A paradox in least-squares estimation of linear regression models

Abstract

This note considers a paradox arising in the least-squares estimation of linear regression models in which the error terms are assumed to be i.i.d. and possess finite rth moment, for r ∈e [1,2). We give a concrete example to show that the least-squares estimator of the slope parameter is inconsistent when the intercept parameter of the model is given. However, surprisingly this estimator is consistent when the intercept parameter is intendedly assumed to be unknown and re-estimated simultaneously with the slope parameter. © 1999 Elsevier Science B.V. All rights reserved.