Econometrica: Sep 2005, Volume 73, Issue 5
Cross‐Section Regression with Common Shocks
Donald W. K. AndrewsThis paper considers regression models for cross‐section data that exhibit cross‐section dependence due to common shocks, such as macroeconomic shocks. The paper analyzes the properties of least squares (LS) estimators in this context. The results of the paper allow for any form of cross‐section dependence and heterogeneity across population units. The probability limits of the LS estimators are determined, and necessary and sufficient conditions are given for consistency. The asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling. The , Wald, and statistics are found to have asymptotic standard normal, χ, and scaled χ distributions, respectively, under the null hypothesis when the conditions required for consistency of the parameter under test hold. However, the absolute values of , Wald, and statistics are found to diverge to infinity under the null hypothesis when these conditions fail. Confidence intervals exhibit similarly dichotomous behavior. Hence, common shocks are found to be innocuous in some circumstances, but quite problematic in others.
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