Limiting behaviour of Dickey-Fuller t-tests under the crash model alternative

We derive the limiting behaviour of Dickey-Fuller's (1981) F-statistics when the trend-break alternative is the crash model that allows for a one time shift in the intercept. We show that both F-statistics are consistent against the crash alternative hypothesis. The power of the F-statistics in finite samples is studied and compared to that of the Dickey-Fuller (1979) statistics, namely, the pseudo-t ratio and the normalized estimator. Copyright Royal Economic Society, 2003