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.

None of this denies that the central bank continually updates its estimate of the current state of the economy. And it should be recalled that our model of the delays in the response of output and inflation implies that the relevant data exist in principle in the quarter prior to the one in which the data must be used under rules (2.1) and (2.2). However, it is reasonable to suppose that the central bank’s estimate of the state of the economy generally differs from the economy’s actual state. In this case, responding to the current estimate of the current state differs from the rules (2.1) and (2.2). If rules of the form (2.1) and (2.2) are applied to the error-ridden current estimates, the interest rate is affected by the measurement error, and a thorough evaluation of these rules would require an analysis of these effects.

Thus we now suppose instead that the Federal Reserve does not respond to output and inflation variations except with a one quarter lag. In this class of rules,
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Considering the effect of such a lag also allows us to compare our results with other papers in this volume since some of these also include the rules we label A\ through D\ in Table 1.
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Even if the Fed had a reasonably accurate estimate of the current state of the economy, there would be good reasons to be interested in lagged-data rules of this form. In particular, the use of such rules would make Fed operations more transparent to the public at large if the public only had this lagged information. By avoiding the use of information that the public does not have, it becomes both easier to describe Fed operations and easier for people to detect when the Fed has departed from the rule. An alternative, of course, might be to respond to internal estimates and publish these estimates of the state of the economy as they become available. The study of this alternative, and its effects on transparency given that this estimate will at least sometimes be wrong, is clearly beyond the scope of this paper.
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We start in Figure 15 by displaying how the variance of inflation varies with a and b when с is set equal to zero. This Figure is quite different from Figure 5 which involves the same parameters and performance criterion in the case of contemporaneous Taylor rules. Unlike what occurs with rules where the interest rate responds contemporaneously, large values of a and b lead to unstable equilibria in the case where the interest rate responds only to lagged output and inflation. Ignoring 6, this can be understood as follows.