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Cross-section Regression with Common Shocks

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  • Donald W.K. Andrews

    () (Yale University, Cowles Foundation)

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.

Suggested Citation

  • Donald W.K. Andrews, 2004. "Cross-section Regression with Common Shocks," Yale School of Management Working Papers ysm401, Yale School of Management.
  • Handle: RePEc:ysm:somwrk:ysm401
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    References listed on IDEAS

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    1. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    2. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    3. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
    4. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    5. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    6. Kloek, T, 1981. "OLS Estimation in a Model Where a Microvariable Is Explained by Aggregates and Contemporaneous Disturbances Are Equicorrelated," Econometrica, Econometric Society, vol. 49(1), pages 205-207, January.
    7. Pepper, John V., 2002. "Robust inferences from random clustered samples: an application using data from the panel study of income dynamics," Economics Letters, Elsevier, vol. 75(3), pages 341-345, May.
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    More about this item

    Keywords

    Asymptotics; Common shocks; Dependence; Exchangeability; Factor model; Inconsistency; Regression;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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