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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

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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.

Information

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

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.

References

REFERENCES

Atak, A., Linton, O., & Xiao, Z. (2011) A semiparametric panel data model for unbalanced data with application to climate change in the United Kingdom. Journal of Econometrics 164, 92–115.CrossRefGoogle Scholar
Bada, O., Kneip, A., Liebl, D., Mensinger, T., Gualtieri, J., & Sickles, R.C. (2022) A wavelet method for panel models with jump discontinuities in the parameters. Journal of Econometrics 226, 399–422.CrossRefGoogle Scholar
Bai, J. (2009) Panel data models with interactive fixed effects. Econometrica 74, 1229–1279.Google Scholar
Baltagi, B.H. (2012) Econometric Analysis of Panel Data . Wiley.Google Scholar
Bartolucci, F., Belotti, F., & Peracchi, F. (2015) Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data. Journal of Econometrics 184, 111–123.CrossRefGoogle Scholar
Boneva, L., Linton, O., & Vogt, M. (2015) A semiparametric model for heterogeneous panel data with fixed effects. Journal of Econometrics 188, 327–345.CrossRefGoogle Scholar
Bosq, D. (1998) Nonparametric Statistics for Stochastic Processes: Estimation and Prediction , 2nd Edition. Springer.CrossRefGoogle Scholar
Cai, Z. (2007) Trending time-varying coefficients time series models with serially correlated errors. Journal of Econometrics 136, 163–188.CrossRefGoogle Scholar
Cai, Z., Fan, J., & Yao, Q. (2000) Functional-coefficient regression models for nonlinear time series. Journal of the American Statistical Association 95, 941–956.CrossRefGoogle Scholar
Chen, B. & Hong, Y. (2012) Testing for smooth structural changes in time series models via nonparametric regression. Econometrica 80, 1157–1183.Google Scholar
Chen, B. & Huang, L. (2018) Nonparametric testing for smooth structural changes in panel data models. Journal of Econometrics 202, 245–267.CrossRefGoogle Scholar
Chen, J., Gao, J., & Li, D. (2012) Semiparametric trending panel data models with cross-sectional dependence. Journal of Econometrics 171, 71–85.CrossRefGoogle Scholar
Chernozhukov, V. & Fernández-Val, I. (2011) Inference for extremal conditional quantile models, with an application to market and birthweight risks. The Review of Economic Studies 78, 559–589.CrossRefGoogle Scholar
Dong, C. & Linton, O. (2018) Additive nonparametric models with time variable and both stationary and nonstationary regressors. Journal of Econometrics 207, 212–236.CrossRefGoogle Scholar
Fan, J., Liao, Y., & Yao, J. (2015) Power enhancement in high-dimensional cross-sectional tests. Econometrica 83, 1497–1541.CrossRefGoogle ScholarPubMed
Feng, G., Gao, J., Peng, B., & Zhang, X. (2016) A varying-coefficient panel data model with fixed effects: Theory and an application to U.S. commercial banks. Journal of Econometrics 196, 68–82.CrossRefGoogle Scholar
Gao, J. & Gijbels, I. (2008) Bandwidth selection in nonparametric kernel testing. Journal of the American Statistical Association 103, 1584–1594.CrossRefGoogle Scholar
Gao, J. & King, M. (2004) Adaptive testing in continuous-time diffusion models. Econometric Theory 20, 844–882.CrossRefGoogle Scholar
Gao, J., Xia, K., & Zhu, H. (2020) Heterogeneous panel data models with cross-sectional dependence. Journal of Econometrics 219(2), 329–353.CrossRefGoogle Scholar
Grossmann, G.M. & Krueger, A.B. (1993) Environmental impacts of a North American free trade agreement. In Garber, P. (ed.), The Mexico–US Free Trade Agreement , pp. 13–56. MIT Press.CrossRefGoogle Scholar
Grossmann, G.M. & Krueger, A.B. (1995) Economic growth and the environment. Quarterly Journal of Economics 110, 353–377.CrossRefGoogle Scholar
Hansen, B. (2000) Testing for structural change in conditional models. Journal of Econometrics 97(1), 93–115.CrossRefGoogle Scholar
Hidalgo, J. & Lee, J. (2014) A CUSUM test for common trends in large heterogeneous panels. In Essays in Honor of Peter C.B. Phillips . Advances in Econometrics, vol. 33, pp. 303–345. Emerald Publishing Limited.CrossRefGoogle Scholar
Horowitz, J.L. & Spokoiny, V.G. (2003) An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599–631.CrossRefGoogle Scholar
Hsiao, C. (1985) Benefits and limitations of panel data. Econometric Reviews 4, 121–174.CrossRefGoogle Scholar
Hsiao, C. (1995) Panel analysis for metric data. In Arminger, G., Clogg, C. C., & Sobel, M. E. (eds.), Handbook of Statistical Modelling in the Social and Behavioral Sciences . Springer.Google Scholar
Hsiao, C. (2014) Analysis of Panel Data , 3rd Edition. Cambridge University Press.CrossRefGoogle Scholar
Hsiao, C. (2018) Panel models with interactive effects. Journal of Econometrics 206, 645–673.CrossRefGoogle Scholar
Hsiao, C. & Pesaran, M.H. (2008) Random coefficient models. In Matyas, L. & Sevestre, P. (eds.), The Econometrics of Panel Data , pp. 185–213. Springer.CrossRefGoogle Scholar
Hsiao, C., Shi, Z., & Zhou, Q. (2022) Transformed estimator for panel interactive effects models. Journal of Business & Economic Statistics 40, 1831–1848.CrossRefGoogle Scholar
Hsiao, C. & Tahmiscioglu, A.K. (1997) A panel analysis of liquidity constraints and firm investment. Journal of the American Statistical Association 92, 455–465.CrossRefGoogle Scholar
Jin, S. & Su, L. (2013) A nonparametric poolability test for panel data models with cross section dependence. Econometric Reviews 32, 469–512.CrossRefGoogle Scholar
Kneip, A., Sickles, R.C., & Song, W. (2012) A new panel data treatment for heterogeneity in time trends. Econometric Theory 28(3), 590–628.CrossRefGoogle Scholar
Lee, J. & Robinson, P.M. (2016) Series estimation under cross-sectional dependence. Journal of Econometrics 188, 346–362.CrossRefGoogle Scholar
Lee, K., Pesaran, M.H., & Smith, R. (1997) Growth and convergence in a multi-country empirical stochastic growth model. Journal of Applied Econometrics 12, 357–392.3.0.CO;2-T>CrossRefGoogle Scholar
Li, D., Chen, J., & Gao, J. (2011) Non-parametric time-varying coefficient panel data models with fixed effects. The Econometrics Journal 14, 387–408.CrossRefGoogle Scholar
Li, D., Su, L., & Qian, J. (2016) Panel data models with interactive fixed effects and multiple structural breaks. Journal of the American Statistical Association 111, 1804–1819.CrossRefGoogle Scholar
Li, Q. & Wang, S. (1998) A simple bootstrap test for a parametric regression function. Journal of Econometrics 87, 145–165.CrossRefGoogle Scholar
Liu, F., Gao, J., & Yang, Y. (2020) Time-Varying Panel Data Models with an Additive Factor Structure. Working Paper 42/20, Monash University.CrossRefGoogle Scholar
Lombardia, M.J. & Sperlich, S. (2008) Semiparametric inference in generalized mixed effects models. Journal of the Royal Statistical Society, Series B (Statistical Methodology) 70(5), 913–930.CrossRefGoogle Scholar
Lu, X. & Su, L. (2022) Uniform inference in linear panel data models with two-dimensional heterogeneity. Journal of Econometrics , forthcoming.Google Scholar
Lumsdaine, R.L., Okui, R., & Wang, W. (2023) Estimation of panel group structure models with structural breaks in group memberships and coefficients. Journal of Econometrics 233(1), 45–65.CrossRefGoogle Scholar
Ma, S., Lan, W., Su, L., & Tsai, C.-L. (2020) Testing alphas in conditional time-varying factor models with high dimensional assets. Journal of Business & Economic Statistics 38(1), 214–227.CrossRefGoogle Scholar
Millimet, D.L., List, J.A., & Stengos, T. (2003) The environmental Kuznets curve: Real progress or misspecified models? Review of Economics and Statistics 85, 1038–1047.CrossRefGoogle Scholar
Moon, H.R. & Weidner, M. (2015) Linear regression for panel with unknown number of factors as interactive fixed effects. Econometrica 83, 1543–1579.CrossRefGoogle Scholar
Newey, W.K. (1997) Convergence rates and asymptotic normality for series estimators. Journal of Econometrics 79, 147–168.CrossRefGoogle Scholar
Pesaran, M.H. (2006) Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74(4), 967–1012.CrossRefGoogle Scholar
Pesaran, M.H. (2015) Time Series and Panel Data Econometrics . Oxford University Press.CrossRefGoogle Scholar
Pesaran, M.H. & Yamagata, T. (2008) Testing slope homogeneity in large panels. Journal of Econometrics 142, 50–93.CrossRefGoogle Scholar
Robinson, P.M. (2012) Nonparametric trending regression with cross-sectional dependence. Journal of Econometrics 169, 4–14.CrossRefGoogle Scholar
Shao, Q.M. & Yu, H. (1996) Weak convergence for weighted empirical processes of dependent sequences. The Annals of Probability 24, 2098–2127.CrossRefGoogle Scholar
Su, L. & Hoshino, T. (2016) Sieve instrumental variable quantile regression estimation of functional coefficient models. Journal of Econometrics 191, 231–254.CrossRefGoogle Scholar
Su, L., Shi, Z., & Phillips, P.C.B. (2016) Identifying latent structures in panel data. Econometrica 84(6), 2215–2264.CrossRefGoogle Scholar
Su, L., Wang, X., & Jin, S. (2019) Sieve estimation of time-varying panel data models with latent structures. Journal of Business & Economic Statistics 37, 334–349.CrossRefGoogle Scholar
Su, L. & Zhang, Y. (2016) Semiparametric estimation of partially linear dynamic panel data models with fixed effects. In Essays in Honor of Aman Ullah . Advances in Econometrics, vol. 36, pp. 137–204. Emerald Publishing Limited.Google Scholar
Sun, S. & Chiang, C.-Y. (1997) Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strong mixing sequences of random variables. Journal of Applied Mathematics and Stochastic Analysis 10, 3–20.Google Scholar
White, H. (2000) Asymptotic Theory for Econometricians , Revised Edition. Emerald Publishing Limited.Google Scholar
Wooldridge, J.M. (2010) Econometric Analysis of Cross Section and Panel Data , 2nd Edition. MIT Press Academic.Google Scholar
Zhang, Y., Su, L., & Phillips, P.C.B. (2012) Testing for common trends in semiparametric panel data models with fixed effects. The Econometrics Journal 15, 56–100.CrossRefGoogle Scholar
Zhang, Y. & Zhou, Q. (2021) Partially linear functional-coefficient dynamic panel data models: Sieve estimation and specification testing. Econometric Reviews 40, 983–1006.CrossRefGoogle Scholar
Zhao, H., Tu, W., & Yu, Z. (2018) A nonparametric time-varying model for panel count data. Journal of Nonparametric Statistics 30(3), 640–661.CrossRefGoogle Scholar
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