Specifying and Estimating New Keynesian Models with Instrument Rules and Optimal Monetary Policies∗

This paper looks at whether sticky-price New Keynesian models with microfounded inertia can usefully describe US data. We estimate a range of models, considering specifications with either internal or external consumption habits, specifications containing Taylor-type rules or an optimal discretionary rule, and specifications where inflation is driven by movements in either the gap or real marginal costs. Among other results, we find that models with external habits produce very similar aggregate behavior to models with internal habits. We also find that modeling monetary policy in terms of an optimal discretionary rule describes US data as well as a forward-looking Taylor-type rule does, and that the data favor the traditional gap-based Phillips curve over specifications containing real marginal costs.