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Working Paper Series
The Taylor Principle, Interest Rate
Smoothing and Fed Policy in the 1970s
and 1980s
WP 02-03
This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/
Yash P. Mehra
Federal Reserve Bank of Richmond
The Taylor Principle, Interest Rate Smoothing and Fed Policy in the 1970s and 1980s*
Yash P. Mehra**
Federal Reserve Bank of Richmond Working Paper No. 02-03
August 27, 2001
Revised: August 1, 2002
JEL Nos. E43, E58
Keywords: real time data, Fed policy, Taylor principle, smoothing
Abstract
Using real time estimates of output gaps or Greenbook forecasts of the unemployment
rate, this article estimates Taylor-type policy rules that predict the actual behavior of the
funds rate during two sample periods, 1968Q1 to 1979Q2 and 1979Q3 to 1994Q4. The
inflation rate response coefficient is close to unity over the first sub-period and well
above unity over the second, suggesting Fed policy violated the Taylor principle during
the first period. The adjustment of the funds rate in response to fundamentals is not as
rapid during the first period as it is during the second. Together these results support the
conventional view that the Fed was “too timid” and “too sluggish” during the late 1960s
and the 1970s. Though the Fed smoothes interest rates, the degree of smoothing exhibited
is far less than what was previously estimated. The funds rate response to its
fundamentals is complete within one year during the first period and within one quarter
during the second.
*The opinions expressed are those of the author and do not necessarily reflect views of
the Federal Reserve Bank of Richmond or the Board of Governors of the Federal Reserve
System. The author would like to thank Mike Dotsey, Marvin Goodfriend, Robert Hetzel,
Bennett McCallum, and Glenn Rudebusch for helpful comments and suggestions.
** Federal Reserve Bank of Richmond, Yash.Mehra@rich.frb.org
2
1. Introduction
During the late 1960s and 1970s inflation steadily increased, whereas during the
early 1980s inflation declined. This contrast in the inflation performance of the U.S.
economy has sparked interest in identifying the nature of monetary policy pursued by the
Federal Reserve. One widely held view is that monetary policy has been broadly
consistent with Taylor-type policy rules in which the funds rate target responds to actual
or expected inflation and the level of the output gap. A key coefficient in these estimated
policy rules is the inflation response coefficient, which measures the long-term response
of the funds rate to the inflation rate. Taylor (1999a) and Clarida, Gali and Gertler (2000)
provide evidence that indicates the inflation response coefficient was below unity during
the late 1960s and 1970s, whereas it was well above unity during the early 1980s. This
empirical result implies that the Fed did not respond aggressively to inflation during the
first period, whereas it did during the second period. This explanation of the poor
inflation performance of the U.S. economy in the 1970s relative to the 1980s has received
further support from recent research on monetary policy rules. That research indicates
that, in order to avoid undesirable economic outcomes, feedback policy rules must satisfy
the Taylor principle, which requires the nominal interest rate eventually increase by more
than one percentage point in response to one percentage point increase in the inflation
rate (Taylor 1999b). This requirement is easily met if the inflation response coefficient in
the feedback policy rules is set above unity.1, 2
1
The exact statement of this requirement in the context of an optimal feedback rule
depends upon the nature of the macro model that underlies the policy rule. For example,
in the context of the “neo-Wicksellian” model derived in Woodford (2000), the feedback
rule must satisfy the following condition aπ + a y (1 − β ) / k > 1 , where aπ is the inflation
response coefficient; a y is the output response coefficient; and β and k are the slope
parameters of the expectational Philips curve (Woodford 2001). This requirement is
easily met if the inflation response coefficient is above unity.
2
Some other consequences of the violation of the Taylor principle are a matter of debate
among economists. While Woodford (2000) has focused on the absence of determinacy
when the Taylor principle is not met, McCallum (2000) has instead emphasized the
absence of expectational stability in models with learning in the same case.
3
The evidence discussed above in Taylor (1999a) and Clarida et al. (2000) that
actual Fed policy may have violated the Taylor principle during the late 1960s and 1970s
is based on policy rules that are estimated using revised data. As documented recently in
Orphanides (1999) and Orphanides and Norden (1999), estimates of inflation and, in
particular, of output gap levels have been substantially revised over time. Hence, policy
prescriptions based on real-time estimates of the variables used in policy rules may differ
substantially from those derived using later estimates, making inferences about the nature
of actual policy suspect. In that context, taking the baseline Taylor rule originally
proposed in Taylor (1993) and using real-time estimates of output gaps prepared by the
Council of Economic Advisors, Orphanides (2000) shows that the funds rate settings that
would have been suggested by the baseline Taylor rule during the 1970s do not greatly
differ from actual policy during that period.3 More recently, Orphanides (2002) has
estimated a forward-looking version of the Taylor rule, using forecasts of the inflation
rate and unemployment rate available to FOMC in real time and assuming partial
adjustment. Since the inflation response coefficient both in the baseline Taylor rule and in
its estimated forward-looking version in Orphanides (2002) is above unity, this finding
raises serious doubts about the stabilization properties of the policy rules that satisfy the
Taylor principle.
Orphanides (2000) uses estimates of output gaps prepared by the Council of
Economic Advisors (CEA) and asserts them as the “official” series used by the Fed. This
assertion has been questioned. Taylor (2000) points out that the Council’s estimates of
potential GDP and its growth rate had become politicized as early as the late 1960s and
hence were ignored by serious economists such as Arthur Burns and Alan Greenspan.
Taylor also argues that real-time output gaps derived from the Council’s estimates (e.g.,
minus 15 percent in 1975) are too pessimistic, being comparable to the Great Depression
(p.# 4, op. cited). In this article, I consider an alternative real-time estimate of the output
gap, generated using a simple linear trend fitted to actual historical data on output. The
hypothesis that potential output during the 1960s and the early 1970s may reasonably be
3
The baseline Taylor rule makes the assumptions that the inflation response coefficient is
1.5, the output response coefficient is .5, the real rate of interest is 2 percent, and the
Fed’s inflation target is 2 percent.
4
approximated by a linear trend is quite consistent with the mainstream contemporary
thinking that macroeconomic time series possessed deterministic time trends. The
alternative real-time output gaps are pessimistic, but not as much as those in Orphanides
(2000).
The baseline Taylor rule originally proposed in Taylor (1993) assumes that the
Fed adjusts the funds rate in response to changes in fundamentals without any delay. In
other words, the policy rule does not assume partial adjustment, implying the absence of
interest rate smoothing. This feature of the baseline Taylor rule is in sharp contrast to the
evidence in previous empirical work that indicates the presence of considerable interest
rate smoothing in Fed behavior i.e., Clarida et. al. (2000) where the forward-looking
Taylor rule is estimated using revised data and Orphanides (2002) where the forwardlooking Taylor rule is estimated using real-time data. This empirical evidence has
recently been challenged. Rudebusch (2001) points out that the presence of monetary
policy inertia would imply a large amount of forecastable variation in interests rates at
horizons of more than three months, which is contradicted by evidence from the term
structure of interest rates. He argues that the monetary policy inertia exhibited in
estimated policy rules may be illusionary, reflecting instead the use of revised data in
estimation and/or the presence of serially correlated shocks that central banks face but are
ignored in estimated policy rules. Some evidence consistent with his view appears in
Lansing (2000,2002) where it is shown the presence of real-time output gap errors can
spuriously generate significant coefficients on the lagged dependent variable in the
estimated policy rules.4
In this article, I reexamine the nature of actual Fed policy during the 1970s and
1980s. In particular, I estimate Taylor-type policy rules using alternative, real-time
estimates of output gaps and then investigate how well estimated rules predict the actual
path of the funds rate and whether or not they satisfy the Taylor principle. To check
robustness of results based on output gaps I also consider results derived using
Greenbook forecasts of the unemployment rate and inflation rate available in real time to
policymakers. The empirical work here focuses on explaining the actual behavior of the
5
funds rate during two sample periods, 1968Q1 to 1979Q2 and 1979Q3 to 1994Q4. The
first period is close to the one studied in Orphanides (2000, 2002) and the second period
is close to the one studied in Clarida et. al. (2000).5 As noted in Rudebusch (2001), it is
easier to identify empirically the degree of monetary policy inertia if the estimated policy
rules control for the influences of serially correlated shocks to policy. The recent
evidence in Mehra (2001) indicates actual policy since the 1980s is well predicted by a
modified Taylor rule that includes the response of policy to inflation scares, discussed in
Goodfriend (1993). Hence for the second period I consider results with and without
capturing the response of policy to inflation scares and examine its implication for the
presence of partial adjustment in estimated policy rules.
The empirical work that is presented here suggests the following observations.
First, Taylor-type policy rules based on alternative real-time output gaps are consistent
with actual policy during these two periods. In the first period, the actual funds rate
settings are predicted well by an estimated Taylor rule in which the funds rate responds to
the lagged inflation rate and the output gap. In the second period, the actual funds rate
settings are predicted well by a modified Taylor rule in which the funds rate responds to
the bond rate, in addition to responding to the lagged inflation rate and the output gap.
The results suggest policy was “preemptive” during the second period as the Fed
responded to the bond rate in an attempt to establish credibility.6 The results continue to
hold if policy rules are estimated, using instead Greenbook forecasts of the inflation rate
and unemployment rate.
Second, the inflation and output response coefficients in these estimated policy
rules have correct signs and are generally significant. If we focus on the backwardlooking Taylor rule in which policy responds to the lagged inflation rate and the output
gap, then the inflation response coefficient is well above unity during the second period,
4
In the context of money demand regressions, Goodfriend (1985) much earlier showed
that measurement error in the variables determining money demand could result in
spuriously significant partial adjustment lags.
5
I truncate the sample in 1994 to exclude the possible influences of the new economy
shifts in trend productivity and the international financial crises on monetary policy in the
last half the 1990s.
6
This result is in line with one in Mehra (2001).
6
but not during the first. This result continues to hold if Taylor rules are estimated using
instead Greenbook forecasts of the inflation rate and unemployment rate.
Third, the extent of partial adjustment estimated here is far less than what was
reported in previous empirical work. In the first period, the estimated Taylor rule
indicates that the Fed adjusted the funds rate to its desired level within one year. Tests
designed to distinguish partial adjustment from serial correlation do not rule out the
hypothesis that the partial adjustment found in the estimated Taylor rule is due to serial
correlation. In the second period, the estimated modified Taylor rule indicates that the
Fed adjusted the funds rate to its desired level within one quarter. The partial adjustment
is found only if the Taylor rule is estimated omitting the response of policy to inflation
scares. Together the results above indicate that the Fed was “too timid” and “too
sluggish” during the first period.
The plan of this article is as follows. Section 2 describes the policy rules and realtime data used in estimation and section 3 presents the empirical results. Concluding
observations are given in section 4.
2. The Model and the Method
2.1. Conventional and Modified Taylor Rules
The conventional backward- and forward looking Taylor rule studied here can be
derived using the following equations.
FRt = a0 + aπ ( Et −1 INFLt + k − INFL*) + a y Et −1 ( yt + k − yt*+k );
( 1)
FRt = ρ FRt −1 + (1 − ρ ) FRt* + vt ; 0 ≤ ρ ≤ 1;
(2)
*
where FR is the actual funds rate; FR* is the Fed’s funds rate target for period t;
Et −1 INFLt + k is the expected inflation rate for period t+k conditional on the information
available in period t-1; INFL* is the Fed’s inflation target; Et −1 ( yt + k − yt*+ k ) is the
expected level of the output gap for period t+k; and v is the disturbance term. The policy
rule in (1) specifies the economic determinants of the funds rate target. The policy rule is
forward looking if k ≥ 0 and backward looking if k < 0 . It is assumed that the Fed has a
target for inflation and a target for the level of output. The Fed raises its funds rate target
7
if past or expected future inflation and output are high relative to their respective target
levels. Equation (2) specifies the actual funds rate as a weighted average of the lastperiod funds rate and the current-period funds rate target, indicating the Fed smoothes
interest rate changes in the short run (Goodfriend [1991]). The magnitude of the partial
adjustment parameter ρ measures the degree of interest rate smoothing in Fed behavior.
If we substitute (1) into (2), we get (3), which is the conventional Taylor rule.
FRt = a00 + ρ FRt −1 + (1 − ρ )aπ Et −1 INFLt +k + (1 − ρ )a y Et −1 ( yt +k − yt*+ k ) + vt
where a00 = ( a0 − aπ INFL* ) (1 − ρ )
(3)
The funds rate in policy rule (3) responds to the inflation rate, the output gap and the
lagged actual funds rate.
Taylor (1999a, p. 339) points out that monetary policy during the early 1980s may
have been tighter than what is indicated by the baseline Taylor rule (Taylor [1993]). Such
a tighter policy response may have been necessary to keep expectations of inflation from
rising and to help establish the credibility of the Fed, as noted in Goodfriend (1993).
Mehra (2001) presents evidence that indicates the Fed responded to inflation scares as
reflected in the bond rate, and that the Taylor rule modified to include such responses
help predict actual policy well during this period. In view of such evidence, the Taylor
rule for this period is estimated including the bond rate as in (4).
FRt = a0 + aπ ( Et −1 INFLt + k − INFL*) + a y Et −1 ( y t + k − yt*+ k ) + ab ( BRt − Et −1 INFt + k )
*
(4)
where BR is the bond rate. If we substitute (4) into (2), we get the modified Taylor rule
(5).
FRt = a00 + ρ FRt −1 + (1 − ρ )aπ Et −1 INFLt + k + (1 − ρ )a y Et −1 ( yt + k − yt*+ k )
+ (1 − ρ )ab ( BRt − Et −1 INFt + k ) + vt
(5)
where a00 = ( a0 − aπ INFL* ) (1 − ρ )
The funds rate in policy rule (5) responds to the bond rate, in addition to responding to
past or expected future inflation rate, the output gap, and the lagged funds rate.
2.2. Partial Adjustment, Serial Correlation, and Interest Rate Smoothing
8
The policy rules in (3) and (5) assume partial adjustment and therefore include the
lagged value of the actual funds rate. The presence of the lagged dependent variable in
these policy rules is often interpreted as reflecting the presence of interest rate smoothing
in Fed behavior, because the Fed’s adjustment of the policy rate to its desired level
suggested by economic fundamentals is spread over time. However, as is well known, the
lagged dependent variable in the policy rule can also arise as a result of the presence of a
serially correlated error term (Griliches [1967]). Consider, for example, the following
specification that assumes no partial adjustment as in (6.1).
FRt = FRt* + vt ; 0 ≤ s ≤ 1;
(6.1)
vt = s vt −1 + µt
(6.2)
where vt is a serially correlated error term and µt is a white noise disturbance term. The
equation (6.1) says the Fed adjusts the actual funds rate to its target ( FRt* ) implied by
economic fundamentals within each time period. If we substitute (6.2) into (6.1), we can
then express the policy rule as in (7).
Serially Correlated Model
FRt = FRt* − sFRt*−1 + sFRt −1 + µt ; 0 ≤ s ≤ 1;
(7)
As can be seen, the lagged dependent variable also appears in the serially correlated
model (7.1), indicating the adjustment of the actual funds rate to its target implied by
economic fundamentals is spread over time, just as in the partial-adjustment model (2).
Hence the presence of the lagged dependent variable in an estimated policy rule does not
necessarily imply the Fed is smoothing interest rates.
In most previous research Taylor rules have been estimated assuming partial
adjustment. However, it is possible that both partial adjustment and serial correlation may
be present in the estimated policy rule. The serial correlation may just be capturing the
responses of policy to economic factors that are not included in the estimated policy rule.
Hence I estimate the policy rules in (3) and (5) allowing for the potential presence of
serial correlation. Furthermore, in order to test whether the lagged dependent variable in
the estimated policy rule is due to partial adjustment or serial correlation, I estimate the
policy rules assuming both partial adjustment and (first-order) serial correlation as in (8).
9
FRt = ρ FRt −1 + (1 − ρ ) FRt* + vt ; 0 ≤ ρ ≤ 1;
(8.1)
vt = s vt −1 + µt ;
(8.2)
0 ≤ s ≤1
where the parameter s is the first-order serial correlation coefficient and where other
variables are defined as before. If we substitute (8.2) into (8.1), we can express the policy
rule as in (9).
FRt = ( ρ + s ) FRt −1 + (1 − ρ )( FRt* − sFRt*−1 ) − s ρ FRt −2 + µt
(9)
where all variables are defined as before. The policy rule in (9) nests partial adjustment
and serial correlation.7 The policy rule is inertial if s = 0, ρ ≠ 0 in (9). The policy rule is
non-inertial but has serially correlated shocks if s ≠ 0, ρ = 0 . Alternatively, the policy
rule is inertial as well have serial correlation if ρ , s ≠ 0 . I provide some evidence on the
extent of partial adjustment by estimating (9), using the determinants of the funds rate
target FRt* alternatively defined in (1) and (4).
2.3. Data, Definition of Economic Variables, and Estimation Procedure
The empirical work here estimates the policy rules in (3) and (5) using quarterly
data over two sample periods, 1968Q1 to 1979Q2 and 1979Q3 to 1994Q4. All interest
rate data used is the average value in the first month of the quarter. The funds rate is the
effective federal funds rate and the bond rate is the nominal yield on ten-year U.S.
Treasury bonds. The real-time estimates of the inflation rate and output gaps during the
sample periods studied are generated using the real-time data compiled by Croushore and
Stark (1999). The real-time quarterly value of the inflation rate for any given quarter
(1968Q1, for example) is the end-of-sample value of the annualized, quarterly percentage
change series constructed using the available real-time price series that starts in 1953Q1
and ends in that quarter. The estimates of potential output for each quarter over 1968Q1
to 1979Q2 are generated fitting each time a linear time trend using historical data on
output available each quarter. Thus the real-time value of the output gap in 1968Q1 is the
end-of-sample value of the residual from the linear time- trend regression, fitted using the
available historical data on real output that begins in 1953Q1 and ends in 1968Q1. A
similar procedure is used to generate estimates of the output gap over 1979Q3 to 1994Q4,
7
This exercise is qualitatively similar to one in Rudebusch (2001).
10
except that a quadratic time trend is employed and the historical output series used starts
in 1959Q1.
For the first period, the procedure of estimating trend output using a linear time
trend is reasonable, because for most of this time period it was thought that economic
time series, including potential output, follow deterministic time trends. Since the
economy grew quite strongly during the 1950s and the 1960s, the linear trend procedure
generates growth estimates of trend output that are optimistic.
The productivity slowdown and the oil price shocks of the 1970s made it clear
that potential output could be influenced by supply shocks and hence could not be
approximated by simple time trends. Initially, this led to the development of alternative
methods over the 1970s, such as the segmented linear trend and the production function
approach. It was during the late 1970s that the new thinking on the econometrics of time
series with unit roots began to undermine the popularity of segmented time trends to
measure the potential, subsequently giving rise to the use of stochastic methods.8 Hence,
for the period 1979Q3 to 1994Q4 I use a quadratic time trend to estimate the level of
output gap, as in Clarida et al. (2000).9
Figures 1 and 2 provide a cursory look at real-time estimates of the inflation rate
and output gaps. In order to get a sense of the size and nature of revisions in measures of
inflation and output over the periods studied, I also chart those measures based on the
data currently available in 2000. Figure 1 charts the data for the period 1968Q1 to
1979Q2 and Figure 2 for 1979Q3 to 1994Q4. If we focus on the inflation rate for the first
period, real-time estimates of the inflation rate do not differ much from those generated
using the revised data (see Figure 1A). In contrast, estimates of the output gap based on
the revised data differ substantially from those derived using real-time data. As can be
seen in Figure 1B, real-time estimates of output gaps are pessimistic in the 1970s, but not
quite so much as argued in Orphanides (2000). The gap between the revised and real-time
estimate of the output gap was about 1 percentage point at the start of the sample in
8
This view of the historical evolution of potential output is in Laxton and Tetlow (1992).
For this period I examine the sensitivity of results to the choice of an alternative detrending procedure used to estimate the potential output. In particular, real-time estimates
of output gaps were also generated using alternatively a linear trend and a HodrickPrescott filter.
9
11
1968Q1, but then it increased considerably during the early 1970s -- exceeding almost 9
percentage points during the first quarter of 1975 (see Figure 1B). In contrast, the output
gap series in Orphanides (2000) shows a gap of 15 percent in the mid-1970s. 10
Figure 2 charts the data for the period 1979Q3 to 1994Q4. As can be seen, the
revised estimates of inflation do not differ consistently from those based on real-time
data. However, estimates of the output gap based on real-time data still differ consistently
from those based on the revised data. In contrast to the first period, real-time estimates of
the output gap appear mostly optimistic following the 1980 recession, indicating the
presence of less slack than indicated by revised estimates. The gap between the revised
and real-time estimates of the output gap has not varied as much, however, in the 1980s
and early 1990s as it did in the 1970s.
The policy rules in (3) and (5) include the lagged value of the funds rate. Ordinary
least squares are inconsistent if the disturbance term in these policy rules is serially
correlated. The presence of serial correlation implies the disturbance term ( vt in (3) or
(5)) is correlated with the lagged funds rate ( FRt −1 ) included in these policy rules
(Johnston 1972). Furthermore, the policy rule in (5) includes the current-period bond rate,
which may also be correlated with the disturbance term. The preliminary work indicated
that in the first period the residuals from the estimated Taylor rule are serially correlated,
whereas no such serial correlation is found in the second period.11 I therefore estimate the
policy rules using the instrument variables procedure. The instrument set used for the
policy rule in (3) consists of a constant, past values of the inflation rate and the output
gap and the period t-2 lagged values of the funds rate. For the modified Taylor rule, the
10
It may be pointed out that estimates of output gaps generated here are reasonable in
that they imply estimates of the natural rate that are in the mainstream contemporary
thinking. For example, for the first half of the 1970s and using the Okun’s Law
coefficient of 3, the natural unemployment rate implied by the output gap is 5.1 percent.
For the full sample period 1968Q1 to 1979Q2, the implied natural rate is 4.9 percent.
11
The autocorrelation function fitted to residuals from the conventional Taylor rule (3)
estimated over the first period 1968Q1 to 1979Q2 is consistent with the presence of firstorder serial correlation. In contrast, the autocorrelation function fitted to residuals from
the modified Taylor rule (5) estimated over 1979Q3 to 1994Q4 indicates the residuals are
not serially correlated (see Table 1 for the first four autocorrelations).
12
instrument set is expanded to include past values of the spread between the bond rate and
the funds rate.
3. Empirical Results
3.1 Estimates of Policy Rules
Table 1 presents instrument variables estimates of the conventional and modified
Taylor rules specified in (3) and (5) and with k set to minus unity. Panel A presents the
estimates for the period 1968Q1 to 1979Q2 and Panel B for the period 1979Q3 to
1994Q4. I estimate the rules smoothing the inflation rate with and without assuming
partial adjustment.12 If we focus on estimates of the conventional Taylor rule for the
earlier period, we see that inflation and output gap variables appear with expected signs
and are statistically significant (see t-values in parentheses below estimates in Panel A,
Table 1). Those estimates indicate that the funds rate rises if the inflation rate rises, or if
actual output is above the potential. The inflation response coefficient is 1.1 to 1.2 and
the output response coefficient is .54 to .65. The statistic ST that tests the hypothesis the
inflation response coefficient is unity is small, implying the policy rule during this period
may have violated the Taylor principle. The estimated partial adjustment coefficient ρ is
.44, indicating 56 percent of a desired change in the policy rate is reflected in the funds
rate within the quarter of the change. This result means that during this period most of the
Fed’s adjustment of the funds rate to its desired level is complete within a year.
Panel B in Table 1 presents estimates of the Taylor rule for the period 1979Q3 to
1994Q4. I present results with and without the bond rate and with and without assuming
partial adjustment. As can be seen, inflation and the bond rate variables have expected
signs and are significant. The inflation response coefficient is 1.7 to 1.9. The statistic ST
that tests the hypothesis the inflation response coefficient is unity is large, suggesting the
inflation response coefficient is above unity. The output gap response coefficient is
positive and generally significant. Finally, as can be seen in Panel B of Table 1, the
lagged dependent variable appears with a positive and statistically significant coefficient
12
Following Taylor (1999a), the smoothed inflation rate is the average value of the
inflation rate over the past four quarters. The quarterly data on the output gap variable is
not smoothed.
13
only if the Taylor rule is estimated without the bond rate. Hence the lagged dependent
variable seems to be picking up the response of policy to inflation scares that is omitted
from the estimated conventional Taylor rule. The estimated modified Taylor rule implies
that during this period 100 percent of a desired change in the policy rate is reflected in the
funds rate within the quarter of the change.
3.2. Assessing the Predictive Accuracy of Policy Rules
I now assess how well these estimated Taylor-type policy rules predict the actual
behavior of the funds rate during the two sample periods considered here. Figures 3 and 4
provide a casual look at the performance of these rules in predicting actual funds rate
settings. Figure 3 charts the funds rate predicted by the conventional Taylor rule in the
late 1960s and the 1970s. I use the Taylor rule with ρ set to zero. Figure 4 does so using
the modified Taylor rule in the 1980s and early 1990s. Actual values of the funds rate are
also charted. These figures clearly indicate that the policy rules estimated here track the
actual settings of the funds rate over these two periods very well.
In order to further assess whether actual funds rate settings systematically differ
from those prescribed by these estimated policy rules, I perform the test of unbiasedness
with the following regression (10).
FRt = f 0 + f1 PFRt + ε t ;
(10)
where FR is the actual funds rate and PFR is the value predicted by the estimated policy
rule. The predicted values used are the dynamic within-sample values, generated using
actual values of the inflation rate and the output gap. The predicted funds rate is an
unbiased predictor of the actual funds rate if f 0 = 0 and f1 = 1 in (10).
Table 2 reports estimates of regression (10). Panel A presents the results for the
period 1968Q1 to 1979Q2 and Panel B does so for the period 1981Q1 to 1994Q4. I
present results using the policy rules estimated with and without partial adjustment. If we
focus on the results for the first sample period, they indicate that the conventional Taylor
rule estimated with partial adjustment provides unbiased forecasts of the actual funds
rate. This result continues to hold even when the Taylor rule is estimated without partial
14
adjustment, suggesting actual policy settings may have been generated by a Taylor rule
with no partial adjustment. This result also implies that in the first period it is difficult to
distinguish between partial adjustment and serial correlation. In contrast, if we focus on
results for the second period 1979Q3 to 1994Q4, only the modified Taylor rule provides
unbiased forecasts of actual funds rate settings. Together these results indicate that during
the late 1960s and the 1970s the Fed was “too timid” as well as probably “too sluggish”
in adjusting the funds rate in response to changes in economic fundamentals including the
inflation rate.
3.3. Additional Results
In this section I present and discuss some additional work that suggests the main
conclusions reached here are robust to changes in the specification of the policy rule. The
policy rules discussed above are estimated without directly allowing for the presence of
serial correlation. I now consider the policy rules that allow both partial adjustment and
(first-order) serial correlation as in (9). Table 3 presents estimates of the conventional and
modified Taylor rules for the two sample periods. As can be seen, the inflation response
coefficient is way above unity only in the second period. In the first sample period, the
coefficients that measure partial adjustment and serial correlation are both positive and
jointly significant, though individually neither coefficient is significant at the
conventional significance level (see F and t-values in Panel A, Table 3). This result
indicates that in this sample period the hypothesis that the policy rule is non-inertial can
not be distinguished from the hypothesis that the policy rule is inertial.13 In contrast, the
coefficients that measure partial adjustment and serial correlation are both zero in the
modified Taylor rule estimated over the second period. The partial adjustment coefficient
is different from zero only if the policy rule is estimated without capturing the response
of policy to the bond rate (see estimates in Panel B, Table 3). This result indicates the
partial adjustment found in the estimated conventional Taylor rules may be capturing the
influences of variables on policy that are omitted from the policy rule.
13
This result is consistent with unbiasedness test results reported in Table 2, which is the
Taylor rule without partial adjustment provides unbiased forecasts of actual policy rate
settings as do the Taylor rule with partial adjustment
15
In order to explore further the role of revised data in generating high estimates of
partial adjustment reported in previous research, Table 4 presents the conventional and
modified Taylor rules estimated using revised data. Rows 1.2 and 2.2 of Table 4 present
instrumental variables estimates of the conventional Taylor rule with partial adjustment
and revised data. In both sample periods, the use of revised data in the estimated
conventional Taylor rule yields an estimate of quarterly partial adjustment that is slower
than what we get with real-time data (compare estimates of (1 − ρ ) in rows 1.1 with 1.2
and 2.1 with 2.2, Table 4). However, the use of revised data has no effect on estimates of
the partial adjustment coefficient if the modified Taylor rule is estimated as in the second
period. Together these results suggest that omitted variables and hence the consequent
presence of serial correlation in estimated conventional Taylor rules may have played a
greater role in generating high estimates of partial adjustment found in previous research
(Taylor 1999a, Clarida et al. 2000).
One key result here is that the inflation response coefficient is close to unity in the
first period. This result is based on the Taylor rule that is backward-looking in the sense
that policy responds to the lagged inflation rate and output gap. It has been suggested that
policy may have been forward-looking during the first period. In fact, Clarida et al.
(2000) report estimates of the forward-looking version of the Taylor rule using revised
data, whereas Orphanides (2002) report estimates using forecasts of the inflation rate and
unemployment rate available to FOMC in real time. The inflation response coefficient
reported in Clarida et al. (2000) is generally below unity, but that reported in Orphanides
(2002), however, is above unity. In order to test whether the results here are sensitive to
the chosen specification, I now consider results from the forward-looking versions of the
Taylor rule estimated using instead the unemployment rate gap as in (11).
FRt* = a + aπ ( Et −1 INFt +1 − INF *) − au ( Et −1URt +1 − NURt +1 )
(11)
where UR is the unemployment rate and NUR is the natural unemployment rate. In order
to estimate (11) I use Greenbook forecasts of the inflation rate and unemployment rate
available to policy makers in real time. However, one also needs estimates of the natural
unemployment rate available to policymakers in real time. Orphanides (2002) estimates a
Taylor rule like (11) assuming the policymakers’ views about the level of the natural
unemployment rate have remained constant in the first period. I however consider the
16
possibility that policymakers’ views about the natural rate might have changed in real
time. Following the suggestion in Friedman (1968) that the unemployment rate fluctuates
around the natural rate irrespective of monetary regime, Hall (1999) has suggested that
the average value of the unemployment rate over the sample period is a good estimate of
the natural rate. Hence I construct real-time estimates of the natural rate for each quarter
in 1968Q1 to 1979Q2 by taking the one-sided simple average of the historical time series
on the unemployment rate.14 Figure 5 charts the natural rate series. Greenbook forecasts
and actual values of inflation and the unemployment rate are also charted there.
Table 5 reports estimates of forward-looking Taylor rules. For the first period I
report results with and without partial adjustment and with and without assuming
constant natural rate. Ordinary least squares are used to estimate the Taylor rule without
partial adjustment. If we focus on the Taylor rule without partial adjustment, then the
estimated inflation response coefficient is close to unity and this result is not sensitive to
whether the natural rate is assumed to be constant or time-varying over the sample period
(see estimates in Panel A, Table 5). In contrast, when we focus on the Taylor rule with
partial adjustment, then the inflation response coefficient is significantly above unity if
the Taylor rule is estimated using least squares and assuming constant natural rate. This
regression is similar in spirit to the one reported in previous research (Orphanides 2002).
But the result that the inflation response coefficient is significantly above unity is subject
to the omitted variable biases arising as a result of the failure to account for the presence
of serially correlated shocks15 and incorrectly assuming constant natural rate. If we use
instrumental variables to estimate the Taylor rule16 and allow varying natural rate, then
the estimated inflation response coefficient is 1.2, not significantly different from unity
14
The historical series used begins in 1953Q1.
As indicated before, least-square estimates are inconsistent in the presence of serial
correlation if the regression contains the lagged dependent variable. The first three
autocorrelation coefficients estimated using the residuals from the Taylor rule (with no
partial adjustment) are large (see si , i = 1, 2,3 in Table 5).
15
16
Since the disturbance term is correlated with the lagged dependent variable due to the
presence of serial correlation, the instrumental variables procedure corrects for the
presence of this correlation. The instrument set used consists of a constant, three lagged
values of Greenbook forecasts of the inflation rate, unemployment rate, and period t-2
lagged values of the actual funds rate.
17
(see estimates and the ST statistic in the pertinent regression, Panel A, Table 5).
Alternatively, if we estimate the Taylor rule assuming both partial adjustment and firstorder serial correlation as in (9) and use non-linear least squares, then the estimated
inflation response coefficient is again 1.2 with a t-value of 5.0. The F statistic that tests
the null hypothesis the inflation response coefficient is unity is small (.89), implying the
inflation response coefficient is not different from unity. Together these results suggest
that greater than unitary inflation response coefficient found in the forward-looking
Taylor rule reported here and in previous research arises, in part, because the estimation
procedure chosen does not properly account for the presence of serially correlated
shocks.
Panel B in Table 5 reports estimates of forward-looking Taylor rules for the
second period. As before, once the Taylor rule is modified to capture the response of
policy to the bond rate, the estimated inflation response coefficient is way above unity
and the partial adjustment coefficient is small and not different from zero (see estimates
in Panel B, Table 5). The modified Taylor rule provides unbiased forecasts of actual
funds rate settings during the second period, with and without partial adjustment.
Figures 6 and 7 chart the values predicted by the forward-looking Taylor rules
estimated without partial adjustment for both the sample periods. Actual values of the
funds rate are also charted there. The figures clearly suggest that the estimated policy
rules track actual policy fairly well. Together the results based on Greenbook forecasts
support the conclusion reached before that the Fed during the first period was “too timid”
and “too sluggish.”
3. Concluding Observations
This paper presents and estimates Taylor-type policy rules for the two sample
periods 1968Q1 to 1979Q2 and 1979Q3 to 1994Q4, using real-time data on inflation and
output gaps or Greenbook forecasts of the inflation rate and unemployment rate available
to policymakers in real time. The results indicate that these policy rules track actual funds
rate settings fairly well during these two sample periods.
Recent research on monetary policy rules indicate that in order to avoid
undesirable inflation outcomes, feedback monetary policy rules like those estimated here
18
should satisfy the Taylor principle, which requires the nominal interest rate eventually
increase by more than one percentage point, in response to one percentage point increase
in the inflation rate. This requirement is easily met if the inflation response coefficient in
the feedback policy rule is well above unity. The policy rules estimated using real-time
data indicate that Fed policy during the late 1960s and the 1970s may have violated the
Taylor principle in that the estimated inflation response coefficient is not different from
unity. This result is in line with the previous evidence in Taylor (1999a) and Clarida et al.
(2000) that used revised data, but not in line with one in Orphanides (2002) based on
real-time data. The use of somewhat different real-time estimates of output gaps and/or
the more careful choice of estimation procedures in the joint presence of serial correlation
and partial adjustment may accounts for different results.
The empirical work here is consistent with the presence of partial adjustment
inertia, suggesting that the Fed has smoothed the adjustment of the policy rate to
economic fundamentals. However, the extent of interest rate smoothing exhibited by the
policy rules estimated here is less than what is indicated by policy rules in previous
empirical work. The partial adjustment coefficients estimated here indicate most of the
adjustment was complete within one year during the late 1960s and the 1970s and within
one quarter during the 1980s and early 1990s. The use of real-time as opposed to revised
data partly accounts for these different results. Another contributory factor may have
been the inadequate attention paid to the empirical problem of distinguishing quarterly
partial-adjustment from serial correlation in the estimated policy rules, emphasized
recently in Rudebusch (2001). The much faster speed of adjustment estimated here
supports the view that in reality the Fed may not be as sluggish as is widely believed.
19
References
Clarida, Richard, Jordi Gali, and Mark Gertler. “Monetary Policy Rules and
Macroeconomic Stability: Evidence and Some Theory,” Quarterly Journal of
Economics, volume 115, February 2000, 147-80.
Croushore, Dean and Tom Stark. “A Real-Time Data Set For Macroeconomists,”
Working Paper, Federal Reserve Bank of Philadelphia, May 1999.
Friedman, Milton. “The Role of Monetary Policy”, American Economic Review, 58,
March 1968, 1-17
Griliches, Zvi. “Distributed Lags: A Survey”, Econometrica, 35, 1967, 16-49
Goodfriend, Marvin. “Reinterpreting Money Demand Regressions,” Carnegie- Rochester
Conference Series on Public Policy, 22, 1985, 207-242.
-------------------------. “Interest Rate Policy and the Inflation Scare Problem 1979-1992,”
Federal Reserve Bank of Richmond Economic Quarterly, Vol. 79, Winter 1993, 1-24.
-------------------------.“Interest Rates and the Conduct of Monetary Policy,” CarnegieRochester Conference Series on Public Policy, 34, 1991, 7-30.
Hall, Robert E. “Comment on Rethinking the Role of NAIRU in Monetary Policy,” in
Monetary Policy Rules, Edited by John B. Taylor, The University of Chicago Press,
1999, 431-34.
Johnston, J. Econometric Methods. McGraw-Hill, New York, 1972.
Lansing, Kevin J. “Learning about a shift in Trend Output: Implications for Monetary
Policy and Inflation,” Federal Reserve Bank of San Francisco, Working Paper 2000 - 16.
--------------------. “Real-Time Estimation of Trend Output and the Illusion of Interest
Rate Smoothing,” Economic Review, Federal Reserve Bank of San Francisco, 2002.
Laxton, Douglas and Robert Tetlow. “A Simple Multivariate Filter for the Measurement
of Potential Output,” Bank of Canada, Technical Report No 59, June 1992.
Mehra, Yash P. “The Bond Rate and Estimated Monetary Policy Rules,” Journal of
Economics and Business, Volume 53, Number 4, July/August 2001, 345-358.
McCallum, Bennett T. “Monetary Policy Analysis in Models Without Money,” Carnegie
Mellon University, Manuscript, November 2000.
20
Orphanides, Athanasios. “Monetary Policy Rules and the Great Inflation,” American
Economic Review, May 2002.
-----------------------------. “Activist Stabilization Policy and Inflation: The Taylor Rule in
the 1970s,” Finance and Economic Discussion Series, 2000-13, Federal Reserve Board,
Washington, D.C.
----------------------------. “The Quest for Prosperity Without Inflation,” Federal Reserve
Board, Washington, D.C., May 1999.
---------------------- and Simon van Norden. “The Reliability of Output Gap Estimates in
Real Time,” Federal Reserve Board, Washington, DC, August 1999.
Rudebusch, Glenn D. “Term Structure Evidence on Interest Rate Smoothing and
Monetary Policy Inertia,” Federal Reserve Bank of San Francisco, January 2001.
Forthcoming in the Journal of Monetary Economics.
Taylor, John B. “Comments on Athanasios Orphanides’ The Quest for Prosperity
Without Inflation,” Stanford University, January 8, 2000.
-------------------. “A Historical Analysis of Monetary Policy Rules,” in Monetary Policy
Rules edited by John B. Taylor. The University of Chicago Press, Chicago, 1999a.
--------------------. “The Robustness and Efficiency of Monetary Policy Rules as
Guidelines for Interest Rate Setting by the European Central Bank,” Journal of Monetary
Economics 43, 1999b, 655-679.
-----------------. “Discretion versus Policy Rules in Practice,” Carnegie-Rochester Series
on Public Policy, December 1993, 195-214.
Woodford, Michael. “The Taylor Rule and Optimal Monetary Policy,” American
Economic Review, May 2001, 232-37.
-------------------------. “A Neo-Wicksellian Framework for the Analysis of Monetary
Policy.” Working Paper, Princeton University, September 2000.
21
Editorial corrections 10/20/02
Table 1
Instrumental Variables Estimates of Policy Rules
Panel A: Sample Period: 1968Q1-1979Q2
Policy Rule
aΠ
ay
ab
ρ
ST
SER
s1 s2
s3
s4
_________________________________________________________________
Taylor Rule
With ρ =0
1.2 .54
1.0
1.26 .6
.1 .0 .0
(6.9)(6.3)
With ρ #0
1.1 .65
(4.7)(6.1)
.44
(3.0)
.3
1.01
.4
-.2
.0
.2
1.79 .4
.5
.5
.1
1.53 -.1
.1
.4 -.2
1.12 -.2 -.1
.2 -.3
Panel B: Sample Period: 1979Q3-1994Q4
Taylor Rule
With ρ =0
With ρ #0
1.7 .32
(14.9)(3.1)
37.8*
1.8 .47
(11.0)(3.0)
.39 26.0*
(3.8)
Taylor Rule With the Bond Rate
With ρ =0
1.9 .37
.79
(25.4)(5.6)(8.5)
149.8*
With ρ #0
1.9 .35
.80
-.11 174.9* 1.13 -.1 .0 .2 -.3
(27.7)(5.8)(9.5) (1.0)
__________________________________________________________________
Notes: The coefficients (with t-values in parentheses) reported above are from
policy rules of the form
FRt = ρ FRt −1 + (1 − ρ )( a + aπ INFt −1 + a y GAPt −1 )
(1)
FRt = ρ FRt −1 + (1 − ρ )( a + aπ INFt −1 + a y GAPt −1 + ab ( BRt − INFt −1 ))
(2)
where FR is the federal funds rate; INF is the inflation rate(smoothed); GAP
is the level of the output gap and BR is the bond rate. Instrumental variables
are used when ρ ≠ 0 or when the bond rate is included; otherwise ordinary least
squares (OLS) are used. For policy rules in (1), the instrument set consists of
a constant, four past values of inflation and the output gap and period t-2
lagged values of the funds rate. For estimating policy rules in (2), the
instrument set is expanded to include past values of the spread. t-values
corrected for the presence of serial correlation. ST is a statistic that tests
aπ = 1 ; it has t-distribution if the rule is estimated with OLS and Chi-square
if IV is used. SER is the standard error of regression; si , i = 1, 2,3,4 are the first
four autocorrelation coefficients. *Significant at the 5 percent level
Table 2
Test of Unbiasedness
Panel A: Sample Period: 1968Q1-1979Q2
r = 0
r # 0
f1
χ2
f0
f1
χ2
f0
_____________________________________________________________
Taylor Rule Estimated
With ρ = 0
-.10
1.0
.62
(.2)
(8.8)
With ρ ≠ 0
.10
(.1)
1.0
(9.1)
.42
-.7
(.9)
1.1
(8.6)
1.25
Panel B: Sample Period: 1981Q1-1994Q4
Taylor Rule
With ρ ≠ 0
-1.0
(1.9)
1.2
8.9*
(20.6)
Taylor Rule With the Bond Rate
With ρ ≠ 0
-.1
1.0
(.6)
(67.9)
2.7
-1.4
(.9)
1.2
63.2*
(8.6)
-.1
1.0
(.3) (56.8)
1.6
__________________________________________________________________
Notes: The coefficients (with t-values in parentheses) reported above are from
regressions of the form FRt = f 0 + f1PFRt + υ t , where FR is the actual federal
funds rate, and PFR is the funds rate predicted by the relevant policy rule.
The predicted values used are the dynamic, within sample values, generated using
policy rules reported in Table 1. The predicted funds rate is an unbiased
f0 =0, f1 =1.0. χ 2 is the Chi-squared statistic with two
degrees of freedom that tests f0 =0, f1 =1.
predictor of actual if
*
Significant at the 5 percent level
Table 3
Estimation With Partial Adjustment and Serial Correlation
Panel A: Sample Period: 1968Q1-1979Q2
Policy Rule
aΠ
ay
ab
ρ
s
F
_______________________________________________________________
Taylor Rule
1.0
.62
.41
.41
15.3*
(3.9) (3.7)
(1.6) (1.6)
Panel B: Sample Period: 1979Q3-1994Q4
Taylor Rule
1.9
(9.3)
.55
(2.7)
.60
(6.5)
Taylor Rule With the Bond Rate
1.9
.36
.78
-.03
(29.1) (5.8) (10.0) (.2)
-.3
(2.0)
-.1
(.7)
22.1*
.9
__________________________________________________________________
Notes: The coefficients (with t-values in parentheses) reported above are from
policy rules of the form
Taylor Rule
FRt * = ( a + aπ INFt −1 + a y GAPt −1 )
FRt = ρ FRt −1 + (1 − ρ ) FRt * +υ t
υ t = sυ t −1 + µt
Taylor RuleWith the Bond Rate
FRt * = a + aπ INFt −1 + a y GAPt −1 + ab ( BRt − INFt −1 )
FRt = ρ FRt −1 + (1 − ρ ) FRt * +υt
υ t = sυ t −1 + µt
where υ and µ are disturbance terms. Instrumental variables are used when the
bond rate is included; otherwise non-linear least squares are used. F is the Fstatistic that tests ( ρ = 0, s = 0).
* Significant at the 5 percent level
Table 4
Additional Results: Estimates With Final Data
Panel A: Sample Period: 1968Q1-1979Q2
Row
aπ
ay
ab
ρ
SER
Number
_______________________________________________________
Taylor Rule
1.1 Real/IV
1.2 Final/IV
1.1
(4.7)
.65
(6.1)
.85
1.3
(3.4) (6.1)
.44
(3.0)
1.01
.60
(8.0)
.78
Panel B: Sample Period: 1979Q3-1994Q4
Taylor Rule
2.1 Real/IV
2.2 Final/IV
1.9
(7.8)
.58
(2.5)
.56
(4.7)
1.57
1.9
(2.6)
.9
(.9)
.84
(7.2)
1.74
-.11
(1.1)
1.13
Taylor Rule With the Bond Rate
3.1 Real/IV
1.9
.35
.80
(27.7) (5.8) (9.5)
3.2 Final/IV
1.8
.3
1.0
.09
1.27
(20.3) (3.3) (9.5)
(.9)
________________________________________________________________
Notes: The coefficients (with t-values in parentheses) reported above are from
policy rules of the form given in Table 1. Real/IV means the relevant policy
rule is estimated using real-time data and instrumental variables. Final means
the final data.
Table 5
Additional Results: Forward-Looking Policy Rules With
Greenbook Forecasts
Panel A: Sample Period: 1968Q1-1979Q2
Policy Rule
aΠ
au
ab
ρ
ST
SER
s1 s2
s3
s4
_________________________________________________________________
Taylor Rule With ρ =0; Non-Linear Least Squares
Constant Natural Rate
1.0 1.0
1.3
1.22 .5 .3 .3 .1
(9.5)(7.5)
Varying Natural Rate
1.1 1.0
.1
1.23 .6 .4 .4 .2
(8.2)(6.4)
Taylor Rule With ρ ≠ 0
Constant Natural Rate; Non-Linear Least Squares
1.4 1.6
.57 4.7*
.77 .1 -.3 .1 .1
(7.4)(7.5)
(8.1)
Varying Natural Rate; Non-Linear IV Estimates
1.2 1.5
.59
.9
.79
.2 -.2 .1 .2
(5.4)(4.9)
(5.7)
Panel B: Sample Period: 1979Q3-1994Q4
Taylor Rule; Varying Natural Rate; Non-Linear IV Estimates
With ρ #0
1.5
.2
.68 2.4
1.75 -.2 -.1 .2 .1
(4.6) (.4)
(7.3)
Taylor Rule With the Bond Rate
With ρ #0
1.8
.5
1.1 .19 48.4* 1.42 -.1
.0 .1 -.1
(14.8)(2.2) (7.6) (1.6)
__________________________________________________________________
Notes: The coefficients (with t-values in parentheses) reported above are from
policy rules of the form
FRt = ρ FRt −1 + (1 − ρ )( a + aπ INFt +gb1 − au (URtgb − NURt ))
FRt = ρ FRt −1 + (1 − ρ )( a + aπ INF
gb
t +1
where
(1)
− au (UR − NURt ) + ab ( BRt − INF ))
gb
t
gb
t +1
(2)
INFt +gb1 is the Greenbook inflation forecast; URtgb is the Greenbook
unemployment rate forecast; and NURt is the natural unemployment rate. The
natural unemployment rate is just the real-time, simple average of the actual
unemployment rates. ST tests aπ = 1 and has F distribution if the rule is
estimated with Least Squares and Chi-Square distribution if the rule is
estimated with IV. SER is the standard error of the regression. See notes in
Table 1
* Significant at the 5 percent level
@FedFRASER