This paper considers a prototypical New Keynesian model, in which the equilibrium is undetermined if monetary policy is "passive." The likelihood-based estimation of dynamic equilibrium models is extended to allow for indeterminacies and sunspot fluctuations. We construct posterior weights for the determinacy and indeterminacy region of the parameter space and estimates for the propagation of fundamental and sunspot shocks. According to the estimated model, U.S. monetary policy post-1982 is consistent with determinacy, whereas the pre-Volcker policy is not. We find that before 1979 indeterminacy substantially altered the propagation of shocks.