Abstract Testing the stationarity of economic time series has become a central issue in empirical economics. This paper evaluates, via Monte Carlo simulation, the empirical power and size of the augmented Dickey-Fuller test for a unit root (ADF test), the most widely used in empirical works, and of the test recently proposed by Kwiatkowski et al. (1992; KPSS test), where the null hypothesis is one of stationarity. The evidence confirms that both procedures suffer from very low power and, more so in the case of the KPSS test, large size distortions, especially in samples of the sizes usually available in practical applications. Moreover, their performance is highly sensitive to the true generating process, as well as to the way one parameterizes each test. It is shown, however, that a combined ADF-KPSS procedure would significantly reduce the number of erroneous conclusions, although at the cost of producing a fairly large number of inconclusive answers.