Abstract
Testing slope homogeneity is important in panel data modeling. Existing approaches typically take the summation over a sequence of test statistics that measure the heterogeneity of individual panels; they are referred to as Sum tests. We propose two procedures for slope homogeneity testing in large panel data models. One is called a Max test that takes the maximum over these individual test statistics. The other is referred to as a Combo test, which combines a certain Sum test (i.e., that of Pesaran and Yamagata in J Econom 142:50-93, 2008) and the proposed Max test together. We derive the limiting null distributions of the two test statistics, respectively, when both the number of individuals and temporal observations jointly diverge to infinity, and demonstrate that the Max test is asymptotically independent of the Sum test. Numerical results show that the proposed approaches perform satisfactorily.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ando, T., Bai, J.: A simple new test for slope homogeneity in panel data models with interactive effects. Econom. Lett. 136, 112–117 (2015)
Bai, J.: Panel data models with interactive fixed effects. Econometrica 77(4), 1229–1279 (2009)
Blomquist, J., Westerlund, J.: Testing slope homogeneity in large panels with serial correlation. Econom. Lett. 121(3), 374–378 (2013)
Breitung, J., Roling, C., Salish, N.: Lagrange multiplier type tests for slope homogeneity in panel data models. Econom. J. 19(2), 166–202 (2016)
Breusch, T.S., Pagan, A.R.: A simple test for heteroscedasticity and random coefficient variation. Econometrica 47(5), 1287–1294 (1979)
Cai, T.T., Liu, W., Xia, Y.: Two-sample test of high dimensional means under dependence. J. R Stat. Soc. Ser. B Stat. Methodol. 76(2), 349–372 (2014)
Chow, T.L., Teugels, J.L.: The sum and the maximum of iid random variables. In: Proceedings of the 2nd Prague Symposium on Asymptotic Statistics, vol 45, pp 394–403 (1978)
Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling extremal events: for insurance and finance, vol 33. Springer Science & Business Media (2013)
Fama, E.F., French, K.R.: Common risk factors in the returns on stocks and bonds. J. Financ. Econ. 33(1), 3–56 (1993)
Feng, L., Jiang, T., Liu, B., Xiong, W.: Max-sum tests for cross-sectional independence of high-dimensional panel data. Ann. Statist. 50(2), 1124–1143 (2022)
Hausman, J.A.: Specification tests in econometrics. Econometrica 46(6), 1251–1271 (1978)
Hsing, T.: A note on the asymptotic independence of the sum and maximum of strongly mixing stationary random variables. Ann. Probab. 23(2), 938–947 (1995)
Juhl, T., Lugovskyy, O.: A test for slope heterogeneity in fixed effects models. Econom. Rev. 33(8), 906–935 (2014)
Laurent, B., Massart, P.: Adaptive estimation of a quadratic functional by model selection. Ann. Statist. 28(5), 1302–1338 (2000)
Li, D., Xue, L.: Joint limiting laws for high-dimensional independence tests. arXiv preprint arXiv:1512.08819 (2015)
Liu, W.D., Lin, Z., Shao, Q.M.: The asymptotic distribution and Berry-Esseen bound of a new test for independence in high dimension with an application to stochastic optimization. Ann. Appl. Probab. 18(6), 2337–2366 (2008)
Pesaran, H., Smith, R., Im, K.S.: Dynamic linear models for heterogenous panels. In: The Econometrics of Panel Data, Springer, pp 145–195 (1996)
Pesaran, M.H., Yamagata, T.: Testing slope homogeneity in large panels. J Econom. 142(1), 50–93 (2008)
Phillips, P.C.B., Sul, D.: Dynamic panel estimation and homogeneity testing under cross section dependence. Econom. J. 6(1), 217–259 (2003)
Swamay, P.A.V.B.: Efficient inference in a random coefficient regression model. Econometrica 38, 311–323 (1970)
Wang, H.J., McKeague, I.W., Qian, M.: Testing for marginal linear effects in quantile regression. J. R Stat. Soc. Ser. B Stat. Methodol. 80(2), 433–452 (2018)
Zellner, A.: An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J. Amer. Statist. Assoc. 57, 348–368 (1962)
Acknowledgements
Guanghui Wang was supported by the Natural Science Foundation of Shanghai (No. 23ZR1419400) and the National Key R &D Program of China (No. 2021YFA1000100, 2021YFA1000101, 2022YFA1003801). Ping Zhao and Long Feng was partially supported by Shenzhen Wukong Investment Company, the Fundamental Research Funds for the Central Universities under Grant No. ZB22000105, the China National Key R &D Program (Grant Nos. 2019YFC1908502, 2022YFA1003703, 2022YFA1003802, 2022YFA1003803) and the National Natural S0cience Foundation of China Grants (Nos. 12271271, 11925106, 12231011, 11931001 and 11971247).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Wang, G., Feng, L. & Zhao, P. New Approaches for Testing Slope Homogeneity in Large Panel Data Models. Commun. Math. Stat. (2024). https://doi.org/10.1007/s40304-023-00371-5
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40304-023-00371-5