Show Me the Money or Taking the Monetary Implications of a Monetary Model Seriously

It has become common practice in applied monetary economics to posit an interest rate rule, i.e. a variant of the Taylor rule, as a component of the economic environment. Since the general equilibrium settting also imposes a money demand relationship (e.g. placing real balances in the utility function or imposing a cash-in-advance setup), the interest rate rule implies that the money supply is endogenous. Rarely are the properties of the money supply implied by the model compared to the data. In this paper, we take the monetary implications of a monetary model seriously (we use a variant of the Christiano, Eichenbaum, and Evans (1997) limited participation model that permits both technology and money shocks) by first modeling the money supply as an exogenous Markov process and then calibrating the parameters of the Markov process to the data. We then examine whether the model produces an interest rate rule similar to the Taylor rule relationship observed in the data. The results from this exercise are instructive: the model is able to duplicate qualitatively the relationship between inflation and nominal interest implied by the Taylor rule but fails dramatically to replicate the correlation between nominal interest rates and output.