In this paper the effects of a shift in the intercept of an autoregressive process on the rejection frequencies of tests for unit roots are investigated using Monte Carlo methods. We consider three groups of tests for unit roots: standard tests (not including structural changes), tests for the unit-root hypothesis allowing for a possible change in the level of the series and tests for the null hypothesis of stationarity against the alternative of unit root. These power values are compared with the equivalent values when no breaks occur. The results show that the standard analysis for unit root can be completely mistaken, mainly when the series contains structural changes. It is advisable to jointly employ tests that allow a change and tests of the null hypothesis of stationarity.

Keywords: empirical power, tests, unit root, structural change.