TCER Working Paper Series

Fiscal Cost to Exit Quantitative Easing: The Case of Japan
Hiroshi Fujiki
Hajime Tomura
September 2015
Working Paper E-99
http://tcer.or.jp/wp/pdf/e99.pdf

TOKYO CENTER FOR ECONOMIC RESEARCH
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Abstract
This paper simulates the cash flows and balance sheets of the Bank of Japan (BoJ)
before and after exiting from Quantitative and Qualitative Monetary Easing (QQE) undervarious scenarios. The simulations show that the BoJ will record significant accounting
losses after exiting QQE. These losses are fiscal costs for the consolidated Japanese
government as they represent increased interest expenses to the public and will arise
because the BoJ will acquire a large amount of Japanese government bonds at very low
interest rates during QQE, whose interest payments will then be insufficient to coverinterest expenses on excess reserves after exiting QQE. Moreover, any cumulative
accounting losses will ensure the BoJ's net asset position remains negative for asustained period of time. We also find that the BoJ's accounting losses will increase withthe duration of QQE and the interest rate elasticity of banknote demand, and decrease if
the BoJ conducts tapering following the ending of QQE. Finally, the effect of tapering
will be significantly stronger if there is no safety channel for the long-term interest rate.

Hiroshi Fujiki
TCER
andChuo University
Department of Commerce
742-1 Higashinakano Hachioji Tokyo
192-0393 Japanfujiki@tamacc.chuo-u.ac.jp

Hajime Tomura
Waseda University
Faculty of Political Science and Economics
1-6-1 Nishiwaseda Shinjyuku-ku Tokyo
169-8050 Japanhtomura@waseda.jp

Fiscal Cost to Exit Quantitative Easing: The Case ofJapan
Hajime Tomura∗

Hiroshi Fujiki

September 14, 2015

Abstract
This paper simulates the cash flows and balance sheets of the Bank of Japan (BoJ)
before and after exiting from Quantitative and Qualitative Monetary Easing (QQE)
under various scenarios. The simulations show that the BoJ will record significant
accounting losses after exiting QQE. These losses are fiscal costs for the consolidated
Japanese government as they represent increased interest expenses to the public andwill arise because the BoJ will acquire a large amount of Japanese government bonds atvery low interest rates during QQE, whose interest payments will then be insuﬃcient
to cover interest expenses on excess reserves after exiting QQE. Moreover, any cumulative accounting losses will ensure the BoJ’s net asset position remains negative for asustained period of time. We also find that the BoJ’s accounting losses will increase
with the duration of QQE and the interest rate elasticity of banknote demand, anddecrease if the BoJ conducts tapering following the ending of QQE. Finally, the eﬀectof tapering will be significantly stronger if there is no safety channel for the long-term
interest rate.

∗

Fujiki (corresponding author):
Department of Commerce, Chuo University, Japan (email:fujiki@tamacc.chuo-u.ac.jp); Tomura: Faculty of Political Science and Economics, Waseda University, Japan(email: tomura.hajime@gmail.com). We thank Will Roberds, Kazumasa Iwata, Ikuko Samikawa, and participants in Summer Workshop on Economic Theory 2015 in Hokkaido for their comments.

1

1

Introduction

The Bank of Japan (BoJ) commenced its “Quantitative and Qualitative Monetary Easing”(QQE) policy in April 2013. The purpose of this policy was to achieve a two percent annual
CPI inflation rate at the earliest possible time, with a time horizon of about two years. The
BoJ has since increased the size of monthly asset purchases after October 2014. To achieve
its target, the BoJ has more than doubled the monetary base and the holdings of Japanese
government bonds (JGBs).

1

The BoJ has also doubled the average remaining maturity of

JGB purchases in place before QQE.
The QQE remains ongoing. In April 2015, two years after the onset of QQE, the BoJ
announced that it expected to achieve the two percent annual inflation target in the first halfof fiscal year 2016; thus, it failed to achieve its target within the desired two-year period.
Nonetheless, the BoJ has not currently made any announcement on a QQE exit strategy. For
example, in June 2015, at the Standing Committee on Audit, House of Councilors, National
Diet of Japan, BoJ Governor Haruhiko Kuroda said that it was too early to discuss an exit
strategy as this would depend on economic and financial market conditions at the time ofexit.
However, we should be cautious about the BoJ’s exit strategy before exit because it
currently holds about 250 trillion yen (50% of nominal GDP) in JGBs. If the BoJ begins
monetary tightening, it could then incur a capital loss associated with the decline in themarket price of its long-term bond holdings, as suggested by Goodfriend (2000) and simulated
by Fujiki, Okina, and Shiratuka (2001). While the BoJ has adopted an amortized cost
method for its accounting since 2004, such that a capital loss will not appear on its balance
sheet, it will still need to maintain current account (reserve) balance at a high level as longas it holds long-term assets purchased during QQE until maturity. In this case, the BoJ willneed to pay interest on excess reserves to control the policy rate. It is then possible that
1

The monetary base increased from 138 trillion yen at the end of 2012 to 326 trillion yen as of July 2015.
Over the same period, its JGB holdings increased from 89 trillion yen to 249 trillion yen.

2the interest expenses on the excess reserves exceed the interest revenues from asset holdings,
causing the BoJ’s net profit after operating costs to become negative. The BoJ’s payments
to the Japanese government will then be zero, or even negative, if it receives government
payments to cover any losses. However, such a situation is not envisioned in present BoJ
law.
In theory, the central bank is only one of many government agencies, so its negative
profit per se should not matter as long as the government and the central bank arrange
a loss-sharing rule in advance, such that the central bank can conduct monetary policy
without any balance sheet constraint. However, Ueda (2004), a then Policy Board member
at the BoJ, points out that if the government can be committed to a rule against the central
bank, then central bank independence should not be an issue. Ueda also raises a concernthat if the central bank runs negative equity, then the government may intervene in thecentral bank’s monetary policy decision making through capital injection to enforce myopic
monetary easing. Indeed, given the fiscal debt currently outstanding in Japan (which theOECD estimates to be 233% of nominal GDP), there is the possibility that fiscal policy willthen dominate monetary policy to maintain a low interest rate on government fiscal debt
(Ikeo 2013; Okina 2015).
In the US, some existing studies examine the US Federal Reserve’s balance sheet as
motivated by its Large-Scale Asset Purchases program operating between 2008 and 2014.
For example, Carpenter et al. (2015) and Greenlaw et al. (2013) simulate the Federal
Reserve’s net profit and net assets after exiting from quantitative easing (QE). In addition,other studies consider the eﬀect of the Federal Reserve’s net assets on price stability. For
example, Del Negro and Sims (2014) argue that the central bank cannot guarantee pricestability if the government is not committed to sharing losses with the central bank because
the central bank may tolerate a high inflation rate simply to earn seigniorage. They showthat this possibility leads to multiple equilibria because of self-fulfilling public expectations.

3

Likewise, Reis (2015) classifies three types of central bank insolvency (negative current profit;
violation of the rule for the distribution of current profit; and intertemporal insolvency),
none of which matters if the government can be committed to sharing losses with the central
bank. However, Reis (2015) also argues that the inflation rate will depend on which type of
insolvency is applied to the central bank as the central bank will adjust seigniorage to achieve
the given condition for its solvency. Regarding a loss-sharing rule between the central bankand the government, Goodfriend (2014) proposes that the Federal Reserve should retain its
profit before the exit from QE to build a loss-absorbing capital buﬀer for exit.
In this paper, we simulate the transition of the BoJ’s balance sheet to analyze how QQE
will account for accounting losses to the BoJ in the course of the exit from QQE. Our analysis
largely draws on Carpenter et al.’s (2015) work in the US and also Iwata et al. (2014), whichapplied Carpenter et al.’s (2014) analysis to Japan for June 2014. Iwata et al. (2014) showsthat QQE will cause accounting losses to the BoJ, even without the expansion of the BOJ’s
asset purchase program in October 2014. The contribution of our analysis is to simulate thetransition of the BoJ’s balance sheet under various scenarios to identify key determinantsof its losses after exiting from QQE. We find that a longer duration of QQE and a higher
interest rate elasticity of banknote demand will increase the BoJ’s accounting losses. Thus,
the BoJ should allow for an increased cost when extending the duration of QQE, and should
not take banknote demand, currently about 17% of nominal GDP, under an eﬀective zerointerest rate for granted. Further, we find that if the BoJ does not cease, but instead tapers
its asset purchase program after exiting QQE, its accounting losses will decrease as it will
also earn profit through the term spread. This eﬀect is significantly stronger if there is nosafety channel, i.e., the eﬀect of the bond supply on the long-term interest rate.
The remainder of the paper is organized as follows. Section 2 models the BoJ’s balance
sheet. Section 3 sets up the simulation, including a description of the data and the calibrationof the parameters. We report the results of the benchmark simulation in Section 4 and4conduct a sensitivity analysis in Section 5. Section 6 concludes the paper.

2

Model of the Bank of Japan’s Accounts

We consider a simple model of the BoJ’s balance sheet, consisting of the following items:

JGBs
Other assets

Reserve balances held by financial institutions
Reserve balances held by the government
Banknotes
Other liabilities
Net assets

Here, reserve balances are current account balances at the BoJ. Other assets and liabilities
comprise various items, including Treasury bills (T-bills), commercial paper and bonds,
exchange-traded funds (ETFs), loans and bills discounted, foreign currency assets, and repos.
To focus on the eﬀect of large-scale purchases of JGBs on the BoJ’s balance sheet, we
simplify the balance sheet by defining the diﬀerence between other assets and liabilities as“net short-term assets”. This approach ignores the presence of long-term assets other thanJGBs, such as ETFs, real estate investment funds (REITs), and stocks, which are included
in “Other assets” on the BoJ’s balance sheet, as described above. As at March 31, 2015, thetotal book value of these items is 7.5 trillion yen while the BoJ’s JGB holdings sum to 220
trillion yen. If a significant capital gain arises for these assets, then the BoJ’s cumulative
accounting profit over time may increase up to a few trillion yen in total. As shown below,
this figure is small compared to the simulated change in the BoJ’s cumulative accounting
profit. Thus, our simplifying assumption does not aﬀect the main results of the model
described below.
In addition, in the model, we ignore the reserve balances held by the government. For
most of the 2000s, the government’s reserve balances are between 1 and 3 % of those held byfinancial institutions at the end of each fiscal year. Thus, ignoring these balances also does5

not significantly aﬀect the results of the model.2
Accordingly, we consider the following simplified BoJ’s balance sheet:

JGBs (Bt )Net short-term assets (St )Reserve balances held by financial institutions (Dt )Banknotes (Ct )Net assets (Et )The notation of each item in the table is in parentheses. The subscript t denotes the
fiscal year. Each variable represents the value at the beginning of the fiscal year. Reservebalances held by financial institutions are split into required reserves (DREQ,t ) and excess
reserves (DEX,t ):DREQ,t + DEX,t = Dt .

2.1

(1)

Demand for banknotes and required reserves

The BoJ supplies required reserves and banknotes passively in response to the demands forbank deposits and cash from the public. We assume the demand for banknotes depends on
nominal GDP and the nominal interest rate:
Ct = µt GDPt ,(2)

where GDPt denotes annual nominal GDP, and µt is the banknotes-to-GDP ratio. Additionally, we assume a regime shift in µt to capture the response of the demand for banknotes
to the interest rate.

{
µ̄
µt =
µ

if t ≤ τ ,if t > τ ,(3)where τ denotes the fiscal year when the BoJ achieves the inflation target. As assumed below,
the BoJ raises the policy rate after this year. This simple specification of the interest rateelasticity is suﬃcient for our simulations, as our scenario analysis does not consider detailed
2

We confirm this result by running simulations under the assumption that the government’s reservebalances are 1% of those held by financial institutions.

6business-cycle fluctuations in the nominal GDP growth rate and the nominal interest rate
after t hits τ .
We set a similar assumption for the demand for required reserves:
DREQ,t = γη t GDPt

(4)

where γ is the average reserve requirement ratio and η t is the bank deposits-to-GDP ratio.
For a similar reason to (3), there is a regime shift in η t when t hits τ :{η̄ if t ≤ τ ,ηt =η if t > τ .

2.2

(5)

Supply of excess reserves

The BoJ’s flow of funds constraint determines the supply of excess reserves, given the BoJ’s
asset purchase policy on JGBs and net short-term assets. The BoJ’s flow of funds constraint
is written as
Dt+1 − Dt = Vt − Rt − Pt + St+1 − St − iST,t St + iCB,t DEX,t+ Jt + Ft + Tt − (Ct+1 − Ct ), (6)where Vt is the purchase value of newly purchased JGBs, Rt is the coupon payments on
JGBs, Pt is the redemption of JGBs held by the BoJ at maturity, iST,t is the short-term
nominal interest rate, iCB,t is the central bank deposit rate on excess reserves, Jt is thepayment of profit to the government, Ft is general and administrative expenses and costs,
such as personnel expenses, and Tt is the corporate and residential taxes incurred by the
BoJ. Note that on the right-hand side of (6), the BoJ’s expenditures have a positive sign
while the revenues have a negative sign. This is because the increment in reserve balanceson the left-hand side of (6) is the BoJ’s cash flow, but with the opposite sign. The new issueof banknotes, Ct+1 − Ct , appears as the last term on the right-hand side of (6) with a minus
sign, as banks obtain new banknotes by withdrawing their reserve balance holdings.
7

We assume that the short-term interest rate is anchored by the interest rate on excess
reserves set by the BoJ:
iCB,t = iST,t .

(7)

We simply assume that general and administrative expenses and costs grow at the same rate
as GDP:Ft = ϕGDPt .

2.3

(8)

Accounting profit and net assets

The BoJ transfers a fraction of its accounting profit to the government as Jt . The BoJ’s
pretax accounting profit, π t , is defined as
π t = Rt + At + iST,t St − iCB,t DEX,t − Ft ,(9)where At is the amortization of the discount on JGBs under the amortized cost method.
Accordingly, the book value of JGBs, Bt , is updated through this method:3
Bt+1 − Bt = Vt − Pt + At .

(10)

For simplicity, we assume that the corporate and residential taxes incurred by the BoJ
are proportional to positive pretax profit:
Tt = κ max{0, π t }.

(11)

Under the current rule, the BoJ pays out a fraction of its after-tax annual accounting profit
to the government the following year, and retains the remainder as part of its net assets.
Thus, the payment of profit to the government, Jt , is determined by the following rule:
Jt = max{0, θ(1 − κ)π t−1 },3

The BoJ has adopted this method since 2004, under which the diﬀerence between the face value andpurchase value of JGBs held to maturity is evenly split over maturity to compute the amortization of the
discount for each year. The amortized discount is then gradually recognized as part of interest revenues eachyear and added to the book value of JGBs, so that the book value equals the face value at maturity.

8

where θ is the proportion of accounting profit to be transferred to the government. Here, we
assume that the BoJ does not make any transfer if it incurs an accounting loss for the year.
The BoJ’s net assets are simply the diﬀerence between the book value of its assets andits liabilities:
Et = Bt + St − Dt − Ct .

(12)

Overall, (1)-(12) determine the transition of the BoJ’s balance sheet and accounting
profit, given the characteristics of the JGBs held by the BoJ (Rt and Pt ), the BoJ’s asset
purchase policy (Vt and St+1 −St ), macroeconomic variables (iST,t and GDPt ), and the timingof the exit from QQE (τ ).

3Simulation setup

Hereafter, we simulate the model by inserting data including the current BoJ’s asset purchasepolicy under simple macroeconomic scenarios. This exercise aims to identify importantfactors that determine the cost to exit from QQE through quantitative sensitivity analysis
under transparent assumptions. The starting month of the simulations is June 2015.

3.1

Timing of the exit from QQECurrently, the BoJ is committed to achieving its inflation target in the first half of fiscal
year 2016. Accordingly, we set τ to 2016 for a benchmark. This assumption implies thatthe BoJ achieves the inflation target at the end of fiscal year 2016 (or March 2017) in themodel, given the annual frequency of the model.

3.2

BoJ’s asset purchase policy before the exit from QQE

In October 2014, the BoJ announced an expansion of QQE, which aims to increase thereserve balances held by financial institutions by 80 trillion yen per year until it achieves this9Table 1: Benchmark assumption on the BoJ’s monthly purchases of JGBs before the achievement of the inflation target
Maturity(years)Purchase value(trillion yen)

20

10

5

2

1.625 2.7

2.55

2.55

10
15
(Inflation-indexed) (Floating-rate)
0.01
0.07

inflation target. Thus, we assume
Dt+1 − Dt = 80 trillion yen if t ≤ τ .

(13)

To achieve this goal, the BoJ is committed to purchasing JGBs worth between 8 and
12 trillion yen each month. It will set a range for the monthly purchase value of JGBs foreach maturity (see Appendix A). Using the median value of this range, we assume the BoJ’s
monthly purchases of JGBs for t ≤ τ as shown in Table 1. The figures in the table imply
Vt = 114.06 trillion yen if t ≤ τ ,(14)which satisfies the range of total monthly purchase value of JGBs described above.
We assume that the terms for the purchases at each maturity, such as the price and the
coupon rate, are the same as in the primary market at the end of May, 2015.4 Under thisassumption, the average maturity of newly purchased JGBs is around eight years, which isconsistent with the BoJ’s policy that sets the average remaining maturity to between sevenand 10 years.
In this regard, an alternative assumption is to follow Carpenter et al. (2015) and use an
estimated yield curve to calculate the price of discounted bonds for each maturity. We do
not select this option as we obtain a negative yield for short maturities if we insert the recent
4

There has been no new issuance of floating-rate JGBs since 2008. For this category, we assume the BoJ
purchase these bonds at the same purchases terms as those most recently issued in the secondary market atthe end of May, 2015. For simplicity, the remaining maturity for this category of bonds is set to seven years
for any year of purchase.

10

ultra-low long-term rate in Japan, which is below 0.5%, into the estimated yield curve.5
Given the JGB purchase policy set by (14), the BoJ adjusts its net short-term assets toincrease the reserve balances held by financial institutions by 80 trillion yen per year. Thus,(6) implies that
St+1 − St = −Vt + Rt + Pt + iST,t St − iCB,t DEX,t − Jt − Ft − Tt
+ Ct+1 − Ct + Dt+1 − Dt if t ≤ τ (15)where Dt+1 − Dt and Vt are set by (13) and (14), respectively.

3.3

BoJ’s asset purchase policy after the exit from QQE

We assume that after the exit from QQE, the BoJ holds JGBs until maturity and does notmake any new purchases:
Vt = 0 if t > τ .

(16)

Following the BoJ’s policy in regular time, we also assume that the BoJ purchases T-bills,
part of net short-term assets in the model, using the revenues from any redeemed JGBs
for one year.6 After that, the BoJ receives reserve balances from the government for the
repayment of T-bills. Thus, reserve balances at the end of fiscal year, Dt+1 , decline through(6) as JGBs held by the BoJ gradually mature.
In addition, the BoJ’s balance of net short-term assets at the exit from QQE is higher
than the value of redeemed JGBs in the previous year. We assume that the BoJ maintains
this excess balance after the exit from QQE, because otherwise the balance of net short-term
assets becomes unrealistically close to zero as JGBs held by the BoJ mature over time.
If reserve balances become insuﬃcient for required reserves, then the BoJ supplies thenecessary amount by adjusting net short-term assets. Overall, the BoJ’s adjustment of net
5

This observation implies that there is nonlinearity in the eﬀect of the long-term interest rate on the yield
curve.
6
As the government rolls over part of its redeemed JGBs, this policy aims to mitigate the imbalance
between demand and supply in the JGB market by rolling over redeemed JGBs for a short period of time.

11

short-term assets is specified asPt − Pt−1






St+1 − St = −Vt + Rt + Pt + iST,t St − iCB,t DEX,t − Jt−Ft − Tt + Ct+1 − Ct + DREQ,t+1 − Dt

if t > τ and Dt+1 ≥ DREQ,t+1 ,if t > τ and Dt+1 < DREQ,t+1
under St+1 − St = Pt − Pt−1 ,(17)where the right-hand side of the second line is derived by substituting Dt+1 = DREQ,t+1 into
(6).

3.4

Data on BoJ’s JGB holdings and balance sheet

The coupon payments (Rt ) and redemption (Pt ) of JGBs depend on the past asset purchasesby the BoJ. The BoJ publishes the face value of its JGBs for each issuance date. We combine
these data with the coupon rate and the maturity for each issuance date published by the
Ministry of Finance. The BoJ, however, does not publish the book value of its JGBs foreach issuance date, but only the book value for each maturity (i.e., each of those listed in
the first row of Table 1). To compute the book value for each issuance date, we divide thebook value for each maturity proportionally to the face value of each issuance date with thesame maturity.
For the initial value of the balance sheet items, we use the Bank of Japan Accounts asat the end of May 2015.

3.5

Benchmark scenario on the path of the inflation rate, theshort-term interest rate, and the nominal GDP growth rate

For a benchmark, we assume that the annual inflation rate remains at 0% until the BoJ hits
the inflation target (i.e., t ≤ τ ) and stays at the targeted rate, 2%, after the achievement of
the target (i.e., t > τ ). The short-term interest rate is set to 0.1% for t ≤ τ , which is the sameas the current interest rate of excess reserves, assumed to rise to 1.25% at t = T + 1 and then12

2.75% for t ≥ T + 2. These figures are based on the spread between the geometric averagesof the overnight call rate and the CPI inflation rate over the period 1990–2013, which was
0.78%. Here we use the Lost Decades in Japan for the sample period.7 We assume that the
BoJ takes two years to raise the short-term interest rate to its long-run level following theexit from QQE, given the negative eﬀect of a sudden large increase in the policy rate. The
nominal GDP growth rate is set to the inflation rate plus 0.3%, which is the spread between
the geometric averages of the two rates over the period 1990–2013 (see Figure 1 for the time
path of the macroeconomic variables in the benchmark scenario).
Even though this simple scenario ignores feedback from the BoJ’s balance sheet to aggregate economic activity, it allows us to run simulations under a more transparent assumption.
In this paper, we choose the latter benefit of considering a simple scenario based on pastdata, given the diﬃculty in precisely forecasting the long-term trend of GDP and othermacroeconomic variables. In addition, we do not use survey forecasts or financial market
data, such as the yield curve, to set the benchmark scenario, because these data reflect the
average expectations over diﬀerent contingencies, including the case in which QQE does notachieve its target. Instead, we take as given the spreads of the macroeconomic variables
to the annual inflation rate to set the benchmark scenario assuming the achievement of theinflation target by QQE.

3.6

Calibration of the remaining parameters

For the demand for banknotes before the achievement of the inflation target, we set µ̄ =0.174, which is the banknotes-to-GDP ratio in 2013. Here, we use the most recent year
for which the Annual Report on National Accounts is available because if we use a sample
average, the diﬀerence between the last data point and the sample average will create an
artificial jump in the BoJ’s net assets. For the period after the achievement of the inflation
target, we set µ = 0.0797. This value is the sample average of the banknotes-to-GDP ratio
7

The sample period ends in 2013, as it is the most recent year in which confirmed GDP data are available.

13

over the 1990s, which is the most recent period before QE in Japan in the 2000s.
We set a similar assumption for the demand for required reserves. The bank depositsto-GDP ratios before and after the achievement of the inflation target (i.e., η̄ and η) are set
to 2.05 and 1.53, respectively. These values are derived from the same sample periods as
those used to set µ̄ and µ. We set γ = 0.00593, which is the average reserve requirement
ratio between 1992 and 2014, as there was a regulatory change in reserve requirement ratios
in October 1991.8 The ratio between the general and administrative expenses and costs andGDP, ϕ, is set to 0.000393, which makes Ft equal 190 billion yen in 2013, as observed in thedata. The corporate income and residential tax rate on the BoJ’s pretax profit, κ, is set to0.275, which is the average rate over the fiscal years between 2012 and 2014. We use only
the most recent three years as the corporate income tax rate changed in 2012. Finally, theproportion of the BoJ’s after-tax accounting profit to be transferred to the government, θ,
is set to 0.75, according to the current rule announced by the BoJ in May 2015.

4

Benchmark results

In this section, we summarize the result of the benchmark simulation. Figure 2 depicts
the transition of the balance sheet items for the BoJ. As shown, reserve balances gradually
decline as JGBs held by the BoJ mature over time. It takes around 20 years until the excess
reserves due to QQE disappear.
Figure 3 displays the major components of the BoJ’s accounting profit. As shown, theBoJ records accounting losses between 2017 and 2032. Accordingly, the payment of profit
to the government becomes zero for this period. The maximum annual loss amounts to 6.19
trillion yen in 2018.
These losses arise because of maturity transformation on the BoJ’s balance sheet. Be8

The reserve requirement ratio diﬀers across diﬀerent categories of bank deposits. To set the value ofγ, we compute the ratio between the sum of required reserves and the balance of bank deposits subject toreserve requirements for each fiscal year, and then take the average over the period 1992–2014.

14

cause the low rates of return on JGBs purchased during QQE are predetermined, the interest
expenses surpass the interest revenues as the BoJ raises the interest rate on reserve balances
to increase the short-term interest rate after QQE. These losses continue until reserve balances suﬃciently decline with the gradual redemption of JGBs.
The fiscal cost of QQE for the consolidated government appears in the BoJ’s accounting
loss. Note that if there were no QQE, the consolidated government would pay interest to
the public on JGBs purchased by the BoJ. Thus, the consolidated government incurs a loss
from QQE when the interest expenses on reserve balances exceed the interest revenues from
JGBs on the BoJ’s balance sheet. A caveat is that this loss is the gross fiscal cost undera given path of the short-term interest rate. To measure the opportunity cost of QQE, weneed to know the precise path of the macroeconomic variables in the instance of no QQE.
Figure 4 illustrates the transition of the BoJ’s net assets. As shown, the accumulationof the accounting losses over 15 years results in an extended period of negative net assets
for the BoJ. In the benchmark simulation, the BoJ recovers positive net assets in 2084 bygradually oﬀsetting the accumulated loss with normal profit from the interest margin between
net short-term assets and banknotes. Does the BoJ remain intertemporally solvent in thebenchmark scenario? Following Del Negro and Sims (2014) and Reis (2015), we computethe BoJ’s net worth, which takes into account the present discounted value of future pretax
profit.9 We use the short-term interest rate for the discount rate, as the BoJ’s assets consistof net short-term assets in the long run.
Figure 5 depicts the time path of the BoJ’s net worth. As shown, given a small spread
between the short-term nominal interest rate and the nominal GDP growth rate in thebenchmark scenario, the present discounted value of future profit is suﬃciently large tooﬀset the negative net assets from the cumulative losses arising after the exit from QQE.

9The BoJ’s tax payments to the government are equivalent to the dividend payouts by a private company
to its shareholders. Thus, we include pretax profit in the computation of the BoJ’s net worth.

15

5

Sensitivity analysis

The benchmark simulation yields an estimate of the BoJ’s future profit based on one of anumber of possible scenarios, rather than a point estimate of the BoJ’s future profit based on
macroeconomic projections. In this section, we discuss the sensitivity of the simulation result
to alternative scenarios concerning the BoJ’s behavior and the macroeconomic environment.

5.1

Longer duration of QQE

Figure 6 shows the BoJ’s balance sheet when QQE lasts until 2018 (i.e., τ = 2018). In thiscase, the BoJ’s JGB holdings reach 500 trillion yen at their peak to achieve the large amountof annual reserve supply targeted under QQE. As a result, the BoJ’s accounting losses after
the exit from QQE increase because of the larger amount of maturity transformation on the
BoJ’s balance sheet, as shown in Figure 7. Thus, the fiscal cost after the exit from QQE
should be taken into account when the BoJ compares the cost and benefit of extending theduration of QQE.

5.2

Interest rate elasticity of banknote demand

In the benchmark scenario, we assume that the banknotes-to-GDP ratio falls to its 1990s
level after the exit from QQE. This assumption aims to capture the elasticity of banknote
demand when the BoJ raises the short-term interest rate following the achievement of QQE.
This assumption is important for the BoJ’s accounting profit after the exit from QQE,
because the BoJ’s profit in normal times stems from purchasing interest-bearing assets to
supply banknotes. The amount of reserve balances is small relative to banknotes in normal
times.
We consider three alternative scenarios for the interest rate elasticity of banknote demand.
The first scenario is that the banknotes-to-GDP ratio remains the same before and after theexit from QQE (i.e., µ̄ = µ = 0.174). Thus, in this scenario, banknote demand does not16respond to an increase in the short-term interest rate.10
The second scenario uses the statistical estimation of the real banknote demand function.
We consider two specifications:ln(RCt ) = a0 + a1 ln(RGDPt ) + a2 (CALLt ) + ε1t ,(18)ln(RCt ) = b0 + b1 ln(RGDPt ) + b2 ln(CALLt ) + ε2t ,(19)

where RCt is real banknote demand, RGDPt is real GDP, and CALLt is the nominal
overnight call rate. Using annual data between 1959 and 2013 for Japan, we find that the second specification includes cointegration with a structural break in 2004. Following Hayashi(2000), we estimate the cointegration coeﬃcients for 1959–2003 using dynamic ordinary
least squares (DOLS). The estimation results are b1 = 1.029 (s.e. = 0.43) and b2 = −0.133(s.e. = 0.010).11 As DOLS does not identify the constant term, we set b0 = −3.31 so thatthe fitted value of (19) coincides with the data in 2003. Given this specification, Figure
8 depicts the comparison between the data and fitted nominal banknote demand based on
the estimation of (19) over the period 1959–2003. In the second scenario, we assume thatthe structural break in the real banknote demand function occurs because of the eﬀective
zero-interest rate policy adopted by the BoJ. Thus, the nominal banknote demand after theexit from QQE is determined by (19) with the DOLS estimates of the coeﬃcients.
The third scenario uses an estimate of the cash stash held in household savings. The
BoJ issues bills in denominations of one, two, five and 10 thousand yen, of which the one
and 10 thousand yen notes are most commonly used. Otani and Suzuki (2008) assume
that people only use 10 thousand yen notes when they hoard cash for savings, and thatthe transaction demands for one and 10 thousand yen notes are proportional to each other.
Under these assumptions, Otani and Suzuki estimate the cash stash using the excess balance
10

Iwata et al. (2014) adopted this same assumption for their simulation of the BoJ’s balance sheet before
and after QQE.
11
Static ordinary least squares (SOLS) estimates are similar to the DOLS estimates (see Appendix B for
details).

17

of 10 thousand yen notes above the transaction demand for these notes, which is assumed
to grow at the same rate as the outstanding balance of one thousand yen notes. They set
1995 as the base year in which they assume there is no cash stash in Japan.12
Figure 9 displays the ratio of the balances of one and 10 thousand yen notes with thenominal overnight call rate in Japan. As shown, this declines as the call rate falls in the late
1990s, and stabilizes when the call rate hits the zero lower bound. This figure is consistent
with the assumption set by Otani and Suzuki. Using Otani and Suzuki’s method, we estimate
the cash stash to be about 35 trillion yen (see Figure 10). For the third scenario, we assume
that only the cash stash disappears as the BoJ raises the short-term interest rate, while thetransaction demand for banknotes remains unaﬀected. This assumption implies that thebanknotes-to-GDP ratio drops to 0.099 at the time of the exit from QQE (i.e., µ = 0.099).
Figures 11 and 12 show the BoJ’s accounting profit and net assets under the benchmark
and the three alternative scenarios. These demonstrate that the demand for banknotes is a
crucial factor in the determination of the BoJ’s accounting profit and the duration in which
the BoJ records negative net assets.

5.3

Tapering after the exit from QQE

In the benchmark simulation, we assume that the BoJ rolls over its JGB holdings for only
one year by purchasing T-bills with the revenues from any redeemed JGBs. As an alternative scenario, we consider the case in which the BoJ decreases its new purchases of JGBs
gradually over a certain period of years after the exit from QQE. In this case, the amountof newly purchased JGBs each year is set to decline linearly so that it becomes zero after
the adjustment period. The average maturity of newly purchased JGBs after the exit from

12

The so-called Jyu-sen problem occurred in Japan in 1995. Jyu-sen is the abbreviation of a nonbank
mortgage loan lender. Japanese banks made real estate loans through Jyu-sens in the late 1980s, and thelosses to Jyu-sens came to the surface in 1995. Thus, Otani and Suzuki (2008) aim to measure the cash
stash associated with the Japanese public’s concerns with the financial health of Japanese banks.

18

QQE is assumed to be 10 years.13
In this case, we need to set a path for the long-term nominal interest rate to compute theyield on JGBs purchased after the exit from QQE. Following Krishnamurthy and VissingJorgensen (2011), we assume the existence of a safety channel such that{
iLT,t = iST,t + min 0.01,{
0.003 − 0.0031 min 0, ln

(

Bt
GDPt

)

}}
− ln(0.041),(20)

where iLT,t denotes the long-term nominal interest rate. On the right-hand side, 0.01 is thelong-run term spread, 0.003 is the term spread under QQE, -0.0031 is the supply elasticityof the long-term interest rate implied by Krishnamurthy and Vissing-Jorgensen’s (2011)
estimate of the safety channel in the US, and 0.041 is the ratio of the book value of JGBs
held by the BoJ and nominal GDP in December 2014.14 The value of the long-run term
spread equals the spread between the geometric averages of the 10-year JGB yield and theovernight call rate over the period 1990–2013, which is before QQE. The value of the term
spread under QQE is based on the fact that the 10-year JGB yield fluctuates around 0.3–
0.5% after the expansion of JGB purchases in December 2014, while the overnight call rate
was set to 0.1% by the interest rate on reserve balances. For the supply elasticity of thelong-term interest rate, we use Krishnamurthy and Vissing-Jorgensen’s US estimate, as there
is no comparable analysis using Japanese data.15
Under (20), the long-term interest rate gradually increases to the long-run level after the
BoJ’s JGB holdings-to-GDP ratio becomes smaller than the level before December 2014.
13

More precisely, the outstanding balance of newly purchased JGBs follows a simple process such that
N Bt+1 = Vt + 0.9N Bt ,where N Bt is the outstanding principal of JGBs purchased after the end of QQE at the beginning of fiscal
year t and Vt is the amount of newly purchased JGBs in fiscal year t.
14
The value of nominal GDP used here is the preliminary quarterly estimate for fiscal year 2014.
15
Strictly speaking, Krishnamurthy and Vissing-Jorgensen (2011) compute the 10-year equivalent supplyof Treasury bonds by using the remaining maturity of each issue of Treasury bonds as a weight. However,they also report that the simple sum of the market values of Treasury bonds is highly correlated with the
10-year equivalent supply of Treasury bonds. Given no public data on the market value of JGBs held by the
BoJ, we use the book value of JGBs in (20).

19

We set this assumption because the long-term interest rate did not show a downward trend
in 2015, despite continuing large-scale JGB purchases each month (see Figure 13). For
simplicity, we set no coupon on JGBs purchased after the exit from QQE, and assume thatthe average yield on these JGBs equals the long-term nominal interest rate, iLT,t .
Figure 14 shows the BoJ’s balance sheet when the adjustment period for the BoJ’s JGB
purchases after the exit from QQE is set at 10 years. Because of the continuation of newpurchases of JGBs, the BoJ’s JGB holdings peak in around 2020.
Figure 15 compares the BoJ’s pretax profit between the benchmark and alternative scenarios with adjustment periods of 10 and 20 years. As shown, tapering shortens the period
in which the BoJ runs accounting losses. This is because the BoJ can profit from the term
spread after the exit from QQE, as shown in Figure 16. Figure 17 illustrates that as a result,the duration of negative net assets is also shortened if the BoJ gradually adjusts its newpurchase of JGBs after the exit from QQE.
The safety channel plays an important role in determining the eﬀect of tapering. Figure
18 and Figure 19 compare the BoJ’s pretax profit and net assets with and without the safety
channel, given that the adjustment period for the BoJ’s JGB purchases is set at 10 years. In
the case of no safety channel, assume that the term spread immediately jumps to the longrun level (i.e., iLT,t = iST,t + 0.01) after the exit from QQE. Figure 20 depicts the long-term
interest rate in the two cases. These figures demonstrate that if the term spread returns to
its pre-QQE level immediately after the exit from QQE, then the BoJ will earn significant
profit from the term spread through continuing purchases of JGBs. As a result, the BoJ willrecord negative net assets only for a short period of time. Thus, tapering saves more fiscal
cost for the consolidated government as the safety channel is less significant.

20

6Conclusion

We simulated the BoJ’s cash flows and balance sheet before and after the exit from QQE
under various scenarios. The simulations show that the BoJ will record significant accounting
losses after the exit from QQE. These losses are fiscal costs for the consolidated government,
as they represent increased interest expenses to the public from the replacement of JGBs withreserve balances as a result of QQE. In addition, these cumulative accounting losses will makethe BoJ’s net assets negative for a sustained period of time, possibly more than 50 years.
Even though the BoJ’s net assets per se do not matter for the consolidated government,
the BoJ and the Ministry of Finance should prepare a loss-sharing rule so that the BoJ’s
accounting losses do not impose a financial constraint on the BoJ or bias the BoJ’s monetary
policy decisions, as argued by Del Negro and Sims (2014).

Loss sharing is not currently

envisioned in BoJ law.
We also found that a longer duration of QQE and a higher interest rate elasticity ofbanknote demand increase the BoJ’s accounting losses significantly. Thus, the BoJ should
consider the consequences on fiscal cost when deciding the duration of QQE, and also should
not take as given current banknote demand under an eﬀective zero interest rate. Finally,
the simulation results suggest that tapering after the exit from QQE mitigates the BoJ’s
accounting losses, and hence the fiscal cost of QQE for the consolidated government, as it
generates profit from the term spread. This eﬀect is significantly stronger if there is no safety
channel for the long-term interest rate.
A caveat is that we consider only simple macroeconomic scenarios to run simulations
under transparent assumptions. Thus, the simulation results in this paper should be taken
as ballpark figures of the BoJ’s future profit based on one of a number of possible scenarios,
rather than a point estimate of the BoJ’s future profit based on macroeconomic projections.
It would be a significant challenge to predict the trend of macroeconomic variables after theexit from QQE. It would also be diﬃcult to model the feedback between the BoJ’s accounting
21

losses and these macroeconomic variables. These issues are left for future research.

22

References[1] Bernanke, Ben S. 2015. “Monetary policy in the future,” Remarks at the IMF’s Rethinking Macro Policy III conference on April 15, 2015, http://www.brookings.edu/
blogs/ben-bernanke/posts/2015/04/15-monetary-policy-in-the-future[2] Carpenter, Seth B., Jane E. Ihrig, Elizabeth C. Klee, Daniel W. Quinn, and Alexander
H. Boote. 2015. “The Federal Reserve’s Balance Sheet and Earnings: A Primer andProjections.” International Journal of Central Banking, 11(2), 2015, 237–283.
[3] Del Negro, Marco, and Christopher A. Sims. 2014. “When Does a Central Bank’s Balance Sheet Require Fiscal Support?” Federal Reserve Bank of New York Staﬀ Report701. Revised: March 2015.
[4] Elliott, Graham. R., Thomas. J. Rothenberg, and James. H. Stock, “Eﬃcient Tests for
an Autoregressive Unit Root.” Econometrica 64 (4), 813–836, 1996.
[5] Fujiki, Hiroshi, Kunio Okina, and Shigenori Shiratsuka. 2001. “Monetary Policy under
Zero Interest Rate: Viewpoints of Central Bank Economists.” Monetary and Economic
Studies, 19 (1), 89–130. Bank of Japan.
[6] Fujiki, Hiroshi, and Kiyoshi Watanabe. 2004. “Japanese Demand for M1 and Demand
Deposits: Cross-Sectional and Time-Series Evidence from Japan,” Monetary and Economic Studies 22(3), 47–77. Bank of Japan.
[7] Goodfriend, Marvin. 2000. “Overcoming the Zero Bound on Interest Rate Policy,” Journal of Money, Credit and Banking, 32(4), 1007–35.
[8] Goodfriend, Marvin. 2014. “Monetary Policy as a Carry Trade.” Monetary and Economic Studies, 32, 29–44. Bank of Japan.

23

[9] Greenlaw, David, James D. Hamilton, Peter Hooper, and Frederic S. Mishkin, “Crunch
Time: Fiscal Crises and the Role of Monetary Policy,” NBER Working Paper No. 19297,
2013.
[10] Gregory, W. Allan, and Bruce E. Hansen. 1996. “Residual-based Tests for Cointegrationin Models with Regime Shifts,” Journal of Econometrics, 70, 99–126.
[11] Hayashi, Fumio. 2000. Econometrics. New Jersey: Princeton University Press.
[12] Ikeo, Kazuto. 2013. Abenomics no keizai bunseki (Economic Analysis of Abenomics).
Tokyo: Nikkei BP. (In Japanese.)[13] Iwata, Kazumasa, and Japan Economic Research Center. 2014. Ryoteki-shituteki kinyu
kanwa seisaku no koka to risuku wo kensyo suru (Examination of the Eﬀect and the
Risk of Qualitative and Quantitative Easing.) Tokyo: Nikkei. (In Japanese.)[14] Krishnamurthy, Arvind, and Annette Vissing-Jorgensen. 2011. “The Eﬀects of Quantitative Easing on Interest Rates: Channels and Implications for Policy,” Brookings
Papers on Economic Activity, 43 (2), 215–287.
[15] Miyao, Ryuzo. 2002. “Liquidity Traps and the Stability of Money Demand: Is Japan
Really Trapped at the Zero Bound?” RIEB Discussion Paper No. 127. Research Institutefor Economics and Business Administration, Kobe University.
[16] ——. 2005. “Use of Money Supply in the Conduct of Monetary Policy: Re-Examining
the Time-Series Evidence,” Japanese Economic Review, 56, 165–187.
[17] Nakashima, Kiyotaka, and Makoto Saito. 2012. “On the Comparison of Alternative
Specifications for Money Demand: The Case of Extremely Low Interest Rate Regimes
in Japan,” Journal of the Japanese and International Economies, 26 (3), 454–471.

24

[18] Okina, Kunio. 2014. Keizai no daitenkan to nihonginkou (Big Change in the Economy
and the Bank of Japan). Tokyo: Iwanami Shoten.
[19] Otani, Akira, and Takashi Suzuki. 2008. “Background to the High Level of Banknotes
in Circulation and Demand Deposits,” Bank of Japan Review 08-E-5.
[20] Reis, Ricardo. 2015. “Diﬀerent Types of Central Bank Insolvency and the Central Roleof Seignorage,” NBER Working Paper Series, 21226.
[21] Ueda, Kazuo. 2004. “The Role of Capital for Central Banks,” the Bank of Japan’s oﬃcial
English translation of the speech at the Fall Meeting of the Japan Society of Monetary
Economics, on October 25, 2003. https://www.boj.or.jp/en/announcements/press/
koen_2003/ko0402b.htm/

25AppendicesA

BoJ’s JGB purchase policy under QQE

In October 2014, the BoJ announced an expansion of QQE, which aimed to increase thereserve balances held by financial institutions by 80 trillion yen per year. In December 2014,
it set a new JGB purchase policy such that it purchases JGBs worth between eight and 12
trillion yen in purchase value per month. The BoJ’s policy on the approximate range of themonthly purchase value for each type of JGBs is shown in Table 2. The average remaining
maturity of the purchased JGBs under this policy is set to be between seven and 10 years.
Table 2: Monthly purchase value of JGBs under QQE
Bond type
Coupon-bearing
bonds

Remaining maturity< 1 year
1–5 years
5–10 years> 10 years

Floating-rate bonds
Inflation-indexed bonds

Approximate range of the purchase valueof JGBs per month (billion yen)100-300
3000-7200
1800-3600
1250-2000
1400(bimonthly)200(bimonthly)

The monthly purchase value for each maturity of JGBs in the model, i.e., the figure in
Table 1, equals the median value of the following range in Table 2: two- and five-year bonds
fall into the second row; 10-year bonds fall into the third row; and 20-year bonds fall into
the fourth row. For two- and five-year bonds, we split into half the median value of therange shown in the second row of Table 2. The figures in Table 1 imply that the average
maturity of newly purchased JGBs before the exit from QQE is 8.2 years. Thus, the BoJ’s
JGB purchase policy in the model satisfies actual policy on the average remaining maturityof purchased JGBs, i.e., between seven and 10 years.

26

B

Estimation of the real banknote demand function

In the literature, Nakashima and Saito (2012) and Miyao (2002, 2005) analyze the interest
rate elasticity of M1 (the sum of banknotes and demand deposits) in Japan by specifying
real M1 as the dependent variable in (18) and (19), respectively. In addition, while Miyao(2002, 2005) set the income elasticity of M1, b1 , to zero, Fujiki and Watanabe (2004) use
cross-sectional data across Japanese prefectures to set the value of b1 . In our analysis, wefollow this literature to estimate the real banknotes demand in Japan.
For the estimation of (18) and (19), we use the following data for 1959–2013:• Ct : the annual average balance of banknotes for each fiscal year.
• N GDPt : GDP deflator for each fiscal year; 1993SNA data for 1993–2013 extended
with the annual growth rates in 1968SNA data for 1959–1992.
• Callt : the annual average overnight call rate; the collateralized rate until 1984 and theuncollateralized rate from 1985.
In the sample period, 2013 is the most recent year in which data on GDP in the Annual
Report on National Accounts is available, and 1959 is the first year in which the call rate
data exist. We define the real balance of banknotes and the real GDP by
Ct,
P GDPtN GDPt
RGDPt =,P GDPt
RCt =

(21)
(22)

respectively.
We first conduct an augmented Dickey–Fuller (ADF) test and find that we cannot reject
the null hypothesis of a unit root with a time trend, except for CALLt (see Table 3). For
CALLt , we cannot reject the null hypothesis of a unit root based on Elliott, Rothenberg
and Stock (1996). (The test statistics is −1.762, and the 10% level critical value is −2.748.)
27

Table 3: ADF test on the components of the real banknote demand functionln(RCt )ln(RGDPt )CALLtln(CALLt )ADF statistics P-value Lag-2.8730.17131-2.5260.3151
1-4.3910.00233-2.4480.3543
1Time trend
Exist
Exist
Exist
Exist

Notes: The sample period is the fiscal years between 1959 and 2013. We
use the dfuller command in Stata 13.

Table 4: Engel–Granger test on cointegration
Test statistics
Eq. (18)-1.992

Critical value
1%
5%
10%
-4.572 -3.903 -3.569

Eq. (19)-1.452-4.572-3.903-3.569Notes: The sample period is the fiscal years between 1959 and 2013. We
use the egranger command in Stata 13.

Next, we conduct the Engel–Granger test and find that we cannot reject the null hypothesis of no cointegration among the variables appearing in each of (18) and (19) (see Table
4).
Given this result, we test a structural break in cointegration using Gregory and Hansen’s(1996) test. In this test, the null hypothesis is no cointegration, and the alternative hypothesis is cointegration with a structural break. While we cannot reject the null hypothesis for(18), we find that there is a structural break in 2004 according to the ADF and Zt statistics(see Table 5).
Given a cointegration relationship for (19) over the period 1959–2003, we estimate thecointegration coeﬃcients using SOLS and DOLS, following Hayashi (2000) (see Table 6).
The estimation result for DOLS does not change significantly, even if we set the number oflags to one year.

28

Table 5: Gregory and Hansen’s (1996) test for a structural break in cointegration

ADF
Zt
Zα

Test statistics for each function
Eq. (18)
Eq. (19)-4.02 (2003)-5.59 (2004)-4.42 (2003)-5.64 (2004)-29.08 (1999)-40.92 (2004)

Critical value
1%
5%
10%
-5.44 -4.92 -4.69-5.44 -4.92 -4.69-57.01 -46.98 -42.49

Notes: The sample period is the fiscal years between 1959 and 2013. We use
the ghansen command in Stata 13. Each set of parentheses in the second andthird columns provide the year of a structural break.

Table 6: Estimation of cointegration coeﬃcients in Eq. (19)

SOLS
DOLS
(s.e.)

b1
1.121
1.029
(.043)

b2
-.090
-.133
(.010)

Notes: The sample period is the fiscal years between 1959 and 2013. We use
the ivreg2 command in Stata 13. The last row shows the standard errors of
the coeﬃcients estimated by DOLS. The number of lags for DOLS is set to two
years.

29

0.05

Figure 1: Benchmark scenario on the path of the inflation rate, the short-term nominalinterest rate, and the nominal GDP growth rate

0.00

0.01

0.02

0.03

0.04

Inflation rate
Short−term nominal interest rate
Nominal GDP growth rate

2016 2020

2030

2040

2050

Fiscal year
Note: The interest rate on reserve balances is the same as the short-term interest rate.

30

500

Figure 2: Balance sheet items of the BoJ in the benchmark scenario

200
100
0

Trillion yen

300

400

Reserves
JGBs
Net Short−term assets
Cash2016 2020

2030

2040
Fiscal year

31

2050

10

Figure 3: Major components of the BoJ’s accounting profit in the benchmark scenario

0
−10

−5

Trillion yen

5Interest on reserves
Interest on JGBs
Interest on short−term assets
Pre−tax profit

2016 2020

2030

2040

2050

Fiscal year
Note: “Interest rate on JGBs” includes the amortization of the discount under the amortizedcost method in each year.

32

0
−20
−40

Trillion yen

20

40

Figure 4: BoJ’s net assets in the benchmark scenario

2016 2020

2030

2040
Fiscal year

33

2050

300
200
0

100

Trillion yen in present value

400

500

Figure 5: BoJ’s net worth in the benchmark scenario

2016 2020

2030

2040

2050

Fiscal year
Notes: The BoJ’s net worth is the sum of net assets recorded on the Bank of Japan Accounts
and the present discounted value of future pretax profit, including losses. The discount rate for
future pretax profit is the short-term nominal interest rate.

34

500

Figure 6: BoJ’s balance sheet when QQE lasts until 2018

200
100

Fiscal year

35

2050

2040

2030

2020

2018

0

Trillion yen

300

400

Reserves
JGBs
Net Short−term assets
Cash

10

Figure 7: Sensitivity of BoJ’s pretax profit to the duration of QQE

0

2050

2040

2030

2020

2018

2016

−10

−5

Trillion yen

5tau = 2016
tau = 2018

Fiscal year
Notes: The solid line is the benchmark; the dotted line is where the BoJ achieves the inflation
target in 2018.

36

Figure 8: Banknote demand based on the pre-2004 cointegration relationship
Fittedvaluebasedonthe1959Ͳ2003realbanknotedemandfunction

Data

90
80
70

Trillionyen

60
50
40
30
20
10
0

Fiscalyear

Notes: Shown until 2013 due to the availability of GDP data. “The fitted value” is derived fromthe estimation of (19). The fitted value after 2013 is the benchmark scenario for the short-term
nominal interest rate and the real GDP growth rate.

37

Figure 9: Ratio of 10,000 and 1,000 yen notes in circulation(10000Ͳyennotesincirculation)/(1000Ͳyennotesincirculation)(leftaxis)
Uncollaterizedcallrate(rightaxis)
9

22

8

20

7
18

6
5

14

4

%

16

3

12

2
10

1
0

8
1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013
Fiscalyear

38

Figure 10: 10,000 yen notes in circulation and transaction demand for 10,000 yen notes
10000Ͳyennotesincirculation

Transactiondemandfor10000Ͳyennotes

90
80
70

Trillionyen

60
50
40
30
20
10
0
1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014
Fiscalyear

Note: “Transaction demand for 10000 yen notes” is the hypothetical balance of 10,000 yen
notes that grows at the same rate as 1,000 yen notes in circulation from 1995.

39

10

Figure 11: Sensitivity of BoJ’s pretax profit to interest rate elasticity of banknote demand

0
−10

−5

Trillion yen

5BenchmarkNo interest−rate elasticity
Return of the 1959−2003 banknote demand function
Disappearance of cash stash

2016 2020

2030

2040

2050

Fiscal year
Notes: The black line is the benchmark; the red line is where the banknotes-to-GDP ratio(µt ) remains the same before and after the exit from QQE; the green line is where the realbanknote demand takes its pre-2004 form after the exit from QQE; and the blue line is where
the nontransaction demand for 10,000 yen banknotes disappears immediately after the BoJ
raises the short-term interest rate after the exit from QQE.

40

40

Figure 12: Sensitivity of BoJ’s net assets to the interest rate elasticity of banknote demand

0
−40

−20

Trillion yen

20

BenchmarkNo interest−rate elasticity
Return of the 1959−2003 banknote demand function
Disappearance of cash stash

2016 2020

2030

2040

2050

Fiscal year
Notes: The black line is the benchmark; the red line is where the banknotes-to-GDP ratio(µt ) remains the same before and after the exit from QQE; the green line is where the realbanknote demand takes its pre-2004 form after the exit from QQE; and the blue line is where
the nontransaction demand for 10,000 yen banknotes disappears immediately after the BoJ
raises the short-term interest rate after the exit from QQE.

41

Figure 13: Term spread in Japan
Uncollateralizedcallrate

10ͲyearJGByield

1.6
1.4
1.2

%

1
0.8
0.6
0.4
0.2
0
2010/01

2011/01

2012/01

2013/0142

2014/01

2015/01

500

Figure 14: BoJ’s balance sheet when new purchases of JGBs are gradually decreased overthe 10 years after the exit from QQE

200
0

100

Trillion yen

300

400

Reserves
JGBs
Net Short−term assets
Cash2016 2020

2030

2040

2050

Fiscal year
Note: The amount of new purchases of JGBs each year after the exit from QQE is linearly
reduced so that it becomes zero after 10 years.

43

10

Figure 15: Sensitivity of BoJ’s pretax profit to the adjustment period for the new purchasesof JGBs after the exit from QQE

0
−10

−5

Trillion yen

5BenchmarkAdjustment period = 10 yrs
Adjustment period = 20 yrs

2016 2020

2030

2040

2050

Fiscal year
Note: The amount of new purchases of JGBs each year after the exit from QQE is linearly
reduced so that it becomes zero after the adjustment period.

44

Short−term nominal interest rateLong−term nominal interest rate (benchmark)Long−term nominal interest rate (adjustment period = 10 years)
Long−term nominal interest rate (adjustment period = 20 years)

0.03
0.02
0.00

0.01

Trillion yen

0.04

0.05

Figure 16: The path of the long-term nominal interest rate with the adjustment of newpurchases of JGBs after the exit from QQE

2016 2020

2030

2040

2050

Fiscal year
Note: The amount of new purchases of JGBs each year after the exit from QQE is linearly
reduced so that it becomes zero after the adjustment period.

45

40

Figure 17: Sensitivity of BoJ’s net assets to the adjustment period for the new purchases of
JGBs after the exit from QQE

0
−40

−20

Trillion yen

20

BenchmarkAdjustment period = 10 yrs
Adjustment period = 20 yrs

2016 2020

2030

2040

2050

Fiscal year
Note: The amount of new purchases of JGBs each year after the exit from QQE is linearly
reduced so that it becomes zero after the adjustment period.

46

10

Figure 18: Sensitivity of BoJ’s pretax profit to the safety channel for the long-term nominalinterest rate

0
−10

−5

Trillion yen

5With the safety channel
Without the safety channel

2016 2020

2030

2040

2050

Fiscal year
Note: For both cases, the amount of new purchases of JGBs each year after the exit from QQE
is linearly reduced so that it becomes zero 10 years after the exit from QQE.

47

40

Figure 19: Sensitivity of BoJ’s net assets to the safety channel for the long-term nominalinterest rate

0
−40

−20

Trillion yen

20With the safety channel
Without the safety channel

2016 2020

2030

2040

2050

Fiscal year
Note: For both cases, the amount of new purchases of JGBs each year after the exit from QQE
is linearly reduced so that it becomes zero 10 years after the exit from QQE.

48

0.05

Figure 20: The path of the long-term nominal interest rate with and without the safety
channel

0.00

0.01

0.02

0.03

0.04

With the safety channel
Without the safety channel

2016 2020

2030

2040

2050

Note: For both cases, the amount of new purchases of JGBs each year after the exit from QQE
is linearly interpolated so that it becomes zero after 10 years.

49