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Durham University

Research & business

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Publication details for Dr Anurag Narayan Banerjee

Banerjee, A.N. & Magnus, J.R. (2000). On the sensitivity of the usual t- and F-tests to covariance misspecification. Journal of Econometrics 95(1): 157-176.

Author(s) from Durham

Abstract

We consider the standard linear regression model with all standard assumptions, except that the disturbances are not white noise, but distributed Full-size image (<1 K) where Full-size image (<1 K). Our interest lies in testing linear restrictions using the usual F-statistic based on OLS residuals. We are not interested in finding out whether θ=0 or not. Instead we want to find out what the effect is of possibly nonzero θ on the F-statistic itself. We propose a sensitivity statistic φ for this purpose, discuss its distribution, and obtain a practical and easy-to-use decision rule to decide whether the F-test is sensitive or not to covariance misspecification when θ is close to zero. Some finite and asymptotic properties of ϕ are studied, as well as its behaviour in the special case of an AR(1) process near the unit root.