Research InstituteDiscussion Paper Series№14
Title：

Asset price stabilization and cost channel in a two-country
new Keynesian modelDaisuke Ida
ida-dai@andrew.ac.jp

2020 年 10 月

http://www.andrew.ac.jp/soken/

Asset price stabilization and cost channel
in a two-country new Keynesian modelDaisuke Ida∗
October 28, 2020

Abstract
This paper studies the role of asset price stabilization in a two-country modelwith incomplete loan rate pass-through. We find that when financial market imperfections are present in the foreign country, world equilibrium determinacy isachieved if home and foreign central banks set smaller weights on asset price stabilization. When the foreign central bank reacts more aggressively to inflation in its
own country, it can cause the worldwide rational expectations equilibrium (REE)
to become more determinate by placing a more aggressive weight on asset pricestabilization. However, irrespective of any combinations of inflation and asset pricestabilization in the foreign country, the worldwide REE becomes indeterminate if
the home central bank reacts more aggressively to domestic asset prices.

Keywords: Incomplete pass-through of the loan rate; Cost channel; Asset price stabilization; Monetary policy; Two-country model;
JEL classification: E52; E58; F41∗

Department of Economics, Momoyama Gakuin University, 1-1, Manabino, Izumi, Osaka 594-1198,

Japan. Tel.: +81-725-54-3131. E-mail: ida-dai@andrew.ac.jp

1

Introduction

The objective of this paper is to explore the role of asset price stabilization in a twocountry new Keynesian (NK) model with incomplete pass-through of the loan rate. A
large number of studies have focused on the role of asset price stabilization in monetary policy analyses. Some studies point out that monetary policy should react to afluctuation in asset prices that deviate from their fundamental values (Cecchetti et al.,
2003; Haugh, 2008). There are studies that assert that the central bank does not haveto stabilize fluctuations in asset prices if monetary policy includes a strong reaction to
inflation rate. (Bernanke and Gertler, 1999; Carstrom and Furest, 2007; Faia and Monacelli, 2007; Gertler and Leahy, 2002; Iacoviello, 2005). Contrary to these studies, somestudies argue that the central bank may obtain gains from asset price stabilization (seeAiraudo et al., 2013; Gali, 2014; Gambacorta et al., 2014; Kannan et al., 2012; Pfajfar
and Santoro, 2014).
These papers focused mainly on the case of a closed economy. But the aftermathof the global financial crisis, which originated in the United States (US), revealed thata change in asset prices in one country can spill over into other countries. However,
it is unclear whether central banks aim to stabilize asset prices may render the world
economy indeterminate. The Taylor principle is required to satisfy the unique rational
expectations equilibrium (REE) in a closed economy (Bullard and Mitra, 2002). Llosa
and Tuesta (2009) showed that the presence of a cost channel renders the determinacy
condition needed to achieve the unique REE more complicated. While Linnemann andSchabert (2006), Bullard and Singh (2008), and Bullard and Schaling (2009) investigatedthe determinacy condition in an open economy model, these papers abstracted the roleof the cost channel.
Recently, Mcknight and Mihailov (2015) examined the role of real money balances
in a two-country sticky price model. They showed how a departure from the separable
utility function between consumption and real money balances significantly changed theworld determinacy condition under forecast-based monetary policy rules. Ida (2019)
examined the impact of an incomplete loan rate pass-through using a two-country model1

and found that an incomplete loan rate pass-through significantly aﬀected the worldwide
equilibrium determinacy.
The results obtained in this paper are summarized as follows. First, we find thatwhen financial market imperfections are present in the foreign country, world equilibrium
determinacy is achieved—as long as home and foreign central banks set smaller weights
on asset price stabilization. Worldwide equilibrium determinacy is not achieved whenfinancial market imperfections are considerably severe in the foreign country. This result
indicates that a smaller weight on asset price stabilization becomes an eﬀective tool forstabilizing the eﬀect of a sunspot shock on the real economy.
Second, we explore the case in which home and foreign central banks cooperatively
employ a stronger response to inflation rates, which leads to a unique worldwide REE.
If the foreign central bank reacts more aggressively to inflation in its own country, it
can make the worldwide REE more determinate by placing a more aggressive weight on
asset price stabilization. However, irrespective of any combinations of inflation and asset
price stabilization in the foreign country, the worldwide REE becomes indeterminate if
the home central bank reacts more aggressively to domestic asset prices.
Third, this paper shows that even in the case in which an interest rate response
to asset prices in each country can be eﬀective, home and foreign central banks fail toachieve the worldwide equilibrium determinacy if either the home or foreign central bankreinforces a policy reaction to its own output gap. In contrast to previous studies, thisstudy emphasizes that a larger weight on asset price stabilization in both countries easily
makes the worldwide REE indeterminate when either central bank responds too strongly
to its own output gap in a two-country model. Nistico (2012) showed the eﬀectivenessof reacting to asset price growth in a perpetual youth NK model, whereas Di Giorgio
and Nistico (2007) argued that such a rule may lead to equilibrium instability in a twocountry NK model with wealth eﬀects. On the other hand, this paper shows the gainthat can be realized from the foreign central bank stabilizing its asset price growth inthat it can expand worldwide determinacy regions.
Fourth, we also examine how the presence of asset price stabilization in each country2

aﬀects the transmission mechanism of structural shocks and volatility in macrovariables.
In contrast to the case in which the central bank does not react to stock prices, volatility
in both output and stock prices declines when each central bank stabilizes its own asset
prices. On the other hand, in such a case, each central bank has to accept an increase
in its own inflation. Thus, even when central banks employ asset price stabilization asa policy rule, they will not be able to overcome the policy trade-oﬀ between inflationand output stabilization. Importantly, we demonstrate that worldwide volatility can be
reduced when the foreign central bank only stabilizes its asset price growth.
Finally, we mention the introduction of financial market imperfections as motivatedby the work of Chowehury et al. (2006). The objective of this paper is to show equilibrium determinacy when both home and foreign central banks simultaneously react to its
own asset prices in a two-country model with incomplete pass-through of the loan rate.
To do this, it is useful to employ a tractable two-country NK model.1 Of course, the proposed model recognizes that the introduction of financial market imperfections motivatedby Chowehury et al. (2006) is actually a shortcut. Nevertheless, in this paper, we would
like to address the fact that this shortcut does have some merits in this paper. First,
we can construct a tractable two-country NK model due to a simple expression of loan
rate dynamics. Such simplification renders the international transmission mechanism ofstructural shocks intuitively understandable. Second, as argued in previous studies, theloan rate curve in this paper corresponds to the reduced form of a microfoundated loan
rate curve (Kobayashi, 2008; Teranishi, 2015). Third, as mentioned by Chowdhury etal, (2006), the specification might simply be regarded as a reduced-form of a financial
accelerator eﬀect.
The remainder of this study is constructed as follows. Section 2 briefly reviews theliterature related to this study. Section 3 describes a log-linearized two-country NK
1

Several scholars have focused on the role of the credit channel or the collateral channel in a medium-

scale open economy (Dedola and Lombardo, 2012; Devereux and Yetman, 2010; Faia, 2008). Kolsa andLombardo (2011) analyzed optimal monetary policy in a medium-scale two-country model with a credit
channel, as argued by Bernanke et al. (1999). However, the models considered in the above studies
appear to be large-scale and, therefore, feature more complicated structures.

3

model in the presence of financial market imperfections. Section 4 calibrates the deepparameters. Section 5 reports the main results of this paper. Section 6 briefly concludes.

2

Related literatureThis section briefly reviews the literature related to our study and clarifies how this study
is related to previous studies in terms of examining the role of asset price stabilization.2
It has been a subject of debate whether or not central banks should react to fluctuationsin asset prices. Bernanke and Gertler (1999) asserted that, based on the framework
developed by Bernanke et al. (1999), the central bank should not stabilize asset prices
unless they aﬀect an increase in future inflation expectations. On the contrary, Cecchetti
et al. (2003) argued that the central bank should respond to asset prices as a precaution
because the bursting of asset price bubbles can cause a severe economic stagnation.
Gali (2014) argued that optimal monetary policy would consider the balance between
stabilization of the real economy and stabilization of the bubble itself, in the presence ofasset price bubbles, in an over-lapping generations model with nominal rigidities.
In terms of the theoretical aspects of the NK model, no consensus regarding thisissue has been reached.3 For instance, several studies support the assertion of Bernanke
and Gertler (1999) (see Carlstrom and Fuerst, 2007; Gilchrist and Saito, 2002; Faia
and Monacelli, 2007; Iacoviello, 2005).4 These studies argue that the central bank canstabilize the economy if it reacts strongly to the inflation rate. Thus, the response to2

This paper focuses on the role of asset price stabilization whereas several other papers consider therole of macro-prudential policy in an open economy (e.g., Davis and Presno, 2017). We would like toconsider the relationship between asset price stabilization and macro-prudential policy as a future work.
3

Castelnuovo and Nistico (2012) argued that the inclusion of a stock-price gap in the monetary policy

rule is consistent with post-WWII stock market boom and bust cycles by using a dynamic stochastic
general equilibrium (DSGE) model with Bayesian techniques.
4

Nistico (2012) showed that in a Blanchard-Yaari NK model, responding to a deviation in stock

prices from their target levels induces equilibrium indeterminacy, whereas responding to a growth instock prices can avoid the indeterminacy problem. See Piergallini (2006) and Nistico (2012) for a detailed
derivation of the Blanchard-Yaari NK model.

4asset prices in the policy rule is redundant when the central bank aggressively raises thepolicy rate in response to inflation.
On the other hand, there are previous studies that assert that the central bank canobtain gains from asset price stabilization (see Airaudo et al., 2013; Gambacorta et al.,2014; Kannan et al., 2012; Pfajfar and Santoro, 2014).5 For instance, Airaudo et al.
(2013) showed that a mild response to asset prices in a monetary policy rule can achievea unique REE and rule out non-fundamental volatility in an NK model with financial
market imperfections. As suggested by Kannan et al. (2012), when the model contains
heterogeneities of households, the central bank can obtain gains by implementing an
augmented monetary policy rule that contains both asset price stabilization and a macroprudential tool such as a credit growth rate.
The above studies focused on the case of a closed economy model. However, the global
crisis, which originated in the US, led to severe economic stagnation, mainly centeredaround the economies of developed countries. As far as we know, very few studies haveexamined whether or not central banks should react to asset prices in an open economy
NK model. It is unclear whether the home central bank should aim to stabilize asset
prices, given a foreign monetary policy rule. Also, should the home central bank react
to both home and foreign asset prices?
Lim and McNeris (2007) examined the role of asset price stabilization in a small
open economy. They focused on the Tobin’s Q channel that implied the eﬀect of Tobin’s
Q on the real economy through a firm’s investment decisions. They argued for theeﬀectiveness of asset price stabilization in monetary policy rules under the Tobin’s Q
channel. Di Giorgio and Nistico (2007) answered these questions in a two-country NK
model.6 According to their model, the stock market is constructed only in the foreigncountry. Therefore, their question is whether the home central bank should stabilize
the movement in foreign asset prices. They showed that the inclusion of foreign asset

5

See also Airaudo (2013a, 2013b).

6

Their model is based on the Blanchard-Yaari NK model because they focused on the eﬀect of thewealth channel of stock prices on the real economy.

5prices in domestic monetary policy rules can lead to preferable outcomes in terms ofequilibrium determinacy and the volatility of macrovariables.
Ida (2011) examined the eﬀectiveness with which the home central bank can respondto both home and foreign asset prices in a two-country model. Ida (2013) exploredthe role of asset price stabilization in a two-country model with local currency pricing
and illustrated the gains from employing asset price stabilization. Ida (2011, 2013) also
focused on the role of Tobin’s Q channel in a two-country model. According to his study,
the gain from such a monetary policy rule is not realized if the monetary policy rule
contains a strong response to output. Ida (2015) compared a Taylor rule and asset pricegrowth with several alternative rules, such as nominal gross domestic product growthtargeting, exchange rate targeting, and so on. However, the above studies did not focus
on the case in which each central bank takes stabilization of its own asset prices into
consideration in a two-country model.
The contribution of this paper is to demonstrate worldwide equilibrium determinacy
when both home and foreign central banks simultaneously react to their own asset prices
in a two-country model with incomplete pass-through of the loan rate. This paper isrelated to Di Giorgio and Nistico (2007), Ida (2011, 2013), and Pfajfar and Santoro(2014). Our study diﬀers as follows. First, while Di Giorgio and Nistico (2007) exploredthe case of wealth eﬀects of foreign asset prices, this paper focuses on the supply sideof asset price fluctuations. Furthermore, in contrast to Di Giorgio and Nistico (2007),
this paper considers the role of incomplete loan rate pass-through associated with thecost channel. Second, while Di Giorgio and Nistico (2007) demonstrated how an asset
price rule in the home country aﬀects equilibrium determinacy in each country, we show
the case in which each central bank stabilizes its own asset prices and thus changes
worldwide equilibrium determinacy. Third, Pfajfar and Santoro (2014) demonstrated
that the gain from employing an asset price rule occurs in the presence of incomplete
pass-through of the loan rate, whereas this paper asks the question whether or noteach central bank should aim to stabilize its own asset prices in a two-country modelwith financial market imperfections. Fourth, in contrast to Ida (2011, 2013), this paper

6

considers the relationship between the degree of imperfect pass-through of the loan rate
and asset price stabilization in terms of worldwide equilibrium determinacy.

3

A two-country NK model with incomplete passthrough of loan rates

This paper incorporates the simple financial market friction associated with a cost channel into a two-country framework. The model in this paper is based on Ida (2015).7
Consider an economy with two large symmetrical countries: home and foreign. There
are two production sectors in each country. The final goods sectors are characterized byperfect competition. The firms in intermediate goods sectors face monopolistic competition and Calvo-type (1983) nominal price rigidity.
In addition, for intermediate firms to pay employee wages, they must borrow funds
from financial intermediaries that are located in the home country. Following Ravenna
and Walsh (2006) and Chowdhury et al. (2006), this paper introduces the role of financial
intermediaries into the model. Financial intermediaries receive deposits from domestic
households and lend funds to domestic firms. When financial intermediaries lend funds
to intermediate goods producers, they incur a monitoring cost.
Our model assumes that there are complete markets in both countries and thathouseholds in both countries can trade a state-contingent bond both domestically andinternationally. Moreover, this paper presumes that only final goods are traded. Finally, unless otherwise noted, analogous equations hold for the foreign country. Foreign
variables are expressed with an asterisk.

3.1

A log-linearized two-country model

The log-linearization of the system is implemented around the steady state. A loglinearized variable around the steady state is expressed by Ĥt = log(Ht /H̄), where H̄
7

The technical appendix provides a detailed derivation of a two-country NK model with incomplete

pass-through of the loan rate. See also Ida (2015, 2019).

7

represents a steady-state value. Additionally, to express in terms of log-deviation fromtheir flexible price equilibrium counterparts, we introduce the following notation:
qt = Q̂t − Q̂ft ; yt = Ŷt − Ŷtf ; ηt = Γ̂t − Γ̂ft ,where Q̂t denotes asset prices, Ŷt represents aggregate output, and Γ̂t denotes the dividend. The superscript f denotes the log-deviation of the natural level.
The log-linearized Euler equation for stock prices is given as follows:
qt = (1 − β)ηt + βEt qt+1 − β(R̂t − Et πt+1 ),(1)

The parameter β denotes the discount factor. The second term on the right-hand side
indicates that future stock prices aﬀect current stock prices. The third term on theright-hand side of Equation (1) is the real interest rate. As we will show, stock prices
in the home country are indirectly influenced by movements in the foreign output gap
through domestic dividends.
The log-linearization of dividends from firms to stockholders is expressed as follows:Γ̂t = Ŷt − (θ − 1)φ̂t .
Parameter θ is the elasticity of substitution for individual goods, which parameter satisfies θ > 1. Using the definition of the dividend gap and substituting the real marginal
cost into the above equation, we obtainηt = [1 − (θ − 1)(σ + ϕ − χ)]yt − (θ − 1)χyt∗ − (θ − 1)R̂tL ,(2)where χ = ϑΩ−1 , ϑ = 2γ(1 − γ)(σa − 1), and Ω = 4γ(1 − γ)(σa − 1) + 1. The parameter adenotes elasticity of substitution between domestic and foreign consumption goods andthe parameter γ represents the degree of trade openness. σ and ϕ are positive parameters,
which are explained in section 4. R̂tL denotes the loan rate associated with the presenceof the cost channel.
In contrast to the framework set forth by Pfajfar and Santoro (2014), there is aspillover eﬀect in an open economy on firm’s dividends to domestic stockholders. Thiseﬀect is captured by the second term of the right-hand side. Thus, it follows from8

Equation (2) that the foreign output gap influences the domestic dividends throughthe terms of trade and consumption risk-sharing. For instance, the foreign output gap
reduces domestic dividends when the parameter σa takes a value above unity. The
foreign output gap increases domestic dividends when the parameter σa takes a valueless than unity. These eﬀects disappear when the parameter σa takes unity. Thus, theforeign output gap aﬀects domestic stock prices through domestic dividends—as long as
the parameter σa is not unity.
Next, the log-linearized lending rate is given as follows:R̂tL = (1 + ψr )R̂t + νt ,(3)

where ψr represents the degree of lending rate pass-through.8 An exogenous loan rate
shock νt is incorporated into the model. The financial market disturbance νt follows an
AR (1) process given by νt = ρν νt−1 + ϵνt with 0 ≤ ρν < 1, where ϵνt is an i.i.d shock withconstant variance σν2 .
It follows from Equation (3) that the lending rate deviates from the policy rate as passthrough of the lending rate becomes incomplete: the higher the value of the parameterψr , the more incomplete the interest rate pass-through becomes. As indicated in theclosed economy model, it is possible that when the economy faces severe financial market
imperfections, monetary tightening might easily increase the inflation rate through the
supply side eﬀect of monetary policy. Note that, as in Ravenna and Walsh (2006),
a wedge between the lending rate and the policy rate disappears when ψr = 0 if an
exogenous loan rate shock is not present.
Inflation adjustment is depicted by the new Keynesian Phillips curve (NKPC), whichplays an important role in inflation dynamics. Following Calvo (1983), price rigidity is
assumed to exist in the intermediate goods sector. Thus, a fraction 1 − ω of all firms
adjusts their prices, whereas the remaining fraction of firms ω do not. An open-economy
NKPC expressed in terms of the real marginal cost is given by
πH,t = βEt πH,t+1 + κφ̂t ,8

See Chowdhury et al. (2006) for a detailed discussion of Equation (3).

9(4)

where κ = (1 − ω)(1 − ωβ)/ω and πH,t is producer price inflation.
The real marginal cost in an open economy is given as follows:φ̂t = R̂tL + (σ + ϕ − χ)yt + χyt∗ ,(5)

As shown in Ravenna and Walsh (2006) and Chowdhury et al. (2006), real marginal costdepends on the lending rate in an economy with a cost channel. Moreover, the foreign
output gap aﬀects the real marginal cost through the terms of trade and consumption
risk sharing in an open economy. As discussed in Clarida et al. (2002) and Pappa (2004),
there exist externalities associated with an open economy as long as the parameter σais not unity. If σa > 1, domestic and foreign goods are substitutes in the ParetoEdgeworth sense. In this case domestic inflation increases in response to an increasein the foreign output gap because a positive output gap in the foreign country induces
an increase in the domestic real marginal cost. On the other hand, if σa < 1, the twogoods are complements. This implies that the domestic inflation rate declines because
a positive foreign output gap reduces the domestic marginal cost. As mentioned earlier,these eﬀects cancel each other out when the parameter σa takes the value of unity.
Substituting Equation (5) into Equation (4), an open-economy NKPC expressed in termsof the output gap is derived as follows:
πH,t = βEt πH,t+1 + κ[R̂tL + (σ + ϕ − χ)yt + χyt∗ ],(6)

The dynamic investment-savings curve, which is derived from the representative
household’s Euler equation for optimal consumption, is given by:
yt = Et yt+1 +σϑ
∗(Et yt+1− yt∗ ) − σ0−1 (R̂t − Et πH,t+1 − R̂tf ),Ωwhere σ0 = σ(1 + ϑ)/Ω.

10

(7)

3.2

Flexible price equilibrium

The set of variables under flexible price equilibrium is given as follows:f∗fR̂tf = σ0 ϑ(Et Ŷt+1− Ŷtf ∗ ) + σ0 (Et Ŷt+1− Ŷtf ),(8)

Q̂ft = (1 − β)Γ̂ft + β(Et Q̂ft+1 − R̂tf ),(9)Γ̂ft = Ŷtf ,(10)(σ + ϕ − χ)Ŷtf + χŶtf ∗ + R̂tf = (1 + ϕ)Zt ,(11)

where the superscript f denotes the log-deviation of the natural level. Equation (8)represents the open economy natural rate of interest that holds the real interest rate
under flexible-price equilibrium. Equations (9) and (10) are stock prices and dividends
under flexible price equilibrium. Equation (11) describes the natural rate of output inan open economy model. In contrast to the natural rate of output shown in Clarida etal. (2002), the natural rate of output in the home country depends on the natural levelof the lending rate.

3.3

Monetary policy rules

To close the model, we describe the monetary policy rules used in this study. This study
employs the standard monetary policy rule suggested by Taylor (1993). In particular,
we consider whether each central bank should react to its own asset prices in terms ofequilibrium determinacy and macroeconomic volatility. More specifically, we specify alog-linearized home monetary policy rule as follows:R̂t = ϕπ πH,t + ϕy yt + ϕq qt + ut ,(12)

where ϕπ is the coeﬃcient of the rate of inflation, and ϕy is the coeﬃcient of the output
gap. Similarly, the foreign monetary policy rule is given by∗R̂t∗ = ϕ∗π πF,t
+ ϕ∗y yt∗ + ϕ∗q qt∗ + u∗t(13)

We can employ another specification of the monetary policy rule for asset price stabilization. Equations (12) and (13) state that each central bank responds to a deviation11

in asset prices from their flexible-price equilibrium counterparts (Di Giorgio and Nistico,2007; Nistico, 2012). In addition, the central bank may employ a monetary policy rulewith the stabilization of asset price growth (e.g., Nistico, 2010). At this point, this paper explores the benchmark case in which each central bank responds to the deviationof asset prices from their flexible-price equilibrium counterparts.

4

Calibration

This section describes the parameters used in this study. The parameter values usedin this paper is are calibrated based on Ida (2015). The degree of price rigidity, ω, isset to 0.75. Following previous studies in the NK literature, the discount factor, β, isset to 0.99. A value of 2.0 is used for the risk aversion coeﬃcient, σ. The elasticity ofhousehold labor supply, ϕ, is set to 1.0. The elasticity of substitution between domestic
and foreign consumption goods, a, is set to 1.5. With regard to the degree of openness,the value of γ is set to 0.2. The elasticity of substitution for individual goods, θ, is set to
5.0, based on the value calibrated in the existing literature. The calibrated parameters
are summarized in Table 1.
[Table 1 around here]
Several studies have reported the value of the degree of financial market imperfection,
ψr . According to Ravenna and Walsh (2006), the value of the parameter ψr is 0.276.
Also, Chowdhury et al. (2006) estimated a value of financial market imperfection of
0.32 for the US. Castelnuovo (2007) used the values ψr ∈ {0.5, 1.7}.9 Therefore, thispaper uses the values ψr ∈ {0, 3}. This paper assumes a slightly larger value of ψr than
do previous studies in order to examine how more severe financial imperfections change
the international transmission mechanism of structural shocks in one country. In thispaper, we mainly focus on how the degree of financial market imperfection in the foreigncountry aﬀects the home country. Therefore, the degree of financial market imperfections
9

Castelnuovo (2007) pointed out that a larger value of the parameter ψr is likely to generate theprice puzzle that an increase in the policy rate increases inflation in the closed economy model.

12

in the home country is set to 0.2, based on the estimation value obtained in the study by
Ravenna and Walsh (2006), whereas we set several values calibrated in the above studies
to that of the foreign countries.
We now describe the parameters for the monetary policy rule. As a benchmark, wechoose 2.0 and 0 for ϕπ and ϕy for each country, respectively. Finally, with regard to thestandard deviation of economic shocks, this paper assumes that σν , σz , and σu are set to0.01, respectively. Also, this paper assumes that the parameters ρν , ρz , and ρu are set
to 0.8, 0.8, and 0.5, respectively. Table 1 summarizes the deep parameters calibrated inthis study.

5

Asset price stabilization in a two-country economy
with the cost channel

This section examines incomplete loan rate pass-through and asset price stabilization ina two-country model. We explore how incomplete pass-through of the loan rate aﬀects
the determinacy of the worldwide equilibrium when each central bank stabilizes its own
asset prices. In this paper, we define the worldwide equilibrium determinacy as the casein which the REE is achieved in both the home and foreign countries. Accordingly,
the worldwide equilibrium is indeterminate if either country faces any indeterminacy
problem.
As noted earlier, Bullard and Singh (2008) and Bullard and Schaling (2009) bothinvestigated the determinacy condition in an open economy model. These papers abstracted the role of the cost channel. Di Giorgio and Nistico (2007) demonstrated how
an asset price rule in the home country aﬀects equilibrium determinacy in each country;
we demonstrate how the case in which each central bank stabilizes its own asset prices
changes worldwide equilibrium determinacy. Therefore, the contribution of this paper isin demonstrating how worldwide equilibrium determinacy is achieved when both central
banks each care about a fluctuation in its own asset prices in the presence of financial
market imperfections.
13Section 5.1 investigates how incomplete pass-through of the loan rate aﬀects thedeterminacy of the worldwide equilibrium when asset price stabilization is consideredby home and foreign central banks. Section 5.2 considers how a stronger response toinflation in each central bank changes the results obtained in Section 5.1. Section 5.3
examines the role of output gap stabilization in this two-country economy. Section
5.4 explores worldwide determinacy when central banks employ a monetary policy rulewith stabilization of asset price growth. Section 5.5 explores the eﬀect of asset pricestabilization on the international transmission mechanism of structural shocks.

5.1

World equilibrium determinacy and asset price stabilization

Figure 1 portrays how the degree of foreign loan rate pass-through changes the world
equilibrium determinacy regions under several parameterizations of ϕq and ϕ∗q . When
financial market imperfections are present in the foreign country, the world equilibrium is
uniquely determinate—as long as both the home and foreign central banks set asset pricestabilization to less than 0.2. It follows from Figure 1 that the reaction of home asset
prices ϕq is smaller than that of ϕ∗q . When ψr∗ = 0.5, given for the value of ϕq , a valueof ϕ∗q that takes 0.15 renders the world equilibrium indeterminate. In particular, whenψr∗ = 1.0, a combination of a suﬃciently smaller value of ϕq and ϕ∗q renders the world
equilibrium indeterminate. In the case in which the incomplete loan rate pass-throughis very severe in the foreign country (i.e., ψr∗ = 1.5), only a combination of a very narrow
range of ϕq and ϕ∗q can yield equilibrium determinacy. Thus, Figure 1 indicates that alarger value of ψr∗ drastically shrinks the worldwide determinacy regions. These results
are not observed in previous studies that focused on the role of asset price stabilizationin an economy with financial market imperfections (e.g., Airaudo, 2013; Bernanke andGertler, 2001; Nistico, 2010; Pfajfar and Santoro, 2014).
[Figure 1 around here]
The intuition from this result is as follows. Suppose that a sunspot shock that induces
14

a boom in both inflation and output occurs in the foreign country. In the case of severe
incomplete loan rate pass-thorough, monetary tightening in reaction to a sunspot shock
results in further inflation through the cost channel. As shown in Llosa and Tuesta(2009), a sunspot shock is likely to generate equilibrium indeterminacy in the presenceof the cost channel. Moreover, in the foreign country, a rise in the inflation rate decreases
asset prices via a decline in the dividend. Thus, the presence of the cost channel generates
a trade-oﬀ between inflation and asset prices. Severe financial imperfections worsen thistrade-oﬀ. In this case, a rule that puts a smaller weight on asset price stabilization might
restrain this channel. However, the foreign country encounters equilibrium indeterminacy
because a stronger response to asset prices dampens the rise in the policy rate, amplifying
the cost channel induced by a larger value of ψr∗ .
A sunspot equilibrium that occurred in the foreign country might be transmitted tothe home country. A foreign sunspot shock generates downward pressure on domestic
inflation and output through an appreciation in the exchange rate. Appreciation in theexchange rate in terms of the home currency leads to a decline in the domestic real
marginal cost, reducing domestic inflation. A decline in home inflation increases homeasset prices. Severe financial imperfections deteriorate this trade-oﬀ via the exchange ratechannel. Therefore, while domestic inflation declines, the home central bank increases
its policy rate in response to the increase in domestic asset prices. Accordingly, a foreign
sunspot shock leads to world equilibrium indeterminacy when both the home and foreign
each central banks employ a stronger response to asset price stabilization.

5.2

Stronger response of inflation and asset price stabilization

Figure 2 portrays the case in which both the home and foreign central banks employ astronger response to inflation when considering the role of asset price stabilization. It
turns out that compared to the case depicted in Figure 1, the worldwide determinacy regions expand if both the home and foreign central banks cooperatively employ a stronger
response to inflation. Even in this case, depicted in the lower right panel of Figure 2,
a unique worldwide REE can be attained if the home and foreign central banks place15

a smaller weight on asset price stabilization in the monetary policy rule. This case isstill observed when ψr∗ = 1.0. Thus, the worldwide determinacy condition cannot be
improved—even if both central banks each react strongly to their own inflation. The
case of ψr∗ = 1.5 is prone to generating world equilibrium indeterminacy. For the caseof ψr∗ = 1.5, while a stronger response to inflation by each central bank can enlarge
the determinacy areas, worldwide equilibrium indeterminacy easily emerges unless eachcentral bank puts a smaller weight on its asset price stabilization.
These results contrast with Bernanke and Gertler (1999) but are consistent with theassertions of Airaudo et al. (2013). However, this paper addresses that the worldwide
determinacy condition can be restored when both central banks employ a milder response
to its own asset prices in the case where a strong cost channel is present in each country.
[Figure 2 around here]
Next, given values for ϕπ , consider how the worldwide equilibrium determinacychanges when the foreign central bank increases the value of ϕ∗π . Figure 3 shows thatlarger values for ϕ∗π can make the worldwide REE more determinate when the foreign
central bank places a more aggressive weight on asset price stabilization.10 However, irrespective of any combinations of ϕ∗q and ϕ∗π , the worldwide REE becomes indeterminate
if the home central bank reacts more aggressively to domestic asset prices for any given
value of ϕπ . The world economy can escape the indeterminacy problem if the foreign
central bank that strengthens its response to inflation reinforces the stabilization of its
own asset prices. Even in such a case, unfortunately, the home central bank that employsa weaker response to home inflation makes the worldwide REE indeterminate if it reacts
strongly to home asset prices.
As noted earlier, Ida (2011) argued that a stronger response to asset prices in the homecountry can enhance social welfare if the home central bank stabilizes not only domestic
asset prices but also foreign asset prices.11 Di Giorgio and Nistico (2007) showed the10

We set ψr = ψr∗ = 0.2 in this simulation.

11

Ida (2013) showed that a stronger response to asset prices increases welfare loss in a two-country

model with local currency pricing.

16

gains achieved when the home central bank responds to foreign asset prices in a twocountry economy with a wealth eﬀect for consumption. However, this paper shows thatworldwide equilibrium determinacy is not retained when both central banks each employ
a larger weight on theirs own asset price stabilization.
[Figure 3 around here]
The intuition from Figures 2 and 3 is as follows. Consider, again, the case in whicha sunspot shock occurs in the foreign country. Figure 3 implies that the foreign central
bank can obtain additional gains from employing asset price stabilization by placing
larger values on ϕ∗π . This is because the foreign central bank can alleviate the tradeoﬀ between inflation and asset prices, which is generated by a severe cost channel as
expressed by larger values of ψr∗ . However, the alleviation of the policy trade-oﬀ in
the foreign country induces an appreciation in the exchange rate in terms of the homecurrency. Therefore, given values for ϕπ and ϕx , the home central bank must place asmaller weight on fluctuations in domestic asset prices in order to achieve a unique REE.
In fact, the worldwide REE becomes indeterminate when ϕq is above 0.15, irrespectiveof any combinations of ϕ∗q and ϕ∗π . In other words, the foreign central bank that responds
strongly to inflation can achieve the REE in its country, whereas the home central bankthat aggressively stabilizes domestic asset prices fails to generate a unique home REE.
As a consequence, a foreign sunspot shock renders the worldwide REE indeterminate
whenever the home central bank responds aggressively to domestic asset prices.

5.3

Responses of the output gap and asset price stabilization

We consider the case in which given a value of ϕx , the foreign central bank reacts strongly
to its output gap. As Figure 4 illustrates, if both central banks stabilize their own asset
prices, the worldwide determinacy areas shrink when the foreign central bank puts astronger weight on the stabilization of its output gap.
[Figure 4 around here]17

As shown in Surico (2008) and Llosa and Tuesta (2009), a stronger policy responseto the output gap is more prone to creating indeterminacy in the presence of the costchannel. Our result is diﬀerent from these studies in that it shows that, even in thecase in which an interest rate response to asset prices in each country is eﬀective, thehome and foreign central banks fail to achieve the worldwide equilibrium determinacy
if either the home or foreign central bank employs a stronger policy reaction to its own
output gap. In addition, Pfajfar and Santoro (2014) demonstrated the eﬀectiveness ofasset price stabilization in an NK model with a cost channel given a response to the
output gap. On the other hand, we show that a larger weight on asset price stabilizationin both countries easily renders the worldwide REE indeterminate when either central
bank responds strongly to its own output gap in a two-country NK model.

5.4

The role of stabilization of the growth rate of asset prices

Finally, this paper considers the role of the stabilization of the asset price growth rate in
the monetary policy rule. We assume that the home central bank employs the monetary
policy rule (12), whereas the foreign central bank incorporates the stabilization of asset
price growth into the monetary policy rule, namely:∗∗R̂t∗ = ϕ∗π πF,t
+ ϕ∗y yt∗ + ϕ∗q (qt∗ − qt−1
) + u∗t(14)

As mentioned earlier, Nistico (2012) considered that the central bank might employ amonetary policy rule with the stabilization of asset price growth and showed that reacting
to asset price growth can alleviate the indeterminacy problem. Di Giorgio and Nistico(2007) also investigated the role of a monetary policy rule that reacts to an asset pricegrowth in a two-country NK model with wealth eﬀects. Accordingly, this paper explores
the asymmetrical monetary policy response in terms of asset price stabilization.12
Figure 5 plots the worldwide determinacy regions when the foreign central bank employs monetary policy rule (14). In contrast to the case depicted in Figure 1, for a
12

We can also consider the case in which both central banks employ a monetary policy rule with anasset price growth. The result of this specification is available from the author upon request.

18

smaller value of ψr∗ , a foreign asset price growth rule can expand the worldwide determinacy regions. In particular, compared to Figure 1, the case in which the values of ϕ∗q
are above 0.2 leads to a unique REE worldwide unless financial market imperfections
are considerably severe in the foreign country. However, in the case of ψr∗ = 1.5, somepositive weight on asset price growth in a foreign monetary policy rule can attain theunique worldwide REE if the home central bank puts a smaller weight on asset pricestabilization in its monetary policy rule.
[Figure 5 around here]
Nistico (2012) showed the eﬀectiveness of reacting to asset price growth in a perpetual
youth NK model, whereas Di Giorgio and Nistico (2007) argued that such a rule mightlead to equilibrium instability in a two-country NK model with wealth eﬀects. On theother hand, this paper shows that the gain from the foreign central bank stabilizing its
asset price growth in that it can expand the worldwide determinacy regions. In contrast
to Di Giorgio and Nistico (2007), our model notes that this gain may be derived from thesituation in which stock markets are present in both countries, but they do not interact
internationally.

5.5

Asset price stabilization and economic dynamics

This section examines the relationship between asset price stabilization and the international transmission of structural shocks. First, we investigate the impulse response
analysis to check the role of asset price stabilization. We consider three cases. The firstcase assumes that the home and foreign central banks do not care about fluctuations inasset prices. The second case focuses on the case in which a stabilization weight on asset
prices is considered only in the home country. The third case presumes that the homeand foreign central banks jointly employ a stronger response to asset price stabilizationin each country.
Figures 6 and 7 illustrate the impulse responses to both foreign productivity and loan
rate shocks. A foreign productivity shock leads to a decline in inflation and an increase19

in output in the foreign country. Since the Case III produces a huge decline in foreign
inflation, the foreign central bank cuts its policy rate more aggressively. Overall, foreign
stock prices seem to be unaﬀected by any combination of home and foreign asset pricestabilization.
[Figure 6 around here][Figure 7 around here]
On the other hand, a foreign productivity shock induces a decline in both inflationand output in the home country. It turns out that when each central bank stabilizes
asset prices in its own country (thus, Case III), as compared to Case II, a decline in bothinflation and output in the home country is alleviated. This is the gain for the homecountry when each central bank stabilizes asset prices in its own country. This policy
implication is also observed in the case of a foreign loan rate shock (e.g., Figure 7).
We also confirm the properties of standard deviations for the three cases. Table 2
shows that, in contrast to the case in which the central bank does not react to stock prices,volatility in both output and stock prices declines when each central bank stabilizes its
own asset prices. On the other hand, in such a case, each central bank has to accept
an increase in its own inflation. Thus, even when central banks employ asset pricestabilization in a policy rule, they cannot overcome the policy trade-oﬀ between inflationand output stabilization.
[Table 2 around here]
Previous studies have argued that, for given foreign monetary policy rule, the home
central bank that stabilizes its asset prices is able to reduce macroeconomic volatility(e.g., Di Giorgio and Nistico, 2007; Ida, 2011; Ida, 2013). This paper also shows thatcompared to making no response to asset prices, a monetary policy rule that contains
asset price stabilization might achieve more preferable outcomes in terms of stabilizationof the output gap, asset prices, and the exchange rate. Importantly, in contrast to
previous studies, compared to the case in which the home central bank only stabilizes its
20

own asset prices, both central banks can obtain welfare gains when they stabilize theirown asset prices. As shown in Table 3, this result is robust to the case in which financial
market imperfections are severe in the foreign country (i.e., ψr∗ = 0.5).
[Table 3 around here]
Finally, we confirm whether the foreign central bank that stabilizes its asset pricegrowth can reduce volatility in worldwide macrovariables. Figure 8 plots the impulse
responses to a foreign productivity shock when the foreign central bank employs diﬀerent
asset price rules. Case I indicates that no central bank responds to their asset prices.
Case II assumes that while the home central bank follows a policy rule with no asset
price response, the foreign central bank employs one with its asset price growth. Case
III implies that the home central bank employs a monetary policy rule that includes
stabilization of the asset price gap, whereas the foreign central bank incorporates thestabilization of its asset price growth into its monetary policy rule.
[Figure 8 around here]
Figure 8 illustrates that Case II can lead to preferable outcomes to the other cases
because of it counteracts the volatility in worldwide macrovariables. This result can also
be confirmed in Table 4. Compared to other regimes, Case II can reduce worldwide
volatility in macrovariables. We reconfirm the findings of Di Giorgio and Nistico (2007)
in a two-country NK model in which both countries have stock markets.13[Table 4 around here]

6

Concluding remarks

A large number of studies have focused on the role of asset price stabilization in monetary policy analyses. The objective of this paper is to explore the role of asset price
13

Note, again, that this gain may be derived from the fact that although stock markets are present

in both countries, they do not interact internationally.

21

stabilization in a two-country NK model with incomplete pass-through of the loan rate.
We focus on worldwide equilibrium determinacy when both the home and foreign central banks simultaneously react to their own asset prices in a two-country model withincomplete pass-through of the loan rate.
The results obtained in the paper are summarized as follows. When financial market imperfections are present in the foreign country, world equilibrium determinacy isachieved if home and foreign central banks set smaller weights on asset price stabilization.
When the foreign central bank reacts more aggressively to inflation in its own country, it
can cause the REE to become more determinate by placing a more aggressive weight on
asset price stabilization. However, irrespective of any combinations of inflation and asset
price stabilization in the foreign country, the worldwide REE becomes indeterminate if
the home central bank reacts more aggressively to domestic asset prices.
There are possible future extensions of the work done in this study. We assumed thatthe exchange rate pass-through is perfectly complete. Thus, the law of one price holds
in this model. However, as argued by Corsetti and Pesenti (2001), Monacelli (2005), andEngel (2009), exchange rate pass-through would be incomplete if firms set their export
prices based on local currency pricing. It is interesting how financial market imperfectionaﬀects an open macroeconomic model in which incomplete exchange rate pass-throughis present.

Acknowledgements
This paper was supported by JSPS KAKENHI Grant Numbers 16H03618 and 17K13766.
All remaining errors are my own.

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26

A

Appendix (Not for publication)

This appendix provides the detailed model description used in the paper. As noted
earlier, this paper incorporates a simple financial market friction associated with a costchannel into a two-country framework. The model in this paper is based on Ida (2015).

A.1

Households

The consumption index for the domestic country, Ct , is given by]a/(a−1)[
Ct = (1 − γ)1/a(a−1)/a(a−1)/aCH,t+ γ 1/a CF,t

,

(A.1)

where CH,t denotes consumption of domestic goods and CF,t denotes consumption offoreign goods. The parameter a denotes elasticity of substitution between domestic andforeign consumption goods, and the parameter γ represents the degree of trade openness.
First, households consider an intra-temporal cost minimization problem and derive
the demand function for each good:
(
)−a
PH,t
CH,t = (1 − γ)
Ct ,
Pt
(
)−a
PF,t
CF,t = γ
Ct ,
Pt

(A.2)
(A.3)

where the home country’s price index is given by[]1/(1−a)1−a1−aPt = (1 − γ)PH,t + γPF,t
,

(A.4)

where PH,t is the price of domestic goods and PF,t is the price of foreign goods.
Next, we consider the household’s dynamic optimization problem. The inter-temporalutility of an infinitely lived representative household is
Ut = Et

∞
∑
j=0

(
β

j

1+ϕ )
1−σ
Ct+j
Nt+j
−ζ
,
1−σ
1+ϕ

(A.5)

where Nt is the household’s labor supply. The parameter β denotes the discount factor,and σ, ζ, and ϕ are positive parameters. The representative household faces the following
27

budget constraint:
Pt Ct + Pt Qt At + Mt+1 + Et µt,t+1 Bt+1 + Dt =Mt + Bt + RtD Dt + Pt At Γt + Πt (B)+ Wt Nt + Pt Qt At−1 + Pt Tt ,(A.6)

where RtD denotes the gross nominal interest rate on deposits, Dt is the deposit infinancial intermediaries, Bt is the nominal bond, µt,t+1 is the stochastic discount factor,
which denotes the bond price of in terms of home currency. Wt and Γt are the nominal
wage and the dividend from intermediate goods firms. Πt (B) denotes the dividend fromfinancial intermediaries and At denotes shares of stock that sell at price Qt . Mt is thenominal money stock and Tt denotes lump-sum transfers. In addition, the representative
household faces the following cash-in-advance constraint:
Pt Ct ≤ Mt − Dt + Wt Nt .

(A.7)

As in Ravenna and Walsh (2006), Equation (A.7 ) states that households enter period
t with cash holdings of Mt . Before households enter goods and financial markets, they
deposit the funds Dt with financial intermediaries. Hence, household’s remaining cash
balances are subject to a cash-in-advance constraint (A.7 ).
The household maximizes its own utility, subject to Eqs. (A.6 ) and (A.7 ). If thenominal interest rate is positive, the first-order conditions of this optimization problem
are(Ct−σ = βEt−σRt Ct+1

)
Pt
,
Pt+1

Wt
ζNtϕ
,
−σ =
Pt
Ct

(A.8)
(A.9)

−σ
Ct−σ (Qt − Γt ) = βEt Ct+1
Qt+1 ,(A.10)

where Rt denotes the nominal interest rate that is set by the home central bank. Equation (A.8 ) represents an Euler equation for consumption.14 The left-hand side of Eq.
14

In competitive bond and deposit markets, the nominal interest rate on bonds is equal to the deposit

rate through the arbitrage condition between bond and deposit markets.

28

(A.8 ) is the marginal utility in period t, whereas the right-hand side of Eq. (A.8 )is the discounted marginal utility of consumption in period t + 1. The Euler equation
requires that in equilibrium, the marginal utility of consumption will inter-temporally
equalize through real interest rate adjustments. Equation (A.9 ) gives the marginal rateof substitution between consumption and a household’s labor supply. Equations (A.10 )represents the dynamics of share prices Qt .

A.2

Firms

Each country has two production sectors. The first is the final goods sector, which produces final goods using intermediate goods and is characterized by perfect competition.
The second is the intermediate goods sector, in which firms face monopolistic competition and Calvo pricing. In addition, intermediate goods firms have to borrow funds
from only home financial intermediaries to pay employee wages. Following Pfajfar andSantoro (2014), it is assumed that domestic firms are completely rationed on the equity
market located in the home country; this assumption allows the model to consider thecase wherein firms borrow funds from home financial intermediaries due to the existenceof financial gaps generated by firms facing a shortage of internal funds.15 Therefore, inthis model, intermediate firms borrow funds from financial intermediaries and also issue
their own securities, which are held by domestic households.
A.2.1

The final goods sector

Each final goods firm employs the following constant elasticity of substitution (CES)
technology:
[∫ 1
Yt =

]θ/(θ−1)
Yt (i)(θ−1)/θ

di,(A.11)

0where Yt is aggregate output and Yt (i) denotes demand for intermediate goods producedby firm i. As in Clarida et al. (2002), both variables are normalized by population size

15

See Pfajfar and Santoro (2014) for a detailed discussion of this problem.

29

1 − γ. Parameter θ is the elasticity of substitution for individual goods, which parametersatisfies θ > 1.
The demand for intermediate goods is()−θ
PH,t (i)Yt (i) =Yt ,PH,t(A.12)

where PH,t (i) is the price for intermediate goods produced by firm i. The price index inthis case is given by[∫ 1]1/(1−θ)1−θ

PH,t =

PH,t (i)di.

(A.13)0

A.2.2

The intermediate goods sector

The intermediate goods sector is characterized by monopolistic competition, and eachfirm produces a diﬀerentiated intermediate good. Firm i’s production function is givenby
Yt (i) = Zt Nt (i),(A.14)

where Zt denotes an aggregate productivity disturbance, which follows an AR (1) process
given by log(Zt ) = ρz log(Zt−1 ) + ϵzt with 0 ≤ ρz < 1. ϵzt is an i.i.d shock with constantvariance σz2 .
Following Calvo (1983), price rigidity is assumed to exist in the intermediate goods
sector. Thus, a fraction 1 − ω of all firms adjusts their prices, whereas the remaining
fraction of firms ω do not. When revising their prices, these firms take into accountuncertainty concerning their next potential opportunity to adjust prices. As such, theintermediate firm’s optimization problem is given by[( opt )1−θ
( opt )−θ ]
∞
∑
PH,t
PH,t
j
Et
ω µt,t+j− φt+j
Yt+j ,
PH,t+jPH,t+jj=0(A.15)

where µt,t+j is the stochastic discount factor, which is given by β j (Ct+j /Ct )−σ . φt denotesopt
the real marginal cost and PH,tis the optimal price index in period t. The first-ordercondition of this optimization problem is as follows:]( opt )−θ
[ opt
∞
∑
PH,t
PH,t
θ
1
j
Et
−
φt+j
(ωβ)
opt Yt+j = 0.
PH,t+jθ−1
PH,t+jPH,t
j=030(A.16)

This paper assumes that intermediate firms must borrow the funds Wt Nt from domestic financial intermediaries at the gross lending rate RtL in order to pay employee
wage. Intermediate firms face the following cost minimization problem:
RtL

Wt
Nt − φt (Zt Nt − Yt ).
PH,t(A.17)

1 Wt LR .
Zt PH,t t(A.18)

Cost minimization leads toφt =In contrast to the standard new Keynesian analysis, because intermediate firms haveto borrow funds from financial intermediaries under the assumption of the cost channel, their real marginal costs also depend on the lending rate. When the central bankraises the nominal interest rate, intermediate firm i’s working capital increases becausemonetary tightening induces a rise in the lending rate. This indicates that a monetary
tightening policy directly increases the real marginal cost.
Finally, as employed in the framework of Pfajfar and Santoro (2014), this paper
assumes that firms fully transfer their profits through dividends to shareholders. In thiscase, dividends to shareholders are given as follows:Γt = Yt − RtL

Wt
Nt = (1 − φt )Yt .
PH,t(A.19)

In contrast to the case of no cost channel, the lending rate aﬀects the dividends tostockholders. Hence, it follows from Eq. (A.10 ) that the lending rate influences the
dynamics of stock prices.

A.3

Financial intermediaries

Domestic financial intermediaries provide deposit services to domestic households. If adomestic household deposits the amount of Dt in period t, it will receive the amount of
Rt Dt at the end of the period. In turn, the financial intermediaries receive deposits fromdomestic households and lend these funds to domestic firms.16
16

As noted earlier, we do not postulate that firms located in home country firms do not lend the funds

from foreign financial intermediaries. Thus, this paper does not assume that financial intermediaries in
one country lends their funds for firms only lend to firms located in the home country.

31

Following Chowdhury et al. (2006), financial intermediaries incurs a monitoring cost,
Ψ(Rt ) when lending funds to intermediate goods producers. As mentioned earlier, thismonitoring cost seems to serve as a shortcut to create incompleteness of loan rate passthrough. For the sake of strictly deriving the loan rate curve with a micro-foundation,
this simplification makes the model description and model solution simple and intuitively
understandable. To capture this argument in the model, following Chowdhury et al.
(2006), it is here assumed that this monitoring cost is diﬀerentiable and satisfies the′′′following properties: Ψ (Rt ) ≥ 0 and Ψ (Rt ) ≥ 0.
Financial intermediaries face the following profit maximization problem:Πt (B) = RtL (1 − Ψ(Rt )eνt )Lt − Rt Dt − kLt ,(A.20)

subject to Lt = Dt , where Lt denotes loans to a firm. The parameter k represents
the management cost, which is constant. In addition, an exogenous loan rate shock νt
is incorporated into the model. The financial market disturbance νt follows an AR (1)process given by νt = ρν νt−1 +ϵνt with 0 ≤ ρν < 1, where ϵνt is an i.i.d shock with constantvariance σν2 . One might consider the exogenous shock νt arised from a loan default rate.
In addition to a simple introduction of financial frictions suggested by Chowdhury etal. (2006), this paper assumes that a simple introduction of an exogenous loan rate
shock can capture structural shocks that tighten demand and supply in the loan market.
Therefore, we assume that this shortcut of an exogenous loan rate shock might be justsimply regarded as a reduced-form of a financial accelerator. The equilibrium for thelending market is Dt = Wt Ntd , where Ntd denotes the demand for labor.

A.4

Market clearing and international risk-sharing condition

We require market clearing conditions of goods market clearing in each country. Domestic
producers sell their final goods to both domestic and foreign households. Since both Yt
and Yt∗ are defined in per capita terms, the clearing conditions for the goods market in32home and foreign countries are∗(1 − γ)Yt = (1 − γ)CH,t + γCH,t,(A.21)∗,
γYt∗ = γCF,t + (1 − γ)CF,t(A.22)

where asterisks denote foreign variables. Substituting Equation (A.2 ) and the corresponding equation in the foreign country into Equation (A.21 ), we obtain
(
Yt =

PH,t
Pt

)−a [

]
)
γ
a ∗
(1 − γ)Ct + γ
S C ,1−γ t t((A.23)

where St = Et Pt∗ /Pt denotes the real exchange rate and Et is the nominal exchange rate.
The stock market clearing condition in each country is (1 − γ)At = 1, and the clearing
condition of the international bond market is given by (1 − γ)Bt + γBt∗ = 0.
Next, we consider a risk-sharing condition between countries. The Euler equation forforeign consumption denominated in domestic currency is[( ∗ )−σ ∗]Ct+1
1
P t Et
= βEt
.
∗
Rt∗
Ct∗
Pt+1
Et+1

(A.24)

By assuming that there exist state-contingent bonds that allow both domestic and foreign
households to trade internationally, combining Eq. (A.24 ) with the Euler equation fordomestic consumption and the definition of the real exchange rate, the real exchange
rate becomes(Ct∗
St = τ
Ct)σ,(A.25)

where τ is a constant term. Equation (A.25 ) states that the real exchange rate adjustsfor the diﬀerence between domestic and foreign consumption.

33

Table 1: Calibrated parameter values for a benchmark caseParameter Description

Value

ω

Degree of price stickiness

0.75

β

Discount factor

0.99

σ

Relative risk aversion coeﬃcient

2.0

ϕ

Elasticity of labor supply

1.0γ

Degree of openness

0.2θ

Elasticity of substitution between individual goods

5.0aElasticity of substitution between home and foreign goods

1.5

ϕπ

Inflation stabilization in the Taylor rule

2.0

ϕy

Stabilization of the output gap in the Taylor rule0σzStandard deviation of a productivity shock

0.01

σν

Standard deviation of a loan rate shock

0.01

σu

Standard deviation of a monetary policy shock

0.01

ρz

Auto-regression coeﬃcient for a productivity shock

0.8

ρν

Auto-regression coeﬃcient for a loan rate shock

0.8

ρu

Auto-regression coeﬃcient for a monetary policy shock

0.5

34

Table 2: Standard deviations of key macrovariables in the case of ψr = ψr∗ = 0.25
Variables

Case I

Case II

Case III

Home inflation

0.17

0.28

0.25

Foreign inflation

0.47

0.47

0.68

Home output gap

0.44

0.51

0.47

Foreign output gap

1.35

1.37

1.27

Home stock price gap

1.80

1.72

1.58

Foreign stock price gap

4.24

4.19

4.02

Real exchange rate

1.33

1.34

1.25

(Note) Case I: ϕq = ϕ∗q = 0; Case II: ϕq = 0.1 and ϕ∗q = 0; Case III: ϕq = ϕ∗q = 0.1.

35

Table 3: Standard deviations of key macrovariables in the case of ψr = 0.25 and ψr∗ = 0.5
Variables

Case I

Case II

Case III

Home inflation

0.18

0.29

0.26

Foreign inflation

0.48

0.48

0.70

Home output gap

0.46

0.53

0.48

Foreign output gap

1.41

1.43

1.31

Home stock price gap

1.84

1.77

1.64

Foreign stock price gap

4.38

4.31

4.18

Real exchange rate

1.39

1.45

1.31

(Note) Case I: ϕq = ϕ∗q = 0; Case II: ϕq = 0.1 and ϕ∗q = 0; Case III: ϕq = ϕ∗q = 0.1.

36

Table 4: Standard deviations of key macrovariables when foreign central bank stabilizes
its asset price growth
Variables

Case I

Case II

Case III

Home inflation

0.18

0.17

0.28

Foreign inflation

0.48

0.45

0.44

Home output gap

0.46

0.44

0.50

Foreign output gap

1.41

1.37

1.39

Home stock price gap

1.84

1.82

1.74

Foreign stock price gap

4.38

4.27

4.20

Real exchange rate

1.39

1.30

1.36

(Note) Case I (Solid line): no asset price responses in both country; Case II (Line witha diamond): no asset price response (home country) and asset price growth response(foreign country); Case III (Line with an asterisk): asset price gap response (homecountry) and asset price gap response (foreign country)37

Figure 1: Worldwide equilibrium determinacy when ϕq and ϕ∗q change under several
values of ψr∗(Note) Dark-shaded areas: determinacy regions; Light-gray areas: indeterminacy
regions38

Figure 2: Worldwide equilibrium determinacy when ϕq and ϕ∗q change under several
values of ψr∗ : The case of ϕπ = ϕ∗π = 4.0(Note) Dark-shaded areas: determinacy regions; Light-gray areas: indeterminacy
regions

39

Figure 3: Worldwide equilibrium determinacy when ϕq and ϕ∗q change under several
values of ϕπ(Note) Dark-shaded areas: determinacy regions; Light-gray areas: indeterminacy
regions40

Figure 4: Worldwide equilibrium determinacy when ϕq and ϕ∗q change under several
values of ϕ∗x

φ*x =-0.2

0.4

0.4
0.3
φ*q

φ*q

0.3
0.2
0.1

0.2
0.1

0

0
0

0.1

0.4

0.2

0.3

0.4

0

0.1

0.2

φq

φq

φ*x =1

φ*x =1.5

0.4

0.3

0.4

0.3

0.4

0.3
φ*q

0.3
φ*q

φ*x =0.5

0.2
0.1

0.2
0.1

0

0
0

0.1

0.2

0.3

0.4

0

φq

0.1

0.2

φq

(Note) Dark-shaded areas: determinacy regions; Light-gray areas: indeterminacy
regions

41

Figure 5: Worldwide equilibrium determinacy when ϕq and ϕ∗q change when the foreign
central bank stabilizes its asset price growth

ψ* =0

ψ* =0.5

r

0.8

0.6
φ*q

φ*q

0.6
0.4
0.2

0.4
0.2

0

0
0

0.2

0.4

0.6

0.8

0

0.2

0.4

φq

φq

*

ψr =1.5

0.6

0.8

0.6

0.8

*

ψr =1

0.8

0.8
0.6
φ*q

0.6
φ*q

r

0.8

0.4
0.2

0.4
0.2

0

0
0

0.2

0.4

0.6

0.8

0

φq

0.2

0.4

φq

(Note) Dark-shaded areas: determinacy regions; Light-gray areas: indeterminacy
regions42

Figure 6: Impulse response to a foreign productivity shock in the case of ψr = ψr∗ = 0.2(Note) Case I (Solid line): ϕq = ϕ∗q = 0. Case II (Line with a diamond): ϕq = 0.1 andϕ∗q = 0. Case III (Line with an asterisk): ϕq = ϕ∗q = 0.1.

43

Figure 7: Impulse response to a foreign loan rate shock in the case of ψr = ψr∗ = 0.2(Note) Case I (Solid line): ϕq = ϕ∗q = 0. Case II (Line with a diamond): ϕq = 0.1 andϕ∗q = 0. Case III (Line with an asterisk): ϕq = ϕ∗q = 0.1.

44

Figure 8: Impulse response to a foreign productivity shock when foreign central bank
employs diﬀerent asset price rules(Note) Case I (Solid line): no asset price responses in both country; Case II (Line witha diamond): no asset price response (home country) and asset price growth response(foreign country); Case III (Line with an asterisk): asset price gap response (homecountry) and asset price gap response (foreign country)

45