On the Cce Estimation of Three-Dimensional Panels With Multi-Level Factors

We consider the common correlated effects estimation of a three-dimensional panel data model with heterogeneous slope coefficients and multi-level interactive fixed effects. We study the asymptotic properties of the heterogeneous slope coefficient estimators and the mean group (MG) estimators. We find that bias correction is indispensable for the MG estimator and show that the MG estimators exhibit different convergence rates depending on the degree of heterogeneity in the slope coefficients. We propose a bias correction procedure and inference method that is uniformly valid irrespective of the degree of slope heterogeneity. We conduct Monte Carlo simulations to evaluate the performance of our estimators and inference methods in finite samples. We apply our new methods to international trade data and find significant heterogeneity in the gravity model even after we control for the multi-level factors.