This paper investigates output convergence for the G7 countries using multivariate time series techniques. We consider both the null hypotheses of no convergence and convergence. It is shown that inferences on output convergence depend on which one of the two null hypotheses is considered. Further, the no convergence results reported in previous studies using the time series definition may be attributed to the low power of the test procedures being used. Our results also highlight some potential problems on interpreting results from some typical multivariate unit root and stationarity tests.