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Monetary Policy and the Term Structure
of Nominal Interest Rates: Evidence
and Theory
Charles L. Evans and David A. Marshall

Working Papers Series
Macroeconomic Issues
Research Department
Federal Reserve Bank of Chicago
December 1997 (WP-97-10)

■ 1

FEDERAL RESERVE B A N K
OF CHICAGO

Monetary Policy and the Term Structure of Nominal
Interest Rates: Evidence and Theory*
Charles L. Evans*

David A. Marshall*

November 3, 1997

Abstract

This paper explores how exogenous impulses to monetary policy affect the yield
curve for nominally risk-free bonds. We identify monetary policy shocks using three
distinct variants of the identified V A R methodology. All three approaches imply simi
lar patterns for the effect of monetary policy shocks on the term structure: A contrac
tionary policy shock induces a pronounced positive but short-lived response in short
term interest rates, with a smaller effect on medium-term rates and almost no effect on
long term rates. Because of their transitory impact, monetary policy shocks account
for a relatively small fraction of the long-run variance of interest rates. The response
of the yield curve to a monetary policy shock is unambiguously a liquidity effect rather
than an expected inflation effect. We then ask whether a dynamic stochastic equi
librium model that incorporates nominal rigidities can replicate these patterns. We
find that the limited participation model of Lucas (1990), Fuerst (1992), and Christiano and Eichenbaum (1995), is broadly consistent with the data, provided modest
adjustment costs are imposed on monetary balances available to satisfy households’
cash-in-advance constraint.

’T his paper represents the views of the authors and should not be interpreted as reflecting the views of
the Federal Reserve Bank of Chicago. We thank Marty Eichenbaum and Larry Christiano for many helpful
discussions. We thank Wendy Edelberg for superlative research assistance at an early stage of this research.
Comments are welcome.
^Federal Reserve Bank of Chicago; Research Department, RO. Box 834, Chicago, IL 60690; (312) 3225812; cevans@frbchi.org
^Federal Reserve Bank of Chicago; Research Department, RO. Box 834, Chicago, IL 60690; (312) 3225102; dmarshall@frbchi.org

1. Introduction
Monetary policy is the natural starting point for an inquiry into the economic determinants
of the nominal term structure. Bond traders and other non-academic observers often cite
monetary policy as a major factor in term structure movements.1 Academic observers have
also argued that the term structure is intimately linked to monetary policy and its goals. For
example, Bernanke and Blinder (1992), Estrella and Hardouvelis (1991), and Mishkin (1990)
explore using the spread between long-term and short-term yields as an indicator ofmonetary
policy, future economic activity and future inflation. However, empirical models of the term
structure typically used in the finance literature do not explicitly incorporate monetary
policy. Rather, they characterize the nominal term structure as driven by unobserved latent
factors. For example, Litterman and Scheinkman (1991), and Dai and Singleton (1997)
estimate three-factor models, with the factors associated with the level, slope, and curvature
of the yield curve. A n open question is whether one or more of these factors corresponds, in
part, to monetary policy shocks.
In this paper, we ask how exogenous impulses to monetary policy affect yields on zerocoupon bonds of various maturities. W e investigate the impact of these shocks on the shape
of the yield curve, as well as on term premiums, and ex ante real rates. Having documented
these empirical patterns, we ask if a dynamic stochastic equilibrium model of aggregate
economic activity can replicate the empirical patterns we find in the data. Standard equi
librium macroeconomic models have had little success at modelling the term structure.2 W e
ask whether the performance of this class of models can be improved by incorporating ex
plicit nominal rigidities. Such an inquiry is a critical step in matching financial factors with
economic determinants.
The fundamental empirical problem in assessing the effects of monetary policy shocks is
the identification problem: how to distinguish exogenous monetary policy shocks from the
endogenous response of the monetary policy instrument to other, nonmonetary, exogenous
*For example, the Wall Street Journal of December 13,1995 describes February 1994 as the month “when
the Fed began raising short-term interest rates and set off the year’s bond-market slaughter.”
2 See, for example, den Haan (1995), Backus, Gregory, and Zin (1989), and Bekaert, Hodrick, and Marshall
(1997b).

impulses. There isdisagreement in the profession on the best way to resolve this identification
problem. Rather than taking a stand on this controversy, we use three different identification
strategies that have been proposed in the literature. All are variants of the identified vector
autoregression (VAR) approach proposed by Sims (1986), Bemanke (1986), and Blanchard
and Watson (1986). In particular, we use the recursive identification strategy of Christiano,
Eichenbaum and Evans (1996a,b), the non-recursive identification strategy advocated by
Sims and Zha (1995a), and the approach of Gali (1992) that utilizes long-run restrictions as
part of the identification strategy.
While these three identification strategies have differing implications for the effect of
monetary policy shocks on real economic variables, it is interesting that their implications
for the effect of monetary policy shocks on the term structure are broadly similar. All
three strategies imply that a contractionary policy shock induces a pronounced positive,
but transitory response in short term interest rates, with a smaller effect on medium-term
rates and almost no effect on long term rates. This finding stands in contrast to the popular
opinion, often expressed in the financial press, that changes in monetary policy systematically
affect long-term bond prices.3 Our empirical results imply that the main effect of monetary
policy shocks is to shift the slope of the yield curve. Because of their transitory impact,
monetary policy shocks account for a relatively small fraction (less than 15%) of the long-run
variance of interest rates. This shock roughly corresponds to the slope factor in the models
of Litterman and Scheinkman (1991), Knez, et. al (1994), and Dai and Singleton (1997).
The response of the yield curve to a monetary policy shock is unambiguously a liquidity
effect rather than an expected inflation effect, since the response of expected future inflation
to the policy shock is opposite to the interest rate response. W e find some evidence that a
contractionary policy shock increases term premiums, at least for the shorter maturities.
Having documented these empirical patterns, we ask whether they are consistent with
a dynamic stochastic equilibrium model that incorporates nominal rigidities. W e focus on
the limited participation model suggested by Lucas (1990), Fuerst (1992), and Christiano
and Eichenbaum (1995). W e calibrate the money-growth process to the results from our
3
Of course, our empirical experiment has a precise definition. Statements about monetary policy in the
financial press undoubtedly confound monetary policy shocks and normal responses of policy to nonmonetary
shocks.

estimated VARs. The theoretical model captures the broad features found in the data. In
particular, a contractionary monetary shock causes a short-lived rise in the short-term yields,
with the response decreasing in the maturity ofthe bond. These responses are unambiguously
liquidity effects, with the real yields rising substantially more than the nominal yields. In
addition, the monetary contraction induces a rise in term premiums, which also decreases
with maturity.
Finally, a number of recent studies are related to our empirical analysis. Each of our
identification strategies have the property that the monetary authority does not respond to
developments in the bond market contemporaneously. The studies by Leeper, Sims and Zha
(1996) and Bernanke, Gertler, and Watson (1997) also maintain this assumption in their
analysis with both short and long-term interest rates. While the focus of the latter article
is on the way the monetary authority’s response function amplifies non-monetary impulses,
they report a number results that are qualitatively similar to our findings. Gordon and
Leeper (1994) and McCallum (1994), however, take the view that the monetary authority
responds contemporaneously to information conveyed in long-term interest rates.
The plan of the remainder of the paper is as follows: In section 2 we describe the three
strategies we use to identify monetary policy shocks. In section 3, we present the implica
tions of each of these strategies for the effect of monetary policy shocks on the yield curve.
Section 4 sets out the equilibrium model with limited participation constraints, describes
our calibration of the model, and compares the implications of the theoretical model to our
empirical results. Section 5 concludes.

2. Identifying monetary policy shocks
Since Sims (1980), numerous proposals have been made for identifying fundamental economic
impulses using V A R methods.4 In an attempt to characterize the facts about monetary policy
and the term structure robustly, we use three alternative strategies for identifying monetary
policy shocks. Each of the three strategies requires estimation of an identified VAR. To
4
The articles mentioned in the introduction are a small subset of the empirical literature that uses VARs to
understand economic fluctuations. Surveys by Watson (1995), Christiano, Eichenbaum, and Evans (1997b),
and Leeper, Sims, and Zha (1996) provide a fuller description of this literature.

conserve space, the discussion in this section focuses on identification issues. For a discus
sion of econometric issues in estimating these models, the reader is referred to Christiano,
Eichenbaum and Evans (1997b) and Sims and Zha (1995b).
The empirical approaches we use are: (1) a recursive strategy studied by Christiano,
Eichenbaum, and Evans (1996a, b); (2) a nonrecursive strategy studied by Sims and Zha
(1995a); and (3) a strategy which employs a combination of long-run and contemporaneous
restrictions studied by Gali (1992). Much of the literature focuses on quarterly time series
analysis, while the frequency of our data analysis is monthly. Consequently, the robust
macroaggregate responses to the three measures of monthly monetary policy shocks is of
some independent interest.

2.1. M onetary policy rules
In allof the identification strategies we use, itisassumed that the monetary policy instrument
is the federal funds rate, denoted F

F t.

W e assume that F

F t

is determined by a relationship

of the form
F F t = f ( n t ) + cret

(2.1)

In (2.1), fit is the information set available to the monetary authority at date t, / is linear
function that describes the monetary authority’s reaction to the state of the economy, and

isan exogenous shock to the monetary policy reaction function with unit variance. The policy
reaction function / incorporates the authority’s preferences regarding counter-stabilization
actions, inflation-fighting activity, and so on. The residual £ reflects random, nonsystematic
factors that affect policy decisions, such as political factors and the personalities, views and
composition of the Federal Open Market Committee.
W e will be considering in detail the responses to monetary policy shocks of bond yields
of various maturities. To insure that the shocks do not change as we move across maturities,
we exclude the bond yields from

Clt .

This requires excluding the bond yield data from the

V A R equations that describe the evolution of the macrodata. Consequently, in all of our
V A R systems, the non-yield equations include no lagged values of the yields. Of course, the
yield equation in each V A R includes lagged values of all of the V A R system’s variables.

Finally, we do not consider specifically a

T a y l o r r u le

for monetary policy in any of our

identification strategies (Taylor 1993). However, it is not possible to observe that the mone
tary policy rule is (2 .1) and be certain that it is inconsistent with a Taylor rule. To see this,
consider a simple-variant of a Taylor rule:

FFt= c*0 + yt+
a i

where

is Taylor’s output gap and

a 2E

[p{+s - pt
\0.t]+

<?£t

(2.2)

is the log price level, so the expectation in brackets

is the s-period-ahead inflation rate. Clearly, in evaluating the conditional expectation of
the s-period-ahead inflation rate, any variable which Granger-causes the inflation rate will
appear in the conditional expectation. Without substantially more structure placed on the
analysis, equations (2.1) and the reduced form implied by (2.2) are indistinguishable.

2.2. Christiano-Eichenbaum -Evans recursive identification strategy
In the Christiano, Eichenbaum, and Evans (1996b)
(denoted

flfEE)

variables. Since

(C E E )

strategy, the information set

includes all lagged variables in the system, plus certain contemporaneous
C E E

(1996b) employs monthly data, we have modified the data vector

only slightly in order to facilitate comparisons with the theoretical model in Section 4.
Specifically, the data vector is given by
where:

E M

Z CEE

(E M , P, P C O M , F F , N B R / T R ,

denotes the logarithm of nonagricultural payroll employment;

A M 2),

denotes the

logarithm of the personal consumption expenditures deflator in chain-weighted 1992 dollars;
P C O M

denotes the smoothed change in an index of sensitive materials prices; F

the federal funds rate;

N B R / T R

credit to total reserves; and A

M 2

denotes

denotes the ratio of nonborrowed reserves plus extended
denotes the log growth rate ofthe monetary aggregate M 2 .5

As Christiano, Eichenbaum, and Evans (1996a) discuss, the inclusion of commodity prices in
a recursively-identified V A R mitigates anomalous responses of the price level from monetary
policy shocks (the “price puzzle” described by Sims (1992) and Eichenbaum (1992)).
5
For all our VARs, the logged data is also multiplied by 100 so that the impulse responses can be
interpreted as percent deviations in all of our figures.

The
P

,and

C E E

monetary policy reaction function includes the contemporaneous values of E

P C O M

in Q $ E E in equation (2.1). Specifically,

F F t

and

e fEE

M ,

A i( L ) Z fJ { E +

01 E

M t

a 2P t

a 3P C O M t

c re fE E

is assumed to be orthogonal to all other right hand-side variables. This identi

fication strategy has two important properties: (1)

E M ,

P ,

and

P C O M

do not respond

contemporaneously to the monetary policy shock, and (2) all of the other variables in the
Z f EE

reSp0n(l contemporaneously to the monetary policy shock. In this sense, the iden

tification of the monetary policy shock e E E B is recursive.
The VARs were estimated over the sample period 1965:1 to 1995:12. Twelve lagged values
were estimated in each equation, with the initial lags beginning in 1964:1. Column one in
Figure 1 displays the impulse response functions for the

C E E

R e c u r s iv e

monetary policy

shocks. Monte Carlo bootstrap methods were used to compute 95% confidence bands. The
confidence bands are displayed around the point estimates of the impulse response functions,
leading to generally asymmetric error bands (as suggested by Sims and Zha 1995).
The monetary policy shock leads to a 46 basis point increase in the federal funds rate
on impact. The funds rate rises to its maximum of 58 basis points in the second month
before falling thereafter. The funds rate response, therefore, is persistent but transitory:
this response pattern holds for each of the identifications we consider. The other variable’s
responses seem consistent with most economists’ prior expectations for a monetary policy
shock. The increase in the federal funds rate occurs simultaneously with reductions in
nonborrowed reserves relative to total reserves as well as M2. Employment and the P C E
deflator are unchanged for several periods before falling persistently. Employment begins to
fall before the P C E deflator, while commodity prices fall almost from the outset. Finally, the
P C E deflator’s response is n e g lig ib ly positive for about six months. Of the three monetary
policy identifications we consider, this is the largest price puzzle in Figure 1.

2.3. Sims-Zha nonrecursive identification strategy
Sims and Zha (1995a) propose an alternative strategy for identifying monetary policy shocks
which is a nonrecursive scheme. In their analysis, the monetary authority’s information
set (denoted fif2) includes all lagged variables in the system, plus certain contemporane
ous variables. Sims and Zha’s empirical analysis used quarterly data. W e use monthly
analogues to their quarterly data series. Specifically, our data vector is given by
(P c m , A T R , F F , P im , P , W , Y ) ,
A T R

where:

P e rn

denotes the log of intermediate goods prices;
Y

denotes the logarithm of crude materials prices;

denotes the log growth rate of total reserves; F

denotes the log of the real wage; and

Z sz

denotes the federal funds rate; P i m

denotes the log of the P C E deflator;

denotes the log of real G D P .6 When Sims and Zha

analyze the federal funds rate as the monetary policy instrument, they select total reserves
to be the monetary aggregate in the analysis. Our analysis follows their variable selection.7
The
and

A T R

monetary policy reaction function includes the contemporaneous values of P c m

in fl f z in equation (2.1). Specifically,

FFf

A\(L)Zf3i + OL\Pcmt + GL2 A T

(2.3)

(j e ^z .

The Sims-Zha strategy isnonrecursive, because e f z isallowed to be correlated with P c m t and
A T R t.

(That is, P c m t and A T

R t

are allowed to respond contemporaneously to a monetary

policy shock.) This correlation implies that

e fz

cannot be recovered as the residual from

an OLS regression. Furthermore, Sims and Zha’s system of equations does not possess any
predetermined variables which can be used as instruments for P c m

and

A T R t

in equation

(2.3). This leads Sims and Zha to full-information estimation methods.
For the remainder of this subsection, let e refer to the vector of structural (SZ) shocks,
6Our real GDP data is interpolated (from Leeper, Sims and Zha (1996)). Sims and Zha used the quarterly
GDP implicit deflator; our use of the PCE deflator is consistent with their choice of a price index with timevarying commodity bundle weights. In all nonrecursive cases we considered, using the PCE deflator resulted
in fewer price puzzles than LSZ’s preferred use of the CPI.
7
We also considered VARs with A M 2 in place of A T R , and the results were similar to the responses
reported in figure 1 .

and

refers to the vector of VAR innovations. That is,

A (L )Z fz

where A ( - ) denotes the matrix polynomial of V A R coefficients. Sims and Zha assume that e
and

are related via a linear transformation

£ t = B 0U t,

where Bo is a square nonsingular matrix. To achieve identification of the S Z monetary policy
shock £ m p i we follow Sims and Zha relatively closely in specifying the B

£Pcm
£m d
£m p
£Pi m
£p
£w/p
Ey
£yield

B n B\2
0 B22
Bz\ B32
Ba 0
B51 0
B qi 0
B71 0
B&i B s 2

B\z B u B 1 5 Bie
Bzz 0 B 2 5 0
Bzz 0 0 0
0 B u B45 B 4 &
0
0 B 5 5 B 5q
0
0
0 Bee

Bn
B27

B47 0
B57 0
Be7 0
0
0
0 B77
0
0
Bzz B&4 B z z B&e B z 7 Bzz

matrix:

UPcm
Utr
Upp
Upim
Up
V-w/p
Uy
Uyield

W e depart from Sims and Zha by excluding personal bankruptcies from the VAR. The first
row indicates that

P e rn

is an

i n f o r m a t i o n v a r ia b le

in the economy (other than the yield shock

£yieid)-

and responds to all structural shocks £
The second row is a money demand

relationship. Our estimation constrains the coefficients on
sign, while

and

u tr

and

u r f

to have the same

u p have opposite signs from u TR.8 The third row is the monetary policy

8These sign restrictions insure that the interest elasticity of money demand is negative, the output

reaction function. Rows four through seven indicate that
the monetary policy shock on impact
on P cm .

P im , P ,

it/, and

respond to

o n ly in d ir e c t ly th ro u g h th e e ffe c t o f m o n e t a r y p o l i c y

Finally, in order to maintain the same identification of monetary policy in each

of our VARs, the yields are influenced by all the other variables but influence no variables
themselves.
The VARs were estimated over the sample period 1964:7 to 1995:12. Six lagged values
were estimated in each equation, with the initial lags beginning in 1964:1. Column two
in Figure 1 displays the impulse response functions for the

monetary policy shocks.

Following Sims and Zha (1995a), Bayesian Monte Carlo methods were used to compute 95%
confidence bands. The confidence bands are displayed around the point estimates of the
impulse response functions, leading to generally asymmetric error bands.
The

monetary policy shock leads to a 50 basis point increase in the funds rate on

impact, rising to 64 basis points in the second period. As with the

C E E

case, the funds rate

falls thereafter. Total reserves fall over this period, although the initial response is close to
zero. Prices fall on impact, with the response larger for crude materials prices and smallest
for the P C E deflator. Real G D P and wages rise negligibly and insignificantly for the first
five months before falling. Broadly speaking, these responses are qualitatively similar to
the recursive results, although there is greater uncertainty as measured by the confidence
bounds.

2.4. G ali id en tificatio n strategy using long-run restrictions
Gali (1992) uses an alternative identification strategy which imposes a mixture of long-run
restrictions and contemporaneous impact restrictions to identify four economic shocks, one
of which is a monetary policy shock. Gali’s empirical analysis used quarterly data, while
our analysis uses monthly data. The monetary policy reaction function can be represented
by equation (2 .1). Specifically, we follow Gali in considering a four-variable autoregression.
The data vector is given by
log difference of GDP;

F F

Z G = (A Y , F F , F F

— A P,

A M

denotes the federal funds rate; F

— A P ),
F — A P

where:

A Y

denotes the

denotes the real interest

elasticity of money demand is positive, and that the price elasticity of demand for nominal balances is
positive.

rate where A P is the log difference of the CPI; and A M — A P denotes real M l balances.
To maintain comparability with the other procedures, we use the level of the federal funds
rate. (Gali used the first difference of the interest rate.) Since Gali’s data is quarterly, we
use the Leeper-Sims-Zha monthly data set for monthly GDP, fed funds rate, CPI and M l .9
Gali’s monetary policy reaction function can be represented as

F F t

and

e f

= A

{ L ) Z f _ l + a xA Y t

a 2{ F F t

is potentially correlated with time

- A

P t)

a 3( A M t

- A P t) +

a e f

(2.4)

variables (like the Sims-Zha system). Identifi

cation is achieved with six restrictions on the covariance structure of the innovations. To
understand Gali’s identifying restrictions, we must provide the other three structural shocks
with economic labels: supply shock, money demand shock, and IS shock. Gali’s restric
tions can be described as follows. First, the monetary policy, money demand and IS shocks
have no long-run effect on output; these restrictions identify the supply shock. Second,
the monetary policy and money demand shocks have no contemporaneous effect on output;
knowledge of the supply shock and these two restrictions identifies the IS shock. Third,
one additional identifying restriction is necessary to identify the remaining two shocks. One
of the restrictions that Gali considers deletes the price data from the monetary authority’s
contemporaneous information set. In equation (2.4), this imposes the coefficient restriction
that <*2 = — 03,leaving only two contemporaneous coefficients to estimate with two available
instruments (the supply and IS shocks). This identifies the monetary policy shock.10
The VARs were estimated over the sample period 1964:8 to 1995:12. Six lagged values
were estimated in each equation, with the initial lags beginning in 1964:2.11 Column three in
9We follow Gali in using the CPI rather than the PCE deflator for two reasons. First, Gali conducted
several sets of unit root and cointegration tests in order to justify his data transformations. Consequently,
we used his P and M l to maintain comparability. Second, the CPI data system delivered more plausible
impulse response functions for most of the shocks than the PCE deflator data system. Since the CPI does
not get revised, its stochastic trend properties may be more consistent with Gali’s unit root assumptions.
10 Gali (1992) alternatively considers: (1 ) deleting only output from the contemporaneous information set
of the monetary authority, and (2 ) explicitly imposing a homogeneity restriction on the money demand
equation in his structural VAR. Gali reported that his results were largely robust across these alternative
identification restrictions, and our implementation of these restrictions also produced qualitatively similar
results.
11 “Double-differencing” to impose the long-run restrictions in identifying the supply shock uses up the

Figure 1 displays the impulse response functions for the G a l i monetary policy shocks. Monte
Carlo bootstrap methods were used to compute 95% confidence bands. The confidence bands
are displayed around the point estimates of the impulse response functions.
The

G a li

monetary policy shock increases the federal funds rate on impact by 41 basis

points. In the second period it increases by 53 basis points, and falls thereafter. M l growth
falls during this period, indicating a liquidity effect. As with the

policy shock, the price

level falls on impact and declines further after about six months. As with the

C E E

policy

shock, real activity (as measured by monthly real GDP) is about flat for four months and
then falls.

3. The response of bond yields to exogenous monetary policy shocks
3.1. Im pulse responses
Figure 2 plots the estimated responses of bond yields to a one-standard-deviation contrac
tionary monetary policy shock. Bond yields are measured as continuously-compounded an
nualized returns on zero-coupon bonds. The yields from 1959:01 -1991:02 are monthly data
taken from McCulloch and Kwon (1993). For the period 1991:03 - 1995:12, we use yields
computed by Robert Bliss using the McCulloch/Kwon procedure. (See Bliss (1994).)*
12 The
solid lines give the point estimates of the impulse responses; the upper and lower dashed
lines give the boundaries of the 95% confidence region. The plots trace the responses over 24
months. Each of these responses is measured in percent deviation from the non-stochastic
steady state. W e display the responses for bond maturities of one month, six months, one
year, 3 years, and 10 years. According to all three of the identification strategies, the policy
shock increases the one-month rate by approximately 20 basis points in the period when
the shock occurs. This response is statistically significant in each case. The one-month
additional lag beginning in 1964:1.
12 McCulloch and Kwon’s (1993) data on zero-coupon bond yields are derived from a tax-adjusted cubic
spline discount function, as described in McCulloch (1975). A more detailed explanation can be found in
McCulloch and Kwon (1993). Unlike McCulloch and Kwon (1993), Bliss (1994) does not tax-adjust the
bond yields. However, under the current tax code, the requisite tax-adjustment in the McCulloch-Kwon
procedure is negligible. From 1987:01 through 1991:02 (the last date where we have an overlap between the
two data sets), the McCulloch/Kwon data and the Bliss data are virtually identical.

rate continues to climb in the following month, and then falls rapidly, with the effect of
the shock insignificant after 6 months. The six-month and the twelve-month rates display
qualitatively similar response patterns, although the magnitude of the response decreases for
the longer-term bonds. When we move to even longer-term bonds, the initial effect dimin
ishes substantially as maturity increases: The initial response of the three-year bond is only
around 9 basis points, falling to less than 5 basis points for the 10 year bonds. The initial
response for this last bond is significant (barely) for only the C E E identification. (Under the
C E E identification, we found that the response to a federal-funds shock of all bonds longer
than 13 years is insignificant at the 5% marginal significance level.) The main qualitative
discrepancy among the three identification strategies is that the bond yield responses die
off somewhat more slowly in the SZ identification than either in the C E E or the Gali iden
tifications. Interestingly, these results are roughly comparable to Cook and Hahn’s (1989)
estimates of the effects on interest rates after a publicly announced change in the federal
funds rate. They find that in response to a 100 basis point increase, short rates rise about
50 basis points, while long rates rise about 10 basis points.
The results are straightforward: There is a significant, relatively large, but relatively
short-lived effect on the short rates, with a decreasing and less significant effect at longer
maturities. In other words, there is not a parallel upwards shift of the term structure in
response to these monetary policy shocks; rather, the shock causes the yield curve to flatten.
A n alternative way to portray these patterns is to look at the effect of a monetary shock
on the shape of the yield curve. One way to summarize this shape is to take a quadratic
approximation of the yield curve at each date. W e do so by regressing all interest rates
at a given date on a constant, maturity, and squared maturity, and treating the parameter
estimates (denoted

i n t e r c e p t , s lo p e ,

and

cu rv a tu re

respectively) as the coefficients of this

quadratic approximation. (Note that these coefficients are time-varying, since the regression
only involves interest rates at a given date, and is re-estimated anew each month.) To
portray the way the shape of the yield curve responds to a monetary shock, we estimate
VARs, analogous to those described above, in which the interest rate is replaced by one of
these three coefficients.
The resulting impulse responses are displayed in Figure 3. A monetary shock raises

the level of the yield curve, decreases the slope, and reduces the curvature. (The positive
response of c u r v a t u r e denotes a reduction in curvature because the average yield curve is
concave, so the average value of c u r v a t u r e is negative.) The positive response of le v e l looks
very much like the response of the one-month interest rate. In the C E E identification, this
response becomes insignificant in about 6 months. The effects on

s lo p e

and

cu rv a tu re

are

significant only for the first four months.

3.2. Variance decompositions
The impulse responses suggest that monetary policy is an important determinant of short
run interest-rate variability, at least for the shorter-term rates. To study this question
directly, consider the variance decompositions displayed in Table 1. The table gives the
point estimates of the fraction of the one-month ahead, six-month ahead, and 24-month
ahead conditional variance of five bond yields attributable to the monetary policy shock, as
identified by each of the three identification strategies. According to this table, monetary
policy shocks account for 17% - 18% of the six-month ahead conditional variance of the
one-month interest rate. The fraction of the six-month ahead variance accounted for by the
monetary policy shock decreases sharply with maturity. It isstill non-trivial for the one-year
interest rate (9% - 11%), but rapidly becomes negligible as maturity lengthens.
The 24-month ahead conditional variance can be interpreted as a proxy for the uncon
ditional interest rate variance. According to the C E E and Gali identifications, monetary
policy shocks account for a relatively smaller fraction of long-run variance of interest rates
(Around 7% for the one-month rate, less for the longer-term rates). This reflects the rapid
decay in the impulse responses implied by these identification strategies. The SZ identifica
tion attributes somewhat more of the long-run variance to monetary policy shocks, due to
the greater persistence of the impulse responses implied by that identification strategy.
The impulse responses and variance decompositions suggest that the monetary policy
shock resembles the “slope” factor identified in the finance literature. In particular, Litterman and Scheinkman (1991) and Dai and Singleton (1997) estimate factor models of the
term structure in which the three factors shift the level, slope, and curvature of the yield
curve, respectively. Litterman and Scheinkman (1991) find that the level factor accounts

for about 90% of the unconditional variability of yields across the maturity spectrum, with
the slope factor accounting for most of the rest. However, Dai and Singleton (1997) note
that the slope factor accounts for a good deal of the short-run variability of the short-term
interest rate. The slope factor is less important for the unconditional variability because it
has only a transitory impact, with a half lifeof about 4 months. (In contrast, the level factor
induces more persistent responses in the yield curve. The half-life of a level-factor impulse is
estimated at approximately 4 1/2 years.) All of these characteristics correspond closely our
result for the monetary policy shock. One might conjecture that the slope factor identified
by Litterman and Scheinkman (1991) and Dai and Singleton (1997) is, in part, driven by
monetary policy.

3.3. Term prem ium s
Monetary policy shocks could affect longer rates either through their effect on expected future
short rates or by affecting term premiums. To distinguish between these two alternatives, let
B ?

denote the T-period continuously-compounded bond yield, and let us define the T-period

term premium,

T P ?,

by
T P J

= fl? - i £
1 t=0

E tH u

(3.1)

That is, the term premium is the difference between the T-period interest rate H ? and the
average of expected future 1-period interest rates over the next T periods. The expecta
tions theory of the term structure is the hypothesis that term premiums are time-invariant.
It can be shown (see Bekaert, Hodrick, and Marshall (1997a)) that the expectations hy
pothesis is equivalent to the hypothesis that the intertemporal marginal rate of substitution
in nominal wealth is conditionally homoskedastic, in the strong sense that

a ll

conditional

higher moments are time-invariant. Of course, the expectations theory has been rejected
decisively in US data,13 so, empirically, T

P ?

varies through time. It is of interest, therefore,

to see whether monetary policy shocks affect longer yields primarily through their effect
13 However, the expectations theory fares far better in other countries. For example, the expectations
theory cannot be rejected using data from the UK, and the rejections are far less decisive with German data.
See Bekaert, Hodrick, and Marshall (1997a), Hardouvelis (1994), Jorion and Mishkin (1991).

on expected future short yields, or whether they directly affect term premiums. This is an
important issue in its own right, and it may serve to indirectly inform us about the way
monetary policy affects the elusive intertemporal marginal rate of substitution in wealth.
To help understand the sources of time-variation in term premiums, we compute the
response of T

P j

to the monetary policy shock in our model as the difference between the

contemporaneous response of R

and the average of the first T -step responses

of R}.

Figure 3, we display these responses, along with the 95% confidence intervals, for T = 6
months through 3 years.14 For all three identification strategies, the point estimates imply
that the six-month term premium responds positively to a contractionary monetary policy
shock, with the maximal response of approximately 10 basis points occurring between two
and five months after the initial impulse. However, the significance of these estimates is
questionable: The maximal response barely creeps into significance for the C E E and Gali
identifications. For the longer maturities, the C E E identification implies a significant and
rather long-lived term premium response. For example, the 12-month term premium rises
to 12 basis points after one year. However, these responses are not found in the other
identification strategies. W e conclude that the evidence for longer term premium responses
is decidedly mixed.

3.4. Real yields, and expected in fla tio n premiums
According to Figures 1 and 2, nominal bond yields and inflation move in opposite directions
in response to a monetary policy shock, so the nominal yield response clearly represents a
liquidity effect, rather than an expected inflation effect. To quantify the magnitude of this
liquidity effect, we compute the response of the real T-month yield to the monetary policy
shock. W e do so by subtracting from the

i th

response of the T-month nominal yield the

average (annualized) inflation response from step i + 1 to step i

+ T.

These computations are

displayed in Figure 4 for T = 6 month through 3 years. According to all three identification
14To estimate the response of term premia, we must estimate a 7-variable VAR, including both the 1-mont
interest rate and the T-period rate. It is problematical to perform this exercise for the longer interest rates,
since it involves summing the first T responses of the long interest rate. In the case of the 10-year rate, for
example, we would have to sum the first 120 responses. We have little confidence in the point estimates over
this long a horizon.

strategies, real yields respond significantly to monetary policy shocks for all maturities dis
played. Notably, both the C E E and Gali identifications imply that the positive response of
the 12-month and 3-year real yields is economically meaningful (about 20 basis points) and
highly persistent, remaining statistically significant for a year or more. (The point estimates
from the SZ identification tell a similar story, although the confidence bands are much wider
for this identification strategy.)

4. Can a dynamic equilibrium model replicate these patterns?
The empirical results for each of the three identification strategies are remarkably similar. A
contractionary monetary shock causes a substantial rise in short-term nominal yields, with a
progressively smaller response as the bond maturity is lengthened. This in turn flattens the
slope and curvature of the yield curve. These responses are rather transient, fully dissipating
between six months and one year. They represent pure liquidity effects: The responses of
real yields are significant, and generally exceed the response of the nominal yields. There is
some evidence that term premiums also respond positively, at least for the shorter yields.
W e now ask whether these patterns are consistent with a dynamic equilibrium of rational
agents. To answer this question, we study the implications for the term structure of nom
inal interest rates of a class of dynamic models that incorporate the limited participation
assumption introduced in Lucas (1990) and studied in Fuerst (1992) and Christiano and
Eichenbaum (1995). The benchmark model we use is a variant of the model analyzed in
Christiano, Eichenbaum, and Evans (1997c). The nominal rigidity in this class of models
is that households must decide how much cash (denoted
b e fo re

“ Q t ') to

use in the goods market

the monetary policy shock is revealed. Furthermore, it is assumed that Q

cannot be

adjusted without cost. Rather, there is a cost in leisure time that must be paid whenever
consumption money is changed from period to period. This adjustment cost allows real
effects of a monetary policy shock to be propagate dynamically through time. The following
is a brief description of the model. (See Christiano, Eichenbaum, and Evans (1997c) for a
more detailed description.)

4 .1 . B a s i c S e t - u p

There are three types of entities: households, firms, and a financial intermediary, plus a
government whose sole function is to create money. The households own the firms and
the financial intermediary, so all profits from these entities are paid to the households.
Households’ purchases of consumption and new capital are subject to a cash-in-advance
constraint, to be described below.
Since the focus of this paper is on the effects of monetary policy, we assume that, unlike
the empirical models of section 2, monetary policy is the only source of randomness in this
economy. Each period, the government injects a quantity of money

X t

as a transfer to

the financial intermediary. The total quantity of money in the economy evolves according
to

M t+i

M t

X t.

For convenience in calibrating the model to the impulse responses

described above in section 3, we assume that net money growth

— 1 evolves

as a stationary moving average process:

X t

+ 90e t

6 \ £ t —l

@ 2 £ t—2

@ z £ t—3

9 ± £ t —4

(4.1)

where x denotes the nonstochastic steady state rate of money growth, and {e(} is a sequence
of i.i.d. standard normal shocks. Equation (4.1) is an exogenous monetary policy rule, while
equation (2 .1) is an endogenous monetary policy rule. Notice that the monetary authority
could be using (2.1) to set the federal funds rate and yet the Wold representation for money
growth would be a moving average of current and lagged exogenous shocks, as approximated
by the finite-order M A in (4.1). The observational equivalence of these rules allows us to
estimate an endogenous monetary policy rule from the data, and then use the equivalent
exogenous policy rule as the driving process in the model. The {0i}*=o coefficients in (4.1)
are computed directly as the impulse response coefficients from row four in Figure l.15 In all
cases we truncate the M A process at an MA(4). As the confidence bands in Figure 1 show,
this truncation seems reasonable.
15 Recall

that the log money growth data has been scaled up by a factor of 100.

4 .2 . H o u s e h o ld s

The representative household’s choice variables in period
cash set aside for purchases

Q t,

money

M t+ 1, capital K t+i ,

bonds with maximum maturity of n periods, denoted

^B3
tj

are: consumption

C t,

labor

L t,

and a portfolio of zero-coupon
^ In this notation B { denotes

a bond purchased at date t paying one dollar at the end of date t

+ j — 1.

The household

takes as given the nominal rental rate on capital, rf,the dollar price bj. of a bond maturing
at the end of period t +
W t

and

— 1,as well as the dollar prices of labor and consumption goods,

P t.

The timing is as follows: At the beginning of period t, the household carries over from
the end of the previous period

M t, K

t, and bonds of maturities 2 through n

(One-period bonds purchased in period

— 1 pay off at the end of period

— 1.) Before

the monetary policy shock in period t is revealed, the household must set aside Q

dollars

to finance purchases subject to the cash-in-advance constraint. The household takes its
remaining financial assets (money holdings

M t

—

and holdings of zero-coupon bonds) to

the financial intermediary. The monetary policy in period t is then revealed. Having seen the
shock, the household rebalances its portfolio by purchasing from the intermediary bonds of
maturities 1 through n. The portfolio constraint facing the household in these transactions
is:.16
(4.2)
j =i

i=2

The household then rents its capital K
a firm for nominal wage

W t-

at nominal rental rate r t and sells its labor L t to

It is assumed that wages are paid in money that can be used

immediately for purchases of consumption and new capital. The cash-in-advance constraint
can therefore be written:

Pt {Ct

( K t+1

- (1 -

6 ) K t)) < Q t + W tL t .

(4.3)

where 6 denotes the capital depreciation rate. Finally, at the end of the period, the firm pays6
1
16As long as b\ < 1 (equivalently, the one-period net nominal interest rate is positive), the household sells
its entire money holdings (net of Qt) to the intermediary.

out all profits to the household as a dividend D t, and the financial intermediary redeems all
maturing bonds B } and pays out all of its profits to the household as a dividend F t . The
flow budget constraint for nominal household wealth can therefore be written:

M t+ i

< F t + D t + B \ + T tK t + Q t + W t L t — P t ( C t + (-Kt+i —(1 —$ ) K t ) ) ■

(4-4)

Let H t denote the time cost of adjusting Q . This adjustment cost is assumed to have the
following form:

Ht = H

+ exp

c( ^ " i_x

'_ Q t_

(4.5)

— l— X

,Q t-1

- 2} ’

where x (the steady state growth rate of money in equation (4.1)) is the net growth rate in
Qt

in a nonstochastic steady state.
In period t, the household chooses C t , Q t, L t, Mi+1, K t+ i, and jl?* | _i to maximize
OO
E - i ^ 2 f t U (Ct , L t , H t )
t =o

subject to (4.2), (4.3), and (4.4), where

U (C ,L ,H )

(.L + H f

+v,)

(1-7)
/(I ~7)-

(4-6)

This utility function has the property that the income effect on leisure is zero. Everything
else equal, this tends to magnify the output response from a monetary shock. Intuitively,
the household’s labor supply does not decrease when money expands. Parameter ijj is the
inverse of the elasticity of labor supply. Parameter 7 is a curvature parameter that affects the
household’s degree of risk aversion. Parameter ipo is purely a scaling parameter. Households
make all date t choices except one as functions of information known at date t and earlier.
The exception, Q t , is restricted to be a function of date t — 1 and earlier information only.

This informational constraint on Q t reflects the limited-participation feature of the model.
Both the informational restriction on the choice of Q t and the cost of adjusting Q t can be
interpreted as ways of capturing, in a representative-agent model, more fundamental microeconomic frictions affecting household portfolio adjustment. For example, Caballero (1993),
Marshall and Parekh (1994), and Schroder (1995) show that extremely small fixed costs of
adjusting an economic choice variable at the individual level can imply extremely sluggish
behavior of the corresponding macroeconomic aggregate. Even small costs of portfolio ad
justment can imply a sluggish response of the aggregate household portfolio to monetary
policy shocks. Unfortunately, it is extremely difficult to formulate dynamic equilibrium
models with cross-sectional heterogeneity that explicitly incorporate fixed adjustment costs.
(The models of Caballero (1993), Marshall and Parekh (1994), and Schroder (1995) are all
partial equilibrium models.) Our formulation is an attempt to incorporate these effects into
an equilibrium model in a tractable fashion.

4.3. Firms

We adopt a Blanchard-Kiyotaki (1987) type of monopolist competition framework. At time
t,

a final consumption good, Yt , is produced by a perfectly competitive firm. It does so by

combining a continuum of intermediate goods, indexed by * € (0 , 1), using the technology:

(4.7)

Yt =

where 1 < fi < oo and Yu denotes the time t input of intermediate good i . 17 Let P t and
P it

denote the time t price of the consumption good and intermediate good i, respectively.

Profit maximization implies the Euler equation:

=
\ P j

Yt '

(4.8)

17The model with competitive identical firms is a special case of this model in which \i is set to unity. This
monopolistic competition paradigm is typically adopted in limited participation models because it implies a
larger output response and a more realistic investment response to monetary policy shocks. However, the
responses of bond yields change very little when fi is set to unity.

Integrating (4.8) and imposing (4.7), we obtain the following relationship between the price
of the final good and the price of the intermediate goods:

Pt =

(4.9)

r rr ' p ; r d i

[Jo

Intermediate good i is produced by a monopolist who uses the following technology:

K % i\ r -

K ° i L ) r > </,

(4.10)

Y it = <

where 0 < a < 1. Here,
i th

and

o th e r w is e
Ku

denote time

labor and capital used to produce the

intermediate good. The parameter (j> denotes a fixed cost of production. We rule out

entry and exit into the production of intermediate good i. Intermediate firms rent capital
and labor in perfectly competitive factor markets. Economic profits are distributed to the
firms’ owner, the representative household.
The firm’s choices are affected by monetary policy through a cash-in-advance constraint.
Firms retain no cash from period to period, but workers must be paid in advance of produc
tion. As a result, firms need to borrow their wage bill, W tL it, from the financial intermediary
at the beginning of the period. Repayment occurs at the end of time period

at the gross

interest rate, R t . Given that the firm’s only source of finance is through the financial inter
mediary, this feature of the model is one possible articulation of the credit channel in the
monetary transmission mechanism.
Profit maximization leads the intermediate good firm to set its price equal to a constant
markup over marginal cost:
P it

implying
W tR t
Pt

where

f^ t

= (1 —a) (K

it/ L i t ) a

_ fL,t

_ fn ,t

(4.11)

/JL

is the marginal product of labor and

fx ,t

a ( L it/ K i t )^

is the marginal product of capital; and we have imposed the equilibrium condition, Pit = Pt

for all z.18 Note that, in equation (4.11), the nominal interest rate R t is determined in part by
the marginal product of la b o r. This reflects the cash-in-advance constraint on labor inputs,
described above. In equilibrium, all intermediate goods firms choose the same labor and
capital combinations, so we henceforth drop the i subscript.

4.4. Financial Intermediary
At time

a perfectly competitive financial intermediary buys and sells bonds with the

household at prices

l?t , j

—

1,...,n. The net amount of funds transferred from households

to the financial intermediary is M
injection, X

t — Q t-

The intermediary also receives a lump sum cash

from the monetary authority. These funds are supplied to the login market at

the gross interest rate

R t.

Demand in the loan market comes from the intermediary good

producers, who seek to finance their wage bill, W tL

Clearing in the loan market requires:

(4.12)

W tL t = M t - Q t + X t .

At the end of the period the intermediary pays off all maturing bonds

to households, and

distributes its profits (revenue from loan repayments minus the cost of paying off maturing
bonds) to households as a dividend F t :

F t

R tW tL t

B\.

The assumption of perfect competition insures that the nominal return earned by the house
hold on one-period bonds equals R t ,the nominal return earned by the intermediary from its
18In deriving equation (4.11), we also use the following characterization of the marginal cost of the inter
mediate good firm:
1
/ T \ a
1 / PC \
a)

u )

one-period loans to the firms. That is,

(4.13)

* 4
4.5. Equilibrium
Let At, ut , and

denote the Lagrange multipliers associated with constraints (4.2), (4.3),

and (4.4), respectively. The first-order conditions of the household are:
For Q

—“ —P U H it+i H ft+1

E t-i

■+ v t + £,t +

(4.14)

= o.

For L

t:
U L ,t + ( v t + Z t) W i =

(4.15)

For C t :
U c ,t

For K

iy t

(4.16)

it ) P t -

t + i:

Z t) P t ( K t+1 -

(1 -

S ) K t) = 0 E k

{^t+1rt+i +

(ut+ l

+ em)^+i(l ~

S )}

(4.17)

For M t+i:
Zt = /3 E t { At+i } .

(4.18)

At6j = 6

(4-19)

X M = 0 E t { X t+ 1b i ~ l } .

(4.20)

For B \ :

For B \ ,j

= 2 ,...,n:

Notice that the conditional expectation in equation (4.14) is with respect to period

— 1

information. This reflects the limited participation feature of the model. Using equations
(4.16) and (4.18) we can eliminate multipliers v t and £t. W e can then use equations (4.11)
and (4.13) to obtain the following equilibrium conditions:

E t -1

{At} —

(3U h ,,£-hlH 't+ 1

E t~ i
-

U c,t

Q t+ i

U c ,t

(4.21)

= P E k |/5A(+2^ i i P t +i + Uc,t+ i(l - 6 )

£1*

J"
+

(4.22)

W tR t

f L<t

f K ,t

X tH

1,... , n

j =

0 j E t { \ t+ j},

(4.23)
(4.24)

Equation (4.24) implies that the marginal utility of nominal wealth is At, and the in
tertemporal marginal rate of substitution (IMRS) in nominal wealth is

. This IMUS

determines the bond yield of maturity j , denoted K [ , according to

, r^At+J-

(4.25)

p i

The behavior of the term structure is therefore determined by the stochastic process for
At. Using (4.13), (4.21), (4.22), (4.23), and (4.24) evaluated at j = 1,we obtain the following
expression for At as a function of the processes for quantity variables:

At —

P (1 -

E t

ju^t+i^+i^- -

p u H)t+2m .

lQt

In the absence of adjustment costs on Q t (that is, ifH

Q t+ 2
Qhi

' =

U c ,t+ 1

(4.26)

0), equation (4.21) implies that the

conditional expectation of Atissimply the expected marginal utility of nominal consumption,
as in the standard model. The marginal product of labor enters equation (4.26) due to the
cash-in-advance constraint faced by the firms on labor inputs.
Note that the model can be solved recursively. According to (4.26), At is a function only
of quantity variables, whose determination does not depend on

\ t o r R%.

Therefore, bond

yields can be computed by first solving for the laws of motion of aggregate quantities, using
techniques standard in the equilibrium business cycle literature, and then using (4.25) and
(4.26) to compute

R f . Details of the solution procedure

we use can be found in the technical

appendix.

4.6. Calibration
In choosing parameters for the model, we adhere closely to the equilibrium business cycle
literature. First, we choose a ,

a = 0.36,

(3,

7 ,ip,

/3 = 1.03-(1/12), 7 = 1,

p , 6,

and

ip = 2 / 3 ,

as follows:

= 1.40,

5-0.00667,

= 0.00667.

The values of a (capital’s share in the Cobb-Douglas production technology), (3 (the monthly
subjective discount factor) and 8 (the monthly capital depreciation rate) are standard choices.
The value of 7 implies a logarithmic specification in (4.6). The value of x implies a yearly
monetary growth rate of 8%. The wage elasticity of labor supply in this model is 1/ ip , so
our choice of ip implies a labor supply elasticity of 1.5. This value is somewhat higher than
most microeconomic estimates (for example, Card (1991), Killingsworth (1983) and Pencavel
(1986), estimate elasticities near zero for males; whereas it is in the range of 0.5 to 1.5 for
females, Killingsworth and Heckman (1986)). However, the implied labor supply elasticity
in most real business cycle models substantially exceeds the value we use (for example,
Christiano and Eichenbaum’s (1992) model parameter estimates imply a Frisch labor supply
elasticity in excess of 5.0). The markup parameter p is at the high end of the range used in
the literature. Rotemberg and Woodford (1995) survey the evidence on markups and select
a markup of this size.

W e set ipQ to imply that in nonstochastic steady state, employment is unity. (This is a
normalization that is without loss of generality.) In particular, we set
a

(3 (1 - a )

//(1 +

) /i(l +

1—a

a(3
x)

- 1

Our calibration implies that ipo = 2.95 . W e set the fixed cost (j> to imply that pure profits
are zero in nonstochastic steady state, as follows:

* = \ r ) Ka’

where

(427)

denotes the nonstochastic steady state stock of capital. Our calibration implies

that K = 181.45, so <(>= 1.86.19
There is no literature to draw on in choosing values for the adjustment cost parameters
c and
and

H '

Furthermore, the adjustment cost function

(•) is constructed so that both

are zero in the nonstochastic steady state, so steady state properties cannot be used

to calibrate c and

In our baseline calibration we choose c and

to imply a reasonable

response of the one-month interest rate to a monetary policy shock. In particular, we set
c = 2 and

= 1. Finally, we choose the coefficients {#i}^=0 in the money growth rule (4.1)

to match the response of the monetary aggregate to a policy shock (as described in section
4.1). The three sets of values are given in Table 2.

4.7. Implications of the model
4.7.1. Macroeconomic variables
Figure 5 displays responses of various macroeconomic aggregates other than the bond yields
to a one-standard-deviation monetary contraction. These responses are qualitatively similar
to the empirical responses displayed in Figure 1, and often correspond quantitatively as
19Equation (4.27) implies that the ratio of the fixed cost <p to the steady state output level is \x —1. Our
parameterization therefore implies that, on average, 40% of output goes to pay the fixed cost.

well.20 The money growth process is displayed in row four of Figure 5 and by construction is
identical to the first five coefficients of the impulse response functions in row four of Figure 1.
Depending on the calibration of the M A process, the price level declines to a level between
20% and 30% below the steady state. By comparison, the price responses in Figure 1 range
between 15% (in the C E E identification to 50% (in the Gali identification). However, these
empirical responses do not appear to have attained the new steady state after 24 months,
while the price response in the model is close to the new steady state after 8 months.
As in the empirical results, the output level in the model declines in response to a
contractionary monetary policy shock. However, the response in the model is both smaller in
magnitude and less persistent than in the data. In particular, the maximal output responses
in the model variants is a decline of about 0.045%, as compared to a decline of around 0.2%
in the empirical exercises. Furthermore, the maximal response in the model is after three or
four months, with the effect of the shock largely dissipated after 10 months. In contrast, the
point estimates in allthree empirical exercises show a sustained response even after 24 months
(although this long-lived response is significant only for the C E E identification). As noted
by Christiano, Eichenbaum, and Evans (1997a), the magnitude of the output response in a
limited participation model of this type is determined largely by the elasticity oflabor supply.
(A monetary injection increases output by relaxing the firm’s cash-in-advance constraint on
labor inputs and clearly the response of labor input to this increase in wages is critical.) For
example, when we increase this elasticity to 2.5 (from our baseline calibration of 1.5), the
maximal output response increases to 0.085%.
Finally, to see whether our specification of the adjustment cost function is reasonable, the
last row of Figure 5 plots the response of the time-cost H t of adjusting Q
state labor supply is normalized to unity, the units for H

(Since the steady

are the fraction of steady-state

labor used in adjusting Q t - ) As can be seen, the maximal adjustment cost engendered by the
monetary policy shock is in the period following the shock, and the magnitude is between
0.0002 and 0.0004 (depending on the model variant). W e conclude that the costs implied by
our specification are trivially small.
20 Output, employment, price and money growth have been scaled up by a factor of 100 so the units are
percent deviations from steady state. This makes the responses directly comparable to Figure 1.

4.7.2. Bond Yields
W e find that the model replicates qualitatively the responses of bond yields to monetary
policy shocks. To preview our results, we find that a contractionary monetary policy shock
causes a positive but transient response in nominal bond yields, and an even bigger positive
response in real bond yields. These responses are largest for the short-term yields, with the
magnitude of the response declining as maturity increases. There is a positive response in
the term premiums for the shorter-maturity bonds. In the rest of this section we describe
these findings in greater detail.
In Figure 6 we display the responses of yields of different maturities to the contractionary
monetary policy shock. In presenting our model’s results, the bond yield responses are
annualized percentage point deviations from steady state. These responses are qualitatively
similar to those found in the data, but the magnitudes are somewhat too large, at least for
the shorter maturities. Consider the C E E calibration of the money growth process: The
contemporaneous response of the one-month yield in the model is 38 basis points, rising to
62 basis points three months after the shock. In contrast, our empirical exercises give a
contemporaneous response of approximately 20 basis points, rising to a maximal response
of 28 or 30 basis points one month later. The contemporaneous response in the model of
the six month yield is 59 basis points, which actually exceeds the contemporaneous response
of the one-month yield. This is largely due to the persistence of the short-rate response
in the model in the model. (Recall that the expectations hypothesis would imply that the
contemporaneous response of the six-month rate should equal the average of the first six
months’responses of the one-month rate.) However, the high contemporaneous response of
the six month rate is also due, in part, to the response of the six-month term premium, as
discussed below. The remaining yields’responses decline in magnitude as maturity increases,
much as in the empirical exercises. The initial responses of the three- and ten-year yields
are 11 basis points and 3 basis points, respectively. These numbers are rather close to the
responses found in the data. The responses implied by the Gali calibration are similar to
those of the C E E calibration. The responses of the one-month yield implied by the Sims-Zha
calibration differs somewhat from the other two, in that the contemporaneous response to
the policy shock is rather small (about 15 basis points). Still, the maximal response in this

calibration (which occurs 4 months after the shock) is over 60 basis points, substantially
exceeding any of the point estimates in the empirical exercises.

4.7.3. Shape of the term structure
Figure 7 displays the model’s implications for the i n t e r c e p t ,

s lo p e

and c u r v a t u r e term struc

ture descriptors. These responses can be computed directly from the individual bond yield
responses as follows. Consider a bond yield of maturity m months, and let R ™ denote its
response j months following a monetary policy shock . The j t h response of the three descrip
tors —
m,

in t e r c e p t , s lo p e

and

c u rv a tu re

— can be computed by projecting i?"1 on a constant,

and m 2. For each of the model parameterizations reported, the i n t e r c e p t increases for

about four months and falls rapidly. The maximal

in t e r c e p t

responses are about 50 basis

points, whereas in the data (Figure 3), the maximal responses are around 18 basis points.
This result highlights again that the model’s implications for short-maturity bond yields ex
ceed the empirical responses. The

s lo p e

response falls, consistent with the declining influence

of the monetary policy contraction on longer-maturity yields. The quantitative responses
of the model and data are quite similar; for example, the

C E E

impact response in Figure

3 is -0.015 and the model’s impact response is -0.013. Finally, the model’s implication for
cu rv a tu re

is qualitatively consistent with the empirical responses in Figure 3. However, the

magnitude of this effect in the model is severely diminished relative to the data.

4.7.4. T erm premiums
The empirical exercises provide some evidence that term premiums increase following a
contractionary monetary policy shock. Our model does imply a positive term-premium
response. As shown in Figure 7, the six-month term premiums in all three variants of the
model display a positive response of 16-18 basis points. This is somewhat larger than the
point estimates in our empirical exercises (in which the maximal response was 8 - 1 0 basis
points). Furthermore, the term-premium response in the model dissipates rapidly, becoming
essentially zero after three or four months. In contrast, the response of the six-month term
premium in the empirical exercises appears to increase over the first four or five months. The

response of term premiums declines monotonically with maturity, being three basis points
for the three-year premium and less than one basis point for the 10-year premium.

4.7.5. Real yields
As in the data, we find that the real yields actually display a more pronounced response
than nominal yields. (This, of course, is a simple implication of the negative response of the
inflation rate.) Figure 8 displays the real yield responses. The responses of shorter-term real
yields in the model are larger and less persistent than in the data. For example the maximal
response of the six- and 12-month real yields in the C E E calibration of the model are 97 basis
points and 53 basis points, respectively. In the data, the maximal responses from the C E E
and SZ monetary policy shocks are under 40 basis points. The Gali identification produces
a maximal response of 45 points (recall that the Gali monetary policy shocks generate the
largest fall in the price level). The maximal response in the model is the contemporaneous
response, while the maximal response in the data occurs 4 - 5 months after the date of the
shock. The response of the three-year yield in the model (18 basis points) is close to that in
the empirical exercises, so the excessive responses in the model appear to be confined to the
shorter-term yields.

4.8. Sources of the Liquidity Effect in the Model
It is of interest to see which elements of the model account for its ability to replicate the
qualitative features found in our empirical exercises. To this end, we experimented with
simpler versions of the model. These results are displayed in Figures 9. First, suppose
money growth were i.i.d., rather than MA(4). That is, we replace equation (4.1) with

(4-28)

x + OoEt

where, to insure that x t has the same variance as before, we set 0 q =

\jY^i=Q O b

The results

of this exercise are in the first column of Figure 9. Not surprisingly, the general response
patterns are quite similar, although the dynamics are less complex. (Basically, all responses

appear to die off exponentially.) The price level response is smaller in the i.i.d. case, but this
is purely an artifact of our normalizing the variances to be equal.21 The most notable effect
of removing serial correlation in money growth is to completely eliminate the term-premium
responses. This in turn reduces the responses of the longer nominal yields, and (along with
the reduced inflation response) reduces the responses of the real yields.
The second column of Figure 9 keeps the MA(4) structure in equation (4.1) (calibrated
to the C E E identification), but sets the Q t adjustment cost (in equation (4.5)) to zero. By
construction, the impact responses of all variables to the contractionary monetary policy
shock are identical to those in the full model. However, the response patterns following the
date of the shock differ substantially. In particular, the smooth responses in our baseline
calibration are replaced by a rapid reversal of the contemporaneous response. Consider the
output response. The initial liquidity effect reduces output, but thereafter the expected
inflation effect dominates. That is, the contractionary shock signals that future inflation will
be lower. (Indeed, our estimated M A process implies a greater reduction in money growth
the period after the shock is observed.) Inflation acts like a distortionary tax, so reduced
expected inflation tends to increase output.
W e next explore the role of the limited participation feature in the model. Consider first
a model

x v ith o u t

the limited participation features — that is, the household now observes

the monetary policy shock before choosing Q

Furthermore, we fix the adjustment cost at

zero, and the money growth rate is i.i.d., as in equation (4.28). This model now behaves as a
conventional cash-in-advance model with i.i.d. shocks. The model’s responses are completely
neutral. No endogenous variables (other than the price level) respond to the policy shock.
That is, there is neither a liquidity effect nor an expected inflation effect.
The third column in Figure 9 suppresses both the limited participation constraint and
the adjustment costs, but assumes that the money growth rate follows the MA(4) process
estimated from the C E E identification. Now, the only effect of a monetary policy shock is
the expected inflation effect: As a result, the contractionary monetary shock causes nominal
21That is, y / z l o
< X^i=o^»> so while the unconditional variance of xt is the same for both processes,
the cumulative effect of a monetary shock on the money stock (and therefore the price level) is greater in
the MA(4) specification.

interest rates to decline. That is, the impact effect of a contractionary monetary policy shock
on bond yields has a counterfactua! response relative to Figure 1. As described above, output
responds positively to this reduced expected inflation. Interestingly, the term premium
responses are virtually identical to those found in the baseline calibration. Evidently, the
term premium responses are driven not by the limited participation feature of the model,
but purely by the serial correlation in the money growth process. As a result of this positive
term premium response, the response of the intermediate-term nominal yields turns positive
after the initial decline.
In the fourth column of Figure 9 we add a

t-adjustment cost (as in equation (4.5)) to

the model in the third column. The adjustment cost not only smooths the impulse responses,
but also attenuates the contemporaneous response: Households do not reduce their demand
for Q t-money as much as they would in the absence of adjustment costs, so less funds flow
from the household to the financial intermediary. On impact the variables other than the
long yields respond like the cash-in-advance model of column three. After the initial impact,
the model’s responses are like the baseline calibration, since unanticipated money movements
axe absent. The impact response of the rc-period long yield incorporates the average of the
first n responses of the one-month yield, which is positive for moderately large n. A s a result,
the impact response of the longer yields is positive. Of course, the positive term premium
response magnifies the impact on the long yields.
Perhaps the most curious result from these exercises is that the term premium response
arises neither from the adjustment costs nor from the limited participation constraint, but
purely from the serial correlation in the money growth process. More generally, it is the
information content in the monetary policy shock that causes term premiums to respond.
Term premiums are a reflection of time-varying conditional higher moments in the logarithm
of the marginal utility of wealth22 (our variable At). While the exogenous shocks in this
model are conditionally homoskedastic, log(At) responds nonlinearly to these shocks. These
nonlinearities in turn can induce conditionally heteroskedastic behavior in log(A£). Evidently,
a monetary policy shock conveys not only information about the conditional first moment
of future money growth, but also information about conditional higher moments of log(A£).
22For a formal derivation of this result, see Bekaert, Hodrick, and Marshall (1997a).

5. C o n c lu sio n s
The results of this paper are straightforward and quite intuitive. W e find clear evidence that
the short-term effect of monetary policy takes the form of a liquidity effect: A monetary
contraction raises interest rates while reducing expected inflation, inducing a pronounced
rise in real interest rates. This effect is rather transitory, dissipating between 6 to 12 months
after the initial impulse. Monetary policy shocks primarily affect short-term interest rates,
with a diminishing effect on longer-term rates. Much of the response of longer-term rates
can be explained by the expectations hypothesis. There is some weak evidence that the
response of the shorter-maturity bonds is enhanced by a positive response of term premiums.
Finally, most of the variance of interest rates is due to sources other than monetary policy.
In particular, monetary policy is a non-trivial source of the short-run variability of short
term rates, but it represents a negligible source of variability for long-term rates. W e are
encouraged by the apparent robustness of these results: These basic patterns emerge under
three rather different identification approaches
W e also find that a simple dynamic equilibrium model, in which nominal rigidities take
the form of a limited participation constraint, is consistent with the broad patterns we have
detected in the data. This suggests that our empirical evidence is in no way anomalous,
but has a simple equilibrium explanation. W e believe that models of this sort may help us
understand the interaction between monetary policy and asset markets generally. Having
said this, we note that the model does require some degree of sluggishness in household
portfolio adjustment. W e have modelled this by imposing a simple adjustment cost. It would
be more satisfactory, from a theoretical standpoint, to be explicit about the microeconomic
frictions that underlie this slow aggregate portfolio adjustment.
W e also note that our model only includes monetary policy shocks. In principle, nonlin
earities of the type we encountered in pricing the zero-coupon bonds imply that the impulse
responses to monetary shocks need not be invariant to the presence of other shocks in the
model. It is an open question whether these nonlinearities substantially affect the economic
analysis. It would be of interest to explore the role of monetary policy in a model of interest
rates that incorporates a full set of exogenous impulses, such as technology shocks, prefer

ence shocks, and shocks to the transactions technology. (This last type of shock can induces
exogenous movements in money demand.) In addition, a model of this sort can be used
to explore the effect of changes in the monetary policy reaction function. Such an analysis
would surely encounter a host of issues not discussed here.

6. T ech n ica l a p p e n d ix : S o lv in g th e m o d e l
W e solve the model using the partial linearization method described in Christiano, Eichenbaum, and Evans (1997c). Let us define

model has two endogenous state variables:
[xt,e t>

Q t/ M t.

K t+ 1

and

The variable qt is stationary. The

qt ]

the exogenous state variables are

£4—3]• W e can reduce the equilibrium conditions of the model to two Euler

equations involving only the processes for these state variables. A linear approximation to the
integrands of these Euler equations is taken, and the resulting system of stochastic difference
equations is solved in the usual manner to yield a linear law of motion for the endogenous
state vector

[ K t+ i,q t ] '

(regarded now as differences from the steady state values):

K t

K t+1
= A
qt

where

and

+
qt-

(6.1)

B [ x t , e t , £ t ~ i , e t- 2 i S t s } '

are coefficient matrices of the appropriate dimensions. All other variables

of interest are known functions of the processes for [ K t , q t - 1]/ and [xt,s(,et-i,£t-2,et-3]7) so
they can be computed exactly once laws-of-motion (4.1) and (6.1) are known. That is, no
other linear approximations are used other than equation (6.1).
In order to compute n-period bond yields, the conditional expectation

E t

[At+n] must

be evaluated. For n equal to 12 months or less we do so by Gauss-Hermite quadrature,
using a two-point discretization23 over {et+i,

For n equal to 36 months or 120

months, the quadrature procedure is computationally infeasible, so we use a Monte Carlo
method. In particular, we simulate a time series (At, K

t , q t - i X t >£t> }t=i°°> and

we regress At+n

23 When the order of the discretization is increased to six, the implications for the impulse responses we
study are virtually unaffected.

on a third-order Chebyshev polynomial function of
fitted regression as an approximation for

E t

using the

[At+n]. As a check on the accuracy of this

procedure, we compute the impulse responses for the 12 month yield using both the Monte
Carlo procedure and the quadrature procedure. The resulting impulse responses are virtually
indistinguishable.

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Handbook o f

Table 1
Fraction of yield variance explained by monetary policy shock
A. C E E Identification

Bond Maturity
Horizon

One month

Six months

One year Three years

Ten years

1-month

16.7%

14.8%

11.0%

6.5%

2.9%

6-months

16.9%

12.9%

10.8%

4.8%

1.5%

24-months

6.9%

5.3%

4.6%

3.0%

1.4%

B. SZ Identification

Bond Maturity
Horizon

One month

Six months

One year Three years

Ten years

1-month

13.6%

12.3%

10.2%

6.6%

1.5%

6-months

18.1%

6.9%

8.7%

7.6%

3.6%

24-months

15.4%

3.7%

11.3%

14.5%

10.3%

C. Gali Identification

Bond Maturity
Horizon

One month

Six-months

One year Three years Ten years

1-month

7.2%

4.9%

3.5%

1.9%

0.0%

6-months

17.1%

13.7%

11.2%

5.0%

3.2%

24-months

7.4%

2.9%

2.2%

0.2%

Notes to Table 1 : The estimated fraction of the one-month ahead, six-month ahead,
and 24-month ahead conditional bond-yield variance attributable to monetary policy shocks
is displayed. Panel A displays results for the C E E recursive strategy for identifying monetary
policy shocks (described in Section 2.2); Panel B displays results for the Sims-Zha nonrecursive identification strategy (described in Section 2.3); and Panel C displays results for the
Gali identification strategy that incorporates long-run restrictions (described in Section 2.4).
For each identification strategy, results are displayed for bonds maturing in one month, six
months, one year, three years, and ten years.

Table 2 : Parameter Calibrations for the M o n e y Growth Process

Identification Strategy 00

CEE

.00041

.00081

.00067

.00038 -.00008

Gali

.00047

.00087

.00082

.00036

.00035

.00016

.00092

.00064

.00099

.00069

Notes for Table 2: This table gives the values of the moving average coefficients {0i}*=o
in money growth process (4.1) implied by our estimates of the C E E recursive strategy for
identifying monetary policy shocks (described in Section 2.2); the Sims-Zha nonrecursive
identification strategy (described in Section 2.3); and the Gali identification strategy that
incorporates long-run restrictions (described in Section 2.4).

C EE Recursive

Sims-Zha

Gali

MP Shock=>EM

MP Shock=>GDP

months
MP Shock=>PCEPriceDeflator

months
MP Shock=>CPIPrice

&
months
MP Shock=>FF

months
MP Shock=>FF

months
MP Shock=>FF
§
o
&

months
MPShock=>GrowthinTR

I
£
months
MPShock=>CommodityPrices
0.036
0.018
•0.054
■0.072
months
MP Shock=>NBRX

0.14•0.14■02*-0.42•0.56■0.70-

0.10- \ /N
0.05-0.00-0.05-0.10------& 0.15-020- / V
_.
,
__
-025months
MP Shock=>CrudeMaterialsPrices
0.50
025
•025
•0.50
& -0.75
-1.0 0 -125
-1.50
months
MP Shock=>IntermediateMaterialsPrices

months
MP Shock=>GrowthinM1
percent

months
MP Shock=>GrowthinM2

0.100.05-0.06-0.10-0.15•020-

r'.*Nv ^ \ ^ ^- __

s
J )

•0.50-0.75
-1.00

months
MP Shock=>RealWages

months

0.15
0.10 0.05
•0.00
-0.05
•0.10
•0.15
•020

Figure 1: Responses of Macroeconomic Variables to Monetary Policy Shocks

months

Notes to Figure 1: For each of the three identification strategies described in section 2, this
figure displays the responses of variables in the V A R system (other than bond yields) to a onestandard deviation monetary policy shock. The first column displays impulse responses for the
CEE recursive identification, described in section 2.2. The responses reported are: employment
(EM), personal consumption expenditure deflator (PCE Price Deflator), federal funds rate (FF),
growth in M 2 money, an index of Commodity Prices, and the ratio of non-borrowed reserves to
total reserves (NBRX). The second column displays impulse responses for the Sims-Zha nonrecursive identification, described in section 2.3. The responses reported are: GDP, personal
consumption expenditure deflator (PCE Price Deflator), federal funds rate (FF), growth in total
reserves (TR), an index of Crude Material Prices, an index of Intermediate Material Prices, and
Real Wages. The third column displays impulse responses for the Gali identification, described
in section 2.4. The responses reported are: GDP, consumer price index (CPI), federal funds rate
(FF), and growth in Ml money. For all variables except the federal funds rate, the responses
are in percentage deviations from the steady state. For the federal funds rate, the units are
percentage points per annum. The solid lines plot the point estimates for the impulse responses;
dashed lines give 95% confidence intervals, as described in sections 2.2 - 2.4.

Sims-Zha

Gali

MP Shock=>FF

6 11
months

S»

11
months

/
1
11
1

°‘
°
-0.2•0.4-

(/
1
1
i

|
Q.

2
©
Q
l

0.80.60.4| 0.2Q. 00"
-0.2-0.4-

/ //
- //

0.80.80.4-

CEE Recursive

--— _______

months

MP Shock=>1-monthyield

months

MP Shock=>6-monthyield

0o)
0)

♦§
1

s?
2L
\y
6

11
months

^
16

0.50.4°J0.2-

✓'

•0.1- \V.
■0.2■........« —
-0.3-.. .it.Trv
6
11 16 21
months

0.50.4^
0.3<5 0.2mP 0.1C
’
-0.1•0.2-0.3-

months

MP Shock=> 12-monthyield

MP Shock=>12-monthyield

______

MP Shock=>12-monthyield

I
&

a
1

months

6 11
months

MP Shock=>3-yearyield

months

MP Shock=>10-yearyield

0.25
0.20

0.15
0.10

a 0.05
•0.05
•0.10

Figure 2: Responses of Bond Yields to Monetary Policy Shocks

21
months

Notes to Figure 2: For each of the three identification strategies described in section 2, this
figure displays the response to a one-standard deviation monetary policy shock of the federal
funds rate (first row) and of the continuously-compounded yields for zero coupon bonds of
maturities one month, six months, one year, three years, and ten years (rows two through six).
The first column displays impulse responses implied by CEE recursive identification (described
in section 2.2); The second column displays impulse responses implied by the Sims-Zha nonrecursive identification (described in section 2.3); the third column displays impulse responses
implied by the Gali identification (described in section 2.4). For all these impulse responses, the
units are percentage points per annum. The solid lines plot the point estimates for the impulse
responses; dashed lines give 95% confidence intervals, as described in sections 2.2 - 2.4.

C E E Recursive

Sims-Zha

Gali

MP Shock=>TS Intercept

months

MP Shock=>TS Slope

MP Shock=>TSSlope

MP Shock=>TS Slope

months

6 11
months

MP Shock=>TS Curvature

MP Shock=>TSCurvature

MP Shock=>TS Curvature

months

MP Shock=>6-monthTermPremium

MP Shock*>6-monthTermPremium

months

6 11
months

MP Shock=>12-monthTermPremium

MP Shock=>12-monthTerm Premium

MP Shock=>12-monthTermPremium

months

MP Shock=>3-yearTermPremium

<D
C
L

&
1

0.25
0.20
0.15
0.10
0.05
•0.05
•0.10
-0.15

Figure 3: Responses of Term Structure Descriptors and Term Premiums to Monetary Policy Shocks

Notes to Figure 3: The interpretation of Figure 3 is identical to that of Figure 2, except that,
instead of displaying responses of bond yields to a monetary policy shock, the first three rows
display responses of the three term structure descriptors in te rc e p t, s lo p e , and c u r v a t u r e . These
term structure descriptors are computed as described in Section 3.1. The last three rows display
the responses of the T-period term premium, T P ] , defined in equation (3.1).

C E E R e c u rsiv e

S im s-Z h a

G a li

MP Shock => 6-month real rate

months

MP Shock => 12-month real rate

months

MP Shock => 3-year real rate

____________________ m n n t h c _______________________________________ m n n t h c ________________________________________m n n t h c

Figure 4: Responses of Real Interest Rates to Monetary Policy Shocks

Notes to Figure 4: The interpretation of Figure 4 is identical to that of Figure 2, except that,
instead of displaying responses of nominal bond yields to a monetary policy shock, the responses
of real bond yields of maturities six months, 12 months, and three years are displayed. The first
column displays impulse responses for the CEE recursive identification, described in section 2.2.
The second column displays impulse responses for the Sims-Zha non-recursive identification,
described in section 2.3. The third column displays impulse responses for the Gali identification,
described in section 2.4. In computing the real bond yields, the CEE identification (column 1)
and the Sims-Zha identification (column 2) compute the inflation rate using the personal
consumption expenditure deflator; the Gali identification (column 3) uses CPI inflation. In all
cases, units are in percentage points per annum.

CEE Recursive

Sims-Zha

Gali

MP Shock => Output, Employment

months

MP Shock => Price

months

MP Shock => 1-month rate

months

MP Shock => Growth in Money

months

MP Shock => Adjustment Cost

Figure 5: Responses of Macroeconomic Variables to Monetary Policy Shocks in the Calibrated Limited
Participation Model

Notes to Figure 5: This figure displays the responses to a one-standard deviation monetary
policy shock, implied by the model described in sections 4.1 - 4.4, of output, the price level, the
one-month interest rate, the growth rate of money, and the adjustment cost of Q , (as given in
equation (4.5)). For output, the price level, and the growth rate of money, the responses are in
units of percentage deviations from the steady state. For the one-month interest rate, the units are
percentage points per annum. For the adjustment cost, the units are fractions of time devoted to
employment in the steady state. The three columns calibrate the law of motion for money growth
(equation (4.1)) to estimates from the CEE identification, the Sims-Zha identification, and the
Gali identification, as given in Table 2. The remaining parameter calibrations are: a = 0.36, P
= 1.03'(1/12), a = 1, \|/ = 2/3, p = 1.40, 6 = 0.00667, x = 000667, c = 2, d = 1.

CEE Recursive

Sims-Zha

Gali

MP Shock => 1-month yield

months

MP Shock => 6-month yield

months

MP Shock => 12-month yield

<D
O

months

MP Shock => 3-year yield

§
g
<D

MP Shock => 3-year yield

0.30-0.25-

0.20 -

0.20-

0.150.10-

0.050.00--

-0.05-0.10 --

-0.050.10
-

I T . . . . .........................

!- ■ ■■

months

MP Shock => 10-year yield

MP Shock => 10-yearyield

Figure 6: Responses ofBond Yields to Monetary Policy Shocks inthe Calibrated Limited Participation Model

Notes to Figure 6: The interpretation of Figure 6 is identical to that of Figure 5, except that
the responses, implied by the model of sections 4.1 -4.4, of the continuously-compounded yields
for zero coupon bonds of maturities one month, six months, one year, three years, and ten years
are displayed. The units are percentage points per annum. The calibration is as in Figure 5.

CEE Recursive

Sims-Zha

Gali

MP Shock => TS Intercept

months

MP Shock => TS Slope

months

6
11
months

MP Shock => TS Curvature

months

MP Shock => 6-month term premium

months

MP Shock => 12-month term premium

0.100C
<D
E
8.

0.0750.0500.025-0.025-

months

6
11
months

MP Shock => 36-month term premium

^
§
S
a
E)A

0.040.030.020.010.00■0.01•
■0.02•0.03-

10
months
MP Shock => 36-month term premium

Figure 7: Responses of Term Structure Descriptors and Term Premiums to Monetary Policy Shocks in the
Calibrated Limited Participation Model

Notes to Figure 7: The interpretation of Figure 7 is identical to that of Figure 5, except that
the responses, implied by the model of sections 4.1 -4.4, of the three term structure descriptors
in te r c e p t, s lo p e , and c u r v a tu r e (rows 1 - 3) and of the 6-month, 12-month, and 36-month term
premiums are displayed. The three term structure descriptors are computed as described in
section 3.1. The T-period term premium, T P ] is defined in equation (3.1). The calibration is as
in Figure 5.

CEE Recursive

Sims-Zha

Gali

MP Shock => 1-month real rate

months

MP Shock => 6-month real rate

months

MP Shock => 12-month real rate

months

MP Shock => 36-month real rate

months

MP Shock => 120-month real rate

c©

O
<D

Figure 8: Responses ofReal Interest Rates to Monetary Policy Shocks in the Calibrated Limited Participation
Model

Notes to Figure 8: The interpretation of Figure 8 is identical to that of Figure 5, except that
the responses, implied by the model of sections 4.1 -4.4, of the real bond yields of maturities one
month, six months, 12 months, three years, and ten years are displayed. The units are percentage
points per annum. The calibration is as in Figure 5.

Lim. Part., Adjust. Costs,iid

Lim. Part., No Adjust Costs, MA(4)

No Lim. Part., No Adjust. Costs, MA(4)

No Lim. Part., Adjust. Costs, MA(4)

MP Shock => Output

1 4

months

MP Shock => Price

0.16•

—

---------

....

0.10-

0.16-

•4X32•

°*°
41.16•

-0.16■

-0.32-

4X3S-

months

MP Shock => 1-month yield

V
-0.7-

0.7-

4X7-

months

MP Shock => 6-month yield

?
?
£

percent

?
_"v.
------------------------

4)26-

“ •
00

(XiO-

0*0percent

|
V

months

MP Shock => 12-month yield

032\

ojoo

032-

032•
|

000

Q-

0.00

_ ------------

1
8.

\ 4X16-

4X16months

months

MP Shock => 3-year yield

0.10006■

“

8
&

8
&
7

months

0.50■

jercent

1.4*

4X10-

006

8i
-006-

4X06■
-aio-

aio-

Oj0
&-

months

MP Shock => 10-year yield

MP Shock «> 10-year yield

MP Shock => 10-year yield

0-025

8
&

8
&
7

Figure 9: Im pulse Responses Im plied by V ariants o f the M odel o f Section 4

8
8.

4X005

-0.060

Lim. Part., Adjust. Costs,iid

Lim. Part., No Adjust. Costs, MA(4)

No Lim. Part., No Adjust. Costs, MA(4)

No Lim. Part., Adjust. Costs, MA(4)

MP Shock => 6-month term premium

months

MP Shock => 12-month term premium

months

MP Shock => 36-month term premium

months

MP Shock => 1-month real rate

0.2

---------------------------------

c
0 a,‘
o
0 -------------CL
-O.tJ-i-.
-.
---.
-.-■
-r—«-.
-.----

0.100

-I---------------------------------

C
g
Q.

oooo----------------------------------------------------------------

•0.040 .-■* ■ . .
---- - -----,
-.
-1
4
7
10

002
.

ooo -

■ota

'■

— .— .— ,— .—

■
—

— .— ----

2.4

C
0
2
0
o.

00
1
. -

— ........ —

•a* - —— ,— ,— .— _

............—

— ,— ,— ,— ,— ,—--------

months

MP Shock => 6-month real rate

0.75

-0.25

months

MP Shock => 12-month real rate

aso

•0.25^ --1
---.-.
-.
-1
-,
---1
-1
-1
-1
4
7
10

months

MP Shock => 3-year real rate

c
©

------------------

o M8. o,.-r=^_________
0.1

'figure 9 (Continued)

Notes to Figure 9: The responses implied by four simple variants of the model of sections 4.14.4 are displayed for the following variables: output (row one); the price level (row two); bond
yields of maturities 1 month, 6 months, 12 months, 3 years, and 10 years (rows three through
seven); term premiums of maturities 6 months, 12 months, and 3 years, as defined in equation
(3.1) (rows eight through ten); and real bond yields of maturities one month, 6 months, 12
months, and three years (rows 11 through 14). The simple model variants are as follows.
Column 1: baseline model of Figure 5, but with money growth i.i.d.; Column 2: baseline model
of Figure 5, but with adjustment cost set equal to zero; Column 3: baseline model of Figure 5,
but without the limited participation constraint, and with adjustment cost set equal to zero;
Column 4: baseline model of Figure 5 without the limited participation constraint, but with
adjustment costs as in Figure 5.

Full text of Working Papers (Federal Reserve Bank of Chicago) : Monetary Policy and the Term Structure of Nominal Interest Rates : Evidence and Theory, Working Paper 1997-10

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