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SPECIFICATION TESTS FOR TIME-VARYING COEFFICIENT PANEL DATA MODELS

Published online by Cambridge University Press:  01 June 2023

Alev Atak ,
Thomas Tao Yang ,
Yonghui Zhang  and
Qiankun Zhou
Alev Atak
Affiliation:
Middle East Technical University
Thomas Tao Yang
Affiliation:
Australian National University
Yonghui Zhang*
Affiliation:
Renmin University of China
Qiankun Zhou
Affiliation:
Louisiana State University
*
Address correspondence to Yonghui Zhang, School of Economics, Renmin University of China, Beijing, China; e-mail: yonghui.zhang@hotmail.com.
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Abstract

This paper provides nonparametric specification tests for the commonly used homogeneous and stable coefficients structures in panel data models. We first obtain the augmented residuals by estimating the model under the null hypothesis and then run auxiliary time series regressions of augmented residuals on covariates with time-varying coefficients (TVCs) via sieve methods. The test statistic is then constructed by averaging the squared fitted values, which are close to zero under the null and deviate from zero under the alternatives. We show that the test statistic, after being appropriately standardized, is asymptotically normal under the null and under a sequence of Pitman local alternatives. A bootstrap procedure is proposed to improve the finite sample performance of our test. In addition, we extend the procedure to test other structures, such as the homogeneity of TVCs or the stability of heterogeneous coefficients. The joint test is extended to panel models with two-way fixed effects. Monte Carlo simulations indicate that our tests perform reasonably well in finite samples. We apply the tests to re-examine the environmental Kuznets curve in the United States, and find that the model with homogenous TVCs is more appropriate for this application.

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Type
ARTICLES
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Econometric Theory , Volume 41 , Issue 1 , February 2025 , pp. 123 - 170
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

We are deeply indebted to the Editor (Peter Phillips), the Co-Editor (Guido Kuersteiner), and three referees for their many constructive comments, which improve the paper substantially. We are grateful to Jiti Gao and participants of the CES 2019 North American conference at Kansas University for helpful comments and discussions. Zhang acknowledges the financial support from the National Natural Science Foundation of China under Grant Nos. 71973141 and 71873033. All errors are the authors’ sole responsibilities. The MATLAB codes for our tests are available upon request.

The original version of this article had an incorrect author name. A notice has been published and the error rectified in the online PDF and HTML version.

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