We estimate a medium-scale DSGE model for the Euro Area allowing and testing for indeterminacy since the introduction of the euro until mid-2023. Our estimates suggest that monetary policy in the euro area was passive, leading to indeterminacy and self-fulfilling dynamics. Indeterminacy dramatically alters the transmission of fundamental shocks, particularly for inflation whose responses are inconsistent with standard economic theory. Inflation increases following a positive supply or a negative demand shock. Consequently, demand shocks look like supply shocks and vice versa, making the dynamics of the model under indeterminacy challenging to interpret. However, this finding is not robust across different assumptions on the way the sunspot shock is specified in the estimation. Both under determinacy and indeterminacy, the model estimates a natural rate of interest that turned positive after the recent inflation episode.