This paper analyzes the stability over time of the econometric process for euro-area inflation since 1970, focusing in particular on the behavior of the so-called persistence parameter (the sum of the coefficients on the lagged dependent variables). Perhaps surprisingly, in light of the Lucas critique, our principal finding is that there appears to be relatively little instability in the parameters of the euro-area inflation process. Full-sample estimates of the persistence parameter are generally close to 1, and we fail to reject the hypothesis that this parameter has been stable over time. We discuss how these results provide some indirect evidence against rational expectations models with strong forward-looking elements, such as the New Keynesian Phillips curve.