every ordinary least squares regression However the table of diagnostic statistics shown above the coefficient estimates is slightly abridged when the model command is not specifically for a linear regression The linear regression model would show autocorrelation diagnostics and other information criteria Results always include the coefficients standard errors and ratios of coefficients to standard errors In the index function models the coefficients are named by the variable that multiplies them in the index function In models which do not use an index function NLSQ MINIMIZE CLOGIT and a few others the parameter label that you provide will appear with the estimate instead Results for index function models include the mean values of the variables that are multiplied by the coefficients Ancillary parameters and user defined parameters will show blanks in this part of the table Note
36. FA Output Status Trace Matrix List Rex Samp 1 40 reje nun lt 0 matr z10 rndm 10 10 matr list z10 rndm 10 10 gt matr list z10 rnda i0 10 Matrix 210 10 10 Figure 9 6 Matrix Result in the Output Window If you double click the object you can display the full matrix in a scaleable window 9 2 4 Matrix Results When MATRIX commands are given in line the default is not to display the results of any matrix computations on the screen or in the output file Itis assumed that in this mode results are mostly intermediate computations The output file will contain instead a listing of the matrix expression and either a confirmation that the result was obtained or just a statement of the expression with a diagnostic in the trace file For example the command MATRIX a Iden 20 produces only an echo of the expression You can request full display of matrices in the output file by placing List before the matrix to be listed Note how this has been used extensively in the preceding examples in Section R12 1 This is a switch that will now remain on until you turn it off with Nolist When the end of a command is reached Nolist once again becomes the default The Nolist and List switches may be used to suppress and restore output at any point When the Nolist specification appears in a MATRIX command no further output appears until the List specification is used At the beginning
37. Grid and Fill Note that the command builder dialog box allows you to specify multiple variables A different line style is used for each variable if you use Fill The time series plot above is an example in which the Lhs variable is the automatically supplied date A different type of point is constructed for each if you are using a cross section Generally PLOT with Fill see the next section creates a figure with one or more line plots joining segments at the points but suppressing any symbols for the points The symbols dots stars etc may be retained with Symbols The Regression command is ignored if more than one variable is being plotted An example is shown in Figure 13 11 PLOT Rhs pn pd ps Lhs year Title Scatter Plot of Price Series Yaxis Prices Grid Fill Symbols Describing Sample Data 13 15 Untitled Plot 10 DER Scatter Plot of Price Series Prices Figure 13 11 Multiple Plots in the Same Figure NOTE This is not a time series plot in spite of the fact that year is the variable on the horizontal axis Although at this point LIMDEP does know that these are time series data it does not know that year is a date variable year is just another variable in the data set If you omit the Lhs variable specification in the command LIMDEP will label the x axis YEAR but this is not with respect to a variable in your data set it is the
38. Matrix W has 1 rows and 1 columns 1 1 7 93237 It is also instructive to see how to compute the restricted least squares estimator using the textbook formulas The result for computing the least squares estimator b subject to the restrictions Rb q 0 is b b X X R R X X R T Rb q where b is the unconstrained estimator To compute this using matrix algebra we use MATRIX r 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 q 0 0 0 MATRIX bu lt X X gt X y 5c r lt X X gt r d r b q be bu lt X X gt r lt c gt d The second hypothesis to be tested is that the elasticities with respect to new and used cars are equal to each other which is Ho Ba Bs To carry out this test using the F statistic we can use any of the devices we used earlier The most straightforward would be to place the restriction in the REGRESS command REGRESS Lhs logg Rhs x Cls b 4 b 5 0 The regression results with this restriction imposed are shown below In order to carry out the test using a t statistic we will require 6 28 Application and Tutorial b b N Va tV55 2V 45 Where vy is the estimated covariance of b and b After computing the unrestricted regression we can use CALC to obtain this result f REGRESS Lhs logg Rhs x CALC List tstat b 4 b 5 sqr varb 4 4 varb 5 5 2 varb 4 5 tc tth 975 degfrdm pvalue 2 1 tds ts
39. OELy x _ OF Bx _ 4F BX _ pana apr Ox Ox IGD B F B x B f B x B That is the vector of marginal effects is a scalar multiple of the coefficient vector The scale factor f B x is the density function which is a function of x The densities for the five binary choice models are listed in Section E18 3 1 This function can be computed at any data vector desired You can request the computation to be done automatically at the vector of means of the current sample by adding Marginal Effects to your command Models for Discrete Choice 15 7 Marginal Effects for Dummy Variables When one of the variables in x is a dummy variable the derivative approach to estimating the marginal effect is not appropriate An alternative which is closer to the desired computation for a dummy variable which we denote z is AF Prob y 1 z 1 Probly 1 z 0 F p x az z 1 F Pp x az z 0 For this type of variable the asymptotic standard error must be changed as well This is accomplished simply by changing the appropriate row of G to x x c pataan pao LIMDEP examines the variables in the model and makes this adjustment automatically 15 2 4 Robust Covariance Matrix Estimation The preceding describes a covariance estimator that accounts for a specific observed aspect of the data The concept of the robust covariance matrix is that it is meant to account for hypothetical unobserved failures of the model a
40. Preview Print 1 G GasolineData lim 2 ModeChoice Income lim 3 strom 1 lim 4 Examples_10 1_to_10 4 lim 5 mrozprobit Ipj 6 C limdepwsrc clogit Ipj 7 psra_wiw2whist_100907_am pj 8 problems Ipj Exit Alt F4 Save the current project with a new name Figure 6 9 Saving the Current Project gt gt gt gt gt gt gt SQ Variables YEAR GASEXP GASPRICE INCOME PNEWCAR PUSEDCAR PPUBTRN POP LOGG LOGPG LOGI LOGPNC LOGPUC LOGPPT T Namelists j Matrices Scalars C Strings E Procedures 2a Ake Application and Tutorial The mini explorer that appears T ing NLOGIT Version 4 0 1 January D prvation read from data file was hta listing in edit window was ree CREATE logg logpg logi logpnc logpuc logppt t Save in O Project Files e c a fs GasolineMarket Ipj File name GasolineM arket Ip Save as type Projects Ipi Cancel Figure 6 10 Mini explorer for Saving the Project 14 31 Application and Tutorial 6 15 When you restart LIMDEP later you can use the File menu to retrieve your project file and resume your work where you left off before The File menu is shown in Figure 6 11 Note that once we have saved our project file the file name will reappear in the Recently Used part of the File menu Limdep GasolineMarket pj SEE Edit Insert Project Model
41. Print 1 E Econometrics banks lim 2 E LIMDEP WIP rpl c lim 3 E LIMDEP WIP rpl2 lim 4 commands 1 lim 5 clogit Ipj 6 E LIMDEP WIPirpl c Ipj 7 CADOCUME 1 Temp data Ipj 8 burnett Ipj Exit Alt F4 Figure 3 2 The File Menu Text Command Document Figure 3 3 The File New Dialog Box NOTE If you have created a text file that contains LIMDEP commands that you will be using instead of creating a new set of commands you can use File Open to open that file If the file that you open has a LIM file extension in its filename then LIMDEP will automatically open an editing window and place the contents of the file in the window You can also use Insert Text File to place a copy of a text file any text file in an editing window that is already open 3 4 Operating LIMDEP 44 Limdep Untitled 1 File Edit Insert Project Model Run Tools Window Help osa S xe elal Bop ee Untitled Proj O X untitled 1 Data U 3333 Rows 3333 Obs f Insert Name 7 lt Q Data SAMPLE 1 100 Variables CREATE X RNN O 1 Namelists Matrices Scalars E Strings E Procedures 3 Output 5 Tables Output Window Figure 3 4 Project Window and Editing Window Note that the editing window shown in Figure 3 4 is labeled Untitled 1 This means that the contents of this window are not associated with a file the commands in an untitled wi
42. The probabilities which enter the log likelihood function are Prob y j Prob y is in the jth range The model may be estimated either with individual data with y 0 1 2 or with grouped data in which case each observation consists of a full set of J 1 proportions po P i NOTE If your data are not coded correctly this estimator will abort with one of several possible diagnostics see below for discussion Your dependent variable must be coded 0 1 J We note that this differs from some other econometric packages which use a different coding convention There are numerous variants and extensions of this model which can be estimated The underlying mathematical forms are shown below where the CDF is denoted F z and the density is fz Familiar synonyms are given as well Paii Fe f ee t 00 fO 0 Bg TT Losi H ee A AQ AOL AQ The ordered probit model is an extension of the probit model for a binary outcome with normally distributed disturbances The ordered logit model results from the assumption that has a standard logistic distribution instead of a standard normal 15 10 Models for Discrete Choice 15 3 1 Estimating Ordered Probability Models The essential command for estimating ordered probability models is ORDERED Lhs y Rhs regressors If you are using individual data the Lhs variable must be coded 0 1 All the values must be present in the data L
43. You the analyst must provide the value of L the number of lags for which the estimator is computed Then request this estimator by adding Pds the value for L to the REGRESS command 14 2 4 Restricted Least Squares This section describes procedures for estimating the restricted regression model y XBpt e subject to RB q R is a JxK matrix assumed to be of full row rank That is we impose J linearly independent restrictions They may be equality restrictions inequality restrictions or a mix of the two Inequality restricted least squares is handled by a quadsratic programming method that is documented in the full manual 14 6 The Linear Regression Model The constrained ordinary least squares estimator is b b X X R R X X R T Rb q where b X X X y is the unrestricted least squares estimator The estimator of the variance of the constrained estimator is Est Var b s2 X X s X X R R X X R R X X where gs y Xb y X b n K J The parameter vector is written b by b2 bg where the correspondence is to your Rhs list of variables including the constant one if it is included The restrictions are then imposed algebraically with CLS linear function value linear function value For example the following imposes constant returns to scale capital coefficient labor coefficient 1 ona hypothetical production function CALC Ran 123457 SAMPLE
44. and ARMAX models time series models with GARCH effects dynamic linear models for panel data nonlinear single and multiple equation regression models seemingly unrelated linear and nonlinear regression models simultaneous equations models LIMDEP is best known for its extensive menu of programs for estimating the parameters of nonlinear models for qualitative and limited dependent variables We take our name from L Mited DEPendent variables No other package supports a greater variety of nonlinear econometric models Among LIMDEP s more advanced features each of which is invoked with a single command are univariate bivariate and multivariate probit models probit models with partial observability selection heteroscedasticity and random effects Poisson and negative binomial models for count data with fixed or random effects sample selection underreporting and numerous other models of over and underdispersion tobit and truncation models for censored and truncated data models of sample selection with one or two selection criteria parametric and semiparametric duration models with time varying covariates stochastic frontier regression models ordered probit and logit models with censoring and sample selection switching regression models 1 2 Introduction to LIMDEP e nonparametric and kernel density regression e fixed effects models random parameters models and latent class models for over 25 different
45. and the sum of squared deviations MATRIX br bu xxi r Iprd r xxi r d CREATE u y x br Compute the disturbance variance estimator CALC 3 s2 1 n Col x Row r wu Compute the covariance matrix then display the results MATRIX 3 vr s2 xxi s2 xxi r Iprd r xxi r r xxi Stat br vr x The preceding gives the textbook case for obtaining the restricted least squares coefficient vector when X X is nonsingular For the case in which there is multicollinearity but the restrictions bring the problem up to full rank the preceding is inadequate See Greene and Seaks 1991 The general solution to the restricted least squares problem is provided by the partitioned matrix equation X X R b X y R O LA q If the matrix in brackets can be inverted then the restricted least squares solution is obtained along with the vector of Lagrange multipliers The estimated asymptotic covariance matrix will be the estimate of o times the upper left block of the inverse If X X has full rank this coincides with the solution above The routine for this computation is MATRIX XX X x sxy xXysr 3 q CALC sk Col x j Row r MATRIX zero Init j j 0 a xx r zero Shorthand for symmetric partitioned matrix 3v xy q ai Ginv a b l ai v br b_1 1 k vr ai 1 k 1 k CREATE u y xbr MATRIX vr wu n k j vr Stat br vr x 9 2 Entering MATRIX Com
46. are marked in the project window with the symbol to indicate that these names are locked Figure 8 12 illustrates This shows the setup of the project window after the tobit example developed above Estimating Models 8 15 A parameter vector is automatically retained in a matrix named b The program will also save the estimated asymptotic covariance matrix and name it varb The reserved matrices are thus b and varb with a third occasionally used and renamed The third protected matrix name will depend on the model estimated A few examples are mu created by ORDERED PROBIT sigma created by SURE and 3SLS pacf created by IDENTIFY All estimators set at least some of these matrices and scalars In the case of the scalars those not saved by the estimator are set to 0 For example the PROBIT estimator does not save rsqrd Matrices are simply left unchanged So for example if you estimate a fixed effects model which creates the third matrix and calls it alphafe then estimate a probit model which only computes b and varb alphafe will still be defined TA mrozprobit L BAR Data U 3333 Rows 1 Obs Sy Data 9 Variables Namelists SQ Matrices E gt B Ph VARB P gt SIGMA gt LASTDSTA b XBAR gt WALDFNS b VARWALD 2 Scalars P gt SSQRD P gt RSQRD Ps SUMSQDEY RHO DEGFRDM SY YBAR KREG NREG LOGL LMDA WALD EXITCODE Kx PL Scalar LOGL 3389 996454 Figure 8 12 Project Window 8 16 Estim
47. calculation is used when observations occur in groups which may be correlated This is rather like a panel one might use this approach in a random effects kind of setting in which observations have a common latent heterogeneity The parameter estimator is unchanged in this case but an adjustment is made to the estimated asymptotic covariance matrix The calculation is done as follows Suppose the n observations are assembled in G clusters of observations in which G the number of observations in the ith cluster is n Thus 2 n n Let the observation specific gradients and Hessians be _ dlogL _ amp logL Sij oB ij Opop The uncorrected estimator of the asymptotic covariance matrix based on the Hessian is Va H Za a Estimators for some models will use the BHHH estimator instead G n a Vs pay Dgs Let V be the estimator chosen Then the corrected asymptotic covariance matrix is Est Asy Var ale Z g X s 4 Note that if there is exactly one observation per cluster then this is G G 1 times the sandwich estimator discussed above Also if you have fewer clusters than parameters then this matrix is singular it has rank equal to the minimum of G and K the number of parameters To request the estimator your command must include Cluster specification where the specification is either the fixed value if all the clusters are the same size or the name of an identifying variable
48. capacity Models with censoring in both tails of the distribution are requested by changing the Limit specification to Limits lower limit upper limit where lower limit and upper limit are either numbers scalars or the names of variables or one of each For example in a labor supply model we might have Limits 20 40 Other options for the tobit model are the standard ones for nonlinear models including Printve to display the estimated asymptotic covariance matrix List to display predicted values Parameters to include the estimate of o in the retained parameter vector Maxit n to set maximum iterations Alg name to select algorithm Tlf Tlb Tlg to set the convergence criteria use Set to keep these settings Output value to control the technical output during iterations Keep name to retain fitted values Res name to retain residuals Marginal Effects Censoring and Sample Selection 16 3 and so on Sample clustering for the estimated asymptotic covariance matrix may be requested with Cluster specification as usual 16 2 2 Results for the Tobit Model You may request the display of ordinary least squares results by adding OLS to the command These will be suppressed if you do not include this request The OLS values will be used as the starting values for the iterations Maximum likelihood estimates are presented in full Note that unlike most of the discrete
49. date labeling that you gave in your DATES command Even if you did not have a variable named year in your data set you can obtain a time series style plot with yearly observations and labeled as such 13 6 8 Options for Scaling and Labeling the Figure Scaling The limits for the vertical and horizontal axes are chosen automatically so that every point appears in the figure Boundaries are set by the ranges of the variables You can override these settings however The options are as follows To set the limits for the horizontal axis use Endpoints lower value upper value To set specific limits for the vertical axis use Limits lower value upper value HINT If you plot variables of very different magnitudes in the same figure or if your series has outliers in it the scaling convention that seeks to include every point in the graph may severely distort your figure Missing values will also severely distort your scatter plot NOTE If the endpoints or limits that you specify push any points out of the figure x or y values are outside the limits then the specifications are ignored and the original default values are used 13 16 Describing Sample Data For example the top panel in Figure 13 12 is the same as Figure 13 9 produced by the command below without the specification of the endpoints and limits The lower panel shows the effect of expanding the limits PLOT Rhs gasp Lhs g Title Gas
50. desktop then close My Computer Now you can double click the icon on the desktop to launch LIMDEP and open the project file at the same time to begin your session 3 2 Operating LIMDEP Limdep Untitled Project 1 DE Fie Edit Insert Project Model Run Tools Window Help osa a ee elal Help Variables Namelists Matrices 5 Scalars E Strings Procedures 3 Output 4 Tables Output Window Figure 3 1 The LIMDEP Desktop 3 2 2 Opening an Editing Window To begin entering commands you should now open an editing window Select New in the File menu to open the File New dialog box as shown in Figure 3 3 Now select Text Command Document and OK to open the editing window which will appear to the right of the project window TIP You can press Ctrl N at any time to bring up the File New dialog box The desktop will now appear as shown in Figure 3 4 and you can begin to enter your commands in the editing window as we have done in an example in the figure We have arranged the various windows for appearance in our figures Your desktop will be more conveniently arranged and will be full screen sized Operating LIMDEP 3 3 44 Limdep Untitled Project 1 Edit Insert Project Model Run Tools Window Help New Ctrl N Open Ctrl O Close Save Save As Save All Open Project Save Project As Close Project Page Setup Print Preview
51. equation models The fitted values are requested by adding Estimating Models 8 17 Keep name to your model command The request for residuals is Res name In each of these cases the command will overwrite the variable if it already exists or create a new one In any model command the specification List requests a listing of the residuals and several other variables TIP To keep fitted values in a text file you can either use List with an output file or use WRITE and write the values in their own file or LIST variable If the current sample is not the entire data set and the data array contains observations on the regressors but not the dependent variable you can interpolate and produce predicted values for these observations by adding the specification Fill to your model command Res Keep and Fill do not compute values for any observations for which any variable to be used in the calculation is missing i e equals 999 Otherwise a prediction is computed for every row for which data can be found TIP Fill provides a very simple way of generating out of sample predictions To provide an example of the Fill feature we will examine some data on gasoline sales in the U S before and after the 1973 1974 oil embargo The data below are yearly series on gasoline sales g per capita income y and index numbers for a number of prices pg is the gasoline price pnc puc and
52. file 2 6 6 5 Command model 8 1 8 10 12 1 Left hand side variable 12 2 Output 12 5 Right hand side variables 12 2 Robust covariance matrix 12 5 Variables 12 2 Constant elasticity 6 1 Constant term 6 19 8 2 Copy Paste 6 6 Correlation 6 17 10 13 Covariance matrix 8 8 8 15 8 16 14 5 CREATE 6 13 7 9 7 10 7 11 to 7 13 7 30 7 31 Functions 7 14 CREATE categorical variable 7 17 Cross section 7 25 Crosstabulation 13 6 Labels 13 6 Weights 13 7 Current sample 7 24 7 25 7 26 l 2 Data area 3 1 7 1 Data editor 6 8 7 1 7 2 Data file variable names 7 6 Data matrix 9 8 9 9 Data missing 7 8 7 30 7 31 Data read 6 6 Data time series 6 16 Descriptive statistics 6 12 13 1 Missing values 13 2 Quantiles 13 2 Weights 13 2 Desktop 2 3 Dialog boxes 4 4 Discrete choice models 15 1 Chi squared 15 2 Hypothesis test 15 2 Log likelihood 15 2 Dummy variable partial effect 15 7 Edit Copy Paste 3 7 Editing window 3 2 3 4 3 6 3 9 Elasticity 6 10 Enter key 3 7 Entropy 15 4 Excel 6 4 7 8 File format 6 4 Exit program 2 5 Exit status 3 11 F statistic 6 23 6 24 6 26 CALC 6 26 File ascii 7 6 File data 7 3 File input 6 5 File menu 2 8 3 2 3 3 6 15 File New 3 3 Filenames 2 6 7 5 Font 3 5 Gasoline market 6 2 6 3 Go button 3 6 3 9 3 11 6 5 6 9 Graphics 5 2 Export 5 2 Hausman test 14 17 14 23 Help 3 14 Windows Vista 3 14 Heteroscedasticity 1 1 8 11 14 9 Histogram 13 4 Continu
53. internally created data that you produce using LIMDEP s random number generators The READ command is provided for this purpose 7 2 1 The Data Area Your data are stored in an area of memory that we will refer to as the data array The data arraay in the student version of LIMDEP or NLOGIT contains 1 000 rows and 99 columns These values are preset and cannot be changed 7 2 2 The Data Editor For initial entry of data LIMDEP s data editor resembles familiar spreadsheet programs such as Microsoft Excel You can reach the data editor in several ways e Click the data editor grid icon on the LIMDEP toolbar e Double click any variable name in the project window e Select the menu entry Project Data Editor The data editor is shown in Figure 7 1 The chevrons next to the observation numbers indicate that these observations will be in the current sample See Section 7 5 7 2 Essentials of Data Management i Data Editor 0 900 Vars 222 Rows 222 Obs New Variable Import Variables 4 4 Figure 7 1 Data Editor The data editor appears with an empty editing area when no variables exist The functions of the data editor are shown in the smaller menu which you obtain by pressing the right mouse button displayed in Figure 7 1 The functions are New Variable Click New Variable to open a dialog box that will allow you to create new variables with transformations as shown in Figure 7 2 This is analogous
54. j 1 20 SAMPLE Z tl 22 F REGRESS LOGL SSORDW REGRTYPE EXITCODE J Il I2 LOGL1 LOGL2 LOGL3 LOGL4 LOGLS LOGL6 LOGL LOGL8S LOGL9 Strings G Procedures Output Tables Output Window logl j logl 3 H AAA A vvv v CALC ENDPROC EXEC v gt gt gt gt gt gt gt gt gt gt gt Scalar LOGL10 28 392127 Figure 10 5 Procedure with Indexed Scalar Names CREATE x some function CALC q x 21 sigma 2 2 In evaluating subscripts for variables the observation refers to rows in the data array not the current sample Expressions may also contain any number of functions other operators numbers and matrix elements A scalar may appear on both sides of the equals sign with the result being replacement of the original value For examples CALC varsum b 1 2 varb 1 1 b 2 2 varb 2 2 2 b 1 b 2 varb 1 2 CALC messy messy 2 pi Gma 5 Gma 1 Sum age If it is necessary to change the algebraic order of evaluation or to group parts of an expression use parentheses nested to as many levels as needed For example CALC func Gma 3 Gma 5 3 x y c f g You may also nest functions For example CALC q Log Phi al a2 Exp a3 a4 Gma z Scientific Calculator 10 9 There are two constants which can be used by name without having been set by you At all points in the program the name pi wil
55. may save the component as a named file The query in each case is Save changes to lt name gt where lt name gt is the name that appears in the title banner of each of the active windows See Figure 2 6 for an example where the query refers to the output window You may also have other 2 6 Getting Started working windows open such as graphs or your scientific calculator and if so you can save these as well This operation is discussed further in Chapter 3 t Limdep clogit pj File Edit Insert Project Tools Window Help lt Q Data lt Q Variables gt gt gt gt gt gt gt gt gt gt b MODE TTME INVC INVT GC CHAIR HINC PSIZE INDJ INDI ASC TASC 250000000 34 5892857 47 7607143 486 165476 110 879762 276190476 34 5476190 1 74285714 R 26A19N47A N Save changes to Untitled Output 1 o cme 433270678 24 9486076 32 3710038 301 439107 47 9783530 447378551 19 6760442 1 01034998 1 335849N1 000000000 000000000 2 00000000 63 0000000 30 0000000 000000000 2 00000000 1 00000000 NNNNNANNAN Idle Figure 2 6 Exiting LIMDEP Saving Window Contents 08 51 4 The filename extension for a saved project window is LPJ The extension for a saved editing window file or output window is LIM When you use LIMDEP s dialog box to save the project editing or output windows LIMDEP will remember the name of th
56. model for z to estimate a For each observation compute o a w a w using the probit coefficients Step 2 Linearly regress y on x and A to estimate B and 0 pos Adjust the standard errors and the estimate of o which is inconsistent The corrected asymptotic covariance matrix for the two step estimator b c is Asy Var b c o X X X I p A X p X AW X W AX X2 X where X X A A diag 6 6 Ada w Aj 1 lt 6 lt 0 and x asymptotic covariance matrix for the estimator of a A consistent estimator of o is e e n The remaining parameters are estimated using the least squares coefficients The computations used in the estimation procedure are those discussed in Heckman 1979 and in Greene 1981 NOTE This is one of our frequently asked questions LIMDEP always computes the corrected asymptotic covariance matrix for all variants of selection models in all model frameworks The estimator of the correlation coefficient p is sign 6 6 6 This is the ratio of a regression coefficient the coefficient on 4 and the variance estimator above Note that it is not a sample moment estimator of the correlation of two variables This ratio is not guaranteed to be between and 1 See Greene 1981 which is about this result But note also that an estimate of p is Censoring and Sample Selection 16 7 needed to compute the asymptotic covariance matr
57. nonlinear procedures that involve time consuming calculations The status window will help you to see how the computation is progressing and if it is near completion Now select the last line in your command set the REGRESS command and click the GO button The regression output appears in the lower half of the window and you can observe the accumulating trace in the upper half of the window This trace in the top half of the window will be recorded as the trace file TRACE LIM when you exit the program Exit status of 0 0 means that the model was estimated successfully 3 12 Operating LIMDEP ai Limdep Output File Edit Insert Project Model Run Tools Window Help osa S ele olalu Sel Status Trace RESET SAMPLE 1 100 CREATE X Rnn 0 1 X Rnn 0 1 REGRESS Lhs Y Rhs One Egit status for this model command is 0 Ordinary least squares regression Model was estimated Dec 21 2005 at 11 17 13AM LHS Mean 2071663E 02 Standard deviation 1 339508 WTS none Number of observs 100 Model size Parameters 2 Degrees of freedom 98 Residuals Sum of squares 92 10805 Standard error of e 9694731 Fit R squared 4814727 Adjusted R squared 4761816 Model test BL d 98 prob 91 00 0000 3 Diagnostic Log likelihood 137 7835 Restricted b 0 170 6216 Chi sq 1 prob 65 68 0000 Info criter LogAmemiya Prd Crt 4220247E 01 Akaike Info Criter 4220779E 01 Autocorrel Durbin W
58. observed data contain a cluster of zeros In the standard censored regression or tobit model the censored range of y is the half of the line below zero For convenience we will drop the observation subscript at this point If y is not positive a zero is observed for y otherwise the observation is y Models of expenditure are typical We also allow censoring of the upper tail on the right A model of the demand for tickets to sporting events might be an application since the actual demand is only observed if it is not more than the capacity of the facility stadium etc A somewhat more elaborate specification is obtained when the range of y is censored in both tails This is the two limit probit model An application might be a model of weekly hours worked in which less than half time is reported as 20 and more than 40 is reported as full time i e 40 or more NOTE The mere presence of a clump of zeros in the data set does not by itself adequately motivate the tobit model The specification of the model also implies that the nonlimit observations will have a continuous distribution with observations near the limit points In general if you try to fit a tobit model e g to financial data in which there is a clump of zeros and the nonzero observations are ordinary financial variables far from zero the model is as likely as not to break down during estimation In such a case the model of sample selecti
59. recomputed based on the GLS estimator and the regression is repeated This iteration continues until the change in r from one iteration to the next is less than 0 0001 The covariance matrix for the slope estimators is the usual OLS estimator s X X based on the transformed data The asymptotic variance for r is estimated by 1 T 1 Results and diagnostics are presented for both transformed and untransformed models NOTE If no other specification is given the estimator is allowed to iterate to convergence which usually occurs after a small number of iterations The updated value of r at each iteration is computed from the Durbin Watson statistic based on the most recent GLS coefficients estimates Iterating these estimators to convergence does not produce a maximum likelihood estimator Other estimation procedures are requested by adding them to the AR1 request ARI Alg Corc requests the iterative Cochrane Orcutt estimator The first observation is skipped and the pseudo difference defined above is applied to the remaining observations We do not recommend this estimator as it needlessly discards the information contained in the first observation with no accompanying gain in speed efficiency or any statistical properties Alternatively ARI Alg MLE requests the maximum likelihood estimator of Beach and MacKinnon 1978 In this model the MLE is not GLS because in addition to the generalized sum of squa
60. requested with OLS Binomial logit model for binary choice These are the OLS values based on the binary variables for each outcome Y i j ah ns Variable Coefficient Standard Error b St Er P Z gt z Mean of X He ak tom cy Gi pe Dy nae ee Characteristics in numerator of Prob Y 1 Constant 56661068 02118790 26 742 0000 AGE 00468710 00029114 16 099 0000 43 5256898 HHNINC 03976003 01726656 2 5303 0213 35208362 HHKIDS 05217181 00680260 7 669 0000 40273000 EDUC 01071245 00131378 8 154 0000 11 3206310 AARRIED 01946888 00757540 2 510 0102 75861817 Standard results for maximum likelihood estimation appear next or first if OLS is not presented These are the results generated for all models fit by maximum likelihood The Hosmer Lemeshow chi squared statistic is specific to the binary choice models It is discussed in Section E18 3 7 The information criteria are computed from the log likelihood logL and the number of parameters estimated K as follows AIC Akaike Information Criterion 2 logL K n BIC Bayesian Information Criterion 2 logL KlogkK n Finite Sample AIC 2 logL K K K 1 n K 1 n HQIC 2 logL Klog logn n 15 4 Models for Discrete Choice Normal exit from iterations Exit status 0 Binomial Logit Model for Binary Choice Maximum Likelihoo
61. rsqrd k 1 1 rsqrd degfrdm Finally in order to obtain the critical value for the F test we use the internal table For the F statistic and t statistics we use CALC list fe Ftb 95 kreg 1 degfrdm 3 te ttb 95 n col x which produces Listed Calculator Results FC TC 2 308273 2 014103 Application and Tutorial 6 25 6 5 7 Hypothesis Tests There are usually several ways to carry out a computation Here we will test a hypothesis using several tools The model is logG B BologPg B3logI BalogPnc BslogPuc BelogPpt Bt The first hypothesis to be tested is that the three cross price elasticities are all zero That is Ho Ba Bs Bo 0 A direct approach is to build the linear hypothesis directly into the model command There is a particular specification for this as shown in the command below NAMELIST xl logpg logi x2 logpnc logpuc logppt x one x1 x2 t REGRESS Lhs logg Rhs x Cls b 4 0 b S 0 b 6 0 This produces the following results The results of the unrestricted regression are shown first followed by x Linearly restricted regression Ordinary least squares regression LHS LOGG Mean 12 24504 Standard deviation 2388115 WTS none Number of observs 52 Model size Parameters 4 Degrees of freedom 48 Residuals Sum of squares 1193176 Standard error of e 4985762E 01 Fit R squared 9589773 Adjus
62. same number of elements It creates the vector of values from the linear combination of the variables in the namelist with coefficients in the row or column matrix Dot products may also be used with other transformations For example CREATE 3 bx12 x1 b1 x2 b2 p Phi x b s The order is not mandatory d z is the same as z d Also if you need this construction a dot product may be used for two vectors or two namelists In the latter case the result is the sum of squares of the variables Essentials of Data Management 7 17 7 3 5 Expanding a Categorical Variable into a Set of Dummy Variables It is often useful to transform a categorical variable into a set of dummy variables For example a variable educ might take values 1 2 3 and 4 for less than high school high school college post graduate For purposes of specifying a model based on this variable one would normally expand it into four dummy variables say underhs hs college postgrad This can easily be done with a set of CREATE commands involving for example hs educ 2 and so on LIMDEP provides a single function for this purpose that simplifies the process and also provides some additional flexibility The categorical variable is assumed to take values 1 2 C The command CREATE Expand variable name for category 1 name for category C does the following e Anew dummy variable is created for each category If the variable to be creat
63. some computations on demand using all four years and then compute other matrices using alldata only for the last three years The sequence might appear as follows SAMPLE All MATRIX commands using demand SAMPLE 32 4 MATRIX commands using alldata The reason for the distinction between data and computed matrices is this Consider the computation of a matrix of weighted sums of squares and cross products F 1 n X WX where X is nxK with n being the sample size and W is an nxn diagonal matrix of weights Suppose n were 10 000 and K were 20 In principle just setting up X and W for this computation would require at least 8 10000x20 10000x10000 or over 800 million bytes of memory before computation even begins But computations of this size are routine for LIMDEP because e F 1 n gt w x x where x is a row of X which is always only 20x20 and e The data needed for the sum already exist in your data area That is by treating this sort of computation as a summing operation not as a formal matrix product we can achieve tremendous efficiencies The important feature to exploit is that regardless of n the result will always be KxK 9 3 2 Computations Involving Data Matrices You can manipulate any sized data matrix with MATRIX There are two simple rules to remember when using large samples e Ensure that in any expression MATRIX name result the target matrix name is not of the order of a data matrix That is
64. stratification variable is not a consecutive sequence of integers 1 2 N then a new stratification variable called _ stratum is automatically created for you The new variable will consist of the consecutive integers Thereafter for the same panel you can use this created variable for your indicator Suppose for example you have a panel data set indicated by postal codes which are not sorted in your data set though we assume that all observations for a particular postal code appear together Then REGRESS 3 3 Str postcode would automatically create the new stratification variable Obviously it is redundant for current purposes but you might have use for it later Looking ahead suppose you were going to fit a linear regression model to one variable in your panel and a probit model to a different one For the first one you can use your postal code to specify the panel But the probit model needs a count variable The next section shows how to obtain this variable The Count Variable In addition to the stratification variable stratum this estimator also always creates a count variable named _groupti If you have a balanced panel the count variable will just equal the The Linear Regression Model 14 15 number of periods But if your panel is unbalanced groupti is exactly what you will need for the other panel data estimators in LIMDEP Using REGRESS to Create Stratification and Count Variables The preceding suggests an
65. that one becomes Constant in the table The prob value shown P Z gt z is the value for a two tailed test of the hypothesis that 8 14 Estimating Models the coefficient equals zero The probability shown is based on the standard normal distribution in all cases except the linear regression model when it is based on the t distribution with degrees of freedom that will be shown in the table e The diagnostics table for the Poisson regression reports some statistics which will be present for all models indicated by the box in the figure 1 left hand side variable 2 number of observations used 3 number of iterations completed 4 log likelihood function or other estimation criterion function e Some results will be computable only for some models The following results listed for the Poisson model will not appear when there is no natural nested hypothesis to test For example they will not normally appear in the output for the tobit model log likelihood at a restricted parameter estimate usually zero chi squared test of the restriction significance level degrees of freedom Pe NS e Finally there are usually some statistics or descriptors which apply specifically to the model being estimated In this example chi squared G squared and two overdispersion tests are statistics that are specific to the Poisson model 8 3 3 Retrievable Results When you estimate a model the estimation res
66. that are most frequently analyzed with cross section and panel data Its range of capabilities include basic linear regression and descriptive statistics the full set of techniques normally taught in the first year of an econometrics sequence and a tremendous variety of advanced techniques such as nested logit models parametric duration models Poisson regressions with right censoring and nonlinear regressions estimated by instrumental variables and the generalized method of moments GMM LIMDEP s menu of options is as wide as that of any other general purpose program available though as might be expected longer in some dimensions and shorter in others Among the signature features of LIMDEP is that you will find here many models and techniques that are not available in any other computer package In addition to the estimation programs you need for your model building efforts you will also find in LIMDEP all the analytical tools you need including matrix algebra a scientific calculator data transformation features and programming language elements to extend your estimators and create new ones This program has developed over many years since 1980 initially to provide an easy to use tobit estimator hence the name LIMited DEPendent variable models With the current release of the program it has spun off a major suite of routines for the estimation of discrete choice models This program NLOGIT builds on the Nested LOGIT model NLOGI
67. the column vector y 0 1 o B 1 o after fitting a tobit model you could use TOBIT face DS CALC theta 1 s MATRIX gamma theta b gt gamma theta Note that the slash used here indicates stacking not division and that gt is a column vector Partitioned Matrices A partitioned matrix may be defined with submatrices For example suppose cl is a 5x2 matrix and c2 is 5x4 The matrix c cl c2 is a 5x6 matrix which can be defined with MATRIX 3c cl c2 The two matrices must have the same number of rows Matrices may also be stacked if they have the same number of columns For example to obtain C F use f c1 c2 C _ Mi Mv _ To obtain M use m m11 m12 m21 m22 Ma Mz Symmetric matrices may be specified in lower triangular form For example suppose M were symmetric so that M21 M12 M could be constructed using m m11 m21 m22 Using Matrix Algebra 9 17 Matrices with Identical Elements If a matrix or vector has all elements identical use a Init r c s This initializes an rxc matrix with every element equal to scalar s This is a way to define a matrix for later use by an estimation program Example 3 in Section R12 1 shows an application This method can also be used to initialize a row r 1 or column c 1 vector Alternatively you could use a c_s fora row vector or a rls for a column vector Identity Matrices To define an rxr identity matrix use
68. the highlighted commands TIP If you have not selected any lines in the editor the two selections in the Run menu will be Run Line and Run Line Multiple Times In this case the line in question is the line where the cursor is located Programs and Procedures 11 3 t Limdep Untitled 1 File Edit Insert Project Model Run Tools Window Help Distal S ele olalu SEM Options TA Untitled Pr View Editor Projects Execution Trace IV Display Tool Bar IV Display Status Bar IV Display Command Bar in 5 5 Idle ai Limdep Untitled 1 File Edit Insert Project Model Tools Window Help Di co bal a e Run Selection Ctrl R Run Selection Multiple Times Run File Run Procedure i Untitled Proj 5 D ata U 3333 Rows 3333 Obs Naw Procedure Sq Data editing window Variables be collected here 5 Namelists G Matrices Scalars G Strings Procedures 3 Output 5 Tables Output Window Stop Running Ctrl Break Figure 11 4 Run Menu 11 4 Programs and Procedures 11 3 Procedures LIMDEP operates primarily as an interpreter This means that commands are submitted one at a time and carried out as they are received This is as opposed to a compiler which would assemble a number of commands in some fashion translate them into its own language then execute them all at once
69. they are conformable CALC 3 x y Cy Dot x y d d and so on Regression Statistics The CALC command has several functions which allow you to obtain certain regression statistics such as an R in isolation from the rest of the least squares computations In the following the list of variables in the parentheses is of the form list independent variables dependent variable The dependent variable is always given last in a list As always if you want a constant term include one You can use a namelist for the independent variables if you wish and the wildcard character may be used to abbreviate lists of variable names The following functions can be computed where X is the list of independent variables Rsq X y R in regression of variable y on X R 1 e e Zi yi y y Xss X y explained sum of squares Ess X y error or residual sum of squares Tss X y total sum of squares Ser X y standard error of regression Lik X y log likelihood function Count for a Panel The number of groups in a panel defined by the stratification variable y is given by Scientific Calculator 10 13 Ngi y number of sequences of consecutive identical values of variable y This examines the sample of values and counts the number of runs of the same value assuming that each run defines a stratum In a sample of 10 if i 1 1 1 2 2 3 4 4 4 the number of runs groups is four 10 7 Correlation Coeffici
70. this section are based on a dichotomous selection mechanism Heckman s approach to estimation is based on the following observations In the selected sample E y x in sample E y X z 1 ED x a wi u gt 0 B x T Efe Ui gt a w B x Poo a w 1 B a w B x Poo gt a w P a wi Given the structure of the model and the nature of the observed data o cannot be estimated so it is normalized to 1 0 We observe the same values of z regardless of the value of Then E y x in sample B x po A Bx Tr 0A 2 There are some subtle ambiguities in the received applications of this model First it is unclear whether the index function B x or the conditional mean is really the function of interest If the model is to be used to analyze the behavior of the selected group then it is the latter If not it is unclear The index function would be of interest if attention were to be applied to the entire population rather than those expected to be selected This is application specific Second the marginal effects in this model are complicated as well For the moment assume that x and w are the same variables Then OELy x 2 1 Ox L B O Aa x Aa 16 6 Censoring and Sample Selection For any variable x which appears in both the selection equation for z and the regression equation the marginal effect consists of both the direct part Bx
71. to enter commands in the matrix calculator window You can type MATRIX commands in the smaller Expr expression window In this dialog mode if your command will not fit on one line just keep typing At some convenient point the cursor will automatically drop down to the next line Only press Enter when you are done entering the entire command In this mode of entry you do not have to end your commands with a 9 4 Using Matrix Algebra Alternatively you can click the fy button to open a subsidiary window that provides a menu of the functions procedures See Figure 9 3 Insert Function Function Category Command Name All Scalar A BHHH x w BHHHIX Y wz C A A1 B1 C01 loads a partitioned matrix Figure 9 3 Insertion Window for Matrix Functions You can select the function you wish to insert in your command You must then fill in the arguments of the function that are specific to your expression E g if you want Chol sigma you can select Chol A from the menu then you must change A to sigma in the command 9 2 2 MATRIX Commands If your MATRIX command is part of a program it is more likely that you will enter it in line rather than in the matrix calculator That is as a command in the text editor in the format MATRIX the desired command Commands may be entered in this format from the editor as part of a procedure or in an input file All of the ap
72. to the CREATE command described in Section 7 3 If you wish simply to type in a column of data a variable in the New Variable dialog box just enter the name at the top of the box and click OK This will create a new variable with a single observation equal to zero which you will replace and all remaining observations missing You will then enter the data editor where you can type in the values in the familiar fashion New Variable xi Name jlogprod Cancel Expression Abst s x Log x 1 Phif y b z sigma Bel x Eal Bc2 x l Byn Namelist r Dot namelist v Exp x Fix x Gmalx 2 Data fil Current sample C All Observations Figure 7 2 New Variable Dialog Box Essentials of Data Management 7 3 The New Variable dialog box also allows you to transform existing variables after they have been entered For example in Figure 7 2 the dialog is being used to create a variable named logprod using two existing variables named y and x and the Log and Phi normal CDF functions After you create and enter new variables the project window is updated and the data themselves are placed in the data area Figure 7 3 illustrates A Untitled Proj BAR R Data Editor Data U 22222 Rows 3 Obs 5 Namelists Matrices Scalars E Strings C Procedures SQ Output 4 Tables Output Window Figure 7 3 Data Editor and Project Window Import Variables Click Import Variab
73. to the next step automatically Step 2 Welcome to the InstallShield Wizard for LIMDEP 9 0 Note LIMDEP is protected by copyright law and international treaties Click Next to continue Step 3 Econometric Software End User License Agreement In order to install LIMDEP 9 0 you must select I accept the terms in the license agreement Click Next to continue Step 4 Welcome to LIMDEP 9 0 This window presents a brief introduction to LIMDEP 9 0 Please take a moment to read this information and click Next to continue Step 5 Destination Folder This window indicates the destination folder for the program C Program Files The complete folder location is C Program Files Econometric Software LIMDEP9 Program Click Next to continue Step 6 Ready to Install the Program This window reviews the installation instructions Click Install to install LIMDEP 9 0 Installation takes about 60 seconds Step 7 InstallShield Wizard Completed Click Finish to complete installation You do not have to restart your computer to complete installation Step 8 The first time you launch LIMDEP you will be presented with the Welcome and Registration dialog box See Section 2 3 1 for a complete explanation of the registration process 2 2 Getting Started Installation also creates a resource folder C LIMDEP9 with three subfolders C LIMDEP9 Data Files C LIMDEP9 LIMDEP Command Files C LIMDEP9 Project Files NOTE All sample data files referenced
74. when it is needed You may also use Output 2 to list fixed effects in an output file This will also produce estimated standard errors for the fixed effects Ifthe number of groups is large the amount of output can be very large The Linear Regression Model 14 19 Standard options for residuals and fitted values include the following All of are available as usual List Keep Fill 3 Wts to display residuals and fitted values name to retain predictions name to retain residuals a submatrix of the parameter VC matrix missing observations weighting variable Printve If your stratification indicators are set up properly for out of sample observations Fill will allow you to extrapolate outside the estimation sample WARNING If you do not have a stratification indicator already in use Fill will not work The _stratum variable is set up only for the estimation sample Thus with Pds T you cannot extrapolate outside the sample Two full sets of estimates are computed by this estimator 1 Constrained Least Squares Regression The fixed effects model above with all of the individual specific constants assumed equal is y a P x This model is estimated by simple ordinary least squares It is reported as OLS Without Group Dummy Variables 2 Least Squares Dummy Variable The fixed effects model with individual specific constant terms is estimated by partitioned ord
75. would replace the title in the figure In this version the title appears as a header and the regression equation is placed in the footer of the figure Untitled Plot 3 p Simple Plot of Gas against Price Figure 13 9 Scatter Plot with Linear Regression 13 6 6 Time Series Plots Time series plots that is plots of variables against the date can be obtained by using DATES and PERIOD to set up the dating then omitting the Lhs part of the PLOT command When you omit the Lhs part of the command it is assumed that this is a time series plot and the adjacent points are automatically connected The figure is also automatically labeled with the dates The Fill specification discussed below is not necessary Figure E4 7 is a time series plot of the three macroeconomic price series for the data above Note the use of the Grid specification to improve the readability of the figure The command is DATES 1953 PERIOD 1953 2004 PLOT Rhs pn pd ps Grid Title Time Series Plot of Price Series Yaxis Prices 13 14 Describing Sample Data Untitled Plot 4 Figure 13 10 Time Series Plot for Several Variables 13 6 7 Plotting Several Variables Against One Variable To plot several variables against a single one just include more than one Rhs variable in the command The command is PLOT Lhs variable on horizontal axis Rhs up to five variables to be plotted 3 other options such as
76. x and some values of x are missing the corresponding values of y will be also When computing a column of predictions LIMDEP returns a missing value for any observations for which any of the variables needed to compute the prediction are missing even if the variable which will contain the predictions already exists at the time This results because when you request a model to produce a set of predictions LIMDEP begins the process by clearing the column in the data area where it will store the predictions Data areas are cleared by filling them with the missing value code 7 14 Essentials of Data Management 7 3 4 CREATE Functions The expressions in CREATE may involve the following functions Common Algebraic Functions Log x natural logarithm Exp x exponent Abs x absolute value Sqr x square root Sin x sine Rsn x arcsine operand between 1 and 1 Cos x cosine Res x arccosine operand between 1 and 1 Tan x tangent Ath x hyperbolic arctangent 2 log 1 x 1 x l lt x lt 1 Ati x inverse hyperbolic arctangent exp 2x 1 exp 2x 1 Gma x gamma function x 1 if x is an integer Psi x digamma log derivative of gamma function I I x Psp x trigamma log 2nd derivative of gamma IT T x Lgm x log of gamma function returned for Gma if x gt 50 Sgn x sign function 1 0 1 for x lt gt 0 Fix x round to n
77. x x But longer matrix expressions may not be grouped in parentheses nor may they appear as arguments in other matrix functions Expressions which must be used in later sums and differences or functions must be computed first There will usually be other ways to obtain the desired result compactly For examples d Sinv a c is invalid but can be computed with d Nvsm a c d a c q is invalid but can be computed with d Msum a c q and d Ginv a q r is invalid but can be computed with d Iprd a q r The functions Msum Mdif Nvsm and Iprd may facilitate grouping matrices if necessary 9 5 Entering Moving and Rearranging Matrices To define a matrix use MATRIX name row1 row2 Elements in a row are separated by commas while rows are separated by slashes For example 9 16 Using Matrix Algebra MATRIX a 1 2 3 4 4 3 2 1 0 0 0 0 1 creates a 4 0 O WwW N 3 4 2 1 To facilitate entry of matrices you can use these two arrangements 0 0 k value k_value a Kx1 column vector with all elements equal to value a 1xK row vector with all elements equal to value Thus in the last row above 0 0 0 0 could be replaced with 4 0 Symmetric matrices may be entered in lower triangular form For example 1 2 3 MATRIX sa 1 2 3 4 5 6 createsa 2 3 5 4 5 6 Matrix elements given in a list such as above may be scalars or even other matrices and vectors For example to compute
78. your LIMDEP session from the Start Programs menu or a shortcut on your desktop the initial screen will show a project window entitled Untitled Project 1 and an empty desktop as shown in Figure 3 1 You can now begin your session by starting a new project or reloading an existing one Figure 3 2 shows the File menu the lower sections show some of our previous work 3 2 1 Opening a Project You can select Open or Open Project in the File menu they are the same at this point to reload a project that you saved earlier or select one of the existing projects known to LIMDEP if any are You may also select New to begin a new project NOTE In order to operate LIMDEP you must have a project open This may be the default untitled project or a project that you created earlier You will know that a project is open by the appearance of a project window on your desktop Most of LIMDEP s functions will not operate if you do not have a project open Note that the window shows that the data area has 3 333 rows Your project window will show a different value This is determined by a setting of the size of the data area TIP You can associate a LIMDEP project file see Section 2 9 with the program and launch LIMDEP directly with your project file Use My Computer or the Windows Explorer to navigate to the folder where you have created your project file its name will be lt the name gt LPJ Drag the icon for the LPJ file to your
79. 08 5 77 338 21129 ASNS 118 1 148 9 253530 1992 112 4 77 040 21505 128 4 123 2 151 4 256922 1993 114 1 76 257 21515 LINS T3379 167 0 260282 1994 116 2 76 614 21797 136 0 141 7 172 0 263455 1995 120 22 717 826 22100 139 0 156 5 175 9 266588 1996 130 4 82 596 22506 141 4 157 0 181 9 269714 1997 134 4 82 579 22944 141 7 TSTS 186 7 272958 1998 122 4 71 874 24079 140 7 150 6 190 3 276154 1999 13739 78 207 24464 139 6 1 520 197 7 279328 2000 WTS end 100 000 25380 139 6 155 8 209 6 282429 2001 171 6 96 289 25449 138 9 158 7 210 6 285366 2002 163 4 90 405 26352 V3 3 152 0 207 4 288217 2003 191 3 105 154 26437 134 7 142 9 209 3 291073 2004 224 5 123 901 27113 133 9 13 353 209 1 293951 6 4 Application and Tutorial 6 3 Read the Raw Data In order to analyze your data you must read them into the program There are many ways to read your data into LIMDEP We will consider two simple ones via an Excel spreadsheet and as portable ASCII text Others are described in the full manual for the software Excel Spreadsheet If your data are given to you in the form of an Excel spreadsheet then you can import them directly into the program The first step is to use the Project menu on the desktop as shown in Figure 6 1 This would then launch a mini explorer You would then locate your file in the menu Finally you can just double click the file name and the data are read into the program Limdep Output Dor Fie Edit Insert fa WG Model Ru
80. 122425 8754652 0622674 CA Namelists Log likelihood E Matrices 3 Restricted b 0 PhB Chi sq 1 prob Ph VARB Info criter Log memiya Prd Crt Ph SIGMA Akaike Info Criter Scalars Autocorrel Durbin Watson Stat 4 Strings Rho cor e e 1 C Procedures E Output Variable Coefficient Standard Error t ratio 4 Tables ge Sh eee G earn NS Cne ee fa ena Nir pa onstant 02910129 09381422 X 95847375 09346887 a Ln 33 33 Figure 4 5 Regression Results in Output Window The dialog box just shown is called a Command Builder because in addition to submitting the necessary information to the program to carry out the regression it literally creates the command you have issued and places it in the output window You can see this result in Figure 14 6 where the REGRESS command is echoed in the output window before the results You can edit copy and paste this command to move it to your editing window where you may change it and use it as if you had typed it yourself LIMDEP Commands 4 7 Limdep Output File Edit Insert Project Model Run Tools Window Help Untitled Proj OX untitled 1 9 Data SAMPLE 1 100 4 Variables CREATE X RNN 0 1 x CREATE Y X RNN O0 1 bY REGRESS Lhs y Rhs one x gt LOGL_OBS 4 Namelists bra aa Status Trace gt VARB plot lhs x rhs y reg grid a gt SIGMA Exit status for this model command is CODATO
81. 16 Autocorrelation 14 5 14 9 14 10 Binary choice 15 1 Marginal effects 15 6 Marginal effect for dummy variable 15 7 Prediction 15 4 Robust covariance matrix 15 7 Binary variables 7 10 7 14 Box Cox transformation 7 9 Browser 2 8 CALCULATE 6 23 6 24 10 1 Algebra 10 6 10 7 Commands 10 2 10 5 10 6 Correlation 10 11 10 13 Functions 10 9 10 10 Matrix dimensions 10 10 Minimum and maximum 10 11 Names 10 7 Normal CDF 10 10 Regression statistics 10 11 Results 6 24 10 4 R squared 10 12 t distribution 10 10 Categorical variable 7 17 Censored regression 16 2 Censoring 16 1 Chi squared test 6 25 Clustering 15 8 Coefficients 8 14 Command 4 1 Command ending 4 2 2SLS 14 11 CALC 6 23 6 24 10 1 CREATE 6 13 7 2 7 9 7 30 CROSSTAB 13 6 DATES 6 16 7 24 7 29 DELETE 7 21 DSTAT 13 1 6 12 ENDPROC 11 4 11 EXECUTE 11 2 11 GOTO 11 5 HISTOGRAM 13 4 INCLUDE 7 24 7 25 6 17 5 4 11 5 KERNEL 13 7 13 8 LOAD 2 7 LOGIT 15 1 15 2 15 3 MATRIX 6 17 6 23 6 26 9 1 9 4 NAMELIST 6 17 6 22 6 26 7 21 7 22 OPEN 2 7 ORDERED CHOICE 15 9 PERIOD 6 16 7 24 7 28 7 29 PLOT 6 16 13 10 13 12 PROBIT 15 1 15 2 16 5 PROC 10 2 11 4 11 5 READ 6 4 6 6 7 1 7 7 REGRESS 3 11 3 12 6 19 6 22 6 25 6 26 7 2 14 1 14 4 REJECT 7 24 7 25 SAMPLE 7 24 7 25 SAVE 2 7 SELECTION 16 4 16 5 SPLOT 7 21 TOBIT 16 1 WALD 6 26 Command builders 4 4 4 5 6 17 8 3 8 4 8 5 12 3 Commands 3 7 3 9 4 1 Command
82. 16 8 159565 F y T leg 2004 224 5 123 901 27113 133 9 133 3 209 1 293951 F Descriptive Statistics for all variables H E Strings DSTAT Rhs E Procedures Transformed Variables Sy Output CREATE logg Tables Logs logi Output Win logpne logpuc logppt 7 t Tutorial lim log gasexp pop gasprice log gasprice log income log pnewcar log pusedcar eh gale ta s year 1953 Define data to be yearly time series Sha set first year as 1953 observations 1953 DATES 1953 This indicates the first year of the data PERIOD 1953 2004 This indicates which years of data to use Time series of four price variables with title and grid for readability PLOT Rhs gasprice pnewcar pusedcar ppubtrn gt Grid Title Time Series Plot of Price Indices Three different ways to display a correlation matrix for four variables STAT Rhs gasprice pnewcar pusedcar ppubtrn Output 2 MATRIX list Xcor gasprice pnewcar pusedcar ppubtrn NAMELIST prices gasprico pnewcar pusedcar ppubtrn MATRIX list Xcor prices Simple regression of logG on a constant and log price Computations to analyse potential biases based on the left out variable formula and plausible values REGRESS Lhs logg Rhs one logpg CALC list spi Cov logPg logI spp Var logPg plim 0 1 spivspp 1 0 Multiple regression including both price and income to confirm expecations about w happ
83. 2 Output from Estimation Programs Results produced by the estimation commands will of course vary from model to model The display in the output window in Figure 8 7 would be typical These are the results produced by estimation of a basic tobit model We converted the dependent variable in the preceding linear model to deviations from the overall mean then forced a tobit model on the resulting variable F3 Output DER Status Trace Begin main iterations for optimization Normal exit from iterations Exit status 0 gt CREATE IDEY I XBR I gt TOBIT Lhs IDEY RHS ONE F C EE HE HE HE HE HE HE HE HE HE HE HE HEHE EEEE HE HE HE HE HE HE HE HE HE EEEE EEEE EEEE EEEE E EEEE EE EEE Estimation Data Analysis Program Tobit Censored FEE IE HEHE HE FE FE HE FE FE FE FE FE FE FE FE FE FE FE FE FE SE FE FE SE SE SEE SE SE SE SE SEE 2E SE 2E SE SE SEE SE SE E36 SEE 2E 5E 38 26 36 36 E 3E 36 96 EE Normal exit from iterations Exit status 0 Limited Dependent Variable Model CENSORED Maximum Likelihood Estimates Model estimated Dec 24 2005 at 02 57 53PM Dependent variable IDEY Weighting variable None Number of observations 200 Iterations completed 5 Log likelihood function 348 2706 Nunber of parameters 4 Info Criterion AIC Finite Sample AIC Info Criterion BIC Info Criterion HQIC Threshold values for the model Lower 0000 Upper infinity IM test df for tobit 11 068 Normality T
84. 2976D 04 Var u 296782D 04 Corr v i t v i s 478868 Lagrange Multiplier Test vs Model 3 188 08 1 df prob value 000000 High values of LM favor FEM REM over CR model Fixed vs Random Effects Hausman Sell _ 2 df prob value 205357 High low values of H favor FEM REM Reestimated using GLS coefficients Original Var e 141468D 05 Var u 325318D 05 Sum of Squares 572940D 06 R squared 747284D 00 HINT Large values of the Hausman statistic argue in favor of the fixed effects model over the random effects model Large values of the LM statistic argue in favor of one of the one factor models against the classical regression with no group specific effects A large value of the LM statistic in the presence of a small Hausman statistic as in our application argues in favor of the random effects model Commands for One Factor Common Effects Models The basic command for estimation of the fixed effects model is REGRESS Lhs dependent variable Rhs independent variables Str stratification or Pds count variable Panel Fixed Effects 14 18 The Linear Regression Model The command for random effects is REGRESS Lhs dependent variable Rhs independent variables Str stratification or Pds count variable Panel Random Effects If the last line specifies only Panel and neither fixed nor random effects then both mod
85. 31 100 CREATE 31 Rnu 1 3 k Rnu 5 2 y Exp 3 6 Log l 4 Log k Rnn 0 4 REGRESS Lhs Log y Rhs one log 1 log k CLS b 2 b 3 1 The following results for restricted least squares are produced The CALC function sets the seed for the random number generator at a specific value so you can replicate the results Ordinary least squares regression LHS LOGY Mean 3 618745 Standard deviation 4 069505 WTS none Number of observs 100 Model size Parameters 3 Degrees of freedom 97 Residuals Sum of squares 1624 362 Standard error of e 4 092187 Fit R squared 9249439E 02 Adjusted R squared 1117841E 01 Model test EF 2y 97 prob 45 6372 Diagnostic Log likelihood 281 2789 Restricted b 0 281 7435 Chi sq E 2 prob 93 6284 Variable Coefficient Standard Error t ratio P T gt t Mean of X Constant 3 20014797 1 06375203 3 008 0033 LOGL 80563172 1 40618551 573 5680 68423500 LOGK 85445443 1 14222281 748 4562 15523890 The Linear Regression Model 14 7 Linearly restricted regression Ordinary least squares regression LHS LOGY Mean 3 618745 Standard deviation 4 069505 WTS none Number of observs 100 Model size Parameters 2 Degrees of freedom 98 Residuals Sum of squares 1629 865 Standard error of e 4 078146 Fit R squared 5892627E 02 Adjus
86. 359708395 1842 77624 Bayes Info Criterion T2953 1 32072 I BIC no model BIC 09270 06744 Pseudo R squared 01923 00000 Pct Correct Pred 62 85223 00000 50 eans y 0 y 1 y 2 y 3 y 4 y 5 y 6 Outcome 3709 6291 0000 0000 0000 0000 0000 Pred Pr 3709 6291 0000 0000 0000 0000 0000 otes Entropy computed as Sum i Sum j Pfit i j logPfit i j Normalized entropy is computed against MO Entropy ratio statistic is computed against MO BIC 2 criterion log N degrees of freedom If the model has only constants or if it has no constants the statistics reported here are not useable A variety of fit measures for the model are listed Fit Measures for Binomial Choice Model Logit model for variable DOCTOR Proportions P0 370892 Pl 629108 27326 NO 10135 N1 17191 LogL 17673 098 LogL0 18019 552 Estrella 1 L L0 2L0 n 02528 Efron McFadden Ben Lerman 02435 01923 54487 Cramer Veall Zim Rsqrd_ML 02470 04348 02504 Information Akaike I C Schwarz I C Criteria 1 29394 1 29574 Predictions for Binary Choice Model Predicted value is 1 when probability is greater than 500000 0 otherwise Note column or row total percentages may not sum to 100 because of rounding Percentages are of full sample Actual Predicted Value Value 0 T Total Actual 0 378 1 4 9757 35 7 10135 37 1 1 394 1 4 16797 61 5 17191 62 9 T
87. 5 EB untitled Plot 3 Histogram for Variable HHHINC fey 5 S 3 gt 2 u 17 526 21 908 26 289 30 674 HHNINC Figure 13 1 Histogram for a Continuous Variable There are other ways to examine continuous data One way is to use RECODE to change your continuous variable into a discrete one Alternatively you may provide a set of interval limits and request a count of the observations in the intervals you define The command would be HISTOGRAM Rhs Limits 10 11 1k where the limits you give are the left boundaries of the intervals Thus the number of limits you provide gives the number of intervals Intervals are defined as greater than or equal to lower and less than upper For example still using our income data HISTOGRAM Rhs educ Limits 0 75 2 5 4 6 9 12 defines five bins for the histogram with the rightmost containing all values greater than or equal to 12 To request K equal length intervals in the range lower to upper use HISTOGRAM Rhs variable Int k Limits lower upper Finally you can use HISTOGRAM to search for the interval limits instead of the frequency counts The command HISTOGRAM Rhs variable Bin p where p is a sample fraction proportion will obtain the interval boundaries such that each bin contains the specified proportion of the observations NOTE If the specified proportion does not lead to an even set of bins then an
88. 6 1982 228 8 3 894 9725 1 976 2 964 3 460 1 000 1 000 1 000 1983 239 6 3 764 9930 2 026 3 297 3 626 1 041 1 021 1 062 1984 244 7 3 707 10421 2 085 3 757 3 852 1 038 1 050 1 117 1985 245 8 3 738 10563 2 152 3 797 4 028 1 045 1 075 1 173 1986 269 4 2 921 10780 2 240 3 632 4 264 1 053 1 069 1 224 We will compute simple regressions of g on one pg and y The first regression is based on the pre embargo data 1960 1973 but fitted values are produced for all 27 years The second regression uses the full data set and also produces predicted values for the full sample We then plot the actual and both predicted series on the same figure to examine the influence of the later data points DATE 1960 PERIOD 1960 1973 REGRESS Lhs g Rhs one pg y Keep gfit6073 Fill PERIOD 1960 1986 REGRESS Lhs g Rhs one pg y Keep gfit6086 PLOT Rhs g gfit6073 gfit6086 Grid Variable 1959 1963 1967 1971 1975 1979 1983 1987 Year G GFIT6O7S GFIT6O86 Figure 8 14 Time Series Plot The following chapters will detail the formulas used in computing predictions residuals and accompanying information When you use List some additional information will be displayed in your output In some cases there is no natural residual or prediction to be computed for example in the bivariate probit model In these cases an alternative computation is done so what is requested by Res or
89. 76 9738 5232 26 8 21 5 LILES 0 1960 12 0 19 112 9770 S125 25 10 22 2 180760 1961 1260 18 924 9843 S15 26 0 23 2 183742 1962 12 6 19 043 10226 5123 28 4 24 0 186590 1963 13 0 18 997 10398 51 0 28 7 24 3 189300 1964 13 6 18 6813 11051 50 9 30 0 24 7 191927 1965 14 8 19 587 11430 49 7 29 8 25 2 194347 1966 1 6 20 038 11981 48 8 29 0 26 1 196599 1967 Ea 20 700 12418 49 3 29 9 27 4 198752 1968 18 6 21 005 12932 50 7 308 7 28 7 200745 1969 20 25 21 696 13060 51 5 30 9 30 9 202736 1970 21 9 21 890 13 56 7 53 0 312 35 2 205089 1971 2322 22 050 14008 55 2 33 10 37 8 207692 1972 24 4 22 336 14270 54 7 33 s 39 3 209924 1973 28 1 24 473 15309 54 8 35 2 39 7 211939 1974 36 1 33 059 15074 57 29 36 7 40 6 213898 1975 39 35 278 15555 62 9 43 8 43 5 215981 1976 43 0 36 777 15693 66 9 50 3 47 8 218086 LOTT 46 9 38 907 15991 70 4 54 7 50 0 220289 1978 50 1 40 597 16674 75 8 55 8 515 222629 LOTS 66 2 54 406 16843 81 8 60 2 54 9 225106 1980 86 7 75 509 16711 88 4 62 3 69 0 227726 1981 OTD 84 018 17046 93 7 76 9 85 6 230008 1982 94 1 79 768 17429 97 4 88 8 94 9 232218 1983 93 1 77 160 17659 99 9 98 7 99 5 234333 1984 94 6 76 005 18922 102 8 LA 5 105 7 236394 1985 Oh ee 76 619 19622 106 1 LEST 110 5 238506 1986 80 1 60 175 19944 1L10226 108 8 117 0 240683 1987 85 4 62 488 19802 114 6 113 1 121 1 242843 1988 88 3 63 017 20682 116 9 118 0 123 3 245061 1989 98 6 68 837 21048 119 2 120 4 129 5 247387 1990 111 2 78 385 21379 121 0 117 6 142 6 250181 1991 1
90. 9 30 11AM LHS LY ean 3 494703 Standard deviation 4 036799 WTS none Number of observs 500 Model size Parameters 4 Degrees of freedom 496 Residuals Sum of squares 8123 764 Standard error of e 4 047043 Fit R squared 9607608E 03 Adjusted R squared 5081815E 02 Model test EL 3 496 prob 16 9239 Diagnostic Log likelihood 1406 454 Restricted b 0 1406 695 Chi sq 3 prob 48 9231 Info criter LogAmemiya Prd Crt 2 803941 Akaike Info Criter 2 803941 Restrictns F 2 494 prob 47 6265 Not using OLS or no constant Rsqd amp F may be lt 0 Note with restrictions imposed Rsqd may be lt 0 Variable Coefficient Standard Error t ratio P T gt t Mean of X Constant 87115229 26637740 10 779 0000 LL 16811718 94623345 1 234 2176 66349271 LK 16811718 94623345 178 8591 16198512 LL2 33357188 1 05355989 Soy Poh 53150388 LK2 31357011 76300427 411 6813 16242739 LKL 02000176 1 26678767 016 9874 10542795 The Linear Regression Model 14 9 14 3 Estimating Models with Heteroscedasticity For the model in which is either known or has been estimated already the weighted least squares estimator is requested with REGRESS Lhs Rhs Wts weighting variable In computing weighted estimators we use the formulas n the current sample size after skipping any missing observations Wi n X W W Scale x W
91. 92 Georgia 304 531 11 530 45 534 71 20 more observations You must include a name for the labels Note that the State name is used for the labels but not for the data 7 2 5 Reading a Spreadsheet File You can read worksheet files such as those created by Lotus WKx or Microsoft Excel XLS directly into LIMDEP without conversion The command is simply READ File name Format WKS or READ File name Format XLS All of the information needed to set up the data is contained within the file However if the columns in your worksheet were created by formulas within the spreadsheet program rather than 7 8 Essentials of Data Management being typed in initially then LIMDEP will not find the transformed data The reason is that the XLS file does not contain the data themselves but merely the formula for recreating the data Since we have not replicated the spreadsheet program inside LIMDEP it is not possible to redo the transformation NOTE Please note the caution about Excel 2007 in Section 6 3 7 2 6 Missing Values in Data Files LIMDEP will catch nonnumeric or missing data codes in most types of data sets In general any value not readable as a number is considered a missing value and given the value 999 NOTE In all settings 999 is LIMDEP s internal missing data code Some things to remember about missing data are A blank in a data file is normally not a missing value it is just a b
92. A y Ely LIMDEP Estimation Results Run log line 6 Current sample contains Predicted Values Observation Observed Y T 0 00000 2 0 00000 3 3 0000 4 4 0000 5 6 0000 6 18 000 8 11 000 9 39 000 0 1 29 000 34 observations 0 39914 0 22733 4 5761 4 5761 6 9559 13 185 6 6922 44 388 20 603 gt observation was not in Predicted Y Residual 0 0 Si TOR O 4 4 5 5 8 3991 2273 5761 5761 9559 8150 3078 3881 3967 For a linear regression the listed items are the familiar ones REGRESS x 1 8 0 9184 1 4813 1 5209 1 5209 1 9396 2 5791 1 9009 3 7930 3 0255 Page estimating sample Prly ooocaoaaoaaoaccoor k y 6709 7967 1644 1881 1499 0426 0375 0453 0162 Lhs g Rhs one pg y Keep gfit6073 List Fill Predicted Values gt observation was not in estimating sample Observation Observed Y 1960 129 70 1961 1313 0 1962 137 10 1963 141 60 1964 148 80 1965 155 90 1966 164 90 1967 171 00 1968 183 40 1969 195 80 1970 207 40 Predicted Y r27 129 134 138 148 160 170 180 187 195 204 98 47 80 04 58 79 39 11 95 73 04 T 2 3 Residual Tts 7243 8315 3032 roo 4 2217 8910 4906 lt 1072 5490 0665 3641 95 Forecast Interval 113 5586 115 8623 121 5356 124 9718 134 9251 147 7508 157 4244 167 4143 175 1447 182 9210 191 1278
93. Category 1 ew variable UNDERHS Frequency Q lt 2 ew variable HS Frequency 23 3 ew variable COLLEGE Frequency 0 lt a ff 4 ew variable POSTGRAD Frequency 29 5 ew variable EDUCO5 Frequency 0 lt 6 ew variable EDUC06 Frequency 22 7 ew variable EDUCO7 Frequency O lt A J 8 ew variable EDUCO8 Frequency 26 Note this is a complete set of dummy variables If you use this set in a regression drop the constant 7 18 Essentials of Data Management Things to note e The empty cells are flagged in the listing but the variable is created anyway e If your list of names is not long enough the remaining names are built up from the original variable name and the category value e The program warns you that this has computed a complete set of dummy variables If you use this set of variables in a regression or other model you should not include an overall constant term in the model because that would cause perfect collinearity the dummy variable trap Thus a model which contained both one and educ_ would contain five variables that are perfectly collinear You may want to avoid the last of these without having to choose one of the variables to omit from the set You can direct the transformation to drop one of the categories by adding 0 after the variable name in the parentheses CREATE Expand variable 0 list of names For our previous example this modification would change the
94. EGRESS 8 2 8 3 8 5 REGRESS command 3 11 3 12 6 22 Regression 3 11 6 1 6 12 6 19 14 1 Autocorrelation 14 9 14 10 Constant term 14 1 Fixed effects 14 15 14 18 Heteroscedasticity 14 9 Hypothesis test 14 8 l 4 Left out variable 6 20 Model 14 1 Multiple 6 22 Panel data 14 12 Plot residuals 14 4 Predictions 14 4 Random effects 14 15 14 21 Residuals 14 3 Residual plot 6 23 Results 14 2 14 3 Restricted 14 5 14 6 Retrievable results 14 3 Robust covariance matrix 14 5 Regression constant term 6 19 Reserved names 4 3 REJECT command 7 24 7 26 Residuals plot 6 21 Residuals 8 16 Plot 8 18 Residuals 12 6 Restricted least squares 9 1 14 6 Restricted regression 6 27 MATRIX 6 27 t statistic 6 28 Retrievable results 8 14 Rhs list 8 1 Robust covariance matrix 12 5 14 5 2sls 14 11 Panel data 14 21 Run menu 3 6 3 7 Sample 7 24 SAMPLE command 7 25 7 27 Sample observations 7 3 Sample selection 16 1 16 4 Heckman estimator 16 6 Model 16 5 PROBIT 16 5 Selection equation 16 5 Two step estimation 16 6 Sandwich estimator 15 7 SAS 2 7 Save 2 5 SAVE command 2 7 Scalars 6 24 8 15 Seed RNG 7 20 Session 3 1 Skewness 13 1 SKIP 7 31 Spreadsheet 6 4 Spreadsheet importing 7 7 Index MATRIX 6 29 Chi squared 6 29 Standard errors 8 14 Stat Transfer 2 7 Stata 2 7 Stratification 14 13 Structural break 6 29 Sums of observations matrix 9 19 Weighted9 20 Syntax command 4 1 Text editing 3 3 3 5 Text edito
95. Edit Insert Project Model Run Tools Window Help osal S e elau AA Untitled 1 f Insert Name I will use this window to collect the commands that I need to analyze my data SAMPLE 1 100 CREATE X RNN 0 1 Y REGRESS Lhs Y Rhs Rnn O0 1 One X Ln 1 6 Idle h Figure 3 10 Editing Window The output window will always contain a transcript of your commands Since you have not generated any numerical results at this point that is all it contains Operating LIMDEP t Limdep Output File Edit Insert Project Model Run Tools Window Help Dora S ele olol Bala Oooo e LG Untitled Proj Untitled 1 Data U 3333 Rows f Insert Name zl SAMPLE 1 100 CREATE X Ron 0 1 X Rnn 0 1 1 RESET 1 SAMPLE 2 CREATE nnc 1 X Rnn 0 1 gt RESET Initializing LIMDEP Version 9 0 1 January 1 2006 gt SAHPLE 1 100 gi CREATE X Rnn 0 1 Z Rnn 0 1 Ek Ln 5 5 Idle 11 12 4 Figure 3 11 Output Window with Command Echo Compute the Regression Before doing this step notice that the top half of the output window has the Trace tab selected If you click the Status tab this will change the appearance of the top half of the window as you ll see later The trace feature in the output window is useful when you execute iterative complicated
96. IMDEP to fit equations to data and test hypotheses about the relationships implied by that estimation process For purposes of documenting the program we use the term model estimation broadly to encompass all those functions that involve manipulation of data to produce statistics to summarize the information the data contain Thus this manual begins with a chapter about computing descriptive statistics which one might not normally consider model building However as data summaries for program purposes we consider these part of the model building functions in LIMDEP The definition of a model in LIMDEP consists of the modeling framework the statement of the variables in the model and what role the variables will play in that model The remainder of this chapter will describe in general terms how to use this format to construct model estimation commands in LIMDEP 12 3 Model Commands LIMDEP s model commands all use the same format The essential parts are as follows Model name _ model variables specification essential specifications for some models optional specifications The Model name designates the modeling framework In most cases this defines a broad class of models such as POISSON which indicates that the command is for one of the twenty or 12 2 Econometric Model Estimation so different models for count data most of which are extensions of the basic Poisson regression model The model variabl
97. IMDEP will look for empty cells If there are any estimation is halted If value j is not represented in the data then the threshold parameter u is not estimable In this circumstance you will receive a diagnostic such as ORDE Panel BIVA PROBIT A cell has almost no observations Empty cell Y never takes value 2 This diagnostic means exactly what it says The ordered probability model cannot be estimated unless all cells are represented in the data Users frequently overlook the coding requirement y 0 1 If you have a dependent variable that is coded 1 2 you will see the following diagnostic Models Insufficient variation in dependent variable The reason this particular diagnostic shows up is that LIMDEP creates a new variable from your dependent variable say y which equals zero when y equals zero and one when y is greater than zero It then tries to obtain starting values for the model by fitting a regression model to this new variable If you have miscoded the Lhs variable the transformed variable always equals one which explains the diagnostic In fact there is no variation in the transformed dependent variable If this is the case you can simply use CREATE to subtract 1 0 from your dependent variable to use this estimator The probit model is the default specification To estimate an ordered logit add Model Logit to the command The standardized logistic distribution mean zero standard devia
98. IZE 1 74285714 TNN T G 2A19N47A Alt F4 INVT GC CHAIR 433270678 24 9486076 32 3710038 301 439107 47 9783530 447378551 19 6760442 1 01034998 1 2 326849n1 000000000 000000000 2 00000000 63 0000000 30 0000000 000000000 2 00000000 1 00000000 NNNNANNNN Idle 08 5 4 2 8 Fast Input of a Data Set with OPEN LOAD File Save or just saving the files upon Exit then File Open offers an extremely fast and easy way for you to transform ASCII or any other raw format data to binary format for quick input The first time you use the data set use File Save or the LIMDEP SAVE command see Chapter 3 to rewrite it in LIMDEP s binary format You can create any new variables you want to before doing so these will be written with the raw data Later instead of reading the raw data set just use File Open or any of the Windows Explorers to retrieve the file you saved earlier If you created any new variables before you saved the data set they will be loaded as well The time savings in reading an ASCII data set which is unformatted are about 90 For a formatted data set it is still at least three times as fast TIP The popular data transfer program Stat Transfer supports LIMDEP and will translate many common system files such as SAS Stata SYSTAT TSP EViews and so on to LPJ style LIMDEP project files 2 8 Getting Started 2 9 Starting LIMDEP from your Desktop or with a Web Bro
99. MA Gamma model for count data NEGBIN Negative binomial regression model POISSON Models for count data Models for Censored Variables BTOBIT Bivariate tobit models GROUPED Regression models for categorical censored data MIMIC Multiple indicators and multiple causes for a latent variable NTOBIT Nested tobit models TOBIT Censored regression models Models for Variables with Limited Range of Variation LOGLINEAR Loglinear models beta gamma Weibull exponential geometric inverse Gaussian LOGNORMAL Lognormal regression model TRUNCATE Truncated regression models Models for Survival Times and Hazard Functions SURVIVAL Survival hazard function models 12 6 Common Features of Most Models There is wide variety in the components and features across the different model classes But there are several elements that are common to nearly all of them Some of those are listed below 12 6 1 Controlling Output from Model Commands These two settings control model results that are generally not reported unless requested Margin requests display of marginal effects Printve requests display of the estimated asymptotic covariance matrix Normally the matrix is not shown in the model results 12 6 2 Robust Asymptotic Covariance Matrices These settings control how the covariance matrix for the coefficient estimator is estimated Cluster spec requests computation of the cluster form of covariance the estimator Str
100. Matrix Functions Again the use of the apostrophe operator here is important in that it sets up the summing operation that allows you to use large matrices That is while logically x y is the same as x y for LIMDEP s purposes they are very different operations The left hand side requires that copies of x and y be made in memory while the right hand side requires only that the sum of cross products be accumulated in memory TIP All sample moments are computed for the currently defined sample If the current sample includes variables with missing data you should make sure the SKIP switch is turned on Missing values in a matrix sum are treated as valid data and can distort your results If you precede the MATRIX command s with SKIP then in summing operations observations with missing values will be ignored The operations described here for manipulating data matrices are logically no different from other matrix operations already described That is in your expressions there is no real need to distinguish data manipulations from operations involving computed matrices The purpose of this section is to highlight some special cases and useful shortcuts Sums Means and Weighted Sums of Observations and Subsamples To sum the rows of a data matrix use name x l or x one The symbol 1 is allowable in this context to stand for a column of ones of length n This returns a Kx1 column vector whose kth element is the sum of th
101. Note the reversal of LIMDEP s usual convention This command puts the Lhs variable on the horizontal axis whereas a regression might be expected to do the reverse You may add a title to the figure by including Title the title to be used The title is placed at the top of the figure The vertical axis of the plot is usually labeled with some variable name You can override this with Yaxis the label to be used up to eight characters This will often be useful when you plot a function or more than one variable 13 6 4 Plotting One Variable Against Another To produce a scatter plot of one variable y against another x variable the PLOT command is given with only a single Rhs variable The command would be PLOT Lhs x Rhs y Figure E4 5 was produced with the commands listed CREATE 32 gasq 100 pop 282429 PLOT Lhs gasp Rhs g Title Simple Plot of Gas against Price Untitled Plot 2 DAR Simple Plot of Gas against Price T aa ime T 6000 6750 7600 8250 G Figure 13 8 Simple Scatter Plot Describing Sample Data 13 13 13 6 5 Plotting a Simple Linear Regression To add a regression line to a figure add Regression to the PLOT command By adding Regression to the preceding command we obtain the plot in Figure E4 6 You can also obtain this by selecting Display linear regression line in the Options page of the command builder In previous versions of LIMDEP the regression equation
102. OAD file E Econometrics Commands Examples Grunfeldi0 1lpj Session has been restored m ma a LHS I Hean 145 9582 WTS none Model size Residuals Fit Model test Diagnostic Info criter Autocorrel Standard deviation Number of observs Paraneters Degrees of freedom Sum of squares Standard error of e R squared Adjusted R squared EF 2 197 prob Log likelihood Restricted b 0 Chi sq 2 prob LogAmemiya Prd Crt Akaike Info Criter Durbin Watson Stat Rho cor e e 1 216 8753 200 3 197 1755850 94 40840 8124080 8105035 426 58 0000 1191 802 1359 151 334 70 0000 9 110149 9 110147 3581853 8209074 4 ce Variable Coefficient Standard Error t ratio P T gt t Mean of XZ t 4 4 4 4 4 Constant Cc 42 7143694 11556216 23067849 Figure 5 1 Output Window 9 51167603 00583571 02547580 4 491 19 803 9 055 0000 0000 0000 1081 68110 276 017150 5 2 Program Output 5 2 Editing Your Output The output window provides limited capability for editing You can select then delete any of the results in the window You can also highlight then use cut or copy in the output window But there is a way to get full editing capability You can select then cut or copy the material from the output window and paste it into an e
103. Page of Command Builder for Linear Regression Model Estimating Models 8 5 The other two tabs in the command builder provide additional options for the linear regression model as shown in Figures 8 4 and 8 5 For this example we ll submit the simple command from the Main page with none of the options Clicking the Run button submits the command to the program and produces the output shown in Figure R8 6 REGRESS Main Options Output Impose and test the restrictions Autocorrelation P Robust YC matrix Phil Perron test Number of periods Model type Standard model Analyze omitted variables C Stepwise regression r Panel data model I t t j Model type Fired Rand T Fixed periods 9 REGRESS Main Options Output Display estimated parameter covariance matrix F Display predictions and residuals Predictions I Keep predictions as variable Data fil Curent sample C All Observations Residuals Perform CUSUMS test F Standardize residuals before plotting or keeping Plot residuals r m I Keep residuals as variable I Keep model results for table as Cancel Figure 8 5 Output Page for Linear Regression Model The regression command that was assembled by the command builder can be seen in the output window directly above the regression output REGRESS Lhs i Rhs one f c d1 d2 d3 d4 8 6 Estimating Models The command builder has done the work of constr
104. Predictions and Residuals 8 16 Using Matrix Algebra Introduction 9 1 Entering MATRIX Commands 9 2 9 2 1 The Matrix Calculator 9 2 9 2 2 MATRIX Commands 9 4 9 2 3 Matrix Output 9 5 9 2 4 Matrix Results 9 6 9 2 5 Matrix Statistical Output 9 7 Using MATRIX Commands with Data 9 8 Table of Contents 9 4 9 5 9 6 9 7 Chapter 10 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Chapter 11 11 1 11 2 11 3 11 4 TOC 3 9 3 1 Data Matrices 9 9 9 3 2 Computations Involving Data Matrices 9 10 Manipulating Matrices 9 11 9 4 1 Naming and Notational Conventions 9 11 9 4 2 Matrix Expressions 9 13 Entering Moving and Rearranging Matrices 9 15 Matrix Functions 9 17 Sums of Observations 9 19 Scientific Calculator Introduction 10 1 Command Input in CALCULATE 10 2 Results from CALCULATE 10 4 Forms of CALCULATE Commands Conditional Commands 10 5 10 4 1 Reserved Names 10 6 10 4 2 Work Space for the Calculator 10 7 10 4 3 Compound Names for Scalars 10 7 Scalar Expressions 10 7 Calculator Functions 10 9 Correlation Coefficients 10 13 Programming with Procedures Introduction 11 1 The Text Editor 11 1 11 2 1 Placing Commands in the Editor 11 1 11 2 2 Executing the Commands in the Editor 11 2 Procedures 11 4 Defining and Executing Procedures 11 5 11 4 1 Executing a Procedure Silently 11 6 11 4 2 Parameters and Character Strings in Procedures 11 7 Part Il Econometric Models and Statistical Analyses Chapter 12 12 1 12 2 12 3
105. Project menu e Select Item into Project Namelist from the Insert menu e Right click the Namelists header in the project window and select New Namelist All these will invoke the dialog box shown in Figure 7 14 New Namelist K Name Constants o Cancel Variables NALT NI NIJ PSIZE PSIZEA TIME Total 4 wW Figure 7 14 New Namelist Dialog Box 7 4 3 Using Namelists Namelists will have many uses as you use LIMDEP to analyze your data Consider the example NAMELIST job butcher baker cndlmakr place north south east west person job place income Note that in the example the namelist person will contain eight variables as the other two namelists are expanded and included with the eighth variable income Your primary use of the NAMELIST command will be for defining variable lists for the estimation commands However a namelist may be used at any point at which a list of variable names is called for Some other applications are in defining data matrices for the MATRIX command and in several CALCULATE and CREATE commands Some examples NAMELIST xlist x1 x2 x3 x4 REGRESS Lhs y Rhs one xlist CALC Col xlist How many variables in list WRITE xlist y1 y2 y3 File DATA DAT MATRIX xtx lt x x gt Computes an X X matrix 7 24 Essentials of Data Management 7 5 The Current Sample of Observations In many cases you will simply analyze the entire da
106. Ps log ofthe peice Pde of gasoline Jogi log ofper capta income te log ofprice index for new cars Pu ected jforused cars cofpprice index for public trepeatation tnd year 1952 _ Wenvtic immeditely Dus ie mato we the bg of the price nds inour regressim model there i at least the potential for a problem of multicolinewty As indication of how seriou the problem is lively to be obtain a time four price series vag nif Cole demand equition Obtain the least squares regression resus a regression of bgG an the log of the price ider logs Report yor Tegressim tenks a Notice atthe coeicimton bagri 5 pee Should t a denmd ove dower What v Bom Sis urey aiene ha veridi othe equtim Conputethe Tinearregressiom of logG an bglord bgPg Repot yourresubs wd comment on The fall regression modelthat you will explore for the rest ofthis eoercise i logG 6 B log y p logi p logiuc p logPuc p logiyt p tte Obtai the Jest squares estimates of the coefficients of the model Repot your resubs Obtain a plot ofthe resihuals as part of your analysis 2 For mare advanced coumes Comps the hes squares regression coeficieras 5 the covariance matricior b nd ag n b Tist ihe hypothesis batal oft coeticimas Sx model swe forthe constart termare aero using an Ftet Obtain the sample Fard the appropriate critical mahue forthe test Use the 95Y sienificance lave Stillusing the full model use an Ftest to test the hypothesi
107. Run Tools Window Help Ctrl N Ctrl O Save Save As Save All Open Project Save Project As Close Project Status Trace Page Setup Current Command Print Preview Print Command 1 G GasolineData lim 2 ModeChoice Income lim 3 strom 1 lim 4 Examples_10 1_to_10 4 lim 5 GasolineMarket Ipj lt 6 mrozprobit pj 7 C imdepwesrc clogit Ipj 8 psra_wiw2whist_100907_am pj Exit Alt F4 Figure 6 11 Reloading the Project As with any software it is a good idea to save your work this way periodically 6 16 Application and Tutorial 6 5 4 Time Series Plot of the Price Variables The PLOT instruction is used to produce the different types of graphs you will obtain Since these are time series data we will first inform LIMDEP of that fact The commands are DATES 1953 This indicates the first year of the data PERIOD 1953 2004 This indicates which years of data to use Then we generate our plot with the command PLOT Rhs gasprice pnewcar pusedCar ppubtrn Grid Title Time Series Plot of Price Indices It is clear from Figure 6 12 that although the price series are correlated that is in the nature of aggregate long period time series data the correlations between the gasoline price and the public transport price seem unlikely to be severe enough to seriously impact the regression However the new and used car price indexes are quite highly
108. SS SS ee aa 1 0 206384 0 00191513 0 104454 0 00638291 0 415292 0 0178458 0 726129 0 039232 1 03697 0 0691 868 1 3478 0 110427 1 65864 0 167168 1 96948 0 222197 2 28032 0 249577 2 59116 0 267021 2 90199 0 282018 3 21283 0 27365 3 52367 0 254416 3 83451 0 232506 4 14534 0 19768 4 45618 0 158283 4 76702 0 134769 5 07786 0 112439 5 38869 0 0818033 Matrix KERNEL 100 2 5 69953 0 0647776 Figure 13 4 Matrix Results KERNEL Variables Namelists 4 Matrices P gt B Ph VARB P gt KERNEL gt LASTDSTA gt GROUPT gt OPERCHAR 4 Scalars Strings E Procedures Sy Output 4 Tables Output Window T 18 Hs You may specify the kernel function to be used with Kernel one of the eight types of kernels listed earlier The bandwidth may be specified with Smooth the bandwidth parameter The default number of points specified is 100 with zj a partition of the range of the variable You may specify the number of points up to 200 with Pts number of points to compute and plot 13 10 Describing Sample Data 13 6 Scatter Plots and Plotting Data This chapter will describe commands for producing high resolution graphs This feature can be used for simple scatter diagrams time series plots and for plotting functions such as log likelihoods You can print the graphics on standard printers and create plotter files for export to word processing programs such as Microsoft Word 13 6 1 Pri
109. SSE K F K n n 2K SSE SSE n n 2K Application and Tutorial 6 29 Where SSE is the sum of squared residuals from the indicated regression and K is the number of coefficients variables plus the constant in the model Superficially this requires us to compute the three regressions then compute the statistic We might not be interested in seeing the actual regression results for the subperiods so we go directly to the sum of squares function using the calculator We proceed as follows PERIOD 1953 2004 CALC ssep Ess x logg k col x PERIOD 1953 1973 CALC ssel Ess x logg nl n PERIOD 1974 2004 CALC sse2 Ess X logg n2 n CALC list f ssep sse1 sse2 k ssel sse2 m1 n2 2 k fe Ftb 95 k n1 n2 2 k The results shown are the sample F and the critical value from the F table The null hypothesis of equal coefficient vectors is clearly rejected Poe E ee eS Listed Calculator Results Poses reo soe Se ee See eee se F 83 664571 FC 2 262304 The second approach suggested is to use a Wald test to test the hypothesis of equal coefficients For the structural change test the statistic would be W b by V Vo b b The difference in the two approaches is that the Wald statistic does not assume that the disturbance variances in the two regressions are the same We compute the test statistic using matrix alg
110. Standard deviation 216 8753 WTS none Number of observs 200 Model size Parameters 5 Degrees of freedon 195 Residuals Sum of squares 918364 3 Standard error of e 68 62624 Fit R squared 9018836 Adjusted R squared 8998709 Model test FL 4 195 prob 448 11 0000 Diagnostic Log likelihood 1126 991 Restricted b 0 1359 151 Chi sq 4 prob 464 32 0000 Info criter LogAmemiya Prd Crt 8 482042 Akaike Info Criter 8 482032 Autocorrel Durbin Vatson Stat 7919530 Rho cor e e 1 6040235 pone Variable Coefficient Standard Error t ratio P T gt t Mean of X foe gt Constant 32 5474569 7 59963603 A k F 05122406 00838401 i A 1081 68110 25889866 01864249 A 276 017150 250 691358 34 3121896 A 10000000 265 680006 19 9233412 f R 10000000 Ln 8 44 Figure 8 6 Regression Output Window Estimating Models 8 7 The command builders are not complete for all models that can be specified by LIMDEP Many features such as the newer panel data estimators are not contained in the command builders In fact you will probably graduate from the dialog boxes fairly quickly to using the text editor for commands The editors provide a faster and more flexible means of entering program instructions 8 2
111. T has now grown to a self standing superset of LIMDEP The student version of LIMDEP that is described in this manual is the full program It is limited in the size of data set that you can analyze and the size of model that you can estimate But beyond those restrictions the student version of LIMDEP is the full program No features are restricted or disabled in any way To the best of our knowledge the code of this program is correct as described However no warranty is expressed or implied Users assume responsibility for the selection of this program to achieve their desired results and for the results obtained William H Greene Econometric Software Inc 15 Gloria Place Plainview New York 11803 January 2008 Preface Preface to the User s Guide for the Student Version of LIMDEP 9 This user s guide is constructed specifically for the student who is using LIMDEP for the first time and is most likely taking their first course in econometrics It is not simply a distillation of the full 2 000 page manual for LIMDEP This guide is divided into two parts Part I is a user s guide to operation of the software There will be several examples drawn largely from econometrics to illustrate the operation of the program However the purpose of this first part is to show you how to use the software rather than to show you specifically how to estimate and analyze econometric models with the program In Part I we are concerned with feat
112. The estimated equation is missing a crucial variable The theoretical result for a demand equation from which income has been omitted would be as follows Model logG a Pprice logPrice Bincome logincome E ae Cov logPrice logIncome B Price Price Var log Price Income plim b where bprice is the simple least squares slope in the regression of logG on a constant and logPg It is clear from the data that the two terms in the fraction are positive If the income elasticity were positive as well then the result shows that the estimator in this short regression is biased upward toward and possibly even past zero We could construct some evidence on what might be expected here Suppose the income elasticity were 1 0 and the price elasticity were 0 1 The terms in the fraction can be obtained with the command CALC list spi Cov logpg logi spp Var logpg plim 0 1 spi spp 1 0 The result is shown here If the theory is right then even if the price elasticity really is negative with these time series data and the positive income elasticity we should observe a positive coefficient on ogPg in the simple regression which we did Listed Calculator Results SPI 223618 SPP 461029 PLIM 385040 Calculator Computed 3 scalar results We proceed to compute the more appropriate regression which contains both price and income and which will either confirm or refute our theory above
113. Variables i Untitled Proj KEk Data U 11111 Rows 52 Obs The command for computing transformed variables is CREATE A single command can be used gt After we place this command in the text editor and execute it the project expands to include the new variables The new project window in shown in Figure 6 8 for all of the transformations listed gt gt CREATE logg log gasexp pop gasprice b logpg log gasprice gt logi log income gt logpne log pnewcar logpuc log pusedcar gt logppt log ppubtrn gt t Year 1953 gt gt gt gt Data Figure 6 8 Project Window E variables YEAR GASEXP GASPRICE INCOME PNEWCAR PUSEDCAR PPUBTRN POP LOGG LOGPG LOGI LOGPNC LOGPUC LOGPPT T Ea Blaesali be 6 14 6 5 3 Saving and Retrieving Your Project Since you have read your data into the program and created some new variables this is a good time to save your project Select File Save Project As next allows you to save the file anywhere you like The Project Files folder is a natural choice See Figures 6 9 and 6 10 for our application Limdep Untitled Project 1 AGI Edit Insert Project Model Run Tools Window Help New Open Close Ctrl N Ctrl O Save Save As Save All aam ntitled Proj EBR U 11111 Rows 52 Obs qyData Open Project Save Projec Close Project Page Setup Print
114. White heteroscedasticity consistent estimator For another example REGRESS Lhs profit Rhs one sales Plot residuals fits a linear model and then plots the residuals If the latter specification is omitted the residuals will not be plotted 12 4 Command Builders In what follows we will describe the model commands that you can use to fit the indicated model In all cases there are command builders that can be used instead of the text editor and command language The command builders are described in Sections 4 4 6 5 4 and 8 2 1 12 5 Model Groups Supported by LIMDEP A few of the various model commands and modeling frameworks supported by LIMDEP and NLOGIT are discussed in the chapters to follow To suggest the breadth of the full menu the following are the model names for the different classes of estimators supported by the program Some such as HISTOGRAM and BURR are quite narrow single purpose instructions while others such as POISSON call for large classes of models that may as in this case contain a large number of different variants The specific models that are presented in Chapters 13 16 in this manual are highlighted in the list The documentation below will present the basic forms of each of these Additional specifications options and model forms are developed in the full manual for LIMDEP Descriptive Statistics CLASSIFY Discriminant analysis classification into latent groups DSTAT Descriptive sta
115. Y i Note that since the outcomes are only ordinal this is not a true expected value Var2 is the probability estimated for the observed Y Estimation results kept by the estimator are as follows Matrices b estimate of B varb estimated asymptotic covariance mu J 1 estimated us Scalars kreg nreg and logl Last Model The labels are b_variables mul The specification Par adds u the set of estimated threshold values to b and varb The additional matrix mu is kept regardless but the estimated asymptotic covariance matrix is lost unless the command contains Par Models for Discrete Choice 15 13 15 3 4 Marginal Effects Marginal effects in the ordered probability models are quite involved Since there is no meaningful conditional mean function to manipulate we consider instead the effects of changes in the covariates on the cell probabilities These are OProb cell j Ox Kum B x f y B x x B where f is the appropriate density for the standard normal logistic density A 1 A Weibull or Gompertz Each vector is a multiple of the coefficient vector But it is worth noting that the magnitudes are likely to be very different In at least one case Prob cell 0 and probably more if there are more than three outcomes the partial effects have exactly the opposite signs from the estimated coefficients Thus in this model it is important to consider carefully the inte
116. a Iden number of rows It may be useful to use a scalar for the number of rows For example suppose that x is the name of a namelist of K variables which will vary from application to application and you will require a to be a KxK identity matrix where K is the number of variables in x You can use the following CALC 3k Col x MATRIX ik Iden k The notation I r produces the same matrix as Iden r Equating One Matrix to Another Use a c to equate a to c To equate a to the transpose of c use a c You would typically use this operation to keep estimation results After each model command the estimated parameter vector is placed in the read only matrix b Thus to avoid losing your coefficient vector you must equate something to b Diagonal Elements of a Matrix in a Vector The function a Vecd c creates column vector a from the diagonal elements of the matrix c Diagonal Matrix Created from a Vector The command a Diag c creates a square matrix a with diagonal elements equal to those of row or column vector c If c is a square matrix the diagonal elements of a will be the same as those of c while the off diagonal elements ofa will be zero 9 6 Matrix Functions There are roughly 50 functions that can be combined with the algebraic operators to create matrix expressions Some of these such as Nvsm are used to combine algebraic results while others such as Root are specialized functions tha
117. a matrices in any way you choose data matrices may share columns An example appears below One useful shortcut which can be used to create a data matrix is simply to associate certain variables and observations with the matrix name by using NAMELIST The variables are defined with the NAMELIST command The rows or observations are defined by the current sample with the SAMPLE REJECT INCLUDE DRAW and PERIOD commands If you change the current sample the rows of all existing data matrices change with it If you change the variables in a namelist you redefine all matrices that are based on that namelist For example suppose the data array consists of the following YEAR CONS INVST GNP PRICES 1995 1003 425 1821 124 5 1996 1047 511 2072 139 2 1997 1111 621 2341 154 7 1998 1234 711 2782 177 6 Two data matrices demand and alldata would be defined by the command NAMELIST demand cons invst gnp alldata year cons invst gnp prices Notice that these data matrices share three columns In addition any of the 31 possible subsets of variables can be a data matrix and all could exist simultaneously 9 10 Using Matrix Algebra The number of rows each data matrix has depends on the current sample For example to have the matrices consist of the last three rows of the data it is necessary only to define SAMPLE 32 4 You can vary the sample at any time to redefine the data matrices For example suppose it is desired to base
118. ace _ with e in the preceding and compute Est Asy Var bna X X X Q X X K where denotes deviations from group means This produces the same results as if the White correction were applied to the OLS results in full model including both regressors and group dummy variables If the variances can be assumed to be the same for all observations in the ith group then each group specific variance can be estimated by the group mean squared residual and the result inserted directly into the formulas above In this case Q becomes a block diagonal matrix in which the ith diagonal block is o I This resembles the time series cross section model discussed at the end of this chapter In practical terms we simply replace e with s in the estimate of the asymptotic covariance matrix To request these estimators add Het or Het Hcl or Het Hc2 or Het Hc3 and Het group respectively to the REGRESS command The asymptotic covariance matrix for the fixed effects estimator may also be estimated with a Newey West style correction for autocorrelation Request this computation with Lags the number of lags up to 10 14 6 4 One Way Random Effects Model The command for the random effects model is REGRESS Lhs dependent variable Rhs independent variables Str stratification or Pds count variable Panel Random Effects This is the base case Other specifications will be added as we proceed 14
119. ady to go back to work See Section 6 5 3 for further discussion Application and Tutorial 6 9 6 4 Tutorial Commands In this tutorial you will used nearly all of the features of LIMDEP that you will need to complete a graduate course in econometrics We will run through a long sequence of operations one at a time and display the results at each step You will want to carry out these operations as we do Rather than type them one at a time it will be more convenient for you to have them available in a text editor where you can execute each one just by highlighting one or more lines and clicking the GO button l The listing below contains all of the commands that we used in this tutorial You can place them in your screen editor by using File Open then making your way to C LIMDEP9 LIMDEP Command Files Tutorial lim Select this file Your screen will then contain all the commands that will be used in the tutorial to follow The text editor does not replicate the boldface in the listing below You can then follow along by highlighting and executing each command or set of commands as they are discussed below Limdep Tutorial lim DER Fie Edit Insert Project Model Run Tools Window Help oea S ee olal AE T GasolineMark Data U 11111 Rows _ Inset Name zl Read the raw data ft Sa Data READ Variables Year GasExp GasPrice Income PNewCar PUgedcer PPubTrn Pop E Namelists 1953 eit 16 668 8883 47 2 26
120. ain covariance and correlation matrices condition numbers and so on More involved procedures can be used in conjunction with the other commands to program new possibly iterative estimators or to obtain complicated marginal effects or covariance matrices for two step estimators To introduce this extensive set of tools and to illustrate its flexibility we will present two examples These are both built in procedures in LIMDEP so the matrix programs are only illustrative The rest of the chapter will provide some technical results on matrix algebra and material on how to use MATRIX to manipulate matrices Example Restricted Least Squares In the linear regression model y XB e the linear least squares coefficient vector b and its asymptotic covariance matrix computed subject to the set of linear restrictions Rb q are b b X X R R X X R Rb q where b X X X y and Est Asy Var b s X X s X X R R X X R J R X X First define the X matrix columns then rows We assume the dependent variable is y NAMELIST x CREATE y the dependent variable SAMPLE as appropriate Next define R and q This varies by the application Get the inverse of X X now for convenience MATRIX rS qQ 3 Xxi lt x x gt Compute the unrestricted least squares and the discrepancy vector MATRIX bu xxi x y d r bu q 9 2 Using Matrix Algebra Compute the restricted least squares estimates
121. aints on some econometrics programs Avoiding it allows LIMDEP to manipulate data matrices of any length The utility of this approach will be clear shortly It is important to keep in mind the distinction between two kinds of matrices that you will be manipulating We define them as follows e Data matrices A data matrix is a set of rows defined by observations and columns defined by variables The elements of the data matrix reside in your data area e Computed matrices A computed matrix is the result of an operation that is based on data matrices or other computed matrices The elements of a computed matrix will reside in your matrix work area which is defined below The distinction is purely artificial since as will soon be evident every numeric entity in LIMDEP is a matrix The important element is that the size of a data matrix is nxK where n is the current sample size and K is a dimension that you will define The size of a computed matrix is K xL where K and L are numbers of variables or some other small values that you will define with your commands 9 3 1 Data Matrices To use your data to compute matrices you will usually define data matrices This amounts to nothing more than labeling certain areas of the data array you do not actually have to move data around whatever that might mean to create a data matrix For LIMDEP s purposes a data matrix is any set of variables which you list You can overlap the columns of dat
122. al you must have lower lt 1 5 upper 1 5 upper lower 5 If upper is not provided it is taken as too If you need upper truncation a transformation which will produce the desired result is Rnr lower The parameters of any random number generator can be variables other functions or expressions as well For example you might simulate draws from a Poisson regression model with CREATE x1 Rnn 0 1 x2 Rnu 0 1 y Rnp Exp 2 3 x1 05 x2 Setting the Seed for the Random Number Generator To reset the seed for the random number generator the same one is used for all distributions use the command CALC Ran seed In this fashion you can replicate a sample from one session to the next Use a large e g seven digit odd number for the seed Using this device will allow you to draw the same string of pseudo random numbers more than once Essentials of Data Management 7 21 7 4 Lists of Variables As part of estimation it is necessary to define two sets of information the variables to be used and the observations LIMDEP s data handling and estimation programs are written to handle large numbers of variables with simple short commands Two methods are provided to reduce the amount of typing involved in giving a list of names the NAMELIST and a wildcard character The NAMELIST feature is used as follows NAMELIST _ name the list of variables names 7 4 1 Lists of Variables in Model Com
123. al commands For example and conditions result from products of these relational operators Thus CREATE v x gt 8 x lt 15 Log q creates v equal to the log of q if x is greater than or equal to 8 and less than or equal to 15 You can also produce an or condition using addition though the conditional command construction may be more convenient For example CREATE sv x 8 x 15 gt 0 Log q does the transformation if x equals 8 or 15 The following algebraic order of precedence is used to evaluate expressions e First functions such as Log are evaluated e Second and which have equal precedence are computed e Third gt gt lt lt are computed e The special operators etc are evaluated from left to right with the same precedence as and Thus for example y x gt 0 equals 1 if y x is greater than 0 and equals 0 otherwise It will usually be useful to use parentheses to avoid ambiguities in these calculations e Fourth and addition and subtraction are computed NOTE LIMDEP does not give the unary minus highest precedence The expression x 2 evaluates to the negative of the square of x which would be negative not the square of negative x which would be positive This is the current standard in software but it is not universal You may use as many levels of parentheses as necessary in order to group items in an express
124. ansport the graph from the screen to your document However the internal components of the figure are not fully formed by this method and the quality of the figure will be inferior to what you will obtain by writing the figure to a wmf file and importing the file into the other program Describing Sample Data 13 11 Limdep Untitled Plot 8 File Edit Insert Project Model Run Tools Window Help Untitled Proj OX Sy Data 29 Variables F TER p Rhs pnc puc ppt Seer gt Title Time Trend of Price Indices Vasabte F a GASEXP GASQ GASP GASCPIU PCINCOMPNC PUC PPT PD 74 25415 16 668 212 8802 47 2 267 16 8 78 26 223 17 029 28 8757 46 5 22 7 18 8 6 28 505 17 21 g g 94 30 229 17 729 102 31393 18 497 32 884 18 316 34 573 18 576 35 757 19 12 36 126 18 924 37 658 19 043 38 815 18 997 4034 18 873 42 874 19 587 45 549 47 029 50 304 53 686 57 009 59 77 62 206 65 44 62 217 i 64 07 278 sas 66 633 TTT 15738 66 5 68 675 7 16128 70 4 70 258 16704 758 63 315 16931 BE 65 358 l 16940 88 4 6R 349 17217 922 ee Figure 13 7 Excel Spreadsheet with LIMDEP mf File Imported 13 12 Describing Sample Data 13 6 3 The PLOT Command The command for producing a basic scatter XY plot of one or more variables against another variable is PLOT Lhs variable on horizontal axis Rhs variables up to five on vertical axis
125. any pair of variables Cov variable variable sample covariance Cor variable variable sample correlation We note for obtaining the correlation between a continuous variable x and a binary variable d one would use the biserial correlation It turns out that the biserial correlation is equal to the ordinary Pearson product moment correlation So no special function is created for this Just use CALC List Cor continuous variable x binary variable d to obtain a biserial correlation coefficient Order Statistics Med variable median of sample values Min variable sample minimum Max variable sample maximum 10 12 Scientific Calculator Qnt qguantile variable the indicated quantile for the variable To locate the minimum or maximum value in the current sample use Rmn variable observation number where minimum value of variable occurs Rmx variable observation number where maximum value of variable occurs Dot Products For any vector matrix with one row or column which we denote c or d or variable in your data set denoted x or y Dot c c c c Dot c d c d Qfr c A c Ac A is a square matrix conformable with c Two forms of the Dot function are Dot x x x x Dot x y x y You may also use the simpler form with the apostrophe and may mix variables and vectors in the function Thus if x and y are variables and c and d are vectors all of the following are admissible assuming
126. ar in the first line of the file The number of observations in the file is determined by reading until the end of the file is reached Obtaining the Path to a File The preceding application is one of several situations in which you will need to specify the full path to a file Sometimes this is hard to locate You can obtain the full path to a file by using Insert File Path For example where is the file TableF1 1 txt that is selected in Figure 7 52 Step one is to make sure that your text editing window is active The file path will be inserted where the cursor is Insert File Path brings up exactly the dialog box shown in Figure 7 5 except that the banner title will be Insert File Path instead of Import When you click Open the full path to the file will be placed in double quotes in the text editor The result is shown in Figure 7 6 amp Untitled 4 f Insert Name v File C Text DataFiles TableFl 1 txt f Figure 7 6 Editing Window with Insert File Path READ 7 6 Essentials of Data Management 7 2 4 General ASCII Files The more general command for reading an ASCII data file is READ Nvar number of variables Nobs number of observations Names names for the variables File the full file name including path Note that the preceding shows the default form of this command This assumes that the file is an ASCII file not a spreadsheet with numbers arranged in rows separated by blank
127. are product To the maximum extent permitted by applicable law Econometric Software disclaims all other warranties and conditions either express or implied including but not limited to implied warranties of merchantability fitness for a particular purpose title and non infringement with respect to the software product This limited warranty gives you specific legal rights You may have others which vary from state to state and jurisdiction to jurisdiction Limitation of Liability Under no circumstances will Econometric Software be liable to you or any other person for any indirect special incidental or consequential damages whatsoever including without limitation damages for loss of business profits business interruption computer failure or malfunction loss of business information or any other pecuniary loss arising out of the use or inability to use the software product even if Econometric Software has been advised of the possibility of such damages In any case Econometric Software s entire liability under any provision of this agreement shall not exceed the amount paid to Econometric Software for the software product Some states or jurisdictions do not allow the exclusion or limitation of liability for incidental or consequential damages so the above limitation may not apply to you Preface to the Student Version of LIMDEP 9 LIMDEP is a general integrated computer package for estimating the the sorts of econometric models
128. arentheses to remove the ambiguity Also in functions which have more than one argument separated by commas such as Eql x y which equals one if x equals y include expression s in parentheses For example Eql x y rt c 2 may not evaluate correctly because of the x y term But Eql xty r c 2 will be fine The supported functions are listed below Basic Algebraic Functions Log x natural log Exp x exponent Abs x absolute value Sqr x square root Sin x sine Cos x cosine Tan x tangent Res x arccosine Rsn x arcsine Ath x hyperbolic arctangent In 1 x 1 x Ati x inverse hyperbolic arctangent exp 2x 1 exp 2x 1 10 10 Scientific Calculator Relational Functions Eql x y 1 if x equals y 0 if not Neq x y 1 Eql x y Sgn x ifx gt 0 0ifx 0 1ifx lt 0 Critical Points from the Normal Family of Distributions In each case when you enter Fen P where P is the probability LIMDEP finds the x such that for that distribution the probability that the variable is less than or equal to x is P For example for the normal distribution Ntb 95 1 645 The P you give must be strictly between 0 and 1 Ntb P standard normal distribution Ttb P d t distribution with d degrees of freedom Ctb P d chi squared with d degrees of freedom Ftb P n d F with n numerator and d denominator degrees of freedom Ntb P u 0 normal
129. ars may be indexed by other scalars in the form ssss iiii where ssss is CALC 31 37 value i pi creates a scalar named value37 and assigns it the value x The procedure in the editor window in Figure 10 5 shows how one might use this feature The data set consists of 10 groups of 20 observations The procedure computes a linear regression model using each subsample Then it catches the log likelihood function from each regression and puts it in a correspondingly named scalar Thus the loop index j takes values 1 2 10 so the scalar names are logl j logll logl10 10 5 Scalar Expressions The rules for calculator expressions are identical to those for CREATE The rules of algebra apply with operations and Box Cox transformation taking first precedence and next followed last by and You may also use any of the functions listed below in any expression This includes the percentage points or critical values from the normal t F and chi squared distributions sums of sample values determinants of matrices or any other algebraic functions Chapter 9 describes how to obtain matrix results You may also use an element of a matrix with its subscript enclosed in parentheses in any scalar calculation Finally any particular observation on any variable in your data area may also be used in an expression For example you might 10 8 Scientific Calculator zi Untitled 1 F Insert Name v PROC CALC Pe a
130. ating Models TIP Each time you estimate a model the contents of b varb and the scalars are replaced If you do not want to lose the results retain them by copying them into a different matrix or scalar For example the following computes a Wald test statistic for the hypothesis that the slope vector in a regression is the same for two groups a Chow test of sorts REGRESS Lhs y Rhs If Male 1 MATRIX bmale b vmale varb REGRESS Lhs y Rhs If Female 1 MATRIX bfemale b vfemale varb MATRIX d bmale bfemale waldstat d Nvsm vmale vfemale d The matrix results saved automatically in b and varb are typically a slope vector b and the estimated asymptotic covariance matrix of the estimator from an index function model For example when you estimate a tobit model the estimates and asymptotic covariance matrix are B V Vo g and O v_ The results kept are B in b Vpp in varb and o in a scalar named s The other parts of the asymptotic covariance matrix are generally discarded We call the additional parameters such as s the ancillary parameters in the model Most of the models that LIMDEP estimates contain one or two ancillary parameters These are generally handled as in this example the slope vector is retained as b the ancillary parameters are kept as named scalars and the parts of the covariance matrix that apply to them are discarded In some applicatio
131. ation about this process is incorporated in the estimation of A Several of the forms of this model which can be estimated with LIMDEP depart from Heckman s now canonical form a linear regression with a binary probit selection criterion model y pxte z a wtu gu N 0 0 0 ou p A bivariate classical seemingly unrelated regressions model applies to the structural equations The standard deviations are o and o and the covariance is po o If the data were randomly sampled from this bivariate population the parameters could be estimated by least squares or GLS combining the two equations However z is not observed Its observed counterpart is z which is determined by Censoring and Sample Selection 16 5 lifz gt 0 O1f 2 lt 0 Z and Z Values of y and x are only observed when z equals one The essential feature of the model is that under the sampling rule E y x z 1 is not a linear regression in x or x and z The development below presents estimators for the class of essentially nonlinear models that emerge from this specification The basic command structure for the models described in this chapter is PROBIT Lhs variable z Rhs variables in w Hold SELECT Lhs variable y Rhs variables in x Note that two commands are required for estimation of the sample selection model one for each structural equation 16 3 1 Regression Models with Sample Selection The models described in
132. atson Stat 2 1569722 cor e e 1 0784861 re poses Variable Coefficient Standard Error t ratio P T gt t Mea 4 Constant 01106059 09695189 114 9094 X 97389103 10209332 9 539 0000 Ln 38 38 Idle Figure 3 12 Regression Output in Output Window The Project Window Note in Figure 3 9 in the project window that the topics Matrices and Scalars have symbols next to them indicating that the topic can be expanded to display its contents But the Variables entry is not marked After you executed your second line in your editing window and created the two variables x and y the Variables topic is now marked with Click this symbol to expand the topic The REGRESS command created another variable Jogl_obs It also created three matrices as can be seen in Figure 3 13 Operating LIMDEP Some other features you might explore in the project window Click the symbol next to the Matrices and or Scalars topics e Double click any name that you find in the project window in any of the three topics e Single click any of the matrix or scalar names and note what appears at the bottom of the window imdep Untitled Project 1 Eak Fie Edit Insert Project Model Run Tools Window Help Dea E ej ofeln aam TA Untitled Project 1 BEAR S H E Variables b
133. author of both LIMDEP and this manual Table of Contents TOC 1 Student LIMDEP 9 0 Combined Table of Contents Part Reference Guide to Using LIMDEP Chapter 1 1 1 1 2 Chapter 2 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 Chapter 3 3 1 3 2 3 3 3 4 3 5 Chapter 4 4 1 4 2 43 4 4 Chapter 5 5 1 5 2 5 3 Chapter 6 6 1 6 2 6 3 6 4 6 5 Introduction to LIMDEP The LIMDEP Program 1 1 References for Econometric Methods 1 2 Getting Started Introduction 2 1 Equipment 2 1 Installation 2 1 Registration 2 2 Execution Beginning the LIMDEP Session 2 3 Components of a LIMDEP Session 2 4 Exiting LIMDEP and Saving Results 2 5 Fast Input of a Data Set with OPEN LOAD 2 7 Starting LIMDEP from your Desktop or with a Web Browser 2 8 Operating LIMDEP Introduction 3 1 Beginning the LIMDEP Session 3 1 3 2 1 Opening a Project 3 1 3 2 2 Opening an Editing Window 3 2 Using the Editing Window 3 4 A Short Tutorial 3 8 Help 3 14 LIMDEP Commands Commands 4 1 Command Syntax 4 1 Naming Conventions and Reserved Names 4 2 Command Builders 4 4 Program Output The Output Window 5 1 Editing Your Output 5 2 Exporting Your Output 5 2 Application and Tutorial Application An Econometrics Problem Set 6 1 Assignment The Linear Regression Model 6 1 Read the Raw Data 6 4 Tutorial Commands 6 9 Using LIMDEP for Linear Regression Analysis 6 12 6 5 1 Obtain Descriptive Statistics 6 12 6 5 2 Transformed Variable
134. ay use this numeric value in any type of file to indicate a missing value Upon reading the data LIMDEP immediately converts any missing data encountered to the numeric value 999 Essentials of Data Management 7 9 7 3 Computing Transformed Variables You will usually need to transform your data for example to obtain logarithms differences or any number of other possibilities LIMDEP provides all of the algebraic transformations you are likely to need with the CREATE command It is often useful to recode a continuous variable into discrete values or to combine discrete values into a smaller number of groups for example to prepare data for contingency tables The RECODE command is provided for this purpose You can use SORT to arrange one or more variables in ascending or descending order 7 3 1 The CREATE Command The CREATE command is used to modify existing variables or compute new ones The essential syntax of the command is CREATE name expression name expression You may also enter your command in a dialog box as shown in Figure 7 10 The dialog box is invoked by selecting Project New Variable or by going to the data editor and pressing the right mouse button which will bring up a menu that includes New Variable You may now enter the name for the new or transformed variable in the Name window If you click OK at this point without entering an expression for the variable the new variable is created and the first obse
135. btaining descriptive statistics is DSTAT Rhs the variables to be described There is a useful short hand the wildcard character in this context means all variables So we will use the simpler instruction DSTAT Rhs The results are shown in the output window shown in Figure 6 7 Application and Tutorial Limdep Output File Edit Insert Project Model Run Tools Window Help 6 13 eee Al osm S seel olal AER a Output Status Trace SAMPLE set to observations 1 to 52 1 missing values were converted to 99 Thana ane maminhlan in the Ante manl amen gt RESET Initializing NLOGIT Version 4 0 1 January 1 gt READ Last observation read from data file was End of data listing in edit window was reached gt DSTAT z Rhs Descriptive Statistics All results based on nonmissing observations 2007 52 Variable All observations in current sample YEAR GASEXP GASPRICE INCOME PNEWCAR PTBEDOAR l 1978 50 70 1019 51 3430 16805 1 87 5673 77 8000 89 3904 225374 15 1548 57 5147 30 8274 5552 03 37 0874 51 0682 69 1902 38077 4 1953 00 7 40000 16 6680 8685 00 44 8000 20 7000 16 8000 159565 2004 00 224 500 123 901 27113 0 141 700 158 700 210 600 293951 PPUBTRN rer This indicates the first wear nf the data Ln 23 23 Figure 6 7 Descriptive Statistics in the Output Window Idle 6 5 2 Transformed
136. cations in order to be identified For example the specific model you want may be a particular case of a broad class of models and in order to specify it you must provide the essential specifications For example the basic command for survival modeling with covariates to provide the model would be SURVIVAL Lhs failtime Rhs one usehours This form of the command is for Cox s proportional hazard model In order to fit a parametric model such as the Weibull model you would use SURVIVAL Lhs failtime Rhs one usehours Model Weibull Note the last specification This is the only way to specify a Weibull model so for this model this specification is essential The Weibull model is requested as a type of survival model by this command Obviously not all models have mandatory specifications the examples above do not But many do The documentation in the chapters to follow will identify these Finally all model frameworks have options which either extend the model itself or control how the model is estimated or how the estimation results are displayed For example the following fits a linear regression model and requests a robust estimator of the covariance matrix of the estimates Econometric Model Estimation 12 3 REGRESS Lhs profit Rhs one sales Heteroscedasticity consistent The latter specification does not change the model specification it requests an additional computation the
137. choice models there is no restricted log likelihood presented The maximum likelihood estimates for a model that contains only a constant term are no less complicated than one with covariates and there is no closed form solution for the B o parameter pair for this model For a general test of the joint significance of all the variables in the model we suggest the standard trio of Neyman Pearson tests which can be carried out as follows First set up the Rhs variables in the model NAMELIST _ xvars the x variables in the model without the constant term CALC kx Col xvars TOBIT Lhs y Rhs one CALC 10 logl This command will produce the Lagrange multiplier statistic TOBIT Lhs y Rhs xvars one Start kx_0 b s Maxit 0 TOBIT Lhs y Rhs xvars one Compute the likelihood ratio statistic CALC List lr 2 logl 10 1 Chi ir kx This computes a Wald statistic MATRIX beta b 1 kx vb varb 1 kx 1 kx List Wald beta lt vb gt beta CALC List 1 Chi wald kx Retained output from the model includes Matrices b varb Scalars s estimated o ybar sy kreg number of coefficients nreg number of observations nonlimts number of nonlimit observations in estimating sample 16 4 Censoring and Sample Selection The diagnostic information for the model also includes Lin and Schmidt s LM test for the model specification against the alternative suggested by C
138. correlated and one might surmise that together in a regression it would be difficult to resolve separate impacts of these two variables Limdep Untitled Plot 1 DER File Edit Insert Project Model Run Tools Window Help z A pea S ee oll AEA r B Untitled Plot 1 Licks PUSEDCAR PPUBTRH Figure 6 12 Time Series Plots To pursue the issue a bit we will compute a correlation matrix for the four price variables As usual there is more than one way to proceed Here are two First the DSTAT command can be extended to request correlations by simply adding Output 2 to the instruction Thus we might use Application and Tutorial 6 17 DSTAT Rhs gasprice pnewcar pusedcar ppubtrn Output 2 This produces the results in Figure 6 13 the descriptive statistics now include the correlations among the price variables PEK Status Trace Current Command Descriptive Statistics All results based on nonmissing observations GASPRICE 51 3430 30 8274 123 901 PNEWUCAR 87 5673 37 0874 141 700 PUSEDCAR 77 8000 51 0682 158 700 PPUBTRN 89 3904 69 1902 210 600 Correlation Matrix for Listed Variables GASPRICE PNEWCAR PUSEDCAR PPUBTRN GASPRICE 1 00000 93605 92277 92701 PNEWCAR 93605 1 00000 99387 98074 PUSEDCAR e222 7 99387 1 00000 98242 PPUBTRN 92701 98074 98242 1 00000 lt M Figure 6 13 Descriptive Statistics with Correlations It is possible to obtain these results with the dial
139. ctions and operations to any level Functions that may appear in expressions are listed in Section 7 3 3 The operators that may appear in CREATE commands are the standard ones and for addition subtraction multiplication and division as well as the special operators listed below N raise to the power a b a Box Cox transformation a b a 1 borlogaifb 0anda gt 0 maximum a b max a b The maximum of a string of operands is obtained just by writing the set separated by s For example 5 3 6 0 1 6 minimum a b min a b percentage change a b 100 a b 1 E g 5 4 25 The following operators create binary variables gt binary variable a gt b lifa gt b and0 else gt binary variable a gt b lifa b and0 else lt binary variable a lt b lifa lt band0 else lt binary variable a lt b lifa lt b and0 else binary variable a b lifa b and0 else binary variable a b 1 ifa is not equal to b For example CREATE a x gt 0 Phi y creates a equal to Phi y if x is positive and 0 else p z gt 0 creates p if zis positive and 0 otherwise zeql z 1 equals if z equals and 0 otherwise To avoid ambiguity it is often useful to enclose these operations in parentheses as in CREATE a x 1 Phi z Essentials of Data Management 7 11 This set of tools can be used in place of conditional commands and sometimes provides a convenient way make condition
140. currently defined sample while INCLUDE adds observations to the current sample You can use either of these to define the current sample by writing your command as REJECT or INCLUDE New expression For a REJECT command this has the result of first setting the sample to All then rejecting all observations which meet the condition specified in the expression For an INCLUDE command this has the effect of starting with no observations in the current sample and selecting for inclusion only those observations which meet the condition In the latter case this is equivalent to selecting cases as may be familiar to users of SAS or SPSS You may enter REJECT and INCLUDE commands from the dialog box shown in Figure 7 16 The dialog box is invoked by selecting Include or Reject in the Project Set Sample menu or by right clicking in the data editor clicking Set Sample then selecting Reject or Include from the Set Sample menu Note in the dialog box the Add observations to the current sample option at the top is the New specification in the command Also by clicking the query button at the lower left you can obtain information about these commands from the online Help file Include Add observations to the current sample C Define a new sample Cancel Using expression Figure 7 16 INCLUDE and REJECT Dialog Box The same Set Sample menu offers All which just generates a SAMPLE All command and Range which
141. d Estimates Dependent variable DOCTOR Weighting variable None Number of observations 27326 Iterations completed 4 Log likelihood function 17673 10 Number of parameters 6 Info Criterion AIC 1 29394 Finite Sample AIC 1 29394 Info Criterion BIC 1 29574 Info Criterion HQIC 1 29452 Restricted log likelihood 18019 55 McFadden Pseudo R squared 0192266 Chi squared 692 9077 Degrees of freedom 5 Prob ChiSqd gt value 0000000 Hosmer Lemeshow chi squared 110 37153 P value 00000 with deg fr 8 ie ia R hee is Variable Coefficient Standard Error b St Er P Z gt z Mean of X rs ia _ ih _ man i A I A Characteristics in numerator of Prob Y 1 Constant 25111543 09113537 22195 0059 AGE 02070863 00128517 16 114 0000 43 5256898 HHNINC 18592232 07506403 2 477 0133 35208362 HHKIDS 22947000 02953694 7 769 0000 40273000 EDUC 04558783 00564646 8 074 0000 11 3206310 AARRIED 08529305 03328573 2 562 0104 75861817 The next set of results computes various fit measures for the model This table of information statistics is produced only for the logit model It is generally used for analysis of the generalized maximum entropy GME estimator of the multinomial logit model but it also provides some useful information for the binomial model even when fit by ML instead of GME The entropy statistics are computed as follows Entropy P log P
142. d Least Squares 14 5 14 2 5 Hypothesis Tests in the Linear Model 14 7 Estimating Models with Heteroscedasticity 14 9 Correcting for First Order Autocorrelation 14 9 Two Stage Least Squares 14 11 14 5 1 Robust Estimation of the 2SLS Covariance Matrix 14 11 14 5 2 Model Output for the 2SLS Command 14 11 Panel Data Models 14 12 14 6 1 Data Arrangement and Setup 14 12 14 6 2 One Way Fixed and Random Effects Models 14 15 14 6 3 One Way Fixed Effects Models 14 18 14 6 4 One Way Random Effects Model 14 21 Models for Discrete Choice Introduction 15 1 Modeling Binary Choice 15 1 15 2 1 Model Commands 15 2 15 2 2 Output 15 2 15 2 3 Analysis of Marginal Effects 15 6 15 2 4 Robust Covariance Matrix Estimation 15 7 Ordered Choice Models 15 9 15 3 1 Estimating Ordered Probability Models 15 10 15 3 2 Model Structure and Data 15 10 15 3 3 Output from the Ordered Probability Estimators 15 11 15 3 4 Marginal Effects 15 13 Table of Contents TOC 5 Chapter 16 Censoring and Sample Selection 16 1 Introduction 16 1 16 2 Single Equation Tobit Regression Model 16 1 16 2 1 Commands 16 2 16 2 2 Results for the Tobit Model 16 3 16 2 3 Marginal Effects 16 4 16 3 Sample Selection Model 16 4 16 3 1 Regression Models with Sample Selection 16 5 16 3 2 Two Step Estimation of the Standard Model 16 6 Index TOC 6 Table of Contents This page intentionally left blank Part Reference Guide to Using LIMDEP Part Reference Guide Chapter 1 Chapter 2 Chap
143. d function is oblivious to centuries You must provide four digit years to this function so there is no ambiguity about 19xx vs 20xx The trend function Trn is used to create equally spaced sequences of values such as 1 2 3 which is Trn 1 1 There are two additional variants used primarily with panel data These are discussed in Chapter R6 Leads and Lags You can use a lagged or leaded variable with the operand variable n observation on the variable n periods prior or ahead The use of square brackets is mandatory n is the desired lag or lead If n is negative the variable is lagged if it is positive it is leaded For example a familiar transformation Nerlove s universal filter is 1 75L where L is the lag operator This would be CREATE filterx x 1 5 x 1 5625 x 2 A value of 999 is returned for the operand whenever the value would be out of the range of the current sample For example in the above command filterx would equal 999 for the first two observations You can change this default value to something else like zero with CREATE LAG the desired value For example CREATE LAG 0 would change the default value for noncomputable lags to zero This must be used in isolation not as part of some other command If you use lags or leads you should modify the applicable sample accordingly when you use the data for estimation LIMDEP makes no internal note of the
144. d same as before Use this to undo a previous DATES command DATES Undated YYYY year for yearly data e g 1951 DATES 1951 YYYY Q year quarter for quarterly data Q must be 1 2 3 or 4 DATES 1951 1 YYYY MM year month for monthly data MM is 01 02 03 12 DATES 1951 04 Note that 1 is a quarter and 5 is invalid The fifth month is 05 and the tenth month is 10 not 1 Once the row labels are set up the counterpart to the SAMPLE command is PERIOD first period last period Essentials of Data Management 7 29 For example PERIOD 1964 1 1977 4 These two commands do not change the way that any computations are done with LIMDEP They will change the way certain output is labeled For example when you use the data editor the row markers at the left will now be the dates instead of the observation numbers NOTE You may not enter a date using only two digits Your dates must contain all four digits No computation that LIMDEP does or command that you submit that involves a date of any sort for any purpose uses two digits Therefore there is no circumstance under which LIMDEP could mistake 20xx for 19xx Any two digit date submitted for any purpose will generate an error and will not be processed The DATES command may be given from the Project Settings Data Type menu item Project Settings Datadrea Data Type Execution Output Observations Quarterly Initial Date
145. dard deviation 2388115 WTS none Number of observs 52 Model size Parameters 7 Degrees of freedom 45 Residuals Sum of squares 1014368 Standard error of e 4747790E O1 Fit R squared 9651249 Adjusted R squared 9604749 Model test F 6 45 prob 207 55 0000 Diagnostic Log likelihood 88 44384 Restricted b 0 1 188266 Chi sq 6 prob 174 51 0000 Autocorrel Durbin Watson Stat 4470769 Rho cor e e 1 7764615 Variable Coefficient Standard Error t ratio P IT gt t Mean of X Constant 26 9680492 2 09550408 12 869 0000 LOGPG 05373342 04251099 1 264 2127 3 72930296 LOGI 1 64909204 20265477 8 L37 0000 9 67214751 LOGPNC 03199098 20574296 a bS 8771 4 38036654 LOGPUC 07393002 10548982 701 4870 4 10544881 LOGPPT 06153395 12343734 499 6206 4 14194132 T 01287615 00525340 2 451 0182 25 5000000 The coefficient on JogPg has now fallen to only 0 05 The implication is that after accounting for the uses of gasoline and the price of a major competitor public transport and income the price elasticity of demand for gasoline really does seem to be close to zero The residuals are still far from random but are somewhat more in that direction than the earlier ones This suggests as surmised earlier that the specification of the model is in need of improvement Application and Tutorial results Note that in this set of comma
146. ded matrices in the output When estimation is done in stages Printve will only produce an estimated covariance matrix at the final step Thus no covariance matrix is displayed for initial least squares results F3 Output ex Status Trace Begin main iterations for optimization Normal exit from iterations Exit status 0 HHH HH HH HHH HHH HHH HHH HH HEH HHH HEHEHE HEHEHE HEHEHE EEE EEKEEEEKEKEKKKRERE Estimation Data Analysis Program Tobit Censored HHH HH HH HHH HH HHH HHH HHH HHH HHH HHH HHH HHH HHH HHH HEH HER HKHR KKK HRKRHRRHE Normal exit from iterations Exit status 0 Limited Dependent Variable Model CENSORED Maximum Likelihood Estimates Model estimated Dec 24 2005 at 03 28 33PM Dependent variable IDEY Weighting variable None Number of observations 200 Iterations completed 5 Log likelihood function 348 2706 Nunber of parameters 4 Info Criterion AIC Finite Sample AIC Info Criterion BIC Info Criterion HQIC Threshold values for the model Lower 0000 Upper infinity LM test df for tobit 11 068 3 Normality Test LM 18 523 2 ANOVA based fit measure 420730 DECOMP based fit measure 449755 3 52271 3 52373 3 58867 3 54940 l e a 4 VYariable Coefficient Standard Error b St Er P Z gt z Mean of X 4
147. ding rxx matrix shown above is displayed in Figure 9 4 Hl Matrix RXX 0 666469 0 138951 0 701385 0 666469 1 0 27401 0 254494 0 138951 0 27401 1 0 0593538 0 701385 0 254494 0 0593538 0 001 Figure 9 4 Matrix Display from Project Window Matrix results will be mixtures of matrix algebra i e addition multiplication subtraction and matrix functions such as inverses characteristic roots and so on and possibly algebraic manipulation of functions of matrices such as products of inverses 9 2 3 Matrix Output The results of MATRIX commands can be matrices with up to 50 000 elements and can thus produce enormous amounts of output As such most of the display of matrix results is left up to your control Matrix results are always displayed in the calculator window When commands are in line results are generally not shown unless you specifically request the display with List See Section 9 2 5 The figures below demonstrate Calculator Expr Kcor num logmth a c F Matrix 7 A Correlation Matrix for Listed Variables HUH LOGHTH A C NUN 1 00000 83136 59147 32994 LOG TH 83136 1 00000 57822 30768 A 59147 57822 00000 30769 C 32994 30768 30769 1 00000 Figure 9 5 Matrix Result in the Calculator Window 9 6 Using Matrix Algebra When the computed result has more than five columns or more than 20 rows it will be shown in the output window as a place holder object
148. distribution with mean p and standard deviation o Probabilities and Densities for Continuous Distributions Phi x probability that N 0 1 lt x Phi x p1 0 probability that N p o lt x NO1 x density of the standard normal evaluated at x Note N zero one Lgf x log of standard normal density 4 In27 x Lgf 0 918938542 NO1 x u o density of normal u co evaluated at x Tds x d prob t with d degrees of freedom lt x Chi x d prob chi squared variable with d degrees of freedom lt x Fds x n d prob F with n numerator and d denominator degrees of freedom lt x Lgp logit probability exp x 1 exp Lgd x logit density Lgp x x 1 Lgp x Lgt P logit of x Log P 1 P for0 lt P lt 1 Xpn x 8 prob exponential variable with mean 1 0 lt x Bds x a B prob beta variable with parameters a B lt x Matrix Dimensions If A is the name of a matrix Row A number of rows in matrix A Col A number of columns in matrix A If X is the name of a namelist then Row X number of observations in current sample n Col X number of variables in the namelist Scientific Calculator 10 11 Sample Statistics and Regression Results The observations used in any of the following are the current sample less any missing observations For the Sum Xbr Var and Sdv functions of a single variable missing data are checked for the particular variable Thus Xb
149. diting window or into any other program such as a word processor that you might be using at the same time The editing window then provides full editing capability so you can place any annotation in the results that you like You can save the contents of the editing window as an ordinary text file when you exit LIMDEP TIP If you wish to extract from your output window a little at a time one approach is to open a second editing window and use it for the output you wish to collect You may have several editing windows open at any time 5 3 Exporting Your Output When you wish to use your statistical results in a report you will generally copy the results from your output window directly into your word processor Results in the window are displayed in the default 9 point Courier New font You can change this to any font you wish using Tools Options Editor All numerical results are shown in this form Graphical results may also be copied directly off the screen They are produced in a wmf windows metafile format You can paste a graph into your word processor then resize the figure to whatever size you like An example appears below in Figure 5 2 An extensive application appears in the next chapter 4 SL a a a 3 2 1 0 1 2 3 Regression is Y 01106 97389X Figure 5 2 Figure Exported From LIMDEP Output Application and Tutorial 6 1 Chapter 6 Application and Tutorial
150. e a namelist However most data manipulation commands allow you merely to give a set of variable names instead mname is the name of a computed matrix sis a scalar It may be a number or the name of a scalar which takes a value A matrix has r rows and c columns Matrices in matrix expressions are indicated with boldfaced uppercase letters The transpose of matrix in a matrix algebra expression C is denoted C The apostrophe also indicates transposition of a matrix in LIMDEP commands The ordinary inverse of matrix C is denoted C The result of a procedure that computes a matrix A is denoted a Input matrices are c d etc In any procedure if a already exists it may appear on both sides of the equals sign with no danger of ambiguity all matrices are copied into internal work areas before the operation actually takes place Thus for example a command may replace a with its own transpose inverse or determinant You can replace a matrix with some function of that matrix which has different dimensions entirely For example you might replace the matrix named a with a or with a s rank trace or determinant Note in these definitions and in all that follows we will make a distinction between a matrix expression in theory such as F 1 n X X and the entities that you manipulate with your LIMDEP commands for example you have created f xx There are thus three sets of symbols We will use bold upper case symbols in mat
151. e are some theoretical complications though The Linear Regression Model 14 13 Data Arrangement Data for the panel data estimators in LIMDEP are assumed to be arranged contiguously in the data set Logically you will have N Nobs VT i l observations on your independent variables arranged in a data matrix T observations for group T observations for group 2 Ty observations for group N and likewise for the data on y the dependent variable When you first read the data into your program you should treat them as a cross section with Nobs observations The partitioning of the data for panel data estimators is done at estimation time NOTE Missing data are handled automatically by this estimator You need not make any changes in the current sample to accommodate missing values they will be bypassed automatically Group sizes and all computations are obtained using only the complete observations Whether or not you have used SKIP to manage missing values this estimator will correctly arrange the complete and incomplete observations Specifying the Stratification for Balanced Panels If you have a balanced panel that is the same number of observations for each group you can use Pds T where you give the specific value of T to define the panel There is no need for a stratification variable For example in one of our applications we use a balanced panel data set with N 10 firms and T 20 years The r
152. e click the lt lt button to select them You may also click the query button at the lower left of the dialog box to obtain a Help file description of the REGRESS command for linear models that is being assembled here The Run button allows you now to submit the model command to the program to fit the model There is also a box on the Main page for the REGRESS command for specifying the optional extension the GARCH model Since the main option box for this specification is not checked this option will not be added to the model command Limdep Grunfeld10 pj Dor File Edit Insert Project Model Run Tools Window Help osla S ee oleln Bap Grunfetdto BR Data U 3333 Rows 200 Obs _STRATUM _GROUPTI LOGL_OBS OBS D2 D3 D4 D5 D1 D6 D7 DB D9 A variables 20 of 900 used Ready REGRESS Main Options Output Dependent variable J Independent variables ONE F C D1 D2 lt 4 Untitled 1 A Insert Name E CREATE D1 Firm 1 Z GARCH models M GARCHIP Q model I GARCH in mean P Q P no of lagged variance terms I Keep cond vars as _ n Q no of lagged squared disturb s Estimating Models Figure 8 2 Project Window for the Grunfeld Data I Weight using variable z I No scaling IF Use least absolute deviations estimator with jo bootstrap replications Figure 8 3 Main
153. e file When you return you will be able to select the file from those listed in the File menu The files listed 1 4 are the last four editing or output window files saved by LIMDEP and the files listed 5 8 are the last four project files See Figure 2 7 Just click the file name in the File menu to open the file You can also save files by using the save options in the File menu NOTE A saved editing window is referred to as a command or input file WARNING Output files and command files are both saved with the LIM extension You will need to make careful note of which files you save are which type Getting Started Limdep clogit pj ies Edit Insert Project Model Run Tools Window Help New Open Close Ctrl N Ctrl O Save As Save All Open Project Save Project As Close Project Page Setup Print Previey Print 1 E LIMDEP WIPrpl c lim 2 E LIMDEP WIP rpl2 lim 3 commands 1 lim L aam Jntitled 1 Insert Name T T Rhs status for this model command is Data Analysis Program Dsta HEH HH HE HHH HHH HHH HHH HHH HHEHEHEHEHKKRKRKHKKRHKRRKREEHE Statistics 4 Problem lim based on nonmissing observations 5 clogit Ipj 6 E LIMDEP WIP rpl c Ipj 7 C DOCUME 1 Tempi data Ipj 8 burnett Ipj 50000000 Exit Figure 2 7 File Menu 5892857 7607143 486 165476 110 879762 276190476 HINC 34 5476190 PS
154. e n observations for the kth variable in x To obtain a row vector instead use name 1 x or one x Do note in most applications this distinction between row and column vectors will be significant You can obtain a sample mean vector with name 1 n x l A matrix function Mean is also provided for obtaining sample means so Mean x 1 n x 1 Note that the Mean function always returns a column vector of means so if you want a row you must transpose the column after using the function 1 n 1 x may be more convenient The Mean Using Matrix Algebra 9 21 function provides one advantage over the direct approach You can use Mean with a list of variables without defining a namelist Thus to obtain the means of z x w log k f21 you could use name Mean z x w Log k f21 To obtain a weighted mean you can use name lt 1 w gt x w where w is the weighting variable Note that this premultiplies by the reciprocal of the sum of the weights If the weights sum to the sample size then you can use 1 n or lt n gt instead of lt I w gt A related usage of this is the mean of a subsample To obtain a mean for a subsample of observations you will need a binary variable that equals one for the observations you want to select and zero otherwise Call this variable d Then name lt 1 d gt x d will compute the desired mean The Mean function also allows weights so you can use Mean x w or Mean
155. e the previous chapter The second step will be carried out 10 times Obviously you could simply be the program That is type the command and look at i Ifi is less than or equal to 10 type it again The point of this discussion is to devise a way to make LIMDEP do the repetitions for you As noted LIMDEP provides several methods of batching commands The example above could be handled as follows CALC 51 0 PROCEDURE CALC i i 1 ENDPROCEDURE EXECUTE n 10 This example initializes i stores the updating command then executes the stored command 10 times There are other ways to do this as well For example a shorter way to display the numbers from 1 to 10 is PROCEDURE CALC List i ENDPROCEDURE EXEC i 1 10 Yet another way to proceed would program the steps literally This would be Programs and Procedures 11 5 CALC i 1 PROCEDURE LABEL 3100 CALC List i i it 1 GO TO 100 i lt 10 ENDPROCEDURE EXECUTE This procedure is only executed once but it contains a loop within it It displays then updates i 10 times The device used in each case and generally will be the procedure Procedures such as these provide a convenient way to store commands The EXECUTE command offers numerous options for how to carry out the procedure and how to decide to exit from the procedure LIMDEP is highly programmable As shown in numerous examples already and throughout the Econometric Modeling Guide you can arrange l
156. earest integer Int x integer part of operand Univariate Normal and logistic Distributions Phi x CDF of standard normal NOI x PDF of standard normal Lgf x log of standard normal PDF 5 log27 x Log N01 x Lmm x N01 Phi E x x lt operand x N 0 1 Lmp x N01 1 Phi E x x gt operand Lmd x z z 1 Lmp x zLmm x where z 0 1 selectivity variable Tvm x 1 Lmm Lmm z Var x x lt operand Tvp x 1 Lmp Lmp z Var x x gt operand Tvr x z 1 z Tvm x zTvp x where z 0 1 selected variance Inp x inverse normal CDF Inf x inverse normal PDF operand is CDF returns density Let x logit log z 1 z Lgp x logistic CDF exp x 1 exp x Lgd x logistic density Lgp 1 Lgp Trends and Seasonal Dummy Variables Tm x1 x2 trend x1 i 1 x2 where i observation number Ind il i2 if il lt observation number lt 72 0 else Dmy p i1 for each pth observation beginning with i1 0 else The Dmy function is used to create seasonal dummy variables The Ind function operates on specific observations as in Essentials of Data Management 7 15 CREATE eighties Ind 22 31 If your data are time series and have been identified as such with the DATES command see Chapter R7 then you may use dates instead of observation numbers in the Ind function as in CREATE eighties Ind 1980 1 1989 4 NOTE The In
157. ebra then obtain the critical value from the chi squared table PERIOD 1953 1973 REGRESS Lhs logg Rhs x quietly MATRIX b1 b vl varb PERIOD 1974 2004 REGRESS Lhs logg Rhs x quietly MATRIX b2 b v2 varb MATRIX db b1 b2 vdb v1 v2 list W db lt vdb gt db CALC list cstar ctb 95 k The results of the Wald test are the same as the F test The hypothesis is decisively rejected Matrix W has 1 rows and 1 columns t 612 92811 Listed Calculator Results Result 14 067140 6 30 Application and Tutorial This page intentionally left blank Essentials of Data Management 7 1 Chapter 7 Essentials of Data Management 7 1 Introduction The tutorial in Chapter 6 showed how to read a simple data file how to obtain transformed variables logs and how to change the sample by setting the period for time series data There are many different options for these operations in LIMDEP This chapter will describe a few of the additional features available in the program for managing your data The sections to follow are 7 2 Reading and Entering Data 7 3 Computing Transformed Variables 7 4 Lists of Variables 7 5 The Current Sample of Observations 7 6 Missing Data 7 2 Reading and Entering Data Most of the analyses of externally created data that you do with LIMDEP will involve data sets that are entered via disk files The alternative is
158. ed already exists it is overwritten e A namelist is created which contains the names of the new variables The name for the namelist is formed by appending an underscore both before and after up to six characters of the original name of the variable e A tabulation of the transformation is produced in the output window The example suggested earlier might be simulated as follows where the commands and the resulting output are both shown CREATE educ Rnd 4 CREATE Expand educ underhs hs college postgrad EDUC was expanded as _EDUC_ Largest value 4 4 New variables were created Category New variable UNDERHS Frequency 28 2 New variable HS Frequency 22 3 New variable COLLEGE Frequency 30 4 New variable POSTGRAD Frequency 20 ote this is a complete set of dummy variables If you use this set in a regression drop the constant As noted the transformation begins with the value 1 Values below 1 are not transformed and no new variable is created for the missing category Also the transformation does not collapse or compress the variable If you have empty categories in the valid range of values the variable will simply always take the value 0 0 Thus if educ had been coded 2 4 6 8 then the results of the transformation might have appeared as shown below EDUC was expanded as _EDUC_ Largest value 8 4 New variables were created
159. egression command is REGRESS Lhs i Rhs one f c Panel Pds 20 Specifying the Stratification for Unbalanced Panels If you will be using unbalanced panels you may use a stratification variable The variable is given in the Str group part of the command The stratification variable group may be any indicator that distinguishes the groups that is a firm number any kind of identification number a telephone number etc 14 14 The Linear Regression Model For example the following could be used for our 100 observation panel mentioned earlier REGRESS Lhs i Rhs one f c Str firm Panel Specifying the Stratification with a Count Variable This and all other panel data estimators in LIMDEP use a count variable to specify the stratification in a panel Your panel is specified with Pds a specific number of periods as discussed above or with Pds a variable which gives the group counts For an example of such a variable suppose a panel consists of three then four then two observations The nine values taken by the variable say ni would be 3 3 3 4 4 4 4 2 2 The panel specification would be Pds ni You may also use this kind of stratification indicator with the linear regression models discussed here The Stratification Variable LIMDEP inspects your stratification variable before estimation of these models begins If you have specified a balanced panel with Pds T or if your
160. egression appears below 14 2 The Linear Regression Model Ordinary least squares regression Model was estimated Dec 13 2007 at 08 34 51AM LHS LOGG Mean 2571288 Standard deviation 2384918 WTS none Number of observs 52 Model size Parameters 6 Degrees of freedom 46 Residuals Sum of squares 1070036 Standard error of e 4823033E 01 Fit R squared 9631123 Adjusted R squared 9591028 Model test EL 57 46 prob 240 21 0000 Diagnostic Log likelihood 87 05475 Restricted b 0 T225 1909 Chi sq 5 prob 171 59 0000 Info criter LogAmemiya Prd Crt 5 954335 Akaike Info Criter 5 955367 Autocorrel Durbin Watson Stat 2512498 Rho cor e e 1 8743751 2i mar e Variable Coefficient Standard Error t ratio P T gt t Mean of X ahi es H Constant 11 5997167 1 48817387 7 795 0000 LOGPG 03438256 04201503 818 4174 3 72930296 LOGINC 1431596815 14198287 9 268 0000 9 67487347 LOGPNC 11963708 20384305 0 071 5601 4 38036655 LOGPUC 03754405 09814077 383 7038 4 10544880 LOGPPT 21513953 11655849 1 846 0714 4 14194132 The statistics reported are as follows e The model framework linear least squares regression e The date and time when the estimates were computed e Name of the dependent variable e Mean of Lhs variable y n xpi edie d N F e Standard deviation of Lhs variable 1 n 1 2
161. els are fit When you fit a random effects model the fixed effects regression may be computed in the background without reporting the results in order to use the estimates to compute the variance components 14 6 3 One Way Fixed Effects Models The two models estimated with this program are one way or one factor designs of the form Yi Wi BXn Er where sz is a classical disturbance with E j 0 and Var s o In the fixed effects model p is a separate constant term for each unit Thus the model may be written Vir Adin Ardy B Xir Ei a B Xi Ein where the os are individual specific constants and the djs are group specific dummy variables which equal one only when j i The fixed effects model is a classical regression model The complication for the least squares procedure is that M may be very large so that the usual formulas for computing least squares coefficients are cumbersome or impossible to apply The model may be estimated in a simpler form by exploiting the algebra of least squares This model adds the covariates X to the model of the previous section Commands for One Way Fixed Effects Models To invoke this procedure use the command REGRESS Lhs y Rhs list of regressors Str stratification variable or Pds number of periods Panel Fixed Effects You need not include one among your regressors The constant is placed in the regression automatically
162. ens when income is omitted from the equation Includes a plot of residuals It Ln 12 117 Idle Figure 6 6 Tutorial Commands in Text Editor 6 10 Application and Tutorial These are the commands contained in the tutorial command file Lines that begin with a question mark are comments If you submit these lines to the program as if they were commands they are ignored Read the raw data READ Year GasExp GasPrice Income PNewCar PUsedCar PPubTrn Pop 1953 7 4 16 668 8883 47 2 26 7 16 8 159565 2004 224 5 T232 90L 2TATS 1334 39 133 3 209 1 293951 Descriptive Statistics for all variables DSTAT Rhs Transformed Variables CREATE logg log gasexp pop gasprice logpg log gasprice logi log income logpne log pnewcar logpuc log pusedcar logppt log ppubtrn t year 1953 Define data to be yearly time series and set first year as 1953 observations 1953 to 2004 DATES 1953 This indicates the first year of the data PERIOD 1953 2004 This indicates which years of data to use Time series of four price variables with title and grid for readability PLOT Rhs gasprice pnewcar pusedcar ppubtrn Grid Title Time Series Plot of Price Indices Three different ways to display a correlation matrix for four variables DSTAT Rhs gasprice pnewcar pusedcar ppubtrn Output 2 MATRIX list Xcor gasprice pnewcar pusedcar ppubtrn NAMELIST prices gasprice pnewca
163. ents There are several types of correlation coefficients that one might compute beyond the familiar product moment measure The nonparametric measures of rank correlation and of concordance are additional examples One might also be interested in correlations of discrete variables which are usually not measured by simple moment based correlations The following summarizes the computations of several types of correlations with LIMDEP Some of these are computed with CALC as described earlier while a few others are obtained by using certain model commands Pearson Product Moment Correlations for Continuous Variables For any pair of variables Cor variable variable sample correlation 10 14 Scientific Calculator This page intentionally left blank Programs and Procedures 11 1 Chapter 11 Programming with Procedures 11 1 Introduction Your first uses of LIMDEP will undoubtedly consist of setting up your data and estimating the parameters of some of the models described in the Econometric Modeling Guide The purpose of this chapter is to introduce LIMDEP s tools for extending these estimators and writing new ones The programs described in this chapter will also help you make more flexible use of the preprogrammed estimators such as in testing hypotheses analyzing specifications and manipulating the results of the estimation procedures 11 2 The Text Editor The tools and methods described in this chapter will make heavy use o
164. er symbol 1 which has special meaning in matrix multiplication Of course the two entities must be conformable for the matrix multiplication but there is no requirement that two matrices be the same type of entity Usually they will be For convenience we will sometimes make the following definitions 9 12 Using Matrix Algebra e Variable names are vnames e Namelists are xnames e Computed matrices are mnames e Scalars are rnames e Numbers are scalars At any time you can examine the contents of the tables of these names in your project workspace just by clicking the particular name in your project window Whenever you create an entity in any of these tables all of the others are checked for conflicts For example if you try to create a variable named q and there is already a matrix with that name an error will occur There are two reserved matrix names in LIMDEP The matrix program reserves the names b and varb for the results of estimation programs These two names may not appear on the left hand side of a matrix expression They may appear on the right however This is known as read only There are a few additional names which are read only some of the time For example after you use the SURE command sigma becomes a reserved name Model output will indicate if a reserved name has been created In the descriptions of matrix operations to follow e xname is the name of a data matrix This will usually b
165. er in the procedure definition at execution time But it is not possible to check the consistency of the parameters in the two lists Thus you can t be prevented from sending a bad command to the Modeler routine above With this device you are free to pass variables namelists matrices model names or any other entities you require Also strings can vary in type from one execution to another though you must be careful to avoid causing conflicts For example assuming that is a scalar in the named procedure one might use 11 8 Programs and Procedures PROC name t then EXEC Proc name x EXEC Proc name 1 2345 which would not cause a conflict Such procedures would generally be useful for creating prepackaged subroutines For example the following procedure computes LM statistics for a given model using two sets of variables PROC Lmtest model y x1 x2 Model 3 Lhs y Rhs x1 MATRIX 3 k2 Col x2 3b2 k2_ 0 Model Lhs y Rhs x1 x2 Start b b2 Maxit 0 ENDPROC You could execute this with something like the following NAMELIST vl one vla ddd 3 v2 11 123 EXEC Proc Lmtest probit y v1 v2 Part Il Econometric Models and Statistical Analysis PART Il Econometric Models and Statistical Analyses Chapter 12 Econometric Model Estimation Chapter 13 Describing Data Chapter 14 The Linear Regression Model Chapter 15 Models for Discrete Choice Chapter 16 Cen
166. erved for the standard deviation of the residuals from a regression LIMDEP will give you a diagnostic if you try to do so and decline to carry out the command Untitled Proj DOR Data U 11111 Rows 100 Obs qj Variables bx b Y 5 Namelists q Matrices E gt B Ph VARB Ph SIGMA Scalars Strings 5 Procedures Sj Output Tables Output Window Figure 4 1 Reserved Names 4 4 LIMDEP Commands 4 4 Command Builders The desktop provides menus and dialog boxes for the functions that you need to manage your data open projects and text windows and so on In almost most all cases there are commands that you can use for these same functions though generally you will use the menus The reverse is true when you analyze your data and do statistical and econometric analysis You will usuall use commands for these procedures However we note for most statistical operations there are also menus and dialog boxes if you prefer to use them For an example in Figure 4 2 you can see an editing window that contains four commands a SAMPLE command followed by two CREATE commands that create a simulated data set on X and Y and a regression command The first three commands have already been executed and the data as you can see in the project window are already created I can now compute the regression by highlighting the REGRESS command and pressing the GO button Limdep Output DER Fie Edit Insert P
167. es The NAMELIST command is used to define a single name which will be synonymous with a group of variables It can be used at any time and applies to the entire set of variables currently in the data array regardless of how they got there Variables are placed in the data array with many commands including READ CREATE MATRIX and any of the model commands The form of the command is NAMELIST _ name list of variable names Several namelists may be defined with the same NAMELIST command by separating the definitions with semicolons e g NAMELIST wl x1 x2 w2 x3 x4 x5 The lists of variables defined by separate namelists may have names in common For example NAMELIST wl x1 x2 w2 x2 x3 By double clicking or right clicking the name of a namelist in the project window you can enter an editor that allows easy modification of namelists See Figure 7 13 for the setup ki Limdep clogit lpj File Edi sert Project odel Run Dy co bel ja eet i POEA T clogit lpj O x zi Untitled 1 f Insert Name X NAMELIST X one gc ttme inve invt Edit Namelist Name ig gt Variables gt LOGL_OBS b Ww H E Namelists px 9 Matrices Total 5 Figure 7 13 Editing a Namelist Essentials of Data Management 7 23 You can also define new namelists with the New Namelist editor There are several ways to reach this editor e Select New Namelist from the
168. es specification generally defines the dependent and independent variables in a model In almost all cases the model will include one or more dependent variables denoted a Lhs or left hand side variable in LIMDEP s command structure Independent variables usually appear on the Rhs or right hand side of a model specification To continue our example a Poisson model might be specified using POISSON Lhs patents Rhs one r_and d which specifies one of the most well known applications of this model in economics The variable one is the constant term We ll return to this below Some model commands will have only one of these two specifications such as DSTAT Rhs patents which requests descriptive statistics for the variable patents As can be seen here we use the term model command broadly to indicate analysis of a set of data whether for description or parameter estimation Other model commands might have only a Lhs variable such as SURVIVAL Lhs failtime which requests a nonparametric life table analysis of a variable named failtime There are also many other types of variable specifications such as Inst a set of variable names which will be used to specify the set of instrumental variables in the 2SLS command Most models can be specified with nothing more than the model name and the identification of the essential variables But some models require additional specifi
169. essarily interested in seeing If you do not request LIMDEP to list the results the program assumes this is the case Several examples below will illustrate this Application and Tutorial 6 19 6 5 5 Simple Regression The REGRESS command is used to compute a linear regression As usual you can also use the Model menu and command builders however we will generally use the commands The essential instruction is REGRESS Lhs one logpg The regression results are displayed in the output window shown in Figure 6 16 NOTE The right hand side of the REGRESS command contains two variables one and the variable that we wish to appear in the model The one is the constant term in the model If you wish for your model to include a constant term and this should be in the vast majority of cases you request it by including one on the right hand side LIMDEP does not automatically include a constant term in the model In fact most programs work this way though there are a few that automatically put a constant term in the model Then it becomes inconvenient to fit a model without one In general LIMDEP requires you to specify the model the way you want it it does not make assumptions for you Status Trace Current Command Ordinary least squares regression LHS LOGG Mean Standard deviation WTS none Number of observs Model size Paraneters Degrees of freedom Residuals Sum of squares Standard error of e
170. est LM 18 523 ANOVA based fit measure 420730 DECOMP based fit measure 449755 3 52271 3 52373 3 58867 3 54940 l pose enn 4 poase ana nn Variable Coefficient Standard Error b St Er P Z gt z Mean of X gt Primary Index Equation for Model Constant 415 387564 44 3490483 9 366 0000 F 17523697 01598256 10 964 0000 1081 68110 Cc 25745128 05517398 4 666 0000 276 017150 Disturbance standard deviation Sigma 170 271654 17 4589668 9 753 0000 Figure 8 7 Output Window for an Estimated Model 8 8 Estimating Models Displaying Covariance Matrices One conspicuous absence from the output display is the estimate of the asymptotic covariance matrix of the estimates Since models can have up to 150 parameters this part of the output is potentially voluminous Consequently the default is to omit it You can request that it be listed by adding Printve to the model command Since covariance matrices can be extremely large this is handled two ways If the resultant matrix is quite small it is included in the output The earlier tobit equation is shown in Figure 8 10 If the matrix has more than five columns then it is offered as an additional embedded matrix with the output as shown in Figure 8 11 for a larger regression model We also included Matrix in this estimation Note that there are two embed
171. extra smaller bin is created if the remaining proportion is more than p 2 For example if p is 22 there will be four bins with 22 and one at the right end with 12 But if the extra mass is less than p 2 it is simply added to the rightmost bin as for p 16 for which the sixth bin will contain 2 of the observations 13 6 Describing Sample Data 13 3 2 Histograms for Discrete Data The data are also inspected to determine the type and the correct number of bars to plot for a discrete variable For a discrete variable the plot can be exact Once again up to 99 bars may be displayed For example the count of doctor visits in the health care data appear as follows HISTOGRAM Rhs docvis Untitled Plot 9 Histogram for Variable DOCVIS Frequency 0 2 4 6 8 10 12 1416 18 20222426 28 30 323436 38 40 42 44 46 4850 625466 58 60 626466 6870 72747678 8082 486 889092 94 Docs Figure 13 2 Histogram for a Discrete Variable The long tail of the skewed distribution has rather distorted the figure The options described earlier can be used to modify the figure However those options are assumed to be used for continuous data which would distort the figure in another way A more straightforward way to deal with the preceding situation is to operate on the data directly For example HISTOGRAM If docvis lt 25 Rhs docvis truncates the distribution but produces a more satisfactory picture of the frequency count
172. extremely helpful tool that should be useful elsewhere in LIMDEP so much so that a special form has been provided for you to use If you have a stratification variable that identifies the group that an individual is in you will need a count variable constructed from this in order to use the other panel data estimators in LIMDEP The preceding suggests that computing a panel data based linear regression might be a good way to create the variable so a method is set up whereby you can use REGRESS without actually computing the regression which you might not have any interest in to compute this variable The method is to use the following command REGRESS Lhs one Rhs one Str the stratification variable Panel Notice that this attempts to regress one on one which is not a regression at all LIMDEP will notice this and respond to such a command with results such as the following No variables specified Stratification and count l variables were created Ngroup 6 Full sample with missing data 20 Stratification variable is _ STRATUM Count variable for N i is _GROUPTI A variable id with the results of the command are shown in Figure 14 1 14 6 2 One Way Fixed and Random Effects Models The next several sections consider formulation and estimation of one way common effects models Yi Qi BX Ey The fixed effects model is Vir yy Adoi B Xi Eis a BX Ein where E
173. f parameters in the full regression with no restrictions In order to compute the statistic this way we need the R s from the two regressions For this application the restricted regression omits the three additional price variables A way we can proceed is NAMELIST x1 logpg logI x2 logpnc logpuc logppt x one x1 x2 t xu x xr one xl t REGRESS Lhs logg Rhs xu CALC rsqu rsqrd REGRESS Lhs logg Rhs xr CALC rsqr rsqrd List f rsqu rsqr Col x2 1 rsqu n Col x Finally since we aren t actually interested in seeing the regressions at this point there is a more direct way to proceed The calculator function Rsq matrix variable computes the R in the regression of the variable on the variables in the matrix which is exactly what we need Thus CALC rsqu Rsq xu logg rsqr Rsq xr logg List f rsqu rsqr Col x2 1 rsqu n Col x An alternative way to compute the test statistic is to use the large sample version which is a chi squared statistic the Wald statistic Formally the Wald statistic is W bo W b2 Where b is the subset of the least squares coefficient vector the three price coefficients and W22 is the 3x3 submatrix of the covariance matrix of the coefficient estimator This is estimated with s X X For the linear regression model the W statistic turns out to be just J times the F statistic where J is the number of restricti
174. f the editing features of the program The various menus described earlier and in the model sections to follow will be of limited usefulness when you are writing your own programs The text editor will be essential 11 2 1 Placing Commands in the Editor LIMDEP s editing window shown in Figure 11 1 is a standard Windows text editor Enter text as you would in any other Windows based text editor You may enter as much text as you like on the editing screen The Edit menu provides standard editing features such as cut copy paste go to and find ai imdep Untitled 1 Insert Project Model Run Tools Window Help Ctrl 2 a c trl C Paste Ctrl Clear Del Delete Insert Name 7 Select All Ctrl A s is the text editing window s Ctrl Add mands can be collected here saci el IA gt X Rnn 0 1 X Rnn 0 1 Find Ctrl F Find Next Replace Go To Ctrl G Figure 11 1 The Editing Window and the Edit Menu 11 2 Programs and Procedures The Insert menu shown in Figure 11 2 can also be used in the editing window The Insert menu allows you to place specific items on the screen in the editing window t Limdep Untitled 1 File Edit POSSA Project Model Run Tools Window Help Be on fee 4 Untitled 1 DAR Item into Project f Insert Name This is the text editing window Variables Commands can be collected here E Namelists CREATE X Rn
175. fact that one variable is a lagged value of another one It just fills the missing values at the beginning of the sample with 999s at the time it is created Moving average and autoregressive sequences can easily be constructed using CREATE but you must be careful to set up the initial conditions and the rest of the sequence separately Also remember that CREATE does not reach beyond the current sample to get observations A special read only variable named _obsno note the leading underscore is provided for creating recursions Consider computing the infinite moving average series t 1 ye x Ox 0 K HOT X 7 16 Essentials of Data Management To do the computation we would use the autoregressive form y x Oy with y 0 The following could be used CREATE If_obsno 1 y 0 Else y x theta y 1 Second consider generating a random sample from the sequence y Oy e where e N 0 1 Simply using CREATE y theta y 1 Rnn 0 1 will not work since once again the sequence must be started somewhere But you could use the following CREATE If _obsno 1 y Rnn 0 1 Sqr theta 2 Else y theta y 1 Rnn 0 1 Matrix Function A transformations based on matrix algebra is used to create linear forms with the data Linear combinations of variables are obtained with CREATE name b x where x is a namelist of variables see Section 7 5 and b is any vector with the
176. fe Xi 0 Var e 1X 0 Cov ir amp js Xi 0 for all ij Cov a xi 4 0 The efficient estimator for this model in the base case is least squares The random effects model is Vir BX Er ti where E u 0 Var u o Cov snui 0 Var uj o 6 tor 14 16 The Linear Regression Model i Data Editor 3 900 Yars 3333 Rows 20 Obs Cell 987321 987321 987321 W a WOW HWW nrDnDMDMMMMDMMNM Ww WwW ww w 1 1 2 2 2 3 3 4 4 4 4 4 4 5 5 5 6 6 6 Figure 14 1 Internally Created Stratification and Count Variables For a given i the disturbances in different periods are correlated because of their common component uj 2 2 Corr j UtiEis uj p Ox 0 The efficient estimator is generalized least squares Before considering the various different specifications of the two models we describe two standard devices for distinguishing which seems to be the more appropriate model for a given data set Specification Tests for the One Factor Models Breusch and Pagan s Lagrange multiplier statistic wr D Eat D ATD YY is used to test the null hypothesis that there are no group effects in the random effects model Arguably a rejection of the null hypothesis is as likely to be due to the presence of fixed effects The statistic is computed from the ordinary least squares residuals from a pooled regression Large values of LM favor the effects model over the classical mode
177. ficient Standard Error t ratio P T gt t Mean of X Constant 20 9557732 59398134 35 2980 0000 LOGPG 16948546 03865426 4 385 0001 3 72930296 LOGI 96594886 07529145 12 829 0000 9 67214751 As a final check on the model we have plotted the residuals by adding PlotResiduals to the REGRESS command REGRESS Lhs logG Rhs one logpg logi Plot residuals The results are striking The residuals are far from a random sequence The long sequences of negative then positive then negative residuals suggests that something is clearly missing from the equation 1005 0505 Reidud o gt 050 5 1004 LE TEEDE EEE N S S E E E S EET 1952 1958 1964 1970 1976 1982 1988 1994 2000 2006 Year Unstandardized Residuals Bars mark mean res and 2s e Figure 6 17 Residual Plot 6 22 Application and Tutorial 6 5 6 Multiple Regression For the full model we use the following setup which combines some of our earlier commands NAMELIST _ x1 logpg logI x2 logpnc logpuc logppt x one x1 x2 t Notice the third namelist is constructed by combining the first two and adding a variable to the list The regression is then computed using REGRESS Lhs logg Rhs x Plot residuals The full results are as follows x Ordinary least squares regression LHS LOGG Mean 12 24504 Stan
178. file must contain the command PROCEDURE at the point at which the procedure is to begin and ENDPROCEDURE at the end of the procedure These might be the first and last commands in the file if you want only to input a procedure If you OPEN such an input file it will simply be loaded into the procedure buffer exactly as if you had typed it But remember the PROCEDURE cannot OPEN any files itself Some notes on procedures e The procedure loader is not a compiler The commands you type are not checked in any way for validity If you type nonsense LIMDEP will dutifully store it for you The problems will show up when you try to execute the procedure But see below procedures can be edited e A procedure may consist of no more than 2 500 nonblank characters When the commands are stored the embedded blanks are removed and comments are stripped off Still it may pay to use short names and always use the four letter convention for model commands e The procedure may contain up to 50 commands but remember that you can combine many CREATE CALC or MATRIX operations in a single command by separating them with semicolons e Only one active procedure can be defined at a time If you issue a PROCEDURE command any procedure which existed before is immediately erased But you can store up to 10 more procedures in a library which is described in the next section e Project files LPJ files always contain not only the active procedure but als
179. file of this form you need only tell LIMDEP where it is The command to read this file is READ File lt the name of the file gt The READ command may be submitted from the text editing window or in the command bar at the top of the screen There are two other ways to import a data file of this form e Use Project Import Variables to open the Import dialog box as shown in Figure 7 5 Select All Files in the file types then locate and select your data file and click Open e In the data editor select Import Variables from the menu invoked by clicking the right mouse button See Figure 7 1 This opens the same Import dialog box described above Essentials of Data Management Look in DataFiles e Fa E TableF2 1 txt E TableF2 2 txt TableF3 1 txt E TableF4 1 txt TableF4 2 txt TableF1 1 txt TableF5 1 txt TableF5 2 txt TableF 1 txt TableF 1 txt TableF7 2 txt TableF8 1 txt TableF9 1 txt TableF9 2 txt TableF11 1 txt TableF13 1 txt TableF14 1 txt TableF14 2 txt TableF15 1 txt TableF18 1 txt TableF20 1 txt TableF20 2 txt TableF21 1 txt TableF21 2 txt lt gt TableF1 1 tet Files of type an Files 7 Cancel Figure 7 5 Import Dialog Box File name When you read a file of this type LIMDEP determines the number of variables to be read by counting the number of names that appe
180. git kernel function and uses a data driven bandwidth equal to h 9Q n where Q min std dev range 1 5 For an example we will compute the kernel density that is a smoothed counterpart to the histogram for income distribution in Figure 13 1 The command is KERNEL Rhs hhninc The results follow The histogram is repeated to show the similarity Once again the very long tail of the distribution distorts the figure We show below how to adjust the parameters to accommodate this problem For the figure below we used Endpoints 0 30 to force the figures to have the same range of variation on the horizontal axis Untitled Plot 11 J 6 HHNING Kemel density estimate for HHNINC Figure 13 3 Kernel Density Estimator for Incomes The kernel density also produces some summary statistics as shown below for the example in Figure in 13 3 Describing Sample Data Kernel Density Estimator for HHNINC Observations 27326 Points plotted 100 Bandwidth 206384 Statistics for abscissa values Mean 3 520836 Standard Deviation 1 769083 Minimum 000000 Maximum 30 671000 Kernel Function Logistic Cross val M S E 000000 Results matrix KERNEL The data used to plot the kernel estimator are also retained in a new matrix named of course kernel Figure 13 4 shows the results for the preceding plot aoe uu DER Data U 27359 Rows 27326 Obs 100 2 Cell hn E
181. h as the squared correlation between the actual and fitted values but neither these nor the one above are fit measures in the same sense as in the linear model 8 Estimates of the coefficients their standard errors and the ratio of each coefficient to its estimated standard error This is asymptotically distributed as standard normal As always the matrices b and varb are saved by the procedure These will be the FGLS estimates of the random effects model ssqrd s from least squares dummy variable LSDV estimator or from FGLS rsqrd R from LSDV sS s from LSDV sumsqdev sum of squared residuals from LSDV rho estimated disturbance autocorrelation from whatever model is fit last degfrdm K sy standard deviation of Lhs variable ybar mean of Lhs variable kreg K nreg total number observations logl log likelihood from LSDV model ssqrdu estimate of o from FGLS ssqrde estimate of o from FGLS ssqrdw estimate of ow from GLS if two way random effects model is fit exitcode 0 0 if the model was estimable ngroup number of groups nperiod number of periods This will be 0 0 if you fit a one way model The Last Model is constructed as usual b_variable Predicted values are based on the last model estimated one or two way fixed or random Models for Discrete Choice 15 1 Chapter 15 Models for Discrete Choice 15 1 Introduction We define models in which the response variable bei
182. h no group specific effects A large value of the LM statistic in the presence of a large Hausman statistic as in our application argues in favor of the fixed effects model 14 24 The Linear Regression Model NOTE Sometimes it is not possible to compute the Hausman statistic The difference matrix in the formula above may not be positive definite The theory does not guarantee this It is more likely to be so but still not certain if the same estimate of o is used for both cases As such LIMDEP uses the FGLS estimator of this however it has been obtained for the computation Still the matrix may fail to be positive definite In this case a 0 00 is reported for the statistic and a diagnostic warning appears in the results Users are warned some other programs attempt to bypass this issue by using some other matrix or some other device to force a positive statistic These ad hoc measures do not solve the problem they merely mask it At worst the appropriate zero value can be replaced by a value that appears to be significant 6 The simple sum of squared residuals based on the random effects coefficients is reported 7 An R measure is reported by popular request N 5T Q 2 R 1 Fie Vin BreXit N wh ee arta Oi y Users are warned this measure can be negative It is only guaranteed to be positive when OLS has been used to fit a model with a constant term There are other measures that could be computed suc
183. he end of the command Finally just highlight the data and names line in the document use Edit Copy in the word processor and Edit Paste in LIMDEP The end result of either of these approaches will be to place the data in the text editor ready for you to use Running the Data File as a Command Set Placing the READ command and data in the text editor then highlighting the material and clicking GO to execute the READ actually involves an extra step You can instruct LIMDEP to do the whole thing at once since the file GasolineData lim contains the command and the data If you use Run Run File from the desktop menu then select the lim file from the mini explorer LIMDEP will read the file and internally by itself highlight the material and press its own GO button This process will carry out the READ command and proceed directly to the confirmation shown in Figure 6 5 Application and Tutorial ch EconometricsAssignment 1 doc Microsoft Word Tools Table MathType Window Help AdobePDF Acrobat Comments Assignment 1 The Linear Regression Model The data listed below are a set of yearly time series chsemations 1053 2004 anthe US Gasoline Market Use these dita to perform the following analyses Read the raw dita irto LIMDEP Genk dees sus oes served dbase etre datata youe 3 Tu Sak are in lerak We wihtofit a ostat ehsticty model which willrequine Obtain the flowing wari is g ofper captalznsolinec IE
184. he mouse cursor to the end of the last line you wish to submit This is the same movement that you use in your word processor to highlight text The highlighted section will change from black text on white to white text on black Then to execute the commands you may do either of the following e Click GO on the LIMDEP toolbar See below If the toolbar is not showing on your screen select the Tools Options View tab then turn on the Display Tool Bar option The GO button is seen in green in the tool bar in Figure 3 6 Limdep Untitled 1 File Edit Insert Project Model Run Tools Window Help osa S e elal Bap This small window accepts a one line command 7 F A Untitled Proj O X _ Data U 222 Rows 222 Obs 4 Untitled 1 EEk S S Data A Insert Name 4 variables I will use this window to collect the 5 Namelists commands that I need to analyze my data 4 Matri deplete SAMPLE 1 100 B CREATE X RNN 0 1 E Strings Procedures J Output Tables Output Window Figure 3 6 Command Bar e Select the Run menu at the top of your screen The Run menu is shown in Figure 3 7 The first two items in this menu are Run Line or Run Selection if multiple lines are highlighted will allow you to execute the selected commands once Run Line Multiple Times or Run Selection Multiple Times if multiple lines are highlighted will allow you to specify
185. hen multiplication for a type of division see below for raising a matrix to a power several forms see below Thus e d equals C x D and ec Ginv c or c lt c gt equals C times its inverse or I and c Ginv c c equals C As will be evident shortly the apostrophe operator is a crucial part of this package When scalars appear in matrix computations they are treated as scalars for purposes of computation not as matrices Thus AsB where s is a scalar is the same as sAB The 1x1 matrix in the middle does not interfere with conformability it produces scalar multiplication 1x1 matrices which are the result of matrix computations such as quadratic forms also become scalars for purposes of matrix multiplication Thus in a r b r a will not require conformability of A and r number columns of A equal number of rows of r if the quadratic form r Br is collected in one term also A r B r A does require conformability but the same expression could be written a r b r a to achieve greater efficiency Also if r happens to be a variable this may be essential The implications of these different forms will be presented in detail below All syntaxes are available for any entity so long as conformability is maintained where appropriate A and B are any matrix w is any vector row or column including if desired a variable and C is any matrix Once again a matrix is any numeric entity
186. hierarchy of operations is 4 gt gt lt lt amp Operators in parentheses have equal precedence and are evaluated from left to right When in doubt add parentheses There is essentially no limit to the number of levels of parentheses They can be nested to about 20 levels It is important to note that in evaluating expressions you get a logical result not a mathematical one The result is either true or false An expression which cannot be computed cannot be true so it is false Therefore any subexpression which involves missing data or division by zero or a negative number to a noninteger power produces a result of false But that does not mean that the full expression is false For example x 0 gt 0 x gt y could be true The first expression is false because of the zero divide but the second might be true and the or in the middle returns true if either expression is true Also we adopt the C language convention for evaluation of the truth of a mathematical expression A nonzero result is true a zero result is false Thus your expression need not actually make logical comparisons For example Suppose x is a binary variable zeros and ones REJECT x will reject observations for which x equals one since the expression has a value of true when x is not zero Therefore this is the same as REJECT x 06 Essentials of Data Management 7 27 REJECT deletes observations from the
187. hs one x yyvyvyvy vvv vey vy FA Output Status Trace 1ne 1 rogram Instruction RESET 1 SAMPLE 2 CREATE gt SAHPIE gt CREATE gt CREATE 0 1 0 x NN O 1 0 0 1 RNN 0 1 1 X File Edit Insert Project Model Run Tools Window Help TA Untitled P a U 11111 Main Options Output Dependent variable fy r GARCH models r Independent variables ONE x I GARCHIP Q model I GARCH in mean P Q 1 F no of laqaed variance terms p Q no of lagged I Keep cond vars as squared disturb s Strings E Procedu Sy Output I Weight using variable I Noscaling Use least absolute deviations estimator with jo bootstrap replications Figure 4 4 Regression Command Builder 4 6 LIMDEP Commands After selecting the variables that I want to appear on the left and right hand sides of my regression equation I press Run and the regression is computed The results are shown in Figure 4 5 Limdep Output DER Fie Edit Insert Project Model Run Tools Window Help psa a Untitled Proj X lt j Untitled 1 Data U 11111 Rows 100 Obs a Data 4 Variables bx bY Plot lhs x rhs y reg grid gt LOGL_OBS Exit status for this model command is CDODATE Y V ss DWN Ase 134 2817 170 7316 72 90 000 1122372 1
188. ht for a selected sample in a sample selection model That is after selection the weights on the selected data points may or may not sum to the number of selected data points As such the weights in SELECT with univariate and bivariate probit criterion equations are rescaled so that they sum exactly to the number of selected observations TIP The scaling will generally not affect coefficient estimates But it will affect estimated standard errors sometimes drastically To suppress the scaling for example for a grouped data set in which the weight is a replication factor use Wts name noscale or just Wts name n WARNING When this option is used with grouped data qualitative choice models such as logit it often has the effect of enormously reducing standard errors and blowing up t ratios The noscale option would most likely be useful when examining proportions data with a known group size For example consider a probit analysis of county voting returns The data would consist of N observations on n pi xi where n is the county size p is the proportion of the county population voting on the issue under study and x is the vector of covariates Such data are heteroscedastic with the variance of the measured proportion being proportional to 1 n We emphasize once again when using this option with population data standard errors tend to become vanishingly small and call upon the analyst to add the additio
189. ic colors math objects etc However once you save then retrieve this window these features will be lost and all that will remain will be the text characters in Courier font 44 Limdep Untitled 1 SEE Ctrlt 2 Ctrl x ala Ctrl C Paste Ctrl nae Del 7 Untitled 1 Select All Ctrl 4 A Insert Name v Include Observations Ctr dd I will use this window to collect the Reject Observations Ctrl Subtract commands that I need to analyze my data Find Ctrl F SAMPLE 1 100 Find Next F3 CREATE X RNN 0 1 5 Replace Go To Ctrl G Object Figure 3 5 Editing Window and the Edit Menu TIP The text editor uses a Courier size 9 font If you are displaying information to an audience or are preparing materials for presentation you might want to have a larger or different font in this window You can select the font for the editor by using the Tools Options Editor Choose Font menu You may then choose a different font and size for your displays This font will be used in the text editing window and in the output window NOTE The editing window is also referred to as a text editor or a command editor 3 6 Operating LIMDEP When you are ready to execute commands highlight the ones you wish to submit with your mouse by placing the cursor at the beginning of the first line you wish to submit and while holding down the left mouse button moving t
190. ic Econometrics McGraw Hill 2003 Johnston J and DiNardo J Econometric Methods 4th Edition McGraw Hill 1997 Stock J and Watson M Introduction to Econometrics 2 Ed Addison Wesley 2007 Wooldridge J Econometric Analysis of Cross Section and Panel Data MIT Press 2002 Wooldridge J Modern Econometrics 2 ed Southwestern 2007 Getting Started 2 1 Chapter 2 Getting Started 2 1 Introduction This chapter will describe how to install LIMDEP on your computer Sections 2 5 to 2 7 describe how to start and exit LIMDEP 2 2 Equipment LIMDEP is written for use on Windows driven computers As of this writing we do not support operation on any Apple Macintosh computers Windows emulation software that allows you to run Windows on Apple machines should allow LIMDEP to operate but we are unable to offer any assurance nor any specific advice 2 3 Installation To install LIMDEP first close all applications Insert the LIMDEP CD in your CD ROM drive The setup program should start automatically If it does not open My Computer or Windows Explorer see Figure 2 2 and double click your CD ROM drive to view the contents of the LIMDEP CD To launch the Setup program double click Setup In either case the installation wizard will start Installation proceeds as follows Step 1 Preparing to Install The InstallShield Wizard checks the operating system and configures the Windows installer Installation proceeds
191. if the clusters vary in size Note this is not the same as the variable in the Pds function that is used to specify a panel The cluster specification must be an identifying code that is specific to the cluster For example our health care data used in our examples is an unbalanced panel The first variable is a family id which we will use as follows Cluster id Models for Discrete Choice 15 9 15 3 Ordered Choice Models The basic ordered choice model is based on the following specification There is a latent regression ye B x F e 0 Efex 0 Var e x 1 The observation mechanism results from a complete censoring of the latent dependent variable as follows Ji 0 ify lt Ho lifum lt y lt u 2ifu lt y lt ph Jif Yi gt Uy The latent preference variable y is not observed The observed counterpart to y is y Four stochastic specifications are provided for the basic model shown above The ordered probit model applies in applications such as surveys in which the respondent expresses a preference with the above sort of ordinal ranking The variance of g is assumed to be one since as long as y B and g are unobserved no scaling of the underlying model can be deduced from the observed data Since the us are free parameters there is no significance to the unit distance between the set of observed values of y They merely provide the coding Estimates are obtained by maximum likelihood
192. iffers from that for ordinary least squares REGRESS only in a list of instrumental variables All options are the same as for the linear regression model see Chapter E5 for details This includes the specifications of AR1 disturbances Plot for residuals etc The list of instruments may include any variables existing in the data set HINT If your equation Rhs includes a constant term one then you should also include one in the list of instrumental variables Indeed it will often be the case that Inst should include one even if the Rhs does not Computations use the standard results for two stage least squares See e g Greene 2008 There are no degrees of freedom corrections for variance estimators when this estimator is used All results are asymptotic and degrees of freedom corrections do not produce unbiased estimators in this context Thus I n Ey B x This is consistent with most published sources but curiously enough inconsistent with most other commercially available computer programs It will show up as a proportional difference in all estimated standard errors If you would prefer that the degrees of freedom correction be made add the specification Dfc to your 2SLS command 14 5 1 Robust Estimation of the 2SLS Covariance Matrix The White and Newey West robust estimators of the covariance matrix of the least squares estimator described in Section 14 2 3 can also be obtained for 2SLS b
193. in this documentation will be found in these folders 2 4 Registration The first time you use LIMDEP you will be presented with the Welcome and Registration dialog box There are two steps to register LIMDEP First provide the registration information requested in the dialog box Carefully input the serial number included with your program This will place the registration information including your serial number in the About box You must complete all three fields of this dialog box in order to begin using LIMDEP See Figure 2 1 Second send your registration information to Econometric Software You can register with Econometric Software by completing the registration card included with your order and faxing or mailing it to us You can also send your registration information to Econometric Software online via our website www limdep com To submit your registration information on our website click Help then select LIMDEP Web Site and proceed to the Registration page LIMDEP 9 0 Welcome and Registration Welcome to IMDEP 9 0 Please provide the registration information requested below Carefully input your serial number When you exit this dialog your registration information will be recorded in the About box Name four name Institution Your company or institution Serial Number Your serial number Figure 2 1 Welcome and Registration Dialog Box Getting Started 2 3 2 5 Execution Beginning the LIMDEP Session Sta
194. inary least squares For the one factor models we formulate this model with N group specific constants and no overall constant NOTE f you have time invariant regressors such as sex or region you cannot compute the fixed effects estimator The fixed effects estimator requires that there be within group variation in all variables for at least some groups In this case you should use Random in your command Program Output for One Way Fixed Effects Models For purposes of the discussion define the four models Model 1 Model 2 Model 3 Model 4 Vit A T Vit Aj T Vit P Xi Yi i PB Xi Eit Eit Eir Eit no group effects or xs group dummies only regressors only xs and group effects Output from this program in the order in which it will appear is as follows 1 Ordinary least squares regression of y on a single constant and the regressors x Xx These K variables do not include one This is Model 3 above Output consists of the standard results for least squares regression The diagnostic statistics in this regression output will also include the unconditional analysis of variance for the dependent variable This is the usual ANOVA for the groups ignoring the regressors See Section E11 5 1 for details The output from this procedure could be used to test the hypothesis that the unconditional mean of y is the same in all groups This test is done by the program See 14 20
195. inear equations Regression based on the Box Cox transformation of variables Nonlinear least squares for nonlinear regression models Nonlinear systems of equations SURE or GMM estimation Analysis of Nonlinear Functions FINTEGRATE GMME MAXIMIZE MINIMIZE WALD Function integration for user specified nonlinear function GMM estimation of model parameters Maximization of user specified functions User defined minimization command Standard errors and Wald tests for user specified nonlinear functions Single Equation Models for Binary Ordered and Multiple Discrete Choices BINARY CHOICESimulation program for all binary choice estimators BIVARIATE BURR CLOGIT COMPLOG GOMPERTZ LOGIT MLOGIT MPROBIT MSCORE NPREG ORDERED PROBIT Bivariate probit models partial observability models Burr model for binary choice Multinomial logit model for discrete choice among multiple alternatives Complementary log log model for binary choice Gompertz model for binary choice Binary and multinomial choice models based on the logistic distribution Multinomial logit model Multivariate probit model Maximum score semiparametric estimation for binary dependent variable Nonparametric regression models Ordered probability models for ordered discrete choice Several forms of binary choice models Econometric Model Estimation 12 5 SEMIPAR Klein and Spady semiparametric estimator for binary choice Models for Count Data GAM
196. into the REGRESS command with Cls b b b 5 0 REGRESS Lhs logg Rhs x CALC list tstat b 4 b 5 sqr varb 4 4 varb 5 5 2 varb 4 5 tc ttb 975 degfrdm pvalue 2 1 tds tstat degfrdm Chow test of structural change For each subperiod and for the full period obtain the residual sum of squares without displaying the whole regression PERIOD 1953 2004 CALC ssep Ess x logg k col x PERIOD 1953 1973 CALC ssel Ess x logg nl n 6 12 Application and Tutorial PERIOD 1974 2004 CALC sse2 Ess x logg n2 n CALC list f ssep ssel sse2 k sse1 sse2 n1 n2 2 k Ftb 95 k n1 n2 2 k Structural change test using Wald approach requires separate regressions and some matrix algebra PERIOD 1953 1973 Compute regressions quietly as I am not interested in seeing the results REGRESS Lhs logg Rhs x quietly MATRIX b1 b vl varb PERIOD 1974 2004 REGRESS Lhs logg Rhs x quietly MATRIX b2 b v2 varb Compute Wald statistic Then display critical value from chi squared table MATRIX db b1 b2 vdb v1 v2 list w db lt vdb gt db CALC list cstar ctb 95 k 6 5 Using LIMDEP for Linear Regression Analysis The following analyses show how to use LIMDEP for the standard applications in analysis of the linear model 6 5 1 Obtain Descriptive Statistics The command for o
197. ion or to change the order of evaluation For example CREATE ma pz pz 1 pz 2 pz 3 4 computes a moving average of a current and three lagged values Parentheses may also be nested to any depth CREATE ratio x y 2 a 2 2 a x c y x y la y a x c y is a valid command which computes ratio You may also nest functions For a few examples the following functions are used to invert certain probability distributions 7 12 Essentials of Data Management Gompertz CREATE t Log 1 w Log a p w Weibull CREATE t Log a 1 p w Normal CREATE t Exp Inp a p w Logistic CREATE t 1 a a i p w Functions may be nested to any depth and expressions may appear in the parentheses of a function Consider for example the following which creates the terms in the log likelihood function for a tobit model CREATE loglik 1 d Log Phi x b sigma d Log 1 sigma N01 y x b sigma Cautions e Any transformation that involves a missing value 999 at any point returns a missing value e It is unlikely to be necessary but if you should require expressions in the parameter list of a two parameter function put them in parentheses The Tm function which computes trend variables is such a function Thus CREATE trend Trn at b x step would confuse the compiler Instead you should use CREATE trend Trn a b x step
198. ions which use your data such as model estimation and data transformation operate only on the current sample For example if you have initially read in 10 observations on x and y but then set the sample to include only observations 1 3 6 and 8 10 nearly all commands will operate on or use only these seven observations Thus if you compute log x only seven observations will be transformed To define the current sample LIMDEP uses a set of switches one for each observation in the data set Thus when you define the sample you are merely setting these switches As such the REJECT command does not actually remove any data from the data set it merely turns off some of these switches The data are not lost The observations are reinstated with a simple SAMPLE All Figure 7 15 shows the process The sequence of instructions in the editing window creates a sample of draws from the standard normal distribution The SAMPLE command chooses the first 12 of these observations then the REJECT command removes from the sample observations that are greater than 1 0 or less than 1 0 This turns out to be observations 6 and 12 as can be seen in the data editor The chevron to the right of the row number in the data editor is the switch discussed above There are two sets of commands for defining the current sample one appropriate for cross section data and the other specifically for time series Essentials of Data Management 7 25 t Limdep Un
199. is as follows Dot products involving variables The procedure is aborted and 999 is returned e Max and Min functions Missing data are skipped e Lik Rsq etc regression functions Same as dot products The matrix algebra program that directly accesses the data in several commands including Essentials of Data Management 7 31 x x for sums of squares and cross products lt x x gt for inverses of moment matrices and many others will simply process them as if the 999s were legitimate values Since it is not possible to deduce precisely the intention of the calculation LIMDEP does not automatically skip these data or abort to warn you It should be obvious from the results You can specifically request this If you do have the SKIP switch set to on during matrix computations the student version does LIMDEP will process MATRIX commands such as x x and automatically skip over missing values But in such a case the computation is usually erroneous so your output will contain a warning that this has occurred and you might want to examine closely the calculations being done to be sure it is really how you want to proceed Figure 7 20 illustrates the results discussed in the previous paragraph The commands are shown in the editing window Variables x and y are random samples of 100 observations from the standard normal distribution The CREATE command changes a few observations in each column to missing values the
200. it logit models begin with an initial set of least squares results of some sort These are suppressed unless your command contains OLS The iterations are then followed by the maximum likelihood estimates in the usual tabular format The final output includes a listing of the cell frequencies for the outcomes When the data are stratified this output will also include a table of the frequencies in the strata The log likelihood function and a log likelihood computed assuming all slopes are zero are computed For the latter the threshold parameters are still allowed to vary freely so the model is simply one which assigns each cell a predicted probability equal to the sample proportion This appropriately measures the contribution of the nonconstant regressors to the log likelihood function As such the chi squared statistic given is a valid test statistic for the hypothesis that all slopes on the nonconstant regressors are zero The sample below shows the standard output for a model with six outcomes These are the German health care data described in detail in Chapter E2 The dependent variable is the self reported health satisfaction rating For the purpose of a convenient sample application we have truncated the health satisfaction variable at five by discarding observations in the original data set it is coded 0 1 10 Ordered Probability Model aximum Likelihood Estimates Dependent variable NEWHSAT Weighting variable No
201. its in your names Other punctuation marks can cause unexpected results if they are not picked up as syntax errors e Names may not contain more than eight characters There are a few reserved words which you may not use as names for variables matrices scalars namelists or procedures These are one used as a variable name the constant term in a model b varb sigma used as matrices to retain estimation results from all models n always stands for the current sample size pi the number 3 14159 _obsno observation number in the current sample used by CREATE _rowno row number in data set used by CREATE s sy ybar degfrdm kreg lmda logl nreg rho rsqrd ssqrd sumsqdev scalars retained after regressions are estimated exitcode used to tell you if an estimation procedure was successful Several of the reserved names are displayed in the project window Note in Figure 4 1 that there are keys next to the three matrix names b varb and sigma These names are locked i e reserved You may not change these entities for example you may not create a matrix named b That name is reserved for program use You are always protected from name conflicts that would arise if you try to name a variable or a matrix with a name which is already being used for something else such as a matrix or scalar or if you try to use one of the reserved names For example you may not name a variable s this is res
202. ity A nonpositive value forces estimation to halt at that point Results Reported by the Random Effects Estimator After display of any previous results including ordinary least squares and the fixed effects estimator a display such as the following Random Effects Model v i t e i t u i Estimates Var e 135360D 02 Var u 578177D 02 Corr v i t v i s 810298 Lagrange Multiplier Test vs Model 3 3721 10 1 df prob value 000000 High values of LM favor FEM REM over CR model Baltagi Li form of LM Statistic 3721 10 Fixed vs Random Effects Hausman 37 62 6 df prob value 000001 High low values of H favor FEM REM Sum of Squares 843423D 01 R squared 990075D 00 will be presented followed by the standard form table of coefficient estimates standard errors etc The results in the table are as follows The Linear Regression Model 14 23 1 Estimates of o and o based on the least squares dummy variable model residuals These are used to estimate the variance components Since there are some potential problems that can arise the sequence of steps taken in this part is documented in the trace file The application shows an example This trace output may be quite lengthy as several attempts may be made to fit the model with different variance components estimators 2 The estimate of p o o2 6 7 based on whatever first round es
203. ix above so this is a potential complication When this occurs LIMDEP uses either 1 or 1 and continues We emphasize this is not an error nor is it a program failure It is a characteristic of the data It may signal some problems with the model When this condition occurs the model results will contain the diagnostic Estimated correlation is outside the range 1 lt r lt 1 Using 1 0 This condition is specific to the two step regression estimators The maximum likelihood estimators discussed below force the coefficient to lie in the unit interval p is estimated directly not by the method of moments To estimate this model with LIMDEP it is necessary first to estimate the probit model then request the selection model The pair of commands is PROBIT Lhs name of z Rhs list for w Hold results SELECT Lhs name of y Rhs list for x For this simplest case Hold may be abbreviated to Hold All of the earlier discussion for the probit model applies See Chapter E18 This application differs only in the fact the Hold requests that the model specification and results be saved to be used later Otherwise they disappear with the next model command The PROBIT command is exactly as described in Chapter E18 The selection model is completely self contained You do not need to compute or save Aj 16 8 Censoring and Sample Selection This page intentinally left blank Index Index Ancillary parameters 8
204. ized dialog boxes specific to a particular model command imdep Untitled Project 1 File Edit Insert Project Mf Run Tools Window Help Data Description p Time Series Linear Models Regression Nonlinear Regression 2515 Binary Choice HREG Censoring and Truncation TSCS Count Data SURE Duration Models 1 3585 3 9 Variables Frontiers 5 Namelists Discrete Choice Matrices Numerical Analysis H E Scalars H E Strings OA Proredires Data Figure 8 1 Model Command Builder with Linear Models Menu We ll illustrate operation of the command builder with a familiar application Grunfeld s panel data set 10 firms 20 observations per firm on three variables investment i profit f and capital stock c The data are contained in the project shown in Figure 8 2 The variables d1 d2 are dummy variables for the 10 firms Figure 8 3 shows the main model specification dialog box Main page which will be quite similar for most of the models The main window provides for specification of the dependent variable the independent variables and weights if desired Weights are discussed in Section 8 3 We will not be using them in this example If desired the model is fully specified at this point Note that the independent variables have been moved from window at the right which is a menu to the specification at the left The highlighted variables D3 D9 will be moved when w
205. just to store is not only feasible but no more complicated than it would be if the data set had only 100 rows instead It is important for you to be aware of how this is done in order to use this program successfully The essential ingredient is the form in which matrix results generally appear in econometrics It is quite rare for an estimator or a procedure to be based upon data matrices per se Rather they almost always use functions of those matrices typically moments i e sums of squares and cross products For example an OLS estimator b X X X y can be viewed as a function of X and y But it is much more useful to view it as a function of X X and X y The reason is that regardless of the number of observations in the data set these matrices are KxK and Kx1 and K is usually small LIMDEP uses this result to allow you to manipulate your data sets Using Matrix Algebra 9 9 with matrix algebra results regardless of the number of observations To underscore the point consider that currently most other econometrics packages provide a means of using matrix algebra But to continue our example in order to do a computation such as that for b directly some of them must physically move the data that comprise X into an entity that will be the matrix X Thus X must be created even though the data used to make X are already in place as part of the data set currently being analyzed It is this step which imposes the capacity constr
206. l based on least squares of any sort or on likelihood methods can be estimated with weights This includes REGRESS PROBIT all LOGIT models and so on The only substantive exceptions are the nonparametric and semiparametric estimators MSCORE NPREG and the Cox proportional hazard model Estimating Models 8 11 NOTE In computing weighted sums the value of the variable not its square root is used As such if you are using this option to compute weighted least squares for a heteroscedastic regression name should contain the reciprocals of the disturbance variances not the standard deviations In maximum likelihood estimation the terms in the log likelihood and its derivatives not the data themselves are multiplied by the weighting variable That is when you provide a weighting variable LIMDEP computes a sum of squares and cross products in a matrix as X WX Yw xx and a log likelihood Log L Y wilog f where w is an observation on your weighting variable The weighting variable must always be positive The variable is examined before the estimation is attempted If any nonpositive values are found the estimation is aborted During computation weights are automatically scaled so that they sum to the current sample size The variable itself is not changed however If you specify that variable w is to be the weighting variable in Wts w the weight actually applied is w N Z w x wi This scaling may or may not be rig
207. l be understood to be the number r 3 14159 Note that this will preempt matrices and scalars named pi so this name should be avoided in other contexts The name pi may also appear in MATRIX and CREATE commands for example MATRIX pii pi Iden 5 CREATE f 1 sg Sqr 2 pi Exp 5 x mu sg 2 When you give a CALC MATRIX or CREATE command the name n is always taken to mean the current sample size You may use n in any scalar calculation For example after you compute a regression the log likelihood function could be computed using CALC 1 n 2 1 Log 2 pi Log sumsqdev n NOTE n and pi have the meanings described above everywhere in LIMDEP Thus you could use pi ina list of starting values as part of a model command or in CALCULATE 10 6 Calculator Functions The functions listed below may appear anywhere in any expression The arguments of the functions can be any number within the range of the function e g you cannot take the square root of 1 as well as matrix elements and names of other scalars Function arguments may also be expressions or other functions whose arguments may in turn be expressions or other functions and so on For example z Log Phi al a2 Log a2 q 2 is a valid expression which could appear in a CALC command The depth of nesting functions allowed is essentially unlimited When in doubt about the order of evaluation you should add p
208. l with no common effects The Linear Regression Model 14 17 A second statistic is Hausman s chi squared statistic for testing whether the GLS estimator is an appropriate alternative to the LSDV estimator Computation of the Hausman statistic requires estimates of both the random and fixed effects models The statistic is H B fels Disav Est Var Disav Est Var B pets B ris Disav Large values of H weigh in favor of the fixed effects model See Greene 2008 for details Note that in some data sets H cannot be computed because the difference of the two covariance matrices is not positive definite The algebra involved does not guarantee this Some authors suggest computing a generalized inverse in such a case which will force the issue But it will not produce an appropriate test statistic The better strategy in such a case is to take the difference between the two estimators to be random variation which would favor the random effects estimator These two statistics are presented as part of the results when you fit both the fixed effects and random effects models The REGRESS command can be stated to request specifically either of the two But if you do not specify either in particular LIMDEP fits both and near the end of the voluminous output presents a table such as the following which contains the LM and H statistics Random Effects Model v i t e i t u i Estimates Var e 32
209. lank Since a data file can be arranged any way you want LIMDEP has no way of knowing that a blank is supposed to be interpreted as a missing value But all other nonnumeric nonblank entries are treated as missing This includes SAS s character the word missing or any other code you care to use There will be occasions when LIMDEP claims it found missing values when you did not think there were any The cause is usually an error in your READ command For example if you have a set of names at the top of your data file and you forget to warn the program to expect them they will be read as missing values rather than as variable names After a data set is READ you are given a count of the variables then existing and a summary of any missing values found When a data set contains missing values you must indicate this in some way at the time the data are read How you do this depends on the type of file you are reading Worksheet file from a spreadsheet program Blank cells in a worksheet file are sufficient to indicate missing data It is not necessary to put any alphabetic indicator in the cell Unformatted ASCII file Any nonnumeric data in the field such as the word missing will suffice Alternatively a simple period surrounded by blanks will suffice Note that in such a file a blank will not be read as missing since blanks just separate numbers in the data file The internal code for a missing datum is 999 You m
210. les Figure 2 3 Tools Menu on Desktop Options View Editor Projects Execution Trace IV Display Tool Bar IV Display Status Bar I Display Command Bar w Cancel Apply Figure 2 4 Options Dialog Box 2 6 Components of a LIMDEP Session When you are operating LIMDEP you are accumulating a project that consists of at least four components e Your data matrices scalars the environment and so on The window associated with this information is the project window usually at the upper left of your screen as in Figure 2 2 e The commands that you have accumulated on the screen in an editing window e The output that you have accumulated in the output window e LIMDEP s session trace file described in Section 2 11 Figure 2 5 shows an example In this session we are analyzing a data set that contains 840 observations on about 20 variables The chapters to follow will describe the various components and how the analysis proceeds Figure 2 5 shows a fairly typical arrangement of a LIMDEP session The screen parts are arranged for the figure It will be more conveniently spaced when you use the program The four parts of the session can be seen in the figure e The project consists of the CLOGIT data which we will use later in several examples e The editing window also referred to as a text or command editor at the upper right shows the one command that we have entered e The output window mostly obsc
211. les to open a dialog box that allows you to import a spreadsheet or other data file This is analogous to the READ command described below Set Sample Click Set Sample to obtain a menu of options for setting the current sample This uses the REJECT INCLUDE and DATES features discussed in Section 7 5 to set the current sample This option is not available until data have been read into the data area HINT The data editor does not automatically reset the current sample After you enter a data set with it the current sample is unchanged Data may be edited in the data editor in the usual fashion for spreadsheets Note however that this means only entering new values or replacing old ones We have not replicated the full transformation functionality in e g Excel Data may be transformed and manipulated using other features in LIMDEP The New Variable option however does provide all the features you might need to transform variables Exit the editor simply by closing the window 7 4 Essentials of Data Management 7 2 3 Reading Data Files Into LIMDEP Data may be entered into LIMDEP from many different kinds of files Formats include simple ASCII files spreadsheet files written by other programs such as Excel and binary as well as other types of files written by other statistical programs The usual way of entering data in LIMDEP if you are not typing them in the data editor is in the form of ASCII text An ASCII file is a te
212. likelihood from the unrestricted model computes the test statistic then computes the tail area to the right of the statistic to determine if the hypothesis should be rejected 10 2 Command Input in CALCULATE CALCULATE is the same as MATRIX in the two modes of input Select Tools Scalar Calculator to open the calculator window shown in Figure 10 1 Calculator Expr Phi 1 96 f Scalar gt CALC list phi 1 96 Result 97500210485177950D 00 Figure 10 1 Calculator Window There are two ways to enter commands in the calculator window You can type CALCULATE commands in the smaller Expr window If your command will not fit on one line just keep typing At some convenient point the cursor will automatically drop down to the next line Only press Enter when you are done entering the entire command In this mode of entry you do not have to end your commands with a Alternatively you can click the fy button to open a subsidiary window the Insert Function dialog box that provides a menu of matrix and calculator functions see Figure 10 2 Select Scalar to display the calculator functions By selecting a function and clicking Insert you can insert a template for the indicated function into your Expr window in the calculator window You must then change the arguments in the function e g the x in the Phi x in Figure 10 2 to the entity that you desire When you have entered your full expression i
213. linear and nonlinear model classes and over fifty other model classes Each of these allows a variety of different specifications Most of the techniques in wide use are included Among the aspects of this program which you will notice early on is that regardless of how advanced a technique is the commands you use to request it are the same as those for the simplest regression LIMDEP also provides numerous programming tools including an extensive matrix algebra package and a function optimization routine so that you can specify your own likelihood functions and add new specifications to the list of models All results are kept for later use You can use the matrix program to compute test statistics for specification tests or to write your own estimation programs The structure of LIMDEP s matrix program is also especially well suited to the sorts of moment based specification tests suggested for example in Pagan and Vella 1989 all the computations in this paper were done with LIMDEP The programming tools such as the editor looping commands data transformations and facilities for creating procedures consisting of groups of commands will also allow you to build your own applications for new models or for calculations such as complicated test statistics or covariance matrices Most of your work will involve analyzing data sets consisting of externally generated samples of observations on a number of variables You can read the data
214. ll zero 9 Test the hypothesis that the elasticities with respect to the prices of new and used cars are equal a Do the test using an F test b Use a t test showing all computations 10 The market for fossil fuels changed dramatically at the end of 1973 We will examine whether the data contain clear evidence of this phenomenon a Use a Chow test for structural break to ascertain whether the same model applies for the period 1953 1973 as for 1974 2004 b More advanced Use a Wald test to test the hypothesis How do the assumptions underlying these two tests differ In the analysis to follow we will work through the problem set in detail You can work through the steps with the presentation by typing the commands into the text editor To save time typing you can just upload the file Tutorial lim that you will find in the C LIMDEP9 LIMDEP Command Files folder The data set that we will use is also provided as file Gasoline txt and Gasoline xls in the folder C LIMDEP9 LIMDEP Data Files The data for the exercise are listed on the following page Application and Tutorial Year GasExp GasPrice Income PNewCar PUsedCar PPubTrn Pop 1953 7 4 16 668 8883 47 2 26 7 16 8 159565 1954 T8 17 029 8685 46 5 2287 18 0 162391 1955 8 6 17 210 9137 44 8 21 5 18 25 165275 1956 9 4 17 729 9436 46 1 20 7 19 2 168221 1957 L032 18 497 9534 48 5 23 2 19 9 171274 1958 10 6 18 316 9343 50 0 24 0 20 9 174141 1959 LIKS 18 5
215. lls so if your data have more than 20 000 groups alphafe will contain the first 20 000 fixed effects computed Estimates of the variances or standard errors of the fixed effects are not kept But a simple method o f computing them is given below Scalars that are kept are ssqrd s from least squares dummy variable LSDV rsqrd R from LSDV sS s from LSDV sumsqdev sum of squared residuals from LSDV rho estimated disturbance autocorrelation from whatever model is fit last degfrdm T K sy standard deviation of Lhs variable ybar mean of Lhs variable kreg K nreg total number observations logl log likelihood from LSDV model exitcode 0 0 if the model was estimable ngroup number of groups nperiod number of periods This will be 0 0 if you fit a one way model The Linear Regression Model 14 21 The Last Model is constructed as usual b_variable Predicted values are based on the last model estimated one or two way fixed or random Predictions are not listed when you use the group means estimator but they can be computed with MATRIX Robust Estimation of the Fixed Effects OLS Covariance Matrix There is a counterpart to the White estimator for unspecified heteroscedasticity for the one way fixed effects model The model is Yi OF Bn Eir Suppose that every has a different variance o In the fashion of White s estimator for the linear model the natural approach is simply to repl
216. mands Lists of variables are used in every model estimation command and a large number of other commands such as WRITE For example nearly all model commands are of the form MODEL COMMAND Lhs a variable Rhs a list of variables Rh2 a list of variables Each of the lists may in principle have 150 or more names in it As such some shorthands will be essential One simple shorthand for lists of variable names is the wildcard character You may use the character to stand for lists of variables in any variable list There are three forms e stands for all variables LIST requests a list of all existing variables DELETE 3 is a global erasure of all data You should use RESET e aaaa stands for all variables whose names begin with the indicated characters any number from one to seven For example If you have variables x1 x2 xa xxx xxy x all five variables xx xxx and xxy then the following command requests simultaneous scatter plots of all variables whose names begin with x SPLOT 3 Rhs x e qaaa stands for variables whose names end with the indicated characters For example if you have xa ya and y REGRESS Lhs y Rhs one a regresses y on one xa and ya 7 22 Essentials of Data Management 7 4 2 Namelists The wildcard character described above will save some typing But namelists will usually be a more efficient approach to specifying a list of nam
217. mands MATRIX commands are typically given as parts of programs that perform larger functions such as in the examples in Section 9 2 1 You also have a matrix calculator that you can access occasionally in a window that is separate from your primary desktop windows project editing and output 9 2 1 The Matrix Calculator You may invoke the matrix calculator by selecting Tools Matrix Calculator as shown in Figure 9 1 Using Matrix Algebra 9 3 ai Limdep Output File Edit Insert Project Model Run MESS osal a see 3 Data qj variables nm lt OF gt NUM a ind 9 16 c in gt MONTHS c67 dmy 8 3 dm gt 77 dmy 8 7 dm gt gt logmth log montl X one a c d e c67 A Open a matrix calculator window Ln 147 205 4 Figure 9 1 Tools Menu for Matrix Calculator The matrix calculator window is shown in Figure 9 2 Calculator DE Expr f 172 374 5 6 Matrix gt MATR list F 1 2 374 5 6 has 3 rows and 3 colugns 2 1 00000 2 00000 4 00000 2 00000 3 00000 5 00000 4 00000 5 00000 6 00000 Figure 9 2 Matrix Calculator Window You can leave the matrix calculator window open while you go to some other function For example you may find it convenient to interrupt your work in the editing output windows by activating the matrix calculator to check some result which perhaps is not emerging the way you expected There are two other ways
218. me model as the reduced form in the previous paragraph Threshold models such as labor supply and reservation wages lend themselves to this approach 15 2 Models for Discrete Choice The probabilities and density functions for the most common binary choice specifications are as follows Probit Bx exp t7 2 E F f Tn dt OB x f B x Logit 2 PRO A f AB x L 1 AB X 1 exp B x 15 2 1 Model Commands The model commands for the five binary choice models listed above are largely the same PROBIT or Lhs dependent variable Rhs regressors LOGIT Data on the dependent variable may be either individual or proportions You need not make any special note of which LIMDEP will inspect the data to determine which type of data you are using In either case you provide only a single dependent variable As usual you should include a constant term in the model unless your application specifically dictates otherwise 15 2 2 Output The binary choice models generate a very large amount of output Computation begins with least squares estimation in order to obtain starting values NOTE The OLS results will not normally be displayed in the output To request the display use OLS in any of the model commands Reported Estimates Final estimates include e logl the log likelihood function at the maximum e logly the log likelihood function assuming all slopes are zero If your Rhs variables d
219. me to display the value at the bottom of the window in the border Double clicking a scalar name will open the New Scalar dialog box which may also be used to replace the value of that scalar See Figure 10 4 zi Untitled 1 f Insert Name v CALC List Phi 1 96 CALC List TailProb Phi i H Matrices lt Q Scalars SSQRD RSORD S Expression SUMSQDEYV 0 841345 ExXITCODE gt TAILPROB Gj Strings 9 Procedures Scalar TAILPROB 0 841345 Figure 10 4 Edit Function of New Scalar Dialog Box 10 4 Forms of CALCULATE Commands Conditional Commands The essential format of aCALCULATE command is CALC name result additional commands 10 6 Scientific Calculator If you wish to see the result but do not wish to keep it just omit name The same applies to the dialog mode in the calculator window Scalar results will be mixtures of algebraic expressions addition multiplication subtraction and division functions such as logs probabilities etc and possibly algebraic manipulation of functions of scalars or expressions All calculator commands may be made conditional in the same manner as CREATE or MATRIX The conditional command would normally appear CALC If logical expression name expression The logical expression may be any expression that resolves either to TRUE or FALSE or to a numeric value with nonzero implying true The rules for
220. mini explorer Look in LIMDEP Command Files e e E faj GasolineData lim File name Files of type All Readable Files lim Ipj sav Cancel Figure 6 2 Mini explorer for Data File Now just double click the file name and the contents of the file will be placed in a new text editing window as shown in Figure 6 3 With the data in this form all that is needed now is Edit Select All then click the GO button o in the desktop toolbar and the data will be read from the screen 6 6 Application and Tutorial Limdep Untitled 2 File Edit Insert Project Model Run Tools Window Help _ osa S olau AEA TUNSWGI Z Untitled 2 Eor f Insert Name GasPrice Income PNewCar PUsedCar PPubTrn 16 6 47 2 16 8 BPRERBRBBPRBEPHPRHH JRE RE REPRE PE PEP PP PP pe Pp wo ee HHH o o D 51 5 Ln 1 55 Figure 6 3 Reading ASCII Data in a Text Editor Using Copy Paste For purposes of this method suppose you have been given the data table in a document file that will allow you to copy and paste the data file exactly the way they appear on the page Figure 6 4 below shows the example for our tutorial The data that we wish to analyze appear on the left hand page To transport these data into LIMDEP we could proceed as follows First start LIMDEP Then we open a text editor in LIMDEP with File New Text Command Document Type the command READ in the top line Do not forget the at t
221. mmands are all independent of the number of observations Finally consider the weighted sum above F 1 n X WX where there are 10 000 observations and 20 variables Once again the result is going to be 20x20 LIMDEP provides many different ways to do this sort of computation For this case the best way to handle it is as follows NAMELIST x the list of 20 variables SAMPLE 3 set up the 10 000 observations CREATE w the weighting variable MATRIX 3f 1 n x w x This would work with 10 or 10 000 000 observations The matrix fis always 20x20 9 4 Manipulating Matrices The preceding described how to operate the matrix algebra package The example in Section 9 1 also showed some of the more common uses of MATRIX This and the following sections will now detail the specifics of LIMDEP s matrix language In addition to the basic algebraic operations of addition subtraction and multiplication LIMDEP provides nearly 100 different functions of matrices most of which can themselves be manipulated algebraically In this section we will list the various conventions that apply to these operations 9 4 1 Naming and Notational Conventions Every numeric entity in LIMDEP is a matrix and you will rarely have to make a distinction among them For example in the expression MATRIX f q rs q and r could be any mix of variables data matrices computed matrices named scalars literal numbers e g 2 345 the numb
222. model The 75 or so different models are specified by changing the model name or by adding or subtracting specifications from the template above At different points other specifications such Rh2 a second list are used to specify a list of variables These will be described with the particular estimators Different models will usually require different numbers and types of variables to be specified in the lists above Note that in general you may always use namelists at any point where a list of variables is required Also a list of variables may be composed of a set of namelists NOTE ON CONSTANT TERMS IN MODELS Of the over 75 different models that LIMDEP estimates only one the linear regression model estimated by stepwise regression automatically supplies a constant term in the Rhs list Jf you want your model to contain a constant term you must request it specifically by including the variable one among your Rhs variables You should notice this in all of our examples below 8 2 Estimating Models ADVICE ON MODEL SPECIFICATION It is fairly rare that a model would be explicitly specified without a constant In almost all cases you should include the constant term Omitting the constant amounts to imposing a restriction that will often distort the results sometimes severely We recall a startling exchange among some of our users in reaction to what appeared to be drastic differences in the estimates of a pr
223. mples from Continuous Distributions Rng m s lognormal with parameters m and s Rnt n t with n degrees of freedom Rnx d chi squared with d degrees of freedom Rnf n d F with n numerator and d denominator degrees of freedom Rne q exponential with mean q Rnw a c Weibull with location a and scale c If c 1 use Rnw a Rnh a c Gumbel extreme value with location a scale c If c 1 use Rnh a Rni a c gamma with scale a and shape c If a 1 use Rni c Rna a b beta with parameters a and b Rnl 0 logistic Rnc 0 Cauchy 7 20 Essentials of Data Management Random Samples from Discrete Distributions Rnp q Poisson with mean q Rnd n discrete uniform x 1 n Rnb 1 p binomial n trials probability p Rnm p geometric with success probability p For sampling from the binomial distribution The limits on n and p are nlog p and nlog 1 p must both be greater than 264 to avoid numerical overflow errors You must provide the a in the Weibull and Gumbel and the 0 logistic and Cauchy functions You may also sample from the truncated standard normal distribution Two formats are Rnr lower sample from the distribution truncated to the left at lower Rnr lower upper distribution with both tails truncated E g Rnr 5 samples observations greater than or equal to 5 Parameters of all requests for random numbers are checked for validity For the truncated norm
224. n 0 1 E Matrices gt Rnn 0 1 Scalars Strings E Procedures 4 Output amp Tables Output Window Insert a text File Figure 11 2 Insert Menu for Text Editor e Insert Command will place a specific LIMDEP command verb at the insertion point where the cursor is A dialog box allows you to select the verb from a full listing with explanation of the verbs e Insert File Path will place the full path to a specific file at the insertion point Several LIMDEP commands use files The dialog box will allow you to find the full path to a file on your disk drive and insert that path in your command e Insert Text File will place the full contents of any text file you select in the editor at the insertion point You can merge input files or create input files using this tool 11 2 2 Executing the Commands in the Editor When you are ready to execute commands highlight the ones you wish to submit Then you can execute the commands in one of two ways e Click the GO button on the LIMDEP toolbar If the toolbar is not displayed click the Tools Options View tab then turn on the Display Tool Bar option See Figure 11 3 e Select the Run menu at the top of your screen See Figure 11 4 When commands are highlighted the first two items in this menu will be Run selection to execute the selected commands once Run selection Multiple Times to open a dialog box to specify the number of times to run
225. n Tools Window Help Data U11111 R iya able S voi Set Sample Look in e Data Files e B EJ Nameli Reset E GasolineData xls Gy Matrici Gy Scalars H E Strings 4 Procedures 4 Output Tables Output Window File name Files of type All Readable Files wk xls M Cancel A FA Output Ln 100 100 Idle Figure 6 1 Reading an Excel Spreadsheet File WARNING For at least 15 years until 2007 the XLS format has served as a lingua franca for exchanging data files between programs Almost any statistical package could read one Beginning in 2007 Microsoft drastically changed the internal format of spreadhseet files and Excel 2007 files are no longer compatible with other software It will be quite a while if ever for software authors to catch up with this change so for the present we note that LIMDEP cannot read an Excel 2007 spreadsheet file If you are using Excel 2007 be sure to save your spreadsheets in the 2003 format Application and Tutorial 6 5 Text Input File A second equally simple way to read your data is simply to read them off the screen in a text editor The file GasolineData lim contains text that is exactly the highlighted command names and data that appear in Figure 6 3 To get these data into the program we can proceed as follows First we start LIMDEP Then use File Open and navigate to the file You will reach the file in the
226. n the regressors but not the dependent variable you can use Fill to obtain predictions for the missing data Remember though that the prediction is 999 missing for any observation for which any of the xs are missing The following commands could be used for computing forecast standard errors This routine uses the matrices b the coefficients and varb estimated covariance matrix kept by the regression and scalar ssqrd which is s squared from the regression The forecast standard errors are the values computed inside the Sqr function in the CREATE command NAMELIST _ x the set of regressors REGRESS Lhs y Rhs x Keep yhat CALC ct Tth 975 degfrdm CREATE lowerbnd yhat ct Sqr ssqrd Qfr x varb upperbnd yhat ct Sqr ssqrd Qfr x varb A plot of the residuals from your regression can be requested by adding Plot to the command Residuals are plotted against observation number i e simply listed If you would like to plot them against another variable change the preceding to Plot variable name These variables can be any existing variables They need not have been used in the regression The residuals are sorted according to the variable you name and plotted against it The plot will show the residuals graphed against either the observation number the date for time series data or the variable you specify using the Plot variable option described above e If there are outliers in
227. n the window press Enter to display the command in the lower part of the window as shown above If your command is part of a program it is more likely that you will enter it in command mode or in what we will label the in line format You will use this format in the editing window That is in the format CALC the desired result Commands may be entered in this format from the editor as part of a procedure or in an input file See Figure 10 3 One difference between the calculator window and display in the text editor or the output window is that in the latter you must include List in your command to have the result actually displayed This is the same as MATRIX See Section R13 3 for details on the List Specification Scientific Calculator 10 3 Insert Function Function Category Command Name All Matrix Ofic A c Ac for vector c VY Phi x probability that N 0 1 less than or equal to x Figure 10 2 Insert Function Dialog Box for Calculator Functions Limdep Output SEE File Edit Insert Project Model Run Tools Window Help oja S ele olol Bap T Untitled Proj lt Untitled 1 Sele Data U 3333 Rows 3333 Obs f Insert Name 24 Data CALC List Phi 1 96 E Variables 5 Namelists Q Matrices Scalars E Strings Procedures H E Output F3 Output Status Trace RESET gt RESET Initializing LIMDEP Ver
228. n with n K degrees of freedom p value Prob t n K gt observed tg e Sample mean of the variable 14 2 1 Retrievable Results The retrievable results which are saved automatically by the REGRESS command are Matrices b slope vector X X X y varb estimated covariance matrix e e n K X X Scalars ssqrd e e n K rsqrd R s 5 sumsqdev sum of squared deviations e e rho autocorrelation coefficient r degfrdm n K sy sample standard deviation of Lhs variable ybar sample mean of Lhs variable kreg number of independent variables K nreg number of observations used to compute the regression n Note this may differ from the sample size if you have skipped observations containing missing values logl log likelihood exitcode 0 0 unless the data were collinear or OLS gives a perfect fit Last Model b_name where the names are the Rhs variables See WALD in Section R11 5 2 14 2 2 Predictions and Residuals To obtain a list of the residuals and fitted values from a linear regression model add the specification List to the command The residuals and predicted values may be kept in your data area by using the specifications Res name for residuals 14 4 The Linear Regression Model and Keep name for predicted values If you are not using the full sample or all of the rows of your data matrix some of the cells in these columns will be marked as missing If you have data o
229. nal measure of interpretation 8 3 2 Model Output Most of the models estimated by LIMDEP are single equation index function models That is there is a dependent variable which we ll denote y a set of independent variables x and a model consisting in most cases of either some sort of regression equation or a statement of a probability distribution either of which depends on an index function x B and a set of ancillary parameters such as a variance term o ina regression or a tobit model The parameters to be estimated are B 6 In this framework estimation will usually begin with a least squares regression of y on x This will often be for the purpose of obtaining the default starting values for the iterations but is sometimes done simply because in this modeling framework the ordinary least squares OLS estimate is often an interesting entity in its own right Model output not including the technical output from the iterations see Section R8 4 will thus consist of the OLS results followed by the primary objects of estimation 8 12 Estimating Models NOTE In order to reduce the amount of superfluous output OLS results are not reported automatically except for the linear regression model To see the OLS outputs when they are computed add OLS to your model command TIP It is important to keep in mind that the OLS estimates are almost never consistent estimates of the parameter
230. nd may involve mathematical expressions of any complexity involving variables lagged variables of the form name lag named scalars matrix or vector elements and literal numbers The operators are the same as above with a few exceptions The ones that may be used are the math and relational operators gt gt lt lt The special operators and are not used here NOTE Logical expressions may not involve functions such as Log Exp etc Concatenation operators which can be used for transformations are amp for and and for or A simple example might be CREATE If x gt 0 expression For a more complex example we compute an expression for observations which are not inside a ball of unit radius CREATE 3 If x142 x242 x242 gt 1 expression The hierarchy of operations is gt lt lt amp Operators in parentheses have equal precedence and are evaluated from left to right When in doubt add parentheses There is essentially no limit to the number of levels of parentheses They can be nested to about 20 levels 7 3 3 Transformations Involving Missing Values NOTE Any mathematical expression that involves a missing value produces a missing value as the result Any transformation that requires a value which turns out to be a cell containing missing data will return a missing value not 0 Thus if you compute y Log
231. ndow are just added to the window during the session When you open a LIM file the file will be associated with the window and its name will appear in the window banner The in the title means that the contents of this window have not yet been saved TIP You can also associate a LIMDEP command file lt the name gt LIM with LIMDEP As in the earlier tip if you use My Computer and your mouse to drag the icon for a LIM file to the desktop then you can double click the icon to start LIMDEP and at the same time open an editing window for this command file Note however that when you do this you must then either open an existing project file with File Open File Open Project or one of the menu entries or start a new project with File New Project OK 3 3 Using the Editing Window LIMDEP s editing window is a standard text editor Enter text as you would in any other Windows based text editor The Edit menu provides standard Undo Cut Copy Paste Clear Select All Find Replace and so on as shown in Figure 3 5 You can also use the Windows clipboard functions to move text from other programs into this window or from this window to your other programs You can for example copy text from any word processor such as Microsoft Word and paste it into the editing window The LIMDEP editing window will inherit all the features in Operating LIMDEP 3 5 your word processor including fonts sizes boldface and ital
232. nds we are avoiding using the reserved names s and rsqrd 0750 0500 4 0250 4 0000 0250 4 Residud 0500 4 07504 M lt 10004 12504 rl EROA RRAHIN ETAREN 1952 1958 1964 1970 1976 Eo 1982 Year VARELAK 1988 1994 2000 Unstandardized Residuals Bars mark mean res and 2s e 2006 Figure 6 18 Residual Plot from Expanded Model 6 23 The least squares coefficients standard errors s and R are all reported with the standard It is also convenient to obtain these results using least squares algebra as shown below MATRIX bols lt X X gt X loge MATRIX e logg X bols CALC list se sqr e e n col X 312 1 e e n 1 var logg MATRIX 3 v s2 lt X X gt Stat bols v x Listed Calculator Results SE 047478 R2 965125 Number of observations in current sample Number of parameters computed here Number of degrees of freedom Variable Coefficient Standard Error b St Er Z gt z i Constant 26 9680492 2 09550408 12 869 0000 LOGPG 05373342 04251099 1 264 2 062 LOGI 1 64909204 20265477 8 137 0000 LOGPNC 03199098 20574296 Selog 8764 LOGPUC 07393002 10548982 4 EOL 4834 LOGPPT 06153395 12343734 499 6181 T 01287615 00525340 2 451 0142 To test the hypothesis that all the coefficients save for the consta
233. ne umber of observations 8140 Log likelihood function 11284 69 umber of parameters 9 Info Criterion AIC 2 77486 Info Criterion BIC 2 78261 Restricted log likelihood 11308 02 cFadden Pseudo R squared 0020635 Chi squared 46 66728 Degrees of freedom 4 Prob ChiSqd gt value 0000000 Underlying probabilities based on Normal Cell frequencies for outcomes Y Count Freq Y Count Freq Y Count Freq 0 447 054 1 255 031 2 642 078 3 1173 144 4 1390 170 5 4233 520 oa t Variable Coefficient Standard Error b St Er P Z gt z Mean of X Index function for probability Constant 1 32892012 07275667 18 265 0000 FEMALE 04525825 02546350 1 777 O55 52936118 HHNINC 35589979 07831928 4 544 0000 32998942 HHKIDS 10603682 02664775 3 979 0001 33169533 EDUC 00927669 00629721 1 473 1407 10 8759203 Threshold parameters for index u 1 23634786 01236704 19 F1 0000 u 2 62954428 01439990 43 719 0000 u 3 1 10763798 01405938 78 783 0000 u 4 1 55676227 01527126 101 941 0000 15 12 The model output is followed by a J 1 x J 1 frequency table of predicted versus actual values This table is not given when data are grouped or when there are more than 10 outcomes Models for Discrete Choice The predicted outcome for this tabulation is the one with the largest predicted probability
234. neither rows nor columns is n This will be simple to achieve since the sorts of computations that you normally do will ensure this automatically e Ensure that when data matrices appear in an expression they are either in the form of a moment matrix i e in a summing operation or they appear in a function that does summing Suppose that x and y are data matrices defined as above with 500 000 rows and 25 columns each i e they are very large Any operation that uses x or y directly will quickly run into space problems For example MATRIX 3Z x y the matrix product equal to the transpose of x times y is problematic since copies of both x and y must be created But the apostrophe is a special operator and Using Matrix Algebra 9 11 MATRIX 3Z x y can be computed because in this form LIMDEP knows that the operation is a sum of cross products and will be only 25x25 The second rule above then amounts to this When data matrices appear in matrix expressions they should always be in some variant of x y i e as an explicit sum or in one of the special moment functions listed in Section 9 7 such as Xdot The apostrophe is a special operator in this setting Although it can be used in multiplying any matrices it is the device which allows you to manipulate huge data matrices as illustrated by the examples given at the beginning of this chapter All of them work equally well with small samples or huge ones The co
235. ng described is inherently discrete as qualitative response QR models This chapter will describe two of LIMDEP s many estimators for qualitative dependent variable model estimators The simplest of these is the binomial choice models which are the subject of Section 15 2 The ordered choice model in Section 15 3 is an extension of the binary choice model in which there are more than two ordered nonquantitative outcomes such as scores on a preference scale 15 2 Modeling Binary Choice A binomial response may be the outcome of a decision or the response to a question in a survey Consider for example survey data which indicate political party choice mode of transportation occupation or choice of location We model these in terms of probability distributions defined over the set of outcomes There are a number of interpretations of an underlying data generating process that produce the binary choice models we consider here All of them are consistent with the models that LIMDEP estimates but the exact interpretation is a function of the modeling framework The essential model command for the parametric binary choice models is PROBIT or Lhs dependent variable Rhs regressors LOGIT A latent regression is specified as y BPxte The observed counterpart to y is y 1 if and only if y gt 0 This is the basis for most of the binary choice models in econometrics and is described in further detail below It is the sa
236. nonmissing cases Use DSTAT Rhs list of variables All to request in addition the skewness and kurtosis measures N DEE ihe x N 1 3 S Daaa AN 1 Sample kurtosis m Sample skewness m 4 Si After the table of results is given you may elect to display a covariance or correlation matrix or both for the variables The request is added to the command Output 1 to obtain the covariance matrix Output 2 to obtain the correlation matrix Output 3 for both covariance and correlation matrices 13 2 Describing Sample Data By adding All to the command we obtain the expanded results that include the skewness and kurtosis measures 13 2 1 Weights Weights may be used in computing all of the sums above by specifying Wts name of weighting variable Weights are always scaled so they sum to the current sample size Thus for example the weighted mean would be X 1 N UA Wy Xp N Z where Ww TA i l ik and zi the weighting variable 13 2 2 Missing Observations in Descriptive Statistics In all cases weighted or otherwise sums are based on the valid observations DSTAT automatically selects out the missing data Most other models save for those in NLOGIT 4 0 and most of the panel data estimators do not routinely do so unless you have the SKIP switch set Each variable may have a different number of valid cases so the table of results gives the number for each one
237. ns you may want the full parameter vector and covariance matrix You can retain these instead of just the submatrices listed above by adding the specification Parameters or just Par to your model command Note for example the computation of marginal effects for a dummy variable in a tobit model developed in the previous section Without this specification the saved results are exactly as described above The specific parameters saved by each command are listed with the model application in the chapters to follow You will find an example of the use of this parameter setting in the program for marginal effects for a binary variable in the tobit model which is in the previous section 8 3 4 Creating and Displaying Predictions and Residuals Most of the single equation models in LIMDEP though not all contain a natural dependent variable Model predictions for any such model are easily obtained as discussed below What constitutes a residual in these settings is a bit ambiguous but once again some construction that typically reflects a deviation of an actual from a predicted value can usually be retained The exact definition of a fitted value and a residual are given with the model descriptions in the chapters to follow There are several options for computing and saving fitted values from the regression models You may request fitted values and or residuals for almost any model The exceptions are e g multiple
238. nt term are zero we need F K 1 n K RK 1 R n K 6 24 Application and Tutorial The value is reported in the regression results above 207 55 But it is easy enough to compute it directly using CALC list f r2 col X 1 1 r2 n col X Listed Calculator Results F 207 553435 In fact this can be made a bit easier because the ingredients we need were automatically computed and retained by the regression command After the REGRESS command is executed the new project window is Untitled Proj E BK Data Y 11111 Rows 52 Obs YEAR GASEXP GASPRICE INCOME PNEWCAR PUSEDCAR PPLUBTRN POP LOGG LOGPG LOGI LOGPNC LOGPUC LOGPPT T LOGL_OBS Namelists Matrices SQ Scalars h SSQRD gt RSQRD ps Ph SUMSQDEY gt RHO gt DEGFRDM Ph sY gt YBAR Ph KREG gt NREG Variables 16 of 900 used Figure 6 19 Project Window b d gt d gt gt gt gt gt gt d gt d gt v The new scalars that appear in the project window are ssqrd s5 rsqrd R s 5 sumsqdev ele degfrdm n K kreg nreg n for the most recent regression computed Thus after the regression comand we could have used CALC list se sqr sumsqdev degfrdm 3r2 1 e e n 1 var logg Of course se and r2 were superfluous since s and rsqrd are the same values For computing the F statistic we could have used CALC 5
239. ntain a The subsequent command will be absorbed into the offending line almost surely leading to some kind of error message For example suppose the illustrative commands we used above were written as follows Note that the ending is missing from the second command SAMPLE 3 1 100 CREATE x Rnn 0 1 y x Rnn 0 1 REGRESS Lhs y Rhs one x This command sequence produces a string of errors Error 623 Check for error in ONE X Error 623 Look for Unknown names pairs of operators e g Error 61 Compilation error in CREATE See previous diagnostic The problem is that the REGRESS command has become part of the CREATE command and the errors arise because this is now not a valid CREATE instruction 4 3 Naming Conventions and Reserved Names Most commands refer to entities such as variables groups of variables matrices procedures and particular scalars by name Note in our examples we have referred to x y abd capital Your data are always referenced by variable names The requirements for names are e They must begin with a letter Remember that LIMDEP is not case sensitive Therefore you can mix upper and lower case in your names at will but you cannot create different names with different mixes E g GwEn is the same as GWEn gwen and GWEN LIMDEP Commands 4 3 e You should not use symbols other than the underscore _ character and the 26 letters and 10 dig
240. nting and Exporting Figures LIMDEP uses the standard Windows interface between input and output devices When a plot appears in a window you can use File Print to send a copy to your printer You can also save the graph as a Windows metafile WMF format by using File Save or File Save As For purposes of illustrating these functions we will use Figure 13 5 which was generated by a PLOT command The figure shows LIMDEP s base format for graphics Every graph generated is placed in its own scalable window as shown in Figure 13 6 apart from the project editing and output windows already open This window will remain open until you close it When you are finished reviewing the figure you should close the window to avoid proliferating windows You will be prompted to save the graph if you have not already done so EB Untitled Plot 7 Figure 13 5 Time Series Plot Using the PLOT Command 13 6 2 Saving a Graph as a Graphics File You may save any figure from a graphics window to disk in the Windows metafile wmf format Use File Save or File Save As This file type is transportable to many other programs including Microsoft Word and Excel For example in Word click the Insert menu and then select Picture then From File to import your wmf file into your Word document The Windows wmf format includes codes that allow you to scale the figure to whatever size you desire TIP Using Edit Copy in LIMDEP then Edit Paste in Word or Excel will tr
241. o not include one this statistic will be meaningless It is computed as logLo n PlogP 1 P log 1 P where P is the sample proportion of ones Models for Discrete Choice 15 3 e The chi squared statistic for testing Ho B 0 not including the constant and the significance level probability that y exceeds test value The statistic is x log logLo Numerous other results listed in detail will appear with these in the output The standard statistical results including coefficient estimates standard errors t ratios and descriptive statistics for the Rhs variables appear next A complete listing is given below with an example After the coefficient estimates are given two additional sets of results appear an analysis of the model fit and an analysis of the model predictions We will illustrate with binary logit and probit estimates of a model for visits to the doctor using the German health care data described in Chapter E2 The first model command is LOGIT Lhs doctor Rhs one age hhninc hhkids educ married OLS Note that the command requests the optional listing of the OLS starting values The results for this command are as follows With the exception of the table noted below the same results with different values of course will appear for all five parametric models Some additional optional computations and results will be discussed later The initial OLS estimates are generally not reported unless
242. o any procedures that you have stored in your procedure library They become part of the project 11 4 1 Executing a Procedure Silently Procedures are often used to produce a final result with many intermediate computations You can suppress intermediate output with EXECUTE Silent This suppresses all output When the procedure is completed the SILENT switches are turned off You can then use MATRIX CALC or whatever other means are necessary to inspect the desired final result from the procedure You might use this in an experiment in which you fit the same model many possibly thousands of times and accumulate a statistic from the execution For example you might investigate whether the mean of a certain statistic is zero with the following procedure The procedure is general you could replace the application specific part with some particular estimation problem It accumulates a result then uses the central limit to test the hypothesis that the statistic being computed is drawn from a distribution with mean zero CALC meanb 0 sb 0 nrep 1000 PROC generate the data set for the model command that computes the statistic CALC meanb meanb the statistic sb sb the statistic 2 ENDPROC Programs and Procedures 11 7 EXECUTE Silent n nrep CALC meanb meanb nrep Sb Sqr sb nrep meanb 2 nrep 1 List z Sqr nrep meanb sb The procedure estimates the same model
243. o so add the specification Names n Essentials of Data Management 7 7 to your READ command where n is the number of lines you need to list the names Then at the absolute beginning of the data set include exactly n lines of 80 or fewer characters containing the variable names separated by any number of spaces and or commas For appearance s sake you might for example position the names above the variables The following reads a data set containing three observations on four variables READ Nobs 3 Nvar 4 Names 2 File MACRO DAT The data set could be Year Consmptn GNP Govt 1961 831 25 996 19 128 37 1962 866 95 1024 82 138 83 1963 904 44 1041 03 153 21 Observation Labels The data file below contains labels for the individual observations as well as the names of the variables You may read a file with observation labels with the following format READ File filename Nobs Nvar Labels the column in the data file that contains the labels The labels column is an extra column in the data It is not a variable For the file below you would use READ 3 3 Nvar 4 Nobs 25 Names 1 Labels 1 This indicates that the labels are in the first column which is probably typical State ValueAdd Capital Labor NFirm Alabama 126 148 3 804 31 551 68 California 3201 486 185 446 452 844 1372 Connecticut 690 670 39 712 124 074 154 Florida 56 296 6 547 19 181 2
244. o the command One way you might use this device would be to draw a function by creating a set of equally spaced values then plotting the function of these values connecting the points to create the continuous function 13 18 Describing Sample Data This page intentionally left blank The Linear Regression Model 14 1 Chapter 14 The Linear Regression Model 14 1 Introduction This chapter will detail estimation of the single equation linear regression model yi XiPi X2Bo xXir Pr i x B 7 1 n The full set of observations is denoted for present purposes as y XB e The initial stochastic assumptions are the most restrictive for the linear model Eje X 0 Ele Vi zero mean Var e X Vale o Vi homoscedastic Cov e s X Cove 0 Vi j nonautocorrelation 14 2 Least Squares Regression The basic command for estimating a linear regression model with least squares is REGRESS Lhs dependent variable Rhs regressors The Rhs list may also include lagged variables and logs of variables This requests a linear ordinary least squares regression of the Lhs variable on the set of Rhs variables The standard output from the procedure is listed in the next section NOTE Remember that LIMDEP does not automatically include a constant term in the equation If you want one be sure to include one among the Rhs variables An example of the standard output for a linear r
245. obit model produced by LIMDEP and Stata The difference turned out to be due to the omitted constant term in the LIMDEP command In a few cases though it is not mandatory by the program you definitely should consider the constant term essential these would include the stochastic frontier and the ordered probit models However in a few other cases you should not include a constant term These are the fixed effects panel data estimators such as regression logit Poisson and so on In most cases if you try to include an overall constant term in a fixed effects model LIMDEP will remove it from the list NOTE With all of the different forms and permutations of features LIMDEP supports several hundred different models They are described fully in the 3 volume documentation for the full program This student version contains all of those models however the manual will only describe a few of the available model specifications In addition to the specifications of variables there are roughly 150 different specifications of the form sss additional information which are used to complete the model command In some cases these are mandatory as in REGRESS Lhs Rhs Panel Str variable This is the model command for the fixed and random effects linear regression model The latter two specifications are necessary in order to request the panel data model Without them the command simply requests linear least sq
246. observations are not the same for x and y The NAMELIST defines zx to be x and a column of ones a two column matrix and zy likewise With SKIP turned on the 2x2 matrix product zx zy shows that there are 88 observations in the reduced sample see the 88 that is 1 1 at the upper left corner and a warning is issued With SKIP turned off in the second computation the missing values are treated as 999s and the resulting matrix has values that appear to be inappropriate t imdep Output DER Fie Edit Insert Project Model Run Tools Window Help WERE ej oleju Bap Alclogit lpj O lt Untitled 1 Data Q 3333 Rows 100 Obs f Insert Name v JE Data SAMPLE 1 100 5a Variabl CREATE X Rnn 0 1 ben ia CREATE If X CREATE lt If Y NAMELIST ZX NAMELIST ZY NOSKIP MATRIK List SKIP Sy Namelists MATRIX List gt sample Status Trace 372 NNCYTP gt NOSKIP gt MATRIX List ZEZY ZX ZY Matrix ZXZY has 2 rows and 2 columns 2 8014 88971 9998225D 06 gt SKIP gt HATRIZ List ZEZY ZX ZY Error 0 Warning missing values skipped reduced number of rows Matrix ZXZY has 2 rows and 2 columns 88 00000 4 02495 20 06916 7 01745 Ln 6 18 Idle Figure 7 20 Matrix Computations Involving Missing Data 7 32 Essentials of Data Management This page intentionally left blank Estimating Models 8 1 Cha
247. of a command the List switch is off regardless of where it was before If you are doing many computations you can suppress some of them then turn the output switch back on in the middle of a command For example Using Matrix Algebra 9 7 MATRIX Nolist xxi lt x1 x1 gt List Root xxi displays only the characteristic roots of the inverse of a particular X X matrix Neither xl x1 nor xxi are displayed Displaying matrices that already exist in the matrix work area requires only that you give the names of the matrices Le MATRIX List abcd qed Note separated by semicolons not commas would request that the matrices named abcd and qed be displayed on your screen You might also want to see the results of a matrix procedure displayed without retaining the results The following are some commands that you might type MATRIX Root xx lists characteristic roots of xx MATRIX a b displays the matrix product ab MATRIX Mean x displays the means of all variables whose names begin with x These commands just display the results of the computations they do not retain any new results 9 2 5 Matrix Statistical Output Your matrix procedures will often create coefficient vectors and estimated covariance matrices for them For any vector beta and square matrix v of the same order as beta the command MATRIX Stat beta v will produce a table which assumes that these are a set of statistical res
248. of a variable nonparametrically that is without any assumption of the underlying distribution The kernel density function for a single variable is computed using fz 5 be EN pet ify h The function is computed for a specified set of values z j 1 M Note that each value requires a sum over the full sample of n values The default value of M is 100 The primary component of the computation is the kernel function K a weighting function that integrates to one Eight alternatives are provided 1 Epanechnikov K z 75 1 22 V5 if z lt 5 0 else 2 Normal K z 6 z normal density 00 lt z lt 3 Logit Kiz A 1 A z default 00 lt z lt 4 Uniform Kiz 5if z lt 1 0 1 else 5 Beta Ziz 1 z 1 z 24 if z lt 1 0 1 else 6 Cosine Kiz 1 cos 27z if z lt 5 0 else 7 Triangle Kiz 1 z if z lt 1 0 else 8 Parzen K z 4 3 872 8 z if z lt 5 8 1 z else 13 8 Describing Sample Data The other essential part of the computation is the smoothing bandwidth parameter h Large values of h stabilize the function but tend to flatten it and reduce the resolution in the same manner as its discrete analog the bin width in a histogram Small values of h produce greater detail but also cause the estimator to become less stable The basic command is KERNEL Rhs the variable With no other options specified the routine uses the lo
249. og boxes in the command builder We begin with Model Data Description Descriptive Statistics on the desktop menu shown in Figure 6 14 and 6 15 Limdep Output Fie Edit Insert Project MOMAR Run Tools Window Help Data Description Descriptive Statistics L Time Series Crosstab D S i amp l EJE Linear Models Histogram Nonlinear Regression Plot ariables Binary Choice Multiple Scatter Plots Censoring and Truncation Plot Matrix Count Data Kernel Density Status Tre Duration Models Frontiers c a i e eee ee ee ee m Current C D Discrete Choice escrip ll resi Numerical Analysis ng observations Figure 6 14 Model Menu for Descriptive Statistics 6 18 Application and Tutorial X pstats Main Options Main Options Variables GASPRICE fi IT Weight using variable PNEWCAR PUSEDCAR Stratify using variable PPUBTRN gt Output I Display covariance matrix I Display correlation matrix I Display sample quantiles I Plot normal quantile I Display skewness and kurtosis measures I Display first order autocorrelation I Display box and whisker plots Figure 6 15 Command Builder for Descriptive Statistics The variables are specified on the Main page then the correlation matrix is requested as an option on the Options page Clicking Run then produces the results that appear in Figure 6 13 A second a
250. oline Consumption vs Price Yaxis Gas_Cons Grid Limits 0 125 Set the vertical axis limits Endpoints 0 1 2 Set the horizontal axis limits Untitled Plot 16 5 a z Figure 13 12 Scatter Plots with Rescaled Axes Describing Sample Data 13 17 The following describe some devices for changing the appearance of the figure and creating particular types of graphs Some of these have been used in the examples above More extensive applications appear below Grids and Lines in the Plotting Field It is sometimes helpful when plotting to put a grid in the figure This makes it easier to relate the points in the graph to the distances on the axes You may request a grid to be placed in the figure with Grid This divides the screen into a grid of rectangles using dotted bars The option was used in the preceding examples You may also put horizontal and or vertical lines in the figure at specific numerical benchmarks The syntax is Spikes up to five value s to put vertical lines at particular values Bars up to five value s to put horizontal lines at particular values The vertical or horizontal line is drawn from axis to axis the full width or height of the box The examples below use these devices to create different types of graphs Connecting Points in the Plotting Field If you are plotting a function or a time series it may also be useful to connect adjacent points To do so add Fill t
251. ommands are translated to upper case immediately upon being read by the program so which you use never matters But note that this implies that you cannot use upper and lower case as if they were different in any respect That is the variable CAPITAL is the same as capital e You may put spaces anywhere in any command LIMDEP will ignore all spaces and tabs in any command e Every command must begin on a new line in your text editor 4 2 LIMDEP Commands e In any command the specifications may always be given in any order Thus READ Nobs 100 File DATA PRJ and READ File DATA PRJ Nobs 100 are exactly the same e You may use as many lines as you wish to enter a command Just press Enter when it is convenient Blank lines in an input file are also ignored e Most of your commands will fit on a single line However if a command is particularly long you may break it at any point you want by pressing Enter The ends of all commands are indicated by a LIMDEP scans each line when it is entered If the line contains a the command is assumed to be complete HINT Since commands must generally end with a if you forget the ending in a command it will not be carried out Thus if you submit a command from the editor and nothing happens check to see if you have omitted the ending on the command you have submitted Another problem can arise if you submit more than one command and one of them does not co
252. on is probably a more appropriate specification 16 2 Single Equation Tobit Regression Model The base case considered here is the familiar tobit model Latent underlying regression y B x s s N 0 0 Observed dependent variable if y lt L then y L lower tail censoring if y U then y U upper tail censoring if Li lt yi lt U then yi y B x E Within this framework the most familiar form is the lower censoring only at zero variant 16 2 Censoring and Sample Selection 16 2 1 Commands The basic command for estimation of the censored regression or tobit model is TOBIT Lhs y Rhs The default value for the censoring limit is zero at the left i e the familiar case Censoring limits can be varied in two fashions To specify upper rather than lower tail censoring add Upper to the model With no other changes this would specify a model in which the observed values of the dependent variable would be either zero or negative rather than zero or positive The specific limit point to use can be changed by using Limit limit value where limit value is either a fixed value number or scalar or the name of a variable For example the model of the demand for sporting events at stadiums with fixed capacities which sell out a significant proportion of the time might be TOBIT Lhs tickets Rhs one price Upper censoring Limit
253. ong sequences of commands to perform intricate analyses Procedures which are similar to small programs greatly extend this capability Procedures will allow you to automate new estimators that are not already present in LIMDEP and to compute certain test statistics that are not routine parts of the standard output The remainder of this chapter will show you how to write and execute procedures 11 4 Defining and Executing Procedures To store a set of commands you begin with the command PROCEDURE or just PROC This tells LIMDEP that the commands that will follow are not to be executed at the time but just stored for later use The end of a procedure is indicated with ENDPROCEDURE or just ENDPROC Once a set of commands has been entered as a procedure you can execute it with EXECUTE or just EXEC The EXECUTE command has a number of options which are discussed below A procedure can be entered at any point just by submitting it from the editing window For example CREATE x Rnn 0 1 y x 1 Rnn 0 2 PROC SAMPLE first last REGRESS Lhs y Rhs one x ENDPROC CALC first 1 last 10 EXEC 11 6 Programs and Procedures At the time the procedure is created the sample limits might not exist The procedure is defined the sample limits are set and finally the procedure is executed The procedure in turn sets the sample and computes a regression You can also load a procedure from an input file The
254. ons three We can compute this by using the built in program written just for this purpose as follows REGRESS Lhs logg Rhs x WALD Fn1 b_logpnc 0 Fn2 b_logpuc 0 Fn3 b_logppt 0 The WALD procedure is used for two purposes first to compute estimates of standard errors for functions of estimated parameters and second to compute Wald statistics The result for our model is Application and Tutorial 6 27 WALD procedure Estimates and standard errors for nonlinear functions and joint test of nonlinear restrictions Wald Statistic 7 93237 Prob from Chi squared 3 04743 a ont k om an a re _ ares am mia agi das a iei pra iati ley ware mi ae Variable Coefficient Standard Error b St Er P 2 gt z iS es ma a _ i ont onl aa Fnen 1 03199098 20574296 155 8764 Fnen 2 07393002 10548982 701 4834 Fnen 3 06153395 12343734 499 6181 The chi squared statistic is given in the box of results above the estimates of the functions The statistic given is the statistic for the joint test of the hypothesis that the three functions equal zero To illustrate the computations we consider how to obtain the Wald statistic the hard way that is by using matrix algebra This would be REGRESS Lhs logg Rhs x MATRIX b2 b 4 6 v22 Varb 4 6 4 6 list w b2 lt v22 gt b2
255. otal 772 2 8 26554 97 2 27326 100 0 15 5 15 6 Models for Discrete Choice This table computes a variety of conditional and marginal proportions based on the results using the defined prediction rule For examples the 97 708 equals 16797 17191 100 while the 63 256 is 16797 26554 100 Analysis of Binary Choice Model Predictions Based on Threshold 5000 Prediction Success Sensitivity actual 1s correctly predicted 97 708 Specificity actual 0s correctly predicted 3 730 Positive predictive value predicted 1s that were actual 1s 63 256 Negative predictive value predicted 0s that were actual Os 48 964 Correct prediction actual 1s and 0s correctly predicted 62 852 Prediction Failure False pos for true neg actual 0s predicted as 1s 96 270 False neg for true pos actual 1s predicted as 0s 2 292 False pos for predicted pos predicted 1s actual Os 36 744 False neg for predicted neg predicted 0s actual ls 51 036 False predictions actual 1s and 0s incorrectly predicted 37 148 Retained Results The results saved by the binary choice models are Matrices b estimate of B also contains y for the Burr model varb asymptotic covariance matrix Scalars kreg number of variables in Rhs nreg number of observations logl log likelihood function 15 2 3 Analysis of Marginal Effects Marginal effects in a binary choice model may be obtained as
256. otential for a problem of multicollinearity As a preliminary indication of how serious the problem is likely to be obtain a time series plot of the four price series 5 We begin with a simple demand equation Obtain the least squares regression results in a regression of logG on the log of the price index JogPg Report your regression results a Notice that the coefficient on log price is positive Shouldn t a demand curve slope downward What is wrong here b Now add the obviously missing income variable to the equation Compute the linear regression of logG on log and logPg Report your results and comment on your findings 6 2 Application and Tutorial 6 The full regression model that you will explore for the rest of this exercise is logG B BologPg B3logl BalogPnc BslogPuc BelogPpt Bit Obtain the least squares estimates of the coefficients of the model Report your results Obtain a plot of the residuals as part of your analysis a For more advanced courses Compute the least squares regression coefficients b s the covariance matrix for b and R using matrix algebra b Test the hypothesis that all of the coefficients in the model save for the constant term are zero using an F test Obtain the sample F and the appropriate critical value for the test Use the 95 significance level 7 Still using the full model use an F test to test the hypothesis that the coefficients on the three extra prices are a
257. ous data 13 5 Discrete data 13 6 Index Hypothesis test 6 25 6 26 tratio 6 27 Structural change 6 28 6 29 Hypothesis test 14 8 Icon 2 3 INCLUDE command 7 24 7 26 Information criteria 15 3 Input file 6 4 Insert in text window 3 3 Installation 2 1 Instrumental variables 14 11 Kernel density 13 7 13 8 Kurtosis 13 1 Labels observation 7 7 Lagged values 7 11 7 15 LM test 14 16 14 23 Least squares 6 23 Likelihood ratio test 10 1 LIM file 3 3 Limited dependent variable 1 1 Lists of variables 6 17 LOAD command 2 7 Logistic 7 14 Logit 15 1 15 2 15 3 Ordered 15 9 Logs data 6 1 6 13 7 11 7 14 Log likelihood 8 14 Looping program 11 4 11 5 Matrix 7 16 9 1 Algebra 9 13 Calculator 9 3 Characteristic roots 9 7 9 18 Command builder 9 4 Creating 9 16 Data 9 8 9 9 Defining 9 14 Determinant 9 19 Diagonal 9 17 Expression 9 13 Identity 9 17 Namelists defining 9 10 Names conventions 9 11 Partitioned 9 16 Product 9 13 Results 9 5 9 6 Statistical output 9 7 Sums 9 10 9 11 9 19 Index Trace 9 19 Transpose 9 13 Windows 9 5 MATRIX command 6 17 6 23 Matrix algebra 9 1 9 13 Maximum 7 9 Mean vector matrix 9 20 9 21 Missing data 7 30 Missing values 7 8 7 12 7 13 Model command 4 1 Models 1 1 8 1 12 1 Model command 8 10 Model constant term 8 2 Model types 12 3 12 4 12 5 Moment matrix 9 11 9 20 Mouse button 3 8 Namelists 7 21 7 22 7 23 NAMELIST 6 17 6 25 Names 4 1 Conven
258. plications given elsewhere in this manual are composed of in line commands as are the examples given in Section R12 1 and in many places in the preceding chapters The essential format of a MATRIX command is MATRIX name result additional commands If you wish to see the result but do not wish to keep it you may omit the name The same applies to the scalar calculator described in the next chapter For example you are computing a result and you receive an unexpected diagnostic We sometimes come across a matrix say rxx that we thought was positive definite but when we try something like MATRIX Sinv rxx a surprise error message that the matrix is not positive definite shows up A simple listing of the matrix shows the problem The 001 in the 4 4 element is supposed to be a 1 0 Now we have to go back and find out how the bad value got there some previous calculation did something unexpected Using Matrix Algebra 9 5 atrix Sinv Rxx Error 185 MATRIX GINV SINV CHOL singular not P D if SINV or CHOL atrix ast gt REX atrix Result has 4 rows and 4 columns 2 3 4 Lj 1 00000 66647 13895 70138 2 66647 1 00000 27401 25449 3 13895 27401 1 00000 05935 4 70138 25449 05935 00100 If you want only to see a matrix and not operate on it you can just double click its name in the project window That will open a window that displays the matrix The offen
259. pproach is to compute and display the correlation matrix To do this since we are computing a correlation matrix we use the MATRIX command There is a matrix function that computes correlations which would appear as follows MATRIX list Xcor gasprice pnewcar pusedcar ppubtrn This produces the following results in the output window Correlation Matrix for Listed Variables GASPRICE PNEWCAR PUSEDCAR PPUBTRN GASPRICE 1 00000 93605 92277 92701 PNEWCAR 93605 1 00000 99387 98074 PUSEDCAR 92277 99387 1 00000 98242 PPUBTRN 92701 98074 98242 1 00000 which are of course the same as those with the descriptive statistics There is another convenient feature of MATRIX that we should note at this point The NAMELIST command below associates the name prices with the four price variables NAMELIST prices gasprice pnewcar pusedcar ppubtrn Now in any setting where we wish to use these four variables we can use the name prices instead This defines a data matrix with these four columns Thus we can now shorten the MATRIX command to MATRIX list Xcor prices Finally note that each MATRIX command begins with list This requests that the result of the matrix computation be displayed on the screen in the output window Why is this needed MATRIX is part of the programming language You might be writing sets of commands that do matrix computations that are intermediate results to be used later that you are not nec
260. ppt are price indices for new and used cars and public transportation and pn pd and ps are aggregate price indices for nondurables durables and services READ Nobs 27 Nvar 10 Names year g Pg y pnc pucspptspd pn ps 1960 129 7 925 6036 1 045 836 810 331 302 1961 131 3 914 6113 1 045 869 846 cae 335 307 1962 137 1 919 6271 1 041 948 874 457 338 314 1963 141 6 918 6378 1 035 960 885 463 343 320 1964 148 8 914 6727 1 032 1 001 901 470 347 325 1965 155 9 949 7027 1 009 994 919 471 353 332 1966 164 9 970 7280 991 970 952 475 366 342 1967 171 0 1 000 7513 1 000 1 000 1 000 483 375 353 1968 183 4 1 014 7728 1 028 1 028 1 046 501 390 368 1969 195 8 1 047 7891 1 044 1 031 1 127 514 409 386 1970 207 4 1 056 8134 1 076 1 043 1 285 527 427 407 1971 218 3 1 063 8322 1 120 1 102 1 377 547 442 431 1972 226 8 1 076 8562 1 110 1 105 1 434 555 458 451 1973 237 9 1 181 9042 1 111 1 176 1 448 566 497 474 1974 225 8 1 599 8867 1 175 1 226 1 480 604 572 513 1975 232 4 1 708 8944 1 276 1 464 1 586 659 615 556 1976 241 7 1 779 9175 1 357 1 679 1 742 695 638 598 1977 249 2 1 882 9381 1 429 1 828 1 824 727 671 648 1978 261 3 1 963 9735 1 538 1 865 1 878 769 719 698 1979 248 9 2 656 9829 1 660 2 010 2 003 821 800 756 1980 226 8 3 691 9722 1 793 2 081 2 516 892 894 839 8 18 Estimating Models 1981 225 6 4 109 9769 1 902 2 569 3 120 957 969 92
261. produces the dialog box shown in Figure 7 17 Set Sample Range Observation rows From fI Cancel To 20 Figure 7 17 Set Sample Range Dialog Box 7 28 Essentials of Data Management TIP If your REJECT command has the effect of removing all observations from the current sample LIMDEP takes this as an error gives you a warning that this is what you have done and ignores the command Interaction of REJECT INCLUDE and SAMPLE REJECT and INCLUDE modify the currently defined sample unless you include New But SAMPLE always redefines the sample in the process discarding all previous REJECT INCLUDE and SAMPLE commands Thus SAMPLE 1 50 200 300 and SAMPLE 1 50 SAMPLE 200 300 are not the same The second SAMPLE command undoes then replaces the first one Any of these three commands may appear at any point together or separately Before any appear the default sample is SAMPLE All TIP If you are using lagged variables you should reset the sample to discard observations with missing data This is generally not done automatically 7 5 2 Time Series Data When you are using time series data it is more convenient to refer to rows of the data area and to observations by date rather than by observation number Two commands are provided for this purpose To give specific labels to the rows in the data area use DATES Initial date in sample The initial date may be one of Undate
262. pter 8 Estimating Models 8 1 Introduction Once your data are in place and you have set your desired current sample most of your remaining commands will be either model estimation commands or the data manipulation commands CREATE CALCULATE and MATRIX We consider the model commands in this chapter and the other commands in Chapter 9 This chapter will describe the common form of all model estimation commands estimation results and how to produce useable output in an output file Section 8 3 contains a general discussion on the important statistical features of the model estimators such as using weights and interpreting resultsinal effects This chapter will also describe procedures that are generally used after a model is estimated such as testing hypotheses retrieving and manipulating results and analyzing restrictions on model parameters In terms of your use of LIMDEP for model estimation and analysis this chapter is the most important general chapter in this part of the manual The chapters in the second part of this manual will provide free standing and fairly complete descriptions of how to estimate specific models but users are encouraged to examine Chapters 8 and 9 here closely for the essential background on these procedures 8 2 Model Estimation Commands Nearly all model commands are variants of the basic structure MODEL COMMAND Lhs dependent variable Rhs list of independent variables 3 Other parts specific to the
263. r the software may not be used on the primary computer by another person while the secondary computer is in use For a multi user site license the specific terms of the site license agreement apply for scope of use and installation Limited Warranty Econometric Software warrants that the software product will perform substantially in accordance with the documentation for a period of ninety 90 days from the date of the original purchase To make a warranty claim you must notify Econometric Software in writing within ninety 90 days from the date of the original purchase and return the defective software to Econometric Software If the software does not perform substantially in accordance with the documentation the entire liability and your exclusive remedy shall be limited to at Econometric Software s option the replacement of the software product or refund of the license fee paid to Econometric Software for the software product Proof of purchase from an authorized source is required This limited warranty is void if failure of the software product has resulted from accident abuse or misapplication Some states and jurisdictions do not allow limitations on the duration of an implied warranty so the above limitation may not apply to you To the extent permissible any implied warranties on the software product are limited to ninety 90 days Econometric Software does not warrant the performance or results you may obtain by using the softw
264. r 11 1 Executing commands 11 2 Textbooks 1 2 Time series 6 16 Time series data 7 28 Tobit 16 1 Hypothesis tests 16 3 Marginal effects 16 4 Results 16 3 Toolbar 3 6 7 1 Trace 2 5 Trace file 3 11 Transformations data 6 1 6 13 7 9 7 30 Trend variable 7 13 7 14 Tutorial commands 6 10 6 11 Two stage least squarres 14 11 Results 14 11 Variable list 7 21 Variable names 7 6 Variables new 7 2 Variables transformed 7 9 Vella F 1 2 Vista 3 14 Wald statistic 6 26 6 29 Weights 8 10 Wts 8 10 Heteroscedasticity 8 11 Scaling 8 11 Window Editing 3 3 Output 3 10 4 6 5 1 5 2 Project 3 13 4 3 6 13 Window editing 3 2 Word processor 3 4 XLS file 6 4
265. r pusedcar ppubtrn MATRIX list Xcor prices Simple regression of logG on a constant and log price Computations to analyse potential biases based on the left out variable formula and plausible values REGRESS Lhs logg Rhs one logpg CALC list spi CovilogPg logl spp Var logPg plim 0 1 spi spp 1 0 Multiple regression including both price and income to confirm expecations about what happens when income is omitted from the equation Includes a plot of residuals REGRESS Lhs logG Rhs one logpg logi Plot residuals Full regression model including all variables NAMELIST _ x1 logpg logI x2 logpnc logpuc logppt x one x1 x2 t REGRESS Lhs logg Rhs x Plot residuals Least squares computations using matrix algebra slopes standard error R squared covariance matrix for coefficients Results are displayed in a table MATRIX bols lt X X gt X logg MATRIX e logg X bols CALC list se sqr e e n col X r2 1 e e n 1 var logg MATRIX V s2 lt X X gt Stat bols v x Application and Tutorial 6 11 F statistic for the hypothesis that all coefficients are zero R squared for the regression CALC list f r2 col X 1 1 r2 n col X CALC list 5 se sqr sumsqdev degfrdm r2 1 e e n 1 var logg F statistic using results retained by the regression Critical values for F and t CALC list f rsqrd k 1 1
266. r x1 and Xbr x2 may be based on different observations You should keep close track of this if your data have gaps or different sample lengths For the remaining functions all observations are used without regard to missing data For example in the covariance function LIMDEP uses all data points so some data may be missing Be careful using these to prevent the 999s from distorting the statistics Sample Moments For any variable in your data area or namelist which contains only one variable name the functions listed below can be used just like any other function such as Sqr 2 If you wish only to display the statistic just calculate it Otherwise these functions can be included in any expression Sum variable sum of sample values Xbr variable mean of sample values Sdv variable standard deviation of sample values Var variable variance of sample values Xgm variable the geometric mean Xgm x Exp 1 nz log x Xhm variable h the harmonic mean using parameter h Xhm x h Zx ui The summing functions Sum Var Sdv Xbr can be restricted to a subsample by including a second variable in the list If a second variable appears the function is compute for nonzero values of that second variable Thus Sum variable dummy is the sum of observations for which the dummy variable is nonzero This allows a simple way to obtain a mean or variance in a subset of the current sample Covariance and Correlation For
267. ragg as well as a test for nonnormality 16 2 3 Marginal Effects The marginal effects in the tobit model when censoring is at the left at zero are computed using ELyx B x 0 B x o6 B x 0 P B x o After some algebra we find OE y x Ox B B x o p The preceding is a broad result which carries over to more general models That is OE y x Ox Prob nonlimit p for all specifications of the censoring limits whether in one tail or both To obtain a display of the marginal effects for the tobit model add Marginal Effects to the TOBIT command A full listing of the marginal effects computed at the sample means including standard errors the estimated conditional mean and the scale factor will be included in the model output 16 3 Sample Selection Model Many variants of the sample selection model can be estimated with LIMDEP Most of them share the following structure A specified model denoted A applies to the underlying data However the observed data are not sampled randomly from this population Rather a related variable z is such that an observation is drawn from A only when z crosses some threshold If the observed data are treated as having been randomly sampled from A instead of from the subpopulation of A associated with the selected values of z potentially serious biases result The general solution to the selectivity problem relies upon an auxiliary model of the process generating z Inform
268. res the log likelihood function contains an extra term the Jacobian for the first observation log 1 p This term becomes deminimus as T gt o so in a large sample the MLE and the other GLS estimators should not differ substantially To use a grid search for the autocorrelation coefficient use AR1 Alg grid lower upper step This requests a simple grid search over the indicated range with a stepsize as given The method used for the grid search is the default Prais Winsten estimator To request the Cochrane Orcutt estimator instead use AR1 Alg grid lower upper step 1 As before the Cochrane Orcutt estimator is inferior to the MLE or Prais Winsten estimator You can request a particular value for p by a simple request ARI Rho specific value When you use this form of the model command the output will still contain an estimated standard error for the estimate of p as if it had been estimated The number of iterations allowed for the first three estimators can be controlled with the specification Maxit maximum The Linear Regression Model 14 11 14 5 Two Stage Least Squares The essential command fitting linear models by instrumental variables is 2SLS Lhs dependent variable Rhs list of right hand side variables all Inst list of all instrumental variables including one The command for computing instrumental variables or two stage least squares estimates d
269. results as follows CREATE Expand educ 0 underhs hs college postgrad EDUC was expanded as _EDUC_ Largest value 4 0 New variables were created Category New variable UNDERHS Frequency 27 2 New variable HS Frequency 26 3 New variable COLLEGE Frequency 21 Note the last category was not expanded You may use this namelist as is in a regression with a constant The note at the end of the listing reminds you of the calculations done The last category is the one dropped Note that 0 new variables were created The reason is that these variables already existed after our earlier example Finally the list of names for the new variables is optional If it is omitted names are built up as in the second example above Continuing the example we might have CREATE educ Rnd 4 CREATE Expand educ EDUC was expanded as _EDUC_ Largest value 4 4 New variables were created Category New variable EDUC01 Frequency 28 2 New variable EDUC02 Frequency 22 3 New variable EDUC03 Frequency 30 4 New variable EDUC04 Frequency 20 ote this is a complete set of dummy variables If you use this set in a regression drop the constant NOTE This transformation will refuse to create more than 100 variables If it reaches this limit you have probably tried to transform the wrong variable Thus the variable must be coded 1 2 up to 99 Essentials of Da
270. rices which are not 1x1 must be conformable for the multiplication Thus if r were a matrix instead of a vector it might not be possible to compute V The operator is used to add matrices Thus to add the two matrices above instead of multiply them we could use l i dt 1 3 5 2 4 5 5 3 5 15 5 The matrix subtraction operator is Thus a c gives A C of course You may also combine the and operators in a command For example the restricted least squares estimator in a classical regression model when the linear restrictions are Rb q is b b X X R R X X R J Rb q This could be computed with NAMELIST x list of variables MATRIX bu lt x x gt x y sr 3rt r sq e 3d r bu q xxi lt x x gt sbr bu xxi r lt rt xxi r gt d Why did we transpose r into rt then use rt which is just r in the last expression Because the apostrophe operator is needed to produce the correct matrix multiplication inside the lt gt operation There are other ways to do this but the one above is very convenient Notice in the preceding that if there is only one constraint r will be a row vector and the quadratic form will be a scalar not a matrix Any of the product arrangements shown in Table R12 1 may appear in any function or expression as if it were already an existing matrix For example Root lt x w x gt computes the characteristic roots of 2 w
271. rix algebra descriptions we will use bold lower case symbols for the parts of LIMDEP commands We will use italic lower case symbols when we refer outside LIMDEP commands to the names of matrices variables namelists and scalars you have created Consider for example the following The sample second moment matrix of the data matrix X is F 1 n X X You can compute this by defining X with a command such as NAMELIST x one age income then using the command MATRIX f 1 n x x After you execute this command you will see the matrix f in your project window listing of matrices The namelist x will also appear in the project window list of namelists You might note we have used this convention at several points above Using Matrix Algebra 9 13 9 4 2 Matrix Expressions Most of the operations you do with matrices particularly if you are constructing estimators will involve expressions products sums and functions such as inverses This section will show how to arrange such mathematical expressions of matrices We have used these procedures at many points in our earlier discussion As noted above every numerical entity in LIMDEP is a matrix and may appear in a matrix expression There are very few functions that require data matrices These will be noted below The algebraic operators are for matrix multiplication for addition for subtraction apostrophe for transposition and also for transposition t
272. rmation about this as well as instructions on how to obtain the patch LIMDEP offers an extensive Help file Select Help Help Topics from the menu to bring up the help editor LIMDEP s Help file is divided into seven parts or books In the first book you will find a selection of Topics that discuss general aspects of operating the program The second book is the Commands list This contains a list of the essential features and parts of all of LIMDEP s commands The third book contains a summary of the various parts of the desktop The fourth book contains descriptions of updates to LIMDEP that were added after the manual went to press Finally there are three books of useful ancillary material a collection of LIMDEP programs some of which appear in the manual for the program a collection of data sets that can be used for learning how to use LIMDEP and for illustrating the applications these include the data sets used in the applications in this manual and finally some of the National Institute of Standards accuracy benchmark data sets The files in the last three books are also available in a resource folder created when LIMDEP is installed The location for the folder is C LIMDEP9 and there are three subfolders Data Files LIMDEP Command Files and Project Files LIMDEP Commands 4 1 Chapter 4 LIMDEP Commands 4 1 Commands There are numerous menus and dialog boxes provided for giving instructions to LIMDEP But ultima
273. roject Model Run Tools Window Help Untitled Proj 0 lt lt untitled 1 Data U 11111 Rows 100 Obs f Insert Name H Data SAMPLE 1 100 49 Variables CREATE X RNN 0 1 YX CREATE Y X RNN O 1 REGRESS Lhs y Rhs one bY E Namelists H E Matrices TE 5 FA Output P gt VARB Ph SIGMA E Scalars E Strings RESET Procedures SAMPLE 3 Output 2 CREATE Tables gt SAMPLE Output Window gt CREATE gt CREATE Status Trace Figure 4 2 Regression Command An alternative way to request the regression is to use the Model menu on the desktop and locate the command builder for the linear regression This is shown in Figure 4 3 When I select this item from the menu this will open a dialog box that lets me construct my linear regression model without typing the commands in the editor The command builder is shown in Figure 4 4 LIMDEP Commands Limdep Output File Edit Insert Project fir Run Tools Window Help Data Description Time Series Linear Models Nonlinear Regression Binary Choice Censoring and Truncation Count Data Duration Models Frontiers Discrete Choice Numerical Analysis Data U 11111 Rows 100 lt 4 Data Variables bx bY Namelists 3 Matrices F gt B h VARB P SIGMA 4 Scalars Strings E Procedures Sy Output E Tables Output Window NN 0O 1 R
274. rpretation of the coefficient estimates Marginal effects for all cells can be requested by including Marginal Effects in the command An example appears below NOTE This estimator segregates dummy variables for separate computation in the marginal effects The marginal effect for a dummy variable is the simple difference of the two probabilities with and without the variable See the application below for an illustration Marginal effects for ordered probability model M E s for dummy variables are Pr y x 1 Pr y x 0 Names for dummy variables are marked by Variable Coefficient Standard Error b St Er P Z gt z Mean of X H 4 These are th ffects on Prob Y 00 at means Constant S000000 sds en Fixed Parameter FEMALE 00498024 00280960 1 773 0763 52936118 HHNINC 03907462 00862973 4 528 0000 32998942 HHKIDS 01131976 00277405 4 081 0000 33169533 EDUC 00101850 00069179 1 472 1409 10 8759203 These are th ffects on Prob Y 01 at means Constant 000000 Fixed Parameter FEMALE 00209668 00118069 1 776 0758 52936118 HHNINC 01647123 00362630 4 542 0000 32998942 HHKIDS 00483428 00119623 4 041 0001 33169533 EDUC 00042933 00029148 1 473 1408 10 8759203 Effects for Y 02 Y 03 and Y 04 are omitted These are th ffect
275. rsqrd degfrdm CALC list fc Ftb 95 kreg 1 degfrdm tc ttb 95 n col x Constrained least squares three coefficients constrained to equal zero Test of hypothesis using F statistic Two ways Built in and using the R squareds REGRESS Lhs logg Rhs x Cls b 4 0 b 5 0 b 6 0 NAMELIST xu x xr one x1 t REGRESS Lhs logg Rhs xu CALC rsqu rsqrd REGRESS Lhs logg Rhs xr CALC rsqr rsqrd list f rsqu rsqr Col x2 1 rsqu n Col x Use the built in calculator function to compute R squared CALC rsqu rsq Xu logg rsqr rsq Xr logg list f rsqu rsqr Col x2 1 rsqu n Col x Testing the hypothesis using the Wald statistic Built in command then using matrix algebra REGRESS Lhs logg Rhs x WALD Fn1 b_logpnc 0 Fn2 b_logpuc 0 Fn3 b_logppt 0 Compute the regression Then use the saved matrices REGRESS Lhs logg Rhs x MATRIX b2 b 4 6 v22 Varb 4 6 4 6 list W b2 lt v22 gt b2 REGRESS Lhs logg Rhs x Cls b 4 b 5 0 Compute a restricted least squares estimator using matrix algebra MATRIX r 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 q 0 0 0 MATRIX bu lt X X gt X y C R lt X X gt R d R b q be bu lt X X gt R lt C gt d Test the hypothesis that two coefficients are equal using a t test This could be built directly
276. rt LIMDEP as you would any other program for example by double clicking the LIMDEP icon on your desktop The opening window is the LIMDEP desktop shown in Figure 2 2 At the top of the screen the main menu is shown above the LIMDEP toolbar Below the toolbar is the command bar discussed in Chapter 3 The open window is the project window The session is identified as your project which will ultimately consist of your data and the various results that you accumulate This is where you will begin your LIMDEP session Operation is discussed in Chapter 3 44 Limdep Untitled Project 1 File Edit Insert Project Model Run Tools Window Help oea 2 Sam ole n SBA Untitled Proj fa Blk Data U 222 Rows 222 Obs Variables Namelists Matrices Scalars Strings G Procedures Sy Output G Tables Output Window Figure 2 2 LIMDEP Desktop Window If you do not see the command bar when you first start the program so that your initial desktop appears as below in Figure 2 3 then select Tools in the desktop menu and Options from the drop down menu In the dialog that appears next as shown in Figure 2 4 tick the option to Display Command Bar to change the desktop menu so that it will then appear as in Figure 2 2 with the command bar included 2 4 Getting Started Limdep Untitled Project 1 File Edit Insert Project Model Run MEWS Window Help Scalar Calculator Matrix Calculator w Tab
277. rvation is set to zero Remaining observations are treated as missing You may enter an expression for the new or transformed variable in the Expression window New Variable OK oc ff ans Cancel 4 Bel xl Bc2 x l Byn Namelist r Cos x Dev x Dmmy p i1 Dot namelist v Esp Fix x Gmafx re 1 dea om Expression Log x 1 Phi y b z sigma 2 Data fil Current sample C All Observations Figure 7 10 New Variable Dialog Box 7 10 Essentials of Data Management A CREATE command operates on the current sample See Section 7 5 If this is a subset of the data remaining observations will not be changed If you are creating a new variable for the subset of observations remaining observations will be undefined missing You can override this feature by using CREATE Fill the rest of the command in your command With this additional setting the transformations listed will be applied to all observations in the data set whether in the current sample or not This is the Data fill option that appears at the bottom center of the dialog box in Figure 7 10 Algebraic Transformations An algebraic transformation is of the form name expression Name is the name of a variable It may be an existing variable or a new variable Name may have been read in or previously created The expression can be any algebraic transformation of any complexity You may nest parentheses fun
278. s tabs and or commas Numbers in the file need not be neatly arranged vertically If there are missing values there must be placeholders for them since blanks just separate values they cannot be interpreted as missing data Use as many as lines as needed for each observation to supply all of the values For example for the following data in a file 12 5 3 4 6 254 3 67 you might use READ File Projec SMALL DAT Nobs 4 Nvar 3 Names x y z There are several optional features and a number of other different types of data files you can use HINT Ifyou do not know the exact number of observations in your data set give Nobs a number that you are sure will be larger than the actual value LIMDEP will just read to the bottom of the file and adjust the number of observations appropriately Variable Names The normal way to enter variable names is in the command as in the example above Names name _1 name_nvar The following name conventions apply names may have up to eight characters must begin with a letter and must be composed from only letters numbers and the underscore character Remember that names are always converted to upper case Reserved names are listed in Section 4 3 Names in the Data File You may find it convenient to make the variable names a part of the data set instead of the READ command Note that this is the basic case described in the tutorial in the previous chapter To d
279. s 6 13 6 5 3 Saving and Retrieving Your Project 6 14 TOC 2 Chapter 7 71 7 2 73 7 4 7 5 7 6 Chapter 8 8 1 8 2 8 3 Chapter 9 9 1 9 2 9 3 Table of Contents 6 5 4 Time Series Plot of the Price Variables 6 16 6 5 5 Simple Regression 6 19 6 5 6 Multiple Regression 6 22 6 5 7 Hypothesis Tests 6 25 6 5 8 Test of Structural Break 6 28 Essential of Data Management Introduction 7 1 Reading and Entering Data 7 1 7 2 1 The Data Area 7 1 7 2 2 The Data Editor 7 1 7 2 3 Reading Data Files Into LIMDEP 7 4 7 2 4 General ASCII Files 7 6 7 2 5 Reading a Spreadsheet File 7 7 7 2 6 Missing Values in Data Files 7 8 Computing Transformed Variables 7 9 7 3 1 The CREATE Command 7 9 7 3 2 Conditional Transformations 7 13 7 3 3 Transformations Involving Missing Values 7 13 7 3 4 CREATE Functions 7 14 7 3 5 Expanding a Categorical Variable into a Set of Dummy Variables 7 17 7 3 6 Random Number Generators 7 19 Lists of Variables 7 21 7 4 1 Lists of Variables in Model Commands 7 21 7 4 2 Namelists 7 22 7 4 3 Using Namelists 7 23 The Current Sample of Observations 7 24 7 5 1 Cross Section Data 7 25 7 5 2 Time Series Data 7 28 Missing Data 7 30 Estimating Models Introduction 8 1 Model Estimation Commands 8 1 8 2 1 The Command Builder 8 3 8 2 2 Output from Estimation Programs 8 7 Model Components and Results 8 10 8 3 1 Using Weights 8 10 8 3 2 Model Output 8 11 8 3 3 Retrievable Results 8 14 8 3 4 Creating and Displaying
280. s of the nonlinear models estimated by LIMDEP Listed below are the results from estimation of a Poisson regression model The example is used at various points in the chapters to follow The model command requests a set of marginal effects These are discussed in the next section READ Nobs 40 Nvar 2 Names num months By Variables 0034 618 m11 39 29 5853 1244 m18 11 01 62m10000211 m40m77512 mi 127 63 1095 1095 1512 3353 0 2244 44882 17176 28609 20370 7064 13099 0 7117 1179 552 781 676 783 1948 0 274 251 105 288 192 349 1208 0 2051 45 0 789 437 1157 2161 0 542 num lt 0 a Ind 9 16 c Ind 17 24 d Ind 25 32 e Ind 33 40 c67 Dmy 8 3 Dmy 8 4 c72 Dmy 8 5 Dmy 8 6 77 Dmy 8 7 Dmy 8 8 p77 Dmy 2 2 logmth Log months X one a c d e c67 c72 c77 logmth Lhs num Rhs x OLS Marginal c67 REJECT CREATE NAMELIST POISSON The following results are reported when your model command contains OLS Poisson Regression Model OLS Results Ordinary least squares regression LHS NUM Mean 10 47059 Standard deviation 15 73499 WTS none Number of observs 34 Model size Parameters 9 Degrees of freedom 25 Residuals Sum of squares 2076 55 Standard error of e 9 114286 Fit R squared 7458219 Adjusted R squared 6644848 abs ie Variable Coefficient Standard Error b St Er P Z gt z Mean of X ls j
281. s on Prob Y 05 at means Constant 000000 wedcn eres Fixed Parameter FEMALE 01803285 01014562 1 777 0755 52936118 HHNINC 14180876 00073836 192 060 0000 32998942 HHKIDS 04218672 00029837 141 390 0000 33169533 EDUC 00369631 00250467 1 476 1400 10 8759203 Summary of Marginal Effects for Ordered Probability Model probit Variable Y 00 Y 01 Y 02 Y 03 Y 04 Y 05 Y 06 Y 07 ONE 0000 0000 0000 0000 0000 0000 FEMALE 0050 0021 0041 0047 0021 0180 HHNINC 0391 0165 0326 a037 e 016A 1418 HHKIDS 0113 0048 0096 0112 0052 0422 EDUC 0010 0004 0008 0010 0004 0037 15 14 Models for Discrete Choice This page intentionally left blank Censoring and Sample Selection 16 1 Chapter 16 Censoring and Sample Selection 16 1 Introduction The models described in this chapter are variations on the following general structure Latent Underlying Regression y B x s N 0 0 Observed Dependent Variable if y lt L then y L lower tail censoring if y 2 U then y U upper tail censoring if Li lt yi lt U then yi y p x F Ei The thresholds L and U may be constants or variables We accommodate censoring in the upper or lower or both tails of the distribution The most familiar case of this model in the literature is the tobit model in which U and L 0 i e the case in which the
282. s that the coefficients an the three ara prices are all zero Test the hypothesis thatthe eleticiies wth repect to the prices ofmew and used cas mee a Do the tetuing mi Fust D Use attest chowing all computations 10 The market for foss fuels charged dramatically at the erd of 1973 We will eamine whether the data ortai clear evidence ofthisphnomma a Use a Chowtes for structural break to ascertain whether the same model applies for the period 1953 1973 as for 1974 2004 gt hors adane Use a Wald tast to test ba pathek How do ta eranpetes underlying these twotests difir p Figure 6 4 Word Processor File Containing the Data Set Gas Pree 16 668 a7 46 5 4a 46 aa 207692 209924 220289 222629 232218 234223 236394 238506 240683 242863 245061 282429 285366 288217 The confirmation in the output window and the appearance of the names of the variables in the project window indicate that the raw data have been read and we can now analyze them Fie Edit Insert Project Model Run Tools Window Help sla al e olaju AEA A GasolineMark Data U 11111 Rows 52 Obs Status Trace lt 4 Data a Current Command gt 3 Variables gt YEAR Command GASEXP GASPRICE INCOME PNEWCAR gt READ PUSEDCAR Last observation read from data file vas PPLIBTRN End of data listing in edit window vas reached gt POP 3 Namelists
283. sion 9 0 1 January 1 gt CALC List Phif1 96 Result 97500210485177950D 00 Output Winde Ln 3 3 Idle Figure 10 3 CALCULATE Command in Text Editor 10 4 Scientific Calculator CALCULATE is similar to CREATE at this point except that instead of calculating whole columns of data you calculate single or scalar values When you give a name to the result it is kept in a work area and you can use it later For example suppose you wanted to have the value of e Euler s constant to use later on You could for example calculate e Exp 1 You could then CREATE etotheax e a x CALC is also similar to MATRIX in that if you wish to see a value without keeping it you may type the expression without giving it a name as in CALC 51 pi Log 25 2 5 1 23 or for the 99 critical value for a two tailed test from the standard normal distribution Ntb 995 Ntb stands for Normal table You also have a t table and so on 10 3 Results from CALCULATE As shown above when you are in the calculator window the result of a calculator expression named or not is displayed on your screen when it is obtained When CALC commands are given in command mode the default is not to display the results of any computations in the output window or in the output file if one is open We assume that in this mode results are intermediate computations for example the increments to the counters in the example in Sec
284. sions 4 2 Reserved 4 2 4 3 Syntax 4 1 Newey West 14 5 Nonlinear models 1 1 NormalCDF 7 14 Normal distribution 7 14 OLS results 8 12 OPEN command 2 7 3 1 Options window 2 4 Ordered choice 15 9 Output 15 11 Marginal effects 15 13 Output 4 6 5 1 5 2 Editing 5 2 Exporting 5 2 Output file 2 6 Output model 8 7 8 12 8 13 Output window 3 10 Output window 8 6 P values 8 14 Pagan A 1 2 Panel data 14 12 Balanced panel 14 12 Count variable 14 14 14 15 Data arrangement 14 13 Fixed effects 14 15 14 18 Hausman test 14 17 14 23 LM test 14 16 14 23 R squared 14 24 Random effects 14 15 14 21 Results 14 19 Stratification 14 13 Path file 7 5 PERIOD command 7 28 7 29 Plot 13 10 Graphics file 13 10 Multiple scatter plots 13 14 Regression 13 13 Scaling 13 15 Scatter plot 13 10 13 12 Time series 13 13 PLOT command 6 16 Title 6 16 Time series 6 16 Plot data 6 16 Plot regression residuals 6 21 6 23 Poisson model 8 12 8 19 Predictions 8 16 12 6 Missing values 8 16 8 17 Probit 10 1 15 1 15 2 Ordered 15 9 Procedure Parameters 11 7 11 8 Silent 11 6 Programming 1 2 Programming 11 1 11 4 Project 2 4 3 1 6 14 Project window 3 4 3 12 3 13 4 3 6 13 6 24 8 4 8 15 R squared 6 24 8 15 Random number generator 7 19 Seed 7 20 Random samples 7 19 Discrete 7 20 Read ASCII data 6 6 Command window 6 6 READ command 6 3 6 6 7 1 7 7 Spreadsheet 7 7 Reading data 7 3 Registration 2 1 2 2 R
285. soring and Sample Selection Part Il Econometric Models and Statistical Analysis This page intentionally left blank Econometric Model Estimation 12 1 Chapter 12 Econometric Model Estimation 12 1 Introduction The primary function carried out by LIMDEP is the estimation of econometric models The first part of the documentation the Reference Guide describes how to use LIMDEP to read a data set establish the current sample compute transformations of variables and carry out other functions that get your data ready to use for estimation purposes Several important tools such as the matrix algebra program scientific calculator and program editor are described there as well This second part the econometric modeling guide will describe some specific modeling frameworks and instructions to be used for fitting these models The organization of this manual is by estimation framework not by model command We have found that users prefer that the program documentation be oriented toward the types of functions they want to perform not to an alphabetical listing of commands As such you will find the arrangement of topics in this manual rather similar to the arrangement of topics in treatises in econometrics such as Greene 2008 We begin with descriptive statistics in Chapter 13 various linear regression models in Chapters 14 and 15 and so on 12 2 Econometric Models This manual is devoted primarily to the methods by which you can use L
286. spec is used with Cluster to specify a stratified two level form of data clustering Robust requests a sandwich estimator or robust covariance matrix for several discrete choice models 12 6 Econometric Model Estimation 12 6 3 Predictions and Residuals Fitted values predictions and residuals from most single equation models are requested as follows List displays a list of fitted values with the model estimates Keep name keeps the fitted values as a new or replacement variable in the data set Res name_ keeps the residuals as a new or replacement variable Prob name saves the probabilities as a new or replacement variable for discrete choice models such as probit or logit Fill requests that missing values or values outside the estimating sample be replaced by fitted values based on the estimated model Describing Sample Data 13 1 Chapter 13 Describing Sample Data 13 1 Introduction This chapter describes methods of obtaining descriptive statistics for one or more variables in your data set Procedures are given for cross sections and for panel data 13 2 Summary Statistics The primary command for descriptive statistics is DSTAT Rhs list of variables This produces a table which lists for each variable xx k 1 K the basic statistics Sample mean x 1 N JEX Xg Standard deviation s J AN DEN x Y Maximum value Minimum value Number of valid
287. ssumptions The intent is to produce an asymptotic covariance matrix that is appropriate even if some of the assumptions of the model are not met It is an important but infrequently discussed issue whether the estimator itself remains consistent in the presence of these model failures that is whether the so called robust covariance matrix estimator is being computed for an inconsistent estimator Section R10 8 in the Reference Guide provides general discussion of robust covariance matrix estimation The Sandwich Estimator It is becoming common in the literature to adjust the estimated asymptotic covariance matrix for possible misspecification in the model which leaves the MLE consistent but the estimated asymptotic covariance matrix incorrectly computed One example would be a binary choice model with unspecified latent heterogeneity A frequent adjustment for this case is the sandwich estimator which is the choice based sampling estimator suggested above with weights equal to one This suggests how it could be computed The desired matrix is aT n log F j n OlogF dlogF n 0 log F i apna gt pal oe Ss Three ways to obtain this matrix are Wts one Choice Based sampling or Robust or Cluster 1 15 8 Models for Discrete Choice The computation is identical in all cases As noted below the last of them will be slightly larger as it will be multiplied by n n 1 Clustering A related
288. t produce complex transformations of matrices Any of the constructions in Table 9 1 can be used as a stand alone matrix For example to obtain the determinant of X WX where W is a diagonal weighting matrix you can use 9 18 Using Matrix Algebra Dtrm lt x w x gt Likewise several such constructions can appear in functions with more than one input matrix This should allow you to reduce some extremely complex computations to very short expressions Characteristic Roots and Vectors a Cvec c characteristic vectors If C is a KxK matrix A has K columns The kth column is the characteristic vector which corresponds to the kth largest characteristic root ordered large to small C must be a symmetric matrix If not only the lower triangle will be used A Root c characteristic roots of a symmetric matrix For symmetric matrix C A will be a column vector containing the characteristic roots ordered in descending order For nonsymmetric matrices use a Cxrt c possibly complex characteristic roots of asymmetric matrix The characteristic roots of a nonsymmetric matrix may include complex pairs The result of this function is a Kx2 matrix The first column contains the real part The corresponding element of the second column will be the imaginary part or zero if the root is real The roots are ordered in descending order by their moduli You can use Cxrt to obtain the dominant root for a dynamic system Then the modul
289. ta Management 7 19 7 3 6 Random Number Generators There are numerous transformations which draw samples using LIMDEP s random number generators The basic generator is the one which will draw a sample from a continuous uniform distribution in the indicated range CREATE name Rnu lower limit upper limit and the one which will create a variable containing a sample from the indicated normal distribution CREATE name Rnn mean standard deviation The sample is placed with the observations in the current sample Note how we used this feature in the examples in Sections 3 3 and 3 4 Random draws may also appear anywhere in an expression as operands whose values are random draws from the specified distribution For example a random sample from a chi squared distribution with one degree of freedom could be drawn with CREATE name Rnn 0 1 2 Random samples can be made part of any other transformation For example the following shows how to create a random sample from a regression model in which the assumptions of the classical model are met exactly CREATE x1 Rnu 10 10 x2 Rnn 16 10 sy 1004 1 5 x1 3 1 x2 Rnn 0 50 The regression of y on xl and x2 would produce estimates of B 100 B2 1 5 and B 3 1 In addition to the Rnn m s normal with mean m and standard deviation s and Rnu u continuous uniform between 7 and u you can generate random samples from continuous and discrete Random Sa
290. ta set that you input But most analyses also involve partitioning the data set into subsamples either by stratification or by excluding or including observations based on some data related criteria This section will describe these two aspects of operation The final section will include a discussion of how the sample is modified either by you or automatically when the data set contains missing observations SAMPLE designate specific observations to be included in a subsample DATES establish the periodicity of time series data PERIOD designate specific time series observations to be included in a subsample REJECT exclude certain observations from the sample based on an algebraic rule INCLUDE include certain observations from the sample based on an algebraic rule In most cases you will read in a data set and use the full set of observations in your computations But it is quite common to partition the sample into subsamples and use its parts in estimation instead You will also frequently want to partition the data set to define data matrices for use in the MATRIX commands NOTE The current sample is the set of observations either part or all of an active data set which is designated to be used in estimation and in the data matrices for MATRIX CREATE etc The commands described in this section are used to designate certain observations either in or out of the current sample With only a few exceptions operat
291. tant 5 33586673 69883851 7 635 0000 C67 74916894 17622269 4 251 0000 29411765 C72 84733072 18996097 4 461 0000 29411765 Cid 36254858 24697201 1 468 1421 14705882 P77 39897106 12475671 3 198 0014 55882353 LOGMTH 84714538 06903915 12 271 0000 7 04925451 MATRIX Stat b varb Number of observations in current sample 34 Number of parameters computed here 10 Number of degrees of freedom 24 H Variable Coefficient Standard Error b St Er P Z gt z B L 533586673 69883851 7 635 0000 B_6 74916894 17622269 4 251 0000 B_7 84733072 18996097 4 461 0000 B_8 36254858 24697201 1 468 1421 B_9 39897106 12475671 3 198 0014 B_10 84714538 06903915 12 271 0000 MATRIX Stat b varb x H Variable Coefficient Standard Error b St Er P Z gt z Constant 533586673 69883851 7 635 0000 C67 74916894 17622269 4 251 0000 C72 84733072 18996097 4 461 0000 C77 36254858 24697201 1 468 1421 P77 39897106 12475671 3 198 0014 LOGMTH 84714538 06903915 12 271 0000 9 3 Using MATRIX Commands with Data LIMDEP s matrix package is designed to allow you to manipulate large amounts of data efficiently and conveniently Applications involving up to three million observations on 150 variables are possible With MATRIX manipulation of a data matrix with 1 000 000 rows and 50 columns which would normally take 400 megabytes of memory
292. tat degfrdm Linearly restricted regression LHS LOGG Mean 12 24504 Standard deviation 2388115 WTS none Number of observs 52 Model size Parameters 6 Degrees of freedom 46 Residuals Sum of squares 1014853 Standard error of e 4697022E 01 Fit R squared 9651083 Adjusted R squared 9613157 Model test FI 5 46 prob 254 47 0000 Autocorrel Durbin Watson Stat 4411613 Rho cor e e 1 7794194 Restrictns F 1 45 prob 02 8841 Not using OLS or no constant Rsqd amp F may be lt 0 Note with restrictions imposed Rsqd may be lt 0 H Variable Coefficient Standard Error t ratio P T gt t Mean of X Constant 26 7523913 1 47691600 18 114 0000 LOGPG 05231601 04095506 S127 2080 3 72930296 LOGI 1 63099549 15903625 10 255 0000 9 67214751 LOGPNC J 06096105 056898ii 1 071 2897 4 38036654 1 1 LOGPUC l 06096105____ 030689811____ 1 071 ___ 2897___4 10544881___ LOGPPT 05636622 11703582 482 6324 4 14194132 T 01262751 00491914 2 567 0137 25 5000000 t Listed Calculator Results TSTAT 146654 TC 2 014103 PVALUE 884061 6 5 8 Test of Structural Break The Chow test is used to determine if the same model should apply to two or more subsets of the data Formally the test is carried out with the F statistic SSE pora SSE
293. ted R squared 9564134 Model test F 3 48 prob 374 03 0000 Diagnostic Log likelihood 84 22267 Restricted b 0 1 188266 Chi sq 3 prob 166 07 0000 Autocorrel Durbin Watson Stat 4220089 Rho cor e e 1 7889955 Restrictns F 3 45 prob 2 64 0606 Not using OLS or no constant Rsqd amp F may be lt 0 Note with restrictions imposed Rsqd may be lt 0 Variable Coefficient Standard Error t ratio P T gt t Mean of X 4 Constant 28 0817710 1 46871226 19 120 0000 LOGPG 13016036 03229378 4 031 0002 3 72930296 LOGI 1 73922391 16247609 10 704 0000 9 67214751 LOGPNC sZ49800D 15 eiaden Fixed Parameter LOGPUC 505L12D 16 pauwe Fixed Parameter LOGPPT 1LI9GID 15 kw wees Fixed Parameter T 01960344 00381652 5 1316 0000 25 5000000 The coefficients on the three prices in the restricted regression are not exactly zero the values are pure rounding error The F statistic is on the boundary not quite statistically significant 6 26 Application and Tutorial Although the restrictions can be built into the REGRESS command there will be cases in which one is interested in applying the theoretical results directly The template formula for computing the F statistic is Raa Recetrictea J L R n K Unrestricted Where J is the number of restrictions and K is the number o
294. ted R squared 4251326E 02 Model test Fl dy 98 prob 58 4478 Diagnostic Log likelihood 281 4480 Restricted b 0 281 7435 Chi sq 1 prob 59 4420 Info criter LogAmemiya Prd Crt 2 831088 Akaike Info Criter 2 831082 Autocorrel Durbin Watson Stat 2 0643771 Rho cor e e 1 0321885 Restrictns F 1 97 prob 33 5678 Not using OLS or no constant Rsqd amp F may be lt 0 Note with restrictions imposed Rsqd may be lt 0 Variable Coefficient Standard Error t ratio P T gt t Mean of X H Constant 210416555 61679283 4 384 0000 LOGL 1 43543661 87473554 1 641 1040 68423500 LOGK 43543661 87473554 498 6198 15523890 You may impose as many restrictions as you wish with this estimator simply separate the restrictions with commas 14 2 5 Hypothesis Tests in the Linear Model The REGRESS and MATRIX commands can be used to test a variety of hypotheses The F statistic for testing the set of J restrictions Ho RB q is F J n K Rb q s R X X R Rb q J e e e e J e e n K where the subscript indicates the sum of squares with the restrictions imposed and b is the unrestricted ordinary least squares estimator This statistic is included in the diagnostic table whenever you use CLS to impose linear restrictions Consider an example where now we make two restrictions hold as equalities SAMPLE 31 500 CALC Ran
295. tely the large majority of the instructions you give to the program will be given by commands that you enter in the text editor This chapter will describe the LIMDEP command language We begin by describing the general form and characteristics of LIMDEP commands Section 4 4 will illustrate how the menus and dialog boxes can also be used to operate the program 4 2 Command Syntax All program instructions are of the form VERB specification specification specification The verb is a unique four character name which identifies the function you want to perform or the model you wish to fit If the command requires additional information the necessary data are given in one or more fields separated by semicolons Commands always end with a The set of commands in LIMDEP consists generally of data setup commands such reading a data file data manipulation commands such as transforming a variable programming commands such as matrix manipulation and scientific calculation commands and model estimation commands All are structured with this format Examples of the four groupings noted are READ File C WORK FRONTIER DAT Nobs 27 Nvar 4 CREATE logq Log output MATRIX identity Iden 5 bols lt X X gt X y REGRESS Lhs logq Rhs one Log k Log l Plot residuals The following command characteristics apply e You may use upper or lower case letters anywhere in any command All c
296. ter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Introduction to LIMDEP Getting Started Operating LIMDEP LIMDEP Commands Program Output Application and Tutorial Essential of Data Management Estimating Models Using Matrix Algebra Scientific Calculator Programming with Procedures TOC 2 Table of Contents This page intentionally left blank Introduction to LIMDEP 1 1 Chapter 1 Introduction to LIMDEP 1 1 The LIMDEP Program LIMDEP is an integrated package for estimating and analyzing econometric models It is primarily oriented toward cross section and panel data But many standard problems in time series analysis can be handled as well LIMDEP s basic procedures for data analysis include descriptive statistics means standard deviations minima etc with stratification multiple linear regression and stepwise regression time series identification autocorrelations and partial autocorrelations cross tabulations histograms and scatter plots of several types You can also model many extensions of the linear regression model such as heteroscedasticity with robust standard errors autocorrelation with robust standard errors multiplicative heteroscedasticity groupwise heteroscedasticity and cross sectional correlation the Box Cox regression model one and two way random and fixed effects models for balanced or unbalanced panel data distributed lag models ARIMA
297. terms and conditions of this agreement Copyright Trademark and Intellectual Property This software product is copyrighted by and all rights are reserved by Econometric Software Inc No part of this software product either the software or the documentation may be reproduced distributed downloaded stored in a retrieval system transmitted in any form or by any means sold or transferred without prior written permission of Econometric Software You may not modify adapt translate or change the software product You may not reverse engineer decompile dissemble or otherwise attempt to discover the source code of the software product LIMDEP and NLOGIT are trademarks of Econometric Software Inc The software product is licensed not sold Your possession installation and use of the software product does not transfer to you any title and intellectual property rights nor does this license grant you any rights in connection with software product trademarks Use of the Software Product You have only the non exclusive right to use this software product A single user license is registered to one specific individual and is not intended for access by multiple users on one machine or for installation on a network or in a computer laboratory For a single user license only the registered single user may install the software on a primary stand alone computer and one home or portable secondary computer for his or her exclusive use Howeve
298. that the selected commands are to be executed more than one time The dialog box queries you for the number of times The commands you have selected will now be carried out In most cases this will produce some output LIMDEP will now automatically open a third window your output window discussed in Section 3 4 Operating LIMDEP 3 7 Limdep Untitled 1 File Edit Insert Project Model fap Tools Window Help Run Selection Ctrl R Run Selection Multiple Times D fa S ae Run File Run Procedure RUC Stop Running Data U 11111 Rows 11111 Obs New Procedure Data Z Untitled 1 MEIR Variables m E Namelists f Insert Name X 9 Matrices Scalars Strings Procedures Sy Output 4 Tables Output Window Figure 3 7 Submitting Commands with the Run Menu If your commands fit on a single line many of LIMDEP s commands do not there are additional ways for you to submit commands e You can type a one line command in the command window then press Enter to submit it The command window or command bar is the small window located below the LIMDEP toolbar The w button at the end of the line allows you to recall and select among the last several such commands you have submitted See Figure 3 6 e You can submit a single line of text in the text editor to the command processor just by placing the cursor anywhere on that line beginning middle or end and then clicking the GO b
299. the data this may severely cramp the figure since the vertical axis is scaled so that every observation will appear e The mean residual bar may not appear at zero because the residuals may not have zero mean They will not if you do not have a constant term in your regression or if you are plotting two stage least squares residuals Since 0 0 will generally not be the midpoint between the high and low residual the zero bar will not be in the center of your screen even when you do have a constant term in the model The Linear Regression Model 14 5 14 2 3 Robust Covariance Matrix Estimation REGRESS will compute robust estimators for the covariance matrix of the least squares estimator for both heteroscedastic and autocorrelated disturbances Although OLS is generally quite robust some researchers have advocated other estimators for finite sample purposes REGRESS can also be used to compute the least absolute deviations estimator Heteroscedasticity The White Estimator For the heteroscedasticity corrected White estimator use Heteroscedasticity in the REGRESS command The White estimator is Est Var b X X x X e7x x x X X i l Autocorrelation The Newey West Estimator The Newey West robust estimator for the covariance matrix of the least squares estimator in the presence of autocorrelation is Est Var b XX x 0 e x x x XX t 1 yy 1 L T J ry X X x Exh ae EFT e ep XX x x x X X
300. the expression are identical to those for CREATE see Section R5 2 2 and REJECT see Section R7 4 as well as MATRIX and all forms of DO In this setting if the condition is true name is computed if it is false name is not computed Thus if name is a new scalar and the condition is false after the command is given name will not exist For example CALC If A 1 1 gt rsqrd q Log Dtr sigma An entire set of CALCULATE commands can be made conditional by placing a semicolon after the condition as in CALC If condition name result result If the condition is false none of the commands which follow it are carried out This form of condition may appear anywhere in a group of CALCULATE commands This will be most useful in iterative programs to condition your CALC commands 10 4 1 Reserved Names You can have a total of 50 scalar results stored in your work area You can obtain a complete list of the names and values assigned to any scalars in the calculator work area by navigating the project window Fourteen of the scalars are used by the program to save estimation results and are reserved The 14 reserved names are ssqrd degfrdm ybar logl kreg sumsqdev rsqrd sy rho lmda nreg theta s exitcode You can see the reserved scalars in the project window in Figure R13 4 They are the ones marked as locked with the gold key icon These scalars save for rho see the hint below are read only
301. timator has been used 3 Breusch and Pagan s Lagrange multiplier statistic for testing the REM against the simple linear regression model with no common effects is lt 2 XTY ENTE 1 OS T r 1 ENE e i l a i i l 1 1 it O ELT fetunay erel PELT DI zee 4 Baltagi and Li s modification of the LM statistic for unbalanced panels is also reported with the results This replaces the term outside the square brackets with 1N ZENIT SE 1 TJ NEE UT LIMDEP s computation of the LM statistic already accounts for unbalanced panels The Baltagi and Li modification evidently has some improved finite sample performance As can be seen in the example above which uses a balanced panel the Baltagi and Li correction has no impact when group sizes are all equal In this case both these complicated statistics reduce to N7T 2 T 1 The prob value is given for the LM statistic To a degree of approximation the same result would apply to the Baltagi and Li form 5 Hausman s chi squared statistic for testing the REM against the FEM is reported next H B rz 7 Busy Est Var B rx Est Var r e J Bax The prob value and degrees of freedom for the Hausman statistic are reported HINT Large values of the Hausman statistic argue in favor of the fixed effects model over the random effects model Large values of the LM statistic argue in favor of one of the one factor models against the classical regression wit
302. tion R13 1 Commands that you give will be listed in your trace file in all cases and in your output window You can request a full display of results both in the output window and in an output file by placing List before the result to be listed You can turn this switch off with Nolist Thus the command CALC tailprob Phi 1 will create a named scalar but will not show any visible numerical results But CALC List tailprob Phi 1 will show the result on the screen in the output window Once the end of a command is reached Nolist once again becomes the default The Nolist and List switches may be used to suppress and restore output at any point When the Nolist specification appears in a CALC command no further output appears until the List specification is used to restore the listing At the beginning of a command the List switch is off regardless of where it was before Scientific Calculator 10 5 To see a result that was computed earlier there are several ways to proceed A CALC command can simply calculate a name Thus in the command format you could just give the command CALC List tailprob You may also open the calculator window and just type the name of the scalar you want to see Finally when you obtain a named scalar result it will be added to the project window You must open the Scalars data group by clicking the When the list of scalars is displayed click any na
303. tion approximately 1 81 is used as the basis of the model instead of the standard normal 15 3 2 Model Structure and Data This model must include a constant term one as the first Rhs variable Since the equation does include a constant term one of the us is not identified We normalize u to zero Consider the special case of the binary probit model with something other than zero as its threshold value If it contains a constant this cannot be estimated Data may be grouped or individual Survey data might logically come in grouped form If you provide individual data the dependent variable is coded 0 1 2 J There must be at least three values Otherwise the binary probit model applies If the data are grouped a full set of proportions po p Pj Which sum to one at every observation must be provided In the individual data case the data are examined to determine the value of J which will be the largest observed value of y which appears in the sample In the grouped data case J is one less than the number of Lhs variables you provide Once again we note that other programs sometimes use different normalizations of the model For example if the constant term is Models for Discrete Choice 15 11 forced to equal zero then one will instead add a nonzero threshold parameter uo which equals zero in the presence of a nonzero constant term 15 3 3 Output from the Ordered Probability Estimators All of the ordered prob
304. tistics TABLES Descriptive statistics for stratified data CROSSTAB Cross tabulations for discrete data HISTOGRAM Histograms for discrete and continuous data KERNEL Kernel density estimation of the density for a variable IDENTIFY Descriptive statistics ACF PACF for time series data SPECTRAL Spectral analysis of a time series Plotting FPLOT Function plot for user specified function MPLOT Scatter plot of matrices PLOT Scatter or time plots of variables against each other SPLOT Simultaneous scatter plots for several variables 12 4 Econometric Model Estimation Linear Regressions and Variants Single Equation FRONTIER HREG QREG REGRESS TSCS 2SLS Stochastic frontier models Heteroscedastic linear regression Quantile regression Linear regression models also OLSQ and CRMODEL Time series cross section covariance structure models Two stage instrumental variable estimation of linear models Multiple Equation SURE 3SLS Linear seemingly unrelated regression models Three stage IV GLS estimator for systems of linear equations Sample Selection Models MATCH SELECT INCIDENTAL SWITCH Propensity score matching to analyze treatment effects Sample selection models with linear and tobit models Incidental truncation selection model Switching regression models Nonlinear Regression Optimization Manipulation of Nonlinear Functions ARMAX BOXCOX NLSQ NLSURE Box Jenkins ARMA and dynamic l
305. titled 1 File Edit Insert Project Model Run Tools Window Help Deal e ola aawl CREATE Sy Data SAMPLE Sy Variables REJECT px Namelists Matrices Scalars QQ Strings E Procedures 0 108296 Sy Output 0 970373 E Tables 0 229617 Output Window 0 715638 0 952213 1 13377 0 496044 0 241646 0 273172 0 509043 0 984089 2 31595 Ln 2 3 Figure 7 15 Current Sample and the REJECT Command 7 5 1 Cross Section Data Initially observations are defined with respect to rows of the data matrix which are simply numbered 1 to 1 000 Sample Definition The SAMPLE Command Designate particular observations to be included in the current sample with the command SAMPLE range range range range A range is either a single observation number or a range of observations of the form lower upper For example SAMPLE 1 12 35 38 44 301 399 You can set the sample in this fashion do the desired computations then reset the sample to some other definition at any time To restore the sample to be the entire data set use SAMPLE All Because of the possibility of missing data being inadvertently added to your data set LIMDEP handles this command as follows All observations are rows 1 to N where N is the last row in the data area which is not completely filled with missing data In most cases this will be the number of observations in the last data set you read
306. transform them in any way you like for example compute logarithms lagged values or many other functions edit the data and of course apply the estimation programs You may also be interested in generating random Monte Carlo samples rather than analyzing live data LIMDEP contains random number generators for 15 discrete and continuous distributions including normal truncated normal Poisson discrete or continuous uniform binomial logistic Weibull and others A facility is also provided for random sampling or bootstrap sampling from any data set whether internal or external and for any estimation technique you have used whether one of LIMDEP s routines or your own estimator created with the programming tools LIMDEP also provides a facility for bootstrapping panel data estimators a feature not available in any other package 1 2 References for Econometric Methods This manual will document how to use LIMDEP for econometric analysis There will be a number of examples and applications provided as part of the documentation However we will not be able to provide extensive background for the models and methods A few of the main general textbooks currently in use are Baltagi B Econometric Analysis of Panel Data 3 ed Wiley 2005 Cameron C and Trivedi P Microeconometrics Methods and Applications Cambridge University Press 2005 Greene W Econometric Analysis 6th Edition Prentice Hall 2008 Gujarati D Bas
307. uares In other cases specifications will be optional as in REGRESS Lhs Rhs Keep yf which requests LIMDEP to fit a model by linear least squares then compute a set of predictions and keep them as a new variable named yf Some model specifications are general and are used by most if not all of the estimation commands For example the Keep name specification in the command above is used by all single equation models linear or otherwise to request LIMDEP to keep the predictions from the model just fit In other cases the specification may be very specific to one or only a few models For example the Cor in SWITCHING REGRESSION Lhs Rh1 Rh2 Cor is a special command used to request a particular variant of the switching regression model that with correlation across the disturbances in the two regimes The default is to omit Cor which means no correlation Estimating Models 8 3 8 2 1 The Command Builder LIMDEP contains a set of dialog boxes and menus that you can use to build up your model commands in parts as an alternative to laying out the model commands directly as shown above Figure 8 1 shows the top level model selection The menu items Data Description etc are subsets of the modeling frameworks that LIMDEP supports We ve selected Linear Models from the menu which produces a submenu offering Regression 2SLS and so on From here the command builder contains special
308. ucting the command and sending it to the program Although the command builders do not remember their previous commands the commands are available for you to reuse if you wish You can use edit copy paste to copy commands from your output window into your editing window then just submit them from the editing window The advantage of this is that you now need not reenter the dialog box to reuse the command For example if you wanted to add a time trend year to this equation you could just copy the command to the editor add year to the Rhs list then select the line and click GO TIP Commands that are echoed to the output window are always marked with the leading gt The command reader will ignore these so you can just copy and paste the whole line or block of lines to move commands to your editing window t imdep Output Dor Fie Edit Insert Project Model Run Tools Window Help Status Trace 13 DELETE ESQ 14 DELETE MEANES gt REGRESS Lhs I Rhs ONE F C D1 D2 HHH HHH HHH HHH HH HHH HH HHH HHH HH JE JE JE JE JE JE JE JE JE JE JE JE HHH JE JE JE JE JE JE EH JE JE JE JE E ME E E E E Estimation Data Analysis Program Linear Regression HHH HH HEH HHH HHH HEH HH HEH HHH HH HHH HHH HHH HHH HHH HHH HHH HHH HHH HHH HHH Eee emmm mmm m me m m E m 8 e E E m e E E m 5 Ordinary least squares regression Model was estimated Dec 24 2005 at 02 50 48PM LHS I Mean 145 9582
309. uld be necessary if c were a data matrix You may string together as many matrices in a product as desired As in the example the terms may involve other matrices or functions of other matrices For example the following commands will compute White s heteroscedasticity corrected covariance matrix for the OLS coefficient vector NAMELIST x list of Rhs variables REGRESS Lhs y Rhs x Res e CREATE 3 esq e 2 MATRIX white lt x x gt x esq x lt x x gt The CREATE command that computes the squared residuals is actually unnecessary The last two lines could be combined in MATRIX white lt x x gt Bhhh x e lt x x gt LIMDEP also provides a function to compute the center matrix for the Newey West estimator Nwst x e computes the Newey West middle matrix for lags L 0 gt White e is the vector of residuals x is a namelist defining the set of variables You may also multiply simple matrices that you enter directly For example as ee 1 3 5 2 4 5 5 sas 1 351 24 55 The multiplication operator sorts out scalars or 1 1 matrices in a product Consider for example V A r Ar A If r is a column vector this is a matrix AA divided by a quadratic form To compute this you could use MATRIX 3v a lt r alr gt a Using Matrix Algebra 9 15 The scanner will sort out scalars and multiply them appropriately into the product of matrices But in all cases mat
310. ults The table contains the elements of beta the diagonal elements of v and the ratios of the elements of beta to the square root of the corresponding diagonal element of v assuming it is positive For example the listing below shows how the Stat function would redisplay the model results produced by a POISSON command from one of our earlier examples NOTE MATRIX Stat vector matrix has no way of knowing that the matrix you provide really is a covariance matrix or that it is the right one for the vector that precedes it It requires only that vector be a vector and matrix be a square matrix of the same order as the vector You must insure that the parts of the command are appropriate The routine to produce model output for a matrix computed set of results can be requested to display variable names by adding a namelist with the appropriate variables as a third argument in the MATRIX Stat b v function If your estimator is a set of parameters associated with a set of variables x they are normally labeled b_1 b_2 etc Adding the namelist to the MATRIX Stat b v x function carries the variable labels into the function An example follows Some results are omitted 9 8 Results from Poisson regression Using Matrix Algebra aka e Variable Coefficient Standard Error b St Er P Z gt z Mean of X aks iia b 4 Cons
311. ults are displayed on the screen and in the output file if one is open In addition each model produces a number of results which are saved automatically and can be used in subsequent procedures and commands The POISSON command above shows an example After the model is estimated scalars named nreg kreg and logl are created and set equal to the number of observations number of coefficients estimated and the log likelihood for the model respectively For another after you give a REGRESS command the scalar rsqrd is thereafter equal to the R from that regression You can retrieve these and use them in later commands For example REGRESS Seiad CALC f rsqrd kreg 1 1 rsqrd mreg kreg to compute a standard F statistic There is an easier way to do this Although your CALCULATOR has 50 cells the first 14 are read only in the sense that LIMDEP reserves them for estimation results You may use these scalars in your calculations or in other commands see the example above but you may not change them The one named rho may be changed Likewise the first three matrices are reserved by the program for read only purposes The read only scalars are ssqrd rsqrd s sumsqdef degfrdm ybar sy kreg nreg logl exitcode and two whose names and contents will depend on the model just estimated The names used for these will be given with the specific model descriptions At any time the names of the read only scalars
312. umulated frequencies To illustrate the use of this feature we use a data set that was employed in the study of health care system utilization Regina T Riphahn Achim Wambach and Andreas Million Incentive Effects in the Demand for Health Care A Bivariate Panel Count Data Estimation Journal of Applied Econometrics Vol 18 No 4 2003 pp 387 405 The raw data were downloaded from the journal s data archive website http ged econ queensu ca jae 2003 v18 4 riphahn wambach million The data which will be used in several applications below are an unbalanced panel of observations on health care utilization by 7 293 individuals The group sizes in the panel number as follows Tj 1 1525 2 2158 3 825 4 926 5 1051 6 1000 7 987 There are altogether 27 326 observations Variables in the file are hhninc household nominal monthly net income in German marks 10000 Hhkids children under age 16 in the household 1 otherwise 0 educ years of schooling married marital status female for female 0 for male docvis number of visits to the doctor doctor number of doctor visits gt 0 hospvis number of visits to the hospital 13 3 1 Histograms for Continuous Data A histogram for the continuous variable Hhninc would appear as follows HISTOGRAM Rhs hhninc You can select the number of bars to plot with Int k This can produce less than satisfactory results however Ts Describing Sample Data 13
313. ure 3 9 with a new project window open and no other windows active Operating LIMDEP 3 9 imdep Untitled Project 1 File Edit Insert Project Model Run Tools Window Help Darla S tee olal AE Variables Namelists Matrices 5 Scalars 9 Strings Procedures SQ Output 4 Tables Output Window Figure 3 9 Initial LIMDEP Desktop Open an Editing Window Select File New then Text Command Document to open an editing window exactly as discussed in Section 3 2 2 See Figure 3 3 Place Commands in the Editing Window Type the commands shown in the editing window of Figure 3 10 These commands will do the following 1 Instruct LIMDEP to base what follows on 100 observations 2 Create two samples of random draws from the normal distribution a y and an x 3 Compute the linear regression of y on x Spacing and capitalization do not matter type these three lines in any manner you find convenient But do use three lines You need not type the comment lines I will use data 3 10 Operating LIMDEP Submit the First Two Commands Highlight the first two lines of this command set Now move the mouse cursor up to the now green button marked GO it is directly below Tools and click the GO button Note that a new window appears your output window see Figure 3 11 You may have to resize it to view the output Limdep Untitled 1 Ef File
314. ured is in the lower half of the split window Getting Started 2 5 e The trace of the session is shown in the center of the screen at the top of the split output window Limdep clogit Ipj File Edit Insert Project Model Run Tools Window Help ojee ee oll Say Dax zi Untitled 1 f Insert Name i DSTAT Rhs Eak Data U 3333 Rows 840 Obs clogit Ipj 3 Variables gt MODE TIME IN C INVT GC CHAIR HINC PSIZE INDJ INDI AASC Tasc Rhs Exit status for this model command is gt gt gt gt gt gt gt b 250000000 34 5892857 47 7607143 486 165476 110 879762 276190476 34 5476190 1 74285714 433270678 24 9486076 32 3710038 301 439107 47 9783530 447378551 19 6760442 1 01034998 000000000 000000000 2 00000000 63 0000000 30 0000000 000000000 2 00000000 1 00000000 S7619NA7K 1 3926949N1 Aannanannann fide 084 Figure 2 5 LIMDEP Data Analysis Session 2 7 Exiting LIMDEP and Saving Results To leave LIMDEP select Exit from the File menu Whenever you exit a session you should save your work At any time in any session you can save all of LIMDEP s active memory tables data matrices etc into a file and retrieve that file later to resume the session When you exit LIMDEP will ask if you wish to save the contents of the editing project and output windows In each case you
315. ures such as how to read a data set how to transform data and what you need to know about missing data Part II is about econometrics The various chapters in Part II follow essentially the sequence of topics that one might encounter in an econometrics course Thus in Part II we will show you how to describe your data then how to use the linear regression model This topic usually takes most of the first semester and it occupies a large section of this part of the manual We then proceed to some of the more advanced topics that would logically appear later in the course such as two stage least squares instrumental variable estimation and basic discrete binary choice models Part II ends with a brief survey of the many somewhat and extremely advanced features that are also available in LIMDEP but not covered in a conventional econometrics course or in this manual Having introduced the manual as above we do emphasize this user s guide is not an econometrics or statistics text and does not strive to be one The material below will present only the essential background needed to illustrate the use of the program In order to accommodate as many readers as possible we have attempted to develop the material so that it is accessible to both undergraduates and graduate students For the latter a text that would be useful to accompany this guide is Econometric Analysis 6 Edition William Greene Prentice Hall 2008 which was written by the
316. us can be obtained with CALC Let C be the relevant submatrix of the structural coefficient matrix in the autoregressive form Then MATRIX rt Cxrt C CALC check rt 1 1 2 rt 1 2 2 Cxrt c gives the same results as Root c if C is a symmetric matrix But if C is nonsymmetric Root c gives the wrong answer because it assumes that C is symmetric and uses only the lower triangle It is always possible to obtain the roots of a symmetric matrix But certain nonsymmetric matrices may not be decomposable If this occurs an error message results The Root function can also be used to find the possibly complex roots of a dynamic equation If C is a vector of elements c c2 cg instead of a symmetric matrix then A Root c reports in a Kx2 matrix the reciprocals of the characteristic roots of the matrix c Cy C3 Co 1 0 0 0 C 0 1 0 o 0 1 0 These are the roots of the characteristic equation 1 c1 z c2 Z cg Z 0 of the dynamic equation Y C1 Y1 C2y2 CoYro other terms The dominant root of the system is the largest reciprocal reported If its modulus is larger than one Using Matrix Algebra 9 19 the equation is unstable Scalar Functions The following always result in a 1x1 matrix a Dtrm c determinant of square matrix a Logd c log determinant of positive definite matrix a Trce c trace of square matrix a Norm c Euclidean norm of vector C a
317. utton The single line does not have to be highlighted for this e For desktop computers this does not apply to most laptop or notebook computers the two Enter keys on your keyboard one in the alphabetic area and one in the numeric keypad are different from LIMDEP s viewpoint You can submit the line with the cursor in it as a one line command by pressing the numeric Enter key The alphabetic Enter key acts like an ordinary editing key Finally the right mouse button is also active in the editing window The right mouse button invokes a small menu that combines parts of the Edit and Insert menus as shown in Figure 3 8 As in the Edit menu some entries Cut Copy are only active when you have selected text while Paste is only active if you have placed something on the clipboard with a previous Cut or Copy Run Line is another option in this menu Run Line changes to Run Selection when one or more lines are highlighted in the editing window and if you make this selection those lines will be submitted to the program If no lines are highlighted this option is Run Line for the line which currently contains the cursor 3 8 Operating LIMDEP 44 Limdep Untitled 1 DE Fie Edit Insert Project Model Run Tools Window Help olsa S ele lt olal Amm This small window accepts a one line command f TA Untitled Proj O X EERTE Data U 3333 Rows 3333 Obs A insat Name Data I will use this window to collect the
318. wever there are a few common variations notably using weights Constant Terms As noted earlier LIMDEP almost never forces a constant term in a model the only case is the linear regression model fit by stepwise least squares For any other case if you want a constant term in a model you must include the variable one in the appropriate variable list The variable one is provided by the program you do not have to create it You can however use one at any point in any model where you wish to have a constant term and any MATRIX command based on a column of ones as a variable in the analysis of data The typical estimation command will appear like the following example REGRESS Lhs y Rhs one x which produces output including Variable Coefficient Standard Error b St Er P Z gt z Mean of X H Constant 00280548254 0070621362 397 6912 X 01489733909 0071169806 2 093 0363 006473082 A MATRIX command based on the same construction might be the following which computes the inverse of a matrix of sums of squares and cross products NAMELIST _ xdata one x MATRIX xxi lt x x gt 8 3 1 Using Weights Any procedure which uses sums of the data including descriptive statistics and all regression and nonlinear models can use a weighting variable by specifying Wts name where name is the name of the variable to be used for the weighting Any mode
319. wser Files with the LPJ and LIM extensions are registered in your Windows system setup This means that whenever you double click any file with a LPJ or LIM extension in any context such as Find File My Computer any miniexplorer or in a web browser Windows will launch LIMDEP and open the file Note however in order to operate LIMDEP you must have a project file open not just a command or input file For example you can create shortcuts by moving any LIM or LPJ files you wish to your Windows desktop These files will then appear as icons on your desktop and you can launch LIMDEP from your desktop Similarly if you open a LIM file on our website or someone else s or a LIM file that is sent to you as an email attachment you can launch LIMDEP and place the indicated file in an editing window If you start LIMDEP in this way you must then use File New Project to open a new project window NOTE Until you open a project no other program functions are available You must now open a project with any of the options in the File menu in order to proceed Operating LIMDEP 3 1 Chapter 3 Operating LIMDEP 3 1 Introduction This chapter will explain how to give commands to LIMDEP and will describe some essential features of operation The sections to follow are 3 2 Beginning the LIMDEP Session 3 3 Using the Editing Window 3 4 A Short Tutorial 3 5 Help 3 2 Beginning the LIMDEP Session When you begin
320. x bY gt LOGL_OBS G Namelists H E Matrices gt B P gt VARB gt SIGMA Scalars H E Strings Procedures H E Output Tables Output Window Figure 3 13 Project Window Exit the Program When you are done exploring select File Exit SAMPLE 1 100 CREATE X Rnn 0 1 REGRESS Lhs Y Rhs Exit status for this mc hary least squares reg was estimated Dec 21 2 Hean Standard deviati Number of observ Parameters Degrees of freed Sum of squares Standard error o R squared Adjusted R squar El lL 98 p Log likelihood Restricted b 0 Chi sq 1 p LogAmemiya Prd Alvailbe Tnfa Cri TZ windows so answer no to the three queries about saving your results There is no need to save any of these 3 14 Operating LIMDEP 3 5 Help NOTE LIMDEP s help feature uses a hlp format file This is was a standard Windows format feature and its operation relies on a Windows utility program With the release of Windows Vista without notification Microsoft made a decision to end support of this format and did not include a version of the help engine in the new operating system Thus the Help procedure in LIMDEP and many other programs is not compatible with Windows Vista But evidently in response to the predictable protest Microsoft has produced a patch for this feature that can be added to the operating system to revive help engines such as ours Please go to http Awww limdep com support faq for more info
321. x d In order to use this construction the parameters of the Mean function must be a namelist followed by a variable Xvem x covariance matrix for X and Xcor x correlation matrix for X 9 22 Using Matrix Algebra This page intentionally left blank Scientific Calculator 10 1 Chapter 10 Scientific Calculator 10 1 Introduction You will often need to calculate scalar results The scientific calculator CALC is provided for this purpose For example you can use CALC to look up critical points for the normal t F and chi squared distributions instead of searching a table for the appropriate value And CALC will give you any value not just the few in the tables Another case will be calculation of a test statistic such as a ratio or likelihood ratio statistic LIMDEP s calculator can function like a hand calculator but it is an integral part of the larger program as well Results you produce with the calculator can be used elsewhere and results you obtain elsewhere such as by computing a regression can be used in scalar calculations The programs listed in the chapters to follow contain numerous examples The example below is a simple application Example Testing fora Common Parameter in a Probit Model Suppose a sample consists of 1000 observations in 10 groups of 100 The subsamples are observations 1 100 101 200 etc We consider a probit model y BotBix te observed y 1 if y gt 0 and 0 otherwise With e N
322. xt file that you can display in a word processing program This section will describe how to read ASCII files You will typically read an ASCII file by instructing LIMDEP to locate the file on one of your computer s storage drives and read the file The next few sections of this chapter will show you how to do that We begin however with a simpler operation that does the same thing Section 6 3 also shows you how to read data into LIMDEP using the text editor Simple Rectangular ASCII File The simplest basic starting point for reading data files instead of from the text editor is the rectangular ASCII file that contains exactly one row of variable names at the top of the file and columns of data below it as shown in the example in Figure 7 4 ID Year Age Educ 1960 23 16 27 1975 44 12 5 3 1990 14 Liss 4 1993 missing 20 Figure 7 4 Sample Data File The sample data set shown illustrates several degrees of flexibility Variable names in a file may be separated by spaces and or commas Names need not be capitalized in the file LIMDEP will capitalize them as they are read The numbers need not be lined up in neat columns in a data file Values in the data set may be separated by spaces tabs and or commas Missing values in a data set may be indicated by anything that is not a number But they must be indicated by something A blank is never understood to be a missing value To read a data
323. y requesting it in the same fashion All necessary corrections for the use of the instrumental variables are made in the computation 14 5 2 Model Output for the 2SLS Command The output for the 2SLS command is identical to that for REGRESS The only indication that 2SLS rather than OLS was used in estimating the model will be a line at the top of the model results indicating that two stage least squares was used in the computations and a listing of the instrumental variables that will appear above the coefficient estimates All retrievable results and methods for testing hypotheses are likewise identical 14 12 The Linear Regression Model 14 6 Panel Data Models This chapter will detail estimation of linear models for panel data The essential structure for most of them is an effects model Yr Ai Ye PK Ex in which variation across groups individuals or time is captured in simple shifts of the regression function i e changes in the intercepts These models are the fixed effects FE and random effects RE models The commands for estimation of these models are variants of the basic structure REGRESS Lhs y Rhs x Panel Str the name of a stratification variable or Pds specification of the number of periods variable or fixed 3 other options 14 6 1 Data Arrangement and Setup Your data are assumed to consist of variables Vito X ity X2its s XKit gt Tiny i lp

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