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 this to be <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image1.png" width="62" height="15" />, for <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image2.png" width="77" height="15" />. Given the fashion in which it arises, we refer to <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image3.png" width="13" height="13" /> as the exponent of cross-sectional dependence. We derive an estimator of <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image3.png" width="13" height="13" /> 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 <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image3.png" width="13" height="13" /> using the S&P 500 data-set, and a large number of macroeconomic variables across and within countries.