  Hierarchical panel data models have recently garnered significant attention.
This study contributes to the relevant literature by introducing a novel
three-dimensional (3D) hierarchical panel data model, which integrates panel
regression with three sets of latent factor structures: one set of global
factors and two sets of local factors. Instead of aggregating latent factors
from various nodes, as seen in the literature of distributed principal
component analysis (PCA), we propose an estimation approach capable of
recovering the parameters of interest and disentangling latent factors at
different levels and across different dimensions. We establish an asymptotic
theory and provide a bootstrap procedure to obtain inference for the parameters
of interest while accommodating various types of cross-sectional dependence and
time series autocorrelation. Finally, we demonstrate the applicability of our
framework by examining productivity convergence in manufacturing industries
worldwide.
