Despite their popularity as theoretical tools for illustrating the effects of nominal rigidities, some have questioned whether models based on staggered price contracts with rational expectations can match the persistence of the empirical inflation process. This article presents some general results about this class of models. It is shown that these models do not have a problem matching high autocorrelations for inflation. However, they fail to explain a key feature of reduced-form Phillips-curve regressions: The positive dependence of inflation on its own lags. It is shown that staggered price contracting models instead predict that the coefficients on these lag terms should be negative.