We show that, in a broad class of menu cost models, the first-order dynamics of aggregate inflation in response to arbitrary shocks to aggregate costs are nearly the same as in Calvo models with suitably chosen Calvo adjustment frequencies. We first prove that the canonical menu cost model is first-order equivalent to a mixture of two time-dependent models, which reflect the extensive and intensive margins of price adjustment. We then show numerically that, in any plausible parameterization, this mixture is well-approximated by a single Calvo model. This close numerical fit carries over to other standard specifications of menu cost models. Thus, for shocks that are not too large, the Phillips curve for a menu cost model looks like the New Keynesian Phillips curve, but with a higher slope.