INTEREST-RATE RULES: Consequences of Simple Policy Rules

When we study rules that can be described by only a small number of parameters, we study the consequences of parameter variation for two sorts of issues. First we analyze the range of parameter which ensure that a determinate rational expectations equilibrium exists; as an extensive prior literature has stressed, determinacy of equilibrium cannot be taken for granted in rational expectations models, especially in the case of a monetary policy defined by an interest-rate rule. (See, e.g., Bernanke and Woodford, 1997, for general discussion of this issue, and illustrations in the context of a model similar to the one that we use here.) Next we study the effect of parameter variation within the range of parameter values for which equilibrium is determinate.

Performance Measures for Alternative Rules

For each of the rules we consider, we compute a number of statistics relating to the variability of inflation, output and interest rates in the unique stationary rational expectations equilibrium associated with that rule. These statistics are reported in Table 1 for a number of rules of particular interest. The significance of the parameters a, b and с that define these rules is explained below.

Among the specific rules included in the table are several that are also considered in other papers in this volume. These are labeled A{ — Д, with i equal to 0 in the case of rules where the interest rate responds to contemporaneous output and inflation, while i equals 1 in the case where it responds with a lag. The table also reports the effects of setting the parameters at the values that represent the best rule (in the sense of minimization of our utility-based loss measure L -f 7Г*2) within each of several families of simple rules discussed below (these are labeled Eq — G0, and E\ — Gi). Finally, we also report the statistics associated with our estimate of actual U.S. policy during the period 1979-1995 (rule Я), and for the unconstrained optimal policy according to our model, discussed in section 3 (rule I).

The statistics reported in Table 1 include the variance of output around trend, the variance of inflation and the variance of the Federal funds rate. In addition to these conventional statistics, we also report the variance of quarterly innovations in the rational forecast of the long-run price level. This is the variance of changes in the variable
which is just the stochastic trend in the price level in the sense of Beveridge and Nelson (1982). (Note that it follows from this definition that the first difference of p°° is also the innovation in this variable.) We include this statistic as an alternative index of the degree of price stability associated with different equilibria. The advantage of this statistic is that it reflects the extent to which agents make capital gains and losses on long term nominal contracts and some analysts have expressed concern over these (e.g., Hall and Mankiw (1994)). Finally, we also report the coefficient of a regression of the innovation at t in the forecast of the long-run price level p°° on the quarter t innovation in the (log) price level at t + 1. (Recall that according to our model, the price level Pt+1 is determined at date t.) This coefficient tells us whether inflation innovations in quarter t eventually lead to a higher price level or whether instantaneous increases in the price level are later offset by subsequent expected reductions in prices. In the case of a random walk in the log price level, we should find Дэо = 1, while if temporary price-level increases are eventually completely offset, we should find /Зсо = 0.