The sensitivity of OLS when the variance matrix is (partially) unknown

We consider the standard linear regression model y = X beta + u with all st andard assumptions, except that the variance matrix is assumed to be sigma( 2)Omega(theta), where Omega depends on nz unknown parameters theta(1),...,t heta(m). Our interest lies exclusively in the mean parameters beta or X bet a we introduce a new sensitivity statistic (B1) which is designed to decide whether (y) over cap(or <(beta)over cap>) is sensitive to covariance missp ecification. We show that the Durbin-Watson test is inappropriate in this c ontext, because it measures the sensitivity of <(sigma)over cap>(2) to cova riance misspecification. Our results demonstrate that the estimator <(beta) over cap> and the predictor (y) over cap are not very sensitive to covarian ce misspecification. The statistic is easy to use and performs well even in cases where it is not strictly applicable. (C) 1999 Elsevier Science S.A. All rights reserved. JEL classification: C12; C22; C51; C52.