EMU and the International Monetary System
Chapter

7 The Euro and Exchange Rate Stability

Editor(s):
Thomas Krueger, Paul Masson, and Bart Turtelboom
Published Date:
September 1997
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Author(s)
Agnès Bénassy-Quéré., Benoît Mojon. and Jean Pisani-Ferry 

This paper deals with a single issue: will EMU increase or reduce exchange rate volatility between European and non-European currencies? As the volatility of exchange rates between the dollar, the yen, and the mark has been the focus of discussions and policy actions within the Group of Seven industrial countries since the early 1980s, this is an issue of some relevance in the discussion on the international implications of EMU.

In addressing this issue, we are concerned with the permanent impact of EMU, which should analytically be distinguished from the transitory effects that could arise from the introduction of the euro. In other words, we do not discuss here whether EMU could initially lead the euro to depreciate (because of a lack of credibility of the ECB, or a diversification of private portfolios and transaction balances arising from the elimination of exchange rate variability and risk within the euro zone) or to appreciate (because the European currency will become an international one and its unified financial market will attract capital flows). These issues have been investigated in the literature (European Commission, 1990; Gros and Thygesen, 1992; Kenen, 1995; Benassy-Quéré, Italianer, and Pisani-Ferry, 1994; Aglietta and Thygesen, 1995), but without reaching firm conclusions, and they are the main focus of some of the papers in this volume (Bergsten; Alogoskoufis and Portes). In order to put aside these transitory issues, we shall assume throughout this paper that the ECB has established its credibility and that whatever portfolio rebalancing that could arise from the introduction of the euro has already taken place. This leaves us with an analytically neat question, to which the literature has repeatedly alluded, but has only recently started to address explicitly (Martin, 1997; and the papers by Cohen and by Ghironi and Giavazzi in this volume).

It was suggested early on by some observers that the creation of EMU could increase exchange rate volatility vis-à-vis the dollar. There are two main grounds for such a claim, which rest respectively on a stochastic stability channel and on a policy preference channel:

  • By removing exchange rate volatility within Europe, monetary union could result in a higher volatility between Europe and the rest of the world. The basic reasoning behind this intuition is that the locking of intra-European exchange rates will prevent them from fulfilling their buffer role, thereby leading to a transfer of shocks to the interest rate of the euro zone and ultimately to the euro-dollar exchange rate. A related motive for increased volatility could be that through aggregating several currencies, EMU could decrease the stability of the fundamental equilibrium exchange rate of the euro in comparison to that of constituting currencies (Collignon, 1997). In other words, there could be a transfer of volatility from intra-European exchange rates to exchange rates between the euro and other currencies.

  • As the euro zone will be comparatively larger and less open than individual member countries, it may collectively attach less weight to exchange rate stability as a policy target (Kenen, 1995). A kind of “reciprocal benign neglect” could thus develop between the United States and Europe, resulting in an increase in exchange rate volatility. Additional arguments stem from the provisions of the Maastricht Treaty, which emphasize the priority of controlling domestic inflation rather than external objectives.

These arguments clearly carry some weight. However, they fall short of being fully convincing. The validity of the volatility transfer argument is disputable: in principle, shocks affecting participant countries in an opposite way (e.g., a negative shock to Germany and a positive shock to France) should not trigger policy reactions from the ECB and therefore not have an impact on the exchange rate of the euro, and symmetric shocks should not affect the volatility of the euro exchange rate either, because the ECB would be able to react in order to offset any undesirable consequence they might have, exactly in the same way as national central banks do in a floating exchange rate regime. Furthermore, the volatility transfer argument has been challenged by Flood and Rose (1995), who have shown that fixing exchange rates does not increase the instability of other macroeconomic variables. If fixing intra-European exchange rates basically removes a source of excessive volatility, there is no reason why this volatility should show up elsewhere in the macroeconomic system, and it could well be that the volatility of the dollar exchange rate would in the end be reduced. Stochastic stability considerations therefore do not lead to concluding unambiguously in favor of the increased volatility hypothesis.

The “reciprocal benign neglect” argument can also be challenged. It is certainly true that because of its lesser openness, policymakers in the euro zone should attach less weight to the union's effective exchange rate than previously to those of the constituent countries. However, this does not imply that they should pay less attention to the exchange rate vis-à-vis the U.S. dollar or the yen. At least, the argument needs to be refined. One reason for being less concerned with the value of the dollar could be that within the framework of the ERM of the EMS, intra-European exchange rates are sensitive to shocks to the dollar-deutsche mark rate (Henning, 1995).1 EMU would obviously remove this factor, but the extent to which this should affect the volatility of the dollar exchange rate depends on whether (under present monetary arrangements) the burden of stabilizing intra-European exchange rates falls on the Bundesbank or on the central banks of other European countries. Furthermore, it was argued by the European Commission (1990) that a single European central bank could also find it easier to embark on exchange rate policy coordination with the U.S. Federal Reserve and the Bank of Japan than would several European central banks acting in a loosely coordinated way, if only because the reduction in the number of players would lower the informational cost of coordinating policies. There is therefore a clear case for examining how changes in European policy preferences could affect global exchange rate stability, but the issue has to be looked at in a precise way.

Although it has been the subject of casual remarks, the link between EMU and global exchange rate stability has until recently not been explored in a systematic fashion within the framework of a clearly specified model. Stochastic simulations with empirical macroeconometric models should provide some indications of the impact of EMU on the volatility of the dollar exchange rate, but since this was not the focus of their study, Masson and Symansky (1992) and Minford, Rastogi, and Hughes Hallett (1992) do not give the corresponding results. Only the European Commission (1990) provides an evaluation of the effects of EMU on the bilateral exchange rates vis-à-vis the dollar, which suggest that its volatility should decrease in comparison to the free-float regime. However, the Commission's results have been criticized for relying on the assumption that most of the observed exchange rate volatility results from noise. Available stochastic simulations therefore fail to provide convincing evidence on the issue.

In this paper, we therefore begin by providing an analytical setup for analyzing the repercussions of supply, demand, and speculative shocks in a world consisting of three countries, two of which decide to form a monetary union. We use it to develop a model in order to analyze the volatility of the real effective exchange rate (REER) of the U.S. dollar under alternative European monetary regimes. We then use a similar setup for dynamic numerical simulations.

European Monetary Regimes and Dollar Exchange Rate Stability: An Analytical Framework

In order to tackle the problem, we need a model that allows us to represent the formation of a monetary union among a subset of countries while remaining sufficiently simple to be solved analytically. This leads us to the realm of three-country models, which are notoriously hard to keep tractable. We shall therefore make a number of simplifying assumptions.

The world economy is made up of three countries called U, G, and F, which represent the United States, Germany, and France. The last two, the union of which forms the euro zone (which will be called Europe for the sake of simplicity), are supposed to be identical in all respects, but can be subject to asymmetric shocks. Furthermore, Europe is supposed to be identical in size and openness to the United States. Initially, France exports a fraction, η, of its GDP’ to Germany and another, η, share to the United States and Germany does the same vis-à-vis France and the United States. The United States exports a fraction,η, of its GDP to Europe, equally divided between France and Germany. Along the baseline, all bilateral trade flows are therefore balanced, with each European country being twice as open as the United States and (ignoring French-German trade) Europe as a whole being as open as the United States. These assumptions are roughly consistent with empirical evidence. This kind of setup is similar to those used by Cohen and Wyplosz (1989) and Canzoneri and Henderson (1991).

We shall consider three alternative exchange rate regimes between France and Germany: a floating exchange rate regime, in which each country separately sets its monetary policy; a monetary union regime, in which the ECB sets the common monetary policy for the two European countries; and an asymmetric system representing the ERM of the EMS, in which the German central bank sets monetary policy while France keeps a fixed French franc-deutsche mark nominal exchange rate.2 Europe is always assumed to be in a floating exchange rate regime vis-à-vis the United States. For countries in a floating exchange rate regime, no coordination is envisaged, that is, the only outcome is a Nash equilibrium. In other words, we only envisage coordination within the framework of fixed exchange rate regimes.

The model for each economy is a standard open economy model with short-run nominal rigidity adapted from Blanchard and Fischer (1989, Chapter 10).3 It has a short run, in which nominal wages are fixed, and a long run, in which they are flexible. Before exogenous shocks occur, full employment is assumed to hold, because wages are set at a level consistent with expected labor market equilibrium. After a shock occurs, there is no immediate wage renegotiation, so the short-run supply curve has a positive slope. Unanticipated shocks may initially give rise to unemployment, but monetary policy is able to react to shocks and attempts to minimize a macroeconomic loss function. In the long run, real wages clear the labor market and the supply curve is vertical. Each country is specialized in the production of one good, which is an imperfect substitute for the production of the other two. Aggregate demand depends on the real exchange rate and the real interest rate, so that goods markets are linked through relative price effects (quantity linkages are ignored for the sake of simplicity). Capital is perfectly mobile between countries, and uncovered interest rate parity holds.

The model is presented in Appendix I. It is made tractable through an Aoki transformation, which consists of defining sum variables that refer to European averages (with E subscripts) and difference variables that capture asymmetries between France and Germany (D subscripts). Finally, U subscripts refer to U.S. variables.

It is assumed that monetary policy aims at minimizing a macroeconomic loss function L(X), where X represents a set of macroeconomic variables. Obviously, the loss function depends in turn on the exchange rate regime. In what follows, we shall alternatively consider separate loss functions for France and Germany, and European loss functions representing the behavior of the ECB. Then, the robustness of the results will be discussed according to the choice of the variables to be included in the loss functions.

Long-Term Equilibrium

Appendix II gives the long-term solution to the model, assuming that shocks may have a permanent component. Except when the nominal exchange rate is fixed (ERM regime), the price flexibility ensures that inflation does not have any real effect. Thus, the only possible aim of monetary policy in the long run is to minimize inflation, and the long-term solution does not depend on the exchange rate regime or on the choice of a particular loss function. It is easily shown that the world real interest rate (which equals the nominal interest rate in this stationary equilibrium) is affected by symmetric worldwide shocks, while shocks affecting Europe and the United States have an asymmetric impact on the real exchange rate of the dollar, and shocks affecting France and Germany have an asymmetrical impact on the real French franc-deutsche mark exchange rate.

Short-Term Equilibrium

The short-term equilibrium is determined by setting nominal wages to zero. This nominal rigidity leads to a positively sloped short-run supply curve:

where y stands for output, p, the price level, and u, a negative productivity shock. Goods market equilibrium implies that supply equals demand, that is,

with q being the real exchange rate; w, the openness ratio (identical in France and Germany, wF = WG = 2η while in the United States, WU = η),rthe real interest rate; and v a positive demand shock.

Combining equations (1) and (2) gives prices as functions of real exchange rates, real interest rates, and shocks:

with Γi=ui+αvi. .

Consumer prices are easily derived:

Equations (1) to (4) describe the functioning of each economy. Equations (5) and (6) represent the interactions through goods and capital markets. Goods market interaction results from changes in the real effective exchange rates:

It is important to realize that, owing to the Aoki transformation, qE is the average real effective exchange rate of France and Germany, which is not identical to the real effective exchange rate of Europe. The latter is simply the opposite of the exchange rate of the dollar (qU=−2qE). In a similar way, qD is not the bilateral real exchange rate between France and Germany (which equals 2(sDpD)), but half the difference of their effective real exchange rates. This is why a 3/2 factor intervenes in the equation for qD.4

The international asset market equilibrium is described by two real interest rate parity conditions that stem from the uncovered interest parity condition:

εF and εD are transitory speculative shocks to the exchange rate equation, which can be seen as representing time-varying risk premiums. We introduce these shocks because we want to represent the effect of speculative shocks that are correlated across currencies.

The model is closed with the three first-order conditions derived from the minimization of the loss function. We now have to choose a loss function.

Central Bank Behavior

As we intend to determine whether European monetary union is likely to affect the stability of the exchange rate vis-à-vis the dollar, a straightforward approach is to explicitly include the real exchange rate in the central bank's loss function. This kind of representation is able to capture recent (and possibly future) policy dilemmas facing the central bank when significant swings in the external value of the currency occur. Article 109 of the Maastricht Treaty explicitly envisages such dilemmas, as it states that the Council may formulate “general orientations” for the exchange rate policy of the euro zone vis-à-vis other currencies (implicitly, the dollar and the yen), but that these orientations “shall be without prejudice to the primary objective of the ESCB to maintain price stability.”

This approach can also be considered a reduced form representation of the traditional trade-off between domestic objectives and the achievement of external equilibrium, under the assumption that the current account essentially depends on the real exchange rate. It was, for example, used by Persson and Tabellini (1996). But we consider it more relevant in the present context to take the real exchange rate as an objective in its own right than to use more traditional ways of including an external variable among the policymakers' main objectives, like including a current account target in the objective function.

Therefore, let the loss function be

where β is a coefficient that measures the relative weight of the real exchange rate objective as compared to the price objective.5 We shall consider other loss functions in the section on robustness. What we need to do here is to determine the weight of this objective for the European central bank, that is, calculate βE from βFand βG

A natural way to proceed is to take as the European loss function a simple average of those of France and Germany:6

French and German prices and real exchange rates can be expressed as functions of the “sum” and “difference” variables, using the property that xF=xE+xD and xG=xExD. Assuming that βGF=β, and rearranging the expression, we obtain

The H term can be dropped from the expression since it only depends on difference variables, which cannot be affected by the monetary policy of the European central bank. Furthermore, equation (5) indicates that the average real effective exchange rate of France and Germany, qE, can be replaced by −qu/2, where − qu is the effective real exchange rate of the euro zone. This leads to the following expression, which is formally similar to equation (7), except for the division by four of the β coefficient:

Moving to monetary union therefore reduces the weight of the effective exchange rate objective. This reduction does not arise from any particular assumption about the behavior of the ECB. Rather, it is the mechanical outcome of the reduction in the openness ratio resulting from the creation of the euro zone, which is half as open as for the two constituent countries individually, and whose central bank is not able to target the real French franc-deutsche mark exchange rate. Note that this result does not mean that the ECB attaches less weight to the exchange rate of the dollar than do the central banks of France and Germany. On the contrary, we explicitly assume here that its preference for keeping the dollar around its equilibrium value does not change.

In minimizing the loss function, we may directly use the real interest rate as the policy instrument when the long-run equilibrium does not require domestic price changes (because as inflation has no real effect in the long run, minimizing the loss function at period t +1 simply leads to equating inflation to zero; thus, piLT=pi andri=ii[E(piLT)pi]=ii ; see Appendix II). This always applies to floating exchange rate regimes, because any required change in the real exchange rate results from corresponding changes in the nominal exchange rate rather than domestic prices. This also applies to fixed exchange rate equilibria in Europe when shocks are either temporary or symmetric (because the long-run real exchange rate remains constant in both cases). The only case in which shocks imply the long-run value of the domestic price to change is that of fixed exchange rate regimes (EMU or ERM) in the presence of permanent asymmetric shocks. We shall therefore use the real interest rate as the policy instruments in all cases but this last one.

ERM in Europe

Which European exchange rate regime should be taken as a benchmark for assessing the effects of EMU is a matter for discussion. There are two reasons for taking a floating rate regime as a benchmark. First, the current wide-band ERM does not differ much from a floating rate regime, de jure at least. Second, many observers consider that, should the EMU perspective be abandoned, Europe would forsake its attempts at exchange rate stabilization and move to a floating rate regime. However, Europe has been attempting to stabilize exchange rates at least since 1979, and the wide-band ERM has de facto been a fixed rate regime since 1993. There are therefore also grounds for comparing exchange rate volatility between Europe and the rest of the world in EMU and the ERM.

Like any target zone system, the ERM has complex features, but for this comparison it will be considered here as an asymmetric system in which the Bundesbank freely defines its monetary policy while the Bank of France maintains a fixed exchange rate with the deutsche mark. This kind of representation does not contradict the conclusions of the literature, and it is adopted in most empirical simulations (European Commission, 1990, or Masson and Symansky, 1992). Furthermore, we disregard the possibility of realignments, we ignore the existence of fluctuation bands, and we assume that the system is perfectly credible and there are no speculative shocks to the French franc-deutsche mark exchange rate. These rather crude assumptions are debatable, especially as they prevent us from taking into account a possible correlation between the deutsche mark-dollar and the intra-ERM exchange rates. They should be relaxed for an empirical evaluation with model simulations. Finally, we assume that the Bundesbank behaves as a Stackelberg leader, that is, that it takes into account the behavior of the Bank of France when making its monetary policy choices. But the loss function of the Bank of France is no longer similar to that of the Bundesbank: its only aim is to keep the deutsche mark-French franc nominal exchange rate stable.

As developed above, the real interest rate can be taken as the policy instrument as long as shocks are either symmetric or temporary. Hence, the monetary policy in the ERM regime can be described as follows:

In the case of permanent, asymmetric shocks, the implications of exchange rate targeting for nominal interest rates must be explicitly taken into account.

Exchange Rate Stability Under Various European Policy Regimes

U.S. Behavior

As the U.S. policy regime does not depend on exchange rate arrangements in Europe, the behavior of the U.S. economy can be represented by a relation between the real exchange rate and the real interest rate that is invariant with respect to policy changes in Europe. To establish this relation, we combine the U.S. goods market equilibrium condition (3) with the first-order condition from the minimization of the U.S. loss function:

with qUrU=1,

The first-order condition for the United States is therefore

Combining equations(3) and (13) gives a relation between the real exchange rate and the real interest rate, which can be represented in a (ruqu) diagram as an upward sloping schedule UU:

with HU=α(1α)2αβUδ+ηθ+αηθandΓU=uU+ανU.

UU is independent of shocks affecting Europe or the dollar exchange rate, but is not independent of domestic U.S. shocks. It represents the reaction of the U.S. central bank, and is upward sloping because the Federal Reserve reacts by raising interest rates to a depreciation of the currency that affects both p and q.

European Behavior Under Floating Exchange Rates and EMU

Similar relations can be derived for Europe under alternative exchange regime assumptions. We begin by comparing a free-float regime and monetary union. The ERM will be introduced thereafter.

Floating Exchange Rate Regime

Minimizing separately the loss functions for France and Germany yields the first-order conditions, which can be expressed in the sum-difference system as

with dpEdrG=dpEdrF=12dpEdrG and

and the same for q. Adding the two conditions therefore yields

and a similar condition for variables pD and qD.

European aggregate behavior can thus be represented by a relation between variables pE and qE, which is similar to equation (13) for the United States and can be calculated using goods market equilibrium conditions (3) and real interest rate parity conditions (6):

with

Relation (16) gives the implicit trade-off between aggregate price and real exchange rate stemming from noncooperative policies conducted independently by French and German authorities.

EMU

The equivalent relation under EMU can simply be obtained by minimizing the aggregate loss function LE=12(pE2+βqE2). . This leads to changing coefficient Ф in equation (16):

with

It is apparent that ФEMUFloat, that is, that the slope of the schedule described by equations (16) and (17) is smaller under EMU than in the free-float regime. This means that moving from the floating rate regime to EMU tilts the European trade-off between price and exchange rate stabilization toward price stabilization and away from exchange rate stabilization.7 The reason for it can be grasped from the expression for Ф in equations (16) and (17): moving from a floating rate regime to monetary union affects the responsiveness to changes in the real interest rate of both exchange rates and prices, that is, it affects the numerator and the denominator of the expression for Ф. Both terms are in fact lowered, since we have both

and

but the reduction in the numerator is proportionally larger because the move to EMU basically affects a country's ability to modify its real exchange rate through monetary policy changes. Since prices are affected by monetary policy both directly and through the exchange rate channel, this effect exceeds the parallel reduction in the control over domestic prices.8

Nash Equilibrium Between Europe and the United States

Whatever the European regime, the euro-dollar exchange rate will result from a noncooperative game between Europe and the United States. In order to calculate the corresponding Nash equilibrium, we need to transform equation (16) into a real exchange rate-real U.S. interest rate relation. Substituting equation (16) into the goods market equilibrium condition (3) and using the real interest rate parity condition (6) leads to the following expression:

where

is a decreasing function of Ф, and ΔE is a combination of shocks:

The model can now easily be used to calculate the impact of supply, demand and exchange rate shocks on the euro-dollar exchange rate. Equations (UU) resulting from U.S. behavior and (EE) resulting from European behavior can be represented as upward- and downward-sloping schedules UU and EE in an (rU, qU) diagram, whose intersection determines the U.S. real interest rate RU and the real effective exchange rate of the dollar QU (Figure 1). Although not conventional, this representation is equivalent to the familiar determination of the Nash noncooperative equilibrium in a two-country game.

Figure 1.Impact of a U.S. Shock

We want to determine whether the responsiveness to shocks of the real exchange rate of the dollar decreases or increases with EMU. To this end, equations (UU) and (EE) can be written as a system of two equations:

where ΓU represents shocks to the United States and ΔE symmetric shocks to France and Germany (see equations UU and EE).

The solution of the above system is

Δ represents shocks affecting Europe and the United States asymmetrically.

It is apparent that dqUdHE>0, and therefore that dqdΔdΦ<0.

Since ФEMUFloat, this demonstrates that forming a monetary union in Europe increases the responsiveness of the real effective exchange rate of the dollar to shocks originating in the United States or affecting European countries symmetrically. Figure 1 depicts it graphically in the case of positive U.S. shocks: the resulting appreciation of the dollar is more pronounced under EMU than under floating exchange rates.

The reason for this result is that under a floating exchange rate regime, France and Germany fail to internalize the externality resulting from their macroeconomic interdependence. Assume for example that Europe is hit by a positive demand shock or an adverse supply shock (vG = vF> 0 or uG = uF > 0). In a floating rate regime, both countries raise their interest rate to stem the inflationary consequences of the shock, but as they do not internalize the externality, they tend to overestimate the impact of their policy.9 In the event, the actual REER appreciation turns out to be lower than expected (because both currencies appreciate vis-à-vis the dollar), and inflation remains higher. Failure to internalize the externality results in a weaker tightening of monetary policy than when countries coordinate. Thus, a side effect of the absence of policy coordination under a floating rate regime is that monetary policy tends to overweight the real exchange rate objective and to stabilize the real effective exchange rate of the dollar.

When the two European countries form a monetary union, they internalize their common externality, and the ECB assesses more accurately the impact of its policy. Therefore, it goes for a higher increase in interest rates than under a floating rate regime, and the resulting appreciation vis-à-vis the dollar is more pronounced. By providing automatic coordination in the response to symmetric shocks, monetary union removes a coordination failure and thereby results in increased real volatility of the dollar.10

Equation (19) also indicates that asymmetric intra-European shocks (uD,vD and εD) do not have an impact on the real exchange rate of the dollar, because the effects of the changes in French and German variables automatically offset. This contradicts the naive version of the volatility transfer argument: as long as we compare two symmetric exchange rate regimes in Europe (i.e., float and EMU), suppressing an intra-European adjustment channel can increase the volatility of French and German macroeconomic variables, but does not have an impact at all on U.S. variables, and in particular has no effect on the (nominal or real) effective exchange rate of the U.S. dollar.

An interesting case is that of speculative shocks. A well-known stylized fact is that the French franc tends to depreciate against the deutsche mark when the deutsche mark appreciates against the U.S. dollar. This asymmetry can be represented in our framework as

where p measures the correlation between speculative shocks to the deutsche mark-U.S. dollar and the French franc-deutsche mark exchange rates. Equation (20) is equivalent to

Such a correlation of shocks does not change the volatility of qE which does not depend on εD. But it increases the volatility of both qF and qG, for a given volatility of qE. As the asymmetry of shocks should disappear in EMU (qF. and qG by definition will have the same volatility), this removal of intra-European Speculative shocks leads to a lower volatility in the exchange rate of each European country in EMU, while the volatility of the average exchange rate remains unchanged.

More generally, an increase in the real effective volatility of the dollar does not necessarily apply to the deutsche mark-dollar and French franc-dollar real exchange rates. Under a floating rate regime, asymmetric shocks in Europe have an impact on the two bilateral dollar exchange rates without affecting the effective exchange rate of the dollar, but this effect vanishes in a monetary union. Depending on the relative size of symmetric versus antisymmetric shocks in Europe, the bilateral euro-dollar real exchange rate could be either more volatile or less volatile than the deutsche mark-dollar and French franc-dollar real exchange rates under a floating rates regime. This is a matter that could only be decided upon empirically.

Behavior Under Fixed Exchange Rates: The ERM Case

The response of the dollar exchange rate when European monetary policies are coordinated through the operation of an asymmetric fixed exchange rate system can be computed in the same fashion as for EMU or floating exchange rates. The derivation of equation (11) leads to the following trade-off for Germany:

As the Bundesbank knows that France will follow a fixed exchange rate policy, it internalizes the externality and behaves exactly in the same way as the European central bank as regards the price/exchange rate trade-off. The only difference is that the Bundesbank does not react in the same way to shocks occurring in France and in Germany. This is clear from the modified (EE) relation:

where HE(Ф)and ΔE are the same as in equation (EE), and ΔD is a combination of “difference” shocks.

Taking the behavior of the Federal Reserve (UU) into account, the dollar real exchange rate can be expressed as a function of shocks:

where ΔE+ΔD+ΓU.

Equation (23) indicates that the reaction of the dollar REER, qUv, to common shocks (ΔD = 0) is the same as in the EMU regime. This is a well-known result from the theory of policy coordination: a fixed exchange rate system behaves in the same way as a monetary union as long as shocks are symmetric (Canzoneri and Henderson, 1991).

The difference arises with asymmetric shocks. In a floating exchange rate or EMU regime, asymmetric shocks do not have an impact on the (nominal or real) exchange rate of the U.S. dollar because shocks to French and German variables offset. However, they do have an impact in an ERM regime because the Bundesbank, whose loss function only includes German variables, reacts asymmetrically to shocks affecting the German and the French economy. Hence, under an ERM regime, asymmetric shocks in Europe lead to real exchange rate fluctuations between the United States and Europe that would vanish in either an EMU or a floating rate regime.

How important can this effect be? It should be expected that as asymmetric shocks tend to be rare among core European countries, they do not account for a large part of the volatility of the dollar-deutsche mark exchange rate, and that moving from the ERM to EMU should not reduce it significantly. But here again, the relevance of this effect is a matter for empirical investigation.

The outcome is similar for correlated speculative shocks: in the ERM regime, a speculative shock to the deutsche mark-U.S. dollar exchange rate that makes the deutsche mark appreciate against both the dollar and the French franc leads to less loosening from the Bundesbank than in EMU. In the ERM regime, the Bundesbank knows that the Bank of France will support part of the stabilization through an increase in its interest rate. This again makes the dollar more volatile against European currencies in the ERM than in EMU.

Summing up, the REER of the dollar appears more volatile in EMU than in a floating regime, while the comparison with the ERM depends on the share of symmetric, asymmetric, and correlated shocks (Table 1).

Table 1.Effect of Shocks on the Real Effective Exchange Rate of the Dollar
ShocksFloatEMUERM
Common shocks
Positive demand shock vF = vG> 0+++++
Negative supply shock uF = uG>0+++++
Asymmetric shocks
Demand shock vF= −vG > 000+
Supply shock uF= −uG> 000+
Correlated speculative shock εD=−ξεG++++
Note: A plus sign indicates dollar depreciation.

Robustness

To what extent are these results robust? Two obvious limitations are (1) the choice of a specific loss function, on which the results might be dependent, and (2) the way the interactions between countries are described in the model. In this section, we address these limitations. We start by describing more precisely the behavior of European countries in the presence of symmetric shocks.

Intra-European Policy Game

To clarify the results of the previous section, it may be useful to present them in a traditional game theory framework, which explicitly shows how the interest rate of each country reacts to shocks and to the interest rate of other countries.

The reaction functions of France and Germany in a floating exchange rate environment can be derived from equation (16) and its equivalent in terms of difference variables:11

with AE=θωE+ϕ1αα, ,

Conversely, under EMU, we have

Figure 2 depicts, in the case of a shock affecting the United States or the two European countries symmetrically, both the free-float Nash equilibrium N and the cooperative EMU equilibrium E, together with the two countries' reaction functions under flexible exchange rates rF(rG) and rG(rF), and the BFBG locus of cooperative equilibria. Note that E is also the equilibrium under fixed exchange rates, with French behavior being represented by the diagonal DD.

Figure 2.Equilibrium with Fixed French Franc-Deutsche Mark Exchange Rate

The figure is similar to usual representations of two-country policy games, but with two differences. The first difference is that, although only the German and the French behavior are represented, the U.S. reaction function is explicitly taken into account. The second difference is that, in contrast to usual results, Figure 2 makes clear that when the European countries set monetary policies independently, they tend to underreact to symmetric shocks. As developed above, this behavior results from the inclusion of the real exchange rate among the policy targets. What if we adopt a more standard loss function instead?

Another Loss Function

Let us now replace the loss function L = p2q2 by the more conventional function A = z2 + βy2 (we drop the country subscripts for the sake of simplification). Using exactly the same method as in the previous section, we derive from the first-order condition a relation between z and y:

where

and

After some algebra, we get

and

We therefore have

Forming a monetary union reduces the percieved effectiveness of momentary policy regarding both consumer prices

and output

because the reduced openness of the euro zone negatively affects the significance of the exchange rate channel for the transmission of monetary policy impulses. But this reduction effect is stronger for consumer prices. This is because consumer prices are affected by the exchange rate both directly (through its effect on the price of imported goods) and indirectly (through its effect on producer prices), while output (and producer prices) are only affected indirectly. This difference, which does not depend on a particular assumption about price elasticities, is crucial to our results.12

Combining equation (26) with equations (7) and (12) gives

Hence,

Substituting into equation (3), we get the following relation between q and r:

For the United States, equation (28) immediately gives a relation between qU and rU that is equivalent to equation (UU) and is also upward sloping:

with

and

Equation (UU′), which represents its reaction, means that the U.S. central bank reacts by raising interest rates to a depreciation of the currency that increases both prices and output.

To get the equivalent relation for Europe, we have to substitute the real interest rate parity condition (10) into equation (28). After some tedious calculation we obtain

where

and

which is formally equivalent to equation (EE), and also downward-sloping. For U.S. shocks as well as demand and speculative European shocks, the resolution is formally similar to that of the (UU, EE) system. Since GEE) is increasing in ΨE and

shocks have a stronger impact on the real effective exchange rate of the dollar when Europe is in a monetary union. This is the same result as with the previous loss function. For European supply shocks, however, things are different because ΩF depends on ΨE. Considering European supply shocks only, we get the following system:

with

the solution of which is

qU is decreasing in ΨE because GEE)BEE) is. We therefore find that European supply shocks have a lesser impact on the real exchange rate of the dollar when Europe forms a monetary union, while demand shocks have a larger impact in EMU.

The intuition behind this result comes from the fact that a demand shock hits both output and prices in the same direction, while a supply shock hits output and prices in opposite directions. Take, for example, an adverse supply shock that has both an inflationary and a contractionary impact. The policy reaction tends to be muted, as authorities agree to accommodate part of the inflationary consequences of the shock in order not to add to its contractionary effects. As Europe forms a monetary union, with the effect that monetary policy loses more of its perceived effectiveness as an instrument to control consumer prices than to control output, the central bank tends to react less aggressively to the inflationary effects of the supply shock. This weaker tightening results in a less pronounced appreciation of the currency.

In the case of a positive demand shock, the monetary authorities increase the interest rates in order to stabilize both output and prices. As consumer prices are more sensitive to exchange rate changes than output, minimization of the loss function results in a limited increase in interest rates, because authorities keep a balance between the deviations from their two policy targets. In the absence of cooperation, this factor limits the extent of interest rate increases and of the resulting exchange rate appreciation. Moving to EMU results in an evening-out of the differences between output and prices as regards the effects of monetary policy. Hence, the monetary authorities accept a larger exchange rate appreciation in order to stabilize both prices and output.

Summing up, we find that as long as demand shocks prevail, or in the presence of U.S. supply shocks, the previous results remain when social welfare is measured in terms of consumer price inflation and output rather than in terms of producer price inflation and the real exchange rate: monetary union in Europe will tend to increase the real effective volatility of the dollar (Table 2). The significant exception is European supply shocks, which tend to be less consequential for the dollar REER when Europe is in a monetary union regime. Which of the effects will on average dominate can only be decided upon on the basis of a quantitative assessment of the size and the probability of the various shocks.

Table 2.Effect of Shocks on the Real Effective Exchange Rate of the Dollar, with the A Loss Function
ShocksFloatEMUERM
Common shocks
Positive demand shock vF = vG> 0+ ++ + ++ + +
Negative supply shock uF = uG> 0+ +++
Asymmetric shocks
Demand shock vF= −vG>000+
Supply shock uF= −uG>000+
Correlated speculative shock εD=−ξεG++++
Note: A plus sign indicates dollar depreciation.

Alternative Spillover Effects

Our representation of the three economies is rather standard and fits the usual macroeconometric models used for forecasting. However, a number of assumptions can be disputed.

A first difference from simplified policy coordination models results from the explicit introduction of two spillover effects, through outputs and prices. In the game-theoretical framework, there is frequently only one exchange rate externality, which is removed under EMU. Thus, cooperation unambiguously leads to smaller reactions of monetary policies to shocks, and thus to a smaller exchange rate volatility. In our model, there are two uneven exchange rate externalities, which are both internalized under EMU. This is why we obtain a different result.

The most important simplification in our model is the equal treatment of the three economies except for openness—for instance, the price elasticity of external trade is assumed equal for intra-European trade and for trade with the United States. This simplification is removed in Cohen's paper in this volume, where the European market is assumed to be more closely integrated than the world market, which results in a higher price elasticity for intra-European trade. In the EMU regime, European countries internalize both a price externality and an output externality, with the former being relatively higher. Thus, monetary union leads to reducing the volatility of the real exchange rate in the presence of demand shocks and to increasing it in the presence of supply shocks. This is exactly the opposite of our result with the (price, output) loss function.

The reason for this difference is twofold. First, Cohen takes output prices and output as arguments of the loss function, which would in our model lead EMU to have neutral effects on exchange rate volatility (because output and output prices move in tandem). Second, Cohen's additional assumption as regards intra-European trade results in the elimination of intra-European externality having more impact on output than on prices.

Other models hinge on further simplifications. For instance, Martin (1997) assumes that there are only supply shocks, and that all interactions between countries arise from the supply side only. He also assumes that purchasing power parity holds, so the real exchange rate is constant by definition. In his model, monetary union removes the supply-side externality between European countries, which has the effect that monetary policy becomes less effective for output stabilization. The smaller variance in monetary policy translates into less variance in prices and nominal exchange rates. In our model, the impact of monetary union on nominal exchange rate volatility is ambiguous (whereas the impact on inflation is not, as price volatility is lower in EMU), but we consider that real exchange rate volatility is more consequential.

Finally, all analytical models involve highly simplified dynamic interactions. In our model, the second period is the long run, so no further inflation is expected, and the real interest rate equals the nominal one. This simplification is removed in simulations that are based on a dynamic model.

Quantitative Evaluations

The above developments only provide qualitative results. In this section, we provide a rough evaluation of the associated quantitative effects. We first give a numerical evaluation of the multipliers from the theoretical model and then we present simulations with a simple dynamic model.

The first approach is to start from equation (19), which gives the theoretical short-run impact of shocks on the REER of the dollar when policy preferences are represented by the loss function L, and to evaluate the impact of moving from a floating exchange rate regime to monetary union in Europe. We take the following values for the parameters:

For a, the elasticity of output to labor input, this corresponds to usual orders of magnitude for a Cobb-Douglas production function. The value for η the openness ratio, is close to the empirical magnitudes for the United States and Europe. For ө, the output/real exchange rate elasticity, and δ, the sensitivity of demand to the real interest rate, the values are usual orders of magnitude corresponding to a wide range of macroeconometric models (see, e.g., Bryant, Helliwell, and Hooper, 1988; or Mitchell and others, 1995).

We can then compute

as a function of β the coefficient of the real exchange rate objective in the European loss function.13 It is apparent that the impact of shocks is larger when Europe is in a monetary union, but the difference does not appear to be large. For example, for β = 0.01 (which means that a 10 percent deviation in the real exchange rate has an equal weight to a 1 percent increase in prices), we obtain

That is, moving to EMU would increase the volatility of the real effective exchange rate of the dollar by less than 3.6 percent.

Figure 3 indicates that the difference is increasing in β, the weight of the exchange rate objective in the loss function, but remains low for values of β that correspond to present behavior in Europe. For example, with β = 0.04 (which means that a 4 percent REER deviation and a 1 percent increase in prices have an equal impact on social welfare), moving to EMU would increase the REER volatility of the dollar by 7 percent. The intuition behind this result is obvious: EMU will only make a difference if European countries attach some weight to real exchange rate stabilization. If central banks only focus on domestic inflation, there is no reason why moving to a monetary union would have a significant impact on exchange rate stability. Obviously, one could argue that moving to monetary union would lead to a reduced value of β because the provisions of the Maastricht Treaty are conducive to reducing the weight of the exchange rate as a policy objective. This would be an additional reason for increased REER volatility.

Figure 3.Ratio of the U.S. REER Elasticity to Shocks, EMU/Float

The increase in REER volatility resulting from EMU also depends on the value of δ, the sensitivity of domestic demand to changes in the real interest rate. For δ = 0, the two regimes would be equivalent. As there is uncertainty regarding the actual value of δ, we plot in Figure 3 the increased volatility of the REER of the dollar as a function of β for two values of δ (0.2 and 0.5). It illustrates that the difference between the two regimes remains low for realistic values of β and δ.

Numerical evaluations can be misleading because of the highly simplified character of the model. We therefore also provide the results of illustrative simulations with a three-country model that resembles the theoretical model but includes dynamic wage and price equations.

The main characteristics of the model are as follows. Wage inflation depends on past wage inflation, consumer price inflation (i.e., a weighted average of GDP deflator and import price inflation), and excess demand, as with a standard augmented Phillips curve. Producer prices are determined by a markup on wages. Excess demand reacts negatively to the ex ante real interest rate (calculated with model-consistent expectations of producer price inflation), and positively to the real effective exchange rate. Identities define the real effective exchange rate as an average of bilateral real exchange rates. Finally, nominal bilateral exchange rates result from uncovered interest rate parity (with one-quarter-ahead model-consistent exchange rate expectations). Although highly simplified, this model captures familiar features of empirical macro-econometric models, from which the values of the parameters are taken. The three countries have similar characteristics except for two well-known stylized facts. First, we introduce a stronger nominal rigidity in the United States, where the average delay for wage inflation adjustments is four quarters instead of two in Europe. Second, the long-term elasticity of final demand to the real interest rate is twice as high in Germany as in France and the United States.

Policy regimes are represented by interest rate reaction functions for the three countries. We consider two regimes in Europe: a floating exchange rate regime and EMU, and two policy rules represented by linear reaction functions (Table 3).

Table 3.Policy Rules Used in the Simulations
Consumer Price Inflation z^

and Excess Demand y
Producer Price Inflation p^

and REERq
United StatesiU=32z^U+12yUiU=32p^U+120qU
Germany with floatiG=54z^G+12yGiG=32p^G+110qG
France with floatiF=54z^F+12yFiF=32p^F+110qF
ECB with EMUiE=32z^E+12yEiE=32p^E+120qE

The policy rules correspond to the loss functions used in the analytical model and involve the same target variables, but the weights attached to the objectives are not formally derived from a loss function. In the first column of Table 3 the monetary policy authority sets its instrument in reaction to deviations from consumer price inflation and to output gap targets, as in the loss function A.14 The weights presented are John Taylor's original coefficients, that is, the real interest rate reacts equally in the United States and in EMU, which have the same openness ratio. When Germany and France are in a floating regime, the weight of consumer price inflation is reduced to account for the higher effectiveness of monetary policy on prices relative to output, consistent with the theoretical model. In the second column, we use the target variables of the loss functions L, giving to the REER a weight equal to half the openness ratio.

The results of the simulations are presented in Figure 4 in the case of a temporary symmetric demand shock in Europe (a rise of demand by 1 percent of GDP lasting four quarters). As expected, the response of the U.S. REER is more pronounced with EMU in Europe than with floating exchange rates, and this is true for both policy rules. This also applies to the deutsche mark-dollar nominal exchange rate. These results hold for a wage shock also, and are robust with respect to reasonable changes in the value of the parameters of the equations.15

Figure 4.Response of U.S. REER and Deutsche Mark-Dollar Exchange Rate to a Symmetric Demand Shock in Europe1

1 Excess demand is increased by I percent over four quarters.

Conclusions

It has been repeatedly suggested by European policymakers and politicians that one of the significant benefits of EMU would be its contribution to greater exchange rate stability between the dollar and European currencies. In this paper, we have investigated whether a simple three-country model could substantiate such a claim.

The short answer is that it does not. On the contrary, there are grounds to consider that in comparison to a floating rate regime in Europe, EMU should increase real exchange rate instability between Europe and its major trading partners, such as the United States or Japan. This result holds for all categories of shocks if one assumes that in addition to their inflation objective, monetary authorities have an explicit real effective exchange rate target. It holds for all but symmetric European supply shocks if it is assumed, rather, that they have an output target.

Three caveats should be kept in mind. First, these results concern the real effective exchange rate of the dollar (or of the euro zone), and not the bilateral real exchange rates vis-à-vis the dollar of the individual European countries. As asymmetric shocks affecting individual European countries offset at the level of the euro zone, EMU could simultaneously increase the real instability of the euro zone's dollar exchange rate and reduce those of the member countries (however, the results are unambiguous for the dollar's REER). The second caveat relates to the baseline situation to which EMU should be compared. We have taken as a baseline a floating exchange rate regime, because we doubt that the ERM would survive if EMU were forsaken. In comparison to an ERM baseline, the effect of a move to EMU would be more ambiguous. Third, the model we have used for deriving these results is highly simplified as, for example, France and Germany are considered identical countries and the representation of domestic markets and international linkages is skeletal. This especially applies to the exchange rate, which is derived from an uncovered interest rate parity condition.

What degree of confidence can we place in such a highly simplified model? We tend to believe that the result we come up with has some relevance. Furthermore, the institutional set-up of the Maastricht Treaty does not weaken this result, as Article 109 explicitly subordinates the pursuit of exchange rate aims to the overriding objective of price stability.

If this proves to be true, monetary union in Europe would at the same time reduce exchange rate instability within Europe and increase it between Europe and the other major monetary regions. As is already the case for the United States (Bergsten and Henning, 1996), European countries would thus have a high degree of real exchange rate stability within Europe, and real exchange rate instability vis-à-vis the dollar and the yen. This could not be inconsequential for trade and investment relations within Europe and across the Atlantic.

The empirical significance of this effect should, however, not be exaggerated. The numerical evaluations provided in this paper, which at this stage of research should be taken as preliminary, suggest that the increase in real exchange rate instability should remain moderate. This is because, as European central banks tend to give priority to price stability rather than to stabilizing the real exchange rate, moving to EMU will not fundamentally alter Europe's policy objectives.

Appendix I Model Equations

The model is written in log-linear form, except for interest rates, with lowercase variables representing deviations from the zero-disturbance equilibrium, and i standing for the country (i = F, G, U).

Goods Market Equilibrium

Demand in each country d increases with the real effective exchange rate q and decreases with the real interest rate r. It is affected by an exogenous demand shock v, which has zero mean. The impact of the real exchange rate is proportional to the degree of openness ω, which is 2η for France and Germany, and η for the United States.

Aggregate supply y is derived from a standard Cobb-Douglas production function under the assumption that the capital stock remains fixed both in the short run and in the long run. Labor, n, is therefore the only production factor. Supply is affected by an adverse exogenous supply disturbance, u, which also has a zero mean.

Goods market equilibrium holds in the short run and in the long run, which implies that in the short run output and employment are demand determined, while they are supply determined in the long run:

Labor Market Equilibrium

As firms maximize profits, the marginal productivity of labor is equal to the product wage w—p (where w is the nominal wage and p is the price of domestic production):

Labor supply is fixed. In the long run, real wages clear the labor market, but in the short run, nominal wages remain at the level set before shocks are observed. As the expected value of supply and demand shocks is zero, the corresponding conditions are

Capital Market

The real interest rate r is defined as the nominal interest rate i less expected inflation:

where E(xLT) represents the expected long run value of variable x. We make the usual rational expectations assumption, that is:

Long-run equilibrium values are supposed to be perfectly anticipated by the agents after the shocks have occurred at the beginning of the short-run period.

Uncovered interest rate parity holds. If sF is the nominal dollar-franc exchange rate (1 U.S. dollar = sF French francs) and sG, the dollar-deutsche mark exchange rate,

where εF and εG are speculative shocks to the exchange rate equation, which can be seen as representing time-varying risk premiums. We introduce these shocks because we want to present the frequently held view that floating exchange rates are responsible for unproductive volatility.

Finally, we define the effective real exchange rate q, which depends on trade patterns, and the consumer price index z, which depends on the openness ratio:

There are altogether 29 variables, and 26 equations for either the short-run or the long-run equilibrium. In order to close the model, we have to determine the interest rate, which is done by assuming that monetary policy aims at minimizing a macroeconomic loss function L(X), where X represents a set of macroeconomic variables:

List of Variables

  • dF,dG,dU Aggregate demand

  • yF,yG,yU Aggregate supply

  • nF,nG,nU Employment

  • wF,wG,wU Wage rate

  • pF,pG,pU Producer prices

  • zF,zG,zU Consumer prices

  • iF,iG,iU Nominal interest rate

  • rF,rG,rU Real interest rate

  • sF,sG Nominal dollar exchange rate

  • qF,qG,qU Real effective exchange rate

Transforming the Model

The model can be made much more tractable by exploiting the symmetry between France and Germany through the usual Aoki transformation. For each variable x, we therefore define the “sum” European variable as

and the “difference” variable as

The model can thus be rewritten with variables xE and xD replacing xF and xG. Obviously, xF =xE+ xD and xG=xExD, which means that country variables can easily be calculated from aggregate sum and difference variables. This transformation allows equations (Al) to (A6) and equation (A9) to be rewritten with i = E, D, U. Only equations (A7) and (A8) are modified:

qE is the average of the effective real exchange rates of France and Germany, which differs from the effective real exchange rate of Europe, −qu

APPENDIX II Long-Term Solution of the Model

Goods market equilibrium conditions in the long run are

where uLT,vLT represent the long-run values of the shocks (we do not necessarily assume that supply and demand shocks are temporary). Real exchange rate stationarity implies that there is only one world real interest rate, which ensures goods market equilibrium:

Equations (A13) and (A14) give the long run real interest rate and the long-run real effective exchange rate of the dollar:

Shocks affecting the United States and Europe symmetrically have an impact on the world real interest rate, while asymmetric shocks have an impact on the real exchange rate of the dollar. Finally, the French franc-deutsche mark real exchange rate depends on asymmetric shocks in Europe:

The authors are grateful to Karim Gebara for efficient research assistance, and to Michel Aglietta, Ralph Bryant, Philippe Martin, Paul Masson, and Bart Turtelboom for discussions on a previous version of this paper. We also wish to thank Marin Bénassy-Quéré for his cooperation.

BIS (1996) provides evidence of the effects of fluctuations in the dollar-deutsche mark exchange rate on intra-European exchange rates.

Realignments and fluctuation bands are ignored.

Canzoneri and Henderson (1991) use a similar model to study policy coordination in the world economy.

An example may help to clarify the reason for this factor. Suppose French price rises by 1 percentage point. The French real effective exchange rate appreciates by 1 percent, while the German one depreciates by 0.5 percent. Thus, the half-difference qD decreases by 0.75 percent, while the half-difference of prices, pD, increases by 0.5 percent. Hence, the 3/2 factor.

The price variable in the loss function is the producer price. Using the consumer price instead does not qualitatively affect the results. The loss function is normalized so that the targets are set to zero.

Masson and Symansky (1992) challenge this approach. They claim that as monetary policy in the euro zone will be based on aggregate variables, the monetary union's loss function should be directly expressed in terms of aggregate variables. However, this distinction is only relevant if the loss function is used for measuring the welfare effects of alternative exchange rate regimes. It is inconsequential if it is used for deriving policy rules, since the first-order condition remains unchanged.

This was already apparent in equation (10). However, the result we have obtained takes into account both changes in the relative weighting of the polity objectives and changes in the transmission channels resulting from the reduced openness of the euro zone.

With δ = 0, that is, no direct domestic demand impact of monetary policy, the two effects would exactly offset.

This is because |dpEdrE|<|dpDdrD|.

In the standard, game-theoretical framework, failure to coordinate frequently results in a tighter monetary policy (and thereby a stronger appreciation vis-à-vis third countries) in reaction to positive demand shocks, because each country thinks it can stabilize its economy through appreciating its exchange rate vis-à-vis its partner. This is not the case here because the monetary authorities target both inflation and the real exchange rate. In the absence of coordination, they overestimate the impact of their monetary policy on the real exchange rate. Thus, the monetary policy underreacts to shocks. The robustness of our result is further discussed in the section on robustness.

With pF = pE+pD,pG = pEpDand the same for qFand qG.

With output prices instead of consumer prices, the reduction in the exchange rate channel in EMU is the same for prices and for output, and EMU no longer modifies the dollar volatility. Nevertheless, the consumer price index seems more representative of the actual monetary policies in Europe (the Maastricht criterion refers to consumer prices).

We take β = 0 for the United States, that is, we assume that the U.S. authorities have no exchange rate objective.

The European Commission (1990) uses a weight of 0.4 for the excess demand objective of European countries.

Some changes of the parameters lead to unstable dynamics and divergence. We exclude these. The range of parameters within which we have simulated the dynamic model is available from the authors on request.

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