Summary: We extend T. A. Lubik and F. Schorfheide’s [Testing for indeterminacy: an application to U.S. monetary policy. American Economic Review 94, 190–217 (2004)] likelihood-based estimation of dynamic stochastic general equilibrium (DSGE) models under indeterminacy to encompass a sample period the includes both determinacy and indeterminacy by implementing a change-point methodology [S. Chib, J. Econom. 86, 221–241 (1998; Zbl 1045.62510)]. By letting the data provide estimates of the dates of the determinacy regimes and allowing the estimates of structural parameters to be the same across regimes, we obtain more precise estimates of the differences in characteristics, such as the impulse responses, across the regimes. The most striking finding about the indeterminacy regime, which is estimated to coincide with the Great Inflation of the 1970s, is that it exhibits the price puzzle, in that the inflation rate rises immediately and in a sustained manner following a positive interest rate shock. Thus, the price puzzle might have been a genuine phenomenon under indeterminacy, rather than a false finding to be excised through specification search and parameter restrictions.