Restoring monotonic power in Wald/LM-type tests

•This paper proposes robust Wald∖LM-type tests for structural breaks with monotonic power.•The modified tests can detect a shift in mean where even multiple structural breaks have occurred.•A partially data-dependent bandwidth choice is proposed.

Wald/LM-type tests for a shift in mean often exhibit nonmonotonic power, due to incorrect estimation of long-run variance. In this paper, we propose a robust estimator of long-run variance that is built on nonparametric regression residuals and always converges to the true long-run variance under both the null and the alternative hypothesis. Monte Carlo experiments show that the modified tests have monotonic power against the mean with single or multiple breaks in finite samples.