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

We propose a two-stage estimation procedure to identify the effects of time-invariant regressors in a dynamic version of the 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 providing analytical standard error adjustments for the second-stage coefficients. The two-stage approach is more robust against misspecification than GMM estimators that obtain all parameter estimates simultaneously. In addition, it allows exploiting advantages of estimators relying on transformations to eliminate the unit-specific heterogeneity. We analytically demonstrate under which conditions the one-stage and two-stage GMM estimators are equivalent. Monte Carlo results highlight the advantages of the two-stage approach infinite samples. Finally, the approach is illustrated with the estimation of a dynamic gravity equation for U.S. outward foreign direct investment.