On the sensitivity of the usual t- and F-tests to covariance misspecification

We consider the standard linear regression model with all standard assumpti ons, except that the disturbances are not white noise, but distributed N(0, sigma(2)Ohm(theta)) where Ohm(0) = I-n. Our interest lies in testing linear restrictions using the usual F-statistic based on OLS residuals. We are no t interested in finding out whether theta = 0 or not. Instead we want to fi nd out what the effect is of possibly nonzero theta on the F-statistic itse lf. We propose a sensitivity statistic phi for this purpose, discuss its di stribution, and obtain a practical and easy-to-use decision rule to decide whether the F-test is sensitive or not to covariance misspecification when theta is close to zero. Some finite and asymptotic properties of phi are st udied, as well as its behaviour in the special case of an AR(1) process nea r the unit root. (C) 2000 Elsevier Science S.A. All rights reserved. JEL cl assification: C12; C22; C51; C52.