Specifying and estimating New Keynesian models with instrument rules and optimal monetary policies

This paper estimates several popular sticky-price New Keynesian models in an effort to understand whether and under what circumstances these models can usefully describe observed outcomes. We estimate and compare specifications that contain different forms of habit formation, specifications that have either the gap or real marginal costs driving inflation, and specifications that use either optimal policymaking or a forward-looking Taylor-type rule to summarize monetary policy. Among other results, we find that the different forms of habit formation lead to very similar aggregate behavior, that optimal policymaking explains the data as well as a Taylor-type rule does, and that the data speak strongly against specifications that have real marginal costs as the driver in the Phillips curve.