Discussion Papers In Economics
And Business

The Effectiveness of the Negative Interest Rate Policy
in Japan: An Early Assessment

Yuzo Honda and Hitoshi Inoue

Discussion Paper 17-02

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Effectiveness of the Negative Interest Rate Policy
in Japan: An Early Assessment

Yuzo Honda and Hitoshi Inoue

Discussion Paper 17-02
March 2017

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Effectiveness of the Negative Interest Rate Policy
in Japan: An Early Assessment*
Yuzo Honda† and Hitoshi Inoue‡

Abstract
This paper examines the effects of the negative interest rate policy (NIRP) introduced by
the Bank of Japan in January 2016. It has effectively stimulated private residential
investment, and in lowering long-term interest rates, it has likely supported private
nonresidential investment. There is also reason to believe that it likely stopped theappreciation of the yen and arrested the downward trend in Japanese stock prices around
August 2016. Overall, we find that the NIRP has had expansionary effects, and therefore
serves as a legitimate policy tool in alleviating Japan’s zero-interest rate lower bound,notwithstanding some potential negative side effects.

Keywords: Negative Interest Rates, Residential/Nonresidential Investment, Foreign
Exchange Rates

JEL Classification Number: E52__________________________* We are grateful to Shin-ichi Kitasaka, Ryuzo Miyao, and Kazuhiko Nishina for theirhelpful comments on an earlier version of this paper, and for the assistance of YoshikoMatsuo in preparing the manuscript.
†Correspondence: Department of Informatics, Kansai University, 2-1-1, Ryozenji-cho,

Takatsuki-shi, Osaka 569-1095, JAPAN, e-mail: honda@kansai-u.ac.jp‡Faculty of Economics, Sapporo Gakuin University, 11-banchi Bunkyodai, Ebetsu, Hokkaido,069-8555, JAPAN, e-mail: inoue12@sgu.ac.jp

The Effectiveness of the Negative Interest Rate Policy
in Japan: An Early Assessment
Yuzo Honda and Hitoshi Inoue

1.

Introduction

Over the period starting in June 2015 until June 2016, the nominal effective exchange
rate of the Japanese yen appreciated by 19.4%, largely because of exogenous negative
shocks from abroad, and many other Japanese macroeconomic indicators deteriorated,
including the rate of inflation. In response to this weakening of the economy, the Bankof Japan (BOJ) decided to adopt a negative interest rate policy (NIRP) in January 2016,
following the example set by the European Central Bank (ECB) and three other
European central banks.1 Since then, the BOJ has started charging private financial
institutions a fee of 0.1% on the portion of their reserves kept with it.
As it has only been about a year since the BOJ introduced the policy, it is still too
early to draw any firm conclusions on the effectiveness of NIRP given the small sample
size of the necessary data. However, this does not lessen in any way the urgent need on
the policy side to evaluate the effectiveness of this important policy tool.
Problematically, the NIRP is an unprecedented macroeconomic policy with little
supporting economic theory or empirical evidence. The purpose of this paper is topreliminarily report on the effects of the NIRP, as recently introduced by the BOJ, on
the Japanese economy, and to discuss any policy implications.
1Our tentative conclusion is that the NIRP overall has empirically observable
expansionary effects. It therefore serves as a legitimate policy tool in alleviating zerointerest rate lower bounds, notwithstanding potential negative side effects. The
remainder of the paper is organized as follows. Section 2 presents a simple analytic
model to consider the effects of the NIRP, comprising a four-asset model based on
Tobin (1969), Yabushita (2009), and Honda (2014). Section 3 discusses some
limitations of this model, and Section 4 provides some empirical evidence on the effectsof the NIRP on the Japanese economy. In Section 5, we provide an interpretation of thestatistical facts and discuss some policy implications. The Appendix includes details ofsome of the mathematical results presented in Section 2.

2.

A Simple Analytic ModelIn this section, we first explain a simple analytic model in which banks act exogenously
and serve as “mechanical tunnels” to transmit monetary policy shocks from themonetary authorities to financial market variables. The assumption of a mechanicaltunnel is purely for analytic convenience, and is not the case in reality. We relax thisassumption and discuss its implications in Section 3.
2.1 Four-Asset Model
We assume the economy comprises four sectors: a private sector, a foreign sector, agovernment, and a central bank. The private sector includes both financial andnonfinancial institutions. For analytical purposes, we regard the income accountvariables as exogenous in determining portfolio choice behavior, and find the market
equilibrium for the stock of assets conditional upon the assumed values of output,2

income, and the remaining flow variables. We also assume prices remain constant andequal the numeraire of one throughout the period. This strategy is identical to that
employed when constructing the well-known liquidity preference/money supply
equilibrium (LM) curve in macroeconomics. The key behavioral assumption here is thatspending and portfolio decisions are independent.
Extending the models in Tobin (1969), Yabushita (2009) and Honda (2014), we
consider a model with four assets, namely, money, bonds, stocks and foreign assets.
2.2 Demand for Assets
The respective demands for money (M), bonds (B), stocks (V), and foreign assets (F)depend on their relative asset yields, gross domestic product (GDP) (Y), and the given
wealth (WS):Money:

M = M(c, i, r, z, Y,WS)

Bonds:

B = B(c, i, r, z, Y,WS)

Stocks:V = V(c, i, r, z, Y,WS)

Foreign assets: F = F(c, i, r, z, Y, WS).

(1)

Money in this model is central bank money, or currency plus private bank demand
deposits held at the central bank. In this model, we assume that the central bank pays
interest (c) on reserves (or money).2 Variable c is exogenous, and its domain extends
from minus to plus infinity. When negative, c is the nominal carrying cost of reserves.
Economic agents then hold money up to some nonpositive point for transaction
purposes, even if its return is negative.
We also assume that bonds, stocks, and foreign assets yield returns of an interest
rate (i), stock returns (r), and foreign asset returns (z), respectively. The domains of3

these variables also extend from minus to plus infinity. The expected rate of return fromholding foreign assets z is then the sum of two components, the interest rate on foreign
bonds and the expected rate of change in the exchange rate E[e/e], where E[*] denotes
the expectation operator. We assume z is exogenous throughout.3
Bank lending is assumed to be a variant of corporate bond lending, and istherefore included in B. For simplicity, we ignore or mechanically treat bank-lending
behavior in this model.4 We also assume that the assets are gross substitutes in standard
microeconomics terminology. That is, the demand for each asset varies directly with its
own rate of return and inversely with all other rates of return. The own-derivatives of
the respective demand functions(M/c, B/i, V/r, F/z),
are then positive, and the cross-derivatives nonpositive.
The total demand for the four assets sums to the total demand for wealth ineconomy W:
W = M(c, i, r, z, Y, WS) + B(c, i, r, z, Y, WS) + V(c, i, r, z, Y, WS) + F(c, i, r, z, Y, WS). (2)Such that the total demand for assets W is a function of all variables on the right-handside of equation (2).
When any one of the returns, c, i, r, or z, changes, the demand for each asset
reacts, but the sum of the changes in demand for each asset are assumed zero. That is:
Mj+ Bj + Vj+ Fj = 0 for j = 1, 2, 3, 4,(3)

where subscript j denotes the partial derivatives of the demand functions, M, B, V, F,
with respect to j-th argument on the right-hand side of equation (1).
Just as there is a budget constraint in standard microeconomics, we have a balance
sheet constraint. That is, we assume that the total demand for assets W in (2) is equal to4the exogenous total supply of assets WS:
W = WS.
As a result, when exogenous total wealth WS increases, we have the following
balance sheet restriction:
M6 + B6 + V6 + F6 = 1,

(4)

where the subscript denotes the partial derivative with respect to total wealth WS, andthe 6-th argument in the respective functions for M, B, V, and F in equation (1). We also
assume that all four assets are normal goods, such that:
𝑀6 > 0, 𝐵6 > 0, 𝑉6 > 0, 𝑎𝑛𝑑 𝐹6 > 0 .
2.3 Supply of Assets
We assume that the central bank exogenously supplies money stock, MS. Firms provide
the supply of stocks, qKS, where q and KS denote the market value price of one unit ofphysical capital and the stock of physical capital, respectively, or alternatively, the stock
price and the total number of stocks outstanding, respectively.
The government and firms supply bonds, PBBS, where PB and BS denote the market
value of one unit of bonds and the total quantity of bonds outstanding, respectively. We
assume that the respective total quantities of stocks and bonds outstanding in theeconomy, KS and BS, are exogenously given. However, their market prices, q and PB, areendogenously determined through arbitrage, as explained below.
The total supply of foreign assets is given by eFS, where e and FS are the exchange
rate (measured in yen per unit of foreign currency) and the total balance of foreign
assets (measured in foreign currency), respectively. We assume that the quantity offoreign assets outstanding, FS, is exogenously given, but that the exchange rate e is5endogenously determined.
2.4 Inverse Relations between Market Prices and Returns
We assume an inverse relation between the bond price, PB, and the interest rate, i:dPB/di<0.

(5)Similarly, we also assume that an inverse relation also holds for capital stocks:
dq/dr<0,(6)

However, unlike conventional models, we assume that the domains for variables i and r
are from minus to plus infinity.
The rationale behind inequalities (5) and (6) is as follows. Suppose an economic
agent holds one unit of bonds. The agent has two possible choices. One is that he/shesells the bond immediately in the market. In this case, he/she obtains the current market
price of the bond, PB. The other is that he/she holds the bond and expects to earn thestream of fixed income produced by this bond in the future. The current value of the
future stream of fixed income is discounted by the bond market interest rate i. We
assume arbitrage works between these two choices, such there must be an inverse
relation between the bond price PB and the market interest rate i, as in inequality (5).
One simple example is a consol bond with a return of one yen per year, such that themarket value PB =1/i. There is indeed an inverse relation between the price of bonds PB
and the interest rate i in this case.
In a similar manner, suppose an economic agent holds one unit of physical capitalthat produces a real return R (assumed exogenous) each year. Once again, the agent has
two possible choices. One is that he/she sells the physical capital in the market. In thiscase, he/she receives q, the current market price of equity. The other choice is that6

he/she holds the capital permanently and expects to earn a stream of fixed real returns R
in the future. We then discount the current value of the future stream of fixed real
returns by the rate of return on capital stocks r, where r is the rate of return on stocks
required for market investors to hold capital stocks in their portfolios. Assuming
arbitrage between the two choices, we have an equation q=R/r. Hence, we have an
inequality (6).
We assume the reproduction cost of one unit of physical capital is one, andremains constant throughout this analysis. Hence, stock prices q in our model also
represent Tobin’s q, which is the ratio of the market value of capital to its reproduction
cost.
2.5 Market Equilibrium
The following four equations give the market equilibrium conditions:
MS = M(c, i, r, z, Y, WS),

(7)

PBBS= B(c, i, r, z, Y, WS),

(8)

qKS = V(c, i, r, z, Y, WS),

(9)eFS= F(c, i, r, z, Y, WS),

(10)

with all but one of these conditions automatically satisfied when the other three are met
because of the balance sheet constraint:
MS+ PBBS + qKS + eFS= WS = W,

(11)

where WS denotes the total supply of wealth. Therefore, we only have to consider any
three of the above four equations; we choose equations (7), (8), and (10). The three
endogenous variables are the interest rate i, returns on capital stocks r, and the foreignexchange rate e. Variables PB, q, and WS are also endogenous because of conditions (5),7

(6), and (11), respectively. The remaining variables in the system, (7) through (10), areexogenous.
Substituting equation (11) into equations (7), (8), and (10), we have:
MS = M(c, i*, r*, z, Y, MS + PB(i*)BS + q(r*)KS + e*FS),(12)

PB(i*)BS = B(c, i*, r*, z, Y, MS + PB(i*)BS + q(r*)KS + e*FS),(13)

e*FS = F(c, i*, r*, z, Y, MS + PB(i*)BS + q(r*)KS + e*FS),(14)

where superscript * indicates the equilibrium value.
2.6 The Effects of an Increase in Interest on Reserves c
We interpret a reserve carrying cost increase as a decrease in the interest on reserves c
across its negative domain. Hence, we are interested in the effects of an exogenous
decrease in interest on reserves c on the equilibrium endogenous variables (i*, r*, e*).
Assuming a smooth differentiable function of our system of equations, weinvestigated the comparative statics of an exogenous increase in interest on reserves c.
The appendix shows that an increase in the interest on reserves raises the interest rate,
di*/dc>0, increases the required rate of returns from stocks, dr*/dc>0, and appreciates
the value of the domestic currency, de*/dc<0.
Lowering the negative interest rate on reserves further into a more negative range
by the central bank then leads to lower interest rates on bonds. It also reduces therequired rate of returns from stocks and depreciates the value of the domestic currency.
However, these conclusions are subject to important qualifications, which are discussed
in the following section.

3.

Limitations of the Overly Simplified Model83.1 Exogenous Financial Sector
In the above overly simplified model, private banks play no role in the transmission
mechanism of monetary policy shocks. Instead, they are exogenous and mechanicalactors. In reality, this is not the case as a decrease in the interest on reserves removes net
profits from banks, which will react to this exogenous negative shock.
First, with reduced profits, banks may become more cautious in taking risks andthus less willing to make loans to their customers. The magnitude of the loss of theirprofits, due to the central bank’s policy change, could be large. Indeed, there is thepossibility that the incentive of private banks to avoid taking risks in making loans
could overwhelm the expansionary monetary policy intent of the central bank. In thatcase, lowering the already negative interest rate on reserves further would not increase,
but rather decrease private bank lending, contrary to the central bank’s intention.
Second, if private banks attempt to avoid any reduction in their net profits, they
will pass their losses on to depositors, and charge larger fees on deposits. Depositors
would then cease depositing their cash into banks and instead hoard any surplus cash.
This sort of disintermediation is likely to cause significant troubles in real terms in theeconomy, and would avoided at all costs by the monetary authorities.5
3.2 Expectations
Variables in financial markets are forward-looking, and expectations play an importantrole in the real world. However, for simplicity, our model ignores the role ofexpectations. When expectations change, they could shift the demand for assets in theequations in (1). Strictly speaking, when we then wish to analyze the effects of a9negative interest policy, we should specify the demands for money M, bonds B, stocks
V, and foreign assets F as:
M = M(c, i, r, z, Y, WS, M(c)),
B = B(c, i, r, z, Y, WS, B(c)),
V = V(c, i, r, z, Y, WS, V(c)),
F = F(c, i, r, z, Y, WS, F(c)),(15)

instead of the corresponding equations in (1), where M(c), B(c), V(c), and F(c)denote the impacts of an increase of interest on reserves on the demands for money,
bonds, stocks, and foreign assets, respectively, through changes in expectations amongmarket participants. In such a complicated model with expectations, our standard
results, di*/dc>0, dr*/dc>0, and de*/dc<0, may no longer hold.
Our simple model with no expectations certainly has some limitations for realworld analysis. It is certainly desirable to extend our model and to incorporate
expectations formally. However, this is beyond the scope of the current paper, andremains an open question.

4.

Some Tentative Empirical Evidence

Given the small passage of time since the introduction of the NIRP by the BOJ in
January 2016, little data have been accumulated. However, in this section, we attempt toprovide some tentative empirical evidence on the effects of the NIRP using the available
data.
4.1. Immediate Impact on Asset Markets
Figure 1 depicts the immediate impact of the NIRP on the stock market. There are three10possible types of reaction, being favorable to the market, unfavorable, or mixed.

<FIGURE 1 ABOUT HERE>

Panels (a) and (b) plot the stock market price indexes for the banking andinsurance industries, respectively, relative to the Nikkei Average Stock Price. We
standardize all indexes to one as of January 28, 2016 to correspond with the time the
BOJ announced the NIRP. In anticipation of a more severe market environment, thestock indexes for both the banking and insurance industries dropped sharply relative to
the Nikkei Average.
By contrast, the real estate industry received news of the NIRP more favorably.
Panels (c) and (d) plot the stock market price index of the real estate industry and JapanReal Estate Investment Trust (J-REIT) index, respectively. As shown, the plots of thestock market prices of both real estate-related industries lie above the Nikkei Average.
Panels (e) and (f) depict the reactions of the indexes of securities and commodity
futures, and other financial services (such as leasing), respectively. In these industries, itappears the news was favorable at first, but then a more negative change was seen in
response.
4.2. Effects on Financial Variables
4.2.1. Market Interest Rates
The BOJ announced the NIRP in January 2016, and it came into effect in February thatsame year. Figure 2 illustrates that both short- (1-month LIBOR; solid line) and longterm (10-year government bonds; dashed line) interest rates fell sharply (some 50 basis
11points for 10-year government bonds) and became negative as soon as the NIRP wasannounced. Subsequently, the long-term interest rate quickly increased to about zero
percent and remained there until September 2016 when the BOJ began to use the longterm interest rate as an operating target and set it to zero percent.

<FIGURE 2 ABOUT HERE><FIGURE 3 ABOUT HERE>

4.2.2. Foreign Exchange Rates
Figure 3 depicts the movements of the nominal effective yen exchange rate using a 26country index (2010 = 100). Largely because of exogenous shocks outside Japan, theyen’s effective exchange rate appreciated by 19.4% from June 2015 to June 2016. Thisappreciation weakened the competiveness of Japanese firms, and the macro indicatorsfor core machinery, retail sales, and production deteriorated over this period. Concerned
about the possibility that the slowdown in spending might lower prices, the BOJ
decided to increase the purchase of exchange-traded funds (ETFs) at its July 2016
meeting. Although we will need to wait until more data is available to confirm whether
this was because of the expansionary monetary policy conducted in July 2016 and/or the
implementation of the NIRP since January 2016, the appreciating trend in the yen,evident since June 2015, finally halted around August 2016, as shown in Figure 3.
After August 2016, the yen’s effective exchange rate began to depreciate. There
are two possible reasons for this. First, with Donald Trump being elected as the new
U.S. president in November 2016, his expected expansionary fiscal policy stance seems
to have contributed to a surge in the value of the U.S. dollar. Second, in December
122016, the U.S. Federal Reserve raised the operating target of the federal funds rate to arange of 0.5% to 0.75%, which also contributed to the U.S. dollar appreciation evident
as at February 2017. Looking at the movements of the nominal effective exchange rateof the euro, we can discern a similar depreciation in the euro relative to the U.S. dollar
over the same period, and this may reconfirm our speculation concerning the reasons forthe depreciating yen.

4.2.3. Stock Prices
Figure 4 provides a graph of the Tokyo Stock Price Index (TOPIX), showing that it
moved closely with the nominal effective foreign exchange rate after 2015. The TOPIX
stopped falling in mid-2016, and rose sharply after November 2016. Again, we await
rigorous analysis to determine whether the NIRP truly contributed to the turnaround ofstock prices in the middle of 2016, as for the effective foreign exchange rate.

<FIGURE 4 ABOUT HERE>

4.3. Effects on Real Variables
4.3.1. Production
In this subsection, we observe the movements of real variables and examine theircorrelation with the NIRP. Figure 5 plots the index of industrial production (IIP). As
shown, the IIP displays a close correlation with movement in the financial variables,
including the effective exchange rate and stock prices. For the most part, the IIP has
declined throughout 2015, but turned around and began to climb toward the middle of13

2016. Around November 2016, there was a further surge in production.

<FIGURE 5 ABOUT HERE>

4.3.2. Residential Investment
Table 1 is the official statement by the Japanese government on preliminary estimates(released February 13, 2017) on seasonally adjusted real GDP for the second (April–June) and third (July–September) quarters of 2016, respectively.

<TABLE 1 ABOUT HERE>As shown in the first and third columns of Table 1, private residential investment
grew by 3.3% and 2.4% over the quarter (percent change from previous quarter),respectively.6 The values in parentheses for private residential investment shown in thesecond and fourth columns in Table 1 are both about 0.1, suggesting that this increase in
private residential investment increased GDP growth by 0.1% per quarter (about 0.4%
annually). These jumps in private residential investment clearly coincided with the
NIRP.

4.3.3. Nonresidential Investment
Despite the sharp appreciation of the yen, nonresidential investment grew by +1.3% in
the second quarter (the first column in Table 1). The growth rate is negative in the third
quarter (-0.3% in the third column of Table1), but relatively small in magnitude, likely
owing to the substantial reduction in the long-term interest rate under the NIRP. Indeed,
14the Ministry of Finance’s “Financial Statements Statistics of Corporations by Industry(April–June, 2016)” reports that the growth rate of fixed investment over the previous
quarter was a respectable +3.1%, seemingly despite a 3.5% fall in sales and a 10.0%
decline in earnings in the second quarter of 2016.7 We conjecture that the lower longterm interest rate associated with the NIRP supported private fixed investment.

4.3.4. Exports
The growth rate in exports of goods and services in the second quarter of 2016 (the firstcolumn in Table 1) was as weak as –1.2% because of the sharp appreciation in the yen.
Around August 2016, the yen appreciation halted, and the growth of exports of goods
and services improved to +2.1% in the third quarter (the third column in Table 1).

5.

Some Interpretation and Policy Implications

This final section summarizes our main findings, provides an interpretation, anddiscusses their policy implications. First, although as small as –0.1% in magnitude, theintroduction of the NIRP in January 2016 substantiality increased residential investment
and thereby supported the growth of the overall Japanese economy. Second, theintroduction of the NIRP lowered the long-term interest rate by roughly 50 basis points,
which likely supported private nonresidential investment.
Third, there are at least two reasons to believe that NIRP likely stopped theappreciating trend in the yen around August 2016. The first is some statistical evidenceby Honda and Inoue (2015). Using Granger causality tests and impulse response
analysis, they showed that differences in U.S. and Japanese bond yields havesignificantly affected, with some lag, the yen–dollar exchange rate over the last 30
15

years. Given that the NIRP substantially lowered both long- and short-term interest rates
in Japan, the NIRP must have widened the spread in yields, pushing the exchange rate
toward a yen depreciation.
The second reason more directly relates to the introduction of the NIRP in January
2016. Figure 6 plots the flow of funds accounts for foreign securities in the insurance
and pension funds sector over the period 2011 to 2016. Clearly, there is a large increasein the first quarter of 2016, immediately after the introduction on NIRP. The average ofthe 20 data points available for the period from the first quarter of 2011 to the fourth
quarter of 2015 is 56.8 billion yen, while that for the last three data points is 4,838.3
billion yen. The difference of –4,781.5 billion yen is significantly different from zero atthe 1%, level, thereby supporting the argument that the NIRP involved significant
portfolio rebalancing effects.8 Facing lower yields on domestic securities, the insurance
and pension funds sector increased its purchase of foreign securities, and in purchasing
foreign assets, they must have bought U.S. dollars and raised the price of the dollar
against the yen.9<FIGURE 6 ABOUT HERE>

Given this, we surmise that it was indeed the NIRP that increased the yield margin
between U.S. and Japanese securities and arrested the rapidly appreciating yen in
August 2016. As Hamada et al. (2010, pp. 30–40) correctly argue, changes in exchange
rates have a great impact on the Japanese real economy. This holds in the present case as
well. If there were no NIRP in January 2016, the growth of the Japanese economy
would probably have been much weaker in the second quarter of 2016.
16

Fourth, NIRP was also likely to have contributed to slowing the downward trend
in stock prices around August 2016. As demonstrated in our analytic model in Section 2,
a NIRP has expansionary effects on stock prices, and these combined with real estate
stimulate the real sector through various channels.
Overall, we found the NIRP has had significant expansionary effects on theJapanese economy.10 It is therefore a legitimate policy tool for alleviating Japan’s zerointerest rate lower bound, notwithstanding the potential negative side effects discussed
earlier.
Finally, using the four-asset model, Honda (2014) showed that an increase incentral bank money has expansionary policy effects. The present paper demonstrates
that a decrease in the interest rate on reserves has the same qualitative effects as anincrease in central bank money. As these comparative statics results are independent, it
implies that each policy tool has independent policy effects.

17Appendix: Effects of an exogenous increase in the interest on reserves c
𝑑𝑖 ∗

𝑑𝑟 ∗

𝑑𝑒 ∗

This appendix provides the basis for the three inequalities, 𝑑𝑐 > 0, 𝑑𝑐 > 0, 𝑎𝑛𝑑 𝑑𝑐 <0, asserted in Subsection 2.6. There are three endogenous variables, (i*, r*, e*), andthree equations in (12), (13), and (14). Differentiating equations (12), (13), and (14)with respect to c, we have:M1− [ 𝐵1 ]F1M2 + M6 BS (dP B /di)
= [B2 − (1 − B6 )BS (dP B /di)F2 + F6 BS (dP B /di)M3 + M6 𝐾 𝑆 (dq/dr)
B3 + B6 𝐾 𝑆 (dq/dr)
F3 + F6 𝐾 𝑆 (dq/dr)

M6 F S(di∗ /dc)
B6 F S ] [(dr ∗ /dc)] , (A1)
(F6 − 1)F S (de∗ /dc)

where Mj, Bj, Vj, and Fj (j = 1, 2, 3, 4, 5, 6) denote the partial derivatives of demand formoney M, bonds B, stocks V, and foreign assets F, with respect to the j-th argument in(1), respectively. Solving this system of equations, we obtain:di∗dc= −F S [𝐹3 (𝑀6 𝐵1 − 𝑀1 𝐵6 ) + 𝑀3 {𝐵1 (1 − 𝐹6 ) + 𝐵6 𝐹1 } + 𝐵3 {𝑀1 (𝐹6 − 1) − 𝑀6 𝐹1 } +(𝑀6 𝐵1 − 𝑀1 𝐵6 )𝐾 𝑆 (dq/dr)]/∆,

(A2)

dr ∗
=
dc
−𝐹 𝑆 [𝑀1 𝐵2 (1 − 𝐹6 ) + 𝑀1 𝐵6 𝐹2 − 𝑀2 𝐵1 (1 − 𝐹6 ) − 𝑀6 𝐵1 𝐹2 − 𝑀2 𝐵6 𝐹1 + 𝑀6 𝐵2 𝐹1 −
{𝑀1 (1 − 𝐵6 − 𝐹6 ) +𝑀6 𝐵1 +
𝑀6 𝐹1 }𝐵 𝑆 (dpB /di)]/
∆,
18

(A3)

de∗
dc

= −[𝑀1 (𝐵2 𝐹3 − 𝐵3 𝐹2 ) + 𝐵1 (M3 𝐹2 − M2 𝐹3 ) + 𝐹1 (𝑀2 𝐵3 − 𝑀3 𝐵2 ) +{𝑀1 (𝐵6 𝐹3 − 𝐹3 − 𝐵3 𝐹6 ) + 𝐵1 (𝑀3 𝐹6 − 𝑀6 𝐹3 ) + 𝐹1 (𝑀6 𝐵3 + 𝑀3 − 𝑀3 𝐵6 )}BS (dpB /di) + {𝑀1 (𝐵2 𝐹6 − 𝐵6 𝐹2 ) + 𝐵1 (𝑀6 𝐹2 − 𝑀2 𝐹6 ) + 𝐹1 (𝑀2 𝐵6 − 𝑀6 𝐵2 )}𝐾 𝑆 (dq/dr) +(𝑀6 𝐹1 − 𝐹6 𝑀1 )BS 𝐾 𝑆 (dpB /di)(dq/dr)]/∆,(A4)

where  denotes the determinant of the (33) matrix on the right-hand side of equation(A1), and is given by:∆ = F S [M2 {B3 (F6 − 1) − B6 F3 } + M3 {B6 F2 + B2 (1 − F6 )} + M6 (B2 F3 − B3 F2 )− 𝑀6 (𝐵3 + 𝐹3

)BS

dpB
𝑑𝑝𝐵
𝑆
(
) + 𝑀3 (𝐹6 + 𝐵6 − 1)𝐵 ()
di𝑑𝑖+ (M6 𝐵2 − 𝑀2 𝐵6 )𝐾 𝑆 (dq/dr) − M6 BS 𝐾 𝑆 (dpB /di)(dq/dr)] .

(A5)First, making use of equations (3) and (4), and the assumption of gross substitutes
between the demands for assets, we can show each of the seven terms on the right-handside of equation (A5) is negative. Hence, ∆ is negative. Second, we can show that eachof the four terms in the numerator on the right-hand side of equation (A2) is also
𝑑𝑖 ∗negative. Therefore, we obtain inequality 𝑑𝑐 > 0.
Third, we can also show that the sum of the first six terms in the square brackets
on the right-hand side of equation (A3) is positive, the sum of the three terms in the
curly brackets on the right-hand side of equation (A3) is also positive, and thus thenumerator of the right-hand side of equation (A3) is negative. Therefore, we have
19

𝑑𝑟 ∗

inequality 𝑑𝑐 > 0.
Finally, the sum of the first three terms in the square brackets on the right-handside of equation (A4) is negative, the sum of the next three terms in the curly brackets
on the right-hand side of equation (A4) is positive, the sum of the three terms in the
curly brackets in front of 𝐾 𝑆 (dq/dr) on the right-hand side of equation (A4) is also
positive, and (𝑀6 𝐹1 − 𝐹6 𝑀1 ) is negative. Therefore, we have inequality

20

de∗
dc

< 0.

Footnotes
1. The BOJ also took additional expansionary monetary policy measures toincrease the purchase of ETFs at its July 2016 meeting.
2. We take c to be a weighted average of the interest payments on reserves at thecentral bank and the return on the currency, which is zero.
3. This assumption is composed of two parts. The first is that the interest rate on
foreign bonds is exogenous to investors. The second is that the expected rate ofchange in the exchange rate remains the same, or E[e/e] is constant, throughout
the period. Alternatively, the time horizon in our model is the period over which
the expected rate of change in the exchange rate is unchanged. Also, note thatthe condition, E[e/e] is constant, is equivalent to the assumption that theelasticity of the expected exchange rate at the end of the period with respect to𝑑𝑒̂the current exchange rate is one, or (𝑑𝑒 )(e/𝑒̂ ) =1, where 𝑒̂ denotes the expectedexchange rate at the end of the period.
4. This is one of the limitations of the present model. It remains an open question
to incorporate private bank behavior into our model as an endogenous variable.
5. There are at least three ways of eliminating or alleviating these side effects.
First, facing the introduction of fees on deposits, depositors may reduce theamount of deposits, but may instead increase their risky investments in theirportfolio choices, and stimulate the real economy. Second, under lower interest
rate environments, some banks with relatively strong balance sheet positions
might aggressively offer lower lending rates to gain new customers, even if they
incur certain losses in the short run. Third, new financial agents might emerge
and enter these financial markets. These include new nonbank and/or foreign
financial firms that do not currently exist in Japanese financial markets.
6. Multiplied by four, these provide rough estimates of the annual growth rates.
7. Financial Statements Statistics of Corporations by Industry (April–June, 2016)
from the Ministry of Finance covers only large corporations with capital
exceeding 10 million yen.
8. This statistical result is robust to changes in the sample size. Varying the size ofthe first sample from three to 20 does not alter the result of the rejection of thenull hypothesis of equal means at the 1% significance level.
9. There is a conundrum concerning the interpretation of the statistical data in theflow of funds accounts for the insurance and pension funds sector. While weobserve a distinct difference in the mean between before and after the
introduction of the NIPR in January 2016 in the BOJ flow accounts data, as
shown in Figure 6, there is a much less marked difference in the corresponding
stock accounts data. To solve this little mystery, recall that there was a sharp
depreciation in the USD against the JPY over the period from June 2015 until
August 2016. With the USD depreciation, the value of dollar assets in the stock
accounts fell, and this obscured the increase in the flow of foreign securities inthe data.
10. See also Honda (2017) for a similar discussion of the effects of the NIPR in theEuro area.
21

References
Hamada, K., M. Wakatabe, and K. Katsuma. 2010. Learn from the Legend Professor.
Tokyo: Toyokeizai Shinposha (in Japanese).
Honda, Y. 2014. “The Effectiveness of Nontraditional Monetary Policy: The Case ofJapan.” Japanese Economic Review 65 (1): 1–23.
Honda, Y. 2017. “On the Effects of a Negative Interest Rate Policy.” Review ofMonetary and Financial Studies, forthcoming (in Japanese).
Honda, Y., and H. Inoue. 2015, “Three Alternative Hypotheses on the Yen-Dollar
Exchange Rate over the Last Thirty Years.” Discussion Papers in Economics andBusiness, No. 15-15, Graduate School of Economics and Osaka School ofInternational Public Policy, Osaka University.
Tobin, J. 1969. “A General Equilibrium Approach to Monetary Theory”, Journal of
Money, Credit and Banking 1 (1): 15–29.
Yabushita, S. 2009. Monetary Economics. Kyoto: Minerva (in Japanese).

22

Table 1: Real GDP Growth Rate and Its Components
2016Q2

2016Q3

0.4

0.3

GDP
Private Consumption

0.2

(0.1)

0.3

(0.2)

Private Residential Investment

3.3

(0.1)

2.4

(0.1)

Private Non-Resi. Investment

1.3

(0.2)

-0.3

(-0.1)

Government Consumption-1.1(-0.2)

0.3(0.0)

Public Investment

1.1

(0.1)

-0.7

(-0.0)

Exports of Goods and Services-1.2(-0.2)

2.1(0.4)

Imports of Goods and Services

-1.0

(0.2)

-0.2

(0.0)

Notes: Data source is seasonally-adjusted quarterly series (percent changes from theprevious quarter) released at February 13, 2017 by the Cabinet Office,
Government of Japan. The figures in parentheses indicate contributions tochanges in GDP.

23

Figure 1: Impact of NIRP on the Stock Market

Notes: All indexes are standardized to one as of January 28, 2016 to correspond withthe time the BOJ announced the NIRP. Dashed lines in all panels denote the
Nikkei Stock Average.

24

Figure 2: Short-term and Long-term Interest Rates

Notes: Solid line denotes the short-term interest rate (one-month LIBOR based onJapanese Yen) and dashed line denotes long-term interest rate (10-year Japanese
government bond rate).

25

Figure 3: Nominal Effective Yen Exchange Rate

Notes: Data source is monthly series, which is standardized to 100 at 2010, released on
the web site of the Bank of Japan. The higher value means the more appreciatedthe currency.

26

Figure 4: Tokyo Stock Price Index (TOPIX)

27

Figure 5: Index of Industrial Production

Notes: Data source is seasonally-adjusted monthly series released on the web site of the
Ministry of Economy, Trade and Industry.

28

Figure 6: Flow of Funds of Foreign Securities in the Insurance and Pension Funds
SectorNotes: Data source is “Outward investment in securities” by the “Insurance and pension
funds” sector in the Flow of Funds Accounts compiled by the Bank of Japan.

29