Title: Exponent of Cross-sectional Dependence for Residuals

Issue: Volume 81 Series B Part 1 Year 2019
Pages: 46 -- 102
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 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.
C21, C32.
Keywords and phrases: Pair-wise correlations, Cross-sectional dependence, Cross-sectional averages, Weak and strong factor models, CAPM and Fama- French factors