We extend Lubik and Schorfheide's (2004) likelihood-based estimation of dynamic stochastic general equilibrium (DSGE) models under indeterminacy to encompass a sample period including both determinacy and indeterminacy by implementing the change-point methodology (Chib, 1998). 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. ; Earlier title: Timing transitions between determinate and indeterminate equilibria in an empirical DSGE model: benefits and implications