Exponent of Cross-Sectional Dependence: Estimation and Inference

46 Pages Posted: 5 Feb 2012

See all articles by Natalia Bailey

Natalia Bailey

Monash University

George Kapetanios

King's College, London

M. Hashem Pesaran

University of Southern California - Department of Economics; University of Cambridge - Trinity College (Cambridge)

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Date Written: January 31, 2012

Abstract

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.

Keywords: cross correlations, cross-sectional dependence, cross-sectional averages, weak and strong factor models, capital asset pricing model

JEL Classification: C210, C320

Suggested Citation

Bailey, Natalia and Kapetanios, George and Pesaran, M. Hashem, Exponent of Cross-Sectional Dependence: Estimation and Inference (January 31, 2012). CESifo Working Paper Series No. 3722, Available at SSRN: https://ssrn.com/abstract=1998062

Natalia Bailey

Monash University ( email )

23 Innovation Walk
Wellington Road
Clayton, Victoria 3800
Australia

George Kapetanios

King's College, London ( email )

30 Aldwych
London, WC2B 4BG
United Kingdom
+44 20 78484951 (Phone)

M. Hashem Pesaran (Contact Author)

University of Southern California - Department of Economics

3620 South Vermont Ave. Kaprielian (KAP) Hall 300
Los Angeles, CA 90089
United States

University of Cambridge - Trinity College (Cambridge) ( email )

United Kingdom

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