Estimation and Inference for Three-Dimensional Panel Data Models

In this paper, we develop estimation and inferential methods for threedimensional (3D) panel data models with homogeneous/heterogeneous coefficients. Our 3D panel data models specify the nature of common shocks through the use of a hierarchical factor structure (i.e., global factors and sector factors). Accordingly, we develop an approach to estimating the hierarchy, thus enabling us to have a better understanding of the relative importance of the two types of unobservable shocks. Second, we propose bias corrected estimators, and give bootstrap procedures to construct the confidence intervals for the parameters of interest while allowing for correlation along three dimensions of idiosyncratic errors. We justify the theoretical findings using extensive simulations. In an empirical study, we examine the twin hypotheses of conditional and unconditional-convergence for manufacturing industries across countries.