Network-Based Clustering for Varying Coefficient Panel Data Models

Abstract

In this article, we introduce a novel varying-coefficient panel-data model with locally stationary regressors and unknown group structure, in which the number of groups and the group membership are left unspecified. We develop a triple-localization approach to estimate the unknown subject-specific coefficient functions and then identify the latent group structure via community detection. To improve the efficiency of the first-stage estimator, we further propose a two-stage estimation method that enables the estimator to achieve optimal rates of convergence. In the theoretical part of the article, we derive the asymptotic theory of the resultant estimators. In the empirical part, we present several simulated examples together with an analysis of real data to illustrate the finite-sample performance of the proposed method.

KEYWORDS:

• Community detection
• Group structure
• Locally stationary
• Two-stage estimation
• Varying-coefficient model

Acknowledgments

The authors would like to thank the editor, associate editor and two anonymous referees for many helpful comments and suggestions, which greatly improved the article.

Additional information

Funding

Dr. Pei’s research was supported by the Fundamental Research Funds of Shandong University (No. 2018GN050), the Taishan Scholar Program of Shandong Province and the National Natural Science Foundation of China (NSFC) (No. 11901351). Dr. Huang’s research was partially supported by National Natural Science Foundation of China (NSFC) (No. 11871323). Dr. Peng’s research was supported in part by CEGR grant of the Research Grants Council of Hong Kong (Nos. HKBU12302615 and HKBU 12303618), FRG grants from Hong Kong Baptist University (FRG2/16-17/042), and National Natural Science Foundation of China (NSFC) (Nos. 11871409 and 11971018). Dr. You’s research was supported by grants from the National Natural Science Foundation of China (NSFC) (Nos. 11971291 and 11471203) and the Program for the Innovative Research Team of Shanghai University of Finance and Economics (IRTSHUFE).