Interpreting the ERM Crisis: Country-Specific and Systemic Issues

I nt er pr et ing t he ER M Cr isis: Count r y-Sp eci…c and Sy st emic I ssues Willem H. Buiter Cambridge University Giancarlo M. Corsetti University of Rome III Paolo A. Pesenti Princeton University January 1996 Revised May 1996 C ont ent s 1 I nt r oduct ion 3 2 A n over v iew of t he anal ysis 2.1 Theory... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 ... and policy . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 7 3 A Cent er -Per ipher y model of cur r ency cr ises 3.1 An int roduct ion t o t he model . . . . . . . . . 3.2 The st ruct ure of t he economy . . . . . . . . . 3.3 Social welfare and commitment technology . . 3.4 Int ernat ional policy spillovers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 . 9 . 11 . 14 . 16 4 N on-cooper at i ve equil ibr ium : t he r ole of dom est ic cr edibilit y 17 4.1 Charact erizing the optimal monetary policy: t he shadow devaluation rat e . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Market expect at ions and wage sett ing . . . . . . . . . . . . . . 20 5 Cur r ent ex planat ions of t he ER M cr isis: an anal yt ical r ev iew 5.1 Shifts in expectat ions and self-ful…lling equilibria . . . . . . . 5.2 Three interpretat ions of t he crisis based on fundament als . . . 5.2.1 German uni… cation shock: the role of learning and expectat ions updating . . . . . . . . . . . . . . . . . . . . 5.2.2 The perceived change in policy-makers’ commit ment t o exchange rate st ability . . . . . . . . . . . . . . . . . 5.2.3 Inherent weakness of disin‡at ion policies based on an ext ernal nominal anchor . . . . . . . . . . . . . . . . . 21 22 24 6 N on-cooper at i ve equil ibr i um : t he syst em ic dim ensi on 6.1 The missing element : modelling t he internat ional policy game 6.2 Monetary st rat egies in t he Center and t he Periphery . . . . . 6.3 The opt imal number and size of exchange rat e realignment s . 6.4 Asymmet ric exchange rat e policies, symmet ric welfare levels . 28 28 30 31 32 7 Cooper at ive equilibr ium and nat ional hor i zont al equi t y 7.1 Welfare implicat ions of t he internat ional monetary spillovers . 7.2 Politically feasible cooperat ion . . . . . . . . . . . . . . . . . . 7.3 Optimal policies and equilibrium under symmet ric cooperat ion 33 33 34 36 1 24 26 27 8 Cur r ency cr ises as syst em ic failur es 37 8.1 Cooperat ive and Nash equilibria compared . . . . . . . . . . . 37 8.2 Policy t ensions, market responses, and exchange rat e crises . . 40 9 I nt er pr et ing t he ER M cr isis in a Cent er -Per ipher y model 42 9.1 The realignment of the lira as a coordinat ion shock . . . . . . 43 9.2 Policy opt ions in Europe and scenarios for the 92-93 crisis . . 45 10 T he r oad ahead 47 A ppendi x 50 2 1 I nt r oduct ion Since 1979, t he Exchange Rate Mechanism (ERM) has represented the cornerst one of monetary policy strategies in Europe, and t he most ambitious experiment in int ernational monetary and exchange rat e cooperation of t he post -Bret t on Woods era. The nat ure of t he ERM has not remained unchanged over time. Originally intended as a syst em of …xed but (frequent ly) adjustable rat es wit h limit ed int ernat ional capit al mobility, it was only in t he second half of t he 1980s t hat t he ERM became t he “ hard” ERM , a regime of stable and narrow currency bands defended by coordinat ed intervent ion among cent ral banks, virt ually without exchange cont rols. Until the fall of 1992, the satisfactory performance of t he new ERM was a key fact or underlying the general appeal of a furt her t ransformation of t he syst em t oward complet e monetary harmonizat ion, and eventual uni…cat ion. Starting in early 1992, however, a sequence of adverse developments of increasing severity undermined the whole process towards European Monet ary Union (EMU). The crisis and revamping of t he ERM between 1992 and 1993 represent s t he key event in t he recent monetary hist ory of Europe — one whose origins, consequences and implications are still at t he core of t he current academic and political debat e, bot h in Europe and elsewhere. The lit erature has provided several complementary interpretat ions of t he ERM crisis. Possibly t he most popular one is based on t he policy con‡ict st emming from the internal reuni…cat ion process in Germany and the policy mix adopted in t hat country during the early 1990s. Other explanat ions of t he collapse in terms of t he behavior of fundament als focus on persistent divergent performances of nat ional price or unit cost levels — presumably re‡ecting divergent national monet ary and …scal policies during t he “ hard” ERM years —; t he liberalizat ion of internat ional …nancial capital movements under t he Single Act ; and t he perceived change in national policy-makers’ commitment to …xed exchange rat es after the results of the …rst Danish referendum in June 1992. Finally, the role of self-ful…lling speculative att acks, t riggered by sudden, and essentially arbitrary, expectat ions shifts in t he …nancial markets, hasbeen emphasized in recent interpretations of t hecollapse of the ERM. In the present stage of internat ional debate on EMU, when European policy makers are about to give shape to the fut ure by (one hopes) drawing lessons from t he experience of the past, an incorrect or even just incomplete int erpret at ion of t he 1992-93 events may be socially, and polit ically, cost ly. 3 Do the existing theories, individually or collect ively, o¤er a reasonablepict ure of the ERM crisis and point t o a su¢ cient ly comprehensive list of factors to be t aken into account? In our view, most int erpret at ions of t he 1992-93 event s miss the following crucial element : t he ERM crisis has been t he crisis of an exchange rate system, rather t han the collapse of a collect ion of unilat eral pegs individually pursued by a number of countries. Theexisting int erpret iveschemestypically focus on t headjust ment problem of a represent at ive count ry, facing an exogenous shock that undermines t he stability of t he current exchange rate parity against t he cent er count ry. The t hesis we develop in t his cont ribut ion is t hat t he conclusions reached within such framework may be incomplet e or misleading, since they ignore t he key role played by struct ural policy spillovers among European count ries, and overlook t he e¤ect s of coordinat ion (or lack t hereof) of monet ary and exchange rate policies among the count ries making up t he periphery of the syst em. In contrast to an approach that focuses exclusively on count ry-speci…c issues, we argue that a systemic view is ultimat ely able t o unravel more coherently, and more convincingly, the “ puzzles” of the ERM crisis. The paper is struct ured in t hree part s. The …rst part (Sect ion 2) presents an overview of the analysis, summarizing our main result s. T he second part (Sect ions 3-5) is devot ed t o an analyt ical review of the current t heoret ical lit erature, focusing on t he role of domest ic credibility in a unilat eral peg framework. The int ernat ional dimensions of t he equilibria, and their implications for the European event s, are explored in t he third part (Sections 6-9). Section 3 provides a simple analyt ical framework, able to encompass — both t echnically and int ellectually — t he recent literat ure on currency crises, while developing it by bringing out t he decisive role of t he st rategic interactions among nat ional policy makers in a mult i-country monetary and exchange rate game. Section 4 characterizes t he domest ic equilibrium on a t heoretical level, while the following section uses our results to review several int erpret at ions of t he ERM crisis. Sections 6 t hrough 9 develop t he analysis of an exchange rate system crisis as an internat ional policy game. Sect ion 6 describes t he internat ional dimension of t he non-cooperative (Nash) equilibrium. The alternat ive to Nash is cooperat ion, rest ricted in a way that, in our view, captures t he relevant inst it utional and historical feat ures of t he ERM and is especially suit able t o describe the int ernat ional policy con‡ict at t he t ime of the crisis (Sect ion 7). Section 8 compares cooperative and Nash equilibria and provides an assessment of t he role of policy coordinat ion in a currency crisis. Section 9 int erpret s the 1992-93 crisis in t he framework of our Cent er-Periphery model. 4 A …nal sect ion recapit ulatest hemain issuesraised in t hepaper, drawing some lessons for the current debat e on the monetary fut ure of Europe. 2 2.1 A n over view of t he analysis T heor y... I t is helpful t o anticipate and synt hesize in an opening sect ion t he main features of our theoretical framework. We model t he ERM as a syst em consist ing of a set of Periphery countries t hat peg t heir currencies against t he currency of t he price-st abilizing Center count ry. Our construction conforms t o the ‘consensus’ view (at t he t ime of the crisis) of the ERM as a disin‡at ion mechanism, where t he exchange rat e against t he D-mark is the nominal anchor for Periphery count ries. In our model, t he Cent er has an uncompromising at titude t owards its own price stability goal, and t he policy-makers’ objective funct ion exhibits no in‡at ionary bias. These charact erist ics qualify the Center as t he nat ural candidate t o receive the mandate of guarant eeing price st abilit y (but not necessarily monet ary st ability) in t he system. Conversely, t he in‡at ionprone Periphery count ries consider …xed exchange rates as an int ermediate t arget toward price st ability. However, policy-makers’ commitment in t he Periphery is only imperfect ly credible, and market participants perceive t he abandonment of t he peg asa possiblepolicy option in the presence of ext ernal shocks. Wit h the German uni…cation scenario in mind, we assume that the source of t ension in the syst em is a large, asymmet ric dist urbance in the form of a demand (e.g., ‘IS’) shock in the Cent er, generat ing pressures for an e¤ective real appreciation of the currency of this count ry. In such a sit uat ion, t he Periphery as a wholewould bene…t from a monetary expansion by t he Center, which would absorb at least part of t he domest ic demand surge and lower int erest rat es in t he syst em. However, the result ing level of internal in‡at ion would be unacceptable t o t he aut horit ies in the Cent er. The Cent er would of course bene…t from a realignment in the syst em, t hat would o¤set t he original demand shock, but a realignment would entail high reputat ion and credibility costs for t he policy makers in t he Periphery countries. Even t hough t he monet ary aut horit ies of the Cent er are unwilling to jeopardize their int ernal nominal targets by cooperating wit h t he Periphery, Periphery count ries have a welfare incent ive t o coordinate t heir monet ary policies among themselves, int ernalizing their reciprocal spillovers (t hat is, the impact of domest ic policies on ot her Periphery count ries’ in‡at ion 5 and employment ). Coordination, however, requires an e¤ect ive enforcement mechanism (t o prevent unilateral deviations from t he agreement ) t hat may not be available t o t he Periphery. Also, t here may be lack of consensus and agreement on how the costs and bene…ts from Periphery-widepolicies— such as a generalized exchange rate realignment against the Center — should be dist ributed among t he individual Periphery count ries. In addressing t he issue of feasibility of int ra-Periphery cooperat ion, we argue t hat , based on t he European experience, special weight should be given t o a principle of national horizontal equity. The principle st ates that nat ional aut horit ies accept t o cooperate only to t he extent that no count ry would excessively bene…t or lose from t he common policy more — in relative t erms — than t he ot hers. A nat ional horizont al equity constraint thus implies t hat no country is willing either to bear a disproport ionat e share of t he cost s of a coordinated realignment, or t o accept an unfair dist ribution of it s bene…ts, even when the corresponding exchange rat e policy would be e¢ cient for t he syst em as a whole. Of course, nat ional horizontal equity is, in principle, consistent with a very large set of Community-wide policy decisions — and realignment schemes, — provided count ries can use appropriate side-payment s t o compensat e t he losers (if only in relat ive t erms) from such decisions. However, internat ional t ransfers contingent on asymmet ric realignment s with selective devaluations t end t o be polit ically quest ionable, and di¢ cult t o implement. It does not come as a surprise that, in t he hist ory of the ERM, t here is no evidence t hat t hey ever represent ed an institut ional reality. Thus, in our model, while post ulating nat ional horizont al equity, we also rule out side-payment s among count ries. We consider two scenarios charact erizing the possible policy responses of t he Periphery countries t o t he Cent er demand shock. In t he …rst scenario, Periphery count ries coordinat e t heir exchange rat e policies – subject t o a nat ional horizontal equity constraint wit hout side-payments – so as t o maximize a common social welfare function. In the alt ernat ive scenario, t here is no cooperat ion, and each count ry unilat erally maximizes it s own objective function. Our model shows t hat , given a realist ic hypothesis about the sign of int ernational policy spillovers (expansionary monetary policy in any Periphery count ry cont ribut es t o lower real int erest rat es in the syst em as a whole, and causes a real appreciat ion of the currencies of all ot her Periphery count ries), t he opt imal coordinated response by t he Periphery is a set of small devaluations by a large number of count ries. If, inst ead, the Periphery count ries do not coordinat e t heir monet ary and exchange rat e policies against t he Center, we will observe large devaluations by a small number of countries. In t he 6 aggregat e, coordinat ed exchange rate policy is generally more expansionary for t he system as a whole t han uncoordinat ed policy actions. Theint uit ion underlying t heseresult s isrooted in theinternat ional spillovers of domestic monet ary policy. The devaluat ion of one count ry (say, It aly) affects t he ot her Periphery countries through two channels. First , a fall in t he price of import s from It aly decreases CPI in‡ation in the rest of t he syst em. Second, by devaluing, Italy cont ributes t o a loosening of t he st ance of ERM-wide monet ary policy, decreasing t he interest rat e in real terms and t herefore boost ing aggregate demand and employment in t he syst em. In t he presence of such spillovers, if a coordinat ed policy response requires a realignment of t he Periphery as a whole vis-à-vis t he Cent er, t he magnit ude of t he realignment will be increasing in t he magnit ude of t he ext ernality: wit h posit ive ext ernalit ies, monetary cooperat ion calls for “ doing more” as regards exchange rate policy. From the vantage point of each single Periphery count ry, however, “ doing more” does not t ranslate int o a large devaluation of it s currency against t he Cent er. In fact , because of t he nat ional horizontal equity constraint (t he expression of t he requirement of polit ical fairness in t he Periphery), t he coordinated response would likely consist of a realignment scheme including many currencies. Given t he st rong impact t hat such a joint devaluat ion has on int erest rat es, t he individual devaluat ion rat e need not be high for domestic stabilizat ion purposes. Conversely, in a scenario without cooperation, provided t hat some count ries devalue and t herefore lower the real interest rates in t he system, some ot her count ries may avoid a realignment alt oget her. In equilibrium, t he average monet ary st ance is less expansionary t han in t he coordinat ed scenario, because the subset of the devaluing countries has only a limit ed impact on t he syst em-wide equilibrium real int erest rate. Nonet heless, for t his very reason, if a country abandons t he peg its individual devaluat ion rate turns out t o be “ excessively” high. 2.2 ... and p ol icy W hat is the cont ribut ion of a syst emic model of currency crises t o t he underst anding of t he 1992-93 events? Consider again t he explanat ion st ressing t he role of t he German uni…cat ion shock. According to this view, t he ERM crisis st ems from t he con‡ict between a Center-country that is unwilling to bear t he in‡at ionary consequences of t he uni…cation, and t he Periphery-count ries t hat dislike the idea of a nominal realignment but are not willing t o sust ain t he costs of a de‡at ion. It is wort h pointing out that such a policy con‡ict wasapparent on several occasions, an important examplebeing t heEuropean 7 meet ing at Bath, on Sept ember 5 and 6, 1992.1 Taking t his con‡ict as a datum, our analysis picks up from where t he ot her cont ribut ions in the lit erature generally st op. By it self, in fact , t he identi…cat ion of an import ant source of tensions calling int o quest ion t he existing ERM parities does not tell us much about the likely modalit ies of adjustment of theseparities. To clarify t his point, recall that, in our analysis, t he opt imal coordinated response by the Periphery t o the aggregate demand shock in t he Center count ry is a set of small devaluat ions by a large number of Periphery countries. Indeed, during t he weekend preceding the Lira devaluat ion, Germany and Italy formulat ed a realignment scheme t hat ent ailed a generalized, small realignment of all ERM currencies against t he D-mark: t he scheme had a D-mark nominal revaluation by 3.5%, coupled wit h a 3.5% devaluat ion of t he lira – so t hat t he lira would have been devalued by 7% against the D-mark. If …nancial agents believed t hat t he Periphery count ries act ed cooperat ively, t heir expect ations would be based on t he forecasted generalized, small realignment s. Empirical evidence support s t his theoretical predict ion: alt hough the credibility of t he ERM was falling in August 1992, all indicat ors of devaluat ion expectations — such as int erest rate di¤erent ials, forward premiums, and average forecast sbased on survey dat a — wereby no means large by historical standards. In our interpretat ion, t he realignment on Sept ember 14, 1992, gave t he privat e sect or a strong signal about t he degree of policy coordination in t he syst em. In our view, it was t he devaluat ion of the lira (or, rat her, the fact t hat it was only t he lira t hat was devalued t hat day) that revealed to t he market s what kind of strategic game the Cent ral Banks were playing. What had been thought of as an internat ional monetary system, turned out to be not hing more t han a collection of individual, unilat eral pegs against t he D-mark. What are the implicat ions for the behavior of privat e market s? Once again, recall t hat restoring equilibrium wit hout coordination requires large devaluat ions by a subset of count ries. Presumably, in t he absence of cooperat ion, t he equilibrium depreciat ion of the lira should have been higher t han t he initial 7% implement ed on Sept ember 14, 1992: in fact , 7% was t he same …gure t hat had been proposed in the cont ext of a general realignment two days earlier, which would have had all countries joining Italy in devaluing t heir currencies. Also, there was a legitimate question as t o whet her ot her count ries should also have devalued in t he new non-cooperat ive equilibrium. As market part icipant s analyzed t he implicat ions of the new policy scenarios, many currencies must have appeared as potent ial candidat es t o sizable, non-cooperative devaluations. In our t heoret ical model, while t he number 8 of count ries involved in a non-cooperat ive realignment is well de…ned, which count riesdevaluecannot bedet ermined. The1992-93 waves of speculat iveat t acks in Europe, apparent ly regardless of t he performance of macroeconomic fundamentals across count ries, were t he logical outcome of such conclusions. Could have the ERM been saved by a joint devaluat ion, implement ing some scheme similar t o t he German-I talian proposal? Our model points out t he possibility that no coordinat ed realignment might have been polit ically accept able under t he nat ional horizont al equity constraint . In ot her words, it is possible that t here exist ed no common realignment scheme t hat would have compensat ed for t he common loss of ant i-in‡ationary credibility. Under t hese circumst ances, count ries could have only “ coordinat ed” on a painfully de‡ationary defense of t he exist ing parit ies. Clearly, insofar as uncoordinated behavior loosens up t he average monet ary policy in t he system (t hrough large, uncoordinated devaluations by a few Periphery count ries), it is bot h individually and collect ively rat ional to switch from (constrained) cooperation to non-cooperation. The model o¤ers an analytical key to int erpret t he evolut ion of European exchange rat es from September 1992 onward, provided we de…ne the Cent er t o includeboth Germany and ot her countries, like the Netherlands, that have long delegated t heir monet ary policies to Germany. Possibly, in t he period under considerat ion, France has acquired t he special position of belonging to t he (soft ) “ Core” of the syst em: a count ry subject t o large-scale speculative at tacks, like t he rest of t he Periphery, but not succumbing to t hem, t hanks t o many episodes of strong and e¤ect ive monet ary cooperat ion (and massive support from Germany). Out side t he “ Core” , t he exit of the lira and t he pound from t he ERM, recurrent speculat ive att acks and devaluat ions since September 1992 weret o a largeext ent there‡ection of each country’s att empt t o rest ore macroeconomic equilibrium in a new European Monetary System (EMS) su¤ering from the loss of it s systemic st ruct ure and nature. 3 3.1 A C ent er -Per ipher y model of cur r ency cr ises A n int r oduct ion t o t he model T he int erpret at ion summarized above is based on a general model of currency crises in a multi-country setup. To emphasize bot h links wit h and depart ures from the existing lit erature, we cast our analysis wit hin t he familiar framework of an internat ional monetary policy game, adopt ing its st andard conventions.2 We believe t hat t he novelty of our approach, namely a syst emic analysis highlighting the role played by internat ional spillovers 9 and st rategic policy int eractions, is more likely t o stand out when present ed against a familiar background. Not ably, in specifying our model, we adopt the view according t o which a …xed exchange rat e policy facilit at es t he process of domest ic disin‡at ion and helps st rengt hen t he reput ation of t he domest ic policy, by “ importing” credibility from t he cent er. Needless t o say, in the post-crisis lit erat ure t he idea of any e¤ect iveness of t he ERM as a ‘commit ment t echnology’ has met wit h increasing skept icism. Yet , from t he mid-Eight ies unt il the 1992-93 crisis, t he ant i-in‡at ionary discipline of an exchange rat e peg as a nominal anchor has provided the most common economic argument in favor of t he ERM.3 To t he ext ent t hat it captures the convent ional view of the ERM shared by both public and privat e agents in the mont hs preceding the crisis, such an approach provides the appropriat e setup wit h which to analyze t he formation of market expect ations, as well as t o int erpret t he unfolding of t he 1992-93 event s. In our framework, t he economy consist s of N + 1 countries, the …rst N of which represent t he Per iphery of t he syst em, while t he last is the Center . All countries in t he syst em are symmetric as regards t echnology and private sector decision rules, including t hose charact erizing labor market behavior. However, t here are crucial macroeconomic dissimilarities between Center and Periphery; speci…cally, the Center has t hree unique charact erist ics. First , it provides a nominal anchor for the syst em as a whole by target ing the level, rather t han t he rate of growth, of the price level. Second, t here is no discrepancy between the target level of out put and pot ent ial (full-employment) out put , so that no in‡at ionary bias (à-la-Kydland-Prescot t / Barro-Gordon) a¤ect s it s economy in a time-consist ent equilibrium. Third, it is assumed t hat all count ries in t he Periphery t rade real goods and services exclusively with t he Center, t hat is, int ra-Periphery t rade is negligible. No such rest rict ion is imposed on t rade in …nancial claims. At a …rst sight, the t hird assumpt ion may appear very unrealist ic; aft er all, concerns wit h the compet it ive gap within t he Periphery have been frequently raised by nat ional policy-makers and by bot h import-compet ing and exporting sect ors in Europe since t he incept ion of t he ERM, a¤ect ing t he determinat ion of Community-wide exchange rat e policies.4 However, t he assumption simply allows us to omit algebra-int ensive but inessent ial considerat ions: t he result s we would obt ain in a more complex set up would not signi…cant ly alt er t he conclusions reached within our framework. For inst ance, one of t he properties of our model is that a devaluat ion in a given Periphery count ry shift s global demand t owards t he count ry’s products and causes a real appreciation in all ot her Periphery count ries, the same qualit at ive result we would obtain in a model focusing directly on int ra-Periphery 10 compet it iveness. In contrast t o t he Cent er, in the Periphery t here is an in‡ationary bias in policy making. Due to t he presence of such a bias, Periphery count ries choose t o reduce t he scope for discret ion in monetary policy by pegging t heir exchange rat es against the currency of the Cent er. Such a policy would obviously be t ime-inconsist ent, unless reneging on t he commitment t o maint ain t he announced exchange rate peg entails a loss of ut ility for t he policy maker: t he higher t he opport unity cost of swit ching to a ‡oat , the higher t he reliability of t he commit ment t o a …xed exchange rat e regime. Our t heoret ical const ruction hinges on t he impact of global shocks originat ing in t he Center on the performance and the policies of t he Periphery count ries. Therefore, t he only source of (exogenous) uncert ainty that is explicit ly modeled is an aggregate demand shock in t he Center count ry — t he German uni…cat ion shock. The emphasis on such a source of uncertainty is mot ivat ed by the st ylized fact s preceding t he collapse of the ERM, in particular t he demand boom associat ed with German uni…cat ion. Nonet heless, our setup could be easily ext ended t o encompass currency subst it ution shocks or supply-side product ivity disturbances. 3.2 T he st r uct ur e of t he economy T he structure of t he economy closely follows t he lit erature on internat ional policy games.5 As t he main feat ures of our setup are well known, in what follows wewill exclusively focus on a semi-reduced form of t he model; a det ailed descript ion of the st ruct ural charact eristics of t he economy is presented in Appendix A-D. Asregardsnotat ion, all variables ot her than int erest rat esare in nat ural logarit hms. All Cent er variables are starred, while t he Periphery count ries are indexed wit h a subscript i, for i = 1; 2; :::; N . Unless otherwise explicitly st ated, Greek let t ers (bot h lowercase and uppercase) refer to const ant , positive parameters. The …rst two equat ions of t he model describe t he levels of employment and CPI in t he i ¡ th Periphery count ry: ni ;t = 1 [si;t ¡ wi ;t + p¤t ¡ Ài;t ] ®2 qi ;t = ®0 n i ;t + wi ;t + ¯ Ài;t (1) (2) where n i ;t is t he level of employment in t he i ¡ th Periphery count ry at t ime t ; si ;t is t he nominal exchange rate (domest ic currency per unit of Cent er currency); wi;t is the domestic nominal wage prevailing at time t ; qi;t is t he domestic CPI in country i ; p¤t is t he GDP de‡ator in the Cent er country. 11 Last , the variable Ài ;t is a country-speci…c shock, whose characteristics will be analyzed below in det ail. The int erpret at ion of these equation is st raight forward. Consider expression (1) …rst. For given nominal wages, employment is increasing in t he nominal exchange rat e, as t his implies a higher rat e of monetary expansion and lower real wages. For a given exchange rat e, employment is decreasing in the level of nominal wage, as this reduces domest ic competitiveness. Ceteris paribus, employment and out put increase with a monetary expansion in t he Cent er which raises p¤t , boost ing the demand for t he Periphery countries’ export s. In expression (2), t he in‡ationary impact of a surge in domest ic employment and a rise in nominal wages is self-explanat ory.6 In t he class of models under considerat ion, the timing of the decisions is t he following. First, the money wage rat e wi ;t is set , before the shock and t he response of the domest ic cent ral bank are observed by privat e agent s. Wages are not renegot iat ed aft er the money supply is announced. Thus, wagecont racts prevailing at t ime t arebased on informat ion available at t ime t ¡ 1 : the economy is characterized by short -run (one-period) nominal wage rigidities. Second, t he shock Ài ;t is observed and the central bank chooses t he level of t he domestic money supply. Under st andard assumptions,7 t he rational-expectat ion wage rate is equal to t he expected money supply wi ;t = E t ¡ 1 mi ;t (3) (where E t ¡ 1 denot es the expect at ion operator conditional on informat ion available at time t ¡ 1) and t he level of employment is equal to t he domest ic monet ary innovat ion n i;t = mi ;t ¡ E t ¡ 1 mi ;t (4) T hus, for given wages, t he semi-reduced form for t he employment level is also a semi-reduced form for money supply. Also, t he domestic de‡ator pi ;t is equal to pi ;t = wi ;t + ®n i ;t = (1 ¡ ®) E t ¡ 1 mi ;t + ®mi;t (5) We can now providea discussion of t he domest ic disturbancet erm Ài;t . As shown in Appendix D, the country-speci…c shock includes two components: 0 1 Ài;t ´ ² t ¡ @®1 X nj ;t + Án ¤t A (6) j6 =i T he …rst component , indexed by ² t ; a¤ect s all Periphery countries symmet rically, as it depends on current and fut ure ant icipat ed dist urbances t o t he aggregat e demand of t he Cent er count ry (e.g., the ‘IS’ shock).8 The second 12 component of the country-speci…c shock (in bracket s) depends – with a negat ive sign – on t he monetary innovat ions (i.e. on t he employment levels) of all the other countries in the syst em. Int uitively, in equilibrium an increase in demand for the Cent er’s out put requires, ceteris paribus, a real e¤ect ive appreciation of t he Center’s currency against t he Periphery. This can be achieved through (a) domestic in‡at ion in t he Center, (b) an appreciat ion of t he nominal exchange rat e of the Cent er against t he Periphery, or (c) a generalized de‡at ion in t he Periphery. Under opt ion (a), the demand boom in t he Center would be absorbed int ernally and would not have signi…cant consequences in the Periphery: heuristically, t he changes in ² t and n¤t would o¤set each ot her in equation (6), leaving Ài ;t una¤ected everywhere in t he Periphery. If t he Cent er is unwilling to t olerat e the in‡ationary consequences of t he int ernal demand boom, t he shock is transmitt ed t o t he Periphery. Consider …rst t he case in which t he Periphery consists of one country only. Equat ion (2) shows t hat , for any given domest ic monet ary policy in t he Periphery count ry (and t hus, for any employment and GDP de‡at or level), t he IS shock in the Center unambiguously leads to in‡ation in t he Periphery. T he mechanism is well known. As t he demand boom in the Cent er raises t he int erest rat es in t he Cent er, capitals ‡ow from t he Periphery to the Center. I f t he monet ary aut horit ies in t he Periphery do not react t o the fall in t he demand for domest ic currency, t he equilibrium exchange rate depreciat es in both nominal and real t erms against the Cent er, and t he CPI level in t he Periphery increases (option b). However, t he monetary aut horit ies of t he Periphery country can also accommodat e the shock by decreasing its money supply and defending t he exchange rat e parity. T he defense of the peg, as shown by eqn.(1), has a recessionary impact on thedomestic economy (opt ion c). In the general caseof N > 1 Periphery count ries, eqn.(6) makes clear t hat — from the vant age point of each individual Periphery count ry — t he impact of the shock originat ing in t heCent er depends not only on t hepolicy response of the Center it self, but also on the monetary behavior of the rest of t he Periphery. In ot her words, while t he relevant shock Ài;t is always “ count ryspeci…c” , it re‡ects t he behavior of all the ot her countries in the system. If ®1 is positive — as we discuss below —, t herole played by a monetary expansion in t he rest of t he Periphery is somewhat analogous to t he role played by a monet ary expansion in t he Cent er. By bringing the e¤ect ive t erms of trade of t he Center closer t o its equilibrium level, an expansion somewhere in t he Periphery represents a “ shock-absorber” for t he rest of t he system.9 13 3.3 Social welfar e and comm it ment t echnol ogy T he lossfunct ion of t he policy maker in t hei ¡ th Periphery count ry is de…ned as follows X1 E t ` i ;t + ¿ (7) ¿= 0 where the single period loss function is ` i ;t ´ i 1h (n i;t ¡ n ¹ i ) 2 + ¾(qi ;t ¡ q¹i ;t )2 + ci I i ;t 2 ( I i ;t = 0 if si ;t = s¹ i ;t 1 otherwise qi ;t = si ;t + p¤t (8) (9) (10) T he single period lossfunction ` i in (8) is quadratic in t he deviat ion of act ual employment and CPI from t heir current t arget levels, n ¹ i and q ¹i ;t respect ively. T he t arget level of employment exceedst herational-expectations equilibrium or “ nat ural” level. As in t his model t he lat t er is normalized t o zero, we have n ¹ i > 0. Following t he standard conventions, such a parametrization of t he model implies the presence of some exogenous (and unremovable) distortions in t he Periphery labor market , that make t he full-employment out put level socially subopt imal. The well-known t heoret ical implicat ion of t he result ing con‡ict between public preferences and equilibrium constraint s is t hat an equilibrium wit h full monet ary discret ion leads to a Paret o-dominat ed allocation, a¤ected by an in‡at ionary bias. The t arget levels for prices and employment , as well as the exchange rate parity (indexed by ¹si ;t ) are known at t ime t ¡ 1, before wages are set. T he t arget price level of t he Periphery count ry (eqn.(10)) has two propert ies. First, as long as t he exchange rate peg is maint ained, t he Center’s price level t arget p¹ ¤t is also t he Periphery’s price level target.10 Second, when t he peg is abandoned, there is ‘drift’ in t he Periphery’s price level t arget: unlike t he Cent er,11 a Periphery count ry does not aut omat ically t ry to recoup an in‡at ion disappointment. Theposit iveconstant ci in eqn.(8) denot essomeexogenously given welfare cost of abandoning the peg: count ry i ’s policy makers su¤er a welfare loss equal t o ci when t he current exchange rat edeviat es(no matt er by how much) from the announced exchange rate parity. For our purposes, these cost s are best underst ood as a proxy for t he wide array of non-quanti…able polit ical int erest s underlying the defense of a given exchange rat e target , ranging from naked nat ional chauvinism t o fears of professional loss of prestige, reput at ion 14 and in‡uence; t hey may also re‡ect a widespread belief that exchange rate st ability is a public good in itsown right , quit eapart from itsant i-in‡ationary implicat ions. In our model, market participants t ake the exist ence of a commitment technology as a datum: the higher t he degree of commit ment by t he policy aut hority t o t he defense of t he peg, t he higher t he lump-sum cost s ci t hat t he policy aut horit y will “ pay” if it abandons it s announced target . An ext remely high value of ci implies that, regardless of int ernal and ext ernal circumstances, t he policy aut hority will subordinat e its other objectives to t he defense of t he current exchange rat e. A negligible value signals that governments will always let t he currency ‡oat or, equivalently, set it at the value most conducive to t he achievement of it s other object ives. Intermediate values can be rationalized in t erms of escape clauses allowing for the possibility of realignments in t he presence of speci…c contingencies, i.e. depending on t he size of t he shock hitt ing the domest ic economy (Obst feld [1991]). For the Center country we posit a one-period social loss in t he following form i 1h ¤ 2 (n t ) + ¾(p¤t ) 2 (11) ` ¤t ´ 2 I n cont rast to eqn.(8), not e, …rst , t hat t he Cent er count ry does not su¤er from an in‡at ionary bias ( n ¹ ¤t = 0); second, the price level t arget is constant and normalized t o zero (p¹ ¤t = 0), that is, in‡at ion does not lead t o a rebasing of t he price level t arget over t ime; third, the policy maker does not t arget any exchange rat e parity (there are no …xed cost s of reneging on an exchange rate commit ment). The Cent er country opt imally (and credibly) pursues full employment while set ting the domestic de‡at or equal to zero in each period. It can be easily veri…ed that t he policy maker in t he Cent er will be able to achieve a social …rst best by following the monetary rule m¤t = 0 (12) n ¤t = m¤t ¡ E t ¡ 1 m¤t = 0 (13) t hat implies in all periods. It also follows that p¤t = w¤t = 0. It is wort h emphasizing t hat , in our speci…cat ion, t he loss funct ion of t he Cent er includes t he domest ic GDP de‡ator inst ead of the domest ic CPI (t hat depends on t he e¤ect ive real exchange rat e against t he Periphery), so t hat t here is no st rat egic int eract ion between Cent er and Periphery as a whole. At a theoretical level, there is no compelling reason to int roduce such asymmet ry between Cent er and Periphery.12 However, in our int erpret at ion 15 of the 1992-93 event s, we want t o emphasize how a syst emic crisis is relat ed t o t he policy con‡ict within t he Periphery, once the con‡ict between Cent er and Periphery is frozen in non-cooperat ivebehavior. To highlight this feat ure of our setup, we cut the Gordian knot and choose to avoid any analysis of t he Cent er-Periphery interact ions. It turns out t hat , while permit t ing us to avoid a great deal of analyt ical complicat ions, including t he GDP de‡at or in (11) instead of t he CPI does not a¤ect t he results of our analysis in any substant ive way. 3.4 I nt er nat i onal p oli cy spi ll over s As intra-Periphery externalit ies play a crucial role in our model, it is import ant to analyze t heir nature and implicat ions in detail. Consider a monetary expansion in one Periphery count ry, indexed by j ; which brings about a real depreciation of it s currency against t he Center.13 T he impact of such a monet ary expansion on the economy of another (any ot her) Periphery country, indexed by i 6 = j , can be split into two components of opposite sign, an expenditure-switching and an expenditure-changing e¤ect . These e¤ects are best underst ood starting from the equilibrium condit ion in t he goods market of the Center. Ot her things equal, a real depreciat ion of t he Periphery country j ’s currency shift s demand in the Cent er away from t he goods produced either in the Center or in t he rest of t he Periphery (t hat is, in any count ry i) and toward country j ’s goods. This is t he expenditureswitching e¤ect associat ed with a monet ary expansion in country j , which lowers aggregat e demand in t he rest of t he Periphery. However, as out put supply in t he Cent er is unchanged, equilibrium requires a fall in t he Cent er’s real int erest rate, r ¤ . Ceter is par ibus, t he fall of r ¤ lowers the real int erest rate in all ot her count ries and boosts demand for t he Periphery’s output . T his is the expenditure-changing impact of a monet ary expansion in country j : it increases global demand by lowering the “ world” int erest rat e.14 Thus, if the elasticity of t he aggregate demand with respect t o t he real exchange rat e is large enough, the expenditure-changing e¤ect of a monet ary expansion by any one Periphery country prevails over t he expenditureswitching e¤ect : it s real exchange rat e appreciat es and t he real int erest rate falls in t he rest of the Periphery. The spillovers associat ed with a monetary expansion by one country may of course have the opposite sign. As is clear from t he expression for t he country-speci…c shock (6), it is the parameter ®1 t hat det ermines t he sign of t he e¤ect of a monetary expansion in one country on employment and price level elsewhere in t he system:15 ®1 is posit ive if and only if t he expenditure-changing e¤ect prevails. As well known, in the empirical lit erature there exist s considerable dis16 agreement on t he sign and t he size of int ernational spillovers.16 However, in t he cont ext of our study, there are compelling reasons t o believe that t he relevant spillovers among the ERM count ries best …t t he patt ern of a prevailing expenditure-changing e¤ect. Ex-post , t here are few doubt s t hat t he ERM devaluat ions in 1992 subst antially contribut ed to the rapid fall of int erest rates bot h in Germany and in the rest of t he system (France and t he UK represent particularly spectacular cases) between 1992 and 1993. A st riking visual representat ion of t his point is provided by Figure 1, that shows t he plot of short -t erm nominal and real interest rates in Germany in t he 1990’s (t he spike in t he graph corresponds t o Sept ember 1992). Insert Figure 1 here To the extent t hat t he impact of the “ swing” of German interest rates on t he economies of the European Periphery is considered as the predominant macroeconomic issue in t he unfolding of t he ERM event s (the consensus view), t here is st rong evidence in support of our assumpt ion that, on balance, t he net e¤ect in t he transmission of monet ary policies in Europe was positive (®1 > 0). It is wort h not icing t hat this assumption does not rule out t he possibility of shifts in demand — from strong- t o weak-currency countries’ goods — following a devaluat ion: rat her, it de-emphasizes t heir relevance vis-à-vis t he impact of a syst em-wide fall in int erest rates. 4 N on-cooper at ive equilibr ium: t he r ole of domest ic cr edibilit y T he analysis of t he equilibrium begins with the determination of t he optimal monet ary policy of a represent at ive Periphery count ry. At any point in time, t he problem faced by the monet ary aut hority of country i can be t hought of as a nested choice. First, t he policy maker will det ermine whet her to maint ain or abandon t he peg, knowing t hat reneging on t he commitment to peg the currency brings about a reduct ion of utility by some …xed amount ci . Second, contingent on t he peg having been abandoned, t he size of t he monet ary expansion is chosen; given t heposit ive relat ion between a count ry’s money supply and it s exchange rate, t his translates into t he det erminat ion of t he opt imal size of t he realignment . At t he t ime when such decisions are t aken, the monetary authority of the Periphery country i t akes into account t he following variables: t he demand shock in the Center, ² t ; the stance of monet ary policy in t herest of thesyst em, t hat is m¤t and mj ;t for all Periphery count ries j 6 = i ; and t he wage level set in the domestic labor market wt . 17 4.1 Char act er izi ng t he opt imal monet ar y poli cy: t he shadow deval uat i on r at e T heopt imal policy rulefor count ry i combinestwo di¤erent monetary regimes. I n one the money st ock isconsist ent wit h t hesurvival of t hepeg. In the ot her one the peg is abandoned and the money supply optimally responds t o fundamentals. Consider …rst t he optimal monet ary policy condit ional on t he peg having been abandoned. If the current exchange rat e parity is no longer a binding target or constraint, t he policy maker will minimize the loss funct ion ` i;t by choosing a money supply such t hat ³ ´ @`i ;t = nFi ;tL ¡ n ¹ i + ¾®0 qiF;tL ¡ q ¹i ;t = 0 @mi ;t (14) where t he superscript “ FL” refers t o “ conditional on abandoning t he peg” .17 I f inst ead t he policy maker decidest o defend t hecurrent parity, t hemonetary policy is implicit ly det ermined by expression (1), positing si ;t = s¹ i ;t : s¹ i ;t ¡ wi ;t ¡ Ài ;t = 0 (15) ®2 where the superscript “ FX” refer t o “ condit ional on defending t he peg” . As regards t he choice of exchange rat e (and monet ary policy) regime, t he policy maker will opt for abandoning t he peg if and only if the loss under a peg is larger t han t he loss associated wit h a devaluation, including t he lump-sum welfare cost ci : i h io 1 nh F X (n i ;t ¡ n ¹ i )2 + ¾(qiF;tX ¡ q ¹i ;t ) 2 ¡ (n Fi ;tL ¡ n ¹ i )2 + ¾(qiF;tL ¡ q ¹i ;t ) 2 ¸ ci 2 (16) T he above expressions complet ely charact erize t he optimal policy. In what follows, we will show t hat t here is a simple yet insight ful way to re-paramet rize the opt imal switching between the two regimes. De…ne t he shadow devaluation rate (henceforth t he SDR) as the di¤erence between t he (optimally chosen) value of the exchange rat e if t he peg were abandoned and t he target exchange rate. The SDR will be denot ed ¢ s~i ;t . By de…nition, t he prevailing exchange rat e conditional on t he abandonment of the peg will be sFi;tL = s¹ i ;t + ¢ s~i ;t : It is st raightforward to show that the shadow devaluat ion rateis increasing in thepredetermined nominal wage, in bot h t heemployment and the price target s, as well as in the count ry-speci…c shock. It is obviously decreasing in the exchange rat e parity t hat is currently defended.18 Not e t hat rearranging t he semi-reduced forms (1) and (2), the SDR can also be writ ten as follows ´ ³ ´ ®2 ³ F L qi ;t ¡ qiF;tX (17) ¢ s~i ;t = ®2 n Fi ;tL ¡ nFi ;tX = ®0 n Fi;tX ¡ 18 T he interpretation of these relationships brings addit ional insight s on t he meaning of ¢ s~i ;t : The shadow devaluat ion rat e is proport ional t o t he ‘employment gap’ (nFi ;tL ¡ n Fi ;tX ), t hat is, t he loss of employment due t o defending t he exist ing parity. It is also proport ional t o t he ‘price level gap’, t hat is, t he in‡at ion bene…t from defending t he peg. I n either cases, the SDR provides a measure of t he welfare opport unity cost of maint aining the exchange rate …xed. Now, by using (17), we can rewrit e t he condition for an optimal choice of exchange rat e regime (16) exclusively in t erms of the shadow depreciat ion rate: si ;t = s¹ i ;t if j¢ ~ si ;t j < cei (18) si ;t = s¹ i ;t + ¢ s~i ;t if j¢ ~ si ;t j ¸ cei where c~i is a constant .19 In ot her words, there exists a threshold value of t he shadow devaluation rate t hat t riggers an optimal realignment. The threshold value ~ ci translat es the welfare cost of abandoning t he peg int o t he metric of t he SDR. Expressions (18) draw a simple pict ure t hat captures the key feat ures of our model. Consider Figure 2. In this Figure, and t hroughout t his paper, we rest rict t he support of t he shock so as t o rule out t he possibility of optimal revaluations.20 On the x-axis we put t he support of t he shock. On t he yaxis we have t he shadow and t he act ual devaluation rat es (both condit ional on private agents’ expect at ions), as well as the “ adjust ed” welfare cost of a devaluat ion cei . The zero on the y-axis corresponds to t he exist ing parity. The level of the shock¹Ài ;t , at which t he shadow depreciation rate crosses t he cost line, divides t he support of the shock in two regions. The policy maker will …nd it optimal to defend t he exchange rat e if t he shock falls in t he region t o t he left. She will opt imally abandon the peg in the region to t he right. By construct ion, the opt imal devaluat ion rat e condit ional on abandoning t he peg coincides with t he shadow one. Thus, the act ual devaluat ion rate will be zero in t he region t o t he left of t he threshold, equal t o t he SDR in t he region t o t he right. Insert Figure 2 here Analytically and conceptually, the SDR provides a unifying framework for di¤erent classesof currency crisismodels. In thecont ext of speculativeatt ack models with an exogenously speci…ed monetary rule, Flood and Garber [1984] showed t hat the privat e sect or will launch a speculative att ack, deplet ing reserves and forcing an abandonment of the …xed parity, as soon as t he path of t he shadow ‡oating exchange rat e crosses t he …xed parity from below. 19 I n our setup, t he government will choose t o abandon the …xed parity, as soon as the shadow ‡oating exchange rate exceeds the …xed rat e by a margin su¢ cient t o cover the sunk devaluation cost .21 4.2 M ar ket exp ect at ions and wage set t i ng T he second stage of the analysis is devot ed t o closing the model by considering t he det erminat ion of nominal wages based on rat ional expect at ions of fut ure domest ic monet ary policies. In t he model under consideration, opt imizing wage set ters will form set t heir wages according t o eqn.(3) above. Since policy makers do not “ tie their own hands” and do not commit themselves t o t he defense of t he exchange rat e target under all possible cont ingencies, market part icipant s will forecast the future monetary policy by combining t wo scenarios, t he …rst one assuming a defense of the …xed exchange rate, t he second one assuming t hat t he peg is abandoned and t hat the opt imal rat e of devaluat ion is chosen. We have observed before t hat t he SDR is a linear, increasing funct ion of t he demand shock Ài;t . Therefore, for any given probability distribut ion for Ài ;t (assumed t o be common knowledge) there exist s a devaluat ion threshold ¹Ài ;t , de…ned as t he level of t he shock such t hat a devaluation will occur for Ài ;t ¸ ¹Ài ;t . As Figure 2 illust rates, by de…nition Ài ;t ¸ ¹Ài ;t if and only if ¢ s~ ¸ c~i . De…ne now the probability of a realignment as ¼i ;t ´ Prf ¢ ~ si ;t ¸ ~ ci g ´ Pr f Ài ;t ¸ ¹Ài ;t g: (19) Wage sett ers’ forecast s will be obtained by taking t he expect at ions of mFi;tX and mFi ;tL conditional on, respect ively, t he defense of the peg (F X according t o t he notat ion of Sect ion 3) and a devaluat ion (F L), and combining them according t o t heir respect ive probabilit ies: h i h wi ;t = E t ¡ 1m i;t = (1 ¡ ¼i ;t ) E t ¡ 1 mFi ;tX jF X + ¼i ;t E t ¡ 1 mFi ;tL jF L i (20) I t bears emphasizing that t he wage rat e obtained according to t he previous expression will be a decreasing function of the devaluat ion t hreshold¹Ài ;t , so far t aken as an exogenous paramet er. To det ermine endogenously the devaluat ion t hreshold under rat ional expect ations, we subst it ut e eqn.(20) into the expression for t he SDR. Then, we evaluat e the SDR at Ài ;t = ¹Ài;t , we equate t he SDR to c~i , and solve for ¹Ài ;t : Algebraic det ails of the solut ion are present ed in Appendix E. Wit hout speci…c assumpt ions on t he distribution of t he shock to fundamentals Ài ;t , very lit t le can be said about t he propert ies of t he devaluat ion 20 t hreshold À ¹ i ;t . An import ant point is that, in general, the expression for t he SDR evaluat ed at t he devaluation t hreshold will be non-linear, so t hat its root s will not be unique. This feat ure is what raises the possibility of multiple instant aneous equilibria, as we discuss below. We choose to illust rat e this point by means of a paramet ric example, assuming a uniform dist ribution of t he shock.22 Insert Figure 3 here Consider Figure 3, where N min and N max represent t he lower and upper boundaries for the count ry-speci…c shock Ài;t . In the t op graph, we plot both t he (modi…ed) welfare cost of a devaluat ion ~ ci and the SDR evaluated at Ài ;t = ¹Ài ;t against all pot ent ial values of¹Ài ;t , that is, t he support of the shock. T here are two crossing point s, ident ifying two possible equilibrium levels for t he devaluat ion t hreshold. Depending on which inst antaneous equilibrium market participants coordinat e t heir expect ations on, we have two possible levels of wages and t herefore two possible levels of t he shadow devaluat ion rate. This is shown in t he graph at t he bot tom of t he Figure, where we include two SDR lines. In each period, once t he wage cont racts are signed, t here can only be one shadow devaluation locus. Before t he cont racts are signed, however, t here could be more than one SDR locus t hat is a rat ional expect at ions equilibrium. 5 Cur r ent explanat ions of t he ER M cr isis: an analyt ical r eview Most cont ribut ions on t he ERM crisis are cast in terms of “ unilat eral peg models” t hat , as our analysis makes clear, can only charact erize partial equilibr ia of t he broader int ernational monet ary game. Even grant ed t he partial equilibrium nature of these models, however, it is our view t hat , in several cases, the models in the lit erat ure are developed under unduly rest rictive assumptions — especially in the de…nition and int erpret at ion of the shock t o fundament als. It is t herefore inst ructive t o re-int erpret the most popular explanat ions of t he ERM crisis wit hin our own framework. The int erpret at ions of t he crisis reviewed in t his section emphasize t he role of domestic credibility, regardless of whet her t he shock det ermining t he currency crisis originat es at home or abroad. Abandoning the peg is ultimat ely a policy decision, based on a rational assessment of costs and bene…ts of a regime swit ch. The cont ingent nat ure of such a decision underlies t he expect at ion game between t he private and t he public sector. This game can have multiple instant aneous equilibria, o¤ering the theoretical founda21 t ions for t he t heory t hat the ERM has succumbed because of dest abilizing self-ful…lling prophecies of a crisis. For a given regime of expect at ions, t he st ability of t he exchange rat e depends on t he perceived distribut ion of t he shocks as well as on t he perceived opportunity cost s of a regime swit ch. 5.1 Shift s i n exp ect at i ons and sel f-ful …lli ng equil ibr ia Consider Figure 3 once again. Suppose that t he economy somehow coordinat es on a high t hreshold, low in‡at ion, equilibrium (on t he right). If a devaluat ion is perceived as a low probability event , workers sett le for a low nominal wage, and employment is, ceteris paribus, high. Only a very adverse realization of the shock (a large value of Ài ;t ) will force the monetary aut horit ies to abandon t he defense of the exchange rate t arget in order to maint ain the level of employment. Nonetheless, the fact t hat the syst em will indeed be safe against devaluation except in t he case of very high values of Ài ;t validates, ex-post , the wage sett ers’ init ial conjecture. Suppose instead that market participants coordinat e on t he bad, high in‡at ion (low ¹Ài ;t ) equilibrium, so that unions perceive a high probabilit y of a devaluation. As t he nominal wage rate is now relat ively high (re‡ect ing t he higher probability of future depreciation and in‡at ion), t he monetary aut horit ies will be forced to use a devaluation t o rest ore competitiveness in t he int ernational markets in response to even mild shocks. Only if t he ext ernal condit ions turn out t o be very favorable, will policy makers prefer t o keep the exchange rat e …xed. It is worth emphasizing t he self-ful…lling nat ure of expectations in both equilibria. If nominal wages are set at a high level, the opt imal response to ext ernal shocks is likely to be a devaluat ion. At the same t ime, the monetary expansion associated wit h a devaluat ion validates ex-post t he in‡ationary expect at ions of market part icipant s t hat generat ed t he original high wage. By the same t oken, if nominal wages happen t o be set at a low level, t he monet ary authorit ies will be helped by t hese favorable int ernal conditions in t heir commitment t o defend the parity. Exchangerate st ability (aswell ast he associated rest rictive monet ary policy) will con…rm, ex-post, the correctness of wage set ters’ expect at ions. In the post-mortem interpret ations of the ERM crisis, unilat eral peg models with mult iple instant aneousequilibria haveprovided a popular t heoret ical foundat ion for t he analysis of self-ful…lling speculat ive att acks in the foreign exchange market s.23 According t o this approach, an exchange rat e crisis due t o self-ful…lling speculat ive behavior consists of a sudden, and complet ely unant icipated, shift from t he good equilibrium t o the right of Figure 3 to t he bad equilibrium to t he left of t he same …gure, for unchanged fundament als. 22 I f a crisis is t riggered by such a shift in expect ations, t he familiar macroeconomic indicators would not give any early indicat ion that a period of exchange rate instability is approaching: up t o t he dawn of a crisis, forwardlooking asset prices in the …nancial markets would re‡ect expectations of a persistence of t he good equilibrium. Indeed, it is apparent t hat …nancial markets did not anticipat e t he magnitude of t he crisis. The interest di¤erent ials between ERM countries and Germany fell on average in 1992; in t he summer, there was some worsening of credibility, but only to a very limit ed ext ent (Rose and Svensson [1994]). Other indicat ors of credibility, based on option prices or survey dat a on exchange rate forecasts, con…rm t hese result s.24 T he popularity of the idea of self-ful…lling speculative att acks is largely due t o its ability to explain these large forecast errors without post ulating irrat ionality or …nancial market ine¢ ciencies. A problem wit h the logical foundations of this view of t he crisis is that , while demonstrat ing the possibility of mult iple inst antaneous equilibria, t he t heory is silent on t he mechanisms underlying the (sudden shift in t he) privat e sector’s coordinat ion on a particular expect at ion regime. T he analysis of a speculat ive att ack as a self-ful…lling prophecy requires a leap from t he t heoretical ident i…cat ion of the existence of mult iple equilibria to the characterization of an economic process (in “ real time” ) t hat the model per se has not hing to say about: modelling expect ations coordinat ing mechanisms requires furt her t heoret ical st ruct ures and/ or ad-hoc assumpt ions. In t he literat ure, expect ations coordination mechanisms are commonly modelled in t erms of exogenous uncertainty: a random variable is assigned an arbit rary dist ribut ion de…ned over possible equilibrium out comes. T he models considered have t he property that, provided fundament als are weak enough, there is, in each period, a posit ive probability t hat a “ self-ful…lling” speculative att ack will occur. Such a black-box approach may be useful in rationalizing t he t iming of t he crisis in a count ry with a credibility problem (Obstfeld [1994] and Obstfeld and Rogo¤ [1995]): what appears, prima facie, as an arbitrary and irrat ional swit ch in currency traders’ beliefs, can be int erpret ed as t he shift from one rational expectation equilibrium to anot her. Nonet heless, if taken too lit erally — i.e. self-ful…lling prophecies were the cause of the crisis — it can only o¤er a super…cial phenomenological explanat ion of t he 1992/ 93 currency crisisand of the persist ent …nancial inst ability t hat followed. Despit e the inherent weakness of t his explanation of t he crisis, it has been argued t hat one is virtually bound to conclude t hat the crisis was indeed t riggered by such self-ful…lling speculative at t acks, because alt ernative explanat ions based on t he analysis of fundamentals tend not t o perform very 23 well empirically.25 Tests have been carried out wit h reference to standard t wo-country (or small open economy) unilateral peg models of currency crisis; fundamentals include various measures of employment , activity, relative prices and …scal de…cit s. The results show t hat t here is no clear evidence of a det eriorat ion of current macroeconomic indicat ors preceding the crisis. Also, fundament als do not seem to di¤er before and aft er the crisis.26 On empirical ground, however, t he issue is not at all straight forward, since expect ations shifts triggered by self-ful…lling prophecies and expect at ions shifts re‡ect ing fundament al shocks are, t o a very large ext ent , observat ionally equivalent . In our opinion, a balanced view of the role played by fundamental imbalances in t he crisis requires …rst and foremost an appropriat e theoret ical and analyt ical framework: the next sect ions are devot ed to a brief discussion of t hese points. 5.2 T hr ee int er pr et at i ons of t he cr isis based on fundament al s T he literature has provided at least three interpretat ions of t he ERM crisis based on economic and polit ical fundament als. The …rst one st resses t he role of the German reuni…cation shock, and of the German …scal-monet ary policy mix that accompanied it. T he second is focused on the perceived weakening of t he political consensus in favor of t he European monet ary project aft er t he …rst Danish referendum. T he t hird one st resses t he role of competitiveness losses implied by a disin‡at ion st rat egy based on a …xed exchange rat e. 5.2.1 G er m an uni…cat ion shock: t he r ole of l ear ni ng and ex pect at ions updat ing T he basic elements of t he …rst st ory are well-known.27 The German domest ic demand boom, partly fueled by the sustained and largely de…cit-…nanced …scal t ransfers from t he West to the Eastern regions of t he country, partly fueled by the conversion of GDR-Marks into D-Marks at the overvalued average rat e of 1:8 to 1, put upward pressures on the German real exchange rate. Given t he Bundesbank’s commit ment t o contain in‡ationary pressures, a D-Mark real appreciat ion would require eit her a nominal devaluat ion or a de‡ation in t he rest of t he ERM. The employment and … scal costs of such a de‡ation undermine t he st ability of the exchange rat e. One of t he most common object ions t o explanat ions of t he crisis based on t he German reuni…cat ion shock concerns t iming. Why does the 1990 German reuni…cat ion shock bring about a crisis in 1992? If such a shock was 24 so import ant, shouldn’t forward-looking …nancial market s have ant icipat ed t he crisis well before 1992? In t he light of our model, t his object ion has litt le ground. Once t he model isspeci…ed appropriat ely, t he role of cur rent aggregat e demand shocks in generating a currency crisis is great ly reduced. Disregard for t he t ime being t he int ernational spillovers and t he policy game, and focus on t he nat ure of the Center demand shock. The relevant shock t o fundamentals ² t is the innovation t o t he present discounted value of current and fut ure I S dist urbances (broadly int erpreted to include t he German monet ary-…scal policy mix following uni…cation), ¸ ¤t in Appendix A. This feat ure of t he model means that considerations about t he st ability of t he dist ribut ion of t he shocks, t heir persistence over time, as well as the learning process should be given appropriate weight in t he analysis of the crisis. In t erms of our reconstruct ion, two speci…c points can be made about the behavior of t he fundamentals. First , privat e agents may have been unable t o disent angle t he permanent and t ransitory components of t he shock. In t his case, it is well known t hat rational forecasts will be charact erized by a t ypical adapt ive pat tern and “ learning” behavior. As the magnit ude and durat ion of the West -t o-East …scal transfers associated wit h German uni…cat ion was only revealed gradually, t he full implicat ions of the shock for t he st ability of t he exchange rat e could only emerge over t ime. Second, German reuni…cation, and the German macroeconomic policy response t o it, was an unprecedented economic and political event. To t he ext ent that the nat ure of the shock made it di¢ cult t o evaluat e the paramet ers of the st ruct ural form, est imat es of it s magnitude and persist ence were likely t o be subject t o drastic revisions over time. To clarify t his point , assume that t he relat ive demand disturbance is generated by a simple …rst-order aut oregressive process ³ ´ ¸ ¤t ¡ ¸ = ½ ¸ ¤t¡ 1 ¡ ¸ + ´ t ; 0 < ½< 1 (21) where the innovat ion ´ t is i.i.d. wit h zero mean. The higher t he coe¢ cient of serial correlat ion (½), the more persistent t he relat ive IS disturbance. It follows that t he (absolute value of the) exogenous shock t o fundamentals in eqn.(6) will be increasing in ½: ²t = ¸ ¤t ¡ ¸ ° º (1 ¡ 2¯ ) 1 ¡ ° ½ (22) A sudden revision of t he paramet er ½implies a jump in t he shock to fundament als ²t for any given realizat ion of ¸ ¤t . This process of revision occurs over t ime and is not necessarily smoot h. 25 The uncompromising at titude of t he Bundesbank — insofar as int erest rate policy was concerned —was fully revealed only at the dawn of t he crisis. I t is wort h recalling t hat even at t he Bath meeting on Sept ember 5-6 1992, t he possibility of an int erest rate cut was considered a feasible policy opt ion by ERM policy-makers, including the Brit ish Chancellor of t he Exchequer.28 T he perceived int ransigence of the German aut horit ies might have t ranslat ed int o a reassessment of t he persist enceof the high interest rate regime, indexed by an upward jump in ½in our setup. As a consequence, in t he framework of Figure 2, ² t and t he entire st ructure of country-speci…c shocks Ài ;t could have suddenly jumped from t he left to t he right of t he devaluat ion threshold ¹Ài ;t , triggering a currency crisis. While we believe that t he int ernational policy game has played a far more important role in the crisis t han learning and revision of expect at ions, (leading us to add t he rules of t he internat ional policy game t o the list of fundamentalsin Section 6 below), one cannot dismisst heimportance of these ot her considerat ions. Our analysis suggest s caut ion in relying too much on empirical evidence on “ contemporaneous shocks” t o fundament als, t hose related t o the German uni…cat ion shock as well as others. The absence of any obvious contemporaneouschangein observablemacroeconomic variablesmay not carry much weight in one’s interpretat ion of the crisis, once t he int ert emporal nat ure of shocks t o fundamentals is t aken int o account appropriat ely. 5.2.2 T he per ceived change in policy-m aker s’ comm it m ent t o ex change r at e st abi lit y T he focus of t he second int erpret at ion of t he crisis as t he result of developments in fundament als, is on t he policy makers’ commitment t o exchange rate stability. At t he beginning of the 1990’s, t he perceived political bene…ts from part icipating in t he ERM were high. Price stability being a nat ional priority, government s t ended to base t he credibility of t heir ant i-in‡ationary policies on t heir ability t o maint ain a st able exchange rat e vis-à-vis t he Dmark. The …rst Danish referendum, and lat er public opinion polls in France, revealed that t he popular consensus over Maast richt was much weaker t han previously believed. The social cost s of de‡ationary policies, exacerbat ed by t heregime of high interest ratesfollowing German reuni…cat ion, suddenly became less bearable. The tempt at ion t o correct domestic imbalances through a devaluation grew stronger. An interpret ation of the crisis in t erms of a polit ical shock helpsexplain its t iming and persistence, insofar as the weakening of popular support for Maastricht spreads t o t he entire EMS. In our t heoret ical framework, t he e¤ect of a downward revision in t he perceived polit ical cost of a devaluation can be modeled as a decrease in t he 26 welfarecost ci (and c~i ). Focusing on a good, low in‡at ion, rat ional expect at ion equilibrium, such as t he one t o t he right of Figure 4, it is apparent t hat a downward shift in c~i increases the probability of a crisis, lowering t he t hreshold À ¹ i ;t and increasing t he equilibrium nominal wages. For t he new level of nominal wages, t he SDR line in t he graph shifts to t he left . Insert Figure 4 here In principle, more could be said in t his respect wit hin a t heoret ical framework wherepolit ical cost saremade explicit in t erms of acceptable primitives. T he lit erat ure provides a few examples of such theoretical exercises. Froot and Rogo¤ [1991] point out t he destabilizing end-game e¤ect s of t he Maast richt time-t able for EMU, insofar as deadlines raise t he temptat ion t o resort t o a …nal realignment before locking in t he exchange rat e irrevocably at a …xed Euro conversion rate. Currie [1992], among ot hers, carries out welfare analysis based on t he social loss function (8), comparing EMU to alt ernative exchange rat e arrangement s. As t he sign of t he net gains from EMU compared to an adjust able peg is qualitatively ambiguous, quant it ative welfare analysis is required t o shed light on the reasons for the expressions of political disagreement on t he Maast richt project. However, any int erpret ation of t he ERM event s wit hin t his framework is cont ingent on (arbitrary) assumpt ions concerning the expect ed monet ary stance of the European cent ral bank following EMU. As shown in Alesina and Grilli [1993], the result s of such a quantitat ive welfare analysis depend crucially on whet her or not , or t o what ext ent , national policy preferences will be re‡ect ed in the behavior of t he European Cent ral Bank. 5.2.3 I nher ent weak ness of disin‡at ion poli cies based on an ext er nal nomi nal anchor T he t hird “ fundament al” explanation points t o an inherent weakness of any price st abilizat ion policy based on pegging t he exchange rate. If eit her in‡at ion has inertia or the new exchange rat e regime is not perfect ly credible, t he policy initially result s in an appreciat ion of the real exchange rat e. Worsening competitiveness a¤ect s the t rade balance, product ion and employment . A successful implement ation of t he policy thus requires a count ry t o push its domestic rate of in‡at ion below that of the Cent er country in order t o o¤set t he init ial real appreciation. Since t he cost s of t he required de‡ation are generally high, t he commit ment t o maint ain the exchange rate parity may not be credible. Such a scheme applies reasonably well t o the It alian and t he English cases. It does not explain, however, why speculat ive at tacks hit the cur27 rency of countries, such as France, where there are no unambiguous signs of a det eriorating ext ernal compet it iveness (convent ionally measured by real exchange rat es based on CPI or unit labor costs).29 A model with one-period wage contract s can only o¤er a stylized account of t hese e¤ect s based on t he consequences of imperfect credibility on t he out put and competitiveness of a count ry. Wit hout an in‡at ionary bias in t he Periphery, t he equilibrium real exchange rat e in our would not change in response t o the Center shock. As long as the commit ment to t he …xed parity is not perfectly credible, a disin‡at ion policy based on an ext ernal nominal anchor causes t he competitiveness of the Periphery countries visa-vis the Center t o det eriorat e. This in‡at ionary bias and the associat ed real exchange rat e overvaluat ion persist s as long as t he imperfect credibility persists. It is also possible to generalize t he t heoretical framework, by including mult i-period wage cont ract s – a rat her demanding approach on technical grounds – or by making t he costs of disin‡at ion policies last ing for more t han one period. Drazen and Masson [1994], for inst ance, adopt a t heoretical framework t hat incorporates hysteresis in unemployment . As a result , a t ough st ance in defense of t he exchange rat e parity increases t he “ nat ural” rate of unemployment over time. Obst feld [1994] discusses a model where t he domest ic policy game is not de…ned in t erms of t he trade-o¤ between in‡at ion and unemployment, but in t erms of t he trade-o¤ between t he dist ort ions of in‡at ion and the dist ort ions due t o a high level of non-lump sum t axation, faced by a government with a high public debt . In bot h examples, t he presence of a st ate variable – the ‘memory’ of past unemployment rat es in one case and t he level of public debt in the ot her case – captures t he cumulative cost of defending t he peg. In both cases, a currency crisis can occur despite st able or even improving current fundament als: it is in fact t he cumulative e¤ect of t he fundamental ‘stock’, not t he marginal e¤ect of its ‘‡ow’, t hat matt ers in determining t he t iming of a devaluation. 6 6.1 N on-cooper at ive equilibr ium: t he syst emic dimension T he m issi ng el ement : m odell ing t he int er nat ional poli cy gam e W hile private-public sect ors interactions at t he domest ic level are certainly an important part of t he process t hat brought down the ERM, explanations 28 of the 92-93 crisis that focus exclusively on the national dimension are bound t o missa key element. As wehaveseen, thedomestic shadow devaluat ion rate complet ely characterizes the monet ary policy of a country. Nonetheless, for any given st ruct ure of spillovers, it is not possible to det ermine an individual count ry’s SDR wit hout knowing the policy st ance of the other count ries in t he system. To t his issue we turn next. Our approach stresses an explanat ion of the crisis in t erms of fundamentals, but augment s t he t radit ional list of fundamentals wit h the r ules of t he int ernat ional monet ary policy game, that is the cooperative or noncooperative design of monetary and exchange rat e policy in the Periphery. W hile our approach does not rule out the possibility of mult iple instant aneous equilibria for given fundamentals, it goes through even if t he domest ic equilibrium is unique. In our discussion, we will assume t hat t he privat e sect ors of each and every country coordinat e on t he same equilibrium. Throughout t he analysis, we will make t he simplifying assumpt ions t hat all policy makers in the Periphery have the same employment target and face the same welfare cost of a devaluat ion: n ¹i = n ¹ and ci = c for all countries i : (23) We also assume that t he private sectors coordinat e their expect at ions on t he same (multi-count ry) equilibrium, t hat is wi ;t ¡ s¹ i = wj ;t ¡ ¹sj for all count ries i; j : (24) E¤ect ively, therefore, all countries in t he Periphery are ex-ante identical. To avoid misleading interpretat ions, it is wort h emphasizing t hat the assumpt ions of symmetry (23) and (24) are only made in order t o highlight t he speci…c role of internat ional policy coordination in t he logic of an exchange rate regime crisis, while abst ract ing from cross-country di¤erences in economic st ructure, inherited economic condit ions, domest ic credibility and subject ive expect ations. Asymmetries between European count ries in t he early 1990s were by no means negligible, and t here is no doubt t hat such di¤erences should be t aken into account in a complet e assessment of t he ERM crisis. Nevert heless, the twelve months spanned by Sept ember 92 and August 93 wit nessed a wave of crises wit hin t he ERM which appear t o be unrelated to visible divergences in macroeconomic policy stance and economic performance among European economies. To t he extent t hat t he 92-93 events in Europe represent the breakdown of a system, rat her than t he crisis of the unilateral exchange rate policies undert aken by a collect ion of isolat ed count ries, intra-Periphery asymmet ries 29 do not help underst and t henatureof t heERM puzzle. Thus, the (admitt edly unrealistic) assumption of symmet ry in our exercise allows us t o focus on t he crucial issues at st ake, while de-emphasizing other factors cont ributing t o t he crisis. As wages are taken as given paramet ers, and t he det erminat ion of market expect at ions is left backst age in what follows, t here is no need to emphasize further the time dimension of our model. Therefore, for not ational convenience we will drop t ime subscript s t hroughout the rest of the paper. 6.2 M onet ar y st r at egi es i n t he C ent er and t he Per ipher y I n t he absence of coordinat ion, each country t akesmonetary ‘act ions’ in ot her count ries as given, and det erminesit sopt imal ‘react ion’. Consider t heCent er …rst. As t he Center opt imally pursues a Friedman-style monet ary rule, its policy strategy complet ely insulat es employment from domest ic and ext ernal dist urbances. The Cent er “ reaction funct ion” is therefore n¤ = 0 (25) I n the Periphery, each country det ermines its opt imal monet ary strategy according t o t he analysis of Sect ion 4.1. Due to t he presence of lump-sum realignment cost s, t he reaction function for t he represent ative Periphery count ry i is discontinuous: by using (14), (15) and t he de…nit ion of t he shock Ài , we can in fact characterize t he Periphery react ion function as follows: 1 ® X ni = ( s¹ i + ¢ si ¡ wi ¡ ²) + 1 nj ®2 ®2 j 6= i ( ¢ si = 0 ¢~ si i f ¢ s~i < ~ c i f ¢ s~i ¸ c~ (26) T his expression makes it clear that t hesign and t he magnitudeof t hespillover e¤ects (t he paramet er ®1 ) are cent ral t o our interpretat ion of the Periphery react ion funct ions and t he Nash equilibrium t hey support . The react ion function (26) shows t hat, if ®1 is positive, t he money stocks of any pair of count ries, j and i, are strategic complements: 30 for a positive ®1 ; t he best response t o count ry j ’s monet ary expansion is a monet ary expansion in count ry i as well. An import ant implicat ion of a dominant expendit ure-changing e¤ect (®1 > 0) is t hat a monet ary expansion in one count ry t ends t o enhance t he st ability of t he peg in all ot her Periphery count ries, because it lowers their shadow devaluat ion rate (and t he welfare gain from a devaluation) for any level of t he exogenous shock.31 30 6.3 T he opt i mal numb er and size of exchange r at e r eali gnm ent s Once monet ary policies are determined on the basis of t he reaction funct ions (26), it is possible t o charact erize t he internat ional dimension of t he non-cooperative (Nash) equilibrium as follows. The support of the shock ² is split int o t hree segment s, de…ned in terms of two thresholds: a lower t hreshold denot ed by ² d and an upper t hreshold denoted by¹² d . In equilibrium, all Periphery countries defend the peg when the shock ² is below t he lower threshold ² d ; all Periphery count ries joint ly devalue their currencies by t he same percent age when the shock is larger than t he upper threshold ¹² d ; some Periphery countries (N F L of t hem) devalue t heir currencies while some (N ¡ N F L ) maintain t he peg when t he shock falls between the two t hresholds (²d and ¹² d ). In t his equilibrium, no Periphery country …nds it optimal t o devalue against the Cent er when some ot her Periphery count ry revalues inst ead. While leaving the analyt ical derivat ion of these result s to Appendix F, we summarize and visualize the properties of t he Nash equilibrium in Figure 5. The graph at t he t op plots t he fract ion of count ries abandoning t he peg (N F L =N ) against t he support of t he shock ². The second graph plots t he shadow devaluat ion rate – which, for each count ry that abandons t he peg, is also that country’s act ual depreciat ion rate – against t he support of t he shock ². The graph at t he bott om present s the informat ion cont ained in t he …rst two graphs in a di¤erent way, by plott ing t he average depreciat ion rate of the Periphery as a whole vis-à-vis the Cent er. Insert Figure 5 here To underst and t he economic intuition underlying t hese graphs, compare Figure 5 wit h Figure 2, where the shadow devaluat ion rat e is plott ed against t he country-speci…c shock Ài . In Figure 2, the higher the country-speci…c shock, the higher the devaluation rat e if the Periphery count ry …nds it opt imal t o abandon t he peg. At t he point Ài = ¹Ài t he country is indi¤erent between devaluing and not devaluing by t he percent age ¢ sei : in other words, at t he t hreshold¹Ài , the welfare bene…ts of a devaluation in t erms of higher employment are exactly o¤set by t he political loss of ant i-in‡ationary reput ation. Now, recall that t he country-speci…c shock is a combinat ion of t he global shock ² and t he monet ary stance in the rest of t he syst em. Thus, Ài can be equal to À ¹ i when the global shock is relatively low and no Periphery count ry expands it s money supply. Equally, Ài can be equal t o ¹Ài when t he global shock is su¢ ciently large and many Periphery count ries follow 31 expansionary policies and devalue. We conclude that there is a continuum of combinat ions of ², t he fundament al shock, and N F L , the number of count ries t hat choose t o devalue, for which a Periphery count ry remains indi¤erent between maint aining the peg and devaluing at t he the const ant rat e ¢ sei = c~. T hus, when we plot the shadow devaluation rat e ¢ sei against the support of t he shock ², as in Figure 5, t he point corresponding t o t he value of Ài = À ¹i in Figure 2 st ret ches over some range of ²; the edges of t his range in Figure 5 are ² d and ¹² d . 6.4 A symm et r i c exchange r at e p oli cies, symm et r ic welfar e l evels Each count ry, taking as given t he behavior of all other count ries, will independently determine whether it is preferable t o peg or ‡oat according t o t he rule given in eqn. (18), t hat is, by comparing the count ry-speci…c shadow devaluat ion rate wit h t he devaluation t hreshold. The model det ermines t he number of countries t hat will devalue in equilibrium. Which count ries will actually abandon t he peg is not det ermined. Only when the shock ² is eit her ext remely high or ext remely low, will t he exchange rat e behavior be ident ical across ex-ante symmetric count ries (eit her they will all peg, or t hey will all devalue by the same amount ). It is important t o st ress that , in the Nash equilibrium we have const ruct ed, Periphery count ries that start o¤ ident ical also share t he same level of welfare ex post for any realizat ion of t he shock, even when their exchange rat e policies di¤er. This lat ter point deserves special att ention. In order to st ress t he role of t he int ernational factors in in‡uencing t he behavior of t he nat ional policy aut horit ies, we have abstract ed from st ruct ural di¤erences at t he nat ional level by assuming perfect ly symmet rical countries. Yet , as st at ed before, for some int ermediate range of the shock, there will be a number of Periphery count ries which …nd it opt imal to abandon the peg while t he other count ries opt imally maintain t he defense of t heir exchange rat e parities. In ot her words, Periphery count ries facing the same global shock will act in a highly asymmet ric way. Ex-ante, the policy-makers in t hePeriphery count riesareall equally credible in their commitment to keep the exchange rat e …xed; t he fundamentals of each economy are exact ly the same, except for di¤erences induced by t he behavior of other count ries. However, because of the internat ional spillovers from domestic policy making, themacroeconomic out look of ex-ante ident ical count ries may vary considerably ex-post. Some economies will have higher in‡at ion, lower unemployment and a depreciat ed currency, while some ot her 32 economies will keep in‡at ion down at the cost of relat ive higher unemployment wit hout devaluing their currencies. The sustainability of t he exchange rate regime in the second group is helped by the behavior of t he …rst group. This is because, under reasonable assumpt ions on t he sign of internat ional policy spillovers, t he monetary expansion induced by a devaluat ion in country j (say, UK) lowers the real int erest rat e in the Center count ry and everywhere in the syst em, reducing …nancial tensions in country i (say, France) t hat does not devalue. At t he same time, t he devaluation of the …rst group of count ries reduces CPI in‡at ion in t he second group. The presence of intra-Periphery spillovers creat es st rat egic int eractions among policy makers: heuristically, t he devaluat ion of count ry j ’s currency will a¤ect the decision of country i t hrough a shift t o the right of this count ry’s SDR for any level of t he shock to fundamentals ². Should t he Periphery count ries try to internalize t hese e¤ect in their policy making? What are t he implicat ions of policy coordinat ion for t he stability of t he exchange rate syst em? This question is addressed by the next sect ion. 7 7.1 Cooper at ive equilibr ium and nat ional hor izont al equit y Welfar e i mpl icat i ons of t he i nt er nat i onal m onet ar y spi ll over s Beforedelving int o theanalysisof t hecooperativeequilibrium, it isimportant t o check whet her t he kind of internat ional policy spillovers we have been focusing on arepositive or negat ivefrom t he point of view of welfarein t heot her count ries in t he system. We have shown t hat , under t he maintained assumpt ion t hat the expenditure-changing e¤ects of a monetary expansion prevail over it s expenditure-switching e¤ects in the rest of the Periphery (®1 > 0), monet ary instruments are strategic complements in t he policy game. We can now show that, in the presence of shocks t o aggregat e demand in t he Center, a monetary expansion in count ry j has a positive external e¤ect on welfare of count ry i . To see t his, it is su¢ cient t o consider the case of a shock t o aggregate demand in t he Cent er that is high enough t o t rigger a common devaluat ion in the Periphery when all countries play Nash. Focus on count ry i. In this count ry, holding domestic money supply (and employment ) const ant, higher values of t he shock ² t ranslate, other things equal, int o a higher depreciat ion 33 rate and t herefore int o a higher domestic CPI level. Now, under our hypot heses about t heint ernational transmission of monetary policy, a devaluation by any other Periphery count ry will induce an appreciat ion of country i ’s currency vis-à-vis the Center, part ly o¤sett ing t he in‡ationary consequences of t he shock t o aggregat e demand in t he Cent er. As the int ernational spillovers of a monet ary expansion in anot her Periphery country reduce count ry i 0s CPI t oward it s current target value, it s opt imal monet ary policy (condit ional on abandoning the peg) becomes more expansionary, bringing employment closer to it s target level and increasing domest ic welfare.32 We may expect t hat, in t he presence of welfare incentives t o coordinate nat ional monetary policies and int ernalize reciprocal spillovers, a system of exchange rat es based on an internat ional agreement like t he ERM could provide t he appropriate inst it utional framework t o do so. Coordinat ion, however, may not be a feasible opt ion: not only because t he cooperat ive equilibrium requires an e¤ect ive enforcement mechanism (to prevent individually rational unilateral deviations from t he agreement ) t hat may not be available t o the count ries in the syst em in all circumst ances, but also because there may be lack of consensus and agreement on how the cost s and bene…ts from coordinated policies should be distributed among t he individual count ries. 7.2 Poli t i call y feasibl e cooper at i on W hat det ermines t he feasibility of int ernational monetary cooperation? We build a scenario making t hree descriptively realistic (in the context of t he ERM) assumpt ions about the nat ure of t he game played by t he Periphery count ries and the Cent er. First, t he Cent er never coordinat es its monetary policy with thePeriphery, while thePeriphery count ries can cooperate among t hemselves. Second, intra-Periphery cooperation is subject t o a national horizontal equity constraint. This constraint requires all cooperat ing count ries (which are ident ical ex-ante) t o be equally well o¤ ex-post. T hird, we rule out side-payments among the Periphery countries. In t his section we brie‡y discuss the rationale underlying these three assumptions. First , in making t he Cent er’s monetary policy always independent of policies in t he Periphery, regardless of whet her t hese are coordinated or not , we abstract from issues regarding cooperat ion between t he Cent er and the Periphery. Our maint ained hypothesis is that cooperat ion is perceived in t he Center as an unaccept able compromise on internal objectives. Some authors have even point ed out t hat a Cent er-Periphery coordinat ion may not be in t he int erest of the Periphery eit her, to t he ext ent t hat internat ional compromises undermines t he anti-in‡ationary credibility of t he conservat ive central bank in t he Cent er count ry (Alesina and Grilli [1993]). 34 Second, t he case we focus on has all Periphery countries cooperating to minimize the sum of t he individual loss functions, internalizing the monetary ext ernalities: Even though all Periphery count ries are st ruct urally identical, t his need not aut omat ically imply t hat in a cooperat ive equilibrium they would eit her achieve equal welfare or adopt t he same policies. Obviously, t he exist ence of t he …xed (sunk) per-country cost of abandoning the parity implies that , for small shocks ²; it might be e¢ cient — as regards t he sum of t he nat ional welfare levels— t o have but a few countries devalue, even if this would make the devaluing countries worse o¤ t han t he remaining count ries t hat st ick t o t heir …xed parities. The quest ion is t hen whet her schemes of cooperat ion with the property t hat ex-ante ident ical countries are not guarant eed to be equally well o¤ ex post can be said t o be characteristic of act ual policy making in Europe. Alt hough technically possible and economically e¢ cient , such schemes would hardly be considered polit ically accept able. First , t here could be considerable disagreement about t he nat ure and t he magnitude of t he common shock as well as about t he severity of the domest ic credibility problem. Second, because of uncertainty regarding the shock and di¢ culty in monitoring individual policy makers’ behavior, complex cooperat ion schemes may create incent ivest o misbehave that subst ant ially reduce t he gainsfrom cooperat ion. For these reasons, we impose in what follows as a “ primitive” a national hor izontal equity constraint in t he joint maximization problem de…ning t he cooperative agreement .33 This constraint st at es that , if the Periphery count ries are symmet ric before t he shock is observed, no Periphery nation would agree on implement ing a cooperat ive act ion t hat would, ex-post, make it worse o¤ t han any ot her Periphery nat ion.34 In other words, no discrepancy in welfare levels among symmet ric Periphery countries is permit ted under any circumst ances.35 Third, a restrict ion of identical ex-post ut ility levels need not t ranslate int o a rest riction of symmet ric use of the policy instruments. In principle, a syst em of redist ribut ive internat ional t ransfers could remove asymmetries in welfare levels generat ed, on impact , by nat ionally di¤erentiated policy measures within a cooperative framework.36 Contingent t ransfers could therefore be used to compensat e t he declining compet it iveness of the count ries t hat do not devalue. It is wort h st ressing t hat such a view neglect s the costs associated wit h the loss of reput ation and anti-in‡at ionary credibility accompanying a realignment. It may well be t hat , under a national horizont al equity constraint , t ransfers would paradoxically run in t he opposite direct ion, from countries t hat keep t he exchange rat e …xed (thus gaining “ more” in t erms of disin‡ation) t o t hose t hat give up the exchange rat e parity. We believe that ruling out these kinds of t ransfers or side-payments as a 35 maint ained hypothesis capt ures a realist ic feat ure of t he actual working of t he ERM. Of course there are many intra-EU transfers, with a wide variety of motivations and goals, many of which are designed to meet speci…c dist ributional or re-st ructuring object ives. However, t o our knowledge, t here is no t ransfer ‡ow cont ingent on t he implementation of coordinated exchange rate policy, or of any ot her aspect of macroeconomic policy.37 In our symmetric context , when all int ra-Periphery ext ernalit ies aret aken int o account and side-payments are ruled out , t he behavior of each single Periphery count ry must beequal to theaveragebehavior of t hePeriphery asa whole: if a realignment occurs, all Periphery count ries realign simult aneously and by t he same amount. We provide an admit t edly ext reme but inst ructive scenario in which dist ributional con‡ict s in designing joint exchange rate policies may act ually inhibit desirable policy init iat ives. Insofar as the realism of our framework is concerned, it is wort h recalling t hat generalized devaluations represent ed an inst it utional reality in the hist ory of the ERM since its very early st ages. Six out of eleven realignments between 1979 and 1987 involved all ERM currencies (excluding the Dut ch guilder, which was realigned only in two cases). The ot her realignment s, which involved only one or two currencies, were typically t riggered by speci…c nat ional cont ingencies rather than represent ing the collective response t o global shocks, such as a sharp fall of t he US dollar.38 Summarizing, we rest rict cooperat ive behavior in t he Periphery t o be symmetric. In our framework, count ries can only agree on symmet ric devaluat ion, that is, devaluation at a common rat e, or no devaluat ion. As we will show, under some circumst ances — that is, when t he nat ional horizont al equity becomes a binding constraint — it may be collectively rational to give up cooperation. If t here is no feasible way t o solve t he dist ribut ional con‡icts involved in coordinat ion, then uncoordinated Nash behavior may be welfare-improving for bot h individual countries and t he ERM as a whole, as long as it leads to a higher overall degree of monetary expansion in response t o t he Cent er shock. 7.3 Opt i mal p oli cies and equil ibr i um under symm et r ic coop er at ion I f all Periphery count ries coordinat e and act symmet rically, t hey e¤ectively behave as if t hey where a single currency area vis-à-vis t he Cent er, by int ernalizing all the cross-count ry e¤ect s on employment and in‡at ion of t heir nat ional monet ary policies. Consider …rst t he opt imal monet ary policy conditional on a coordinated symmet ric abandonment of t he peg. Given t hat 36 t he common objective funct ion is t he equally weight ed sum of domestic objective funct ions, the opt imal money supply in t he representat ive Periphery count ry i sat is…es nCi S ¡ n ¹ + ¾(® + ¯ Á) (qCi S ¡ q ¹i ) = 0 (27) where the superscript CS refers to coordinated symmet ric behavior by t he Periphery count ries. Policy makers will resort t o a coordinat ed symmetric revaluat ion or devaluat ion of the domestic currencies if and only if XN 1 nh i= 1 2 i (nFi X ¡ n ¹ )2 + ¾(qiF X ¡ q ¹i )2 ¡ h (n Ci S ¡ n ¹ )2 + ¾(qiC S ¡ q¹i )2 io ¸ Nc (28) Following our analyt ical scheme int roduced in Sect ion 4.1— algebraic det ails are present ed in Appendix G — this policy rule can be writ ten in t erms of t he SDR: ¢ s~Ci S ¸ ~ cC S (29) where ~ cC S is a constant .39 As in the case where individual count ries play Nash, t he optimal choice of exchange rat e regime requires the comparison of t he SDR with t he cost of abandoning the peg expressed in t he appropriate met ric. The SDR under policy-coordination is of course di¤erent from the SDR under Nash behavior, as it corresponds to a di¤erent opt imal monet ary policy. Expressing t he SDR as a funct ion of t he shock to fundamentals, it is st raightforward to show t hat there exists a threshold value of t he shock ¹² C S such that t he Periphery will jointly devalue for ² ¸ ¹² C S , and jointly maint ain t he peg for ² · ¹²C S . 8 8.1 Cur r ency cr ises as syst emic failur es Cooper at i ve and N ash equi li br ia compar ed We compare the Nash and t he cooperat ive equilibria in Figures 6a and 6b. Each Figure includes t hree graphs, plot ting the shadow depreciation rat e, t he number of count ries devaluing and the average devaluation rate for both equilibria against t he support of t he shock. The two … gures are drawn for di¤erent values of t he parameters: in particular, t he in‡ationary bias in t he Periphery of t he syst em is “ worse” in Figure 6a compared t o 6b. In each graph, t he solid line refers t o t he non-cooperat ive equilibrium, t he broken 37 line t o t he cooperative equilibrium. Insert Figure 6a and 6b here There are three result s worth emphasizing. First, the level of the shock t hat triggers a generalized devaluat ion in t he Periphery of t he system is smaller under cooperat ion t han under Nash — compare the posit ion of t he relevant threshold values¹² C S < ¹² d in both Figures 6a and 6b. This result st ems from t he assumption of positive ext ernal e¤ects of domest ic monetary policy. Intuitively, as Canzoneri and Henderson [1991] put it, “ when policy makers impose posit ive ext ernalit ies on one anot her, cooperation calls for doing more, rather t han less” . Thus, for any dist ribut ion of the shock, a simultaneous realignment by all count ries is ‘more likely’ under symmetric cooperative behavior t han under Nash. However, symmet ric coordinat ion need not imply more frequent realignments tout-court, as, under Nash, uncoordinat ed devaluat ions by a subset of count ries are possible also for ² · ¹² d . In Figure 6b, for instance, when ² is bet ween ² d and¹² C S ; some count ries will devaluein a Nash equilibrium, whileall Periphery count ries will maint ain t he peg under a cooperative agreement .40 Our second point refers t o the magnit ude of realignments rat her t han on t heir likelihood or “ t iming” . Provided that a coordinat ed realignment occurs, t he average devaluat ion by t he Periphery count ries as a group will be larger in a coordinated equilibrium than under Nash, even when t he individual count ry’s optimal depreciat ion rate (conditional on abandoning t he peg) is higher in a Nash equilibrium. Such a result is shown by the graphs at the bot tom of Figure 6a and 6b, where, t o t he right of t he t hreshold ¹² C S , t he broken line (Coordination) is always above the solid line (Nash). The nat ure of t he ext ernal e¤ect of a Periphery country’s monet ary policy on t he ot her Periphery count ries’ welfare provides t he rationale for t his result . For shocks large enough t o make all countries devalue in both equilibria, t he average money supply in t he Periphery will be larger in a symmet ric cooperat ive equilibrium than in a Nash equilibrium. The (common) devaluation rat e will correspondingly be higher in the symmetric cooperat ive equilibrium. A for tiori, for smaller shocks (yet large enough to make all countries devalue in a coordinated symmet ric equilibrium), a Nash equilibrium result s in a suboptimally low average monetary expansion in t he Periphery, implying an average depreciat ion lower than in t he case of symmetric coordination. Nevert heless, it is possible that an individual count ry devalues more in a Nash equilibrium t han in a coordinat ed symmet ric equilibrium. Such a possibility is illust rated by the plots of individual devaluat ion rat esin the middle 38 of bot h Figures 6a and 6b. I n t hese plot s, there is a range of realizat ions of t he shock for which the solid line is above t he broken line. In t his case, t he subset of countries that devalue in a Nash equilibrium do so at an individual rate higher than t he common devaluation rat e in a symmetric coordinat ed equilibrium. Note t hat, as shown by Figure 6a, this is a possibility also when Periphery count ries resort t o coordinat ed devaluations much “ before” any count ry would devalue in a Nash allocation (² d > ¹² C S ). The explanation of t his result has to be found in t he di¤erent ial impact of coordinated and non coordinat ed devaluat ions on the real interest rat e in t he system as a whole. An uncoordinated devaluation by a few count ries has a limit ed impact on the real int erest rate in t he system. T hus, out put st abilizat ion by the countries t hat opt for a ‡oat requires a relative large jump in t heir exchange rates. A coordinat ed devaluation by many countries, inst ead, brings down the syst em-wide real interest rat e substant ially. T he bene…t from a large individual country exchange rate depreciat ion for out put stabilization purposes is much lower, compared to its costs in t erms of in‡at ion. Our t hird and last point refers to an import ant e¤ect of t he nat ional horizontal equity constraint . When this const raint is binding, there may exist a range of realizations of the shock for which no count ry devalues in a coordinated symmetric equilibrium, while some countries devalue in a Nash equilibrium. This is illust rat ed by Figure 6b, where, for values of the shock between ² d and ¹² C S , no symmetric devaluation is possible, while some Periphery count ries would …nd it optimal t o devalue when playing Nash. In such a range, monetary policy in the syst em as a whole is less expansionary in a symmetric coordinated equilibrium than in a Nash equilibrium. The implicat ions of this result deserve special att ent ion, as t hey stress t he possibility that , for given wages, ex post welfare could be higher in a Nash equilibrium t han in a coordinat ed symmet ric equilibrium. This will be t he case for values of ² that are not large enough t o t rigger a coordinat ed symmet ric devaluation, but large enough t o induce an uncoordinat ed devaluat ion by some count ries in a Nash equilibrium. For such values of t he shock, no-cooperat ion dominates symmetric (const rained) cooperat ion, from t he point of view of t he Periphery count ries as a group and indeed from t he point of view of t he syst em as a whole. This is an import ant result for our int erpret at ion of the ERM crisis. We will return on t his point shortly. 39 8.2 Poli cy t ensi ons, mar ket r esp onses, and exchange r at e cr i ses I s t here a speci…c role for policy coordinat ion in t he crisis of an exchangerate syst em? An exchange rate arrangement is primarily a mechanism for policy coordination. If t he relat ions between Cent er and Periphery are assumed to befrozen in non-cooperat ivebehavior, theonly coordinat ion options available are t hose open t o t he Periphery count ries among themselves. To t he extent t hat cooperative behavior prevails in t he Periphery of t he system (and Periphery countries are ex-ante perceived as su¢ ciently similar t o each ot her), t he outcome can be described by using the results from our analysis. Int uitively, in response t o a demand shock in the Cent er, t he Periphery will t end not to implement a joint (symmetric cooperat ive) devaluation, unless t he recessionary costs of defending the exchange rat e are high enough t o o¤set the collect ive political cost of reneging on the commit ment to peg. Condit ional on abandoning t he peg, the common devaluat ion rate will be set in a way t hat fully int ernalizes all int ra-Periphery int ernational spillovers. As the real exchange rate of the Periphery as a whole falls markedly, there is only a limit ed need t o use the exchange rate for st abilization purposes: t he common devaluat ion rat e will be small in equilibrium. A crisis of t heexchange rat esyst em isprimarily a crisis of t hecooperat ion agreement that de…nes and sust ains it . In our t heoretical framework, there are at least two ways in which a crisis may emerge. First, t o the ext ent t hat t he coordination scheme lacks an e¤ect ive enforcement mechanism, individual countries always have an incentive to renege on t he agreement and play according t o t heir individual reaction funct ions. Although the hypot hesis of an exchange rate crisis st emming from individually deviant behavior raises an issue of logical consist ency — why did the deviant countries accept t o be part of t he syst em in the …rst place? —, it is not unrealist ic.41 Consider a realizat ion of the shock slight ly larger t han ² d in Figure 6a. While coordinat ion requires a generalized devaluation, nat ional policy makers may be t empted t o “ save” t heir currency. After all, as Figure 6a suggest s, in a Nash equilibrium just t o t he right of ² d ; it may t ake the devaluat ion of just one currency t o absorb the shock and save t he rest of the Periphery from t he embarrassment of reneging on t he announced exchange rat e t arget s. If market part icipant s’ beliefs are based on t he assumption of symmetric cooperative behavior, t hey will expect , for a shock in the range under considerat ion, t o observe a sizable appreciation of t he Center’s real exchange rate, to be achieved through cooperative small uniform devaluat ions of all currencies in t he Periphery. In such a situation, a large devaluation by one count ry provides a st rong signal to market part icipant s that national policy 40 makers are no longer act ing cooperat ively. If t he Periphery as a whole reverts t o undilut ed Nash, some count ries will maint ain their exchange rate parit y vis-à-vis t he Center. For t he ot hers, t he equilibrium devaluat ion rat e needs t o be large. Since, on average, the monet ary stance of t he syst em is not as expansionary as under coordinat ion, real int erest rates do not fall as much: devaluing count ries will use their exchange rate instrument t o t arget a sustained increase in t he level of aggregat e demand. Ult imat ely, large-scale currency crises in a number of count ries will be required to modify appreciably the e¤ect ive t erms of t rade of t he Center. Note t hat in this …rst int erpret ation of a currency crisis ² d falls t o t he right of ¹² C S : t herefore, the national horizontal equity constraint is not binding, nor it plays any role in t he st ory. In our second interpretat ion of the emergence of a crisis, illustrat ed in Figure 6b, nat ional horizont al equity is inst ead an import ant issue. Consider a realization of t he shock in the range (² d ,¹² C S ): a shock which is sizable but not large enough t o just ify a collective devaluation put s the system under considerablest ress. If a cooperative defenseof the peg prevails, t hePeriphery count ries perceive t hat t he individual gains from a unilateral devaluation are high. Implement ing a coordinat ed but select ive (t hat is, non-universal) devaluat ion is a problem when there are no instrument s t o dist ribut e its costs and bene…ts evenly across nations. For realizat ions of t he shock in t he range (² d ,¹² C S ), the loss in welfare from const rained cooperat ive behavior is partly avoided in a Nash equilibrium. A Nash equilibrium would accomplish what symmetric coordination cannot: some subset of countries would devalue, making the monet ary stance in t he system more expansionary (alt hough not by enough to maximize the sum of t he nat ional welfare functions). If policy makers realize t hat t he syst em is in such a stat e, it could be collect ively rat ional t o revert to Nash, and thus to implement uncoordinat ed large devaluations. Even if, in t he eye of an observer, t hese devaluations may look like a disorderly response by domest ic policy makers t o market pressures, they would nonet heless be consist ent with (const rained) welfare maximizat ion both at t he level of t he individual Periphery count ry and from t he point of view of t he Periphery as a collect ive. Yet again, a realignment involving only one country would signal to the privat e market s t hat t he exchange rat e mechanism as a coordination device has ground to a halt. What is t he role of markets in a crisis of t he exchange rate syst em? T he answer t o this question is complex, because market s play bot h an act ive and a passive role. As regards t heir act ive role, in our theoretical framework, privat e sect or expectat ions are re‡ected in t he level of the predet ermined nominal variables. Higher nominal wages, ceteris par ibus, reduce t he stabil41 ity (and viability) of a peg: all threshold values for t he shock determining both coordinat ed or uncoordinated opt imal switches between exchange rate regimes are funct ions of t he predetermined nominal variables. On the ot her hand, once privat e expect at ions are formed, exchange rat e policies are t he out come of rat ional decision making by t he national authorities, who assess t he costs and bene…ts of defending t he peg, given t he current realization of t he shock t o the fundament al. In t his sense, the behavior of t he …nancial market s may be seen as a passive re‡ect ion of policy makers’ choices, and a currency crisis would be nothing but t he expression, in the …nancial market s, of t he tensions that lead to t he breaking up of t he int ernational agreement on policy coordinat ion. Can a syst em of …xed exchange rat es survive a crisis t hat puts into quest ion its viability as a policy coordinating mechanism? The answer t o this quest ion depends on two considerat ions. First, in t he light of the crisis, privat e agents may modify t heir prior s about t he likelihood of future cooperative behavior in t he policy game. The levels of wages and domest ic int erest rat es vary with t he market ’s perception of the nature of the ongoing game among policy makers. Therefore, the post-crisis …xed exchange rate syst em may be intrinsically more or less fragile, depending on the perceived changes in t he nature of t he game. Second, as a result of a crisis, policy makers may form coalitions, that is, new agreement s among subset s of the players replace t he old agreement . For example, a subset of a few Periphery count ries may either join an enlarged Center or form a unilat eral …xed exchange rat e area vis-à-vis the Cent er (t he Core) which systematically excludes t he ot hers Periphery count ries. T he emergence of such coalitions might be more plausible if t here is some exante het erogeneity among t he Periphery count ries. Through t he mechanisms analyzed in t hediscussion of t he Nash allocation, the stability of t he bilat eral exchange rat es in the Core vis-a-vis an IS shock in the Cent er clearly bene…ts from the free ‡oat of t he Core vis-à-vis the outsiders’ currencies. 9 I nt er pr et ing t he ER M cr isis in a Cent er Per ipher y model T he Center-Periphery model shows that, for a given exogenous shock t o t he conventional fundament als, represent ed by ², t he equilibrium outcome is not independent of t he nature and ext ent of policy coordination in the Periphery of the syst em. The goal of this sect ion is t o explore t he contribution of this insight t o an underst anding of t he 92-93 exchange rat e crisis. 42 9.1 T he r eali gnment of t he li r a as a coor di nat i on shock At t he end of 1991, it became clear that, in t he absence of a realignment in the ERM, t he Bundesbank would pursue t he goal of price stability by using its interest rate inst rument s wit h litt le regard for the consequences for t he domest ic real economy and wit h ut t er disregard for the internat ional implicat ions of such a policy. Figure 1 provides a striking synthesis of t he policy con‡ict between Germany and the ot her ERM members. The int erest rate in Germany increases relent lessly up to t he crisis. This con‡ict, reinforced by the tensions generat ed by t he …rst Danish referendum and t he dollar crisis in August, had led, during the summer of 1992, to expect at ions of a generalized devaluation vis-à-vis the D-Mark, by a magnit ude that was variable across country (It aly, Spain and Portugal show t hehighest interest di¤erent ials) but modest overall, and signi…cant ly smaller t han the magnit udes of the depreciat ions that were actually realized in t he following weeks. In t he …rst half of Sept ember, a massive speculat ive att ack against t he lira t ook place. Bot h the adverse cyclical condit ions and t he increasing public debt t o GDP ratio suggest ed that the It alian government would have welcomed a devaluation. Unless the Bundesbank had st ood decisively in defense of t he exist ing parities, a realignment was widely considered unavoidable. The speculat ive att ack against the lira intensi…ed aft er the EC meet ing in Bath on t he 5th and 6t h of Sept ember, on which occasion t he con‡ict on exchange rat e mat t ers among European policy makers was widely report ed by the press. During t he week following the event, t he Bundesbank and t he Bank of It aly put forward a proposal for a generalized realignment involving a 3.5% revaluat ion of t he D-mark and a 3.5% devaluation of t he lira against all ot her currencies in the ERM (that is, a 7% devaluation of the lira against t he D-mark). Therealignment should have been mat ched by a cut in the German int erest rates by a magnit ude that was to depend on t he number of count ries joining in the realignment as well as on the size of t hese realignment s. At …rst sight , t he German proposal may look like a bargaining scheme, wit h the Bundesbank o¤ering a subst ant ial int erest rat e cut in exchange for a generalized devaluat ion of the ERM currencies vis-à-vis t he D-mark. Our model shows how misleading such an interpretation can be. The German proposal need involve no bargaining or compromise. A decrease in t he community-wide interest rate following a generalized realignment is an equilibrium (endogenous) out come in our model, in which there is no bargaining and t he Cent er (Germany) does not modify its non-cooperat ive policy st rat egy vis-à-vis the Periphery. There need not be any quid pro quo involved. As Germany aft er reuni…cat ion wasunwilling t o modify it spolicy mix, t he 43 only way in which the rest of the Community could rescue t heir economies from t he adverse domest ic implicat ions of high German int erest rates was t o engineer domest ic monetary expansions and depreciate their currencies. T his could have been done in a coordinated way, for inst ance (but not necessarily) along t he lines of t he German-It alian proposal. I n principle, t he realignment scheme could have also involved di¤erent iat ed rat es of exchange rate devaluation, to account for het erogeneity among individual Periphery count ries. Not e that, according t o our analysis, t he init ial and solit ary I talian devaluat ion by 7% could hardly have been considered to be part of a sustainable equilibrium. Assuming, for t he sake of argument , that t he Bundesbank proposal could indeed have produced a sust ainable ERM-wide parity grid, t he devaluat ion of t he lira by 7% would have made sense only in the cont ext of a generalized realignment . As t he lira was t he only currency t o be devalued in a period of rampant rumors and leaks about disagreements and polemics among ERM member countries,42 t he new parity grid est ablished in Sept ember 14th 1992 could have hardly been convincing in t he eye of …nancial market s. In t he light of these considerations, one should not dismiss the hypot hesis that t he realignment of t he lira on Sept ember 14, 1992 was indeed an important component of t he shock to t he ERM fundament als, insofar as it conveyed information about a possible change in the rules of t he ERM monet ary policy game (a switch from cooperative to non-cooperat ive behavior) and t hus led private market s t o revise their views on t he current and fut ure level of EC-wide int erest rates. Wit h the …rst It alian devaluation it became apparent t hat German rat es would only fall signi…cant ly in response t o sharp devaluat ions by a number of ot her count ries. Our model shows t hat uncoordinated realignments deliver less monet ary expansion t han coordinated realignment s, even if all of t he devaluat ions that charact erize t he new Nash equilibrium are implement ed fully. A fortiori, t he uncoordinat ed realignment(s) of a disequilibrium scenario will deliver rat her lit t le syst em-wide monetary relaxat ion. Thus, t he partial resolution of t he uncert ainty about the degree of cohesion among t he ERM countries clearly pointed to a persist ence of relat ively high int erest rates. Doubt s about the sustainability of such a regime must have suddenly grown st ronger in quite a few count ries. As Padoa-Schioppa [1994] puts it: ” [the cause of the ERM crisis] was plainly traceable to what in the academic jargon is called a ’co-ordination failure’ [...]. There was the refusal to accept a general realignment and even to call a meeting of the Monetary Committee or of the ministers and 44 central-bank governors when, in September 1992, a general realignment might have calmed the markets. The general procedure, once embarked on, did not produce a credible new grid. At various time, and in various ways, through unhelpful declarations that excited mar kets as well as through policy decisions that caused unnecessar y friction, the system was destabilized by its very custodians.” 43 9.2 Poli cy opt i ons in Eur ope and scenar i os for t he 9293 cr isis Anecdotal evidence of a low level of cohesion and coordinat ion in t he face of t he t ensions in the ERM in 1992 is overwhelming. I t …rst became public knowledge with the devaluat ion of t he lira. Why were European count ries unable t o agree on coordinat ed policy action? At a t heoret ical level, our model addresses this issue by focusing on pot ent ial con‡ict s regarding the dist ribut ional consequences of a coordinat ed realignment . A devaluat ion by one count ry has a posit ive ext ernal e¤ect on welfare in t he rest of t he Periphery. There is scope for disagreement and con‡ict about how t he costs and bene…ts of coordinat ed policies are to be dist ributed among t he members of an exchange rat e system. Taking our model at face value, let usfocus on thescenario in which, faced wit h a sizable shock to German demand, symmetric coordination would lead t o a generalized defense of t he exchange rate regime, while Nash behavior would bring about uncoordinated devaluat ions by some count ries. The …rst bit of relevant evidence is t hat Germany was keen on implementing a generalized ERM realignment, while being utt erly opposed to any revision of its own monet ary policy. The second bit of evidence is that apparently no count ry (with t he except ion of Italy) was willing to discuss the t erms of an ERM-wide realignment , while considerable pressure was put on Germany to do exact ly what it did not want t o do. In t he EC meet ing of Bath at t he beginning of Sept ember 1992 “ Schlesinger was not so much ignored as scorned, says a participant [to the EC meeting in Bath], for his apparent willingness to ‘so easily put monetary union at r isk’ with the …rst ERM realignment since 1987. [...] ‘Realignment was a dirty word in Bath’ Schlesinger was later bitterly to complain to a German colleague.” 44 As it became absolut ely clear t hat Germany would not give in to t he ot her ERM countries’ request t o loosen its monet ary policy, t here were two 45 possible courses of act ion open to the Periphery count ries. The …rst one was to engage in a possibly very painful defense of t he existing parit ies, at t he cost of further domest ic de‡at ion and worsening …scal imbalances. T he second one was t o engineer some monetary expansion in t he Periphery. This could have been achieved eit her in a coordinat ed way (implying bargaining and compromising on whet her, and by how much, each particular country should have devalued), or, in the spirit of t he brightest libertarian tradit ion, “ each one to his own” . In t he second scenario, the quest ion arises as to which countries would have t o give in and devalue. Besides the lira, a reasonable set included t he pound, t he peset a and t he escudo. Not e that , as far as the French franc is concerned, t he uncert ainty regarding the polit ical support for the Maast richt Treaty played a role in delaying t he speculat ive at t ack on t his currency until aft er the referendum result – a t iny majority for the oui to Maastricht. Perhaps, t herewas no need at all t o guesswhich part icular currency would have been morevulnerable to a speculativeatt ack. Our model predicts that a non-coordinated equilibrium requires a few count ries t o devalue by a sizable amount ; it cannot predict which currencies will be devalued. Thus, each currency is a potent ial candidat e for a devaluation, regardless of how sound its domest ic fundament als look. The rest of the st ory is well known: during t he…rst t en days of t hecrisis, thelira and t hepound withdrew from theERM, t he peset a devalued by 5%, t he defense of t he French franc required massive int ervention by both French and German authoritiesand Spain, Portugal and I reland reint roduced temporary capital cont rols. In t he following months, several ERM currencies su¤ered repeated att acks.45 Subst ant ial devaluations were oft en the only possible response. We st ress two caveat s. The …rst one regards the de…nition of t he Cent er of the syst em. This, of course, may include more than one country, provided t hat t heir monet ary policies are fully coordinat ed. T his is the case for Germany, the Netherlands and, to a cert ain ext ent , Belgium. The second caveat concerns the evidence of a coalition or cooperative arrangement between Germany and France. France clearly cannot, for t he period under consideration, be considered part of t he (hard) Center. Yet , unlike all ot her Periphery countries, which were e¤ect ively left to fend for t hemselves, France bene…ted in t he defense of it s parity from massive German support, putt ing it in the special position of belonging t o the ext ended Cent er or “ soft Core” of the syst em. Wit h t he except ion of France, t he survival of t he ERM was clearly linked, once t he crisis had st art ed, t o each individual count ry’s willingness t o peg its exchangerate to t heD-Mark, wit h lit t le or no int ra-community support . T he di¢ culty of this t ask was magni…ed by a widespread feeling t hat t he st rength 46 of the polit ical support for Maastricht had somehow dwindled with the …rst Danish referendum. From September 1992 t ill August 1993, t he working of t he ERM is well described in t erms of uncoordinat ed at tempt s to det ermine t he new equilibrium exchange rates, that is, by t he (somewhat messy and st aggered implement at ion of the) Nash scenario of our model. 10 T he r oad ahead I n the mid 1990s, we have witnessed somet hing of a shift of support , wit hin both the political and intellect ual milieu, from ext ernal to internal nominal anchors. It appears rather hard to …nd the same ent husiasm for …xed exchange rat e policies t hat charact erized t he late 1980s. As a new chapt er of European monet ary hist ory is being writ t en, t he academic debate on its t heoretical underpinnings has indeed been increasingly devot ed to in‡at ion t argeting, opt imal contract s and cent ral bank independence, wit h reduced emphasis on target zones and other forms of exchange rat e management as st abilizat ion instrument s, reputat ion-building schemes and ant i-in‡ationary devices. The crucial t urning point a¤ecting int ellectual opinions and policy priorit ies is the crisis of t he ERM in 1992/ 93. Still, t o consider t he ERM crisis as the ult imat e proof of the unsust ainability (or undesirability) of …xed exchange rat es is t o miss the point. This paper has developed in det ail the view that the key event that triggered t he collapse of t he ERM was a shift in the at t it ude toward exchange rat e and monet ary policy coordination and cooperat ion among European policy makers, and t he perception of t his shift by market participants. Wit h most of t he exist ing lit erat ure, we share t he view t hat — unless t he commitment to t he exchange rat e peg is indeed complet ely unquestioned — t he oxymoronlike “ ‡exible peg” is in it self dest abilizing, and cont ains the seeds of it s own destruct ion. We do not believe, however, t hat if a collapse can occur it necessarily will occur. Asymmetric disturbances per se need not be disruptive of internat ional monet ary arrangement s. Almost by de…nit ion, a crisis of an exchange rate syst em is a sympt om of insu¢ cient or ine¤ect ive policy coordination. As regards the implicat ions for t he future of t he ERM and EMU, what t he 1992-93 event s have painfully revealed is the intrinsic fragility of t he European monet ary architecture. What should replace the current (non-) syst em? The Cent er is current ly showing an uncompromising att it ude t owards monet ary stability in a monet ary union. T he tradit ional debate bet ween the “ monetarist” and “ economist” approach46 to European monetary issues has long made us aware of t he fact t hat , for the Center (t he home of 47 t he ‘economist ’ approach), the ‘convergence’ process is virt ually a goal in its own right , rat her t han a means t o the end of monetary union. The transit ion t owards monet ary union, rat her than monet ary union itself, is the crux of t he process. Not e t hat any convergence-cent ered approach to the transit ion t o monet ary union re‡ect s a view of monet ary union as a coming t ogether of count ries that are e¤ectively replicas of each ot her rat her than as a process of int egration of het erogeneous economies. The part icular furt her slant given t o this approach by t he Center in addit ion makes t he convergence process asymmet ric, with the st ate of monet ary union to be reached t hrough t he addition of homogenized Periphery regions to a pre-exist ing core on the terms of the core. The st at ement s of German …scal and monet ary aut horit ies in t he fall of 1995 leave no doubt about t heir stance on these issues. Is it possible t o replace e¤ect ive and active policy coordination among European count ries with t he kind of mechanical policy coordinat ion t hat is implicitly required by numerical ceilingson public sector debts and by t argets for in‡at ion rat es, exchange rat es and int erest rat es? Despit e the well-known object ions to the logic and e¤ect iveness of t he Maast richt convergence crit eria, such t est s of good macroeconomic behavior may be useful in fost ering good policy management , provided that they are applied sensibly and ‡exibly. After all, solvency, low in‡at ion and …nancial st ability are reasonable pre-requisit es for a count ry that want s t o join a monetary union. An obsessively mechanical reading of t he Maastricht crit eria, however, t ends t o focus t he at t ent ion exclusively on domest ic problems, denying the relevance of t he issue of reconstruct ing a system of European monetary cooperation. One key lesson from t he 1992-93 crisis is that , in t he absence of e¤ect ive int ernalization of t he policy spillovers, nominal or real macroeconomic convergence between Cent er and Periphery do not insulat e the syst em from currency crises. Even if a country were able t o satisfy t he Maast richt crit eria exactly, it could still be vulnerable t o speculative att acks. Moreover, recent episodes show that, without cooperat ion, count ries t hat att empt t o achieve convergence may …nd t hemselves subject ed to t he …nancial equivalent of t he t ort ures of Tantalus. There are plenty of …nancial shocks beyond t he control of a national policy maker t hat may hamper convergence; careless political st atement s by in‡uential foreigners are a good example. Through t heir impact on interest rat es, speculative pressures generat ed by a t hrowaway comment or an infelicitously timed opinion in Frankfurt can rapidly reduce t he e¤ect iveness of domestic policy measures in Rome. Finally, it is apparent t hat monet ary union, if and when it comes, will init ially involve but a st rict subset of all EU members. A whole range of Center-Periphery (and int ra-Periphery) issues will therefore have to be dealt wit h. Even t hough t hespecial problems associat ed with a two-speed or multi48 speed monet ary union are only transit ional or t emporary, in nat ure, no one doubts t hey are likely t o be acut e. The year 1995 has already given us a taste of t he t ensions t hat are likely t o arise. We have ment ioned before the debate on the “ unfair” compet it ive advant age acquired by weak-currency count ries against st rong-currency count ries as a result of t he large devaluat ions since September 1992. T he suggest ion was even made that these “ competitive devaluat ions” sanct ioned t heimposit ion of count ervailing dut ies wit hin the EU. Rebut ted forcefully by several economist s (including the EU Commissioner Mario Monti) as inconsist ent wit h the Single Market legislat ion, the case for “ devaluation aid” and compensatory t ransfers failed to convince the economists and the o¢ cials of t he Commission, who in the fall of 1995 concluded t hat, if anything, st rong-currency count ries such as France, the Benelux and Germany had gained in compet it iveness t hrough low in‡at ion, lower int erest rates and low labor costs. In hist orical perspect ive, political cohesion has been theengineof progress in European economic and monet ary integrat ion. Political cohesion is what has tradit ionally overcome t heskept icism of market s as well as the objections of the “ expert s” . The insu¢ cient and solit ary realignment of t he lira in 1992 revealed t o both markets and expert s t hat European policy makers were no longer able or willing t o give a coherent, coordinat ed response to monetary t ensions. A renewed ability t o do so will be t he …rst import ant indicat or t hat t he Maastricht design has not been swept away on waves of speculative frenzy. 49 A ppendix T his appendix presents t he struct ure of t he model underlying our analysis. All variables ot her t han int erest rates are in nat ural logarit hms. All variables referring t o t he Center country are st arred, while t he Periphery countries are indexed with a subscript i , for i = 1; 2; :::; N . Unless ot herwise explicitly st ated, Greek let ters (bot h lowercase and uppercase) refer to const ant , posit ive paramet ers. A ) T he Cent er count r y Out put supply in the Cent er, denoted by y , is a det erministic funct ion of employment , n ¤, subject t o decreasing ret urns to scale: y¤t = (1 ¡ ®)n ¤t 0< ®< 1 (A.1) ¤ Labor is supplied inelast ically, while pro…t-maximizing compet it ive …rms equat e the marginal product of labor t o t he real wage. The money wage in t he Center is denot ed w¤ , while p¤ is the Cent er’s GDP de‡ator: wt¤ ¡ p¤t = ¡ ®n¤t (A.2) Real aggregat e demand in t he Cent er depends on t he e¤ective real exchange rat e of the Periphery vis-à-vis the Center z (de…ned below), t he Center’s real interest rat e r ¤ , and an aggregat e demand shock ¸ ¤ : yt¤ = ¸ ¤t ¡ ±zt ¡ º r t¤ (A.3) T he real interest rat e in t he Cent er is it s nominal interest rate i ¤ minus t he expect ed proportional rat e of change in its consumer price index, q¤ : r ¤t ´ i ¤t ¡ E t qt¤+ 1 + qt¤ (A.4) where E t denot es t he expect ation operator condit ional on information available in period t. The Center’s consumer price index is de…ned as follows. Let si ;t be t he nominal spot exchange rat e of t he i t h Periphery count ry (expressed as i t h count ry’s currency per unit of Center’s currency) and let st be the nominal e¤ective exchange rate of the Periphery vis-à-vis t he Center, that is, st ´ 1 XN si;t N i= 1 (A.5) Given t he assumpt ion of symmet ry, in eqn.(A.5), t he e¤ect ive nominal exchange rat e is simply t he arit hmet ic average of the nominal exchange rat es 50 in t he Periphery. Similarly, let pi ;t be t he GDP de‡at or of t he i t h Periphery count ry (in local currency). The real exchange rat e of the Periphery country i vis-à-vis the Cent er is de…ned as zi ;t = si ;t ¡ pi ;t + p¤t (A.6) T he e¤ective real exchange rat e of the Periphery vis-à-vis the Cent er, z, is t hen given by 1 XN zt ´ zi ;t N i= 1 (A.7) It is convenient t o de…ne p~t t he “ e¤ective price level” of the Periphery as a whole, measured in t he Center’s currency, that is, 1 XN (pi ;t ¡ si;t ) N i= 1 p ~t ´ (A.8) Assuming a const ant share of import s in consumpt ion, ¯ (which applies to each of t he Periphery countries as well as to t he Center), t he Cent er’s CPI is de…ned as follows qt¤ ´ (1 ¡ ¯ )p¤t + ¯ p~t = p¤t ¡ ¯ zt 0< ¯ < 1 2 (A.9) We rest rict the propensity t o import ¯ t o be less t han one half, which is equivalent to assuming home bias in consumption in our model. As will become clear later, this assumption rules out the possibility that real int erest di¤erent ials and real expect ed depreciat ion between Cent er and Periphery move in opposit e direct ions. Assuming a const ant velocity money demand funct ion, equilibrium in t he money market requires m¤t = p¤t + yt¤ = w¤t + n ¤t (A.10) where m ¤ denotes the Cent er’s nominal money st ock. At t he end of period t ¡ 1, t hat is before t he Center money stock m¤t is det ermined and observed, wage sett ers choose t he money wage prevailing in period t. Their objective function is t o minimize t he forecasted deviat ion of employment from t he full-employment level (here normalized to zero). Therefore, t hey solve Et¡ min ¤ wt 1 1 ¤2 (n ) 2 t 51 (A.11) subject t o eqn.(A.10). Since n ¤t = m¤t ¡ w¤t ; t his implies t hat nominal wages are equal t o t he expect ed money supply, and employment (or out put ) is function only of monet ary innovat ions: wt¤ = E t ¡ 1 m¤t (A.12) n ¤t = m¤t ¡ E t ¡ 1 m¤t (A.13) B ) T he Per ipher y count r ies Periphery count rieshave the samet echnology as the Cent er. Thus, using self-explanatory not at ion, the supply-side equat ions characterizing t he Periphery are given below. yi;t = (1 ¡ ®)n i ;t (A.14) wi ;t ¡ pi ;t = ¡ ®n i;t (A.15) We assume that Periphery countries import (export ) goods and services exclusively from (t o) the Cent er count ry. This is t he reason why only t he bilateral real exchange rate of country i relative to the Center, zi , enters into t he demand equat ion for country i 0s output : yi ;t = ¸ + ±zi ;t ¡ º r i ;t (A.16) Di¤erent from t he demand equat ion in the Cent er country (A.3), t he paramet er ¸ in equat ion (A.16) is const ant . In ot her words, we abstract from count ry-speci…c and t ime-speci…c IS shocks hit t ing t he Periphery count ries. The only source of exogenous uncert ainty is t herefore a perturbat ion of aggregat e demand in t he Cent er, which a¤ects all Periphery countries symmetrically. The other behavioral parameters ±; º and ¯ are ident ical in both t he Cent er and t he Periphery. Real int erest and exchange rat es in t he i t h country are r i ;t = i i ;t ¡ E t qi ;t + 1 + qi ;t (A.17) qi ;t = pi;t + ¯ zi;t (A.18) By analogy wit h t he Center, real money balances, money wages and employment in the Periphery are det ermined as follows mi ;t ¡ pi;t = yi ;t (A.19) wi ;t = E t ¡ 1 mi ;t (A.20) 52 n i;t = mi ;t ¡ E t ¡ 1 mi ;t (A.21) We …nally assume t hat asset s denominat ed in di¤erent currencies are perfect substitut es in private agent s’ port folios, so t hat t he uncovered int erest parity condit ion holds: i i;t = i ¤t + E t si;t + 1 ¡ si ;t (A.22) Note t hat , given (A.22), wit h perfect capital mobility t he uncovered int erest parity condit ion must hold for any pair of currencies in t he syst em. C) Shocks t o fundament als, m onet ar y i nnovat ions and t he r eal ex change r at e In t his section, we present a semi-reduced form of our model, expressing all endogenous variables as funct ions exclusively of exogenous, predet ermined or cont rol variables. First, consider the bilat eral real int erest rate di¤erent ial between t he i t h country and the Cent er count ry r i ;t = r ¤t ¡ ¯ (E t zt + 1 ¡ zt ) + (1 ¡ ¯ )(E t zi ;t + 1 ¡ zi ;t ) (A.23) By t aking t he sum over t he N periphery count ries, t he average int erest rate di¤erent ial between t he Periphery and t he Center will be P r i ;t = r t¤ + (1 ¡ 2¯ )(E t zt + 1 ¡ zt ) N i (A.24) According t o the previous expression, the real interest rat e di¤erent ial and t he expected rate of depreciation of t he real exchange rat e between Cent er and Periphery move in t he same direct ion if and only if ¯ < 1=2, that is, if there is home bias in consumpt ion (see eqn.(A.9)). We maint ain this assumption throughout . A few intermediate steps are helpful t o characterize t he reduced form equat ion for the Cent er’s e¤ect ive real exchange rat e. First, using eqn.(A.24) t oget her wit h t he aggregat e demand functions (A.3) and (A.16), and t he resource const raint of t he economy as a whole, P µP ¶ yi ;t i ni ;t ¡ yt¤ = (1 ¡ ®) ¡ n ¤t N N we obtain a …rst order st ochast ic di¤erence equat ion in zt : i µP zt = ° E t zt + 1 + Á where ° ´ ¶ n i ;t ¤ ¡ nt ¡ N i v(1 ¡ 2¯ ) < 1 2± + v(1 ¡ 2¯ ) 53 à (A.25) ! ° (¸ ¡ ¸ ¤t ) º (1 ¡ 2¯ ) (A.26) 1¡ ® 2± + v(1 ¡ 2¯ ) (A.27) Á´ As t he e¤ective real exchange rate zt is a forward looking variable, we impose a no-bubble t erminal condit ion. Solving equation (A.26) with such a boundary condition yields µP zt = Á ¶ ni ;t ¡ n ¤t + ² t N i (A.28) where ² t is de…ned as X1 ° ° ¿E t (¸ ¤t+ ¿ ¡ ¸ ) v(1 ¡ 2¯ ) ¿= 0 ²t ´ (A.29) The e¤ective real exchange rat e depends bot h on the di¤erence between t he current monetary innovat ions in t he Periphery and in the Cent er (which equals the di¤erence between the employment levels in t he Periphery and t he Center) and, t hrough t he forward looking variable ² t , on current and expect ed future real demand shocks in the Center relative to the Periphery. T hus, a demand (IS) shock in the Center larger than in the Periphery causes t he Cent er’s real exchange rat e t o appreciat e, while a money supply shock in t he Cent er larger t han in t he Periphery causes the Cent er’s real exchange rate to depreciat e. The st ochastic variable ² t is the exogenous shock to t he fundament als of our internat ional economy. It bears emphasizing t hat t he current realizat ion of ² t is t he present discounted value of current and expect ed future demand dist urbances over t he in…nit e horizon. D ) B ilat er al r eal exchange r at es and r eal int er est r at es Next , it is st raightforward (albeit algebraically t edious) t o show that t he bilateral real exchange rat e of Periphery country i vis-à-vis the Cent er is 0 1 zi ;t = »(1 ¡ µ) ni ;t + @² t ¡ »µ X nj ;t ¡ Án¤t A (A.30) j6 =i where the paramet ers µ and » are de…ned as à µ´ ±¡ º ¯ 2± + º (1 ¡ 2¯ ) ! 1 ; N »´ 1¡ ® Á = > 0 ± + º (1 ¡ ¯ ) 1¡ Nµ (A.31) Note that the sign of µ is ambiguous. Using (A.16) and (A.30), the semi-reduced form of t he real interest rate in country i becomes 8 r i;t 0 19 = X 1< = : ¸ + [±»(1 ¡ µ) ¡ (1 ¡ ®)] n i ;t + ±@² t ¡ »µ nj ;t ¡ Án ¤tA ; º j6 =i (A.32) 54 I nspection of equation (A.32) brings out an import ant feat ure of our frameP work: for given monetary policies in t he rest of the syst em, n ¤t and j 6= i n j ;t , t he spillovers from a posit ive demand shock in t he Cent er result in an increase of t he real int erest rate in count ry i . That is t o say, positive demand shocks in t he Center count ry direct ly translat e int o negat ive demand shocks in t he Periphery t hrough their e¤ect on the real int erest rate. Finally, it is useful t o write t he semi-reduced form equat ions for t he CPI as 0 1 qi ;t = [® + ¯ »(1 ¡ µ)] n i ;t + wi;t + ¯ @² t ¡ »µ X n j ;t ¡ Án ¤t A (A.33) j6 =i and t he bilat eral nominal exchange rat e vis-à-vis the Cent er as 0 si;t = [® + »(1 ¡ µ)] n i;t + wi ;t ¡ w¤t ¡ ®n¤t + @² t ¡ »µ 1 X n j ;t ¡ Án ¤t A (A.34) j6 =i Other things equal, a depreciat ion of it s nominal exchange rat e raises both employment and t he CPI in count ry i . In t he main t ext , we adopt the following not at ional simpli…cat ions: ®0 ´ ® + ¯ »(1 ¡ µ) (A.35) ®1 ´ »µ (A.36) ®2 ´ ® + »(1 ¡ µ) (A.37) Ài ;t ´ ² t ¡ ®1 X n j ;t ¡ Án ¤t (A.38) j6 =i I t is t herefore immediat e to derive equations (1) and (2) in the main t ext by rearranging equat ions (A.33) and (A.34) above. E) Equi libr ium devaluat ion t hr esholds To det ermine the devaluat ion thresholds, we proceed as follows. First, we writ e t he formula for t he shadow devaluation rat e as: ¢~ si ;t = n ¹ i + (A ¡ ¤ ) wi ;t + (A ¡ ¯ ¤ ) Ài ;t + ¤ q¹i ;t ¡ A s¹ i ;t A where A= 1 + ¾®20 ®2 ¤ = ¾®0: 55 (A.39) (A.40) Second, market participant s’ wage expect ations can be rewrit ten by rearranging eqn.(20) as a function of a given t hreshold¹Ài;t à wi ;t = E t ¡ 1 mi ;t à + ¼i ;t ! si ;t ¡ [EÀi ;t jÀi;t < ¹Ài ;t ] = (1 ¡ ¼i ;t )A + (1 ¡ ¼i ;t )A + ¼i ;t ¤ n ¹ i + ¤ (q ¹ i;t ¡ ¯ [E Ài;t jÀi ;t ¸ ¹Ài ;t ]) (1 ¡ ¼i;t )A + ¼i;t ¤ ! (A.41) Third, we replace wi ;t in t he de…nit ion of the shadow devaluat ion rate ¢ s~i ;t with expression (A.41). Rearranging the realignment rule (18), country i will devalue its currency if t he following condition holds: à µ A¡ ¤ A A¡ ¯¤ A ! " # n ¹ i + ¤ (q ¹ i;t ¡ s¹ i ;t ) Ài ;t + ¡ (1 ¡ ¼i ;t ) A + ¼i ;t ¤ ¶" # (1 ¡ ¼i ;t ) A [EÀi ;t jÀi;t < ¹Ài ;t ] + ¼i ;t ¤¯ [E Ài ;t jÀi ;t ¸ ¹Ài ;t ] ¡ ¸ c~i (1 ¡ ¼i ;t ) A + ¼i ;t ¤ (A.42) T his is the key-expression t o the endogenous ident i…cation of t he devaluat ion t hreshold ¹Ài;t ; so far t aken as a given parameter. The equilibrium int erior value(s) of the devaluat ion t hreshold under rational expect at ions can be found by taking expression (A.42) to hold wit h equality and solving for Ài ;t = ¹Ài ;t : F) M ult i-count r y N ash equilibr ium Our t hree-step solution st rat egy focuses on equilibrium outcomes involving (possibly) devaluations by some count ries. First , conject ure the existence of a realization of the shock, say ² = ^², such t hat each Periphery count ry is indi¤erent between maint aining t he peg and abandoning it. By condit ions (18), it is obvious t hat this is possible if and only if t he SDR — eqn.(A.39) above — is equal to c~ for each count ry in the Periphery, when evaluated at ^² : ¢ s~i [^²] = ~ c i = 1; 2; :::; N (A.43) Given t hat the Periphery countries are indi¤erent between a peg and a ‡oat , denote by N F L the number of countries t hat decide t o realign. Since t he count ries that chooset o abandon the peg devalue(optimally) by a percent age c~, the average actual depreciation rat e is 1 XN NFL NFL (si ¡ s¹ ) = ¢ s~i [^²] = c~ N i= 1 N N 56 (A.44) Second, consider the aggregat ereact ion funct ion of the Periphery, namely P P ni 1 · i si = ¡ ²¡ N ®2 N i P P ¸ wi i ni + ®1 (N ¡ 1) N N i (A.45) Using eqn.(A.44), it is possible t o evaluate the previous expression at ² = ^². Solving for t he average employment rate in t he Periphery yields P " 1 NFL ni (^²) = c~¡ ^² + N ®2 ¡ ®1 (N ¡ 1) N i P i ( s¹ i ¡ wi ) N # (A.46) Third, consider t he shadow devaluat ion rat e (A.39) and take its average across Periphery countries. For our conject ure to be true, it must be the case t hat P P ~i 1· wi i ¢s (^²) = ~ c= n ¹ + (A ¡ ¤ ) i + N A N P P P µ ¶ ¹i ¹i ¸ i ni i q i s + (A ¡ ¯ ¤ ) ^² ¡ ®1 (N ¡ 1) (^²) + ¤ ¡ A (A.47) N N N where A and ¤ are t he paramet ers de…ned in eqn.(A.40) above. Subst it ut ing eqn.(A.46) int o (A.47) and rearranging, t he percentage of count ries that in equilibrium must abandon t he peg is given by " # XN s XN wi ¡ q NFL 1 ¹ i ¡ wi ¹i = n ¹ + - 1^² ¡ - 2 ¡ ¤ ¡ A~ c N c~- 3 N N i= 1 i= 1 (A.48) where t he - 0s coe¢ cient s are funct ions of t he parameters of the model, as summarized below: à - 1 ®2 (A ¡ ¯ ¤) »µ(N ¡ 1) = = (A ¡ ¯ ¤ ) 1 + ®2 ¡ ®1 (N ¡ 1) ®+ Á ! ®1 (N ¡ 1) - 1 - 3 = - 2¡ A (A.49) ®2 The proport ion of count ries abandoning t he peg in equilibrium is a linear function of target exchange rat e, t he target price level, t he predet ermined wage rat es and t he realizat ion of the shock. As we conject ured, equat ion (A.48) implies t hat each country is indeed indi¤erent between abandoning or maint aining t he announced exchange rat e parity, provided that the required number of countries N F L devalue in t he aggregat e (for expositional convenience, we ignore t he const raint that N F L be an int eger). Not e t hat , with ex-ant e ident ical count ries, it is not possible to det ermine which particular count ries will implement a devaluat ion. - 2 = A+ 57 Nonetheless, t he range of shocks for which our conject ure is valid is limited by the fact t hat N F L must lie between 0 and the number of Periphery count ries. The boundaries of t his range can t hus be det ermined by sett ing N F L = 0 and N F L = N in equation (A.48), and solving for t he corresponding t hreshold values, ²d and ¹² d : For shocks larger t han ¹² d ; all count ries in t he Periphery will devalue by t he same optimal rat e ¢ s~i ;t ¸ c~. For shocks smaller than¹² d ; t he Periphery count ries will maint ain the peg. G) Cooper at ive equi libr ium under t he nat ional hor izont al equit y const r aint The optimal monetary policy in t he case of coordinat ed symmetric behavior of t he N countries in the Periphery implies the following react ion functions: if ¢ s~Ci S · ~ cC S , ni = ¹si ¡ wi ¡ ² ®+ Á (A.50) while if ¢ ~ sCi S ¸ c~C S , ¹si + ¢ ~ sCi S ¡ wi ¡ ² t ni = : ®+ Á (A.51) Under symmetric cooperation, t he relevant shadow devaluation rat e is ¢ s~Ci S = ³ ´ i 1 h CS CS CS CS n ¹ + A ¡ ¯ ¤ ² + A (w ¡ s ¹ ) ¡ ¤ (w ¡ q ¹ ) i i i i AC S (A.52) where 1 + ¾(® + ¯ Á)2 ¤ C S ´ ¾(® + ¯ Á) (A.53) ®+ Á Solving for the equilibrium yields t he following condit ion: the Periphery will joint ly devalue for ² ¸ ¹² C S , and joint ly maint ain the peg for ² · ¹²C S . T he t hreshold of t he shock at which a generalized devaluation occurs is easily obt ained as ACS ´ ¹² C S ´ ACS~ cC S ¡ n ¹ ¡ A C S (wi ¡ s¹ i ) + ¤ C S (wi ¡ q¹i ) ACS ¡ ¯ ¤ CS 58 (A.54) N ot es 1 For a reconstruct ion and chronology of the ERM events see Kenen [1995], ch.7, and Buiter, Corset ti and Pesent i [1996], ch.3. 2 The st andard references are Hamada [1976], Cooper [1985], Buit er and Marst on [1985] and Canzoneri and Henderson [1991]. Recent developments are surveyed in Currie and Levine [1993], Ghosh and Masson [1994] and Persson and Tabellini [1995]. 3 As Begg and Wyplosz [1993] writ e, “ despite inconclusiveformal evidence, most st udent s of the EMS have accepted the German dominance hypothesis. T he frequency of t his conclusion seems to arise from the usual view that if you don’t see what you believe then buy adequate glasses” (p.23). 4 Among t he most recent cases, it is wort h recalling that in 1995 French and Belgian indust ries – and a number of leading polit icians from these two count ries – have been bitt erly complaining about the competitive advant age acquired by Brit ish, Italian and Spanish industry as a result of t he large devaluat ions since Sept ember 1992. As an example, according t o the est imat es (report ed by t he Financial Times, Sept ember 18, 1995) by Jacques Calvet , head of Peugeot , for every 1 per cent fall in t he value of t he lira or st erling, t he company’s pre-t ax pro…ts fell by between FFr35m and FFr140m. 5 See e.g. Canzoneri and Henderson [1991]. 6 However, note that an increase in wages is directly in‡ationary but indirect ly de‡at ionary, as it reduces employment and t herefore domest ic prices along t he short -run Phillips curve. 7 See Appendix A and B. 8 For future reference, t he formula for ² t as the innovation t o the present discount ed value of t he demand shock is: ²t ´ X1 ° ° ¿E t (¸ ¤t+ ¿ ¡ ¸ ) º (1 ¡ 2¯ ) ¿= 0 Here ¸ ¤t is t he IS shock in t he Cent er during period t, ¸ is the common value of the IS ‘shock’ in t he Periphery, and ° ; º and ¯ are positive parameters wit h ¯ < 1=2 and ° < 1. See Appendix C for det ails. 9 When wemove from thepart ial-equilibrium approach considered so far to general-equilibrium considerations, it should be clear t hat t he policy stance of every country in the syst em is joint ly det ermined as a function of t he exogenous shock t o fundament als ² t . 10 In choosing the policy t arget q ¹i ;t and s¹ i ;t , the policy maker is aware of t he link between t hem: for a given value of t he Center’s GDP de‡at or p¤t , …xing q¹i ;t and s¹ i ;t is equivalent to t arget ing some level of t he real exchange rat e. In principle, one could use t his fact to explore the implicat ions of choosing an “ incorrect ” , misaligned exchange rate target. However, in what follows we 59 shall rat her focus on t he case where t here is no inescapable con‡ict between t he object ives for the int ernal and the ext ernal value of the currency. T he count ry t herefore target s q ¹ i;t = s¹ i;t + p¹ ¤t : 11 As we discuss below, p¹ ¤t is a const ant (normalized t o zero) in our model. 12 Indeed, most analyses of internat ional monetary games, including our own in Buiter, Corset ti and Pesenti [1995] and [1996], focus precisely on t he case in which t he Cent er country target s t he CPI and not t he de‡ator. 13 Wit h predet ermined wages, count ry j ’s GDP de‡at or increases wit h its nominal money st ock, but less t han proport ionally and it s real output expands. Theincreasein aggregat edemand t hat matchest heincreasein supply requires a real depreciat ion and a fall of the real int erest rate. 14 In our model, all goods market interaction among t he Periphery passes t hrough t he Cent er. If t he fall in t he demand for the Cent er’s output is large responding t o a depreciat ion of country j ’s bilat eral real exchange rate, for a given domestic supply in t he Center, t he real int erest rate will have to fall substant ially to clear t he market for Center output. This decline in t he real int erest rate is t ransmit ted t o t he ot her Periphery count ries. They now face excess demand at their old bilat eral real exchange rat e wit h t he Cent er and will experience a real appreciat ion. Similar considerat ions apply also in t he more general case in which int ra-Periphery trade is considered. 15 The result depends on t he relat ive size of the elasticities of aggregate demand with respect to the real int erest rate and the real exchange rat e, normalized by t he (constant ) share of income devot ed t o domest ic consumpt ion. 16 See for inst ance Frankel [1988] and Ghosh and Masson [1994], ch.2. 17 In principle, the identi…cat ion of an opt imal monet ary policy is rat her di¢ cult when t he objective funct ional of t he policy maker is de…ned over an in…nite horizon. Nonet heless, in our setup t heint ertemporally optimal policy is obt ained by t aking into account the single-period loss funct ion ` i ;t only. Among t he feat ures of our model which allow this considerable simpli…cat ion of the analysis, not e t hat current and anticipat ed future policy act ions are assumed not t o bea¤ected by t hepast hist ory of the game (that is, t he act ual sequences of past policy act ions). 18 See Appendix E, eqn.(A.39). 19 Theconst ant can beshown t o beequal t o t hesquareroot of 2ci =(1 + ¾®20 ) : 20 The escape clause speci…ed in our analysis does not preclude the possibility of a revaluation of the central parity as well as of a devaluation. We simplify t he analysis by considering realizat ions of t he shock for which t he relevant alt ernat ive for the country i ’s policy makers is between a peg and a devaluat ion against t heCenter. In other words, we restrict t he support of t he shock t o be such t hat a revaluat ion by country i will never be optimal, ruling 60 out by const ruction shocks t o fundament als that would correspond to large negat ive value of the shadow depreciat ion rat e (so that ¢ ~ si ;t ¸ ¡ ~ ci ). T he ext ension to the general case is simply a corollary of the analysis to follow. 21 See t he discussion in Cavallari and Corset ti [1996]. 22 See also Obst feld [1994]. 23 See t he discussion in Eichengreen and Wyplosz [1993]. 24 See for instance Champa and Chang [1995] and Kenen, Mercurio and Pesenti [1996]. 25 See, for inst ance, Eichengreen, Rose and Wyplosz [1994]. 26 Not e that , on logical grounds, the fact that fundamentals do not seem t o di¤er before and aft er a currency crisis can be alternat ively interpreted as evidence against an int erpret at ion based on self-ful…lling speculative att acks. I t is su¢ cient ly clear, at least since Obst feld [1986], t hat multiple instant aneous equilibria are based on t he policy maker validating ex-post t he initial privat e sect or conject ures. To t he extent t hat monetary and int erest rate policy is among t he fundament als, these should indeed di¤er aft er the crisis in t he presence of a successful self-ful…lling at t ack. 27 For a discussion, see Gros and Thygesen [1992]. 28 In the reconst ruct ion of Muehring [1992], “ near the end of the conference in the British spa town of Bath on Saturday, September 5, Br itish Chancellor of the Exchequer Norman Lamont asked Bundesbank president Helmut Schlesinger once more for a commitment to cut German interest rates, which could be included in the postmeeting communiqué. Schlesinger, containing his mounting anger, replied that it was impossible. When Lamont continued to press him, the normally un‡appable Bundesbank president suddenly stood up to leave, only to be restrained by an almost equally annoyed Theo Waigel, the German …nance minister. ‘My dear Norman, - Waigel snapped - you have asked us that question four times, and four times we have given you the same answer. We do not see the need for wasting any more time. So if you ask again, I will get our helicopter ready to take us back’.” In private conversation, Schlesinger recalls t o have said: “ The Bundesbank committ ee decided t he day before not t o lower, but authorized me to say t hat we would not increase” . 29 In t he case of France, one could nonet heless argue t hat the incipient loss of compet it iveness was suppressed through a high and rising unemployment rate, which creat ed doubt s about t he polit ical sust ainability of t he franc for t policy. 30 Player j ’s action, n j , is a st rat egic complement with respect to player i’s action n i (i 6 = j ) if t he magnitude of t he opt imal action of player i increases whenever player j increases t he magnitude of her act ion, t hat is, if and only if @n i =@n j > 0 (see Bulow, Geanakoplos and K lemperer [1985]): In t he two61 player case t he react ion curve of player i would be upward-sloping. When ®1 is negat ive, t hen @ni =@n j < 0; count ry j ’s action is instead a st rat egic substitut e wit h respect to count ry i ’s act ion. 31 It can be easily shown t hat @¢ s~i =@nj < 0 if ®1 > 0. 32 Formally, t he response of count ry i 0s welfare t o a monetary expansion in count ry j conditional on bot h countries lett ing their currencies ‡oat can be calculat ed by di¤erentiat ing count ry i 0s loss function wit h respect t o country j 0s employment, and evaluating this expression at the equilibrium level of employment and prices under a ‡oat: ³ ´ @`Fi L =@n j = ¡ ¾ qiF L ¡ q ¹i ¯ ®1 I f the support of fundament als shocks ² is such t hat revaluat ions are never opt imal, t he Nash equilibrium price level will be above it s t arget level q¹i (and Nash equilibrium employment will be below it s t arget level n ¹ ). T he expression above is t herefore negative for large ² when ®1 is positive: a monetary expansion in count ry j increases welfare in count ry i : 33 Such assumpt ion is obviously based on positive, not normat ive, considerat ions. 34 A discussion of thehist orical roleof a (st rong form of ) national horizont al equity is in De Cecco [1988]. The aut hor focuses on t he hypot hesis according t o which cooperative act ions are pursued only if they preserve t he relative positions, in t erms of economic and political power, of t he four main members of t he EMS. A general discussion of dist ribut ive issues and economic int egration is in Guerrieri and Padoan [1988]. 35 If t hePeriphery count ries were not all equal ex-ante, t his constraint could be generalized t o t he requirement of “ fair” outcomes (ex-post ), such t hat no Periphery count ry would t olerat ea cooperat ive act ion t hat reduces itswelfare (relat ively t o ot her count ries) below some predet ermined level, unanimously agreed upon. 36 Not e that the lit erature on EMU mainly discusses int ernational transfers in t heframework of t het heory of opt imal currency areas. Int ernational t ransfers cont ingent on relat ive aggregate demand can help reduce the short-run cost of IS shocks due t o domest ic nominal rigidit ies in a …xed exchange rate syst em, thus increasing t he st ability and viability of the syst em. At a theoretical level, our model highlights a di¤erent role of contingent internat ional t ransfers, as side-payments that could make asymmet ric coordinat ed policies feasible by compensat ing t he countries t hat sust ain the largest adjustment costs in a realignment . While in principle sound, however, the assumpt ion of int ra-Periphery side-payments of the kind required t o support cooperat ion wit h nat ionally di¤erent iat ed policy actions would hardly be defensible on empirical grounds. 62 37 The nearest we get to such exchange rate cooperation-cont ingent t ransfers are the Monetary Compensatory Amounts (MCA’s) of t he Common Agricultural Policy. Even t hey don’t …t t he bill, on closer inspection, as they (a) are limited t o the agricultural sect or and (b) are not cont ingent on t he implement ation of cooperat ive exchange rate policies, but simply respond to gaps between the value of the Green currency and the value of the act ual currency, regardless of the nature of t he exchange rate arrangements t hat generates t hese gaps. 38 See t he discussion in Giavazzi and Giovannini [1989]. 39 In t erms of t he not ation adopt ed in t he Appendix, c~C S is equal to t he square root of 2c (® + Á) =A C S : 40 Figure6a showst hepossibility t hat , for somecon…gurat ion of parameters (implying a stronger in‡at ionary bias than in Figure 6b), t he trigger point for a generalized devaluat ion under symmet ric cooperat ion is lower t han t he t hreshold at which at least one country realigns under Nash. In t his case, a cooperative agreement delivers lessexchange rat est ability for any level of t he shock in t he Center. Policy makers will bene…t in this case from “ smooth” and frequent realignment s (a familiar pat tern during t he early st ages of t he ERM). 41 Thisquestion of course point s at political economy considerations, st ressing t he role of policy makers’ changing at titudes t owards t he internat ional agreement . 42 As Peter Kenen [1995] writ es, “ t he Germans were apparent ly interest ed in a more general realignment but pursued the matt er rat her casually — t oo casually perhaps to impress t he French with t he urgency of t he issue... I t may be object ed t hat France would have vet oed a general realignment , even if France had pressed for one, because t he French believed t hat t he franc was immune t o contagious speculation. What would have happened, however, if t he German chancellor had warned the French president t hat t he Bundesbank could not be expect ed t o support t he franc — if he had called at tent ion t o t he so-called Eminger let ter. (One might also ask what would have happened if t he German chancellor, not t he Italian prime minister, had telephoned John Major about t he devaluat ion of t he lira — and added t he same sort of warning about fut ure Bundesbank support for the pound)” (p.160). 43 Padoa-Schioppa [1994], p. 14-15. 44 Muehring [1992], p. 7. 45 Similar problems were also faced by both Scandinavian count ries t hat kept t heir currencies pegged against t he mark, obviously not because of t he disappearance of fait h in the willingness and ability of t he ERM members t o cooperat e in the defense of the peg, as no such (implicit ) agreement to 63 cooperate ever exist ed for them. Count ry-speci…c t riggers were undoubt edly part of theexplanation (t hecollapseof it s t rading arrangement swit h t heFSU for Finland and t he collapse of domestic consumpt ion demand for Sweden). Bandwagon and cont agion e¤ect s may also bear some of the blame. 46 In the intellect ual hist ory of European monet ary integrat ion, two schools of t hought have been contrasted wit h each ot her, at least since the timeof t he Werner Report. The …rst one advocates gradualism in the implement at ion of t he inst it utional reforms and in t he change of policy regimes. Gradualism here means that t he process of integrat ion is primarily a process of convergence of economic structure and performance in di¤erent count ries, to be mat ched, and indeed followed by, appropriat e inst it utional development s. T he second school instead st resses the role of inst it ut ional innovat ions in promoting economic int egration, and advocates …xed deadlines and uncondit ional inst it utional reforms which would lead and encourage t he behavioral changes required for convergence. 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