Exponent of Cross‐Sectional Dependence: Estimation and Inference

Abstract

SummaryThis paper provides a characterisation of the degree of cross‐sectional dependence in a two dimensional array, {xit,i = 1,2,...N;t = 1,2,...,T} in terms of the rate at which the variance of the cross‐sectional average of the observed data varies with N. Under certain conditions this is equivalent to the rate at which the largest eigenvalue of the covariance matrix of xt=(x1t,x2t,...,xNt)′ rises with N. We represent the degree of cross‐sectional dependence by α, which we refer to as the ‘exponent of cross‐sectional dependence’, and define it by the standard deviation, , where is a simple cross‐sectional average of xit. We propose bias corrected estimators, derive their asymptotic properties for α > 1/2 and consider a number of extensions. We include a detailed Monte Carlo simulation study supporting the theoretical results. We also provide a number of empirical applications investigating the degree of inter‐linkages of real and financial variables in the global economy. Copyright © 2015 John Wiley & Sons, Ltd.