Various Asymptotic Distributions of the Error-Components Test for Cross-Sectional Correlation

Abstract

In the two seminal papers Anderson and Hsiao (1981, 1982), the linear panel regression model without cross-sectional correlation is thoroughly discussed. This uncorrelatedness assumption is now often examined in empirical work, using tests such as those by Pesaran, Ullah, and Yamagata (2008), Hsiao, Pesaran, and Pick (2012), or Pesaran (2015). All these tests in turn improve upon the so-called error-components test suggested in Breusch and Pagan (1980). In this chapter, the author revisits this error-components test and derives its asymptotic distribution under various scenarios: (a) both time-series dimension T and cross-sectional dimension N go to ∞ jointly (Phillips & Moon, 1999); (b) T → ∞ while N is fixed, and (c) N → ∞ while T is fixed. To the best of the author’s knowledge, the results under Scenarios (b) and (c) are new. Moreover, while the distributions under (a) and (b) are normal, that under (c) is not and it is even asymmetric. The critical values under (c) can be simulated. A Monte Carlo experiment is performed and it aims to throw light on the choice among the critical values suggested in the three scenarios, given a T and an N.

Citation

Sin, C.(.-y. (2022), "Various Asymptotic Distributions of the Error-Components Test for Cross-Sectional Correlation", Chudik, A., Hsiao, C. and Timmermann, A. (Ed.) Essays in Honor of M. Hashem Pesaran: Panel Modeling, Micro Applications, and Econometric Methodology (Advances in Econometrics, Vol. 43B), Emerald Publishing Limited, Leeds, pp. 145-175. https://doi.org/10.1108/S0731-90532021000043B007