Optimal and Sustainable Exchange Rate Regimes
A Simple Game-Theoretic Approach
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

This paper examines the question of how to design an optimal and sustainable exchange rate regime in a world economy of two interdependent countries. It develops a Barro-Gordon type two-country model and compares noncooperative equilibria under different assumptions of monetary policy credibility and different exchange rate regimes. Using a two-stage game approach to the strategic choice of policy instruments, it identifies optimal (in a Pare to sense) and sustainable (self-enforcing) exchange rate regimes. The theoretical results indicate that the choice of such regimes depends fundamentally on the credibility of monetary policy commitments by the two countries’ authorities. The nature of shocks to the economies and the substitutability between goods produced in the two countries also play some role. International coordination on instrument choice is necessary to design optimal and sustainable exchange rate regimes.

Abstract

This paper examines the question of how to design an optimal and sustainable exchange rate regime in a world economy of two interdependent countries. It develops a Barro-Gordon type two-country model and compares noncooperative equilibria under different assumptions of monetary policy credibility and different exchange rate regimes. Using a two-stage game approach to the strategic choice of policy instruments, it identifies optimal (in a Pare to sense) and sustainable (self-enforcing) exchange rate regimes. The theoretical results indicate that the choice of such regimes depends fundamentally on the credibility of monetary policy commitments by the two countries’ authorities. The nature of shocks to the economies and the substitutability between goods produced in the two countries also play some role. International coordination on instrument choice is necessary to design optimal and sustainable exchange rate regimes.

I. Introduction

In the debate over the relative merits of fixed and flexible exchange rate systems, economists have focussed on such issues as the role of exchange rate flexibility in current account adjustment, the importance of monetary policy autonomy in pursuing national objectives, the need to enhance monetary policy credibility, and the public-goods nature of exchange rate stability. The theoretical literature has established that optimal exchange rate arrangements depend on a number of criteria, including the structural characteristics of an economy (such as wage-price flexibility, factor mobility, openness of goods markets, and financial integration), the nature of shocks to the economy (such as nominal vs. real shocks and country-specific vs. global shocks), and the relative importance of price stability, exchange rate stability, etc., as policy objectives. Recent studies have attempted to evaluate the welfare outcomes of different international monetary arrangements (with or without policy coordination) from the perspective of both individual economies and the world as a whole. These studies have often involved game-theoretical modelling. See Frenkel, Goldstein, and Masson [1991], McKibbin and Sachs [1991], Goldstein, Isard, Masson, and Taylor [1992], and Tavlas [1992] for some of the issues involved. This paper attempts to synthesize these studies and offer a theoretical framework for evaluating welfare outcomes of noncooperative exchange rate regimes.

The paper extends the Barro-Gordon [1983] closed-economy model to a two-country world economy and examines the question of how to design optimal and sustainable exchange rate regimes. It attempts to identify optimal exchange rate regimes (from a global welfare perspective) within which each sovereign national authority benefits most by pursuing an independent monetary policy to accomplish its own objectives. Although policymakers in our model act noncooperatively to pursue their objectives in a given exchange rate regime, they can coordinate and agree on their choice of regime in order to secure a Pare to- optimal outcome. An exchange rate regime is sustainable if it is a Nash equilibrium, where no incentive exists for either policymaker to deviate from the chosen exchange rate regime. We will indeed show that our model identifies optimal and sustainable exchange rate regimes, using a two-stage game approach suggested by Hamada [1985]. Going backward, the second stage of a two-stage game obtains each authority’s maximum, noncooperative welfare for each exchange rate regime, and the first stage involves determining Nash-equilibrium exchange rate regimes. We will argue that the optimal choice of regime depends fundamentally on the credibility of monetary policy commitments by the two countries’ authorities. Other important factors include the nature of real shocks to the economies (global or country-specific), the substitutability between domestic and imported goods, and the relative importance given to exchange rate stability in a policymaker’s objectives.

The organization of the paper is as follows. Section II sets up a two-country macroeconomic model consisting of two monetary authorities and private agents and explains each decision-maker’s objective. It also describes the role of monetary policy credibility and defines the flexible, managed, and fixed exchange rate regimes. Sections III, IV, and V examine the cases of symmetric credibility, asymmetric credibility, and no credibility under alternative exchange rate regimes. These sections explain solution procedures and evaluate the equilibrium solutions of the key macroeconomic variables. Section VI deals with the strategic choice problem of exchange rate regimes in a two-stage game framework and focusses on the role of international coordination concerning the choice of exchange rate regimes. It also examines how the rational calculation of the authorities leads them to decide whether or not to establish the credibility of low-inflationary policy, and how some of the paper’s conclusions might be modified if the authorities attach some importance to exchange rate stability in their policy objectives. Section VII offers concluding remarks.

II. The Model

In this section, we present a formal model, explain the maximization problems of the decision-makers, interpret the role of credibility, and define the exchange rate regimes to be considered in the model. The model is standard and kept sufficiently simple so that decision rules or policies and equilibrium outcomes can be compared under different assumptions of credibility and different exchange rate regimes.

1. The Two-Country Model

The model is an extension of the Barro-Gordon [1983] closed macroeconomic framework to a two-country world macroeconomic model. The model’s structure is similar to those of Rogoff [1985], Turnovsky and d’Orey [1986, 1989], Canzoneri and Henderson [1988], and Giavazzi and Giovannini [1988, 1989]. The model includes many popular elements (such as nominal wage contracts and Lucas supply functions) but does not consider pertinent dynamics (such as those generated by capital accumulation and sticky prices), or imperfect/incomplete information. The two economies are assumed to be symmetric in size and structure. These simplifications enable us to sharply focus on the essential role of credibility in the choice of exchange rate regimes. The model is described as follows:

mtqt=φ(yt+ptqt)λit+ut,(1)
yt=σ(itqt+1|t+qt)+δ(st+pt*pt)+β(yt*yt)+vt,(2)
yt=γ(ptqt|t1)+wt,(3)
qt=θpt+(1θ)(pt*+st),(4)
mt*pt*=φ(yt*+pt*qt*)λit*+ut*,(5)
yt*=σ(it*qt+1|t*+qt*)δ(st+pt*pt)β(yt*yt)+vt*,(6)
yt*=γ(pt*qt|t1*)+wt*,(7)
qt*=θpt*+(1θ)(ptst),(8)
itit*=st+1|tst,(9)

where

mt = nominal money supply in logarithmic form,

yt = real output, measured as a deviation from the natural rate level and expressed in logarithmic form,

pt = price of domestically produced goods in logarithmic form,

qt = general price index in logarithmic form,

qt+1 | t = one-period ahead expectation of the general price index in logarithmic form,

it = nominal interest rate expressed in natural units,

st = spot exchange rate, measured as units of home currency per unit of foreign currency and expressed in logarithmic form,

st+1 | t = one-period ahead expectation of the logarithm of the spot exchange rate,

ut, vt, wt = mutually and serially uncorrelated disturbances with zero means.

Foreign variables are expressed with asterisks (*) and home variables without. The Greek letters are positive constants.

Equations (1) and (5) describe the money market equilibrium conditions in the two countries. Money balances on the left hand side and output on the right hand side are deflated by the country’s general price index. The income elasticity of money demand, φ, is assumed not to be excessively greater than unity (so that A2 to be defined later is positive). The disturbance ut or ut* summarizes serially uncorrelated shocks affecting money demand and/or supply.

Equations (2) and (6) represent goods demand in the two countries. Goods demand depends negatively on the real interest rate, it - qt+l | t + qt, and positively on the real exchange rate, st + pt* - pt, and foreign output relative to domestic output, yt* - yt. The real interest rate, which affects business capital investment and households’ durables purchases (including housing demand), is defined as the nominal interest rate, it, minus the expectation of one-period ahead rate of inflation in general price indices, qt+1 | t - qt. Business firms undertaking capital investment and households purchasing durable goods form the expectation of general prices. The terms involving the real exchange rate and relative output capture net exports. The stochastic disturbance vt or vt* represents serially uncorrelated demand shocks.

Equations (3) and (7) define goods supply in terms of standard Lucas supply functions. Each economy is assumed to be specialized in the production of a distinct good. Since labor is the only variable input used for production in each country, output supply depends positively on the inverse of the real wage the firm faces, pt - qt | t-1. Here, qt | t-1 is interpreted as the time t nominal wage set by labor and management in a wage contract negotiation held at time t-1. Note that the same, one-period forward notation, qt+1 | t, is used to indicate price expectations set by business firms undertaking capital investment and by households purchasing durable goods. The term wt or wt* denotes serially uncorrelated supply shocks.

Equations (4) and (8) define the general price index in the two countries. The definition embodies the assumption that θ and 1 - θ are fixed expenditure shares spent on domestic and imported goods. It is assumed that people have preferences for domestic goods in their spending so that 1/2 ≤ θ ≤ 1.

Equation (9) is the usual condition for uncovered interest rate parity. The two economies are perfectly integrated financially so that the nominal interest rate differential, it - it*, equals the expectation of the one-period rate of change in the nominal exchange rate, st+1 | t - st. 1/ Exchange market traders set this expectation, which is nothing but the forward premium due to the assumed absence of an exchange risk premium.

Equations (1)-(9) contain nine endogenous variables, two monetary policy instruments, and three expectations variables, yt, yt*, pt, pt*, qt, qt*, it, it*, st, mt, mt*, qt+1 | t, qt+1 | t*, and st+1 | t. The home and foreign monetary authorities choose two out of the three variables, mt, mt*, and st, as their policy instruments, letting the remaining variable be determined endogenously. A chosen combination of instruments defines the exchange rate regime (see below). The model is closed by specifying how private agents set the three expectations variables, qt+1 | t, qt+1 | t*, and st+1 | t. An important feature of the model is that it formulates both monetary policy and private behavior explicitly, allowing us to focus on the interactions between them.

2. Maximization Problems of the Authorities and Private Agents

The objectives of the home and foreign monetary authorities are to set their respective monetary policies so as to maximize

Et[Σj(1+ρ)jUt+j],Ut+j =Δyt+j -(ω/2)(Δqt+j)2,j=0,1,2,..,(10a)
Et[Σj(1+ρ*)jUt+j*],Ut+j* =Δyt+j* -(ω*/2)(Δqt+j*)2,j=0,1,2,..,(10b)

Here, Δxt = xt - xt-1 (xt is any variable). That is, the authorities try to raise the growth rate of real output and stabilize domestic inflation as much as they can. The objective functions indicate that the authorities have the Barro-Gordon inflationary bias. 1/ The parameter ρ (or ρ*) is the subjective rate of time preference, and ω (or ω*) is a relative weight attached to the objective of inflation stability. At this point of the analysis, the authorities are assumed not to attach any weight to exchange rate stability in their objectives. This issue will be taken up in Section VI.

Private sector agents set their expectations of the one-period ahead general price indices and spot exchange rates. Private individuals are aggregated into three representative decision-makers: the home price-expectations setter, the foreign price-expectations setter, and the global exchange market trader. Here, the price-expectations setter represents the interests of business firms undertaking capital investment, households purchasing durable goods, and labor and management negotiating on nominal wages. The objectives of private agents are to set the values of their expectations so as to minimize the prediction errors of the general price index or spot exchange rate. That is, they maximize

Vt= -Et(qt+1qt+1|t)2,(11a)
Vt*=Et(qt+1*qt+1|t*)2,(11b)
Wt=Et(st+1st+1|t)2,(11c)

with respect to qt+1 | t, qt+1 | t*, and st+1 | t, respectively, in each period. 1/

3. Credibility

The ability of each authority to make a credible commitment to a given monetary policy has important implications for the choice of exchange rate regimes. For example, our intuition tells us that a credible authority should not manage or fix the exchange rate against the currency of a non-credible country because the latter’s authority cannot pursue a stable and low-inflationary monetary policy. Another example is that a fixed exchange rate system cannot be maintained unless the authority fixing the exchange rate is credible, since fixing the rate requires a (time-inconsistent) commitment.

This paper considers two polar cases where each authority has either full credibility of monetary policy commitment or no such credibility at all. This leads to three types of international policy games:

Symmetric Credibility: Both countries’ monetary authorities can commit themselves credibly to their respective policy rules, to which private agents respond optimally.

Asymmetric Credibility: Only one authority can make a credible commitment to a monetary policy rule, while the other authority cannot, so that the latter and private agents respond optimally to the former authority’s policy rule.

No Credibility: Neither authority can make a credible policy commitment.

The concept of “credibility” in this paper is defined in terms of an authority’s ability to carry out any given (time-inconsistent) policy as well as other players’ belief that it will indeed implement the policy. Since such policy behavior is common knowledge, it introduces a certain leader-follower relationship to international policy games. In the case of symmetric credibility, both authorities, while acting as Nash-Cournot players with each other, behave as Stackelberg leaders vis-à-vis private agents. In the case of asymmetric credibility, the credible authority behaves as the sole leader and the other, non-credible, authority and the private agents act as Nash-Cournot players with each other and respond optimally to the former authority’s policy rule as Stackelberg followers. In the case of no credibility, the authorities and private agents all play a Nash-Cournot game. The question of how an authority acquires credibility, thus assuming a leadership role vis-à-vis private agents (and, perhaps, the other authority), will be taken up in Section VI.

4. Exchange Rate Regimes

We examine three exchange rate regimes, depending on whether the authorities use the money supply or the exchange rate as their policy instruments, and whether or not the exchange rate is fixed. The first examined is a freely flexible exchange rate regime where both authorities use their respective money supplies as policy instruments, allowing the exchange rate to be determined freely in the market. This is the regime most often studied in the literature on international macroeconomic policy interdependence. The second is a managed exchange rate regime where one authority uses the money supply as its policy instrument and the other uses the exchange rate (see Giavazzi and Giovannini [1989]). This regime introduces another type of asymmetry to the relationship between the authorities, since they use different monetary policy instruments. The third is a fixed exchange rate regime where one authority fixes the exchange rate while the other uses the money supply as its policy instrument. Since fixing the exchange rate requires a commitment, the regime cannot be maintained unless the authority fixing the rate is credible. 1/ The paper focusses only on these three polar exchange rate regimes and does not take up other cases where the authority controls a combination of the exchange rate and the money supply. 1/

Throughout the paper, we assume that all decision-makers can observe the current disturbances and that the authorities make their decisions noncooperatively when setting their respective monetary policies. We obtain and compare noncooperative outcomes under different assumptions of credibility and different combinations of monetary policy instruments (i.e., exchange rate regimes). The private-sector expectations are rational in equilibrium; the implication is that monetary policy cannot raise the equilibrium growth rate of real output systematically above the natural growth rate.

III. Symmetric Credibility

Let us first consider the case where both the home and foreign authorities can credibly commit themselves to their money supply or exchange rate rule. By virtue of their ability to make credible commitments, the authorities act as Stackelberg leaders vis-à-vis private agents. The private agents respond optimally to the authorities’ committed policy rules. In what follows, we obtain the equilibrium solutions for real output, the general price indices, and the exchange rate, all in the form of rates of change, under alternative exchange rate regimes. 2/

1. The Flexible Exchange Rate Regime

Under the flexible exchange rate regime with symmetric credibility, each authority can commit itself in advance to a linear money supply rule. This is a contingent rule that relates linearly the money supply growth rate, Δmt or Δmt*, to the shocks to the economies. It is assumed that every decision-maker can observe current and past shocks. The exchange rate is determined endogenously in the market.

Since Δmt and Δmt* are policy variables, the reduced form solutions to (1)-(9) can be expressed as

Δyt=Ψ1(ΔmtΔutΔqt|t1)+Ψ2(Δmt*Δut*Δqt|t1*)+Ψ3Δvt+Ψ4Δvt*+1+λλ(Ψ1Δwt+Ψ2Δwt*)+λ(Ψ1Δ2qt+1|t+Ψ2Δ2qt+1|t*)+(λΨ1σΨ3)(Δst+1|t+Δqt+1|t*Δqt+1|t),(12a)
Δyt*=Ψ1(Δmt*Δut*Δqt|t1)+Ψ2(ΔmtΔutΔqt|t1)+Ψ3Δvt*+Ψ4Δvt+1+λγ(Ψ1Δwt*+Ψ2Δwt)+λ(Ψ1Δ2qt+1|t*+Ψ2Δ2qt+1|t)(λΨ1σΨ3)(Δst+1|t+Δqt+1|t*Δqt+1|t),(12b)
ΔqtΔqt|t1=Π1(ΔmtΔutΔqt|t1)+Π2(Δmt*Δut*Δqt|t1*)+Π3Δvt+Π4Δvt*+1+λγ{(Π111+λ)Δwt+Π2Δwt*}+λ(Π1Δ2qt+1|t+Π2Δ2qt+1|t*)+(λΠ1σΠ3)(Δst+1|t+Δqt+1|t*Δqt+1|t),(12c)
Δqt*Δqt|t1*=Π1(Δmt*Δut*Δqt|t1*)+Π2(ΔmtutΔqt|t1)+Π3Δvt*+Π4Δvt+1+λγ{(Π111+λ)Δwt*+Π2Δwt}+λ(Π1Δ2qt+1|t*+Π2Δ2qt+1|t)(λΠ1σΠ3)(Δst+1|t+Δqt+1|t* -Δqt+1|t),(12d)
ΔstΔst+1|t=Γ1{(ΔmtΔutΔqt|t1)(Δmt*Δut*Δqt|t1*)} -Γ2(ΔvtΔvt*){φΓ1(1+2β)Γ2}(ΔwtΔwt*)+(λΓ11)(Δ2qt+1|tΔ2qt+1|t*)+(λΓ1+σΓ21)(Δst+1|t+Δqt+1|t*Δqt+1|t),(12e)

where

Ψ1=γ2{σA1+2δ+σ(2θ1)A2}>0,
Ψ2=γ2{σA12δ+σ(2θ1)A2},
Ψ3=γ2{λA1+λ+2(1θ)(1φ)A2}>0,
Ψ4=γ2{λA1λ+2(1θ)(1φ)A2},
Π1=12{σA1+2δ+σ(2θ1)+2γ(1+2β)(1θ)A2}>0,
Π2=12{σA12δ+σ(2θ1)+2γ(1+2β)(1θ)A2},
Π3=12{λA1+(2θ1)λ2φ(1+γ)(1θ)A2},
Π4=12{λA1(2θ1)λ2φ(1+γ)(1θ)A2},
Γ1=2δ+σ(2θ1)+γ(1+2β)A2>0,
Γ2=2φ(1θ)+(2θ1)+γφA2>0,
A1=σ(1+λ+γφ)+γλ>0,
A2={2δ+σ(2θ1)}(1+λ+γφ)+γ(1+2β){λ+2(1θ)(1φ)}>0,

and Δ2xt=Δ(xtxt1)=xt2xt1+xt2 (xt is any variable).

To find equilibrium, we first obtain the private agents’ optimal responses to Δmt and Δmt*. At each time t, the private agents maximize Vt, Vt*, and Wt defined by (11) over qt+1 | t - qt, qt+1 | t* - qt*, and st+1 | t - st, respectively, using (12) and taking Δmt and Δmt* and other private agents’ expectations as given. These maximization problems yield the following reaction functions of the private agents:

qt+1|tqt=EtΔqt+1,qt+1|t*qt*=EtΔqt+1*,st+1|tst=EtΔst+1,(13)

where Etxt+1 is the mathematical expectation of xt+1 (any variable at time t+1) given information available at time t. These are the usual rational expectations conditions widely used in many macroeconomic models. The private agents give full credibility to the home and foreign monetary authorities by way of setting the rational expectations of one period-ahead rates of change in prices and exchange rates as Stackelberg followers.

Next, the two monetary authorities, as Stackelberg leaders, take the private agents’ optimal responses (13) into consideration and set the linear contingent rule for the money supply growth rate. Then, real output growth no longer depends on money supply growth at time t and the authority’s objective now reduces to stabilizing the rate of general price inflation. Complete stabilization is accomplished by setting the money supply rule in the following way: 1/

Δmt=μt=Δut+B1Δvt+B2Δvt*+B3Δwt+B4Δwt*,(14a)
Δmt*=μt*=Δut*+B1Δvt*+B2Δvt+B3Δwt*+B4Δwt,(14b)

where

B1 =Π1Π3Π2Π4Π12Π22,B2= -Π1Π4Π2Π3Π12Π22,B3=Π1γ(Π12Π22) -1+λγ,B4 =Π2γ(Π12Π22).

Then, the equilibrium solutions for real output, prices, and the exchange rate are expressed as

Δyt=ηt=(Ψ3+B1Ψ1+B2Ψ2)Δvt+(Ψ4+B2Ψ1+B1Ψ2)Δvt*+B5Δwt+B6Δwt*,(15a)
Δyt*=ηt*=(Ψ3+B1Ψ1+B2Ψ2)Δvt*+(Ψ4+B2Ψ1+B1Ψ2)Δvt+B5Δwt*+B6Δwt,(15b)
Δqt=0,(15c)
Δqt*=0,(15d)
Δst=ξt={Π3Π4Π1Π2Γ1+Γ2}(ΔvtΔvt*)+{1(1+λ+γφ)γ(Π1Π2)Γ1+(1+2β)Γ2}(ΔwtΔwt*),(15e)

where

B5=Ψ1Π1Ψ2Π2γ(Π12Π22),B6= -Ψ1Π2Ψ2Π1γ(Π12Π22).

The best contingency rule prescribes zero inflation for both countries at all dates, although real output and the exchange rate fluctuate randomly over time. It is also clear that the equilibrium solutions for real output, general prices, and the exchange rate depend only on real shocks because the money supply is set so as to always offset nominal shocks, ut or ut*. This property holds in all exchange rate regimes considered in the paper.

The time t utility of the authority, then, turns out to be

Ut=ηt,Ut*=ηt*.

Taking the unconditional expected value, 1/ we find

U=EUt=0,U*=EUt*=0.

The private agents’ expected utilities are

Vt=0,Vt*=0,Wt=Σ,(16a)

where

Σ={Π3Π4Π1Π2Γ1+Γ2}2Var(vtvt*)+{1(1+λ+γφ)(Π1Π2)γ(Π1Π2)Γ1+(1+2β)Γ2}2Var(wtwt*).(16b)

The home and foreign price-expectations setters achieve the maximum utility of zero (bliss point) because the general price index is stabilized completely in both countries, while the global exchange market trader achieves a negative utility due to unpredictable exchange rate fluctuations.

2. The Managed Exchange Rate Regime

The managed exchange rate regime to be considered in this paper is asymmetric, in the sense that one country’s authority uses the exchange rate and the other country’s authority uses the money supply as policy instruments. 1/

On the assumption that the home authority makes a money supply commitment, Δmt, and the foreign authority makes an exchange rate commitment, Δst, the reduced form solutions to (1)-(9) can be expressed as

Δyt=(Ψ1+Ψ2)(ΔmtΔutΔqt|t1)(Ψ2/Γ1)(ΔstΔst+1|t) +(Ψ3Γ2Ψ2/Γ1)Δvt+(Ψ4+Γ2Ψ2/Γ1)Δvt*+[(1+λ)Ψ1/γ{φΓ1(1+2β)Γ2}Ψ2/Γ1]Δwt+Ψ2[(1+λ)/γ+{φΓ1(1+2β)Γ2}/Γ1]Δwt*+[λ(Ψ1+Ψ2)Ψ2/Γ1]Δ2qt+1|t(17a)+(Ψ2/Γ1)Δ2qt+1|t*+[λΨ1σΨ3+(λΓ1+σΓ21)Ψ2/Γ1](Δst+1|t+Δqt+1|t*Δqt+1|t),
Δyt*=(Ψ1+Ψ2)(ΔmtΔutΔqt|t1)(Ψ1/Γ1)(ΔstΔst+1|t) +(Ψ3Γ2Ψ1/Γ1)Δvt*+(Ψ4Γ2Ψ1/Γ1)Δvt+Ψ1[(1+λ)/γ{φΓ1(1+2β)Γ2}/Γ1]Δwt*+[(1+λ)Ψ2/γ{φΓ1(1+2β)Γ2}Ψ1/Γ1]Δwt+(Ψ2/Γ1)Δ2qt+1|t*(17b)+[λ(Ψ1+Ψ2)Ψ1/Γ1]Δ2qt+1|t+[σΨ3+(σΓ11)Ψ1/Γ1](Δst+1|t+Δqt+1|t*Δqt+1|t),
ΔqtΔqt|t1=(Π1+Π2)(ΔmtΔutΔqt|t1)(Π2/Γ1)(ΔstΔst+1|t)+(Π3Γ2Π2/Γ1)Δvt+(Π4+Γ2Π2/Γ1)Δvt*+[(1+λ)Π1/γ{φΓ1(1+2β)Γ2}Π2/Γ11/γ]Δwt+Π2[(1+λ)/γ+{φΓ1(1+2β)Γ2}/Γ1]Δwt*+[λ(Π1+Π2)Π2/Γ1]Δ2qt+1|t(17c)+(Π2/Γ1)Δ2qt+1|t*+[λΠ1σΠ3+(λΓ1+σΓ21)Π2/Γ1](Δst+1|t+Δqt+1|t*Δqt+1|t),
Δqt*Δqt|t1*=(Π1+Π2)(ΔmtΔutΔqt|t1)(Π1/Γ1)(ΔstΔst+1|t)+(Π3+Γ2Π1/Γ1)Δvt*+(Π4Γ2Π1/Γ1)Δvt+[(1+λ)Π1/γ+{φΓ1(1+2β)Γ2}Π1/Γ11/γ]Δwt*+[(1+λ)Π2/γ{φΓ1(1+2β)Γ2}Π1/Γ1]Δwt+(Π1/Γ1]Δ2qt+1|t*(17d)+[λ(Π2/Γ1)Π1/Γ1]Δ2qt|t1+[σΠ3+(σΓ21)Π1/Γ1](Δst+1|t+Δqt+1|t*Δqt+1|t),

where ψj, Γj and Πj have been defined previously. On the other hand, if the home authority manages the exchange rate and the foreign authority controls its money supply, the reduced form solutions are the same as (17) except that the home and foreign variables have to be reversed due to the assumed symmetry of the economic structures of the two countries.

The solution procedure under the managed exchange rate regime is basically the same as that of the flexible exchange rate regime; the only difference is that the foreign authority’s policy instrument is now the exchange rate. It turns out that the equilibrium solutions are indeed identical to those of the flexible exchange rate regime and, thus, we obtain (14) and (15). This implies that, with symmetric credibility, the flexible and managed exchange rate regimes are effectively the same. Each authority accomplishes complete price stability and obtains a maximum possible level of welfare of zero. The private agents’ utilities are also the same as those under the flexible exchange rate regime, i.e., (16).

3. The Fixed Exchange Rate Regime

Under the fixed exchange rate regime with symmetric credibility, one authority makes a fixed exchange rate commitment and the other authority makes a money supply commitment. The authority fixing the rate abandons monetary policy autonomy while the latter retains it. 1/

The reduced form solutions to be used are the same as those under the managed exchange rate regime, (17). The solution procedure is simpler than that of the managed rate regime in that one authority sets the exchange rate at a constant level in all periods without solving any maximization problem. An anticipated outcome of this regime is that the authority committed to fixed exchange rates cannot stabilize the rate of inflation and, therefore, incurs a welfare loss.

On the assumption that the home authority makes a money supply commitment and the foreign authority fixes the exchange rate, the growth rates of the money supply in the two countries can be expressed as

Δmt=Δut1Π1+Π2{(Π3Γ2Π2/Γ1)Δvt+(Π4+Γ2Π2/Γ1)Δvt*+[(1+λ)Π1/γ{φΓ1(1+2β)Γ2}Π2/Γ11/γ]Δwt+Π2[(1+λ)/γ+{φΓ1(1+2β)Γ2}/Γ1]Δwt*},(18a)
Δmt*=Δut*1Π1+Π2{(Π4Γ2Π1/Γ1)Δvt*+(Π3+Γ2Π1/Γ1)Δvt+[(1+λ)Π2/γ{φΓ1(1+2β)Γ2}Π1/Γ1]Δwt*+[(1+λ)Π1/γ+{φΓ1(1+2β)Γ2}Π1/Γ11/γ]Δwt}.(18b)

The equilibrium solutions for real output and prices are summarized as:

Δyt=ηtΨ1Π2Ψ2Π1Γ1(Π1+Π2)ξt,(19a)
Δyt*=ηt*+Ψ1Π1Ψ2Π2Γ1(Π1+Π2)ξt,(19b)
Δqt=0,(19c)
Δqt*=Π1Π2Γ1ξt.(19d)

The home authority completely stabilizes the general price index in all periods, while the foreign authority achieves the zero rate of inflation on the average with fluctuations around it. The foreign average inflation rate is zero because the fixed rate commitment allows the foreign authority to import zero inflation, on the average, from the home country. The home country provides a nominal anchor for the foreign country. However, the fixed rate commitment does not allow the foreign authority to pursue an independent monetary policy and stabilize inflation.

The above result indicates that the home authority’s welfare is at its maximum, while the foreign authority’s welfare is lower due to variable inflation:

U=EUt=0,U*=EUt*={(Π1Π2)/Γ1}2Σ/ω*0,

where Σ has been defined in (16b). This means that the fixed exchange rate regime is not as desirable as the flexible or managed exchange rate regime from the viewpoint of the foreign authority fixing the exchange rate.

However, the foreign authority’s welfare becomes as high as its potential if Σ = 0; that is, if the two country’s real shocks are identical (i.e., vt = vt* and wt = wt*) or if goods produced in the two countries are perfect substitutes (i.e., δ → ∞ so that Π34 → 0 and Π12 → 1/(1+λ+γφ)). In either one of these special cases, we obtain Σ = 0 and the foreign authority does not lose much by abandoning its monetary policy autonomy and pegging the exchange rate to the. home, nominal-anchor currency. To put it differently, a credible authority experiencing country-specific shocks and producing goods distinct from goods abroad has nothing to gain from sacrificing monetary policy autonomy to undertake fixed rate commitments. 1/

The fixed exchange rate regime also changes the private agents’ welfare. We obtain

Vt=0,Vt*={(Π1Π2)/Γ1}2Σ0,Wt=0.

The home price-expectations setter and the global foreign exchange market trader achieve the bliss utility of zero due to perfect stabilization of home prices and exchange rates. The foreign price-expectations setter, on the other hand, receives a lower level of utility due to unpredictable inflation variability. In one of the special cases mentioned above (where Σ = 0), however, the welfare of the foreign price-expectations setter becomes its potential maximum.

IV. Asymmetric Credibility

Next, let us consider the case of asymmetric credibility. Assume that only the home authority can make a credible commitment to a monetary policy rule while the foreign authority cannot. The home authority sets its policy rule as a Stackelberg leader and the foreign authority and the private agents, as Stackelberg followers, respond optimally to the home authority’s policy rule. More specifically, the home authority sets a policy rule in advance to maximize its objectives by taking into consideration the optimal responses of the foreign authority and the private agents. In response to the policy commitment by the home authority, the latter two parties set their choice variables in each period, as Nash-Cournot players with each other and as Stackelberg followers vis-à-vis the credible home authority. 1/

1. The Flexible Exchange Rate Regime

Under the flexible exchange rate regime with asymmetric credibility, the credible home authority makes a money supply commitment, while the non-credible foreign authority and the private agents set the values of money supply and expectations, respectively, in each period.

Therefore, the solution can be obtained in two procedures, using the reduced form expressions in (12). First, the reaction functions of the foreign authority and the private agents are derived from their respective maximization problems. The foreign authority’s objective is to set Δmt* in each period to maximize Ut*, given Δmt, qt+1|t - qt, qt+1 | t* - qt*, and st+1|t - st, which yields the reaction function:

Δqt*=(Ψ1/Π1)/ω*.(20)

The private agents’ reaction functions have already been derived in (13).

Second, the home authority sets the contingency rule for Δmt to maximize its discounted expected utility subject to the reaction functions (13) and (20). This maximization problem yields the money supply solutions,

Δmt=μt,Δmt*=(Ψ1/Π1)/ω*+μt*.

The equilibrium solutions for real output, prices, and the exchange rate are

Δyt=ηt,Δyt*=ηt*,Δqt=0,Δqt*=(Ψ1/Π1)/ω*,Δst=(Ψ1/Π1)/ω*+ξt.(21)

Thus, the credible home authority again completely stabilizes the rate of inflation at zero while the non-credible foreign authority stabilizes it at a higher rate. Credibility allows the home authority to accomplish complete price stability. On the other hand, the lack of credibility forces the foreign authority to inflate, because it cannot take the private reactions (13) as given when setting the money supply and, hence, it is led to maintain a high growth rate of money supply (without affecting real output in a systematic way). But its inflation rate, (ψ11)/ω*, is not too excessive in comparison to the rate that would be obtained in a Barro-Gordon type of closed-economy model, which is γ/ω* (> (ψ11)/ω*). 1/ This is because in a two-country world under flexible exchange rates, the foreign authority controls the money supply to reduce price inflation indirectly by keeping its currency from depreciating too much, which indeed mitigates inflationary pressure in the foreign country. Such a mechanism does not exist in a closed-economy framework. The credible home authority sets a zero-inflation money supply rule without being adversely affected by foreign inflation; it can insulate its own economy from inflation abroad by allowing home currency appreciation.

The welfare outcome is that the home authority achieves the maximum utility of zero, while the utility level of the foreign authority is lower at - (ψ11)2/2ω* (< 0). The private agents’ utility levels are the same as those of symmetric credibility, (16).

2. The Managed Exchange Rate Regime

Under the managed exchange rate regime, the home credible authority makes either a money supply or an exchange rate commitment and the foreign authority and private agents set the values of the remaining policy instrument and expectations, respectively, responding optimally to the home authority’s policy commitment. This case is interesting, because both the choice of monetary policy instruments and the degree of credibility are asymmetric between the two authorities.

a. Money Supply Commitment

Let us first take up the case where the home authority sets a credible rule for the money supply, Δmt, and the foreign authority sets the exchange rate, Δst, in each period in response to the home authority’s money supply rule. The relevant reduced form solutions are (17).

The equilibrium solutions turn out to be the same as those of the flexible rate regime above. That is, we obtain the solutions identical to (21). The credible home authority completely stabilizes inflation at zero, while the non-credible foreign authority stabilizes inflation at a positive rate of (ψ11)/ω*, which is still lower than the closed-economy inflation rate, γ/ω*. The reason for the moderate rate of inflation in the foreign country is similar to that under the flexible rate regime; although the foreign authority is forced to inflate without stimulating real output in equilibrium, it can avoid excessive currency depreciation and mitigate inflationary pressure by directly managing the exchange rate. Essentially, as long as the credible authority sets a money supply rule (Δmt), the choice of the follower authority’s policy instrument (whether Δmt* or Δst) does not matter. That is, in the case of asymmetric credibility, the flexible and managed exchange rate regimes bring about identical welfare outcomes, if the credible authority controls the money supply and plays the role of a nominal anchor for the world economy.

b. Exchange Rate Commitment

Next is the case where the credible home authority makes an exchange rate commitment, and the non-credible foreign authority sets the money supply in each period. In this case, the relevant reduced form solutions to be used are identical to (17) with the home and foreign policy instruments reversed.

The solutions are obtained in two procedures. First, the foreign authority maximizes Ut* over Δmt* and the private agents maximize Vt, Vt*, and Wt over qt+1 | t - qt, qt+1 | t* - qt*, and st+1 | t - st, by taking all other players’ choice variables (including the committed rule for Δst) as given. The first-order condition of the foreign authority’s maximization problem is the same as (20), and those of the private agents are derived in (13).

Second, the home authority sets the rule for Δst to maximize its own utility subject to (20) and (13). This yields the equilibrium solutions for the money supplies:

Δmt=μt,Δmt*=γ/ω*+μt*.

The equilibrium solutions for real output, prices, and the exchange rate are

Δyt=ηt,Δyt*=ηt*,Δqt=0,Δqt*=γ/ω*,Δst=γ/ω* +ξt.

The solutions indicate that the credible home authority committed to an exchange rate rule completely stabilizes inflation at zero, while foreign inflation, though stable, is excessively high at γ/ω*, a rate identical to the closed-economy inflation rate. Foreign inflation is excessive because the home authority attempts to stabilize general prices by allowing rapid appreciation of its own currency, thus exporting inflation to, and exercabating the existing inflationary pressure (due to the lack of credibility) in, the foreign country. Since the home authority manages the exchange rate, the foreign authority which controls the money supply cannot counteract effectively against rapid currency depreciation; as a result foreign inflation becomes excessive. Exchange rate management has an adverse effect on the non-credible foreign authority. 1/ This is in sharp contrast to the case where the home authority controls the money supply (the flexible rate regime or the managed rate regime with home-authority money supply commitment). The result is also a significant departure from the case of symmetric credibility discussed in Section III.

It turns out that the welfare outcomes of the private agents are the same as those in the case of home-authority money supply commitment or under the flexible exchange rate regime; their welfare measures are summarized in (16).

3. The Fixed Exchange Rate Regime

Since the fixed exchange rate regime requires a commitment, it cannot be maintained without a credible authority. The credible home authority makes fixed exchange rate commitments, and the non-credible foreign authority sets the money supply in each period. This means that the credible authority sacrifices its ability to pursue a potentially anti-inflationary monetary policy and that the non-credible foreign authority uses its own independent (potentially inflationary) monetary policy. The anticipated outcome is not desirable.

The maximization problems of the foreign authority and private agents are the same as those in the case of home-authority exchange rate commitment under the managed exchange rate regime. Hence, their reaction functions are (20) and (13). Then the home authority simply sets Δst = 0. The result is

Δmt =γω*+Δut1Π1+Π2{(Π4Γ2Π1/Γ1)Δvt+(Π3+Γ2Π1/Γ1)Δvt*+[(1+λ)Π2/γ{φΓ1(1+2β)Γ2}Π1/Γ1]Δwt+[(1+λ)Π1/γ+{φΓ1(1+2β)Γ2}Π1/Γ11/γ]Δwt*},
Δmt* =γω*+Δut*1Π1+Π2{(Π3Γ2Π2/Γ1)Δvt*+(Π4+Γ2Π2/Γ1)Δvt+[(1+λ)Π1/γ{φΓ1(1+2β)Γ2}Π2/Γ11/γ]Δwt*+Π2[(1+λ)/γ+{φΓ1(1+2β)Γ2}/Γ1]Δwt},

and

Δyt=ηtΨ1Π1Ψ2Π2Γ1(Π1+Π2)ξt,Δyt*=ηt* +Ψ1Π1Ψ2Π2Γ1(Π1+Π2)ξt,Δqt=γ/ω* -Π1Π1Γ1ξt,Δqt*=γ/ω*.

The equilibrium solutions indicate that the home authority suffers from excessively high and variable inflation and the foreign authority experiences equally excessive but stable inflation. Ironically, the welfare of the credible home authority is lower than that of the non-credible foreign authority. This is because the foreign authority, which lacks credibility but can stabilize the rate of inflation by adjusting its money supply in each period, is pushed to inflating the economy at a constant exchange rate, just as in a closed-economy framework. The home authority, on the other hand, completely forgoes the opportunity to use an independent, credible monetary policy; it no longer pursues a low-inflation policy nor counteracts against disturbances. By fixing the exchange rate, the home authority is forced to not only import the high inflation of the non-credible foreign authority but also abandon monetary policy autonomy for stabilization. 1/

The fixed exchange rate regime changes the welfare of the private agents in a way similar to the case of symmetric credibility. Since home inflation is now variable, the home price-expectations setter receives a negative welfare (when Σ > 0), while other private agents receive a maximum possible level of welfare:

Vt={(Π1Π2)/Γ1}2Σ,Vt*=0,Wt=0.

V. No Credibility

This section considers the case where no monetary authority makes a credible policy commitment. Without credibility the authorities can no longer take private-sector reactions (13) as given and must set their monetary policies as Nash-Cournot players vis-à-vis private agents. Also, a fixed exchange rate regime cannot be maintained due to the absence of a credible authority.

With no credibility, welfare measures of private agents under the flexible and managed exchange rate regimes turn out to be the same. They are also identical to those obtained in the case of symmetric credibility (Section III) and asymmetric credibility (Section IV).

1. The Flexible Exchange Rate Regime

Under the flexible exchange rate regime with no credibility, the home and foreign authorities set the money supply in each period to maximize their objectives, by taking each other’s money supply and private expectations as given subject to the reduced form solutions (12). The first-order conditions of the maximization problems yield

Δqt=(Ψ1/Π1)/ω,Δqt*=(Ψ1/Π1)/ω*,(22)

which constitute the authorities’ reaction functions.

Combining (22) with private agents’ reaction functions (13), the flexible rate solution with no credibility is obtained as

Δmt=(Ψ1/Π1)/ω+μt,Δmt*=(Ψ1/Π1)/ω*+μt*,

and

Δyt=ηt,Δyt*=ηt*,Δqt=(Ψ1/Π1)/ω,Δqt*=(Ψ1/Π1)/ω*,
Δst=(Ψ1/Π1)(1/ω1/ω*)+ξt.

The rate of inflation in each country is positive but not as high as in the case of a closed-economy model. The reason for moderate inflation has already been suggested in the previous section; under the flexible rate regime, each authority attempts to reduce price inflation by competitively appreciating its own currency, thereby importing low inflation from abroad. Although both authorities cannot appreciate their currencies simultaneously, the equilibrium is characterized by a positive but moderate rate of money growth and inflation.

2. The Managed Exchange Rate Regime

The equilibrium is presented here on the assumption that the home authority controls the money supply and the foreign authority controls the exchange rate. We use the reduced form solutions (17) to derive equilibrium.

The home authority, the foreign authority, and private agents maximize Ut over Δmt, Ut* over Δst, and Vt, Vt*, and Wt over qt+1 | t - qt, qt+1 | t* - qt*, and st+1 | t - st, respectively, each taking all other players’ choice variables as given, subject to (17). These maximization problems yield

Δmt=γ/ω+μt,Δmt*=(Ψ1/Π1)/ω*+μt*,

and

Δyt=ηt,Δyt*=ηt*,Δqt=γ/ω,Δqt*=(Ψ1/Π1)/ω*,Δst=γ/ω(Ψ1/Π1)/ω*+ξt.

The equilibrium solutions indicate that both authorities can stabilize inflation but at different rates; home inflation is excessively high while foreign inflation is moderately high. Foreign inflation is moderate because the foreign authority can appreciate its own currency by managing the exchange rate; it directly sets the exchange rate in such a way as to keep imported goods prices from soaring. Home inflation is excessive because the home authority lacks a direct instrument to counteract against home currency depreciation and thus ends up importing inflation from abroad. Exchange rate management by either authority, where no credibility exists, has a beggar-thy-neighbor effect, since the rate-managing authority is made better off, and the counterpart authority worse off.

VI. Choice of Exchange Rate Regimes

A number of interesting results emerge from the above analytical exercises. This section summarizes the results in the form of payoff matrices, discusses the problem of the strategic choice of exchange rate regimes, identifies conditions under which an authority will decide to establish its credibility, and examines the situation in which the authority assigns some utility weight to exchange rate stability.

1. Summary of the Results: The Payoff Matrices

Tables 1, 2 and 3 summarize our results. They represent the cases of symmetric credibility, asymmetric credibility, and no credibility, respectively. Three strategies are available to each authority: controlling the growth rate of the money supply (Δm), managing the exchange rate (Δs), and fixing the exchange rate (Δs = 0). A combination of these strategies determines the exchange rate regime. 1/ The expressions U and U* in each cell in the tables are the payoffs per period for the home and foreign authority, and V, V*, and W are the payoffs for the private agents. Note that the payoffs of {Δs, Δs} and {Δs, Δs=0} are not defined because the two authorities cannot simultaneously manage or fix the exchange rate. Also note that Table 3 does not report the payoff under the fixed exchange rate regime due to the absence of a credible authority.

Table 1.

Payoff Matrix for the Case of Symmetric Credibility

article image
Note: Σ =[Γ1(Π3Π4)/(Π1Π2)+Γ2]2Var(vtvt*)+[{1/(Π1Π2)(1+λ+γφ)}Γ1/γ+(1+2β)Γ2]2Var(wtwt*)0.
Table 2.

Payoff Matrix for the Case of Asymmetric Credibility

article image
Note: 0<Ψ1/Π1<γ.Σ =[Γ1(Π3Π4)/(Π1Π2)+Γ2]2Var(vtvt*)+[{1/(Π1Π2)(1+λ+γφ)}Γ1/γ+(1+2β)Γ2]2Var(wtwt*)0.
Table 3.

Payoff Matrix for the Case of No Credibility

article image
Note: 0<Ψ1/Π1<γ.Σ =[Γ1(Π3Π4)/(Π1Π2)+Γ2]2Var(vtvt*)+[{1/(Π1Π2)(1+λ+γφ)}Γ1/γ+(1+2β)Γ2]2Var(wtwt*)0.

Table 1 (symmetric credibility) shows that both authorities attain the highest payoff of zero under the flexible or managed exchange rate regime. This is because each credible authority implements a linear monetary policy rule to ensure stable and zero inflation in either regime. Therefore, the authorities are indifferent between the two regimes. (Exchange rate management has no beggar-thy-neighbor effect when the counterpart authority is credible because the latter can control its own inflation.) Under the fixed exchange rate regime, the rate of inflation of the rate-fixing country is zero on the average but variable so that its payoff is negative, unless Σ = 0 (i.e., the shocks are completely identical between the two countries or purchasing power parity holds). The payoff for the authority controlling the money supply under the fixed rate regime is zero.

The table also indicates that the private agents are indifferent between the flexible and managed exchange rate regimes; price-expectations setters obtain the bliss payoff of zero and the global exchange market trader receives a negative payoff (unless Σ = 0). The fixed exchange rate regime, however, changes the payoffs in favor of the exchange market trader and against the price-expectations setter in the country fixing the rate.

Table 2 (asymmetric credibility) describes the payoff matrix when only the home authority is credible. Under the flexible or managed exchange rate regime, the home authority always obtains the maximum payoff of zero because it can make a commitment to ensuring stable and zero inflation. The foreign authority’s payoff depends on whether the home authority controls the money supply or the exchange rate; foreign inflation is moderately high and its payoff moderately low if the home authority controls the money supply, whereas foreign inflation is excessively high and its payoff very low if the home authority manages the exchange rate. Therefore exchange rate management by the credible home authority has an adverse effect on the non-credible foreign authority, though exchange rate management by the foreign authority has no such effect on the home authority. The question is: How can the foreign authority keep the home authority from managing the exchange rate? This question will be addressed later in a two-stage game framework. 1/

Under the fixed exchange rate regime, the credible home authority’s payoff is extremely low and the foreign authority’s payoff is the same as that when the home authority manages the exchange rate. The reason the home authority’s payoff is extremely low is two-fold; first the home authority imports excessive inflation from the foreign country by fixing the exchange rate, and second the home authority abandons monetary policy autonomy, thereby foregoing the opportunity to counteract against shocks to the economy (the case of Σ > 0). Even when Σ = 0, the fixed rate regime is not attractive to the home authority because of importation of high foreign inflation. The credible authority can only lose if it decides to fix the exchange rate against the currency of an inflationary country. The result is intuitively plausible.

The payoffs of the private agents, reported in Table 2, show a pattern similar to Table 1. The private agents are indifferent between the flexible and managed exchange rate regimes. The fixed rate regime makes the home price-expectations setter worse off due to the resulting inflation variability (if Σ > 0) and the exchange market trader better off due to exchange rate stability. If Σ = 0, however, the private agents are completely indifferent among the three exchange rate regimes.

Table 3 (no credibility) shows that the authorities’ payoffs are strictly negative tinder any exchange rate regime. (The fixed exchange rate regime cannot be maintained.) It turns out that an authority’s payoff is determined completely by the counterpart authority’s choice of instrument. Each authority is made worse off if its counterpart manages the exchange rate; exchange rate management has a beggar-thy-neighbor effect. The private agents are indifferent between the flexible and managed rate regimes.

2. Strategic Choice of Exchange Rate Regimes: The Two Stage Game

We now examine the problem of the strategic choice of exchange rate regimes. This paper offers the first formal attempt in the literature to apply a two-stage game approach, suggested by Hamada [1985], to the choice of exchange rate regimes in a popular macroeconomic framework. 1/ The approach is useful in finding Nash-equilibrium strategies (i.e., sustainable exchange rate regimes), and focussing on a set of Pare to-dominant regimes that are Nash when there is a multiplicity of Nash equilibria.

The first stage of the two-stage game consists of a game to choose one of the three strategies (types of policy instruments): controlling the money supply, managing the exchange rate, and fixing the exchange rate. The second stage consists of a game to set the actual rule or value of the instrument chosen in the first stage.

Tables 1, 2 and 3 above provide information concerning the second stage. The task in the first stage, then, is to find Nash-equilibrium combinations of strategies in each Table. Since it is the authorities who choose the exchange rate regime strategically, the payoffs for the private agents are irrelevant in this part of the exercise.

It is apparent from each of the three tables that all instrument combinations, except those yielding “undefined” outcomes and those involving Δs=0 (when Σ > 0), are Nash equilibria. 1/ This means that the authorities have the incentive to choose the flexible or managed exchange rate regime as a self-enforcing regime as long as Σ > 0. When Σ = 0, the fixed exchange rate regime is also self-enforcing in the case of symmetric credibility (but not in the case of asymmetric credibility).

When symmetric credibility exists (Table 1), the flexible and managed exchange rate regimes are Nash equilibria and Pareto comparable; they are self-enforcing and equally desirable for the authorities. If the real shocks to the two economies are identical (global shocks) or if the goods produced in the two countries are perfect substitutes (the law of one price, or purchasing power parity) so that Σ = 0, the fixed rate regime is also a Nash equilibrium and Pareto comparable to other regimes. This last point is consistent with the literature emphasizing the importance of symmetry of the shocks and similarity of industries as prerequisites for a system of fixed exchange rates. 2/

In the case of asymmetric credibility (Table 2), the flexible and managed rate regimes are Nash equilibria but not equally desirable. The instrument combinations {Δm, Δm*} and {Δm, Δs}, which are Pareto comparable to each other, are Pareto superior to the combination {Δs, Δm*}. That is, a regime where the credible home authority controls the money supply is Pareto superior to the regime where it manages the exchange rate (because of the adverse effect on the foreign authority). To achieve a Pareto-superior outcome, the home authority should avoid exchange rate management, make a money supply commitment, and establish itself as a nominal anchor in the world economy. How can we induce the home authority to take this course of action, given that it can obtain the same payoff of zero regardless of whether it manages the exchange rate or controls the money supply and hence has no private incentive to avoid exchange rate management? 1/ We suggest that it can be accomplished through international coordination and mutual agreements on the choice of policy instruments (and hence the exchange rate regime), because the regime agreed upon is sustainable (i.e., self-enforcing). That is, once the home authority agrees to control the money supply, it has no incentive to deviate from it. The foreign authority may control the money supply or manage the exchange rate, so that either the flexible or managed exchange rate regime can emerge. The fixed exchange rate regime never emerges; it is neither a Nash equilibrium nor Pareto optimal.

In the case of no credibility (Table 3), the flexible rate regime is Pareto superior to the managed rate regime. Exchange rate management has a beggar-thy-neighbor effect on the counterpart authority and, hence, is not desirable. To ensure a Pareto-superior outcome, again, international coordination concerning the choice of exchange rate regime is required because this outcome is not automatically guaranteed by the authorities’ unilateral choice.

It is important to emphasize that this type of international coordination does not require coordinated (or joint) determination of the values or rules of the particular instruments chosen, but only requires the policymakers to agree on the choice of instruments. The purpose of international coordination here is to establish an international monetary framework in which the national authorities can pursue their independent policy objectives noncooperatively and, at the same time, obtain desirable welfare outcomes. Thus it must be distinguished from the widely discussed notion of international policy coordination where the authorities set policy values or rules cooperatively for joint maximization of world welfare. 2/

3. Establishing Credibility

So far each authority’s ability or inability to make a credible policy commitment has been assumed to be exogenously given. Comparisons of Tables 1, 2, and 3, however, suggest that an authority has an incentive to unilaterally acquire credibility and change the payoff matrix in a way favorable to itself. We now explore the possibility that each authority may decide whether or not to acquire credibility. Such a decision endogenously determines the leader-follower relationship and affects the choice of exchange rate regimes.

The discussion here is intuitive. We assume that each authority decides to acquire its credibility and obtain a higher payoff if the benefit of doing so exceeds the cost. The benefit accruing to an authority of making a credible policy commitment is the difference in payoffs between the case of symmetric credibility and that of no credibility, which is denoted as US - UN (Here and in what follows, US, UA, and UN refer to the home authority’s payoffs with symmetric, asymmetric, and no credibility, respectively, and U*S, U*A, and U*N refer to the foreign authority’s payoffs.) When the home authority unilaterally acquires credibility for a given instrument combination, its payoff rises without affecting foreign payoff, that is, UA = US = UN and U*A = U*S = U*N. The benefit accruing to the foreign authority of acquiring its own credibility is defined similarly.

How is the cost defined? One way of defining the cost would be to introduce the idea that it is costly to build up the reputation that an authority is credibly committed to anti-inflationary monetary policy. For example, to convince the public that the monetary commitment is credible, the authority will have to pay a price in the form of high unemployment or low real output. The less credibility the authority has initially, the higher the price will be. 1/ Essentially, the authority cannot enhance credibility without investing, i.e., making a sustained effort and incurring a cost, to accomplish it. 2/

Let us denote such a cost as Z (for the home authority) or Z* (for the foreign authority). Then, each authority has the incentive to invest to acquire credibility if

USUN>Z,U*SU*N>Z*.(23)

According to this simple idea, the case of symmetric credibility obtains if US - UN > Z and U*S - U*N > Z* the case of asymmetric credibility obtains if US - UN > Z and U*S - U*N < Z* and the case of no credibility obtains if US - UN < Z and U*S - U*N < Z*.

A second way to define the cost of acquiring credibility is to formulate the opportunity cost of implementing a committed policy rule in an infinitely repeated game framework. Here, we assume that an authority continues to receive the payoff of US as long as it sticks to its policy commitment, while if it deviates from the commitment the payoff becomes higher (denoted by UD) in the period of defection but lower (UN) in all the subsequent periods. 1/ The authority, therefore, decides not to deviate from its policy commitment if the temporary gain from defection, UD - US, falls short of the permanent loss, (US - UN)/ρ, where ρ is the subjective rate of time preference.

In this second formulation, the opportunity cost of building up a reputation of credibility is defined as Z = ρ(UD - US). Then the authority has the incentive to acquire credibility if (23) holds. This implies that the lower the subjective rate of time preference, the greater incentive there is for the authority to acquire credibility. In this example, it turns out that the authority chooses to acquire credibility as long as ρ < 1. 2/

The above discussion, though intuitive, sheds important light on the question of how each authority decides whether or not to acquire credibility. Once such a decision is made and the payoff matrix determined, we can identify optimal and self-enforcing exchange rate regimes.

4. Exchange Rate Stability as a Policy Objective

In our theoretical model above, it was assumed that an authority’s objectives are to raise real output growth and stabilize price inflation as much as it can. It did not regard exchange rate stability as beneficial.

However, one of the policy issues concerning the current flexible rate experience is the potentially adverse effects caused by serious misalignments and excessive volatility of exchange rates. It has been argued that real exchange rates often move for reasons unrelated to changes in underlying economic factors, such as bandwagon effects and speculative bubbles. Exchange rate instability is alleged to raise exchange risk, inhibiting international trade and investment. It reduces the role of money as an international unit of account and, thus, generates inefficiency in global markets. Thus a case could be made that there is a welfare gain from exchange rate stability. 1/ Indeed, the industrialized countries have increasingly geared their monetary policies towards exchange rate stabilization in recent years.

We now examine briefly the possible implications of including exchange rate stability as one of the policy objectives.

In Section III we argued that, when two authorities are credible (symmetric credibility), a fixed exchange rate regime is neither a Nash equilibrium nor Pareto optimal as long as Σ > 0. Only when Σ = 0, does the fixed rate regime become one of the optimal and sustainable regimes. The implication is that if Σ is sufficiently small and the utility weight attached to exchange rate stability in the policy objectives is sufficiently large, the fixed rate regime can Pareto-dominate other regimes.

When only one authority is credible (asymmetric credibility), scope for fixed exchange rates is more limited. The reason is that fixing the rate is very costly to the rate-fixing authority; it not only imports excessive inflation from abroad but also forgoes the opportunity to stabilize inflation. This means that for a fixed rate regime to be chosen, the utility weight attached to exchange rate stability must be very large to offset the cost. To the extent that resulting exchange rate stability inhibits the objective of price stability, the outcome may not be desirable and may reduce the credibility of an anti-inflationary monetary policy.

To summarize, we can find some scope for fixed exchange rates when there exists at least one country with strong anti-inflationary credibility which provides a nominal anchor for the international monetary system. When no authority is credible, there is no such scope.

VII. Concluding Remarks

This paper has focussed on the question of how to design optimal and sustainable exchange rate regimes in a world economy of two interdependent countries. For this purpose we have developed a simple game-theoretic model of Barro-Gordon type and compared noncooperative equilibria under different assumptions of credibility and different exchange rate regimes. A two-stage game approach to the strategic choice of exchange rate regimes turns out to be very useful, because it allows us to identify sustainable (Nash or self-enforcing) and optimal (in a Pareto sense) exchange rate regimes. The basic message of this approach is that it is in the best interest of the policymakers to agree on an exchange rate regime in which they can not only set their monetary policies freely (or noncooperatively) but also secure the best welfare outcomes from the perspectives of both individual economies and the world as a whole. We also examined the decision-making process whereby a country’s authority chooses whether or not to acquire credibility, since its outcome affects the choice of exchange rate regimes.

Some of the detailed, innovative results of the paper can be summarized as follows. The first, general result is that regardless of the degree of credibility, the flexible and managed exchange rate regimes are always Nash equilibria and, hence, sustainable (self-enforcing). It is possible to choose a Pareto-superior regime from these sustainable ones through international coordination. For example, the IMF, the OECD, the G7, and the Economic Summits can help shape a desirable exchange rate regime by providing a forum in which the choice of industrial countries’ policy instruments is appropriately coordinated. They do not have to coordinate on their monetary policies, but have only to agree on an international monetary framework in which monetary policies can be set noncooperatively.

Second, when both authorities are fully credible (symmetric credibility), the flexible and managed exchange rate regimes yield identical welfare outcomes for the authorities and, as a result, coordination concerning the choice of exchange rate regimes is unnecessary. The fixed exchange rate regime is not a Nash equilibrium as long as Σ > 0. When Σ = 0, the fixed regime becomes a Nash equilibrium and Pareto-comparable to the flexible and managed regimes. In fact, a fixed exchange rate regime can only become optimal and sustainable when symmetric credibility exists and Σ = 0, i.e., when both authorities are credible and real shocks to the economies are global or goods produced in both countries are perfect substitutes. Two anchor countries with different (country-specific) real shocks or dissimilar product mixes should not be tied together through fixed exchange rates.

Third, when one authority is credible and the other is not (asymmetric credibility), the fixed exchange rate regime cannot be a Nash equilibrium. To ensure a Pareto-superior outcome, the credible authority should control the money supply and play a nominal anchor role without trying to manage the exchange rate. Exchange rate management has an undesirable effect on the counterpart, non-credible authority. Once the credible authority agrees to control the money supply, the non-credible authority may control the money supply or manage the exchange rate. Thus, either a flexible or a managed exchange rate regime, with the anchor country pursuing a stable and low-inflationary policy, emerges as an optimal, sustainable regime in the case of asymmetric credibility.

Fourth, when neither authority is credible (no credibility) only the flexible exchange rate regime is Pareto optimal. Since exchange rate management by one authority has a beggar-thy-neighbor effect on the other, the managed exchange rate regime is Pareto inferior. No scope exists for fixed exchange rates as an optimal and sustainable regime.

Finally, each authority has an incentive to unilaterally acquire credibility and change the structure of the payoff matrix, if the benefit of doing so exceeds the cost. The lower the cost of pursuing an anti-inflationary monetary policy and the lower the subjective rate of time preference, the more incentive there is for the authority to establish and maintain its policy credibility. Such rational calculations by the authorities are an important factor determining the exchange rate regime.

Although we do not claim that the model employed is perfectly general or robust, its theoretical predictions are quite plausible. However, the model itself may contain biases that favor a flexible exchange rate regime over a fixed rate regime. It did not include those elements which would potentially work against a flexible rate regime, such as currency misalignments, speculative bubbles, imperfect and/or incomplete information, the public goods aspect of exchange rate stability, and the explicit role of fixed exchange rates as a device to enhance credibility. Inclusion of these elements may bolster the case for a fixed rate regime.

As the European Community countries plan to create European Monetary Union by the end of this century, the world appears increasingly headed toward a multiple currency system. What will the future international monetary system look like? The framework presented in this paper offers a useful guide for examining the factors that shape exchange rate regimes and thus may assist in designing a desirable future international monetary system.