COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 798 "On the Performance of Least Squares in Linear Regression Donald W.K. Andrews July 1986 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. |
