# RDP 9806: Policy Rules for Open Economies 4. Other Instrument Rules

This paper is part of a project to evaluate policy rules in alternative macroeconomic models. As part of the project, all authors are evaluating a list of six rules to see whether any performs well across a variety of models. Each of the rules has the general form:

where a, b, and c are constants. Table 1 gives the values of the constants in the six rules.

Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 Rule 6 a 2.0 0.2 0.5 0.5 0.2 0.3 0.8 1.0 0.5 1.0 0.06 0.08 1.0 1.0 0.0 0.0 2.86 2.86 ∞ 531.59 4.42 2.62 1.86 ∞ ∞ 5.18 6.55 3.43 4.05 ∞ ∞ ∞ 6.53 2.77 1.81 ∞ ∞ ∞ 7.59 3.91 4.22 ∞ ∞

All of these rules are inefficient in the current model. There are two separate problems. First, the rules are designed for closed economies, and therefore do not make the adjustments for exchange-rate effects discussed in the last section. Second, even if the economy were closed, the coefficients in most of the rules would be inefficient. To distinguish between these problems, I evaluate the rules in two versions of my model: the open-economy case considered above, and a closed-economy case obtained by setting δ and γ to zero. The latter is identical to the model in Ball (1997).

Table 1 presents the variances of output and inflation for the six rules. For comparison, I also include variances for some of the efficient rules in the last section. The six new rules fall into two categories. The first are those with c, the coefficient on lagged r, that are equal to or greater than one (rules 1, 2, 5 and 6). For these rules, the output and inflation variances range from large to infinite, both in closed and open economies. This result reflects the fact that efficient rules in either case do not include the lagged interest rate. Including this variable leads to inefficient oscillations in output and inflation.

The other rules, numbers 3 and 4, omit the lagged interest rate (c = 0). These rules perform well in a closed economy. Indeed, rule 4 is fully efficient in that case; rule 3 is not quite efficient, but it puts the economy close to the frontier (see Ball 1997). In an open economy, however, rules 3 and 4 are inefficient because they ignore the exchange rate. Rule 4, for example, produces an output variance of 1.86 and an inflation variance of 4.05. Using an efficient rule, policy can achieve the same output variance with an inflation variance of 3.54.

Recall that the set of efficient rules does not depend on the variances of the model's three shocks. In contrast, the losses from using an inefficient rule generally do depend on these variances. For rules 3 and 4, the losses are moderate when demand and inflation shocks are most important, but larger when the exchange-rate shock is most important. That is, using r as the policy instrument is most inefficient if there are large shocks to the r/e relation. In this case, r is an unreliable measure of the overall policy stance.

## Footnote

In the closed-economy case, I continue to assume β + δθ = 1. Therefore, since δ is zero, β is raised to one.