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Université Laval - The Software DAD

1. Indication Vector or parameter Status of choice Distribution 1 Distribution 2 Variable of interest y y 2 Compulsory Weight Variable w w Optional Group Variable al c2 Optional Index of group ki ki Optional s s Compulsory On the first execution bar you will find 1 Compute to provide the critical relative poverty lines and the crossing points of the sample normalised dominance curves When the option with STD is specified the standard deviation on the estimates of the critical relative poverty lines and on the estimates of the crossing points of the normalised FGT curves are also given 2 Range to specify the range of A over which to check the presence of critical values With this command you can also specify the incremental step of research for these crossing points 3 Graph to draw the normalised FGT curves for the two distributions with parameter A 42 Curves ee DADS 7 Curves A number of curves are useful to present a general descriptive view of the distribution of living standards Many of these curves can also serve to check the robustness of distributive orderings in terms of poverty inequality social welfare and equity 7 1 Quantiles and normalised quantiles Remark The application for computing the normalised quantiles is similar in structure to the one for computing quantiles The p quantile at a percentile p of a continuous population is given by Ol p F p
2. Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional rho P Compulsory p p Compulsory On the first execution bar you find e The command Compute to compute L k p To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the Lorenz curve To specify a range for the horizontal axis choose the item Graph Management gt Change range of x from the main menu 47 Curves Re AN e The command Range to specify the range of the horizontal axis To compute the standard deviation choose the option for computing with standard deviation Case 2 Two distributions To compute the Lorenz curve with two distributions l From the main menu choose the item Curves gt Lorenz curve 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Vectors or parameters Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable wl w2 Optional Group Variable a c2 Optional Index of group ki ko Optional rho Pi P2 Compulsory p Pi p2 Compulsory On the first execution bar you find 1 The command Crossing to search the fi
3. The first execution bar contains the command Compute To compute the standard deviation choose the option for computing with standard deviation 5 3 2 The S Gini social welfare index Casel One distribution To compute the S Gini index of social welfare for one distribution l From the main menu choose the following item Welfare and inequality Social welfare indices S Gini index 2 In the configuration of the application choose 1 for the number of distributions 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows 32 Inequality Poverty and Social Welfare Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional rho P Compulsory On the first execution bar you will find The command Graph Case 2 Two distributions Management Change range of x from the main menu To compute the S Gini with two distributions The command Compute to compute the S Gini index To compute the standard deviation choose the option for computing with standard deviation to draw the value of index according to a range of parameter p To specify such a range for the horizontal axis choose the item Graph l From the main menu choose the item Welfare and inequality Social
4. 1 From the main menu choose the item Distribution gt Density function 56 Distribution ee DADS 2 Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of y Compulsory interest Weight Variable w Optional Group Variable c Optional Index of group k Optional Parameter y Compulsory Smoothing Optional parameter On the first execution bar you find e The command Compute to compute f y To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of the function as a function of y To specify a range for the horizontal axis choose the item Change range of x from the main menu Graph management gt e The command Range to specify the range of the horizontal axis To compute the standard deviation choose the option for computing with standard deviation 8 3 The joint density function The gaussian kernel estimator of the joint density function f x y is defined as 2 2 A 1 n 1 I 2 yi f xyJ gt 2 Wa P 3 a a i To reach this application l From the main menu choose the item Distribution J oint density function 2 Choose the different vectors and parameter values as follows 57 Distribution Indication Variables or Status of choice parameter
5. The user then has sik possibilities for computing the mean as shown in the following table The mean Variable of weighting Variable of Index of Interest Variable groups group For the 10 households 1 1 x E Na ra dp yi Without No selection 1 weighting For the 10 households 1 Wil webbing yj wi No selection 109 For households living in town VI ith h 1 3 Without weighting Yi W out Ci weighting For households living in town V1 h h h 1 With weighting Yi Wi Ci For households living in town V2 h 1 5 Without weighting Yi Without Si 2 weighting For households living in town V2 we 6 with weighting Yi i Ci 2 This choice does not affect the results since not variable of groups has been selected Finally to compute the standard deviation on the estimate of the mean you just need to select the option of computing with STD 13 Inequality Poverty and Social Wel 5 Inequality poverty and social welfare 5 1 The inequality indices The software DAD can compute the following four types of inequality indices 1 The Atkinson index 2 The S Gini index 3 The Atkinson Gini index 4 The Generalised Entropy index y is the living standard of observation i We assume that the n observations have been ordered in increasing values of y such that y lt y 41 Yi 1 0 1 The variable c indicates the group to which observati
6. e g 5 4 1 The decomposition of the FGT index The FGT poverty index for a population composed of K groups can be written as follows K Pi z a X Q k P k z k 1 where P k z Q is the FGT poverty index for subgroup k and k is the proportion of the population in this subgroup The contribution of group k to the poverty index for the whole population equals k P k z To perform the decomposition of the FGT index l From the main menu choose the item Welfare and inequality Decomposition FGT Decomposition 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Poverty line z Compulsory alpha a Compulsory Indices of groups kj ko Compulsory separated by 35 Inequality Poverty and Social Welfare Remark The indices of the subgroups separated by the dash should be integer values For example we may have two subgroups coded by the integers 1 and 2 In this case we should write in the field Indices of groups the values 1 2 before proceeding to the decomposition 5 4 2 The decomposition of the FGT index for two groups To perform the decomposition of the FGT index for two groups l From main menu choose the item
7. 5 R p tez les tapes 2 et 3 pour les autres variables 6 From the main menu of SPSS select File gt Save as Dans A Bureau El A c E Poste de travail Decalue JSci SamplingD Mes documents dpsfb950029 ps liste Services e eal Yoisinage r seau exemple nuevo tempo L correspondance Help DAD 4 0 Personnel tempo3 CI Dad4 0 26mars ift 21133 Rapport_AU test I DADA EXE Inegalit roma testa Nom data3 dat Paste Type Fixed ASCII dat Annuler dd A Gunite vaneble names ka spreadsheet 9 Indicate that the type of the file is Fixed ASCII dat 7 Note SPSS does not include in the ASCII file the name of the variables that you have saved You can add these names by editing the saved file with a text editor such as WordPad Write on the first line the names of the vectors and save the file again it is useful to have the names of variables before reading them in DAD Any way it is strongly recommended to edit the file with a simple text editor and to check the format and the separating type of the decimals If the separator of decimals is comma it should be specified during the procedure of loading of the data in DAD 10 Follow the instructions in the User s Manual of DAD3 0 to download the ASCII file in DAD 11 When the SPSS database contains a high number of vectors or columns it is useful to save just those that will be useful in DAD To save just a few SPSS vectors of
8. 0 1 Cow L k 0 1 C k2 0 2 Cow Lk 0 1 C kp 1 Cow L k 130 2 C k gt 0 1 Cow Lk 0 2 C k gt 0 2 Cow L k1 1 C k2 0 1 Cow L kj 1 C k0 2 gt Cov Lk 31 C kp 51 7 6 The CPG curve The CPG curve at p for a subgroup k and poverty line z is EWG y 0 SOP G k p3z f yw Case 1 One distribution To compute the CPG curve for one distribution l From the main menu choose the item Curves gt CPG curve 2 In the configuration of application choose 1 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional Poverty line z Compulsory p P Compulsory On the first execution bar you find e The command Compute to compute G k p z To compute the standard deviation choose the option for computing with standard deviation 53 Curves ee DAD S 2 e The command Graph to draw the curve as a function according of p To specify a range for the horizontal axis choose the item Graph Management gt Change range of x from the main menu To compute the standard deviation choose the option for computing with standard deviation Case 2 Two distributions To reach the application for two distributions 1 From the main men
9. 2 Range to specify the range of poverty lines over which to check for the presence of critical poverty lines With this command you can also specify the incremental step of research for these crossing points 3 Graph to draw the FGT curves for the two distributions 6 2 Inequality dominance Distribution dominates distribution 2 in inequality at order s over the conditional range of proportions of the mean A FE only if P Aw gt P 42 0 V e h a where s 1 These are normalised stochastic dominance curves at order s or normalised FGT curves for amp s 1 This section checks for the points at which there is a reversal of the above dominance conditions for inequality orderings Said differently it provides the crossing points of the FGT curves that is the values of A and P 1 Aw a for which P App sO P5 Ap250 when sign P 1 Jur P n Jz sign P A u2 0 P A n Ju sat for a small n These crossing points at A can also be referred to as critical relative poverty lines when the poverty lines are a proportion of the mean and when the indices are normalised by the poverty line To check for those crossing points l From main menu choose the item Dominance Inequality Dominance 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows 41 Dominance O MM
10. Welfare and inequality Decomposition Entropy decomposition 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional theta 0 Compulsory Indices of groups kj ko Compulsory separated by The following information appears in the output window 1 The entropy index for the whole population 38 Inequality Poverty and Social Welfa 2 The entropy index for between group inequality 7 0 3 The entropy index within every subgroup k 4 The proportion u k u for every subgroup 5 The absolute contribution to total inequality of inequality within every subgroup that is U k u Ok K 8 6 The relative contribution to total inequality of inequality within every subgroup To compute the standard deviations for these statistics choose the option computing with standard deviation 39 Dominance 6 Dominance p This section looks at the primal dominance conditions for the poverty and inequality orderings of two distributions of living standards Corresponding dual dominance conditions are considered in the section on Curves 6 1 Poverty dominance Distribution 7 dominates distribution 2 at order s over the conditional range al if only
11. Choose the different vectors and parameter values as follows Indication Status of choice parameters Basic variable Interest variable T or B Compulsory Weight variable Group variable ndek of group o h Compulsory p 67 Redistribution O DAD S 2 On the first execution bar you find 1 The command S Gini to compute Tax Ix P Ly 1 P Ty P Ly49 P 2 The command Crossing to seek the first point at which the curves Ly _7 p and Ly p or Ly4p p and Ly p cross DAD indicates the co ordinates of that first crossing and their standard deviation if the option of computing with standard deviation is chosen 3 The command Difference with this command to compute Tax Ly_7 p Lx p Ly p p Lx p 4 The command Range to specify a range of p for the search of the first intersection between the two curves The command also allows to specify the range of the horizontal axis in the drawing of a graph 5 The command Graph to draw the following curves as a function of p Tax Ly 7 p Lx p Ly p p Lx p 9 6 The coefficient of concentration Let a sample contain n joint observations y 7 on a variable y and a variable T Let The S Gini coefficient of concentration of T for the group k is denoted as Cr k p and defined as observations be ordered in increasing values of y in such a way that y lt y it i CPt h p MI where V wk j ICr k p 1 Uy h i 6
12. Progressivity and equity across different taxes and or tranfers and subsidies 3 Checks for the robustness of distributive comparisons 4 Estimation of stochastic dominance curves of the primal and dual types for poverty social welfare inequality and equity dominance 5 Robustness of decompositions into population subgroups and factor components 6 Estimation of popular dual curves ordinary and generalised Lorenz curves Cumulative Poverty Gap curves quantile curves normalised quantile curves curves of quantiles of poverty gaps concentration curves 7 Estimation of popular primal curves cumulative distribution functions poverty deficit curves poverty depth curves etc 8 Estimation of differences in curves and indices 9 Estimation of critical poverty lines for absolute and relative poverty comparisons 10 Estimation of crossing points for dual curves 11 Provision of asymptotic standard deviations on all estimates of indices points on curves critical poverty lines crossing points etc allowing for dependence or independence in the samples being compared These standard deviations are currently computed under the assumption of identically and independently distributed sample observations but the computations take into account the randomness of the sampling weights when such weights are provided by the user 12 Allowance for sampling errors in the poverty lines specified to compute absolute and rel
13. between a Lorenz curve and a concentration curve HM kj p C kp D To compute this difference 1 From the main menu choose the item Curves gt Difference 2 Choose the different vectors and parameter values as follows Indication Vectors or parameters Status of choice Distribution 1 Distribution 2 Ranking variable y Compulsory Variable of interest yi T Compulsory Weight Variable al w2 Optional Group Variable cl c2 Optional Index of group ky ko Optional rho Pi P2 Compulsory p Pi p2 Compulsory On the first execution bar you find 1 The command Crossing to search the first intersection of the two curves If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To seek an intersection over a particular range use the command Range The command Difference to compute the difference I kj p C k2 pa 2 The command Graph to draw the difference L p C p according to p 3 The command Range to specify the range for the search of a crossing between the two curves The command also specifies the range of the horizontal axis 4 The command S Gini to compute the difference I kj p I k2 p 5 The command Covariance to compute the following covariance matrix 52 Curves DADS Cow U k 0 1 C k gt
14. data follow the next steps 12 Click on the button Paste the following window appears Ri Syntax SPSS Syntax Editor S S 5 lt Gelb 44 gt Of Fa WRITE OUTFILE C WINDOWS Bureau data3 dat TABLE ALL EXECUTE 13 Delete on the second line TABLE AII and replace it by followed by the name of vectors that you wish to save and finally by a dot g Syntax2 SPSS Syntax Editor S a S 5 lt Bl le 44 gt Of Z WRITE OUTFILE C WINDOWS Bureau datad dat chemo time EXECUTE 14 From the main menu of this last window select Run All The file that will then be saved will contain only the desired vectors of data
15. index according to the parameter If you wants to specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To compute the Atkinson index of two distributions 1 Ja 3 From the main menu choose the item Welfare and inequality gt Inequality indices gt Atkinson index In the configuration of application choose 2 for the number of distributions Choose the different vectors and parameter values as follows 16 Inequality Poverty and Social Welfare Indication Vectors or parameters Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable W w2 Optional Group Variable cl c2 Optional Index of group k ko Optional epsilon E E2 Compulsory On the first execution bar you find only one command Compute To compute the standard deviation of this index choose the option for computing with standard deviation 5 1 2 S Gini index Denoting the S Gini index of inequality for the group k by I k p and the S Gini social welfare index by k p we have u k 6 k p m OP Vaa Lo I k p E where SEPI Dph and V w Case 1 One distribution h i To compute the S Gini index of inequality for only one distribution l From the main menu choose the following item Welfare and inequality gt Inequality
16. item Curves gt concentration curve 2 Inthe configuration of application choose 1 for the number of distributions 3 Choose the different vectors and parameter values as follows 49 Curves ee DAD 3 1 Indication Variables or Status of choice parameters Variable of interest T Compulsory Ranking variable y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional rho P Compulsory p p Compulsory On the first execution bar you find e The command Compute to compute the concentration curve C k p To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the concentration curve To specify a range for the horizontal axis choose the item Graph Management gt Change range of x from the main menu e The command Range to specify the range of the horizontal axis To compute the standard deviation choose the option for computing with standard deviation Case 2 Two distributions To compute the concentration curve of two distributions 1 From the main menu choose the item Curves gt Concentration curve 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows 50 Curves RL Indication Vectors or parameters Status of ch
17. p gt Lx p Cr p Ype p IR Approach A transfer B is more IR progressive than a tax T if Cx B P gt Cx r p vpe p To reach this application 1 From the main menu choose the item Redistribution Transfer vs Tax 2 Choose the approach to be either TR or IR 3 Choose the different vectors and parameter values as follows Variables or Status of choice parameters Compulsor Compulsory Gross income X Variable of transfer B Compulsory Reo TP Commoy p gt E e Redistribution On the first execution bar you find jue The command S Gini to compute 2Ix P ICr Pp 1ICg P ICxr P 1Cx P where C p is the coefficient of concentration 2 5 The command Crossing to seek the first point at which the progressivity ranking of the tax and transfer is reversed DAD indicates the co ordinates of that first reversal and their standard deviation if the option of computing with standard deviation is chosen These co ordinates are TR Approach IR Approach rr ee ee eee C p Ly P The command Difference to compute TR Approach IR Approach Cr p Cp p 2Lx p Cx B P Cx r p The command Range to specify a range of p for the search of the first reversal of the progressivity ranking The command also allows to specify the range of the horizontal axis in the drawing of a graph The command Graph to draw the following curves as a function of p TR Approa
18. progressivity of two taxes or two transfers 3 Comparing the progressivity of a transfer and a tax 4 Estimating horizontal inequity 5 Estimating redistribution 6 Estimating a coefficient of concentration 9 1 Estimating the progressivity of a tax or a transfer Let A X be gross income B T beatax C B bea transfer 1 TR progressivity A tax T is TR progressive if Ly p Cr p gt 0 Vp p A transfer B is TR progressive if Cp p Ly p gt 0 Vp b 2 IR progressivity A tax T is IR progressive if Cy_7r p Lxy p gt 0O NDE bz A transfer B is IR progressive if Cyip p Ly p gt O Ype bz To reach this application 1 From the main menu choose the item Redistribution Tax or transfer 2 Specify if you wish to estimate the progressivity of a tax or of a transfer 3 Choose the approach to be either TR or IR 4 Choose the different vectors and parameter values as follows Redistribution o MPZ Indication Status of choice parameters Gross income Compulsor Tax transfer Compulsory Weight Variable Group Variable Index of group h Compulsory On the first execution bar you find 1 The command S Gini to compute TR Approach IR Approach Tax ICr P Ix p Ix P ICx_r P Ix P ICR P I P ICy Pp where IC p is the S Gini coefficient of concentration and 1 p is the S Gini index of inequality 2 The command Crossing to seek the first intersection of the concentrati
19. software to manage better the computer s memory Remark If the separation mark of columns is a comma the separation mark of the decimals cannot also be a comma Once those three steps are done click on button OK to confirm the information The next window appears to ask for the name and the directory of the file mssetup t CI cores J Acrobat3 Cserve Aol25i E dictionnaire Aol25ia dist apros E docal CoreJavaBook E emacs a Type Jan Files z Annuler Once the name and the directory have been selected click on the button Open Another window is opened to indicate the number of observations that is effectively loaded After the loading of the data base the editing window is opened To rename the vectors or modifying their values consult the previous section concerning the construction of a new data base with DAD 2 3 Loading a second data base As already mentioned for many applications in DAD we can use simultaneously two data bases To activate a second data base the user should load another file To activate a second data base follow these steps Introduction O DAD 3 1 1 In the main menu click on the command File and select the item Load a second file 2 The procedures to follow after this are identical to those presented for loading the first file Remark The active file in the software DAD is the last file loaded Because of this you can only edit or modify the last file that
20. to which you have copied the file jav3 1 In the following instructions we suppose that jav31 zip was put on the c drive Menu for DAD 3 1 Wed Apr 25 15 58 32 EDT 2001 programName DAD 3 1 args cp Intro_an C JAV3 1 JRE 1 1 LIB SWINGALL JAR xecFilename C JAV3 1 JRE 1 1 BIN JREW EXE The important changes appear in the last two lines For your convenience these changes have already been made in the file DAD3 1 3 Launch again DAD3 1 The software should now execute properly Introduction DAD 3 1 Ni 2 DAD and the data base A data base used in DAD is a set of vectors of data where each vector represents a specific variable The length of each vector determines the number of observations for that variable Each data base contains a set of vectors whose number of observations must be the same 2 1 Constructing a data base with DAD After opening DAD we find the following fey DAD loj x File Edit Welfare and inequality 9 Redistribution Dominance Curves Distribution A Writing field B Principal menu C Control for editing of data For the construction of a new data base with DAD it is sufficient to follow these steps 1 In the principal menu click on the command File and select the option New File A window appears in order to ask the user to indicate the following information Introduction ee Make By default the number of columns
21. vectors is equal to 3 likewise the number of lines observations equals ten It is possible to modify these numbers and to choose those corresponding to the desired new data base To confirm your choice click on the button Make new file After confirming these choices the edition window of the data takes the following form 3 q 8 8 0090600606909090 0000000000 009090090090 By defaults all the values of the new data set are initialised to zero To begin editing the new vectors follow these steps 1 Click on the cell vector 1 index 1 The colour of this cell changes to blue Introduction O DAD S 1 2 Click in the writing field Notice that the cursor begins to flicker 3 Write the new value of the cell As a general rule with DAD the decimal part should be separated by a dot 4 Press Enter Note that the selected cell is now vector 1 index 2 5 Write the value of the cell and repeat the procedure until all of the vector 1 is initialised 6 To edit another vector select the first cell of this vector and repeat steps 2 up to 5 If you want to modify the value of one cell you should follow these steps 1 Select the cell subject to modification by clicking on it 2 Click in the writing field and write the new value of the cell 3 Press Enter Remark I DAD edits the data set by page Each page contains 30 observations If you want to edit the next 30 observations you shoul
22. was loaded although you will have access to both files for making distributive comparisons 2 4 Saving a file You can save an active file on the hard disk or on a CD ROM or floppy disk The procedure is simple Begin with the command File and select the item Save File The next window appears to enquire for the name and the directory where you would like to save the file Sauvegarde Fichier ki x Dans gt C3 gt 2 a f se mssetup t 9 cores GA Cserve G dictionnaire G dist E docal CoreJavaBook C emacs gt wa o Type An Files sad Annuler After making your choice of the name and directory click on the button Save to save the active file Remark the saved file with software DAD is an ASCII file Columns are separated by spaces and the decimal part is separated by a dot 2 5 Erase a file To delete the active file click on the button File and then select the item Erase the file 2 6 Printing a file To print the active file click on the button File and then select the item Print the file 2 7 Exit the application To exit the application click on the button File and then select the item Quit Introduction O MPA 3 Modifying the data base The software DAD offers the possibility to modify the dimension of a data base and also to generate a new vector of data using logical or arithmetic operators 3 1 The addition of new column or line To add a new line a
23. where p F y is the cumulative distribution function at y For a discrete distribution let the n observations of living standards be ordered such that YI Sya SS yi Sin SS yai WE pelF yi F yii then we define Q p yj The normalised quantile is defined as Or p Q p u Case 1 One distribution To compute the quantiles of one distribution 1 From the main menu choose the item Curves gt Quantile 2 Inthe configuration of application choose 1 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional p P Compulsory 43 Curves ee DAD S 2 On the first execution bar you find e The command Compute to compute the quantile at a point p To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of the curve according to the parameter p To specify a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To compute the quantiles of two distributions l From the main menu choose the item Curves gt Quantile 2 In the configuration of application choose 2 for the number of distributions 3 Choose the d
24. 8 Redistribution O DAD 3 1 One distribution To compute the coefficient of concentration for only one distribution l From the main menu choose the following item Redistribution Coefficient of concentration 2 In the configuration of the application choose 1 for the number of distributions 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Indication Status of choice parameters Ranking variable Variable of interest Index of group On the first execution bar you find e The command Compute to compute the coefficient of concentration To compute the standard deviation of this index choose the option for computing with standard deviation e The command Graph to draw the value of the coefficient as a function of the parameter p To specify a range for the horizontal axis choose the item Graph management Change range of x from the main menu Two distributions To reach this application l From the main menu choose the item Redistribution Coefficient of concentration 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows 69 Redistribution O PPA Vectors or parameters Status of choice Distribution 1 Distribution 2 Variable of interest Compulsory 2 Weight variable 1 Optional WwW w a Compulsory Only o
25. A S A 5 aa e Jem Pa aa a SI 7 From the main menu of Excel select File Saveas 8 Indicate that the type of the file is Formatted Text Space delimited A Bureau z e m Q X Ci E Took E Poste de travail 3 Mes documents History za Yoisinage r seau B gt Mes Documents Favorites gt File name DATA 4 prn Web Folders Save as type Kab hah Ae NT 9 Follow the instructions in DAD s User s Manual to read the ASCII file intoDAD Outputting SPSS8 0 DATA to use in DAD3 1 DAD can easily read an ASCII or text file The following steps explain what can be done to transform an SPSS file into an ASCII file which can then be read by DAD 1 The following window shows an example of an SPSS data file composed of four vectors of data entitled EXPED FED NFED and CALEQ The aim is to output these vectors in an ASCII file data 4 SPSS Data Editor Of x File Edit View Data Transform Statistics Graphs Utilities Window Help fe NETE NET NET NA AA era n e a NA ross s s NA i ceso so soa r CO arsmo sso rams meta sos TO 1 sero meso soas 70 NE NE NE NE NA NA saa momo rasan aa TO NA NAGA NANA NANA DANA KA gt SPSS Processor is ready h 2 The first step consists of selecting these vectors by clicking on EXPEQ the name of the first variable maintaining pressed the right button of the mouse and slipping up to CALEQ the
26. Distributive Analysis oe Universit Laval DAD DISTRIBUTIVE ANALYSIS ANALYSE DISTRIBUTIVE USER S MANUAL by Jean Yves Duclos E mail jyves ecn ulaval ca Abdelkrim Araar E mail aabd ecn ulaval ca Carl Fortin E mail cfortin gel ulaval ca Mai 2000 Universit Laval Introduction O DAD 3 1 1 Introduction DAD is a software designed to facilitate the analysis and the comparisons of social welfare inequality poverty and equity across distributions of living standards Its features include the estimation of a large number of indices and curves that are useful for distributive comparisons as well as the provision of asymptotic standard errors to enable statistical inference The features also include basic descriptive statistics and provide simple non parametric estimations of density functions and regressions The main facilities of DAD are the 1 Estimation of indices of Poverty Watts CHU FGT S Gini normalised and un normalised or absolute and relative poverty indices with absolute and relative poverty lines Social Welfare Atkinson S Gini Atkinson Gini Inequality S Gini Atkison Entropy Atkinson Gini Redistribution progressivity vertical equity reranking and horizontal inequity 2 Decomposition of Poverty across population subgroups Inequality across population subgroups or by factor components e g by type of consumption expenditures or source of income
27. Welfare and inequality Decomposition FGT Decomposition for two groups 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Poverty line z Compulsory alpha a Compulsory Indices of the 2 subgroups separated kj ko Compulsory by In the output window you will find the following information 1 The FGT index for the whole population 2 The FGT index for each of the two subgroups 3 The difference in the indices of the two groups P 1 z a PO z a 4 The percentage difference in the contribution of the two population subgroups OPA z 0 2 P 2 250 P z3 To compute the standard deviations for these statistics choose the option computing with standard deviation 36 Inequality Poverty and Social Welfar 5 4 3 The decomposition of the S Gini index of inequality Let J components yj add up to y that is Aj Yi LY j l We can decompose the S Gini index of inequality as follows J U I p eS p j l es lj The contribution of the j component is LIC ji p Hy where IC ji p is the coefficient of concentration of the jih component and u F is its mean To perform the decomposition of the S Gini index of inequality 1 From mai
28. able w w2 Optional Group Variable cl c2 Optional Index of group k ko Optional rho Pi P2 Compulsory The first execution bar contains only one command Compute To compute the standard deviation of this index choose the option for computing with standard deviation 5 1 3 The Atkinson Gini index Denoting the Atkinson Gini index of inequality for the group k by I k e p and the S Gini social welfare index by k p we have I k p uk amp k p where H k 18 Inequality Poverty and Social Welfare ys Ga oo serene and p21 n PS p of glenn i l k p 3 gt and pel 4k and V w h i Case 1 One distribution To compute this index of inequality for only one distribution l From the main menu choose the following item Welfare and inequality Inequality indices Atkinson Gini index 2 In the configuration of the application choose 1 for the number of distributions 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable Cc Optional Index of group k Optional epsilon E Compulsory rho P Compulsory The only command on the first execution bar is Compute which computes the Atkinson Gini index To comp
29. arameter values as follows On the first execution bar you find Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional Poverty line z Compulsory p p Compulsory e The command Compute to compute g p z To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of g p z as a function of p To specify a range for the horizontal axis choose the item Graph Management Change range of x from the main menu 45 Curves ee DAD S 2 To compute the standard deviation choose the option for computing with standard deviation Case 2 Two distributions To reach the application for two distributions l From the main menu choose the item Curves poverty gap Quantile 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Vectors or parameters Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable y w2 Optional Group Variable cl c2 Optional Index of group ki ko Optional Poverty line z Z2 Compulsory p pi p2 Compulsory On the first execution bar you find 1 The command Crossing to
30. ative poverty indices DAD s environment is user friendly and uses menus to select the variables and options needed for all applications The software can load simultaneously two data bases can carry out applications with only one data base or two and can allow for dependence or independence of data bases and vectors of living standards in computing standard errors on differences in indices and curves Introduction DAD 3 1 The data bases can be built with the software or can be loaded from a hard disk or a floppy or CD ROM driver The data bases can be edited new observations can be added and new vectors of data can be generated using arithmetical or logical operators 1 1 Features of version 3 1 of DAD gt More effective data handling resulting in better memory use and increased capacity to deal with large data bases gt Optimised algorithms for processing data yielding a much increased speed of execution for several computations gt Provision of a new additional output window which adds significantly to the amount of information provided and results in a higher quality of output display gt Addition of a few options for the estimation of indices and curves Introduction l DAD 3 1 1 2 Installation and required equipment DAD is conceived to run on operating systems Windows 95 98 and NT A PC of 100MHz or more is also required The steps for installation of this software are as follows DAD Version 3 1 Di
31. ch IR Approach Cr p Cp p 2Lx p Cx B P Cx r p 65 Redistribution O 9 4 Horizontal inequity A tax or a transfer T causes reranking and is therefore horizontally inequitable if Tax Cy r p Ly r p gt 0 for at least one value of pe lov Transfer Cy 7 p Ly 7 p gt O for at least one value of pe lo z To reach this application l From the main menu choose the item Redistribution Horizontal inequity 2 Specify if you are using a tax or a transfer 3 Choose the different vectors and parameter values as follows parameters Gross income X Tax transfer Weight variable w Group variable c Index of group of k Optional interest ho Compulsory On the first execution bar you find 1 The command S Gini to compute Tax Ix r P ICx r f Ixg P ICx4g P 2 The command Difference to compute Tax Cxy r p Lx r p Cy pl p Lx B p Redistribution KN DADS1 3 The command Range to specify the range of the horizontal axis in the drawing of a graph 4 The command Graph To draw the following curves as a function of p Tax Cy r P Lx r Pp Cx B P Ly g D 9 5 Redistribution A tax or a transfer T not caused a redistribution if Tax Ly r p Lx p gt 0 vpe p Transfer Ly p p Lx p gt 0 Yp p To reach this application 1 From the main menu choose the item Redistribution Redistribution 2 Specify if you are using a tax or a transfer 3
32. d click on the button You can also indicate a page number and click on the button to edit this page Remark 2 By default the name of the different vectors is vector 1 vector 2 etc To give anew name to a vector follow these steps 1 Click on the cell Vector i 2 Delete the text Vector i and write the new name of this vector 2 2 Loading an ASCII data base To load an ASCII data file you should click on the command File select the command Load a file and choose the item ASCII file The following window appears asking for some information concerning the data file E Configuration D x Separation mark of columns Separation mark of decimal qot 0 i Number of columns 4 Number of lines Default Configuration OK Introduction O DADS 1 1 In the field Separation mark of columns indicate the type of separation between the different columns of the data base If the type of separation is not one or several spaces then click the button 7 for selecting another type of separation won non such as comma semi colon or colon mom 2 In the field Separation mark of decimal indicate the type of separation between the integer value and the part of the decimals 3 By default the number of columns is set to 4 but you must indicate the exact number of columns of the ASCII data file 4 Indicating the number of lines is optional but indicating can help the
33. d inequality Inequality indices gt Entropy index 2 In the configuration of the application choose 1 for the number of distributions 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional theta 0 Compulsory In the first execution bar you find the following choices e The command Compute computes the Generalised Entropy index To compute the standard deviation of this index choose the option for computing with the standard deviation 21 Inequality Poverty and Social Welfare e The command Graph to draw the value of index according to the parameter 0 to specify such a range for the horizontal axis choose the item Graph Management gt Change range of x from the main menu Case 2 Two distributions To calculate the Generalised Entropy index for two distributions l From the main menu choose the item Welfare and inequality Inequality indices Entropy index 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Vectors or parameters Status of choice Distribution 1 Dis
34. does not include in the ASCII file the name of the variables that you have saved You can add these names by editing the saved file with a text editor such as WordPad Write on the first line the names of the vectors and save the file again it is useful to have the names of variables before reading them in DAD 9 Follow the instructions in the User s Manual of DAD3 1 to download the ASCII file in DAD 10 When the SPSS database contains a high number of vectors or columns it is useful to save just those that will be useful in DAD To save just a few SPSS vectors of data follow the next steps 11 Click on the button Paste the following window appears Ri Syntax2 SPSS Syntax Editor Iof x File Edit View Statistics Graphs Utilities Bun Window Help siale gt mb aa gt zl WRITE OUTFILE C WINDOW S Bureau data4 dat TABLE ALL EXECUTE 8 SPSS Processor is ready A 12 Delete on the second line TABLE AII and replace it by followed by the name of vectors that you wish to save and finally by a dot Bs Syntax2 SPSS Syntax Editor sjala lt mp al _ OI Fal WRITE OUTFILE C WINDOWS Bureau datad dat exped caleg EXECUTE 13 From the main menu of this last window select Run gt All The file that will then be saved will contain only the desired vectors of data Outputting SPSS10 1 DATA to use in DAD3 1 DAD can easily read an ASCII or text file The following s
35. e computation of inequality indices Indicates the name of the variable used to compute the index of inequality indicates the weight variable Indicates the vector that contains group indices in this application the choice of such a vector is optional Indicates the selected group index by default its value equals one Indicates to the user the names and the values of the parameters The parameter names typically refer to the definition of indices and curves e g epsilon is the inequality aversion parameter in the Atkinson class of indices Indicates the options selected for this execution 3 The third and last block contains the results of the execution gt Index value gt Indicates the value of the Atkinson index of inequality The value within parentheses indicates the standard deviation for this index One can select a number of decimal values for the printing of results To do this choose the command Option gt Decimal number The following window appears Choose the desired number of decimals and confirm the choice by clicking on the button OK gt Number of digit iof x 73 The edition and printing of results E 7V When another execution is performed a new window appears with the information concerning this new execution One can return to and edit the information on the previous executions by clicking on the button lt lt for previous executions gt gt and similarly on l
36. e window of inputs Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional Poverty line z Compulsory rho P Compulsory On the first execution bar you will find Case 2 Two distributions To compute the S Gini index with two distributions The command Compute to compute the S Gini index To compute the standard deviation choose the option for computing with standard deviation The command Graph to draw the value of index according to a range of poverty lines z To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu l From the main menu choose the item Welfare and inequality Poverty indices S Gini index 2 Inthe configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Vectors or parameters Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable w w2 Optional Group Variable cl e2 Optional Index of group ky ko Optional Poverty lines z Z2 Compulsory rho Pi P2 Compulsory 28 Inequality Poverty and Social Welfare The first execution bar contains the command Compute To compute
37. egression The gaussian kernel regression of y on x is as follows Li K y yj 7 Px LiK y yi 9 P ylx where K t 1 2m exp 1 2 t To reach this application l From the main menu choose the item Distribution gt Non parametric regression 2 Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Exogenous Variable X x Compulsory Endogenous Variable Y y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional Level of X or p y Compulsory Smoothing parameter p Optional On the first execution bar you find Remark The option Level vs Percentile allows the estimation of the expected value of y either at a level of x or at a p quantile for x such that F x p where p is the percentile value for x e The command Compute to compute ylx To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw ylx as a function of x To specify a range for the horizontal axis choose the item Graph management Change range of x from the main menu e The command Range to specify the range of the horizontal axis 59 Redistribution O DADS1 9 Redistribution This section regroups the following applications l Estimating the progressivity of a tax or a transfer 2 Comparing the
38. execution bar contains the command lt Compute gt To compute the standard deviation of this index choose the option for computing with standard deviation 4 To compute the normalised index choose this option in the window of inputs 5 2 2 The Watts poverty index The Watts poverty index PW k z for the population subgroup k is defined as 25 Inequality Poverty and Social Welfare E wh lost y 2 PW k z n k Lwi i where z is the poverty line and x max x 0 Case 1 One distribution To compute the Watts index l From the main menu choose the item Welfare and inequality Poverty indices Watts index 2 Inthe configuration of application choose 1 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional Poverty line z Compulsory In the first execution bar you will find e The command Compute to compute the Watts index To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of index according to a range of poverty lines z To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Tw
39. h a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To compute the CHU index with two distributions 1 From the main menu choose the item Welfare and inequality Poverty indices gt CHU index 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Vectors or parameters Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable wi w2 Optional Group Variable cl c2 Optional Index of group ki ko Optional Poverty lines z Z2 Compulsory epsilon E E2 Compulsory The first execution bar contains the command Compute To compute the standard deviation choose the option for computing with standard deviation 30 Inequality Poverty and Social Welfare 5 3 The social welfare indices DAD can compute the following types of social welfare indices 1 Atkinson index 2 S Gini index 3 Atkinson Gini index 5 3 1 The Atkinson social welfare index Case 1 One distribution To compute the Atkinson index of social welfare for one distribution 1 In the configuration of the application choose 1 for the number of distributions Indication Variables or Status of choice parameters Variable of interes
40. if P 6 a gt P G a V teko loras These are stochastic dominance curves at order s or FGT curves with a s 1 This section checks for the points at which there is a reversal of the dominance conditions Said differently it provides the crossing points of the dominance curves that is the values of and P G a for which P G a P G a when sign P 6 n50 P C n a sign P 6 15 P C 1 for a small n The crossing points of can also be referred to as critical poverty lines To check for the crossing points of the dominance curves of two distributions l From main menu choose the item Dominance Poverty Dominance 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Indication Vector or parameter Status of choice Distribution 1 Distribution 2 Variable of interest yi y 2 Compulsory Weight Variable w we Optional Group Variable c c2 Optional Index of group k ko Optional S Compulsory 40 Dominance ee DADS On the first execution bar you will find l Compute to provide the critical poverty lines and the crossing points of the sample dominance curves When the option with STD is specified the standard deviation on the estimates of the critical poverty lines and on the estimates of the crossing points of the FGT curves are also given
41. ifferent vectors and parameter values as follows Indication Vector or parameter Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable iyi w Optional Group Variable cl c2 Optional Index of group ki ko Optional p Pi p2 Compulsory On the first execution bar you find 1 The command Crossing to check if the two quantile curves intersect If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To seek an intersection over a particular range of p use the command Range to specify this range 2 The command Difference to compute the difference Oj p Q2 p2 44 Curves 3 The command Graph to draw the difference Q p Q gt p along values of the parameter p 4 The command Range to specify the range for the search of a crossing between the two curves The command also specifies the range of the horizontal axis 7 2 Poverty gap quantile The poverty gap quantile at a percentile p is amp p z z Q p Case 1 One distribution To compute the poverty gap quantile for one distribution l From the main menu choose the item Curves Poverty gap quantile 2 Inthe configuration of application choose 1 for the number of distributions 3 Choose the different vectors and p
42. indices gt S Gini index 2 In the configuration of the application choose 1 for the number of distributions 3 After confirming the configuration the application appears Choose the different vectors and values of parameters as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional rho P Compulsory 17 Inequality Poverty and Social Welfare Two choices appear on the first execution bar e The command Compute to compute the S Gini index To compute the standard deviation of this index choose the option for computing with standard deviation e The command Graph to draw the value of the index according to the parameter p To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To reach the S Gini application with two distributions l From the main menu choose the item Welfare and inequality Inequality indices S Gini index 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Vectors or parameters Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Vari
43. lity gt The value in parentheses indicates the standard deviation of this index The second Window of results can be activated from the main menu with the command Option gt Advanced results by default this option is initially activated Advanced Result iof x Options The Atkinson index B Session Date Sun May 10 10 04 52 EDT 1998 Execution Time 0 55 sec File Name beninl dat OBS 1612 Variable of interest Expend Weight Variable Without weigths Group Variable No selection Index of Group 1 Parameters epsilon 0 5 Options With STD Result Index Value 0 11064447 0 00752240 lt lt Finish gt Caleul 1 1 The window contains the name of the application and the results of the execution We can divide these results displayed in the last figure in three blocks 1 General information this first block is composed of gt Session date Indicates the time at which the results were computed gt Execution time Indicates the computation time 72 The edition and printing of results O DAD3 1 2 The block of inputs composed by gt File name gt OBS gt Parameter used gt Variable of interest gt Variable of weight gt Group variable gt Index of group gt Parameter gt Options indicates the name of the file that is used indicates the number of observations indicates the value of the parameter used for this computation see also the illustrations for th
44. n menu choose the item Welfare and inequality Decomposition gt S Gini decomposition 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Weight Variable w Optional rho P Compulsory Indices of variables Index 1 index2 Compulsory separated by Remark In the input window note that vectors are coded with numbers To indicate the components that add up to y enter the code of these vectors in the field Indices of variables separated by The following results appear in the output window 37 Inequality Poverty and Social Welfare 1 The S Gini index for y 2 The coefficients of concentration for every component of y 3 The ratio u 7 u for every component of y 4 The contribution for every component 5 4 4 The decomposition of the Generalised Entropy index of inequality The Generalised Entropy index of inequality can be decomposed as follows 0 K Oz gt fe Mk 6 1 8 k 1 u y where k isthe proportion of the population found in subgroup k u k isthe mean income of group k 1 k is the inequality within group k 1 0 is population inequality if each individual in subgroup k is given the mean income of subgroup k u k To perform the decomposition of the entropy index l From the main menu choose the item
45. name of the last variable data 4 SPSS Data Editor iof x File Edit View Data Transform Statistics Graphs Utilities Window SPSS Processor is ready 3 From the main menu of SPSS select DATA Templates The following window appears Template DEFAULT kd OK gt Template Description amp pply J Close Name DEFAULT M Type H N elp Type Comma8 7 MV Value labels Missing Values None M Missing values Alignment Right Column format Define Template i Missing Values eet Value Labels Column Format Remove 4 Click on the button type When the following window appears choose the format Numeric Width 20 or more Decimal Places 4 or more After this click on the button Continue and Ok Define Variable Type DEFAULT eeeeeee 5 By clicking on the button OK the SPSS window takes the following form data 4 SPSS Data Editor f e E a CO o o a e NANG al ral al a al E E al al El EA KIE 6 From the main menu of SPSS select File gt Save as Dans Z Bureau kd E c E Poste de travail Mes documents 3 data4 dat al Voisinage r seau 3 data44 dat C Dad 2 dd dat T ere 2 ddd dat Nom data 4 dat Type Fixed ASCII dat x Paste Jv Write variable names to spreadsheet Annuler 7 Indicate that the type of the file is Fixed ASCII dat 8 Note SPSS
46. ne command appears on the first execution bar Compute to compute the concentration coefficients and their difference for each of the two variables of interest To compute the standard deviation of those estimates choose the option for computing with standard deviation 70 The edition and printing of results US 10 The edition and printing of results Results appear in two distinct windows The first window forms part of the principal application as indicated in the next figure by Windows of outputs E Function to compute 1 nso I ormpte Trae Rage a seve int Resetsessin The Atkinson index File name benin1 dat Parameter used 0 5 Variable of Interest Expend OBS 1612 0 11064447 0 00752240 Windows of outputs The information provided in this window is 1 The name of the application The Atkinson index in this example 2 The block of inputs composed by gt File name indicates the name of the file that is used gt Parameter used indicates the value of the parameter used for this computation see also the illustration section for the computation of inequality indices gt Variable of interest Indicates the name of the variable used to compute the index of inequality The edition and printing of results MOT gt OBS indicates the number of observations 3 The block of results composed by gt Index value Indicates the value of the Atkinson index of inequa
47. new observation to the data base choose the command Edition and select the item Insert a new line The values on this new line are initialised to zero by default As explained before you can edit these new values if you wish You can add a new column by choosing the command Edition and select the item Insert a new column The values of this new column are set to zero by default and can also be edited 3 2 Generating new vectors It is possible that the user needs to generate a new vector in the active data base The following steps describe the necessary procedures for this l In the main menu choose the command Edition and select the item Edition of columns The next window appears for the specification of the type of operation that you wish to apply A Operation t Type of operation Series 1 Series 2 v Series 1 Vector 1 Series 2 Vector 1 Number 10 Results Vector 1 Execution D B C 1 Choose the type of operation you need to carry out by clicking on the icon A 2 Select the vectors to be used to generate the new vector by clicking on the icons B and C 3 If a number is used to generate the new vector write its value after Number By default this number is set to 10 4 Select the vector of results by clicking on the icon D Introduction O DADS 1 Remark If the vector of results has to be stored in a new vec
48. o compute the standard deviation choose the option for computing with standard deviation Case 2 Two distributions To compute the Atkinson Gin social welfare with two distributions 4 From the main menu choose the item Welfare and inequality Social welfare indices gt Atkinson Gini 5 In the configuration of application choose 2 for the number of distributions 6 Choose the different vectors and parameter values as follows Indication Vector or parameter Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable wl w2 Optional Group Variable cl c Optional Index of group ki ko Optional Pi Po Compulsory epsilon E E2 Compulsory 34 Inequality Poverty and Social Welfare The first execution bar contains the command Compute To compute the standard deviation choose the option for computing with standard deviation 5 4 The decomposition of inequality and poverty DAD can perform the following types of decomposition l The decomposition of the FGT poverty index across several population subgroups 2 A more detailed decomposition of the FGT poverty index across two specific population subgroups 3 The decomposition of the S Gini index of inequality across sources of income types of expenditures etc 4 The decomposition of the generalised entropy index across population subgroups 66 components
49. o distributions To compute the Watts index with two distributions l From the main menu choose the item Welfare and inequality Poverty indices gt Watts index 2 In the configuration of application choose 2 for the number of distributions 26 Inequality Poverty and Social Welfare 3 Choose the different vectors and parameter values as follows Indication Vector or parameter Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable l T Optional Group Variable cl e2 Optional Index of group ky ko Optional Poverty lines z Z2 Compulsory The first execution bar contains the command Compute To compute the standard deviation choose the option for computing with standard deviation 5 2 3 The S Gini poverty index The S Gini poverty index P k z p for the population subgroup k is defined as P k z p z n r a i n k z y and Mh wh IV F i where z is the poverty line and x max x 0 Case 1 One distribution To compute the S Gini index l From the main menu choose the item Welfare and inequality Poverty indices S Gini index 2 Inthe configuration of application choose 1 for the number of distributions 3 Choose the different vectors and parameter values as follows 27 Inequality Poverty and Social Welfare 4 To compute the normalised index choose this option in th
50. oice Distribution 1 Distribution 2 Ranking variable yi y Compulsory Variable of interest T T2 Compulsory Weight Variable wl w Optional Group Variable cl c2 Optional Index of group ky ko Optional rho Pi P2 Compulsory p pi p2 Compulsory On the first execution bar you find 1 The command Crossing to search the first intersection of the curves If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To seek an intersection over a particular range use the command Range 2 The command Difference to compute the difference in the concentration curves 3 The command Graph to draw the difference in the curves as a function of p 4 The command Range to specify the range for the search of a crossing between the two curves The command also specifies the range of the horizontal axis 5 The command S Gini to compute the difference IC kj P IC k2 Pp 6 The command Covariance to compute the following covariance matrix Cov C k 0 1 C2 k2 0 1 Cov C7 k7 0 1 C2 k2 0 2 sere Cov C7 k7 0 1 Co k251 Cov C7 k7 0 2 C2 k2 0 1 Cov C7 k7 0 2 C2 k2 0 2 Cov Cjl kj l C2 k2 0 1 Cov Cjl kj l C2 k2 0 2 DAN Cov C k l C2 k2 1 51 Curves ee DAD 31 7 5 The distance between two curves This application computes the difference
51. on and Lorenz curves DAD indicates the co ordinates of that first intersection and their standard deviation if the option of computing with standard deviation is chosen 3 The command Difference to compute pO TR Approach IR Approach Lx p Cr P Cx Lx P Cpl p Lx p Cx p p Lx p 4 The command Range to specify a range of p for the search of the first intersection between the two curves The command also allows to specify the range of the horizontal axis in the drawing of a graph 5 The command Graph to draw the following differences as a function of p PO TR Approach IR Approach Lx p Cr P CP L Col p Ex MORAG 61 Redistribution O DAD 3 1 9 2 Comparing the progressivity of two taxes or transfers Let A X be gross income B T1 and T2 be two taxes C Bl et B2 be two transfers 1 TR Approach T1 is more TR progressive than T2 if Cr2 p Cr p gt 0 Ype pil Bl is more TR progressive than B2 if Cgpi p Cp2 p gt 0 Ype p 2 IR approach T1 is more IR progressive than T2 if Cy r p Cx r2 p gt 0 NDE pl Bl is more IR progressive than B2 if Cy4p p Cyx p2 p gt O NDE pb To reach this application l From the main menu choose the item Redistribution Transfer Tax vs Transfer Tax 2 In front of the indications Tax Transfer 1 and 2 specify the two vectors of taxes or transfers 3 Choose the approach to be either TR or IR 4 Choose the differen
52. on i belongs The sampling weights are defined as e wew if c k wk 0 if c k where k represents a population subgroup 5 1 1 The Atkinson index Denote the Atkinson index of inequality for the group k by I k e it can be expressed as follows LA k k Li Yi ngja j MSCS where u k _ ji LW i l Lw op gt ife l ande20 k 4 1 n W i l P wihin y gt ife 1 k i l i Exp 15 Inequality Poverty and Social Welfare Case 1 One distribution If you wish to compute the Atkinson index of inequality for only one distribution follow these steps 1 From the main menu choose the following items Welfare and inequality Inequality indices Atkinson index In the configuration of the application choose 1 for the number of distributions After confirming the configuration the application appears Choose the different vectors and values of parameters as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional epsilon E Compulsory In the first execution bar you find the following two choices The command Compute to compute the Atkinson index If you also want the standard deviation of this index choose the option for computing with a standard deviation The command Graph to draw the value of the
53. pulsory alpha a Compulsory 4 To compute the normalised index choose that option in the window of inputs On the first execution bar you find e The command Compute to compute the FGT index To compute the standard deviation of this index choose the option for computing with standard deviation 24 Inequality Poverty and Social Welfare e The command Graph1 to draw the value of the index as a function of a range of poverty lines z To specify the range and the horizontal axis choose the item Graph Management Change range of x from the main menu e The command Graph2 to draw the value of FGT ee as a function of the parameter a To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To compute the FGT index with two distributions l From the main menu choose the item Welfare and inequality Poverty indices gt FGT index 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Vector or parameter Status of choice Distribution 1 Distribution 2 Variable of interest yi y2 Compulsory Weight Variable w w2 Optional Group Variable cl e2 Optional Index of group ky ko Optional Poverty lines z Z2 Compulsory alpha 04 04 Compulsory The first
54. rst intersection of the curves If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To seek an intersection over a particular range use the command Range 2 The command Difference to compute the difference L kj py L k2 p2 3 The command Graph to draw the difference Lj k p In ky p as a function of p 48 Curves 1 DAD 3 1 4 The command Range to specify the range for the search of a crossing between the two curves The command also specifies the range of the horizontal axis 5 The command S Gini to compute the difference Z kj P 1 k2 p 6 The command Covariance to compute the following covariance matrix p g Cov L k1 0 1 Lo k2 0 1 Cov L k1 0 1 Lo k2 0 2 Cov L k1 0 1 L gt k2 1 Cow L k1 0 2 Lo k2 0 1 Cov L k 0 2 Lo k2 0 2 Cov Lj kj 1 Lal ko 0 1 Cov Ly kj 1 Lal ko 0 2 Cow Ljl kj 1 Lal ko l 7 4 The concentration curve The concentration curve for the variable T ordered in terms of y at p and for a population subgroup k is wT IO lt O k p C k p wT i l where I y lt Q k p 1 if y lt Q k p and O otherwise Q k p is the p quantile of y for the subgroup k Case 1 One distribution To compute the concentration curve for one distribution l From the main menu choose the
55. s Variable of x Compulsory interest Variable of y Compulsory interest Weight Variable w Optional Group Variable c Optional Index of group k Optional Parameter x Compulsory Parameter y Compulsory Smoothing a Optional parameter On the first execution bar you find e The command Compute to compute the estimate of the joint density function To compute the standard deviation choose the option for computing with standard deviation 8 4 The distribution function To reach this application 1 From the main menu choose the item Distribution gt Distribution function 2 Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of y Compulsory interest Weight Variable w Optional Group Variable c Optional Index of group k Optional Parameter y Compulsory On the first execution bar you find e The command Compute deviation to compute the estimate of the distribution function To compute the standard deviation choose the option for computing with standard 58 Distribution ee DADHI e The command Graph to draw the distribution function according as a function of y To specify a range for the horizontal axis choose the item Graph management Change range of x from the main menu e The command Range to specify the range of the horizontal axis 8 5 Non parametric r
56. search the first intersection of the curves If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To seek an intersection over a particular range use the command Range 2 The command Difference to compute the difference g z7 P1 82 Z2 P2 3 The command Graph to draw the difference g z p g7 Z p as a function of p 4 The command Range to specify the range for the search of a crossing between the two curves The command also specifies the range of the horizontal axis 7 3 Lorenz curve and generalised Lorenz curve The Lorenz curve at p for a population subgroup k is given by 46 Curves A DAD 3 1 E wiy 1O lt 0 p Lik p n k wry ivi i l where J y lt Q k p 1 if y lt Q k p and O otherwise Q k p is the p quantile of the subgroup k The generalised Lorenz curve at p for a population subgroup k is GL k p U L k p Remark The application for the Lorenz curve is similar in structure to the one for the generalised Lorenz curve Case 1 One distribution To compute the Lorenz curve for one distribution 1 From the main menu choose the item Curves gt Lorenz curve 2 Inthe configuration of application choose 1 for the number of distributions 3 Choose the different vectors and parameter values as follows
57. standard deviation TOBA OAMS The window is made of two windows the window of inputs and the window of outputs with two execution bars B and C The execution bar B includes commands specific to the application and the execution bar C includes commands concerning the edition of results The option at icon E allows you to specify a weighting vector in order to weight your observations The options represented by icons F and G allow you to compute an estimate for one specific group or sub sample or sub vector The following example illustrates those different options 12 Introduction 4 2 Example Suppose that you wish to compute the mean of a vector of a variable y with yj denoting the i observation of y We call the vector to be used the variable of interest The following table indicates the observations of y for a sample of ten households The vector w weighting variable is the weight to be these observations We can also assign to each of these observations a code c that indicates the subgroup of the population to which the i observation belongs For example code 1 may indicate that households live in town V1 and code 2 that they live in town V2 Observation yj Cj Ww Variable of interest Variable Weighting i of groups variable 1 500 1 3 2 200 2 1 3 300 1 1 4 1000 1 2 5 700 2 3 6 450 1 1 7 300 1 1 8 200 2 3 9 300 2 2 10 400 1 1
58. stributions 1 File for distribution 1 File for distribution 2 New File New File Configuration OK Each data base represents one distribution Generally you should indicate the following information l The number of distributions 2 The name of the file representing the first distribution 3 The name of the file representing the second distribution 4 When two distributions are to be used you should indicate if the two distributions represent dependent or independent samples Confirm your choice by clicking on the button Confirm the configuration Once the choice is confirmed you can reach the desired application 11 Introduction DAD _ O Xx Welfare and Graph inequality Donginance Redistribution Curves Distribution Management The name of the application The window of inputs F D Variable of interest Bal E Weighting variable Without weight BA Variable otarops emen TO B pee Command 1N Command 2 Etc Delete Print Save Load Window of outputs STD Standard Deviation Main menu First bar of execution Second bar of execution Choice of variable of interest Choice of weighting vector Choice of vector for the group indices Index value for the desired group Option to compute with or without
59. stributive Analysis a a E E AAT ETT EE Ampere aaa a T Pahna Ba Tom dnih rasamu dara la ores pala ariii Arer Pr biota 1 Insert the CD ROM that contains the DAD installation file and click on the icon Install The following window appears Click on the button continue and specify the installation directory Remark You must choose the button Yes when the following message appears The object of this message concerns the software compiler but not the software DAD itself 3 Warning X This installer is for in house evaluation on Distribution violates the J Express licens Did you create this installation package es we 2 At the end of the procedure of installation you can run this software like any other programs by clicking on the button Start and selecting item Program gt DAD Distributive Analysis Important remark If after having installed DAD3 1 you cannot launch the software it is probably because you do not have the appropriate version of JDK JAVA Development Kit installed on your computer To resolve this problem follow these steps 1 Copy the file jav31 zip on your disk decompress it and extract it onto the drive CA This should create a directory c jav3 1 jre and install JDK files 2 Edit the file DAD3 1 after installing DAD3 1 this file is located in the directory C Program Files DADIN Jexpress as follows this will specify the directory
60. t lt to view the output of subsequent executions To print these results choose from the main window the command Option gt Print session The printing window appears just choose the name of printer and confirm by clicking on the button OK Impression FLexmark Optra 5 1650 74 Outputting Excel DATA to use in DAD3 1 DAD can easily read an ASCII file The following steps explain how to transform an excel file into an ASCII file which can then be read by DAD 1 The following window shows an example of an Excel data file composed of four vectors columns of data entitled EXPED FED NFED and CALEQ 1006 07 499 12 196 43 i 1562 76 710 65 282 65 2553 91 912 69 263 49 1378 83 5031 95 1511 31 3620 64 2975 6 3523 01 1128 57 2394 44 5533 38 564 3 223 05 340 45 2773 49 407 66 147 96 339 7 1114 78 136 54 2527 45 2 Inthe first step select the vectors from A to D by clicking on A maintaining pressed the right button of the mouse and slipping up to D A Ed Microsoft Excel Data 4 a G File Edit view Insert Format Tools Data Window Help Os SRY Be Jas NGO The following window appears Indicate a column width equal to 16 or more By clicking on the button OK the following Excel window takes the following form Ed Microsoft Excel Data 4 OF x File Edit view Insert Format Tools Data Window Help la x DGHH EDDY BEN err 4 we PAT EXPEQ A B a bd MANAN NA DAT
61. t vectors and parameter values as follows parameters Gross income Compulsor Tax transfer 1 Compulsory Group Variable c Optional tho Compulsory po Compulsory 62 Redistribution o DAD3 1 On the first execution bar you find 1 The command S Gini to compute TR Approach IR Approach ICr P ICra P ICx 12 P 1Cx r1 P IC p2 P 1IC BI P IC y4R2 P ICy pi P where IC p is the S Gini coefficient of concentration 2 The command Crossing to seek the first intersection of the two concentration curves DAD indicates the co ordinates of that first intersection and their standard deviation if the option of computing with standard deviation is chosen 3 The command Difference to compute TR Approach IR Approach Tax Cr2 Pp Cri PD Cy _71 P Cx_r2 P Gaul p Cant E a mi 4 The command Range to specify a range of p for the search of the first intersection between the two curves The command also allows to specify the range of the horizontal axis in the drawing of a graph 5 The command Graph To draw the following curves as a function of p TR Approach IR Approach Tax Cr2 p Crif p Cx r P Cx r2 P Cpg p Cp2 p Cx4BI P Cx B2 P 63 Redistribution O PA 9 3 Comparing the progressivity of a transfer and of a tax Let A X be gross income B T bea tax C B a transfer TR Approach The transfer B is more TR progressive than a tax T if Cpl p Lx
62. t y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional epsilon E Compulsory On the first execution bar you will find The command Graph parameters To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu From the main menu choose the following item Welfare and inequality Social welfare indices Atkinson index After confirming the configuration the application appears Choose the different vectors and parameter values as follows The command Compute to compute the Atkinson index To compute the standard deviation choose the option for computing with standard deviation to draw the value of index according to a range of 31 Inequality Poverty and Social Welfare Case 2 Two distributions To compute the Atkinson with two distributions l From the main menu choose the item Welfare and inequality Social welfare indices gt Atkinson index 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Vector or parameter Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable W w2 Optional Group Variable cl c2 Optional Index of group ki ko Optional epsilon E E gt Compulsory
63. teps explain what can be done to transform an SPSS file into an ASCII file which can then be read by DAD 1 The following window shows an example of an SPSS data file composed of four vectors of data entitled chemo time and status The aim is to output these vectors in an ASCII file sa SPSS Data Editor tS 5 gt ele 44 Er aE 1 00 F900 E a 100 100 1 00 1 00 l 100 23 00 100 1 00 1 00 1 00 keanaan zy p 5 5 5 2 There are two windows in SPSS10 1 that represent the data The first window activated witch the option Data View see the green arrow contain the data at that time the second window activated by the option Variable View see the blue arrow contain information concerning variables of the data as shown in the following window t DPT Data Liiu Harane B fa Piarre ja Tima farke None Kurang u Serius 00 Censoeed po 2 In column lt TYPE click on the first cell after this click on the small gray square the following window appears sa SPSS Data Editor Yariable Type LJ S J S eu 3 Choose the width of the column for example 20 and the number of decimals for example 4 Select the dot as such as a decimal separator and click on the button OK Le aim of this procedure is to format the data before saving them in ASCII format 4 Repeat steps 2 and 3 for the remaining variables
64. the standard deviation choose the option for computing with standard deviation 4 To compute the normalised index choose this option in the window of inputs 5 2 4 The Clark Hemming and Ulph CHU poverty index The poverty index P k z for the population subgroup k is defined as P IN I Ewo ga E if 1 and 20 Lw P k z A n k xk Lj inyi zZ exp 1 if e l k Lw i Y f YSZ where z is the poverty line and y z otherwise Case 1 One distribution To compute the CHU index l From the main menu choose the item Welfare and inequality Poverty indices gt CHU index 2 In the configuration of application choose 1 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional Poverty line z Compulsory epsilon E Compulsory 29 Inequality Poverty and Social Welf 1 4 To compute the normalised index choose this option in the window of inputs On the first execution bar you will find e The command Compute to compute the CHU index To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of index according to a range of poverty lines z To specify suc
65. tor start by adding a new column Denote vector by S1 i and vector 2 by 2 1 The following table then presents the type of operations available and their results Type of operation Results Series 1 Series 2 S1 i S2 i Series 1 Series 2 S1 i S2 Series 1 Series 2 S1 i S2 i Series 1 Series 2 S1 i S2 i Series 1 Number S1 i Number Series 1 Number S1 i Number Series 1 Number S1 i Number Series 1 Number S1 i Number Exp Series 1 Exp S1 i Log Series 1 Log S1 i Series 1 Series 2 1 if S1 i S2 i otherwise 0 Series 1 Number 1 if S1 i S2 i otherwise 0 Series 1 gt Series 2 1 if S1 i gt S2 i otherwise 0 Series 1 gt Number 1 if S1 i gt S2 i otherwise 0 Series 1 lt Series 2 1 if S17 lt S2 i otherwise 0 Series 1 lt Number 1 if S1 i lt S2 i otherwise 0 5 Finally click on the button Execution to generate the new vector 10 Introduction i 4 Applications in DAD 4 1 Introduction to applications Remember that DAD can activate one or two data bases Once a data base is activated the user can then call different applications of DAD Before you reach those applications however you must indicate how many data bases are to be used in the application and which ones This is done through the following window E Configuration of distributions Number of di
66. tribution 2 Variable of interest yi y Compulsory Weight Variable wi 72 Optional Group Variable a 2 Optional Index of group ki ko Optional theta 9 05 Compulsory The first execution bar contains the command lt Compute gt To compute the standard deviation of this index choose the option for computing with standard deviation 22 Inequality Poverty and Social Welfar 5 2 Poverty indices DAD can compute the following four types of poverty indices 1 FGT index 2 Watts index 3 S Gini index 4 CHU index DAD offers four possibilities for fixing the poverty line l A deterministic poverty line set by the user 2 A poverty line equal to a proportion of the mean 3 A poverty line equal to a proportion m of a quantile Q p 4 An estimated poverty line that is asymptotically normally distributed with a standard deviation specified by the user For the first possibility just indicate the value of the deterministic poverty line in front of the indication Poverty line For the three other possibilities proceed as follow e Click on the first execution bar on the button Computation of line e Choose one of the three following options a b c Proportion of mean the proportion m should be indicated Proportion of quantile indicate the proportion m and the quantile Q p by indicating the desired percentile p of the population Estimated line indicate the estimate of the poverty line z and i
67. ts standard deviation stdz To compute the poverty line in the case of two distributions e Click on the first execution bar on the button Computation of line e Choose one of these three following options a b c Proportion of mean indicate the proportions mjand mp for the distributions 1 and 2 respectively Proportion of quantile indicate the proportions m and m3 and specify the desired quantiles by indicating the percentiles of population pj and p gt Estimated line indicate the estimates of the poverty lines z and zz and their standard deviations stdz and stdz 23 Inequality Poverty and Social Welfare 5 2 1 The FGT index The Foster Greer Thorbecke poverty index FGT P k z a for the population subgroup k is as follows 1 n P k 2 0 Ew z Yi m yi i i where z is the poverty line and x max x 0 The normalised index is defined by P k z 0 P k za z Case 1 One distribution To compute the FGT index l From the main menu choose the item Welfare and inequality Poverty indices gt FGT index 2 In the configuration of application choose 1 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable c Optional Index of group k Optional Poverty line z Com
68. u choose the item Curves CPG curve 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Vectors or parameters Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable w2 T Optional Group Variable cl 2 Optional Index of group ki ko Optional Poverty line z Z2 Compulsory rho Pi P2 Compulsory p ki ko Compulsory On the first execution bar you find l The command Crossing to search the first intersection of the curves If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To seek an intersection over a particular range use the command Range 2 The command Difference to compute the difference G k1 P 52 Gal ka p23 Z 54 Curves DAD 3 1 3 The command Graph to draw the difference G k p z G2 k2 p z2 asa function of p 4 The command Range to specify the range for the search of a crossing between the two curves The command also specifies the range of the horizontal axis 5 The command S Gini to compute the difference P z p P zr P 6 The command Covariance to compute the following covariance matrix Cov Gy kj 0 1 z1 Go ky 50 1 z2 Co
69. ute the standard deviation of this index choose the option for computing with standard deviation Case 2 Two distributions To reach the Atkinson Gini application with two distributions 4 From the main menu choose the item Welfare and inequality Inequality indices Atkinson Gini 5 In the configuration of application choose 2 for the number of distributions 19 Inequality Poverty and Social Welfar 6 Choose the different vectors and parameter values as follows Indication Vectors or parameters Status of choice Distribution 1 Distribution 2 Variable of interest yi y2 Compulsory Weight Variable y 7 Optional Group Variable cl c2 Optional Index of group k ko Optional rho Pi P2 Compulsory epsilon E E2 Compulsory The first execution bar contains only one command Compute To compute the standard deviation of this index choose the option for computing with standard deviation 20 Inequality Poverty and Social Welfare 5 1 4 The Generalised Entropy index of inequality The Generalised Entropy index of inequality for the group k is as follows 0 ikos pi YEN arl if 0 0 1 i lt on yk jag pe if 0 0 rwk i yi l i ka L yi Di gg A if 0 1 wk TMK HK 1 i Case 1 One distribution To compute the Generalised Entropy index of inequality for only one distribution l From the main menu choose the following item Welfare an
70. v Gy k 0 1 z1 G kp 0 2 z2 ves Cov Gj kj 0 1 zi Go kos 1 z2 Cov G kj 0 2 z Go ko 0 1 Z2 Cov Gy k1 0 2 2 Go k2 0 2 z2 TR Cov Gy ky 51 z G2 k2 0 l z2 Coy Gy ky 31 z1 G2 k2 0 2 z2 gt Cow Gy krt z G k2 1 z2 55 Distribution 8 Distribution This section describes the following applications 1 Descriptive statistics 2 Density function 3 J oint density function 4 Distribution function 5 Non parametric regression 8 1 Descriptive statistics This application computes basic descriptive statistics for the data base the mean the standard deviation and the minimum and the maximum values of the vectors To reach this application l From the main menu choose the item Distribution gt Statistics 2 Choose the data base if you have activated two data bases 3 Choose the weight variable if the observations must be weighted 4 Choose the group variable and the index of group if you would like to compute the statistics for a specific group The results are as follows Name of variable 1 Mean Standard deviation Minimum Maximum Name of variable 2 Mean Standard deviation Minimum Maximum 8 2 Density function The gaussian kernel estimator of a density function f y is defined as fly wi Exp Swoi V27 A p i where is a bandwidth which acts as a smoothing parameter To reach this application
71. welfare indices S Gini index 2 Inthe configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Indication Vector or parameter Status of choice Distribution 1 Distribution 2 Variable of interest yi y Compulsory Weight Variable w w2 Optional Group Variable g e2 Optional Index of group ki ko Optional rho Pi P2 Compulsory The first execution bar contains the command Compute To compute the standard deviation choose the option for computing with standard deviation 33 Inequality Poverty and Social Welfare 5 1 3 The Atkinson Gini social welfare index To compute the Atkinson Gini social welfare index 1 J 3 Indication Variables or Status of choice parameters Variable of interest y Compulsory Weight Variable w Optional Group Variable C Optional Index of group k Optional epsilon E Compulsory rho P Compulsory From the main menu choose the following item Welfare and inequality Social welfare indices S Gini index In the configuration of the application choose 1 for the number of distributions After confirming the configuration the application appears Choose the different vectors and values of parameters as follows On the first execution bar you will find the command Compute to compute the Atkinson Gini index T

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Université Laval - The Software DAD