Estimation and Inference for Multi-dimensional Heterogeneous Panel Datasets with Hierarchical Multi-factor Error Structure

Given the growing availability of large datasets and following recent research trends on multi-dimensional modelling, we develop three dimensional (3D) panel data models with hierarchical error components that allow for strong cross-sectional dependence through unobserved heterogeneous global and local factors. We propose consistent estimation procedures by extending the common correlated effects (CCE) estimation approach proposed by Pesaran (2006). The standard CCE approach needs to be modified in order to account for the hierarchical factor structure in 3D panels. Further, we provide the associated asymptotic theory, including new nonparametric variance estimators. The validity of the proposed approach is confirmed by Monte Carlo simulation studies. We also demonstrate the empirical usefulness of the proposed approach through an application to a 3D panel gravity model of bilateral export flows