Panel Data Estimation and Inference: Homogeneity versus Heterogeneity

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.