Bank of Japan Working Paper Series

Broad
Perspective Broad-Perspective Review Series
Review

The Bank of Japan's Large-Scale
Government Bond Purchases and theFormation of Long-Term Interest Rates

Takashi Nakazawa*
takashi.nakazawa@boj.or.jp

Mitsuhiro Osada**
mitsuhiro.osada@boj.or.jp

No.24-E-10
September 2024

Bank of Japan
2-1-1 Nihonbashi-Hongokucho, Chuo-ku, Tokyo 103-0021, Japan* Monetary Affairs Department** Monetary Affairs Department (currently Financial System and Bank Examination

Department)
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The Bank of Japan's Large-Scale Government Bond Purchases
and the Formation of Long-Term Interest Rates *Takashi Nakazawa‡

Mitsuhiro Osada†

September 2024
Abstract
This paper quantitatively examines the effects of the Bank of Japan's (BOJ's) purchasesof Japanese government bonds (JGBs) – especially the large-scale purchases since theintroduction of Quantitative and Qualitative Monetary Easing in 2013 – on the formationof long-term interest rates in Japan using time series analysis. The results can besummarized as follows. First, having quantified the effect of BOJ JGB purchases taking
market participants' expectations about the future path of such purchases into account, wefind that the effect of JGB purchases on interest rates has been driven by the increase in
JGB holdings (i.e., the stock effect), which affects market participants' risk allocation,rather than by the daily conduct of JGB purchases (i.e., the flow effect), which affects
supply and demand in the secondary market. Second, in addition to the flow and stock
effects, the Yield Curve Control framework introduced in September 2016 had the effectof restraining interest rate increases when long-term interest rates approached the upperbound of the announced range. This effect tended to be larger when the BOJ took
countermeasures and market participants expected such countermeasures. Finally, ouranalysis of interest rates at different maturities suggests that the framework of government
bond purchases and Yield Curve Control had an effect on interest rates across a wide
range of maturities, and that the recent large-scale monetary easing had the effect ofpushing down the entire yield curve.
JEL Classification: G12, E44, E52, E58
Keywords: unconventional monetary policy, long-term interest rates, government bondpurchases, flow effect, stock effect, announcement effect, yield curve control*

The authors thank Takuto Arao, Ichiro Fukunaga, Yuichiro Ito, Sohei Kaihatsu, Junko Koeda, Kazuhiro
Masaki, Teppei Nagano, Jouchi Nakajima, Koji Nakamura, Kaori Ochi, Nao Sudo, Kosuke Takatomi,
Yoichi Ueno, and Hiroki Yamamoto for helpful comments on this paper. The authors are also grateful to
Daiki Date, Yasuhiro Kubokura, and Kento Yoshizawa for their dedicated support at an early stage of theanalysis. Any remaining errors are the authors' own. The views expressed in this paper are those of theauthors and do not necessarily represent those of the Bank of Japan.

‡

Monetary Affairs Department, Bank of Japan (takashi.nakazawa@boj.or.jp)†

Monetary Affairs Department (currently Financial System and Bank Examination Department), Bank ofJapan (mitsuhiro.osada@boj.or.jp)

1

These tools are often referred to as “unconventional” or “nonstandard” policies. Since
I will argue that these tools should become part of the standard toolkit, I will refer tothem here as “new” or “alternative” monetary tools. ― Ben S. Bernanke [2020]
QE has now been used numerous times in the past two decades for extended periods when
the policy rate was at the effective lower bound, so I would say it is no longer
unconventional. ― Christopher J. Waller [2024]

1. Introduction
The Bank of Japan (BOJ) introduced Quantitative and Qualitative Monetary Easing(QQE) in April 2013, under which it has conducted large-scale purchases of Japanese
government bonds (JGBs); in September 2016, the BOJ introduced the framework ofyield curve control (YCC), in which it sets both short-term and long-term interest rates aspolicy rate targets, and since then has conducted JGB purchases in a more flexible mannerin order to achieve its long-term interest rate target; in this sense, YCC is a form ofquantitative easing. Subsequently, in March 2024, the BOJ decided to end the frameworkof QQE with YCC, judging that achieving the price stability target of 2 percent in asustainable and stable manner had come in sight. During this period, the BOJ's JGB
purchases had pushed down the yield curve as a whole, which had a positive impact on
economic activity and prices.1
The history of quantitative easing as a monetary policy tool – not only in Japan,
but worldwide – dates back to March 19, 2001, when the BOJ introduced its Quantitative
Easing Policy (QEP). At that time, the BOJ changed its operating target for money market
operations from the short-term interest rate (uncollateralized overnight call rate) to aquantitative indicator, the outstanding balance of the current accounts at the BOJ, andintroduced forward guidance that the policy would continue until the year-on-year change
in the consumer price index (excluding fresh food) registered stably a zero percent or an
increase year on year. However, the quantitative expansion at that time mainly focusedon the supply of short-term funding. During this period, the BOJ also decided to increase
the amount of its long-term government bond purchases, but this was not intended to pushdown long-term interest rates but to facilitate the smooth supply of short-term funding(Shirakawa [2002] and Ueda [2005]).2 Subsequently, the U.S., Europe, and other major

1

For details on the impact on economic activity and prices, see the BOJ's September 2016 "Comprehensive
Assessment" and the March 2021 "Assessment for Further Effective and Sustainable Monetary Easing." In
the March 2021 Assessment, the simulation results show that the BOJ's large-scale monetary easing boosted
the level of real GDP by about 0.9 to 1.3 percent on average and the year-on-year rate of change in consumer
prices by about 0.6 to 0.7 percentage point on average. Moreover, developing a variant of the BOJ's
macroeconomic model (Q-JEM) that takes the term structure of interest rates into account, Izawa et al.
[2024] reassessed the results of the present paper and obtained more or less the same results.
2
During the global financial crisis, following the collapse of Lehman Brothers in September 2008, theBOJ increased its purchases of long-term JGBs, but regarded this as a measure to ensure financial market
stability.

2

advanced economies increasingly conducted government bond and risky asset purchases
in response to the global financial crisis of the late 2000s, and such "unconventional"
tools have come to be regarded as part of the standard toolkit (Bernanke [2020] and Waller[2024]). Against this background, there has been a growing body of academic research
about the effects on long-term interest rates, with recent studies reaching a consensus that
central bank holdings of government bonds have the effect of pushing down long-term
interest rates (Bernanke [2020] and BIS [2023]).
Following these developments in academic research, this paper conducts anempirical analysis of the effect of the BOJ's JGB purchases, especially the large-scalepurchases since the introduction of Quantitative and Qualitative Monetary Easing in 2013,
on the formation of long-term interest rates in Japan. The main results are threefold. First,
quantifying the effect of JGB purchases taking market participants' expectations about
the future path of the purchases into account, we find that the effect of JGB purchases oninterest rates has been driven by the increase in JGB holdings (i.e., the stock effect), which
affects market participants' risk allocation, rather than by the daily conduct of JGB
purchases (i.e., the flow effect), which affects supply and demand in the secondary market.
Second, quantifying the effect of the YCC framework introduced in September 2016using a model incorporating the probability that the targeted long-term yield will exceed
the YCC range implied by option prices as a proxy, we find that, in addition to the flow
and stock effects described above, the framework of QQE with YCC had the effect ofrestraining interest rate increases when long-term interest rates approached the upperbound of the announced range. This effect tended to be larger when the BOJ took
countermeasures and market participants expected such countermeasures. Third,
examining interest rates at different maturities, we find that government bond purchases
and YCC had an effect on interest rates across a wide range of maturities, and that thelarge-scale monetary easing since 2013 had the effect of pushing down the entire yield
curve.
The remainder of this paper is organized as follows. Sections 2 and 3 provide an
overview of previous studies about the effect of government bond purchases and YCC
and how they affect the formation of long-term interest rates in Japan. In Section 4, weconstruct a time series model consistent with the literature and quantify the effect on longterm interest rates and the entire yield curve. Section 5 concludes.

2. The Effect of Government Bond Purchases
How central bank purchases of government bonds work
Central bank purchases of government bonds affect the formation of long-term interest
rates in the market through various channels as discussed in previous studies. It is useful3

to review these channels based on the following three perspectives.3 The first perspective
focuses on policy actions and distinguishes between (i) the flow effect, in which central
bank purchases of government bonds in the secondary market affect the supply anddemand for government bonds at the time of purchase, and (ii) the stock effect, in which
the central bank's large-scale holdings of government bonds have a persistent effect on
the supply of government bonds in the market. This classification is useful in practicebecause it corresponds to the actual policy measures (monthly purchases of government
bonds and holdings on the balance sheet). The second focuses on the mechanism throughwhich the effects materialize: (i) the liquidity effect through the impact on market liquidity,(ii) the portfolio-balance effect through the impact on market participants' risk allocation,and (iii) the signaling effect through the impact on market participants' expectations about
the future path of short-term interest rates implied by the stance of monetary policy. In
academic research, many studies construct a structural model based on such theoreticalconcepts. The third perspective focuses on the timing that the effects materializes anddistinguishes between (i) the implementation effect, which occurs when the central bankpurchases take place and holdings arise, and (ii) the announcement effect, which arises
prior to implementation as market participants anticipate future central bank actions andincorporate them into prices.4 Many previous studies have pointed to the importance of
the announcement effect and highlight that it is important to consider market expectations
when interpreting the empirical results of event studies.
It should be noted that these perspectives are not mutually exclusive and that thedifferent effects are closely related. It is therefore useful to consider these perspectives
together when examining the effects of government bond purchases (Chart 1). 5 For
example, the flow effect of government bond purchases is closely related to the liquidity
effect and the implementation effect, as it could push down yields on the targeted assets
by affecting supply and demand at the time of the purchases. In addition, the stock effectof government bond holdings is linked to the portfolio balance effect, which refers to theeffect that central bank purchases of government bonds from market participants (i.e.,
economic agents other than the central bank) push down long-term interest rates byabsorbing duration risk from the market. Finally, the announcement effect affects the3

There are numerous other studies providing an overview of the different channels from a similar
perspective to this paper. Example from the 2000s include Eggertsson and Woodford [2003], Bernanke etal. [2004], Ueda [2005], Ugai [2007], and Shirakawa [2008], while more recent examples are the studies
by Bernanke [2020], Aoki [2023], BIS [2023], Logan [2024], and Schnabel [2024].

4"Announcement" here refers not only to the actual announcements of policy measures by central banks,
but also to all actions and information by central banks that could affect the formation of market
expectations.
5

As shown in Chart 1, there is a considerable overlap between these classifications, and it is important tonote that since there are no strict definitions, the meaning of each classification may differ somewhat
depending on the author and situation. In addition to the channels shown in Chart 1, other channels havebeen pointed out, such as the default risk channel and the inflation channel, which operate through changes
in expectations regarding economic developments. See, for example, Krishnamurthy and Vissing-Jorgensen[2011] and Ueda [2012].

4

formation of long-term interest rates through announcements of future purchases andholdings of government bonds, which may indicate the future stance of monetary policy.
If the effects of future purchases and holdings are priced in, the liquidity and portfolio
balance effects may arise before the actual purchases and holdings materialize. If this also
creates market expectations that monetary easing will continue further, the effect oninterest rates is called the signaling effect.6

Chart 1. Effects of Government Bond Purchases on Long-term Yields
Flow effect

Stock effectLong-termyieldsPortfolio balance
effectTerm
premium

Implementation effectLiquidity effectAnnouncement effectSignaling effect

Expected
short-term
ratecomponent

Signaling effect and the expected short-term rate component of long-term yields
Based on these considerations, many studies examine long-term yields by constructing
term structure models of interest rates and decomposing long-term interest rates into two
components: (i) the average of the expected future path of short-term interest rates (theexpected short-term rate component), and (ii) the term premium, which is obtained as theresidual. The reason why this approach is widely used is that, by definition, the expectedshort-term rate component captures the signaling effect, while the term premium capturesother effects, so that the results are easy to interpret.
Chart 2 shows the expected short-term rate component of long-term JGB yields
estimated using the term structure model of interest rates proposed by Imakubo and

6

The reason why central banks have started to adopt unconventional monetary policy tools is that shortterm interest rates fell near the effective lower bound, so that it was no longer possible to conduct monetary
policy using the conventional tool, namely, setting short-term interest rates. Trying to push down mediumand long-term interest rates by creating the expectation that short-term interest rates will remain low for along period (through the signaling effect) through forward guidance on short-term interest rates and/or aquantitative commitment is something that has been discussed since the introduction of Japan's zero interest
rate policy in 1999. See, for example, Fujiki and Shiratsuka [2002], Bernanke and Reinhart [2004], andUeda [2005].

5

Nakajima [2015], which takes the effective lower bound on short-term interest rates into
account.7

Chart 2. The Expected Short-term Rate Component of Long-term Yields, by Maturity

2.5

Clarification of theIntroduction
conduct of fixed-rateof
NIRP
Introduction Introduction
Introduction purchase operations forconsecutive daysof QQEof CMEof YCC

Introduction Introductionof QEP% of ZIRP

1-year3-year5-year10-year

2.0
1.5
1.0
0.5
0.0
-0.5
CY 97

99

01

03

05

07

09

11

13

15

17

19

21

23

Note: Latest data are as of May 2024.
Source: Bloomberg.

As pointed out in previous studies (e.g., Ugai [2007] and Aoki [2023]), theexpected short-term rate component of long-term JGB yields declined significantly after
the introduction of quantitative easing in the 2000s, suggesting that a signaling effect wasseen through the impact on market expectations that the future path of short-term interest
rates would remain low for a long period.8 On the other hand, the expected short-term
rate component tended to rise after the introduction of Comprehensive Monetary Easing

7

In this paper, we make the following two changes to the term structure model of interest rates proposedby Imakubo and Nakajima [2015] in light of the recent situation. First, since the effective lower bound on
short-term interest rates has declined since the introduction of the negative interest rate policy, the lower
bound from January 2016 onward is regarded to be whichever is the lowest at a particular point in time of
the following rates: the 1- to 6-month overnight index swap (OIS) rates, the call rate, and minus 0.1 percent,which is the interest rate applied to policy rate balances in the current accounts held by financial institutions
at the BOJ (i.e., the effective lower bound is assumed to change over time). Second, while 2-, 5-, 7-, and10-year JGB yields were used to estimate the term structure model, since the 10-year JGB yield was thetarget of YCC, the 15-year yield is used instead of the 10-year yield to ensure that the estimation results are
not directly affected by YCC.
8

After the introduction of the zero interest rate policy (ZIRP) in 1999, the expected short-term ratecomponent also declined due to the policy duration effect induced by the commitment to "continue the zerointerest rate policy until deflationary concerns are dispelled" (see for example, Fujiki and Shiratsuka [2002]
and Ugai [2007]). For the U.S., Bauer and Rudebusch [2014] and others report that Large-Scale Asset
Purchases (LSAPs) had the effect of pushing down long-term interest rates through their impact on the
expected short-term rate component.

6

(CME) and Quantitative and Qualitative Monetary Easing (QQE). This may be due to theeffects of the rise in U.S. interest rates seen at that time and expectations of an
improvement in economic activity as a result of monetary easing.
Chart 3 shows that the term premium of long-term JGB yields hovered at around
0.5 to 1.0 percent with some large swings during the 2000s, then declined significantly
from around 2012. It has remained in negative territory for the past decade since 2015.
This result is in line with the findings of previous studies. Oda and Ueda [2007] find thatgovernment bond purchases before 2005 did not have any statistically significant effectthrough the term premium but did have the effect of reducing long-term interest rates byleading to a decline in the expected short-term rate component. One of the reasons why,as pointed out by Shirakawa [2002], is that the BOJ's JGB purchases were still small
relative to the overall amount outstanding in the market. On the other hand, many studies
suggest that the large-scale JGB purchases since 2013 have had the effect of reducing
long-term yields, mainly due to a decline in the term premium (e.g., Fukunaga et al.
[2015], Katagiri and Takahashi [2017], and Sudo and Tanaka [2021]).

Chart 3. Term Premium of Long-term Yields, by Maturity

2.5%

Introduction
Introduction Introduction of NIRP Introductionof QQEof CMEof YCC

Introduction Introductionof QEPof ZIRP

Clarification of the
conduct of fixed-rate
purchase operations forconsecutive days

1-year3-year5-year10-year

2.0
1.5
1.0
0.5
0.0
-0.5
CY 97

99

01

03

05

07

09

11

13

15

17

19

21

23

Note: Latest data are as of May 2024.
Source: Bloomberg.

Flow effect of government bond purchases
As shown in Chart 4, the BOJ's monthly JGB purchases increased after (i) the introductionof the QEP in March 2001 and (ii) the introduction of CME in October 2010, but the sizeof the increases was small compared to (iii) the increase after the introduction of QQE in

7

April 2013 and (iv) the expansion of QQE in October 2014. Subsequently, (v) after the
introduction of YCC in September 2016, the amount of JGB purchases declined
somewhat, but (vi) when interest rates came under upward pressure in domestic andforeign financial markets from 2022 onward. JGB purchases increased again substantially,
partly due to the conduct of fixed-rate purchase operations at the upper bound of thetargeted fluctuation range of YCC.

Chart 4. BOJ's Monthly JGB Purchases

25

Introduction

tril. Introduction Introductionof QEPyen of ZIRP

Introduction Introduction of NIRP Introductionof QQEof CMEof YCCClarification of the
conduct of fixed-rate
purchase operations forconsecutive days

20
15
10
5
0
CY 97

99

01

03

05

07

09

11

13

15

17

19

21

23

Note: Latest data are as of April 2024. Based on the settlement day of operations.
Source: Bank of Japan.

The large purchases through fixed-rate purchase operations conducted frequently
since 2022 are the result of the clarification of how the BOJ would conduct fixed-rate
purchase operations for consecutive days and the upper bound of the targeted fluctuation
range, decided at the April 2022 Monetary Policy Meeting.
Apart from these unique circumstances under YCC, central bank purchases ofgovernment bonds generally have a liquidity effect by directly affecting supply anddemand in the secondary market at the time of purchase. In particular, BOJ purchases of
longer-maturity JGBs since 2013 may have had the effect of pushing down long-term
interest rates to some extent. Previous studies have also pointed out that the effects ofasset purchases, including purchases not only of government bonds but also a wide rangeof other assets, tend to be stronger in times of stress, when liquidity and risk premiums
increase.99For example, BIS [2023] highlights the effects of central banks' large-scale asset purchases in the wakeof the COVID pandemic, while Logan [2024] and Schnabel [2024] argue that the effects of asset purchasesvary across economic and financial conditions. Regarding the effect of asset purchases on corporate bond8

At the same time, however, previous studies have also pointed out that suchliquidity effects are essentially temporary and limited to the targeted asset and/or its
substitutes. For example, Bernanke [2020] points out that the liquidity effect should
theoretically be short-lived, while various empirical results suggest that the effect ofgovernment bond purchases tends to be persistent, which is more consistent with the stock
effect in theory. In this regard, Sudo and Tanaka [2021], using a dynamic stochastic
general equilibrium model, show that in Japan the stock effect dominates the flow effect,
accounting for more than 90 percent of the interest rate reduction effects. On the other
hand, as pointed out in BIS [2023], when a central bank conducts government bondpurchases, market participants pay attention to its stance with regard to purchases, which
affects expectations with regard to the central bank's future monetary policy stance andgovernment bond purchases and hence interest rate formation.

Stock effect of government bond holdings
When examining the effect of central bank government bond holdings (i.e., the stock
effect) on long-term interest rates through the portfolio balance effect, there are threepoints to consider from a theoretical perspective. First, there are preferred-habitat
investors who have preferences for specific maturities (Vayanos and Vila [2021]). In
particular, pension funds and insurance companies, due to their liability structure, are notindifferent to the maturity structure of their assets and tend to prefer bonds with relatively
long maturities. When the supply of longer-maturity bonds in the market decreases,
imperfect substitution between bonds with different maturities pushes down long-term
interest rates.10 Second, the concept of interest rate risk (duration risk) is important forinvestors to manage their balance sheets (Krishnamurthy and Vissing-Jorgensen [2011]).
The longer the maturity of a bond, the greater its interest rate risk. Therefore, central bankpurchases of longer-maturity bonds have a larger effect on long-term interest rates thanpurchases of shorter-maturity bonds, even when the amounts purchased are the same.
Chart 5 shows the outstanding amount of JGBs held by economic agents. While
the overall amount has been on an upward trend, holdings by the BOJ have increased
substantially since the introduction of QQE in 2013, so that the share of BOJ holdings in
the total amount outstanding has exceeded 40 percent since 2017 and recently reachedaround 50 percent. On the other hand, in terms of holdings by economic agents other thanyields, some studies (e.g., Gilchrist and Zakrajšek [2013] and Gilchrist et al. [2021]) highlight the default
risk channel, which refers to the effect of central banks' crisis response measures on credit risk premiums
through the impact on market expectations with regard to an improvement in economic activity. As forcorporate bond purchases in Japan, empirical findings by Ochi and Osada [2024] suggest that both the flow
and stock effects of such purchases improve the functioning of corporate bond markets.
10

A growing number of studies on the effects of central bank purchases of government bonds rely on thepreferred-habitat model of Vayanos and Vila [2021], originally published in 2009. See, for example,
Krishnamurthy and Vissing-Jorgensen [2011], Gagnon et al. [2011], and D'Amico and King [2013] for theUnited States, Altavilla et al. [2015] for Europe, and Fukunaga et al. [2015] for Japan.

9the BOJ, holdings by depository financial institutions as well as households and firms
have been declining. Moreover, looking at the amount of JGBs outstanding on a riskadjusted basis (i.e., the 10-year equivalent value) shows that the BOJ has absorbed interest
rate risk from the market, as it has increased its purchases of longer-maturity JGBs since2013 and the average duration of its holdings has increased substantially. That said, since2019, the average duration of non-BOJ holdings has also increased, and the amount ofinterest rate risk in the rest of the JGB market has increased somewhat.

Chart 5. Total Amount of JGBs Outstanding, by Economic Agent
Par amount

1,600

Ten-year bond equivalent value(taking interest rate risk into account)tril. yentril. yen

years

1,200

1,600
BOJ
Insurance coporations and pension funds
1,400
Depository corporations
Overseas
Households and nonfinancial corporations, etc 1,200

1,000

1,000

800

800

600

600

400

400

200

200

0
CY 97 99 01 03 05 07 09 11 13 15 17 19 21 23

0
CY 97 99 01 03 05 07 09 11 13 15 17 19 21 23

1,400

BOJ

12
11

Others10

Average remaining maturity of
JGBs held by BOJ (right scale)

9
8
7
6
5
4
3
2
1
0

Notes: 1. The left chart shows the outstanding amount of JGB holdings in the Flow of Funds Accounts (on a market value basis).
Treasury discount bills are not included before April 2010. Latest data are as of the October-December quarter of 2023.
2. Figures for the right chart are obtained by converting the amount outstanding of different maturities into the equivalentamount of 10-year bonds containing the same amount of interest rate risk. Latest data are as of the January-March quarterof 2024. Figures for the BOJ’s JGB holdings prior to May 2001 are estimates based on certain assumptions (see Appendix
A for details of the calculation method).
Source: Bank of Japan.

Third, government bond purchases have an announcement effect (e.g., Bernanke[2020]). That is, by shaping market participants' expectations about the future supply of
government bonds, purchases affect long-term yields in a forward-looking manner. The
demand-supply curve analysis in Chart 6 illustrates this point. As noted above, an increasein central bank holdings of government bonds reduces the amount of interest rate risk inthe market and lowers long-term interest rates (term premiums) as market participants
take on additional interest rate risk. Moreover, if market participants anticipate further
purchases of JGBs by the BOJ in the future, the demand curve will shift so that the10expected future decline in interest rates materializes in advance. In this case, the decline
in interest rates due to the stock effect may occur before the actual purchases are made asa result of the announcement effect.

Chart 6. Stock Effect of Government Bond Holdings (Conceptual Illustration)
Interest rate

Expected future
supply curve

Supply curve after JGB
purchases

Supply curve without
JGB purchases(1) JGB purchases

Demand curve(1) Reduction of interest rate
(Effect of BOJ's JGB holdings)(2) Additional impact oninterest rate(2) Demand increasein anticipation offurther JGB purchases

Amount of JGB outstanding (or interest rate risk) in the market

A number of studies have sought to quantify the stock effect of government bondholdings taking the announcement effect into account. Specifically, focusing on the
United States, Li and Wei [2013] and Ihrig et al. [2018] empirically examine howannouncement shocks with regard to the Federal Reserve's (Fed's) future Treasury
holdings affect the U.S. term premium through market participants' expectations. Thesestudies assume that (i) market participants anticipate the Fed's future Treasury holdings
based on the expectation that the Fed will follow its announced purchase plan, and (ii)they also form expectations about outstanding Treasury securities in the rest of the market.
The longer the Fed continues to purchase Treasury securities (i.e., the more open-ended
the purchases are), the larger the effect of the Fed's announcement on long-term interest
rates at the time of the announcement.11 Another study along these lines is that by Chunget al. [2023], who develop a variant of the Fed's FRB/US macroeconomic model thatassumes that the Fed follows a relatively mechanical rule in its Treasury purchases andincorporates a mechanism for how expected changes in the future size of the Fed's balance11

Li and Wei [2013] and Ihrig et al. [2018] use a similar framework to analyze the effects of the Fed'spurchases of mortgage-backed securities (MBS) in addition to Treasury securities.

11sheet affect the current term premium.12 They then use the model to estimate the effectof the Fed's bond-purchase policy on market developments, economic activity, and prices.
Following these studies, in this paper we construct indicators of the expected BOJ
holdings of JGBs in the future using certain assumptions in order to quantify the stock
effect, taking the effect of market participants' expectations with regard to future
developments into account.13 Specifically, we assume that market participants anticipate
future (two-year ahead) BOJ holdings of JGBs at each point in time based on the BOJ's
actual and planned monthly purchases of JGBs. In addition, we make mechanicalassumptions about the amount of JGB issuance during this period and calculate theexpected future share of BOJ holdings, which is shown in Chart 7. The calculated future
share rose sharply when QQE was introduced in April 2013. Thus, the expected sharechanges significantly at the time of policy announcements as market participants'
expectations are incorporated ahead of actual changes in the share of JGB holdings.
Chart 7. Expected BOJ Holdings of JGBs (Share of Total, 10-year Equivalent)

50%

Introduction

Introduction
Introductionof QEPof ZIRP

Introduction Introduction of NIRP Introductionof QQEof CMEof YCCClarification of the
conduct of fixed-rate
purchase operations forconsecutive days

Share of BOJ holdings(Risk amount based)

45
40

Expected future shareof BOJ holdings(Risk amount based)

35
30
25
20
15
10
5
0
CY 97

99

01

03

05

07

09

11

13

15

17

19

21

23

Notes: See Appendix A for details on how the data are constructed. Latest data are as of April 2024.
Source: Bank of Japan.

In Section 4, we will quantify the effects of the BOJ's JGB purchases on long-term
interest rates through the various channels discussed in this section, taking the effectthrough market participants' expectations into account. Such a quantitative assessment of
the policy effects based on theoretical considerations will provide a useful perspective for
12

More concretely, the Fed's Treasury-purchase rule in Chung et al. [2023] is (i) that the Fed begins to
expand its balance sheet when the federal funds rate reaches the effective lower bound of the short-term
interest rate, and (ii) that the Fed begins quantitative tightening after a certain period of time after
developments in economic activity and prices improve and the short-term interest rate is raised. Since thepolicy rule for the short-term interest rate depends on economic and inflation conditions, expectations withregard to future purchases of Treasury securities also depend on economic and inflation conditions.

13

See Appendix A for details on how we construct the data.

12

drawing policy implications.

3. The Effect of Yield Curve Control
Developments in long-term interest rates under the YCC framework
QQE with YCC, introduced by the BOJ in September 2016, is a framework that promotes
the formation of a market yield curve in line with the Guideline for Market Operations,which sets the short-term policy rate at minus 0.1 percent and the target 10-year JGB yieldat around zero percent, through large-scale JGB purchases. With the introduction of YCC,
the BOJ introduced fixed-rate purchase operations as a new tool that allows the BOJ toconduct operations to make the yield curve consistent with the Guideline for Market
Operations when necessary, such as when interest rates rise sharply.
Although the BOJ did not explicitly state a targeted fluctuation range for the 10year JGB yield under YCC from the introduction of YCC until July 2018, market
participants perceived the range to be around ±0.1 percent based on the actual conduct of
fixed-rate purchase operations and the fact that the yield in practice remained within thisnarrow range. Subsequently, when the BOJ decided on "Strengthening the Framework forContinuous Powerful Monetary Easing" in July 2018, it also allowed the targeted longterm yield to fluctuate up to about double the previous fluctuation range of around ±0.1
percent. In March 2021, when the BOJ decided to conduct "Further Effective andSustainable Monetary Easing," it clarified the fluctuation range to be around ±0.25
percent and introduced "fixed-rate purchase operations for consecutive days" to strictly
limit the upper bound of long-term interest rates when necessary.
Moreover, in early 2022, the rises in interest rates seen globally also put upward
pressure on long-term yields in Japan, which rose to around 0.25 percent at that time.
Under these circumstances, in April 2022, the BOJ decided to clarify the conduct of fixedrate purchase operations for consecutive days, and decided to offer to purchase 10-year
JGBs at 0.25 percent through fixed-rate purchase operations every business day, unlessthere was a high probability that no bids would be submitted. Subsequently, the BOJ
decided to increase flexibility in the conduct of YCC through the following intermittent
steps: in December 2022, the fluctuation range was expanded to ±0.5 percent; in July
2023, while using the fluctuation range of ±0.5 percent as reference, the target level atwhich fixed-rate purchase operations are offered was set at 1.0 percent; and in October
2023, the BOJ decided to promote the formation of a yield curve consistent with theguideline through nimble responses, while using the upper limit of the long-term yield of
1.0 percent as reference.14 In March 2024, as noted earlier, the BOJ judged that the YCC
framework had fulfilled its role and changed the monetary policy framework, as achieving
the price stability target of 2 percent in a sustainable and stable manner had come into
14

In October 2023, the BOJ decided to determine the offer rate for fixed-rate purchase operations at eachoffer, taking market rates and other factors into account.

13

sight.
Chart 8 presents long-term interest rates during this period. While they weregenerally within the targeted fluctuation range before 2022, the long-term JGB yield
hovered near the upper limit of the range when the yield came under upward pressure due
to interest rate developments in foreign financial markets. During this period, the 10-year
swap rate (overnight index swap, OIS, rate) tended to diverge significantly from the 10year JGB yield, far exceeding the 10-year JGB yield.

Chart 8: Long-term Yields and the Targeted Fluctuation Range under YCC
1.2

Clarification of the
conduct of fixed-rate
purchase operations forconsecutive days

Introductionof YCC%

Changes inmonetary policy
framework

Offer rate of fixed-rate purchase
operations for consecutive days
Targeted fluctuation range under YCC

1.0
0.8

JGB yields (10-year)

0.6

OIS rate (10-year)

0.4
0.2
0.0
-0.2
-0.4
-0.6
CY 15

16

17

18

19

20

21

22

23

24

Note: Latest data are as of May 22, 2024. The broken line for the "Targeted fluctuation range under YCC" denotes
the period from September 21, 2016, to July 31, 2018, when the targeted fluctuation range was not explicitly
stated but perceived to be around ±0.1 percent, and the period from July 31, 2018, to March 19, 2021, when it
was twice the size of the preceding period, i.e., around ±0.2 percent.
Source: Bloomberg.

How YCC works
The YCC framework can be regarded as a type of government bond purchase program inthat it affects the formation of interest rates in the market through large-scale JGB
purchases. As such, the mechanisms through which it operates are the same as the QQE
program that preceded it, and the considerations in the preceding section on the effect onlong-term interest rates also apply to YCC.15 On the other hand, QQE with YCC differs

15

Employing the preferred-habitat model of Vayanos and Vila [2021], Lucca and Wright [2024] examine
the effects of the Reserve Bank of Australia's Yield Target policy, which is not identical but similar to the
BOJ's YCC. Based on the model, they classify the effects into (i) broad channels and (ii) narrow and supernarrow channels. Broad channels include the signaling effect, which is the effect on the yields of various

14

from QQE without YCC in that it guides long-term interest rates not through the purchaseof JGBs based on a pre-announced plan, but by directly targeting the level of long-term
JGB yields, which may affect the formation of long-term interest rates in a different
manner than QQE without YCC.
In particular, under the previous QQE framework in which the amount of JGB
purchases was scheduled, the fluctuations in JGB yields were greater, the greater thefluctuations in demand for government bonds. On the other hand, under the YCC
framework, which targets the level of long-term JGB yields, the amount of purchases isdetermined endogenously in response to changes in the demand for government bonds,
so that, in principle, fluctuations in interest rates should be smaller. Chart 9 illustrates thismechanism through a simple demand-supply curve analysis.

Chart 9. Effect of YCC on Interest Rate Volatility (Conceptual Illustration)
Interest rate

Supply curve when JGB purchases
are inelastic to demand changes

Demandcurve
Demand changes for somereason(2) Interest rate tends to be
more stable under YCC

Supply curve under
YCC(1) Interest rate changes
substantially if the amount of JGB
purchases is not adjusted flexibly

Amount of JGB outstanding (or interest rate risk) in the market

If the scheduled amount of JGB purchases is decided at each monetary policy
meeting, as was the case with QQE before the introduction of YCC, the supply curve will
be vertical because the amount of JGBs held by the rest of the market is fixed in the shortrun. In this case, if the demand for JGBs changes for some reason, that is, if the demand
curve shifts, long-term yields will change significantly in response to the change indemand. On the other hand, under YCC, which targets the long-term JGB yield, theassets (not limited to the purchased asset) through market participants' expectations about the future pathof the short-term interest rate, and the portfolio-balance effect, which is the effect on the entire yield curveof government bonds through influencing the supply of interest rate risk in the market. Narrow and supernarrow channels include asset-specific liquidity effects, i.e., asset purchases affect the supply-demandbalance of only the targeted assets or issues.

15

narrower or stricter the targeted fluctuation range is, the more horizontal the supply curve
will be, restraining interest rate changes when the demand curve shifts. (Instead, theamount of JGB purchases will change substantially.) Moreover, if market participantssufficiently understand this mechanism of YCC, interest rate changes will be smaller evenin the absence of actual JGB purchases. In other words, if market participants fully expectthat interest rate changes will be suppressed, the mechanism may operate in advance byflattening the slope of the demand curve, thereby making interest rates less volatile.
While academic research on this kind of setup is still scarce, since the introduction of
YCC, central banks in other countries have looked into the feasibility of adopting a similar
policy framework, and a number of studies have empirically examined the impact of
YCC. 16 First, with regard to the effects on the volatility of long-term interest rates,
Hattori and Yoshida [2023], for example, use intraday trading data to empirically examine
the effect of YCC on volatility and find that the stochastic nature of long-term interest
rate movements changed after the introduction of YCC in that interest rates became
stationary and less volatile. A similar observation applies when looking at the volatility
in 10-year JGB yields since 2013, as seen in Chart 10. In terms of the real-world
implications of this reduction in the volatility of market interest rates, it is likely that it
reduced the uncertainty firms faced with regard to funding costs, which in turn likely had
a positive impact on the real economy by making it easier for firms to formulate businessplans.17
Chart 10. Historical Volatility of Long-term Interest Rates
0.03

Standard deviation in day-to-day changes, percentage point

0.02

JGB yields (10-year)

0.01

OIS rate (10-year)
0.00
October 5, 2010
(introduction of CME)
to April 3, 2013

April 4, 2013
(introduction of QQE)
to September 20, 2016

Source: Bloomberg.

September 21, 2016
(introduction of YCC)
to April 26, 2022

April 27, 2022
(clarification of the
conduct of fixed-rate
purchase operations forconsecutive days)
to December 19, 2022

16

See, for example, the discussions in Federal Open Market Committee [2020] and Reserve Bank ofAustralia [2022]. While there are few cases of similar policies in the past, the Fed's yield curve targetingfrom 1942 to 1951 (at 2.5 percent for long-term bonds) is often cited as an example (Amamiya [2017] andRose [2021]).

17

According to the BOJ's March 2021 "Assessment for Further Effective and Sustainable Monetary
Easing," low interest rate volatility may have a positive impact on business fixed investment (BOJ [2021]).

16

Second, some studies focus on the effectiveness of YCC. Specifically, they argue
that if market participants sufficiently understand the YCC mechanism, it may be possible
to control interest rates while reducing the amount of JGB purchases. For example,
Bernanke [2016] and Higgins and Klitgaard [2020] suggest that using long-term interest
rates as the direct target of operations means that a small amount of JGB purchases may
have a sufficient effect to push down interest rates. Further, using a term structure modelof interest rates that takes investors' preferred habitat into account, Koeda and Ueno
[2022] show that as long as market participants have confidence in the long-term interest
rate target of YCC, the long-term interest rate will remain close to the target even in theabsence of actual JGB purchases, and that this effect occurs across the entire yield curve.
It should be noted, however, that whether this mechanism, which relies on market
participants' expectations formation, works depends on the circumstances. This is
illustrated by the study by Lucca and Wright [2024] examining the Reserve Bank ofAustralia's (RBA's) yield target policy for 3-year Australian government bonds conductedfrom 2020 to 2021. While they found that the policy had a stabilizing effect on interest
rates when the policy was first introduced, once the inflation rate rose far above the RBA's
forecasts after 2021 and the market lost confidence in the continuation of the yield target
policy, arbitrage along the yield curve no longer worked sufficiently, so that government
bond purchases no longer had the effect of pushing down yields on government bonds
with maturities other than those subject to RBA purchases. Similarly, in Japan, the degreeof market functioning deteriorated when from around mid-2022 to early 2023 long-term
interest rates rose close to the upper bound of the targeted fluctuation range under YCC
and arbitrage between the OIS rates and JGB yields as well as across different issues andmaturities of JGBs became difficult, and such a deterioration in market functioning may
have spread to other financial markets (see for example, Fukuma et al. [2024], Shiratsuka[2024], and Ochi and Osada [2023, 2024]).18
Finally, YCC may affect the effectiveness of other policy tools. For example,
reviewing the RBA's experience in conducting its yield target policy, RBA [2022] argues
that, in the early period after the introduction of yield targeting, the policy helped toreinforce the message that the RBA was committed to continued monetary easing, as it
was highly consistent with the RBA's forward guidance at the time of keeping the policy
rate unchanged at low levels for the time being.

Effects of setting a targeted fluctuation range under the YCC framework
Having discussed the possible effects of YCC on long-term interest rates from atheoretical perspective, we now outline our strategy for empirically quantifying the effect18

In response to this situation, the BOJ has implemented the Securities Lending Facility (SLF) in a flexible
manner taking the degree of functioning of the JGB market into account, and, as noted above, since
December 2022 has also increased flexibility in the conduct of YCC.

17

using a time series model.
In the construction of the empirical model, the choice of explanatory variables iskey. In the case of quantifying the effect of JGB purchases, it is natural to expect that therelationship between the amount of JGB purchases or holdings and long-term interest
rates is monotonic; that is, the larger the amount, the greater is the effect of pushing downinterest rates. However, the effect of YCC differs depending on the situation, implyingthat the choice of the appropriate proxy variable to capture the effect is not straightforward.
We therefore need to consider how YCC works in different situations. First, when market
participants fully expect long-term interest rates to remain within the targeted range, longterm interest rates are likely to be formed based on the relationship between the BOJ’s
JGB holdings and the long-term yield, as shown in Chart 6. In this case, the effect of YCC
is essentially the same as the effect of JGB purchases. On the other hand, in a situation inwhich the level of long-term interest rates is close to the upper or lower bound of thetargeted range, or in which market participants increasingly expect that, in the absence of
YCC, long-term interest rates would change beyond the targeted range in the future, theeffect of YCC is likely to be enhanced by market participants' expectations that the BOJ
will take measures to keep long-term interest rates within the targeted range throughnimble responses. In fact, when interest rates came under upward pressure from 2022
onward, the BOJ implemented YCC in a strict manner so that long-term interest rates did
not exceed the upper bound of the targeted range by conducting fixed-rate purchase
operations for consecutive days, which kept long-term interest rates lower than theywould have been in the absence of such a response. We can interpret this to mean that
YCC works by influencing the shape of the demand and supply curves, as shown in Chart
9.19,20
Against this background, we construct indicators of the probability that the longterm yield will exceed the YCC range (for the upper and lower bounds, respectively) frommarket data, and then, using the empirical approach described in the following section,
test the hypothesis that when the probability increases, the effect of YCC also increases.
Specifically, we use option price data to calculate the probability that the long-term yield

19

This situation implies that market participants' confidence in YCC does matter. In this context, thestructural model proposed by Koeda and Ueno [2022] suggests that the stricter the implementation of YCC,
the greater is the effect of YCC through the flattening of the slope of the demand curve (where the slope ofthe demand curve represents the price semi-elasticity of the demand for government bonds by preferredhabitat investors). Such a structural model could be used, for example, to conduct a counterfactual analysisof the effect of increasing the degree of confidence in YCC. However, such an analysis is beyond the scopeof this paper as it would require various additional assumptions.

20

In addition, as noted earlier, the YCC framework, through the signaling effect, potentially also pushes
down the expected short-term rate component of long-term interest rates in a way that reinforces forward
guidance. Koeda and Wei [2023] find evidence of the signaling effect of YCC by conducting acounterfactual analysis using a term structure model of interest rates that incorporates macroeconomic
variables.

18

in the market will exceed the YCC range in the next three months.21 Chart 11 shows that,in the early period after the introduction of YCC, there was a considerable probability thatthe long-term yield might exceed the lower bound but not the upper bound of the YCC
range (i.e., ±0.1 percent). Subsequently, the probability that the long-term yield might
exceed the upper bound increased in 2018 due to speculation about a widening of the
YCC range. From 2022, when the economy started to recover from the COVID pandemic
and increases in foreign interest rates exerted upward pressure on Japanese long-term
interest rates, the probability that the long-term yield might exceed the upper bound roseto over 90 percent in the second half of 2022. In Chart 11, the probability that the longterm yield might exceed the upper bound and the probability that it might exceed the offer
rate for fixed-rate purchase operations for consecutive days are shown separately for theperiod from July to October 2023, as an upper bound for the YCC range of about 0.5
percent was used as reference, while the offer rate for fixed-rate purchase operations was
set at 1.0 percent during this period.

Chart 11. Probability that the Long-term Yield Might Exceed the YCC Range in the
Next Three Months
100 %Offer rate of fixed-rate purchase
operations for consecutive days：

Targeted Fluctuation
range undrer YCC：±0.1%±0.2%＋0.25% ＋0.5% ＋1.0％±0.25%

±0.5%

＋1.0%

Probability that the offer rate of
fixed-rate purchase operations forconsecutive days is exceeded
Probability that the upper bound of
the YCC range is exceeded

90
80
70

Probability that the lower bound of
the YCC range is exceeded

60
50
40
30
20
10
0
CY16

17

18

19

20

21

22

23

24

Note: Latest data are as of March 18, 2024. The part of the "Probability that the upper bound of the YCC range is
exceeded" shown in a broken line represents the period during which the BOJ conducted fixed-rate purchase
operations every business day. For details on the estimation, see Appendix B.
Sources: Bloomberg; LSEG Eikon.

21

See Appendix B for details on how the data are constructed.

19

4. Empirical Results using Time Series Analysis
In this section, based on the discussion above, we construct time-series models of JGB
purchases and YCC that are consistent with the theoretical considerations. Using various
specifications, we quantitatively assess the effects of JGB purchases and YCC on longterm interest rates and the entire yield curve.

4.1. Effect of JGB Purchases and YCC on Long-term Interest Rates
Specifications with QE dummies
We start by providing an overview of the effects of past quantitative easing frameworks
using specifications with simple dummy variables representing these frameworks as
explanatory variables. Specifically, we employ ordinary least squares regression models
with the following specification for long-term interest rates:𝑦𝑐𝛼 ∙ 𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠

𝛽 ∙ 𝑄𝐸𝑑𝑢𝑚𝑚𝑖𝑒𝑠

𝜀,where for the dependent variable (𝑦 ) we use the 10-year JGB yield (𝑖 ) and its twocomponents: the expected short-term rate component (𝐸𝑆 ) and the term premium(𝑇𝑃 ), estimated using a term structure model of interest rates following previous
studies. In addition, we use three variables to control for the major determinants ofdevelopments in long-term interest rates (𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠 ): the 10-year U.S. Treasury yield,
the uncollateralized overnight call rate, and the inflation rate (year-on-year change in the
consumer price index, excluding fresh food and energy and the effects of the consumption
tax hikes). 22 In addition, we use five QE dummies for past QE frameworks(𝑄𝐸𝑑𝑢𝑚𝑚𝑖𝑒𝑠 ): (i) the Quantitative Easing Policy (QEP) from March 2001 to February
2006, (ii) Comprehensive Monetary Easing (CME) from October 2010 to March 2013,(iii) Quantitative and Qualitative Monetary Easing (QQE) from April 2013 to December
2015, (iv) QQE with the Negative Interest Rate Policy (NIRP) from January 2016 toAugust 2016, and (v) QQE with Yield Curve Control (YCC) from September 2016 to
March 2024, where the variables take 1 for the corresponding period (and 0 for otherperiods).
Chart 12 shows the estimation results. In Model 1, where the dependent variable
is the 10-year JGB yield, the coefficients on all QE dummies are negative, indicating thatthe various QE policies tended to lower the long-term interest rate. In particular, the effectis large and significant in the periods after the introduction of QQE. Next, when we split
the dependent variable into the expected short-term rate component and the term premium

22

While there are various other variables that we could include as determinants of long-term interest rates,in our analysis we focus on these three variables, which are often cited as the primary drivers of short-term
movements in 10-year interest rates in practice. The adjusted R-squared of the model using only these threevariables is around 0.85, indicating that these three variables have high explanatory power.

20

(Models 2 and 3), the results are generally similar to those of Model 1; that said, while
the coefficients on the QEP and CME dummies are significant in the estimation for the
expected short-term rate component, they are not in that for the term premium. This may
reflect the fact that JGB purchases in these periods were targeted at issues with relatively
short remaining maturities; it is also consistent with the results of previous studies
suggesting that JGB purchases affect yields mainly through the signaling effect (e.g., Ugai
[2007] and Oda and Ueda [2007]). Similar results are obtained in the estimations using
data for the period up to March 2013 before the introduction of QQE (Models 4 to 6).

Chart 12. Estimation Results: Specifications with QE Dummies
(1)

(2)

(3)

(4)

(5)

(6)

Dependent variable

10-yearyield

10-yearexpected shortterm ratecomponent

10-yearterm
premium

10-yearyield

10-yearexpected shortterm ratecomponent

10-yearterm
premium

Constant

0.558 ***

0.587 ***

-0.0180.495 ***

0.733 ***

-0.23210-year U.S. Treasury yields

0.203 ***

0.061 ***

0.151 ***

0.230 ***

0.023

0.220 ***

Uncollateralized overnight callrate

0.485 **

0.576 ***

-0.1210.271

0.694 ***

-0.514 **CPI (less fresh food and energy)

0.014

0.082 ***

-0.067 ***0.089 ***

0.025

0.091

QEP

-0.151 **-0.159 ***0.011-0.164 **-0.168 ***

0.005

CME

-0.094-0.181 ***0.097-0.022-0.288 ***0.292 **

QQE

-0.569 ***-0.325 ***-0.260 **

―

―

―

NIRP

-1.010 ***-0.708 ***-0.328 *

―

―

―

YCC

-0.907 ***-0.410 ***-0.529 ***

―

―

―

Adjusted R-squared
AIC

0.931
-0.5260.827-1.0320.798-0.2090.746-0.3190.747-1.1260.482-0.086Time dummy：

Estimation Period

January 1997 to March 2024

January 1997 to March 2013

Note: ***, **, and * denote statistical significance at the 1, 5, and 10 percent levels, respectively.
Sources: Bank of Japan; Ministry of Internal Affairs and Communications; Bloomberg.

Stock and flow effects of JGB purchases
These results indicate that the BOJ's JGB purchases have had a substantial effect since
the introduction of QQE, when the large-scale purchases began. To examine whether theeffect of JGB purchases is caused by stock or flow effects, we next conduct estimations
using the following specification in which JGB holdings and the amount of JGB
purchases are used as explanatory variables instead of the QE dummies for each period:𝑦𝑐

𝛼 ∙ 𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠𝛾 ∙ 𝐽𝐺𝐵𝑠𝑡𝑜𝑐𝑘𝛾 ∙ 𝐽𝐺𝐵𝑓𝑙𝑜𝑤𝜀.

We start by checking for the existence of stock effects. To this end, based on thediscussion in Section 2, we include three relevant variables in the specification as21

indicators of the BOJ's JGB holdings (𝐽𝐺𝐵𝑠𝑡𝑜𝑐𝑘 ): (A) the share of the BOJ's JGB
holdings in the total amount of JGBs outstanding, (B) the risk-adjusted share of the BOJ's
JGB holdings in the total amount of JGBs outstanding (10-year bond equivalent), and (C)the expected future share of the BOJ's JGB holdings (adjusted for interest rate risk, 10year bond equivalent).23, 24

Chart 13. Estimation Results: Stock Effect of JGB Purchases
(1)

(2)

(3)

(4)

(5)

10-year yield

Dependent variable
Constant-0.307 ***0.390 ***

0.310 ***

0.522 ***

0.480 ***

10-year U.S. Treasury yields

0.329 ***

0.255 ***

0.270 ***

0.229 ***

0.240 ***

Uncollateralized overnight call rate

1.329 ***

0.697 ***

0.759 ***

0.738 ***

0.719 ***CPI (less fresh food and energy)-0.152 ***-0.002-0.019

0.020

0.013

A

Share of BOJ's JGB holdings in total

B

Risk adjusted share of BOJ's JGB
holdings in total

C

Expected 2-year ahead share of BOJ's
JGBs holdings in total-0.018 ***-0.025 ***-0.022 ***-0.024 ***(adjusting for interest rate risk)

B-A

Difference between the actual shares
when adjusting and not adjusting forinterest rate risk

-0.026 **C-B

Expectation of future changes in
JGB holdings-0.016 ***Adjusted R-squared
AIC

0.847
0.259

0.918
-0.3640.926-0.4650.933-0.5670.935-0.596

January 1997 to March 2024

Estimation Period

Note: ***, **, and * denote statistical significance at the 1, 5, and 10 percent levels, respectively.
Sources: Bank of Japan; Ministry of Internal Affairs and Communications; Bloomberg.

Chart 13 presents the estimation results. While the coefficients on the indicators of
the BOJ's JGB holdings are statistically significant in Models 2 to 4, the estimated23

We perform unit root tests on the stock indicators and find that the null hypotheses that each indicator isa non-stationary process are not rejected. Therefore, we additionally conduct cointegration tests to confirm
that the models are not spurious regressions and find that the null hypothesis of no cointegration is rejected
for each model (in Chart 13) at the 5 percent confidence level.
24

While many previous studies use JGB holdings in the rest of the market relative to nominal GDP, theratio we employ uses the total JGBs outstanding as the denominator; i.e., we calculate the share of the BOJ's
JGB holdings as (1 - JGB holdings in the rest of the market) ÷ total JGBs outstanding. The reason is that,given that the amount of JGBs outstanding has continued to increase, the former is more likely to have atrend than the latter, which is calculated as a share. Nakamura and Yagi [2017] note that panel data for 23
OECD countries do not show a simple relationship between total outstanding government debt and longterm interest rates, and that empirical analyses should take market participants' expectations of future fiscal
consolidation into account. Meanwhile, Ichiue and Shimizu [2012] argue that it is important to consider thefinancial assets held by the government and the share of government debt held by foreign investors.

22coefficients are larger when the amount of risk is taken into account (Model 3) and when
future expectations are also taken into account (Model 4), and the fits of the models (interms of the adjusted R-squared) are also higher when they are taken into account. To
examine whether the amount of risk and future expectations, which are considered
important for understanding the stock effect, contain additional information, we
additionally estimate Model 5, which decomposes the expected future share of the BOJ's
JGB holdings (C) into the actual share of the BOJ's JGB holdings without adjusting forinterest rate risk (A), the difference between the actual shares when adjusting and not
adjusting for interest rate risk (B-A), and expectations of future changes in the BOJ's JGB
holdings (C-B). We find that each of these plays a significant role in lowering interest
rates. In fact, at the time of the introduction of QQE, the BOJ announced that it would
double its holdings of long-term JGBs over the next two years, and market participants
appear to have formed expectations incorporating this policy announcement relatively
quickly. Thus, Models 4 and 5, which take such future expectations into account, arelikely to provide more accurate results in terms of the timing of the stock effect. Thissuggests that considering the announcement effect is key in the results.
Next, we check for the existence of the flow effect. To do so, we consider themonthly change in the BOJ's JGB holdings (seasonally adjusted), which indicates the net
flow of JGB purchases (i.e., taking redemptions of JGB holdings into account), as anindicator of the BOJ's JGB purchases (𝐽𝐺𝐵𝑓𝑙𝑜𝑤 ), and add it to Model 4 in Chart 13.25
Chart 14 shows the estimation results. In Model 1, the coefficient on the stock
indicator, the expected future share of BOJ holdings, is similar in magnitude andstatistical significance to the results in Chart 13, while we do not obtain a significant
coefficient estimate for the flow indicator, the monthly change in JGB holdings. Moreover,the coefficient has the wrong sign. We obtain the same result in Model 2, where theestimation period is different, while in Model 3, which uses data from before theintroduction of QQE, the coefficient is negative but not significant. That said, in Model4, when the dependent variable is split into the expected short-term rate component andthe term premium, the monthly change in JGB holdings has a significant negative effectin the specification using the expected short-term rate component, while the coefficient
has the wrong sign in the specification using the term premium. This suggests that
information on the actual pace of purchases may affect long-term interest rates throughthe signaling effect, i.e., through influencing market participants' expectations about thepolicy stance for the future path of short-term interest rates. This tendency is also
observed in Model 5, in which the expected future share of BOJ holdings is decomposed

25

Another potential indicator of BOJ JGB purchases is the gross flow of JGB purchases. We therefore
conducted a robustness check using the amount of purchases of JGBs with a remaining maturity of 9 to 10
years (excluding purchases through fixed-rate purchase operations) as a ratio to new JGB issuance, which
is obtained using issue-specific data. However, the results were insignificant and in some of thespecifications the estimated coefficient had the wrong sign.

23

(C) into the actual share of BOJ holdings taking interest rate risk into account (B) and
expectations of future changes in JGB holdings (C-B). Meanwhile, expectations of futurechanges in JGB holdings contain both flow and stock information in the sense that they
are based on the assumption that the current pace of purchases will continue. That said,
the effect of such expectations on the term premium is significantly negative, while thecoefficient on the expected short-term rate component has the wrong signs. This result
suggests that expectations regarding future JGB purchases affect long-term interest rates
through the portfolio-balance effect.

Chart 14. Estimation Results: Flow Effect of JGB Purchases
(1)

(2)

(3)

Dependent variable(4)10-year yield
10-year(sum ofexpected
estimatedcoefficients ） short-term rate

10-year yield(5)

component

10-yearterm
premium

10-year yield
10-year(sum ofexpected
estimatedcoefficients ） short-term ratecomponent

10-yearterm
premium

Constant

0.515 ***

0.500 ***

0.590 ***

0.525

0.478 ***

0.047

0.513

0.468 ***

0.046

10-year U.S. Treasury yields

0.234 ***

0.240 ***

0.252 ***

0.242

0.077 ***

0.165 ***

0.245

0.080 ***

0.165 ***

Uncollateralized overnight callrate

0.695 ***

0.591 ***

0.521 ***

0.689

0.797 ***

-0.1080.698

0.805 ***

-0.107

CPI (less fresh food and energy)

0.029 *

0.060

0.092 **

0.021

0.088 ***

-0.067 ***0.010

0.079 ***

-0.068 **Expected 2-year ahead share of
BOJ's JGBs holdings in total-0.024 ***-0.023 ***-0.039 *-0.025-0.009 ***-0.016 ***Risk adjusted share of BOJ's JGB
holdings in total-0.025-0.009 ***-0.016 ***Expectation of future changes in
JGB holdings-0.0120.002-0.014 *(adjusting for interest rate risk)

Monthly change in JGB holdings

0.067-0.003-0.0590.075-0.074 **0.149 ***

-0.116-0.237 ***0.122

Adjusted R-squared
AIC

0.935
-0.5830.878-0.4330.749-0.332――0.826-1.0300.778-0.122――0.833-1.0720.777-0.117

Estimation Period

January 1997 to
March 2024

January 1997 toAugust 2016

January 1997 to
March 2013

January 1997 to March 2024

January 1997 to March 2024

Note: ***, **, and * denote statistical significance at the 1, 5, and 10 percent levels, respectively.
Sources: Bank of Japan; Ministry of Internal Affairs and Communications; Bloomberg.

Effect of setting the targeted fluctuation range under the YCC framework
Next, we quantitatively analyze the effect of setting the targeted fluctuation range under
YCC on long-term interest rates. Specifically, as noted above, we examine the hypothesisthat the effect of YCC increases as the probability of long-term interest rates exceeding
the upper (or lower) bound of the YCC range increases. To do so, we use the following
specification, which includes the probability that long-term interest rates might exceed
the upper (or lower) bound of the YCC range as an explanatory variable:

24

𝑇𝑃

𝑐

𝛼 ∙ 𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠𝛾 ∙ 𝐽𝐺𝐵𝑠𝑡𝑜𝑐𝑘𝛾 ∙ 𝐽𝐺𝐵𝑓𝑙𝑜𝑤

𝛿 ∙ 𝑌𝐶𝐶𝑒𝑓𝑓𝑒𝑐𝑡𝑠𝜀In the specification, we use the term premium as the dependent variable, since theeffect of setting the YCC range is not expected to affect the expected short-term ratecomponent, and add an explanatory variable that captures the effect of YCC(𝑌𝐶𝐶𝑒𝑓𝑓𝑒𝑐𝑡𝑠 ) to the term premium model in Chart 14. Specifically, we use the monthly
amount of fixed-rate purchase operations (as a percentage of monthly new JGB issuance,
hereafter referred to as the fixed-rate purchase operations share), which can also be
regarded as a flow variable, and the probability that the targeted long-term yield exceeds
the upper (or lower) bound of the YCC range, which is priced into the options market, as
discussed in Section 3. 26 As these probabilities increase, market participants'
expectations that the likelihood of a response by the BOJ to prevent interest rates fromrising (or falling) in the future increases are factored into market prices in advance. In
addition, since the effect of YCC is likely to have further strengthened after the BOJ'sclarification in April 2022 of how it will conduct fixed-rate purchase operations forconsecutive days, we also use a specification that includes the probability that the longterm yield might exceed the offer rate of fixed-rate purchase operations for consecutive
days as an explanatory variable. As for the expected future share of BOJ holdings, we use
two specifications shown in Chart 14.
The estimation results, presented in Chart 15, show that the coefficients on boththe fixed-rate purchase operations share and the probability that the upper (or lower)bound of the YCC range might be exceeded are significant and have the right sign in allmodels.27 The coefficients on the probability that the long-term yield might exceed theoffer rate of fixed-rate purchase operations for consecutive days are also significant andsomewhat larger than those on the probability that the long-term yield might exceed theupper bound of the YCC range, indicating that the fixed-rate purchase operations have astronger effect. In fact, in periods of upward pressure on Japanese long-term interest rates
after the introduction of YCC, the expected short-term rate component increased due toheightened expectations of future monetary tightening (Charts 2 and 11). In response tothis, the BOJ undertook measures such as fixed-rate purchase operations, which had the26

In our regressions, we use the logit transformation of the probabilities that the long-term yield exceeds
the upper or lower bound of the YCC range (or the offer rate of fixed-rate purchase operations forconsecutive days).
27

Due to possible reverse causality, our regression may suffer from endogeneity. When the term premiumrises for some reason, this may increase the probability that the long-term yield as a whole exceeds theupper bound of the YCC range (and/or the offer rate of "fixed-rate purchase operations for consecutive
days") and therefore also increase the fixed-rate purchase operations share as the BOJ conducts measures
such as fixed-rate purchases operations. This may result in an underestimation of the negative coefficientson these explanatory variables (in absolute value). That said, since the upward pressure on interest rates
during periods when the probabilities actually increased was mainly due to the rise in foreign interest rates
and the rise in inflation in Japan, it seems reasonable to regard the probability as an exogenous variable inour estimation.

25

effect of pushing down the term premium.

Chart 15. Estimation Results: Effects of YCC on the Term Premium
(1)

(2)

(4)

10-year term premium

Dependent variable
Constant

(3)

0.000

0.005

0.016

0.024

0.177 ***

0.174 ***

0.176 ***

0.172 ***

Uncollateralized overnight call rate

-0.298-0.301-0.315-0.320

CPI (less fresh food and energy)-0.008-0.007

0.001

0.004

10-year U.S. Treasury yields

Expected 2-year ahead share of BOJ's JGBs
holdings in total(adjusting for interest rate risk)-0.011 ***-0.011 ***Risk adjusted share of BOJ's JGB
holdings in total-0.009 **-0.010 **Expectation of future changes in
JGB holdings-0.016 ***-0.018 ***Monthly change in JGB holdings-0.0070.062-0.0050.076

Ratio of fixed-rate purchase
operations to JGB issuance-0.004 ***-0.004 ***-0.002 **-0.002 **Probability that the upper bound of the
YCC range is exceeded (from Sep.
2016 to Mar. 2024)-0.048 ***-0.050 ***Probability that the upper bound of the YCC
range is exceeded (from Sep. 2016 to Apr.
2022, from Nov. 2023 to Mar. 2024)-0.045 ***-0.047 ***Probability that the offer rate of fixed-rate
purchase operations for consecutive days is
exceeded (from May. 2022 to Oct. 2023)-0.059 ***-0.062 ***Probability that the lower bound of the
YCC range is exceeded

Adjusted R-squared
AIC

0.033 ***

0.027 ***

0.033 ***

0.025 **

0.818
-0.3120.818-0.3110.819-0.3180.820-0.319Estimation Period

January 1997 to March 2024

Note: ***, **, and * denote statistical significance at the 1, 5, and 10 percent levels, respectively.
Sources: Bank of Japan; Ministry of Internal Affairs and Communications; Bloomberg; LSEG Eikon.

Quantitative assessment of the effect of JGB purchases
Finally, based on the results of the above estimations, we quantitatively assess the effectof large-scale JGB purchases on long-term interest rates from two perspectives: the effectof the amount of JGB purchases (flow and stock effects) and the effect of setting the YCC
range. Specifically, these effects are quantified using five models based on the following
three approaches. The first approach is to quantify the effect of YCC as the difference
between actual developments in the long-term yield and the counterfactual evolution of
the long-term yield in the absence of YCC, using estimation results based on data for theperiod prior to the introduction of YCC and assuming that the coefficients in the model26

remained unchanged. The results based on this approach are shown as Model 1 in Chart
16. The second approach is to quantify the effect using a full model in which thedependent variable is the 10-year yield and the explanatory variables include both theeffect of JGB purchases and the effect of YCC (Models 2 and 4 in Chart 16). The lastapproach is similar to the second approach, but the model is estimated separately for the
expected short-term rate component and the term premium, and the estimated coefficientsare then summed (Models 3 and 5 in Chart 16).28
Chart 16. Estimation Results: Final Models
(1)

(2)

(3)

(4)

(5)

10-yearyield(sum of10-yearestimated
expected short10-year
coefficientterm rate
term premiums）component

10-year yield

10-yearyield(sum of10-yearestimated
expected short10-year
coefficientterm rate
term premiums）component

10-year yield

10-year yield

Constant

0.499 ***

0.524 ***

0.475

0.465 ***

0.010

0.512 ***

0.495

0.476 ***

0.019

10-year U.S. Treasury yields

0.241 ***

0.232 ***

0.247

0.082 ***

0.165 ***

0.238 ***

0.238

0.078 ***

0.159 ***

Uncollateralized overnight call rate

0.590 ***

0.634 ***

0.776

0.776 ***

0.645 ***

0.798

0.798 ***CPI (less fresh food and energy)

0.060 ***

0.050 ***

0.090

0.090 ***

0.045 ***

0.082

0.082 ***

Expected 2-year ahead share of BOJ's JGBs
holdings in total (adjusting for interest rate risk)-0.023 ***-0.022 ***-0.020-0.010 ***Risk adjusted share of BOJ's JGB
holdings in total-0.024 ***-0.018-0.009 ***Expectation of future changes in
JGB holdings-0.012 ***-0.014Monthly change in JGB holdings-0.141 **-0.208

Dependent variable-0.011 ***-0.009 **-0.014 ***-0.208 ***Ratio of fixed-rate purchase operations
to JGB issuance―-0.001-0.002-0.002 *0.000-0.002-0.002 **Probability that the upper bound of the
YCC range is exceeded (from Sep. 2016 toApr. 2022, from Nov. 2023 to Mar. 2024)―-0.009 ***-0.042-0.042 ***-0.007 *-0.046-0.046 ***Probability that the offer rate of fixed-rate
purchase operations for consecutive days is
exceeded (from May. 2022 to Oct. 2023)―-0.025 ***-0.054-0.054 ***-0.021 ***-0.059-0.059 ***Probability that the lower bound of the YCC
range is exceeded―-0.0030.032

0.032 ***

0.009

0.025

0.025 **

Adjusted R-squared
AIC

0.878
-0.4410.937-0.609――0.813-0.2910.938-0.621――

Estimation Period

January 1997 toAugust 2016

0.824
-1.0220.833-1.077January 1997 to March 2024

Note: ***, **, and * denote statistical significance at the 1, 5, and 10 percent levels, respectively.
Sources: Bank of Japan; Ministry of Internal Affairs and Communications; Bloomberg; LSEG Eikon.

Chart 16 presents the estimation results of the final models. Starting with thecontrol variables, we find that the coefficients on the 10-year U.S. Treasury yield arestable at around 0.25 in all models. The coefficients on the uncollateralized overnight call28

To improve the accuracy and interpretability of the quantitative results, we exclude explanatory variables
that have the wrong sign.

27

0.813
-0.290rate range from 0.5 to 0.8, depending on whether we use the 10-year yield or the expectedshort-term rate component as the dependent variable. Similarly, the coefficients on the
inflation rate range from 0.04 to 0.09, but we can ignore the difference as the coefficientsare quite small relative to those on the other control variables.
Turning to the coefficients on the stock variables of JGB purchases, in particular
the share of BOJ holdings and the expected future share of BOJ holdings, these are
generally stable at around -0.02 in all models. On the other hand, expectations of futurechanges in JGB holdings over the next two years have an effect only on the term premium,and the coefficients on this variable are smaller than those on the share of BOJ holdings.
Next, looking at the coefficients on the flow variables of JGB purchases, Models 4 and 5,
which include the monthly change in JGB holdings as an additional explanatory variable,
show that JGB purchases had an effect on the expected short-term rate component, which
contrasts with expected future changes in JGB holdings, which did not have an effect.
Moreover, the coefficients are fairly large at around -0.1 to -0.2. Finally, regarding theeffect of YCC, Models 2 to 5 find that the fixed-rate purchase operations share has theeffect of pushing down interest rates, although the coefficients are small. Meanwhile, theprobability that the long-term yield might exceed the upper (or lower) bound of the YCC
range had a significant effect on the long-term yield, mainly through the effect on theterm premium. The same is true for the probability that the long-term yield might exceed
the offer rate of fixed-rate purchase operations for consecutive days, and the coefficient
is somewhat larger than that for the probability that the upper bound might be exceeded.
Chart 17 presents developments over time in the effect of JGB purchases and theeffect of the YCC range based on the coefficients obtained in Models 1 to 5. The chartshows the following. First, the magnitude of and developments in the effect of JGB
purchases are generally similar across all models since the coefficients on the share of
BOJ holdings are roughly similar. Since the introduction of QQE in 2013, JGB purchases
have pushed down long-term interest rates significantly, with the reduction following the
introduction of YCC in 2016 reaching about 1 percent in all models. On the other hand,
while the effect of the YCC range varies somewhat from model to model, it graduallystrengthened from the introduction of YCC in 2016 to 2018 and temporarily declined in
2022. Subsequently, it had a large effect in restraining long-term interest rates when
upward pressure on interest rates increased from 2022 onward. On the other hand, thediffusion index for the degree of JGB market functioning in the Bond Market Survey
deteriorated substantially during this period, suggesting that as the effect of YCC
strengthened, this had a negative impact on the price discovery function of the market andliquidity.29

29

Studies examining the effect of large-scale JGB purchases on market functioning and liquidity in detailinclude Fukuma et al. [2024]. Meanwhile, Ochi and Osada [2024] examine how the functioning of corporatebond markets works as a transmission channel between the large-scale bond purchases and the real economy.

28

Chart 17. Effects of JGB Purchases and YCC Based on the Final Models
Effect of JGB purchases
Effect of setting the YCC range(Sum of stock and flow effects)
Introduction Clarification of theof YCC conduct of fixed-rate
purchase operations
Introduction
for consecutive daysof QQE%

0.5

0.0
Model1-0.5

Clarification of the
conduct of fixed-rate
purchase operations forconsecutive days
%pt

Introductionof YCC

0.5 %

25

0.0

0

-0.5

-25

Model2Model3

-1.0

-50

-1.0

Model4Degree of bond market
functioning (right scale)

Model5-1.5
CY 97 99 01 03 05 07 09 11 13 15 17 19 21 23

-1.5
CY 15

-75
16

17

18

19

20

21

22

23

24

Note: Based on the estimation results for each model in Chart 16.
Sources: Bank of Japan; Ministry of Internal Affairs and Communications; Bloomberg; LSEG Eikon.

Chart 18. Sources of Changes in the Long-term JGB Yield(Average of Models 4 and 5)
3 %

2

1

0
Other
U.S. Treasury yield
Effect of the YCC range
Effect of BOJ's JGB purchases (flow effect)
Effect of BOJ's JGB holdings (stock effect)10-year JGB yield

-1

-2
CY 97

99

01

03

05

07

09

11

13

15

17

19

21

23

Note: Figures are calculated based on the average of the coefficients obtained in Models 4 and 5 in Chart 16.
Sources: Bank of Japan; Ministry of Internal Affairs and Communications; Bloomberg; LSEG Eikon.

In addition, to separately assess the flow and stock effects of JGB purchases, we
decompose changes in the long-term yield using the results of Models 4 and 5, which takethe signaling effect of the flow of JGB purchases into account. The results are shown inChart 18.30 For the calculation, we use the simple average of the results obtained from30

The results in the April 2024 issue of the BOJ's Outlook Report (Charts B6-4 and B6-5 in Box 6, "Impactof the BOJ's JGB Purchases on the Yield Curve") correspond to the results of Models 2 and 3 in Chart 16.

29

each model. The results show that (i) the stock effect of JGB purchases graduallystrengthened after the introduction of QQE and has generally been at around 1 percent
since the introduction of YCC, and (ii) the YCC range restrained the long-term yield when
there was upward pressure on Japanese long-term interest rates. In addition, (iii) the flow
effect of JGB purchases, unlike the stock effect, had the effect of pushing down the
expected short-term rate component, particularly during the period when the BOJ
increased JGB purchases after the introduction of QQE.

4.2. Effect of JGB Purchases and YCC on the Entire Yield Curve
Finally, by extending the above analytical framework to JGBs of different maturities, wequantify the effect of JGB purchases and the YCC framework on the entire yield curve.
Specifically, we estimate Model 5 in Chart 16 using maturities ranging from 1 to 9 years
for the expected short-term rate component, the term premium, and U.S. Treasury yields.
Charts 19 and 20 show the coefficients and their standard deviations for the main
explanatory variables (see Appendix C for detailed estimation results).
Starting with the effect of JGB purchases, Chart 19 shows that the impact of boththe flow (monthly changes in JGB holdings) and the stock (the share of the BOJ's JGB
holdings in total JGBs) on the expected short-term rate component tends to be larger forlong maturities. However, the incremental increase for longer maturities graduallydiminishes, implying that expected short-term interest rates are pushed down mainly overthe medium term. On the other hand, while the impact of the expected future share of
BOJ holdings on the term premium also tends to be larger for longer maturities, the impact
appears to be particularly large for maturities of more than 5 years, indicating that thestock effect mainly impacts longer maturities. These results are in line with the theoreticalpredictions of preferred-habitat models such as the one proposed by Koeda and Ueno
[2022].
Turning to the effects of YCC, which are shown in Chart 20, the estimation results
indicate that fixed-rate purchase operations had an effect on the term premium only for
10-year JGBs, i.e., JGBs that were subject to BOJ purchases. In fact, such an effect oninterest rates was observed only for new issues, which were subject to the fixed-rate
purchase operations, so that spreads between new issues (on-the-run issues) and existing
issues of similar maturity (off-the-run issues) widened. These findings indicate that theestimated effect of the fixed-rate purchase operations corresponds to the asset-specificliquidity effect (super-narrow channel) discussed by Lucca and Wright [2024].31 On theother hand, the results also show that the probability that the upper bound of the YCC
range is exceeded has an effect on the term premium across a wide range of the yield
In order to conduct a more detailed analysis of the flow and stock effect, we here focus on Models 4 and 5,
which are extension of those models, and use Models 2 and 3 as benchmarks.
31

Similarly, Koeda and Wei [2024], employing panel data estimation using issue-specific data, find thatthe conduct of fixed-rate purchase operations affected only the yields of specific JGB issues.

30

curve, including not only 10-year yields but also medium-term yields. Finally, we findthat the effect of the probability that the offer rate of fixed-rate purchase operations forconsecutive days is exceeded is even larger, and that the effect of the probability that thelower bound of the YCC range is exceeded is symmetrical to the corresponding results
for the upper bound.

Chart 19. Estimation Results, by Maturity: Effects of JGB Purchases (Flow and Stock Effects)
Coefficients

0.05

Coefficients

0.005

0.005

Coefficients

0.005

0.00
-0.05
-0.10

0.000

0.000

0.000
Monthly change in
JGB holdings (effecton expected shortterm component)-0.005-0.005-0.010-0.010Coefficients-0.005-0.010

-0.15
-0.20

Risk-adjusted share of
BOJ holdings (effect on
expected short-term
component)-0.015-0.25-0.30
1 2 3 4 5 6 7 8 9 10
years

-0.0201 2 3 4 5 6 7 8 9 10
years

-0.015

Risk-adjusted
share of BOJ
holdings (effect onterm premium)-0.020-0.015
Expectation of futurechanges in JGB holdings(effect on term premium)-0.020-0.025

1 2 3 4 5 6 7 8 9 10
years

1 2 3 4 5 6 7 8 9 10
years

Chart 20. Estimation Results, by Maturity: Effects of YCC
0.005

Coefficients

0.004

0.06

Ratio of fixed-rate
purchase operations to
JGB issuance (effecton term premium)

0.003
0.002

Coefficients

0.06

Probability that the upperbound of the YCC range is
exceeded (effect on term
premium)

0.04
0.02

0.04
0.02

Coefficients
0.06
Probability that the offer
rate of fixed-rate purchase
operations for consecutive
days is exceeded (effecton term premium)

0.04
0.02

0.00

0.00

0.00

-0.02

-0.02

-0.02

-0.04

-0.04

-0.04

-0.002

-0.06

-0.06

-0.06

-0.003

-0.08

-0.08

-0.08

0.001
0.000
-0.001-0.004
1

2

3

4

5

6

7

8

9 10
years

-0.10

-0.10
1

2

3

4

5

6

7

8

9 10
years

1 2 3 4 5 6 7 8 9 10
years

Coefficients

Probability that the lower
bound of the YCC range
is exceeded (effect onterm premium)-0.10
1 2 3 4 5 6 7 8 9 10
years

Note: The shaded areas in Charts 19 and 20 denote the 90 percent confidence intervals.
Sources: Bank of Japan; Ministry of Internal Affairs and Communications; Bloomberg; LSEG Eikon.

Finally, we decompose changes in the entire yield curve following the introductionof QQE into the contribution of different sources of change. Specifically, we additionallyestimate Models 4 and 5 in Chart 16 for maturities ranging from 1 year to 9 years andsum the coefficients of these two models for each maturity. The results are presented in
Chart 21 and indicate that the large-scale monetary easing under QQE and YCC pushed
down not only the 10-year yield but also yields for a wide range of maturities (i.e., theentire yield curve), and that the main channel was the stock effect.

31

Chart 21. Sources of Changes in the Entire Yield CurveQQE with YCC
QQE
0.4

%

0.4

0.2

0.2

0.0

0.0

-0.2

-0.2

-0.4

-0.4

-0.6

-0.6

-0.8

-0.8

%

-1.0

-1.0
1

2

3

4

5

6

7

8

1

9 10
years

2

3

4

Other
U.S. Treasury yields
Effect of YCC range
Effect of BOJ's JGB purchases (flow effect)
Effect of BOJ's JGB holdings (stock effect)
Changes in yield curve

5

6

7

8

9

10

years

Notes: 1. In the left-hand panel, figures are the average from April 2013 to August 2016 relative to theaverage from January 2012 to March 2013. In the right-hand panels, figures are the average
from September 2016 to March 2024 relative to the average from January 2012 to March 2013.
2. Figures are calculated based on the average coefficients of Models 4 and 5 in Chart 16 for eachmaturity from 1 year to 10 years. In the estimations, U.S. Treasury yields for the corresponding
maturities are used.
Sources: Bank of Japan; Ministry of Internal Affairs and Communications; Bloomberg; LSEG Eikon.

5. Conclusion
This paper presented an empirical analysis of the effect of the BOJ's JGB purchases onlong-term interest rates in Japan, taking academic developments on central bankpurchases of government bonds into account. The main results can be summarized in thefollowing three points. First, having quantified the effect of JGB purchases taking market
participants' expectations about the future path of such purchases into account, we findthat the effect of JGB purchases on interest rates has been driven by the increase in JGB
holdings (i.e., the stock effect), which affects market participants' risk allocation. In
contrast, the effect of the daily conduct of JGB purchases (i.e., the flow effect), which
affects the supply and demand in the secondary market and market expectations about the
future stance of monetary policy, appears to have been relatively modest. Second, withregard to the YCC framework introduced in September 2016, in addition to the flow andstock effects described above, we find that it had the effect of restraining interest rateincreases when the long-term yield approached the upper bound of the YCC range. Thiseffect tended to be larger when the BOJ took countermeasures and market participants
expected such countermeasures. Third, our analysis of interest rates at different maturities
suggested that government bond purchases and YCC had an effect on interest rates across32

the entire yield curve.
The aim of this paper was to present a tractable time series model that is consistent
with theory and previous research results, and to obtain quantitative results that are as
robust as possible. That said, such a time series model is a non-structural reduced-form
model without any assumptions about the economic structure, and it is necessary to beaware of so-called model risks, such as the risk that the proxy variables we use for stockand flow effects are not always representative or that the estimation results may be biased
due to omitted variables.32 In particular, sensitivities in the model may vary over time,
and the model may not be able to accurately capture changes in market expectations if
they change dramatically. 33 , 34 This means that the results presented here should beinterpreted with considerable caution. On the other hand, since our model is relatively
simple and easy to understand, it is useful in practice for quantitatively assessing theeffects of policy measures on the entire yield curve from time to time. Moreover, while
we incorporate new ideas based on developments in recent academic research, our results
are similar to those in the BOJ's September 2016 "Comprehensive Assessment" and the
March 2021 "Assessment for Further Effective and Sustainable Monetary Easing," inwhich the BOJ attempted to quantity the effects of its quantitative easing policies using
time series models. Thus, our finding that the BOJ's large-scale JGB purchases under
QQE and YCC have pushed down the entire yield curve are likely to be relatively robust.
In March 2024, the BOJ decided that its large-scale monetary easing under the
QQE with YCC framework had fulfilled its role, and decided to shift to a monetary policy
framework that uses short-term interest rates as the primary policy tool.35 Under thisframework, long-term interest rates are essentially formed in financial markets, and theeffect of the targeted range on long-term interest rates presented in Chart 18 is likely to

32

While there are many studies that use sophisticated methods to identify monetary policy shocks, theymay, as highlighted by Bernanke [2020], be subject to model risk or their shock identification strategies
may not detect macroeconomic effects well. In practice, it would be useful to examine the advantages anddisadvantages of different approaches, including the one employed in this paper.

33

In times of higher interest rate volatility and lower risk tolerance among investors, the slope of thedemand curve in the JGB market (in Chart 6) would likely steepen, which would lead to an increase in thecoefficients for the impact of JGB purchases on interest rates above the historical average captured by themodel.

34

Waller [2024] points out that the effect of government bond purchases on the market can differ
substantially depending on central banks' communication accompanying such purchases or quantitative
tightening, such as whether they are open-ended or closed-ended, and the degree to which such purchases
or tightening are predictable. The model in this paper incorporates this idea and uses the expected share of
future JGB holdings as one of the variables based on the assumption that market participants anticipate thefuture path of JGB purchases over the next two years. However, this means that if the way market
participants incorporate information and form expectations changes, the assumptions of the model would
also need to be changed, which would potentially change predictions derived by the model.
35

The Fed and the ECB also currently conduct monetary policy using short-term interest rates as theirprimary policy tool, while maintaining the size of their balance sheets at ample levels. See, for example,
the Fed's "Principles for Reducing the Size of the Federal Reserve's Balance Sheet," published in January
2022.

33

disappear.36 On the other hand, regardless of the amount of JGB purchases in the nearterm, the BOJ's JGB holdings are expected to remain at a high level for the time being.
Given the estimation results in this paper, this would imply that the BOJ's JGB purchaseprogram will continue to affect the formation of the yield curve, mainly through the stock
effect. That said, it is important to note that, as discussed above, the quantitative resultspresented in this paper should be interpreted with considerable latitude. Recent studies
have highlighted that the magnitude of the effect on long-term interest rates may differ
between periods in which the central bank increases and decreases its holdings of JGBs.37
Keeping these points in mind, it is important to further deepen our understanding of theeffects of central bank purchases and holdings of government bonds on long-term interest
rates.

36

At the March 2024 Monetary Policy Meeting, the BOJ decided that in the case of a rapid rise in longterm interest rates, it will make nimble responses by, for example, increasing the amount of JGB purchases,
regardless of the monthly schedule of JGB purchases. Although it is difficult to quantify the effect of thisstatement using the analytical framework in this paper since it does not indicate a specific target level forthe long-term yield in advance, it is expected to contribute to the stable formation of long-term interest rates
in a manner similar to the setting of an upper bound under YCC.

37

See, for example, Schnabel [2023, 2024] and Ramsden [2023]. At a recent event (the US Monetary
Policy Forum), Kristin Forbes, a professor at MIT, presented an event study analysis (Du et al. [2024])
using data from seven central banks that have already reduced their government bond holdings, including
the Fed and the ECB, and pointed out that announcements of reductions in government bond holdings
significantly raise long-term interest rates, but that, the quantitative magnitude of the effect is relatively
small compared to the effect of the announcements of increases in government bond purchases. She thendiscussed with Fed officials the reasons for and background to this in terms of differences in economic andfinancial conditions and central bank communication. (See also, for example, Waller [2024] and Logan[2024]).

34

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Purchases: Evidence on the Importance of Local Supply," Journal of Financial

35

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38

Appendix A. Estimation Method for the Expected Future Share of the
BOJ's JGB Holdings (Adjusted for Interest Rate Risk)
This appendix presents the method we use for constructing the expected future share of BOJ
holdings of JGBs (adjusted for interest rate risk) introduced in Section 2 and used in theanalysis in Section 4. Specifically, we first calculate (1) the risk-adjusted share of the BOJ's
JGB holdings, which takes interest rate risk with respect to the BOJ's JGB holdings into
account. Next, (2) we estimate the expected future share of the BOJ's JGB holdings (adjusted
for interest rate risk) based on the actual and the announced amount of purchases by the BOJ.

A.1. Risk-adjusted share of the BOJ's JGB holdings
The amount of interest rate risk of a bond (the change in the bond price when the interest
rate changes by one unit) depends on its remaining maturity and the level of the interest
rate.38 Performing a quadratic approximation using a Taylor expansion around interest rate
𝑟 for bond price 𝑃, the change in the bond price when the bond interest rate changes by 𝛥𝑟using bond duration 𝐷 and convexity 𝐶 can be expressed as follows:
𝑃 𝑟

𝛥𝑟

𝑃

𝑃 𝑟

1 𝑑𝑃
𝛥𝑟
𝑃 𝑑𝑟

11𝑑 𝑃
𝛥𝑟
2 𝑃 𝑑𝑟

𝐷𝛥𝑟

1
𝐶 𝛥𝑟
2

(A.1)

where, approximating convexity 𝐶 by 𝐷 for simplicity, the amount of interest rate risk
( 𝛥𝑃/𝑃) of each bond issue for a 1% rise in interest rates (𝛥𝑟 1%) can be calculated as afunction of its remaining maturity D (𝑅 ).39 We use this approximate relationship to convert
the BOJ’s JGB holdings and overall JGB issuance to a risk amount basis.
We start by calculating the BOJ’s JGB holdings by maturity (remaining maturity)using the "Japanese Government Bonds Held by the BOJ" statistics on the BOJ's JGB
holdings published monthly by the BOJ.40 In other words, the amount of JGB holdings bymaturity can be calculated using information on JGB holdings by issue and the scheduled
redemption date of JGBs of each issue.
38

The possibility that bonds are redeemed or sold prior to maturity in response to changes in interest
rates should also be taken into account. However, with some exceptions in the past, the BOJ holds JGBs
until maturity without selling them. Given this, the BOJ employs the amortized cost method for thevaluation of JGBs.
39

Specifically, 𝑅 can be calculated as 𝑅

𝛥𝑃/𝑃

0.01𝐷

0.0001𝐷 /2.

40

Treasury discount bills are excluded from the analysis because purchases and holdings of such assets
likely have little impact on long-term interest rates. Floating-rate bonds and inflation-indexed bonds,
which only account for a small share of BOJ holdings, are also excluded, and only fixed-rate JGBs areincluded.
The "Japanese Government Bonds Held by the BOJ" statistics do not contain data prior to May 2001. We
therefore retroactively estimate the amount of interest rate risk held by the BOJ for the period prior to
May assuming a linear relationship between the interest rate risk amount and semiannual data on the
average remaining maturity of JGBs, and then convert them to monthly data through linear interpolation.

39

In converting JGB holdings to an interest rate risk basis, we follow previous studies(e.g., Li and Wei [2013]) and standardize the amount of JGBs outstanding to the equivalentamount of 10-year bonds that contain the same amount of interest rate risk (i.e., the 10-year
equivalent value). Specifically, risk-adjusted JGB holdings (𝐽𝐺𝐵𝑅𝐼𝑆𝐾 ) for each maturity arecalculated by multiplying the amount of JGB holdings (𝐽𝐺𝐵 ) for each maturity by the 10year JGB equivalent risk amount (𝑅 /𝑅 ) and adding them together for all maturities toobtain the aggregate risk-adjusted value (𝐽𝐺𝐵𝑅𝐼𝑆𝐾 ).
𝐽𝐺𝐵𝑅𝐼𝑆𝐾𝑅
𝑅

𝐽𝐺𝐵𝑅𝐼𝑆𝐾

𝐽𝐺𝐵

(A.2)

A.2. Expected Future Share of the BOJ's JGB Holdings
Next, we construct the expected future share of the BOJ's JGB holdings (adjusted for interest
rate risk) taking market participants' expectations based on the actual purchase amount andannounced planned amount of purchases by the BOJ into account.
There are several possible ways to incorporate market participants' expectations of
the BOJ's future JGB holdings. The first is to use surveys of market participants. Equiza etal. [2023], who examine the effect of the ECB's asset purchases, for example, obtain market
participants' expectations of the future pace of government bond purchases at each date froma monthly survey of economists conducted by Bloomberg and use these to estimate expected
future government bond holdings. 41 The second approach is to assume that market
participants forecast the future path of purchases based on publications such as central bankreleases. An example of a study following this approach is that by Ihrig et al. [2018], whoanalyze the effect of the FRB's three quantitative easing programs (LSAP1, LSAP2, andLSAP3) implemented in the U.S. in the wake of the global financial crisis. They estimate
the expected future outstanding amount of the FRB's government bond holdings assumingthat market participants form their expectations based on the FRB's announcements (about
the total purchases of assets such as long-term government bonds and the pace of thosepurchases). For our analysis in Section 4, we tried to estimate the long-term interest rate
model from 1997 but were unable to obtain survey-based information on market participants'
expectations for the entire period. Therefore, as in Ihrig et al. [2018], we make various
assumptions regarding the formation of market participants' expectations using available
information on the BOJ's purchases of JGBs.
Specifically, we estimate the expected future (two-year ahead) share of BOJ holdings

41

Since Bloomberg’s survey does not provide the expected maturity structure of purchases, the amountof interest rate risk of future holdings is calculated by combining future pace of purchases at each datewith information on the maturity structure announced separately by the ECB.

40

based on the following assumptions for each subperiod. 42 (1) For the period after the
introduction of the QEP (from March 2001 to September 2010 43 ), we assume that themonthly pace of purchases at each point announced by the BOJ would continue over the next
two years. (2) After the introduction of CME (from October 2010 to March 2013), the BOJ
established its Asset Purchase Program as a temporary measure, so we add the scheduledpurchase amount of that program to the former purchase expectations.44 (3) For the period
between the introduction of QQE and the introduction of YCC (from October 2010 to August2016), we assume that market participants expected the pace of purchases over the next two
years to be in line with the announced monthly pace of JGB purchases (at an annual pace ofabout 50 trillion yen until October 2013, and about 80 trillion yen from November 2014).
Finally, (4) for the period after the introduction of YCC (from September 2016 onward), theJGB holdings in two years' time implied by the monthly pace of purchases announced in the"Schedule of Outright Purchases of Japanese Government Bonds" released monthly by BOJ
is used. Since the "Schedule of Outright Purchases of Japanese Government Bonds"
indicates only the upper and lower limits of the purchase amount for each remaining maturity,
the average of the upper and lower limits is used as the scheduled purchase amount.45 Chart
A.1 shows the expected amount of the BOJ's JGB purchases over the next two years basedon the above assumptions.

42

Li and Wei [2013] and Ihrig et al. [2018], using a term structure model of interest rates, argue thatshocks to the expected future bond supply have the effect of pushing down the current term premium, andthat the more distant the future shock occur, the more its effect is discounted. Therefore, in their models,
shocks that occur in the distant future only have a negligible effect on the current term premium.
Consequently, in our analysis we focus on the expected JGB holdings over the next two years only.
43

Before the introduction of the QEP (i.e., prior to March 2001), asset purchases were not linked directly
to monetary policy. Given this, the amount of JGB holdings two years ahead is calculated assuming thatthe monthly purchases of long-term JGBs at each point in time would continue for the next two years.

44

We assume that under the CME Asset Purchase Program monthly JGB purchases were implemented
at a constant pace until the target amount of purchases announced at each point in time was reached.
45

From April 2021 to November 2022, the planned amount of purchases was published instead of therange.

41

Chart A.1. Expected Amount of the BOJ’s JGB Purchases and Redemptions
over the Next Two Years (Per Month)

12

tril.
yen

Introductionof QEP

Introduction Introductionof QQEof CME

10Expected amount of JGB
purchases

8

Expected amount of JGB
redemptions

Introductionof YCC

6
4
2
0
CY 97

99

01

03

05

07

09

11

13

15

17

19

21

23

Note: Latest data are as of April 2024.
Source: Bank of Japan.

The expected amount of the BOJ's JGB holdings over the next two years can becalculated by subtracting the expected redemption amount of JGBs over the next two years
from the expected purchase amount calculated above and adding it to the amount of JGB
holdings at each point in time. The redemption amount is calculated by adding up (1) theamount of holdings at each point in time whose redemption date falls within the next two
years and (2) the portion of scheduled purchases over the next two years that will mature
within the next two years.46
Taking interest rate risk into account, we calculate the expected JGB holdings for eachmaturity, and then convert them to the 10-year equivalent amount using the above equation(A.2) and finally aggregate the amounts.47
46

For the period prior to June 2001, data for BOJ JGB holdings by maturity is not publicly available. We
therefore assume that the ratio of the redemption amount over the next two years to the outstanding
amount of JGBs is constant and equals the average for the period from June 2001 to May 2002.
47

In order to calculate expected JGB holdings by maturity, it is necessary to make assumptions regarding
the composition of future JGB purchases by maturity.
For the period since the introduction of QQE, we use the BOJ's purchase schedule by remaining maturity(up to 1 year, more than 1 year and up to 3 years, more than 3 years and up to 5 years, more than 5 years
and up to 10 years, more than 10 years and up to 25 years, and more than 25 years) published each month.
On the other hand, this information was not available for the period before the introduction of QQE.
Therefore, we use the actual maturity structure of each month's purchases (moving averages for the six
months before and after the purchases to smooth out short-term fluctuations). For the period before May

42

Lastly, expected future JGB issuance by the government, which is the denominatorof the expected future share of the BOJ's JGB holdings (adjusted for interest rate risk) in the
total amount of JGBs outstanding, is calculated based on the simplifying assumption that at
each point in time the pace of issuance over the next two years is the same as that over the
past two years. The maturity structure of JGBs is assumed to remain constant on a stockbasis. Chart 7 shows the expected future share of the BOJ's JGB holdings (adjusted forinterest rate risk) based on the above assumptions.

References
Equiza, J., R. Gimeno, A. Moreno, and C. Thomas [2023], "Evaluating Central Bank Asset
Purchases in a Term Structure Model with a Forward-looking Supply Factor," BANCO DEESPAÑA Working Papers, No.2303.
Ihrig, J., E. Klee, C. Li, M. Wei and J. Kachovec [2018], "Expectations about the Federal
Reserve’s Balance Sheet and the Term Structure of Interest Rates," International Journal ofCentral Banking, 14(2), 341-390.
Li, C., and M. Wei [2013], "Term Structure Modeling with Supply Factors and the Federal
Reserve's Large-scale Asset Purchase Programs," International Journal of Central Banking,9(1), 3-39.

2001, when issue-specific information is not available, we assume perfect foresight and that market
expectations are equal to the realized value two years ahead. (Here, the realized value refers to the ratioof the BOJ's JGB holdings adjusted for interest rate risk to the BOJ's JGB holdings not adjusted for interest
rate risk).

43

Appendix B. Estimation Methodology for the Probability that the LongTerm Yield Might Exceed the YCC Range
This appendix explains how we calculate the probability that the long-term yield might
exceed the YCC range introduced in Section 3 and used in the analysis in Section 4.
Specifically, we (1) estimate the expected future interest rate distribution using data frominterest rate swaptions with the 10-year OIS rate as the underlying price and (2), using this
distribution, calculate the probability that the long-term interest rate might exceed the upperor lower bound of the YCC target range 3 months ahead priced in by market participants.
The expected future interest rate distribution is estimated employing the approach
proposed by Malz [2014] utilizing the "volatility smile" -- the tendency of a plot of therelationship between the implied volatility (IV) and the strike price to be a convex curve -incorporated into swaption prices.48
Specifically, we start by expressing the price 𝑐 𝑡, 𝑋, 𝜏 of a European call option attime 𝑡 using the following equation:

𝑐 𝑡, 𝑋, 𝜏𝑒𝐸 max 𝑆

𝑋, 0

𝑒

𝑠

𝑋 𝜋 𝑠 𝑑𝑠

(B.1)

where, for a 3-month interest rate swaption with a 10-year OIS rate as the underlying price,
𝑆 is the price of the underlying asset (=OIS rate) at time 𝑡, 𝑋 is the strike price, 𝜏 is theremaining term ( 𝜏 𝑇 𝑡 when the maturity of the underlying asset is 𝑇 ), 𝜋 𝑠 is theprobability density function for the future distribution of the underlying asset price, and 𝑟
is the risk-free rate. Here, the probability density function 𝜋 𝑋 , which we ultimately wantto calculate, integrated over the cumulative distribution function Π 𝑋 is derived by partial
differentiation of the option price by strike price 𝑋 as follows:Π 𝑋

𝜋 𝑠 𝑑𝑠 ＝1𝑒𝜕𝑐 𝑡, 𝑋, 𝜏
∂X

(B.2)

Using this equation, we can calculate the expected future interest rate distribution
using option price data, if the relationship with the strike price can be derived. However, inpractice, strike prices 𝑋 of traded options are discrete, so that a continuous relationshipbetween option prices and strike prices cannot be observed. We therefore need to somehow
estimate option prices corresponding to strike prices at which no trades take place throughinterpolation. However, since the relationship between option prices and strike prices is
48

This method proposed by Malz [2014] can be also applied to the future distribution of the exchange
rate, as recently done by Yoneyama et al. [2024].

44highly nonlinear, it is not easy to make accurate interpolated estimates (Jiang and Tian[2005]). For this reason, in practice, probability densities are often estimated by interpolating
IV data that show continuous changes with respect to the strike price, and then convert thevalues to option prices (Malz [2014]).
In this paper, we use IV quote data for 3-month forward 10-year interest rate
swaptions, which we obtain from LSEG Eikon. For IVs corresponding to the 11 strike prices
for which data are available (namely, ATM =at the Money: when the strike price equals themarket price, ATM ±25 bps, ATM ±50 bps, ATM ±100 bps, ATM ±150 bps, and ATM ±200bps), we estimate the cubic spline function, which is often used in previous research, forinterpolation. 49 Looking at the estimated IV functions in Chart B.1, the functions are
relatively smooth, and a so-called "volatility smile" shape can actually be observed, withvolatility bottoming out around ATM and increasing at both ends.
Chart B.1. IV Function Calculated from Swaption Data
180

IV, bps160

IV (interpolated data)
IV (quote data)

140

120

100

80
-200 -150
bps

-100

-50

ATM

+50

+100 +150 +200

Note: As of January 13th, 2023.
Sources: Bloomberg; LSEG Eikon.

Chart B.2 shows the expected future interest rate distribution calculated from theobtained IV function. Since there is a one-to-one relationship between option prices and the49

Note that when nonparametric methods such as spline interpolation are used, extreme unevenness canbe observed in the value of the IV at each strike price, and the interpolated IV can also be negative. We
check that the interpolated IV in this paper is non-negative for all periods.

45

IV, it is possible to numerically calculate the expected distribution at each point in time.50,51
The chart shows that the expected distribution at the beginning of 2022 was concentrated
around zero percent under the YCC framework. However, at the beginning of 2023, whenlong-term yields came under upward pressure, the distribution shifted significantly to theright and the dispersion became larger with a thicker right tail. This indicates that uncertainty
about future interest rate levels had increased, and that some investors were increasingly
expecting the abolition of YCC and a significant rise in interest rates.
Chart B.2. Expected Future 10-year Interest Rate Distribution 3 Months Ahead
60%
As of January 13th, 2022
As of January 13th, 2023

50
40
30
20
10
0
-0.5

0.0

0.5

1.0

Note: The circles denote the median of each distribution.
Sources: Bloomberg; LSEG Eikon.

1.5

2.0
2.5
yields, %The probability that long-term interest rates exceed or fall below a specific level threemonths from now can be calculated using the expected interest rate distribution at each point
in time calculated as described above. Chart 11 shows the probabilities at each point in timethat long-term interest rates exceed the upper or lower bounds of the YCC targeted range oroffer rate for fixed-rate purchase operations three months later (see Chart 8 for the targetedrange at each point in time).

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The call option price 𝑐 𝑡, 𝑋, 𝜏 can be represented by the option valuation function
𝑉 𝑆 , 𝑋, 𝜏, 𝜎 𝑡, 𝑋, 𝜏 with the IV as a variable using the Black model. However, in Japan, yields havebeen negative in recent years. Since the Black model does not take this possibility into account, it cannot
depict option prices. For this reason, LSEG Eikon converts option prices and IVs using a normal model(the Bachelier model) that assumes that swap rates follow a normal distribution as its standard model.
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In calculating the distribution, we assume the risk-free rate 𝑟 to be zero since short-term interest rates
in Japan are around zero percent.
Since IVs for LIBOR-based swaptions were used prior to May 25, 2022, we use the LIBOR-OIS spreadto convert the distribution to an OIS-based distribution, assuming a parallel shift in the overall distribution.
For missing portions of the IV data for the 11 strike prices, parameters were estimated using only available
data and interpolation estimation was performed.

46

References
Malz, A. M. [2014], "A Simple and Reliable Way to Compute Option-Based Risk-Neutral
Distributions," Federal Reserve Bank of New York Staff Reports, No.677.
Jiang, G. J., and Tian, Y. S. [2005], "Model Free Implied Volatility and Its Information
Content," Review of Financial Studies, 18, 1305-1342.
Yoneyama, A., A. Tsuchiya., and N. Fukuma [2024], "Changes in Risk Perceptions on Yen
Interest Rates and Exchange Rates Observed in Options Markets: Developments in Implied
Probability Distributions amid Rate Hikes in the United States and Europe from 2022 to2023," Bank of Japan Review, 24-E-8.

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Appendix C. Detailed Estimation Results of Interest Rate Functions
Chart C.1. Detailed Estimation Results for Model 5 in Chart 16(1) Dependent Variable: Expected Short-term Rate Component for Each Maturity
Dependent variable1-year2-year3-year4-year5-year6-year7-year8-year9-year10-yearConstant

0.075 ***

0.102 ***

0.145 ***

0.192 ***

0.240 ***

0.291 ***

0.341 ***

0.388 ***

0.433 ***

0.476 ***

10-year U.S. Treasury yields

0.005

0.018 ***

0.029 ***

0.040 ***

0.048 ***

0.056 ***

0.063 ***

0.069 ***

0.074 ***

0.078 ***

Uncollateralized overnight call rate

0.708 ***

0.811 ***

0.853 ***

0.875 ***

0.886 ***

0.875 ***

0.858 ***

0.838 ***

0.818 ***

0.798 ***CPI (less fresh food and energy)

0.020 ***

0.034 ***

0.047 ***

0.057 ***

0.065 ***

0.071 ***

0.075 ***

0.078 ***

0.080 ***

0.082 ***

Risk-adjusted share of BOJ's JGB
holdings in total-0.004 ***-0.005 ***-0.006 ***-0.007 ***-0.008 ***-0.008 ***-0.009 ***-0.009 ***-0.009 ***-0.009 ***Monthly change in JGB holdings-0.049 **-0.081 ***-0.113 ***-0.139 ***-0.163 ***-0.177 ***-0.187 ***-0.195 ***-0.202 ***-0.208 ***Adjusted R-squared
AIC
Estimation Period

0.692-1.6360.758-1.5270.790-1.4120.808-1.3210.819-1.2430.826-1.1860.830-1.1420.832-1.1100.833-1.0890.833-1.077January 1997 to March 2024

(2) Dependent Variable: Term Premium for Each Maturity
Dependent variable1-year2-year3-year4-year5-year6-year7-year8-year9-year10-yearConstant

0.053 **

0.045 **

0.023

0.001

-0.053-0.077-0.087-0.056

0.001

0.019

10-year U.S. Treasury yields

0.010

0.027 ***

0.047 ***

0.075 ***

0.103 ***

0.126 ***

0.146 ***

0.157 ***

0.157 ***

0.159 ***

Risk-adjusted share of BOJ's JGB holdings
in total

0.000-0.002-0.002-0.003-0.002-0.003-0.004-0.006 *-0.008 **-0.009 **Expectation of future changes in JGB
holdings-0.006 ***-0.005 ***-0.005 ***-0.006 ***-0.007 ***-0.009 ***-0.010 ***-0.011 ***-0.013 ***-0.014 ***Ratio of fixed-rate purchase operations to
JGB issuance0.001 **

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

-0.002 **Probability that the upper bound of the YCC
range is exceeded (from Sep. 2016 to Apr. 2022,
from Nov. 2023 to Mar. 2024)-0.010 **-0.011 **-0.019 ***-0.026 ***-0.035 ***-0.040 ***-0.043 ***-0.044 ***-0.044 ***-0.046 ***Probability that the offer rate of fixed-rate
purchase operations for consecutive days is
exceeded(from May. 2022 to Oct. 2023)-0.016 ***-0.019 ***-0.032 ***-0.042 ***-0.048 ***-0.054 ***-0.056 ***-0.056 ***-0.056 ***-0.059 ***Probability that the lower bound of the YCC
range is exceeded-0.010 *

0.001

0.010

0.018 *

0.023 **

0.027 **

0.027 **

0.028 **

0.026 **

0.025 **

0.450
-2.0850.609-2.1980.687-1.7820.731-1.3400.760-1.0460.773-0.7470.773-0.4880.785-0.3450.803-0.3280.813-0.290Adjusted R-squared
AIC
Estimation Period

January 1997 to March 2024

Notes: 1. ***, **, and * denote statistical significance at the 1, 5, and 10% levels, respectively.
2. In the estimations, U.S. Treasury yields for the corresponding maturities are used.
Sources: Bank of Japan; Ministry of Internal Affairs and Communications; Bloomberg; LSEG Eikon.

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