Exponent of Cross-Sectional Dependence: Estimation and Inference

• Published in: Journal of applied econometrics (Chichester, England) England), 2016-09, Vol.31 (6), p.929-960
• Main Authors: Bailey, Natalia, Kapetanios, George, Pesaran, M. Hashem
• Format: Article
• Language: English
• Subjects: Monte Carlo simulation
• ISSN: 0883-7252; 1099-1255
• DOI: 10.1002/jae.2476

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 = (x 1t , x 2t , ..., 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 (N α–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.