Exponent of Cross-sectional Dependence: Estimation and Inference

Abstract

(DISCLAIMER: Not all mathematical symbols in the abstract will display properly - please see the abstract in the pdf). 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 this to be 0(N2α-2), for 1/2<α≤1. Given the fashion in which it arises, we refer to α as the exponent of cross-sectional dependence. We derive an estimator of α 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 α using the S&P 500 data-set, and a large number of macroeconomic variables across and within countries