Monetary Policy Rules (I) : How Good is Simple?

This is a technical appendix to a group of papers being prepared, one of which is "Monetary Policy Rules in a Small Forward-Looking Macro Model." The present paper, the first of several, attempts to quantify the relative advantage of simple, Taylor-style interest rate rules vs. feedback rules derived from principles of optimal control theory. The vehicle for analysis is a small estimated annual model of inflation and output based on staggered real price contracting theory. By definition, constrained optimal rules are second best. The reaction parameters in both feedback rules are chosen to minimize an asymptotic loss function defined over a convex combination of the unconditional variances of output, inflation, and the nominal short-term interest rate chosen as the instrument. For illustration, we generate inflation-output volatility tradeoff frontiers by varying the relative weights in the loss function. For the estimated model at hand, best is not much better than second-best: the tradeoff frontiers for the optimal and simple optimal rules not being far apart. The performances of optimal and second-best rules, imputed from (a) sample estimates of volatility tradeoffs before and after the 1979 policy regime shift and (b) the asymptotic tradeoff implied by Taylor'd static rule can be evaluated by simulations. The main drawback of Taylor's static rule is that, after a shock, it takes the economy twice as long to return to equilibrium.The main shortcoming of simple rules is that they engender more oscillations than the more flexible optimal rules. The model is annual; but it is doubtful that our earth-shaking findings will be overturned with a quarterly model