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On the Performance of Least Squares in Linear Regression with Undefined Error Means

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Abstract

This paper considers the linear regression model with multiple stochastic regressors, intercept, and errors that have undefined means. This model is of interest from a robustness perspective as a polar case. Generally, least squares estimators are inconsistent in this context. It is shown, however, that this inconsistency is restricted to the estimation of the intercept, if the regressors are highly variable. Rates of convergence of the least squares slope estimators are determined, and are shown to exceed the standard rate, n^{-1/2}, in certain contexts. The results place no restrictions on the temporal dependence of the errors, and require an unusually weak exogeneity condition between the regressors and errors. Implications of the results for robustness theory are discussed.

Suggested Citation

  • Donald W.K. Andrews, 1986. "On the Performance of Least Squares in Linear Regression with Undefined Error Means," Cowles Foundation Discussion Papers 798, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:798
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d07/d0798.pdf
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    1. Andrews, Donald W. K., 1985. "A Zero-One Result for the Least Squares Estimator," Econometric Theory, Cambridge University Press, vol. 1(1), pages 85-96, April.
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    Cited by:

    1. Phillips, Peter C. B. & Loretan, Mico, 1991. "The Durbin-Watson ratio under infinite-variance errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 85-114, January.
    2. Peter C.B. Phillips & Mico Loretan, 1990. "Testing Covariance Stationarity Under Moment Condition Failure with an Application to Common Stock Returns," Cowles Foundation Discussion Papers 947, Cowles Foundation for Research in Economics, Yale University.

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