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

In: Essays in Honor of M. Hashem Pesaran: Panel Modeling, Micro Applications, and Econometric Methodology

Author

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  • CY (Chor-yiu) Sin

Abstract

In the two seminal papersAnderson 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.

Suggested Citation

  • CY (Chor-yiu) Sin, 2022. "Various Asymptotic Distributions of the Error-Components Test for Cross-Sectional Correlation," Advances in Econometrics, in: Essays in Honor of M. Hashem Pesaran: Panel Modeling, Micro Applications, and Econometric Methodology, volume 43, pages 145-175, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-90532021000043b007
    DOI: 10.1108/S0731-90532021000043B007
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    More about this item

    Keywords

    Cross-sectional correlation; cross-sectional dimension; double-indexed central limit theorem; error-components test; joint limit; time-series dimension; C12; C21; C23;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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