Econometric Analysis of Panel Data

1. Econometric Analysis of Panel Data • Random Regressors • Pooled (Constant Effects) Model • Instrumental Variables • Fixed Effects Model • Random Effects Model • Hausman-Taylor Estimator

2. Random Regressors • Pooled (Constant Effects) Model • Other classical assumptions remained. • OLS is biased; Instrumental variables estimation should be used. • IV estimator is consistent.

3. Constant Effects Model Instrumental Variables Estimation

4. Constant Effects Model • Instrumental Variables Estimation • Instrumental Variables: Zi • Included Instruments: X1i • # Zi≥ # Wi

5. Constant Effects Model Instrumental Variables Estimation

6. Constant Effects Model Instrumental Variables Estimation HAC Variance-Covariance Matrix

7. Constant Effects Model • Hypothesis Testing of Instrumental Variables • Test for Endogeneity • Test for Overidentification • Test for Weak Instruments

8. Random Regressors • Fixed Effects Model • Other classical assumptions remained. • Can not estimate the parameters of time-invariant regressors, even if they are correlated with model error. • The random regressors x2 has to be time-varying.

9. Fixed Effects Model • The Model • Instrumental Variables • #Zi≥ #Xi (Zi must be time variant)

10. Fixed Effects Model • Within Estimator • Panel-Robust Variance-Covariance Matrix

11. Example: Returns to Schooling Cornwell and Rupert Model (1988) Data (575 individuals over 7 ears) Dependent Variable yit: LWAGE = log of wage Explanatory Variables xit: Time-Variant Variables x1it: EXP = work experience (+EXP2)  exogenousWKS = weeks worked  endogenousOCC = occupation, 1 if blue collar IVIND = 1 if manufacturing industry IVSOUTH = 1 if resides in south IVSMSA = 1 if resides in a city (SMSA) IVMS = 1 if married IVUNION = 1 if wage set by union contract IV Time-Invariant Variables x2i: ED = years of education  endogenousFEM = 1 if femaleBLK = 1 if individual is black

12. Random Regressors • Random Effects Model • Other classical assumptions remained. • Mundlak approach may be used when • Instrumental variables must be used if

13. Random Effects Model The Model

14. Random Effects Model • (Partial) Within Estimator • Panel-Robust Variance-Covariance Matrix

15. Example: Returns to Schooling Cornwell and Rupert Model (1988) Data (575 individuals over 7 years) Dependent Variable yit: LWAGE = log of wage Explanatory Variables xit: Time-Variant Variables x1it: EXP = work experience (+EXP2)  exogenousWKS = weeks worked  endogenousOCC = occupation, 1 if blue collar IVIND = 1 if manufacturing industry IVSOUTH = 1 if resides in south IVSMSA = 1 if resides in a city (SMSA) IVMS = 1 if married IVUNION = 1 if wage set by union contract IV Time-Invariant Variables x2i: ED = years of education  endogenousFEM = 1 if female IVBLK = 1 if individual is black IV

16. Hausman-Taylor Estimator • The Model • Time-variant Variables: x1it, x2it • Time-invariant Variables:x3i, x4i • Fixed effects model can not estimate b3 and b4; Random effects model has random regressors: x2 and x4 correlated with u.

17. Hausman-Taylor Estimator Fixed Effects Model

18. Hausman-Taylor Estimator • Fixed Effects Model • Within Residuals

19. Hausman-Taylor Estimator • Random Effects Model

20. Hausman-Taylor Estimator • Instrumental Variables • Hausman-Taylor (1981) • Amemiya-Macurdy (1986)

21. Hausman-Taylor Estimator Instrumental Variable Estimation

22. Example: Returns to Schooling Cornwell and Rupert Model (1988) Data (575 individuals over 7 ears) Dependent Variable yit: LWAGE = log of wage Explanatory Variables xit: Time-Variant Variables x1it: EXP = work experience  endogenous (+EXP2)WKS = weeks worked  endogenousOCC = occupation, 1 if blue collar, IND = 1 if manufacturing industrySOUTH = 1 if resides in southSMSA = 1 if resides in a city (SMSA)MS = 1 if married  endogenousUNION = 1 if wage set by union contract  endogenous Time-Invariant Variables x2i: ED = years of education  endogenousFEM = 1 if femaleBLK = 1 if individual is black