Massive Money Injection in an Economy with Broad
Liquidity Services: The Japanese Experience 2001-2006
Mitsuru Iwamura
Waseda University

Shigenori Shiratsuka
Bank of Japan

Tsutomu Watanabe∗
Hitotsubashi University

September 4, 2006

Abstract
This paper presents a model with broad liquidity services to discuss the consequences ofmassive money injection in an economy with the zero interest rate bound. We incorporate Goodfriend’s (2000) idea of broad liquidity services into the model by allowing the amounts of bonds
with various maturities held by a household to enter its utility function. We show that the satiation of money (or the zero marginal utility of money) is not a necessary condition for the
one-period interest rate to reach the zero lower bound; instead, we present a weaker necessary
condition that the marginal liquidity service provided by money coincides with the marginal liquidity service provided by the one-period bonds, both of which are not necessarily equal to zero.
This result implies that massive money injection would have some influences on an equilibriumof the economy even if it does not alter the private sector’s expectations about future monetary
policy. Our empirical results indicate that forward interest rates started to decline relative to thecorresponding futures rates just after March 2001, when a quantitative monetary easing policy
started by the Bank of Japan, and that the forward and futures spread has never closed until thepolicy ended in March 2006. We argue that these findings are not easy to explain by a model
without broad liquidity services.
JEL Classification Numbers: E31; E43; E52
Keywords: Liquidity trap; zero interest rate policy; quantitative monetary easing policy; broadliquidity services∗ Correspondence:

Tsutomu Watanabe, Institute of Economic Research, Hitotsubashi University, Kunitachi, Tokyo
186-8603, Japan. Phone: 81-42-580-8358, fax: 81-42-580-8333, e-mail: tsutomu.w@srv.cc.hit-u.ac.jp.

1

Introduction

Recent researches on the optimal monetary policy in an economy with the zero interest rate boundhave found the importance of a central bank’s commitment about future monetary policy (Woodford(1999), Jung et al. (2005), Eggertsson and Woodford (2003) among others). In a usual environment,a central bank conducts monetary easing by lowering the current overnight interest rate through an
additional injection of money to the market. However, this does not work well once the overnightinterest rate reaches the zero lower bound. Further monetary easing in such a situation could be
implemented only through central bank’s announcements about the future path of the overnightinterest rate. Specifically, it has been shown that the optimal monetary policy rule is characterized by“history dependence” in the sense that a central bank commits itself to continuing monetary easing
even after the economy returns to a normal situation.
Somewhat interestingly, the Bank of Japan’s (BOJ’s) policymaking since the spring of 1999 has
some similarities with the findings provided by these theoretical studies (see Table 1 for recent monetary policy events).1 One of the keywords frequently used by the BOJ oﬃcials and other market
participants during this period was Jikanjiku eﬀects, or temporal-axis eﬀects.2 This is an idea thatfurther monetary easing could be implemented by expanding a flat “zero-rate zone” in the yield
curve. The length of the zero-rate zone has been regarded as an indicator of monetary easing, which
at least partially replaces the role played by the current level of the overnight interest rate in a normal
situation.3
1 Iwamura et al. (2005) evaluates the BOJ’s monetary policy in 1999-2004 by comparing it with the optimal monetary
policy rule.
2 Temporal-axis eﬀects is a literal translation of jikanjiku eﬀects, while the BOJ oﬃcially use “policy duration eﬀects”
as its English translation. These two translations are both closely related to the zero-rate zone in the yield curve.
Interestingly, the word “policy duration eﬀects” implicitly assumes that the zero-rate zone is created and expanded
by a central bank’s commitment about future monetary policy. For example, as far as the “policy durations eﬀects”
are concerned, the zero-rate zone is expanded only when a central bank’s commitment about future easing successfully
alters the market’s expectations. There does not seem to exist any recognition that the zero-rate zone in the yield curve
could be expanded by massive money injection.
3 The idea of “temporal-axis eﬀects” had an important influence upon various aspects of developments in Japanesemoney markets during this period. First, the Bank of Japan has repeatedly announced that it would continue monetaryeasing (zero interest rate policy or quantitative monetary easing policy) for longer periods than expected by market
participants. For example, Governor Hayami announced in April 1999, just after the introduction of the zero interest
rate policy, that the BOJ will continue that policy until “deflationary concerns are dispelled”. Also he announced in
March 2001, when the BOJ introduced the quantitative monetary easing policy, that it will continue that policy until“the core CPI records a year-on-year increase of zero percent or more on a stable basis”. Second, market participants andmass media have been paying a special attention to the length of the zero rate zone in the yield curve as an importantsource of information about future monetary policy. In some sense, its length has been regarded as an indicator ofmonetary easing, given that the current level of the overnight interest rate (which is already zero) does not provide any
useful information about the degree of monetary easing. Third, the BOJ tended to purchase longer and longer-termbonds over time during this period. Bonds located in the zero-rate zone in the yield curve are already equivalent tomoney, so financial institutions were not willing to conduct an exchange between these bonds and money. Given that,

2

The purpose of this paper is to closely look at recent developments in the yield curve, paying aparticular attention to developments in the zero-rate zone in the yield curve. One might say thisis a simple task, given that the length of the zero-rate zone is determined solely by the market’s
expectations about future monetary policy, as emphasized by the above mentioned theoretical studies.
For example, if one detects a longer zero-rate zone in the yield curve, it should be regarded as anevidence that market participants update their belief about future monetary policy and now believethat monetary easing will be continued longer than it was believed before.
However, there is a serious mismatch between the optimal monetary policy rule described in thetheoretical literature and the actual policy decisions made by the BOJ, and it creates a complication.
The BOJ switched its operational target in March 2001 to the current account balance (CAB) from theovernight interest rate (“quantitative monetary easing policy”), and has raised the CAB target fairly
frequently since then, starting from 5 trillion yen at the beginning of 2001 to 30-35 trillion yen three
years later (see Figure 1). According to Eggertsson and Woodford (2003), such an additional injectionof money would have no eﬀects upon an equilibrium of the economy when the overnight interest
rate is already zero, simply because the marginal utility of money equals to zero as well. However,in a more realistic setting where portfolio rebalancing eﬀects work to some extent, an additional
injection of money would lead to an increase in demand for longer-term (or riskier) bonds even when
the overnight interest rate is already zero, thereby raising prices for those bonds (Meltzer (2001),
Goodfriend (2000), Clouse et al. (2003)). An important point to note here is that an additional
money injection, particularly large-scale one, would lead to an expansion in the zero-rate zone in
the yield curve through the portfolio rebalancing channel, even if it does not alter at all the market’
expectations about future monetary policy (namely, no eﬀects through the expectation channel). This
paper seeks to discriminate these two channels by looking at the spread between forward and futuresinterest rates around the very end of the zero-rate zone in the yield curve, and investigate a mechanism
behind the observed expansion of the zero-rate zone during the period of the quantitative monetaryeasing policy.
The rest of this paper is organized as follows. Section 1 presents a model with broad liquidity
services in order to investigate the consequences of massive money injection in an economy with thezero interest rate bound. We incorporate Goodfriend’s (2000) idea of broad liquidity services into thethe BOJ was forced to purchase bonds located outside the zero-rate zone, whose yields were still above zero.

3

model by allowing the amounts of bonds with various maturities held by a household to enter its utility
function. First, we show that the satiation of money (or the zero marginal utility of money) is not anecessary condition for the one-period interest rate to reach the zero lower bound; instead, we present
a weaker necessary condition that the marginal liquidity service provided by money coincides with themarginal liquidity service provided by the one-period bonds, both of which are not necessarily equal
to zero. Second, we show that massive money injection through an open market operation would
have some influences on the yield curve even if it does not alter the private sector’s expectations
about future monetary policy, as long as a central bank purchases bonds located outside the zero-ratezone. Third, we show that the forward and futures spread would become positive (i.e., the forward
interest rate is lower than the corresponding futures rate) when a central bank conduct massive money
injection, although it would become zero in a limiting case in which the base money is supplied up to
the satiation level.4
Section 3 turns to empirical analysis. Our empirical results indicate that forward interest rates
started to decline relative to the corresponding futures rates just after March 2001, when a quantitative
monetary easing policy started by the Bank of Japan, and that the forward and futures spread has
never closed until the policy ended in March 2006. We argue that these findings are not easy to
explain by a model without broad liquidity services. Section 4 concludes the paper.

2

A Model of Broad Liquidity

Eggertsson and Woodford (2003) shows that an additional provision of the base money would have noeﬀects on an equilibrium of the economy, given that the overnight interest rate has already reachedthe zero lower bound (“Irrelevance Proposition”).5 In the model of Eggertsson and Woodford (2003),
an additional money injection becomes ineﬀective simply because the marginal utility of money iszero in an economy with the zero overnight interest rate. An additional money injection will neverchange the marginal utility of money, which is already zero, thereby having no eﬀects on households’
4 Bernanke (2001) and McGough et al. (2005) argue that a central bank should use a long-term interest rate asits policy instrument in a case when the overnight interest rate reaches the zero lower bound. In responding to this
proposal, Woodford (2005) argues that massive money injection might have some impacts on long-term interest rates,
but its impacts on the real economic activities would be limited if the operation does not alter the private’s sectors
expectations about future monetary policy. Our analysis is closely related to this debate.
5 Given this proposition, an expansion of the zero-rate zone occurs only when the private sector changes their expectations about the future path of overnight interest rates. Based on this understanding, most of recent empiricalresearches on the Japanese yield curve interpret the observed expansion of the zero-rate zone in the yield curve as
coming from changes in the market’s expectations (Fujiki and Shiratsuka (2002), Okina and Shiratsuka (2004), Marumo
et al. (2003), Nagayasu (2004), Oda and Ueda (2005)).

4

behaviors, and consequently no eﬀects on an equilibrium of the economy.
Then one may wonder why the marginal utility of money must be zero when the overnight interest
rate is zero. Consider a situation that a household carries over its wealth to the next period. The
household receives interest as a return if it purchases a one-period bond. On the other hand, if thehousehold carries over through money, it receives no interest but is allowed to enjoy liquidity service
provided by money. No-arbitrage condition between money and one-period bonds immediately implies
that the marginal utility of money should be equal to the overnight interest rate, and that the marginalutility must be zero if the overnight interest rate is zero. However, this argument depends crucially on
the assumption that liquidity services are provided only by money. If one relaxes this assumption byinstead assuming that even other financial assets, including overnight bonds, provide liquidity services
as money does, then the zero overnight interest rate does not necessarily imply the zero marginal utilityof money. If this is the case, an additional money injection into an economy with the zero overnightinterest rate could have some impacts on an equilibrium.
Goodfriend (2000) argues that we need to have a model in which liquidity services are provided
by other financial assets in order to fully understand the consequences of an open market operationin an economy with the zero overnight interest rate. Specifically, Goodfriend (2000) proposes the ideaof “broad liquidity service”. The assumption that money is the only financial asset that provides
liquidity services might not be a good approximation to actual financial activities, in the sense that
financial assets other than money is used as collateral in those activities. According to the definitionof Goodfriend (2000), any asset that contributes to reducing external finance premium (i.e., the wedge
between internal and external financing costs) must be regarded as providing liquidity services to someextent. Broad liquidity services are defined as those services provided not only by money but also byother financial assets. According to his definition, “all assets provide broadly defined services to one
degree or another” (Goodfriend (2000), p.1020).
We introduce broad liquidity services simply by assuming that bonds with various maturities enter
the household’s utility function as its arguments.6 This treatment mimics the MIUF (Money in the
Utility Function) approach for liquidity services provided by money. Needless to say, this assumes
much of what we would like to explain, thus clearly not a satisfactory treatment,7 but still captures
6 Our model does not diﬀer from the standard model in other respects, including the assumption of complete capital
markets.
7 See Goodfriend (2004) for an attempt to describe the endogenous emergence of broad liquidity services provided byvarious financial assets in an economy with imperfect information.

5

an important aspect of liquidity services provided by various financial assets without sacrificing thetractability of the model. In the rest of this section, we use this approach to investigate how the yield
curve is formed, how it is aﬀected by open market operations, and how it is distorted by the zerointerest rate bound, in an economy with broad liquidity services.

2.1

Household’s optimization

Let us consider a representative household that seeks to maximize a discounted sum of utilities of the
form
E0

"∞
X
t=0

#
¡ h ¢
β ut zt ; ξt ,
t

(2.1)

where u(·) is an increasing and concave function, β is the discount factor, and ξt represents exogenous
stochastic disturbances. The variable zth represents a vector of endogenous variables that is defined
by
zth ≡

"

h

h
h
h
BN̄ ,tB2,tBn,tMth B1,t
ct ,
,
,
,...,
,...,
Pt
Pt
Pt
Pt
Pt

#

(2.2)

where ct is the private consumption expenditures, Mth is the household’s nominal end-of-period balances in the base money, and Pt is the price level. We assume that the government issues zero-coupon
nominal bonds, each of which pays one yen when it matures, and denote the face value of bonds, withh.
n periods to maturity, held by the household at the end of period t by Bn,t

The representative household is subject to a flow budget constraint of the form
N̄
¢ X
¡ h
¢
¡
d
h
h
+
≤ Pt dt + B1,t−1(1 + in,t )−1 Bn,t
− Bn+1,t−1,
Pt ct + Mtd − Mt−1

(2.3)

n=1

h
where dt is the household’s real disposable income, and B1,t−1
represents the amount of repayment forbonds that mature in period t. The representative household allocates the sum of disposable income
and the repayment between consumption expenditures and the purchases of government bonds. Thehhterm Bn,t− Bn+1,t−1
represents the change from the previous period in the face value of bonds thatmature in period t + n, namely, an amount of net purchase of those bonds in period t. Those new
bonds are evaluated by the market price in period t, (1 + in,t )−1 , where in,t is the yield to maturity
for bonds with n periods to maturity.
The household optimization problem defined above implies the following first-order conditions. Wehdiﬀerentiate with respect to Mth , Bn,tand ct , and then substitute a market clearing condition of the

6

form
zth = zt ,where zt represents supply quantities of goods, the base money, and bonds with various maturity,
defined by:¸∙BN̄ ,tMt B1,t B2,t
Bn,t
.
,
,
,...,
,...,
zt ≡ yt ,
Pt
Pt
Pt
Pt
Pt
The first-order conditions with respect to Mth and ct imply
1 = Et (q1,t ) + φm (zt ; ξt ) ,(2.4)

where φm (zt ; ξt ) represents the marginal utility of money, or equivalently the marginal liquidity service
provided in period t, by the base money, which is defined by φm (zt ; ξt ) ≡ ∂u(zt ; ξt )/∂(Mt /Pt ). The
variable qj,t is a nominal stochastic discount factor that is defined by∙¸
j uc (zt+j ; ξt+j ) Pt
for j ≥ 0.
qj,t ≡ Et β
uc (zt ; ξt ) Pt+jh
Similarly, the first-order conditions with respect to Bn,tand ct imply


n−1
X
1
= Et 
qj,t φn−j (zt+j ; ξt+j ) + qn,t  ,1 + in,t
j=0

(2.5)

(2.6)

where φn−j (zt+j ; ξt+j ) represents the marginal liquidity service provided in period t + j by bonds withn − j periods to maturity, which is defined by φn−j (zt+j ; ξt+j ) ≡ ∂u(zt+j ; ξt+j )/∂(Bn−j,t+j /Pt+j ).
Equation (2.6) implies that the yield for bonds with one period to maturity is given by1= Et (q1,t ) + φ1 (zt ; ξt ) .
1 + i1,t(2.7)

Together with equation (2.4), we eliminate Et (q1,t ) to obtain an arbitrage condition between money
and these one-period bonds of the formφm (zt ; ξt ) =i1,t+ φ1 (zt ; ξt ) .
1 + i1,t(2.8)

This equation reduces to a standard money demand relationship in which money demand is a decreasing function in the short-term (namely, one-period) nominal interest rate i1,t , if the marginal liquidity
service provided by the one-period bonds φ1 (·) is equal to zero. Otherwise, however, money demand
inversely depends on the marginal liquidity service provided by the one-period bonds.
7

We make the following assumptions about the marginal liquidity services provided by bonds withvarious periods to maturity. First, we assume thatφm (zt ; ξt ) ≥ φ1 (zt ; ξt ) ≥ φ2 (zt ; ξt ) ≥ · · · ≥ φN̄ (zt ; ξt ) ≥ 0.

(2.9)

This simply states that the marginal liquidity service provided by the base money should be not beless than the one provided by the one-period bonds; the marginal liquidity provided by the one-periodbonds should not be less than the one provided by the two-period bonds, and so on. These assumptions
must be easy to accept. Second, we assume that the derivative of φn (zt ; ξt ) with respect to the realmoney balance mt (≡ Mt /Pt ), namely φnm (zt ; ξt ) ≡ ∂φn (zt ; ξt ) /∂mt should satisfy
φnm (zt ; ξt ) ≤ 0

forn = 1, . . . , N̄ .

(2.10)

In other words, the base money and bonds with various periods to maturity are substitutes. The
representative household with ample money (and ample liquidity service provided by money) would
have little need to obtain additional liquidity services from bonds, which is represented by a lower
marginal liquidity service provided by bonds.8 Third, we assume that
|φmm (zt ; ξt ) | ≥ |φ1m (zt ; ξt ) | ≥ |φ2m (zt ; ξt ) | ≥ · · · ≥ |φN̄ m (zt ; ξt ) | ≥ 0.

(2.11)

Figure 2 shows the schedules of φm (zt ; ξt ), φ1 (zt ; ξt ), φ2 (zt ; ξt ) and so on, as a function of mt under
the additional assumption (the assumption for simplification) of linearity. As shown in the figure,the marginal liquidity service provided by the base money is greater than the one provided by the
one-period bonds if mt < m̄1 but these two become identical once mt exceeds m̄1 , which is a directreflection of (2.11). Similarly, m̄2 represents a “junction” for two-period bonds, and m̄3 for threeperiods bonds, and so on. These junctions should satisfy¯,
m̄1 > m̄2 > · · · > m̄N̄ > m̄

(2.12)¯ is the level of the base money where the marginal liquidity service provided by the basewhere m̄money equals to zero, namely the satiation level of money.

8 A similar assumption is adopted by Goodfriend (2000), but in an informal way.

8

2.2

Necessary conditions for zero interest rates

Consider a necessary condition for the one-period nominal interest rate in period t, i1,t , to reach thezero lower-bound. Substituting i1,t = 0 into equation (2.8) leads to
φ1 (zt ; ξt ) = φm (zt ; ξt ) .

(2.13)

An important point to note here is that the satiation of the base money, φm (zt ; ξt ) = 0, is not a necessary condition for the one-period interest rate to be zero. Previous studies on the zero bound on nominal interest rates, including Eggertsson and Woodford (2003) and Jung et al. (2005) among others,
typically ignore liquidity services provided by bonds, thereby implicitly assuming that φ1 (zt ; ξt ) = 0.
In their case, equation (2.13) reduces to φm (zt ; ξt ) = 0, implying that the satiation of money is indeed
a necessary condition for the one-period interest rate to be zero. The one-period bond provides neither
liquidity service nor interest to its holders in their models; thus an arbitrage argument between money
and the one-period bonds implies a zero marginal liquidity service (or, zero marginal utility) even formoney. However, this kind of arbitrage argument does not necessarily imply the satiation of money
in a more general setting in which not only money but also bonds provide liquidity services. In thissetting the one-period bonds are still attractive to investors because of its liquidity service, even whenits interest rate reaches the zero lower bound. Then an arbitrage argument requires that the marginalliquidity service provided by money should be equal to the marginal liquidity service provided by the
one-period bonds (which is positive), as shown in equation (2.13). Note that, as shown in Figure 2,
mt must be greater than m̄1 for the one-period interest rate to be zero, but still could be smaller than¯ (namely, the satiation level).
m̄
Turning to the two-period bonds, a similar necessary condition for its yield to maturity, i2,t , tobe zero could be obtained in the following way. Under the assumption of perfect foresight,9 a simple
substitution of equation (2.4) into equation (2.6) leads to1= [1 − φm (zt ; ξt )] [1 − φm (zt+1 ; ξt+1 ) + φ1 (zt+1 ; ξt+1 )] + φ2 (zt ; ξt ) .
1 + i2,tNote that, given the inequality constraint (2.9), the right-hand side of the above equation equals tounity if and only if10
mt ≥ m̄2 ; mt+1 ≥ m̄1 ,9 The rest of this section assumes perfect foresight unless otherwise mentioned.
10 Observe that φm (zt ; ξt ) = φ2 (zt ; ξt ) if mt ≥ m̄2 , and that φm (zt+1 ; ξt+1 ) = φ1 (zt+1 ; ξt+1 ) if mt+1 ≥ m̄1 .

9

implying that this is a necessary condition for the two-period nominal interest rate, i2,t , to reach thezero lower bound.
A similar argument indicates that the yield to maturity for the N -period bonds is given by(" j−1
#
)
N
−1
N
−1
Y
X
Y
1
=
[1 − φm (zt+j ; ξt+j )] +(1 − φm (zt+k ; ξt+k )) φN −j (zt+j ; ξt+j ) + φN (zt ; ξt ),1 + iN,t
j=0
j=1
k=0

(2.14)

and, given the inequality condition (2.9), the right-hand side of equation (2.14) could be equal tounity if and only if
mt ≥ m̄N ; mt+1 ≥ m̄N −1 ; · · · ; mt+N −1 ≥ m̄1 .

(2.15)

This simply states that the yield to maturity for the N period bonds could reach the zero lower
bound only when a large-scale money injection is conducted in period t, and it is expected by market
participants in period t that substantial monetary easing will be continued up until period t + N − 1.
This result sharply diﬀers from those obtained in the previous researches that pay no attention tobroad liquidity services. First, a simple substitution of φn (·) = 0 (n = 1, . . . , N ) into equation (2.14)
implies that the right-hand side of (2.14) could be equal to unity only when φm (·) = 0 holds in eachperiod from t to t + N − 1. In this sense, a necessary condition for iN,t = 0 in their models is thesatiation of money in every period. Second, i1,t , . . . , i1,t+N −1 would be zero if mt , . . . , mt+N −1 are all
equal to m̄1 . One may think this would be enough to make iN,t to be zero. But this is not true simply
because such a path of the one-period nominal interest rate does not satisfy equation (2.15), which
requires more monetary easing not only in the current period but also in the future periods. This isin a sharp contrast with the results obtained in the previous studies in that iN,t does indeed become
zero if mt , . . . , mt+N −1 are all equal to m̄1 .

2.3

Open market operations

If the condition (2.15) is satisfied, the yield to maturity would equal to zero for all bonds startingfrom 1-period bonds up to N -period bonds. In other words, the yield curve in period t contains a flat“zero-rate zone.” This has been the key feature in the Japanese financial markets since the springof 2001 until very recently, as we will closely see in the next section. Given such an environment,
the Bank of Japan sought to expand the zero-rate zone in the yield curve by conducting a series oflarge-scale open market operations.
10We consider the eﬀects of an additional large-scale open market operation when the yield tomaturity equals to zero for all bonds up to N -period bonds, using a theoretical framework prepared in
the previous subsections. Specifically, we are interested in the conditions under which an additional
operation would expand the zero-rate zone. First, it is important to note that the purchase of bonds
with less than N periods to maturity has no consequences on financial prices, as has already been
pointed out by many researchers and practitioners. In our model with broad liquidity services, theexistence of the zero-rate zone up to the N -period bonds (i1,t = i2,t = · · · = iN,t = 0) implies
φm (zt ; ξt ) = φ1 (zt ; ξt ) = φ2 (zt ; ξt ) = · · · = φN (zt ; ξt ).
Note that all bonds up to the N -period bonds are equivalent to money in the sense that they pay nointerest to their holders, and that they provide the same marginal liquidity service as money does.
Given this, the purchase of bonds with less than N periods to maturity is nothing but an exchangeof two identical financial assets, therefore yielding no consequences on an equilibrium in the financial
markets. On the contrary, a central bank may not be able even to purchase such bonds if market
participants need to pay some transaction costs for each financial transactions including those with acentral bank.11
Second, consider the purchase of bonds with longer than N periods to maturity. Specifically,
suppose that a central bank purchases the N + 1-period bonds. As explained earlier, all bonds up to
the N -period bonds are equivalent to money, so that they can be regarded as “money”. The purchaseof the N + 1-period bonds is nothing but an exchange between those bonds and “money”. An increase
in “money” leads to a decrease in the marginal liquidity service for money and those bonds included
in “money” by the same amount. Then the market price of “money” should decline so as to restore
an equilibrium in the financial market. However, given that the price of “money” is already equal tounity (namely, zero interest rates), there is no room for a further increase. The only way to restore an
equilibrium in this circumstance is to make the interest rate for the N + 1-period bonds suﬃciently
lower to create an additional demand for “money”, which should coincide with an additional supply of“money” injected though the open market operation. This is the portfolio rebalancing eﬀect of open
market operations discussed by Goodfriend (2000).
To evaluate this eﬀect, we investigate the impact of an open market operation in period t upon
11 The Bank of Japan failed to purchase short-term bonds, and was thus forced to purchase longer-term bonds in2004-2005.

11

various interest rates in period t, under the assumption that the market’s expectation about futureinterest rates are not aﬀected by the open market operation in period t. We start by looking at a simple
case in which mt = m̄1 so that i1,t is already zero, but the market expects in period t that mt+1 < m̄1
so that i1,t+1 will still be positive. We want to see what will happen on i2,t if an additional money
is injected through an open market operation in period t, although the market expectation about therelevant future interest rates (i1,t+1 in this case) does not change in response to the operation. As wesaw in the previous subsection, a necessary condition for i2,t = 0 is that mt ≥ m̄2 and mt+1 ≥ m̄1 ,suggesting that a further increase in mt would lower i2,t to a level closer to zero. To see this, we
express the price of two-period bond in period t in a slightly diﬀerent way.12
¶µ
¶
¸
µ
∙
1
1
φ2 (zt ; ξt )1
1
+ φ1 (zt ; ξt ).
=−1 + i2,t
1 + i1,t
1 + i1,t+1
φ1 (zt ; ξt ) 1 + i1,t+1(2.16)

The first term on the right-hand side of this equation does not change in response to the operation,
because i1,t is already zero, and the market expectation about i1,t+1 is not altered by the operation.
Turning to the second term on the right-hand side of the equation, the expectations theory implies
that this term should be always equal to zero. This is indeed true if φ1 (·) and φ2 (·) are both equal
to zero, as assumed in models without broad liquidity services. Then these models imply that anopen market operation without changing i1,t+1 has no eﬀects on i2,t . However, this is not true any
more in our setting. For example, when mt is equal to m̄1 , φ2 (·) is small relative to φ1 (·), so thatthe second term on the right-hand side should be negative. If mt increases through the operation,
however, φ2 (·)/φ1 (·) monotonically approaches unity, and the second term turns to positive.13 Thisimplies that an increase in money through the open market operation lowers i2,t .14
The above argument could be extended to the open market purchase of the N + 1-period bonds,
whose market price is given by
¶µ
¶
¸
µ
∙
1
1
φN +1 (zt ; ξt )1
1
+ φ1 (zt ; ξt ).
=−1 + iN +1,t
1 + i1,t
1 + iN,t+1
φ1 (zt ; ξt )1 + iN,t+1
Suppose that i1,t , i2,t , . . . , iN,t are all equal to zero, and that an open market operation in period t does
not alter the market’s expectations about the future path of money supply. Then a similar argument
12 We obtain this equation by substituting (2.4) into (2.6).
13 If m = m̄ , then φ (·)/φ (·) = 1, and the second term should become positive. Figure 3 shows the value of thet2
2
1
second term as a function of mt in a case in which the marginal liquidity service schedules for money and various bonds
are linear as given in Figure 2.
14 This could be understood in the following way. The market price of the two-period bonds in period t consists of twoparts: the discounted value of the market price of the one-period bonds in period t + 1 and the marginal liquidity service
provided by the two-period bonds in period t (φ2 (zt ; ξt )). The latter part increases relative to φ1 (zt ; ξt ) in response to
an increase in mt , thereby contributing to a rise in the market price of the two-period bonds in period t.

12

as before implies that an increase in money though the purchase of the N + 1-period bonds in periodt leads to an increase in the term φN +1 (zt ; ξt ) /φ1 (zt ; ξt ),15 thereby raising the market price of theN + 1-period bonds in period t.

2.4

Forward and futures interest rates

If the second term on the right-hand side of (2.16) is positive, it implies
1 + i2,t< 1 + i1,t+1 .
1 + i1,t
The right-hand side of this equation represents the one-period forward rate in period t that starts inperiod t+1 and ends in period t+2, while the left-hand side represents the corresponding futures rate.
This equation simply states that the forward rate in period t could be lower than the corresponding
futures rate if substantial monetary easing is conducted in period t.
The market price for the three-period bonds similarly implies
1−
1 + i3,tµ¸∙
φ3 (zt ; ξt )1
= φ2 (zt ; ξt )−φ2 (zt ; ξt ) 1 + i1,t+2∙¸
φ2 (zt+1 ; ξt+1 )1+[1 − φm (zt ; ξt )]φ1 (zt+1 ; ξt+1 )−.
φ1 (zt+1 ; ξt+1 ) 1 + i1,t+2

1
1 + i2,t¶µ

1
1 + i1,t+2¶(2.17)

If the right-hand side of this equation is positive, it implies
1 + i3,t< 1 + i1,t+2 .
1 + i2,t
The left-hand side represents the one-period forward rate that starts in period t + 2 and ends in period
t+3, while the right-hand side represents the corresponding futures rate. The right hand-side of (2.17)
is likely to be positive when the following conditions are satisfied. First, the base money in period t,
mt , should be close to m̄3 so that φ3 (zt ; ξt )/φ2 (zt ; ξt ) becomes as close as its maximum value (namely,
unity). Similarly, the market’s expectation formed in period t about the base money in period t + 1,
mt+1 , should be close to m̄2 so as to make φ2 (zt+1 ; ξt+1 )/φ1 (zt+1 ; ξt+1 ) as close as its maximum(namely, unity). These two conditions indicate that substantial monetary easing not only in periodt but also in period t + 1 are necessary conditions for the futures and forward spread to be positive.
Second, the base money in period t + 2 should be less than m̄1 so as to keep i1,t+2 at a positive level.
If mt+2 should exceed m̄1 , then the expressions in the two squared brackets on the right-hand side are
15 Specifically, m increases from m̄tN to mt = m̄N +1 .

13both equal to zero even if both φ3 (zt ; ξt )/φ2 (zt ; ξt ) and φ2 (zt+1 ; ξt+1 )/φ1 (zt+1 ; ξt+1 ) equal to unity.
In fact, i3,t is equal to zero in this case, as we saw in subsection 2.2. In other words, the futures andforward spread becomes zero as soon as the three-period bonds enter the zero-rate zone. This implies
that the futures and forward spread is likely to be positive around the end of the zero-rate zone.
The market price for the n-period bonds implies
¶µ
¶
¸
∙
1
1
φn (zt ; ξt )1
= φn−1 (zt ; ξt )−1 + in−1,t
1 + i1,t+n−1
φn−1 (zt ; ξt ) 1 + i1,t+n−1
(
)
¸
∙
n−2
X j−1
Y
φn−j (zt+j ; ξt+j )1, (2.18)[1 − φm (zt+k ; ξt+k )] φn−1−j (zt+j ; ξt+j )+−φn−1−j (zt+j ; ξt+j ) 1 + i1,t+n−1
j=1

1−
1 + in,t

µ

k=0

and
1 + in,t< 1 + i1,t+n−1
1 + in−1,tholds if the right-hand side of (2.18) is positive. A necessary condition for this is that substantial
monetary easing is conducted in period t as well as in periods t + 1, t + 2, and so on. For example,
a decline in the forward rate relative to the futures rate would be limited if an increase in the basemoney in period t is perceived by the market to be a temporary one. The future and forward spread
would increase over time as market participants gradually update their belief about the future pathof the base money.
Figure 4 illustrates how the forward and futures spread depends on the real money balance inperiod t, mt , and the expected real balance in period t + 1, mt+1 , for the case of the two-period bonds.
1+i

1coincides with the corresponding futures rate 1+i1,t+1, if
First, we note that the forward rate 1+i2,t1,tmt exceeds m̄2 and mt+1 exceeds m̄1 . In other words, the spread is zero within the zero-rate zone.
¯ . This is the situation the previous
Second, the spread is again zero if mt exceeds the satiation level m̄studies on the optimal monetary policy rule in a liquidity trap, including Eggertsson and Woodford(2003), have been focusing on. Third, the spread would be positive if mt is close to, or greater thanm̄2 and mt+1 is less than m̄1 . In other worlds, the spread could become positive outside the zero-ratezone, if a large-scale open market operation (but not so large to reach the satiation level) is conducted.
This is the new possibility our analysis focuses on.

14

3

Forward and Futures Spreads in 2001-2006

We show that a massive injection of monetary base distorts yield curve in our analysis using the modelof broad liquidity in the previous section. More precisely, a massive provision of monetary base reduceforward interest rates, thus possibly inducing forward interest rates lower than futures interest rates.
In addition, a spread between forward and futures interest rates, observed at period t and startingfrom n-period ahead, depends on market expectations regarding the future path of monetary basefrom period t to t + n. This implies that the spread does not necessarily expand at the time of themassive injection of monetary base, but at the time when market expectations regarding the future
path of monetary base do change. In this section, we examine these predictions using the Japanesedata during the period of quantitative monetary easing policy, from 2001 through 2006.

3.1

Preliminary analysis

We start by comparing the forward and futures yield curves on some typical days. Figure 5 shows these
two yield curves on February 5, 1999, April 13, 2000, September 25, 2000, June 27, 2001, June 30,
2005, and June 9, 2006. The forward yield curves represent the three-month rates starting from each
day measured on the horizontal axis, which is estimated using the Nelson-Siegel method (see Appendix
A for more details). On the other hand, the futures yield curves represent the corresponding futuresinterest rates, taken from the Euro yen three month futures rate.
A simple comparison between the two yield curves shows the following. First, we do not see any
significant discrepancies between the two before the start of a quantitative monetary easing policy inMarch 19, 2001.16 Specifically, the two lines are located very close to each other on the three days;
February 5, 1999 (just before the start of a zero interest rate policy); April 13, 2000 (the period inwhich financial markets restored its stability after the end of the fiscal year); September 25, 2000
(just after the termination of the zero interest rate policy). However, the two lines start to deviate
from each other after the start of the quantitative monetary easing policy, as shown in the figure forJune 27, 2001. The futures yield curve overlaps with the forward one for the maturities shorter than
one year, while the futures curve is located well above the forward one for longer maturities. Such a
discrepancy between the two yield curve is observed as well on June 30, 2005, when the CAB (current
16 As we see later, however, there were some phases in which the discrepancies emerged even before the start of thequantitative monetary easing policy, including the end of December 1999 when the spread widened due to the Y2K
problem.

15

account balance) target was 30-35 trillion yen.17 However, it disappears again on June 9, 2006, whenthe quantitative monetary easing policy ended and the CAB reduced to about 10 trillion yen.
Figure 6 shows scatter plots with time-to-settlement (relative to the policy duration measured by
P D, which is defined in the next subsection) on the horizontal axis, and futures and forward spreadon the vertical axis. We show the result for the full sample period (February 2, 1999 to June 30, 2006)
as well as the results for five subsamples. We clearly see a hump-shaped curve in each of them. More
importantly, these hump shaped curves tend to reach their peaks when period-to-maturity coincides
with P D. In other words, the spread is very close to zero for short maturities, but it tends to increase
monotonically as the maturity approaches P D. Such a tendency is most clearly seen in the period of
QMEP under Governor Hayami, and the period of QMEP under Governor Fukui. These observations
are consistent with the theoretical predictions obtained in the previous section.

3.2

Indicators for spreads between futures and forward rates

We propose two indicators to detect spreads between futures and forward rates: horizontal spreads
for HSP and vertical spreads for V SP , illustrated in Figure 7. We first estimate the policy duration,
P D, as a flattened zone in the short-end of a forward rate curve. We then measure the verticaldistance between the futures rate curve and the forward rate curve at P D. We compute a forward
rate and a futures rate at P D as F W P D and F T P D, respectively, and V SP is defined as a spread
between F T P D and F W P D. We measure the horizontal distance at F W P D. We define P D∗ as thetime-to-settlement of futures contract that futures rate is equal to F W P D. We compute HSP as adiﬀerence between P D and P D∗ .
We formally define the above mentioned indicators: P D, P D∗ , F W P D, F T P D, HSP , andV SP . First, we follow the definition of P D in Okina and Shiratsuka (2004), based on estimates ofthe extended Nelson-Siegel model regarding the instantaneous forward rate (IFR) for a settlement at
period m, denoted by r(m), below:
¡m¢
¡ m¢
¡m¢
¡ m¢
¡ m¢
+ β2
exp −
+ β3
exp −
,
r(m) = β0 + β1 exp −
τ1
τ1
τ1
τ2
τ2

(3.1)

where β0 , β1 , β2 , β3 , τ1 and τ2 are parameters to be estimated from the data. We expect β0 , τ1 andτ2 to be positive. Using the estimates of the extended Nelson-Siegel model, P D is defined as:
P D = τ2 ,17 This was the period just before the market’s started to expect the termination of the policy.

16

(3.2)

The estimate of τ2 corresponds to the duration of the flattened zone of r(m) in the short end, andreflects the market expectations of how long the BOJ will commit to a zero interest rate.
Next, we measure the vertical distance between a forward rate curve and futures rate curve at
P D. F W P D and F T P D are defined as 3-month forward rates starting from P D for both euro yen
TIBORs/yen swap rates and euro-yen futures rates.
FWPD = 4

Z P D+1/4

r(s)ds,

(3.3)

s=P D

FTPD =

P D − tn
tn+1 − P D
F T (tn ) +F T (tn+1 ),tn+1 − tn
tn+1 − tn(3.4)

where F T (t) is 3-month euro yen futures rates for the time-to-settlement of t, and tn and tn+1 areadjacent time-to-settlements that include PD in their interval, i.e. tn ≤ P D < tn+1 . Thus, the verticalspread, VSP, is defined as
V SP = F T P D − F W P D.

(3.5)

Finally, we measure the horizontal distance at F W P D. We define P D∗ as the time-to-settlementof euro yen futures that euro yen futures rate is equal to F W P D. More precisely, P D∗ satisfies theequation below,
tk+1 − P D∗P D ∗ − tk
F T (tk ) +F T (tk+1 ) = F W P D,
tk+1 − tk
tk+1 − tk(3.6)

where tk and tk+1 are adjacent time-to-settlements that include P D∗ in their interval, i.e. tk ≤ P D∗ <tk+1 . Thus, P D∗ is computed as
P D∗ =(tk+1 − tk )F W P D − tk+1 F T (tk ) + tk F T (tk+1 ).
F T (tk+1 ) − F T (tk )(3.7)

The horizontal spread, HSP, is defined as
HSP = P D − P D∗ .

(3.8)

Note that the long-term forward rate, LF R, is also an informative indicator, defined in Okina andShiratsuka (2004). This indicator is equal to β0 in equation (3.1) and is considered as a proxy forthe summation of expected inflation and expected economic growth, or expected nominal economic
growth.
LF R = β0 ,

17

(3.9)

3.3

Time-series movements of HSP and VSP

We first look at the day-by-day changes in F W P D and F T P D, as well as the changes in P D andP D∗ , around the start of the quantitative monetary easing policy in March 19, 2001 (see the twocharts on the left-hand side of Figure 8).18 Note that there was a discrepancy between F W P D and
F T P D, or between P D and P D∗ , even before the start of the policy. This probably reflects the factthat the BOJ’s injected money in response to a temporary increase in liquidity demand just before
the end of the fiscal year (namely, the end of March). As is consistent with this interpretation, these
spreads almost disappeared at the beginning of April, as soon as the new fiscal year started. More
importantly, however, the spread started to widen again in April, and continued to increase over the
next three months. If we look more closely at the changes in P D and P D∗ during this period, we seethat P D rose almost consistently during this period while P D∗ did not show any significant change.
A similar tendency could be seen in F W P D and F T P D, although less clearly. These observations
suggest that money injection during this period contributed to lowering forward interest rates, andextending the zero-rate zone in the yield curve, while keeping the market’s expectations about futuremonetary policy unchanged.
Turning to the changes in these four variables around the end of the policy in March 9, 2006, we
see more clearly that a decrease in the base money lead to a narrower spread, both in terms of thevertical and horizontal ones, until it finally disappeared at the end of May. Note that the current
account balance at the BOJ has been declining only gradually even after the decision to terminate
the policy was made in March 9.19 This is consistent with the gradual decline in the spread during
this period.
Let us next examine the developments in HSP and V SP from 2001 through 2006 in Figure 9. In
this figure we plot P D and P D∗ in the top panel, F W P D and F T P D in the second top panel, HSP
and V SP in the second bottom panel, and LF R in the bottom panel.
Looking at the top panel, P D jumps upward after the introduction of QMEP and remains highthroughout 2001, while P D∗ does not respond significantly and rather start declining around the turnof the year from 2001 to 2002. After the sharp decline in P D in mid-2003, P D and P D∗ converge to
18 All figures used in Figure 8 are the moving average over thirteen days. Also note that FWPD and FTPD are
depicted using diﬀerent vertical axes (the left axis for F W P D and the right axis for F T P D).
19 Even at the end of June, more than three months after the decision, the current account balance is above 15 trillion
yen, much higher than the level before the start of the quantitative monetary easing policy (about 4 trillion yen).

18

almost same level at around one year. They then start rising again, but P D increases slightly fasterthan P D∗ . After the second half of 2005, they drop again, as market expectations rise regarding theearly termination of QMEP.20
In the second top panel, F W P D and F T P D generally show reverse relationship between P D andP D∗ . However, most significant movements can be seen in the sharp rise in both F W P D and F T P D
after the termination of QMEP, suggesting growing market expectations regarding the early exit fromzero interest rates. In the second bottom panel, HSP and V SP generally show similar movements,and especially during the period of QMEP under Governor Hayami, two indicators move very closely.
To sum up, both HSP and V SP steadily expand from 2001 through the summer of 2003 when
the series of increase in the target level of the current account balance at the BOJ. HSP and V SP ,however, do not necessarily move in response to the increases in the target level. Especially, HSP and
V SP are generally insensitive to rapid rises in the target level of the current account balance at theBOJ. Given that LF R follows declining trend from late 2002 through mid-2003, such developments
in HSP and V SP suggest that market expectations regarding the future path of the current accountbalance at the BOJ remain virtually unchanged.

3.4

Granger causality test

We next examine the time-series relation between policy duration indicators and monetary policy
actions. To this end, we focus on two variables as indicators for monetary policy actions. The firstone, RSV , is the outstanding balance of current accounts at the BOJ, and the second one, OP E, isthe maturity of outstanding amounts of outright purchasing operations of commercial bills.
We carry out Granger causality test using the above two variables as well as two sets of policy
duration indicators: P D, P D∗ and F W P D, F T P D. Figure 10 and 11 respectively report F -values for
Granger causality tests for a relationship among two sets of variables using subsamples of 60 businessdays ending at each date on the horizontal axis and the four-variable VAR model with five-day lag
length.
According to these figures, relationships among these variable are highly sensitive to the choice ofsample period. We find almost no evidence regarding the changes in the current account balance at
20 It should be noted that estimates of P D ∗ tend to become unstable before significant liquidity events, such as theY2K problem and the end of fiscal year. This is because short-end of forward rate curve shows a hump-shape reflecting
increased concern over liquidity availability, and forward rates at shorter than P D become higher than that at P D,
thus making it very diﬃcult to find P D∗ within the interval of zero to P D.

19

the BOJ Granger cause other variables.

4

Conclusion

This paper has presented a model with broad liquidity services to investigate the consequences ofmassive money injection in an economy with the zero interest rate bound. We incorporate Goodfriend’s(2000) idea of broad liquidity services into the model by allowing the amounts of bonds with various
maturities held by a household to enter its utility function. Our main findings can be summarized asfollows. First, we show that the satiation of money (or the zero marginal utility of money) is not anecessary condition for the one-period interest rate to reach the zero lower bound; instead, we present
a weaker necessary condition that the marginal liquidity service provided by money coincides with themarginal liquidity service provided by the one-period bonds, both of which are not necessarily equal
to zero. Second, we show that massive money injection through an open market operation would havesome influences on the yield curve even if it does not alter the private sector’s expectations about
future monetary policy, as long as a central bank purchases bonds located outside the zero rates
zone. Third, we show that the forward and futures spread would become positive (i.e., the forward
interest rate is lower than the corresponding futures rate) when a central bank conduct massive money
injection, although it would become zero in a limiting case in which the base money is supplied up to
the satiation level.
We have also conducted empirical analysis to check the implications of the model. Our empiricalresults indicate that forward interest rates started to decline relative to the corresponding futures rates
just after March 2001, when a quantitative monetary easing policy started by the Bank of Japan, andthat the forward and futures spread has never closed until the policy ended in March 2006. We argue
that these findings are not easy to explain by a model without broad liquidity services.21

21 Our findings have the following implications. First, the zero-rate zone in the yield curve has been expanded in
2001-2006 mainly through the portfolio rebalancing channel, not through the expectation channel. This is consistent
with the fact that the eﬀects of monetary stimulation through quantitative easing have been very limited. Second, theyield curve provides less useful information on the private sector’s expectations about future monetary policy when theovernight interest rate has reached the zero lower bound, in the sense that forward interest rates would deviate fromthe corresponding futures rates.

20References[1] Bernanke, Ben S., “Deflation: Making Sure “It” Doesn’t Happen Here,” Before the National
Economists Club, Washington, D.C., November 21, 2002.
[2] Bernanke, Ben S., Vincent Reinhart, and Brian Sack, “Monetary Policy Alternatives at the ZeroBound: An Empirical Assessment,” Brookings Papers on Economic Activity 2: 2004, 1-78.
[3] Clouse, James, Dale Henderson, Athanasios Orphanides, David Small and Peter Tinsley, “Monetary Policy When the Nominal Short-Term Interest Rate is Zero,” Topics in Macroeconomics 3(1), Article 12, 2003.
[4] Eggertsson, Gauti, and Michael Woodford, “The Zero Bound on Interest Rates and Optimal
Monetary Policy,” Brookings Papers on Economic Activity 1: 2003, 139-211.
[5] Fujiki, Hiroshi, Kunio Okina, and Shigenori Shiratsuka, “Monetary Policy under Zero Interest
Rate —Viewpoints of Central Bank Economists—,” Monetary and Economic Studies, 19 (1), 89130, 2001.
[6] Fujiki, Hiroshi, and Shigenori Shiratsuka, “Policy Duration Eﬀect under the Zero Interest Rate
Policy in 1999-2000: Evidence from Japan’s Money Market Data,” Monetary and Economic
Studies, 20 (1), 1-31, 2002.
[7] Goodfriend, Marvin, “Overcoming the Zero Bound on Interest Rate Policy,” Journal of Money,
Credit, and Banking 32 (4), 1007-1035, 2000.
[8] Goodfriend, Marvin, “Narrow Money, Broad Money, and the Transmission of Monetary Policy,”Federal Reserve Bank of Richmond, 2004.
[9] Hanes, Christopher, “The Liquidity Trap and U.S. Interest Rates in the 1930s,” Journal of Money,
Credit, and Banking, forthcoming.
[10] Iwamura, Mitsuru, Takeshi Kudo, and Tsutomu Watanabe, “Monetary and fiscal policy in aliquidity trap: The Japanese experience 1999-2004,” NBER Working Paper Series 11151, 2005.
[11] Jung, Taehun, Yuki Teranishi and Tsutomu Watanabe, “Optimal Monetary Policy at the ZeroInterest-Rate Bound,” Journal of Money, Credit, and Banking 37 (5), 813-835, 2005.
21

[12] Kimura, Takeshi, Hiroshi Kobayashi, Jun Muranaga, and Hiroshi Ugai, “The Eﬀect of ‘Quantitative Monetary Easing’ at Zero Interest Rates,” IMES Discussion Paper Series, No. 2002-E-22,
2002.
[13] Marumo, K., T. Nakayama, S. Nishioka, and T. Yoshida, “Extracting Market Expectations on
the Duration of the Zero Interest Rate Policy from Japan’s Bond Prices,” Financial Markets
Department Working Paper 03-E-2, 2003.
[14] Meltzer, Allan H., “The Transmission Process,” In Deutsche Bundesbank ed. The Monetary
Transmission Process: Recent Developments and Lessons for Europe, London: Palgrave, 2001.
[15] McGough, Bruce, Glenn D. Rudebusch, and John C. Williams, “Using a Long-Term Interest
Rate as the Monetary Policy Instrument,” Journal of Monetary Economics 52, 2005.
[16] Nagayasu, Jun, “The Term Structure of Interest Rates and Monetary Policy During a Zero
Interest Rate Period,” Monetary and Economic Studies 22 (2), 19-43, 2004.
[17] Nelson, Charles R., and Andrew F. Siegel, “Parsimonious Modeling of Yield Curves,” Journal ofBusiness, 60 (4), 473-489, 1987.
[18] Oda, Nobuyuki, and Kazuo Ueda, “The Eﬀects of the Bank of Japan’s Zero Interest Rate Commitment and Quantitative Easing on the Yield Curve: A Macro-Finance Approach,” Bank ofJapan Working Paper Series No. 05-E-6, 2005.
[19] Okina, Kunio, and Shigenori Shiratsuka, “Policy Commitment and Expectation Formation:
Japan’s Experience under Zero Interest Rates,” North American Journal of Economics and Finance 15, 75-100, 2004.
[20] Söderlind, Paul, and Lars E. O. Svensson, “New Techniques to Extract Market Expectations
from Financial Instruments,” Journal of Monetary Economics 40 (2), 383-429, 1997.
[21] Woodford, Michael, “Commentary: How Should Monetary Policy Be Conducted in an Era ofPrice Stability?” in New Challenges for Monetary Policy, Kansas City: Federal Reserve Bank ofKansas City, 1999.
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22

Appendix A Indicators for the Policy Duration Eﬀect in Okina and Shiratsuka (2004)
Okina and Shiratsuka (2004) derive indicators for the policy duration eﬀect using the estimates of theextended Nelson and Siegel’s (1987) model, proposed by Söderlind and Svensson (1997). They apply
the model to euro-yen Tokyo interbank oﬀered rates (TIBOR) and yen swap rates: euro-yen TIBORs
for 1-month to 12-month contracts, and yen swap rates for 1-year to 12-year contracts.
As shown in equation (3.1), the instantaneous forward rate (IFR), based on the extended NelsonSiegel model, includes four terms. For your reference, we show equation (3.1) again below:
¡ m¢
¡m¢
¡ m¢
¡m¢
¡ m¢
r(m) = β0 + β1 exp −
+ β2
exp −
+ β3
exp −
,
τ1
τ1
τ1
τ2
τ2

(A.1)

where β0 , β1 , β2 , β3 , τ1 and τ2 are parameters to be estimated from the data. We expect β0 , τ1 andτ2 to be positive.
The first term is a constant β0 . The second term is an exponential function β1 exp(−m/τ1 ). Whenβ1 takes a negative (positive) value, this term produces an upward-trending (downward-trending)shape in the short end of the IFR curve. A large (small) value of τ1 means that this exponential eﬀect
decays more slowly (quickly). The third term is β2 (m/τ1 ) exp(−m/τ1 ), producing a U-shape (humpshape) when β2 takes a negative (positive) value. The fourth term produces a U-shape (hump shape)
when β3 takes a negative (positive) value. τ2 controls the rate of convergence of the fourth term, as
does τ1 for the second and third terms. The important features of equation (A.1) are that the limits offorward and spot rates when maturity approaches zero and infinity, respectively, are equal to β0 + β1
and β0 .22
To detect market expectations on the duration of the policy commitment as well as the impactsof the policy, Okina and Shiratsuka (2004) define four indicators for the policy duration eﬀect below,
using the estimates of the extended Nelson-Siegel model.
P D = τ2 ,1
RP D =
PD

Z PD

(A.2)
r(s)ds,

(A.3)

s=0

22 In our estimation, we exploit the first feature to keep the very short end of the IFR curve from becoming negative,by imposing the restriction that the overnight uncollateralized call rate be equal to β0 + β1 . This restriction is suﬃcient
to prevent the zero-bound of nominal interest rates from influencing the estimates. We also use the second feature tocompile an indicator for policy duration eﬀect since it corresponds to the restriction that forward rates for settlements
very far into the future be constant.

23

SL = arctan(r 0 (2τ2 )),(A.4)

LF R = β0 ,(A.5)

The first indicator, P D, corresponds to the duration of the flattened shape of r(m) before its
second stage increase reflects the market expectations of how long r(m) will stay close to zero, andthus how long the BOJ will commit to a zero interest rate. The second indicator, RP D, computes spot
rates at P D, showing the flatness of r(m) in the short-end and the confidence of market participants
regarding the strength of BOJ’s commitment to a zero interest rate. The third indicator, SL, shows
sharpness of r(m) in medium-term, indicating market expectations as to how rapidly the economy
will recover from the zero interest rate conditions. The fourth indicator, LF R, is equal to β0 , or the
long-term forward rate, and is considered as a proxy for the summation of expected inflation and
expected economic growth, or expected nominal economic growth.23 This is deemed to reflect market
expectations for long-term economic performance.
Figure A-1 updates four indicators up to end-June 2006, which includes the periods of ZIRP
and QMEP. We see a significant change in market expectations during the summer of 2003. The
forward rate curve shifts upward in the medium to long term, as evidenced by increased SL and
LF R, indicating brightening market expectations for the long-term performance of the economy. At
the same time, P D shortens, partly because such positive expectations in turn shorten the expected
duration of the policy commitment to a zero rate or to quantitative monetary easing.
Looking at the period after the second half of 2005, P D declines steadily and RP D and SL shift
upward, reflecting growing expectations of the termination of quantitative monetary easing policy.
Shortly before the termination of QMEP, P D stop declining, while SL start increasing rapidly, suggesting that the forward rate curve steepens in the medium-term. After the termination, RP D startrising, reflecting growing market expectations about the exit from zero interest rates. In contrast
to the summer of 2003, LF R generally remains unchanged until the termination of QMEP, while it
moves up slightly after the termination.

23 Given the possibility of time-varying risk premiums, we must be cautious in interpreting time-series movements of

estimates.

24

Table 1: Policy events

Date

Changes in Policy Guidelines

September 9, 1998

Reduction of targeted O/N rate (0.5 Æ 0.25 %)November 13, 1998

Introduction of new money market operations

February 12, 1999

Introduction of zero interest rate policy

April 13, 1999

Governor’s announcement of the commitment to zero interest
rate until deflationary concerns are dispelled

October 13, 1999

Expansion of the range of money market operations

August 11, 2000

Termination of zero interest rate policy

February 9, 2001

Reduction of ODR (0.5Æ0.375%), introduction of new methodof liquidity provision

February 28, 2001

Reduction of targeted O/N rate (0.25Æ0.125%) and ODR(0.375Æ0.25%)*1

March 19, 2001

Decision to introduce quantitative monetary easing policy

August 14, 2001

Increase in the target CAB (5Æ6 trill. yen) *1

September 18, 2001

Increase in the target CAB (6Æabove 6 trill. Yen)

December 19, 2001

Increase in the target CAB (above 6Æ10-15 trill. yen)

September 18, 2002

Introduction of stock purchasing plan

October 30, 2002

Increase in the target CAB (10-15Æ15-20 trill. yen)

(March 20, 2003)

Installation of Governor Fukui

April 30, 2003

Increase in the target CAB (17-22Æ22-27 trill. yen) *2

May 20, 2003

Increase in the target CAB (22-27Æ27-30 trill. yen)

October 10, 2003

Increase in the target CAB (27-30Æ27-32 trill. yen)

January 20, 2004

Increase in the target CAB (27-32Æ30-35 trill. yen)March 9, 2006

Termination of QMEP*1

Note: 1.

ODR denotes the official discount rate, CAB denotes the current account balance, and

QMEP denotes quantitative monetary easing policy.
2.

The target CAB was raised from 15-20 trillion yen to 17-22 trillion yen on April 1,

2003, considering necessary adjustment due to the establishment of the Japan Post.

25

Figure 1: Current account balance at the BOJ(trillion yen)
40
Iraqi war

35

End offiscal year

End offiscal mid-year

30
Y2K

25

End offiscal year

Y2K
(leap year)

20
15

9-11
terror attack

Computer system failure ofMizuho Financial Group10
Financial difficulties
of Enron

5
0
1998

1999

2000

2001

2002

2003

2004

2005

Note: Shaded lines indicate the target or target range of the current account balance.

26

2006

Figure 2: Marginal Liquidity Service

0.12

φm

0.10

φ1
φ2

0.08

φ3
0.06

φ4
0.04

0.02

0.00
0

m1

m2

27

m3

m4

m

mt

Figure 3: Futures-Forward Spread

0.004
0.002
0.000
-0.002-0.004-0.006-0.008-0.010-0.012-0.0140

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

i= 0.00i= 0.0128

i= 0.031i= 0.05

Figure 4: Forward versus Futures Interest Rates

m t +1m

m2

Forward=Futures
Forward>Futures

m1

Forward<Futures

m1

m2

29

m

mt

Figure 5: Short-end of yield curves

(%)
2.5

(%)
0.6

February 5, 1999

June 27, 2001

3M forward rates
0.5

2.0

Euro yen futures
0.4

1.5
0.3
1.0
0.2

3M forward rates
0.5

0.1

Euro yen futures

0.0

0.0
0

1

(%)
2.0

2
(time-to-settlement, years)

3

0

1

2
(time-to-settlement, years)

(%)
0.8

April 13, 2000

3

June 30, 2005

3M forward rates
1.5

0.6

1.0

0.4

Euro yen futures

3M forward rates
0.5

0.2Euro yen futures

0.0

0.0
0

1

(%)
2.0

2
(time-to-settlement, years)

3

0

(%)
2.0

September 25, 2000

1.5

1.5

1.0

1.0

1

2
(time-to-settlement, years)

3

June 9, 2006

3M forward rates

3M forward rates
0.5

0.5

Euro yen futures

Euro yen futures
0.0

0.0
0

1

2
(time-to-settlement, years)

3

0

30

1
2
(time-to-settlement, years)

3

Figure 6: Spreads between futures and forward rates
ZIRP: 99/2/12-00/8/13

Full sample
60

60

99/2/12-9/30
99/10/1-12/30
00/1/4-3/31
00/4/1-8/10

b/w ZIRP and QMEP40

40

QMEP under Hay ami
QMEP under Fukui
Post-QMEP

20
0
-20

-40
-60
-3

-2

-1
0
1
(Difference from PD, year)

2

3(Spreads between futures and forward, bps)

(Spreads between futures and forward, bps)

ZIRP

20

0

-20

-40

-60
-3

Between ZIRP/QMEP: 00/8/11-01/3/16

3

QMEP under Hayami: 01/3/19-03/3/19

00/8/12-9/29

40

40(Spreads between futures and forward, bps)

00/10/2-12/29
01/1/4-3/16

20

0

-20

-40

-60
-3

-2

-1
0
1
(Difference from PD, year)

2

20

0

-20

01/3/19-8/13
01/8/14-9/17
01/9/18-12/18
01/12/19-02/10/29
02/10/30-03/3/19

-40

-60

3

-3

-2

QMEP under Fukui: 03/3/20-06/3/8
60

40

40

20

0
03/3/20-4/28
03/4/30-5/19
03/5/20-10/9
03/10/10-04/1/19
04/1/20-06/3/8

-20

-40

-60
-3

-2

-1
0
1
(Difference from PD, year)

2

-1
0
1
(Difference from PD, year)2

3

Post-QMEP: 06/3/9-06/6/30

60(Spreads between futures and forward, bps)

(Spreads between futures and forward, bps)

-1
0
1
2
(Difference from PD, year)

60

60(Spreads between futures and forward, bps)

-2

20

0

-20

-40

-60

3

-3

31

-2

-1
0
1
(Difference from PD, year)

2

3

Figure 7: Indicators for spreads between forward and futures interest rates(interest rate)
HSP

futures rates
forward rates

FTPD
VSP
FWPD

PD *
PD
(time-to-settlement)

32

0.00

2001/06/15

2001/05/31

0.00

33
1.20

2006/06/29

PD

2006/06/14

2006/05/30

2006/05/15

2006/04/25

2006/04/10

1.00

2006/03/24

1.50

2006/03/08

PD*

2006/02/21

2.50

2006/02/06

FTPD

0.90
0.95

0.45
0.80
0.85

0.35
0.40
0.70
0.75

0.30
0.35
0.60
0.65

0.25
0.30
0.50
0.55

0.20
0.25
0.40
0.45

0.15
0.20
0.30
0.35

0.10
0.15
0.20

0.05
0.10
0.10

0.00
0.05
0.00
2006/06/29

2006/06/14

2006/05/30

2006/05/15

2006/04/25

2006/04/10

2006/03/24

2006/03/08

2006/02/21

2006/02/06

2006/01/20

2006/01/04

2001/06/15

2001/05/31

2001/05/16

2001/04/26

2001/04/11

2001/03/27

2001/03/09

2001/02/22

2001/02/06

2001/01/22

2001/01/04

0.50

FWPD

2006/01/20

0.45

2006/01/04

0.40

2001/05/16

2001/04/26

2001/04/11

2001/03/27

2001/03/09

2001/02/22

2001/02/06

2001/01/22

2001/01/04

Figure 8: HSP and VSP around the beginning and end of QMEP

FWPD
0.25

FTPD
0.15

1.40
PD

2.00
PD*

1.00

0.80

0.60

0.40

0.50

0.20
0.05

Figure 9: Policy duration indicators(years)3.0
QMEP under Hayami

ZIRP

QMEP under Fukui

2.5
2.0
1.5
1.0
PD*
0.5
0.0

PD

1999

2000

2001

2002

2003

2004

2005

2006

(%)
1.2
1.0

FTPD

0.8

FWPD

0.6
0.4
0.2
0.0

1999

2000

2001

2002

2003

2004

2005

(years)
2.5

2006
(bps)
50

HSP

2.0

40

VSP
1.5

30

1.0

20

0.5

10

0.0

0

-0.5

1999

2000

200

2002

2003

199

2000

200

200

200

2004

2005

2006

-10

(%)
3.0
2.5
2.0
1.5
1.0
0.5
0.0

200

200

200

Note: In the top and bottom panels, shaded lines indicate the upper and lower bounds of theconfidence interval of the estimate (estimates ± 2*standard errors), respectively.

34

Figure 10: Granger causality tests: horizontal gaps
(F-val)12ZIRP
10Granger causality to DPD
QMEP (Hayami)

QMEP (Fukui)
DPD*
DRSV
DOPE

8
6
4
2
0

1999

2000

2001

(F-val)
12

2002

2003

2004

2005

2006

2004

2005

2006

Granger causality to DPD*
DPD

10

DRSV
DOPE

8
6
4
2
0

1999

2000

2001

(F-val)
12

2002

2003

Granger causality to DRSV
DPD
DPD*
DOPE

10
8
6
4
2
0

1999

2000

2001

(F-val)
12

2002

2003

2004

2005

2006

Granger causality to DOPE
DPD
DPD*
DRSV

10
8
6
4
2
0

1999

2000

2001

2002

2003

2004

2005

2006

Notes: 1. Granger causality tests are conducted using subsamples of 60 business days ending at
each date on the horizontal axis with 5-day lag length.
2. Horizontal lines shows F-values for 1-percent, 5-percent and 10-percent significancelevel from top to bottom.

35

Figure 11: Granger causality tests: vertical gaps
(F-val)10ZIRP
8Granger causality to DFWPDQMEP (Hayami)

QMEP (Fukui)
DFTPD
DRSV
DOPE

6
4
2
0

2000

2001

(F-val)
10

2002

2003

2004

2005

2006

Granger causality to DFTPD
DFWPD
DRSV
DOPE

8
6
4
2
0

2000

2001

(F-val)
10

2002

2003

2004

2005

2006

Granger causality to DRSV
DFWPD
DFTPD
DOPE

8
6
4
2
0

2000

2001

(F-val)
10

2002

2003

2004

2005

2006

Granger causality to DOPE
DFWPD
DFTPD
DRSV

8
6
4
2
0

2000

2001

2002

2003

2004

2005

2006

Notes: 1. Granger causality tests are conducted using subsamples of 60 business days ending at
each date on the horizontal axis with 5-day lag length.
2. Horizontal lines shows F-values for 1-percent, 5-percent and 10-percent significancelevel from top to bottom.

36

Figure A-1: Policy duration indicators(years)
3.5

PD
QMEP under Hayami

ZIRP

3.0

QMEP under Fukui

2.5
2.0
1.5
1.0
0.5
0.0

1999

2000

2001

(%)
0.8

2002

2003

2004

2005

2006

2003

2004

2005

2006

2003

2004

2005

2006

2003

2004

2005

2006

RPD

0.6
0.4
0.2
0.0

1999

2000

2001

( degree )
60

2002

SL

50
40
30
20
10
0

1999

2000

2001

(%)
3.5

2002

LFR

3.0
2.5
2.0
1.5
1.0
0.5
0.0

1999

2000

2001

2002

Note: Bold lines are estimates, and shaded lines indicate their upper and lower bounds,
respectively, of the confidence interval (estimates ± 2*standard errors).

37