The Zero Lower Bound and Monetary Policy in a Global Economy: A

The Zero Lower Bound and Monetary Policyin a Global Economy: A Simple

Analytical Investigation∗

Ippei Fujiwara,a Nao Sudo,b and Yuki TeranishibaFinancial Markets Department, Bank of Japan

bInstitute for Monetary and Economic Studies, Bank of Japan

How should monetary policy cooperation be designed whenmore than one country is simultaneously facing zero lowerbounds on nominal interest rates? To answer this question,we examine monetary policy cooperation with both opti-mal discretion and commitment policies in a two-countrymodel. We reach the following conclusions. Under discretion,monetary policy cooperation is characterized by the intertem-poral elasticity of substitution (IES), a key parameter meas-uring international spillovers, and no history dependency. Onthe other hand, under commitment, monetary policy featureshistory dependence with international spillover effects.

JEL Codes: E52, F33, F41.

1. Introduction

The world economy now faces the largest economic downturn sinceWorld War II. To prevent the economy from deteriorating fur-ther, most central banks in developed economies simultaneouslyreduced policy interest rates to unprecedented low levels at speedsnot previously seen. As shown in figure 1, the Bank of Japan

∗Copyright c© 2010 Bank of Japan. We thank Klaus Adam, Larry Chris-tiano, Jordi Galı, Paolo Pesenti, Frank Smets, and Carl Walsh and participantsat the Monetary Policy Challenges in Global Economy Conference 2009, FederalReserve Board and Bank of Italy seminars for helpful discussions, and espe-cially Andy Levin as the editor for helpful comments and suggestions. Viewsexpressed in this paper are those of the authors and do not necessarily reflectthe official views of the Bank of Japan. Author e-mails: [email protected];[email protected]; and [email protected].

103

104 International Journal of Central Banking March 2010

Figure 1. Policy Interest Rates

Notes: All data are from central banks: the call rate for Japan, the federal fundrate for the United States, the main refinancing operations fixed rate for the euroarea, the bank rate for the United Kingdom, and the overnight rate target forCanada.

(BOJ), the Bank of England (BOE), and the Federal Reserve Board(FRB) have virtually cut their policy rates to the lowest possiblelevel.1 Under such circumstances, with very little room for fur-ther monetary easing, how should monetary policy cooperation bedesigned? Is there any role for the home (foreign) central bank toassist the inactive foreign (home) monetary policy in the presenceof the zero lower bound?

Reflecting on the recent economic experience in Japan, therehave been several studies on monetary policy in the presence of

1“Lowering of the Bank’s target for the uncollateralized overnight call rate by20 basis points; it will be encouraged to remain at around 0.1 percent” (Decem-ber 12, 2008, Statements on Monetary Policy, BOJ); “The Bank of England’sMonetary Policy Committee today voted to reduce the official Bank Rate paidon commercial bank reserves by 0.5 percentage points to 0.5%” (March 5, 2009,News Release, BOE); “The Committee will maintain the target range for thefederal funds rate at 0 to 1/4 percent and anticipates that economic conditionsare likely to warrant exceptionally low levels of the federal funds rate for anextended period” (March 18, 2009, Press Release, FRB). The European CentralBank (ECB) and the Bank of Canada (BOC) have also set their policy rates atvery low levels.

Vol. 6 No. 1 The Zero Lower Bound and Monetary Policy 105

a liquidity trap. Most, however, focus on the closed economy. Forexample, Reifschneider and Williams (2000), Eggertsson and Wood-ford (2003), Jung, Teranishi, and Watanabe (2005), Adam and Billi(2006, 2007), and Nakov (2008) outline the characteristics of desir-able monetary policy under a zero lower bound on nominal interestrates for a closed economy. Regarding the liquidity trap in the openeconomy, Svensson (2001, 2003) and Coenen and Wieland (2003)investigate the zero interest rate policy in open economies and stressthe importance of the depreciation of nominal exchange rates for acountry caught in a liquidity trap. On the other hand, Nakajima(2008) shows that nominal exchange rates should appreciate for acountry adopting a zero interest rate policy under optimal commit-ment. These studies, however, only consider the situation where asingle country is at the zero bound. They do not provide a frame-work capable of examining the current global situation. As far as weknow, there have been no studies on the desirable conduct of mon-etary policy when more than one country is simultaneously facingzero lower bounds on nominal interest rates.

The design of optimal monetary cooperation in the presence ofthe zero lower bound is more complicated and substantially differentfrom studies that consider the zero lower bound in a closed economy.For example, we need to consider possible gains from policy cooper-ation when only one country moves away from the zero bound. Weset up a two-country dynamic general equilibrium model where bothcountries are at the zero lower bound because of temporary decreasesin the natural rate of interest. We provide a tractable framework forthe analysis of monetary policy cooperation with both discretionand commitment under the Markov equilibrium used in Eggertssonand Woodford (2003). The dynamic model considered in this papercollapses to a finite number of linear simultaneous equations. In ourpaper, the optimal monetary policy, which is obtained by minimizingthe quadratic social loss under policy cooperation, is characterizedby an optimally chosen home policy interest rate when the homecountry is free from the zero lower bound while the foreign countryis subject to the zero lower bound.

Our main conclusions are as follows. Under discretion, mone-tary policy cooperation is affected by the intertemporal elasticity ofsubstitution (IES), a key parameter measuring internationalspillover. The optimal exit policy depends greatly on whether IES


is larger or smaller than unity. When home goods and foreign goodsare complements (substitutes)—that is, when the inverse of IESis smaller (greater) than unity—the country that has escaped theliquidity trap earlier chooses expansionary (contractionary) mone-tary policy to boost economic activity in the country that is stillcaught in the liquidity trap. However, discretionary policy does nothave history dependence regardless of the value of IES. Under com-mitment, optimal policy cooperation has history dependence. Bycommitting to easing future monetary conditions, the two centralbanks mitigate the effects of the adverse shocks. Meanwhile, thelevel of policy interest rates changes with IES.

Admittedly, our conclusion is not independent from severalimportant assumptions. First, preferences of agents in the homecountry and foreign country are identical. Second, we assume thatthere are only home goods and foreign goods in the economy, andthat there are no non-tradable goods. Third, there is a completeinternational financial market so that agents in both countries canachieve the risk sharing. Fourth, agents in both countries set pricesin their own currency (“producer-currency pricing”). Thanks tothese assumptions that are used commonly in the literature, suchas in Clarida, Galı, and Gertler (2002), we can provide an intuitivedescription of the monetary policy.

The remainder of the paper is as follows. In section 2, we describethe two-country model used for analysis in this paper. Section 3 clar-ifies the equilibrium concept and how a dynamic two-country modelcan be represented by analytically tractable static equations. Section4 investigates the nature of the optimal monetary policy under dis-cretion, and section 5 inquires into that under commitment. Finally,section 6 summarizes the findings in this paper and refers to futurepossible extensions.

2. The Model

The two-country model considered in this paper is very standard, asfound in Clarida, Galı, and Gertler (2002) and Benigno and Benigno(2003). Because we adopt the assumption of complete internationalfinancial markets and assume a Markov equilibrium, it is convenientto make use of history notation. That is, let st ∈ S denote all thepossible states of the world that can occur in period t. Let


st = (s0, s1, . . . , st)

denote the history up until period t of the realized states of theworld. The set of states, S, contains only two elements. One is asso-ciated with a low level of the natural rate of interest and the otheris associated with a “normal” level of the natural rate of interest.We denote the probability of history st by μ(st).

2.1 Households

A representative household in the home country H has the followingpreferences:

∞∑t=0

βt∑st

μ(st){u[C(st)] − v [h(st)]},

where 0 < β < 1. C(st) and h(st) denote consumption and thesupply of labor in history st, respectively. The household budgetconstraint is given by

W (st)h(st) + Π(st) + B(st−1)

≥∑st+1

Q(st+1, st)B(st+1, s

t) + P (st)C(st),

where W (st) and Π(st) denote the wage rate and lump-sum prof-its and taxes in home currency units. Furthermore, the objectB(st+1, s

t) is an Arrow security. It is the quantity of home currencyto be delivered in period t+1 if state st+1 is realized, conditional onhistory st. The associated price is Q(st+1, s

t). Finally, P (st) denotesthe price of consumption goods.

Aggregate consumption is given by

C(st) =[CH(st)

n

]n [CF (st)1 − n

]1−n

, (1)

where 0 ≤ n ≤ 1 is the relative size of the home country. CH(st)and CF (st) denote the consumption of home and imported goods


in the home country, respectively. Furthermore, CH(st) and CF (st)are defined as

CH(st) =[∫ 1

0CH(st, i)

ε−1ε di

] εε−1

(2)

and

CF (st) =[∫ 1

0CF (st, i)

ε−1ε di

] εε−1

,

where ε > 1.Similarly, the lifetime utility of a representative household in the

foreign country, F , is defined by

∞∑t=0

βt∑st

μ(st){u[C∗(st)] − v [h∗(st)]},

where superscript ∗ denotes foreign variables. The budget constraintis given by

W ∗(st)h∗(st) + Π∗(st) +B∗(st−1)

E(st)

≥∑st+1

Q(st+1, st)B∗(st+1, s

t)E(st)

+ P ∗(st)C∗(st).

In the above expression, E(st) denotes the exchange rate, namely,units of home currency per unit of foreign currency.

The household maximizes utility subject to its budget constraint,taking as given prices, wages, exchange rates, and rates of return.

2.2 Firms

The ith, i ∈ (0, 1), intermediate good is produced by a monopolistusing the following technology:

Y (st, i) = Z(st)h(st, i),


where Z(st) is the common technology and the only stochastic dis-turbance. The marginal cost of production for the ith monopolist isgiven by

MC(st) = [1 − τ(st)]W (st)

Z(st)PH(st), (3)

where τ(st) denotes a tax subsidy associated with the supply oflabor, financed by a lump-sum tax on households. The ith monopo-list maximizes profits subject to its demand curve derived from con-sumer preferences as in equation (2), and the Calvo (1983) price fric-tions. In particular, the monopolist may optimize its price, P (st, i),with probability 1 − θ, and with probability θ it sets its price asfollows:

P (st, i) = P (st−1, i).

We assume similar production technology for the foreign countryas well.

2.3 Market Clearing

Clearing in the labor market requires

h(st) =∫ 1

0h(st, i)di.

Clearing in the home homogeneous goods market requires

nY (st) = nCH(st) + (1 − n)C∗H(st). (4)

Clearing in financial markets requires

B(st+1, st) + B∗(st+1, s

t) = 0.

Following the argument in Yun (2005), output of the homogeneoushome good is related to aggregate employment by

Y (st) = Δ(st)Z(st)h(st), (5)


where the relative price distortion term Δ(st) is

Δ(st) =∫ 1

0

[PH(st, i)PH(st)

]−ε

di.

Under the Calvo price frictions, its dynamics are defined by

Δ(st) =1

(1 − θ){

1−θ[1+πH(st)]ε−1

1−θ

} εε−1

+ θ[1+π(st)]εΔ(st−1)

,

where

πH(st) =PH(st)

PH(st−1)− 1.

We have similar clearing conditions for the foreign country.

2.4 Financial Market Equilibrium Condition

From the first-order necessary conditions with respect to holdings ofArrow securities, we have

u′[C∗(st+1)]q(st)u′[C∗(st)]q(st+1)

=u′[C(st+1)]u′[C(st)]

,

where the real exchange rate q(st) is defined by

q(st) =E(st)P ∗(st)

P (st).

Under the symmetric preferences assumption, the real exchange rateis always unity. As a result, equilibrium relative consumption alsoequals unity with suitable initial wealth conditions under a unitelasticity of substitution between home and foreign goods,2 namely,

C(st) = C∗(st). (6)

2For a formal proof of this point, see the proposition in Nakajima (2008).


2.5 Equilibrium Conditions

We adopt a standard sequence-of-markets equilibrium concept, usingthe following functional forms:

u(C) =C1−σ

1 − σ, v(h) =

h1+ω

1 + ω,

where σ, ω > 0. It is important to note that, in our model, σ equalsthe inverse of the intertemporal elasticity of substitution (equiva-lently, the degree of risk aversion) following the notation of Rotem-berg and Woodford (1997) and not the notation of Eggertsson andWoodford (2003) where σ is the intertemporal elasticity of substitu-tion. From the first-order necessary conditions in the optimizationproblem mentioned above, we can derive the system of log-linearizedequations as follows.3 The aggregate supply conditions are given bythe New Keynesian Phillips curves:

πH(st) = γHxH(st) + γH,F (1 − n)xF (st) + β∑st+1

μ(st+1)πH(st+1)

(7)

for the home country and

π∗F (st) = γH,F nxH(st) + γF xF (st) + β

∑st+1

μ(st+1)π∗F (st+1) (8)

for the foreign country, where

γH =(1 − θ)(1 − βθ)[1 + ω + (σ − 1)n]

θ(1 + ωε),

γF =(1 − θ)(1 − βθ)[1 + ω + (σ − 1)(1 − n)]

θ(1 + ωε),

and

γH,F =(1 − θ)(1 − βθ)(σ − 1)

θ(1 + ωε).

3For details of the derivations, see, for example, Clarida, Galı, and Gertler(2002), Benigno and Benigno (2003), and Nakajima (2008).


For aggregate demand conditions, we derive the dynamic IS curvesas follows:

iH(st) =∑st+1

μ(st+1){

[1 + (σ − 1)n]xH(st+1)+ (σ − 1)(1 − n)xF (st+1) + πH(st+1)

}(9)

− [1 + (σ − 1)n]xH(st) − (σ − 1)(1 − n)xF (st) + rn(st)

for the home country. For the foreign country, we have

iF,t(st) =∑st+1

μ(st+1){

[1 + (σ − 1)(1 − n)]xF (st+1)+ (σ − 1)nxH(st+1) + π∗

F (st+1)

}(10)

− [1 + (σ − 1)(1 − n)]xF (st) − (σ − 1)nxH(st) + r∗n(st).

Here, the inflation rates of the home goods and the foreign goods,πH(st) and π∗

F (st), are defined as follows:

πH(st) ≡ lnPH(st) − lnPH(st−1),

π∗F (st) ≡ lnP ∗

F (st) − lnP ∗F (st−1).

The output gaps xH(st) and xF (st) are defined by the log-deviation of outputs from their flexible price levels Yn(st) andY ∗

n (st):4

xH(st) ≡ log[Y (st)] − log[Yn(st)],

xF (st) ≡ log[Y ∗(st)] − log[Y ∗n (st)].

rn(st) and r∗n(st) are called the natural rates of interest. They are

defined as the real interest rates that arise when both the homegoods price and foreign goods price are flexible. Namely, we have

11 + rn(st)

≡∑st+1

[βuH(Yn(st+1), Y ∗

n (st+1))uH(Yn(st), Y ∗

n (st))

],

11 + r∗

n(st)≡

∑st+1

[βuF (Yn(st+1), Y ∗

n (st+1))uF (Yn(st), Y ∗

n (st))

].

4Yn(st) and Y ∗n (st) are the natural levels of output that arise when prices

of both the home goods and foreign goods PH(st) and P ∗F (st) are flexible. See

Clarida, Galı, and Gertler (2002) for related discussions.


Here, uH and uF are the marginal utilities of the household withrespect to home goods consumption and foreign goods consump-tion, respectively. It is notable that the natural rate of interest ineither of the countries is a function of the flexible level outputs inboth countries, Yn(st) and Y ∗

n (st). Therefore, each of the naturalrates of interest is affected by the exogenous shocks occurring inboth countries, such as technology shocks or government expendi-ture shocks.5 In the following analysis, we examine the equilibriumresponse of the economy when these natural rates of interest followthe law of motion, such that they fall below the steady state in aparticular period and revert back to the steady state in subsequentperiods with fixed probabilities. The probabilities are assumed to beindependent of each other for analytical convenience.

The equilibrium conditions are equations (7)–(10) with home andforeign monetary policy equations, which are formalized to max-imize social welfare. From the second-order approximation of thenon-linear equilibrium conditions and welfare of the households inthe two countries, we can derive the periodic social loss function:6

L(st) =γHn

θxH(st)2 +

2γH,F n(1 − n)θ

xH(st)xF (st)

+γF (1 − n)

θxF (st)2 + nπH(st)2 + (1 − n)π∗

F (st)2. (11)

We set the parameters as follows. One period in the model corre-sponds to a quarter. We set β = 0.99, ε = 7.88, θ = 0.66, ω = 0.47,and n = 0.5. For σ, three values are considered: σ = 0.5, 1, and5.988.7

2.6 International Spillover

Let us discuss international spillover. We show how internationalspillover is related to σ. For this, we derive two equilibrium

5Thus, fiscal policy is included in the natural interest rate shock in our model.6For the derivation of the welfare loss function under policy cooperation, see

Clarida, Galı, and Gertler (2002) and Benigno and Benigno (2003).7For comparison with the literature, we choose σ−1 = 2 and σ−1 = 0.167,

which are used by Eggertsson and Woodford (2003) and Jung, Teranishi, andWatanabe (2005), respectively.


conditions. The first equation is the optimality condition for thehome country households’ labor supply:

v ′[h(st)] = u′[C(st)]W (st)P (st)

(12)

= C(st)−σ MC(st)Z(st)1 − τ(st)

[PH(st)PF (st)

]1−n

,

where we used equation (3) and the definition of the consumer priceindex derived as the Hicksian demand function from equation (1).The other is the equation that relates consumption of the home coun-try household to the home country output, which is derived fromequations (4), (5), and (6), together with the Marshallian demandfunctions derived from equation (1):

C(st) =[PH(st)PF (st)

]1−n

Δ(st)Z(st)h(st). (13)

Note that only PF (st), which is expressed under the law of one priceas

PF (st) = E(st)P ∗F (st),

enters equations (12) and (13) as the foreign variables. When σ = 1,PF (st) and therefore the terms of trade, defined as PF (st)/PH(st),disappear from equations (12) and (13). In this case, the marginalcost in the home country is determined only by variables of thehome country, and there is no spillover from the foreign country.When σ �= 1, however, the foreign variable affects the home vari-ables through the terms of trade. As shown by Clarida, Galı, andGertler (2002), spillover takes place through the two channels. Thefirst channel is the “terms-of-trade effect,” in which a rise in foreignoutput reduces the marginal cost of the home country, via appre-ciation of the terms of trade, working through the terms of trade,in equation (12). The second channel is the “risk-sharing effect,” inwhich an increase in foreign output increases the marginal cost ofthe home country by raising the consumption of the home coun-try household, working through the terms of trade in equation (13).Note that these two cancel out when σ = 1, and the two countriesbecome insular.


3. A Markov Equilibrium under a Global Liquidity Trap

Following Eggertsson and Woodford (2003), we analytically investi-gate optimal monetary policy under a Markov equilibrium for bothdiscretionary policy and commitment policy. To see the propertiesof the policies, we consider an experiment in which the two naturalrates of interest rn(st), r∗

n(st) ∈ {r, r} in the home and foreign coun-try, respectively, fall unexpectedly and simultaneously at period 0from their steady-state value r to a negative value r, and then simu-late the optimal response of the policy rates to these adverse shocks.Here, we set r = 1−β

β > 0 and r = −0.04/4 < 0. We assume thateach natural rate of interest reverts back to its steady-state valuewith a fixed probability in every subsequent period, and that it staysthere for good once it returns to the steady state. More precisely, forthe home natural rate of interest rn(st), when rn(st) = r at period t,rn(st+1|st) remains r at period t+1 with constant probability p andreturns to its steady-state value r with constant probability 1 − p.For the foreign natural rate of interest r∗

n(st), we assume that theforeign country shock r∗

n(st) = r does not revert back to the steadystate until the home country shock disappears. The foreign naturalrate of interest returns to its steady-state value r with constantprobability 1 − q after the home country shock rn(st+1|st) returnsto its steady-state value r. Thus, in our setting, the home coun-try shock always disappears earlier than the foreign country shockdoes.

Here, the state of the economy is characterized by the signs ofthe natural rates of interest in the two countries. We employ thesubscript zz for the state where rn(st) = r and r∗

n(st) = r hold, nzfor the state where rn(st) = r and r∗

n(st) = r hold, and nn for thestate where rn(st) = r and r∗

n(st) = r hold.8 Table 1 shows the tran-sition probability of the states in our model economy. For each row,the column reports the transition probability that the state changesfrom the current state to the other state. Notice that the state nnis an absorbing state, and the economy stays at the state nn withprobability one once it reaches this state.

8Note that the state zn defined as rn(st) = r and r∗n(st) = r does not exist.


Table 1. Transition Probability

zz nz nnzz p 1 − p 0nz 0 q 1 − qnn 0 0 1

For the tractability of our analysis on optimal commitment pol-icy, we further assume that central banks fix their policy rates withina state,9 but that they can change their policy interest rates acrossdifferent states.10 For sufficiently large adverse shocks to the nat-ural rate of interest, it is natural to predict the following: (i) Thetwo central banks cooperatively set the policy interest rate of thecountry in which the adverse shock still prevails to zero; that is,iHzz = iFzz = iFnz = 0, and (ii) they set both of the policy interestrates to the steady-state level of the natural rates of interest whenboth of the two adverse shocks die out; that is, iH,nn = iF,nn = r.In this experiment, we assume these conditions (i) and (ii) actuallyhold by making r sufficiently negative to ensure that these conditionsare consistent with the optimality of the monetary policy imple-mentation. Thanks to condition (ii), we have one other condition:(iii) xH,nn = xF,nn = πH,nn = π∗

F,nn = 0, because the economy isperfectly stabilized in this case.11 Given these conditions (i), (ii), and(iii), optimal monetary policy is characterized by the optimal choiceof iH,nz that maximizes social welfare. Admittedly, the choice setdiffers between discretionary policy and commitment policy.

Under this Markov equilibrium, the dynamic system of equationsconsisting of equations (7)–(10) collapses to a system of eight staticequations. As for the equilibrium conditions during the state zz, weobtain

9Because there are no endogenous state variables, dependency on the laggedvariables stems solely from the history-dependent policy. Therefore, as long aswe impose this condition, the solution below is consistent with the non-linearequilibrium conditions derived in the previous section.

10Fujiwara et al. (2009) relax this condition and analyze the case in which thecentral banks can also adjust their policy rates even within a state.

11Another way to justify this condition is to set the Ramsey planner’s discountfactor very close to unity. Together with the condition that there is no variation inthe policy interest rates within the state, this condition yields iH,nn = iF,nn = r.


πH,zz = γHxH,zz + γH,F (1 − n)xF,zz + β[pπH,zz + (1 − p)πH,nz],(14)

π∗F,zz = γH,F nxH,zz + γF xF,zz + β

[pπ∗

F,zz + (1 − p)π∗F,nz

], (15)

0 = [1 + (σ − 1)n][pxH,zz + (1 − p)xH,nz − xH,zz]

+ (σ − 1)(1 − n)[pxF,zz + (1 − p)xF,nz − xF,zz]

+ pπH,zz + (1 − p)πH,nz + r, (16)

and

0 = [1 + (σ − 1)(1 − n)][pxF,zz + (1 − p)xF,nz − xF,zz]

+ (σ − 1)n[pxH,zz + (1 − p)xH,nz − xH,zz]

+ pπ∗F,zz + (1 − p)π∗

F,nz + r. (17)

For the state nz, we have

πH,nz = γHxH,nz + γH,F (1 − n)xF,nz + βqπH,nz, (18)

π∗F,nz = γH,F nxH,nz + γF xF,nz + βqπ∗

F,nz, (19)

iH,nz = [1 + (σ − 1)n](qxH,nz − xH,nz)

+ (σ − 1)(1 − n)(qxF,nz − xF,nz) + qπH,nz + r, (20)

and

0 = [1 + (σ − 1)(1 − n)](qxF,nz − xF,nz)

+ (σ − 1)n(qxH,nz − xH,nz) + qπ∗F,nz + r. (21)

Now, we have eight unknowns—πH,zz, π∗F,zz, xH,zz, xF,zz, πH,nz,

π∗F,nz, xH,nz, and xF,nz—for the eight equations above. Here, iH,nz is

the policy variable that is chosen by the home central bank.

4. Optimal Monetary Policy under Discretion

Under discretion, the home central bank chooses iH,nz to maximizesocial welfare, taking expectations as given for the state nz. The


policy interest rate set by the home country central bank at thestate nz, iH,nz, is chosen to minimize the contemporaneous loss:

LDnz =

γHnH

θx2

H,nz +2γH,F nHnF

θxH,nzxF,nz

+γF nF

θx2

F,nz + nHπ2H,nz + nF π∗2

F,nz, (22)

subject to the following five constraints:

πH,nz = γHxH,nz + γH,F (1 − n)xF,nz,

π∗F,nz = γH,F nxH,nz + γF xF,nz,

iH,nz = −[1 + (σ − 1)n]xH,nz − (σ − 1)(1 − n)xF,nz + r,

0 = −[1 + (σ − 1)(1 − n)]xF,nz − (σ − 1)nxH,nz + r,

and

iH,nz ≥ 0.

Assuming that the non-negativity constraint on iH,nz doesnot bind, because there are four constraints with four unknownvariables—πH,nz, π∗

F,nz, xH,nz, and xF,nz—the optimal discretionarypolicy is obtained by choosing iH,nz to minimize the loss function inequation (22). When the non-negativity constraint binds, iH,nz is setto zero. Because expectations are taken as given by the two centralbanks at the state nz, the probability p does not directly affect theoptimal monetary policy. However, iH,nz indirectly depends on q,since the economic structure at the state nz is affected by the futureexpectation associated with q.

Simulation results are shown in tables 2, 3, 4, and 5. Tables 2 and3 demonstrate how policy interest rate, output, and inflation changewith the expected duration of the adverse shock in the foreign coun-try, namely, q, for the state zz and the state nz, respectively. Here,we fix the other parameters, including p = 0.25. Similarly, tables4 and 5 demonstrate how the variables change with the expectedduration of the adverse shock in the home country, namely, p, for thestate zz and the state nz, respectively, keeping the other parameters,including q = 0.25.

Under discretion, the optimal monetary policy iH,nz is character-ized by the size of the international spillover, which is captured by


Table 2. Policy Interest Rate, Output Gap, and Inflationunder Discretion at State zz for Various Sizes of q

q = 0.0 q = 0.5 q = 0.75 q = 0.90

σ = 1 πH,zz −0.4 −0.4 −0.4 −0.4xH,zz −1.4 −1.4 −1.4 −1.4iH,zz 0.0 0.0 0.0 0.0πF,zz −1.0 −2.2 −14.7 6.6xF,zz −2.5 −4.0 −16.5 3.4iF,zz 0.0 0.0 0.0 0.0

σ = 0.5 πH,zz −0.4 −0.1 8.7 −0.3xH,zz −2.7 −2.7 4.6 −0.9iH,zz 0.0 0.0 0.0 0.0πF,zz −1.1 −2.5 −17.5 6.3xF,zz −4.2 −6.4 −23.2 3.6iF,zz 0.0 0.0 0.0 0.0

σ = 5.988 πH,zz −0.5 −0.7 −3.4 −0.7xH,zz −0.2 0.2 1.2 −2.4iH,zz 0.0 0.0 0.0 0.0πF,zz −0.7 −1.7 −8.5 7.0xF,zz −0.6 −1.2 −4.2 2.9iF,zz 0.0 0.0 0.0 0.0

Note: Variables are presented in terms of percentage points at annual rates.

the parameter σ.12 We first describe this using table 3. When σ = 1,the output and inflation in the home country are perfectly stabilizedat the state nz by setting iH,nz = 1−β

β , regardless of the value of q.Because the output gap and inflation in the foreign country do notaffect those of the home country in this case, the expected durationof the foreign adverse shock does not affect the home variables. For

12The key parameter of interdependence across countries may change accord-ing to the model specification. In this paper, we employ the standard new openmacroeconomy model of Clarida, Galı, and Gertler (2002), Corsetti and Pesenti(2001), or Corsetti and Pesenti (2005) in which many of the properties of inter-national spillover are studied. In this model, the interdependence is well capturedby the inverse of the intertemporal elasticity of substitution parameter σ. How-ever, when we assume a different utility following Greenwood, Hercowitz, andHuffman (1988), for example, the other parameters may play a key role, affectingthe interdependence effects across countries.


Table 3. Policy Interest Rate, Output Gap, and Inflationunder Discretion at State nz for Various Sizes of q

q = 0.0 q = 0.5 q = 0.75 q = 0.90

σ = 1 πH,nz 0.0 0.0 0.0 0.0xH,nz 0.0 0.0 0.0 0.0iH,nz 4.0 4.0 4.0 4.0πF,nz −0.2 −1.0 −10.0 5.7xF,nz −1.0 −2.2 −11.4 2.8iF,nz 0.0 0.0 0.0 0.0

σ = 0.5 πH,nz 0.1 0.3 6.5 0.1xH,nz 0.1 0.1 5.9 0.8iH,nz 2.4 2.5 0.7 4.2πF,nz −0.2 −1.1 −11.7 5.5xF,nz −1.3 −3.0 −15.1 3.4iF,nz 0.0 0.0 0.0 0.0

σ = 5.988 πH,nz −0.1 −0.3 −2.2 −0.3xH,nz 0.1 0.3 1.0 −1.2iH,nz 6.4 5.9 6.6 3.7πF,nz −0.2 −0.8 −5.8 6.0xF,nz −0.3 −0.9 −3.1 1.8iF,nz 0.0 0.0 0.0 0.0


the foreign country, on the other hand, output gap and inflationvary with q, because longer q implies that the foreign adverse shockstays longer. When q increases from 0.0 to 0.75, the output gap andinflation in the foreign country decrease monotonically. On the otherhand, they take positive values when q = 0.90. In this case, underour restricted solution, the longer expected adverse shock togetherwith the zero interest rate induces too much easing in terms ofthe real interest rate since an elasticity of the inflation to outputgap increases as q increases.13 When σ �= 1, there is internationalspillover and the home central bank sets iH,nz, depending on σ,

13As we see below, we have the similar situation for the case where p takes alarge value for both underdiscretion and undercommitment under a given zerointerest rate.


Table 4. Policy Interest Rate, Output Gap, and Inflationunder Discretion at State zz for Various Sizes of p

p = 0.0 p = 0.5 p = 0.75 p = 0.90

σ = 1 πH,zz −0.2 −1.0 −9.9 5.7xH,zz −1.0 −2.2 −11.4 2.8iH,zz 0.0 0.0 0.0 0.0πF,zz −1.0 −2.2 −14.7 6.6xF,zz −2.5 −4.0 −16.5 3.4iF,zz 0.0 0.0 0.0 0.0

σ = 0.5 πH,zz −0.1 −1.1 −33.7 4.9xH,zz −1.9 −4.6 −61.0 3.8iH,zz 0.0 0.0 0.0 0.0πF,zz −1.1 −2.7 −40.3 6.2xF,zz −3.9 −7.1 −68.0 4.7iF,zz 0.0 0.0 0.0 0.0



because of two reasons. First, the two central banks focus on themonetary policy coordination, and the home country sets the policyinterest rate to maximize the global welfare rather than the homecountry welfare. Second, there is the interaction between the twocountries through the economic structure, as we discussed above.Consequently, the size of iH,nz is characterized by σ.14 To illustratethis, we rewrite the IS equation for the foreign country at the statenz as follows:

14More precisely, under the cooperative policy, the two central banks maximizethe welfare given by equation (11). Under the non-cooperative policy, each centralbank maximizes its own welfare. Admittedly, the two optimal policy interest ratescan differ since objectives are different. See Clarida, Galı, and Gertler (2002) forthe comparison of the two policies in the case where two countries are not in theliquidity trap.


Table 5. Policy Interest Rate, Output Gap, and Inflationunder Discretion at State nz for Various Sizes of p

p = 0.0 p = 0.5 p = 0.75 p = 0.90

σ = 1 πH,nz 0.0 0.0 0.0 0.0xH,nz 0.0 0.0 0.0 0.0iH,nz 4.0 4.0 4.0 4.0πF,nz −0.4 −0.4 −0.4 −0.4xF,nz −1.4 −1.4 −1.4 −1.4iF,nz 0.0 0.0 0.0 0.0

σ = 0.5 πH,nz 0.1 0.1 0.1 0.1xH,nz 0.1 0.1 0.1 0.1iH,nz 2.5 2.5 2.5 2.5πF,nz −0.4 −0.4 −0.4 −0.4xF,nz −1.8 −1.8 −1.8 −1.8iF,nz 0.0 0.0 0.0 0.0

σ = 5.988 πH,nz −0.3 −0.3 −0.3 −0.3xH,nz −0.5 −0.5 −0.5 −0.5iH,nz 6.2 6.2 6.2 6.2πF,nz −0.3 −0.3 −0.3 −0.3xF,nz −0.5 −0.5 −0.5 −0.5iF,nz 0.0 0.0 0.0 0.0


iF,nz = [1 + (σ − 1)(1 − n)](qxF,nz − xF,nz)

+ (σ − 1)n(qxH,nz − xH,nz) + qπ∗F,nz + r.

We first consider the case in which the two countries are insular(σ = 1). When the zero-lower-bound constraint is binding, this ISequation is reduced to

0 = (q − 1)xF,nz + qπ∗F,nz + r.

In this case, as we discussed in section 2.6, there is no spillovereffect across countries. Thus, the home central bank does not haveany international spillover affecting the dynamics of the output gapxF,nz and inflation π∗

F,nz in the above equation.We now turn to the case in which there is an interdependence

between the two countries (σ �= 1) and the zero lower bound isbinding:


0 = [1 + (σ − 1)(1 − n)](qxF,nz − xF,nz)

+ (σ − 1)n(qxH,nz − xH,nz) + qπ∗F,nz + r.

It is obvious from the third term on the right-hand side of the aboveequation that if σ > (<)1, the deflationary pressure to the foreignoutput gap and inflation is mitigated by decreasing (increasing) thehome output gap xH,nz, to net out the negative natural rate ofinterest in the foreign country. In particular, while the foreign out-put and inflation are negative, the home central bank sets its policyrate higher (lower) than the case of σ = 1 when σ > (<)1, sothat the home output declines (rises) compared with the case ofσ = 1. By setting the appropriate policy interest rate, the negativeoutput gap of the foreign country is reduced even in the liquiditytrap, and the welfare loss of the two countries associated with theadverse shocks is reduced.15 This result is consistent with the exist-ing literature that discusses the spillover of monetary policy acrosscountries. For instance, Corsetti and Pesenti (2001), using a frame-work similar to ours, report that a foreign monetary expansion has anegative (positive) impact on home output when σ > (<)1, becausethe two goods are substitutes (complements) and the marginal util-ity of home goods decreases (increases) with the consumption offoreign goods. Based on their arguments, therefore, to increase theoutput gap in the home country, foreign output needs to be lower(higher) for σ > (<)1.

Table 5 shows the case for p. The role of international spillover isclearly observed in how the home policy interest rate is set depend-ing on σ. In contrast to q, the expectation about the adverse shockin the home country p does not affect the economy at the state nz,since the state nz has realized already. This result contrasts sharplywith that under the quasi-optimal commitment policy, as shown inthe later section. This is because the central banks take the valuesof future variables as given under discretionary policy.

15Table 3 shows that when q is sufficiently large, the adverse shock in theforeign country causes the positive output and inflation, rather than negativeoutput and inflation in the foreign country. In this case, the home central banksets iH,nz lower (higher) than the case of σ = 1 for σ > (<) 1, so as to mitigatethe inflationary pressure in the foreign country.


As shown in tables 2 and 4, the variables at the state nz affectthose at the state zz through the agents’ expectations. When σ = 1,the home variables at the state zz are independent from the vari-ations in q, and dependent on the variations in p, because longerduration of the adverse state in the foreign country does not influ-ence the home country. The foreign variables, on the other hand,vary with both p and q, because both duration parameters affectthe expected duration that the foreign adverse shock prevails. Whenσ �= 1, the home country is affected by q, because of the presence ofthe spillover effect from the foreign country.

To summarize the results under discretion, the nature of the opti-mal cooperative monetary policy is characterized by internationalspillover. When two countries are not insular, a country can miti-gate the deflationary pressure of the other country by boosting orcontracting its own economy.

5. Quasi-Optimal Policy under Commitment

We next discuss our commitment policy. We call the commitmentmonetary policy under our setting a quasi-optimal commitment pol-icy, since we restrict the state dynamics as explained above. Underquasi-optimal commitment policy, the home central bank undercooperation chooses iH,nz to minimize the present discounted valueof the social loss in equation (11) expressed as

LC(st) = L(st) + β∑st+1

μ(st+1|st)L(st+1|st)

+ β2∑st+2

μ(st+2|st+1)L(st+2|st+1) . . . .

= L(st) +∞∑

k=1

∑st+k

βkμ(st+1|st)L(st+1|st), (23)

subject to equations (14)–(21), and the zero-lower-bound constraint

iH,nz ≥ 0.

The analytical form of this loss function (23) is shown in theappendix.


Table 6. Policy Interest Rate, Output Gap, and Inflationunder Commitment at State zz for Various Sizes of p

p = 0.0 p = 0.5 p = 0.75 p = 0.90

σ = 1 πH,zz −0.0 −0.0 −5.1 4.7xH,zz −0.6 −0.8 −6.3 2.1iH,zz 0.0 0.0 0.0 0.0πF,zz −1.0 −2.2 −14.7 6.6xF,zz −2.5 −4.0 −16.4 3.4iF,zz 0.0 0.0 0.0 0.0

σ = 0.5 πH,zz 0.2 −0.2 −27.4 4.4xH,zz −1.1 −2.9 −51.1 3.3iH,zz 0.0 0.0 0.0 0.0πF,zz −1.1 −2.5 −36.9 6.3xF,zz −3.7 −6.4 −61.3 4.6iF,zz 0.0 0.0 0.0 0.0



Simulation results are shown in tables 6, 7, 8, and 9. Tables 6 and7 demonstrate how policy interest rate, output, and inflation changewith the expected duration of the adverse shock in the home coun-try, namely, p, for the state zz and the state nz, respectively. Here,we fix the other parameters, including q = 0.25. Similarly, tables 8and 9 demonstrate how the variables change with the expected dura-tion of the adverse shock in the foreign country, namely, q, for thestate zz and the state nz, respectively, keeping the other parameters,including p = 0.25.

Under commitment, the optimal monetary policy iH,nz is char-acterized by the history dependency as well as the internationalspillover. As table 7 shows, in contrast to discretion displayed intable 3, the policy interest rate is affected by p even though thestate nz has realized already. This is a pure effect of the mone-tary policy commitment, since the central banks take the values of


Table 7. Policy Interest Rate, Output Gap, and Inflationunder Commitment at State nz for Various Sizes of p

p = 0.0 p = 0.5 p = 0.75 p = 0.90

σ = 1 πH,nz 0.1 0.3 0.4 0.4xH,nz 0.4 1.1 1.4 1.4iH,nz 3.0 0.8 0.0 0.0πF,nz −0.4 −0.4 −0.4 −0.4xF,nz −1.4 −1.4 −1.4 −1.4iF,nz 0.0 0.0 0.0 0.0

σ = 0.5 πH,nz 0.3 0.4 0.4 0.4xH,nz 0.8 1.4 1.4 1.4iH,nz 1.0 0.0 0.0 0.0πF,nz −0.4 −0.4 −0.4 −0.4xF,nz −1.5 −1.4 −1.4 −1.4iF,nz 0.0 0.0 0.0 0.0

σ = 5.988 πH,nz −0.1 0.1 0.1 0.4xH,nz 0.3 0.6 0.6 1.4iH,nz 5.4 4.0 3.7 0.0πF,nz −0.3 −0.4 −0.4 −0.4xF,nz −0.6 −0.8 −0.8 −1.4iF,nz 0.0 0.0 0.0 0.0


future variables into consideration under commitment. The homecountry’s output gap and inflation increase with p, since greaterpolicy stimulus is needed to offset the contractionary impact of thelonger expected duration of the adverse shock in the home country.In addition to this history dependency, there is the internationalspillover effect. When σ > (<)1, the home policy interest rate iH,nz

is set higher (lower) than the case of σ = 1, being consistent withthe discussion in the previous section.

Next we discuss the relationship between iH,nz and q, shown intable 9. Lower q implies a shorter expected duration of the state nz,during which the home central bank is able to maintain its accom-modative monetary policy. When σ = 1, there is no foreign effect.Thus the home central bank sets a lower value for iH,nz for a smallerq, only to mitigate the effect of the adverse shock in the home coun-try at the state zz. As q increases, the home policy interest rate


Table 8. Policy Interest Rate, Output Gap, and Inflationunder Commitment at State zz for Various Sizes of q

q = 0.0 q = 0.5 q = 0.75 q = 0.90

σ = 1 πH,zz −0.0 −0.1 −0.2 −0.3xH,zz −0.6 −0.9 −1.1 −1.3iH,zz 0.0 0.0 0.0 0.0πF,zz −1.0 −2.2 −14.7 6.6xF,zz −2.5 −4.0 −16.5 3.4iF,zz 0.0 0.0 0.0 0.0

σ = 0.5 πH,zz 0.0 0.4 9.2 −0.2xH,zz −1.6 −1.7 5.3 −0.8iH,zz 0.0 0.0 0.0 0.0πF,zz −1.1 −2.4 −17.2 6.3xF,zz −3.9 −6.0 −22.7 3.6iF,zz 0.0 0.0 0.0 0.0

σ = 5.988 πH,zz −0.3 −0.5 −3.4 −0.6xH,zz −0.2 0.4 1.2 −2.3iH,zz 0.0 0.0 0.0 0.0πF,zz −0.8 −1.7 −8.5 7.0xF,zz −0.8 −1.4 −4.2 2.8iF,zz 0.0 0.0 0.0 0.0


becomes less accommodative, because the accommodative periodbecomes longer in the good state for the home country. When σ �= 1,there is an international spillover effect as well as history depen-dency, and the relationship between the expected duration and thepolicy interest rate becomes less evident.

Similarly to the results under discretion, the variables at thestate nz affect those at the state zz through the agents’ expecta-tions. Under commitment, however, even when σ = 1, the homevariables at the state zz vary with q as well as with p, reflectingthe fact that setting of the policy interest rate is history dependentunder commitment policy.

In summary, the monetary policy cooperation under commit-ment is characterized by the history dependence existing studieshave found in a closed economy, which is contrary to the results


Table 9. Policy Interest Rate, Output Gap, and Inflationunder Commitment at State nz for Various Sizes of q

q = 0.0 q = 0.5 q = 0.75 q = 0.90

σ = 1 πH,nz 0.2 0.2 0.1 0.1xH,nz 0.7 0.4 0.2 0.0iH,nz 1.2 3.3 4.0 4.1πF,nz −0.2 −1.0 −9.9 5.7xF,nz −1.0 −2.2 −11.4 2.8iF,nz 0.0 0.0 0.0 0.0

σ = 0.5 πH,nz 0.2 0.6 6.8 0.2xH,nz 1.0 1.0 6.5 0.8iH,nz 0.0 1.5 0.6 4.3πF,nz −0.2 −1.1 −11.6 5.5xF,nz −1.0 −2.7 −14.7 3.4iF,nz 0.0 0.0 0.0 0.0

σ = 5.988 πH,nz 0.0 −0.1 −2.2 −0.2xH,nz 0.4 0.5 1.0 −1.2iH,nz 4.5 5.4 6.6 3.7πF,nz −0.2 −0.8 −5.8 6.0xF,nz −0.5 −1.0 −3.1 1.8iF,nz 0.0 0.0 0.0 0.0


under discretion.16 However, similar to the outcomes under discre-tion, the level of these low optimal policy rates is determined by thesize of σ. An additional finding in the two-country model is thatthere are two ways to mitigate the effect of adverse shocks. One isthe international spillover channel through which one of the centralbanks affects the output and inflation in the other country throughthe interdependence of the two countries. The other is the intertem-poral (or history-dependent) channel through which both centralbanks commit to lower future policy interest rates to mitigate theadverse shocks.

16As shown in Adam and Billi (2007), if an economy falls into a liquiditytrap again after being in the steady state, optimal discretionary policy may havehistory dependency.


Table 10. Expected Social Welfare Loss at the Statezz for Various Sizes of p under Discretion

(numbers are multiplied by 107)

p = 0.0 p = 0.5 p = 0.75 p = 0.90

σ = 1 70 516 43,549 22.413σ = 0.5 107 875 411,564 18,900σ = 5.988 34 260 11,316 29,073

6. Welfare Analysis

Tables 10, 11, 12, and 13 report the expected welfare loss given by(23) under discretion policy and quasi-optimal commitment policy,for various sizes of p and q. The loss, in general, tends to be smallwhen the expected durations of the adverse shocks are small. Thecomparisons among the tables illustrate the gains from the com-mitment. Clearly, the welfare loss is smaller under the quasi-optimalcommitment policy than it is under discretion for every combinationof p and q, as implied by Woodford (2003).

7. Conclusion

How should monetary policy cooperation be designed when morethan one country is simultaneously facing zero lower bounds on nom-inal interest rates? To answer this question, we provided a tractableframework within a two-country dynamic general equilibrium modelunder a Markov equilibrium. Analysis of the nature of optimal policycooperation in such a situation provides the key feature of the policy

Table 11. Expected Social Welfare Loss at the Statezz for Various Sizes of q under Discretion


q = 0.0 q = 0.5 q = 0.75 q = 0.90

σ = 1 87 382 23,753 11,247σ = 0.5 146 556 43,070 10,548σ = 5.988 40 204 8,434 12,375


Table 12. Expected Social Welfare Loss at the Statezz for Various Sizes of p under Commitment


p = 0.0 p = 0.5 p = 0.75 p = 0.90

σ = 1 68 434 33,572 19,505σ = 0.5 99 677 314,317 17,420σ = 5.988 33 233 10,581 23,507

under optimal discretionary and commitment policies. Under discre-tion, optimal monetary policy cooperation is characterized by no his-tory dependency and international spillover in which the parameterof IES plays an important role. On the other hand, under commit-ment, monetary policy is characterized by history dependence. Itis recommended that the country commits to low future nominalinterest rates. Quantitatively, the size of σ affects the optimal levelof interest rates.

Yet, in practice, making credible commitments to future policy isa difficult task in open economies. Central banks need to effectivelyinform citizens not only in the home country but also in foreigncountries about the nature of the commitments. At the same time,agents across the globe would fully understand the statements madeby the central banks, regardless of whether these are written in theirown language or not. Thus, because of these potential obstacles inimplementing cooperative commitment policy in open economies, itis equally important for central banks to understand the paths ofthe policy interest rates under optimal discretion policy.

There are several possible extensions to this study. First, weshould investigate the nature of policy cooperation for a global

Table 13. Expected Social Welfare Loss at the Statezz for Various Sizes of q under Commitment


q = 0.0 q = 0.5 q = 0.75 q = 0.90

σ = 1 76 374 23,748 11,245σ = 0.5 117 530 43,033 10,547σ = 5.988 36 202 8,434 12,373


liquidity trap with a less-restrictive model framework. In this paper,we assume that central banks maintain policy interest rates withina state to obtain analytical solutions and clear policy implicationsin a tractable manner. Although we believe that there should notbe qualitatively significant differences, it would be worth analyz-ing policy cooperation without this restriction.17 Second, to suggestreal monetary policy implementations, it is important to incorpo-rate more empirical realism through estimation and a richer modelstructure. Third, it would be intriguing to gauge the gains fromcooperation for a global liquidity trap by comparing the welfare lossunder cooperation with that under non-cooperation. Here, it wouldalso be interesting to think of a situation where one country deviatesfrom cooperation. We will address these issues in future research.

Appendix. Loss Function under Commitment

By substituting equations (14)–(21) into equation (23) and usingthe formula for the geometric series, we can obtain the loss functionthat the central banks under commitment aim to minimize:

LC(st) = Lt(st) + βEtLt+1(st+1) + β2EtLt+2(st+2) + . . . ..

=γHnH

θx2

H,zz +2γH,F nHnF

θxH,zzxF,zz

+γF nF

θx2

F,zz + nHπ2H,zz + nF π∗2

F,zz

+ βp

[γHnH

θx2

H,zz +2γH,F nHnF

θxH,zzxF,zz

+γF nF

θx2


F,zz

]

+ β(1 − p)[γHnH

θx2

H,nz +2γH,F nHnF

θxH,nzxF,nz

+γF nF

θx2


F,nz

]

17Our accompanying paper, Fujiwara et al. (2009), provides the solution of theoptimal monetary policy using a model with a general setting.


+ β2p2[γHnH

θx2

H,zz +2γH,F nHnF

θxH,zzxF,zz

+γF nF

θx2


F,zz

]

+ β2[(1 − p)q + p(1 − p)]

×[γHnH

θx2

H,nz +2γH,F nHnF

θxH,nzxF,nz

+γF nF

θx2


F,nz

]· · ·

+ βkpk

[γHnH

θx2

H,zz +2γH,F nHnF

θxH,zzxF,zz

+γF nF

θx2


F,zz

]

+ βk

⎡⎣(1 − p)

k−1∑j=0

q(k−1)−jpj

⎤⎦

×[γHnH

θx2

H,nz +2γH,F nHnF

θxH,nzxF,nz

+γF nF

θx2


F,nz

]. . . .

Then we have for p �= q,

LC(st) =1

1 − βp

[γHnH

θx2

H,zz +2γH,F nHnF

θxH,zzxF,zz

+γF nF

θx2


F,zz

]

+(1 − p)q − p

[1

1 − βq− 1

1 − βp

]

×[γHnH

θx2

H,nz +2γH,F nHnF

θxH,nzxF,nz

+γF nF

θx2


F,nz

],


and for p = q,

LC(st) =1

1 − βp

[γHnH

θx2

H,zz +2γH,F nHnF

θxH,zzxF,zz

+γF nF

θx2


F,zz

].

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Documents

The Zero Lower Bound and Monetary Policy in a Global Economy: A