We show that in weakly identi…ed models (1) the posterior mode will not be a consistent estimator of the true parameter vector, (2) the posterior distribution will not be Gaussian even asymptotically, and (3) Bayesian credible sets and frequentist con…dence sets will not coincide asymptotically. This means that Bayesian DSGE estimation should not be interpreted merely as a convenient device for obtaining as-ymptotically valid point estimates and con…dence sets from the posterior distribution. As an alternative, we develop a new class of frequentist con…dence sets for structural DSGE model parameters that remains asymptotically valid regardless of the strength of the identi…cation. The proposed set correctly re ‡ects the uncertainty about the structural parameters even when the likelihood is ‡at, it protects the researcher from spurious inference, and it is asymptotically invariant to the prior in the case of weak identi…cation. We thank Marco del Negro and Frank Schorfheide for providing access to their data. We thank Yanqin Fan, Ulrich Müller and Frank Schorfheide for helpful conversations and participants at Vanderbilt University, the NBER Summer Institute, the Seminar on Bayesian Inference in Econometrics and Statistics, and the Triangle Econometrics conference for helpful comments. The views expressed here are those of the authors and do not necessarily re ‡ect those of the Federal Reserve Bank of Philadelphia or of the Federal Reserve System.