Three-dimensional heterogeneous panel data models with multi-level interactive fixed effects

Abstract

We consider a three-dimensional (3D) panel data model with heterogeneous slope coefficients and multi-level interactive fixed effects consisting of latent global factors and two types of local factors. Our model nests many commonly used 3D panel data models. We propose an iterative estimation procedure that relies on initial consistent estimators obtained through a novel defactored approach. We study the asymptotic properties of our estimators and show that our iterative estimators of the slope coefficients are “oracle efficient” in the sense that they are asymptotically equivalent to those when the factors were known. Some specification testing issues are also considered. Monte Carlo simulations demonstrate that our estimators and tests perform well in finite samples. We apply our new method to the international trade dataset.