In this paper, we consider and examine the performance of two-step LM unit root tests with trend-breaks. In the first step, we jointly test for the existence and location of breaks using a maximum F-test. In the second step, we utilize the identified breaks and test for a unit root. A transformation procedure is adopted so that the tests with trend-breaks are invariant to nuisance parameters. We show that the two-step LM unit root tests have better properties of size and power than endogenous break unit root tests. In addition, the two-step test can be conveniently applied to allow for multiple breaks.
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