13) have different performances under both the null and local alternatives. Common practice in empirical research is to apply multiple tests if none is uniformly superior. We show that this approach tends to produce contradictory evidence for the tests considered, making it unclear whether to reject the null. To address this problem, we advocate a combined testing procedure. Simulation evidence shows that the combined test has good size control and closely tracks the more powerful test. An empirical application reinvestigates whether there is a unit root in OECD inflation rates. We find evidence that inflation is stationary for long observation periods, but we cannot reject nonstationarity in most subsets of countries for the last three decades.