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Cross-section Regression with Common Shocks

  • Donald W.K. Andrews

    ()

    (Yale University, Cowles Foundation)

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.

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Paper provided by Yale School of Management in its series Yale School of Management Working Papers with number ysm401.

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Date of creation: 28 Jul 2004
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Handle: RePEc:ysm:somwrk:ysm401
Contact details of provider: Web page: http://icf.som.yale.edu/

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  1. 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 205-07, January.
  2. 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.
  3. Gary Chamberlain & Michael Rothschild, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," NBER Working Papers 0996, National Bureau of Economic Research, Inc.
  4. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  5. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-65, July.
  6. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, 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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