Optimal Interest-Rate Rules: I. General Theory

This paper proposes a general method for deriving an optimal monetary policy rule in the case of a dynamic linear rational-expectations model and a quadratic objective function for policy. A commitment to a rule of the type proposed results in a determinate equilibrium in which the responses to shocks are optimal. Furthermore, the optimality of the proposed policy rule is independent of the specification of the stochastic disturbances. Finally, the proposed rules can be justified from a “timeless perspective,” so that commitment to such a rule need not imply time-inconsistent policy. We show that under fairly general conditions, optimal policy can be represented by a generalized Taylor rule, in which however the relation between the interest-rate instrument and the other target variables is not purely contemporaneous, as in Taylor’s specification. We also offer general conditions under which optimal policy can be represented by a “super-inertial” interest-rate rule, and under which it can be represented by a pure “targeting rule” that makes no explicit reference to the path of the instrument. ∗An earlier version of this work was delivered by the second author as the Jacob Marschak Lecture at the 2001 Far Eastern Meeting of the Econometric Society, Kobe, Japan, July 21, 2001. We thank Ed Nelson, Julio Rotemberg and Lars Svensson for helpful discussions, and the National Science Foundation, through a grant to the NBER, for research support. Both positive and normative accounts of monetary policy are often expressed in terms of systematic rules for determining the central bank’s operating target for a short-term nominal interest rate. For example, the “Taylor rule” (Taylor, 1993) expresses the Fed’s operating target for the federal funds rate as a linear function of a current inflation rate and a current measure of output relative to potential. Alternatively, “inflation targeting” is often described as a commitment to adjust a nominal interest-rate instrument as necessary in order to bring about an inflation projection (say, over a two-year horizon) consistent with the central bank’s inflation target (e.g., Vickers, 1998; Svensson, 1999a). A common feature of such prescriptions is that a precise criterion is given that should be checked each time an interest-rate decision is made, in order to determine whether the central bank’s current interest-rate target is acceptable or not, given the observed or projected behavior of variables such as inflation and the “output gap” (i.e., the variables that define the bank’s stabilization objectives, rather than any “intermediate” targets). This paper considers the optimal choice of a criterion of this form to guide monetary policy deliberations. The question has been extensively discussed in recent years. However, most of the recent literature assumes some low-dimensional parametric family of policy rules, and then optimizes over the coefficients of the rule, using an economic model to compute the equilibrium associated with each possible set of parameters. A characteristic weakness of such work, in our view, is that the conclusions reached about the optimal values of certain parameters are likely to be strongly influenced by the parametric family of rules considered, i.e., by which other kinds of feedback are assumed not to be possible. Hence we propose here to take a different approach. We propose first to characterize the best possible pattern of equilibrium responses to disturbances — solving an optimization problem in which the structural equations of one’s model of the economy appear as constraints — and then ask what kind of policy rule can bring about the desired equilibrium. This alternative approach is standard in the theory of public finance, and is also used in See, e.g., the papers in Taylor (1999). This includes our own previous studies, such as Rotemberg and Woodford (1999).