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

Donald Andrews ()

No 798, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Keywords: Least squares estimator; linear regression; stable distribution; fat-tails; consistency; robustness (search for similar items in EconPapers)
Pages: 54 pages
Date: 1986-07
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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