Stability tests for cointegrating coefficients are known to have very low power with small to medium sample sizes. In this paper we propose to solve this problem by extending the tests to dependent cointegrated panels through the stationary bootstrap. Simulation evidence shows that the proposed panel tests improve considerably on asymptotic tests applied to individual series. As an empirical illustration we examined investment and saving for a panel of European countries over the 1960-2002 period. While the individual stability tests, contrary to expectations and graphical evidence, in almost all cases do not reject the null of stability, the bootstrap panel tests lead to the more plausible conclusion that the long-run relationship between these two variables is likely to have undergone a break.