# Exponent of Cross-sectional Dependence for Residuals

Natalia Bailey (), George Kapetanios () and M Pesaran ()

Sankhya B: The Indian Journal of Statistics, 2019, vol. 81, issue 1, No 3, 46-102

Abstract: Abstract In this paper, we focus on estimating the degree of cross-sectional dependence in the error terms of a classical panel data regression model. For this purpose we propose an estimator of the exponent of cross-sectional dependence denoted by α, which is based on the number of non-zero pair-wise cross correlations of these errors. We prove that our estimator,α~$, \tilde {\alpha }$, is consistent and derive the rate at which it approaches its true value. We also propose a resampling procedure for the construction of confidence bounds around the estimator of α. We evaluate the finite sample properties of the proposed estimator by use of a Monte Carlo simulation study. The numerical results are encouraging and supportive of the theoretical findings. Finally, we undertake an empirical investigation of α for the errors of the CAPM model and its Fama-French extensions using 10-year rolling samples from S&P 500 securities over the period Sept 1989 - May 2018.

Keywords: Pair-wise correlations; Cross-sectional dependence; Cross-sectional averages; Weak and strong factor models; CAPM and Fama-French factors; C21; C32 (search for similar items in EconPapers)
Date: 2019
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Related works:
Working Paper: Exponent of Cross-sectional Dependence for Residuals (2018)
Working Paper: Exponent of cross-sectional dependence for residuals (2018)
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