Exponent of Cross-Sectional Dependence: Estimation and Inference
定义了横截面依赖指数α，衡量数据横截面平均方差随N变化的速率，提出偏差校正估计量并推导渐近性质，通过蒙特卡洛模拟和全球经济实证应用验证。
Summary This paper provides a characterisation of the degree of cross‐sectional dependence in a two dimensional array, { x i t , 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 x t =( x 1 t , x 2 t ,..., x N t )′ 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, , where is a simple cross‐sectional average of x i t . 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. Copyright © 2015 John Wiley & Sons, Ltd.