Combined estimation of semiparametric panel data models

Abstract

The combined estimation for the semiparametric panel data models is proposed. The properties of estimators for the semiparametric panel data models with random effects (RE) and fixed effects (FE) are examined. When the RE estimator suffers from endogeneity due to the individual effects correlated with the regressors, the semiparametric RE and FE estimators may be adaptively combined, with the combining weights depending on the degree of endogeneity. The asymptotic distributions of these three estimators (RE, FE, and combined estimators) for the semiparametric panel data models are derived using a local asymptotic framework. These three estimators are then compared in asymptotic risk. The semiparametric combined estimator has strictly smaller asymptotic risk than the semiparametric fixed effect estimator. The Monte Carlo study shows that the semiparametric combined estimator outperforms semiparametric FE and RE estimators except when the degrees of endogeneity and heterogeneity of the individual effects are very small. Also presented is an empirical application where the effect of public sector capital in the private economy production function is examined using the US state level panel data.