Exponent of Cross-Sectional Dependence: Estimation and Inference

This paper provides a characterisation of the degree of cross-sectional dependence in a two dimensional array, {x(it),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 x(t)=(x(1t),x(2t),...,x(Nt)) rises with N. We represent the degree of cross-sectional dependence by , which we refer to as the exponent of cross-sectional dependence', and define it by the standard deviation, is a simple cross-sectional average of x(it). We propose bias corrected estimators, derive their asymptotic properties for > 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 (c) 2015 John Wiley & Sons, Ltd.