On the observational (non)equivalence of money growth and interest rate rules

In this paper, we discuss the observational equivalence between two monetary policy rules: a constant money growth rule and an interest rate rule. From the equilibrium conditions of a sticky prices model, we consider: (i) the Taylor rule parameter implied by the model with exogenous money supply; and (ii) the parameter of the money growth process implied by the model with an interest rate rule. We then compare the parameters of the two monetary rules in each case to evaluate the equivalence property. We show that the two monetary policy rules are not observationally equivalent (except in a very implausible empirical case) and therefore that the way of modeling monetary policy is of importance.