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, {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, Std(x̄t) = O (Nα–1), where x̄t 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.