IFDP
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International Finance Discussion Papers

TITLES

1986
Taxation of Capital Gains on Foreign
Exchange Transactions and the Nonkneutrality
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

SS

34

AUTHOR(s)

Garry J. Schinasi

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 Fraga
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.


11

Tf we analyse this solution, we find that the sign of @* depends

on

ems 2 1, , that is, om (194P8)2 & I

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

inflation as the French in relation to output, or €TM>€, @" 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 d not 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*

¢-3)
in order to achieve the agreed exchange rate. Corresponding to the

identity

m=da+ (m-d)


a1

si. gens 2 12

ex

If next we also substitute eq. (49) for 1,, we have

cx
— OP
eo 1+2€02 ]

Moz ON

Se. eens = x

In addition, y = 0 implies q@"* = 0 . Thus, in case of eq. (49) and

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

L = yl¥ + (1-yL = 0

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

6)
yield e&"S = @¥ and y = O if eq. (49) holds. Furthermore, @E"S=@N

means the same inflation rate for Germany in or out of the EMS because
I* = I§-o@€ is then independent of this presence in the EMS. Based on
y= 0, qMEMS = Cy-1)0@E"S also yields

x
1+2€02

53. quens = _

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

s4. 0 gene
ex ox


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 I 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 tuo goods, q and qTM, are p
and p*TM, 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 (i and iTM) and the inflation rates (p,, !, Pa.
and 1*). The superscript a designates anticipated values. In the
present illustration, there is one extra complication : namely, the tuo
countries also consume a third good coming from the United States,
whose price is p¥**TM. The price of dollars in marks is e*. The equations

are as follows :


32
6. I resort to this indirect form of argument in order to avoid the
overly complex, fully reduced forms of eqs. (40) and (41) Cor

eqs. (48), and (41a) of the previous footnote, in case € = e*j, as

indicated befare.

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

Alberto GIOVANNINI (1986). GIAVAZZI 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¥S - 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).


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 6 exceeds the positive value of qTM 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*TM

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¥ - @TM* Cor @ @¥),

based on eq. (26).

The EMS solution, on the other hand, places the tuo
countries, mot 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

be wherever the correct 45-degree €&"5 line intersects the contract

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

whether @£"$ 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.

I will next introduce a basic simplification in the analysis,

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


24

T+xb2

}
T,+ p- woe

ane
res

- x68"

I, + «6e"
“
o

rv": T+P,

I’-z

FIGURE 2


2@
the slopes of RR and R¥RTM are symmetrical in figure 1, they imply €=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" - p,
and 1TM* [(28) and (28)] show us that there exists some negative value
of I, 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 :

Exd
14+2€02

For the latter event to happen, it is :

1+€02
Po
1+2€02

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

the EMS is quite obvious. In either of our last examples, the

survival of the system would depend on a realignment bringing @€"s

down to @" 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 = 0 into eq. (48), we get


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.

GIAVAZZ1, 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",
ENSAE and Unité de Recherche, document de travail n° 8507, INSEE,

Paris, and CEPR discussion paper n° 81.


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. b= G-yL+yL*

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 salve for e€"$ and y, we get

Oo. gens « ( y & 13 - Ci-y) €l, )
40. @ =
e

y Gi-y) + [C1-A) € + A €*] of

and

et CIE - we Of"S)2 - € Clg + we EEMSDA

2 Ce eensye2

The full solution for @ and y based on these two interdependent equations

is apair of very complicated expressions, which we will avoid

using. Based an (40) and (41), we have :

we. gttt = gtent sg gine eg (<P Ele)

y(l-y) + [C-y) € + y EF] of


2a, tagtas _

17, q-q¥ = ———— @ = o€
lta,
where
@ = et+p¥ -p,
Next the definitions of inflation can be written in the form:
18. 1 = po+S Cp¥S-0.5p,-0.5 p¥) + (1-W-0.56) &
and

19, ITM = p¥+$ (p¥8-0.5p,-0.5pTM) - (1-W-0.56) =

The two can then be conveniently restated as :

20. 1 = potl gta Cq-q*)

and
21. 1TM = p¥tly-« Cq-q*)
where
1, = $ (p¥8-0.5 (py+p¥))
and
« = (1--0.56)/e {see eq. (17)]


ry

FOOTNOTES

The only basic step in this derivation is

a, (i - i@ + p - pt, + p¥p - pTM) = as (pp - p¥ - e) = - as @

See MELITZ (1985).

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

capital mobility.

This equation of A and y, which means letting the weights of L and L*
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 = LLTM, in which 16
terms like A and 1-A of eq. (36) ever appear. It was the minimisation
of LLTM -- 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


gE"S and q®E"S, on the other hand, are independent of 1, and
they are spaced on either side of the horizontal axis. The vertical

distance between q&®"5 ard g¥E"S is greater than the one between the q”

and q®* because €&"* exceeds €¥. g®"S is somewhat higher above the

origin than qTM* is below it because y is greater than 0.S.

It is important to see that nothing but a realignment can affect
the positions of the IE"S - p, and I*E"S lines in figure 2, whereas
the positions of q®&"S and q¥TM"S in figure 3 depend on the
intervention coefficient y as well. fi realignment alters the distance
between these tuo quantity lines, while a change iny situates them
differently ata given distance apart. This brings us to ar

interesting point.

As 1, 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 Sermany
still views its inflation rate as too high. But around point 2, the
shoe is on the opposite foot. Germany might be unhappy about 1 - ¥
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
qTME"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 peint 1 and the q&"® line
therefore converges with the horizontal axis Cwhile the qTM&"S line

drops down to the position of the dashed qTM&"S line in the figure),


This has a major advantage, as Matthew CANZONERI and Dale

HENDERSON (1985) and Gilles OUDIZ (1985) have shown, since it makes
it possible to view q as 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 (p, and p¥), based on eqs

(5) and (6). Hence, the two demand for money equations imply that by
controlling 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 tuo national interest rates, i
and i*. Eq. (7), 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 ard
exchange rate anticipations are forward-looking. People expect p and
pTM 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 corre
inflation while the Germans would like to get rid of it altogether. For
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 :0


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

2. q¥ = -a, Cp¥t+e-p) + a, (p¥¥te"-p) - a, Ci*-p¥e+p*) + a, q
3. m-p = ug 4, m¥-p* = pq®
S. P= Potp.y 6. pTM = p¥+p¥,
Po > 0 px > 0
7. ef,-e = i-i* 8. pt,-P = p-p.,
9. p¥p-pTM = p¥-p¥, 10. e3,+p¥?-p?, = e_,+p¥,-p.

11, 1 = WCp-p_,) + & (p¥*-p¥¥+e*-e% t+e-e_ |)
1 1

+ C1W-$) (p¥-p¥, te-e_, >

12. 1% = WCp—p¥,) + S Cp*_pettex—ex,

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

Os<¥c1 B+ OC

13. L = (qt+e Cl-p,)?] 14. LE = — [CqTM)2+ e*C1*D2]

mie
mie

There are various simplifications here. In the first two
equations, I 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

(4), I suppose no interest-rate-elasticity of demand for money.


16

y (i-y + €* oF) 1, + x € of IF

43. 1€"8 - p, =
° y C-y) + [Ct-y) € + ¥ €f] of

and

Ci-y) Cy + € o@) IN + C1-y) € o I,
y Cl-y) + [Ci-y) € + y EF] of

44, [NERS =

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)]. With @ positive, French output is

positive and German output negative ; with @ 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 (which is not necessarily optimal based on (41)), q&"S will be
Positive, qTM¥€"$ will be negative, and the mean value of the two will be

exactly zero.

Figure 1 depicts the situation. RR, which corresponds to eq.
(22), is the Nash reaction function for France. R¥R® is the similar

German one and corresponds to eq. (23). F is the French bliss point, 6


& (p¥8-p'$+0.S5e-0.5e_,) feq.C11)]

and

& (pU8-p¥$-0.5e+0.5e_,) [eq.c12)]

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 depends on
the idea that the factors affecting s in the relevand period come from
the outside world. But the assumption is quite innocuous for two
reasons. First, France and Germany can be supposed to have l.ttle
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 :

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

C1)
in order to eliminate various terms, ue find


22

Then if we substitute eq. (50) [rather than (49)] for I,, we get eE"%=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 tuo
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. | have assumed in this discussion that the EMS is dynamicaily
stable even though the French and German rates of inflation 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

. ?)
the opposite conclusion.


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: J.nternational 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.


1
Min 3 (q#+eCl-p,)?]

I-py = Igtx Cq-qTM)

and qTM fixed

and

1
min 5 [Camdesencrmye ]

ITM = [,+p¥-xCq-qTM)

and q fixed

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

equations are :

€o0e cx
22. qh = qay I,
1+€02 1+ £02
and
Boe ety
23. gah = Hn is
1+EMoe 1+e¥ oe

where I$ = I,+pTM

The two have the following solutions :

tof Mok IE + C1¢E¥O2) 1g]
1+ CEeteTM) of

24. qh =


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 écus, 0.5 (py-p¥)

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,t+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 €, I, and I*.

I

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

the system. This means solving the following problem :


ay

oO

be read in a normative way. Thus seen, it teils 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 buy insisting on the
possibility of a change in the future causing the system to beccme
beneficial oncemore. Indeed, I think this argument has a lot of merit
since a choice of regimes is fundamentally involved, and such choices
should rest on long-run possible changes, not 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
fer 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.


France would remain dissatisfied : q®"* would then be zero, but !EnS

- Py would still be positive, while France could have the zero value

of I ~ pg it wants outside of the EMS. Symmetrical reasoning
Peint é€. Even if y rose to one, and q*€"S therefcre converged with
the horizertal axis (while the q®"* line rose to the level of the
dashed q®"® line}, the Germans would not be pleased. Althcugh q¥e"s
would then be zero I¥*€*S would be negative, while the Germans could
obtain the zero vaiue of I*TM 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

¢s)
realignment. Nothing can save the EMS around points 1 and 2, in

the terms of our problem.

The one feature of the example that might arcuse 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 she
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-ccoperative solut:on
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
of 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


both of them in marks. But why not in francs ? Why should the Europeans
be akle 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
amalysis. 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 eTM. Let the hypothetical écu/dollar, S$, be defined as

follows :
( FF DM y° ( D ye
$= - — —
DM ¢ $

Then in logarithms, it becomes

15. s = 0.SeteTM
where s is the log of S and e and eTM have the preceding significations
Wherever eTM 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 @ terms of the inflation rates [in eqs. Ci1) and (12)]. Letting

16. p¥S = p¥¥ts,
these Pour terms become respectively

a, (p¥S+0.Se-p) feq. (1)]

a, (p¥S-0.5e-p*) {eq. (2)]

v


19

and

te
———— P
e(l+2€ x]

46. eN = 3

and from (42),

ee [(Cy-1) 1, +¥ p¥]
yG-yd + €

47, qens— quens =

eu [C2 yx - 1) 1, + ype]
ely (-y) + € of]

48, eENs

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

independence of @" 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 tong as I, is positive,

y must be somewhat above 0.5, and therefore @£"* must be higher than é¥.

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


EHS
4

gr
qe

gem(ee?

4,4"

= ye em®
(eT) bE MS

yw

TES e

= - <a (1-7)
"2 ea I*"

ems

FIGURE 3


We have now entered a period of dollar depreciation after four
to five years of dollar appreciation. This paper makes an attempt to
show that this change in policy environment could lead to tensions
within the European Monetary System (EMS). What I have done is tc
cons:ruct a special theoretical example where, depending upon the extent
of dollar depreciation, either Germany or France achieves "“bliss" by
leaving the EMS. In either of these tuo cases, the best the EMS can do
is to 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 «reading this example. It can be viewed as a prediction about the
future, as I 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 mational interests may cali

for moving 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
impazt of the dollar depreciation without altering the franc-mark
exchange rate. This inability to adjust in other waus 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.


12

we can also urite
q = q¢ + Cq-q4)

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

Doing so, we have

32. q-q4 = - y (qs-qts—ggens)

and

33. q¥-q¥4 = (1 - y) (qd-q¥d-gaens)

where 0 ¢ y « 1 and @€"8 is obviously the value of e+p§-p, deriving from
the agreed value of e in the EMS. Tt can be checked out that (32) and

(33) will yield
q-q® = 9 gens

as they must. The coefficient y 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 both

(3)
countries do not engage in any sterilization. This means not only
that they must treat q4¢ not qa Cque not q¥) as their

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


joint loss function to be

36. L = CI-AD L +

where A is the weight

minimisation of (36), of

on their contract curve.

The problem is

C1-AD

fo

q=yee

qwedy- lee
T-poti,teeed

I*s1¥ -ee @

The solution

ather

a}
a
te

(

©

and

38. y= A
However, ¥
the

EMS solution would

Cournot-Nash one.

is perfect or

(a? + € Cl-p 02] +

14

AL*
of German welfare in the aggregate. The
course, must lead the two countries to a point

then

[eqtoe + ef CE2G

wl>

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

A e* IE - Ci-Ad EL, \

cannot rest on some arbitrarily given
not necessarily be
Suppose,

nearly so for

Boeya+ at tametrnejpe!

A in eq. (38) or else

as good or better than the

for example, that the Cournot-Nash solution

Germany but not France Cas in one of our


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.


IFDP
NUMBER
269
268

267

266

265

264

263

262

261

260

259

258

257

256

255

254

International Finance Discussion 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 Nordic Countries

Money Demand in Open Economies: A Currency
Substitution Model for Venezuela

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


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

additional aspects of the EMS.

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¥S. That is,
only the changes in I, resulting from movements in p¥S and not p, or p¥TM

(e)
are in question. The IN - p, 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 paint 0, where I, equals zero, p¥® is equal to
O.S Cp, + p¥) +; at point 1, I, has the negative vaiue of eq. (49) ;
at point 2, it has the larger negative value of eq. (SO). There

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

The lines [#E"S 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. Our previous formulas for

the EMS assume optimal values of @€"$ and yx. 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@€*"$, if not y,


ABSTRACT

This paper analyses the possibility of increased tensions in the
Europeé.n 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.


w

German welfare Caiong with € and €*). Herce eq. (39) is not
surprising. I avoid LLTM, since its use, as such, would be
mathematically unwieldy, as it would involve a polunomial of the

fourth order.

With € = €*, eq. (41) becomes

eC1IE + 14) CIE - 1, - 2 0 @ SES)

2Ce eEnsye

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

necessarily exceed 0.5 if only

1§ - I, = p¥ exceeds 2 w @ GEMS.

But @*"§ is positively related to y and even for y as low as 0.5,

4
paca 48% yy
1+ 4€

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

Further, for y as low as 0.5, eq. (48) says

2ta
gens = px
e[1 +4 € oo]
which is greater than
2t oa
ey = «

e[2@+4€ &]


26

constant until the next realignment. Accordingly, the IM®"* and

I€"S- p, lines in the figure, resting on e€"$ at the initial

position, are depicted as parallel to the previous price lines. The

I€"S - py line exceeds the I" - ps one because the initial @e&"s

exceeds €¥, and by the same token, the I¥€"$ line is always below

the I1TM* one (by an exactly equal amount).

It is impossible to infer from the figure uhere 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. It 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[,. Im 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 qTM*
follow. These two curves are also parallel lines, of slope - € x, as
indicated by the relevant equations (which 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 :hey
are necessarily in negative space. (In fact, their values must

correspond to those at point N in figure 1).


and

25. q¥¥ =

Tt follows that

~eTMa[ fo@ 1, + C1+E02 18]
1+ Cete*) o@

awCe*[S-€1,)

26. qh-qu" = ——-__-_
1+CE+E*) of
and
eS,
27. eM = “ Ce*IB-E1,)
@  1+CE+ETM) oF
Further
C1ite¥oe®) 1, + ef o@ IE
28. IN-py = 1g + x Cq¥-qu") = ————__*
1 + Cete*) of
Cite®) IB + €o@ 18
29. 1 = 18 - w Cq¥-qey) = ———_*__

From a comparison

30. q¥ =

31. gah =

1 + Ce+e*) of

of (28) and (29) with (24) and (25), we discover :

te CIN-p,)

MQ AN

18


13

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

Min ( (qe)? + € CI-p.d2 ]

a
o
rie

IT - py = 1, + woeens

and

1
Min = [ Cq¥4o? + em CEH? ]
que 2

I¥ = 18 - wosens

If they do so, the solution will be q% =q¥* = 0. Consequently, based

cn (32) and (33), the EMS will yield

34, qi"S = y 9 Gens

and

35. qTMEMS = -Ci-y) @a@ens

This solution remains incomplete as long as we do not know y and EMS.

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 LTM. Let us consider this