6/10/15. Session 2: The two- way error component model. Session 2: The two- way error component model. Two- way error component regression model.

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1 Session 2: The two- way error component model! First: a look back!! general panel data linear model Individuals (country, group) time! so far, one- way error component models! pooled model! fixed effects models! between! within! random effects models! various es;ma;on methods! swar! walhus! amemiya! nerlove Session 2: The two- way error component model! What is the main purpose of panel data analysis (in microeconomics)?! increased precision in es;ma;on! more data (pooling)! modeling unobserved heterogeneity! in individuals! over ;me! splieng error into idiosyncra;c part and unobserved heterogeneity! idiosyncra;c error is usually assumed to be well- behaved! homogeneous! exogeneous (uncorrelated with anything else)! individual heterogeneity! heterogenous! endogeneous (correlated with regressors) Two- way error component regression model! general panel data linear model Individuals (country, group) time! we combine the unobserved individual effects model and the unobserved 1me effects model Individuals (country, group) time 1

2 ! Unobserved effects model (separate error terms for each individual and for each ;me period) " models individual heterogeneity that is constant over ;me and ;me period heterogeneity that is constant for all individuals " Can be es;mated in two ways: as fixed effects or as random effects " Es;ma;on as fixed effects (within or least squares dummy variable) " Es;ma;on as random effects! Estimation as fixed effects (within or least squares dummy variable)! Estimation as fixed effects (within or least squares dummy variable)! Within estimator can not estimate the effect of time-invariant and individual invariant variables (because Q transformation sweeps them out) 2

3 Two- way fixed effects models for Grunfeld data Two- way fixed effects models for Grunfeld data Fixed effects for unobserved individual heterogeneity Two- way fixed effects models for Grunfeld data Fixed effects for unobserved time period heterogeneity 3

4 " Es;ma;on as random effects " We can define a corresponding transforma;on matrix " with homoscedas;c, but correlated disturbances " Es;ma;on as random effects " this yields the following correla;ons " Es;ma;on as random effects " can be tackled as a general least squares problem (GLS) resul;ng in " various feasible GLS es;mators are equivalent to OLS on par;ally demeaned data " with 4

5 Two- way random effects models for Grunfeld data Two- way random effects models for Grunfeld data Partially demeaning parameters 1: Swamy and Aurora 2: Wallace and Hussain 3: Amemiya Various computa?onal approaches " Linear model approach " Ordinary Least Squares " Weighted Least Squares " Generalized Least Squares (feasible GLS) " Least squares es;ma;on typically involves three steps: " data- transforma;on or first stage es;ma;on " parameter es;ma;on using OLS " variance- covariance es;ma;on of the es;mates (VCE) to correct for panel structure " parameter es;mates are some;mes refined using itera;vely reweighted least squares / Maximum likelihood es;ma;on 5

6 Various computa?onal approaches " es;ma;on of models with variable coefficients Various computa?onal approaches " es;ma;on of models with variable coefficients Various computa?onal approaches " es;ma;on of models with variable coefficients " general methods of moments es;ma;on " mostly for dynamic panel models " general feasible generalized least squares es;ma;on " used for variance covariance es;ma;on for es;mates " robust es;ma;on for cluster structure " requires n much larger than T 6

7 " Test of Poolability " standard F- test comparing the model with variable coefficients with the pooled model " Tests for individual and ;me effects " Lagrange mul;plier tests " four different types implemented in plm package " Tests for individual and ;me effects " F tests " comparing within and pooling models 7

8 " Hausman tests " mainly used to compare fixed and random effects models " applicable to compare any two panel models " Tests of serial correla;on " a rich list in plm package " Tests of serial correla;on " a rich list in plm package 8

9 " Tests of cross- sec;onal dependence " Unit root tests " Robust covariance matrix es;ma;on " tests in the package lmtest 9

10 Panel data: CigareDe consump?on in US! a panel of 46 observa;ons from 1963 to 1992 " total number of observa1ons : 1380 " number of different variables: 9 of which two are iden1fiers! state: state abbrevia;on! year; the year! price: price per pack of cigare^es! pop: popula;on! pop16: popula;on above the age of 16! cpi: consumer price index (1983=100)! ndi: per capita disposable income! sales: cigare^e sales in packs per capita! pimin: minimum price in adjoining states per pack of cigare^es " Source: Online complements to Baltagi (2001). h^p:// " References: " Baltagi, B. H. (2001) Econometric Analysis of Panel Data, 2nd ed., John Wiley and Sons. " Baltagi, B.H. and D. Levin (1992) Cigare^e taxa;on: raising revenues and reducing consump;on, Structural Changes and Economic Dynamics, 3, " Baltagi, B.H., J.M. Griffin and W. Xiong (2000) To pool or not to pool: homogeneous versus heterogeneous es;mators applied to cigare^e demand, Review of Economics and Sta;s;cs, 82, Summary " Two- way error component models " unobservable individual and ;me effects model " fixed effects models " within " random effects models " different es;ma;on procedures " various tests 10