Exponent of Cross-sectional Dependence: Estimation and Inference

An important issue in the analysis of cross-sectional dependence which has received renewed interest in the past few years is the need for a better understanding of the extent and nature of such cross dependencies. In this paper we focus on measures of cross-sectional dependence and how such measures are related to the behaviour of the aggregates defined as cross-sectional averages. We endeavour to determine the rate at which the cross-sectional weighted average of a set of variables appropriately demeaned, tends to zero. One parameterisation sets the exponent of the cross-sectional dimension, N, being between 1/2 and 1. We refer to this as the exponent of cross-sectional dependence. We derive an estimator of this exponent from the estimated variance of the cross-sectional average of the variables under consideration. We propose bias corrected estimators, derive their asymptotic properties and consider a number of extensions. We include a detailed Monte Carlo study supporting the theoretical results. Finally, we undertake an empirical investigation of the exponent of cross-sectional dependence using the S&P 500 data-set, and a large number of macroeconomic variables across and within countries.