Estimation for time-invariant effects in dynamic panel data models with application to income dynamics

Abstract

A two-step estimation procedure is proposed to estimate the time-invariant effects, i.e., the slopes of the time-invariant regressors, in dynamic panel data models. In the first step, generalized method of moments (GMM) is used to estimate the time-varying effects, and the second step is to run cross-sectional OLS regression of the time series average of the residuals from the GMM estimation on the time-invariant regressors to estimate the time-invariant effects. It is shown that the OLS estimator of time-invariant effects is N-consistent and asymptotically normally distributed. A consistent estimator for the asymptotic variance of the estimator is also provided, which is robust to errors with heteroscedasticity and works well even if the errors are serially correlated. Monte Carlo simulations confirm the theoretical findings. Application to income dynamics highlights the importance of estimating time-invariant effects such as education, race and gender in return to schooling.