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

We present a sequential approach to estimating a dynamic Hausman-Taylor model. We first estimate the coefficients of the time-varying regressors and subsequently regress the first-stage residuals on the time-invariant regressors. In comparison to estimating all coefficients simultaneously, this two-stage procedure is more robust against model misspecification, allows for a flexible choice of the first-stage estimator, and enables simple testing of the overidentifying restrictions. For correct inference, we derive analytical standard error adjustments. We evaluate the finite-sample properties with Monte Carlo simulations and apply the approach to a dynamic gravity equation for US outward foreign direct investment.