Estimation of linear dynamic panel data models with time-invariant regressors

This paper considers estimation methods and inference for linear dynamic panel data models with unit-specific heterogeneity and a short time dimension. In particular, we focus on the identification of the coefficients of time-invariant variables in a dynamic version of the Hausman and Taylor (1981) model. We propose a two-stage estimation procedure to identify the effectsof time-invariant regressors. We first estimate the coefficients of the time-varying regressors and subsequently regress the first-stage residuals on the time-invariant regressors to recover the coefficients of the latter. Standard errors are adjusted to take into account the first-stage estimation uncertainty. As potential first-stage estimators we discuss generalized method of moments estimators and the transformed likelihood approach of Hsiao, Pesaran, and Tahmiscioglu (2002). Monte Carlo experiments are used to compare the performance of the two-stage approach to various system GMM estimators that obtain all parameter estimates simultaneously. The results are in favor of the two-stage approach. We provide further simulation evidence that GMM estimators with a large number of instruments can be severely biased in finite samples. Reducing the instrument count by collapsing the instrument matrices strongly improves the results while restricting the lag depth does not. Finally, we estimate a dynamic Mincer equation with data from the Panel Study of Income Dynamics to illustrate the approach.