Panel Data Estimation and Inference: Homogeneity versus Heterogeneity

2025-02-05

AI Summary

This paper addresses the joint modeling of cross-sectional dependence and temporal autocorrelation in panel data. We propose a unified high-dimensional inference framework applicable to both homogeneous and heterogeneous settings. Methodologically, we extend the Beveridge–Nelson decomposition to high-dimensional infinite-order moving average (HDMA(∞)) processes, yielding a unified data-generating process capable of capturing both strong and weak cross-sectional dependence as well as long-memory dynamics. Theoretically, we develop a uniform asymptotic theory based on Gaussian approximation and Edgeworth expansion, rigorously establishing consistency, asymptotic normality, and third-order accuracy of common correlated effects (CCE)-type estimators under nonstationary, high-dimensional, and heterogeneous conditions. Empirically, our method demonstrates substantial improvements in both Monte Carlo simulations and real-data applications over existing approaches, achieving superior robustness and statistical efficiency.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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 properties by revisiting the common correlated effects (CCE) estimators, and a classic nonstationary panel data process. Finally, we verify our theoretical findings via extensive numerical studies using both simulated and real datasets.

Problem

• Analyzing cross-sectional dependence and autocorrelation in panel data
• Comparing homogeneous and heterogeneous panel data estimation methods
• Developing inference tools for high-dimensional time series settings

Innovation

• Uses HDMA(∞) for cross-sectional dependence modeling
• Extends Beveridge-Nelson decomposition to high dimensions
• Applies Gaussian approximation for homogeneity testing