LM-Type tests for a Unit Root Allowing for a Break in Trend

We consider LM-type tests for a unit root allowing for a break in trend at an unknown date. In addition to the minimum LM test statistic, we propose new LM-type tests based on the least squares estimator of the break date under the null. We examine asymptotic behavior under the null hypothesis with and without a break. For all the endogenous break tests considered, the limiting distribution when there is a break in slope is not the same as when there is no break. Other authors have obtained similar results in the context of DF-type tests. Since this discrepancy is smaller for the LM-type based on the least squares estimator, smaller size distortions are to be expected when using this test statistic. Simulation experiments confirm the superiority in terms of size, power and break date estimation of the proposed method