A Taylor rule and the Greenspan era.

There is considerable interest in determining whether monetary policy actions taken by the Federal Reserve under Chairman Alan Greenspan can be summarized by a Taylor rule. The original Taylor rule relates the federal funds rate target to two economic variables: lagged inflation and the output gap, with the actual federal funds rate completely adjusting to the target in each period (Taylor 1993). (1) The later assumption of complete adjustment has often been interpreted as indicating the policy rule is "non-inertial," or the Federal Reserve does not smooth interest rates. Inflation in the original Taylor rule is measured by the behavior of the GDP deflator and the output gap is the deviation of the log of real output from a linear trend. Taylor (1993) shows that from 1987 to 1992 policy actions did not differ significantly from prescriptions of this simple rule. Hence, according to the original Taylor rule, the Federal Reserve, at least during the early part of the Greenspan era, was backward looking, focused on headline inflation, and followed a non-inertial policy rule.

Recent research, however, suggests a different picture of the Federal Reserve under Chairman Greenspan. English, Nelson, and Sack (2002) present evidence that indicates policy actions during the Greenspan period are better explained by an "inertial" Taylor rule reflecting the presence of interest rate smoothing. (2) Blinder and Reis (2005) state that the Greenspan Fed focused on a "core" measure of inflation in adjusting its federal funds rate target. Clarida, Gali, and Gertler (2000), among others, have shown that a forward-looking Taylor rule that relates the current funds rate target to "expected" inflation and output developments appears to fit the data quite well over the period spanning the tenures of Chairmen Paul Volcker and Alan Greenspan. Orphanides (2001) argues that policy evaluations using policy rules estimated with the final revised data may be misleading.

This article estimates a Taylor rule that address three key features of the Greenspan period highlighted in recent research: the Federal Reserve under Greenspan was forward looking, focused on core inflation, and smoothed interest rates. Furthermore, this article uses the real-time data for economic variables and investigates whether results based on the final, revised data change when the real-time data are used. We also examine whether the use of real-time data leads to a better explanation of policy actions during the Greenspan period.

A Taylor rule incorporating the above-noted three features is shown below in equation (1.3).

[FR*.sub.t] = [[alpha].sub.0] + [[alpha].sub.[pi]][[pi].sub.t,j.sup.c] + [[alpha].sub.y](ln [y.sub.t,k] - ln [y*.sub.t,k]), (1.1)

[FR.sub.t] = [rho] [FR.sub.t-1] + (1 - [rho]) [FR*.sub.t] + [v.sub.t], (1.2)

[FR.sub.t] = [rho] [FR.sub.t-1] + (1 - [rho]){[[alpha].sub.0] + [[alpha].sub.[pi]][[pi].sub.t,j.sup.c] + [[alpha].sub.y] (ln [y.sub.t,k] - ln[y*.sub.t,k])} + [v.sub.t], (1.3)

where [FR.sub.t] is the actual federal funds rate, [FR*.sub.t] is the federal funds rate target, [[pi].sub.t,j.sup.c] is the j-period ahead forecast of core inflation made at time t, ln y is the log of actual output, ln y* is the log of potential output, and [v.sub.t] is the disturbance term. Thus, the term (ln [y.sub.t,k] - ln [y*.sub.t,k]) is the k-period ahead forecast of the output gap. Equation (1.1) relates the federal funds rate target to expected values of two economic fundamentals: core inflation and the output gap. The funds rate target is hereafter called the policy rate. The coefficients [[alpha].sub.[pi]] and [[alpha].sub.y] measure the long-term responses of the funds rate target to the expected inflation and the output gap. They are assumed to be positively signed, indicating that the Federal Reserve raises its funds rate target if inflation rises and/or the output gap is positive. Equation (1.2) is the standard partial adjustment equation, expressing the current funds rate as a weighted average of the current funds rate target [FR*.sub.t] and last quarter's actual value [FR.sub.t-1]. If the actual funds rate adjusts to its target within each period, then [rho] equals zero, which suggests that the Federal Reserve does not smooth interest rates. Equation (1.2) also includes a disturbance term, indicating that in the short run, the actual funds rate may deviate from the value implied by economic determinants specified in the policy rule. If we substitute equation (1.1) into (1.2), we get (1.3), a forward-looking "inertial" Taylor rule. (3)

This article estimates the Taylor rule (1.3) using final as well as real-time data. The real-time data consists of the Greenbook forecasts of core CPI inflation and the Congressional Budget Office (CBO) estimates of the output gap. (4) The policy rule estimated using the final data covers all of the Greenspan period from 1987:1 to 2005:4, whereas the rule estimated using the Greenbook forecasts spans part of the Greenspan period from 1987:1 to 2000:4, given the five-year lag in release of the Greenbook forecasts to the public. (5)

The empirical work presented here suggests several conclusions. First, policy response coefficients in the estimated inertial Taylor rule ([[alpha].sub.[pi]], [[alpha].sub.y], [rho]) are all positively signed and statistically significant. The key points to note are: (a) the estimated long-term inflation response coefficient [[alpha].sub.[pi]] is well above unity, which suggests that the Greenspan Fed responded strongly to expected inflation; (b) the estimated output gap response coefficient [[alpha].sub.y] is generally below unity, suggesting the presence of a relatively weak response to the output gap; and (c) the estimated partial adjustment coefficient [rho] is well above zero, indicating the presence of interest-rate smoothing. The conclusion suggested by the estimated Taylor rule, namely, the Greenspan Fed responded strongly to expected inflation developments ([[alpha].sub.[pi]] > 1) but relatively weakly to the output gap ([[alpha].sub.y] < 1), is in line with the recent work by Boivin (2006), who, using a different estimation methodology, reports time-varying estimates of inflation and the output gap response coefficients from 1970 to 1995. For the period since the mid-1980s, the reported estimated policy coefficients are stable and close to values as reported in this article. (6)

Second, the hypothesis that the Greenspan Fed paid attention to expected inflation and output gap developments is supported by additional test results. Those tests favor a forward-looking inertial Taylor rule over the one in which the Federal Reserve focuses on lagged inflation and the output gap. Furthermore, the results somewhat support the hypothesis that the Greenspan Fed was focused on core rather than on headline inflation.

Third, the Taylor rule estimated using the Greenbook core CPI inflation forecasts and the CBO's estimates of real-time output gap has a lower standard error of estimate and predicts policy actions better than the Taylor rule estimated using actual future inflation and the final, revised data on the output gap. However, there still remain several periods during which policy actions differ significantly from prescriptions of the simple Taylor rule. Hence, despite its better fit, the forward-looking inertial Taylor rule estimated here may not be considered a complete description of policy actions taken by the Greenspan Fed.

The rest of the article is organized as follows. Section 1 discusses estimation of the Greenspan policy rule and the real-time data that underlie the estimated policy rule. Section 2 discusses estimation results, and concluding observations are in Section 3.

1. EMPIRICAL METHODOLOGY

Estimation of the Forward-Looking Inertial Taylor Rule

One key objective of this article is to investigate whether monetary policy actions taken by the Federal Reserve under Chairman Greenspan can be summarized by a Taylor rule according to which the Federal Reserve was forward looking, focused on core inflation, and smoothed interest rates. We model the forward-looking nature of the policy rule by relating the current value of the funds rate target to the four-quarter-average expected inflation rate and the contemporaneous output gap. The policy rule incorporating these features is reproduced below in equation (2.3).

[FR.sub.t] = [rho] [FR.sub.t-1] + (1 - [rho]){[[alpha].sub.0] + [[alpha].sub.[pi]][bar.[pi].sub.t,[bar.4].sup.c] + [[alpha].sub.y](ln [y.sub.t] - ln [y*.sub.t])}, + [v.sub.t] (2.3)

where [bar.[pi].sub.t,[bar.4].sup.c] is the average of one-to-four-quarter-ahead forecasts of core CPI inflation made at time t and other variables as previously defined. (7)

The estimation of the policy rule in equation (2.3) raises several issues. The first issue relates to how we measure expected inflation and the output gap. The second issue relates to the nature of data used in estimation, namely, whether it is the real-time or final, revised data. As discussed earlier, the use of revised as opposed to the real-time data may affect estimates of policy coefficients and may provide a misleading historical analysis of policy actions (Orphanides 2001, 2002). …

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