Exponent of Cross-Sectional Dependence for Residuals
58 Pages Posted: 11 Oct 2018
Date Written: January 30, 2019
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 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.
JEL Classification: C21, C32
Suggested Citation: Suggested Citation