In this paper we propose a set of new panel tests to detect changes in persistence. The test statistics are used to test the null hypothesis of stationarity against the alternative of a change in persistence from I(0) to I(1), from I(1) to I(0) and in an unknown direction. The limiting distributions of the panel tests are derived, and small sample properties are investigated by Monte Carlo experiments under the hypothesis that the individual series are independently cross-section distributed. These tests have a good size and power properties. Cross-sectional dependence is also considered. A procedure of de-factorizing, proposed by Stock and Watson (2002), is applied. The defactored panel tests have good size and power. The empirical results obtained from applying these tests to a panel covering 21 OECD countries observed between 1970 and 2007 suggest that inflation rate changes from I(1) to I(0) when cross-correlation is considered.