HIAS-E-13

The First Arrow Hitting the Currency Target:
A Long-run Risk Perspective
Takashi Kano
Hitotsubashi University, Tokyo Center for Economic Research, Japan

Kenji Wada
Hitotsubashi University

November 9, 2015

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
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http://hias.ad.hit-u.ac.jp/
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The First Arrow Hitting the Currency Target:
A Long-run Risk Perspective
Takashi Kano†

Kenji Wada‡† Hitotsubashi University, Tokyo Center for Economic Research, Japan‡ Hitotsubashi University

Current Draft: November 9, 2015
Abstract
This paper reconsiders the successful currency outcome of the first arrow of the Abenomics. The
Japanese yen depreciation against the U.S. dollar after the introduction of the first arrow comoves tightly
with long-term yield diﬀerentials between Japan and the United States. The estimated term structureof the sensitivity of the currency return of the Japanese yen to the two-country interest rate diﬀerential
indeed shifts up and becomes steeper after the onset of the Abenomics. To explain this structural change
in the term structure of the Fama regression coeﬃient, we employ a long-run risk model endowed with realand nominal conditional volatilities as in Bansal and Shaliastovich (2013). Under a plausible calibration,
the model replicates the structural change when nominal uncertainty dominates real uncertainty in the
U.S. bond market. We conjecture that the arrow was shot oﬀ from the U.S. side, not the Japan side.
Key Words : Japanese yen/U.S. dollar exchange rate; Term structure; Fama regression; Long-run risk;
Abenomics
JEL Classification Number : E31, E37, F41†

The first author wishes to thank a grant-in-aid for scientific research from the Japan Society for the Promotion of
Science (number 24330060) and financial support from Hitotsubashi Institute for Advanced Study.
†
Contacting address: Graduate School of Economics, Hitotsubashi University, Naka 2-1, Kunitachi-city, Tokyo,186-8601, Japan. Emails: tkano@econ.hit-u.ac.jp (T.Kano), 2112279c@g.hit-u.ac.jp (K.Wada)1. Introduction
One of the most striking events that international financial markets recently encountered
might be the sharp depreciation of the Japanese yen (JPY) against the U.S. dollar (USD) started
at the end of 2012. Since 78.97 JPY/USD was recorded on October 2012, the JPY keeps depreciating
to 123.17 JPY/USD by August 2015. The depreciation rate of the JPY within the two-year window
is 56.0 %. Given the prolonged appreciation of the JPY against the USD after the Lehman shockand the subsequent global financial crisis (GFC), the change in the direction of one of the major
currencies was so drastic that identifying a fundamental source behind the rapid JPY depreciation
is a serious challenge for researchers of exchange rates in both academia and policy circles.
Many insist that the JPY depreciation was a unique direct consequence of the aggressive
monetary easing adopted by the Bank of Japan (BOJ). This view has gotten strong popularity
among academic researchers and market commentators in Japan because the JPY depreciation
just started on November 2012, when most market participants expected a radical change in themonetary policy regime of the BOJ due to a strong political pressure from an anticipated new
government run by the Liberal Democratic Party (LDP).1 Soon after the then LDP Governor Abe
won the general election of the Lower House of the Diet on December 2012, the “first arrow” — thebold monetary easing by the BOJ for fighting against chronic deflation in Japan — was announced
by new BOJ Governor Kuroda in accordance with Prime Minister Abe under his new economic
policy initiative subsequently known as the“Abenomics.”2 This eﬀect of the first arrow on the JPY
depreciation is frequently cited as a successful outcome of the Abenomics.
In this paper, we develop a new view toward the exchange rate implication of the first arrow.
We start our discussion relying on an empirical finding by Kano and Morita (2015). Kano andMorita observe that the JPY depreciation after the first arrow has no correlation with the 1 and2 year short-term interest rate diﬀerentials between Japan and the United States, rather it goes intandem closely with the 5 and 10 year long-term ones. As reported by Kano and Morita, Figure
1 plots (the minus of) the logarithm of the JPY/USD rate along with the nominal government
bond interest rate diﬀerentials with the 1, 2, 3, 5, 7, and 10 year maturities between Japan andthe United States since January 2012. Notice that after the first arrow shot oﬀ on November 2012
the interest rate diﬀerentials of the Japanese Government Bond (JGB) and the U.S. Treasury Bill(USTB) sharply falls over all maturities. The fall in the two-country interest rate diﬀerential ismore striking with longer maturities of 5, 7, and 10 years than with shorter maturities of 1, 2, and3 years. The JPY spot rate depreciates against the USD along tightly with such sharp falls in thelonger-term interest rate diﬀerentials, not in the shorter-term ones.
1
Ueda (2013) emphasizes a significant role of the enormous political pressure placed on the BOJ in the large asset
price movements in Japan between November 2012 and May 2013.
2
Ueda (2013) provides detailed chronology and typology of the BoJ’s unconventional monetary policy measures.

1

To scrutinize more deeply the data association between the JPY/USD rate and the term
structure of the two-country interest rate diﬀerentials, we conduct simple Fama regression exercises∗
below. Let St denote the JPY/USD spot rate at period t, yt,n the JGB rate to maturity n, yt,nthe
USTB rate to maturity n. We then regress the JPY depreciation rate st+1 − st ≡ log St+1 − log St
on the interest rate diﬀerential to maturity n:∗
st+1 − st = αn + βn (yt,n − yt,n
) + ϵt,n ,(1)where αn is constant, βn is the Fama regression coeﬃcient, and ϵt,n is an i.i.d. error term. We also
estimate an alternative Fama regression specification with the one-period excess currency return∗rxt+1 ≡ st+1 − st + yt,1
− yt,1 as the dependent variable:∗
rxt+1 = αnrx + βnrx (yt,n − yt,n
) + ϵrxt,n ,(2)

where αnrx is constant, βnrx is the Fama coeﬃcient, and ϵrxt,n is an i.i.d. error term. We investigate
the monthly data of the JGB rates, the USTB rates, and the JPY/USD rate spanning the period
between January 2008 and August 2015. We estimate the two specifications using (i) the wholesample, (ii) the first subsample before the Abenomics between January 2008 and November 2012,
and (iii) the second subsample after the Abenomics between December 2012 and August 2015.
Table 1 reports the OLS point estimates of the Fama coeﬃcients to maturity n and thecorresponding standard errors for specification (1) in panel (a) and for specification (2) in panel (b),respectively. The first two raws of panel (a) basically repeat the conventional argument of a randomwalk exchange rate: in the whole sample after the Lehman shock the JPY depreciation rate against
the USD has no statistically significant relation with the two-country interest rate diﬀerential over
all the maturities. The third and fourth raws of the same panel show that this covariance structure
between the currency return and the interest rate diﬀerential is essentially preserved in the firstsub-sample period before the Abenomics, while the slope of the term structure becomes slightly
steep over maturities. The term structure of the Fama regression coeﬃcient, however, drasticallychanges its shape in the second sub-sample period after the onset of the Abenomics. The fifth andsixth raws of panel (a) uncover that (i) the level of the term structure shifts up and (ii) the slope ofthe term structure becomes steeper. In particular, the point estimate of the Fama coeﬃcient to the
10 year maturity is 2.269 at the conventional statistical significance level. The OLS regression of thealternative specification, which is reported in panel (b), conveys the almost same inferences as drawn
in panel (a) except the fact that the negative dependence of the one-period excess currency returnon the interest rate diﬀerentials to the shorter maturities of 1, 2, and 3 years become statisticallysignificant in the first sub-sample period.3
3

Hence, a risk premium explanation for the failure of the uncovered interest parity condition, especially, at the2

Figure 2 confirms the structural change in the term structure of the Fama regression coeﬃcients between the two sub-sample periods graphically. The solid blue line represents the estimatedterm structure of the Fama coeﬃcient in currency return specification (1) in the first sub-sample
period, while the dotted blue line the estimated term structure of the Fama coeﬃcient in excess currency return specification (2). The solid and dotted red lines correspond to the second sub-sample
period after the Abenomics. Confirm that the term structure of the Fama coeﬃcient is almost flatand there is no strong data association between the currency return and the yield diﬀerential before
the Abenomics. In the second sub-sample period, the term structure shits up over all maturities
and its slope becomes steeper enough to make the correlation between the currency return and the
10 year yield diﬀerence a large positive with a statistical significance.
A relevant economic model for the exchange rate eﬀect of the first arrow of the Abenomics,
therefore, needs to explain the above structural change in the term structure of the sensitivityof the currency return to the two-country interest rate diﬀerential. A successful economic model
should have an implication on a relation between a nominal exchange rate and a term structureof two-country nominal bond yield diﬀerential. To accomplish this task, we exploit the long-run
risk (LRR, hereafter) model recently developed by Bansal and Shaliastovich (2013, hereafter BS).
Relying on the Kreps-Porteus, Epstein-Zin recursive preference, the BS model allows persistentcomponents of both the consumption growth rate (real LRR) and the inflation rate (nominal LRR)
with the corresponding conditional volatilities. When nominal LRR aﬀects negatively real LRR, themodel predicts that the sensitivity of a nominal bond yield to nominal long-run uncertainty (i.e.,
conditional volatility attached to the nominal LRR) changes the sign over diﬀerent maturities. In
particular the nominal bond yield loading on nominal uncertainty is negative at shorter maturities,
while it becomes positive at longer maturities because of a rise in an inflation premium. The
covariance between the excess currency return and the yield diﬀerential then tends to be less negative
and, under plausible parameter values, could be positive at longer maturities. In this case, thedepreciation rate is associated positively with the yield diﬀerentials with longer maturities. Hence,a currency with a higher long-term yield tends to depreciate.
Importantly, the model predicts the relative size of real and nominal uncertainty mattersfor the shape and slope of the term structure of the Fama coeﬃcient. Specifically, when nominal
uncertainty dominates real uncertainty, the term structure of the Fama coeﬃcient shifts up andbecomes steeper. Under a plausible calibration of the model following the BS estimates, we showthat the model indeed can replicate fairly well the structural change in the term structure of theFama coeﬃcient observed in the data when we lower the relative size of real uncertainty to nominal
uncertainty. The model, thus, predicts that there should be a change in the component of market
uncertainty in the two countries between the two sub-sample periods.
shorter maturities, is also applicable to our sample.

3

We, then, ask the following question: where did this change in the component of economic
uncertainty occur, in Japan, or the United States or both? We first emphasize the fact that a fallin the long-term interest rate diﬀerential between the two countries after the first arrow is mostly
originated from a rise in the long-term USTB rates but not from a fall of the corresponding JGB
rates. We, thus, confirm that the fall in the long-term interest rate diﬀerential is mainly caused by
the U.S. side but not from the Japan side.4 Using a U.S. 10-year term premium recently estimatedby Adrian et al. (2013), we discuss a high possibility that there was a change in the component ofmarket uncertainty in the United States coincidently around the onset of the Abenomics: before
2012 the U.S. market faced both real and nominal uncertainty, while after 2012 nominal uncertainty
dominates the U.S. bond market. We, therefore, conjecture that the arrow was shot oﬀ from the
U.S. side, not the Japan side.
In the next section, we introduce and explain the BS model in details. Section 3 derives thetheoretical implication of the model for the term structure of the Fama coeﬃcient and reports theresults of our calibration exercise. After discussing our conjecture on the possibility of the U.S.
origin of the first arrow, we conclude in Section 4.

2. A long-run risk approach to the first arrow
2.1. The Bansal and Shaliastovich modelThis paper borrows the LRR model of nominal bond yields and currency returns from BS.
We construct our hypothesis that the sign flipping of the nominal bond yield loading on nominal
uncertainty predicted by the BS model could be a key mechanism to understand the sharp depreciation of JPY against USD after the first arrow. Although the model of this paper is completely
identical with that of BS, we nevertheless introduce the model below for detailed explanation.
Consider two countries in each of which the representative agent lives in nfinite periods. Let
mt+1 and m∗t+1 denote the logarithms of the home and foreign real stochastic discount factors (SDFs)∗
and πt+1 and πt+1
the home and foreign inflation rates. As discussed by Backus et al. (2001), no
arbitrage opportunity under frictionless markets determines the home currency depreciation rate
against the foreign currency, st+1 − st , by the diﬀerence in the nominal SDF between the foreign
and home countries:∗
st+1 − st = m∗t+1 − mt+1 − πt+1
+ πt+1 .
(3)
The real SDF in each country is characterized by the representative agent’s maximizing the4This observation of a negligibly weak response of the long-term JGB rate to the first arrow echoes the findingsof Fujiwara et al.(2015) using a Japanese consensus survey data.

4

Kreps-Porteus, Epstein-Zin recursive preference over consumption
!
" θ
1−γ
1−γ θ1 1−γ
Ut = max (1 − δ)Ct θ + δ(Et Ut+1
)
,
Ct

θ≡

1−γ
,
1 − ψ1subject to the budget constraint
Wt+1 = (Wt − Ct )Rc,t ,where δ ∈ (0, 1) is the subjective discount factor, γ ≥ 1 is the risk aversion parameter, ψ ≥ 0 is theintertemporal elasticity of substitution (IES), and Et is the mathematical conditional expectation
operator, Wt is the wealth of the household, and Rc,t+1 is the gross return on the consumption claim(i.e., the asset delivering aggregate consumption as its dividends).
Let rc,t+1 denote the rate of return of the consumption claim (i.e., the logarithm of the gross
return on the consumption claim). The logarithm of the real SDF implied by the recursive utility
is then derived asθ
mt+1 = θ log δ − ∆ct+1 + (θ − 1)rc,t+1 ,(4)ψwhere ∆ct+1 ≡ log Ct+1 − log Ct is the consumption growth rate.5 Let pct describe the wealthconsumption ratio (or, equivalently, the price-dividend ratio of a claim to the aggregate consumption). As discussed by Bansal and Yaron (2004) and Bansal at al. (2007), the rate of return of theconsumption claim, rc,t+1 , is linearly approximated as
rc,t+1 ≈ κ0 + κ1 pct+1 − pct + ∆ct+1 ,(5)where approximating constants κ0 and κ1 are given as nonlinear functions of the deterministic
steady state level of the wealth-consumtpion ratio, pc,
¯ as
κ1 =

exp(pc)¯,
1 + exp(pc)¯and κ0 = log(exp(pc)¯ + 1) − κ1 pc,¯

where κ1 ∈ (0 1).6
Given real SDF (4), the equilibrium price of any real asset must satisfy the Euler equation
Et exp(mt+1 + rt+1 ) = 1,

(6)where rt+1 ≡ log(Rt+1 ) is the one-period real rate of return. Similarly, the equilibrium price of any
5

The full derivation of the real SDF (4) is provided by, for example, Bansal and Yaron (2004) and Bansal et al.
(2007).
6
Following Bansal et al.(2007), we numerically solve the steady state wealth-consumption ratio pc¯ by a nonlinear
root finding program.

5

nominal asset must satisfy the Euler equation$
Et exp(m$t+1 + rt+1
) = 1,(7)$$
where rt+1
≡ log(Rt+1) is the one-period nominal rate of return and m$t+1 = mt+1 − πt+1 is thenominal SDF.

As specified by BS, we assume that consumption growth rate ∆ct+1 and inflation rate πt+1
follow exogenous stochastic processes including persistent AR(1) components∆ct+1 = µc + xc,t + σc ηc,t+1 ,πt+1 = µπ + xπ,t + σπ ηπ,t+1(8)where µc and µπ are constants, ηc,t+1 and ηπ,t+1 are i.i.d. standard normal temporary shocks
to the consumption growth and inflation rate, and σc and σπ are the standard deviations of theconsumption growth rate and inflation rate temporary shocks, respectively. Random variables xc,tand xπ,t are the persistent components of the consumption growth and inflation rate. These real andnominal LRR components are specified as a first-order vector autoregression (VAR) with stochastic
volatilities. Let xt denote a 2 × 1 random vector including the LRRs as its elements: xt ≡ [xc,t xπ,t ]′ .
Random vector xt follows
xt+1 = Πxt + Σt et+1 ,(9)where Π is the VAR coeﬃcient matrix specified as#$ρc ρcπ
Π=
.
0 ρπ

(10)

Parameters ρc and ρπ , therefore, govern the persistence of the real and nominal LRRs. Parameterρcπ captures the non-neutral eﬀect of expected future inflation on expected future consumption
growth. As in BS, we assume the expected future inflation predicts negatively the expected future
consumption growth. Hence, ρcπ is assumed to be negative.
In eq.(9), 2 × 1 random vector et+1 is i.i.d. standard normal shocks to the real and nominal
LRRs. Conditional volatility matrix Σt is diagonal and time-varying
#

$
σxc,t
0
Σt =
,
0 σxπ,t(11)

where σxc,t and σxπ,t reflect time-varying uncertainty in the real and nominal LRRs. The conditional

6

volatilities follow a VAR
#

$
# $
#
$
2
2
2
σxc,t+1
σxc
σxc,t= (I2 − Φ) 2 + Φ 2+ Σw wt+1 ,2
σxπ,t+1
σxπ
σxπ,t

(12)

2
2
where σxc
and σxπ
are the unconditional means of the real and nominal volatilities, and Φ and Σw
capture the persistence and the scale of the standard normal volatility shocks wt+1 = [wc,t+1 wπ,t+1 ]′ .
In particular, Φ and Σw are orthogonal

#

vc 0
Φ=
0 vπ

$

#

$
σwc 0
and Σw =
.
0 σwπ

(13)

Finally, approximating constants κ0 and κ1 are endogenously solved as a fixed point of the implicit
equation of the deterministic steady state value of the wealth-consumption ratio pc:¯
22pc¯ = A0 (pc)¯ + Asc (pc)σ¯ xc+ Asπ (pc)σ¯ xπ

where A0 (pc),¯ Asc (pc),¯ and Asπ (pc)¯ are implicit functions of pc.
¯
2.2. Equilibrium bond yields
An equilibrium of the model is solved with an undetermined coeﬃcient method. Given state
2
2variables xc,t , xπ,t , σxc,t, and σxπ,t, we make an educated guess of the equilibrium wealth-consumption
ratio
2
2
pct = A0 + Axc xc,t + Axπ xπ,t + Asc σc,t
+ Asπ σπ,t.
(14)
To solve unknown coeﬃcients A0 , Axc , Axπ , Asc , and Asπ , notice that Euler equation (6) also needs
to be satisfied for the one-period return on the consumption claim rc,t+1 :Et exp(mt+1 + rc,t+1 ) = 1.
Substituting real SDF (4), rate of return on the consumption claim (5), and wealth-consumption
ratio (14) into the above Euler equation and using the stochastic processes of the exogenous statevariables provide five coeﬃcient restrictions for solving the five unknowns in eq.(14). In particular, the sensitivity of the equilibrium wealth-consumption ratio toward the four state variables is7characterized by the four coeﬃcientsAxc =1 − ψ11 − κ 1 ρcAxπ = κ1 ρcπ> 0,
1 − ψ1< 0,(1 − κ1 ρc )(1 − κ1 ρπ )%&2(1 − γ)(1 − ψ1 )
κ1
Asc =
< 0,
2(1 − κ1 vc )1 − κ 1 ρc'
(2
(1 − γ)(1 − ψ1 )
κ21 ρcπAsπ =< 0.
2(1 − κ1 vπ )(1 − κ1 ρc )(1 − κ1 ρπ )Under the conventional calibration in the LRR literature, the IES is greater than one, i.e., ψ > 1.
In this case, the intertemporal substitution eﬀect dominates the wealth eﬀect. Hence, a higher
expected future consumption growth leads to a higher investment to the consumption claim and ahigher wealth-consumption ratio as the positive loading Axc implies. The assumed negative nonneutrality of the expected future inflation on the expected consumption growth (i.e., ρcπ < 0)results in a negative wealth-consumption loading on the nominal long-run risk (i.e., Axπ < 0): a
higher expected future inflation implies a lower expected future real growth and a lower wealthconsumption ratio. When the degree of the risk aversion is greater than one (i.e., γ > 1), higher real
as well as nominal volatilities raise the uncertainty on future consumption dividends. Because theequilibrium price of the consumption claim falls, the wealth-consumption ratio responds negatively
to the real and nominal volatilities (i.e., Asc , Asπ < 0). 7
As usual, the real market prices of risks are derived as the forecast error of the real pricing
kernel. Substituting equilibrium wealth-consumption ratio (14) into real SDF (4), we can calculate
the forecast errors of the real SDF
mt+1 −Et mt+1 = −λc σc ηc,t+1 −λπ σπ ηπ,t+1 −λxc σxc,t ec,t+1 −λxπ σxπ,t eπ,t+1 −λsc σwc wc,t+1 −λsπ σwπ wπ,t+1 ,
where
%
&
%
&
1
κ1
1
κ21 ρcπλc = γ, λπ = 0, λxc = γ −> 0, λxπ = γ −< 0,
ψ 1 − κ 1 ρc
ψ 1 − κ 1 ρπ
%
&
%
&2
1
κ1
κ1
λsc = γ −(1 − γ)< 0,ψ
2(1 − κ1 vc ) 1 − κ1 ρc
%
&
% 2
&2
1
κ1
κ1 ρcπλsπ = γ −(1 − γ)< 0.
ψ
2(1 − κ1 vπ ) 1 − κ1 ρπConstant A0 can be solved through the coeﬃcient restriction log δ + κ0 + (1 − ψ1 )µc + A0 (κ1 − 1) + κ1 [Asc (1 −2222vc )σxc+ Asπ (1 − vπ )σxπ
] + θ2 (1 − ψ1 )2 σc2 + θ2 κ21 A2sc σwc+ θ2 κ21 A2sπ σwπ
= 0.
7

8

The real market price of the temporary consumption growth risk is positive (i.e., λc > 0) due tothe positive risk aversion parameter (γ > 1). Since the instantaneous inflation shock has no impact
on the real pricing kernel, its real market price is zero: λπ = 0. Under the early resolution of
uncertainty (i.e., γ > ψ1 ), the real market price of the expected future consumption growth risk ispositive (i.,e., λxc > 0), while that of the expected inflation risk is negative (i.e., λxπ < 0) with
the negative non-neutrality of the expected inflation on the consumption growth. The real market
prices of the real and nominal volatility risks are both negative: λsc , λsπ < 0.
Similarly, the nominal market prices of risks are calculated as the forecast error of the nominal
pricing kernel.
m$t+1 −Et m$t+1 = −λc σc ηc,t+1 −λ$π σπ ηπ,t+1 −λxc σxc,t ec,t+1 −λxπ σxπ,t eπ,t+1 −λsc σwc wc,t+1 −λsπ σwπ wπ,t+1 ,where the nominal market price of the instantaneous inflation shock is equal to one: λ$π = 1. The
other nominal market prices of risks are the same as the corresponding real market prices of risks.
To derive the real bond yields to diﬀerent maturities, let pt,n denote the logarithm of the priceof the real bond to maturity n. Similarly to the equilibrium wealth-consumption ratio, we solve
equilibrium real bond price pt,n by an undetermined coeﬃcient method. We construct an educatedguess of the equilibrium real bond price to maturity n:22pt,n = −B0,n − Bxc,n xc,t − Bxπ,n xπ,t − Bsc,n σc,t
− Bsπ,n σπ,t.

The corresponding real bond yield to maturity n, which is denoted by yt,n , is simply given as theinverse of the real bond price divided by maturity n:
yt,n =*
1)
2
2
B0,n + Bxc,n xc,t + Bxπ,n xπ,t + Bsc,n σc,t
+ Bsπ,n σπ,t.
n

To find the equilibrium real bond yield loadings, let hn,t→t+1 (= pt+1,n−1 − pt,n ) denote the corresponding one-period holding return of the real bond to maturity n. The real bond price implies thecorresponding one-period holding return
hn,t→t+1 = (B0,n − B0,n−1 ) + (Bxc,n − ρc Bxc,n−1 )xc,t + (Bxπ,n − ρπ Bxπ,n−1 − ρcπ Bxc,n−1 )xπ,t ,2
2+(Bsc,n − vc Bsc,n−1 )σc,t+ (Bsπ,n − vπ Bsπ,n−1 )σπ,t− Bxc,n−1 σc,t ec,t+1 − Bxπ,n−1 σπ,t eπ,t+1−Bsc,n−1 σwc wc,t+1 − Bsπ,n−1 σwπ wπ,t+1 − Bsc,n−1 (1 − vc )σc2 − Bsπ,n−1 (1 − vπ )σπ2 .

The Euler equation implies that under the real pricing kernel, the conditional moment condition
Et exp(mt+1 + ht→t+1,n ) = 1

9

must be satisfied. The above moment condition then yields five coeﬃcient restrictions as theequilibrium diﬀerence equations of five unknowns B0,n , Bxc,n , Bxπ,n , Bsc,n , and Bsπ,n :Bxc,n = ρc Bxc,n−1 +1,ψBxπ,n = ρπ Bxπ,n−1 + ρcπ Bxc,n−1 ,
+ 1
,2
%
&%
&2
−γ
1
1
κ1
1
ψ
Bsc,n = vc Bsc,n−1 − (1 − γ) γ −−κ1 − Bxc,n−1 ,2ψ
1 − κ 1 ρc
2 1 − κ 1 ρc
%
&.2
1
1
κ21 ρcπBsπ,n = vπ Bsπ,n−1 − (1 − γ) γ −2ψ(1 − κ1 ρc )(1 − κ1 ρπ )
#
$2
1
−γ
1
ψ
2
−
κ ρcπ − Bxπ,n−1 ,2 (1 − κ1 ρc )(1 − κ1 ρπ ) 1
%
&2
1
θ
2
2
B0,n = B0,n−1 + Bsc,n−1 (1 − vc )σxc
+ Bsπ,n−1 (1 − vπ )σxπ
− m̄ −
θ−1−
σc2
2
ψ
1
1
2
2
− [(θ − 1)κ1 Asc − Bsc,n−1 ]2 σwc− [(θ − 1)κ1 Asπ − Bsπ,n−1 ]2 σwπ,22where m̄ is the unconditional mean of the real pricing kernel. The restriction that the real bondprice to the zero maturity should be zero (i.e., pt,0 = 0) imposes the zero restrictions on the initial
real bond yield loadings B0,0 = Bxc,0 = Bxπ,0 = Bsc,0 = Bsπ,0 = 0. Starting with the initialconditions, recursion of the equilibrium diﬀerence equations solves the equilibrium real bond yields
to any maturity n.
The agent holds the real bond for hedging an expected future consumption risk. A lower
expected consumption growth increases the demand for the real bond and, hence, raises the realbond price and falls the real bond yields to all maturities: Bxc,n > 0. With the negative nonneutrality of expected future inflation to expected future consumption growth (i.e., ρcπ < 0), a
higher expected inflation deteriorates the agent’s perspective of the future consumption growth,raises the real bond price, and falls the real bond yield: Bxπ,n < 0. Careful investigation uncovers
that under the early resolution of uncertainty, the real bond yield loading on the real and nominal
volatilities are negative: Bsc,n < 0 and Bsπ,n < 0. Because a higher real volatility implies thatthe future consumption dividend is more uncertain, the agent desires to invest more into the realbond. Through this “flight to quality” (hereafter FTQ) eﬀect, the real bond price rises and thereal bond yield falls. The FTQ eﬀect also produces the negative sensitivity of the real bond yield
to the nominal volatility: the higher the inflation volatility, the higher the real volatility under thenegative non-neutrality of expected inflation on future consumption growth. Thus, the real bondprice rises and the real bond yield falls in response to a rise in the nominal volatility.
The exactly same steps are applicable to derive the equilibrium nominal bond yield to maturity10$n, yt,n
:

*
1) $
$
$
$
2
$
2
B0,n + Bxc,nxc,t + Bxπ,nxπ,t + Bsc,nσc,t+ Bsπ,n
σπ,t
.
(15)
n
The nominal Euler equation then provides five coeﬃcient restrictions as the equilibrium diﬀerence
$
$
$
$
$
equations of five unknowns B0,n
, Bxc,n, Bxπ,n, Bsc,n, and Bsπ,n
:
$
yt,n
=

$
$
Bxc,n
= ρc Bxc,n−1
+

1
,
ψ

$
$
$
Bxπ,n
= ρπ Bxπ,n−1+ ρcπ Bxc,n−1
+ 1,
+ 1
,2
%
&%
&2
−
γ
1
1
κ
1
1
ψ
$
$
$
Bsc,n
= vc Bsc,n−1− (1 − γ) γ −−κ1 − Bxc,n−1,2ψ
1 − κ 1 ρc
2 1 − κ 1 ρc
%
&.2
1
1
κ21 ρcπ$$Bsπ,n = vπ Bsπ,n−1 − (1 − γ) γ −2ψ(1 − κ1 ρc )(1 − κ1 ρπ )
#
$2
1
−γ
1
ψ
2
$
−
κ ρcπ − Bxπ,n−1 ,2 (1 − κ1 ρc )(1 − κ1 ρπ ) 1
%
&2
1
θ
1
$
$
$
2
$
2
B0,n = B0,n−1 + Bsc,n−1 (1 − vc )σxc + Bsπ,n−1 (1 − vπ )σxπ − m̄ + µπ −θ−1−
σc2 − σπ2
2
ψ
2
02 2
02 2
1/
1/
$
$
− (θ − 1)κ1 Asc − Bsc,n−1
σwc − (θ − 1)κ1 Asπ − Bsπ,n−1σwπ22The restriction that the nominal bond price to the zero maturity should be zero (i.e., p$t,0 = 0)$$$
imposes the zero restrictions on the initial nominal bond yield loadings B0,0
= Bxc,0= Bxπ,0=$$
Bsc,0 = Bsπ,0 = 0. Starting with the initial conditions, recursion of the equilibrium diﬀerence
equations solves the equilibrium nominal bond yields to any maturity n.
The hedging purpose for the expected future consumption risk also explains the positive$
nominal bond yield loading: Bxc,n> 0. Because the expected future inflation directly aﬀects thenominal pricing kernel negatively, the nominal bond yield loading on an inflation expectation is$positive: Bxπ,n> 0. Moreover the real volatility creates a FTQ eﬀect and falls the nominal bond$yields: Bsc,n < 0.
The most outstanding characteristic of the BS model is that the sign of the nominal bondyield loading on the nominal volatility changes over maturities. In particular, Bsπ,n is negative atshorter maturities, while it becomes positive at longer maturities. To understand the reason behind
this sign flipping of the nominal bond yield sensitivity to the inflation volatility, notice that thenominal bond yield to maturity n is1$yt,n= yt,n + Et
n

n
1

1
πt+i − Vt
2n
i=1

+ n
1

πt+i

i=1

11

,

1
+ Covt
n

+ n
1
i=1

mt+i ,

n
1
i=1

πt+i

,

.

where Vt and Covt are the mathematical conditional variance and covariance operators. Our discussion has already suggested that the nominal volatility lowers the real bond yield yt,n through a
FTQ eﬀect (i.e., Bsπ,n < 0). The third term of the RHS reflects a Jensen’s inequality adjustment
and its sensitivity to the nominal volatility decreases in maturity n.8 The fourth term captures an
inflation premium, which is given as the covariance between the multi-period real pricing kernel
and inflation. It could be shown then that the inflation premium term becomes larger at longer
maturities and gradually dominates both the FTQ eﬀect and the Jensen’s inequality adjustment as
the maturity becomes longer.

3. Revisiting the first arrow hitting the currency target
Why did the depreciation rate of the JPY against the USD drastically increase its sensitivity
to the two-country yield diﬀerentials at longer maturities right after the introduction of the firstarrow of the Abenomics? The model resolves this question by revealing important roles of real andnominal LRR uncertainty in the term structure of the Fama coeﬃcient. We now characterize theequilibrium term structure of the Fama regression coeﬃcient.
3.1. Term structure of the Fama coeﬃcient
We assume throughout the rest of the paper that the two countries share the identical structural parameters. For any random variable for the home and foreign countries vt and vt∗ , let ṽt denotethe corresponding cross-country diﬀerential: ṽt ≡ vt − vt∗ . Notice that the equilibrium depreciation
rate (3) then can be rewritten as∗∗∗
st+1 − st = Et (m∗t+1 − πt+1
) − Et (mt+1 − πt+1 ) + (m∗t+1 − Et m∗t+1 ) − (πt+1− Et πt+1)− (mt+1 − Et mt+1 ) + (πt+1 − Et πt+1 ),1
1
2
2= ỹt,1 + λ2sc σ̃xc,t+ λ2sπ σ̃xπ,t+ λc σc η̃c,t+1 + λ$π σπ η̃π,t+1 + λxc σxc,t ẽc,t+1 + λxπ σxπ,t ẽπ,t+122+ λsc σwc w̃c,t+1 + λsπ σwπ w̃π,t+1 .
(16)

Using nominal bond yield equation (15), we can derive the unconditional covariance between the
depreciation rate and the cross-country yield diﬀerential to maturity n:$$$$
Cov(st+1 − st , ỹt,n) = Cov(ỹ1,t, ỹt,n) + Cov(rxt+1 , ỹt,n
),

(17)

8
Notice that the nominal bond yield is an log inverse of the expected multi-period nominal SDF. Hence an increasein the variance of the multi-period nominal SDF through a higher variance of future inflation lowers the nominalbond yield through the log transformation.

12

where
1 $
1 $
1 $
$
$
$
2
Bxc,1 Bxc,nV (x̃c,t ) + Bxπ,1
Bxπ,nV (x̃π,t ) + Bsc,1
Bsc,nV (σ̃xc,t
)
n
n
n
1 $
$
2
+ Bsπ,1Bsπ,nV (σ̃xπ,t
),
n
1 2 $
1
$
2
$
2
Cov(rxt+1 , ỹt,n)=λsc Bsc,n V (σ̃xc,t) + λ2sπ Bsπ,nV (σ̃xπ,t
).
2n
2n
$
$
Cov(ỹ1,t, ỹt,n
)=

(18)
(19)

Eq.(17) implies that the unconditional covariance between the depreciation rate and the yield diﬀerential to maturity n can be decomposed into two unconditional covariance terms, (i) that between
the yield diﬀerential to the one-period maturity and that to maturity n (eq.18) and (ii) that between
the excess currency return and the yield diﬀerential to maturity n (eq.19). Observe that except alonger maturity the former covariance is always positive. The latter covariance, however, is negativeat least to short maturities because the first and second terms of the RHS of eq.(19) are negative
over short maturities. This negative association between the excess currency return and the yielddiﬀerential to short maturities is indeed the fundamental source of the Fama puzzle: a currency
with a higher short-term yield tends to appreciate.
The crucial implication of BS model is that the Fama puzzle becomes less severe at longer
maturities. To see this, remember that the nominal bond yield loading changes its sign fromnegative to positive at longer maturities. The covariance between the excess currency return andthe yield diﬀerential then tends to be less negative and, under plausible parameter values, could bepositive at longer maturities. In this case, the depreciation rate is associated positively with theyield diﬀerential with longer maturities. Therefore, a currency with a higher long-term yield tends
to depreciate.
3.2. Benchmark calibration
To see whether the model indeed generates an upward-sloping term structure of the Fama
regression coeﬃcients, we calibrate the model simply following BS. Table 1 summarizes our benchmark calibration of the model. All the parameter values except the standard deviations of the realand nominal volatility shocks, σwc and σwπ , stem from the results of the BS estimation of the modelwith quarterly data of the United States and the United Kingdom spanning the period between 1969∗
and 2010. In particular, τxc ≡ Cov(ec,t+1 , e∗c,t+1 ), τxπ ≡ Cov(eπ,t+1 , e∗π,t+1 ), τsc ≡ Cov(wc,t+1 , wc,t+1),∗
and τsπ ≡ Cov(wπ,t+1 , wπ,t+1 ) are the unconditional instantaneous correlation coeﬃcients in thereal and nominal LRR shocks and the real and nominal volatility shocks between the two countries.9 We also follow the results of BS’s minimum distance estimation to calibrate these correlation
9

Under the assumption of the identical structural parameters in the two countries, we can calculate variance terms
2σ 2 (1−τ )2σ 2 (1−τ )2σ 2 (1−τ )2σ 2 (1−τ )22V (x̃c,t ) = xc1−ρ2 xc , V (x̃π,t ) = xπ1−ρ2 xπ , V (σ̃xc,t) = wc1−v2 sc , and V (σ̃xπ,t) = wπ1−v2 sπ .
c

π

c

13

π

coeﬃcients. We calibrate σwc and σwπ to higher values of 7.95e-07 and 2.51e-07 than the corresponding BS estimates of 1.85e-07 and 1.81e-07, respectively. This calibration reflects our priorbelief that during the GFC after the Lehman shock in 2008, both real and nominal uncertainty
greatly increased relative to that during the Great Moderation period.
Figure 3 indeed displays the term structure of the Fama regression coeﬃcients at maturities
1, 2, 3, 5, 7, and 10 years implied by the benchmark specification of the model. The solid blueline depicts the sizes of the population regression coeﬃcients of the depreciation rate on the two$$country yield diﬀerential to maturity n, i.e., Cov(st+1 − st , ỹt,n)/V (ỹt,n), while the dotted blueline the sizes of the population regression coeﬃcients of the one-period excess currency return on$$
the two-country yield diﬀerential to maturity n, i.e., Cov(rx$t+1 , ỹt,n)/V (ỹt,n). Observe that thebenchmark model replicates the actual data shape of the term structure of the Fama coeﬃcient
before the first arrow fairly well: as reported in Figure 2, the Fama coeﬃcient is negative at shorter
maturities up to 3 years but turns to be positive at longer maturities after 5 years. The excess
currency return regression coeﬃcients clearly uncover that this upward-sloping term structure of
the Fama coeﬃcient reflects the key theoretical property of the model: the negative correlation
between the excess currency return and the yield diﬀerential generated by the real and nominal
conditional volatilities, as in eq.(19), gradually weakens because nominal uncertainty increases the
inflation premium eﬀect enough to dominate the FTQ eﬀect as well as the Jensen’s inequality eﬀect
when the yield maturity becomes longer.
3.3. Roles of real and nominal uncertainty
Why did the term structure of the Fama coeﬃcient shift up and become steeper after the firstarrow? We now draw our theoretical inference from the model: real uncertainty in expected future
consumption growth was mitigated around the first arrow and nominal uncertainty in expected future
inflation rate and/or future monetary policy path dominated domestic and international financial
markets after the first arrow.
To see this theoretical prediction, recall that a fall in real uncertainty mutes the FTQ eﬀect$(i.e., Bsc,n< 0) and leads to a higher nominal bond yield. As shown by eq.(19), the covariance
between the excess currency return and the yield diﬀerential then rises over all maturities. Nominal
uncertainty then dominates this covariance. Besides, as shown by BS, the slope of the nominalbond yield loading on the nominal volatility is positive and quite steep over maturity n.10 Thismeans that given a fall in real uncertainty the positive association between the excess currency
return and the yield diﬀerential enlarges especially at longer maturities. The term structure of theFama regression coeﬃcient, hence, becomes steeper.
10

See their Figure 4.

14

To check the validity of the theoretical prediction, we calculate the term structure of theFama regression coeﬃcient with an alternative calibration of the model. In the new calibration, wechange only the size of real uncertainty specifying that the standard deviation of the real volatility
σwc falls from 7.95e-07 to 1.85e-07.11 We call the new calibrated model the nominal uncertainty
model. Figure 3 also plots the term structure of the Fama coeﬃcient as the solid red line and theexcess currency return regression coeﬃcient as the dotted red line, respectively predicted by thenominal uncertainty model. For comparison, we also plot the results from the benchmark modelas the solid and dotted blue lines. The figure clearly reveals three facts. First, comparing with theterm structure of the Fama coeﬃcient under the benchmark model, the nominal uncertainty model
generates a much higher and steeper term of structure. Second, although the nominal uncertainty
model tends to over-evaluate the Fama coeﬃcients at 7 and 10 year maturities, it tracks the actual
data shape of the term structure of the Fama coeﬃcient fairly well.12 Finally, as the third fact, themost part of the upward-sloping term structure of the Fama coeﬃcient reflects the upward-sloping
term structure of the covariance between the excess currency return and the yield diﬀerential as
observed in the data.
We therefore conclude that the BS model can capture the most data aspects of the term
structure of the Fama regression coeﬃcient before and after the first arrow of the Abenomics. In
particular, the lens of the BS model provides us with a novel picture of the currency outcome of
the Abenomics: the main cause of the sharp depreciation of the JPY against the USD and its tightlinkage with longer-term yield diﬀerentials between the two countries after the first arrow would
be a mitigation of real uncertainty prevailed since the Lehman shock and a resulting dominance of
nominal uncertainty in the bond markets of the two countries. But which country matters moresignificantly?
3.4. Discussion: where did the first arrow shoot oﬀ ?
Figure 4 plots that the 10-year JGB rate as the blue line, the 10-year USTB rate as the redline, and the 10-year interest rate diﬀerential between Japan and the United States as the green line
in our whole sample period. The shaded areas display the periods when the Fed conducted the threequantitative easing (QE) policies (i.e., QE1, QE2, and QE3). The figure reveals four important
facts. First, the long-term JGB rate sticks around 1 % along a downward trend line and has no11
This calibration of σwc comes from the corresponding estimate of BS. BS estimate σwc using quarterly data of
the United States spanning the period between 1969 and 2010. Hence, their calibration represents the average size ofthe real uncertainty in the United States mostly before the GFC. Hence our exercise reflects the standard conjecturethat during the GFC real uncertainty sharply increased in the United States.
12
Koijen et al. (2010) also point out that a version of the BS model tends to generate counterfactually large
nominal bond yields at longer maturities. Because we calibrate the model based on the estimates of BS with U.S.and
U.K. quarterly data, it might be possible to resolve this over-valuation of long-term nominal bond yields if we fit themodel to Japanese data. We will leave this empirical task as a future research agenda.

15

big action around the onset of the Abenomics. We can observe a tiny dip of the JGB rate between
January and April 2013 but the rate gets back to the trend line very quickly. Second, contrary to
the JGB rate, the long-term USTB rate has a lot of actions. The USTB rate sharply falls from 4% to 2 % before 2013 and sharply increases above 3 % after May 2013 due to the “taper tantrum.”
Third, the USTB rate tends to increase during each QE period, although QE1 generates a sharp fallin the long-term USTB rate at the beginning of the program. Fourth, the movement of the yielddiﬀerential between Japan and the United States is mainly dominated by the action in the USTB
rate not the JGB rate. In particular, we can confirm that the fall in the yield diﬀerential after theend of 2012 is dominated mostly by the large increase in the USTB rate, not by the small fall in
the JGB rate. These facts throw serious doubt on the popular claim across the policy debates inJapan that the first arrow, which hit the currency target of the Japanese yen, shot oﬀ from theJapan side. The data of the long-term yields of the two countries clearly uncover that rather thearrow shot oﬀ from the U.S. side.
A natural question is then the following: what factors explain such active movements of
the long-term USTB rate in our sample? To figure out this question, it is quite informative todecompose the USTB rate fluctuations into the components of the risk-neutral rate and the term
premium. Adrian et al. (2013) recently estimate the USTB term premium by estimating their aﬃneterm structure model. Figure 5 plots their estimates of the 10-year treasury term premium andthe corresponding risk neutral rate.13 The shaded areas again exhibit the three U.S. QE periods.
According to their estimates, it is useful to split the whole sample into the first and second partsat the mid 2012 with respect to the term premium. Each part is well characterized by high term
premiums. More specifically, the term premium keeps being high after the onset of the Lehman
shock, then sharply falls from above 2 % on June 2011 to below 0% on May 2012. After August2012 the term premium starts increasing and peaks out on December 2013.
Importantly, we observe that each QE tends to raise the term premium during the the program. This rise in the term premium in fact is the main cause of the tendency that each QE creates
an upward pressure on the long-term USTB rate. This observation leads to our conjecture: theselarge scale bond purchasing programs are recognized to a great degree by market participants as
uncertainty about the U.S. monetary policy through enlarging market disagreements about long-run
perspective on inflation rates.
14

On the one hand, the main risk factor prevailed the U.S. market in the first sub-sample
13

Thanks to the authors, the daily and monthly estimates are downloadable at the Federal Reserve Bank of New
York website with URL http://www.newyorkfed.org/research/data_indicators/term_premia.html.
14
Abrahams et al. (2015) report empirical evidence that the large scale asset purchasing programs of the Fed decline
the 2 and 10 year real and nominal bond yields on several days right after the policy announcements, especially inthe case of QE1. We completely agree with their inference that the QE policies in total has a short-run compressing
eﬀect on the U.S. medium- and long-term bond yields.

16period is both real and nominal uncertainty. As observed by Abrahams et al. (2015), a variety
of indicators for real economic activity including the unemployment rate and consumer confidence
highly comove with the term premium inferring a sharp rise in real uncertainty after the Lehman
shock and the subsequent GFC. As suggested by Figure 5, the policy response of the Fed withunconventional monetary policies including QEs is likely to contribute to developing high nominal
uncertainty. As predicted by the BS model, this co-existence of real and nominal uncertainty is the
crucial characteristic to figure out the low and flat term structure of the Fama regression coeﬃcientestimated in the first sub-sample period. On the other hand, the main risk factor behind mounting
up the term premium in the second part of the sample is evident: uncertainty about the future pathof Fed’s unconventional monetary policy due to tapering QE3. As mentioned by Abrahams et al.
(2015) and Bernanke (2015), the sharp rise in the term premium obviously reflects the taper tantrum
episode of the early summer of 2013. Nominal uncertainty with respect to the long-run perspectiveof Fed’s monetary policy and inflation rate prevailed in the U.S. long-term bond market during
this period of time. The LRR model indeed consistently understands that the dominance of U.S.
nominal uncertainty generates both the increase in U.S. long-term yield and the JPY depreciation.

4. Conclusion
In sum, the paper draws an inference that the arrow comes from the U.S. side not the Japanside. The two-country data of the term structure of the nominal government bond yield shows
no clear evidence for a significant role that the first arrow from the BOJ plays in the drastic
depreciation the JPY against the USD after the onset of the Abenomics. The conjecture of thispaper casts serious doubt on the popular notion of the successful outcome of the Abenomics for thecurrency target.
Our inference, of course, is subject to several important reservations. First, we adopt theestimate of the LRR model by BS with quarterly data of the United Kingdom and the United States.
More careful investigation requires us to estimate the BS model using Japanese data. Second,
to derive the theoretical implication for the upward-sloping nominal bond yield over maturities
the BS model depends crucially on the negative non-neutrality of the expected future inflation
toward expected future consumption growth (i.e., ρcπ < 0). It is diﬃcult to justify this maintained
assumption theoretically with a solid micro-foundation as well as empirically with data of advanced
countries. Even with these reservations we hope that the exercise of this paper will deepen our
understanding of the fundamental mechanism behind the recent depreciation of the JPY against
the U.S. dollar from the novel long-run risk perspective.

17

References
Abrahams, M., Adrian, T., Crump, R.K., Moench, E., 2015, Decomposing real and nominal yield
curves, Federal Reserve Bank of New York Staﬀ Report No.570.
Adrian, T. Crump, R.K., Moench, E., 2013, Pricing the term structure with linear regressions,
Journal of Finance Economics 110, 110 − 138.
Backus, D.K., Foresi, S., Telmer, C. I., 2001, Aﬃne term structure models and the forward premium
anomaly, Journal of Finance 56, 279 − 304.
Bansal, R., Kiku, D., Yaron, A., 2007, Risks for the long run: estimation and inference, Duke
University and University of Pennsylvania.
Bansal, R., Shaliastovich, I., 2013, A long-run risks explanation of predictability puzzles in bondand currency markets, Review of Financial Studies 26, 1 − 33.
Bansal, R., Yaron, A., 2004, Risks for the long run: a potential resolution of asset pricing puzzles,
Journal of Finance 59, 1481 − 1509.
Bernanke, B. S., 2015, Why are interest rates so low, part 4: term premiums, Ben Bernanke’s Blog
April 13.
Fujiwara, I., Nakazono, Y., Ueda, K., 2015, Policy regime change against chronic deflation? Policy
option under a long-term liquidity trap, Journal of the Japanese and International Economies
37, 59 − 81.
Kano, T., Mortia, H., 2015, An equilibrium foundation of the Soros chart, Journal of the Japaneseand International Economies 37, 21 − 42.
Koijen, R.S.J., Lustig, H., Nieuwerburgh, S.V., Verdelhan, A., 2010, Long run risk, the wealthconsumption ratio, and temporal pricing of risk, American Economic Review 100(2), 552 − 556.
Ueda, K., 2013, Response of asset prices to monetary policy under Abenomics, Asian Economic
Policy Review 8, 252 − 269.

18

Table 1:

Estimated Term Structure of Fama Coeﬃcients

Sample Period

1 yearYields to Maturity
2 years
3 years 5 years 7 years 10 years∗(a) st+1 − st = αn + βn (yt,n − yt,n
) + ϵt,n

2008/1-2015/8

β̂n
s.e.

0.304
0.684

0.158
0.675

0.068
0.614

0.361
0.534

0.496
0.503

0.523
0.539

2008/1-2012/11

β̂n
s.e.

-0.3050.693-0.4270.694-0.342
0.636

0.120
0.559

0.269
0.530

0.343
0.563

2012/12-2015/8

β̂n
s.e.

1.092
3.792

0.873
2.169

1.296
1.543

1.708
1.144

1.765
1.118

2.269∗
1.243∗(b) rxt+1 = αnrx + βnrx (yt,n − yt,n
) + ϵt,n

2008/1-2015/8

β̂nrx
s.e.

-0.7690.666-0.7890.657-0.6340.598-0.088
0.525

0.138
0.495

0.150
0.531

2008/1-2012/11

β̂nrx
s.e.

−1.374∗∗0.665−1.392∗∗
0.666−1.090∗0.616-0.3950.553-0.1530.527-0.1210.561

2012/12-2015/8

β̂nrx
s.e.

0.258
4.217

0.474
2.378

1.093
1.630

1.638
1.279

1.733
1.163

2.320∗
1.297∗
Note 1. rxt+1 ≡ st+1 − st + yt,1
− yt,1 is the one-period excess currency return.
Note 2. ∗∗ and ∗ stands for the 5 and 10 % levels of statistical significance.

19

Table 2:

Baseline Calibration of Bansal and Shaliastovich Model

Parameters

ValuesPreferenceδγψSubjective Discount Factor
Risk Aversion
Intertemporal Substitution Elasticity

0.994
12.00
1.810

Consumption Growth
µc
σc
ρc
ρcπ
σxc

Mean Consumption Growth
Temporary Consumption Growth Shock Std.
Persistent Consumption Growth AR(1) Coef.
Non-neutrality Coef. of Expected Inflation
Persistent Consumption Growth Shock Std.

4.9e-03
4.6e-03
0.810-0.047
1.09e-03

Inflation Rate
µπ
σπ
ρπ
σxπ

Mean Inflation Rate
Temporary Inflation Shock Std.
Persistent Inflation Rate AR(1) Coef.
Persistent Inflation Shock Std.

9.0e-035.5e-03
0.988
1.11e-03

Conditional Volatilities
vc
vπ
σwc
σwπ

Consumption Growth Volatility AR(1) Coef.
Inflation Rate Volatility AR(1) Coef.
Consumption Growth Volatility Shock Std.
Inflation Rate Volatility Shock Std.

0.994
0.979
7.95e-07
2.51e-07

Two-country Shock Correlations
τxc
τxπ
τsc
τsπ

Corr Coef. in Persistent Consumption Growth ShockCorr Coef. in Temporary Inflation Rate ShockCorr Coef. in Consumption Growth Volatility ShockCorr Coef. in Inflation Rate Volatility Shock

0.820
0.990
0.940
0.960

Note. All the parameters except σwc and σwπ are calibrated from the corresponding estimates of Bansal andShaliastovich (2013).

20

JGB-USTB Interest Rate Differential %
-2.5

-2

-1.5

-1

-0.5

0

0.5

JP-US 2
JP-US 3
JP-US 5
JP-US 7
JP-US 10-log JPY/USD

Figure 1: JPY/USD rate and Term Structure of Interest Rate Diﬀerentials between Japan and the United States

JP-US 1

201201
201202
201203
201204
201205
201206201207
201208201209201210201211
201212
201301
201302
201303
201304
201305201306201307
201308
201309201310201311
201312
201401
201402
201403
201404
201405201406201407
201408
201409201410201411
201412
201501
201502
201503
201504
201505201506201507
201508
-2.15

-2.1

-2.05

-2

-1.95

-1.9

-1.85

-1.8

-1.75

-log JPY/USD-2.000-1.500-1.000-0.500

0.000

0.500

1.000

1.500

2.000

2.500

3.000

1 yearFigure 2: Term Structure of the Fama Regression Coeﬃcients Before and After the Abenomics: Data

One-period Excess Return Reg. After

7 yearOne-period Excess Return Reg. Before

5 yearDepreciation Rate Reg. After3 yearDepreciation Rate Reg. before

2 year10 year!2.000%%!1.000%%0.000%%

1.000%%

2.000%%

3.000%%

4.000%%

1%year%Figure 3: Term Structure of the Fama Regression Coeﬃcients: Model

One!period%Excess%Return%Reg:%Nominal%Uncertainty%

7%year%Deprecia3on%Rate%Reg:%Nominal%Uncertainty%

5%year%

One!period%Excess%Return%Reg:%Benchmark%

3%year%Deprecia3on%Rate%Reg:%Benchmark%2%year%10%year%

-3

-2

-1

0

1

2

3

4

JGB 10 Years
USTB 10 Years
Yield Differential: 10 Years

Figure 4: JGB rate, USTB rate, and Interest Rate Diﬀerential: 10 Year Maturity

QE

200801
200803
200805
200807
200809200811
200901
200903
200905200907
200909200911
201001
201003
201005201007
201009201011
201101
201103
201105
201107
201109201111
201201
201203
201205
201207
201209201211
201301
201303
201305201307
201309201311
201401
201403
201405201407
201409201411
201501
201503
201505201507
201509

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Term Premium
Risk Neutral Rate

Figure 5: U.S. 10 Year Term Premium and Risk Neutral Rate: Adrian et al.(20013) estimates

QE

200801
200803
200805
200807
200809200811
200901
200903
200905200907
200909200911
201001
201003
201005201007
201009201011
201101
201103
201105
201107
201109201111
201201
201203
201205
201207
201209201211
201301
201303
201305201307
201309201311
201401
201403
201405201407
201409201411
201501
201503
201505201507