On the relation between monetary interdependence and exhange rate volatility

JOURNAL

OF THE JAPANESE

AND

INTERNATIQNAL

ECONOMIES

1,

351-372 (1987)

On the Relation between Monetary Interdependence and Exhange Rate Volatility* TAKAHIKO Tokyo

Keizai

MUTOH

University,

Tokyo,

Japan

Received April 16, 1986; revised January 27, 1987

Mntob, Takahiio-On the Relation between Monetary Interdependence change Rate Volatility

and Ex-

A simplified two-country macromodel is developed to analyze the relationship between the international linkage of interest rates and the exchange rate volatility. A fundamental trade-off exists between them in that the weaker the international linkage of capital, the more volatile the behavior of the foreign exchange rates. Depending on the degree of capital mobility, the foreign exchange rates may be so volatile that it is impossible for macroeconomic policy to have a systematic influence on the level of the foreign exchange rates, undermining the effectiveness of the macroeconomic policy. J. Japan. ht. &on., December 1987, l(4), pp. 351372. Tokyo Keizai University, Tokyo, Japan. e 1987 Acacdmic PESS, IW. Journal

of Economic

Literature

1.

Classification Numbers 431, 133, 441.

INTRODUCTION

International interdependenceof interest rates has becomeone of the major concernsof the world economyof today. During the first half of the 198Os,it was often pointed out that the high-interestrate policy employed by the United States was transmitted to the rest of the world by way of international capital movements. Using a portfolio equilibrium model, Fukao and Okubo (1982)examinated the effect of the U.S. long-term * I express my special thanks to Professors Tetsuro Shizuki, Takashi Toyoda, Kyoji Fukao, and Hiroshi Yoshikawa. Drs. Jenny Corbett, Christopher Allsopp, David So&ice, and Chris Gilbert also gave me useful suggestions during my stay at Oxford University. My thanks also to Professor Michihiro Oyama, editor of this journal, and to an anonymous referee for many useful comments. Needless to say, all remaining errors are my own. 351

0889-1583187 $3.00 Copyright 0 1987 by Academic Press, Inc. All rights of reproduction in any form reserved.

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interest rate on the Japaneselong-term interestrate. They reportedstatistically significant influencesof the former on the latter. In contrast, Ueda (1983)was relatively skeptical whether changesin the U.S. interest rate influencedthe Japaneseinterest rate through portfolio markets. Despite its importance in the formation of macroeconomicpolicy, formal analysisof the causesand consequencesof internationalinterest rate linkagesseemsto be still at a developingstage.The purposeof this paper is to offer a two-country framework which, although admittedly highly simple, may be useful in understandingthe way in which monetary policy in one country could be transmitted to another under the flexible exchangerate system. We would like, in particular, to analyzethe interrelationship between the international interest rate linkage and the behavior of the foreign exchangerate. Needlessto say, there arepossibly many channelsthroughwhich international interest rate linkage could occur. If, for instance,one country’s interest rate policy (in terms of money supply)is directly affectedby the monetary policy of the foreign authorities, one would naturally observe some linkage of the two country’s interest rates. An alternative view might emphasizethe fact that a rise in the foreign interestrate may depreciate the domestic currency, which in turn raisesthe domesticprice level andthereforeincreasesthe demandfor the domestic money stock. A third possibility, with which we shall deal in this paper, has to do with the reshufflingof the portfolio composedof the internationally traded assets. Although considerableliterature has beenaccumulatedon this last possibility, the approachtaken here may claim some advantage,for the relatively simple structure of our model will make it possibleto analyzethis somewhatcomplicated problem from the standpointof the two-country macroeconomicmodel. In order to analyze the interest rate linkage, it is crucial to analyzethe relationshipbetweenexchangerate expectationsand the determinationof interest rates in the two countries.If the expectationof the exchangerate change is static or close to static, a high international dependenceof interest rates is the inevitable result (Mundell (1963)).In contrast, if exchangerate expectationsare nonstatic, it is possiblethat the interest rate linkage would be reduced, becausea monetary shock in one country might be absorbedby movementsin foreign exchangerate expectationsas well as movementsin the exchangerate itself. If, however, the burdenof absorbingthe shock is exclusively borneby the adjustmentof the foreign exchangerates, the behavior of the foreign exchangerate could become highly volatile. Monetary independence(in the senseof low or negligible interest linkage) would then be possible only at the cost of highly volatile exchangerates. This paper will show that this is a possibility. It will be shown, in

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particular, that a trade-off exists between international interest rate dependenceon the one hand, and the volatility of the behavior of foreign exchangerates on the other. The weaker the international linkage of interest rates, the more volatile the behavior of foreign exchangerates.If, in the extreme, the interest rate of one country is completely independent of the interest rate of the other country, the behavior of the foreign exchangerate betweenthe two countriesmay exhibit, underfairly plausible conditions, highly volatile propertiesincluding random walk. 2.

MODEL

Consider a two-country world linked by a flexible exchangerate with capital mobility. The monetary equilibrium of the home country is denoted by the equality of the demandand supply of the home country’s money stock, m = -b&

- b&+

+ tst+l

- sJ + p + y

b, > bz > 0,

(1)

where m, p, and y denotethe supply of money stock, the price level, and the national income of the home country (in terms of natural logarithm), respectively. sr denotesthe (log of the) home country’s foreign exchange rate in period t, while t~t+l denotesthe exchangerate of period t + 1 as expectedin period t. As usual, s measures(in log terms) the home currency price of a unit of the foreign currency. It is implicitly assumedthat the holding of securities (either home securities or foreign securities) involves uncertainty as to the developmentof the price of these securities. In addition to the transactionsmotive, the agentswish to hold money stocks in order to avoid this uncertainty.’ The monetary equilibrium of the foreign country is likewise denotedas m* = -b:$

- b;(i, - rsr+l + sJ + P* +

Y*

b; > b: > 0,

(2)

wherethe asteriskrefers to the foreign country. Throughoutthe paperwe shall assumefor simplicity that the income and the price level are exogenous. In this sense,our analysis is a partial equilibrium one. The right-handsidesof Eqs. (1)and (2) arethe conventionaldemandfor money functions except that they dependnot only on the domestic interest rate but also on the overseasinterest rate adjustedfor the expected 1 Ideally, therefore, the relationship between the expectations as to the future price of the securities and the expectations as to the future development of the foreign exchange rate must be simultaneously analyzed.

354

TAKAHIKO

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rate of depreciationof the home currency. This reflects the assumption that capital is intematiomtlly mobile, leaving room for the domesticinterest rate to be instantaneouslyaffectedby the foreign interest rate.*As we shall see, however, the interrelationship between the domestic and the foreign interest rates cannot be properly analyzedby the money market equilibria of the two countries alone. Indeed, if one treats the foreign exchangerate (as well as its expectation)as exogenous,(1) and (2) will produce a rather implausible prediction that one country’s monetary expansionwill always be transmittednegativelyto another(i.e., an increase in the supply of money in one country will reducethe interest rate of that country, but it will always raise the interest rate of the other country). In orderto obtain reasonableresults, one has to take into accountthe simultaneousdetermination of the exchangerate. Turning now to the determinationof the foreign exchangerate, we shall assumethat the foreign exchangerate is determinedby the equality of the demandand the supply of foreign exchange.Let us assumethat thereare two kinds of securities, issued either by the home country or by the foreign country. Residentsof the home country demandthe foreign exchange(i.e., the foreign money as medium of exchange)either because they demand foreign securities or becausethey demandforeign goods. Therefore, their demandfor the foreign exchangeis

4dif + &+I - s,l -

q2it

-

FL1

-

d'~,-~

-

wt

41,

q2,

d'

>

0,

(34

whereF; = ql[iT + t~,+l - s,] - q2it denotesthe stock of the home country’s residents for the foreign issued securities. F; - F:-, denotes the increasein the home country’s demandfor the foreign securities stock, and hence the demand for the foreign exchangedue to capital account transactionsduring period t. With respectto the internationaltrade, we assumethat the international tradecontract is made with one period lag. d’st-, + w, denotesthe home country’s import function with wt being its intercept: we shall treat the latter as a time-independentrandom variable.Taken together,the last two z The inclusion of the foreign interest rate (adjusted for expected exchange rate changes) makes it possible to analyze the instantaneous linkage of each country’s interest rate due to the reshufhing of portfolio composed of internationally traded assets. If, in contrast, we included only the domestic interest rate in the money demand function, each country’s interest rate would be independent at least instantaneously: international dependence of interest rates is explained, in that event, by the effect of the foreign exchange rate (which itself is associated with changes in the international interest rate differentials) on the price level and hence the real supply of money. Because, as assumed in Dombusch (1976), price adjustment would generally take time, instantaneous linkage of interest rates would be difficult to explain by such a model.

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RATE VOLATILITY

terms denotethe import of the home country, and hencethe demandfor the foreign exchangedue to international trade. Foreign country residents demandthe domestic currency (and therefore supply the foreign currency)as a medium of exchangeeither because they want to purchasethe securities issuedby the home country or becausethey want to buy the home country’s products. Their demandfor the domestic currency (i.e., their supply of the foreign currency) is likewise denotedas -q:iT + q2*[it- ,St+l + s,] + d”~,-~ - FjZl - zr,

(3b)

whereF:?l denotesthe first two terms of (3b)laggedby oneperiod, and z1 denotesthe random term associatedwith the foreign country’s demand for the home country’s products. Taking the difference between(3a) and (3b), we obtain the excessdemand for foreign exchangeduring period t (i.e., the foreign country’s currency demandedfor the purpose of international transactions). We assumethat the foreign exchangerate is determinedat a level where the excessdemandis equal to zero.3The equilibrium condition of the foreign exchangemarket is then

(41+ 4T)iF-

(q2

+

&it

+

(41

+

qz*Mtst+l

-

s,)

-

dst-l

-

F,-I

=

ur,

(3)

where d = d’ + d” > 0,

F,-, = F;-1 - F:-*,,

u* = w, - Zt.

Equation (3) is basically the sameforeign exchangemarket equilibrium condition asused, for instance,by Driskill and MacCafferty (1982)for the casewhereall the q’s areof the samevalue. F denotesthe home country’s net foreign assets. Equation (3) is rather conventional in that the foreign exchangerate is determined at a level where the demand for and the supply of foreign exchangeare equated.Consideringthat internationalcapital transactions are carried out in a highly organizedmarket where informationsare trans’ We assume, by implication, that neither country’s residents hold overseas money as a part of their assets. Overseas money stocks are demanded only for the purpose of international transactions. In the foreign exchange market, private agents obtain that amount of the foreign money needed for buying either overseas securities or overseas products in return for domestic money stocks. When buying the overseas securities or products by using the overseas money stocks thus obtained, these money stocks are handed over to the opposite party who naturally is a resident of the country where those money stocks are originally issued.

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mitted very rapidly, it will be appropriateto assumethat the q’s arelarger than d.4 Can we further assumeanything in order to restrict the model?Because investment in foreign securities involves a foreign exchangerate risk whereasinvestment in domestic securitiesinvolves no such risk, it might be possible to assumethat q2

2

41

and

4: 2 d.

Such an assumption may not always be valid, however, for there is no reasonto assumethat foreign investment is always riskier than investing in domestic securities. Rather than make such an assumption, we shall classify the casesaccording to whether this assumptionholds or not. An additional assumption with respect to the parametervalues concernsthe behavior of the q’s as their valuestend to increaserelative to d. In this paper, we shall use the terminology “the perfect capital mobility” to meanthe casewhere eachand every valueof the q’s becomesinfinitely large. With respect to the behavior of the q’s, we shall assumethat

will hold as each and every value of the q’s become infinitely large so that the economy approaches the perfect capital mobility case. Justificationof this assumptionis as follows. Supposethe valuesof all the q’s areinfinitely large. This meansthat the equilibrium of the foreign exchangemarket is dominatedby the demand and supply of the foreign exchangedue to the capital account transactions. Supposein that situation the rate of return from investing in the home securities(i.e., it) is different from the rate of return from investing in the foreign securities (i.e., i: adjustedfor the expectedchangein the foreign exchangerate). This meansthat those (either domestic or foreign residents)who hold home securitieswill wish to reshuf!Ietheir portfolio entirely in favor of the foreign securities.In the foreign exchangemarket, this would imply that all the agentsdemandthe foreign currency (supply the home currency) while nobody will supply the foreign currency (demand the home currency) as far as the capital account transactionsare concerned:with the dominanceof the capital account transactionsin the foreign exchangemarket, equilibrium of the foreign exchangemarket is impossibleto definewithout further assumptions.For suchan assumption we shall employ the one we havejust mentioned above. Under this assumption, the equilibrium condition of the foreign exchangemarket (3) 4 For empirical estimates of the relative value of q to d, see Fukao (1983) and Mutoh (1985).

MONETARYINTERDEPENDENCEAND

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becomes (3)

it = i: + tst+l - st

as the economy approachesthe perfect capital mobility case in which each and every q becomesinfinitely large. The expression (3) has often been referred to as showing the perfect substitutability of the relevant securities. It has also been referred to (especiallyin the literature concerningthe “efficient market hypothesis” in the foreign exchange market) as showing the risk neutrality of the preferenceof the agents.In the context of open economy macroeconomics, it has sometimes been regardedas expressing the perfect capital mobility (Mundell (1963)as well as Dornbusch (1976)may be quoted in this context). Our terminology of the perfect capital mobility follows the last tradition. The equations (l), (2), and (3) complete the model. As developedin Appendix 1, this system can be interpreted within the framework of a two-country model in which residents of both countries allocate their portfolio among (a) the money of the country in which the agentsare residents,(b) the home country’s securities,and (c) the foreign country’s securities.With respectto the home country’s residents,their demandfor money is specifiedas the right hand side of (I), and their demandfor the foreign country’s securities is specifiedas in (3a). Their demandfor the home country’s securities (which does not appearexplicitly in the model in the text) is determined as residual due to the wealth constraint. The impact of any change of the endogenousvariables on the wealth is assumedto be absorbedby changesin the demandfor the home securities. The samekind of behavior is assumed,mutatis mutandis, with respectto the foreign residents.5 3.

LINKAGE

OF INTEREST

RATES

Our model is composed of three equations that determine simultaneously the domestic and foreign interest rates and the foreign exchange rate. In solving the model, we shall assumefor simplicity that all the other variablesmay be treated asexogenous.An attempt to treat the price level and/or income simultaneouslyis desirable,but we shall leaveit for future 5 The specitication of each asset demand function in our model, therefore, is not in line with Tobin-type portfolio selection theory, according to which each and every asset demand function should in principle depend on the same hind of variables. Our specification of the money demand may be regarded as an example of the Keynesian money demand function where all the wealth effects are usually assumed as absorbed by the demand for another asset due to the wealth constraint.

358

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studies.As mentionedearlier, our analysisto follow shouldbe interpreted as partial equilibrium analysis as far as this aspectis concerned. In order to solve the model, we shall expressthe equilibrium condition of the foreign exchangemarket (3) in the form h - if - (1 - h)it + g(,s,+~ - s3 - (1 / q) * (G,-I + u,) = 0,

(4)

where q, h, and G,-i are definedas

4 = 41+ 42+ 4: + qz*, h = (41+ qT)q-’

0
0 bz. FF denotesthosepairs of the domestic interest rate and the expected rate of depreciationof the domestic currency which equilibrate the foreign exchangemarket or Eq. (4). 1t

tst*1-St

FIGURE

1

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359

The slope of FF, which is equal to g/(1 - h), dependson the relations betweenthe 4’s. If it is assumedthat q2 > 41, then its slopeis positive but lessthan 45”, becauseg/(1 - h) is equal to (ql + qT)/(q2 + q$) < 1. Figure 1depicts this case.(For the sakeof symmetry, we shall hereafterassume that q: > q; holds if q2 > q,.) Starting from an initial equilibrium, let the foreign interest rate rise by 1% from the initial equilibrium at A. For any level of the equilibrium domestic interest rate, the MM locus must shift horizontally to left by 1% in order for the domestic money market to be in equilibrium. The FF locus must shift upwardto left, becausethe increasein the foreigninterest rate must depreciatethe domestic currency for the foreign exchangemarket to be in equilibrium. For any level of the home country’s interestrate, the horizontal shift must be h/g = (q, + q?)/(q, + qf)%, i.e., larger than l%, becauseof the assumptionqT > qz. The new equilibrium of the money market and the foreign exchange market takes place at B where, by construction, the domestic currency is depreciatedand the domestic interestrate is higherthan the initial equilibrium. The domestic interestrate is positively linked with the foreign interest rate: further, a rise in the foreign interest rate will generallyresult in a depreciation of the domestic currency. The international linkage of the two countries’ interest ratesoccurs instantaneously,reflectingthe reshuffling of the portfolio of each country’s residents. A specialcaseoccurs when the value of h is equalto that of g, or when qT = qf. In this particular case,the horizontal shift of FF is the same as that of MM, which meansthat the domestic interest rate is not affected instantaneouslyby the rise in the foreign interest rate. (The sameis true, mutatis mutandis, for the casewhere 1 - h = g; this is the casewhere a rise in the domestic interest rate will have no instantaneouseffect on the foreign interest rate.) An intuitive account is readily madeby looking at (1) and (4). An increasein the foreign interest rate in Eq. (4) with h andg beingequaland with given i, and tsr+1,will be accompaniedby a declinein the expectedexchangerate change(,s~+,- s,)that completely offsets the initial rise in the foreign interest rate. If the complete offset takes place and thereforethere is to be no changein the rate of yield from investment abroad(i? + r~t+~ - sJ, then Eq. (1) implies that no excessdemandwill develop in the domestic money market, and hencethere will be no upward pressureon the domestic interest rate.6 At first sight, casessuch as h = g or 1 - h = g (i.e., q: = q2* or q1 = q2) may seem very special. They may not be so special, however, as the limiting casewhere the capital is highly mobile in the sensethat all the 6 Because G,-, in (4) includes s,-,, and because s,-, is affected by i:,, the foreign interest rate has a lagged effect on the domestic interest even if qT = q;. This lagged effect disappears only if the q’s become infinitely large. For details, see below.

360

TAKAHIKO

MUTOH

values of the q’s tend to be very large. (If the values of the q’s are very large, then g, h, and 1 - h all convergeto t in the limit underour assumption of the limiting behavior of the 4’s.) In this context, we concludethat the high capital mobility weakens the interest rate linkage. The foreign exchangerate in this case servesas a genuineshockabsorberto external shocks. To go back to the case where the values of the q’s are finite, suppose the assumptionq2 > ql, hitherto maintained,is reversed.The slopeof FF in this caseis steeperthan 45”. An increasein the foreign interestrate will again depreciate the home country’s currency but the home country’s interest rate will be lowered rather than raised. There will then be a negativecorrelation betweenthe domestic and the foreign interest rates. Simultaneousdetermination of domestic and foreign interest rates is explainedwith the aid of Fig. 2. In Fig. 2 we shall treat all the variables (including, implicitly, the expecteddepreciationof the home currency)as endogenous.II locus derives from (1) and (4), and it shows the pairs of domestic and the foreign interest rates which equilibrate the domestic money market. 1*1* derivesfrom (2)and (4), andit depicts the equilibrium locus of the money market of the foreign country. It is shownat the end of this sectionthat the slopeof II is less steepthan that of 1*1* if both curves are positively sloped, and vice versa if they are negatively sloped. In

it A

1

it* FIGURE

2

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conformity with Fig. 1, we depict in Fig. 2 the casewhere both II and 1*1* are positively sloped. An increasein the supply of the foreign money, given the price and income levels, wilI shift the 1*1* locus to the left, lowering both domestic and foreign interest rates. The extent to which the domestic interest rate is affectedby the foreign monetaryexpansiondependson the slopeof the II locus. If, for instance, II is horizontal, then the domestic interest rate will not be affected by the increasein the foreign money supply. There are two possible cases in which II is horizontal, making the domestic interest rate independentof the foreign interest rate. The first concernsthe value of bZ and the secondconcernsthe value of the q’s. If the value of b2 is zero, as in the first case, it is obvious that the domestic interest rate is not affectedby the foreign interest rate, because the domestic demand for money is not affected by the foreign interest rate. This does not mean, however, that the foreign interest rate is not affectedby the domestic interestrate. In order for the foreigninterest rate to be illdependentof the domestic monetary policy, it must be true that b$ is zero. Turning now to the secondpossibility, the slopeof both the II locus and 1*1* is affectedby the degreeof capital mobility, i.e., the value of the q’s. As seenfrom the discussionof Fig. 1, the II locus becomeshorizontal if capital mobility is high. The samereasoningas usedfor II is applicable also to the foreign country, so that 1*1*becomesvertical at the sametime. Therefore, if the capital mobility is very high, the interestratesof the two countriesbecomecompletely independentof eachother, althoughcapital is free to move between the two countries. Formally, the analysisup to this stagecan be developedin the following way. Solving (1) and (2) for t~t+l - st, and substitutingthem respectively into (4) yields the solution for domestic and foreign interest rates as: -um,glb2 - q-l(G,-I + u,) um,*glb; - q-‘(G,-, + IJ,)1 ’

where and

um,=m-p-y all = -[h + gbfbg-‘l/D

um:

> 0

a12 = [h - g]/D ~21 = -[I a22

- h - g]/D

= [Cl - h) + gb,b;‘]lD

< 0

=

m*

-

p*

-

y*

(5)

362

TAKAHIKOMUTOH D = (h - g)(l - h - g) - (1 - h + gblb;‘)(h

+ gbfb;-‘)

= -&b*b:(b*b:)-’ + (1 - h)b:b;-1

+ hblb;’

+ (1 - g)] < 0.

Equation (5) shows the explicit solution of the intersection of II and 1*1* in Fig. 2. The fact that D in the aboveformula is negativeensuresthat II (whose slope is Q/U& is less steepthan 1*1* (whoseslope is aii/u2i) when they are positively sloped, and vice versawhen they arenegatively sloped. Because~11is positive and ~22is negative,Eq. (5)predicts that a monetary expansion(i.e., an increasein urn or urn* due to an increasein m or m*) in one country will lower the interest ratesof the country where the monetary expansiontakes place. What happensto the interest rate of the other country dependson the sign of aI2 and ~221. If the international capital mobility is high, both h andg will convergeto 4, which meansthat both al2and ~221 will be zero: accordingly,the other country’s interestrate will not be affected in that instance.To the extent that capital mobility is low, the two interest rates will be correlated either positively or negatively, dependingon the parametervalue of ~21and u12.7

4.

VOLATILITYOFTHEFOREIGNEXCHANGERATE

In order to analyze the effects of monetary impacts on the foreign exchangerate, we may substitutefrom (1) and (2) into (4) to get t&l

- St - t-1St + St-1 - @q)-‘st-1

= Nt - Ntml + q-b,,

(6)

where a = g + [hb;B + (1 - h)b2B*]/E > 0 B = b, + bZ

B* = bf + b;

E = b,b: - b2b; > 0 Nt = -e*

- umt + e * urn,*

e = [hbl + (1 - h)bz](uE)-’

> 0

’ Moreover, because q-*(G,-, + u,) converges to zero as q becomes infinite, it is determined by “urn,” alone when the capital mobility is infinitely large. In other words, the interest rate of the current period is determined by the monetary policy of the current period alone under the assumptions of our model when the capital mobility is high.

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363

and e* = [hb2*+ (1 - h)b:](uE)-r > 0. N, may be termed as the “relative money supply,” althoughin fact it is a combination of the two country’s Marshallian k’s. With income and the price levels given exogenouslyconstant, we may dub N1 as the relative money supply. An increase in the value of N1 means that the foreign country follows a more expansionary monetary policy relative to the home country. Equation (6) can be solved for the dynamics of the foreign exchange rate, once appropriate exchange rate expectation hypothesis is introduced. Equation (6) is essentially the sameequation as usedin a number of articles by Driskill and MacCtierty (1980, 1982,and others). If we introduce, as Driskill and MacCafferty do, the rational expectation hypothesis, then the behavior of the system is governedby the following characteristicequation that correspondsto the homogeneouspart of (6) x2 - 2x + (1 - d(aq)-1) = 0,

(7)

where X denotesthe characteristicroots of the system. Noting that a is larger than g, the constant term of (7) is positive but less than unity, because

aq > gq = 41+ d > 4 where the last inequality derives from our assumption that the q’s are generally larger than d. Therefore, (7) has one stable and one unstable characteristic root. Following the conventionin rational expectations,one may choosethe stable characteristic root to represent the unique solution path of the foreign exchangerate. By referring to Eq. (5), the solution path of the interest rates will be uniquely determined. In any case,the dynamic behavior of each endogenousvariable will be convergentto the corresponding steady-statevalue. To the extent that the dynamic behavior of the endogenousvariables is convergent, there is no reason to characterize their behavior as being volatile. Volatility occurs, however, as the value of the q’s increasesrelative to d. If q is so large that the constant term of (7) is virtually unity, then (6) breaksdown to tsr+l - (s, + r-d + sr-1 = Nt - Nt-1.

(6’)

As we have seenearlier, there is no internationallinkage of interest rates

364

TAKAHIKO

MUTOH

if the capital mobility is extremely high in the sense that the value of q is virtually infinite. The monetary shock originating in one country will neither raise nor lower the interest rate of the other country. What is the factor, then, that absorbs the monetary shock when the value of q is very large? It is the foreign exchange rate. The important point to notice here is that the characteristic equation corresponding to Eq. (6’) is no more stable. In fact, (6’) shows that the corresponding characteristic equation is simply (X - l)* = 0 so that the characteristic roots are both unity. A remarkable point to notice here is the fact that, as shown in the Appendix 2, it is not possible to determine a unique solution path that satisfies the initial condition (6’). In order to determine a unique solution path, one has to add a further condition. We shall arbitrarily postulate the following: tSt+1

=

t-1St

+

ct.

(8)

Equation (8) simply says that the exchange rate prevailing in period t + 1 will be expected to be equal to the right-hand side of (8).* What is meant by C, in (8) can be interpreted, for instance, that the government (say, the foreign exchange authority) is successful in persuading (fooling, so to speak) the private agents that the next period (period f + 1) exchange rate is going to be the right-hand side of (8). Alternatively, one can suppose that C, refers to private agents’ “psychology” with respect to the development of the foreign exchange rate. In either case, one cannot offer any “economic” reasons because of which C, takes on a particular value. In fact, C, can take any value: the essential point is that private agents believe it, and that they form their expectations accordingly. It is only in that instance that the foreign exchange market determines the current period (i.e., period t) foreign exchange rate. Without postulating that the value of C, is somehow determined, the foreign exchange market cannot determine anything.9 Only when ,s,+~ is determined somehow will (6’) determine a unique solution for the equilibrium foreign exchange rate. The form of the solution path will depend on the way the exogenous variable of the system 8 In order for (8) to make any sense, it must be true that the information that influence the value of C, arrive at the agents before the foreign exchange market actually opens at period r. Formally, this means that ,s,+, = E[s,+ila,], where n,i3 s,, but C, E R,, I owe this particular point to Hiroshi Yoshikawa, whom I thank. 9 That C, is determined essentially arbitrarily (i.e., not necessarily “economically”) concerns the volatile nature of the foreign rate. This point is naturally related to what is called “bubbles” in the foreign exchange market. With respect to the evaluation of the theory of bubbles, see footnote 14.

MONETARY

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develops. If we assume, for simplicity, that ,Nt+kis equal to Nt(k = 1, 2 9 - . .), then the solution that satisfies(6’) (under the postulate(8)) isi

s, = --[Iv1- iv,-11+ SF-1 + Ct $t+k = -(Nt

- N,-,)

+ St-1 + c, + k[(N, - N,-1) + t-lSt - ‘f-i]

(9) (lo)

k = 1, 2, . . .; C, is an arbitrary constant.

Equation (8) saysthat only when an arbitrary constant C, is given, will the expectedforeign exchangerate be determinedas the right-handside of (8). Oncethe expectedexchangerate is given by (8), then Eq. (6’) gives (9)as the solution path of the foreign exchangerate. By its very nature, C, can be given at any arbitrary level, and the solution path of the exchange rate is determined accordingly. What matters in the determinationof the foreign exchangerate in this particular caseis the volatile psychologyof the agents.Such is the peculiar property of this “hysteresis” solutionthat occurs when the characteristic root is unity. Under the assumed“perfect” capital mobility, the foreign exchange market basically loses its ability to determine the level of the foreign exchangerate.” The level of the foreign exchangerate is essentially determined, in that instance, either by the ability of the governmentto let the public believe what is going to happenin the next period, or by the pure psychology (which itself is essentially noneconomic)of the private agents.In either case,the level of the foreignexchangerate is determined essentially by the value of C,, which itself is not necessarilydetermined by “economic” forces.i2There is no reasonto believethat the behaviorof the foreign exchangerate in this particular case should somehowreflect what arebelievedto be “fundamentals,” suchas the balanceof payments and the economic growth rate. This gives the fundamentally very volatile nature of the foreign exchangemarket under the assumptionof “perfect” capital mobility. As a first approximation, it may be possibleto treat C, as the realizedvalueof a time-independentrandom variable distributed with mean zero. If that is 10See Appendix 2 for mathematical formalities. I1 It is perhaps Hahn (1%) who first pointed out explicitly that the relative price becomes indeterminate when the relevant assets are perfectly substitutable. See also Giavazzi and Wyplosz (1985) and Mutoh (1987) about the indeterminacy when the characteristic root of the relevant system is unity. By using a currency substitution-type model, Wallace (1979) (as summarized by Krueger (1983), p. 94) argues the essential indeterminacy of the foreign exchange rate. Our model can be regarded as reconfuming Wallace’s point. I2 “Economic forces” here mean all the information as summarized by (l), (2), and (4). What I mean by “noneconomic” or by “psychology” refers to anything else that is not incorporated explicitly in the model above. Therefore, the term noneconomic must be interpreted rather broadly.

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the case,then, the actual path of the foreign exchangerate is goingto be a random walk processwith drift (trend)parameter[N1- N,-,I. Even if the actual value of the drift parameterhappenedto be zero at any time period, the variance of the dynamic processof the foreign exchangerate will be infinitely large, becausethe actual value of the foreign exchangerate is goingto be the sum of the infinite seriesof all the past C,‘s. Further, there is no presumptionthat the processN, - N,-l itself is zero or constant.It may well be that this term itself is distributed independentlyof time with some meanI In that case, the foreign exchangerate will againfollow a random walk, even if C, is constantly zero.r4 In contrast to the highly volatile behavior of the foreign exchangerate, the dynamic behavior of each country’s interest rate is under complete control of each country’s monetary authorities. In fact, there is no “dynamics” of interest rates: Eq. (5) shows that the term that may cause dynamics of interest rate (i.e., G,-1) disappearswhen the value of q is infinitely large. The behavior of our system is in striking contrast dependingon the degreeof capital mobility. If the capital mobility is reasonablylow, the monetarypolicy of one country is not independentof the monetarypolicy of the other country: international interest rate linkage exists. However, the dynamic behavior of the interest rates as well as that of the foreign exchangerate is systematicin the sensethat, at any point in time, there is a tendencyfor each variable to convergeto the steady state. If, on the other hand,capital mobility is very high, then the interestrate linkage disappears.Monetary policy can be pursuedwithout foreign hindrance; however, the behavior of the foreign exchangerate is no longer under control of the monetary authorities. Except for moral persuasion, 13 This will be the case if, for instance, each country followed a “weak” k% rule, in which each country makes it a rule to increase the money supply at a predetermined growth rate on the average (i.e., expected value of monetary growth rate be at a certain predetermined level, although the actual monetary growth rate is influenced also by random factors). I4 Volatility of the foreign exchange rates has been explained by a number of hypothesis. The overshooting hypothesis is one of the first attempts to theorize the volatility. A recent development in this field is the theory of bubbles, which usually emphasizes the role of the unstable characteristic root of the dynamic system that determines the behavior of the exchange rates. For details about the theory of bubbles, see Dombusch (1982) and especially Okina (1984). Our interpretation of the volatility is based on the idea of the theory of bubbles, but we do not emphasize the role of unstable characteristic root. Rather, we would like to emphasize that volatility occurs only when the foreign exchange speculation is in some sense too active, making the characteristic roots neither stable (Le., smaller than one) nor unstable. Indeed it is in this case that one does not have any strong reason to drop one of the characteristic roots. Various criteria, as suggested by Taylor (1977), McCallum (1983), and others, in order to avoid bubbles (i.e., to ensure uniqueness) of the rational expectation solution do not seem helpful in this special but yet reasonably realistic (“hysteresis”) case of the high capital mobility.

MONETARY INTERDEPENDENCE AND EXCHANGERATEVOLATILITY

367

the monetary authorities do not have any effective means to control the level of the foreign exchange rate.

5.

SOME POLICY IMPLICATIONS

The theoretical implications of our model of course depend very much on the specification that has been employed. Our analysis has been carried out in a framework in which both income and price level are treated as exogenous. In that sense our analysis is a partial equilibrium approach. To the extent, for instance, that the determination of income, price, and the interest rate are simultaneously affecting each other, the conclusions of this paper will have to be modified. The conclusion of this paper, particularly that of the perfect capital mobility case, will be relevant only when these variables (income and/or price) can be regarded as state variables as far as the equilibrium of the portfolio market is concerned. Another point to note is the treatment of the wealth effect. In our analysis, all the wealth effects with respect to the home residents are assumed to be absorbed by the demand for the securities issued by the home country. The wealth effect with respect to foreign residents is similarly treated. Although these assumptions do justice to the wealth constraint of the residents of each country, it has been crucial for our conclusion that the foreign interest rate has no influence on the domestic interest rate under perfect capital mobility. Otherwise, a rise in the foreign interest rate would change the valuation of domestic wealth through the exchange rate change, and the demand for the domestic money stock would eventually be affected. There would then be an international interest rate linkage through a mechanism different from our own. (The conclusion about the volatility of the exchange rate must also be modified.) The relevant question to be asked, in a sense, is an empirical one: the share of the foreign currency denominated assets in the total financial assets. We are not prepared to answer this empirical question in this paper. Bearing these reservations in mind, we now attempt to draw some policy implications of this paper. Let us first note that the behavior of our model is in striking contrast depending on the degree of capital mobility. If international capital mobility is somewhat low, in the sense that the parameter value of 4 is reasonably small in magnitude relative to d, the predictions of our model are not so different from widely accepted views such as those of Dornbusch (1976). The only difference lies in the fact that our model does not share the long-run neutrality property due to the simplifying assumption which treats the price level as exogenous. If we endogenized the price level dynamics (such as used by Dombusch), we would be able to obtain essentially the same result with respect to the overshooting of the foreign exchange rates. Further, despite the short run

368

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overshooting,the behavior of the foreign exchangerates would be essentially “systematic” (althoughdisrupted by random factors) in the sense that at any moment in time the exchangerate is on the stable dynamic adjustmentpath toward the steady state. With respect to the international interest rate linkage, our model predicts, again if the value of q is reasonablysmall, that an instantaneous interest rate linkage could exist: this does not precludethough, and our model is in conformity with the widely acceptedview in this respect,that each country’s interest rate may be differentiated from the other country’s interest rate in the short run, if not in the long run. If the international capital mobility is so high that the value of d relative to q is virtually zero, the behavior of our model is very different from the above.First of all, there is no suchthing as the “steady-statelevel” of the foreign exchangerate in this case.The actualpath of the foreign exchange rate may well be a very volatile processsuch as random walk, and there will be no tendency for the actual exchangerate to converge. Further, each country’s interest rate level is independentof the other country, despite the fact that capital is free to move betweencountries. The fact that no steady-stateexchangerate exists implies that one cannot define the “overshooting” of the foreign exchangerate properly. The term overshootingrefers to the possibility that the short run level of the foreign exchangerate exceedsthe level that is validated in the long run. If one cannot properly define the long run, it is natural that one cannot properly define the overshootingat all. Open economy macroeconomicmodels have often emphasizedthe effect of the foreign exchangerate on the current balanceand henceon the effective demand. The famous article by Mundell (1%3) put a particular emphasison this point in order to analyze the relative effectivenessof monetary and fiscal policy under a capital mobile flexible exchangerate economy. The implication of Dombusch (1976)is that, becauseof the existence of exchangerate overshooting, there exists some short run period during which the foreign exchangerate may be maintained-by an expansionary monetary policy-at levels below (i.e., depreciated)the long run PurchasingPower Parity Rate at which the current balanceis presumably balanced. Interpreted in this way, the Dombusch model shares,and to someextent reconfirms,the Mundellian conclusionthat the effectivenessof the monetary policy under flexible exchangerates derives, at least partly, from its influenceon the foreign exchangerate. Becauseour model doesnot treat the income level as endogenous,one cannotexplicitly compareour resultswith the traditional view. We could, however, draw someimplications of our model with respectto the effectivenessof macroeconomicpolicy tools. We shall only statethe implications of the particular casein which the international capital mobility is very high (in the sensethat d/q of our model is virtually zero).

MONETARY

INTERDEPENDENCE

AND

EXCHANGE

RATE

VOLATILITY

369

First, with respectto monetary policy, it has beenshownthat it cannot exert a systematic influence on the level of the foreign exchangerate. If capital mobility is very high, the behavior of the foreign exchangerate dynamics may well be a highly volatile process reflecting the arbitrary psychologyof the agents.Although Mundell-Dornbusch effectivenessof the monetary policy hingeson the assumptionthat monetary policy may exert an influence on foreign exchangerates in a systematic and somewhat persistentway, their conclusion may not apply if capital mobility is very high. The same observationsapply to the effectivenessof fiscal policy which, accordingto Mundell, is impotent to regulateeffective demand. Since this view by Mundell again hinges on the assumptionthat fiscal expansionexerts appreciatingforce on the foreign exchangerate in a systematic and persistentway, it is called into questionfrom the standpoint of this article. Second,despite the doubts about the effectivenessof monetarypolicy in regulating the foreign exchangerates, monetary policy may still be effective in regulatingeffective demandthrough its effect on investment demand. The casefor monetary policy becomesstrongeras the international mobility of capital becomes higher, becausethe high mobility of capital may imply, somewhat different from the conventional view, weaker international linkage of interest rates. Monetary policy, in terms of regulatingeachcountry’s interest rate independentlyof others, regains effectivenessin the case of extremely high capital mobility. As we have alreadyseen,however, suchan independenceof monetarypolicy is to be obtained only at the cost of highly volatile foreign exchangerates. The important choice for the monetary authorities lies between the stable exchangerates coupled with some interest rate linkage on the one hand andvolatile exchangerates coupledwith a relatively independentinterest rate policy on the other. APPENDIX

1

The model in the text can be interpretedas derived from the following two-country general equilibrium model. In what follows, any variable with a tilde denotesa demandfunction for the relevant variable (e.g., &? denotesthe demand for money function). The subscripts0 and 1 denote the beginning-of-periodand end-of-periodvalues,respectively. The notations are as follows: W M B F

private financial wealth money stock domestic public bond held by the domestic private foreign public bond held by the foreign private

370

TAKAHIKO

F* B* Dl - Do G T X, ZM Ll - Lo Y E

MUTOH

domestic public bond held by the foreign private foreign public bond held by the foreign private open market purchase of the domestic public bond by the domestic monetary authorities government purchase of the goods and services tax export and import of the home country new issue of the public debt during a period income expenditure (i.e., consumption + investment).

With these notations in mind, we have the following twelve identities: (1) (2) (3) (4) (5) (6)

wo = MO + eo + co W, = MI + B, + F, Ml - M,, = D, - D,, G = T + L1 - Lo Lo = B. + D,, + F$ Y = E + T + W, - W.

Further, ket:

we have the following

(7)Y=Z?+G+&Zii (8) M, = ti, (9) L1 = I?, + D1 + E:

(1’) (2’) (3’) (4’) (5’) (6’)

W,* = M; + B$ + F$ wf 3 Aa: + zg + PI” MT -M,fzD;--D; G* = T” + L: - L$ L; = B$ + D: + F; Y* 3 E* + T* + W: - W,*.

six equilibrium

conditions

for each mar-

(7’) Y* = E* + G* + Z% - 8 (8’) MT = Ai’? (9’) L: = BI + D: + fir.

All in all, we have 18 equations, with which the following remarks are in order: (a) Out of the 6 equilibrium conditions, one is dependent on the others due to the budget constraints (l)-(6) and (I’)-(6’). We shall choose to drop (9’). (b) Dropping (9’), one can note that (7) and (7’) are interpreted as determining Y and Y*, respectively; that (8) and (8’) determine the interest rates; and that (9), the equilibrium condition for the market for the public bond issued by the domestic government, determines the foreign exchange rate. This is evidently the “asset market view” of foreign exchange rate determination. (c) Alternatively, however, one can note that (7) and (7’) determine Y and Y*; (8) and (8’) determine the interest rates and that the following equation (lo)-instead of (9)-determines the foreign exchange rate, because (1) through (9) clearly imply (10): 8 - Ziii = (8, - F,,) - (r;=; - F:).

(10)

MONETARY

INTERDEPENDENCE

AND EXCHANGERATEVOLATILITY

371

This may be called the foreign exchangemarket view of the foreign exchange rate determination, but this view is, as the derivation shows, consistentwith the assetmarket view. The model in the text is interpreted as treating(8), (8’), and (10)as a subsystemof the model in this Appendix.

2

APPENDIX

During period t, the equilibrium foreign exchangerate must satisfy the following conditions: IS?+1

- St= [Nt - iv,-,1 f r-1st- St-1

tSf+Z tst+3

-

-

&St+1

as,+2

+ +

tSt+t

sr

(2-I)

=

LN,+1

-

NJ

(2-2)

=

wt+2

-

at+11

(2-3)

As we do in the text, let us for simplicity assumethat ,Nt+k= Nt (k = 1, 2, 3, - . .). this means that the right-hand side of (2-2), (2-3), . . . all vanish. A generalsolution that satisfies(2-3)-and all the equationsthat follow-is of the form: $t+k = z,, + &k (k = 1, 2, 3, . . .),

(2-4)

where ZOand ZI are constantsthat shouldbe determinedin principle by the initial conditions. In order to determine the value of theseconstants,we substitutefrom (2-4)into (2-2)to yield that tSt+l - st must be equal to Z1. From (2-l), we then know that Z1 must be equal to the right-hand side of (2-l), or the coefficient associatedwith the first order term of the right-handsideof (9) in the text. We may therefore determinethe value of Z,, but this is all we can do. We have already exhaustedall the initial conditions, so that no independent condition is left free to determine the value of Zo. ZOmay therefore take any value. The only problem remaining is to give some appropriate interpretation (not necessarilyof an “economic” nature)concerningZo. In the text, we have chosento postulatethat Z. is equal to the 0th order term of the right-hand side of (lo), which is consistentto postulateas (8).

REFERENCES DORNBUSCH,

1176.

R. (1976). Expectations and exchange rate dynamics, J. Polit. Econ. 84,1161-

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D~RNBUSCH, R. (1982). “Flexible Exchange Rates and Interdependence,” NBER Working Paper, No. 1035, Cambridge, Nov. DIUSKILL, R., AND MACCAFFERTY, S. (1982). Spot and forward rates in a stochastic model of the foreign exchange market, .Z. Znt. Econ. 12, 313-331. DRISKILL, R., AND MACCAFFERTY, S. (1980). Speculation, rational expectations and the stability of the foreign exchange market, J. Znt. Econ. 10, 92-102. FRANKEL, J., AND FROOT, K. (1986). “The Dollar as a Speculative Bubble: A Tale of Fundamentalists and Chartists,” NBER Working Paper, No. 1854, Cambridge. FUKAO, KYOJI (1983). Determinants of foreign exchange rates and speculation, KinyuKenkyu (Bank ofJapan) 2(4), 27-66, Dec. [In Japanese] FUKAO, MITSUHIRO, AND OKUBO, T. (1982). International linkage of interest rates: The case of Japan and the United States, Znt. Econ. Rev. 25(l), 193-207. GIAVA~ZI, F., AND WYPLOSZ, C. (1985). The zero root problem: A note on the dynamic determination of the stationary equilibrium in linear models, Rev. Econ. Stud., 353-357. HAHN, F. H. (1966). Equilibrium dynamics with heterogeneous capital goods, Quart. .Z. Econ., 633-646. KRUEGER, A. (1983). “Exchange Rate Determination,” Cambridge Univ. Press, London. MCCALLUM, B. T. (1983). On non-uniqueness in rational expectations models: An attempt at perspective, J. Monet. Econ. 11, 139-168. MUNDELL, R (1%3). Capital mobility and stabilization policy under fixed and flexible exchange rates, Can. J. Econ. Polit. Sci. 29, 227-257. MUSSA, M. (1979). Empirical regularities in the behavior of exchange rates and the theories of the foreign exchange market, Carnegie-Rochester Corlf Ser. Public Policy 11, 9-58. MUTOH, T. (1985). Foreign exchange speculation and market efficiency under rational expectations: Some empirical tests for Japan, Keizai Kenkyu, pp. 44-52, Jan. MUTOH, T. (1987). “Logical Structure of the Rational Expectation Hypothesis and the Indeterminacy of Solutions,” mimeo. OBSTFELD, M., AND ROGOFF, K. (1986). Ruling out divergent speculative bubbles, J. Monet. Econ., 349-62 OKINA, K. (1984). Rational expectations, bubbles and foreign exchange market, Bunk of Japan, Monet. Econ. Stud. 2(l), 81-118. TAYLOR, J. B. (1977). “Conditions for Unique Solutions in Stochastic Macroeconomic Models with Rational Expectations,” Econometrica 45(6), 1377-85. UEDA, K. (1983). Flexible exchange rates and the monetary interdependence, in “Open Economy Macroeconomics and the Japanese Economy” (“Kokusai Macro-Keizaigaku to Nihon Keizai”) (K. Ueda, Ed.), Chap. 6, Toyo Keizai Shinpo Sha, Tokyo. [In Japanese] WALLACE, N. (1979). Why markets in foreign exchange are different from other markets, Federal Reserve Bank of Mineapolis, Quart. Rev. 3(4), 1-7.