AN ALTERNATIVE DERIVATION OF MUNDLAK'S FIXED EFFECTS RESULTS USING SYSTEM ESTIMATION

Abstract

Mundlak (1978, Econometrica 46, 69–85) showed that the fixed effects estimator can be obtained as generalized least squares (GLS) for a panel regression model where the individual effects are random but are all hopelessly correlated with the regressors. This result was obtained by partitioned inversion after substituting the reduced form expression for the individual effects as a function of the means of all the regressors. This note shows that Mundlak's result can be obtained using system estimation without using partitioned inversion. System estimation has proved useful for deriving two-stage least squares (2SLS) and three-stage least squares (3SLS) counterparts for the random effects panel models by Baltagi (1981, Journal of Econometrics 17, 189–200). It also has been used for obtaining an alternative derivation of the Hausman tests that is robust to heteroskedasticity of unknown form (see Arellano, 1993, Journal of Econometrics 59, 87–97) and more recently, for obtaining generalized method of moments (GMM) estimators for dynamic panel models (see Arellano and Bover, 1995, Journal of Econometrics 68, 29–51; and Blundell and Bond, 1998, Journal of Econometrics 87, 115–143, to mention a few). We also show that a necessary and sufficient condition for ordinary least squares (OLS) to be equivalent to GLS is satisfied for this model.