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

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This paper examines estimation methods and inference for linear dynamic panel data models characterized by unit-specific heterogeneity and a limited time dimension. It emphasizes the identification of coefficients for time-invariant variables within a dynamic version of the Hausman and Taylor model. A two-stage estimation procedure is proposed to determine the effects of time-invariant regressors. Initially, coefficients for time-varying regressors are estimated, followed by regressing the first-stage residuals on the time-invariant regressors to recover their coefficients. Standard errors are adjusted to account for uncertainty from the first-stage estimation. The paper discusses potential first-stage estimators, including generalized method of moments estimators and the transformed likelihood approach by Hsiao, Pesaran, and Tahmiscioglu. Monte Carlo experiments compare the two-stage method's performance against various system GMM estimators that estimate all parameters simultaneously, with results favoring the two-stage approach. Additional simulation evidence indicates that GMM estimators with many instruments can be biased in finite samples, while reducing instrument count by collapsing matrices significantly enhances results. The approach is illustrated through the estimation of a dynamic Mincer equation using data from the Panel Study of Income Dynamics.