Unbalanced Panel Data Models - univie.ac.at

1 IntroductionUnbalanced Panel data ModelsUnbalanced panels with StataUnbalanced Panel data ModelsBaltagi Textbook - Chapter 9 Markus MayerDepartment of EconomicsUniversity of ViennaJune XX, 2010 Presented by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataAgenda1 Introduction2 Unbalanced Panel data ModelsThe Unbalanced One-Way Error Component ModelThe Unbalanced Two-Way Error Component ModelTesting for Individual and Time EffectsThe Unbalanced Nested Error Component Model3 Unbalanced panels with StataPresented by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataBalanced

2 Vs. Unbalanced PanelIn abalanced Panel , the number of time periodsTis thesame for all individualsi. Otherwise we are dealing with anunbalanced introductory texts restrict themselves to balancedpanels, despite the fact, that Unbalanced panels are the example, in large Panel data sets like the SOEP, there arealways some individuals, who drop out of the reason for the absence of data is important. We have tomake a distinction betweenrandomly missingdata andnonrandomly by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with PanelPresented by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataOne-Way Error Component ModelTwo-Way Error Component ModelTesting for Individual and Time EffectsNested Error Component ModelOne-Way Error Component model 1/5 model for 2 cross-sections

3 Andunequalnumber of time-seriesobservationsn1andn2.(y1y2)=(X 1X2) +(u1u2)In this case, thevariance-covariance matrixis given by = 2 In1+ 2 Jn1n1000 2 In1+ 2 Jn1n1 2 Jn1n20 2 Jn2n1 2 In2+ 2 Jn2n2 Presented by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataOne-Way Error Component ModelTwo-Way Error Component ModelTesting for Individual and Time EffectsNested Error Component ModelOne-Way Error Component model 2/5 Generalform of regression model :yit= +X it +uituit= i+ iti= 1.

4 ,N;t= 1,..,Tiand in vector notationy=Z + OLS of the Unbalanced data is given by OLS= (Z Z) 1Z isBLUE, if the variance component 2 is equal to it is positive, OLS is still unbiased and consistent, but itsstandard by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataOne-Way Error Component ModelTwo-Way Error Component ModelTesting for Individual and Time EffectsNested Error Component ModelOne-Way Error Component model 3/5 Methods for estimating the variance components.

5 For balanced model ,ANOVA estimators are best quadraticunbiased estimators (BQU) of the variance component. Forunbalanced one-way model , BQU estimators of the variancecomponents are a function of the variance components itself,we loose desired properties except functions of sufficient statistics andconsistentandasymptotically efficient, but it does not take into account theloss of degrees of freedomdue to the regression coefficients inestimating the variance by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataOne-Way Error Component ModelTwo-Way Error Component ModelTesting for Individual and Time EffectsNested Error Component ModelOne-Way Error Component model 4/5 Under normality of disturbances.

6 MINQUE andMIVQUE procedures for estimating the variance components areidentical, therefore we focus on MIVQUE. It is a linearcombination of the variance components,p 2 +p 2. Itrequires a priori values of the variance components. Theestimator has only minimum variance properties, if the a priorivaues are the true values. We therefore call the MIVQUE locally best or locally minimum variance .Presented by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataOne-Way Error Component ModelTwo-Way Error Component ModelTesting for Individual and Time EffectsNested Error Component ModelOne-Way Error Component model 5/5 Comparison of estimators by usingMonte Carlosimulations.

7 For the estimation of the regression coefficients, ANOVA-typefeasible GLS estimators compare well with the morecomplicated estimators like the estimation of the variance remainder component 2 ,the estimation methods show no big to the balanced case, better estimates of thevariance components do not imply better estimates of theregression a balanced Panel out of an Unbalanced Panel leadsto an enormous loss in by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataOne-Way Error Component ModelTwo-Way Error Component ModelTesting for Individual and Time EffectsNested Error Component ModelTwo-Way Error Component model 1/3 Regression model with unbalancedtwo-wayerror componentdisturbances.

8 Yit=X it +uiti= 1,..,Nt;t= 1,..,Tuit= i+ t+ itwhereNtis the number of individuals observed in t andDtaNt Nmatrix obtained fromINby omitting the rowscorresponding to individuals not observed in by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataOne-Way Error Component ModelTwo-Way Error Component ModelTesting for Individual and Time EffectsNested Error Component ModelTwo-Way Error Component model 2/3 This way, we can construct the matrix gives thedummy-variable structurefor the incomplete data model .

9 = Presented by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataOne-Way Error Component ModelTwo-Way Error Component ModelTesting for Individual and Time EffectsNested Error Component ModelTwo-Way Error Component model 3/3 Fixed EffectsModel: For fixed iandt, we have to run theabove regression with the matrix of dummies. This will oftenbe infeasible for large panels . TheWithintransformation is abit more complicated for the two-way case, than for theone-way EffectsModel: Using vector notation, the incompletetwo-way random effects model is given asu= 1 + 2 +.

10 An ANOVA-type quadratic unbiased estimator (QUE) of thevariance components based on the Within residuals leads tounbiased 2 , even for random effects by Markus MayerUnbalanced Panel data ModelsIntroductionUnbalanced Panel data ModelsUnbalanced panels with StataOne-Way Error Component ModelTwo-Way Error Component ModelTesting for Individual and Time EffectsNested Error Component ModelTesting for Individual and Time EffectsWe employ theLM testfor the Unbalanced two-way errorcomponent modelThe LM statistic is asymptotically distributed as22under thenull statistic can easily computed using least squares variance component