Applications of Data Analysis (EC969) Week 3 Lecture 1: Gains from
Contents
1. is that the income is shared equally by all members i e no member has a greater claim to the household income than the others Household income model Household income comprises of the sum of income of all earning members in the household These consist of earnings such as wages profits etc and non earning income such as interest and dividends welfare receipts or gifts When individuals get married or cohabit with someone their economic well being is likely to change as another person s income is added y 21Week3Lecturel but the total income now needs to be shared between two persons and there are some gains because of economies of scale sharing one apartment television household chores If marriage or cohabitation were completely random events then we could estimate the economic gains from marriage or cohabitation by regressing household income on marital status But there are some factors which may affect household income as well as marital status so we need to control for these These are factors such as education region of residence employment level past labour market experience marital status presence of children For example college graduates are expected to earn higher pay than those with only O level or A level either as a reflection of their higher human capital accumulation or signalling their higher ability Education is also a determinant of marital status as educational institutions serve as marriage markets and peo2. Applications of Data Analysis EC969 Simonetta Longhi and Alita Nandi ISER Contact slonghi and anandi essex ac uk Week 3 Lecture 1 Gains from marriage and cohabitation Input dataset Week3Lecturel dta Do file Week3Lecturel do I Research question We want to estimate and compare the gains in economic well being from marriage and cohabitation for men and women in England In other words we want to estimate the effect of marital status on household income a measure of economic well being for men and women To identify this effect we will need to 1 Compute household income that is comparable for single and multiple person households 2 Control for other observable characteristics in the household income model that may be correlated with marital status 3 Account for any unobservable factors in the household income model that may be correlated with marital status The background paper for this exercise is Light 2004 We thus want to estimate the parameters in the following model and based on those estimate the economic gains from marriage and cohabitation Y f P B Married B Cohabiting BX BA a E 1 where i i 1 2 n represents individuals time t 1 2 T Y household income for person i at time and a the unobserved factors X A are vectors of time varying and time invariant observed factors and Married Cohabiting are 0 1 dummy variables representing marital status Equ
3. Are unobserved effects zero for men Are these zero for women Next the Random Effects Estimator Estimate the model using random effects separately for men and women What is the estimated value of the coefficient for ethnicity variable Should we use the Random Effects or Fixed Effects estimator Using a Hausman test do you think we should use the Random Effects or the Fixed Effects model There may be heteroskedasticity or within panel serial correlation in the time varying error component What would you do to produce correct estimates of standard errors for a first difference fixed effect and random effects estimator that is robust against heteroskedasticity or within panel serial correlation Reference Light Audrey 2004 Gender Differences in the Marriage and Cohabitation Income Premium Demography 41 2 263 284 Taylor Marcia Freed ed with John Brice Nick Buck and Elaine Prentice Lane 2010 British Household Panel Survey User Manual Volume A Introduction Technical Report and Appendices Colchester University of Essex Wooldridge Jeffrey 2001 Econometric Analysis of Cross sectional and Panel Data MIT Press 9 Week3Lecturel Optional How to create dataset Week3Lecures1 dta This consists of data from different BHPS data files i individual respondent data collected from all waves windresp ii household sample file from all waves whhsamp iii
4. describe inspect tabulate summarize 6 Week3Lecturel BHPS data does not have any system missing Instead all missing values are assigned negative values e g 1 for don t know 8 for not applicable see documentation for the complete list Stata will not recognize these as missing values So we need to recode these to missing Set all missing values to system missing Hint use mvdecode or recode First we need to compute the dependant variable Note the income is in nominal terms and so we need to deflate the income by a price index One such price index is the implied GDP deflator name of the variable in the dataset is deflator It is the GDP calculated at the current prices divided by the GDP calculated at the prices for some given year This variable is not included in the BHPS but we have provided it using the Blue Book 2009 produced by the Office of National Statistics Compute the equivalised household income Compute the real equivalised household income Compute the log of real equivalised household income Next we need to create the independent variables The dataset has these variables not necessarily in the format that we want to use All categorical variables need to be transformed into 0 1 dummy variables to be included For example highest educational attainment variable edu_highest has five categories We need to create four 0 1 dummy variables for the four categories the fifth on
5. e is the omitted category And easy method to create 0 1 dummies from a categorical variable is as follows tab var gen newvar If var had n categories then this will create n 0 1 dummies called newvarl newvarn When you are thinking of transforming the existing variables into new ones that you need for your estimation check the variable label and value labels of the variables Also if there are categorical variables then you may want to reduce the number of categories so that none of the categories has too few observations and the categories reflect what you want to say For example if you are interested in seeing the difference between people living in London vis a vis other areas but the region variable has 19 categories then you should collapse all categories into just two London and other than London The variables that we need for the analysis are 1 Married Cohabiting 2 Region of residence Collapse into fewer categories 3 Any children present in the household 4 Hours worked 5 Education 6 Age And some of its polynomials say age squared 7 Time year dummies 8 Living with at least one parent 9 Ethnicity Collapse into fewer categories 7T7IWeek3Lecturel 10 Currently enrolled in school Now the dataset is ready Examine the final data set Again use any or all of these summarize describe inspect tabulate But with a panel data set we can see the data patterns better if we use
6. ent However we have used the BHPS provided household income which includes the income of all household members In case of students the other household members could be their roommates So it would be a good idea to drop those who are currently enrolled keep if enrolled 0 III Estimation Estimate the effect of marital status on household income using pooled OLS fixed effect and first difference methods Do this for men and women separately Compare the estimated gains from marriage by each of these methods Which one yields the greatest estimate of the gains from marriage SlIWeek3Lecturel Based on any one of the estimators answer the following What is the estimated gain from marriage for men and women Is the gain from marriage higher or lower than that from cohabitation for men Is the gain from marriage higher or lower than that from cohabitation for women What is the estimated value of the coefficient for ethnicity variable Why is year 1991 omitted from the first difference estimation Stata conducts an F test for the Null Hypothesis that unobserved effect is zero or constant for everyone sigma_u and sigma_e are the estimated variance for the unobserved effect and the time varying error term and rho is the fraction of the total variance that is explained by variation ina You can see the results at the bottom of the output following fixed and random effects estimation
7. household response files from all waves whhresp iv household grid information from all waves windall and v time invariant fixed individual level data collected xwavedat Data from these three files have been merged together If you wanted to create these yourself here is a guide to do that See Week3Lecturel_dataprep_DoFile pdf which contains the corresponding do file for this For each wave do steps 1 5 1 Get information about the individual that was asked in the individual questionnaire from windresp dta employment status enrolment status highest educational qualification work hours weight region of residence 2 Get other information about the individual that was coded from the household grid from windall dta marital status person number of spouse father and mother age number of own children in the household interview outcome 3 Get information on strata and primary sampling unit from whhsamp dta 4 Get information about the household that was asked in the household questionnaire from whhresp dta monthly household income McClement s scale household size number of children in the household 5 Merge all these datasets sequentially for each wave keep only those observations present in all datasets Points to remember about merging e Datasets being merged should be sorted on the variable or variables that are being used to merge these e Check _merge to see how many cases were available in both how many in only one e
8. icient than the first difference estimator if the time varying error component is homoskedastic and serially uncorrelated The first difference estimator yields more efficient estimates under less strict conditions it only requires the first difference of the error term to be serially uncorrelated and homoskedastic So suppose the time varying error component is a random walk 1 e serially correlated as follows Ei Ein FMi where 77 is white noise i e a normal variable with zero mean and variance one Then A is not serially correlated and so the first difference method yields efficient estimators Random effects model Random effects estimator is consistent only if the unobserved heterogeneity is not correlated with the independent variables Under this assumption estimating the model in 2 using OLS will also yield consistent estimators but not the most efficient random effects estimator will be more efficient This is because the random effects estimator is computed using using generalized least squares GLS or rather feasible GLS FGLS which takes into account the serial correlation in the error structure In Stata the code to estimate the model using Random Effects using Feasible Generalized Least Squares is xtreg depvar indepentvar re In Stata the code to estimate the model using Random Effects using MLE is xtreg depvar indepentvar mle Why and when to use random effects If the independent variable
9. identically distributed then using vce robust option produces consistent standard errors If observations are distributed independently across clusters but not independently within clusters then using vce cluster clustervar produces consistent standard errors If there is heteroskedasticity or within panel serial correlation in the time varying error component then we should use the vce robust or vce cluster panelvar option to get Huber White or sandwich robust standard errors Both yield the same result Clustering on the panel variable produces an estimator of the VCE that is robust to cross sectional heteroskedasticity and within panel serial correlation that is asymptotically equivalent to that proposed by Arellano 1987 Stata Help xtreg depvar indepentvar fe vce robust xtreg depvar indepentvar fe vce cluster panelvar II Setting up the data As you have realised the data needs to be in long format We have provided the long form dataset pid is the unique person identifier and wave is the interview year or time identifier The dataset is called Week3Lecture1 dta In the model above we have suggested some independent variables that are likely to affect household income This dataset contains all the variables needed for the above model If you would like to include others you will need to extract those separately from the BHPS data files and merge with this dataset Examine the data Use any or all of these
10. iminate the individual specific fixed effects and use the within individual changes in income and marital status to estimate J and 2 Fixed Effect Method This method involves subtracting the across time mean of a variable from the value at any point in time fixed effect transformation or within transformation and estimating the resulting differenced equation by OLS The differenced equation is as follows Alog Y p AMarried 8 ACohabiting B ARe gion f AAnykids B AAge B AHoursworkal 2 AEducation B AYear A 3 T where Alog Y log Y gt be Y and T is the total number of time periods observed and s l similarly for all other variables First Difference Method In this method we take the difference of each variable between two time points first differencing transformation and estimate the resulting differenced model using OLS The differenced equation is as follows Alog Y p AMarried B ACohabiting PA Re gion f AAnykids BAAge B AHoursworkal 8 AEducation B AYear A 4 where Alog Y log Y log Y _ and similarly for all other variables and k the time difference is the same for all observations As you can see the effect of is eliminated in both estimation methods So even if is correlated with marital status OLS will yield consistent estimates of 2 and Also note any time invariant regressor will also be eliminated and we will not be able to esti
11. ivalised Household Income Household income in a single person and multiple person households is not comparable in terms of economic well being because of sharing rules and economies of scale In other words an individual s economic well being when living alone and when living in a two person household with the same household income is not the same First in a multiple person household the income is shared As we do not know how the income is shared it is generally assumed to be shared equally among all members If the household income in a two household is 1000 then each person in the two person household has access to 500 only However certain goods and services can be shared among different members e g television apartment cooking and other household activities So the individuals in the two member 1 Week3Lecturel household may have access to 1500 worth of goods and services in total and 750 per person Thus the actual difference between a person in the single person household and in the two person household is not 1000 500 500 but only 1000 750 250 Thus if we want to compare the income between a single adult household and a two adult household we need to normalise the income of these households to that of some common household structure This normalised income is called equivalised income and the normalising factor is known as equivalence scale All scales must declare a particular household type as the base o
12. mate its coefficient using these methods More generally we will only be able to estimate parameters of those variables which change for at least some individuals and so the coefficients are estimated only on the basis of those cases where these variables have changed You can use xttab and xtsum commands to identify time varying and time invariant variables more in section IT What would happen if in our dataset there were hardly any individuals or none at all whose marital status changed Stata code to estimate a model using fixed effect method is xtreg depvar indepentvar fe 41Week3Lecturel But to use this and any other xt commands such as xttab and xtsum i e commands that start with xt we first need to set up the data as a panel dataset i e xtset the data In this Stata command you tell Stata which is the individual identifier idvar and which is the time identifier timevar xtset idvar timevar For the first difference mode we need to compute the first differences We can do that easily in Stata once Stata knows this is a panel dataset i e after we have xtset the data generate diffdepvar Dl depvar generate diffindepvar Dl indepvar Estimate first difference estimator by simply running OLS on the differenced data regress diffdepvar diffindepvar First difference Vs fixed effects methods These methods yield the same estimates when T 2 but not always when T gt 2 Fixed effects estimator is more eff
13. merge is created by Stata at every merge and so if you don t drop _merge or rename it to something else after each merge Stata will produce an error message saying _merge already exists and will not allow you to perform merge until you have dropped _merge or renamed it In addition to these variables always remember to include the appropriate unique identifiers in each of the datasets pid hid amp pno 6 Now using a foreach loop create a dataset for all waves in the long form as in week 1 7 Get information about gender race ethnicity and sample origin from xwavedat dta and merge this with the long form dataset in step 6 keep only those present in both datasets 8 Create the following variables i Create a 0 1 dummy variable that takes on 1 if currently employed using JBHAS did paid work last week and JBOFF no work last week but has job ii Hours worked variable which is zero for all those who are not employed using employed dummy created in i and JBHRS iii Create a categorical variable for highest qualification using QFEDHI iv Create a 0 1 dummy variable if individual is currently enrolled in school or further education v Create a categorical variable to represent the country of residence using REGION vi Create a variable that captures the implicit GDP deflator for each year wave Finally change value labels to make them consistent with variable names and if you want keep only those that are necessary for the
14. ple may look for similar educational attainment in their mates Similarly individuals working in London and other economically thriving urban regions where there are more opportunities of higher paying jobs are likely to earn higher pay And these regions with their higher population density may also provide larger marriage markets We thus want to estimate the parameters in the following model specifically B and B2 Here as in Light 2004 we have controlled for presence of children age hours worked education current enrolment status ethnicity and year In addition we have also controlled for region of residence log Y 6 Married B Cohabiting P Re gion f Anykids B Age B Hoursworkal p Education B Ethnicity p Year a 2 Generally the model of log of income and not income itself is assumed to be linear So here we have used log household income instead of household income Note Light 2004 also estimates the effect of the duration of marriage single status or cohabitation on household income In this exercise we have ignored this 3 Estimation and unobserved factors If the unobservables or the error terms and are not correlated with marital status then we can consistently estimate economic gains from marriage and cohabitation 2 and 2 using Ordinary Least Squares OLS for 2 In other words if marital status is endogenous to household income then we cannot consistently estima
15. r norm and the equivalence scale for such a household is 1 Different equivalence scales exist depending on the assumptions they make about the extent to which some goods and services can be shared by different people i e economies of scale Also some of the equivalence scales treat children differently from adults as they assume that adults are likely to put a higher pressure on household resources than children So equivalence scales are different for households of different sizes and composition One such equivalence scale is the McClements scale Here is the scoring rule used in the McClements Equivalence scale before housing costs McClements Household member Bauivalence Scales before housing costs Head 0 61 Spouse 0 39 Other second adult 0 46 Third Adult 0 42 Further adult 0 36 Dependent child aged 0 1 0 09 2 4 0 18 5 7 0 21 8 10 0 23 11 12 0 25 13 15 0 27 16 0 36 Source Taylor et al 2010 Table 29 pp App2 4 The equivalence factor for each household is the sum of the scores in the table for each household type For example a couple with no children will have an equivalence scale of 0 61 Head 0 39 Spouse 1 0 In the BHPS the equivalence for each household is computed using the table above and already provided with the dataset Some of the other most commonly used equivalence scales are OECD scale US poverty line equivalence scale The implicit assumption
16. s are not correlated with the individual effect then we can use both random and fixed effects and get consistent estimates of the coefficients However if this assumption does not hold then only fixed effect methods and FD methods yield consistent estimates So we can construct a Hausman test to determine which method to use Random 5 Week3Lecturel effect has another advantage over fixed effects methods we can estimate the coefficients of time invariant variables In Stata the command hausman performs the Hausman s specification test To use the command we have to 1 Estimate the model that is consistent whether or not the hypothesis is true 2 Store the estimation results of the first model consistent_estimate 3 Estimate the model that is efficient and consistent under the hypothesis that you are testing but inconsistent otherwise 4 Store the estimation results of the second model efficient_estimate 5 Use hausman consistent_estimate efficient_estimate to perform the test In our specific case the consistent_estimate will be the fixed effects model while the efficient_estimate will be the random effect model You can use the same command to perform other kinds of test Just make sure that the first set of results is the consistent one and the second set of results is the efficient one Remember always consistent first and efficient under HO second Robust estimators If observations are independently but not
17. some of the xt commands The xt series of commands provide tools for analyzing panel data also known as longitudinal data or in some disciplines as cross sectional time series when there is an explicit time component From Stata Help First we need to tell Stata that this is a panel dataset and which variable identifies the person and which variable identifies the time variable xtset pid wave You can use xtdescribe to see what this panel data looks like in terms of whether it is a balanced or unbalanced panel what percentage of observations have a particular pattern of occurring in the dataset See what Stata has to offer Which of the variables do not vary with time Hint Use xtsum and xttab Sample selection Our population of interest is England and so keep if region lt 17 The dataset consists of those who were interviewed face to face i e in person or via telephone or by proxy when someone else answered from them Studies show that sometimes how people respond to a question varies by who answers the question and the interview mode So we have decided to drop all those cases who were not interviewed face fo face IVFIO is one for those who were interviewed face to face keep if ivfio While Light 2004 includes those who are currently enrolled it may not be a good idea for us The reason is as follows In her paper she has computed the household income for just the person and his her spouse partner if pres
18. subsequent analysis 9 Sample selection drop the ECHP sub sample 10 Week3Lecturel
19. te 2 and pusing OLS The reason is as follows OLS estimates these parameters by comparing the income of single persons with the income of married and cohabiting persons But if those who are single are different but this is not observed and so cannot be controlled for from those who are married or cohabiting in terms of their earnings potential then the OLS estimates of the economic gains from marriage and cohabitation will merely reflects the differences in these earnings potentials For example a woman who is highly motivated may search intensively for a spouse or partner and as well as for a better quality job Such a woman will be more likely to be married or cohabiting as well as be in a high paid job Suppose that if none of the men earn anything then if we compare single and married women we will find that the household incomes of the latter are higher than the former and erroneously conclude that there are economic gains from marriage cohabitation 31Week3Lecturel In this model we have hypothesised that the error term comprises of two parts an individual effect and a time varying component amp Other terms used to describe this individual effect are unobserved component latent variable unobserved heterogeneity individual heterogeneity If we assume that is correlated with marital status but is not then we can consistently estimate and 2 using first difference or fixed effect methods These methods aim to el
Download Pdf Manuals
Related Search