Panel Data Estimation and Inference: Homogeneity versus Heterogeneity

TL;DR

This paper develops a unified framework for panel data estimation that accounts for both homogeneity and heterogeneity, incorporating high-dimensional dependence and autocorrelation, with theoretical and empirical validation.

Contribution

It introduces a comprehensive toolkit for analyzing high-dimensional panel data with dependence structures, extending existing methods to accommodate heterogeneity and nonstationarity.

Findings

Unified approach to homogeneity and heterogeneity in panel data

Extended Beveridge-Nelson decomposition for high-dimensional processes

Validated theoretical results with simulations and real data

Abstract

In this paper, we define an underlying data generating process that allows for different magnitudes of cross-sectional dependence, along with time series autocorrelation. This is achieved via high-dimensional moving average processes of infinite order (HDMA($\infty$)). Our setup and investigation integrates and enhances homogenous and heterogeneous panel data estimation and testing in a unified way. To study HDMA($\infty$), we extend the Beveridge-Nelson decomposition to a high-dimensional time series setting, and derive a complete toolkit set. We exam homogeneity versus heterogeneity using Gaussian approximation, a prevalent technique for establishing uniform inference. For post-testing inference, we derive central limit theorems through Edgeworth expansions for both homogenous and heterogeneous settings. Additionally, we showcase the practical relevance of the established asymptotic theory by (1). connecting our results with the literature on grouping structure analysis, (2). examining a nonstationary panel data generating process, and (3). revisiting the common correlated effects (CCE) estimators. Finally, we verify our theoretical findings via extensive numerical studies using both simulated and real datasets.