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.
Highlights
Interest in the analysis of cross-sectional dependence applied to households, firms, markets, regional and national economies has become prominent over the past decade, especially so in the aftermath of the latest financial crisis given its effects on the global economy
We present 10-year rolling estimates of α applied to excess returns on securities included in the Standard & Poor’s 500 (S&P 500) data set as well as α estimates applied to the residuals obtained from the capital asset pricing model (CAPM) and its Fama-French extensions used extensively in the finance literature
We focus on the exponent of cross-sectional dependence of the residuals obtained from different versions of the CAPM model, and provide rolling estimates of the exponent of the cross-sectional dependence of the errors from CAPM and related APT models
Summary
Interest in the analysis of cross-sectional dependence applied to households, firms, markets, regional and national economies has become prominent over the past decade, especially so in the aftermath of the latest financial crisis given its effects on the global economy. Bailey, Kapetanios, and Pesaran (2016, BKP hereafter) give a thorough account of the rationale and motivation behind the need for determining the extent of cross-sectional dependence, be it in finance, micro or macroeconomics They focus on the asymptotic behaviour of the variance of the cross section average of the observations on a double array of random variables, say xit, indexed by i = 1, 2, . They analyse the rate at which this variance tends to zero and show that it depends on the degree or exponent of cross-sectional dependence which they denote by α They explore a factor model setting as a vehicle for characterising strong and semi-strong covariance structures as defined in Chudik et al (2011). They relate these to the degree of pervasiveness of factors in unobserved factor models often used in the literature to model cross-sectional dependence
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