The Prospect of a Depreciating Dollar and Possible Tension Inside the EMS

International Finance Discussion Papers Number 279

Revised: February 1986

THE PROSPECT OF A DEPRECIATING DOLLAR AND POSSIBLE TENSION INSIDE THE EMS

by

Jacques Melitz

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment by a writer that he has had access to unpublished materia:.) should be cleared with the author or authors.

ABSTRACT

This paper analyses the possibility of increased tensions in the European Monetary System (EMS) as a result of the recent dollar depreciation. The analysis employs a static, fairly stylised macroeconomic model in which the EMS is characterized as a means of achieving a cooperetive outcome even though policymakers in member countries weigh output-inflation tradeoffs differently. Compared with the Nash (noncooperative) equilibrium, such cooperation is shown to have been welfare-improving for member countries before the depreciation of the dollar began. However, the inflationary consequences of the dollar depreciation in Europe give rise to the possibility that even if there is an optimal realignment afterwards, the members will not be able to achieve

a better output-inflation tradeoff within the EMS than outside of it.

THE PROSPECT OF A DEPRECIATING DOLLAR

AND POSSIBLE TENSION INSIDE THE EMS

by

Jacques Melitz* I.N.S.E.E. 18, boulevard Adolphe-Pinard 75675 Paris Cedex 14, France

First version: December 1985

Revised: February 1986

*This paper was prepared while the author was a visiting scholar at the Division of International Finance. I have benefited a great deal from discussions with Gilles Oudiz and the participants at the Bellagio conference on "Economic Policy in Closed and Open Economies" (January 1986), especially from the comments of my official discussant, Francesco Giavazzi. This paper represents the views of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal. System or members of its staff.

We have now entered a period of dollar depreciation after four to five years of dollar appreciation. This paper makes an attempt ta show that this change in policy environment could lead to tensions within the European Monetary System CEMS). What I have done is ts cons:ruct a special theoretical example where, depending upon the extent of doltar depreciation, either Germany or France achieves “bliss"“ by leaving the EMS. In either of these two cases, the best the EMS can do is ty duplicate the non-cooperative solution. But even if the EMS does so, :he system has no particular advantage, and this is true for either country, the one which is not so blessed as well as the other. Hence, if there are any political rigidities in the system or other costs of upholding it, the EMS would not survive. There are two ways of treading this example. It can be viewed as a prediction about the Futuire, as [ have suggested above. Regarded in this way, the example spells trouble for the EMS. The second way, which is perhaps less obvinus but equally important, is as policy advice. Read in this other way, the argument tells both countries that national interests may call

for inoving out of the EMS.

The example has two critical features. The first is a difference in the policy preferences of Germany and France. The Germans are supposed to have a lower tolerance for inflation than “the French. The second is a supposed inability of either country to neutralise the impact of the dollar depreciation without altering the franc-mnark exchange rate. This inability to adjust in other ways can be interpreted as a reflection of a combination of inertia and problems of forecasting. In other words, the difficulty may be seen as being that other means of adjustment are too slow to take effect while the shock of the dollar

appreciation is impossible to foresee sufficiently far ahead of time.

The paper will be divided into five sections. The first will present the basic model. The next will derive and compare the non-cooperative and the EMS solutions. The third will analyse the impact of a dollar depreciation, and the fourth will provide a graphical interpretation of the analysis. This last interpretation will’ add

to the argument. The last section is a conclusion.

I will begin with a modified version of a model that | have used before in order to explain the EMS [MELITZ (1985)]. In the simplest form of this model, there are only two countries, France and Germany, both of which produce a good that differs from the other’s and which both of them consume. The respective prices of the two goods, q and q*®, are p and p™, where the starred notation applies to Germany. The interest rates in the two countries are i and i*, their money stocks are m ard m*, the exchange rate or the number of francs per mark is e, and the tuo countries” respective utility losses resulting from deviatiors from desired values are L and L*. All variables are Logarithms except the two interest rates Ci and i*) and the inflation rates (py. I, p¥, and [*). The superscript a designates anticipated values. In the present illustration, there is one extra complication : namely, the two countries also consume a third good coming from the United States, whose price is p®®. The price of dollars in marks is e*®. The equations

are as follows

fo

1. q = a, (p¥te-p) + a, Cp¥¥te*+e-p) - a, Ci-p?,+p) + a,q™

2. q¥ = -a, Cp¥t+e-p) + a, (p¥*+e¥-p) - a, Ci™-p¥*#tp*) + a, q 3. m—p = uq 4. m*®*-p* = uq* S. P = PotP., 6. p¥ = p¥+p*, P, > 0 px¥ > 0 7. ef,-e = i-i* 8. p?,-P = P-P_, 9. p¥i-p™ = p¥-p*, 10. e?, +p¥?-p?, = e_,+p¥™,-p.,

11. 1 = WCp-p_,) + & Cp¥*¥-p¥¥+e*-e* +e-e_,)

+ C1tH-$) (p¥-p*, +e-e_, )

12. 1% = WCp¥—-p¥,) + S Cp¥¥-p¥¥+eR-e*, )

+ C1-U-$) Cp-p_,-ete_,)

Oa5<W<¢t w+oecl

13. L= {q?t+e Cl-p,)? ] 14. L® = — [Cq¥)2+ e*C1*)2 ]

mle ml

There are various simplifications here. In the first two equations, | ignore U.S. output as an influence’ on the aggregate demand in both countries. This simply does away with a constant term in these two equations. In the next two equations, (3) and

C4), 1 suppose no interest-rate-elasticity of demand for money.

This has a major advantage, as Matthew CANZONER! and Dale

HENDERSON (1985) and Gilles OUDIZ (1985S) have shown, since it makes it possible to view qas the policy instrument in France, q™® as the one in Germany. p and p® in eqs. (3) and (4) are respectively given by

core inflation in France and Germany (Cp, and p¥), based on eqs. CS) and (6). Hence, the two demand for money equations imply that by centrolling money, the French and German authorities also directly

control home output. The demands for goods equations, (1) and (2), in this view, essentially determine the two national interest rates, i and i®,. Eq. C?), stating the interest rate parity condition, next determines the exchange rate e. This supposes perfect capital mobility. Eqs. (€8), (¢€9), (10), in turn, describe anticipations. They suppose that price anticipations are backward-Looking and exchange rate anticipations are forward-looking. People expect p and p* to go up as much next period as they did the last one, while they expect the terms of trade next period to return where they were tie last one. Eqs. (11) and (12) are the inflation rates that enter tne utility functions of the authorities. The welfare functions (13) and (14) are fundamental. They introduce the basic asymmetry that I referred to previously : the French would like to Limit inflation to core inflation while the Germans would like to get rid of it altogether. Far the moment, both of them not only experience core inflation, but import inflation through the appreciation of the home-currency price of

the U.S. good.

The system, as thus stated, would require treating e* as exogenous. This is troublesome in a way since it introduces an asymmetry between Germany and France that has no particular foundation. The exogeneity of e*, if maintained, would mean that the price of the

U.S. good, if given to both countries in dollars, would also be given :o

both of them in marks. But why not in francs ? Why should the Europeans be able to do nothing about the price of the U.S. good in marks while they can do something about it francs ? The asymmetry that would result from retaining this feature would run right through the rest of the analysis. But the problem can be avoided by resorting to the notion of an evenly weighted average exchange rate of francs and marks. This average -- some hypothetical écu -- can then be treated as exogenous instead of e®. Let the hypothetical écu/dollar, S$, be defined as

follcws

5 ( FF DM y° ( DM yr DM § $ Then in logarithms, it becomes

15. s = 0.5e+e*

where s is the log of S and e and e™® have the preceding significations.

Wherever e* occurs, s minus 0.Se may be substituted. This will alter

the two a, terms of the demands for goods [in eqs. (1) and €2)] and the

two 4 terms of the inflation rates [in eqs. €11) and (€12)]. Letting 16. p¥S = p¥¥+s,

these Pour terms become respectively

a, Cp¥S+0.Se-p) feq. (€1)]

a, (p¥8-0.5e-p*) feq. (2)]

V1

6 (p¥8-p¥$+0.5e-0.5e_,) feq.C11)] and

$ (p¥8-p¥$-0.5e+0.5e_,) feq.(12)] i

No asymmetry between Germany and France now results from treating the

price of the U.S. good in écus, p¥S, as exogenous.

The exogeneity of s is itself a simplification, which depenis on the idea that the factors affecting s in the relevand period come from the outside world. But the assumption is quite innocuous Por two reasons. First, France and Germany can be supposed to have little effect on U.S. policy behavior. Second, most of the news regarding s in the period of the EMS (since 1979) can be considered as stenming from the U.S. We could endogeneise s, of course, by modelling the

U.S. explicitly, but all of the essential results would stay the sane.

To proceed, we need to solve for the reduced forms of the | and i* terms in the two loss functions. As a preliminary, we must then solve

for e. Let us begin with the simplifying assumption P., = p¥, = p¥§ = e_, = 0.

Next if the subtract eq. (2) from eq. (1), and use eqs. (5) through (10)

C1) in order to eliminate various terms, we find

2a,t+a,tas _

17. q-q*® = = ee lta, where @ = e+p*® -p, Next the definitions of inflation can be written in the form: 18. I = pot+S Cp¥S-0.5p,-0.5 p¥) + (1-W-0.56) @ and

19. I = p§+ Cp¥S-0.S5p,-0.Sp¥) - (1-W-0.56) €

The two can then be conveniently restated as:

20. I = potl,+ta Cq-q*®)

and

21. 1% = p¥+lo-w Cq-q®) where

1, = $ (p¥S-0.5 (Cp,+p*)) and

R i

C1-W-0.56)/6 [see eq. (17) }

We shall assume that I, is positive because of dollar appreciation

that is, the inflation of the price of the U.S. good in écus, p¥S, will be supposed to exceed core inflation in Europe in eécus, 0.5 (pop). Later on, in section III, we will switch to the assumption of dollar depreciation and consider I, negative. But as the situation stands nou, both Germany and France undergo inflation as a result of the rising écu price of the U.S. good as well as through core inflation [see eqs. (21) and (22)]. The only other factor affecting their inflation rates is the movement in their bilateral terms of trade. This last is the only factor

that they can affect.

The policy problem can be seen at a glance. Since France warts I-p, = 0, it would like e to be such that wee = -I, in eq. (21). Eut

Germany wants I* = 0, therefore it wants wee = I[,+p® in eq. (22). Evidently e cannot satisfy both of these values at once. Further, while both countries want an appreciation of their currency relative to the

other, Germany wants a larger appreciation than France.

For the rest of the analysis, we will focus on eqs. (13) and

(14), the two utility-loss functions, and (17), (20), and (21), the

reduced forms for e, I, and I*™.

{I

Consider first the non-cooperative or Cournot-Nash solution to

the system. This means solving the following problem :

1 Min — [q?+€Ci-p,)? J 2

I-p, = I,tw Cq-q™)

and q™® fixed

and

1 Min — [Cq¥)@+e*C1*)2 ] q* 2

I™ = [,+p¥-x«Cq-q*)

and q fixed

The result is a French reaction function for q as a function of q® and a German reaction function for q*® as a function of q. The two

equations are

Exe ex 22. qh = ———— g¥¥ - ——__ | 1+€62 1+f02 and EM Qe ER oy 23 quy = yoo 1s 1+e¥oe 1+E¥ oe

where I¥ = I,+p¥

The two have the following solutions

~Ea[ eMoP 1B + C1+E*%OF) 15) 1 + CE+E™) of

24. qh =

and

~EMel Eo2 1, + CL+ E02 1¥] 1 + CE+E*) of

eS. q¥s =

It follows that

wCe*l¥-e1,)

26. qh -qai c= 1+CE+e*) 02

and

Ce*1¥-€1,)

it 27, eX = — ——_* @ 1+CE+E®) of

Further

C1tE%o2) 1, + Ef of If 1 + Cete*) of

28. I%¥-p, = I, + w Cqh-q¥4) =

Cito®> IB + € of 18 1 + CE+E*®) o@

29. 18 = 18 - w Cq¥-q¥¥) =

From a comparison of C28) and (29) with (24) and (25), we discover :

30. qh = -&&e CIN-p,)

SL. q¥N = -E¥qy] *N

18

11

If we analyse this solution, we find that the sign of e*% depends

on

ex[*

, € 1, , that is, €* CI,+p¥)> € I, <

Thus, if only the Germans are at least as much concerned with

inflation as the French in relation to Output, or €*>€, e% is necessarily positive. We can also see, quite independently, that both inflation rates must be positive. But if so, from eqs. (30) and (31), both outputs are necessarily negative. This last result simply reflects the counterproductive effort of both countries to neutralise the inflationary forces coming from the movement of the dollar by appreciating their own currency relative to the other. Germany wins this battle in a sense, because it wants to do so more badly, but it does so at the cost of a@ greater loss of output than France. As we

shall see immediately, the EMS solution is more sensible.

In order to find this next solution, a bit of preliminary material is necessary. Let us suppose momentarily that each country’s instrument is domestic credit not money, or donot m, where m-d depends on an intervention rule. This intervention rule basically represents the way tne EMS proposes to reconcile d-d® with the required value of m-—m*®

C2) in order to achieve the agreed exchange rate. Corresponding to the

identity

m= d+ Cm-d)

le

we can also write

q = q? + Cq-q4)

Subsequently, we can express the intervention rule in terms of q-q9,

Doing so, we have

32. q-q¢ = - y Cqt-qts-ggens)

and

33. q¥-q¥¢ = (1 - y) (q4-q¥d_ggensy

where 0 ¢ y ¢ 1 and GE"$ igs obviously the value of et+p¥-p, deriving from the agreed value of e in the EMS. It can be checked out that (32) and

(33) will yield

q-q™ = 6 eens

as they must. The coefficient vy therefore simply reflects the agreement between Germany and France about the distribution of the burden of

intervention.

As I have shown elsewhere, this system will work as long as bath

C3) countries do not engage in any sterilization. This means not only

that they must treat q? not q Cq™s not q*®) as their

basic instrument, but that they must disregard q-q* in setting q¢?.

13

Quite exactly, the problem they must solve is the following :

Min [ Cq¢)# + € CI-p,)? J

Q ° Mle

I - py = 1, + woeens and

1 Min — [ Cq¥¢)2 + e* Cre? ] qua 2

I" = 18 - q@gens

If they do so, the solution will be q? =q¥* = Q. Consequently, based

cn €32) and (33), the EMS will yield

34, qens =ye eens

and

35. qMEMS = -C1-y) eens

This solution remains incomplete as long as we do not know y and eens,

These two values were necessarily set by a joint agreement at the time of the last realignment. At this time France and Germany Supposedly reached their agreement by minimising some joint loss

Function consisting of a combination of L and L®. Let us consider this

joint Loss function to be

36. L = C1-A) L + AL*

where r is the weight of German welfare in the aggregate. The

Minimisation of C36), of course, must lead the tun countries to a point

on their contract curve.

The problem is then

C1-AD » Min [q2 + € Cl-pod?] + -— [Cqho2 + €* C192] eo 2 2 : q =yee q* = Cy - lige f-p, =i, +xee I*#=1*¥ -~we@ @

The solution to this problem with @ and y both as a function of the

gather Ls 37, gens zs 8 ( MN e* 13 - Ci-Ad EL, ; e se -2y A+ A+ CCL-AD C+ A E*] OF and 38. yA

However, y cannot rest on some arbitrarily given A in eq. (38) or else the EMS solution would not necessarily be as good or better than the Cournot-Nash one. Suppose, for example, that the Cournot-Nash solution

is perfect or nearly so for Germany but not France Cas in one of our

1s

later examples). Then any arbitrarily chosen A far below one will necessarily be inferior to Cournot-Nash as far as Germany is concerned. The right way to obtain the EMS solution therefore is to set y = A from

the start. That is, we must begin with the hypothesis 39. L = Ci-y) L+ y L®

and thereby equate the French burden of intervention between realignments with the weight of German welfare on the occasion of any

€4) realignment right at once. Then if we solve for eE&"S and y, we get

y &* 1% - Ci-y) €l,

40. ec&Ms = hal ( ——— ) y Ci-y) + [C1-A) € + A E*] o@

and

e* CIE - w @ @E"S)2 - € C1, + we |EENSD2

2 Ce eFNS 2

The full solution for @ and y based on these two interdependent equations is a pair of very complicated expressions, which we will avoid

using. Based on C40) and (41), we have

y &€ I - C1-y) € 1,

42. qEns - queens = 9 eens =a ( yCi-y) + [Cl-y) € + y €*] of

16

y U-y + oD 1, + € of IF

43. [€"8 - p, = ° y Cl-y) + [Ci-y) € + xy €*] &

and

Cl-y) Cy + € of) 18 + Cl-y) € o I, y Cl-y) + [Ci-y) € + x €*] 02

44, [NEMS =

If we compare this EMS solution with the non-cooperative one, we can see little difference in regard to inflation, which is still positive in both countries. But otherwise the situation is

quite different. French and German output necessarily have opposite signs [see eqs. (34) and €35)]. Withe positive, French output is

positive and German output negative ; with e negative, the opposite is true. In any case, both countries cannot have negative output, as happens under Cournot-Nash. This is understandable, since there is no Longer any attempt at a competitive appreciation on either side. Hence, if either country departs from the common zero-output objective on the low end, the other will do so on the high one. In the case of y equal 0.50 Cwhich is not necessarily optimal based on (419), q&"5S will be Positive, q*E°"S will be negative, and the mean value of the two will be

exactly zero.

Figure 1 depicts the situation. RR, which corresponds to eq. C22), is the Nash reaction function for France. R*R® is the sirilar

German one and corresponds to eq. (23). F is the French bliss point, G

18 the German one. These two points, of course, reflect the fact that both countries would like zero output for themselves but positive output for the other one in order to benefit from the exchange rate appreciation and the consequent deflationary pressure this would bring. them. The positive value of q at point G exceeds the positive value of ge at Foint F because the Germans desire more deflationary pressure than the French. Nis the Nash solution and thus corresponds to the values of q ard q*

implicit in eqs. (24) and (25). The 4S-degree e* line traces all of the

combinations of q and q® that are compatible with q*¥ - q™* Cor 6 e*),

based on eq. (26).

The EMS solution, on the other hand, places the two countries, not at N, but somewhere on their contract curve going from F to G. In accordance with eqs. (34) and (35), all points on this curve necessarily yield opposite signs of q® and q. I do not

indicate the exact EMS solution in the figure, but this point must

pe wherever the correct 45-degree e£"5 line intersects the contract

curve. Hence it is to the left or the right of point H, depending on

whether e£"$ is greater or less than e%. As it stands, however, the illustration clearly shows the essential superiority of the EMS solution. The general superiority of this solution rests on the

reasoning in footnote 4. Itl

I will next introduce a basic simplification in the analysis,

which is to suppose € = €*. In this case, from (26) and (27), we have

19

and

- f e& 46. es = ——____________ p¥ e {i+ 2 € x] and from (42), ~- Pd 47. qens— quens = cate xy - 1) 1, + ¥ Pol

y¥Cl-yd+ € &

eu (C2 y- 1) 1, + x-pE] efy (i -y) + € &]

48. e&Ns

Thus e” is strictly independent of I, whereas e€"$ is not. It is this

independence of e” from I, that makes the analysis much simpler. The result is that a change in I, will not affect the exchange rate that

would exist in the absence of the EMS.

We must also observe that with € = €™, as long as I, is positive,

“y must be somewhat above 0.5, and therefore e£"* must be higher than e".

¢5) The proof of these two propositions follows by footnote below. Since

2a the slopes of RR and R*R*® are symmetrical in figure 1, they imply c=e™,

and it follows that the EMS solution in the figure is to the right of H.

We are how prepared to introduce dollar depreciation and a consequent move of I, into the negative range. The equations for I* - Po and I** [(€28) and (29)] show us that there exists some negative value of [, for which I"-p, will be zero, and some other, larger negative value for which I*®" will be zero and I" - p, negative. In the former case, q” would also be zero and France would find bliss. In the latter, q®** would be zero and Germany would find bliss. The required level of I,

for the first event to happen is :

ae « 43. 1, =---——p ° 1+2€02 °°

For the latter event to happen, it is

1+€02 SO. I, = - ——— Pp 1+2€02

The problem that a depreciation of the dollar can then pose for

N

the EMS is quite obvious. In either of our last examples, the survival of the system would depend on a realignment bringing e€"s

down to e” and leaving the otherwise perfectly happy nation without any responsibility for intervention whatever. But in this circumstance, the other nation would also derive no benefit from the system, as we shall

Let us begin by verifying that the EMS could and would indeed produce the required values in order to match the Cournot-Nash solutions

in our two previous examples. If we plug y = O into eq. (48), we get

at

Si. gens = ~ 2

If next we also substitute eq. (49) for [,, we have

Ex e[1+2€e2 ]

52. eens = px = @é

9

In addition, y = O implies qe"* =o. Thus, in case of eq. (49) and

y = 0, we obtain L = O, and therefore

L = ylL® + C1-yL = 0

It follows that the minimisation of L with respect to € and y must

(6) yield ef"S = @% and y= Oif eq. (49) holds. Furthermore, e&NS=—N

means the same inflation rate for Germany in or out of the EMS because I* = 13-wee is then independent of this presence in the EMS. Based on

y = 0, qeE"S = Cy-1)eeE"S also yields

S3. queens = + _ oe ”

1+2€02

which is exactly the value we get for q™" after setting € = €*® and substituting (49) for I, [see eq. (25)]. Hence Germany will also be no

better off in or out of the EMS.

Similarly, if we set y = 1, we get

$4. gens = 2 = eK oN

22

Then if we substitute eq. (SO) [rather than (49)] for I,, we get e&%=eN once more. Everything else follows : from the conclusion L*® = 0, we obtain L = O with y = 1, and the French will be no better off in -or out

of the EMS.

Thus the EMS could survive in either one of our difficult set of circumstances. But would it do so ? The fact remains that the system would then cease to yield any advantages. There are a least two reasons why it might therefore crack. The first has to do with the fact that the survival of the system would require a return to the conditions of the European “snake”, thus placing one country in a position of dominance. In the case of eq. (49), this country would be France. In the case of eq. (50). It would be -- more familiarly so -- Germany. Politically speaking, however, it is not clear that either solution is Feasible. In the light of the evolution of the EMS since the Bremen agreement in the last seven years, neither France nor Germany may be in a position to accept a realignment entirely on the other’s terms with complete endorsement on its part of its own exclusive responsibility for defending the parity. In other words, y values in the vicinity of zero or one may not be politically feasible. Second, there are economic costs of maintaining the EMS, of which capital controls are the foremost example. I have assumed in this discussion that the EMS is dynamicaily stable even though the French and German rates of inflatian differ. But it is not clear that this stability is possible without capital controls, and efforts to deal with the question have generally come to

. C7) the opposite conclusion.

23 A graphical illustration of the argument will make a number of things clearer. [t will also permit bringing into view some important,

additional aspects of the EMS.

Iv

Figure 2 traces the excess over desired inflation in France and Germany as a function of I, both in and out of the EMS. More exactly, the figure traces these excess values as a function of p¥’. That is, only the changes in I, resulting from movements in p¥S and not P, or p®

C8) are in question. The IN - ps and I lines concern the situation

under Cournot-Nash or outside the EMS. They thus show simple

one-for-one reductions in inflation with reductions in I, Cas they

must, of course, since I, has no effect on @*, based on the simplifying assumption € = €*). At point 0, where I, equals zero, p¥S is equal to 0.5 Cp, + p¥) ; at point 1, I, has the negative vaiue of eq. (49) ; at point 2, it has the larger negative value of eq. ¢S0). There

is therefore French bliss at point 1, German bliss at point 2.

The lines [*ENS and I&"S-p,> have a somewhat different interpretation, and it is one that brings us in touch with something that has escaped us thus far. These lines relate to what happens in

the EMS in the absence of realignment. Cur previous formulas for

the EMS assume optimal values of e&"S and y. Thus they assume continuous realignment as the parameters of the situation change.

But the rules of the EMS do not allow such continuous adaptation. On the

contrary, these rules require keeping at least e@&"S, if not y,

¥ < y 8K NY iy oN ig Hy he SO " 5 Sc iH Q aS wl) ¥ Ps b Ho . oo ‘ae IA IN \ & aon aor ig & ew ss) are, yi > ee av TN) ee 2 ©} iv oy “¢ we w ri 94 ge? Woe + KH

@

ee

Ss Tr. I,+P

I"-2

FIGURE 2

w cou)

gq,"

1)

-

qin®

4

EMS

qr

2 *% Ss

FIGURE 3

26

constant until the next realignment. Accordingly, the I*®"* and IE"S- p> lines in the figure, resting on eE&"S at the initial position, are depicted as parallel to the previous price lines. The IE"S - p, line exceeds the I" - py one because the initial ens exceeds e"%, and by the same token, the I**£"S line is always below the [*®* one Cby an exactly equal amount).

It is impossible to infer from the figure where a realignment must happen following a fall in p¥* or as I, moves down. But since 1 and

2@ bliss points, this is necessarily somewhere at a distance from either

of these two points. Let us assume that either France or Germany

will call for a realignment as soon as it finds itself in a

position which is inferior to Cournot-Nash. [t immediately follows

that France will call for a realignment in the vicinity of point 1,

and Germany will do so in the vicinity of point 2. This explains the

hypothetical intervals in the diagram where a realignment must happen.

Figure 3 adds to our understanding. It shows French and German

output as a function of I[,. In the case of Cournot-Nash, undesired

inflation leads to a contraction in output ; less than desired inflation

leads to an expansion of output. The negative slopes of q™’ and q™™

follow. These two curves are also parallel lines, of slope - € x, as

indicated by the relevant equations Cwhich are repeated for

convenience at the bottom of the figure), and the two necessarily

run respectively through points 1 and 2. At the initial position shey

are necessarily in negative space. (In fact, their values inst

correspond to those at point N in figure 1).

n

gE™S and q®**"S, on the other hand, are independent of I, and they are spaced on either side of the horizontal axis. The vertical!

distance between q®"5 ard g®°"S is greater than the one between the 4%

and q®* because e&"S exceeds e”%. gq&"S is somewhat higher above the

origin than q¥®* is below it because y is greater than O.S.

It is tmportant to see that mothing but a realignment can affect the positions of the I1F"§ - p, and I*E"S lines in figure 2, whereas the positions of q&"S and q¥E"S in figure 3 depend on the intervention coefficient y as well. A realignment alters the distance between these tuo quantity lines, while a change iny situates them differently ata given distance apart. This brings us to an

interesting point.

As I, approaches point 1, we might imagine, fcr example, that France would tend to pull back from its agreement about y, while Gernany might allow France to do so because an immediate realignment would only lead to a devaluation of the mark at atime when Germans still views its inflation rate as too high. But around point @, the shoe is on the opposite foot. Germany might be unhappy about 1 - y while France might be willing to make concessions in order to avoid the realignment that would otherwise force an immediate appreciation of the franc at a time when France considers its price level as already too low. On these grounds, some adjustment of q&"* and q@E"S could take place without any realignment. But this sort of adjustment will not take the EMS very far. Even in the extreme case where y drops to zero in the vicinity cf point 1 and the q&"S line therefore converges with the horizental axis Cwhile the q¥&"S line

drops down to the position of the dashed q™—="S line in the figure),

France would remain dissatisfied : q®"§ would then be zero, but !JE"S - Pp, would still be positive, while France could have the zero value of I - py it wants outside of the EMS. Symmetrical reascring applies st Point ¢. Even if y rose to one, and q*°"S theref:re converged sith the horizertal axis Cuhile the q&"* line rase to the levei of the dashed q®"® line), the Germans would not be pleased. Althcugh ge" would then be zero IFE™S would be negative, while the Germans could obtain the zero vaiue of I*® they want outside of the EMS. Perfect flexibility of y, therefore, may narrow the interval where a realignment is essential, but cannot obviate the necessity for a

(9) realignment. Nothing can save the EMS around points 21 and 2, in

the terms of our problem.

The one feature of the example that might arouse discomfort is the required appreciation of the franc in the danger zone. This feature necessarily follows in the example from the fact that the EMS sets che franc lower thar it would otherwise be. Since the exchange rate that would exist independently of the EMS does not change, the forces that would require the EMS to adapt itself to the non-cocperative solution necessarily require an appreciation of the franc. It would be possible to modify this feature of the example only by complicating it. The essential point is independent : as long as there are divergent tendencies in the EMS, the depreciation of the dollar can be an element cf stress. Indeed, under the conditions that I have designed, a dollar

depreciation might cause the system to fall apart.

Finally, as indicated at the start, the message should not be

interpreted strictly as a prediction of Possible troubie, but can also

fo

ive)

be read in a normative way. Thus seen, it tells both countries to keep in mind the possibility cf moving out cf the system. Admittedly, one could always argue in favor of preserving the EMS by insisting on the possibility of a change in the future causing the system to beccme beneficial oneemore. !ndeed, I think this argument has a lot of merit since a choice of regimes is fundamentally involved, and such choices should rest on long—srun possible changes, net only the current Situation. Still, the weight of the argument depends on its

recognition on both sides. If either country becomes complacent whenever current circumstances happen to favor it, the ground

fcr a mutually satisfactory intertemporal compromise will be urdercut. Thus, it remains sound advice to both countries never to

close off the possibility of moving out of the system.

rT) i!

FOOTNOTES

The only basic step in this derivation is

a, (i - i® + p - po, + p¥e - p¥™) = az Cp, - p§ - e) = - as e€

See MELITZ (1985).

. MELITZ (1985). Any sterilization is a problem since we assume perfecrt

capitai mobility.

This equation of A and y, which means letting the weights of L and !_* in eq. (39) be endogenous, is much more plausible than it might seen. For any case, the equation should be interpreted as a linear approximation to the Nash bargaining solution L = LL®, in which 16 terms Like A and 1-A of eq. (36) ever appear. It was the minimisation of LL*® -- no other loss function -- that was shown by John Nash in 1950 to lead to a result that is necessarily as good or superior to the non-cooperative one. If we were actually to approximate L_* linearly, the intervention coefficient y would indeed appear

as a critical term in the relative weights of French and

German welfare (Caiong with € and €*). Herce eq. (29) is not Surprising. I avoid LL®™, since its use, as such, would be mathematicaliy unwieldy, as it would involve a polunomial of the

fourth order.

With € = €*®, eq. (41) becomes

ecig + 1,) CIS - 1, - 2 aw @ €EMS) +

1 (41a) yr - é -

2Ce eFRS 2

This equation says that as long as the sum I® + I, is positive, y will

necessarily exceed 0.5 if only I - I, = p® exceeds 2 w @ GEMS,

But e€"S is positively related to y and even for y as tow as 0.5

>

which is less than p¥. Therefore y is necessarily greater than 0.5.

Further, for y as low as GO.5, eq. €48) says

ete ecEns = m

eo {1 + 4 € &]

which is greater than

2c

e[2@+4€ ]

6.

32 I resort to this indirect form of argument in order to avoid the overly complex, fully reduced forms of eqs. (40) and (41) for eqs. (48), and (41a) of the previous footnote, in case € = €*j], as

indicated befare.

- See MELITZ and Philippe MICHEL (1985) and GIAVAZZI and

Alberto GIOVANNINI (1986). GIAVAZZ! and Marco PAGANO (1985) seem to come to the opposite conclusion that capital controls can be avoided, but they do so only by implicitly assuming official

indifference to the effect of the interest rate on output.

- Remember that I, = $[p¥® - 0.5 Cp, + p¥)]

. Besides explaining some possible retardation of the realignment, the

; hypothesis of some Flexibility of y at times of stress may be useful

in explaining why the pressure for realignment may come from the country in the weaker position. Thus, if Germany fails to intervene around point 2, France may be the one to press for a realignment near this point. The discussion in this section may be profitably compared

with OUDIZ (1985).

33 REFERENCES CITED

CANZONERI, Matthew and Dale HENDERSON (1985). “Strategic aspects of macroeconomic policy making in interdependent economies", Chapters |

and II of a book in preparation for the Brookings Institution.

SIAVAZZI, Francesco and Alberto GIOVANNINI (1986). “European currency

experience", Economic Policy, to appear.

GIAVAZZI, Francesco and Marco PAGANO (1985). “Capital controls and the.

European Monetary System", in Capital controls and foreign exchange

legislation, Occasional paper, Euromobiliare, Milano.

MELITZ, Jacques (1985). "The welfare case for the European Monetary System", Journal of International Money and Finance, December, Pp. 485-506.

MELITZ, Jacques and Philippe MICHEL (1985). "The dynamic stability of the European Monetary System", ENSAE and Unité de Recherche,

document de travail n° 8503, INSEE, Paris.

NASH, John (1950). "The bargaining problem", Econometrica, April, 18,

355-62.

OUDI2, Gilles (1985). “European policy coordination : an evaluation", EINSAE and Unité de Recherche, document de travail n° 8507, INSEE,

Paris, and CEPR discussion Paper n° 81.

IF DP NUMBER

280

279

278

277

276

275

274

273

272

270

International Finance Discussion Papers ee ee ton rapers

TITLES

1986

Taxation of Capital Gains on Foreign

Exchange Transactions and the NonFneutrality

of Changes in Anticipated Inflation

The Prospect of a Depreciating Dollar and Possible Tension Inside the EMS

The Stock Market and Exchange Rate Dynamics Can Debtor Countries Service Their Debts? Income and Price Elasticities for Exports

of Developing Countries

Post-simulation Analysis of Monte Carlo Experiments: Interpreting Pesaran's (1974)

Study of Non*nested Hypothesis Test Statistics

A Method for Solving Systems of First Order Linear Homogeneous Differential Equations When the Elements of the Forcing Vector

are Modelled as Step Functions

International Comparisons of Fiscal Policy: The OECD and the IMF Measures of Fiscal Impulse

An Analysis of the Welfare Implications of Alternative Exchange Rate Regimes: An Intertemporal Model with an Application

1985 (partial listing)

Expected Fiscal Policy and the Recession of 1982

Elections and Macroeconomic Policy Cycles

Assertion Without Empirical Basis: An Econometric Appraisal of Monetary Trends

in ... the United Kingdom by Milton Friedman

and Anna J. Schwartz

ne ee

34

AUTHOR(s)

Garry J. Sohinasi

Jacques Melitz

Michael K. Gavin Jaime Marquez

Caryl McNeilly

Neil R. Ericsson

Robert A. Johnson

Garry Schinasi

Andrew Feltenstein David Lebow Anne Sibert

William H. 3ranson Arminio Fraza Robert A. Johnson

Kenneth Rogoff Anne Sibert

David F. Hendry Neil R. Ericsson

Please address requests for copies to International Finance Discussion

Papers, Division of International Finance, Stop 24, Board of Governors of the Federal Reserve System, Washington, D.C. 20551.

IF DP NUMBER 269

268

267

266

265

264

263

261

260

259

258

257

256

255

254

International Finance Discussion Papers ee cston Papers

TITLES Canadian Financial Markets: The Government's Proposal for Reform

Was It Real? The Exchange Rate Interest Differential Relation, 1973-1984

The U.K. Sector of the Federal Reserve's Multicountry Model: The Effects of Monetary and Fiscal Policies

Optimal Currency Basket in a World of Generalized Floating: An Application to the Nordie Countries

Money Demand in Open Economies: Substitution Model for Venezuela

A Currency

Comparing Costs of Note Issuance Facilities and Eurocredits

Some Implications of the President's Tax Proposals for U.S. Banks with Claims on Developing Countries

Monetary Stabilization Policy in an Open Economy

Anticipatory Capital Flows and the Behaviour of the Dollar

Simulating Exchange Rate Shocks in the MPS and MCM Models: An Evaluation

Trade Policy for the Multiple Product Declining Industry

Long Memory Models of Interest Rates, the Term Structure, and Variance Bounds Tests

Currency Substitution and the New Divisia Monetary Aggregates: The U.S. Case

The International Transmission of Oil Price Effects and OPEC's Pricing Policy

U.S. Banks' Lending to Developing Countries: A Longer-Term View

Conditional Econometric Modelling: An Application to New House Prices in the United Kingdom

35

AUTHOR(s) Garry J. Schinasi Richard Meese Kenneth Rogoff

Hali J. Edison

Hali J. Edison Erling Vardal

Jaime Marquez Rodney H. Mills

Allen B. Frankel

Marcus H. Miller Arnold Kling Arnold Kling Catherine Mann Gary S. Shea Jaime Marquez Jaime Marquez Henry S. Terrell

Rod Mills

Neil R. Ericsson David F. Hendry