Does it Matter to Assume that U.S. Monetary Authorities Follow a Taylor Rule?; Franck Portier (UCL/TSE)

Abstract

The specification of the monetary policy rule is not a marginal element in New Keynesian models, but crucially determine allocations properties. We show that assuming that monetary authorities follow a Taylor rule does seriously bias estimation of New Keynesian type models.

We make the distinction between feedback rules and state dependant rules. Feedback rules relate the policy instrument to some endogenous variables of the model. The Taylor rule is a feedback rule. State dependant rules relate the policy instrument to the state of the economy.

Using a simple abstract models, we illustrate three results. First, and quite obviously, a state dependant rule can always replicate allocations generated by a feedback rule model. In that sense, it is not constraining to assume that policy makers follow a state dependant rule or in other words, a state dependent rule is never misspecified. Second, a feedback rule cannot always replicate allocations generated by a state dependant rule model, because the former rule is constrained to  guarantee determinacy. Therefore, a feedback rule should be used only if one believe that the actual policy maker is indeed constrained to such a rule. Third, even when the estimation is not constrained by determinacy, assuming wrongly that the policy is a feedback rule leads to biases in the estimation.

We therefore identify two sources of bias. The model coefficients will be biased if the true policy rule is misspecified. We refer to this as the misspecification bias. Imposing determinacy of the model solution in the estimation restricts the parameter space in a way that is dependant on the specific rule assumed. We refer to this as the determinacy bias. We estimate a simple New Keynesian model and show that we face a determinacy bias. We study some extensions of that model (including a HANK one) and show that the determinacy bias is pervasive. Finally we estimate the Smets-Wouters model and show that there is no determinacy bias, but a strong misspecification bias.