This paper estimates two optimization-based sticky-price New Keynesian models and assesses how well they describe U.S. output, inflation, and interest rate dynamics. We consider models in which either internal habit formation influence consumption behavior, and in which Calvo-pricing and inflation indexation generate price and inflation inertia. Subject to constraints dictated by household and firm behavior, monetary policy is set under discretion and the model's time-consistent equilibrium is employed to estimate key behavioral parameters. We find that specifications estimated on consumption data perform better than specifications estimated on output data and that models with external habit formation out-perform models with internal habit formation. Nevertheless, even the best fitting specification displays characteristics that are inconsistent with the data.