Cross-section Regression with Common Shocks

Donald Andrews ()

No 1428, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This 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) and instrumental variables (IV) 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 and IV 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 re-centering and scaling. t, Wald, and F statistics are found to have asymptotic standard normal, chi^2, and scaled chi^2 distributions, respectively, under the null hypothesis when the conditions required for consistency of the parameter under test hold. But, the absolute values of t statistics and Wald and F 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. Models with factor structures for errors, regressors, and IV's are considered. Using the general results, conditions are determined under which consistency of the LS and IV estimators holds and fails in models with factor structures. The results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units. Extensions to generalized method of moments estimators are discussed.

Keywords: Asymptotics; Common shocks; Dependence; Exchangeability; Factor model; Inconsistency; regression (search for similar items in EconPapers)
JEL-codes: C10 C12 C13 (search for similar items in EconPapers)
Pages: 43 pages
Date: 2003-06
New Economics Papers: this item is included in nep-ecm and nep-fin
Note: CFP 1153.
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

Published in Econometrics (September 2005), 73(5): 1551-1585

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Journal Article: Cross-Section Regression with Common Shocks (2005)
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