Semiparametric Spatial Autoregressive Panel Data Model with Fixed Effects and Time-Varying Coefficients

Abstract

This article considers a semiparametric spatial autoregressive (SAR) panel data model with fixed effects and time-varying coefficients. The time-varying coefficients are allowed to follow unknown functions of time, while the other parameters are assumed to be unknown constants. We propose a local linear quasi-maximum likelihood estimation method to obtain consistent estimators for the SAR coefficient, the variance of the error term, and the nonparametric time-varying coefficients. The asymptotic properties of the proposed estimators are also established. Monte Carlo simulations are conducted to evaluate the finite sample performance of our proposed method. We apply the proposed model to study labor compensation in Chinese cities. The results show significant spatial dependence among cities and the impacts of capital, investment, and the economy’s structure on labor compensation change over time.

Keywords:

• Concentrated quasi-maximum likelihood estimation
• Local linear estimation
• Time-varying coefficient

Acknowledgments

The authors are grateful for the editor, the associate editor and anonymous referees for their constructive comments and suggestions on earlier versions of this submission. The authors also acknowledge seminar participants for their comments and suggestions. This project was undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government.

Supplementary Materials

The online supplementary material includes useful lemmas and additional simulation results. Specifically, Appendix B provides the main lemmas directly related to the proofs of the main theorems in the article. Appendix C contains additional lemmas which are used to show Appendix B. Last, additional numerical results are reported in the tables of Appendix D.

Additional information

Funding

Xuan Liang and Jiti Gao thank to the Australian Research Council Discovery Grants Program under grant numbers: DP150101012 & DP170104421 for its financial support. Xuan Liang also acknowledges the financial support of the ANU RSFAS Cross-Disciplinary Grant.