Maturity Structure and Supply Factors
in Japanese Government Bond Markets∗
Ichiro Fukunaga†, Naoya Kato‡, and Junko Koeda§
June 12, 2015

Abstract
Using our constructed database on the amount outstanding of Japanese
Government Bonds (JGBs) categorized by holder and remaining maturity,
we examine the effects of changes in the holders and maturity structureson the term structure of interest rates and the risk premium on longterm bonds. Both approaches using single-equation regressions and a term
structure model confirm that the net supply of JGBs, the issuance (supply)by the government minus the demand by the preferred-habitat investors
including the Bank of Japan (BOJ), had significant effects on long-term
interest rates. The regression approach implies that the net supply effects
were stronger in the zero interest rate periods, while this relationship was
not found using the model approach. We also calculate the net supply
effects of the BOJ’s JGB purchases as part of its Quantitative and Qualitative Monetary Easing and compare the results with those obtained froma simple event-study analysis.
Keywords:
Japanese Government Bonds; Term structure of interest
rates; Preferred habitat; Unconventional monetary policy
JEL classification: E43, E44, E52, E58, G11, G12, H63∗

The authors would like to thank Kazuo Ueda, Christopher Waller, the participants at the2015 BOJ-IMES Conference, and the staff at the Bank of Japan, for their helpful comments.
Takako Yoshiba helped to prepare the data. The views expressed in this paper are those of theauthors and do not necessarily reflect the official views of the Bank of Japan.
†
Director and Senior Economist, Institute for Monetary and Economic Studies, Bank ofJapan. E-mail: ichirou.fukunaga@boj.or.jp‡
Associate Director, Institute for Monetary and Economic Studies, Bank of Japan. E-mail:naoya.katou@boj.or.jp§
Associate Professor, School of Political Science and Economics, Waseda University. E-mail:jkoeda@waseda.jp

1

Introduction

After the recent global financial crisis, many central banks in advanced economies
lost their conventional monetary policy tools near the zero lower bound on shortterm interest rates. To provide further monetary accommodation, they have
moved to unconventional tools, such as forward guidance and government bondpurchases, aimed at affecting longer-term interest rates.1 The Bank of Japan(BOJ) introduced these unconventional tools long before the global financial crisis,2 but since April 2013, it has implemented more aggressive monetary easing measures, the “Quantitative and Qualitative Monetary Easing (QQE),” toovercome prolonged deflation and achieve the price stability target.3 Under the
QQE, the pace of the BOJ’s purchases of Japanese Government Bonds (JGBs)
has accelerated and the remaining maturity of its JGB purchases has extended
significantly, while clear forward guidance on the continuation of the policy has
been provided.
In general, a central bank’s purchases of government bonds are considered tolower long-term interest rates through three channels: the signaling channel, thescarcity channel, and the duration channel.4 The signaling channel captures the1
Many central banks in advanced economies purchased private as well as public assets,
especially in an earlier part of the post-crisis period, mainly to restore the functioning of financial
markets and intermediation rather than provide monetary accommodation.
2
The BOJ first introduced a zero interest rate policy in 1999 after a domestic banking crisis,
and then implemented a quantitative monetary easing policy from 2001 through 2006 withforward guidance on the continuation of the policy. After the global financial crisis in 2008,
the BOJ again cut the policy rate to virtually zero and established an asset purchase program
under its “Comprehensive Monetary Easing.”
3
The BOJ’s price stability target was set at 2 percent in terms of the year-on-year rate ofchange in the consumer price index in January 2013. Before that, the “price stability goal in
the medium to long term” was set at 1 percent (in a positive range of 2 percent or lower). A
crucial feature of the QQE is that it aims to raise inflation expectations through a strong andclear commitment to achieving the price stability target as well as massive purchases of JGBs,
and thereby to lower real interest rates. In this paper, however, our analyses focus on nominal
rather than real interest rates. For an analysis of real interest rates and inflation risk premia
in Japan, see for instance Imakubo and Nakajima (2015).
4This classification follows IMF (2013). Krishnamurthy and Vissing-Jørgensen (2011) classify the channels through which the Federal Reserve’s quantitative easing policies affected abroader range of long-term interest rates, including the interest rates on corporate bonds andreal interest rates. Joyce et al. (2012) survey the theoretical and empirical literature on thetransmission mechanisms of quantitative easing policies.

1role of bond purchases as a credible commitment by the central bank to keepinterest rates low and thus serves as a complement to forward guidance. The
bond purchases may support the credibility because market participants may
perceive that it would be difficult for the central bank to raise rates rapidly witha large amount of long-term assets on its balance sheet. The scarcity channel
captures the effect of a shortage of bonds with particular maturities available
for trading, caused by the central bank’s purchase of these particular bonds,
on the corresponding yields. The duration channel captures a downward shiftof the entire yield curve through a decrease in the price of duration risk (riskpremium) caused by the central bank’s purchases of longer-term bonds. Amongthese channels, the signaling channel had been considered as the main channel
until recently. Theoretically, according to the expectation hypothesis, changes inthe supply of bonds should affect yields only to the extent that expectations of
future short-term interest rates are changed, that is, only through the signaling
channel.5 Similarly, Eggertsson and Woodford (2003) argue that the central
bank’s open-market operations would be irrelevant if they did not change theexpected future conduct of monetary or fiscal policy. Empirically, at least forJapan, existing studies on the earlier quantitative easing policy imply that theeffects through the scarcity and duration channels, often combined and referred
to as the portfolio rebalance channel, were smaller or less clear-cut than thosethrough the signaling channel.6
Recent studies motivated by the implementation of large-scale bond purchasesby many central banks in advanced economies, however, pay more attention to
the scarcity and duration channels. A theoretical background of the scarcity
channel is the preferred-habitat theory, first set forth by Modigliani and Sutch(1966), which assumes that bond markets are segmented due to the existence of“preferred-habitat” investors with preferences for particular maturities and thus
the interest rate for a given maturity is determined by the supply and demand of
5

Gürkaynak and Wright (2012) discuss various implications and limitations of the expectation hypothesis and standard affine term structure models.
6
For details, see for instance Ugai (2007) and Ueda (2012a, c).

2bonds with that particular maturity. Based on this assumption, Vayanos and Vila
(2009) construct a model of the term structure of interest rates in which the term
structure and bond risk premia are determined through the interaction between
the preferred-habitat investors and risk-averse arbitragers and thereby the duration channel generated by the arbitragers’ aversion to duration risk as well as the
scarcity channel is incorporated.7 Two important predictions of this theoreticalframework are as follows: (i) the “net supply” of more and longer-term government bonds, which is defined as the issuance (supply) by the government minus
the demand by the preferred-habitat investors, leads to a higher risk premiumand steeper yield curve; and (ii) the above “net supply” effects are stronger when
the arbitragers’ risk aversion is higher. In the real world, the preferred-habitat
investors include long-term investors such as pension funds and insurance companies as well as central banks that implement large-scale bond purchases as an
unconventional monetary policy tool. The preferred-habitat theory can explaina variety of episodes in which a shock to the net supply of government bonds
affected long-term interest rates,8 including the recent bond purchases by central banks in advanced economies, and appears to be increasingly accepted bypolicymakers as well as academic economists.9
In this paper, we examine how the net supply of JGBs affected the term structure of interest rates and the risk premium on long-term JGBs using Japanesemonthly data from January 1992 to September 2014, which includes the period
after the QQE was introduced.10 First we construct a database on the amount7

The model of Vayanos and Vila (2009) can be positioned within the literature on “limits of arbitrage” surveyed by Gromb and Vayanos (2010) that investigates how costs faced byarbitragers, that is, shocks to the demand and supply of government bonds with particular maturities absorbed by the risk-averse arbitragers in this model, can prevent them from eliminating
mispricings.
8
Greenwood and Vayanos (2010) present two recent episodes that strongly support the relevance of the preferred-habitat theory: the U.K. pension reform of 2004 and the U.S. Treasury
buyback program of 2000–01.
9Kohn (2009) and Yellen (2011) mentioned the preferred-habitat theory as a key mechanism
behind the effects of the Federal Reserve’s large-scale asset purchases on long-term interest
rates.
10
Our sample period does not include the period after the expansion of the QQE was announced on October 31, 2014.

3

outstanding of JGBs categorized by holder and remaining maturity, from which
various net supply measures are calculated. To examine the net supply effects, we
use two approaches: single-equation regressions and a term structure model. The
former approach can flexibly control various factors that affect long-term interest
rates, while the latter is more rigorously related to the preferred-habitat theory.
Both approaches confirm that the net supply effects are statistically significant,consistently with prediction (i) above on the preferred-habitat theory. Moreover,
the regression approach implies that the net supply effects were stronger when
the arbitragers’ risk aversion was higher, and this relationship is incorporated in
the model approach, consistently with prediction (ii) above.11 However, while theregression approach implies that the net supply effects were stronger in the zerointerest rate periods when the arbitragers’ risk aversion was relatively high, thisrelationship was not found using the model approach, because the model estimation results imply that the effects were weaker in the zero interest rate periods
given the arbitragers’ risk aversion. Finally we calculate the net supply effects of
the BOJ’s JGB purchases as part of the QQE from both approaches and compare
the results with those obtained from a simple event-study analysis.
Our regression approach is closely related to Greenwood and Vayanos (2014),
who examine the effects of the supply and maturity structure of U.S. government debt on bond yields and returns based on the preferred-habitat theory.
Unlike us, however, they focus on the gross supply of government debt and do
not use data on the bonds held by preferred-habitat investors to construct net
supply measures. Kuttner (2006) examines the effects of changes in the Federal
Reserve’s holding of long-term securities on the holding-period excess returns,
and Chadha et al. (2013) examine the effects of the average maturity of U.S.
Treasury bonds held outside the Federal Reserve on forward long-term yields andterm premium. D’Amico et al. (2012) examine the effects through the scarcity
channel and duration channel on several components of long-term U.S. Treasury
11

Strohsal (2013) examines the net supply effects under time-varying risk aversion using
German daily data and obtains results consistent with prediction (ii) above on the preferredhabitat theory.

4

yields. Besides these, there are many regression analyses that estimate the effects of government debt or a central bank’s purchases of government debt on
long-term interest rates, including Laubach (2009) for U.S. government debt12
and D’Amico and King (2013) and Meaning and Zhu (2011) for the Federal Reserve’s purchases,13 although they examine the effects through broader channels
than those motivated by the preferred-habitat theory.14 Meanwhile, our term
structure model approach is based on a model extended from Hamilton and Wu(2012a),15 who incorporate preferred-habitat investors into an arbitrage-free term
structure model as a discrete-time version of Vayanos and Vila (2009) and estimate it using U.S. data. Also motivated by the preferred-habitat theory, Li andWei (2013) estimate an arbitrage-free term structure model with U.S. Treasury
and mortgage-backed securities supply factors as well as observable yield factors
and evaluate the effects of the Federal Reserve’s large-scale asset purchase programs. While all the papers mentioned above conduct empirical analyses using
U.S. data, similar analyses using Japanese recent data including the period under the QQE are very limited.16 Moreover, similar analyses using data on private
12
Following Laubach (2009), Kameda (2014) estimates the effects of government debt andbudget deficit on long-term JGB yields using Japanese data. Ichiue and Shimizu (2012) examine
the determinants of long-term bond yields, including fiscal conditions, using panel data for 10
developed countries.
13
To examine the effects of a central bank’s purchases of government bonds on long-term
interest rates, many studies use event-study methodologies: for instance, Gagnon et al. (2011),
Krishnamurthy and Vissing-Jørgensen (2011), Swanson (2011), Neely (2010), and Cahill et al.
(2013). Those studies using Japanese data include Ueda (2012b) and Lam (2011). Some ofthese studies use regression analyses as well as event-study analyses.
14
In this relation, Krishnamurthy and Vissing-Jørgensen (2012) show that when the supplyof the U.S. government debt is low, the value that investors assign to the liquidity and safety
attributes offered by Treasury bonds is high, and thus the yield on Treasuries is low relative tothe yield on corporate bonds that offer less liquidity and safety. This implies that preferredhabitat theory can be applied to not only within government bonds market but also between
government bonds and other bonds markets. Meanwhile, Greenwood, Hanson, and Stein (2010)
show that when the supply of long-term bonds by the government is low, private firms issue
a larger fraction of their debt long-term given the existence of preferred-habitat investors forlong-term bonds.
15
The model used in this paper is the same as in Koeda (2015), which extends Hamilton andWu (2012a) by allowing the coefficients in yield-curve factor dynamics as well as the prices ofrisk to change at the zero lower bound regime, using latent factors instead of observable factors,
and so on. In this paper, we estimate the model using Japanese data slightly different from
Koeda (2015).
16
Iwata and Fueda-Samikawa (2013) extensively examine the effects of the QQE on financial

5preferred-habitat investors as well as a central bank are limited even in the U.S.17
The remainder of the paper is organized as follows. First, we discuss our
JGB data in Section 2. Then, the results from a regression approach and a term
structure model approach are reported in Sections 3 and 4, respectively. Finally,
we show the results calculated from both approaches as well as a simple eventstudy analysis for the net supply effects of the BOJ’s JGB purchases in Section 5.
Section 6 concludes. Appendix A explains the construction of the JGB database
discussed in Section 2 and Appendix B describes the term structure model usedin Section 4.

2

Data on JGB Outstandings and Yields

In this section, we discuss data on the holders and maturity structures of JGBs
and the term structure of JGB yields. The details of the data construction on
the amount outstanding of JGBs categorized by holder and remaining maturity
are described in Appendix A.
Figure 2-1 presents the amount outstanding of marketable fixed-rate JGBs18
divided by nominal GDP from January 1992 to September 2014, which corresponds to the main sample period of our analyses in the following sections.19 The
upper panel shows those with all maturities, and the lower panel shows those withmarkets, including the analysis following Chadha et al. (2013). BOJ (2015) assesses the effectsof the QQE on Japan’s economic and financial developments during the two years since theintroduction of the policy.
17
Using the U.S. flow of funds data, Carpenter et al. (2014) identify the types of investors
that are selling to the Federal Reserve and investigate their portfolio adjustment after thesesales, without examining the effects on interest rates. Saito and Hogen (2014) conduct similar
analyses using Japanese data. Using a comprehensive dataset on the sovereign investor base for
45 advanced and emerging market economies, Jaramillo and Zhang (2013) examine the effects
on bond yields of “real money investors” which include institutional investors as well as nationaland foreign central banks.
18
The fixed-rate JGBs cover the majority of the government debt in Japan (around 75 percentof the central government bonds and 60 percent of the general government gross debt as of 2013).
We do not use data on floating-rate bonds, inflation-linked bonds, financial bills, Treasury bills(T-bills), or any other discount bonds in our analyses. Also, we exclude directly underwrittenbonds and focus on marketable bonds.
19
To avoid an endogeneity problem in our analyses, we use the amount outstanding data
mostly in face-value terms rather than market-value terms.

6remaining maturities less than 10 years. Besides the total amounts issued by thegovernment, Figure 2-1 shows those held by four sectors: the BOJ, insurancecompanies, pension funds, and “arbitragers.” Throughout the paper, we regard
insurance companies and pension funds as well as the BOJ as “preferred-habitat
investors,” because these private investors clearly prefer to hold long-term bonds
to match their long-duration liabilities at least in our sample period as shown below. Accordingly, we define “arbitragers” as all JGB holders excluding the BOJ,
insurance companies, and pension funds. Specifically, domestic banks, households, and foreigners are included in the arbitragers. The share of arbitragers in
the total amount outstanding of fixed-rate JGBs has been within the range of 40
and 50 percent since the mid-1990s as shown in Figure 2-2.
As shown in Figure 2-1, the ratio of the amount outstanding of JGBs held by
the arbitragers to GDP increased generally in parallel with the total debt-to-GDP
ratio before the BOJ introduced the QQE in April 2013. However, it started tofall as the BOJ accelerated the pace of its JGB purchases as part of the QQE.20
This movement in the arbitragers’ debt-to-GDP ratio represents the movementin volume of the net supply of JGBs, which is defined as the issuance (supply)by the government minus the demand by the preferred-habitat investors, and it
will be used as a net supply measure in our analyses.
Figure 2-3 shows the maturity structures of JGBs held by the arbitragers, private preferred-habitat investors (insurance companies and pension funds),21 andthe BOJ from 2004 to the end of our sample period (September 2014). While
the arbitragers’ maturity structure has been relatively stable, the maturity structures of the preferred-habitat investors (both private and the BOJ) have changed
remarkably. Private preferred-habitat investors, especially life insurance companies, steadily increased their holdings of JGBs with maturities over 10 years.
20

Before the introduction of the QQE, the BOJ gradually increased its purchase of JGBs as
part of its monetary easing measures after the global financial crisis. Concurrently, pension
funds have decumulated their assets including JGBs to finance their increasing pension payments since around 2008, and this has been an increasing factor in the arbitragers’ debt-to-GDP
ratio (Figure 2-1) and their share (Figure 2-2).
21
The “private” preferred-habitat investors actually include Japan Post Insurance (privatizedin 2007) and public pension funds. See Appendix A for details.

7

They have needed to match the duration of assets to their long duration of liabilities under regulations and accounting standards that force them to reduce
their holdings of risky assets such as stocks.22 The BOJ has increased its holdingof JGBs with maturities between 3 years and 10 years since the implementationof the QQE, while it has reduced the share of those with maturities less than 3
years in its JGB portfolio.
The average maturities of JGBs held by each sector as well as the total average
maturities are shown in Figure 2-4. Insurance companies have sharply extended
their average maturities while reducing the share of medium-term bonds in their
JGB portfolio with maturities less than 10 years (shown in the lower panel). The
BOJ has drastically extended its average maturity since the implementation of
the QQE, especially in its JGB portfolio with maturities less than 10 years.23 As aresult, the arbitragers’ average maturities, which had increased since around 2009,
leveled off in their JGB portfolio with all maturities and started to decline in thatwith maturities less than 10 years. These average maturities of the arbitragers
are used as key net supply measures for explaining term spreads in our analyses
in Section 3. In Figure 2-5, the changes in the arbitragers’ average maturities
since 2008 are decomposed into the changes in the average maturities of private
preferred-habitat investors, the BOJ, and the total issuance by the government
as well as the changes in weights among them. Before 2013, while the private
preferred-habitat investors’ maturity extension had been a decreasing factor in
the arbitragers’ average maturity, the maturity extension of the total issuanceoffset and overwhelmed it,24 which extended the arbitragers’ average maturity
22

In addition to the prolonged low profitability of stocks since the bursting of the bubble
economy in 1990s, mark-to-market accounting (introduced in 2000) and solvency margin regulations (revised in 2012, when the risk coefficient for changes in domestic stock prices wasraised from 10 percent to 20 percent) intensified Japanese life insurers’ stance of reducing risks
associated with stockholdings. See, for instance, Severinson and Yermo (2012) and Kan et al.
(2013).
23
After the end of our sample period (not shown in Figure 2-4), the BOJ further extended
its average maturity as it announced that “the average remaining maturity of the Bank’s JGB
purchases will be extended to about 7-10 years” on October 31, 2014 as an expansion of the
QQE.
24
The average maturity of the total issuance by the Japanese government exceeded that insome other developed countries during this period, as shown in Figure 2-6.

8

as a result. After 2013, the BOJ’s maturity extension was added as anotherdecreasing factor, but it was offset by the effect of the increase in the BOJ’sshare that had a relatively shorter average maturity than the arbitragers as wellas the effect of the maturity extension of the total issuance. Meanwhile, the BOJ’s
maturity extension overwhelmingly affected the arbitragers’ average maturity intheir JGB portfolio with maturities less than 10 years.
Finally, Figures 2-7 and 2-8 show the data on JGB yields. Throughout the
paper, we use the zero-coupon yields calculated by Bloomberg. As shown in
Figure 2-7, the 1-year and 3-year yields have been very low since the zero interest
rate policy was first implemented in 1999. The 10-year and 20-year yields havesteadily declined since the mid-2000s, while the pace of decline in the 10-yearyield has been faster than in the 20-year yield. In Figure 2-8, it can be clearlyseen that the yield curve for relatively shorter maturities flattened between 2009
and 2013, and then the yield curve for maturities longer than 6 years flattened
after 2013 as a result of the QQE.

3

Regression Approach

In this section, we examine the effects of the net supply of JGBs on the term
structure of interest rates and the risk premium on long-term bonds by a regression approach. As the dependent variables representing the term structure, we
focus on two measures of term spreads: the difference between zero-coupon yields
on 10-year and 3-year JGBs and the difference between yields on 20-year and 10year JGBs. The corresponding net supply measures we mainly use are the average
maturity of JGBs with maturities less than 10 years held by the arbitragers (defined in Section 2) and the average maturity of JGBs with all maturities heldby the arbitragers, respectively. As the dependent variables representing the risk
premium, we use 1-year and 3-year holding excess returns of 10-year JGBs. The
corresponding net supply measures are the ratio of JGBs with maturities lessthan 10 years held by the arbitragers to nominal GDP as well as the average9maturity of those JGBs held by the arbitragers. Unless otherwise mentioned, we
use monthly data from January 1992 to September 2014.
Our regression approach is closely related to Greenwood and Vayanos (2014,
GV henceforth). However, besides the difference between gross and net supply
measures mentioned in Introduction, our choices of dependent variables and net
supply measures differ slightly from GV. They use long-term yields or returns
rather than term spreads or excess returns as dependent variables while usinga short-term (1-year) yield as a control variable (or alternatively, they use thespreads between long-term and short-term yields as dependent variables). We do
not use the 1-year yield either for term spreads or as a control variable because it
was very low and moved little due to the zero interest rate policy for a significant
part of our sample period. Regarding the net supply measures, we do not use
the maturity-weighted debt-to-GDP ratio, GV’s main supply measure, because
its movement was predominantly driven by the strong upward trend of the debtto-GDP ratio in Japan. While the maturity-weighted debt-to-GDP ratio canbe decomposed into the average maturity and the debt-to-GDP ratio, we use
only the average maturity for the equations of term spreads and both the average
maturity and the debt-to-GDP ratio separately for the equations of excess returns.
Besides GV, we follow Laubach (2009) in controlling the economic fundamentals
for the term spreads and Cochrane and Piazzesi (2005) in using their proposed
return-forecasting factor as an explanatory variable for the holding-period excess
returns.
There are mainly two econometric issues that need to be addressed in our
regression approach. First, some of our net supply measures and control variables have a unit root, while the null hypotheses of a unit root are rejected forour dependent variables except for the 10-year/3-year yield spread. For the 10year/3-year spread equation, we identify a single cointegrating relationship andestimate it by the fully-modified ordinary least squares (FM-OLS) method. For
the other equations, we report level-regression results estimated by OLS witht-statistics using Newey and West (1987) standard errors to deal with serially10correlated errors. Second, the arbitragers’ average maturities could be endogenous and affected by (as well as affecting) term spreads. We calculate average
maturities mostly in face-value terms rather than market-value terms to avoid
this endogeneity problem, but the concern still remains even with the face-value
average maturities. In general, a widening of term spreads is likely to induce thegovernment to shift the issuance of its debt toward shorter maturities, while it
induces private preferred-habitat investors to hold government bonds with longer
maturities. Both of these tendencies generate a negative relationship between
term spreads and the arbitragers’ average maturities and thus would bias ourregression outcomes toward smaller net supply effects. We address this issue by
taking the instrumental variable estimation approach.
In what follows, we present the estimation specifications and results for the
10-year/3-year spread, the 20-year/10-year spread, and the holding-period excess
returns, in turn.

3.1

Regression of the 10-year/3-year Yield Spread

Our baseline specification of the regression equation of the 10-year/3-year yieldspread, yt3,10 , is expressed as follows:
yt3,10 = β + βx x10
t + β1 z1t + β3 z3t + ut ,(1)

where x10
t is the average maturity of JGBs with maturities less than 10 years heldby the arbitragers, z1t is the 10-year/3-year spread of nominal GDP trend growth,and z3t is the equity premium. β, βx , β1 , and β3 are parameters to be estimatedand ut is the error term. Following Laubach (2009), we try to control the expected
trend growth in real consumption, the expected inflation, and the time variation inrisk aversion as fundamental determinants of nominal long-term interest rates.25
Due to unavailability of data on expected long-term trend growth and inflation
25

In the Ramsey model of optimal growth with a representative household with CES utility,
the real rate of return on capital net of depreciation is determined by the net growth rate of percapita consumption, the intertemporal elasticity of substitution, and households’ rate of time
preference. For details, see Laubach (2009).

11

for our entire sample period, we use a backward moving average with triangularweights of nominal GDP growth as a proxy for the combined expected real trend
growth and inflation. The spread is simply calculated as the difference between
the 10-year moving average and the 3-year moving average. For risk aversion, we
use an equity premium, a measure of expected excess return of risky over riskfree assets, as a proxy.26 We do not control the short-term deviations from thenatural rate of interest caused by nominal rigidities as well as the counter-cyclicalmonetary policy rule, which would provide little information in addition to thenominal trend growth spread for the long-term yield spread. Other candidates
for control variables are discussed below.
As summarized in Table 3-1, according to the Dickey-Fuller test, the null
hypothesis of a unit root for all the above dependent and explanatory variables
cannot be rejected at the 5 percent critical level. We then conduct Johansen’s
cointegration test and confirm the existence of a single cointegrating relationshipin the above set of variables.
Before estimating the identified cointegrating relationship of equation (1),we conduct the first-stage regression of the arbitragers’ average maturity on instrumental variables to deal with the possible endogeneity problem mentioned
above. Following GV, we use the debt-to-GDP ratio, which is driven mostly
by the accumulation of past deficits rather than the current market conditions,as an instrumental variable. Specifically, the ratio of JGBs (less than 10 years)
held by the arbitragers to nominal GDP is used here. In addition, we include
a linear trend in instrument variables to control the strong upward trend in thedebt-to-GDP ratio. The results of this first-stage regression are summarized inTable 3-2. We also confirm the existence of a single cointegrating relationshipin the obtained fitted values with the other explanatory variables and dependent
26

Following Laubach (2009) and Kameda (2014), we use the equity premium based on thedividend yield as a proxy for the risk aversion. More specifically, our measure is computed as theratio of the dividend component of national income (SNA data) to the sum of the market valueof “shares and other equities” (flow of funds data) held by households, minus the 10-year JGB
yields. For this equity premium as well as GDP, we linearly interpolate the original quarterly
data to obtain monthly data.

12

variable in equation (1).
As the second-stage regression, we estimate the cointegrating relationship ofequation (1) by the FM-OLS method to obtain asymptotically unbiased estimates.27 The results are also summarized in Table 3-2. The estimated coefficienton the arbitragers’ average maturity is positive and significant at the 1 percent
critical level. This implies that the net supply of relatively longer-term (but lessthan 10 years) JGBs tends to widen the 10-year/3-year spread, which is consistent with the preferred-habitat theory. The nominal trend growth spread also
has a significantly positive relationship with the long-term yield spread, whichis consistent with the neoclassical growth theory. The coefficient on the equity
premium is negative but statistically insignificant. The estimated (insignificant)sign implies that an increase in households’ (final investors’) risk aversion tended
to shift their demand from equity to 10-year JGBs rather than to 3-year JGBs in
our sample period. Figure 3-1 shows the decomposition of the fitted values (adjusted by the constant term) into three explanatory variables, from which we cansee that the decrease in the arbitragers’ average maturity together with shrinking
trend growth spread have contributed to tightening of the 10-year/3-year spreadin recent years.
Table 3-3 summarizes the results from the specifications using alternative
measures of the net supply of JGBs, while the two control variables are the sameas in the baseline specification. We could not identify a single cointegrating
relationship in some of these specifications, but we report level-regression results
estimated by OLS with t-statistics using Newey and West (1987) standard errors
in Table 3-3. The column titled “baseline” shows the OLS estimation result of thebaseline specification, in which the estimated coefficients are not much changed
from the FM-OLS estimation result shown in Table 3-2 but the coefficient on theequity premium becomes significant at the 5 percent critical level. Column (i)shows the result using the original (not instrumented) data of the arbitragers’
27

In the FM-OLS estimation, we estimate the long-run covariance matrices in the cointegrating equation and stochastic regressors innovations using a kernel approach with a Bartlett
kernel and Newey-West fixed bandwidth.

13average maturity. Reflecting the downward bias due to the endogeneity problem
mentioned above, the estimated coefficient on the average maturity is smaller
and insignificant.28 In column (ii), the change in the ratio of JGBs (less than
10 years) held by the arbitragers to nominal GDP, smoothed by the HodrickPrescott filter, is included as an additional net supply measure that captures
the movements in volume of the net supply. However, the estimated coefficienton this measure is insignificant, while the signs and significance of the average
maturity and control variables are maintained. In column (iii), we use the shareof JGBs with maturities in excess of 3 years held by the arbitragers in their JGBs
with maturities less than 10 years (the share of maturities of 3 to 10 years withinthose less than 10 years) as an alternative net supply measure.29 The estimatedcoefficient on this measure is positive but insignificant.
Column (iv) shows the result using the average maturities of JGBs with maturities less than 10 years held by the BOJ and those issued by the government
minus the holdings of private preferred-habitat investors separately (the latter
equals the holdings of the arbitragers and the BOJ). The estimated coefficienton the BOJ’s average maturity is significantly negative, which is consistent withthe preferred-habitat theory. The absolute value of the estimated coefficient canbe regarded as relatively large compared with the estimated coefficient on theother component of the net supply, considering that the BOJ’s share in JGBs
with maturities less than 10 years is around 15 percent on average since the data
became available in 2001 (while the share of the arbitragers plus the BOJ isaround 65 percent). This result may imply some heterogeneity between the BOJ
and other (private) preferred-habitat investors and may also reflect the downward bias caused by the endogenous interaction between the term spread andthe average maturities of the government and private preferred-habitat investors
28

The estimated coefficient on the original average maturity is significant when we use theusual (not Newey-West) standard error (the t-statistic is 2.24). Meanwhile, the same coefficientestimated by FM-OLS is even smaller (0.08) and insignificant.
29
Modigliani and Sutch (1967) point out that the average maturity fails to distinguish changes
occurring at the short end of the maturity range from those at the long end. They use in theiranalysis the proportion of the total volume of outstanding debt accounted for by issues fallingwithin a specified maturity range as an alternative measure of maturity composition.

14

as mentioned above.30 In Section 5, we calculate the effect of the BOJ’s JGB
purchases and maturity extension as part of the QQE based on this result as wellas the baseline result and other approaches.
Table 3-4 summarizes the results using alternative sets of control variables,
while the net supply measure is the same as in the baseline specification. Column(v) shows the result using the real trend growth spread (based on real GDP) andthe trend inflation spread (based on the consumer prices index) instead of thenominal trend growth spread. For both variables, backward moving averages withtriangular weights are used and the spread is calculated as the difference between
the 10-year moving average and the 3-year moving average. The estimated coefficients on both variables are significantly positive, while the adjusted R-squared isslightly lower than in the baseline regression. In columns (vi) and (vii), the volatility of the 10-year/3-year JGB zero-coupon yield spread (dependent variable) andthe corresponding spread of the U.S. Treasury bonds are included, respectively,
as an additional control variable. However, the estimated coefficients on these
additional variables are insignificant with wrong signs.
Finally in Table 3-5, we show the results of sub-sample regressions using thebaseline specification. In column (viii), the sample period is limited to the three
sub-periods under the zero lower bound of the short-term nominal interest rate:from March 1999 to July 2000, from March 2001 to June 2006, and from December 2008 to September 2014 (the end of the sample period), which correspond to
the “zero lower bound (ZLB) regime” in the term structure model in Section 4.
In column (ix), the sample period is further limited to the last sub-period after
December 2008. In both results, the estimated coefficients on the arbitragers’
average maturity are larger than that in the full sample period, which imply
that the net supply effect on the 10-year/3-year spread was stronger in the zero
lower bound periods including the recent period after the global financial crisis.
30

Kuttner (2006) shows that the effect of changes in the Federal Reserve’s holdings of longterm securities had a larger and statistically significant effect on the holding-period excess
returns than those in the composition of privately held debt because the latter includes thepotentially endogenous issuance of new Treasury securities.

15

A possible interpretation based on the preferred-habitat theory is that the arbitragers’ increasing aversion to the duration risks strengthened the net supply
effect through the deepened market segmentation in the zero lower bound periods.
To consider the possibility of the time-varying effect of the net supply dependingon the risk aversion, we estimate another specification in which the arbitragers’
average maturity in the baseline specification is replaced with the product of theaverage maturity and the equity premium. The latter in the product is used as
an independent variable representing the risk aversion and was generally higher
in the zero lower bound periods. According to the result shown in column (x),the estimated coefficient on this risk-weighted net supply measure is positive andsignificant at the 1 percent critical level, while the signs and significance of otherexplanatory variables are maintained. This result together with the baseline result implies that the net supply effect on the 10-year/3-year spread was stronger
when the risk aversion was higher, which supports the above conjecture based on
the preferred-habitat theory.

3.2

Regression of the 20-year/10-year Yield Spread

Our baseline specification of the regression equation of the 20-year/10-year yieldspread, yt10,20 , corresponds with that of the 10-year/3-year spread equation, andis expressed as follows:
yt10,20 = β + βx xt + β2 z2t + β3 z3t + ut ,(2)

where xt is the average maturity of JGBs (with all maturities) held by arbitragers,31 z2t is the 20-year/10-year spread of nominal GDP trend growth, andz3t is the equity premium. As summarized in the upper part of Table 3-1, according to the Dickey-Fuller test, the null hypothesis of a unit root for the dependent
variable is strongly rejected at the 1 percent critical level, while those for all ex31

We use the arbitragers’ average maturity of JGBs with all maturities rather than thoseover 10 years because the issuance of JGBs with maturities over 10 years was very limited in
the early part of our sample period (especially before 1998).

16

planatory variables cannot be rejected.32 Accordingly, we report level-regression
results estimated by OLS with t-statistics using Newey and West (1987) standard
errors.
As in the case of the 10-year/3-year spread equations, we conduct two-stage
least square regression to deal with the possible endogeneity problem. In thefirst-stage regression, the arbitragers’ average maturity is regressed on the arbitragers’ debt-to-GDP ratio, the one-month lagged share of JGBs with maturities
in excess of 10 years held by the arbitragers in their total holdings of JGBs, anda linear trend, as summarized in Table 3-6. In the second-stage regression, we
estimate equation (2) using the fitted values of the first-stage regression. The
results are also summarized in Table 3-6. The estimated coefficient on the arbitragers’ average maturity is positive and significant at the 1 percent criticallevel, which implies that the net supply of relatively longer-term JGBs tends towiden the 20-year/10-year spread as well as the 10-year/3-year spread, consistently with the preferred-habitat theory. The nominal trend growth spread also
has a significantly positive relationship with the super-long-term yield spread,consistently with the neoclassical growth theory. The coefficient on the equity
premium is significantly positive rather than negative, in contrast to the result
for the 10-year/3-year spread. It may be naturally understood that an increase ininvestors’ risk aversion tends to widen the 20-year/10-year spread because they
become averse to the duration risk for this super-long-term spread. In our sample
period, the increasingly risk-averse investors tended to shift their demand fromequity to 10-year JGBs rather than to 20-year JGBs or 3-year JGBs. Figure 3-2
shows the decomposition of the fitted values (adjusted by the constant term) into
three explanatory variables, from which we can see that the increase in the arbitragers’ average maturity has contributed to the widening of the 20-year/10-year
spread since around the recent financial crisis.
Table 3-7 summarizes the results from the specifications using alternative
measures of the net supply of JGBs, while the two control variables are the32

According to Johansen’s cointegration test, we can identify a single cointegrating relationship in the three explanatory variables in equation (2).

17same as in the baseline specification. The column titled “baseline” shows exactly
the same result in Table 3-6. Column (i) shows the result using the original(not instrumented) data of the arbitragers’ average maturity. The estimatedcoefficient on the average maturity is slightly smaller than that obtained fromthe instrumental variable estimation, although the difference is much smaller thanin the case of the 10-year/3-year spread equations. In column (ii), the change
in the ratio of JGBs held by the arbitragers to nominal GDP, smoothed by the
Hodrick-Prescott filter, is included as an additional net supply measure. However,
the estimated coefficient on this measure is insignificant, while the signs andsignificance of other explanatory variables are maintained. In column (iii), we use
the share of JGBs with maturities in excess of 10 years held by the arbitragers intheir total holdings of JGBs as an alternative net supply measure. The estimatedcoefficient on this measure is positive and significant at the 1 percent criticallevel.
Column (iv) shows the result using the average maturities of JGBs held by
the BOJ, those held by private preferred-habitat investors, and those issued by
the government, separately. The estimated coefficients on the average maturitiesof the BOJ and private preferred-habitat investors are significantly negative, consistently with the preferred-habitat theory. The magnitudes of these estimatedcoefficients generally correspond to their shares in the total outstanding of JGBs
(The BOJ’s share is around 15 percent on average since the data became available in 2001, while the private preferred-habitat investors’ share is around 40
percent.) On the one hand, there may be some downward bias caused by theendogeneity problem in the estimated coefficient on the private preferred-habitat
investors’ average maturity. On the other hand, since the BOJ’s average maturity has been far below 10 years, its effect on the 20-year/10-year spread may belimited compared with the private preferred-habitat investors’ average maturity
that has increased to well over 10 years as shown in Figure 2-4 in Section 2.
Table 3-8 summarizes the results using alternative sets of control variables,
while the net supply measure is the same as in the baseline specification. Column

18(v) shows the result using the real trend growth spread and the trend inflation
spread instead of the nominal trend growth spread. The estimated coefficienton the real trend growth spread is significantly positive, while that on the trend
inflation spread is insignificant. In columns (vi) and (vii), the volatility of the
20-year/10-year JGB yield spread (dependent variable) and the corresponding
spread of the U.S. Treasury are included, respectively, as an additional control
variable. While the estimated coefficient on the former is insignificant, that on
the latter is strongly significant and positive, in contrast to the result for the
10-year/3-year spread, and greatly improves the adjusted R-squared from thebaseline result.
Finally in Table 3-9, we show the results of sub-sample regressions using thebaseline specification. As in the results for the 10-year/3-year spread, column(viii) shows the result when the sample period is limited to the three sub-periods
under the zero lower bound of the short-term nominal interest rate, and column(ix) shows the result when the sample period is further limited to the last subperiod after December 2008. The estimated coefficient on the arbitragers’ average
maturity is little changed in the zero lower bound periods and is smaller in the last
sub-period than that in the full sample period, in contrast to the result for the 10year/3-year spread. Meanwhile, column (x) shows that the estimated coefficienton the risk-weighted net supply measure, the product of the arbitragers’ average
maturity and the equity premium, is significantly positive, as in the result forthe 10-year/3-year spread. The latter result implies that the net supply effect on
the 20-year/10-year spread was stronger when the arbitragers’ risk aversion was
higher, while the former implies that the effect was not stronger in the zero lower
bound periods when the risk aversion represented by the equity premium washigher. One possible factor that could reconcile these seemingly conflicting results
is the share of JGBs held by the arbitragers in the total amount outstanding,which declined in the early 1990s and then dropped again after the recent financial
crisis (especially their share in JGBs with maturities over 10 years) as shown in
Figure 2-2 in Section 2. When the presence of the arbitragers is small, the net

19

supply effect would not change so much in response to changes in the arbitragers’
risk aversion. Another possibility is that long-term (as well as short-term) interest
rates become less responsive to any factors, including the net supply shocks, when
the short-term interest rate is constrained by the zero lower bound. We checkthis possibility in Section 4 using a term structure model that explicitly considers
the zero lower bound regime as well as the normal regime.

3.3

Regression of Holding-Period Excess Returns

Next, we present the estimation specifications and results for the holding-period
excess returns. Our specifications of the 1-year and 3-year holding excess returns10of 10-year JGBs, rx10
t+1,12 and rxt+1,36 , respectively, are expressed as follows:

10
9
1
rx10
t+1,12 ≡ (10 × yt − 9 × yt+12 ) − yt10
= β01 + βx x10
t + βxx xxt + β4 z4t + u1t ,(3)

7(10 × yt10 − 7 × yt+36
)
− yt3
3
10
= β03 + βx x10
t + βxx xxt + β4 z4t + u3t ,

(4)

rx10
t+1,36 ≡where ytn is the yield on n-year JGBs in period (month) t, x10
t is the average
maturity of JGBs with maturities less than 10 years held by the arbitragers,
xx10
t is the ratio of those JGBs held by the arbitragers to nominal GDP, andz4t is the return-forecasting factor proposed by Cochrane and Piazzesi (2005).33
10
We use xx10
t as well as xt as net supply measures to capture the volume aswell as maturity structure of the net supply. As mentioned in the beginningof this section, the product of these two measures corresponds to the maturityweighted debt-to-GDP ratio, the main supply measure used by GV. Regarding thereturn-forecasting factor, it is constructed from the fitted value of a regressionPof (1/4) 5n=2 rxnt+1,12 on a constant and the 1- through 5-year forward rates.
33

Kuttner (2006) uses Cochrane and Piazzesi (2005)’s return-forecasting factor as a control
variable in his regression of the holding-period excess returns on the maturity structure of theFederal Reserve’s holding securities.

20

Since we use the realized (ex-post) holding-period excess returns as dependent
variables, the end of the sample period is September 2013 for the 1-year holding
excess return equation (3), and is September 2011 for that of 3-year holding excess
return equation (4).
As summarized in the upper part of Table 3-1, according to the Dickey-Fuller
test, the null hypotheses of a unit root for the dependent variables are rejected
at the 5 percent critical level, while those for all explanatory variables cannot berejected.34 Accordingly, we report level-regression results estimated by OLS witht-statistics using Newey and West (1987) standard errors. The results are summarized in Table 3-10. Regarding the 1-year holding excess return, the estimatedcoefficients on the arbitragers’ average maturity and their debt-to-GDP ratio areboth positive but only the latter coefficient is significant, which implies that alarger volume of the net supply of JGBs tends to increase the risk premium on
the 10-year bond, which is consistent with the preferred-habitat theory. Whenthe sample period is limited to the three sub-periods under the zero lower boundof the short-term nominal interest rate, as shown in column (ii), the estimated coefficients on the two net supply measures are larger than those in the full sample
period, although the coefficient on the average maturity is still insignificant. Regarding the 3-year holding excess return, as shown in column (v), the estimatedcoefficients on the two net supply measures are both positive and significant at
the 1 percent critical level, which implies that a relatively longer-term and alarger volume of the net supply of JGBs tends to increase the risk premium on
the 10-year bond. When the sample period is limited to the three sub-periods
under the zero lower bound, as shown in column (vi), the estimated coefficientson the two net supply measures are larger than those in the full sample period,
while the signs and significance are maintained. This implies that the net supply
effect on the risk premium was larger in the zero lower bound periods.
We then consider the possibility of the time-varying effect of the net supply
depending on the arbitragers’ risk aversion by estimating two alternative specifi34

According to Johansen’s cointegration test, we can identify a single cointegrating relationship in the three explanatory variables in equations (3) and (4).

21

cations. First, as in the analysis of term spreads, the two net supply measures are
replaced with the product of the two measures and also the equity premium. As
shown in columns (iii) and (vii) for the 1-year and 3-year holding excess returns,
respectively, the estimated coefficients on these risk-weighted net supply measures
are both positive but insignificant. Second, following GV, the product of the two
net supply measures and the measure of the change in the arbitragers’ wealthduring the holding periods in addition to the two net supply measures is included
as an explanatory variable. The wealth measure is defined as the product of thearbitragers’ maturity-weighted debt-to-GDP (the product of the two net supply
measures) in 1 year (or 3 years) before and the 1-year (or 3-year) holding excess
return. As shown in columns (iv) and (viii) for the 1-year and 3-year holding
excess returns, respectively, the estimated coefficients on these wealth measures
are both negative, although only the coefficient in the 1-year return equation issignificant. This implies that net supply effects on the risk premium are stronger
when the arbitragers have lost their wealth and thus their risk aversion heightens.
Throughout this section, from our regression approach, we can conclude thatthe net supply effects on the term structure of interest rates and the risk premium
on long-term bonds are statistically significant in most alternative specifications,consistently with the preferred-habitat theory. Moreover, many regression results
imply that the effects are stronger when the short-term interest rate is constrainedby the zero lower bound and the arbitragers’ risk aversion is higher.

4

Term Structure Model Approach

In this section, we report the results from a term structure model that incorporates preferred-habitat investors.35 In the model, yields at all maturities are
expressed as affine functions of three yield-curve factors. Moreover, we consider
the zero lower bound (ZLB) regime as well as the normal regime, allowing the35

The model used in this paper is the same as in Koeda (2015), which is an extension ofHamilton and Wu (2012a). The model of the normal regime described in the text is the sameas in Hamilton and Wu (2012a).

22

coefficients on the yield-curve factor dynamics and the prices of risk to differ
between the two regimes. Using this model, we examine the effects of the modelimplied net supply measures of JGBs on term spreads and holding-period excess
returns as in our regression approach in Section 3. We also use this model in
Section 5 to derive the term premium and examine the effects of the BOJ’s JGB
purchases and maturity extension.
Here we just give a brief outline of the model of the normal regime. Detailsof the model including the ZLB regime are described in Appendix B and Koeda(2015).
There are two types of investors in the JGB market: arbitragers and preferredhabitat investors. The arbitragers choose a fraction, znt , of their JGB portfolio in
each maturity n (from 1 to N) to maximize the mean-variance expected returns
on the portfolio, as follows:noγ
E(rt,t+1 |ft ) − Var(rt,t+1 |ft ) ,z1t ,···,zNt
2
max

where rt,t+1 = ΣN
n=1 znt rn,t,t+1 is the arbitragers’ rate of return from period t toperiod t + 1 on their JGB portfolio and ft is a 3 × 1 vector of yield-curve factors
assumed to follow a VAR (1) process: ft+1 = c + Φft + Σut+1 . The parameter γ
captures the arbitragers’ risk aversion. In the ZLB regime, arbitragers explicitly
consider the possibility of a regime shift to the normal regime in their optimization
problem, as described in Appendix B.
On the other hand, the preferred-habitat investors demand JGBs with a particular maturity depending solely on the corresponding yield on that particularmaturity: they demand more of the bonds when the yield on that maturity bonds
increases. Meanwhile, the government would also decide to issue its bonds witha maturity depending on the yield on that particular maturity: it issues lessof the bonds when the yield on that maturity bonds increases. Therefore, thenet supply of the JGBs with maturity n, the issuance by the government minus

23

preferred-habitat investors’ demand, can be expressed as
xnt = ςt,n − αn yt,n ,for each n, where xnt is the net supply of the JGBs with maturity n divided by
the arbitragers’ net wealth, ςt,n is an affine function of ft , and the parameter αnrepresents the sensitivity to the n-period log yield, yt,n . Then, in the market
equilibrium where znt = xnt for all n, the n-period log bond prices, pt,n , and log
yields, yt,n , can be expressed as an affine function of ft aspt,n = −n yt,n = ān + b̄n ft ,for all n, given that the risk-free one-period rate, yt,1 , is assumed to follow anaffine function of ft .
From this model, we can derive the term spread between j- and k-period yields(j > k), yt,j − yt,k , and the expected k-period holding excess return of j-periodbonds, Et (rxjt+1,k ), as follows:
yt,j − yt,k = c̃j,k + Γ̃j,k ft
(
)

N
X
b̄j−1 b̄k−1
0
0
+γ
−
ΣΣ
znt b̄n−1 ,jk
n=2
Et (rxjt+1,k )= cj,k + Φj,k ft + γ b̄j−1 ΣΣ

0

N
X

0

znt b̄n−1 ,

(5)
(6)

n=2

where c̃j,k , Γ̃j,k , cj,k , and Φj,k are combinations of parameters in the model. The
point here is that znt (= xnt ) is included in the third term on the right-hand sideof equations (5) and (6).36 We regard this term as the model-implied net supply
measure in each equation.
We estimate the model using monthly data of the zero coupon yield (the sameas in Section 3) on 3-month, 3-year, 5-year, and 10-year JGBs. As in Koeda(2015), we apply Hamilton and Wu (2012b) minimum chi-squared estimation to36

As described in Appendix B, the price of risk can be expressed as a function of zt in thismodel.

24

estimate the term structure model coefficients.37 Meanwhile, some deep parameters including γ representing the risk aversion are not estimated in the model. In
this paper, we try to estimate γ in equations (5) and (6) by OLS, using the actual data of term spreads and ex-post holding-period excess returns as dependent
variables, respectively.38 We construct the model-implied net supply measures
as explanatory variables for the above regressions, by plugging in the data on
JGB’s maturity structure described in Section 2 for znt in the third term on theright-hand side of equations (5) and (6). In these regressions, the sample period isfrom January 1992 to September 2014, as in the regression analysis in Section 3.
We distinguish between the normal and ZLB regimes, the latter of which consistsof three sub-periods: from March 1999 to July 2000, from March 2001 to June
2006, and from December 2008 to September 2014,39 by using dummy variables.
In what follows, we first check the model-implied relationship between thematurity structure (znt ) and the net supply measures in term spreads and holdingperiod excess returns, based on Koeda (2015). Then given these net supply
measures and the estimated yield-curve factors, we try to estimate γ in equations(5) and (6), and discuss the results including the size, significance, and difference
between the normal and ZLB regimes.

4.1

Regression of the 10-year/3-year Yield Spread

First we examine the effects of the model-implied net supply measure on the 10year/3-year spread. The net supply measure, the third term on the right-handside of equation (5), increases when the average maturity of JGBs held by thearbitragers is extended. We check how the change in the maturity structure lessthan 10 years (znt for n ≤ 10) is related to the net supply measure, using the37

We first estimate the term structure model coefficients under the normal regime using thedata from February 1992 to February 1999 and then, given the normal-regime parameters, theterm structure model coefficients under the ZLB regime are estimated using the data from
December 2008 to September 2014.
38
In these regressions, we relax the model assumption by allowing the net supply of the JGBs
to depend on not only bond yields but also other possible exogenous shocks.
39
The identification of the ZLB regime is based on Hayashi and Koeda (2014).

25

data on JGB’s maturity structure described in Section 2 for znt . Suppose a shockcauses the arbitragers to extend their maturity by buying 10-year bonds andselling 1-year bonds by a 1 percent share of their holding JGBs with maturities
less than 10 years (at the same time, the preferred-habitat investors shorten theirmaturity by selling 10-year bonds and buying 1-year bonds) under the normal
regime. Then, the net supply measure widens the 10-year/3-year yield spread by
about 0.23 basis point, given the estimated term structure model coefficients andassuming the parameter value of the arbitragers’ risk aversion to be γ = 100.40 If,
on the other hand, the arbitragers shorten their maturity (the preferred-habitat
investors extend their maturity) by carrying out the opposite transaction under
the ZLB regime, the net supply measure tightens the 10-year/3-year yield spreadby about 0.06 basis point. Note that these figures in terms of the 10-year/3-yearyield spread are very small because we focus here on the effect of the net supply
measure (the third term in equation (5)) and do not take account of the changes
in the yield-curve factors (the second term).41 The asymmetry between the two
regimes reflects the model estimation results in which the yield-curve factors are
more volatile and yields are more responsive to the yield-curve factors under thenormal regime, as in Koeda (2015). Therefore, according to this model, the net
supply effect on the 10-year/3-year spread is stronger under the normal regime
than the ZLB regime, unless the degree of the arbitragers’ risk aversion changes
significantly between the two regimes.
Then, given the model-implied net supply measure and yield-curve factors, weestimate γ in equation (5) by OLS. We also estimate the coefficients on the yieldcurve factors under the two alternative assumptions: they are identical or different
between the two regimes.42 As summarized in Table 4-1, in both specifications
40

Hamilton and Wu (2012a) calibrate this parameter to 100 based on their estimation results
using U.S. data.
41
When we calculate the effects of the BOJ’s JGB purchases and maturity extension in
Section 5, we take account of the changes in the yield-curve factor as well as the net supply
measure.
42
The coefficients Γ̃in,k in equation (5) are estimated in the term structure model and differ
between the two regimes. However, we do not use these estimated coefficients but re-estimate
them in the single-equation regression to improve the fit of the regression.

26

with and without the coefficient dummies for the ZLB regime on the yield-curve
factors, the estimated coefficient on the net supply measure, γ, is significantly
positive. Since γ represents the arbitragers’ risk aversion in this model, thisresult implies not only that the net supply effect is significantly positive but alsothat the effect is stronger when the arbitragers’ risk aversion is higher. However,the size of estimated γ, differs greatly between the two specifications. Table
4-1 also shows the result when the sample period is limited to the three subperiods under the ZLB regime, in column (iii). The estimated coefficient on the
net supply measure is positive but insignificant at the 10 percent critical level.
In sum, the net supply of relatively longer-term (but less than 10 years) JGBs
tends to widen the 10-year/3-year spread, consistently with the preferred-habitat
theory. However, the result of the above sub-sample regression as well as thecalculated asymmetry in the model-implied net supply measure between the two
regimes imply that the net supply effect was not stronger in the zero lower boundperiods, in contrast to the regression analysis in Section 3.43

4.2

Regression of the 20-year/10-year Yield Spread

Next, we examine the effects of the model-implied net supply measure on the
20-year/10-year spread. As before, we first check how the change in the maturity
structure (znt for all n) is related to the net supply measure in the 20-year/10-year
spread equation (5), using the data on JGB’s maturity structure described in Section 2 for znt . If the arbitragers extend their maturity by buying 20-year bonds
and selling 1-year bonds by a 1 percent share of their total JGB holdings (atthe same time, the preferred-habitat investors shorten their maturity by selling
20-year bonds and buying 1-year bonds) under the normal regime, the net supply measure widens the 20-year/10-year yield spread by about 0.16 basis point,
given the estimated term structure model coefficients and assuming the parame43

To address the possible endogeneity problem mentioned in Section 3, we also conduct twostage least square estimation using the same instrumental variables as in Section 3 or the lagsof the model-implied net supply measure. The results are generally unchanged from those using
the original (not instrumented) model-implied net supply measure shown in Table 4-1.

27

ter value of the arbitragers’ risk aversion to be γ = 100. If, on the other hand, thearbitragers shorten their maturity (the preferred-habitat investors extend theirmaturity) by carrying out the opposite transaction under the ZLB regime, thenet supply measure tightens the 20-year/10-year yield spread by about 0.13 basis
point. Although the asymmetry between the two regimes is smaller than in 10year/3-year spread, the net supply effect on the 20-year/10-year spread is slightly
stronger under the normal regime than the ZLB regime, given the degree of thearbitragers’ risk aversion.
Then, given the model-implied net supply measure and yield-curve factors, weestimate equation (5) by OLS. As summarized in Table 4-2, in both specifications
with and without the coefficient dummies for the ZLB regime on the yield-curve
factors, the estimated coefficient on the net supply measure, γ, is significantly
positive. The size of estimated γ, however, differs greatly between the two specifications. When the sample period is limited to the three sub-periods under the
ZLB regime, the estimated γ is significantly positive and its size is close to (butsmaller than) that obtained from the specifications with the coefficient dummieson the yield-curve factors in the full sample period. In sum, the net supply of
relatively longer-term JGBs tends to widen the 20-year/10-year spread, again
consistently with the preferred-habitat theory. However, the result of the above
sub-sample regression combined with the calculated asymmetry in the modelimplied net supply measure between the two regimes imply that the net supply
effect in the zero lower bound periods was not necessarily stronger than that in
the full sample period.

4.3

Regression of Holding-Period Excess Returns

We then examine the effects of the model-implied net supply measure on theholding-period excess returns, the third term on the right-hand side of equation(6). As shown in the analysis of the one-period holding excess return in Koeda(2015), the net supply measure increases when the average maturity of JGBs heldby the arbitragers is extended, but there is asymmetry in this relationship between
28

the two regimes: the net supply measure is more sensitive to the arbitragers’
average maturity under the normal regime than the ZLB regime.
Keeping this relationship in mind, given the model-implied net supply measures and yield-curve factors, we estimate equation (6) using the actual data on
the ex-post 1-year and 3-year holding excess returns of 10-year JGBs by OLS.
The results are summarized in Table 4-3. Regarding the 1-year holding excess
return, the estimated coefficient on the net supply measure, γ, is significantly
positive only in the specifications without the coefficient dummies for the ZLB
regime on the yield-curve factors. Even in this specification, the size of estimatedγ differs greatly from the results obtained from the term spread equations as wellas the other specification of the holding-period excess returns. When the sample
period is limited to the three sub-periods under the ZLB regime, the estimatedγ is positive but insignificant. Results similar to these are also obtained for the
3-year holding excess return. Therefore, we could not obtain a robust and reliable estimate of γ to examine the net supply effects on the holding-period excess
returns from this term structure model approach.44

5Effects of the BOJ’s JGB Purchases

Based on the analyses in Sections 3 and 4, we can extract the effects of the
BOJ’s purchases of JGBs and maturity extension as part of the QQE, whichstarted in April 2013, on term spreads.45 The idea is simple: we just plug inthe contributions of the BOJ’s JGB purchases and/or maturity extension to thevarious net supply measures in the regression equations in the preceding two
sections, and calculate the cumulative net supply effects through our sample
period after the implementation of QQE based on the estimated coefficients. We
briefly summarize and compare these calculation results in the latter part of thissection.
44

Due to this difficulty in estimating γ, Koeda (2015) reports her results with some alternativevalues of γ.
45
We do not calculate the effects of the BOJ’s JGB purchases on holding-period excess returns
because the data near the end of our sample period (1 year or 3 years) are not available.

29

In general, however, it is difficult to identify the effects of a central bank’s bondpurchases on long-term interest rates in the data. As mentioned in Introduction,
there are various channels of transmission of the effects including those that are
not captured by our analyses based on the preferred-habitat theory. Moreover,
the timing and persistence of the effects are hard to identify. As shown in Figure 2-7 in Section 2, long-term interest rates actually started to decline before
the QQE was implemented. This was probably because market participants had
widely anticipated since the Prime Minister Abe took office near the end of December 2012 that he would appoint a new BOJ governor who would take a moreaggressive monetary easing policy, including the BOJ’s purchases of more andlonger-term JGBs, compared to the governor at the time whose term was going
to expire in April 2013.46 These “anticipated” net supply effects are not captured, at least directly, in our analyses. Regarding the persistence of the net
supply effects, it should be distinguished between the instantaneous response ofbond prices to a central bank’s ongoing purchase operations (the “flow effects”)
and persistent changes in bond prices resulting from movements along the bonddemand curve (the “stock effects”), as investigated by D’Amico and King (2013).
While our analyses using monthly data in the preceding sections focus mainlyon the stock effects, the flow effects may also be important, as they could reflect
some impairments in liquidity and functioning of the government bond markets
as well as updates of market participants’ expectations about the details of thecentral bank’s operations.
In what follows, before showing the results calculated from our analyses in thepreceding sections, we conduct a simple event-study analysis of the BOJ’s outrightpurchases of JGBs using daily data, for a reference of comparison. While many
event-study analyses in the literature focus on a number of official announcements
regarding the framework of asset purchase programs that affect market participants’ expectations about the net supply of the government bonds, we cannot
do so for this analysis of the QQE because there was no major change in the46

The anticipations of market participants in this period are discussed in, for instance, Ito(2014).

30

framework of JGB purchase program in the QQE after the initial announcement
on April 4, 2013 until the end of our sample period. Instead, we include eachoffer date of market operations by the BOJ in our event set. Therefore, ourevent-study analysis below may mainly capture the flow effects rather than theannouncement effects of the BOJ’s JGB purchases.

5.1

Event-Study Analysis

As mentioned above, our baseline event set includes all dates of offer of the
BOJ’s outright purchases of JGBs during the period between April 4, 2013 andSeptember 30, 2014, which amounts to 173 events.47 We also use an alternative
event set that focuses on the outright purchases of JGBs with maturities over
10 years, which amounts to 87 events. Since long-term interest rates started to
decline before the QQE was implemented as mentioned above, we also examine
an extended period from January 4, 2013 to September 30, 2014, in which thebaseline events and alternative events increase to 185 and 90, respectively.48
Regarding the response window, we use one-day and two-day windows aroundthe offer date: the former is measured from the closing level of the working dayprior to the offer date to the closing level of the offer date, and the latter ismeasured from the closing level of the two working days prior to the offer dateto the closing level of the offer date. We use the two-day window because manymarket participants anticipate the details (purchase amount, JGB maturity, etc.)of the operation to some extent in the previous working day of the offer date. At
the same time, however, setting a wider window increases the risk to contain theeffects unrelated to the BOJ’s purchases on long-term interest rates. We calculate
the cumulative changes in long-term interest rates during the response window ofeach event as a measure of the effects of the BOJ’s JGB purchases. Specifically,
47

The corresponding dates of exercise of the operations are generally two working days after
the offer dates.
48
The market operations conducted in the period prior to April 4, 2013 include those under
the asset purchase program in “Comprehensive Monetary Easing” as well as those conducted
as a regular operation tool.

31

we examine the effects on the 10-year yield, 20-year yield, 10-year/3-year spread,and 20-year/10-year spread on JGBs, which are all the zero-coupon yields as in
the analyses in the preceding sections.
The results are summarized in Table 5-1. The upper table shows the results forthe extended period from January 2013, and the lower table shows the results forthe period after the implementation of QQE in April 2013. Since the numbers ofevents in the period between January and April 2013 are small (12 in the baseline
event set and 3 in the alternative event set), the cumulative changes during the
response windows are generally not much different between the upper and lower
tables. In contrast, total cumulative changes through the two periods are very
different, as shown in the bottom line in each table, because the zero-coupon
yields decreased greatly in the period between January and April 2013 (23.8 basis
points for 10-year yield) and then lowered only slightly (3.1 basis points) after the
implementation of QQE until the end of our sample period.49 Therefore, while
the effects (cumulative changes during the response windows) in the extended
period (shown in the upper table) are generally comparable with total cumulativechanges in the same period, the effects in the period after the implementationof QQE (the lower table) are much larger than total cumulative changes in thecorresponding period. The latter implies that the interest rates actually increased
on non-event days reflecting many factors including rising inflation expectations,a rebound in the economic outlook, and improvements in market risk sentiment.50
From the comparison between the alternative event sets and response windows, we can see that the effects in the two-day window of the alternative (narrower) event set are the largest. This implies that the interest rates decreased
remarkably on the day before the offer date of the outright purchases of JGBs
with maturities over 10 years. From the comparison between the interest rate
49

After the end of the sample period (September 30, 2014), the long-term interest rates
decreased greatly again, especially after the expansion of QQE was announced on October 31,
2014. The decrease in the 10-year zero-coupon yield from September 30, 2014 to March 31,
2015 was 13.2 basis points.
50
Similar results of the decomposition between event days and non-event days are also obtained in event-study analyses using the U.S. data, such as Gagnon et al. (2011).

32

measures, it is shown that the effects on the 20-year yield are larger than thoseon the 10-year yields, while the effects on the 10-year/3-year spread are larger
than the 20-year/10-year spread. These relationships are generally consistent
with total cumulative changes through the extended period from January 2013.

5.2

Results from Regression and Term Structure Model
Approaches

We then show the results calculated from the analyses in Sections 3 and 4 for theeffects of the BOJ’s JGB purchases and maturity extension on term spreads. As
mentioned above, we plug in the BOJ’s contribution to the various net supply
measures in the regression equations and calculate the monthly cumulative net
supply effects. The results are summarized in Table 5-2. The upper table shows
the results for the extended period from January 2013, and the lower table shows
the results for the period from April 2013. As in Table 5-1, the calculated cumulative effects are generally not much different between the upper and lower tables
because the BOJ’s holding of JGBs and its average maturity changed little in the
period between January and April 2013.
The results for term spreads from the regression approach in Section 3 are
calculated using the estimated coefficients in the baseline and an alternative specification (the baseline estimation shown in Tables 3-2 and 3-6 and the alternative
specification using the BOJ’s average maturity separately as shown in columns(iv) of Tables 3-3 and 3-7) and two sub-sample regressions with the baseline specification (the zero lower bound periods and the period after the global financial
crisis as shown in columns (viii) and (ix) of Tables 3-5 and 3-9). In the baseline
specification, we calculate the pure contribution of the BOJ’s maturity extension(not including the contribution of changes in its share in the outstanding JGBs)
to the arbitragers’ average maturity, which is represented by the white bars in
Figure 2-5 in Section 2, and then multiply it by the estimated coefficients on the(instrumented) arbitragers’ average maturity.
Regarding the effect on the 10-year/3-year spread, the result using the baseline
33

estimation is 16.2 basis points for the extended period, as shown in column (i) of
Table 5-2. The result from the alternative specification (column (ii)) is slightly
larger, possibly reflecting the downward bias caused by the endogeneity problem
remaining in the baseline result. The results from the sub-sample regressions(columns (iii) and (iv)) are much larger than the baseline result, reflecting thelarger estimated coefficients. Regarding the effect on the 20-year/10-year spread,the result using the baseline estimation is 27.6 basis points for the extended
period. In contrast to the effects on the 10-year/3-year spread, however, theresult from the alternative specification is smaller, and those from the sub-sample
regressions are also smaller or not much larger than the baseline result. As aresult, except the baseline results in column (i), the effects on the 10-year/3-year
spread are larger than those on the 20-year/10-year spread. Overall, these results
obtained from the regression approach are broadly comparable with the range
resulting from the event-study analysis (column (vi)) and the actual changes inthe term spreads through the extended period from January 2013 (column (vii)).
The results for term spreads from the term structure model approach in Section 4 are calculated using the estimated coefficients in the specification with thecoefficient dummies for the ZLB regime on the yield-curve factors (columns (i)of Tables 4-1 and 4-2). We calculate the contribution of changes in the maturity
structure of JGBs held by the BOJ to the model-implied net supply measure,and then multiply it by the estimated coefficients on the net supply measure. In
addition, we also take account of the effects of changes in the yield-curve factors on the term spreads under some assumptions of the relationship between
the maturity structure and the yield-curve factors.51 The results are shown incolumn (v) of Table 5-2 as ranges depending on the assumption of the above
relationship. In both the results for the 10-year/3-year and 20-year/10-year term
spreads, the ranges of the effects are relatively small compared with the resultsfrom the regression approach and the event-study analysis. This may reflect the51

Specifically, we assume that the correlation between the maturity structure that was mostinfluenced by the BOJ’s JGB purchases and the first yield-curve factor is in the range between
0.1 and 0.6, judging from the data.

34

model estimation results in which the yield-curve factors are less volatile andthe yields are less responsive to the yield-curve factors under the ZLB regime.
Also in contrast to the results from the regression approach, the effect on the
10-year/3-year spread is smaller than the effect on the 20-year/10-year spread.
This may partly reflect the large difference in the estimated coefficients on themodel-implied net supply measures between the two term-spreads equations.
Finally, we calculate the effect of the BOJ’s JGB purchases on the 10-year
term premium derived from the term structure model in Section 4. The term
premium is defined as the actual bond yield minus the average expected future
short-term interest rates over the life of the bond.52 Then the derived term premium is regressed on the arbitragers’ average maturity, the change in the ratioof the arbitragers’ holding JGBs (less than 10 years) to nominal GDP, the equity
premium, the consumer price index inflation, the output gap, and the constant.53
The estimated coefficients on the two net supply measures, the arbitragers’ average maturity and the change in the arbitragers’ debt-to-GDP ratio, are bothsignificantly positive. Using these estimated coefficients, we calculate the effectsof the BOJ’s JGB purchases and maturity extension on the 10-year term premium. The result is shown in the bottom line in Table 5-2. The effect of thematurity extension is 38.0 basis points and the effect of increase in the JGB purchases as well as the maturity extension is 60.0 basis points (both for the extended
period). These results are broadly comparable with the cumulative changes in
the 10-year yield calculated in the event-study analysis shown in Table 5-1 (-56.5

52

To calculate the expectations components in the n-period term premium, we obtain
1, 2, ..., n period forecasts of the future short-term interest rates at each month via two-regime
three-variable VAR forecasting. See Appendix B for details.
53
The estimation result is as follows:
10
10
3
5
6
tpt = 0.764 [3.20]x10
t + 118.2 [3.23]xxxt − 0.287 [−3.31]z t + 0.076 [0.76]z t + 0.067 [1.11]z t− 1.660 [−1.49] + ut ,10
3
10
where tp10
t is the 10-year term premium, and xt and zt are the same as in equation (1). xxxt
is the change in the ratio of JGBs (less than 10 years) held by the arbitragers to nominal GDP(smoothed by the Hodrick-Prescott filter), zt5 is the consumer price index inflation, and zt6 isthe output gap estimated by the OECD. The values in the brackets present the Newey-Westadjusted t-statistics. The adjusted R2 is 0.497. The sample period is from January 1992 toSeptember 2014.

35

to -27.4 basis points for the extended period).54

6

Concluding Remarks

In this paper, we have examined how the net supply of JGBs affected the term
structure of interest rates and the risk premium on long-term JGBs using ourconstructed database on the amount outstanding of JGBs categorized by holder
and remaining maturity. Both approaches using single-equation regressions anda term structure model confirm that the net supply of JGBs had significant
effects on long-term interest rates, consistently with the preferred-habitat theory.
The regression approach implies that the net supply effects were stronger in thezero interest rate periods, while this relationship was not found using the model
approach. We also calculated the net supply effects of the BOJ’s JGB purchases
as part of the QQE from both approaches and compared the results with thoseobtained from a simple event-study analysis.
Based on our analyses in this paper, several directions for future research could
be pursued. First, we have left the problem of when and how the effectivenessof the net supply of JGBs on long-term interest rates changed. A clear solution
to this problem would provide useful implications for the future normalizationof unconventional monetary policy as well as the government debt management
policy. Second, there are several channels through which a shock to the net supply of JGBs affects long-term interest rates. It would be essential to empiricallydisentangle these channels for more accurately measuring the size, timing, andpersistence of the net supply effects. On the theoretical side, there would be
more room for improvement in specifications of the preferred-habitat theory, including a consideration of some heterogeneity among preferred-habitat investors,
54

BOJ (2015) estimates the effects of the BOJ’s JGB purchases on real interest rates using
several approaches. According to its regression approach, the cumulative effect from March2013 to December 2014 was minus 80 basis points in terms of 10-year yields. This result seems
broadly comparable with our results on the nominal 10-year term premium, considering thatthe long-term inflation expectations of economists and market participants increased by around
40 to 50 basis points during the corresponding period.

36and for developing other theories on the effects of a central bank’s purchases ofgovernment bonds on long-term interest rates.55 Third, while we focus mostly on
the gradual and persistent changes in interest rates using monthly data, daily or
intra-day fluctuations and instantaneous responses to a net supply shock such as
the effect of a central bank’s ongoing purchase operation are also important, as
discussed in Section 5. In this regard, how the scarcity channel captured in our
analyses relates to short-term liquidity would be an important problem left for
future consideration. Finally, given the significant net supply effects on long-term
interest rates, some normative and policy implications could be derived from thisresult. The current situation in Japan is that the BOJ extends the maturity of
its holding of JGBs to achieve the price stability target and the private preferredhabitat investors extend their maturity to match their long-duration liabilities,
while the government extends the maturity of its debt to reduce the risks associated with refinancing. In terms of overall social welfare, however, there might
be some room to improve the situation by pursuing better coordination among
these entities.56 We hope that our analyses in this paper will serve as a usefulstarting point for future research and policy discussions.

55

For instance, Williamson (2014) constructs a model in which short-maturity government
debt has a greater degree of pledgeability than long-maturity government debt and collateralis collectively scarce, and then a central bank’s purchases of long-maturity government debt
could flatten the yield curve.
56
Greenwood et al. (2014) discuss the government debt management policy in the U.S. andsuggest revised institutional arrangements to promote greater cooperation between the Treasury
and the Federal Reserve when the conventional monetary policy is constrained by the zero lower
bound.

37

Appendix
A

Database on JGBs

In this appendix, we explain how to construct the database on the amount outstanding of JGBs categorized by holder and remaining maturity.
A type of JGBs that is used in our analyses throughout the paper is fixedrate JGBs, which cover the majority of the government debt in Japan (around 75
percent of the central government bonds and 60 percent of the general government
gross debt as of 2013). In particular, we use 2-year, 4-year, 5-year, 6-year, 10-year,
20-year, 30-year, and 40-year fixed-rate JGBs. We do not use 15-year floating-ratebonds, inflation-linked bonds, financial bills, Treasury bills (T-bills), or any otherdiscount bonds. We exclude directly underwritten bonds and focus on marketablebonds. Besides the total issuance of JGBs, we consider three sectors: the Bank ofJapan (BOJ), insurance companies, and pension funds. Regarding the maturity
structure, we use face-value outstanding of JGBs issued/held by each sector,57
and categorize them into six categories along with their remaining maturity:58“less or equal than 1 year,” “longer than 1 year but less than 3 years,” “longer
than 3 years but less than 5 years,” “longer than 5 years but less than 7 years,”“longer than 7 years but less than 10 years,” and “longer than 10 years.” Ourdatabase has a form of “sector (four)” by “maturity category (six)” matrix forevery end of month from January 1992 to September 2014, which corresponds tothe main sample period in our analyses. Due to unavailability of data, for some
sectors and some sample periods we estimate the maturity structure using thedata on the total amount outstanding of JGBs held by the sectors. The overview
of our database and data availabilities is summarized in Table A.
Using the above database, we calculate the average maturity of JGBs held by57

To avoid the endogeneity problem in our regression analyses, we basically use the data inface-value terms. However, we cannot obtain some data of this type. In this case, we estimate
it based on the data in market-value terms. The details are explained later.
58
It is possible to calculate remaining maturities more precisely for total issuance and JGBs
held by the BOJ. We use these six categories because data for insurance companies are only
available in these categories.

38the arbitrager, which is used as a key net supply measure in our analyses. As
explained in Section 2, we define “arbitragers” as investors excluding the BOJ,
insurance companies, and pension funds. The average maturity of JGBs held byarbitragers is calculated as the weighted sum (or difference) of average maturity of
total issuance of JGBs, the BOJ’s average maturity, insurance companies’ average
maturity, and pension funds’ average maturity.59 The weights are based on theshare of JGBs held by each sector. As explained later, our maturity structure data
only cover the period from September 2003 to September 2014 due to the data
limitation. To calculate the arbitragers’ average maturities between January 1992
and August 2003, we assume that the maturity structure of JGBs held by eachsector is exactly the same as that for total issuance. We calculate the arbitragers’
average maturity using the step adjustment method for the period, and connect
it with the data from September 2003 to September 2014.
In the following, we explain the detail of data construction method sector by
sector.

A.1

Total Supply

We collect the issuance data from the Ko-Shasai Binran (Japanese Bond Handbook)60 on every single JGB issued between January 1979 and September 2014.61
This database provides data on characteristics of each bond, including bond type,
series number, date of issue, date of redemption, amount of issue in face-value
terms, and direct underwriter (if any).62 To focus only on the marketable bonds,
we exclude the data with direct underwriters. We also collect retirement by purchase data63 from the Ministry of Finance to calculate the remaining outstand59

The average maturity of JGBs with maturities less than 10 years held by the arbitragers
are calculated in the same way, except that data with maturities less than 10 years are used.
60
The handbook is semiannually published by the Japan Securities Dealers Association (available only in Japanese).
61
We exclude bonds redeemed before 1992.
62
For example, the Financial Investment and Loan Program is one of the largest direct
underwriters in our early sample period.
63
We use only the data of retirement by purchase from the market. The data are available on
the website of the Ministry of Finance as part of its “Notification of the Ministry of Finance”(available only in Japanese).

39

ing.64 The data include the bond type, series number, date of purchase, and thepurchase amount in face-value terms. Subtracting retirement by purchase datafrom the corresponding bond issuance data, we calculate the remaining maturity
and the remaining amount in face-value terms of every single JGB for each endof month,65 and categorize the amount into six maturity categories. Finally, we
sum up it for every remaining bond to build up the total issuance data.

A.2

Bank of JapanThe BOJ has released the statistics titled “Japanese Government Bonds heldby the Bank of Japan” every month since June 2001.66 This statistics reports
the information on JGBs held by the BOJ at the end of the previous month,including bond type, series number, and amount of holding in face-value terms.
This statistics does not include JGBs that are directly underwritten by the BOJ.67
We combine these data and the bond characteristics data explained in Section
A.1 and, in the same way as total supply, obtain the data series on amountoutstanding of JGBs with maturity structure from May 2001 to September 2014.
Since we cannot know the maturity structure of JGBs held by the BOJ until
May 2001, we instead construct the data on total amount outstanding of JGBs
held by the BOJ between January 1992 and April 2001. The data in these periods
are based on the flow of funds statistics,68 which report the amount outstandingof JGBs held by the BOJ in market-value terms.69 Using this statistics, we firstinterpolate the data linearly, and calculate the year-on-year growth rate of JGBs
held by the BOJ for each month. Then we backwardly estimate the total amountoutstanding of JGBs held by the BOJ in face-value terms given this growth rate
64

Since prematurity redemption for fixed-rate JGBs has never been observed in Japan, theamount outstanding of marketable fixed-rate JGBs only decreases when the Ministry of Financeconducts a retirement by purchase other than the redemption at maturity.
65
We do not break the stream of each bond’s cash flows into principal and coupon payments
to construct the future cash flows as in Greenwood and Vayanos (2014).
66
The statistics are available on the website of the BOJ.
67
Before 1998, the BOJ directly underwrote JGBs to roll them over.
68
The statistics are available on the website of the BOJ.
69
The statistics includes 15-year floating-rate bonds, inflation-linked bonds, and JGBs thatwere directly underwritten by the BOJ.

40

and the data after May 2001.

A.3

Insurance Companies

The data on total amount outstanding of JGBs held by insurance companies are
based on the flow of funds statistics. Since the data in flow of funds statistics
are in market-value terms, we avoid using them directly. The detail estimation
method is as follows. After December 1997, we calculate the share of JGBs heldby insurance companies in the net issuance of JGBs,70 and multiply this by the
total amount of issuance in face-value terms we explained in Section A.1. Before
November 1997, due to the discontinuity in the statistics, we first calculate theyear-on-year growth rate of JGBs held by insurance companies that are defineddifferently, and backwardly estimate the total amount outstanding of JGBs heldby insurance companies given this growth rate and the data after December 1997.
As for the maturity structure, we estimate it based on the disclosures ofindividual insurance companies. Insurance business law in Japan requires every
insurance company to disclose the amount outstanding of JGBs and T-bills71 byperiod remaining at least once each business year.72 In the data, companies report
six categories of amount outstanding of JGBs and T-bills based on the remaining
maturity mentioned above. To estimate the maturity as precisely as possible,
we consider separately the structure of private life insurance company, nonlife
insurance company, and Japan Post Insurance.73 As for the maturity structure70

The net issuance of JGBs is defined as the total issuance of JGBs minus the amount of
JGBs held by government agencies.
71
The evaluation method of JGBs and T-bills is mixed, and it differs along with the purposeof holding; bonds declared as held-to-maturity debt are evaluated in terms of face value, andother securities are evaluated in terms of market value.
72
Insurance companies disclose these data through annual or semiannual reports. Theirreports are mostly available on their homepage, but many companies release them only inJapanese.
73
We treat Japan Post Insurance, a subsidiary of the Japan Post, as a preferred-habitat
investor in this paper. As for the Japan Post Bank, another subsidiary of the Japan Post, we
treat it as arbitragers. Although its investment strategy may be different from other majorbanks, its average maturity is not much different from that of major domestic banks. In orderto obtain marketable JGBs held by Japan Post Insurance, we subtract the amount outstandingof directly underwritten JGBs from the total amount outstanding of JGBs held by Japan
Post Insurance. The amount outstanding of directly underwritten JGBs held by Japan Post

41

of JGBs held by private life insurance companies, we sum up the data for 11 major
life insurance companies, and obtain the shares of each maturity category in the
total amount outstanding of JGBs and T-bills from September 2003 to September
2014, using linear interpolation and the seasonality adjustment method. The
same method is applied for four major nonlife insurance companies and Japan
Post Insurance, respectively.74 We then multiply this by the corresponding total
amount outstanding of JGBs of these three insurance categories, respectively,75
and obtain the data on amount outstanding of JGBs and T-bills categorized bymaturity structure from September 2003 to September 2014. Finally, we sum up
these three insurance categories, and subtract the total amount outstanding ofT-bills held by insurance company, which is based on the flow of funds statistics,
from the amount outstanding of JGBs and T-bills with maturity of “less or equal
to 1 year” to obtain the amount outstanding of JGBs.

A.4

Pension Funds

The data on the total amount outstanding of JGBs held by pension funds are
estimated based on the flow of funds statistics, which are in market-value terms as
well. After December 1997, we calculate the share of JGBs held by pension funds
plus public pensions in the net issuance of JGBs, and multiply this by the total
amount we explained above. Before November 1997, due to the discontinuity inthe statistics, we cannot obtain exact data on pension funds. We assume thatthe share between 1992 and 1997 is equal to the average share of JGBs held bypension funds in total issuance between 1997 and 2014. Using this assumption,
we obtain the data on the total amount outstanding of JGBs held by pension
Insurance is estimated based on the Ko-Shasai Binran (Japanese Bond Handbook).
74
Since it is almost impossible to collect data from every insurance company in Japan, we only
use the data of major insurance companies, and assume them to be a representative value. We
use the data of 11 major life insurance companies and four major nonlife insurance companies
besides that of Japan Post Insurance.
75
Total amount outstanding of JGBs in each insurance category is calculated exactly thesame way as we explained above, and the sum of total amount outstanding of JGBs of thesethree categories is equal to the total amount outstanding of JGBs held by insurance companies.
To obtain the total amount outstanding of JGBs held by Japan Post Insurance, we use its
disclosure as well as the flow of funds, because of discontinuity in the statistics.

42

funds from January 1992 to September 2014.
As for the maturity structure, since there is no disclosure of JGBs’ maturity
structure information in pension funds, we use as a proxy the maturity structure
information from the NOMURA Bond Performance Index, which is used by many
pension funds as a benchmark index for passive management of JGBs.76 The
information is available through the disclosures of fund-of-funds style investment
trusts in which the index is used as a underlying fund. The annual disclosure
reports the information on JGBs held by the index, including bond type, serial
number, and amount of holding in face-value terms.77 We combine these data
and the bond characteristics data explained in Section A.1, and, in the same way
as for total supply, obtain the data series on the amount outstanding of JGBs,
categorized by maturity structure, using linear interpolation and the seasonality
adjustment method, from May 2006 to May 2014. Since each category of maturity
structure in these periods is slightly changed with the constant slope, we assume
that the maturity structures from September 2003 to April 2006 as well as from
June 2014 to September 2014 are equally changed like those between May 2006
and May 2014. Combining this assumption with the total amount outstandingof JGBs held by pension funds, we can also calculate the data on the amountoutstanding of JGBs categorized by maturity structure in these periods.

76

For example, the Government Pension Investment Fund declares that it uses this index asa benchmark in its annual disclosure.
77
We use information from the “Nomura Domestic Bond Index Fund Nomura BPI DC.” Thedata are available through the Electronic Disclosure for Investors’ NETwork (EDINET) system
in Japan.

43

B

Term Structure Model in Section 4

In relation to Section 4 in the text, this appendix summarizes the underlying
model and report estimated parameters in Table B. For a full description of themodel, derivations, estimation strategy, and discussions on estimated results, see
Koeda (2015). Following Vayanos and Vila (2009), we assume that there are
two types of agents in the government bond market: preferred-habitat investors
and arbitragers. Arbitragers maximize the mean-variance expected returns on
their government bond portfolio, while preferred-habitat investors prefer to holdparticular maturities of government bonds. The bond market equilibrium price isdetermined by equating arbitragers’ net demand and preferred-habitat investors’
net supply for different maturities of bonds.
Specifically, the model follows a discrete-time version of Vayanos and Vila
(2009) discussed by Hamilton and Wu (2012a, HW henceforth). It extends HW
by (i) allowing the coefficients in yield-curve factor dynamics as well as the pricesof risk to change at the zero lower bound (ZLB) regime to allow greater model
flexibility, (ii) using latent factors instead of observable factors to improve model
fit to the data, (iii) writing out arbitragers’ portfolio optimization problem at the
ZLB regime solving for the bond market equilibrium price, and (iv) carrying out
estimation using JGB data.
Bond pricing in “normal” time (in the absence of the ZLB) follows the same
specification as HW. HW define the arbitragers’ rate of return from period t toperiod t + 1 on their portfolio (rt,t+1 ) by
rt,t+1 =NX

znt rn,t,t+1 ,

(7)

n=1

where znt is a fraction of their portfolio in the bond of maturity n and rn,t,t+1 isthe holding-period return from period t to t + 1 on the n-period bond.
At the ZLB, arbitragers face two types of regimes: the ZLB regime where
the ZLB binds, and the normal regime where the ZLB does not bind (denotedby s = 0 and s = 1, respectively). They maximize the mean-variance expected
returns weighted by transition probability that the ZLB will continue to bind in44the next period (π00 ) or that it will be lifted (π10 ). These transition probabilities(πi0 for i = 0, 1) are assumed to be exogenous and constant and add up to 1
P
( i=0,1 πi0 = 1). The arbitragers’ optimization problem at the ZLB regime canbe given as
max

z1t ,...,z NtX

πi0 [E (rt,t+1 |st+1 = i, st = 0, ft )i=0,1

− (γ/2) V ar (rt,t+1 |st+1 = i, st = 0, ft )],(8)subject toNX

znt = 1,(9)n=1where γ captures arbitragers’ risk aversion. ft are the yield-curve factors assumed
to follow a VAR (1) process
ft+1 = ci + Φi ft + Σi ut+1 ,with normalization that gives the identity matrix Σ1 and a 3 × 1 vector of zeros
c1 and, for parsimonious purpose, we assume that Σ0 is a diagonal matrix. We
can approximately solve for zt = (z2t , ..., zN t )0 , that is, the arbitragers’ demand
equation. zt depends on expected excess one-period holding returns on different
maturities of bonds. Given zt , the arbitragers’ demand for the short-term bond,
z1t , can be derived by equation (9).
The preferred habitat’s net supply of bonds (xnt ) is modeled in the samemanner as the normal-time model, except that the supply-equation coefficientsare allowed to take different values at the ZLB regime.
0xnt ≡ ςt,n
− αn0 yt,n , for n = 1, ..., N,(10)0where yt,n is the log yield and ςt,n
= ςn0 + ϑ0n ft .

By equating the demand and supply functions for each maturity of bonds, theequilibrium log bond prices can be derived as follows.

45

p0t,n = ā0n + b̄0n ft , for n = 1, ..., N,X
ā0n = ā01 +πi0 āin−1 + b̄in−1 ci −Σi λi + (1/2) b̄in−1 Σi Σi0 b̄i0n−1 ,

(11)
(12)

i=0,1

b̄0n

=

X

i=0,1


πi0 b̄in−1 Φi −Σi Λi + b̄01 ,(13)

with the prices of risk coefficients given by
λi = γΣi0

N
X
n=2

N
X
 
 
b̄i0n−1 ςn0 + αn0 /n ā0n , Λi = γΣi0b̄i0n−1 ϑ0n + αn0 /n b̄0n .
n=2Thus, at the equilibrium, bond prices in the ZLB regime follow the standard
affine term structure model with regime shifts. Furthermore, by arbitragers’
FOCs, it can be shown, the prices of risk can be expressed as a function of zt ,λit ≡ λi + Λi ft = γΣi0NXznt b̄i0n−1 .

(14)

n=2

B.1

Risk Premium (Holding-Period Excess Returns)

At the bond market equilibrium, the model-implied expected k -period holding
excess log return of j -period bonds under the normal regime (rx1t+1,j,k ) can be
expressed as
Et rx1t+1,j,k≡ Et p1t+1,j−k − p1t,j + p1t,k= Et ā1j−k + b̄1j−k ft+k − ā1j − b̄1j ft + ā1k + b̄1k ft ,=c1j,k + Φ1j,k ft + γ b̄1j−1 Σ1 Σ10NX

znt b̄10
n−1 ,

n=2

where p1t,j is the j-period log price. The second equality holds because bondprices are modeled as an exponential affine function of yield-curve factors. The
third equality holds by using the recursive equations for ā1j and b̄1j and arbitragers’FOCs, and also by solving for the conditional expectation term (Et ā1j−k + b̄1j−k ft+k )

1
1
1
and
Φ
≡
b̄
−
b̄
with c1j,k ≡ ā1j−k + ā1k − ā11 − ā1j−1 − 12 b̄1j−1 Σ1 Σ10 b̄10
j−1
1 +
j,k
k
k

b̄1j−k (Φ1 ) − b̄1j−1 Φ1 .

Similarly, the corresponding excess log return under the ZLB regime can be46

expressed as
Et rx0t+1,j,k≡ Et p0t+1,j−k − p0t,j + p0t,k

st+k
st+k
= Et āj−k+ b̄j−kft+k − ā0j − b̄0j ft + ā0k + b̄0k ft ,=c0k + Φ0k ft + γX

πi0 b̄ij−1 Σi0 Σi0

i=0,1

N
X

znt b̄i0n−1 ,

n=2

where
c0k ≡ ā0k − ā01 + (π00 )k
+

k−1
X

(

ā0j−k +

k
X

Φ

i=1

(π00 )l (1 − π00 ) ā1j−k + Φ

−

i=0,1

+

k

Φ


0 i−1

+ (1 − π00 )k b̄1j−k Φ1(π00 )l (1 − π00 ) b̄1j−k Φ1

l=1

B.2

l
 X
1 k−l

+ (1 − π00 )k ā1j−k
c0

!



πi0 āij−1 + b̄ij−1 ci + (1/2) b̄ij−1 Σi Σi0 b̄i0j−1 ,Φ0k ≡ b̄0k − b̄01 + (π00 )k b̄0j−k Φ0
k−1
X

c0

)

i=1

l=1

X


0 i−1

k−l

k

l X
πi0 b̄ij−1 Φi .
Φ0 −
i=0,1

Term Spread

The model-implied j-period log bond price under the normal regime can be expressed as
p1t,j = c1j−1 + Γ1j−1ft − b̄1j−1 Σ1 λ1t , for j = 1, ..., N,= c1j−1 + Γ1j−1ft − γ b̄1j−1 Σ1 Σ10NX

znt b̄10
n−1 ,

n=2

where the first equality holds by the pricing equation (equations (11)–(13)) andthe second equality holds by arbitragers’ FOCs with c1j−1 ≡ ā1j−1 + b̄1j−1 c1 +
1 1
1
1
1
1
1
b̄ Σ1 Σ10 b̄10
j−1 +ā1 and Γj−1 ≡ b̄j−1 Φ + b̄1 . This implies that the term spread
2 j−1

47

between j- and k-period bonds (j > k) can be expressed asyt,j − yt,k = c̃1j,k + Γ̃1j,k ft + γ(1/j) b̄1j−1 − (1/k) b̄1k−1



1

ΣΣ

10

N
X

znt b̄10
n−1 ,

n=2

where yt,j = −p1t,j /j, c̃1j,k ≡ c1k−1 /k − c1j−1/j, and Γ̃1j,k ≡ (1/k) Γ1k−1 − (1/j) Γ1j−1 .
Similarly, the j-period log bond price under the ZLB regime can be expressed
asp0t,j = c0j−1 + Γ0j−1 ft −γX

πi0 b̄ij−1 Σi Σi0NXznt b̄i0n−1 , for j = 1, ..., N,

n=2

i=0,1


P
where c0j−1 ≡ ā01 + i=0,1 πi0 āij−1 + b̄ij−1 ci + (1/2) b̄ij−1 Σi Σi0 b̄i0j−1 and Γ0j−1 ≡Pii0i=0,1 πi0 b̄j−1 Φ + b̄1 . Then the term spread between j- and k-period bonds canbe expressed asyt,j − yt,k = c̃0j,k + Γ̃0j,k ft + γX

πi0 b̄ij−1 /j − b̄ik−1 /k Σi Σi0


i=0,1

N
X
n=2

znt b̄i0n−1!

,

where yt,j = −p0t,j /j, c̃0j,k ≡ c0k−1 /k − c0j−1/j and Γ̃0j,k ≡ (1/k) Γ0k−1 − (1/j) Γ0j−1 .

B.3

Term Premium

We decompose the long-term bond yields into the expectations and term premiumcomponents. Following the typical definition in the literature, the term premiumof an n-period bond yield is defined as the actual n-period bond yield minus theaverage expected future short-term interest rates over the life of the bond (i.e.,o nPn−1
1
Et
j=0 r1,t+j ). To calculate the expectations components, we first obtainn
1, 2, ..., n period forecasts of the future short-term interest rates at each month

via two-regime three-variable VAR forecasting. Our model assumes that (i) if
the initial regime is normal, then the corresponding VAR forecasting is reduced
to a simple one-regime VAR forecasting. And (ii) if the initial regime is ZLB,
then the regime shifts from ZLB to normal with the probability of 1 − π00 in thenext period; once the regime shifts to normal, however, it remains normal for the48

rest of the forecasting period. This implies that there are n + 1 possible paths ofregimes and expected future yield-curve factors when the initial regime is ZLB.
The conditional expectation on n-period ahead yield-curve factors is computedby taking the average of possible values of expected yield-curve factors weighted
by probability.

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53

Figure 2-1

Amount Outstanding of Marketable Fixed-Rate JGBs Held by Each Sector/GDP(1) With all maturities
180
160

140
120

% of nominal GDP
Total
Bank of Japan
Insurance companies
Pension funds
Arbitragers

100

80
60
40

20
0
CY 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14(2) With maturities less than 10 years
180
160
140
120
100

% of nominal GDP
Total
Bank of Japan
Insurance companies
Pension funds
Arbitragers

80
60
40
20
0
CY 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14
Note: Seasonally adjusted data. For details on data sources and the data calculation method, see Appendix A.

Figure 2-2

Share of Arbitragers in Marketable Fixed-Rate JGBs

80

% of arbitragers in marketable fixed-rate JGBs

70
60
50
40
30
20

With all maturities
With maturities over 10 years
With maturities less than 10 years

100
CY 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14
Note: Seasonally adjusted data. For details on data sources and the data calculation method, see Appendix A.

Figure 2-3

Maturity Structure of JGBs Held by Each Sector(1) Arbitragers
100% of their holdings of JGBs

90

80
70
60
50
40
30
20
10
0
CY 04

Over 10 years05

06

7–10 years07

5–7 years08

1–3 years1011

3–5 years

1–3 years

09

10

11

3–5 years

1–3 years

09

10

09

(2) Private preferred-habitat investors
100

3–5 years

12

Less or equal than 1 year13

14

% of their holdings of JGBs
Over 10 years

90

7–10 years

5–7 years

Less or equal than 1 year

80

70
60
50
40
30

20
10
0
CY 04

05

(3) Bank of Japan
100

06

07

08

12

13

14

% of its holdings of JGBs

90
80
70
60
50
40
30
20
10

Over 10 years

0
CY 04

05

06

7–10 years07

5–7 years
08

11

Less or equal than 1 year
12

13

14

Note: Seasonally adjusted data. For details on data sources and the data calculation method, see Appendix A.

Figure 2-4

Average Maturities of JGBs Held by Each Sector(1) With all maturities
16

Years
Total

14

Bank of Japan
Insurance companies

12

Pension funds
Arbitragers

10
8
6
4
2
CY 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14(2) With maturities less than 10 years
8

Years
Total

7

Bank of Japan
Insurance companies

6

Pension funds
Arbitragers

5

4

3

2
CY 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14
Note: Seasonally adjusted data. For details on data sources and the data calculation method, see Appendix A.

Figure 2-5

Decomposition of the Arbitragers' Average Maturities(1) Arbitragers' average maturity of JGBs with all maturities
0.30

Years, change over the month, and contribution

Contribution: Weights and others
Contribution: Private preferred-habitat investors' average maturity
Contribution: The BOJ's average maturity
Contribution: Average maturity of total issuance
Change over the month: Arbitragers' average maturity

0.25
0.20
0.15
0.10
0.05
0.00

-0.05
-0.10
-0.15
CY 08

09

10

11

12

13

14

(2) Arbitragers' average maturity of JGBs with maturities less than 10 years
0.10

Years, change over the month, and contribution

0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
-0.08
-0.10
CY 08

Contribution: Weights and others
Contribution: Private preferred-habitat investors' average maturity
Contribution: The BOJ's average maturity
Contribution: Average maturity of total issuance
Change over the month: Arbitragers' average maturity (less than 10 years)
09

10

11

12

13

14

Figure 2-6

Average Remaining Maturity of Government Debt in Developed Countries

18

Years

Japan
United States
United Kingdom
Germany
France

16

14

12

10

8

6

4

2

0
CY 97

99

01

Source: Ministry of Finance of Japan.

03

05

07

09

11

13

Figure 2-7

Zero-Coupon Yields
7%, monthly average, annualized
20-year

6

Implementation of QQE(Apr. 2013)10-year3-year5

1-yearEnd of our sample period(Sep. 2014)

4

3

2

1

0

-1
CY 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15
Note: The graph is based on the zero-coupon yield data calculated by Bloomberg. The shaded area indicates zero
lower bound periods.

Figure 2-8

Yield Curves
7%, monthly average, annualized

6
Jan. 1992
5

Feb. 1999
Jan. 2009
Jan. 2013

4

Sep. 2014
3

2

1

0

0

2

4

6

8

10

12

14

Note: The graph is based on the zero-coupon yield data calculated by Bloomberg.

16

18

20
Years

Figure 3-1

Decomposition of the 10-year/3-year Yield Spread
3.0
2.5
2.0

%

%
Equity premium
Nominal GDP trend growth spread (10-year/3-year)
Arbitragers' average maturity (less than 10 years)
Fitted (right scale)
Actual (right scale)

2.5
2.0

2.0
1.8
1.6

1.5
1.4

1.5

1.0

1.0

0.5

0.5

0.0

1.2
1.0
0.8
0.6

0.0

-0.5
0.4

-0.5

-1.0

-1.0
CY 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14-1.5

Note: The constant term is adjusted. For details on the results of the estimation, see Table 3-2.
The arbitragers' average maturity in the above figure is the original (not instrumented) data.

0.2
0.0
CY

Figure 3-2

Decomposition of the 20-year/10-year Yield Spread
2.0
1.8
1.6

%

%
Equity premium
Nominal GDP trend growth spread (20-year/10-year)
Arbitragers' average maturity
Fitted (right scale)
Actual (right scale)

1.6
1.4

3.0
2.5

1.2
2.0

1.4

1.0

1.2

0.8

1.0

0.6

0.8

0.4

0.6

0.2

1.5
1.0
0.5
0.0

0.4

0.0

0.2

-0.2

0.0
CY 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14-0.4 -1.0

Note: The constant term is adjusted. For details on the results of the estimation, see Table 3-6.
The arbitragers' average maturity in the above figure is the original (not instrumented) data.

-0.5

1.8
1.6
1.4
1.2

0.8
0.6
0.4
0.2

Table 3-1: Unit root and cointegration tests(1) Unit Root Test
SeriesAugmented Dickey-Fuller test statistic

Level

First difference

10-year/3-year JGB zero-coupon yield spread–2.261–13.931 ***20-year/10-year JGB zero-coupon yield spread–4.434 ***—Arbitragers' average maturity(less than 10 years), IV–1.068–2.907 **Arbitragers' average maturity, IV–0.625–8.250 ***–0.848–13.956 **–0.937–2.105 **Equity premium–1.438–6.988 ***Ex-post 1-year holding excess return–3.088 **—Ex-post 3-year holding excess return–2.936 **—Ratio of JGBs (less than 10 years)
held by the arbitragers to nominal GDP–0.168–2.907 **Return-forecasting factor–2.538–13.006 ***Nominal GDP trend growth spread(10-year/3-year)
Nominal GDP trend growth spread(20-year/10-year)(2) Johansen's Cointegration Test
Series: 10-year/3-year JGB zero-coupon yield spread, arbitragers' average maturity (less than 10 years, original),
nominal GDP trend growth spread (10-year/3-year), equity premium
Null hypothesis

Trace statistic

None62.845 ***At most 1

29.202

Series: 10-year/3-year JGB zero-coupon yield spread, arbitragers' average maturity (less than 10 years, IV),
nominal GDP trend growth spread (10-year/3-year), equity premium
Null hypothesis

Trace statistic

None65.962 ***At most 1

26.366

Note: *** and ** indicate statistical significance at the 1 percent and 5 percent levels, respectively.

Table 3-2: Baseline regression of 10-year/3-year yield spread(1) First-Stage Regression(2) Second-Stage Regression

Dependent variable: Arbitragers' average maturity(less than 10 years), original
Ratio of JGBs (less than 10 years)
2.148 ***
held by the arbitragers to nominal GDP[3.72]–0.011 ***Linear trend[–7.79]5.197 ***
Constant[65.80]Dependent variable: 10-year/3-year JGB zero-coupon yield spread
Arbitragers' average maturity(less than 10 years), IV
Nominal GDP trend growth spread(10-year/3-year)

0.326 ***
[3.28]
17.365 ***[5.00]–0.059[–1.31]–0.197[–0.41]Equity premiumConstant

Sample period

1992M01–2014M09

Sample period

1992M02–2014M09

Estimation method

OLS

Estimation method

FM-OLS

Adjusted R-squared

0.822

Adjusted R-squared

0.653

Note: ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Note: Newey-West adjusted t -statistics are presented in the brackets.

Table 3-3: Regression of 10-year/3-year yield spread (Alternative 1)
Dependent variable: 10-year/3-year JGB zero-coupon yield spread
Baseline
Arbitragers' average maturity(less than 10 years), IV
Arbitragers' average maturity(less than 10 years), original

0.281 ***
[3.20]

Alternative net supply measures
(i)

0.111
[1.27]

Change in the ratio of JGBs (less than 10 years)
held by the arbitragers to GDP, smoothed

Share of 3- to 10-year JGBs held byarbitragers within less than 10 years
BOJ's average maturity(less than 10 years)
Arbitragers' and BOJ's average maturity(less than 10 years)
Nominal GDP trend growth spread(10-year/3-year)

(ii)

(iii)

(iv)

0.286 ***
[3.32]
5.160[0.41]

0.667[0.86]–0.158 *[–1.79]0.224 *
[1.90]

18.004 ***[4.40]–0.066 **[–2.01]
0.002[0.00]

18.528 ***[4.53]–0.122 ***[–3.43]0.811 **
[1.99]

17.593 ***[3.76]–0.070 **[–2.00]–0.021[–0.05]18.804 ***[4.59]–0.125 ***[–2.84]0.885 *
[1.73]

18.620 ***[4.59]–0.128 ***[–3.64]0.922 **
[2.15]

Estimation method

OLS

OLS

OLS

OLS

OLS

Adjusted R-squared

0.647

0.612

0.646

0.609

0.615

Equity premiumConstant

Notes: 1. Sample period: 1992M01-2014M09.
Notes: 2. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Notes: 2. Newey-West adjusted t -statistics are presented in the brackets.

Table 3-4: Regression of 10-year/3-year yield spread (Alternative 2)
Dependent variable: 10-year/3-year JGB zero-coupon yield spread
Baseline
Arbitragers' average maturity(less than 10 years), IV

0.281 ***
[3.20]

Nominal GDP trend growth spread(10-year/3-year)
Real GDP trend growth spread(10-year/3-year)
Trend inflation spread(10-year/3-year)
Volatility of 10-year/3-year
JGB zero-coupon yield spread
10-year/3-year U.S. Treasury
zero-coupon yield spread

18.004 ***[4.40]

Alternative control variables
(v)

(vi)

(vii)

0.395 ***
[3.54]

0.319 ***
[3.09]

0.307 ***
[3.26]

17.454 ***[4.08]

17.979 ***[4.54]

11.293 ***[2.70]
0.242 ***
[2.99]–0.286[–0.65]–0.066 **[–2.01]
0.002[0.00]–0.041[–1.13]–0.489[–0.96]–0.067 **[–2.04]–0.112[–0.25]–0.037[–0.95]–0.043[–1.00]–0.113[–0.26]

Estimation method

OLS

OLS

OLS

OLS

Adjusted R-squared

0.647

0.619

0.648

0.651

Equity premiumConstant

Notes: 1. Sample period: 1992M01-2014M09.
Notes: 2. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Notes: 2. Newey-West adjusted t -statistics are presented in the brackets.

Table 3-5: Regression of 10-year/3-year yield spread (Alternative 3)
Dependent variable: 10-year/3-year JGB zero-coupon yield spread
Baseline

Sub-sample regressions(viii)(ix)

Arbitragers' average maturity(less than 10 years), IV
The product of the average maturity
and the equity premium

0.281 ***
[3.20]

0.752 ***
[5.92]

0.686 ***
[4.09]

Nominal GDP trend growth spread(10-year/3-year)

18.004 ***[4.40]–0.066 **[–2.01]
0.002[0.00]

3.821[1.09]–0.003[–0.10]–1.907 ***[–3.63]11.971 ***[3.14]
0.006[0.19]–1.743 ***[–3.26]Equity premiumConstant

Time-varying
net supply(x)0.184 ***
[3.83]
18.848 ***[4.78]–0.763 ***[–4.66]
1.099 ***
[14.15]

1999M03-2000M07

Sample period

1992M01-2014M09 2001M03-2006M06 2008M12-2014M09 1992M01-2014M09
2008M12-2014M09

Estimation method

OLS

OLS

OLS

OLS

Adjusted R-squared

0.647

0.562

0.766

0.646

Note: ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Note: Newey-West adjusted t -statistics are presented in the brackets.

Table 3-6: Baseline regression of 20-year/10-year yield spread(1) First-Stage Regression(2) Second-Stage Regression

Dependent variable: Arbitragers' average maturity, original
1.717 ***
Arbitragers' debt-to-GDP ratio (-1)[4.02]
Share of JGBs over 10 years held by
16.630 ***arbitragers in their total holdings (-1)[10.09]–0.007 ***Linear trend[–7.07]4.345 ***
Constant[34.34]

Dependent variable: 20-year/10-year JGB zero-coupon yield spread
0.347 ***
Arbitragers' average maturity, IV[3.87]
Nominal GDP trend growth spread
7.264 *
(20-year/10-year)[1.74]
0.109 ***
Equity premium[3.96]–1.309 **Constant[–2.50]Estimation method

OLS

Estimation method

OLS

Adjusted R-squared

0.864

Adjusted R-squared

0.222

Notes: 1. Sample period: 1992M01-2014M09.
Notes: 2. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Notes: 2. Newey-West adjusted t -statistics are presented in the brackets.

Table 3-7: Regression of 20-year/10-year yield spread (Alternative 1)
Dependent variable: 20-year/10-year JGB zero-coupon yield spread
Baseline
Arbitragers' average maturity, IV

0.347 ***
[3.87]

Arbitragers' average maturity, original
Change in the ratio of JGBs held by thearbitragers to GDP, smoothed
Share of JGBs over 10 years held byarbitragers in their total holdings

Alternative net supply measures(i)

0.314 ***
[5.75]

(ii)

(iii)

0.480 ***
[2.81]
21.552[1.17]

4.905 ***
[3.81]

BOJ's average maturity
Private preferred-habitat investors'
average maturity
Average maturity of total issuanceNominal GDP trend growth spread(20-year/10-year)(iv)–0.081 ***[–3.02]–0.189 *[–1.91]0.673 ***
[2.60]

7.264 *
[1.74]
0.109 ***
[3.96]–1.309 **[–2.50]4.557[1.38]
0.104 ***
[4.28]–1.093 ***[–3.37]

10.736 *[1.76]
0.109 ***
[4.01]–2.053 **[–2.10]2.281[0.60]
0.031[1.19]
0.293 *
[1.66]

10.248 **[2.05]
0.061 **
[2.17]–1.857 **[–2.18]Estimation method

OLS

OLS

OLS

OLS

OLS

Adjusted R-squared

0.222

0.293

0.231

0.179

0.328

Equity premiumConstant

Notes: 1. Sample period: 1992M01-2014M09.
Notes: 2. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Notes: 2. Newey-West adjusted t -statistics are presented in the brackets.

Table 3-8: Regression of 20-year/10-year yield spread (Alternative 2)
Dependent variable: 20-year/10-year JGB zero-coupon yield spread
Baseline
Arbitragers' average maturity, IV
Nominal GDP trend growth spread(20-year/10-year)
Real GDP trend growth spread(20-year/10-year)
Trend inflation spread(20-year/10-year)
Volatility of 20-year/10-year
JGB zero-coupon yield spread
20-year/10-year U.S. Treasury
zero-coupon yield spread

0.347 ***
[3.87]
7.264 *
[1.74]

Alternative control variables
(v)

(vi)

(vii)

0.303 ***
[4.48]

0.343 ***
[3.89]

0.320 ***
[3.82]

7.105 *
[1.80]

7.753 **
[2.00]

7.045 *
[1.83]
0.021[0.47]

0.080[0.15]

0.109 ***
[3.96]–1.309 **[–2.50]0.104 ***
[3.51]–1.036 **[–2.58]0.112 ***
[3.50]–1.299 **[–2.53]0.337 ***
[3.16]
0.072 ***
[2.93]–1.228 **[–2.57]

Estimation method

OLS

OLS

OLS

OLS

Adjusted R-squared

0.222

0.223

0.219

0.328

Equity premiumConstant

Notes: 1. Sample period: 1992M01-2014M09.
Notes: 2. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Notes: 2. Newey-West adjusted t -statistics are presented in the brackets.

Table 3-9: Regression of 20-year/10-year yield spread (Alternative 3)
Dependent variable: 20-year/10-year JGB zero-coupon yield spread
Baseline
Arbitragers' average maturity, IV
The product of the average maturity
and the equity premium
Nominal GDP trend growth spread(20-year/10-year)
Equity premiumConstant

Sub-sample regressions(viii)(ix)

0.347 ***
[3.87]

0.350 ***
[4.61]

0.275 ***
[3.41]

7.264 *
[1.74]
0.109 ***
[3.96]–1.309 **[–2.50]0.633[0.24]
0.027[0.93]–0.954 **[–2.50]–0.444[–0.06]–0.005[–0.14]–0.461[–1.09]Time-varying
net supply(x)0.128 ***
[4.91]
3.062[0.88]–0.546 ***[–4.45]0.524 ***
[4.64]

1999M03-2000M07

Sample period

1992M01-2014M09 2001M03-2006M06 2008M12-2014M09 1992M01-2014M09
2008M12-2014M09

Estimation method

OLS

OLS

OLS

OLS

Adjusted R-squared

0.222

0.499

0.517

0.233

Note: ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Note: Newey-West adjusted t -statistics are presented in the brackets.

Table 3-10: Regression of holding-period excess returns

Arbitragers' average maturity(less than 10 years), original
Ratio of JGBs (less than 10 years)
held by the arbitragers to nominal GDP
The product of the average maturity,
the debt/GDP, and the equity premium

Dependent variable:
ex-post 1-year holding excess return of 10-year JGBs

Dependent variable:
ex-post 3-year holding excess return of 10-year JGBs

(i)

(ii)

(iv)

(v)

(vi)

1.202
[0.98]
5.976 **
[2.06]

2.697[1.59]
8.114 *
[1.82]

2.944 **
[2.30]
14.193 ***[3.05]

2.056 ***
[5.19]
6.170 ***
[4.41]

2.809 ***
[4.76]
8.250 ***
[4.14]

(iii)

0.215
[1.25]

The wealth measure
Return-forecasting factor
Constant
Sample period
Adjusted R-squared

218.480 ***[5.08]–5.246[–0.98]
1992M012013M09

0.334

242.678 *[1.89]–11.879[–1.43]
1999M03-2000M07
2001M03-2006M06
2008M12-2013M09

0.109–0.015 **[–2.52]224.066 ***[5.16]
0.699[0.57]

199.875 ***[4.89]–13.439 **[–2.31]105.429 ***[10.07]–8.115 ***[–4.27]

1992M01-

1992M01-

1992M01-

2013M09

2013M09

2011M09

0.330

0.353

0.742

163.674 ***[4.04]–12.112 ***[–4.05]
1999M03-2000M07
2001M03-2006M06
2008M12-2011M09

0.491

(vii)

0.045
[0.64](viii)
2.777 ***
[3.03]
9.028 **
[2.22]–0.017[–0.53]

122.355 ***[11.82]
1.553 ***
[4.22]

135.630 ***[9.11]–11.786 ***[–2.67]

1992M01-

1995M01-

2011M09

2011M09

0.690

0.709

Notes: 1. Results are based on OLS regressions.
Notes: 2. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Notes: 2. Newey-West adjusted t -statistics are presented in the brackets.
Notes: 3. The wealth measure is defined as the product of arbitragers' maturity-weighted debt-to-GDP in 1 year (or 3 years) before and the 1-year (or 3-year) holding excess return.

Table 4-1: Regression of 10-year/3-year yield spread from the term structure model approach
Dependent variable: 10-year/3-year JGB zero-coupon yield spread

Model-implied net supply measure
Yield-curve factor 1
Yield-curve factor 2
Yield-curve factor 3
ZLB dummy × yield curve factor 1
ZLB dummy × yield curve factor 2
ZLB dummy × yield curve factor 3
Constant
ZLB dummy

(i)

(ii)

(iii)

121.034 *[1.83]

397.825 ***[4.68]

137.725[1.09]

0.142 ***
[41.27]–0.036 ***[–9.05]–0.023 ***[–8.74]–0.051 ***[–12.26]
0.069 ***
[16.68]0.022 ***
[8.53]
1.399 ***
[44.60]–0.416 ***[–17.35]

0.082 ***
[17.68]0.004[1.40]–0.000[–1.50]0.091 ***
[70.11]0.034 ***
[47.05]–0.001 ***[–8.03]1.019 ***
[32.17]0.980 ***
[50.78]

1999M03-2000M07

Sample period

1992M01-2014M09 1992M01-2014M09 2001M03-2006M06
2008M12-2014M09

Adjusted R-squared

0.961

0.706

0.960

Notes: 1. Results are based on OLS regressions.
Notes: 2. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Notes: 2. t -statistics are presented in the brackets.

Table 4-2: Regression of 20-year/10-year yield spread from the term structure model approach
Dependent variable: 20-year/10-year JGB zero-coupon yield spread

Model-implied net supply measure
Yield-curve factor 1
Yield-curve factor 2
Yield-curve factor 3
ZLB dummy × yield curve factor 1
ZLB dummy × yield curve factor 2
ZLB dummy × yield curve factor 3
Constant
ZLB dummy

(i)

(ii)

(iii)

2811.477 ***[4.96]

294.300 ***[3.10]

2603.564 ***[7.33]

0.019 ***
[3.53]–0.045 ***[–5.23]0.029 ***
[4.99]–0.009[–1.05]0.031 ***
[3.34]–0.028 ***[–4.82]
1.050 ***
[13.03]–0.690 ***[–4.17]0.014 ***
[3.66]–0.013 ***[–4.99]0.001 ***
[3.18]

0.009 **
[2.54]–0.015 ***[–7.27]0.001 ***
[6.01]

0.737 ***
[47.79]0.391 ***
[7.13]

1999M03-2000M07

Sample period

1992M01-2014M09 1992M01-2014M09 2001M03-2006M06
2008M12-2014M09

Adjusted R-squared

0.333

0.187

0.415

Notes: 1. Results are based on OLS regressions.
Notes: 2. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Notes: 2. t -statistics are presented in the brackets.

Table 4-3: Regression of holding-period excess returns from the term structure model approach
Dependent variable:
ex-post 1-year holding excess return of 10-year JGBs
Model-implied net supply measure
Yield-curve factor 1
Yield-curve factor 2
Yield-curve factor 3
ZLB dummy × yield curve factor 1
ZLB dummy × yield curve factor 2
ZLB dummy × yield curve factor 3
Constant
ZLB dummy

Dependent variable:
ex-post 3-year holding excess return of 10-year JGBs

(i)

(ii)

(iii)

(iv)

(v)

(vi)

–9.066[–1.13]9.391 ***
[5.32]

36.686[0.33]–4.673 ***[–2.90]6.818 ***
[16.18]14.184[0.93]

0.553 ***
[2.98]
1.468 ***
[6.96]–0.865 ***[–6.20]0.208[0.85]–1.255 ***[–5.59]0.887 ***
[6.36]
8.638 ***
[2.76]–7.264 **[–2.47]0.566 ***
[5.94]
0.215 ***
[3.47]
0.016 **
[2.55]

0.750 ***
[2.95]
0.204 **
[2.29]
0.024 **
[2.58]

0.301 ***
[13.07]0.137 ***
[8.76]
0.009 ***
[5.95]

0.416 ***
[10.33]0.205 ***
[10.31]0.012 ***
[8.20]

1.272 **
[2.28]

0.030[0.01]

0.496 ***
[13.25]0.346 ***
[8.13]–0.216 ***[–7.70]–0.074[–1.36]–0.136 ***[–2.90]0.227 ***
[8.08]
6.082 ***
[9.66]–4.991 ***[–8.38]1.190 ***
[8.74]

0.542[1.18]

1999M03-2000M07

Sample period

1999M03-2000M07

1992M01-2013M09 1992M01-2013M09 2001M03-2006M06 1992M01-2011M09 1992M01-2011M09 2001M03-2006M06
2008M12-2013M09

Adjusted R-squared

0.422

0.309

0.273

2008M12-2011M09

0.857

Notes: 1. Results are based on OLS regressions.
Notes: 2. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively.
Notes: 2. t -statistics are presented in the brackets.

0.760

0.641

Table 5-1: Event-study analysis(1) From Jan. 4, 2013 to Sep. 30, 2014 (Extended period)
10-yearyield

bps
10-year/3-year
spread20-year/10-year
spread

–57.6

–35.8

–11.1

–27.4

–30.6

–16.4

–3.2

Two-day

–56.5

–73.2

–52.5

–16.7

One-day

–41.8

–46.3

–32.3

–4.5

Total changes through the period (427 days)

–26.9

–43.8

–25.6

–16.9

EventsWindows

Offer of outright purchases of
JGB operations by the BOJ(185 events)

Two-day–46.5

One-day

Offer of outright purchases of
JGB operations with maturities
over 10 years by the BOJ(90 events)

20-yearyield(2) From Apr. 4, 2013 to Sep. 30, 2014bps
10-yearyield

10-year/3-year
spread20-year/10-year
spread

–35.6

–23.8

–2.8

–23.2

–23.0

–11.1

+0.2

Two-day

–49.9

–71.4

–46.2

–21.5

One-day

–40.7

–48.6

–30.8

–7.9

Total changes through the period (367 days)

–3.1

–3.0

–4.7

+0.1

EventsWindows

Offer of outright purchases of
JGB operations by the BOJ(173 events)

Two-day–32.8

One-day

Offer of outright purchases of
JGBs operations with maturities
over 10 years by the BOJ(87 events)

20-yearyield

Note: The table shows the cumulative changes in the zero-coupon yields and spreads during the response window of each
event. The one-day window is measured from the closing level of the working day prior to the offer date to the closing
level of the offer date, and the two-day window is measured from the closing level of the two working days prior to theoffer date to the closing level of the offer date.

Table 5-2: Effects of BOJ's JGB purchases(1) From Jan. 2013 to Sep. 2014 (Extended period)bps
Regression approach

JGB term spread(10-year/3-year)
JGB term spread(20-year/10-year)
Term premium (10-year)

Model approach

Event-study
analysis

Actual changes
through the period

Baseline

Alternative
specification

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

–16.2

–22.9

–37.4

–34.1

–9.7 to –2.1

–52.5 to –16.4

–25.6

–27.6

–16.8

–27.9

–21.9

–14.2 to –13.9–16.7 to –3.2

–16.9

–38.0
<–60.0>

—

—

—

—

—

–27.0

Sub-sample regressions(2) From Apr. 2013 to Sep. 2014bps
Regression approach

JGB term spread(10-year/3-year)
JGB term spread(20-year/10-year)
Term premium (10-year)

Model approach

Event-study
analysis

Actual changes
through the period

Baseline

Alternative
specification

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

–16.0

–22.6

–37.0

–33.8

–9.2 to –2.0

–46.2 to –11.1

–4.7

–27.7

–16.9

–27.9

–22.0

–13.3 to –12.9–21.5 to +0.2

+0.1

–37.6
<–56.1>

—

—

—

—

—

–2.0

Sub-sample regressions

Note: In the regression approach, the effects of BOJ's maturity extension are presented, except that the values in the angular brackets are
Note: the effects of the increase in JGB purchases as well as the maturity extension.

Table A: Overview of our JGB database and data availabilities
Total issuanceTotal amount of JGBs
(face-value terms)

Maturity information

Data sources

Bank of Japan

Insurance companies

Private life insurancecompanies

Nonlife insurancecompanies

Japan Post Insurance

Pension funds

Available from May
2001. Before May
2001, data are
estimated based on
the data in marketvalue terms provided
by the flow of funds
statistics.

Estimated (1) based
Estimated based on the on the data in marketAvailable as a sum of Estimated based on the Estimated based on thedata in market-value
value terms provided
those of private life
data in market-value
data in market-value
terms provided by the by the flow of funds
insurance companies, terms provided by the terms provided by theflow of funds statistics, statistics from 1997 tononlife insurance
flow of funds statistics. flow of funds statistics.
and disclosures.
2014 and (2) withcompanies, and Japan Discontinuity is
Discontinuity is
Discontinuity is
assumption of a
Post Insurance
adjusted.
adjusted.
adjusted.
constant share from1992 to 1997.

Available

Available from May
2001

Estimated (from Sep.
2003 to Sep. 2014)
based on disclosures.

Estimated (1) basedon the informationfrom the benchmark
index from May 2006
to May 2014 and (2)with an assumption ofa constant trend from
Sep. 2003 to Apr.
2006 and June 2014
to Sep. 2014.

Japan Securities
Dealers Association,"Ko-Shasai Binran(Japanese Bond
Handbook)."Bank of Japan,"Japanese
Government Bonds
held by the Bank ofJapan", "Flow ofFunds Statistics."

Disclosures by each
Disclosures by each
Disclosures by Japan
company; Bank ofcompany; Bank of
Post Insurance; BankJapan, "Flow of Funds Japan, "Flow of Funds of Japan, "Flow of
Statistics."
Statistics."
Funds Statistics."

Disclosure by the
Nomura Domestic
Bond Index Fund
Nomura BPI DC;
Bank of Japan, "Flowof Funds Statistics."

Available

Available as aweighted average of
those of private life
Estimated (from Sep.
insurance companies, 2003 to Sep. 2014)nonlife insurance
based on disclosures.
companies, and Japan
Post Insurance—

Estimated (from Sep.
2003 to Sep. 2014)
based on disclosures.

Table B: Estimated parameters of the term structure model in Section 4Note: c¹ and ∑¹are a 3×1 vector of zeros and a 3×3 identity matrix.