Double Bootstrap Test for a Structural Break When the Disturbance Variance Changes with the Break*

In this paper we consider the Wald test statistic proposed by Watt (1979) for testing equality between the sets of regression coefficients in two linear regression models when the disturbance variances may possibly be unequal. This test can be also used as a test for a structural break. As shown by Ohtani and Toyoda (1985) and Honda and Ohtani (1986), the test based on the Wald test statistic suffers from severe size distortion in small samples when the disturbance variances of the two regression models are unequal. To tackle this problem, we apply two kinds of bootstrap methods, i.e., the usual bootstrap and the double bootstrap. Through simulation studies, we show that the size distortion is substantially improved when the bootstrap methods are utilized.