Profile GMM estimation of panel data models with interactive fixed effects

This paper studies panel data models with interactive fixed effects where the regressors are allowed to be correlated with the idiosyncratic error terms. We propose a two-step profile GMM estimation procedure to estimate the parameters of interest. In the first step we obtain a preliminary consistent estimate of the slope coefficient via a nuclear-norm-regularization (NNR) based profile GMM procedure. In the second step, via an iterative procedure, we conduct post-NNR profile GMM estimation of the slope coefficient, factors, and factor loadings, with an improved convergence rate for the estimate of the slope coefficient. We establish the asymptotic properties of the preliminary estimates and the iterative estimates, and propose an efficient profile GMM estimator. We also study the determination of the number of factors and propose Hausman tests for the exogeneity of the regressor. Monte Carlo simulations suggest that the proposed estimation and testing methods work well in the determination of the number of factors, the estimation of the model parameters and the test for exogeneity. As an empirical application, we apply our model and method to study the price elasticity of U.S. imports.