Various studies have considered the risk properties under Quadratic loss, of estimators of the scale parameter after a preliminary test for exact linear restrictions on the regression coefficients. This loss function is symmetric though, arguably, under-estimation of the scale has greater consequences than over-estimation. In this paper we consider the LINEX loss function, which allows for an asymmetric penalty. We derive the exact risk of estimators of the error variance after a pre-test of exact restrictions and we numerically evaluate the derived expressions. The results are compared with those under quadratic loss so that the effects of the asymmetry can be ascertained.