INTEREST-RATE RULES: Rules Using Only Lagged Data 2


Inflationary shocks now lead to delayed increases in interest rates which imply delayed reductions in inflation. The rule then requires that subsequent interest rates fall so that inflation rises once again. For a sufficiently strong reaction of interest rates to lagged inflation, i.e., a high value of a, the resulting oscillations are explosive. Thus, the parameters that minimize the variance of тг in the case of a contemporaneous rule no longer do so when the government can only react with a delay. In particular, this minimization now requires that a be equal to about 15.
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INTEREST-RATE RULES: Rules Using Only Lagged Data

One criticism sometimes leveled (see, e.g., McCallum (1997)) against all rules of the kind considered thus far is that they require the Fed to make use of data about current output and inflation that it does not actually have when it sets the current interest rate. There are two reasons why such variables may simply be unobservable by the central bank. These are that some important economic data is collected retrospectively and that even the data that are collected concurrently need to be processed before their message about the economy as a whole can be distilled. A further difficulty with responding to contemporaneous variables may be that, even if these are observable immediately, the political process of responding to them takes time.
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INTEREST-RATE RULES: Rules that Involve a Lagged Inter est-Rate 2

The result is that the economy stays on a non-explosive path in which increases in inflation are matched by subsequent reductions in inflation which ensure that the interest rate does not explode. In fact, higher values of с actually increase the range of values of a for which a determinate equilibrium exists, by helping to solve the problem of indeterminacy discussed above.

The figure also shows that, within the range being considered, the goal of inflation stabilization is furthered by setting a to as large as possible. The variance of inflation reaches its minimum value (over the range of rules shown in the figure) when a equals 20 and с takes a positive value less than one. If the range of the figure were extended, the optimum would involve even higher values of a. Thus, the key to inflation stabilization remains making sure that the interest rate reacts vigorously to inflation.
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