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

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

Constant Effects Model Instrumental Variables Estimation

Constant Effects Model Instrumental Variables Estimation –Instrumental Variables: Z i –Included Instruments: X1 i –# Z i ≥ # W i

Constant Effects Model Instrumental Variables Estimation

Constant Effects Model Instrumental Variables Estimation HAC Variance-Covariance Matrix

Constant Effects Model Hypothesis Testing of Instrumental Variables –Test for Endogeneity –Test for Overidentification –Test for Weak Instruments

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.

Fixed Effects Model The Model Instrumental Variables –#Z i ≥ #X i (Z i must be time variant)

Fixed Effects Model Within Estimator –Panel-Robust Variance-Covariance Matrix

Example: Returns to Schooling Cornwell and Rupert Model (1988) Data (575 individuals over 7 ears) –Dependent Variable y it : LWAGE = log of wage –Explanatory Variables x it : Time-Variant Variables x1 it : –EXP = work experience (+EXP 2 )  exogenous WKS = weeks worked  endogenous OCC = occupation, 1 if blue collar  IV IND = 1 if manufacturing industry  IV SOUTH = 1 if resides in south  IV SMSA = 1 if resides in a city (SMSA)  IV MS = 1 if married  IV UNION = 1 if wage set by union contract  IV Time-Invariant Variables x2 i : –ED = years of education  endogenous FEM = 1 if female BLK = 1 if individual is black

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

Random Effects Model The Model

Random Effects Model (Partial) Within Estimator –Panel-Robust Variance-Covariance Matrix

Example: Returns to Schooling Cornwell and Rupert Model (1988) Data (575 individuals over 7 years) –Dependent Variable y it : LWAGE = log of wage –Explanatory Variables x it : Time-Variant Variables x1 it : –EXP = work experience (+EXP 2 )  exogenous WKS = weeks worked  endogenous OCC = occupation, 1 if blue collar  IV IND = 1 if manufacturing industry  IV SOUTH = 1 if resides in south  IV SMSA = 1 if resides in a city (SMSA)  IV MS = 1 if married  IV UNION = 1 if wage set by union contract  IV Time-Invariant Variables x2 i : –ED = years of education  endogenous FEM = 1 if female  IV BLK = 1 if individual is black  IV

Hausman-Taylor Estimator The Model –Time-variant Variables: x1 it, x2 it –Time-invariant Variables:x3 i, x4 i –Fixed effects model can not estimate  3 and  4; Random effects model has random regressors: x2 and x4 correlated with u.

Hausman-Taylor Estimator Fixed Effects Model

Hausman-Taylor Estimator Fixed Effects Model –Within Residuals

Hausman-Taylor Estimator Random Effects Model

Hausman-Taylor Estimator Instrumental Variables –Hausman-Taylor (1981) –Amemiya-Macurdy (1986)

Hausman-Taylor Estimator Instrumental Variable Estimation

Example: Returns to Schooling Cornwell and Rupert Model (1988) Data (575 individuals over 7 ears) –Dependent Variable y it : LWAGE = log of wage –Explanatory Variables x it : Time-Variant Variables x1 it : –EXP = work experience  endogenous (+EXP 2 ) WKS = weeks worked  endogenous OCC = occupation, 1 if blue collar, IND = 1 if manufacturing industry SOUTH = 1 if resides in south SMSA = 1 if resides in a city (SMSA) MS = 1 if married  endogenous UNION = 1 if wage set by union contract  endogenous Time-Invariant Variables x2 i : –ED = years of education  endogenous FEM = 1 if female BLK = 1 if individual is black