Homogeneity and Sparsity Analysis for High-Dimensional Panel Data Models

Abstract

In this article, we are interested in detecting latent group structures and significant covariates in a high-dimensional panel data model with both individual and time fixed effects. The slope coefficients of the model are assumed to be subject dependent, and there exist group structures where the slope coefficients are homogeneous within groups and heterogeneous between groups. We develop a penalized estimator for recovering the group structures and the sparsity patterns simultaneously. We propose a new algorithm to optimize the objective function. Furthermore, we propose a strategy to reduce the computational complexity by pruning the penalty terms in the objective function, which also improves the accuracy of group structure detection. The proposed estimator can recover the latent group structures and the sparsity patterns consistently in large samples. The finite sample performance of the proposed estimator is evaluated through Monte Carlo studies and illustrated with a real dataset.

Keyword:

• ADMM algorithm
• Group detection
• Heterogeneity
• Panel data
• Penalized regression

Supplementary Materials

The supplementary material contain additional simulation results and all mathematical proofs.

Acknowledgments

The authors are thankful to the Editor, Associate Editor, and two referees for their constructive comments that substantially improve this work.

Disclosure Statement

The authors report there are no competing interests to declare.

Funding

Additional information

Funding

Wu Wang’s research was partially supported by the Natural Science Foundation of China (12201627), and the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (22XNKJ10). Zhongyi Zhu’s work was partially supported by the Natural Science Foundation of China (12071087, 12226308).