This paper examines the relationship between cyclical output and inflation in models commonly used for monetary policy analysis. This includes models that incorporate the New Keynesian, Fuhrer–Moore and backward-looking Phillips curves. The main finding is that these models imply a strong negative relationship between inflation and output, a result that is at odds with the data. The fact that New Keynesian models yield counterfactual implications is not new; the novelty of the paper lies in the fact that the finding extends to the other variants, such as the backward-looking Phillips Curve, which have been put forward as displaying superior dynamics.