This paper addresses the stability throughout different phases of the business cycle of the relationship involving the inflation rate and the real output growth. Thanks to a new methodology developed in this article, we analyze the presence of what we call short-run attractor regimes. These regimes characterize period of time where the impulse responses for a set of stationary time series are collinear. We find that inflation does not impact real output in the long-run but that short-run relationships are subject to change in regimes.