Are structural vector autoregressions (VARs) useful for discriminating between macro models? Recent assessments of VARs have shown that these statistical methods have adequate size properties. In other words, in simulation exercises, VARs will only infrequently reject the true data generating process. However, in assessing a statistical test, we often also care about power: the ability of the test to reject a false hypothesis. Much less is known about the power of structural VARs. This paper attempts to fill in this gap by exploring the power of long-run structural VARs against a set of DSGE models that vary in degree from the true data generating process. We report results for two tests: the standard test of checking the sign on impact and a test of the shape of the response. For the models studied here, testing the shape is a more powerful test than simply looking at the sign of the response. In addition, relative to an alternative statistical test based on sample correlations, we find that the shape-based tests have greater power. Given the results on the power and size properties of long-run VARs, we conclude that these VARs are useful for discriminating between macro models.