Exponent of Cross-sectional Dependence for Residuals - Natalia Bailey; George Kapetanios; M. Hashem Pesaran (Center for Economic Studies and ifo Institute (CESifo), 2018)
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, ᾶ; is consistent and derive the rate at which ᾶ 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: C21; C32; 330; pair-wise correlations; cross-sectional dependence; cross-sectional averages; weak and strong factor models; CAPM and Fama-French factors