Exponent of Cross-Sectional Dependence for Residuals

58 Pages Posted: 11 Oct 2018

See all articles by Natalia Bailey

Natalia Bailey

Monash University

George Kapetanios

King's College, London

M. Hashem Pesaran

University of Southern California - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: January 30, 2019

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 ̃; is consistent and derive the rate at which α ̃approaches its true value. We evaluate the fi nite 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.

JEL Classification: C21, C32

Suggested Citation

Bailey, Natalia and Kapetanios, George and Pesaran, M. Hashem, Exponent of Cross-Sectional Dependence for Residuals (January 30, 2019). USC-INET Research Paper No. 19-01, Available at SSRN: https://ssrn.com/abstract=3256904 or http://dx.doi.org/10.2139/ssrn.3256904

Natalia Bailey (Contact Author)

Monash University ( email )

23 Innovation Walk
Wellington Road
Clayton, Victoria 3800
Australia

George Kapetanios

King's College, London ( email )

30 Aldwych
London, WC2B 4BG
United Kingdom
+44 20 78484951 (Phone)

M. Hashem Pesaran

University of Southern California - Department of Economics ( email )

3620 South Vermont Ave. Kaprielian (KAP) Hall 300
Los Angeles, CA 90089
United States

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