INTEREST-RATE RULES: Framework for Analysis 5

To complete our model specification, we posit that interest rates are set according to a
Here rt is the continuously-compounded nominal interest rate (identified with log Rt in terms of our theoretical model, and with the Federal funds rate in our empirical implementation of the model), r* is the steady-state value of r implied by the policy rule, and 7r* is the steady-state inflation rate implied by the rule read more.

In equilibrium, the steady state nominal interest rate r* must equal the sum of the equilibrium steady state real interest rate p and the steady state inflation rate 7Г*. Thus, if p is independent of the monetary policy rule (as our model implies8), the monetary authority’s choice of 7r* implies a value for r*. Thus the pair of values 7Г* and r* represent only a single free parameter in the specification of the policy rule, which we shall treat in the subsequent discussion as the choice of 7Г*.

The aim of our paper is to discuss the effects of alternative rules of the form of (1.23). In our discussion, we will generally treat separately the effects of the parameters а{, Ьг and c*, which indicate how the interest rate reacts to the history of the economy, and the effects of the choice of 7Г*. This is because, in our log-linear approximation to the model’s equilibrium conditions, the parameter тг* has no effect upon the implied responses to shocks (and hence upon the equilibrium variability of the various state variables), while the parameters aiy bx, have no effect upon the implied steady state (and hence upon the average equilibrium values of the state variables).

We may thus study separately the determination of the steady state and the determination of fluctuations around the steady state, and different parameters of the policy rule matter for each of these investigations. Our overall welfare criterion (discussed in the next subsection) depends, however, upon both aspects of equilibrium, and so upon both sets of policy parameters.

Our complete model of the economy consists of the IS and AS equations (1.11) and (1.22) together with the monetary policy rule (1.23). To evaluate the effect of changing the monetary rule we need to know both the parameters of the model as well as the stochastic process for the two structural disturbances, Gt and Yts, the first of which affects only our IS equation while the second affects only our AS equation. In Rotemberg and Woodford (1997, 1998) we describe both our method for estimating and calibrating the behavioral parameters as well as our approach to reconstructing the structural disturbances and their stochastic process. Here we give an outline of this approach.