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Economic Quarterly—Volume 96, Number 2—Second Quarter 2010—Pages 123–151

Inflation Measure, Taylor
Rules, and the
Greenspan-Bernanke Years
Yash P. Mehra and Bansi Sawhney

R

ecent research has highlighted several aspects of monetary policy under Chairman Alan Greenspan, noting that the Federal Reserve was
forward looking, smoothed interest rates, and focused on core inflation.1 Some analysts have estimated Taylor rules that incorporate these salient
features of monetary policy, and have shown that monetary policy actions
taken by the Federal Reserve in the Greenspan era can broadly be explained
by these estimated Taylor rules. Using a core measure of consumer price inflation (CPI), Blinder and Reis (2005) estimate a Taylor rule over 1987:1–2005:1,
showing that the estimated policy rule tracks actual policy actions fairly well.
Using Greenbook forecasts of core CPI inflation, Mehra and Minton (2007)
estimate a forecast-based Taylor rule that shows this estimated policy rule
also fits the data over 1987:1–2000:4.2 More recently however, Taylor (2007,
2009) has argued that monetary policy was “too loose” during most of the
period from 2002–2006, in the sense that the actual federal funds rate was too
low relative to the level simulated by a smoothed version of the original Taylor
rule.3 In this simulation exercise, Taylor (2007) assumes response coefficients
Mehra is a senior economist and policy advisor at the Federal Reserve Bank of Richmond.
Sawhney is a professor of economics at the Merrick School of Business, University of Baltimore. The opinions in this paper do not necessarily reflect those of the Federal Reserve
Bank of Richmond or the Federal Reserve System.
1 Blinder and Reis (2005) have hailed Chairman Greenspan’s focus on core, rather than headline, inflation as a “Greenspan innovation.” The measure of core inflation used excludes food and
energy prices.
2 The sample period used in Mehra and Minton (2007) ends in 2000, given the five-year lag
in the release of the Greenbook forecasts to the public.
3 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

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Federal Reserve Bank of Richmond Economic Quarterly

of 1.5 and .5 on inflation and the output gap, as in the original Taylor rule, but
instead uses headline CPI as a measure of inflation.4
This article highlights another aspect of monetary policy in the Greenspan
era: The measure of inflation used in monetary policy deliberations has also
been refined over time. This can be seen in the semiannual monetary policy
reports to Congress (Humphrey-Hawkins reports), where inflation forecasts
by the members of the Federal Open Market Committee (FOMC) have been
presented using different measures of inflation over time. Thus, through July
1988, inflation forecasts used the implicit deflator of the gross national product,
thereafter switching to the CPI. In February 2000, the CPI was replaced by the
personal consumption expenditures (PCE) deflator measure of inflation and
from July 2004 onward inflation forecasts employed the core PCE deflator
that excludes food and energy prices.
Though these different measures of inflation may move together in the
long run, over short periods these inflation measures may behave differently
because of factors such as energy prices and changes in coverage and definitions. As a result, the Fed’s inflation target may vary depending on the
measure of inflation used, thereby affecting the desired setting of the federal
funds rate.5 Previous empirical work has not paid much attention to this issue,
as most analysts estimate Taylor rules under the assumption that the measure
of inflation used in policy deliberations did not change during the Greenspan
years.6
target each period as shown below (Taylor 1993):
F Rt

=

F Rt

=

rr ∗ + α π π t−1 − π ∗ + α y yt − yt∗ t−1
2.0 + 1.5 π t−1 − 2.0 + .5 yt − yt∗ t−1 ,

where rr ∗ is the real interest rate (assumed to be 2 percent), π is actual inflation, π ∗ is the
Fed’s inflation target (assumed to be 2 percent), yt − yt∗ is the output gap, α π is the inflation
response coefficient (assumed to be 1.5), and α y is the output response coefficient (assumed to
be .5). Inflation in the original Taylor rule was measured by the behavior of the gross domestic
product (GDP) deflator, and the output gap is the deviation of the log of real output from a linear
trend. According to the original Taylor rule, the Federal Reserve is backward looking, focused on
headline inflation, and follows a “non-inertial” policy rule.
4 Using the policy response coefficients from the original Taylor rule and headline CPI as a
measure of inflation, Poole (2007) also shows that the actual federal funds rate is too low relative
to the level prescribed for most of the period from 2000:1–2006:4 (see Figure 1 in Poole [2007]).
Poole, however, does not conclude that policy was too easy because he alludes to the change in
the measure of inflation used in monetary policy deliberations during this subperiod.
5 Kohn (2007) has highlighted these considerations.
6 While Blinder and Reis (2005) and Mehra and Minton (2007) estimate Taylor rules using
a core measure of CPI inflation, the measure of inflation used in Taylor (2007, 2009) is headline
CPI and the one used in Smith and Taylor (2007) is the implicit deflator for GDP. An exception
is the paper by Orphanides and Wieland (2008), in which a forecast-based Taylor rule is estimated
using the semiannual Humphrey-Hawkins inflation forecasts. More recently, Dokko et al. (2009)
and Bernanke (2010) have highlighted the issue of the measurement of inflation used in monetary
policy deliberations.

Mehra/Sawhney: Inflation, Taylor Rules, Greenspan-Bernanke Years

125

This article re-examines the issue of whether monetary policy actions
taken during the Greenspan years can be described by a stable Taylor rule. It
considers two Taylor rules that differ with respect to the measure of inflation
used in implementing monetary policy. According to both these rules, the
Greenspan Fed was forward looking, smoothed interest rates, and linked the
federal funds rate target to expected inflation and the unemployment gap.
However, according to one Taylor rule, the Federal Reserve used headline
CPI inflation, and, according to the other, it used core CPI until 2000 and core
PCE thereafter. The later specification departs from the usual assumption
that a Taylor rule has to be estimated using a single measure of inflation.7
Both the policy rules employ real-time data on economic fundamentals such
as the pertinent inflation measure and the unemployment gap. As noted by
Orphanides (2001, 2002), in evaluating historical monetary policy actions
using estimated Taylor rules, the use of ex post revised, as opposed to realtime, data on economic variables can give misleading inferences about the
stance of monetary policy.
A Taylor rule incorporating the above-noted features is shown below in
(1.3):
F Rt∗ = α 0 + α π Et π c + α u urt − urt∗ ,
t+j
F Rt = ρF Rt−1 + (1 − ρ) F Rt∗ + ν t ,
F Rt

(1.1)

(1.2)

= ρF Rt−1 + (1 − ρ) α 0 + α π Et π c + α u urt − urt∗
t+j

+ νt ,
(1.3)

where F Rt is the actual federal funds rate, F Rt∗ is the federal funds rate target,
Et π c is the expectation of the j -period-ahead core inflation rate made at time
t+j
t conditional on period t −1 dated information, ur is the actual unemployment
rate, ur ∗ is the non-accelerating inflation unemployment rate (NAIRU), and ν t
is the disturbance term. Thus, the term urt − urt∗ is the current unemployment gap. Equation (1.1) relates the federal funds rate target to two economic
fundamentals, expected inflation and the current unemployment gap. Hereafter, the funds rate target is called the policy rate. The coefficients α π and α u
measure the long-term responses of the funds rate target to expected inflation
and the unemployment gap; the inflation response coefficient is assumed to
7 The estimation of a Taylor rule using an inflation series that employs two or more measures
of inflation may mean that the intercept term in the estimated Taylor rule is no longer a constant.
This may happen if different measures of inflation exhibit different trend behaviors during the
course of the estimation period and, hence, the Fed’s inflation target expressed in these different
inflation measures is no longer similar in magnitude.

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Federal Reserve Bank of Richmond Economic Quarterly

be positive and the unemployment gap response coefficient is assumed to be
negative, indicating that the Federal Reserve raises its funds rate target if it
expects inflation to rise and/or the unemployment gap to fall. Equation (1.2)
is the standard partial adjustment equation, which expresses the current funds
rate as a weighted average of the current funds rate target, F Rt∗ , and the last
quarter’s actual value, F Rt−1 . If the actual funds rate adjusts to its target
within each period, then ρ equals zero, suggesting 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 (1.1) into (1.2), we get (1.3)—a forward-looking “inertial” Taylor
rule.
As in Clarida, Gali, and Gertler (2000), the Taylor rules are estimated
assuming rational expectations and using instrumental variables over 1987:1–
2004:4; this sample period spans most of the Greenspan era.8 The key feature of the estimation procedure used here is that the instrument set includes,
among other variables, Greenbook inflation forecasts based on different inflation measures. This strategy differs from the one used in Boivin (2006) and
Mehra and Minton (2007), where forward-looking Taylor rules are estimated
directly using Greenbook forecasts. Given the five-year lag in the release of
Greenbook forecasts to the public, the current strategy enables one to estimate
the Taylor rules over most of the Greenspan era (1987:1–2004:4) and then examine their predictive content for the longer sample period (1987:1–2006:4)
that includes the Bernanke years.9 We end the sample in 2006 in order to
compare results in previous research that indicate monetary policy was too
loose over 2002–2006.
The empirical work presented here suggests several observations. First,
a Taylor rule that is estimated using a time-varying measure of core inflation
8 There is considerable evidence that the policy rule followed by the Greenspan Fed differed
from the one followed by the Volcker Fed in one important way. In its attempts to build credibility,
the Volcker Fed responded strongly to long-term inflationary expectations imbedded in long bond
yields, in addition to responding to inflation and unemployment, the two fundamental variables
suggested by a Taylor rule (Mehra 2001). The long bond rate is generally not significant if the
Taylor rule is estimated using data from the Greenspan era because the Greenspan Fed had by
then achieved credibility. For this reason we estimate the Taylor rule using observations only from
the Greenspan era. This strategy is also consistent with the observation that in criticizing the
Greenspan Fed, Taylor (2007) uses a policy rule that includes only inflation and unemployment
(output) gap variables.
9 We, however, do compare the robustness of our results to this alternative method of estimating the Taylor rule using Greenbook inflation forecasts. Although estimates of policy response
coefficients differ, the estimates yield qualitatively similar conclusions about the relevance of the
inflation measure. In particular, the Taylor rule that is estimated using Greenbook forecasts of
core CPI until 2000 and core PCE thereafter tracks actual policy well over 2000:1–2006:4 and
passes the test of parameter stability. That is not the case if the Taylor rule is estimated using
Greenbook forecasts of headline CPI inflation. Furthermore, as measured by the root mean squared
error criterion, the Taylor rule with Greenbook forecasts of the time-varying inflation measure fits
the data better than the Taylor rule with Greenbook forecasts of headline CPI.

Mehra/Sawhney: Inflation, Taylor Rules, Greenspan-Bernanke Years

127

(CPI until 2000 and PCE thereafter) yields reasonable estimates of inflation
and unemployment gap response coefficients. The estimated inflation response coefficient, α π , is positive and way above unity, suggesting that the
Greenspan Fed responded strongly to expected inflation. The estimated unemployment gap response coefficient, α u , is negative and statistically significant,
suggesting that the Federal Reserve also responded to slack. The Chow test
of parameter stability does not indicate a shift in the estimated parameters
around 2000 when the Federal Reserve switched from CPI to PCE.10 Also,
the estimated Taylor rule tracks the actual path of the federal funds rate fairly
well, especially over the period from 2002–2006.
In contrast, a Taylor rule that is estimated using headline CPI inflation does
not provide reasonable estimates of policy response coefficients and depicts
parameter instability over 1988:1–2004:4. The estimated Taylor rule based
on headline CPI inflation is consistent with the actual funds rate being too
low relative to the level prescribed by the estimated Taylor rule over 2002–
2006, as in Smith and Taylor (2007) and Taylor (2007). These results indicate
that the choice of the measure of inflation used in estimated Taylor rules is
not innocuous. Furthermore, one should employ real-time information for
evaluating historical monetary policy actions.
Second, during most of the period from 2001–2006, inflation measured
by headline CPI was higher than what would be indicated by core PCE data,
reflecting in part the effects of the rise in oil prices on headline inflation. The
tests of parameter stability here indicate that the Greenspan Fed did not adjust
the federal funds rate target in response to increases in the headline measure
of CPI inflation.11 The lack of policy response to increases in headline CPI
inflation reflected the Greenspan Fed’s belief that oil price increases were
transitory12 and that core inflation is a better gauge of the underlying trend
inflation.13
Third, the core measure of PCE inflation has been substantially revised
over the years. In particular, real-time estimates of core PCE inflation over
10 Although the core PCE index was given prominence in Humphrey-Hawkins forecasts in
July 2004, the hypothesis here that the Greenspan Fed in fact paid attention to core measures of
inflation implies that the FOMC started paying attention to core PCE much earlier.
11 Several analysts and policymakers have noted that the Greenspan Fed’s policy of focusing on core inflation continued through the Bernanke years. See, for example, Kohn (2009) and
Bernanke (2010).
12 During this subperiod most other economists also thought oil price increases were transitory
and hence did not expect the rise in oil prices to lead to persistent increases in headline inflation.
For example, despite the actual increase in headline CPI inflation, the Survey of Professional
Forecasters forecasts of headline CPI inflation did not increase appreciably over 2003:1–2006:4.
See Dokko et al. (2009) for additional evidence on this issue.
13 This belief is consistent with the empirical evidence documented by several analysts that,
for the period since the early 1980s, it is core rather than headline inflation that better approximates
the trend component of inflation. Some of that empirical evidence is reviewed in Mishkin (2007)
and Kiley (2008) and updated in Mehra and Reilly (2009).

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Federal Reserve Bank of Richmond Economic Quarterly

2002:1–2005:4 are substantially lower than those indicated by ex post revised
data (vintage 2009). The counterfactual simulations of the federal funds rate
generated using the ex post revised data do suggest that deviations of the
policy rule are somewhat larger than those generated using the real-time data.
However, it would be misleading to conclude from such evidence that the
Greenspan Fed had followed an easier stance on monetary policy.
Our results complement the recent work of Orphanides and Wieland
(2008), who argue that policy actions taken over 1988–2007 have been consistent with a stable Taylor rule and that policy was not too loose over 2001–
2007. They, however, estimate a forecast-based Taylor rule using publicly
available forecasts of inflation and unemployment contained in semiannual
Humphrey-Hawkins reports. As indicated before, the Humphrey-Hawkins inflation forecasts used CPI until 1999, switching thereafter to the PCE measure.
The evidence in this article implies that a forward-looking Taylor rule estimated using actual real-time inflation and unemployment data yields identical
results, in particular the conclusion that policy actions are consistent with a
stable Taylor rule, provided we allow for the change in the measure of inflation
used in monetary policy deliberations.14
The rest of the paper is organized as follows. Section 1 discusses the empirical methodology and reviews the data on the behavior of different measures
of inflation during the Greenspan era. Section 2 presents empirical results,
reproducing the evidence in Taylor (2007, 2009) that the Greenspan Fed set
a funds rate low relative to the Taylor rule. We show that the result in Taylor
disappears if one uses the time-varying measure of inflation employed by the
FOMC. Section 3 concludes.

1.

EMPIRICAL METHODOLOGY

Estimation of the Forward-Looking Inertial
Taylor Rule
The 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, smoothed interest rates, and refined the measure
of inflation used in monetary policy deliberations. We model the forwardlooking nature of the policy rule by relating the current value of the funds rate
14 Using somewhat different approaches, Dokko et al. (2009) and Bernanke (2010) also show
that actual policy is much closer to the one prescribed by the original Taylor rule if the measure of
inflation used in the policy rule is the one employed by the FOMC in monetary policy deliberations
and if real-time data are used. Bernanke (2010) generates the predictions of the policy rate using
the Greenbook inflation forecasts until 2004 and the Humphrey-Hawkins forecasts thereafter. Dokko
et al. (2009) generate the predictions of the policy rate employing real-time estimates of core PCE
inflation.

Mehra/Sawhney: Inflation, Taylor Rules, Greenspan-Bernanke Years

129

target to the expected average annual inflation rate and the contemporaneous
unemployment gap. The policy rule incorporating these features is reproduced
below in equation (2.3):
F Rt = ρF Rt−1 + (1 − ρ) α 0 + α π Et π c + α u urt − urt∗
¯4
¯

+ νt ,

(2.3)

where the expected average annual inflation rate, Et π c , is measured by the
¯4
¯
average of one-through-four-quarter-ahead expected values of core inflation
made at time t, and other variables are defined as before.15
The estimation of the policy rule (2.3) raises several issues. The first
issue relates to how we measure expected inflation and the unemployment
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 indicated earlier, the use of
revised as opposed to real-time data may affect estimates of policy coefficients
and may provide a misleading historical analysis of policy actions. The third
issue is an econometric one, arising as a result of the potential presence of
serial correlation in the error term ν t . Rudebusch (2002, 2006) points out that
the Federal Reserve may respond to other economic factors besides expected
inflation and the unemployment gap and, hence, a Taylor rule estimated while
omitting those other factors is likely to have a serially correlated error term.
The presence of serial correlation in the disturbance term, if ignored, may
spuriously indicate that the Federal Reserve is smoothing interest rates.
To understand how a serially correlated disturbance term may mistakenly
indicate the presence of partial adjustment, note first that if the funds rate
does partially adjust to the policy rate as shown in (1.2) and the disturbance
term has no serial correlation, then the reduced-form policy rule in (1.3) or
(2.3) has the lagged funds rate as one of the explanatory variables. Hence, the
empirical finding of a significant coefficient on the lagged funds rate in the
estimated policy rule may be interpreted as indicating the presence of interest
rate smoothing. But now assume that there is no partial adjustment, ρ = 0 in
(2.3), but instead the disturbance term is serially correlated as shown below
in (3.1):

ν t = sν t−1 + ε t ,

(3.1)

15 In particular, the four-quarter average of expected inflation rates is defined as π c =
¯ ¯
t,4

π c + π c + π c + π c /4, where π c j = 1, 2, 3, 4 is the j -quarter-ahead expected value of
t,1
t,2
t,3
t,4
t,j
core inflation made at time t.

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Federal Reserve Bank of Richmond Economic Quarterly

F Rt

= sF Rt−1 + α 0 + α π Et π c + α u urt − urt∗
¯4
¯
∗
−s α 0 + α π Et−1 π c + α u urt−1 − urt−1
¯4
¯

+ εt .

(3.2)

If we substitute (3.1) into (2.3), it can be easily shown that we get the
reduced-form policy rule (3.2) in which, among other variables, the lagged
funds rate also enters the policy rule. Hence, the empirical finding of a significant coefficient on the lagged funds rate in the estimated policy rule may be
interpreted as arising as a result of interest rate smoothing when in fact it is
not present. In view of these considerations, the policy rule here is estimated
allowing for the presence of both interest rate smoothing and serial correlation,
namely, we allow both partial adjustment and a serially correlated disturbance
term. It can be easily shown that the policy rule incorporating both partial
adjustment and serial correlation can be expressed
F Rt

= α 0 (1 − s) (1 − ρ) + (s + ρ) F Rt−1
+ (1 − ρ) α π Et π c + α u urt − urt∗
¯4
¯

∗
−s (1 − ρ) α π Et−1 π c + (1 − ρ) α u urt−1 − urt−1
¯4
¯
−sρF Rt−2 + ε t .

(4)

Note, if there is no serial correlation (s = 0 in [4]), we get the reducedform policy rule shown in (2.3), and if there is no partial adjustment (ρ = 0
in [4]), we get the policy rule shown in (3.2). Of course, if both s and ρ
are not zero, we have a policy rule with both partial adjustment and serial
correlation.16
In previous research, a forward-looking policy rule such as the one given
in (2.3) has often been estimated assuming rational expectations and using a
generalized method of moments procedure (Clarida, Gali, and Gertler 2000).
We follow this literature and estimate the policy rule assuming rational expectations, namely, we substitute actual future core inflation for the expected
inflation term and use an instrumental variables procedure to estimate policy
coefficients. Given the evidence that the Greenbook forecasts are most appropriate in capturing policymakers’ real-time assessment of future inflation
developments, we include the Greenbook forecasts in the instruments.17 In
16 Estimating the policy rule allowing for the presence of serial correlation produces more
robust estimates of policy parameters including the partial adjustment coefficient. Moreover, the
policy rule is estimated using the quasi-differenced data, as can be seen in equation (3.2). This
quasi-differencing of data minimizes the spurious regression phenomenon noted in Granger and
Newbold (1974).
17 Romer and Romer (2000) have shown that the Federal Reserve has an informational advantage over the private sector, producing relatively more accurate forecasts of inflation than does
the private sector. Bernanke and Boivin (2003) argue that one needs a large set of conditional
information to properly model monetary policy. In that respect, the Greenbook forecasts include

Mehra/Sawhney: Inflation, Taylor Rules, Greenspan-Bernanke Years

131

Figure 1 Actual Inflation (Real-Time)
Panel A: Headline CPI and Core CPI (4Q Average)
7
Headline CPI
Core CPI

5
3
1
1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

1996

1997

1998

1999

Panel B: Headline CPI Minus Core CPI
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
1988

1989

1990

1991

1992

1993

1994

1995

Panel C: Headline CPI and Core PCE
4.0
Headline CPI
Core PCE

3.0
2.0
1.0
2000

2001

2002

2003

2004

2005

2006

2005

2006

Panel D: Headline CPI Minus Core PCE
2.0
1.5
1.0
0.5
0.0
-0.5
2000

2001

2002

2003

2004

addition, we estimate the policy rule allowing for the presence of both interest rate smoothing and serial correlation as in (4) and use the nonlinear
instrumental variables procedure. The instruments used are the three lagged
values of Greenbook inflation forecasts, the federal funds rate, levels of the
unemployment gap, and the spread between the 10-year Treasury bond yield
and the federal funds rate. As indicated earlier, the policy rule is estimated
over 1988:1–2004:4, given the five-year lag in the release of the Greenbook
forecasts to the public.18
real-time information from a wide range of sources, including the Board staff’s “judgment,” not
otherwise directly measurable.
18 The estimation period begins in 1988:1 because the instrument set includes the lagged
values of economic variables. As a check on the adequacy of the instruments variables procedure, we ran the first-stage regressions for the endogenous variables (expected inflation and the

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Real-Time Versus Vintage 2009 Core Inflation
Panel A: Core CPI (4Q Average)

5.5

Real-Time
Vintage 2009

5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1988

1989

1990

1992

1993

1994

1995

1996

1997

1998

1999

Panel B: Core PCE (4Q Average)

2.50
2.25

1991

Core PCE
Vintage 2009

2.00
1.75
1.50
1.25
1.00
2000

2001

2002

2003

2004

2005

2006

Data
We estimate the policy rule in (4) using real-time data on core inflation and the
unemployment gap. The data on core inflation came from the real-time data
set maintained at the Philadelphia Fed.19 The data on real-time estimates of
the NAIRU were those prepared by the Congressional Budget Office (CBO).20
The Greenbook forecasts of core inflation used in the instrument list are those
prepared for the FOMC held near the second month of the quarter.
contemporaneous unemployment gap). In the first stage regressions, the R-squared statistics are
fairly large, ranging from .45 to .97, suggesting the endogenous variables are highly correlated
with the instruments.
19 The empirical work used the preliminary estimates of core PCE inflation, usually released
by the end of the first month of a quarter. The Greenbook forecasts used as instruments were
the ones prepared for the FOMC meetings held near the second month of a quarter. This timing
means that the Board staff preparing the Greenbook forecasts had information about the preliminary
estimates of core inflation rates in previous quarters. However, none of the conclusions reported
here would change if we had used third release estimates, usually reported by the end of the third
month of the quarter.
20 In January of each year from 1991–2006, the CBO released estimates of the NAIRU. For
the period 1987–1990, the estimates used are those given in the 1991 vintage data file. For 1991,
we used the pertinent series on the NAIRU from the 1992 vintage data file and so on for each
year thereafter.

Mehra/Sawhney: Inflation, Taylor Rules, Greenspan-Bernanke Years

133

Figure 3 Unemployment Gap
2.5
Real-Time
2009 Vintage

2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

1.5
Real-Time
2009 Vintage

1.0
0.5
0.0
-0.5
-1.0
-1.5
2000

2001

2002

2003

2004

2005

2006

Panel A in Figure 1 charts the four-quarter averages of real-time headline
and core CPI inflation rates from 1988:1–1999:4, and Panel C charts the averages of headline CPI and core PCE inflation rates from 2000:1–2006:4. As
can be seen, headline and core CPI inflation series stay together for most of
the period before 2000 (see Panel B). However, over 2000:1–2006:4, headline
CPI inflation remained above core PCE inflation (see Panel D), suggesting
that a policy rule that relates the policy rate to headline CPI inflation is likely
to prescribe a higher federal funds rate target than a policy rule that relates the
policy rate to core PCE inflation, ceteris paribus. Hence, given the different
behavior of headline CPI inflation and core PCE inflation rates over this subperiod, the measure of inflation used in the estimated Taylor rule will matter
for predicting the stance of monetary policy.
Figures 2 and 3 chart real-time and 2009 vintage estimates of economic
fundamentals that enter the Taylor rules; Figure 2 charts the four-quarter average of core CPI and core PCE inflation rates, whereas Figure 3 charts the
unemployment gap. Two observations are noteworthy. First, core PCE inflation data have been extensively revised over the years, and there are big
discrepancies between real-time and revised estimates of core PCE inflation.
In particular, real-time estimates of the four-quarter average of PCE inflation

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Greenbook Inflation Forecasts and Actual Future Inflation
(4Q Average)
Panel A: Core CPI: Greenbook Forecasts and Actual Future Inflation
5.5
Actual Real-Time
Forecast

5.0
4.5
4.0
3.5
3.0
2.5
2.0
1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

Panel B: Core PCE: Greenbook Forecasts and Actual Future Inflation
Actual Real-Time
Forecast

2000

2001

2002

2003

2004

rates were substantially below the 2009 vintage estimates over 2002:1–2005:4
(see Figure 2, Panel B). Second, the unemployment gap data is also revised,
but discrepancies between the real-time and 2009 vintage estimates are small
and do not increase appreciably over 2001–2006 (see Figure 3).
Figure 4 charts Greenbook inflation forecasts and actual future inflation;
Panel A charts inflation forecasts of core CPI inflation and Panel B charts those
of core PCE.As can be seen, Greenbook inflation forecasts of core CPI inflation
do track actual core CPI inflation, with the exception of the short period 1994–
1997 when the Greenbook forecasts turned out to be too pessimistic. For the
later period, the Greenbook forecasts of core PCE inflation do not fare as
well in predicting actual core inflation. In particular, in 2003:1–2004:4, the
Greenbook forecasts of core PCE inflation indicated deceleration in expected
inflation, but actual core PCE inflation turned out to be much higher than what
the Board staff predicted. The fear of expected deflation implicit in Greenbook
forecasts of declining future inflation is used by some analysts to argue that
the Greenspan Fed may have kept the federal funds rate target too low for too
long during this subperiod. However, it is for a very short span that actual
core inflation was higher than what the Board staff forecasted. The result

Mehra/Sawhney: Inflation, Taylor Rules, Greenspan-Bernanke Years

135

Table 1 Estimated Taylor Rules
Row
1

End Period
1999:4

Inflation
Core CPI + PCE

2

2004:4

Core CPI + PCE

3

1999:4

Headline CPI

4

2004:4

Headline CPI

5

1999:4

Core CPI

6

2004:4

Core CPI

απ
1.6
(5.3)
1.9
(8.2)
1.5
(2.9)
.1
(.3)
1.6
(5.4)
1.6
(3.1)

αy
−1.3
(4.3)
−1.4
(5.5)
−1.0
(2.3)
−2.4
(−4.9)
−1.3
(4.3)
−1.4
(3.0)

ρ
.56
(3.3)
.52
(6.4)
.72
(5.8)
.40
(2.6)
.56
(3.3)
.60
(4.3)

s
.62
(2.9)
.67
(3.6)
.61
(3.2)
.97
(3.3)
.62
(2.9)
.75
(4.4)

SER
.322
.331
.352
.347
.322
.324

Notes: Rows labeled 1 through 4 contain nonlinear instrumental variables estimates of
policy coefficients from the forward-looking policy rule given below in (a) and use realtime data on inflation and the unemployment gap:
F Rt

=

α 0 (1 − s) (1 − ρ) + (s + ρ) F Rt−1 + (1 − ρ) α π Et π c + α u urt − urt∗
¯¯
4

∗
−s (1 − ρ) α π Et−1 π c + (1 − ρ) α u urt−1 − urt−1
¯¯
4

− sρF Rt−2 + εt . (a)

The instruments used are three lagged values of Greenbook inflation forecasts, the funds
rate, unemployment gap, the growth gap, and the spread between nominal yields on 10year Treasury bonds and the federal funds rate. Parentheses contain t-values. SER is the
standard error of estimate. Estimation was done allowing for the presence of first-order
serial correlation in ν t , and s is the estimated first-order serial correlation coefficient.
The sample periods begin in 1988:1 and end in the year shown in the column labeled
“End Period.”

here—that a rational expectations version of the Taylor rule estimated using
real-time data tracks the actual funds rate target well—implies that the fear of
deflation may have played a limited role in keeping the funds rate target low
during this subperiod.

2.

EMPIRICAL RESULTS

This section presents and discusses policy response coefficients from Taylor
rules that are estimated using different measures of inflation. It also examines
the stability of policy response coefficients using the Chow test with the break
data around 2000, when the Greenspan Fed switched from focusing on CPI
to PCE inflation measure.

Estimates of Policy Response Coefficients
Table 1 presents estimates of policy response coefficients (α π , α u ) from the
Taylor rule in equation (4) for two sample periods, 1988:1–1999:4 and

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Federal Reserve Bank of Richmond Economic Quarterly

1988:1–2004:4. Rows 1 and 2 present estimates using the time-varying measure of core inflation, and rows 3 and 4 present estimates for headline CPI
inflation measure. Focusing first on estimates of the Taylor rule with the
time-varying measure of core inflation, all estimated policy response coefficients are correctly signed and statistically significant. In particular, the
inflation response coefficient α π is generally well above unity, suggesting that
the Greenspan Fed responded strongly to expected inflation. Furthermore, in
both sample periods, estimated policy response coefficients remain correctly
signed and are statistically significant, suggesting parameter stability.21,22
Focusing on estimates of the Taylor rule with headline CPI inflation, we
find that estimated policy response coefficients are sensitive to the sample period. For the sample period ending in 1999:4, the estimated policy response
coefficients are correctly signed and statistically significant. The estimated
inflation response coefficient is 1.5, well above unity, and the estimated unemployment gap response coefficient is close to unity. However, the estimated
policy response coefficients are not stable across the two sample periods. In
particular, the estimated inflation response coefficient falls below unity and
is no longer statistically significant when the policy rule is estimated over
1988:1–2004:4 (see Table 1, Row 4). This result is similar in spirit to the one
in Smith and Taylor (2007), who estimate a Taylor rule over 1984:1–2005:4
and find that the estimated inflation response coefficient declined significantly
in 2002, leading them to conclude that the Greenspan Fed had become less
responsive to inflation.

Parameter Stability
We formally test for stability of policy response coefficients in the Taylor
rule over 1988:1–2004:4 using the Chow test and treating the break date as
unknown. Since the FOMC switched to the PCE measure of inflation in
21 Other estimated coefficients of interest are also correctly signed. The estimated serial correlation coefficient, s, is generally positive and statistically significant, indicating the presence of
serially correlated errors in the estimated policy rules. As noted in Rudebusch (2006), the presence
of serial correlation may reflect influences on the policy rate of economic variables to which the
Federal Reserve may have responded but that are omitted from the estimated policy rule. Furthermore, even after allowing for the presence of serial correlation, the estimated partial adjustment
coefficient, ρ, is positive and well above zero, suggesting that the continued role of partial adjustment in generating a significant coefficient on the lagged value of the funds rate. This result is in
line with the one in English, Nelson, and Sack (2002). However, the magnitude of the estimated
partial adjustment coefficient, ρ, reported here is somewhat smaller than what is found in previous
research.
22 The empirical work employed the inflation series using CPI until 2000:4 and PCE thereafter. The estimates of the policy response coefficients do not change much if the policy rule is
alternatively estimated using CPI until 2000:1 and PCE thereafter. Furthermore, the test of parameter stability discussed in the next section was implemented for all break dates over 2000:1–2001:4.
As discussed later, the estimated policy rule employing the time-varying measure of inflation did
not indicate a break in policy response coefficients for any of the break dates.

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137

Table 2 Test for Stability of Policy Coefficients in Policy Rules
Breakpoint
2000Q1
2000Q2
2000Q3
2000Q4
2001Q1
2001Q2
2001Q3
2001Q4

Policy Rule
Core CPI + Core PCE
(A)
.86
.95
.46
.30
.41
.17
.65
.75

Policy Rule
Headline CPI
(B)
.04
.02
.01
.01
.00
.00
.00
.00

Policy Rule
Core CPI
(C)
.22
.19
.16
.17
.05
.01
.19
.35

Notes: The values reported are p-values of a test of the null hypothesis in which policy
coefficients, including the intercept in the policy rule, were stable against the alternative
in which coefficients changed at the indicated date. Since the test is implemented including dummy variables in the policy rule given in equation (a) in the Table 1 Notes,
the reported p-values are a test of the null hypothesis in which coefficients on slope
dummies, including the intercept, did not change at the indicated date.

2000, we look for a break in the estimated Taylor rule around that period.
In particular, for each date between 2000:1–2001:4, we include intercept and
slope dummies on policy response coefficients in the Taylor rule in equation
(4) and test their joint significance for a possible break in the estimated relation.
Table 2 reports the p-value for a test of the null hypothesis in which Taylor rule
coefficients were stable against the alternative in which coefficients changed at
the indicated date. The column labeled (A) reports p-values generated using
the Taylor rule that employed the time-varying measure of core inflation,
whereas the column labeled (B) does so for the Taylor rule with headline CPI
inflation. As can be seen, there is no date in the interval 2000:1–2001:4 at
which one could claim to find a statistically significant break in the Taylor
rule if one uses a time-varying measure of core inflation. In contrast, there are
several dates one could find the evidence of a break in relation if the Taylor
rule is estimated using headline CPI inflation (see column B). The latter result
is similar in spirit to the one in Smith and Taylor (2007).23
23 The test for parameter stability was implemented using intercept and slope dummies. In
the case of the policy rule that was estimated using the time-varying measure of inflation, both the
intercept and slope dummy coefficients were not different from zero, suggesting that there was no
shift in the intercept of the policy rule in response to change in the measure of inflation employed.
In contrast, when the policy rule is estimated using headline CPI, the slope dummy coefficient on
the inflation response coefficient is relatively small, suggesting that the Federal Reserve did not
respond as aggressively to headline inflation as it did before. This result is in line with the inflation
response coefficient becoming insignificant when the policy rule is estimated over 1988:1–2004:4
(compare estimates across rows 3 and 4, Table 1).

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Figure 5 Forward-Looking Taylor Rule
Actual and Predicted Fund Rate (Dynamic Predictions, Core CPI and Core PCE, and Unemployment Gap)
10.0
Actual
Predicted

7.5

5.0

2.5

0.0
1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

1998

2000

2002

2004

2006

Residual
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
1988

1990

1992

1994

1996

Predicting the Policy Rate Using a Taylor Rule based
on Core Inflation: Was the Fed Off the Taylor Rule
over 2001:1–2006:4?
In order to evaluate whether monetary policy actions over 2000:1–2006:4 can
be explained by a Taylor rule, we generate predictions of the policy rate using
the estimated Taylor rules. We consider two Taylor rules that differ with
respect to the measure of inflation, and we generate both dynamic and static
predictions. The dynamic predictions are generated using the policy rule as
shown in (5):
p

p

F Rt = ρF Rt−1 + 1 − ρ
ˆ
ˆ

α 0 + α π π c 4 + α u urt − urt∗
ˆ
ˆ ¯ t, ¯ ˆ

,

(5)

where F R p is the predicted funds rate and the other variables are defined as
before. As can be seen in the prediction equation given in (5), in generating
the current quarter predicted value of the funds rate, we use last quarter’s
predicted value of the federal funds rate rather than the actual value, while
using current-period values of the other two economic fundamentals. As a
result, the current funds rate is a distributed lag on current and past values of
expected inflation and the unemployment gap.

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139

Figure 6 Forward-Looking Taylor Rule
10.0

Actual and Predicted Fund Rate (Static Predictions, Core CPI and Core PCE, and Unemployment Gap)
Actual
Predicted

7.5

5.0

2.5

0.0
1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

1998

2000

2002

2004

2006

Residual

1.00
0.75
0.50
0.25
0.00
-0.25
-0.50
-0.75
-1.00
-1.25
1988

1990

1992

1994

1996

In contrast, the static predictions of the policy rate are generated while
also paying attention to recent policy actions, in addition to economic fundamentals. In particular, the static predictions are generated using the estimated
policy rule as shown in (6):
p

F Rt = ρF Rt−1 + 1 − ρ
ˆ
ˆ

α 0 + α π π c 4 + α u urt − urt∗
ˆ
ˆ ¯ t, ¯ ˆ

.

(6)

The policy rule shown in (6) is similar to the one in (5) with the exception that
(6) uses last quarter’s actual value of the federal funds rate. Thus, in the static
exercise the current forecast is influenced in part by actual policy actions, the
magnitude of the influence of policy on the forecast being determined by the
size of the partial adjustment coefficient, ρ.24
24 Since the dynamic predictions are generated by paying attention only to expected inflation and the unemployment gap, they are better at revealing certain types of misspecification. In
particular, if the federal funds rate equation is misspecified because it is estimated ignoring the
influences of some other economic fundamentals, then the dynamic predictions generated using
such a policy rule are likely to be poor proxies for the actual behavior of the federal funds rate.
Hence, the dynamic predictions are better at gauging the fit of the estimated policy rule than are
the static predictions.

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 7 Forward-Looking Taylor Rule
10

Actual and Predicted Fund Rate (Dynamic Predictions, Headline CPI, and Unemployment Gap)
Actual
Predicted

9
8
7
6
5
4
3
2
1
1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2000

2002

2004

2006

Residual

3
2
1
0
-1
-2
-3
-4
1988

1990

1992

1994

1996

1998

Figures 5 and 6 respectively chart the dynamic and static predictions of
the funds rate from the Taylor rule that is estimated using the time-varying
measure of core inflation.25 Actual values of the funds rate and the prediction
errors are also charted there. Two observations need to be highlighted. First,
the estimated policy rule predicts very well the broad contours of the policy rate
over 1988:1–2006:4. The mean absolute error is .47 percentage points when
dynamic predictions are used and .30 percentage points when static predictions
are used. The root mean squared error is .60 percentage points when dynamic
predictions are used, whereas it is only .38 percentage points when static
predictions are used. Secondly, focusing on the period from 2000:1–2006:4,
there is no evidence of persistently large prediction errors, and most prediction
errors are small in magnitude (below twice the root mean squared error),
suggesting that the actual funds rate is well predicted and, hence, that the
Greenspan-Bernanke Fed was “on” a Taylor rule.
25 The predictions begin in 1988:1. For generating the prediction for 1988:2, we use last

quarter’s actual funds rate. For later periods, the predicted values are generated using last period’s
predicted value and current period estimates of expected inflation and the unemployment gap.

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141

Figure 8 Forward-Looking Taylor Rule
Actual and Predicted Fund Rate (Static Predictions, Headline CPI, and Unemployment Gap)

10

Actual
Predicted

9
8
7
6
5
4
3
2
1
1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2000

2002

2004

2006

Residual

1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
1988

1990

1992

1994

1996

1998

Predicting the Policy Rate Using a Taylor Rule Based
on Headline CPI Inflation: Was the Fed Off the
Taylor Rule over 2001:1–2006:4?
Figures 7 and 8 respectively chart the dynamic and static predictions of the
policy rate from the Taylor rule estimated using headline CPI inflation. Two
observations are noteworthy. First, this Taylor rule does not predict well the
broad contours of the policy rate. The mean absolute error is 1.1 percentage
points and the root mean squared error is 1.5 percentage points, based on
dynamic prediction of the policy rate. The summary measures of predictive
performance improve somewhat when they are calculated using the static
prediction errors—the mean absolute error is .46 percentage points and the root
mean squared error is .56 percentage points. Secondly, focusing on the period
from 2000:1–2006:4, there is clear evidence of persistently large negative
prediction errors, and many of these prediction errors are large in magnitude
(see lower panels, Figures 7 and 8). According to this Taylor rule, the actual
funds rate remained consistently below the level prescribed, implying policy
was too loose for most of the period over 2000:1–2006:4—a result that is in
line with the ones in Smith and Taylor (2007) and Taylor (2007).

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 9 Counterfactual Simulations
Actual and Predicted Fund Rate (Dynamic Predictions, Core PCE Inflation, Real-Time Versus Final Data)
7
6
5
4
3
2
1

Actual
Predicted (Real)
Predicted (Final)

0
2000

2001

2002

2003

2004

2005

2006

Residual

1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5

Real

Final

V2P

V2N

-2.0
2000

2001

2002

2003

2004

2005

2006

Role of Data Revisions
Figure 2 shows that data on core PCE inflation have been extensively revised
over the years, particularly for the period 2002–2005 when real-time estimates
of core PCE inflation are substantially below the 2009 vintage estimates. Figures 9 and 10 chart, respectively, the counterfactual dynamic and static simulations of the policy rate generated using 2009 vintage data on economic
fundamentals.26 For a comparison, the predictions generated using real-time
data are also charted. As can be seen, deviations of the policy rule using the
2009 vintage data are somewhat larger than those generated using real-time
data. However, it would be misleading to conclude from such evidence that
the Federal Reserve was too loose.27
26 The policy rule is estimated using real-time data over 1988:1–2004:4. The dynamic predictions are, however, generated using not real-time but 2009 vintage estimates of core PCE inflation
and the unemployment gap.
27 Many analysts have examined other indicators of inflation available in real time and conclude that monetary policy was not inflationary, despite the low level of the federal funds rate
target. For example, Dokko et al. (2009) have examined the commercially available inflation forecasts of the private sector as well as the inflation forecasts made by the individual members the
FOMC published in the Humphrey-Hawkins reports over 2003–2006. They concluded that all those
inflation forecasts were consistent with the Federal Reserve’s informal inflation target of between

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143

Figure 10 Counterfactual Simulations
Actual and Predicted Fund Rate (Static Predictions, Core PCE Inflation, Real-Time Versus Final Data)
7
6
5
4
3
2
1

Actual
Predicted (Real)
Predicted (Final)

0
2000

2001

2002

2003

2004

2005

2006

Residual

1.00
0.75
0.50
0.25
0.00
-0.25
-0.50
-0.75
-1.00

Real

Final

V2P

V2N

-1.25
2000

2001

2002

2003

2004

2005

2006

Role of Deflation Fears
Some analysts, focusing on the Taylor rule estimated using CPI inflation measure, contend that, over the period 2002:1–2005:4, the Greenspan Fed may
have kept the federal funds rate too low for too long in order to avoid the
consequences of a Japanese-style deflation. According to this explanation,
internal forecasts of the U.S. inflation rate indicated the possibility of deflation, which led the Greenspan Fed to keep the short-term interest rate low
for an extended period of time. There is some limited support for this view
in Figure 4, which shows that the Greenbook forecasts of core PCE inflation
indicated substantial deceleration of expected inflation for most of the period
over 2002:1–2005:4. However, actual core PCE inflation did not decline to
levels indicated by the Greenbook forecast. Also, as shown above, the actual
funds rate is close to what is prescribed by a forward-looking Taylor rule estimated using real-time data on the fundamentals, namely, core PCE inflation

1.5 percent to 2 percent. Others focusing on the bond market measures of inflationary expectations
point out that, over this subperiod, long-term rates exhibited considerable stability that is consistent
with the presence of a noninflationary policy stance, despite the low level of the federal funds
rate.

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 11 Forward-Looking Taylor Rule
Actual and Predicted Fund Rate (Dynamic Predictions, Core CPI, and Unemployment Gap)

10

Actual
Predicted

9
8
7
6
5
4
3
2
1
1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2002

2004

2006

Residual

2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
1988

1990

1992

1994

1996

1998

2000

and the unemployment gap. The empirical work here suggests that, while the
fear of deflation may have played some role, the actual funds rate remained
low for fundamental reasons once we recognize that the Greenspan Fed was
focused not on headline CPI but on a core measure of PCE inflation.

Headline CPI Versus Core CPI
The result here—that a forward-looking Taylor rule estimated using a headline measure of CPI inflation does not depict parameter stability during the
Greenspan years—continues to hold if the Taylor rule is instead estimated
using a core measure of CPI inflation. In fact, several analysts, including
Blinder and Reis (2005), have estimated Taylor rules using a core measure
of CPI inflation. But, as shown below, the use of a core measure of CPI
inflation does generate reasonable estimates of policy response coefficients;
the estimated policy rule, however, does not depict parameter stability in the
Greenspan years. Table 1 presents policy response coefficients estimated using core CPI inflation data and Table 2 presents p-values of the Chow test
of parameter stability (see column C). As can be seen, estimated policy response coefficients appear reasonable. However, the estimated policy rule still

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145

Figure 12 Forward-Looking Taylor Rule
Actual and Predicted Fund Rate (Static Predictions, Core CPI, and Unemployment Gap)

10

Actual
Predicted

9
8
7
6
5
4
3
2
1
1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2000

2002

2004

2006

Residual

1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
1988

1990

1992

1994

1996

1998

exhibits parameter instability in 2001; the test results indicate a reduction in
the size of the inflation response coefficient, consistent with the observation in
Taylor (2007) that the Greenspan Fed did not react strongly to inflation after
2001. Figures 11 and 12 chart the dynamic and static simulations of the federal
funds rate using the estimated Taylor rule based on the core measure of CPI
inflation. As can be seen, the actual funds rate is considerably below the value
prescribed by this policy rule for most of the subperiod from 2001:1–2006:4.
Using the metric of summary error statistics based on dynamic predictions, we
calculate the mean absolute error as .70 percentage points and the root mean
squared error as .86 percentage points. By this metric, the Taylor rule estimated using core CPI does better than the Taylor rule estimated using headline
CPI inflation. However, neither of these Taylor rules depict parameter stability and both are consistent with policy by being “too loose” over most of the
period 2002:1–2006:4.

Forward- Versus Backward-Looking Taylor Rules
The empirical work here has used forward-looking Taylor rules to show that
the measure of inflation chosen matters for predicting actual policy actions

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 13 Backward-Looking Taylor Rule
Actual and Predicted Fund Rate (Core CPI and Core PCE and Unemployment Gap)

10.0

Actual
Predicted

7.5

5.0

2.5

0.0
1988

1990

1992

1994

1998

2000

2002

2004

2006

1998

2000

2002

2004

2006

1996
Residual

1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
1988

1990

1992

1994

1996

over 2002:1–2006:4, namely, a Taylor rule estimated using the time-varying
measure of core inflation tracks actual policy better than a Taylor rule estimated
using headline CPI inflation. However, it may be noted that the above result
continues to hold if one estimates and compares backward-looking Taylor
rules. Namely, a backward-looking Taylor rule estimated using the timevarying measure of core inflation tracks actual policy actions much better
than does a Taylor rule with headline CPI inflation (see Figures 13 and 14).
However, backward-looking Taylor rules generally do not depict parameter
stability, even when they are estimated using the time-varying measure of core
inflation.28
28 The Taylor rules considered in this exercise were estimated using smoothed lagged values
of inflation and unemployment gap variables, as in the original Taylor rule. We also estimated
versions in which we include a lagged value of the federal funds rate, thereby directly allowing
interest rate smoothing. This specification gave qualitatively similar results.

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147

Figure 14 Backward-Looking Taylor Rule
Actual and Predicted Fund Rate (Headline CPI and Unemployment Gap)

10

Actual
Predicted

9
8
7
6
5
4
3
2
1
1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2000

2002

2004

2006

Residual

3
2
1
0
-1
-2
-3
1988

1990

1992

1994

1996

1998

Discussion of Results
The empirical results above suggest that monetary policy actions in the
Greenspan era can be summarized by a stable Taylor rule according to which
the Federal Reserve was forward looking, smoothed interest rates, and focused
on a core measure of inflation measured by CPI until 2000 and PCE thereafter.
The estimated Taylor rule does not depict any parameter instability, despite
the switch in the measure of inflation used in monetary policy deliberations.
In contrast, Taylor rules that do not allow for this switch in the measure of
inflation, and are instead estimated using CPI inflation (headline or core), depict parameter instability around 2000, indicating that the Greenspan Fed did
not react strongly to expected (CPI) inflation.
Within the context of a Taylor-type policy rule, a switch in the measure of
inflation is likely to affect the policy rule mainly by altering the constant term
of the policy rule if the switch leads to a different inflation target expressed
in a new inflation measure. This occurs because the constant term in a Taylor
rule has embedded in it the Fed’s estimate of its inflation target. However,
the constant term in a Taylor rule also has embedded in it the Fed’s estimate
of the economy’s real rate of interest. To see it, rewrite equation (1.1) as

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Federal Reserve Bank of Richmond Economic Quarterly

F Rt∗ = rr ∗ + π ∗ + α π Et π c − π ∗ + α u urt − urt∗ , where rr ∗ is the
t+j
real rate and π ∗ is the inflation target. If we substitute the above equation into
equation (1.2), we get equation (1.3), where the constant term is now defined as
α 0 = rr ∗ + (1 − α π ) π ∗ . The constant term thus has embedded in it the Fed’s
estimates of the real rate of interest as well as its inflation target. However, as
is well known, given a reduced-form estimate of the constant term, we can’t
recover the Fed’s estimates of the real rate as well as its inflation target without
bringing in additional information.
The switch in the measure of inflation from core CPI to core PCE does
not appear to be associated with any significant shift in the estimated Taylor
rule used to explain monetary policy actions in the Greenspan years.29 One
possible explanation of why the switch did not lead to any significant shift in
the estimated Taylor rule is that while the switch may have lowered the Fed’s
inflation target expressed in core PCE inflation, it may have also caused the
Greenspan Fed to raise its assessment of the economy’s real rate of interest,
thereby leaving the constant term of the estimated Taylor rule unchanged.30

3.

CONCLUDING OBSERVATIONS

This article shows that the measure of inflation used in estimating Taylor
rules to explain historical monetary policy actions is not innocuous. The
FOMC under the chairmanship of Alan Greenspan refined the measure of
inflation used in monetary policy deliberations, switching from focusing on
CPI to focusing on PCE in the early 1980s. Moreover, Chairman Greenspan
encouraged both the FOMC and the financial markets to focus on core rather
than headline inflation in implementing policy. As noted in Blinder and Reis
(2005), during the Greenspan era an oil shock was considered a “blip” in
the inflation process that did not affect long-term inflationary expectations
and therefore should be ignored, leading the Fed to focus on core rather than
headline inflation in the implementation of monetary policy.
If we estimate a Taylor rule that uses real-time data and we employ the
time-varying measure of core inflation, then the estimated policy rule depicts
29 This result is consistent with the test results of parameter stability discussed above. For
each possible break date between 2000:1–2001:4, the Chow test of parameter stability was performed including intercept as well as slope dummies on response coefficients in the policy rule.
For all the break dates, the intercept dummy was not statistically different from zero, which is
consistent with the absence of a change in the constant term of the policy rule.
30 Using the metric of comparing means, the sample mean of core PCE inflation rates over
1987:1–2005:4 is 2.5 percent, which is lower than the value (3.1 percent) computed using core CPI
inflation rates over the same period. Given the differential trend behavior of these two inflation
measures, the Greenspan Fed having an inflation target of, say, 2 percent based on the behavior
of core PCE inflation is equivalent to its having an inflation target of 2.6 percent based on the
core CPI inflation measure. Hence, the switch from CPI to PCE measure of inflation could have
been associated with a downward shift in the constant term of the estimated Taylor rule around
2000.

Mehra/Sawhney: Inflation, Taylor Rules, Greenspan-Bernanke Years

149

parameter stability in the Greenspan era and predicts very well the actual path
of the federal funds rate over 2001:1–2006:4. In contrast, a Taylor rule that
is estimated using headline CPI inflation depicts parameter instability and
indicates the actual funds rate was too low relative to the level prescribed, as
headline CPI inflation remained above core PCE inflation during most of this
short period. Hence, in evaluating monetary policy actions in the Greenspan
era, it is important to pay attention to these two real-time features of monetary
policy deliberations, namely, the focus on core rather than headline inflation
measures and the switch from CPI inflation to PCE inflation.
Following John Taylor’s (2007) work, many analysts and some policymakers have begun to contend that, over 2002:1–2005:4, the Federal Reserve
may have lowered the federal funds rate too low for too long, suggesting that
monetary policy was too loose as seen through the lens of a Taylor rule. The
popular explanation of this easier stance on monetary policy during this period
is that the Greenspan Fed feared deflation. In fact, the Greenbook forecasts of
core PCE inflation indicated substantial deceleration in expected inflation during this subperiod, which did not materialize. However, the result here—that
a forward-looking Taylor rule estimated using real-time core PCE inflation
data tracks the actual funds rate well—implies that the actual funds rate was
determined for fundamental reasons. In real time, the Fed’s preferred measure
of core PCE inflation fluctuated in a low narrow range.
The core measure of PCE inflation has been extensively revised over the
years. In particular, the most recent 2009 vintage data indicates that over 2002–
2006, core PCE inflation did not decelerate as much and was substantially
higher than what the Federal Reserve knew in real time. When seen through
the lens of a Taylor rule, policy deviations using the 2009 vintage data are
somewhat larger than those generated using the real-time data. However, it
would be misleading to conclude from such evidence that monetary policy
was too easy. Several other indicators of inflationary expectations that were
available in real time indicate policy was noninflationary over this subperiod.

REFERENCES

Bernanke, Ben. 2010. “Monetary Policy and the Housing Bubble.” Speech at
the Annual Meeting of the American Economic Association, Atlanta,
Georgia (January 3).
Bernanke, Ben, and Jean Boivin. 2003. “Monetary Policy in a Data-Rich
Environment.” Journal of Monetary Economics 50 (April): 525–46.

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Blinder, Alan S., and Ricardo Reis. 2005. “Understanding the Greenspan
Standard.” Presented at the Symposium “The Greenspan Era: Lessons
for the Future,” sponsored by the Federal Reserve Bank of Kansas City
in Jackson Hole, Wyoming (August 25–27).
Boivin, Jean. 2006. “Has U.S. Monetary Policy Changed? Evidence from
Drifting Coefficients and Real-Time Data.” Journal of Money, Credit
and Banking 38 (August): 1,149–73.
Clarida, Richard, Jordi Gali, and Mark Gertler. 2000. “Monetary Policy
Rules and Macroeconomic Stability: Evidence and Some Theory.”
Quarterly Journal of Economics 115 (February): 147–80.
Dokko, Jane, Brian Doyle, Michael T. Kiley, Jinill Kim, Shane Sherlund, Jae
Sim, and Skander Van den Heuvel. 2009. “Monetary Policy and the
Housing Bubble.” In the Finance and Economics Discussion Series
2009-49. Washington, D.C.: Federal Reserve Board.
English, William, William R. Nelson, and Brian P. Sack. 2002. “Interpreting
the Significance of the Lagged Interest Rate in Estimated Policy Rules.”
Mimeo, Board of Governors (April 24).
Granger, C.W.J., and P. Newbold. 1974. “Spurious Regressions in
Econometrics.” Journal of Econometrics 2 (July): 111–20.
Kiley, Michael T. 2008. “Estimating the Common Trend Rate of Inflation for
Consumer Prices and Consumer Prices Excluding Food and Energy
Prices.” In the Finance and Economics Discussion Series 2008-38.
Washington, D.C.: Federal Reserve Board.
Kohn, Donald L. 2007. “John Taylor Rules.” Speech at the Conference on
John Taylor’s Contributions to Monetary Theory and Policy, Federal
Reserve Bank of Dallas (October 12).
Kohn, Donald L. 2009. “Policy Challenges for the Federal Reserve.” Speech
at the Kellogg Distinguished Lectures Series, Kellogg School of
Management, Northwestern University, Evanston, Illinois (November
16).
Mehra, Yash P. 2001. “The Bond Rate and Estimated Monetary Policy
Rules.” Journal of Economics and Business 53: 345–58.
Mehra, Yash P., and Brian D. Minton. 2007. “A Taylor Rule and the
Greenspan Era.” Federal Reserve Bank of Richmond Economic
Quarterly 93 (Summer): 229–50.
Mehra, Yash P., and Devin Reilly. 2009. “Short-Term Headline-Core
Inflation Dynamics.” Federal Reserve Bank of Richmond Economic
Quarterly 95 (Summer): 289–313.

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Mishkin, Frederic S. 2007. “Headline versus Core Inflation in the Conduct of
Monetary Policy.” Speech at the Business Cycles, International
Transmission and Macroeconomic Policies Conference, HEC Montreal,
Montreal, Canada (October 20).
Orphanides, Athanasios. 2001. “Monetary Policy Rules Based on Real-Time
Data.” American Economic Review 91 (September): 964–85.
Orphanides, Athanasios. 2002. “Monetary Policy Rules and the Great
Inflation.” American Economic Review 92 (May): 115–20.
Orphanides, Athanasios, and Volker Wieland. 2008. “Economic Projections
and Rules-of-Thumb for Monetary Policy.” Federal Reserve Bank of St.
Louis Review (July): 307–24.
Poole, William. 2007. “Understanding the Fed.” Federal Reserve Bank of St.
Louis Review 89 (January/February): 3–14.
Romer, Christina, and David Romer. 2000. “Federal Reserve Information
Advantage and the Behavior of Interest Rates.” American Economic
Review 90: 429–57.
Rudebusch, Glenn D. 2002. “Term Structure Evidence on Interest Rate
Smoothing and Monetary Policy Inertia.” Journal of Monetary
Economics 49 (September): 1,161–87.
Rudebusch, Glenn D. 2006. “Monetary Policy Inertia: Fact or Fiction?”
International Journal of Central Banking 2 (December): 85–135.
Smith, Josephine M., and John B. Taylor. 2007. “The Long and the Short
End of the Term Structure of Policy Rules.” Mimeo, Stanford University.
Taylor, John. 1993. “Discretion Versus Policy Rules in Practice.”
Carnegie-Rochester Series on Public Policy 39 (December): 195–214.
Taylor, John. 2007. “Housing and Monetary Policy.” Presented at the Policy
Panel at the Symposium on Housing, Housing Finance, and Monetary
Policy sponsored by the Federal Reserve Bank of Kansas City in
Jackson Hole, Wyoming (September).
Taylor, John. 2009. “The Financial Crisis and the Policy Responses: An
Empirical Analysis of What Went Wrong.” Working Paper 14631.
Cambridge, Mass.: National Bureau of Economic Research (January).

Economic Quarterly—Volume 96, Number 2—Second Quarter 2010—Pages 153–177

Monetary Policy with
Interest on Reserves
Andreas Hornstein

I

n response to the emerging financial crisis of 2008, the Federal Reserve
decided to increase the liquidity of the banking system. For this purpose,
the Federal Reserve introduced or expanded a number of programs that
made it easier for banks to borrow from it. For example, commercial banks
were able to obtain additional loans through the Term Auction Facility, which
the banks would then hold in their reserve accounts with the Federal Reserve.
As a result of the combined financial market interventions, the balance sheet
of the Federal Reserve increased from about $800 billion in September 2008
to more than $2 trillion in December 2008. Over the same time period, the
reserve accounts of commercial banks with the Federal Reserve increased
from about $100 billion to $800 billion. In late 2008 the Federal Reserve also
announced a program to purchase mortgage-backed securities (MBS) and debt
issued by government-sponsored agencies. Since then, outright purchases of
agency MBS and agency debt have essentially replaced short-term borrowing
by commercial banks on the asset side of the Federal Reserve’s balance sheet,
and the volume of outstanding reserves increased again to about $1.1 trillion
by the end of 2009. Given the magnitude of outstanding reserves, there is some
concern these reserves might limit policy options once the Federal Reserve
decides to pursue a more restrictive monetary policy. Yet, another change in
the available policy instruments might lessen this concern: Starting in October
2008, the Federal Reserve began to pay interest on the reserve accounts that
banks hold with the Federal Reserve System.
How should one think about monetary policy when reserve accounts earn
interest? To study this issue, I introduce a stylized banking sector into a simple
baseline model of money that is at the core of much research in monetary
I would like to thank Anne Davlin, Huberto Ennis, Bob Hetzel, Thomas Lubik, John Weinberg,
and Alex Wolman for helpful comments and Nadezhda Malysheva and Sam Henly for excellent
research assistance. Any opinions expressed in this paper are my own and do not necessarily reflect those of the Federal Reserve Bank of Richmond or the Federal Reserve System.
E-mail: andreas.hornstein@rich.frb.org.

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economics. In this framework I address an admittedly rather narrow theoretical
question, but this question is fundamental to any theory of monetary policy.
Namely, does the payment of interest on reserves affect issues of price level
determinacy? An indeterminate price level might be undesirable since it can
give rise to price level fluctuations driven by self-fulfilling expectations. In
this context it is shown that the amount of outstanding reserves has only limited
implications for the conduct of monetary policy.
Price level determinacy is studied in a theoretical framework that specifies
not only monetary policy, but also fiscal policy, e.g., Leeper (1991) or Sims
(1994). Monetary policy is described as setting a short-term nominal interest
rate in response to inflation, and fiscal policy is described as setting the primary surplus in response to outstanding government debt. For the baseline
monetary model without a banking sector, one obtains price level determinacy
if monetary policy is active, that is, it responds strongly to the inflation rate,
and fiscal policy is passive, that is, it responds strongly to government debt.1
Price level determinacy is also obtained when monetary policy is passive and
fiscal policy is active. For the modified model with a banking sector, I find
that this characterization of price level determinacy is not materially affected,
whether or not interest is paid on reserves. I obtain a determinate price level
when monetary policy is sufficiently active and fiscal policy is sufficiently
passive, or vice versa. Furthermore, the magnitude of outstanding reserves
may not matter at all, and if it does matter the impact of reserves is small.
Earlier theoretical work on paying interest on reserves was concerned
that this policy would lead to price level indeterminacy. Sargent and Wallace
(1985) argue that, depending on how interest on reserves is financed, an equilibrium might not exist or the price level might be indeterminate.2 In terms of
the above characterization of monetary and fiscal policy, these results obtain
because the assumed financing schemes for interest on reserves make monetary and fiscal policy both passive or both active. My results are in line with
the recent work of Sims (2009), who studies the monetary and fiscal policy
coordination problem when interest is paid on money in a baseline monetary
model. The results are also related to Woodford’s discussion (2000) of monetary policy as an interest rate policy in environments where the role of money
is diminished over time.
The framework of this article is not suited to address the question of
whether interest on reserves allows a separation of monetary policy from
credit policy as suggested by Goodfriend (2002) and Keister, Martin, and
McAndrews (2008). In this article I use a reduced form representation of liquidity preferences by households to model distinct household demand
1 The terminology follows Leeper (1991).
2 Smith (1991) raises similar concerns on price level determinacy in an extended version of

the environment studied by Sargent and Wallace (1985).

A. Hornstein: Interest on Reserves

155

functions for cash, bank demand deposits, and government bonds, but the
model of the financial system’s attitude toward the liquidity of assets in the
financial system is even more rudimentary. First, I do not allow for credit
risk; and second, the banks’ attitudes toward liquidity risk are captured by
one exogenous parameter, the desired ratio of liquid assets to deposits. The
fact that the volume of reserves is of only limited relevance for price level
determinacy therefore does not say anything about the ability of reserves to
enhance the liquidity of the financial system.
The analysis of the conduct of monetary policy when interest is paid on
reserves is based on a stylized model of the economy. Before proceeding
with this analysis I will review the mechanics of the Federal Reserve’s interest
rate policy in the next section. This section also provides an opportunity to
describe how the interventions of the Federal Reserve in financial markets in
2008 affected its ability to conduct interest rate policy. Section 2 then reviews
Leeper’s joint analysis (1991) of monetary and fiscal policy in a baseline
monetary model, and Section 3 adds a stylized banking sector to the baseline
monetary model. The banking model of this section introduces the payment
of interest on reserves into a simplified version of the environment studied by
Canzoneri et al. (2008). Section 4 concludes.

1. THE MECHANICS OF INTEREST RATE POLICY
Most central banks implement monetary policy through an interest rate policy.
That is, they target a short-term interest rate and adjust their target in response
to changes in economic conditions. Federal Reserve monetary policy appears
to be well-approximated by a policy rule that increases the targeted interest
rate more than one-for-one in response to an increase of the inflation rate and
decreases the targeted interest rate in response to declines in economic activity
as measured by a declining gross domestic product growth rate or an increasing
unemployment rate. This kind of behavior has become known as the Taylor
rule. The short-term interest rate that the Federal Reserve targets is the federal
funds rate—that is, the interest rate that U.S. banks charge each other for
overnight loans. This section provides a short review of the mechanics of how
the Federal Reserve influences the federal funds rate, and how paying interest
on reserves affects its ability to target this rate. The review takes a very stylized
view of the federal funds market, as in Ennis and Weinberg (2007). For a more
detailed description of the process see Ennis and Keister (2008).
Commercial banks are required to hold particular assets (reserves) against
their outstanding liabilities. How many reserves a bank has to hold depends
on the types and amounts of its outstanding liabilities. Assets that qualify as
reserves are vault cash and accounts with the central bank. Banks hold accounts with the central bank not only to satisfy reserve requirements, but also
to facilitate intraday transactions. Private agents engage in transactions and

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 The Market for Reserves

Federal Funds Rate

RP

S'

S

R
D
RR

Reserves

use their bank accounts to settle payments associated with these transactions.
Since not everybody is using the same bank, these payment settlements result
in corresponding payment settlements between banks during a business day.
Banks use their accounts with the central bank to implement these settlements.
A payments transfer from one bank to another can be settled through a debit
(credit) to the paying (receiving) bank’s account with the central bank. Total
inflows and outflows to a bank’s account with the central bank during a day
need not balance, and at the end of the day a bank’s account may have increased or decreased. Furthermore, there is some randomness to settlement
transactions and the bank is uncertain as to its end-of-day balance with the
central bank.
The uncertainty about payment flows creates a problem for banks since
they have to hold a certain balance with the central bank at the end of the day
in order to satisfy their reserve requirement. Suppose that at the beginning of
the day a bank has some amount of money and has to decide how much to
allocate to its reserve account and how much to borrow/lend overnight with
other banks at the federal funds rate. If the bank does not allocate enough
to its reserve account and at the end of the day its balance falls short of its
reserve requirement, it can borrow from the central bank at a penalty rate,

A. Hornstein: Interest on Reserves

157

RP .3 Alternatively, if at the end of the day the bank’s reserve account exceeds
its reserve requirement, then the bank foregoes some interest income if the
interest rate paid on reserve accounts, RR , is lower than the federal funds rate.
The optimal response of banks to this settlement uncertainty creates a
precautionary demand for reserves, D, that depends on the federal funds rate
(Figure 1). The federal funds rate cannot exceed the penalty rate since banks
can always borrow at the penalty rate. If the federal funds rate is below the
penalty rate but above the interest rate paid on reserves, then the foregone
interest income represents an opportunity cost to holding reserve balances.
This opportunity cost, however, is declining in the federal funds rate and
banks are willing to hold more reserves at lower federal funds rates. Finally,
if the federal funds rate is equal to the interest on reserves, then there is no
opportunity cost to holding reserves and the demand for reserves becomes
infinitely elastic. The equilibrium federal funds rate is bounded by the penalty
rate and the interest rate on reserves, and, given the demand for reserves, it is
determined by the supply of reserves, S.
In the short run the Federal Reserve controls the federal funds rate through
actions that affect the supply of reserves. The particular operating procedure
for the Federal Reserve has been that the market desk at the New York Federal
Reserve Bank forecasts the daily demand for reserves and then injects or
withdraws reserves in order to equalize the predicted federal funds rate with
the federal funds rate target set by the FOMC. Except for unusual events,
the “effective” federal funds rate during the day—that is, the rate at which
intrabank loans occur—is usually very close to the federal funds target rate
(Figure 2a).4 At times, when the Federal Reserve injects large amounts of
liquidity for reasons other than interest rate policy, this is no longer true.
For example, in response to the events of September 11, 2001, the Federal
Reserve wanted to ensure the stability of the financial system and injected
large amounts of reserves. This action resulted in an effective federal funds
rate that was substantially below the target rate (Figure 2b). At the time,
this divergence between perceived liquidity needs and interest rate policy was
not considered to be a problem since the liquidity provision was viewed as
temporary and to be reversed in a short period of time.
3 In the United States, banks can borrow from the Federal Reserve against pre-approved
collateral at the discount window. The discount rate is set higher than the federal funds target
rate, usually 100 basis points (bp). As part of the response to the financial crisis, the Federal
Reserve kept the discount rate at 25bp above the target federal funds rate from April 2008 until
February 2010. A bank’s effective borrowing rate is presumably higher than the discount rate since
a bank’s borrowing from the discount window is seen as a negative signal on the bank’s balance
sheet condition.
4 Interbank lending proceeds through bilateral arrangements and, during the day, the negotiated
lending rates can fluctuate substantially. The effective federal funds rate is a value-weighted average
of the different loan rates.

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Target and Effective Federal Funds Rate

Panel A: January 2000--January 2010
8
Federal Funds Target

7

Effective Federal Funds Rate

Rate (100bp)

6
5
4
3
2
1
0
2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

Panel B: June 2001--December 2001
8
Federal Funds Target

6

Rate (100bp)

7

Effective Federal Funds Rate

5
4
3
2
1
June 01

July 01

Aug 01

Sep 01

Nov 01

Oct 01

Dec 01

Panel C: August 2008--January 2010

Federal Funds Target
Effective Federal Funds Rate
Rate on Required Reserves
Rate on Excess Reserves

Rate (100bp)

3

2

1

Aug 08

Sep 08

Nov 08

Jan 09

Apr 09

June 09 Aug 09

Oct 09

Dec 09

Jan 10

Notes: The data are described in the Appendix.

After the September 2008 bankruptcy of Lehman Brothers, the Federal
Reserve increased liquidity substantially in response to the widening financial
crises. This was accomplished through the expansion of existing programs,
such as the Term Auction Facility and swap lines to foreign central banks, and
the creation of new facilities, such as the Commercial Paper Funding Facility.
As a result, the Federal Reserve’s balance sheet more than doubled over three
months and the supply of reserves increased almost tenfold. Even if banks’

A. Hornstein: Interest on Reserves

159

demand for liquid assets increased at the time, the increase in the supply of
reserves was large enough to drive the effective federal funds rate significantly
below the stated federal funds target (Figure 2c).
Unlike the events of September 11, 2001, the divergence in this case between effective and target federal funds rates created a problem for the conduct
of interest rate policy since the increased liquidity provision was not viewed
as a short-lived measure. To deal with this problem, the Federal Reserve in
October 2008 started paying interest on reserves.5 The Federal Reserve Board
initially set the interest rate on reserves below the target federal funds rate,
but by early November 2008, after several modifications, the interest rate on
reserves was essentially the target federal funds rate.6
The rationale for this policy is based on the discussion above that suggests
that paying interest on reserves puts a floor to the federal funds rate (Figure 1).
Thus, even if the Federal Reserve increases the supply of reserves to a point
where the demand for reserves becomes infinitely elastic, e.g., S in Figure
1, the federal funds rate should not fall below the rate paid on reserves. This
suggests that with interest on reserves the Federal Reserve can separate the
provision of liquidity from its interest rate policy, e.g., Goodfriend (2002).
Furthermore, once the Federal Reserve pays interest on reserves, it has the
choice between two policy instruments: It can continue to target a market
interest rate, such as the federal funds rate, above the interest paid on reserves;
or it can increase the supply of reserves sufficiently and bring the federal funds
rate down to the interest paid on reserves and then adjust the interest rate it
pays, e.g., Lacker (2006). The first approach targets a lending rate for banks
that still contains some counterparty risk, while the second approach sets the
risk-free lending rate for banks.
The actual experience with interest on reserves does not completely support this argument. Since November 2008, the effective federal funds rate
has been consistently below the interest rate paid on reserves. In fact, starting in December 2008, the FOMC decided to announce a target range for
the federal funds rate between 0 and 25bps. This continues to be the policy
as of the writing of this article. On the positive side, since February 2008,
the effective federal funds rate has traded closer to the interest rate paid on
5 In 2006 Congress authorized the Federal Reserve to pay interest on reserves starting in
2011. At the time, the main motivation for paying interest on reserves was to eliminate the “tax
distortion” implied by the absence of interest payments on reserves. For example, banks would
engage in activities whose sole purpose was to minimize their holdings of “reservable” accounts.
6 On October 6, 2008, the Federal Reserve Board announced that it would pay interest on
the depositary institutions’ reserve account at 10bp (75bp) below the federal funds rate target for
required (excess) reserves. On October 22, the Board changed the rate paid on excess reserve
balances to the lowest Federal Open Market Committee (FOMC) target rate in effect during the
reserve maintenance period less 35bp. Finally, on November 5, 2008, the rate on required reserves
was set equal to the average target federal funds rate over the reserve maintenance period, and
the rate on excess balances was set equal to the lowest FOMC target rate in effect during the
reserve maintenance period.

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Federal Reserve Bank of Richmond Economic Quarterly

reserves. Various reasons have been advanced for this divergence between the
effective federal funds rate and the interest rate on reserves. For example, in
late 2008 participants in the federal funds market may have been preoccupied
with events other than trying to exploit all profit opportunities in the market for
overnight credit. More recently it has been argued that the low effective federal
funds rate originates from particular lenders in the federal funds market—the
government-sponsored enterprises (GSEs) Fannie May and Freddy Mac—
who do not have interest-bearing reserve accounts with the Federal Reserve
(for example, Bernanke [2009] or Bech and Klee [2010]). Arbitrage competition of depository institutions that can borrow from the GSEs and deposit
the proceeds in their interest-bearing reserve accounts should eliminate any
spreads between the effective rate and the reserve rate. This competition appears, however, to be limited since the GSEs apparently only engage in lending
activities with a limited number of banks.
For the analysis of an interest rate policy when reserves are paying interest,
I will abstract from the issues just discussed and assume that the interest rate
paid on reserves is the market interest rate. First, for monetary policy I am
interested in the opportunity cost to banks, which is the rate on reserves. For
this analysis it is irrelevant that nonbank institutions drive the effective rate
below the rate on reserves; and even if arbitrage by depositary institutions
does not completely eliminate the spread between the rate on reserves and
the effective rate, it will at least bound that spread. Second, for the types
of aggregate models used in monetary policy analysis, there is no meaningful
concept of counterparty risk. Thus, there is no risk premium that distinguishes
the interbank lending rate from the riskless rate paid by reserves. Third, these
models are not specified in terms of overnight interest rates, but interest rates
on short-term government debt. Given that the choices for the policy rates
tend to be highly persistent over short periods, this seems like a reasonable
approximation. Figure 3 displays the effective federal funds rate and several
other short-term interest rates from 1980 to present.7 As is apparent from
Figure 3, most of the time the different short-term interest rates track the
federal funds rate quite closely.
In what follows I will study an interest rate policy that pays interest on all
reserves at the market interest rate. In particular, I will study the implications
of interest on reserves for price level determinacy, and to what extent the
amount of outstanding reserves matters. Before proceeding to the model with
interest on reserves I first outline the framework of analysis for the case without
interest on reserves.
7 All data are described in detail in the Appendix.

A. Hornstein: Interest on Reserves

161

Figure 3 Selected Short-Term Interest Rates
25
Effective Federal Funds Rate
Three-Month Treasuries

20

Nonfinancial Three-Month
Commercial Paper
Three-Month CDs, Secondary Market

Rate (100bp)

Prime Bank Lending

15

10

5

0
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010

Notes: The data are described in the Appendix.

2. A SIMPLE FRAMEWORK FOR THE ANALYSIS OF
MONETARY AND FISCAL POLICY
The following model of an endowment economy has been used extensively
in the study of monetary policy. There is one consumption good, ct , and
the consumption good is in exogenous supply. There are two nominal assets
issued by the government: fiat money, Mt , and bonds, Bt . The price of the
consumption good in terms of fiat money is Pt , and since the consumption
good is the only good, Pt is also the price level. Inflation is the price level’s rate
of change from one period to the next, π t+1 = Pt+1 /Pt . Bonds pay interest
at the gross rate Rb,t , but fiat money does not. I define real balances and real
bonds in units of the consumption good as mt = Mt /Pt and bt = Bt /Pt .
Households can use both, money and bonds, to save, but holding money
also provides some transactions services when households purchase consumption goods. If it was not for the transactions services, households would not
want to hold money when bonds pay a positive interest rate since money
does not pay any interest. The demand for real balances, equation (1), depends negatively on the opportunity cost of holding money, i.e., the foregone

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Federal Reserve Bank of Richmond Economic Quarterly

interest income, and positively on the real transactions volume, ct . The demand
for bonds is determined by the Euler equation (2), which equates households’
willingness to exchange consumption today for consumption tomorrow with
the rate at which households can do that using bonds. The latter is the real rate
of return on bonds—that is, how much of the consumption good you obtain
tomorrow if you invest one unit of the consumption good today in a nominal
bond. Equations (1) and (2) can be derived from simple dynamic representative agent economies that explicitly specify the preferences of households
and their budget constraints, e.g., Leeper (1991) or Sims (1994):
= M Rb,t+1 ct ,
ct Rb,t+1
1 = β
,
ct+1 π t+1
Rb,t vt−1 − Rb,t − 1 mt−1
− τt,
vt =
πt
vt = b t + m t .

mt

(1)
(2)
(3)
(4)

Equation (3) represents the government’s budget constraint. On the lefthand side is the new real debt issued to make interest payments and retire
the outstanding debt on the right-hand side. Since debt is nominal, inflation
reduces the real amount of debt to be repaid. Furthermore, the government
does not pay interest on fiat money. Finally, if the government collects lump
sum taxes, τ t , then less new debt needs to be issued.8 Equation (4) defines
total real government debt as the sum of interest-paying real bonds and noninterest-paying real balances.
To close the model I assume that there is an exogenous endowment of the
consumption good such that one can take the time path for consumption as
given. I also assume that monetary policy chooses the nominal interest rate
in response to the inflation rate, and fiscal policy chooses taxes in response to
outstanding real bonds,
Rb,t+1 = f (π t ) and τ t = g (bt ) .

(5)

I characterize the equilibrium time paths for inflation, the interest rate,
real balances, real bonds, real debt, and lump sum taxes, xt =
π t , Rb,t , mt , bt , vt , τ t . An equilibrium is then a bounded time path for the
variables {xt } that solves the dynamic system defined by equations (1)–(5).9
8 A negative lump sum tax represents a transfer payment to the household. We can interpret lump sum taxes as the government’s primary surplus, that is, lump sum tax revenues minus
spending net of interest payments.
9 The equilibrium time paths for real balances and debt have to remain bounded, since they
represent solutions to a dynamic optimization problem. Technically, real balances and debt have
to satisfy transversality conditions, which state that the limiting value of the discounted future

A. Hornstein: Interest on Reserves

163

Monetary policy is said to be active (passive) if the nominal interest rate
responds strongly (weakly) to an increase of the inflation rate. Fiscal policy
is said to be active (passive) if lump sum taxes respond weakly (strongly)
to an increase of real bonds. For a local approximation of the difference
equation system, Leeper (1991) shows that for positive interest rates there
exists a unique equilibrium if monetary policy is active and fiscal policy is
passive, or conversely if monetary policy is passive and fiscal policy is active.10
The existence of a unique equilibrium in terms of the inflation rate and real
balances implies price level determinacy. If both policies are passive then
the equilibrium is indeterminate, and if both policies are active an equilibrium
will not exist.11 Sims (1994) shows that these results hold globally in Leeper’s
model (1991), and not only for local approximations.
The point of this analysis is that price level determinacy is jointly determined by monetary and fiscal policy. To illustrate this point, Figure 4, Panel
A1 displays the different regions that characterize equilibrium in terms of the
responsiveness of monetary and fiscal policy to the inflation rate and real debt
for a standard parameterization of the model.12 The horizontal axis displays
the elasticity of lump sum taxes with respect to real debt, γ , and the vertical axis displays the elasticity of the nominal interest rate with respect to the
inflation rate, α. The northeast and southwest regions represent parameter
combinations for which there exist unique equilibria. The southeast region
represents parameter values in which a continuum of equilibria exists, and the
northwest region represents parameter values in which no equilibrium exists.
The intuition for this decomposition of the policy parameter space is fairly
straightforward. Substituting the interest rate policy rule (5) into the Euler
equation (2) shows that the difference equation describing the dynamics of
inflation is independent of fiscal policy. If monetary policy is active, i.e.,
it responds strongly to past inflation, then this difference equation defines a
unique bounded solution for inflation. Furthermore, if fiscal policy is passive,
marginal utility of real balances and debt has to be zero. Thus, real balances and debt cannot
grow too fast relative to the time discount factor.
10 For a constant consumption path, c = c, and given policy targets for inflation and the
t
debt-consumption ratio, equations (1)–(5) define a unique time-invariant solution for the endogenous
variables, xt = x, the steady state. I define a local approximation to the equilibrium in terms of
small deviations from the steady state, which transforms the dynamic system of equations into a
linear difference equation system. For a description of conditions for the existence and uniqueness
of a bounded solution to linear difference equation system see, e.g., Sims (2000).
11 Indeterminacy or nonexistence of an equilibrium raises an issue as to how useful the proposed theory is for the analysis of monetary policy. After all, we are trying to explain a particular
outcome for the economy. Indeterminacy can be resolved by refining the equilibrium concept. For
example, we might assume that decisions are coordinated on an extraneous random variable that
has no relevance for the feasibility of outcomes, a sunspot. This gives rise to fluctuations as a
result of self-fullfilling expectations. If no equilibrium exists for certain combinations of monetary
and fiscal policy then we might conclude that some policy rules are simply not feasible in the
long run (Sargent and Wallace [1981]).
12 Figure 4 is based on a parameterization of the economy described in Section 3.

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Price Level Determinacy
Panel A1:
Fiscal Policy Targets Bonds b, Baseline
4-

4-

Monetary Policy

Monetary Policy

5-

Panel B1:
Fiscal Policy Targets Total Debt v, Baseline
5-

3210 -I
0

I

I

I

10

15

210 -I
0

I

5

3-

20

I

I

I

I

5

10

15

20

Fiscal Policy

Fiscal Policy

Panel B2:
Fiscal Policy Targets Total Debt v, Banks with Rm=1
5-

4-

4-

Monetary Policy

Monetary Policy

Panel A2:
Fiscal Policy Targets Bonds b, Banks with Rm=1
5-

3210 -I
0

I

I

I

10

15

210 -I
0

I

5

3-

20

I

I

I

I

5

10

15

20

Fiscal Policy

Fiscal Policy

Panel B3:
Fiscal Policy Targets Total Debt v, Banks with Rm=Rb
5-

4-

4-

Monetary Policy

Monetary Policy

Panel A3:
Fiscal Policy Target Bonds b, Banks with Rm=Rb
5-

3210 -I
0

I

I

I

I

5

10

15

20

Fiscal Policy

3210 -I
0

I

I

I

I

5

10

15

20

Fiscal Policy

i.e., lump sum taxes respond strongly to government debt, then iteration on
the transition equation for government debt defined by the government budget
constraint (3) defines a unique bounded path for government debt. Conversely,
if fiscal policy is active, i.e., lump sum taxes respond weakly to debt, then
the unique bounded solution for debt from the government budget constraint
defines debt as the discounted present value of future lump sum taxes and
seigniorage revenue from money creation. This in turn defines a time path for
the price level and thus the inflation rate. The implied time path for inflation
need not be the same as the unique time path for inflation implied by an active
monetary policy. Thus, active monetary and fiscal policies are inconsistent

A. Hornstein: Interest on Reserves

165

with the existence of an equilibrium. But if monetary policy is passive, then
the difference equation describing the dynamics of inflation is consistent with
a continuum of bounded solutions for inflation, in particular the inflation rate
implied by the government budget constraint. This case is therefore also
known as the fiscal theory of the price level. Finally, if monetary and fiscal
policy are both passive, then there exists a continuum of bounded solutions to
the system of difference equations, that is, the equilibrium is indeterminate.
Since for positive interest rates there is a uniquely defined demand for real
balances, one can think of the interest rate as being supported by open market
operations that supply the amount of money that is demanded at the given
interest rate, equation (1). If the demand for real balances is characterized by
a “liquidity trap”—that is, the demand is flat at a zero interest rate—then open
market operations do not affect the equilibrium outcome.

3.

INTEREST ON RESERVES AND THE CONDUCT OF
MONETARY POLICY

I now describe a simple endowment economy with a banking sector that generalizes the baseline model described in the previous section. In this model
banks are required to hold reserves, and one can study if and how the conduct
of monetary policy needs to be changed once market interest rates are paid on
reserves. I will limit attention to the question of how the payment of interest
on reserves affects price level determinacy, that is, existence and uniqueness
of an equilibrium.

An Economy with a Banking Sector
Consider a representative agent with preferences over a cash good, c, a credit
good, k, real balances, mh , real demand deposits, d, and real government
bonds, bh . Including these financial assets in preferences introduces a wedge
into the asset pricing equations because the assets pay a liquidity premium.
There is also a generic asset, a, that does not provide any liquidity services.
The demand deposits are offered by a competitive banking sector that uses
reserves and government bonds to service the demand deposits. The banking
sector also makes loans, l, to the representative agent that are used to finance
purchases of the credit good. Fiscal policy affects the evolution of government
debt. The environment is a simplified version of Canzoneri et al. (2008).
Household Demand for Assets

The representative agent’s preferences are
β t ln ct + γ k ln kt + γ m ln mh,t + γ d ln dt + γ b ln bh,t
t=0

(6)

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Federal Reserve Bank of Richmond Economic Quarterly

and the budget constraint is
ct + kt + mht + dt + bht + at − lt + τ t
≤ yt + mh,t−1 + dh,t−1 Rdt + bh,t−1 Rbt + at−1 Rt − lt−1 Rl,t /π t , (7)
where the nominal interest rate for asset j = m, d, b, and l is Rj , the nominal
interest rate on the generic asset is R, exogenous income is y, and lump
sum taxes are τ . Real balances, demand deposits, and government bonds
are assets that provide liquidity services in addition to being a store of value.
The liquidity services are represented as direct contributions to a household’s
utility. The generic asset does not provide any liquidity services and is not
included in the household’s utility function. By assumption the household has
to take out a loan to purchase the credit good
k t ≤ lt .

(8)

The optimal choices of the household imply the following asset demand
equations:
Rt+1
(9)
ct ,
mht = γ m
Rt+1 − 1
Rt+1
dt = γ d
ct ,
(10)
Rt+1 − Rd,t+1
Rt+1
bht = γ b
ct ,
(11)
Rt+1 − Rb,t+1
Rt+1
ct .
(12)
lt = γ k
Rt+1 − Rl,t+1
Note that the household’s demand for real balances is well-defined even at a
zero nominal bond rate. The household’s demand for real balances depends
on the interest rate of the generic asset and not the bond rate. Furthermore,
since bonds provide liquidity services, the bond rate will always be below the
generic asset rate. Thus, even if the bond rate is zero the household demand
for real balances is uniquely defined. There is no liquidity trap for household
demand of real balances.
Intertemporal optimization with respect to the generic financial asset implies the Euler equation
ct
Rt
1= β
,
(13)
ct+1 π t+1
where the term in square brackets is the marginal rate of substitution between
consumption today and tomorrow. In the endowment economy equilibrium
consumption of the cash and credit good is exogenous. With exogenous consumption, this Euler equation determines inflation conditional on the nominal
interest rate for the generic asset.
Two remarks are in order. First, I deviate from the standard asset pricing
setup to get potentially well-specified demand functions for real balances and

A. Hornstein: Interest on Reserves

167

demand deposits. Putting the assets into the utility function is one way to
get well-defined demand functions. Alternatively, I could have assumed that
these assets lower transactions costs and introduced the relevant cost terms in
the budget constraint as in Goodfriend and McCallum (2007). Second, I want
to have a simple model of bank lending, so just assume that the “credit” good
has to be purchased through a one-period loan taken out from the bank.
Bank Demand and Supply of Assets

A bank takes in demand deposits that provide transactions services for the
household and represent a liability to the bank. The bank’s assets consist of
loans made to the household, and bond and reserve holdings, bb and mb . The
balance sheet of a bank is
lt + bbt + mbt = dt .

(14)

Banks need to hold reserves and bonds to service demand deposits:
bbt + mbt = ϕdt .

(15)

This equation represents an assumption on the bank’s technology, namely
what and how many assets the bank needs in order to generate the demand
deposit services for the household. I assume that the bank uses liquid assets,
i.e., bonds and reserves, in order to service demand deposits, but it need not
hold 100 percent liquid assets, ϕ < 1. Furthermore, bonds and reserves are
perfect substitutes in the production of demand deposit services.
Banks may also be forced to satisfy a reserve requirement that is imposed
by a government regulator:
mbt ≥ ρdt .

(16)

Alternatively, the reserve ratio can reflect special precautionary preferences
of banks for reserves. I assume that ρ < ϕ, otherwise banks would not hold
other liquid assets besides reserves.13
I can assume that there is a representative bank that behaves competitively
since the banking technology described above is characterized by constant
returns to scale. Whereas banks receive interest on their bond holdings, the
payment of interest on reserves (IOR), Rm ≥ 1, is a policy choice. If bonds
pay interest at a higher rate than do reserves, Rb > Rm ≥ 1, then banks would
prefer to hold bonds only against their demand deposits, but they are forced to
hold at least a fraction, ρ, of their demand deposits in the form of reserves. If
IOR is paid, I assume that interest is paid at the bond rate such that banks are
13 Canzoneri et al. (2008) provide a more elaborate model of a banking sector that uses

resources and not just assets to service demand deposits, and they allow for imperfect substitution
between reserves and government bonds.

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Federal Reserve Bank of Richmond Economic Quarterly

indifferent between reserves and bond holdings, Rm = Rb .14 To summarize,
the bank demand for reserves and bonds is determined by interest rates and
reserve requirements as follows
mbt
mbt
bbt

= ρdt if Rb,t+1 > Rm,t+1 ≥ 1,
∈ [ρdt , ϕdt ] if Rb,t+1 = Rm,t+1 or Rb,t+1 = 1,
= ϕdt − mbt .

(17)
(18)
(19)

In any case, the zero profit condition for making loans and demand deposits
determines the deposit rate
Rd,t+1 = (1 − ϕ) Rl,t+1 + (ϕ − ρ) Rb,t+1 + ρRm,t+1 .

(20)

This model for banks’ reserve demand exhibits features of a “liquidity
trap.” First, at a zero bond rate the demand for reserves is indeterminate.
Note, however, that the range of indeterminacy is bounded by the required
reserve ratio and the desired liquid asset ratio. Second, once IOR is paid at
the bond rate, the demand for reserves becomes indeterminate even at positive
bond rates. Even though the banks’ demand for reserves may be indeterminate
within a range, the banks’ joint demand for reserves and bonds is always
uniquely determined.
Does the proposed “banking” technology make sense? For commercial
banks the ratio of cash (including reserves with the Federal Reserve System)
plus Treasury holdings relative to deposits has been remarkably stable from
1973 to the end of the 1980s (Figure 5). There was a sharp increase in the
early 1990s and then a downward trend that has been reversed since last fall.
At the same time, there was a steady decline of the ratio of cash relative to
total deposits. Since excess reserves were small relative to required reserves
before 2008, this must reflect a steady decline in the required reserve ratio.
Simultaneously with the introduction of IOR in the fall of 2008 and associated with various credit and liquidity programs, the amount of reserves
banks hold with the Federal Reserve System has increased dramatically. These
higher reserve holdings have not been accompanied by a corresponding decline of other liquid assets, such as treasuries or MBS, or by an increase of
demand deposits (Figure 5). In terms of the proposed simple model this would
have to be interpreted as a substantial increase in the desired ratio of liquid
assets to deposits, ϕ.
Government Supply of Assets

The government budget constraint is
bt + mt = Rb,t bt−1 + mh,t−1 + Rm,t mb,t−1 /π t − τ t ,

(21)

14 In principle the policymaker could decide to make IOR greater than the bond rate, R >
m
Rb , and reserves would dominate bonds as an asset for banks. I do not consider this case.

A. Hornstein: Interest on Reserves

169

Figure 5 Liquid Asset Shares
0.7

Assets/Deposits, Excluding Large Time Deposits

0.6

0.5

0.4

0.3

0.2

0.1

Cash
Cash and Treasuries and Agency Securities
Cash and All Securities

0.0
1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

Notes: The data are described in the Appendix.

where b = bh + bb is the total amount of government bonds issued and
m = mh + mb is the monetary base. In an equilibrium the total amount of
government debt has to equal the sum of bank and household bond holdings,
and the monetary base has to equal the sum of bank reserves and household
cash holdings.
Simplifying the Model

It is possible to simplify the exposition of the model considerably.15 First,
given the exogenous endowment of the cash and credit good, I can use the
household demand for loans, (12), and the zero profit condition for banks,
(20), to get an expression for the deposit rate:
Rd,t+1 = Rd Rt+1 , Rb,t+1 , Rm,t+1 .
15 For the detailed derivation, see Hornstein (2010).

(22)

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Federal Reserve Bank of Richmond Economic Quarterly

I can use this function in the household’s demand for deposits, (10), and obtain
the banks’ demand for reserves:
mbt

= ρD Rt+1 , Rb,t+1 , Rm,t+1 ct if Rb,t+1 > Rm,t+1 = 1,

mbt

∈ [ρ, ϕ] D Rt+1 , Rb,t+1 , Rm,t+1 ct if Rb,t+1 = Rm,t+1 or Rb,t+1 = 1.

(23)

Aggregate demand for real balances, the monetary base, is then the sum of
household demand (9) for cash and bank demand for reserves (23):
mt = M Rt+1 , Rb,t+1 , Rm,t+1 ct .

(24)

The demand for monetary base inherits a “flat” indeterminacy range from the
banks’ reserve demand if the bond rate is zero or interest is paid on reserves.
Analogously to the total demand for real balances, I can define a total
demand for government bonds by households and banks:
bt = B Rt+1 , Rb,t+1 , Rm,t+1 ct .

(25)

Corresponding to the aggregate demand for real balances, the aggregate demand for bonds also inherits a “flat” indeterminacy range from the banks’
demand for bonds. Aggregate demand for total government debt is the sum
of the demand for real balances and bonds, equations (24) and (25),
vt = V Rt+1 , Rb,t+1 , Rm,t+1 ct .

(26)

As pointed out above, banks’demand for reserves and bonds together is always
determinate and the same then applies to the demand for total government debt
(money and bonds).
The reduced form of the economy can now be represented by the following
set of equations:
= M Rt+1 , Rb,t+1 , Rm,t+1 ct ,
ct Rt+1
,
1 = β
ct+1 π t+1
Rb,t vt−1 − Rb,t − 1 mt−1
˜
− τt,
vt =
πt
˜
mt = M Rt+1 , Rb,t+1 ct ,
˜
mt

vt
vt

= V Rt+1 , Rb,t+1 , Rm,t+1 ct ,
= bt + mt .

(27)
(28)
(29)
(30)
(31)
(32)

Equation (27) is the aggregate demand for real balances. Equation (28) is
the household Euler equation for the generic asset, (13). Equation (29) is
the government budget constraint in terms of total debt outstanding v, and m
˜
denotes non-interest-bearing government debt. Without interest on reserves,
non-interest-bearing debt is aggregate real balances, m = m; and with interest
˜
on reserves, non-interest-bearing debt is cash holdings by households, m =
˜
mh . Equation (31) is the aggregate demand for government debt. Equation

A. Hornstein: Interest on Reserves

171

(32) defines total government debt as the sum of real balances and bonds. The
baseline model, (1)–(4), is obtained from Section 2 if one assumes that bonds
and demand deposits do not provide any liquidity services, γ b = γ d = 0;
eliminates the credit good, γ k = k = 0; and eliminates the banking sector.

Price Level Determinacy with Interest on Reserves
I now show that the simple baseline model from Section 2 and the just described
model with a banking sector have very similar implications for how monetary
and fiscal policy affect price level determinacy. Whether or not interest is paid
on reserves, the model with banking does not materially affect this result. In
particular, it appears that the volume of bank reserves does not matter.
The reduced form representation of the economy with a banking sector,
equations (27)–(32), appears to be slightly more complicated than the simple
baseline model, equations (1)–(4), but the structure of the two economies is
very similar. In order to close the model with banking, I again assume that
there are fixed endowments of the consumption good, cash and credit; and
specify monetary and fiscal policy as responding to inflation and government
debt, equation (5). I again study the local properties of the linearized dynamic
system defined by equations (27)–(32) and the policy rules (5). In the baseline
model, fiscal policy responds to the stock of outstanding real bonds, b, that is,
interest-bearing government debt. For reasons that will immediately become
apparent, I also consider a fiscal policy that responds to the total stock of
government debt, v. I can also do that for the simple baseline model and,
comparing Panels A1 and B1 of Figure 4, it is clear that this has no substantial
impact on the issue of equilibrium existence and uniqueness.
In order to characterize the implications of monetary and fiscal policy
for price level determinacy I need to parameterize the model with banking.
Relative to the baseline model, I need to make assumptions on households’
steady-state asset holdings (real balances, m , bonds, b, and deposits, d); banks’
required reserve ratio, ρ, and desired liquidity, ϕ; and on steady-state rates of
return on the generic asset, R, bonds, Rb , and money, π . I follow Canzoneri
et al.’s (2008) calibration of the 1990–2005 U.S. economy. The time period
is assumed to be a quarter. The household steady-state ratios of real balances,
bonds, and demand deposits to consumption are mh /c = 0.3, bh /c = 0.9, and
d/c = 2.45. Steady-state nominal interest rates on reserves, bonds, and the
generic asset are Rm = 1, Rb = 1.011, and Ra = 1.015. Steady-state inflation
is π = 1.007. The reserve ratio is ρ = 0.05 and reflects the ratio of vault
cash and bank deposits with the Federal Reserve. The desired liquidity ratio
is ϕ = 0.30 and reflects the ratio of bank holdings of treasury debt, agency
debt, agency MBS, and total reserves to total deposits.

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Federal Reserve Bank of Richmond Economic Quarterly

Fiscal Policy Targets Total Debt

Suppose first that fiscal policy targets total debt, v, and that no interest is paid
on reserves. Comparing Panels B1 and B2 of Figure 4 it is apparent that the
parameter regions that characterize equilibrium existence and uniqueness are
qualitatively similar to the baseline model. Price level determinacy is obtained
in the northeast region (active monetary policy and passive fiscal policy) and
the southwest region (passive monetary policy and active fiscal policy) of the
parameter space.
Now suppose that fiscal policy continues to target total debt, but interest
is paid on reserves. Because of interest on reserves, total demand for real
balances is indeterminate for a range that depends on the reserve ratio and the
desired liquidity ratio of banks. Even if the total supply of real balances falls
into that range, this does not create a problem for the conduct of monetary
policy.
Consider equations (28)–(31) of the reduced form together with the monetary and fiscal policy rules. These equations are sufficient to determine
an equilibrium in terms of the inflation rate, interest rates, and total debt,
π t , Rt+1 , Rb,t+1 , vt , if the equilibrium exists. The allocation of total government debt between interest-bearing reserves and interest-bearing debt is
irrelevant. In particular, the magnitude of reserves at banks does not matter,
as long as the reserves remain within the range of indeterminacy.
Comparing Panels B2 and B3 of Figure 4 shows that paying interest on
reserves has some impact on the issue of price level determinacy. If there is
price level determinacy in the northeast region of the parameter space without
IOR, then for a given active monetary policy, fiscal policy with IOR has to be
somewhat more passive in order for the equilibrium to remain unique.16 Conversely, in the southwest region of the parameter space, for a given monetary
policy, fiscal policy with IOR needs to be more active to obtain price level
determinacy.
Fiscal Policy Targets Real Bonds

Now suppose that fiscal policy targets the stock of real bonds, b, rather than
total debt, v, but no interest is paid on reserves. Comparing Panels A2 and
B2 of Figure 4 shows that for any given monetary policy, fiscal policy can be
somewhat more active before losing price level determinacy, either because
of nonexistence or nonuniqueness. But now it appears that there is a problem
if interest is paid on reserves, since the demand for government bonds—
16 Recent projections of rapidly expanding fiscal deficits might suggest that fiscal policy has
shifted toward a more active stance, that is, taxes are responding less strongly to outstanding debt.
If monetary policy were to remain active, fiscal and monetary policy could become inconsistent,
that is, an equilibrium would not exist. Thus, the payment of interest on reserves might require a
further adjustment of either monetary or fiscal policy to maintain the existence of an equilibrium.

A. Hornstein: Interest on Reserves

173

Figure 6 Monetary Policy Targets Reserves

Panel A: Fiscal Policy Targets Bonds b and IOR, δ < 0

_

10
Fiscal Policy

_

8

_

6

_

4

_

2

_

_

_

0

_

_

0

_

_

1

_

2

_

3

_

Monetary Policy

_

4

_

5

12

14

16

18

20

Panel B: Fiscal Policy Targets Bonds b and IOR, δ = 0

_

_

8

_

6

_

4

_

2

_

_

_

0

_

_

0

_

_

1

_

2

_

3

_

Monetary Policy

_

4

_

5

10

12

14

16

18

20

Fiscal Policy

Panel C: Fiscal Policy Targets Bonds b and IOR, δ > 0

_

10
Fiscal Policy

_

8

_

6

_

4

_

2

_

_

_
_

0

_

_

1

_

_

2

_

_

3

0

Monetary Policy

_

4

_

5

12

14

16

18

20

and relatedly the demand for real balances—becomes indeterminate for some
range. A well-defined demand for government bonds is, however, needed,
since fiscal policy is supposed to respond to the stock of outstanding bonds.
I can resolve the indeterminacy of the demand for bonds through the
introduction of an additional policy rule that determines their equilibrium
values. For example, the central bank might conduct open market operations
(OMO) that adjust real balances in response to the inflation rate:
mt = h (π t ) ,

(33)

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Federal Reserve Bank of Richmond Economic Quarterly

with an elasticity of δ. In other words, because the money demand equation,
(27), no longer determines real balances, monetary policy can choose real
balances.17
Figure 4, Panel A3 graphs the parameter regions for price level determinacy when monetary policy does not adjust real balances in response to the
inflation rate, δ = 0. The impact of paying interest on reserves relative to not
paying interest on reserves, Figure 4, Panel A2, is similar to the case when
fiscal policy targets total debt and not bonds only.
How much paying IOR matters now also depends on the new OMO parameter, δ. Figure 6 displays the parameter regions for price level determinacy
when fiscal policy targets real bonds and the OMO parameters are δ = 100
(Panel A), δ = 0 (Panel B), and δ = −100 (Panel C). Given that the OMO
response to real balances is essentially a response to bank reserves, one might
think that with IOR, monetary policy would have to target both inflation and
bank reserves. This interpretation has to be qualified for two reasons. First,
bank reserves matter only because I have assumed that fiscal policy targets
bonds and not total debt. Second, the graphs in Figure 6 are based on very
extreme values for the OMO policy parameter. For δ values that are of similar magnitude as the monetary and fiscal parameters, α and γ , the parameter
regions for price level determinacy are essentially the same.

4.

CONCLUSION

This article addresses the question of whether paying interest on the reserve
accounts that banks hold with a central bank affects the conduct of monetary
policy. For this purpose I introduce a stylized model of banks that hold reserves
into a standard baseline model of money. This model suggests that paying
interest on reserves does not drastically change the implications of monetary
policy, implemented as an interest rate policy, for price level determinacy.
Furthermore, the amount of outstanding reserves does not appear to be critical
for issues of price level determinacy.
The scope of the article is rather narrow. For example, I do not study
how the payment of IOR affects the dynamic response of the economy to
shocks for given monetary and fiscal policy rules. The model can be used
to address this issue if features are added that make money non-neutral, for
example, a New Keynesian Phillips curve based on sticky prices. Preliminary
results for such an augmented model suggest that for the same monetary and
fiscal policy rules the dynamic response of inflation and output to shocks does
17 We usually think of OMO as determining nominal quantities. I have chosen a policy rule
that chooses real balances to keep the exposition simple. One could interpret the proposed policy
rule as responding to inflation and to the price level. Alternatively, one could simply start with a
policy rule that sets the nominal money stock and study the more complicated system.

A. Hornstein: Interest on Reserves

175

depend on whether or not interest is paid on reserves, but the differences are
not substantial.
The effects of financial market interventions by central banks, however,
cannot be studied in this framework. Since the model’s concept of liquidity
for the financial sector is rather narrow, the model has nothing to say about
central bank provision of liquidity to banks through an increase of the banks’
reserve accounts. For example, the model does not provide any rationale for
the Federal Reserve’s program to purchase agency MBS as opposed to other
government debt. Indeed, the simple banking model assumes that agency MBS
and treasuries provide the same liquidity services to banks.18 For a critical
review of the Federal Reserve interventions in specific financial markets that
gave rise to the expansion of the Federal Reserve’s balance sheet, in particular,
the volume of reserve liabilities, see Hamilton (2009).

APPENDIX
Figure 2 displays daily data for the federal funds target set by the FOMC and
the effective federal funds rate from January 2000–February 2010. In addition,
Panel C of Figure 2 also displays the interest rate that was paid on required
reserves and on excess reserves from September 2008 on. Figure 3 displays
monthly averages from January 1980–February 2010 for the following shortterm interest rates: the effective federal funds rate, the three-month constant
maturity Treasury rate, the three-month nonfinancial commercial paper rate,
the rate for three-month certificates of deposit in the secondary market, and
the prime bank lending rate. Figure 5 displays monthly liquid asset ratios
of all commercial banks, domestically chartered and foreign related institutions, from January 1973–January 2010 based on the Federal Reserve Board’s
H.8 table. Securities in bank credit include Treasury and agency securities
and other securities. A large part of agency securities consists of MBS issued by GSEs such as the Government Mortgage Association (Ginnie Mae,
GNMA), the Federal National Mortgage Association (Fannie Mae, FNMA),
or the Federal Home Loan Mortgage Corporation (Freddie Mac, FHLMC).
Other securities include private label MBS, among others. Cash includes vault
cash and reserves with the Federal Reserve. The liquid asset ratio is calculated
relative to bank deposits excluding large time deposits. All series are from
Haver.
18 Given that the GSEs Fannie Mae and Freddie Mac have become wards of the federal
government, this does not appear to be such an unreasonable assumption. Indeed, the only reason
to distinguish between Treasury debt on the one hand and agency-issued debt and MBS on the
other hand appears to be political: GSE-issued debt does not count toward the congressionally
mandated federal debt limit.

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Federal Reserve Bank of Richmond Economic Quarterly

REFERENCES
Bech, Morten L., and Elizabeth Klee. 2010. “The Art of a Graceful Exit:
Interest on Reserves and Segmentation in the Federal Funds Market.”
Finance and Economics Discussion Series 2010-07. Washington, D.C.:
Divisions of Research & Statistics and Monetary Affairs, Federal
Reserve Board.
Bernanke, Ben. 2009. “The Fed’s Exit Strategy.” Wall Street Journal, July 21.
Canzoneri, Matthew B., Robert Cumby, Behzad Diba, and David
L´ pez-Salido. 2008. “Monetary Aggregates and Liquidity in a
o
Neo-Wicksellian Framework.” Journal of Money, Credit and Banking 40
(December): 1,667–98.
Ennis, Huberto M., and John A. Weinberg. 2007. “Interest on Reserves and
Daylight Credit.” Federal Reserve Bank of Richmond Economic
Quarterly 93 (Spring): 111–42.
Ennis, Huberto M., and Todd Keister. 2008. “Understanding Monetary
Policy Implementation.” Federal Reserve Bank of Richmond Economic
Quarterly 94 (Summer): 235–63.
Goodfriend, Marvin. 2002. “Interest on Reserves and Monetary Policy.”
Federal Reserve Bank of New York Economic Policy Review 8 (May):
77–84.
Goodfriend, Marvin, and Bennett T. McCallum. 2007. “Banking and Interest
Rates in Monetary Policy Analysis: A Quantitative Exploration.”
Journal of Monetary Economics 54 (July): 1,480–507.
Hamilton, James D. 2009. “Concerns about the Fed’s New Balance Sheet.”
http://dss.ucsd.edu/˜jhamilto/fed concerns.pdf (April 18).
Hornstein, Andreas. 2010. “Technical Appendix for ‘Monetary Policy with
Interest on Reserves.”’ Mimeo, Federal Reserve Bank of Richmond.
Keister, Todd, Antoine Martin, and James McAndrews. 2008. “Divorcing
Money from Monetary Policy.” Federal Reserve Bank of New York
Economic Policy Review 14 (September): 41–56.
Lacker, Jeffrey. 2006. “Central Bank Credit in the Theory of Money and
Payments.” Speech presented at The Economics of Payments II
Conference, New York. http://www.richmondfed.org/press room/
speeches/president jeff lacker/2006/lacker speech 20060329.cfm
(March 29).
Leeper, Eric M. 1991. “Equilibria Under ‘Active’ and ‘Passive’ Monetary and
Fiscal Policies.” Journal of Monetary Economics 27 (February): 129–47.

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Sargent, Thomas, and Neil Wallace. 1981. “Some Unpleasant Monetarist
Arithmetic.” Federal Reserve Bank of Minneapolis Quarterly Review 5
(Fall): 1–17.
Sargent, Thomas, and Neil Wallace. 1985. “Interest on Reserves.” Journal of
Monetary Economics 15 (May): 279–90.
Sims, Christopher. 1994. “A Simple Model for Study of the Determination of
the Price Level and the Interaction of Monetary and Fiscal Policy.”
Economic Theory 4 (3): 381–99.
Sims, Christopher. 2000. “Solving Linear Rational Expectations Models.”
http://sims.princeton.edu/yftp/gensys/.
Sims, Christopher. 2009. “Fiscal/Monetary Coordination when the Anchor
Cable has Snapped.” Presentation at the Princeton Conference on
Monetary and Fiscal Policy, Princeton University, May 22.
Smith, Bruce D. 1991. “Interest on Reserves and Sunspot Equilibria:
Friedman’s Proposal Reconsidered.” Review of Economic Studies 58
(January): 93–105.
Woodford, Michael. 2000. “Monetary Policy in a World without Money.”
International Finance 3 (July): 229–60.

Economic Quarterly—Volume 96, Number 2—Second Quarter 2010—Pages 179–199

Are Wages Rigid Over the
Business Cycle?
Marianna Kudlyak

T

he search and matching model of the labor market has become a leading
model of unemployment in macroeconomics. Recent work (Shimer
2005) shows that under common parameter values the standard search
and matching model cannot account for the cyclical volatilities of vacancies
and unemployment observed in the data.1 This difficulty is related to the
flexibility or, alternatively, rigidity of real wages over the business cycle.2 In
this article, I review empirical evidence on wage flexibility as it relates to
search and matching models.
The search and matching model introduces frictions into the labor market
in the sense that workers and employers cannot costlessly contact each other.
In an economy with frictions, market prices are not competitively determined,
and the standard search and matching framework assumes that wages are determined by a particular solution to a bargaining problem between workers
and employers, the Nash bargaining solution. Under this bargaining, wages
increase when productivity is high, thus limiting incentives for job creation.
Hall (2005) and Shimer (2005) show that replacing the Nash bargaining solution with an alternative wage determination procedure that makes wages more
rigid amplifies the volatility of unemployment and vacancies the model can
generate.
I am grateful to Andreas Hornstein, Arantxa Jarque, Damba Lkhagvasuren, Aysegul Sahin,
Pierre-Daniel Sarte, Roman Sysuyev, and Antonella Trigari for their generous comments and
discussions. All views and errors are mine alone. I thank Nadezhda Malysheva and Devin
Reilly for help in editing the earlier draft. The views expressed here are those of the author
and do not necessarily reflect those of the Federal Reserve Bank of Richmond or the Federal
Reserve System. E-mail: marianna.kudlyak@rich.frb.org.
1 The “standard search and matching model” refers to the model studied by Shimer (2005)

and developed in Mortensen and Pissarides (1994). Pissarides (2000) provides a textbook exposition
of the standard search and matching model.
2 The terms “rigid” and “acyclical” are used interchangeably and imply a lack of response
to a cyclical indicator.

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Federal Reserve Bank of Richmond Economic Quarterly

This line of research motivates important questions: How flexible, or rigid,
are real wages over the business cycle? Is observed wage rigidity consistent
with the wage rigidity needed to amplify the fluctuations in the textbook search
and matching model?
In the job creation decision, a firm takes into account not only the initial
wage in a newly formed match but also the entire expected stream of future
wages to be paid in the match. Thus, job creation in frictional labor markets
places the focus on the cyclical behavior of the expected present discounted
value of wages. The volatility of unemployment in the model depends on the
intensity of job creation through changes in the job finding rate. As Shimer
(2004) emphasizes, what is relevant for the volatility of job creation, and, thus,
of unemployment, is the rigidity of the present discounted value of wages that,
at the time of hiring, a firm expects to pay to a worker over the course of the
employment relationship.
A large empirical literature exists that studies the behavior of individual
wages over the business cycle. The literature finds that the wages of newly
hired workers are more cyclical than wages of workers in ongoing employment
relationships (for example, Bils [1985] and Carneiro, Guimar˜ es, and Portugal
a
[2009]).
One crucial aspect of the existing empirical literature is that it provides
evidence on the cyclical behavior of the current wage, but not on the cyclical
behavior of the expected present discounted value of future wages within a
match formed in the current period. Emphasizing the importance of the future
wages to be paid in the long-term employment relationships, Kudlyak (2007)
estimates the cyclicality of the user cost of labor, which is the difference
between the expected present discounted value of wages paid to a worker
hired in the current period and the value paid to a worker hired the following
period. Kudlyak constructs the user cost of labor from the individual wage
and turnover data. She finds that the user cost of labor is more cyclical than
wages of newly hired workers. Haefke, Sonntag, and van Rens (2009) argue
for the importance of the elasticity of the expected present discounted value
of wages with respect to the expected present discounted value of productivity
in newly formed matches, which they refer to as permanent values of wages
and productivity, respectively. They do not estimate the elasticity directly but,
using model simulations, conclude that the elasticity of the current period wage
of newly hired workers with respect to current period productivity “constitutes
a good proxy for the elasticity of the permanent wage with respect to permanent
productivity for the case of instantaneously rebargained wages” and “can be
seen as a lower bound for [the elasticity of the permanent wage with respect
to permanent productivity] in the case of wage rigidity on the job.”
Pissarides (2009), Haefke, Sonntag, and van Rens (2009), and Kudlyak
(2009) study whether the search and matching model can simultaneously
match the empirical wage and unemployment statistics. Pissarides (2009)

M. Kudlyak: Are Wages Rigid Over the Business Cycle?

181

and Haefke, Sonntag, and van Rens (2009) compare the elasticity of wages
in the model to the elasticity of wages of newly hired workers in the data.
They conclude that making wages in the model rigid enough to generate the
observed volatility of unemployment requires more rigid wages than are found
in the data. Kudlyak (2009) shows that the free entry condition in the model
ties together match productivity and the user cost of labor. She calibrates the
model to match the estimated cyclicality of the user cost of labor and concludes that the model calibrated to wage data cannot generate the empirical
volatilities of the vacancy-unemployment ratio.
In summary, in the model, the rigid expected present discounted value
of wages in newly formed matches amplifies the response of firm’s surplus
to productivity shocks. This increases the volatility of job creation and thus
of unemployment. The success of the model in generating the empirical
volatilities of vacancies and unemployment depends on whether the required
rigidity of the relevant measure of wages is consistent with the data. The
studies reviewed suggest that wages in the data may not be as rigid as required
for generating empirical volatilities of vacancies and unemployment in the
standard search and matching model.
The remainder of the paper is structured as follows. Section 1 summarizes
the textbook search and matching model and the unemployment volatility puzzle. Using an example, I demonstrate the importance of the expected present
discount value of wages for the job creation decision. Section 2 surveys empirical evidence on the cyclicality of individual wages of the newly hired workers
and wages of workers in ongoing relationships. Then I review empirical evidence on the cyclicality of a measure of wages that takes into account the
expected present discounted value of future wages. Section 3 concludes.

1.

SEARCH AND MATCHING MODEL

The Standard Model
An economy is populated by a continuum of firms and a continuum of measure
1 workers. Both firms and workers are risk neutral and infinitely lived. Firms
maximize the present discounted value of profits. Workers maximize the
present discounted value of wages and do not value leisure. Firms and workers
discount the future with a common discount factor β, 0 < β < 1. Time is
discrete.
A firm can choose to remain inactive or to start production, which requires
only labor input. To start production, a firm must enter the labor market and
hire a worker. Upon entering the labor market, a firm opens a vacancy and
searches for a worker. During each period a firm must pay a per vacancy cost,
c. An unemployed worker receives a per period unemployment compensation,
b, and costlessly searches for a job. Employed workers earn wages and cannot
search. When a firm with an open vacancy and an unemployed worker meet,

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Federal Reserve Bank of Richmond Economic Quarterly

they form a match that immediately becomes productive. While matched,
all firm-worker pairs have the same constant return to scale production technology, which uses a unit of labor indivisibly supplied by the worker. Each
firm-worker match produces per period output z, thus z is also aggregate productivity. z evolves stochastically according to the first-order Markov process.
Every period, a firm-worker pair separates exogenously with probability δ.
Given the number of unemployed workers, u, and the number of vacancies,
v, the number of newly created matches in the economy is determined by a
matching function, m(u, v). It is assumed that m(u, v) = Kuα v 1−α , where
0 < α < 1 (Petrongolo and Pissarides 2001) and K is a positive constant. Let
v
θ denote labor market tightness, i.e., θ ≡ u . Let q(u, v) ≡ m(u,v) = Kθ −α
v
denote the probability of filling a vacancy for a firm. Let μ(u, v) ≡ m(u,v) =
u
Kθ 1−α denote the probability of finding a job for an unemployed worker.
Thus, the unemployment in this economy evolves according to the following
equation, given u0 :
ut+1 = ut + (1 − ut ) δ − μ (ut , vt ) ut .
Dropping the time subscripts and using to denote the next period values,
I summarize the value functions of a worker and of a firm as follows. The
value function of a firm with a worker is
J (z) = z − w (z) + β (1 − δ) Ez J z ,

(1)

where z´ denotes productivity in the next period and Ez is a conditional expectations operator. Equation (1) takes into account that in each period with
probability δ, the firm-worker match separates and the firm obtains a value of
an inactive firm, which is 0. The value function of an opened vacancy is
V (z) = −c + q (θ (z)) J (z) + (1 − q (θ (z))) βEz V z .

(2)

The value function of an employed worker is
W (z) = w (z) + β (1 − δ) Ez W z + βδEz U z .

(3)

The value function of an unemployed worker is
U (z) = b + βEz μ(θ (z ))W (z ) + (1 − μ(θ (z )))U (z ) .

(4)

There are two important conditions in the standard model. First, there is
free entry for firms, i.e., firms enter the labor market and post vacancies until
the value of an open vacancy, V (z), equals the value of an inactive firm, 0.
From (2) free entry implies the following condition:

M. Kudlyak: Are Wages Rigid Over the Business Cycle?

183

c
= J (z) .
(5)
q (θ (z))
Second, wages are rebargained every period in new and ongoing matches
according to the Nash bargaining rule. The Nash bargaining rule yields the
following division of the surplus from the match, S(z) ≡ J (z) + W (z) −
V (z) − U (z), in every period:
J (z) = (1 − η)S(z),
W (z) − U (z) = ηS(z),

(6)
(7)

where η is a worker’s bargaining power, 0 < η < 1. Equations (6)–(7) imply
that each party obtains a constant share of the surplus from the match.
Using equations (1)–(5) yields the following equation for the surplus:
S(z) = z − b + βEz ((1 − δ) − Kθ (z )1−α η)S(z ).

(8)

Combining (5) and (6) yields the job creation condition
c
= (1 − η) S (z) .
(9)
Kθ (z)−α
Combining (8) with the job creation condition yields the following equation for the evolution of the vacancy-unemployment ratio:
c
c
= (z − b)(1 − η) + βEz ((1 − δ) − Kθ (z )1−α η)
. (10)
−α
Kθ (z)
Kθ (z )−α
Equation (8) links the evolution of the vacancy-unemployment ratio, θ ,
to the productivity shock, z. Using this equation and common parameter
values, Shimer (2005) shows that the standard search and matching model
cannot generate the volatilities of vacancies and unemployment observed in
the data. In particular, in the U.S. data, the standard deviation of the vacancyunemployment ratio is 20 times larger than the standard deviation of labor
productivity. The standard search and matching model predicts the volatility
of the vacancy-unemployment ratio as almost one-to-one to the volatility of
the productivity. Since productivity shocks are the driving force in the model,
the model is said to lack an internal propagation mechanism.3 This failure
of the standard search and matching model to generate empirical volatilities
of vacancies and unemployment is often referred to as the unemployment
volatility puzzle (Pissarides 2009).
3 See Hornstein, Krusell, and Violante (2005) for a detailed inspection of the mechanism.
See also Costain and Reiter (2008).

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Federal Reserve Bank of Richmond Economic Quarterly

Rigid Wages Within Matches
To understand what measure of wages affects allocations in the search and
matching model, consider the following modification of the standard model.
In the standard search and matching model, wages in both newly formed and
ongoing matches are set in each period using the Nash bargaining rule. In
the modified model, wages in newly formed matches are set using the Nash
bargaining rule but wages in ongoing matches remain constant and equal to
the wage at the time of hiring. We will see that the modified model delivers the
same equation for the vacancy-unemployment ratio, thus the same allocations,
given the initial conditions, as the standard model despite the fact that in the
modified model wages in ongoing matches are rigid. The modified model is
a discrete time version of the argument presented in Shimer (2004).4
In the standard model, given that all matches are equally productive, wages
of new hires and existing workers are equal in each period. This implies that
when the aggregate productivity is zt , the value of a firm with a worker in an
ongoing match that started in period t0 , J t0 (zt ), equals the value of a firm in
the newly formed match, J t (zt ). Similarly, when the aggregate productivity
is zt , the value of an employed worker in an ongoing match that started in
period t0 , W t0 (zt ), equals the value of a newly hired worker in t, W t (zt ). In
the modified model, these values are not necessarily equal. Dropping the time
subscripts, using z0 to denote the aggregate productivity at the time a match
is formed and using to denote the next period values, we can summarize the
value functions in the modified model as follows:
J z0 (z) = z − w (z0 ) + β (1 − δ) Ez J z0 z ;
V (z) = −c + Kθ (z)−α J z (z) + 1 − Kθ (z)−α βEz V z ;
W z0 (z) = w (z0 ) + β (1 − δ) Ez W z0 z + βδEz U z ;
U (z) = b + βEz Kθ z

1−α

W z´ z + 1 − Kθ z

1−α

U z

.

In the modified model the free entry condition, (5), and the surplus division
rule, (6)–(7), are required to hold only for the values at the time of hiring,
which can be denoted as J z (z) for a firm and W z (z) for a worker. Thus, in the
modified model, equations corresponding to equations (6), (7), and (9) are as
follows:
J z (z) = (1 − η)S z (z),

(11)

4 See also Haefke, Sonntag, and van Rens (2009) and Pissarides (2009) for insightful dis-

cussions of this example and Rudanko (2009) for a model with endogeneous wage rigidity within
ongoing matches.

M. Kudlyak: Are Wages Rigid Over the Business Cycle?
W z (z) − U (z) = ηS z (z),

185
(12)

c
(13)
= (1 − η)S z (z),
q(θ (z))
where S z (z) is the surplus from a newly formed match when the aggregate
productivity is z, S z (z) ≡ J z (z) + W z (z) − V (z) − U (z).
To demonstrate that this modified model delivers exactly the same allocations as the standard model (in which wages are rebargained in all matches
every period), it suffices to show that it delivers the same equation for the
vacancy-unemployment ratio as the standard model, (10). Using equations
for J z0 (z),W z0 (z), and U (z), one can derive the following equation for the
total surplus of the newly formed match:
S z (z) = z − b + β(1 − δ)Ez S z (z ) + βηEz μ(θ (z ))S z (z ),
where z´is productivity in the next period.
Note, however, that J z (z ) = J z (z ) +
1
1−β(1−δ)

1
1−β(1−δ)

(14)

(w(z ) − w(z)), where

w(z) is a present discounted value of wages paid to a worker

hired when the aggregate productivity is z. Similarly, W z (z ) = W z (z ) −
1
(w(z ) − w(z)). Then S z (z ) = J z (z ) + W z (z ) − U (z ) =
1−β(1−δ)
J z (z ) + W z (z ) − U (z ) = S z (z ). Substituting S z (z ) for S z (z ) in (14)
yields
S z (z) = z − b + βEz ((1 − δ) − μ(θ (z ))η)S z (z ),

(15)

where S z (z) is the surplus from a newly created match when the aggregate
productivity is z and S z z is the surplus from a newly created match when
the aggregate productivity is z .
Substituting S z (z) from the job creation condition (13) into (15) yields
exactly the same equation for the vacancy-unemployment ratio, θ, as in the
standard model, equation (10):
c
c
= (z − b)(1 − η) + βEz ((1 − δ) − μ(θ (z ))η)
.
q(θ(z))
q(θ (z ))
The two models considered above have important similarities. Both models deliver the same total surplus at the time of hiring, and it is split between a
worker and a firm by the same rule. However, they differ in how the wages are
determined within ongoing employment relationships. In the standard model,
wages are renegotiated for every match in every period. Because all matches
are equally productive, this implies that newly hired workers and workers in
existing employment relationships receive the same wages. In the modified
model, wages of newly hired workers are determined based on the aggregate

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Federal Reserve Bank of Richmond Economic Quarterly

productivity at the time of hiring. Once set, the wage remains rigid throughout the duration of the match. The modified model generates wages of newly
hired workers that are more responsive to the aggregate conditions than wages
of the workers in ongoing relationships. However, in the modified model, the
rigidity of wages within employment relationships does not affect allocations.
Thus, this example shows that the rigidity of wages in ongoing matches is not
sufficient to amplify the volatility of the vacancy-unemployment ratio.
To understand what kind of wage rigidity has an effect on allocations in
the model, rewrite the job creation (13) using (1 − η)S z (z) = J z (z) and using
the expression for J z (z) in the sequential form. This yields:

c
= Et
q(θ(zt ))

∞
τ =t

(β(1 − δ))τ −t zτ − Et

∞

(β(1 − δ))τ −t wt,τ (zt ), (16)

τ =t

where wt,τ is a period τ wage of a worker hired in period t. Equation (16)
shows the relationship between the labor market tightness, θ (zt ), and the
expected present discounted value of wages, Et ∞ (β (1 − δ))τ −t wt,τ (zt ),
τ =t
given productivity zt . Note that Et ∞ (β (1 − δ))τ −t zτ is a function of zt
τ =t
alone. Both θ (zt ) and Et ∞ (β (1 − δ))τ −t wt,τ (zt ) change in response to
τ =t
changes in zt . The extent of the response of θ (zt ) to zt depends on the extent of
the response of the expected present discounted value of wages to be paid in a
new employment relationship that starts at t. However, it does not depend on
the change of wages within the employment relationship if this change does
not affect the expected present discounted value of wages to be paid in a new
match.

2.

EMPIRICAL EVIDENCE ON CYCLICAL
BEHAVIOR OF WAGES

This section reviews the empirical evidence on wage cyclicality. First, I present
the empirical evidence on the behavior of individual wages over the business
cycle, distinguishing wages of new hires from wages of workers in ongoing
employment relationships (often referred to as job stayers). Second, I present
the empirical evidence on the history dependence of wages. Then, I present
the evidence on the cyclical behavior of a measure of wages that takes into
account both the initial wage and the expected value of future wages paid in the
newly formed matches. Finally, I summarize the quantitative implications of
the evidence for the volatility of vacancies and unemployment in the standard
search and matching model.

M. Kudlyak: Are Wages Rigid Over the Business Cycle?

187

Cyclicality of Wages of New Hires and Wages of
Existing Workers
Below I provide a statistical model of individual wages with a particular emphasis on how wages depend on the unemployment rate. Then I survey results
from the empirical studies that include information on individual workers and
from the studies that include information on workers and their employers.5
The findings show that wages of newly hired workers are more procyclical
than wages of job stayers. All of these studies refer to current wages and not
to the expected present discounted value of future wages.
General Framework

In labor economics the standard statistical model for wages is Mincer regression, which attributes variation in the logarithm of wages to the observable
characteristics of a worker—years of schooling, a quadratic polynomial in
labor market experience, and other factors (Mincer 1974). These variables are
supposed to reflect productivity (or human capital) differences. The literature
that studies the behavior of individual wages over the business cycle includes
the contemporaneous unemployment rate as a business cycle indicator. What
is of interest for the questions in this article are the differences, if any, of the
responses of wages of workers in ongoing matches (job stayers) and wages of
new hires to changes in the unemployment rate.
The individual wage equation that distinguishes between the cyclical response of wages of job stayers and wages of new hires is specified as follows:
nh
nh
ln wit = Xi α + Xit γ + βUt + β nh Ut ∗ Iit + δIit + ηi + vit ,

(17)

where wit is a real wage of worker i in t, Xi is a vector of observable individualspecific explanatory variables that remain fixed over time, Xit is a vector of
individual controls that vary with time, Ut is a measure of the unemployment
nh
rate, and ηi and vit are the unobservable error terms. Iit is a dummy variable
that takes value 1 if an individual is a new hire, and 0 otherwise. The new hire
is defined as a worker who has been employed at a firm for less than a specified
period, usually one year. Error terms are assumed independent of each other
and of all explanatory variables in X. The variables commonly included in Xit
are a quadratic in worker labor market experience and a quadratic in tenure
(for job stayers). Because of the structure of the survey data, the time period
is typically one year.
5 Given a large literature, this survey does not aim to summarize all works on the real wage

cyclicality. An interested reader is referred to the surveys in Abraham and Haltiwanger (1995) and
Brandolini (1995).

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Federal Reserve Bank of Richmond Economic Quarterly

The coefficient on the unemployment rate is interpreted as a semi-elasticity,
which indicates a percent change in wage in response to a one percentage point
increase in the unemployment rate. If the semi-elasticity is positive, the wage
is called procyclical, i.e., it moves positively with the business cycle. For job
stayers the cyclicality is measured by β. If the cyclicality of wages of new
hires differs from the cyclicality of job stayers, then the coefficient on the
interaction term, β nh , is statistically significantly different from zero and the
cyclicality of new hires is measured by β + β nh .
Evidence from Worker Survey Data

Most of the existing evidence on the cyclicality of individual wages comes
from studies that use individual level survey data: the National Longitudinal
Survey (NLS), the Panel Study of Income Dynamics (PSID), and the National
Longitudinal Study of Youth (NLSY). These data allow tracking individual
workers’ histories across time and contain information on individual workers’
characteristics, including education, age, sex, and job characteristics such as
industry and occupation.6
Bils (1985) is the first study that examines the cyclicality of individual
wages while separating the wages of job stayers from the wages of new hires.
He also distinguishes between new hires who are hired from another job and
new hires who are hired from unemployment. Using the individual data on
men from NLS for the period 1966–1980, Bils finds that as the unemployment
rate increases by one percentage point, individual wages of white male workers on average decrease by 1.59 percent. Once the job changers are explicitly
accounted for, the results show that wages of job changers are much more
procyclical than wages of job stayers. In particular, wages of job stayers decrease by 0.64 percent while wages of job changers decrease by 3.69 percent
in response to one percentage point increase in the unemployment rate. Similarly, wages of workers who move in and out of employment are also more
procyclical than wages of workers who do not change jobs.
Shin (1994), using a different estimation procedure for the NLS data on
men’s wages from 1966–1981, estimates separate equations for workers who
remain with the same employer from t − 1 to t and for workers who change
their employer. Similarly to Bils, Shin finds substantially procyclical wages
for workers who change employers and much less procyclical wages for job
stayers. Solon, Barsky, and Parker (1994) estimate wage cyclicality using data
from the PSID for the period 1967–1987. They find that the point estimate
of the cyclicality of men’s real wages is between −1.35 percent and −1.40
percent. In the sample restricted to workers who did not change employers,
6 The type of data set, which contains information on the cross section of individuals over
time, is called panel data.

M. Kudlyak: Are Wages Rigid Over the Business Cycle?

189

the coefficient reduces to −1.24 percent. Consistent with Bils (1985), Solon,
Barsky, and Parker find that wages of job stayers are less procyclical than
wages of all workers.
The usual measure of wages used in the studies is the average hourly
wage, which is constructed by dividing total annual earnings by total annual
hours worked. However, if workers are more likely to hold more than one
job in expansions, then the constructed average hourly wage may be more
procyclical than actual wages within employment relationships. Devereux
(2001) conducts a detailed examination of the cyclicality of wages of job
stayers and, in contrast to the earlier studies, focuses on the wages of workers
who have only one job at a time. Using PSID data from 1970–1992 on men’s
earnings, Devereux finds that the cyclicality of the average wage of these
workers is −0.54 percent. These findings confirm that wages of job stayers
are less procyclical than wages of job changers.7
Evidence from Matched Firm-Worker Data

Controlling for a firm fixed effect is important if there are changes in the composition of firms over the business cycle with respect to the level of wages
they offer. For example, if the firms that hire in economic booms are predominantly high-wage firms and the firms that hire in economic busts are low-wage
firms, then the failure to control for the firm’s fixed effect may lead to biasing
the estimates of the cyclicality away from zero even when wages are acyclical. Researchers often use occupation and industry fixed effects to control for
changes in the composition of jobs over the business cycle, which is readily
available from worker survey data. Most of the studies employ individual
worker survey data that do not allow identification of the firm’s fixed effect.
To allow identification of a firm fixed effect, the data must contain information
on more than one worker from the same firm and on firm identifiers. Only
recently have longitudinal firm-worker data for the U.S. economy become
available; however, to my knowledge, there are no studies of wage cyclicality
using these data yet.
Carneiro, Guimar˜ es, and Portugal (2009) use administrative firm-worker
a
data from Portugal. They estimate a model in levels similar to (17), controlling
for an individual worker’s qualification, education, age, and a quadratic in
time trend. Their findings are very similar to the findings by Bils (1985). In
particular, controlling for a worker and a firm fixed effects, they find that the
cyclicality of wages of workers who have been with their employer for less
than a year is −2.77 percent. The cyclicality of wages of workers who have
been with an employer for more than a year, job stayers, is −1.41 percent.
Importantly, accounting for both firm and worker fixed effects delivers results
7 Shin and Solon (2007) find similar evidence in the NLSY data.

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very similar to the results from accounting only for worker fixed effect. In
particular, the cyclicality of wages of new hires from the regression with only
a worker fixed effect is −2.73 percent, while with only a firm fixed effect it is
−3.53 percent. The cyclicality of wages of job stayers from the regressions
with only a worker fixed effect is −1.50 percent, while from the regression
with only a firm fixed effect it is −2.94 percent. Using the same data set,
Martins, Solon, and Thomas (2010) investigate the cyclicality of wages of
newly hired workers in a subset of occupations into which firms frequently
hire new workers. The estimated cyclicality of the wages of newly hired
workers in these entry jobs is −1.8 percent. The authors conclude that the
wages of new hires in the entry jobs are substantially procyclical.8
The results from the studies that allow controlling for firm fixed effects
confirm the earlier findings that wages of newly hired workers are more cyclical
than wages of existing workers.
Cyclicality of Wages of Job Stayers and Job Changers and
Match Quality

Gertler and Trigari (2009) suggest that the difference in the cyclicality of
wages of new hires and existing workers can be explained by the differences
in the quality (or, alternatively, productivity) of newly formed and ongoing
matches. In particular, Gertler and Trigari argue that separately controlling
for firm and worker fixed effects cannot account for match quality, which must
be controlled for by the interaction term—a worker-job fixed effect. Gertler
and Trigari use individual male worker data from the Survey of Income and
Program Participation over the period 1990–1996. The data consists of four
panels from 1990, 1991, 1992, and 1993, each lasting approximately three
years and containing information from interviews conducted every four
months. The data allow for identifying if a worker changes employer. Gertler
and Trigari estimate a wage equation similar to equation (17) except that, instead of controlling for a worker fixed effect, ηi , they control for the unobserved
firm-worker effect, which simultaneously captures two effects: a worker fixed
effect that does not change from job to job and a joint worker-firm effect. After the authors control for a worker-firm fixed effect, the coefficient on the
interaction term between the unemployment rate and the dummy for new hire
becomes small and statistically insignificant. Gertler and Trigari interpret the
results as evidence of an omitted variable, a worker-firm specific fixed effect.
If a job change is systematically associated with the movement from low to
high quality match, then the omitted variable is negatively correlated with the
interaction term, biasing the estimates. They conclude that a large part of the
8 Martins, Solon, and Thomas (2010) conclude that the cyclicality is of the similar magnitude
as the cyclical elasticity of employment.

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191

higher procyclicality of wages of new hires is probably due to the comparatively higher quality of these matches. Gertler and Trigari suggest that the
existing literature does not provide conclusive evidence that the newly hired
workers have more cyclical wages than the existing workers in the same firm.
This finding raises questions, which I discuss at the end of this section,
about what heterogeneity in the data should be controlled for when calculating
the statistics and how to bring the model to match these statistics.

Dependence of Wages on the Past Labor
Market Conditions
Literature surveyed so far finds evidence that the wages of new hires are more
sensitive to the aggregate labor market conditions than the wages of workers
in ongoing employment relationships. A closer look at workers in ongoing
employment relationships shows that their wages depend not only on current
labor market conditions, but also on the history of labor market conditions
during the entire employment relationship.
Beaudry and DiNardo Regressions

Beaudry and DiNardo (1991) estimate the following equation for individual
wages:
ln wj t0 t = Xj t0 t α + γ start Ut0 + γ c Ut + γ min min {Uτ }tτ =t0 + ηj + ν j t , (18)
where wj t0 t is an hourly wage of a worker j in year t who was hired in year
t0 , Xj t0 t is a vector of the individual- and job-specific characteristics, Uτ is
the unemployment rate in year τ , ηj is an individual-specific fixed effect,
and ν j t is an individual- and time-varying error term. ν j t is assumed to be
serially uncorrelated as well as uncorrelated across individuals. The vector
of individual- and job-specific characteristics, Xj t0 t , includes a quadratic in
experience, a quadratic in tenure, years of schooling, and dummies for industry, region, race, union status, marriage, and standard metropolitan statistical
area. The equation is estimated using the individual data on men’s wages
from PSID, 1976–1984, and two cross-sectional samples from the Current
Population Survey (CPS).
The main finding of Beaudry and DiNardo (1991) is that when all three
measures of the unemployment rate are included, the effect of the minimum
unemployment rate is the most significant, both statistically and economically.
Thus, whenever the labor market conditions improve, wages increase. In particular, controlling for worker fixed effect in the PSID sample, the coefficient
on the minimum unemployment rate is −2.9 percent, the coefficient on the
unemployment rate at the start of the job is −0.6 percent and insignificant, and
the coefficient on the contemporaneous unemployment rate is −0.7 percent.

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Federal Reserve Bank of Richmond Economic Quarterly

If, however, only the contemporaneous unemployment rate is included, then
the results are consistent with earlier studies—the coefficient on the contemporaneous unemployment rate is −1.4 percent.
Subsequent studies replicate the findings of Beaudry and DiNardo (1991)
for different time periods and using different data sets. McDonald and
Worswick (1999) find support in Canadian data. Grant (2003) estimates an
equation similar to (18) and adds the maximum unemployment rate experienced by a worker from the start of the job. Grant finds that both the minimum
unemployment rate and the contemporaneous unemployment rate have an effect on wages. In particular, in the sample of young men from NLS from
1966–1983, when all three unemployment rates are included, the coefficient
on the minimum unemployment rate is −2.29 percent while the coefficient
on the contemporaneous unemployment rate is −2.37 percent. This finding
leads Grant to conclude that wages depend both on the past and on the contemporaneous labor market conditions.
Devereux and Hart (2007) study the history dependence in wages in British
data, the New Earnings Survey Panel, for the period 1976–2001. They estimate
a model similar to (18) that also includes the maximum unemployment rate
but employ a different estimation procedure from the studies above. They find
that both the minimum unemployment rate and the contemporaneous unemployment rate are statistically significant and negative. The authors conclude
that the British real wage data exhibit both the history dependence as described
in Beaudry and DiNardo (1991) and the dependence on the contemporaneous
labor market conditions.
Hagedorn and Manovskii (2009) find that the dependence on the past unemployment rates in model (18) disappears if one controls for the quality of a
match. They argue that the quality of a match can be learned from the number
of job offers a worker receives throughout the total duration of the job, which
can be approximated by the sum of the aggregate vacancy-unemployment ratios experienced by a worker throughout the job. In addition, if a worker
switches job-to-job, then the sum of labor market tightnesses experienced
during a previous job also helps predict the quality of the current match. Using the NLSY, the authors find that if these controls are included in Beaudry
and DiNardo’s (1991) equation, (18), the coefficients on the past unemployment rates are insignificant both economically and statistically, while the new
controls have a large positive effect.

Evidence from Matched Firm-Worker Data

Baker, Gibbs, and Holmstrom (1994) provide compelling evidence on the
history dependence of wages in the study of the wage policy of a large firm
over the period 1969–1988. The authors find that there is a substantial cohort
effect in wages, where the cohort is defined as the employees who enter the

M. Kudlyak: Are Wages Rigid Over the Business Cycle?

193

sample in a given year.9 That is, much of the variation in wages between
cohorts comes from the differences in starting wages, which implies that wages
depend on the history of the labor market conditions from the start of the job.
The authors investigate whether the differences in the starting wage can be
driven by observable or unobservable worker characteristics. To check for the
possible impact of unobservable characteristics, they examine whether cohorts
that entered with lower starting wages are promoted less and exit more. They
find no evidence of this and no evidence that composition effect can fully
account for either the differences in starting wages or the persistent effect of
external labor market conditions from the start of the job on wages.
Using a large matched employer-employee data set from Northern Italy,
Macis (2006) provides a detailed empirical investigation of the dependence of
wages on the unemployment rates from the start of the job, controlling for both
firm and worker fixed effects. Using a model similar to (18), Macis finds that
wages are correlated with both the best and the worst labor market conditions
from the start of the job, as well as with the contemporaneous unemployment
rate.

Cyclicality of a Measure of Wages that Takes into
Account Future Wages
The studies reviewed above estimate the cyclicality of the current wage. These
studies find that wages of newly hired workers are more procyclical than wages
of workers in ongoing employment relationships, and wages depend on the
history of labor market conditions from the start of the job. As discussed
earlier, what is relevant for job creation is the expected present discounted
value of wages paid in a newly formed match. Nevertheless, from the evidence
presented so far we can form some intuition about the cyclical behavior of the
measure of wages that takes into account both the initial wage and the expected
value of future wages.
Consider a firm that decides whether to hire a worker in the current period
or to hire in the following period. In addition, suppose that in the current
period unemployment is high but is expected to return back to its lower level
in the following period. Since wages of newly hired workers are procyclical,
the hiring wage in the employment relationship that starts in the current period
is low. Because of the history dependence of wages, the future wages in this
relationship are also expected to be lower than the wages in the matches formed
in the future periods. Thus, by hiring now a firm locks in a worker to a stream
9 In the study, the authors cannot identify whether the entrants are the new hires at the firm
or are internally promoted. They argue that it is plausible that both categories of workers are
treated in the same way by the firm. Their comparison of wage patterns of these workers with
industry wages supports this view.

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Federal Reserve Bank of Richmond Economic Quarterly

of wages that is lower as compared to a stream of wages to be paid to a worker
hired the following period. Consequently, the wage costs associated with
hiring in the current period are comparatively lower because the initial wage is
low and because of the future wage savings. Similarly, if in the current period
the unemployment rate is low and is expected to increase in the following
period, the total wage costs associated with hiring in the current period are
comparatively higher than the total wage costs associated with hiring in the
following period. This argument, developed in Kudlyak (2009), suggests that
the relevant measure of wages that a firm takes into account at the time of
hiring is low when unemployment is high and high when unemployment is
low, which is the opposite of being rigid. To gauge the quantitative importance,
we need empirical estimates of this cyclical volatility.
Using the free entry condition for firms, Haefke, Sonntag, and van Rens
(2009) argue for the importance of the elasticity of the expected present discounted value of wages with respect to the expected present discounted value
of productivity in newly formed matches, which they refer to as permanent
values of wages and productivity, respectively. They do not estimate the
elasticity directly but aim at providing the empirical bounds for this statistic.
Using simulations of the standard model, Haefke, Sonntag, and van Rens conclude that “the elasticity of the current period wage of newly hired workers
with respect to current period productivity . . . constitutes a good proxy for the
elasticity of the permanent wage with respect to permanent productivity for
the case of instantaneously rebargained wages.” Using the simulations of a
model, similar to the modified model presented in Section 1 above, they argue
that “the elasticity of the current period wage of newly hired workers with
respect to current period productivity . . . can be seen as a lower bound for [the
elasticity of the permanent wage with respect to permanent productivity] in
the case of wage rigidity on the job.” Haefke, Sonntag, and van Rens (2009)
proceed to estimate the elasticity of wages of newly hired workers with respect
to productivity using a large data set on wages of newly hired workers from
nonemployment from the CPS. The estimated model for wages is similar to
the models presented above except that, instead of using the series of unemployment, they use the series of labor productivity as a cyclical indicator. They
find that the elasticity of wages of newly hired workers from nonemployment,
0.8, is substantially larger than the elasticity of wages of all workers, 0.2.10
Kudlyak (2009) provides an estimate of the cyclical behavior of the measure of wages that takes into account the initial wage and the expected present
value of future wages to be paid in a newly formed match. The firm’s hiring
decision can be thought of as a decision to hire in the current period versus
10 Haefke, Sonntag, and van Rens (2009) document that the elasticity of wages of job-to-job
movers is similar to the elasticity of wages of newly hired workers from nonemployment or even
larger.

M. Kudlyak: Are Wages Rigid Over the Business Cycle?

195

waiting one more period and hiring then. In equilibrium, the marginal productivity of an additional worker equals the user cost of labor, which is the
difference between the expected present discounted values of the costs associated with creating a match with a worker in the current period and the costs
associated with creating a match the following period. In a model with search
and matching, these costs consist of expenses on hiring a worker, i.e., costs
associated with vacancy posting, and wage payments to a worker.
Using individual wage data from the NLSY, Kudlyak (2009) estimates
the cyclicality of the wage component of the user cost of labor, which equals
the wage at the time of hiring plus the expected present discounted value of
the differences from the next period onwards between the wages paid to the
worker hired in the current period and the worker hired the following period.11
The estimated cyclicality of the wage component of the user cost of labor is
−4.5 percent as compared to the cyclicality of wages of newly hired workers
of −3 percent. The greater cyclicality obtains because at the time of hiring,
a firm to some degree locks in a worker to a stream of wages that depends
on the economic conditions from the start of the job. Thus, the rigidity of
wages within employment relationships actually amplifies the fluctuations of
the expected present discounted value of wages to be paid to a newly hired
worker as compared to the fluctuations in the initial wage in newly formed
matches.

Discussion
To gauge whether the wage data exhibit enough rigidity to amplify fluctuations
in the standard search and matching model, the empirical estimates from wage
data must be contrasted with the statistics obtained from the model. This task
is conducted in Pissarides (2009), Haefke, Sonntag, and van Rens (2009), and
Kudlyak (2009).
Pissarides (2009) compares the elasticity of wages with respect to productivity obtained from the standard search and matching model using common
parameter values to the elasticity of wages of newly hired workers with respect
to productivity in the data. He finds that the elasticity of wages of new hires
with respect to productivity in the data is close to 1. This is consistent with
the elasticity of wages generated by the standard search and matching model
with Nash bargaining. He concludes that any solution to the unemployment
volatility puzzle should be able to generate this near-proportionality of wages
of new hires and productivity. Thus, a model with more rigid wages will not be
able to match the data. The same conclusion is reached by Haefke, Sonntag,
and van Rens (2009), who compare their estimates of the elasticity of wages
11 See Kudlyak (2007) for more details on the estimation.

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of newly hired workers with respect to productivity to the statistics from the
standard search and matching model.
Kudlyak (2009) calibrates the elasticity of the wage component of the user
cost of labor in the model to the empirical estimate and examines how much
volatility of vacancies and unemployment the calibrated model can generate.
She concludes that the data lack required rigidity to amplify the fluctuations
of vacancies and unemployment in the model.
Statistics Conditional on Match Quality

Gertler and Trigari (2009) find that, conditional on match quality, there is no
difference between the cyclicality of wages of new hires and existing workers.
They argue that their finding implies that assuming the same cyclicality for new
hires’ and existing workers’ wages within each firm in the standard search and
matching model is consistent with the existing micropanel data evidence on
new hires’ wages once the empirical evidence controls for match quality, i.e.,
match productivity. Their finding that, conditional on match quality, there is no
difference between the cyclicality of wages of new hires and existing workers
is consistent with the evidence that the wages that firms pay to newly hired
workers are (unconditionally) more procyclical than the wages of workers in
ongoing matches. Note, however, that if the conditional statistics are used for
calibrating the model, i.e., if the wage statistics from the model are compared
to the conditional wage statistics in the data, then the driving force of the
model—productivity—as well as other statistics in the model should also be
conditioned accordingly.
Gertler and Trigari’s evidence suggests a possible source of the difference between the cyclicality of wages of new hires and wages of the existing
workers—the difference between the quality of a newly formed match and of
an existing match. It implies that there is economically significant cyclical
heterogeneity in match quality between newly formed and ongoing matches.
In contrast, in the standard search and matching model, newly formed and
ongoing matches are homogeneous, i.e., they are equally productive in every
period. Thus, for the model to generate cyclical volatilities, the finding calls
for a modification of the model to incorporate the cyclical heterogeneity.

3.

CONCLUSION

What matters for the hiring decision of a firm over the business cycle is the
cyclicality of the expected value of wages paid in newly formed matches.
Most of the existing studies are concerned with the cyclicality of the current
wage. The evidence on the cyclicality of the expected present value of future
wages to be paid in a newly formed match is scarce.
The data provide evidence of the difference between the cyclicality of
wages of newly hired workers and of wages of workers in ongoing matches.

M. Kudlyak: Are Wages Rigid Over the Business Cycle?

197

In particular, the studies document that a one percentage point increase of the
unemployment rate is associated with approximately a 3 percent decrease in
wages of newly hired workers. Wages of workers in ongoing matches are
less responsive to the contemporaneous labor market conditions and depend
on the history of the labor market conditions from the start of the job, i.e.,
they are more rigid as compared with the wages of newly hired workers. This
wage rigidity within employment relationships may, in fact, make the expected
present value of wages to be paid in newly formed matches more cyclically
volatile than the wage of new hires.
Haefke, Sonntag, and van Rens (2009), using simulations from the model,
argue that the wage measure that takes into account future wages in a match
is likely more volatile than wages of new hires. Kudlyak (2009) provides an
estimate of the cyclicality of the user cost of labor, which takes into account
hiring wage and the expected future wages to be paid in the employment relationship. She finds that a one percentage point increase in the unemployment
rate is associated with a 4.5 percent decrease in the expected difference between the present value of wages to be paid in a match created in the current
period and in a match created in the following period.
The evidence suggests that the measure of wages relevant for job creation
is rather procyclical. In fact, using the existing empirical evidence and also
providing new estimates, recent studies find that, quantitatively, the data may
not exhibit the required rigidity necessary to generate the empirical volatility
of unemployment in the standard search and matching model.

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Economic Quarterly—Volume 96, Number 2—Second Quarter 2010—Pages 201–229

Changes in Monetary Policy
and the Variation in Interest
Rate Changes Across Credit
Markets
Devin Reilly and Pierre-Daniel G. Sarte

T

he conduct of monetary policy is most often interpreted in terms of the
federal funds target rate set by the Federal Open Market Committee
(FOMC), at least until recently when this rate effectively reached its
zero bound and additional actions were then implemented. The federal funds
rate is the interest rate at which private depository institutions, typically banks,
lend balances held with the Federal Reserve to other depository institutions
overnight. By targeting a particular value for that rate, the Federal Reserve
seeks to adjust the liquidity provided to the banking system through daily
operations. Because the federal funds rate applies to overnight transactions
between financial institutions, it represents a relatively risk-free rate. As such,
it serves to anchor numerous other interest rates that reflect a wide array of
credit transactions throughout the U.S. economy, such as deposits, home loans,
and corporate loans.
Because the federal funds rate anchors interest rates in many different
types of credit transactions, monetary policy actions that move the funds rate
in a given direction are expected to move other interest rates in the same
general direction. However, the extent to which changes in the federal funds
rate affect conditions in different credit markets may vary significantly from
market to market. For example, changes in the federal funds rate may be
closely linked to changes in the three-month Treasury bill rate, but potentially
less so to changes in home loan rates. In that sense, changes in monetary policy,
We wish to thank Kartik Athreya, Sam Henly, Yash Mehra, and John Weinberg for helpful
comments and suggestions. The views expressed in this article are those of the authors and
do not necessarily represent those of the Federal Reserve Bank of Richmond or the Federal
Reserve System. All errors are our own. E-mail: pierre.sarte@rich.frb.org.

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Federal Reserve Bank of Richmond Economic Quarterly

as reflected by broad liquidity adjustments through the federal funds market,
will be more effective in influencing credit conditions in some markets than
others. Thus, this article attempts to assess empirically the extent to which
interest rate changes in various credit markets reflect changes in monetary
policy. It also explores whether these relationships have changed over time.
As a first step, we construct a panel of 86 time series spanning a diverse
set of monthly interest rate changes, including Treasury bill rates, corporate
interest rates, repurchase agreement rates, and mortgage rates, among others. The panel of interest rate changes covers the period July 1991–December
2009. The empirical framework then uses principal component analysis to
characterize co-movement across these interest rate changes. The basic intuition underlying the exercise is as follows: If changes in monetary policy
tend to move a broad array of interest rates in the same general direction, then
changes in these interest rates will share some degree of co-movement.
Having characterized the common variation in interest rates using principal components, we ask two questions. First, looking across all interest rate
changes, which series tend to be mostly driven by common changes in interest rates rather than idiosyncratic considerations? In particular, idiosyncratic
changes in a given interest rate series are orthogonal to the principal components and, therefore, unlikely to reflect a common element such as a change in
monetary policy. Therefore, one expects that monetary policy will have only
a limited effect on interest rates in which changes are mostly idiosyncratic.
Second, recognizing that the common variation across interest rate changes
may reflect a broad set of aggregate factors, how closely is the common change
component of each interest rate series (which may play a more or less important role in the characterization of different interest rates) related to changes
in monetary policy? Furthermore, has this relationship changed over time?
Our results indicate that most of the variation across our sample can be explained by a small number of common components. For most credit markets,
including mortgage, repurchase agreement, Treasury, and London Interbank
Offered Rate (LIBOR) rates, four components explain approximately 70 percent or more of the variation in interest rate changes. One notable exception is
the auto loan market, in which interest rate variation is almost entirely idiosyncratic. For most of the series in our sample, the common variation in interest
rate changes is relatively highly correlated with the federal funds rate. This
suggests that common movements in interest rates reflect, to a large extent,
changes in monetary policy, as defined by the federal funds rate, rather than
other aggregate disturbances. That said, there nevertheless remains a moderate
number of rates for which the common components, while explaining a significant portion of their variability, are not highly correlated with the federal
funds rate. We interpret this finding in mainly two ways. First, these rates,
which include corporate bond and mortgage rates, are driven to a greater degree by aggregate factors that may be somewhat disconnected from monetary

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

203

policy. Second, these rates, to the extent that they include longer term rates,
reflect monetary policy more indirectly through changes in expected future
short rates. For example, changes in beliefs regarding future productivity will
likely affect the perceived path of future federal funds rates.
The rest of this article is organized as follows. In Section 1, we review the
relevant literature. Section 2 outlines the principal component methodology
and calculations used in our analysis. Section 3 describes the data set used
in the empirical work. Section 4 presents our findings, while Section 5 offers
concluding remarks.

1.

LITERATURE REVIEW

Several recent papers have utilized principal component analysis or similar
techniques to explore the behavior of various interest rates and macroeconomic
variables over time. Diebold, Rudebusch, and Aruoba (2006) and Bianchi,
Mumtaz, and Surico (2009), among others, use a latent factor model to explore
the interaction between yield curves and several macroeconomic variables,
including a monetary policy instrument. The approach used is similar to
using principal components to obtain the factors; however, it differs in that
principal component analysis requires factors to be orthogonal to each other,
but remains agnostic about the form of the factor loadings. The models used
in these and other papers restrict the factor loadings by extending an approach
for modeling yield curves from Nelson and Siegel (1987). These papers have
also restricted their attention to government bond yields.
Perhaps more closely related to our paper is Knez, Litterman, and
Scheinkman (1994). This article investigates the behavior of money market instruments utilizing a factor model that is less restrictive on the loadings
than the previous papers discussed. The authors find that much of the total
variation in their data set can be explained by three or four factors, and that
each factor can be interpreted as a parameter that characterizes systematic
movements in the yield curve. It differs from our analysis in that the data
set used is much narrower, including only Treasury bills, commercial paper,
certificates of deposit, Eurodollar deposits, and bankers’ acceptances, all with
maturities of less than one year. Additionally, they examine the returns of
these securities, whereas we analyze the changes in interest rates across a
variety of credit markets.
Finally, G¨ rkaynak, Sack, and Swanson (2005) and Reinhart and Sack
u
(2005) examine the immediate impact of a variety of forms of FOMC communication on several financial variables, including interest rates, equity prices,
and others. They use principal components to extract common components
from a set of changes in these variables around FOMC statements, testimonies,
and other releases. They find that a small number of factors appears to explain a significant amount of the variation in response to all types of FOMC

204

Federal Reserve Bank of Richmond Economic Quarterly

communication. Our analysis does not limit itself to changes in interest rates
around FOMC communication, and explores a broader array of rates than
these two articles.

2.

PRINCIPAL COMPONENTS

Consider a panel of (demeaned) observations on interest rate changes across N
credit markets over T time periods, which we summarize in an N × T matrix,
X. Let Xt denote a column of X (i.e., a set of observations on all interest
rate changes at date t). As explained in Malysheva and Sarte (2009), the
nature of the principal component problem is to ask how much independence
there really is in the set of N variables. To this end, the principal component
problem transforms the Xs into a new set of variables that will be pairwise
uncorrelated and of which the first will have the maximum possible variance,
the second the maximum possible variance among those uncorrelated with the
first, and so on.
We denote the j th principal component of X by fj , where
fj = λj X,

(1)

and λj and fj are 1 × N and 1 × T vectors, respectively. In other words,
different principal components of X simply reflect different linear combinations of interest rate changes across sectors. Moreover, the sum of squares of
a given principal component, fj , is
fj fj = λj

(2)

XX λj ,

where XX = XX represents the variance-covariance matrix (when divided
by T ) of interest rate changes in the data set.
Let k = (λ1 , ..., λk ) denote an N × k matrix of weights used to construct
the first k principal components of X, f1 , .., fk , which we arrange in the k × T
matrix Fk = (f1 , ..., fk ) . Thus, Fk = k X and the principal component
problem is defined as choosing sets of weights, k , that solve
max
k

k

XX

k

subject to

k

k

= Ik .

(3)

The solution to the above problem has the property that each set of weights,
λj , solves1
XX λj

= μj λj ,

(4)

where λj λj = 1 ∀j . Put another way, the sets of weights that define the different principal components of X in equation (1) are eigenvectors, λj , of the the
variance-covariance matrix of interest rate changes, XX , with corresponding
eigenvalues given by μj . In addition, because the variance-covariance matrix
1 See the Appendix in Malysheva and Sarte (2009).

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

205

of X is symmetric, these eigenvectors are orthogonal to each other, λj λi = 0
∀i = j .
Combining equations (2) and (4), note that
fj fj = λj μj λj = μj .

(5)

Therefore, the eigenvalue μj is the sum of squares of the principal component fj in (2). Then, given that principal components are ranked by the
extent of their variance, the first such component, f1 , is obtained using the
weights, λ1 , associated with the largest eigenvalue of XX . The second principal component is obtained using the weights corresponding to the second
largest eigenvalue of XX , and so on.
Proceeding in this way for each of the N principal components of X using
the weights given by (4), observe that
⎡
⎤
μ1 0 ... 0
⎣ 0 μ2 ... 0 ⎦ .
(6)
N XX N =
0 0 ... μN
If the rank of XX were k < N , there would be N − k zero eigenvalues and
the variation in interest rate changes would be completely captured by k independent variables. In fact, even if XX has full rank, some of its eigenvalues
may still be close to zero so that a small number of (or the first few) principal components may account for a substantial proportion of the variance of
interest rate changes.
The Appendix at the end of the article shows that the principal component
problem defined in (3) can be derived as the solution to the least square problem
T

T −1

min

{f1 ,...,fk }T ,
t=1

k

et et subject to

k

k

= Ik ,

(7)

t=1

where
Xt =

k Fk,t

+ et .

(8)

Hence, it follows that
XX

=

k

FF

k

+

ee ,

(9)

where F F = Fk Fk , in which case we can think of the principal components
as capturing some portion k F F k of the variation in interest rate changes,
XX .
Given the decomposition expressed in (8), each interest rate change in the
data set can be written as
rti =

i
k Fk,t

+ eti ,

(10)

where i is the ith row of k . In that sense, i Fk,t captures the importance
k
k
of the principal components in driving each individual series. The objective
of the article then is to address two key aspects of interest rate changes.

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Federal Reserve Bank of Richmond Economic Quarterly

First, having computed a set of principal components, Fk,t , that account
for most of the fraction of the variation in the Xs, we wish to assess the
extent to which a given series of interest rate changes, rti , is driven by
these components rather than its own disturbance term, eti . The important
consideration here is that the principal components, Fk,t , in (10) are common
to all interest rate changes (i.e., they do not depend on i) and, therefore, will be
directly responsible for co-movement across interest rate changes. In contrast,
even if there remains some covariation across the shocks, eti , this covariation
will, by construction, play a larger role in explaining idiosyncratic variations
in interest rate changes. In that sense, changes in monetary policy will more
likely be reflected in the co-movement term i Fk,t in equation (10) rather
k
than eti .
Formally, we compute how much of the variance of rti , denoted σ 2 rit ,
is explained by the variance of i Fk,t ,
k
i
k

Ri2 (F ) =

i
k

FF
σ 2 rit

(11)

.

The series of interest rate changes with Ri2 (F ) statistics close to 1 are driven
almost entirely by forces that determine mainly the covariation across interest
rate changes. In contrast, series of interest rate changes with Ri2 (F ) statistics
close to zero generally reflect considerations that are likely more idiosyncratic
to each series.
Suppose that we were interested in a subgroup of M series—say all mortgage interest rates or all repurchase agreement rates. We can compute an
analogous R 2 statistic for that credit market segment by using a 1 × N weight
vector, w, that associates positive weights to the series of interest and zeros
2
elsewhere. The implied RM (F ) statistic is then given by
2
RM (F ) =

w

w

FF

w

XX w

.

(12)

2
As before, RM (F ) statistics close to 1 indicate a subgroup of credit markets
(defined by the weights, w) that are mostly affected by common forces across
interest rates, w k Fk,t , rather than conditions specific to that subgroup, wet .
Second, because the covariation across interest rate changes reflects not
only changes in monetary policy but also other aggregate considerations (including those potentially driven by systemic issues), the next step is to relate changes in each interest rate series captured by principal components to
changes in monetary policy. Hence, in each credit market, i, we compute the
correlation between i Fk,t and changes in the effective federal funds rate,
k
f ed
rt ,

ρ i = corr(

i
k Fk,t ,

f ed

rt

).

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

207

f ed

Evidently, rt may not capture all of the relevant aspects of changes in
monetary policy and serves here only as an approximate guide. For instance,
going forward, we may be more interested in the relationship between i Fk,t
k
and the interest on reserves. More generally, to the extent that other measurable
aspects of changes in monetary policy matter, say represented in a vector Zt ,
one could instead compute the projection,
i
k Fk,t

= Zt β + u i ,
t

and its associated Ri2 (Z) statistic.

3. THE DATA
Our analysis focuses on a data set that includes 86 time series on interest
rate changes, all seasonally adjusted and expressed at an annual rate. These
include a wide array of rates with monthly observations spanning back to July
1991. A full list of rates and associated descriptive statistics can be found in
the Appendix (Table 5). The data come primarily from Haver Analytics and
Bloomberg. While we analyze these rates individually, for ease of presentation
we also place them into eight broad categories and investigate the average
behavior in each of these credit markets.
The first group includes LIBOR rates based on the U.S. dollar, with maturities ranging from one month to one year. These are reference rates based
on the interest rates at which banks are able to borrow unsecured funds from
other banks in the London interbank market. We refer to the second group in
our data set as the deposit group, which contains averages of dealer offering
rates on certificates of deposit with maturities from one to nine months, as well
as bid and effective rates on Eurodollar deposits for maturities of overnight to
one year. Our third group includes a variety of Treasury bill, note, and bond
rates. There are two secondary market rates (three- and six-month), which are
the average rates on Treasury bills traded in the secondary market. We also
include auction highs on three- and six-month Treasury bills. However, the
majority of rates in this group are yields on nominal Treasury securities with
maturities ranging from three months to 30 years. These are interpolated by the
U.S. Treasury from the daily yield curve for noninflation indexed securities,
based on closing market bid yields on actively traded Treasury securities.
Our panel also contains a variety of corporate borrowing rates. We include
one-month and three-month rates for nonfinancial and financial commercial
paper in this group. These rates are calculated by the Federal Reserve Board
using commercial paper trade data from the Depository Trust and Clearing
Corporation. Also included are Aaa and Baa Moody’s corporate bond yields,
which are based on outstanding corporate bonds with remaining maturities of
at least 20 years. Finally, Citigroup Global Markets provides corporate bond
yields that cover a variety of industries and ratings.

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Federal Reserve Bank of Richmond Economic Quarterly

We include two smaller groups, one of which contains three rates for longterm government (state and local) and agency bonds. The other relatively small
group in our panel includes two series of interest rate changes for new and
used car loans. These are simple unweighted averages of rates commonly
charged by commercial banks on auto loans.
The final two groups we utilize are mortgage rates and repurchase agreement rates. The former spans a variety of mortgage rates, including new
homes, existing homes, adjustable rate loans, and fixed rate loans. The repurchase agreement group (which also includes reverse repurchase rates) is based
on transactions that involve Treasury, mortgage-backed, or agency securities,
with maturities ranging from one day to three months.

4.

EMPIRICAL FINDINGS

Given the computation of principal components described in Section 1, the
next section assesses the extent to which a small number of principal components, out of potentially 86, captures the variation in interest rates across
different credit markets. We then gauge the contribution of common changes to
individual interest rate variations, as captured by the Ri2 (F ) statistic described
above. In other words, in each credit market, we assess how much of the variation in its interest rate, rti , is explained by its component related to common
interest rate movements, i Fk,t . The next subsection then relates the common
k
component of individual interest rate changes, i Fk,t , to changes in the fedk
f ed
f ed
eral funds rate, rt , by examining their correlation, corr( i Fk,t , rt ).
k
Finally, in the last subsection, we examine the robustness of our findings over
different sample periods.

Accounting for Interest Rate Variations with a Small
Number of Factors
This subsection examines the degree to which a small number of factors potentially captures most of the variation in interest rates across credit markets.
We carry out this assessment in mainly two ways. First, we ask how much of
i
the variation in average interest rate changes, N −1 N
i=1 rt , is explained by
the first few principal components. Second, following Johnston (1984), we
ask how much of the sum of individual variations in the Xs is explained by
these components. The total individual variation in interest rate changes is
given by
T

T

( rt1 )2 +
t=1

T

( rt2 )2 + ... +
t=1

( rtN )2 = tr(
t=1

XX ).

(13)

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

209

From equation (6), observe that
N

= tr(

μj

N

xx

N)

i=1

= tr(
= tr(

XX

N)

N

(14)

XX ).

In other words, the sum of the eigenvalues of the covariance matrix of interest rate changes, XX , is precisely the sum of individual variations in these
changes. It follows that
μ1
N
i=1 μj

,

μ2
N
i=1 μj

, ...,

μN
N
i=1 μj

(15)

represent the proportionate contributions of each principal component to the
total individual variation in interest rate changes. In addition, since principal
components are orthogonal, these proportionate contributions add up to 1.
The analysis reveals that the first four principal components (i.e., k = 4)
of the panel of interest rate changes constructed for this article explain 99
i
percent of the variation in average interest rate changes, N −1 N
i=1 rt , and
78 percent of the their total individual variation,

4
k=1 μk
N
i=1 μj

= 0.78. In other

words, a small number of components effectively accounts for the variation in
the data set. The findings discussed in the remainder of the article are based on
these first four principal components. However, our conclusions regarding the
effects of changes in monetary policy in different credit markets, in particular
the qualitative ranking of credit markets most influenced by changes in the
federal funds rate, are robust to considering either fewer than four or up to
eight principal components.
As discussed in the prior section, we summarize the behavior of our interest
rate series into eight main categories. Figure 1 depicts average changes in
these eight broad credit markets over time. Recession peaks and troughs
are indicated in the figures by vertical dashed lines. The average changes in
rates differ in both persistence and volatility across the eight groups. At two
extremes, changes in mortgage rates appear to be relatively stable relative to
other rates, whereas auto loan rates are considerably more volatile than any
other group. Table 1A provides basic summary statistics for each category
of credit markets, as well as for the effective federal funds rate. Consistent
with Figure 1, Table 1A indicates that auto loan rates are by far the most
volatile rates while mortgage rates are least volatile. In addition, many of
these interest rate changes, including auto loan, deposit, and mortgage rates,
present evidence of kurtosis. That is, much of the variance in these interest rate
changes stems from infrequent extreme observations as opposed to relatively
common deviations. Some of the series also show evidence of skewness. For

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Average Interest Rates in Different Credit Market Segments
Deposit Rates

LIBOR Rates
200

200

Number of Rates = 04

Number of Rates = 14

0

0

-100

-100

-200

100

Rate Changes (bp)

Rate Changes (bp)

100

1992

1994

1996

1998

2000

2002

2004

2006

2008

-200
2010

1992

1994

1996

1998

Treasury Rates

2006

2008

2010

2004

2006

2008

2010

Corporate Rates

Rate Changes (bp)

100

Rate Changes (bp)

2004

Number of Rates = 15

Number of Rates = 15

0

100

0

-100

-100

-200

-200
1992

1994

1996

1998

2000

2002

2004

2006

2008

1992

2010

1994

1996

1998

2000

2002

Date

Date

Government/Agency Bond Rates

Auto Loan Rates
200

200

Number of Rates = 03

Number of Rates = 02

Rate Changes (bp)

100

Rate Changes (bp)

2002

200

200

0

100

0

-100

-100

-200

-200
1992

1994

1996

1998

2000

2002

2004

2006

2008

1992

2010

1994

1996

1998

2000

2002

2004

2006

2008

2010

2008

2010

Date

Date

Mortgage Rates

Repurchase Agreement Rates

200

200

Number of Rates = 09

Number of Rates = 24

100

Rate Changes (bp)

Rate Changes (bp)

2000

Date

Date

0

-100

100

0

-100

-200

-200
1992

1994

1996

1998

2000

2002

Date

2004

2006

2008

2010

1992

1994

1996

1998

2000

2002

2004

2006

Date

example, deposit, auto loan, and LIBOR rates are all left skewed, indicating
the presence of large negative changes in the time series.
Table 1B presents analogous summary statistics for individual Treasury
bill rates of different maturities. Interestingly, the standard deviations of the
rates increase for maturities of three months to three years, and then decrease
at higher maturities. In addition, shorter-term rates, namely three months
and six months, are left skewed and thus have historically experienced large

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

211

Table 1 Changes in Rates by Category
Table 1A: Changes in Rates, by Credit Market
Series
Mean
Std. Dev. Skewness Kurtosis
Federal Funds
−2.60
19.87
−1.27
6.49
LIBOR
−2.68
25.67
−1.62
12.98
Deposit
−2.59
27.38
−1.90
17.87
Treasury
−2.35
22.71
−0.33
4.08
Corporate
−2.24
26.10
0.34
11.54
Government/Agency
−2.14
22.72
0.05
3.99
Auto
−3.73
48.41
−1.37
15.58
Mortgage
−1.94
19.45
0.82
15.03
Repurchase Agreements −2.56
30.03
−0.98
9.13

Min.
−96
−219
−285
−111
−179
−86
−392
−110
−225

Max.
53
94
140
65
227
77
172
200
168

Table 1B: Changes in Treasury Rates, by Maturity
Series
Mean
Std. Dev. Skewness Kurtosis
Three-Month Bill
−2.55
21.96
−1.06
4.99
Six-Month Bill
−2.63
22.16
−0.69
4.11
One-Year Bill
−2.70
23.41
−0.43
3.66
Two-Year Note
−2.70
36.06
−0.03
2.86
Three-Year Note
−2.65
26.85
0.11
2.76
Five-Year Note
−2.42
26.06
0.13
2.85
Seven-Year Note
−2.22
24.63
0.13
3.28
10-Year Note
−2.04
23.43
−0.08
4.35
20-Year Bond
−1.74
20.75
−0.18
5.37
30-Year Bond
−1.74
19.86
−0.36
6.00

Min.
−89
−77
−79
−69
−69
−77
−93
−111
−109
−110

Max.
49
54
60
63
65
60
61
65
58
51

Notes: Basis points, monthly at annual rate.

negative changes. Finally, changes in Treasury rates with maturities less than
one year and more than 10 years also have relatively large kurtosis statistics.

Contribution of Common Changes to Individual
Interest Rate Variations
Figure 2 shows a histogram of the Ri2 (F ) statistic discussed in Section 1.
This statistic captures the extent to which common movements across interest
rates, as summarized by i Fk,t for each individual interest rate, drive changes
k
in these individual rates. Two main observations stand out. First, changes in
interest rates across credit markets tend to reflect factors common to all interest
rate changes. In particular, the median Ri2 (F ) statistic is 0.814. Second, this
first observation notwithstanding, the data also include interest rates in which
variations appear almost exclusively driven by idiosyncratic considerations
rather than common changes. This is true, for example, of auto loan rates.
2
Table 2A presents the RM (F ) statistics for the eight broad categories of
credit markets described earlier. These range from 0.03 for auto loan rates

212

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Importance of Common Changes in Individual Interest Rates

12

Distribution of R 2(F) Across Credit Markets
i

Percent of Total

10

8

6

4

2

0

0.0

0.2

0.4

0.6

0.8

2

R i (F)

to 0.92 for LIBOR rates.2 In other words, changes in auto loan rates are
explained almost exclusively by idiosyncratic considerations. Put another
way, factors that explain co-movement across interest rate changes, one of
which is expected to be monetary policy, appear to have little influence over
interest rate variations in the auto loan credit market. At the other extreme,
changes in LIBOR and deposit rates are almost exclusively driven by forces
responsible for the co-movement across interest rates. Somewhere between
these two extremes, observe that the common components explain about 68
percent of the variation in government and agency bond rates and mortgage
rates.
Table 2B presents the same Ri2 (F ) statistics for Treasury bill rates of
different maturities. As indicated in the table, the principal components play
a large role in explaining the variation in these rates across all maturities. In
this case, the Ri2 (F ) statistics range from 0.71 to 0.91. Around 78 percent of
the variation in 30-year Treasury bill rates is explained by forces common to
all interest rates. Interestingly, the common component of the three-month
2 A listing of all R 2 (F ) statistics can be found in the Appendix (Table 6).
i

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

213

Table 2 Importance of Principal Components in Different Interest
Rate Categories
2
Table 2A: Average RM (F ) by Credit Market Segment
2
Series
Average Ri (F )
Auto
0.030
Mortgage
0.682
Government/Agency
0.685
Repurchase Agreements
0.754
Treasury
0.835
Corporate
0.839
Deposit
0.860
LIBOR
0.917
2
Table 2B: Average Ri (F ) for Treasury Securities
2
Series
Average Ri (F )
Three-Month Bill
0.710
Six-Month Bill
0.846
One-Year Bill
0.866
Two-Year Note
0.856
Three-Year Note
0.873
Five-Year Note
0.902
Seven-Year Note
0.913
10-Year Note
0.907
20-Year Bond
0.844
30-Year Bond
0.781

Notes: Monthly rates.

Treasury bill rates explains a lower fraction of the variation in that rate than
does the corresponding common component in the 30-year rate. However,
since common sources of movement in Treasury bill rates reflect changes
not only in monetary policy but also in other aggregate factors, one cannot
conclude from Table 2B that changes in the federal funds rate exert a greater
influence on the 30-year rate than the three-month rate. For the same reason, it
does not follow from Table 2B that changes in monetary policy broadly affect
Treasury bill rates to the same degree across all maturities.
One should recognize that in each credit market category (defined by
weights, w), changes in interest rates that stem from sources that are common
across all credit markets, w k Fk,t , will not necessarily correspond to the behavior of average changes in these rates, wXt . This is shown, for example, in
Figure 3 where the difference between the common component of auto loan
rate changes and average auto loan rate changes is evident. More important,
having extracted the component of each rate change that is related to common
sources, Figure 4 plots these common change components against changes in
the effective federal funds rate for each of the eight broad credit markets defined above. It is apparent that the different components capturing the effects

214

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Common and Average Rate Variations in Selected Credit
Markets
Auto Loan Rates
150
100
50
0
-50
-100
-150
Common Change Component
Actual Rate Change

-200
-250
1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2004

2006

2008

2010

Mortgage Rates
150
100
50
0

-50
-100
-150
Common Change Component
Actual Rate Change

-200
-250
1990

1992

1994

1996

1998

2000

2002

of common forces look different across various credit market segments. However, the volatility of these change components tends to be similar to that of the
effective federal funds rate. The question then is: What does the distribution
of correlations between the different common change components in interest
rates and changes in the effective federal funds rate look like? As mentioned
earlier, changes in the effective federal funds rate may constitute only a rough
summary of changes in monetary policy. A more general approach might be
to examine a projection of common changes across individual interest rates
on different aspects of changes in monetary policy, although ultimately not all
relevant aspects of monetary policy are easily quantifiable or measured. For
now, however, we focus on the effective federal funds rate.

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

215

Figure 4 Common Rate Change Components and Federal Funds Rate
Changes
LIBOR Rates

Deposit Rates

300

150

Common Change Component
Change in Federal Funds Rate

200

Common Change Component
Change in Federal Funds Rate

100
50

100
0
0

-50
-100

-100
-150
-200
-200
-300

-250
1992

1994

1996

1998

2000

2002

2004

2006

2008

1992

2010

1994

1996

Treasury Rates

1998

2000

2002

2004

2006

2008

2010

2004

2006

2008

2010

Corporate Rates
150

150

Common Change Component
Change in Federal Funds Rate

100

Common Change Component
Change in Federal Funds Rate

100
50

50
0

0

-50

-50

-100

-100

-150

-150
-200

-200

-250

-250
1992

1994

1996

1998

2000

2002

2004

2006

2008

1992

2010

1994

1996

Government/Agency Bond Rates

1998

2000

2002

Auto Loan Rates

150

150

Common Change Component
Change in Federal Funds Rate

100

Common Change Component
Change in Federal Funds Rate

100

50

50

0

0

-50

-50

-100

-100

-150

-150

-200

-200

-250

-250
1992

1994

1996

1998

2000

2002

2004

2006

2008

1992

2010

1994

Mortgage Rates

1996

1998

2000

2002

2004

2006

2008

2010

Repurchase Agreement Rates

150

150

Common Change Component
Change in Federal Funds Rate

100

Common Change Component
Change in Federal Funds Rate

100

50

50

0

0

-50

-50

-100

-100

-150

-150

-200

-200

-250

-250
1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

Co-movement in Interest Rate Changes and the
Federal Funds Rate
Figure 5 shows the histogram of the correlations between common change
components in each interest rate, i Fk,t , and changes in the federal funds
k
rate. While some of the common change components in interest rates seem
highly correlated with changes in the federal funds rate, there are also many

216

Federal Reserve Bank of Richmond Economic Quarterly

Figure 5 Changes in the Federal Funds Rate and Common Changes in
Interest Rates
Distribution of Correlations of Common Change
Components with Federal Funds Rate Changes
16
14

Percent

12
10
8
6
4
2
0
0.0

0.2

0.4

0.6

0.8

Correlation

other interest rates for which that is not the case. The median correlation
in this case is 0.60 while the mean is 0.50. Table 3A provides a ranking of
correlations across the eight credit market segments examined in this article.3
Interestingly, the common change components least correlated with
changes in the federal funds rate are found in the government and agency
bond and corporate credit markets. This finding may be interpreted in mainly
two ways. First, although the common change components play an important
role in driving corporate rates in Table 2A, these components likely reflect aggregate disturbances (or internal co-movement) that are somewhat unrelated
to monetary policy. Second, to the extent that these rates include longerterm rates, they reflect monetary policy more indirectly through changes in
expected future short rates. For example, changes in beliefs regarding future
productivity will likely affect the perceived path of future federal funds rates.
In contrast, we also see in Table 3A that the common change components
in deposit and LIBOR rates are relatively highly correlated with changes in
3 A listing of all correlations between
(Table 6).

iF
k k,t and

rtfed can be found in the Appendix

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

217

Table 3 Correlation of Changes in Federal Funds Rate with Common
Components by Interest Rate Category
Table 3A: Correlation of Common Components for Credit Markets
with Changes in Federal Funds Rate
Series
Correlation
Government/Agency
0.131
Corporate
0.212
Mortgage
0.315
Treasury
0.501
Deposit
0.616
LIBOR
0.632
Repurchase Agreements
0.756
Auto
0.769
Table 3B: Correlation of Common Components for Treasury Securities
with Changes in Federal Funds Rate
Series
Correlation
Three-Month Bill
0.776
Six-Month Bill
0.730
One-Year Bill
0.640
Two-Year Note
0.485
Three-Year Note
0.400
Five-Year Note
0.290
Seven-Year Note
0.220
10-Year Note
0.155
20-Year Bond
0.066
30-Year Bond
0.070
Notes: Monthly rates.

the federal funds rate. Moreover, Table 2A also suggests that the variations
in these rates are, for the most part, accounted for by common sources of
variations across interest rates. We conclude, therefore, that changes in monetary policy, as captured by changes in the federal funds rate, have played a
fundamental role in driving deposit and LIBOR rates.
Table 3B provides the same statistics for Treasury rates of different maturities. As expected, the correlation between the common change component
of Treasury bill rates and changes in the federal funds rate is decreasing in
maturity, starting at 0.78 for the three-month rate and ending at 0.07 for the
30-year rate. Therefore, even if the common change component of 30-year
rates plays a large role in explaining its variations (recall Table 2B), Table 3B
is consistent with the conventional view that 30-year rates reflect other more
fundamental aggregate changes in the economy rather than contemporaneous
changes in policy.
Figure 6 summarizes the results thus far in the form of a scatter plot with
Ri2 (F ) on the x-axis and corr( i Fk,t , rtfed ) on the y-axis. A point near the
k

218

Federal Reserve Bank of Richmond Economic Quarterly

Figure 6 Effects of Monetary Policy Across Credit Markets
2

R i (F) vs. Correlation of Common Change Components
with Federal Funds Rate Changes
1.0

0.8

Used Auto Loans

Correlation

1M Agency
Repo

2M CDs

New Auto Loans

0.6

Treas. Repo - 1 Day
1Y ARMs - FHLMC

0.4

3Y Treas. Note
New Home Loans, Eff. Rate
5Y Treas. Note
30Y FHLMC Fixed Mortgage

0.2

Government/Agency Bond

0.0
0.0

Mortgage Bond Yield

0.1

0.2

0.3

0.4

0.5

0.6

0.7

20Y Treas. Bond

0.8

0.9

1.0

2
R i (F)

lower left-hand corner, where both statistics are near zero, would indicate that
changes in interest rates are entirely disconnected from changes in the federal
funds rate and, in essence, driven by more idiosyncratic considerations. The
opposite is true near the top right-hand corner where both statistics are close
to 1. Interestingly, the common components for auto loan rates have high
correlations with changes in the federal funds rate, so that the common variation in these rates seems related to changes in monetary policy to a nontrivial
extent, but also have extremely low Ri2 (F ). Put another way, although the
common variation in auto loan rates is related to changes in the federal funds
rate, their overall variation is ultimately driven by idiosyncratic considerations. There are also several rates in the lower right-hand corner of the plot.
Variation in these rates is explained almost entirely by the common variation.
However, the common components for these rates appear disconnected from
monetary policy, as defined by the federal funds rate. Some of these rates
include corporate bonds, fixed-rate mortgages, and long-term Treasury notes
and bonds, and all of them have maturities of at least five years. Finally, Figure
6 also includes several rates near the top right-hand corner of the graph, namely
several deposit, repurchase agreement, and Treasury bill rates, in which

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

219

Table 4 Correlation of Changes in Federal Funds Rate with Common
Components by Interest Rate Category Over Different
Sample Periods
Table 4A: Correlation of Common Components for Credit Markets
with Changes in Federal Funds Rate
Correlation
Credit Market Segment
Government/Agency
Corporate
Mortgage
Treasury
LIBOR
Deposit
Repurchase Agreements
Auto

1991:7–2001:2
0.26
0.33
0.41
0.55
0.67
0.67
0.72
0.75

2001:3–2009:12
0.03
0.14
0.24
0.47
0.60
0.58
0.79
0.79

Table 4B: Correlation of Common Components for Treasury Securities
with Changes in Federal Funds Rate
Correlation
Treasury Security
Maturity
1991:7–2001:2
2001:3–2009:12
Three-Month Bill
0.76
0.80
Six-Month Bill
0.72
0.75
One-Year Bill
0.65
0.64
Two-Year Note
0.54
0.45
Three-Year Note
0.48
0.34
Five-Year Note
0.40
0.20
Seven-Year Note
0.35
0.12
10-Year Note
0.30
0.04
20-Year Bond
0.22
−0.06
30-Year Bond
0.23
−0.06
Notes: Monthly rates.

variations therefore appear closely related to changes in contemporaneous
monetary policy.

Robustness Across Different Sample Periods
To analyze if this behavior has changed over time, we split the data into two
subsamples: July 1991–February 2001 and March 2001–December 2009. We
then calculate the correlations of the common components with changes in the
effective federal funds rate over these two periods. We chose the breakpoint to
be February 2001 to keep the subsamples roughly the same size, and because
this is the month prior to the National Bureau of Economic Research peak of
the 2001 recession. Table 4A shows the correlations for the eight broad groups

220

Federal Reserve Bank of Richmond Economic Quarterly

Figure 7 Common Changes in Interest Rates and the Yield Curve
Yield Curve, 10-Year over Three-Month Treasuries
5
Common Change Component
Actual Yield Curve
4

3

2

1

0

-1
1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

described previously for each subsample. The ordering of the correlations for
each credit market is essentially the same across the two periods. The most
noticeable differences are seen in the mortgage, corporate, and government
and agency bond markets. For these three groups, the correlations are moderately higher in the first subsample, indicating that disturbances less directly
related to the contemporaneous federal funds rate have become more important in explaining common variation in these interest rate changes over time.
This finding runs somewhat counter to the view in Taylor (2007) that an easy
monetary policy kept long-term interest rates too low, thereby contributing to
the housing boom. Rather, it is more consistent with the emphasis given by
Bernanke (2010) to the role of other factors in keeping long-term interest low
during the early 2000s.
The only two groups that saw an increase in correlations over the two periods are auto rates and repurchase agreement rates, though the increases are
relatively small. Table 4B shows the analogous correlations for the common
components of individual Treasury rates of different maturities. Interestingly,
short-term Treasury bill rates have similar correlations across the two periods. However, at longer maturities, correlations between the common components and the federal funds rate have decreased in the later period, with the

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

221

correlations for 20-year and 30-year Treasury bonds becoming slightly negative in the recent subsample.
As a final examination, we plot the common change component of the
yield curve against the yield curve calculated from the raw data. These are
shown in Figure 7. We define the yield curve as the 10-year Treasury note
yield less the three-month Treasury bill yield. The main periods in which the
two series deviate from each other are at their relative peaks and troughs, in
particular in 1992, 2000, and 2006. However, overall the two series co-move
strongly together, indicating that much of the spreads in rates of different
maturities over time resides in how common shocks affect those rates rather
than more idiosyncratic considerations.

5.

CONCLUDING REMARKS

In this article, we use principal component methods to assess the importance of
changes in the federal funds rate in driving interest rate changes across a variety
of credit markets. Our findings suggest that most of the variability in interest
rate changes across these markets can be explained by a small number of
common components. In particular, four components explain approximately
80 percent of the total variation in interest rate changes. One notable exception
is the auto loan market, in which interest rate variation is almost entirely
idiosyncratic.
For most of our sample, the common variation in interest rate changes
is relatively highly correlated with federal funds rate changes. This suggests
that common movements in interest rates to a large extent reflect changes
in monetary policy rather than other aggregate disturbances. That said, there
nevertheless remains a moderate number of rates for which the common components, while explaining a significant portion of their variability, are not
highly correlated with the federal funds rate. Therefore, these rates, which
include mainly those with longer maturities such as mortgage rates, are driven
to a greater extent by aggregate forces other than short-term changes in monetary policy. Finally, the analysis also suggests that movements in the auto
loan market are almost entirely driven by idiosyncratic considerations rather
than changes in the federal funds rate.

APPENDIX
This appendix shows that the solution to the principal component problem (3)
also solves the least square problem described in (7). In particular, combining

222

Federal Reserve Bank of Richmond Economic Quarterly

equations (7) and (8) gives
T

min

T

{f1 ,...,fk }T ,
t=1

−1

(Xt −

k

k Fk,t )

(Xt −

k Fk,t )

subject to

k

k

= Ik .

t=1

Suppose that k were known. Then the solution for Fk,t
given by the standard least square formula,
Fk,t (

k)

=(

k)

k

−1

(16)
would simply be

k Xt .

Substituting this solution into (16) yields
T

min T

−1

k

Xt [Ik −

k(

k)

k

k ]Xt ,

t=1

or equivalently,
T

max T −1
k

Xt

k(

k)

k

k Xt .

t=1

Now, note that this last expression is a scalar. Hence, we can re-write the
problem as
T

max tr T

−1

Xt

k(

k

k)

k Xt

tr Xt

k

k(

k

k)

k Xt

,

t=1

or
T

max T −1
k

.

t=1

Using the properties of the trace operator, this last expression can also be
expressed as
T

max T
k

−1

tr (

k

k)

−1/2

k (Xt Xt )

k(

k

k)

−1/2

,

t=1

or
T

max tr (
k

k

−1/2
k)

−1
kT

(Xt Xt )(

k

k)

−1/2

k(

k

k)

−1/2

.

t=1

Given the notation introduced in the text, one can observe that T −1 T (Xt Xt )
t=1
is simply XX = XX . It follows that the least-square problem defined in (16)
is equivalent to solving max k k XX k subject to k k = Ik .

Mean
−2.6
−2.6
−2.7
−2.7
−2.7
−2.6
−2.6
−2.6
−2.7
−2.7
−2.5
−2.5
−2.6
−2.6
−2.5
−2.6
−2.6
−2.6
−2.7
−2.5
−2.5
−2.5
−2.5
−2.6
−2.6
−2.7

Std. Dev.
19.9
28.0
25.2
23.8
25.8
29.2
29.1
26.4
25.7
29.8
32.3
28.8
26.5
20.4
24.9
29.1
26.7
26.2
27.3
21.2
21.0
20.8
20.8
22.0
22.2
23.4

Skewness
−1.3
−2.5
−1.9
−1.2
−0.5
−2.8
−1.6
−2.2
−1.5
−1.4
−3.0
−1.9
−0.9
−1.6
−3.8
−2.2
−1.1
−0.9
−0.5
−1.1
−0.7
−1.0
−0.7
−1.1
−0.7
−0.4

Kurtosis
6.5
19.8
15.2
7.5
4.5
23.7
12.9
17.4
9.8
11.0
30.6
20.5
9.0
8.0
33.2
19.9
11.6
8.2
5.2
5.0
4.2
4.6
4.2
5.0
4.1
3.7

Min
−96
−219
−178
−122
−98
−241
−172
−196
−154
−164
−285
−220
−143
−103
−229
−225
−152
−116
−106
−86
−73
−83
−75
−89
−77
−79

Max
53
88
94
65
74
98
119
80
71
124
140
136
109
43
55
125
129
109
98
46
51
45
52
49
54
60

223

Rate
Federal Funds [Effective] Rate
One-Month London Interbank Offer Rate: Based on U.S.$
Three-Month London Interbank Offer Rate: Based on U.S.$
Six-Month London Interbank Offer Rate: Based on U.S.$
One-Year London Interbank Offer Rate: Based on U.S.$
One-Month Certificates of Deposit, Secondary Market
Two-Month Certificate of Deposit
Three-Month Certificates of Deposit, Secondary Market
Six-Month Certificates of Deposit, Secondary Market
Nine-Month Certificate of Deposit
One-Month Eurodollar Deposits, London Bid
Three-Month Eurodollar Deposits, London Bid
Six-Month Eurodollar Deposits, London Bid
U.S. Dollar: Eurocurrency Rate, Short-Term
U.S. Dollar: Seven-Day Eurocurrency Rate
U.S. Dollar: One-Month Eurocurrency Rate
U.S. Dollar: Three-Month Eurocurrency Rate
U.S. Dollar: Six-Month Eurocurrency Rate
U.S. Dollar: One-Year Eurocurrency Rate
Three-Month Treasury Bills, Secondary Market
Six-Month Treasury Bills, Secondary Market
Three-Month Treasury Bills
Six-Month Treasury Bills
Three-Month Treasury Bill Market Bid Yield at Constant Maturity
Six-Month Treasury Bill Market Bid Yield at Constant Maturity
One-Year Treasury Bill Yield at Constant Maturity

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

Table 5 Monthly Changes (in Basis Points)

Table 5 (Continued) Monthly Changes (in Basis Points)
Std. Dev.
26.1
26.9
26.1
24.6
23.4
20.8
19.9
20.8
22.2
21.2
23.3
23.1
18.4
21.7
28.6
27.6
28.6

Skewness
0.0
0.1
0.1
0.1
−0.1
−0.2
−0.4
−0.1
−1.1
−1.0
−1.7
−2.2
−0.3
1.6
0.3
0.5
−0.7

Kurtosis
2.9
2.8
2.9
3.3
4.4
5.4
6.0
5.4
6.1
6.1
10.8
15.4
7.6
15.0
4.6
6.7
9.7

Min
−69
−69
−77
−93
−111
−109
−110
−109
−94
−98
−148
−165
−107
−76
−89
−116
−179

Max
63
65
60
61
65
58
51
59
68
56
64
61
63
157
118
124
112

−1.6
−2.3
−2.1
−1.9
−2.2
−2.3

23.8
28.1
30.1
33.6
30.1
27.3

−0.1
0.4
1.8
1.1
0.7
1.3

7.0
6.8
16.0
12.9
12.0
11.3

−115
−127
−80
−130
−147
−80

90
133
222
227
188
181

−2.7
−2.5
−1.3
−4.2
−3.3
−2.5
−1.9

24.7
26.2
16.0
65.2
21.2
37.9
13.2

−0.1
0.0
0.7
−1.1
0.3
0.9
−0.3

3.8
3.2
4.6
9.4
3.8
8.3
4.7

−86
−85
−49
−392
−59
−110
−63

77
69
64
172
74
200
34

Federal Reserve Bank of Richmond Economic Quarterly

Mean
−2.7
−2.7
−2.5
−2.2
−2.0
−1.7
−1.7
−1.9
−2.7
−2.7
−2.6
−2.6
−1.7
−1.7
−2.4
−2.3
−2.8

224

Rate
Two-Year Treasury Note Yield at Constant Maturity
Three-Year Treasury Note Yield at Constant Maturity
Five-Year Treasury Note Yield at Constant Maturity
Seven-Year Treasury Note Yield at Constant Maturity
10-Year Treasury Note Yield at Constant Maturity
20-Year Treasury Bond Yield at Constant Maturity
30-Year Treasury Bond Yield at Constant Maturity
Long-Term Treasury Composite, Over 10 Years
One-Month Nonfinancial Commercial Paper
Three-Month Nonfinancial Commercial Paper
One-Month Financial Commercial Paper
Three-Month Financial Commercial Paper
Moody’s Seasoned Aaa Corporate Bond Yield
Moody’s Seasoned Baa Corporate Bond Yield
Citigroup Global Markets: U.S. Broad Investment Grade Bond Yield
Citigroup Global Markets: Credit (Corporate) Bond Yield
Citigroup Global Markets: Credit (Corporate) Bond Yield: AAA/AA
Citigroup Global Markets:
Credit (Corporate) Bond Yield: AAA/AA 10+ Years
Citigroup Global Markets: Credit (Corporate) Bond Yield: A
Citigroup Global Markets: Credit (Corporate) Bond Yield: BBB
Citigroup Global Markets: Credit (Corporate) Bond Yield: Finance
Citigroup Global Markets: Credit (Corporate) Bond Yield: Utility
Citigroup Global Markets: Credit (Corporate) Bond Yield: Industrial
Citigroup Global Markets:
Gov’t Sponsored Bond Yield, U.S. Agency/Supranational
Citigroup Global Markets: Gov’t Agency Bond Yield
Bond Buyer Index: State/Local Bonds, 20-Year, Genl Obligation
Auto Finance Company Interest Rates: New Car Loans
Auto Finance Company Interest Rates: Used Car Loans
Citigroup Global Markets: Mortgage Bond Yield
Home Mortgage Loans: Effective Rate, All Loans Closed

Table 5 (Continued) Monthly Changes (in Basis Points)
Std. Dev.
14.2
13.7

Skewness
−0.3
−0.3

Kurtosis
4.2
4.8

Min
−56
−67

Max
35
35

−2.1
−1.9
−1.8
−2.1
−1.3
−2.5
−2.6
−2.6
−2.6
−2.5
−2.6
−2.6
−2.6
−2.6
−2.6
−2.6
−2.6
−2.5
−2.7
−2.6
−2.6
−2.5
−2.6
−2.6
−2.6
−2.5
−2.6
−2.6
−2.6

20.6
13.7
13.3
20.6
14.5
43.1
25.2
23.3
23.6
43.3
27.1
23.4
22.8
43.0
25.5
22.9
22.8
44.2
29.1
23.5
23.0
39.8
24.6
22.9
23.4
43.5
27.0
24.0
23.9

0.5
−0.3
−0.4
0.6
0.6
−0.5
−1.5
−2.4
−2.2
−0.4
−1.1
−2.2
−1.9
−0.3
−0.8
−1.9
−1.9
−0.4
−1.0
−1.8
−1.9
−0.3
−1.1
−2.2
−2.2
−0.7
−1.0
−2.2
−2.2

4.0
4.3
5.2
4.0
4.3
5.6
9.7
13.2
12.0
5.6
7.7
11.8
10.3
5.1
6.5
9.7
10.3
5.1
6.9
9.4
10.3
6.0
6.9
11.6
11.3
7.3
6.8
11.8
10.8

−76
−55
−67
−76
−39
−165
−140
−140
−135
−180
−130
−135
−125
−140
−110
−117
−116
−153
−120
−120
−120
−145
−115
−130
−125
−225
−115
−130
−125

64
35
36
64
56
168
69
59
48
168
82
58
48
168
85
62
62
168
90
60
56
168
72
59
43
168
82
58
41

225

Mean
−2.0
−1.9

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

Rate
Purchase of Newly Built Homes: Effective Rate, All Loans
Purchase of Previously Occupied Homes: Effective Rate, All Loans
Contract Rates on Commitments:
Conventional 30-Year Mortgages, FHLMC
Purchase of New Single-Family Home: Contract Interest Rate
Purchase of Existing Single-Family Home: Contract Interest Rate
FHLMC: 30-Year Fixed-Rate Mortgages: U.S.
FHLMC: 1-Year Adjustable Rate Mortgages: U.S.
Treasury Repo - One Day
Treasury Repo - One Week
Treasury Repo - One Month
Treasury Repo - Three Months
Treasury Reverse Repo - One Day
Treasury Reverse Repo - One Week
Treasury Reverse Repo - One Month
Treasury Reverse Repo - Three Months
MBS Repo - One Day
MBS Repo - One Week
MBS Repo - One Month
MBS Repo - Three Months
MBS Reverse Repo - One Day
MBS Reverse Repo - One Week
MBS Reverse Repo - One Month
MBS Reverse Repo - Three Months
Agency Repo - One Day
Agency Repo - One Week
Agency Repo - One Month
Agency Repo - Three Months
Agency Reverse Repo - One Day
Agency Reverse Repo - One Week
Agency Reverse Repo - One Month
Agency Reverse Repo - Three Months

226

Table 6 R-Squared and Correlation of Factor Components with
Federal Funds Rate (Monthly Data)

R2
0.010
0.051
0.457
0.459
0.513
0.514
0.558
0.618
0.643
0.648
0.655
0.655
0.670
0.671
0.672
0.680
0.689
0.697
0.710
0.711
0.722
0.725
0.734
0.740
0.750

Correlation
0.750
0.772
0.595
−0.027
0.363
0.359
0.634
0.683
−0.118
0.446
0.632
0.447
0.600
0.597
0.435
0.538
0.608
0.819
0.776
0.778
0.030
0.528
0.786
0.789
0.163

Federal Reserve Bank of Richmond Economic Quarterly

Rate
Auto Finance Company Interest Rates: New Car Loans
Auto Finance Company Interest Rates: Used Car Loans
Treasury Repo - One Day
Bond Buyer Index: State/Local Bonds, 20-Year, Genl Obligation
Purchase of New Single-Family Home: Contract Interest Rate
Purchase of Newly Built Homes: Effective Rate, All Loans
Treasury Reverse Repo - One Day
Two-Month Certificate of Deposit
Moody’s Seasoned Baa Corporate Bond Yield
Purchase of Existing Single-Family Home: Contract Interest Rate
Agency Repo - One Day
Purchase of Previously Occupied Homes: Effective Rate, All Loans
MBS Repo - One Day
MBS Reverse Repo - One Day
Home Mortgage Loans: Effective Rate, All Loans Closed
FHLMC: One-Year Adjustable Rate Mortgages: U.S.
Agency Reverse Repo - One Day
U.S. Dollar: Eurocurrency Rate, Short-Term
Three-Month Treasury Bill Market Bid Yield at Constant Maturity
Three-Month Treasury Bills, Secondary Market
Citigroup Global Markets: Mortgage Bond Yield
Nine-Month Certificate of Deposit
Three-Month Treasury Bills
Agency Repo - One Week
Citigroup Global Markets: Gov’t Agency Bond Yield

Table 6 (Continued) R-Squared and Correlation of Factor Components with Federal Funds Rate (Monthly
Data)

Correlation
0.761
−0.037
0.060
0.020
0.766
0.752
0.070
0.762
0.781
−0.053
0.770
0.796
0.779
0.777
0.802
0.808
0.769
0.756
0.772
0.781
0.756
−0.042
0.788
0.066
0.163
0.730
0.733
0.485
0.738
0.793
0.638

227

R2
0.751
0.764
0.768
0.769
0.772
0.772
0.781
0.786
0.793
0.793
0.795
0.799
0.803
0.804
0.807
0.810
0.810
0.812
0.815
0.815
0.821
0.833
0.836
0.844
0.845
0.846
0.849
0.856
0.856
0.857
0.861

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

Rate
MBS Reverse Repo - One Week
Citigroup Global Markets: Credit (Corporate) Bond Yield: Utility
Citigroup Global Markets: Credit (Corporate) Bond Yield: Finance
Moody’s Seasoned Aaa Corporate Bond Yield
Treasury Repo - Three Months
Treasury Reverse Repo - One Week
30-Year Treasury Bond Yield at Constant Maturity
Agency Reverse Repo - One Week
MBS Repo - One Week
Citigroup Global Markets: Credit (Corporate) Bond Yield: BBB
Treasury Reverse Repo - Three Months
One-Month Nonfinancial Commercial Paper
Agency Repo - Three Months
Treasury Repo - One Month
MBS Reverse Repo - One Month
MBS Repo - One Month
Agency Reverse Repo - Three Months
MBS Reverse Repo - Three Months
MBS Repo - Three Months
Treasury Reverse Repo - One Month
Treasury Repo - One Week
Citigroup Global Markets: Credit (Corporate) Bond Yield: AAA/AA 10+ Years
Agency Reverse Repo - One Month
20-Year Treasury Bond Yield at Constant Maturity
Citigroup Global Markets: Gov’t Sponsored Bond Yield: U.S. Agency/Supranational
Six-Month Treasury Bill Market Bid Yield at Constant Maturity
Six-Month Treasury Bills, Secondary Market
Two-Year Treasury Note Yield at Constant Maturity
Six-Month Treasury Bills
Agency Repo - One Month
U.S. Dollar: Seven-Day Eurocurrency Rate

Table 6 (Continued) R-Squared and Correlation of Factor Components with Federal Funds Rate (Monthly
Data)

Correlation
0.640
0.207
0.076
0.204
0.074
0.400
0.715
0.572
0.754
0.543
−0.016
0.529
0.603
0.598
0.693
0.588
0.290
0.155
0.099
0.220
0.564
0.578
0.566
0.610
0.534
0.035
0.619
0.646
0.017
0.601

Federal Reserve Bank of Richmond Economic Quarterly

R2
0.866
0.868
0.870
0.870
0.873
0.873
0.882
0.886
0.886
0.888
0.889
0.892
0.894
0.897
0.898
0.901
0.902
0.907
0.912
0.913
0.916
0.917
0.926
0.934
0.934
0.936
0.937
0.938
0.939
0.948

228

Rate
One-Year Treasury Bill Yield at Constant Maturity
FHLMC: 30-Year Fixed-Rate Mortgages: U.S.
Long-Term Treasury Composite, Over 10 Years
Contract Rates on Commitments: Conventional 30-Yr Mortgages, FHLMC
Citigroup Global Markets: U.S. Broad Investment Grade Bond Yield
Three-Year Treasury Note Yield at Constant Maturity
One-Month Financial Commercial Paper
U.S. Dollar: One-Month Eurocurrency Rate
Three-Month Nonfinancial Paper
One-Month Eurodollar Deposits, London Bid
Citigroup Global Markets: Credit (Corporate) Bond Yield: Industrial
U.S. Dollar: One-Year Eurocurrency Rate
One-Month London Interbank Offer Rate: Based on U.S.$
One-Month Certificates of Deposit, Secondary Market
Three-Month Financial Commercial Paper
One-Year London Interbank Offer Rate: Based on U.S.$
Five-Year Treasury Note Yield at Constant Maturity
10-Year Treasury Note Yield at Constant Maturity
Citigroup Global Markets: Credit (Corporate) Bond Yield: AAA/AA
Seven-Year Treasury Note Yield at Constant Maturity
U.S. Dollar: Three-Month Eurocurrency Rate
U.S. Dollar: Six-Month Eurocurrency Rate
Six-Month Eurodollar Deposits, London Bid
Three-Month London Interbank Offer Rate: Based on U.S.$
Three-Month Eurodollar Deposits, London Bid
Citigroup Global Markets: Credit (Corporate) Bond Yield: A
Six-Month Certificates of Deposit, Secondary Market
Six-Month London Interbank Offer Rate: Based on U.S.$
Citigroup Global Markets: Credit (Corporate) Bond Yield
Three-Month Certificates of Deposit, Secondary Market

Reilly and Sarte: Monetary Policy and the Variation in Interest Rates

229

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