The Syndrome of Exchange-Rate-Based Stabilization and the Uncertain Duration of Currency Pegs

BoardofGovernors ofthe Federal Reserve System International Finance Discussion Papers Number 548 April 1996 T]{ESYNDROMOEFEXCIIANG~-RATE-BASESDTABILIZATIONS ANDTHEUNCERTAINDURATIONOFCURRENCYPEGS EnriqueG. Mendoza and Martin Uribe Note: International FinanceDiscussion Papers are preliminary materials circulated to stimulate discussion and criticalcomment. References inpublications to International Finance Discussion P+ers (other d~anan acknowledgment that the writer had accessto unpublished material) should becleared with the authororauthors.

ABSTRACT This paperconductsaquantitativeexamination ofthe hypothesisthat uncertain duration of currency pegscauses thesharp realappreciations and business cycles thataffect chronically countries using fixedexchange ratesasan instrumentto stop high inflation. Numerical solutions of equilibrium dynamics ofatwo-sector smaliopen economy with incomplete markets showthat uncertain duration rationalizesthe syndromeof exchange-rate-based stabilizations without price orwage rigidities. Three elements ofthe modelarecritical forthese results: (a) a strictly-convex hazard rate function describing time-dependent devaluation probabilities,(b)the wealth effects introducedby incomplete insurance markets, and (c)the supply-sideeffects introduced viacapital accumulation and elastic laborsupply. Uncertain duration alsoentails largewelfare costs, compared to the perfect-foresight credibility framework, althoughtemporary disinflation are welfare-improving. The model’spotential empirical relevance isexamined furtherby reviewing Mexico’spost-war experience with the collapse of six currency pegs.

The Syndrome ofExchange-R::te-Based Stabilizations and the UncertainDuration of Currency Pegs EnriqueG. Nlendozaand Martin Uribel 1.Introduction The chronic economic crises and currencycollapses that affect developing economies, dramatically exemplified bythe collapse oftheMexican peso inDecember of 1994,are one ofthe most widely studied issuesin international macroeconomics. One key question that research inthis area has aimed to answer is:why do disinflation programsbased on fixed exchange ratesset inmotion a perverse dynamic processthat often leadsto the breakdownofthe program itself? Inthe Mexican case, for example. a stabilization planthat practically fixedthe peso-dollar exchange rate, and successfully tightened fiscaland monetary policies, hadbeen inplace for seven years priorto the collapse. During this period. thereal exchange rateappreciated sharply, investment andconsumption boomed, and external imbalanceswidened markedly. Thesethree phenomena definethe syndromeof exchange-ratebased stabilizations(ERBS) documented extensively in international studiesby Kiguel and Liviatan (1992)and Vegh(1992)), andobserved inthe fiveprevious attempts atfixingtheexchange rate undertaken inM&ico since 1945.Z Early studiesby Dornbusch (1982)and Rodriguez (1982), based on adaptiveexpectations and sticky prices. attribute ERBS syndrometo inflationary inertia. A fixedexchange rate causes aboom in domestic absorption because it lowersthereal interestrate, as interestparity forcesthe nominal interest rate to fall and inflationary expectationsadjustslowly. Persistent inflationcombined with the currency peg produces the real appreciation. Adifferentapproach based ontwo-sector inter-temporalequilibrium . ‘We thank David Bowman, Guillermo Calve, Allan Drazen, Sebastian Edwards, Jon Faust, Graciela Kamirlsky, John Rogers, and seminar participants at Banco de Mexico, the Federal Reserve Boar me Wharton Schoolof Business, and the Winter 1996Meetings of the Society for Economic Dynamics and Controlforhelpfulcommentsandsuggestions. Thispaperreflects onlythe authors’views and not thoseof the Board ofGovernors ofthe Federal ReserveSystem or other members of itsstaff. ‘Mexico’s long post-war experience with fixed-exchange-rates is examined in Section 4. Gomez-Oliver (1981)and Aspe(1993)also review post-warMexican currencv. crises.

-2models, asthose developed by Dornbusch (1983) and Greenwood (1984), suggests that real appreciation and large external deficits can be features oftransitional dynamics inducedby sustained stabilization and structural reforms (as inUribe (1995) and Rold6s(1995)). Equilibrium models that examine the consistency between fiscal and exchange-rate policies byHelpman and Razin (1987) and Drazen and Helpman (1988) provideathird explanation forthe real effects of disinflation. This literature emphasizes wealth effects resulting from thetiming ofexpected cuts inthe inflationtax and government expenditures. Calvo (1986)proposed an alternative view inwhich ERBS syndrome resultsfrom the lackof credibility ingovernment policies. Policies lackcredibility because ofchronic failures of stabilization plansand mishandling of financial policies. Broadly defined,the credibility problem, also known asthe temporariness hypothesis,refers to a situation inwhich apolicy is implemented, butagents question whether itcan bemaintained. Forexample, inCalve’smodel agentsexpect the collapse ofa fixedexchange-rate regimeat a futuredate, and this acts likeatemporary tax on savings, which, via intertemporal substitution,rationalizes ERBS syndrome. Thus, this setup shares with the price-inertia approach the viewthatthe syndrome isawarning signalsuggestingthat acurrency peg isunsustainable, butwith the key differences that(a) real appreciation isan endogenous outcome, ratherthan the exogenous trigger ofthecrisis, and (b) economic policies are partofthe problem ratherthan the solution. Several studieshaveexamined the empirical relevance of the Dombusch-Rodriguez model and the equilibrium models(see forexample Edwards (1993) and (1996), Femandez (1985), and Mendoza (1995)). While themodels helpto explain the experience of countries where price inertiaor structural change were important,the experience of countries where, as inM4xico in 1994,crisisemerged despite the dismantling of indexation mechanisms and rapid structural change remains apuzzle. Similarly, lack ofconsistent fiscaladjustment during acurrency pegwas relevant inexplaining the collapse ofthe I disinflation programs examined by Helpman and Razin (1987), but is lessrelevant forexplaining the Mexican crash andthe Argentinean recession of 1994-95,sincethese countries tightened fiscal policy

-3considerably. The objective ofthis paper isto examine whether the credibility hypothesis can helpto explain these puzzles. Despite significantdevelopments inthetheory of credibility, littleisstillknown about its quantitative implications.Early studiesaddressingthis issueby Reinhart and V6gh(1994, 1995) simulated perfect-foresight models, inwhich itisknownthat apolicy change announced atdate twillbe reversed atsome datet+j. These studieshighlightedflaws ofthe basic credibility model, thusjustifying extensions adding pricestickiness and supply-sideeffects via labor supplyand capital accumulation (see Lahiri(1995), Rebeloand Vegh (1995), Rold6s(1995), and Uribe (1995)). However, empirical research inthisarea waschallenged byrecent theoretical studiesshowing that perfect-foresight models are inadequateforassessing the relevance of lackofcredibility because ofthe probabilistic nature ofthe credibility problem. In practice, agentsdo notknowthe date inwhich astabilization planwill fail, but only attach acertain probability tothatevent. Thus,the credibility problem isreally aproblem of “uncertainduration”ofa policy regime, as inDrazen and Helpman (1988) and Calvo and Drazen (1993). Uncertain duration isa key distinctionbecause italters the qualitativepredictions of perfectforesightcredibility models, and hence itaffectstheirquantitativeassessment. Calvo and Drazen (1993) showed that, rulingout risk-neutrality, the predictionsofpetiect-foresight models extend to uncertainduration models onZyifinsurance marketsarecomplete. They examined a small open, endowment economy where thegovernment abolishestariffs butagents attach some probability to their reinstatement. Undercomplete markets,theresultsofthe perfect-foresight analysis ofCalvo (1988)are reproduced: consumptionjumps when thetariff iscut,and remains constant until itcollapses when the trade reform fails(Figure la). The assumption of complete markets isatoddswith the reality ofcountries considered candidates forthe credibility problem,3and hence itisnotsurprising that several features of economi~ fluctuations inthesecountries challenge thepredictionsofcomplete-markets, orperfect-foresight, 3CalvoandMendoza(1996)reviewmassiverunsonpublicdebtthatplayedakeyroleintheMexicancrisis.

-4credibility models. In particular, economic booms, widening external imbalances, and real appreciations do not occur indiscretejumps, and they are significantly largerthan whatcan beaccounted for bythe intertemporal substitution channel emphasized under complete markets. Rebelo and V6gh (1995) showed that frictions on preferences andtechnology can help produce gradual consumption booms, but even then investment and money balances idjust indiscretejumps. Moreover, the perfect-foresight model isfar from explaining the sizeofthe observed boom-recession cycles, unless it isaugmented by exogenous inflation stickiness.The latter,however, leavesthe largereal appreciations unexplained and weakens the case forthecredibility hypothesis. Inthe more realistic case that insurance markets are incomplete, Calvo and Drazen (1993) showed that uncertain duration produces outcomes that differ markedly from perfect-foresight outcomes, depending on the strengthof income effects introduced bymarket incompleteness relative to intertemporal substitution effects. The former depend inturn onthe sizeoftariff revenue rebatesandon the households’degree ofrisk aversion (orthe reciprocal ofthe intertemporal elasticity of substitution in the classic setup with isoelastic,time-separable utility). Iftariff revenue isfully rebated, consumption rises on impactwhen thetariff isreduced, and then fallsgradually until itcollapses when the tariff is increased again (Figure 1b). The same occurs iftariff revenue isnot rebated and the coefficient of relative risk aversion (CRRA) is iessthan 1. Iftariff revenue isnotrebated and CRRA > 1,there isa gradual boom forthe duration of thetariff cut(Figure Ic). Thus, uncertainduration explains quaZitativeZythe gradual booms and real appreciations observed inthe data. However, whether the quanlitafivepredictions ofthe model are also consistent with thedata isstill unknown. Moreover, Calvo and Drazen (1993) examined only demand-driven uncertain-duration effects, and thus the implicationsof uncertain duration inageneral equilibrium settingare stillunexplored. This paper extendstheoretical work on uncertainduration to examine the quantitative implications of amodel inwhich lackofcredibility ismodelled asthe probability of abandonment ofa currency peg. The modeldescribes the general equilibriumof a smallopen economy with the featuresof

-5production. laborsupply,and capital and debtaccumulation examined inthe credibility literatureand in international real business cycie (RBC) theory. Insurancemarkets are incomplete and money enters through atransactions-costs technology. The model’sequilibrium stochastic processes are simulated numerically using a recursive, near-exact-solution method given an exogenous hazard function governing the probability ofdevaluation. The introductionof uncertain duration inthis manner linkscredibility models to empirical work on balance-of-payments crises. This isaccomplished bycalibrating the model to mimic the probabilities ofdevaluation under fixedexchange ratesestimated by Blancoand Garber (1986),Goldberg (1994), and Kleinand Marion (1994). These studies showthat devaluation probabilities are “J-shaped,”sothat currency pegsare expected to fail with more probabilitynearthe datesof introduction and abandonment than inthe period inbetween. Thus, we askthequestion: ifthe probability of devaluation issetto estimates derived from thedata, are equilibrium allocationsproduced byan uncertain duration model consistent with the sty]izedfacts? Simulation resultssuggest that uncertain duration issufficient to cause economic fluctuations and realappreciations similarto those attributed to ERBSsyndrome. Moreover, the patternsofbooms followed byrecessions, with the latterstarting insomecasesprior to the currency crisis, andthe existence of periods of real-exchange-rate stability inbetweensharp appreciations, are also replicated by themodel. These results follow from comparing the simulationswith the stylized facts identified inthe empirical literature on ERBS syndrome, and fromacase studybased onthe six failed currency pegs implemented in Mexico since 1945. The wealth effects associated with seignorage andtransaction costs under incomplete markets, the supply-side effects introduced bythegeneral-equilibrium nature ofthe model, andthe “J-shaped” hazard rate function defining devaluation probabilities,are critical forthe favorable resultsofthe simulations. These elements ofthe modelalso implythatthe welfare costsof uncertain duration largely exceed the trivial costs of lack ofcredibility obtained inperfect-foresight studies(see Calvo (1988)). In

-6contrast with these studies, stabilizations of uncertain duration improvewelfare, starting from ahighinflation equilibrium. Uncertain duration iscostly inthe sensethat itabsorbsa large fraction ofthe benefits ofa fully-credible disinflation. The restofthe paper isorganized asfollows. Section 2describes the model, and discusses simulation issues. Section3 presentsthe quantitative analysis and examines policy implications. Section 4compares Mexican datato the model’spredictions. Section 5concludes. 2. Uncertain Duration ofaC P aS O E Preferences, Technology,andFinancialMarkets Households maximize expected lifetime utility,which takesthe conventional isoelasticform: 7 F(+w‘-’. (c,T ‘+(1-(A)) ~ ( Eo~ f t=o l-u I C(C,T,C(N=)G (1-U)(C(N)p- p (2) [ J- Households are infinitely-lived and consume atraded good(C,?)and a nontraded good (C,?. They supply labor inelastically tothe industrythat produces traded goods, inthe amount L’;and trade offthe remaining “timesupply”between providing laborto the nontraded goods industry(L,~ orenjoying leisure(Q. The totaltime constraint is[,= J-L,N-LT. The expectations operator &applies to the probability ofduration ofacurrency peg,asdefined below. Preferences between CTand C’Nare represented byaconstant-elasticity-of-substitution (CES) function, where l/l+P isthe elasticity of substitution between traded and nontraded goods, and u isthe share oftraded goods inconsumption of the aggregate C, defined bythe CES composite good inequation (2). Leisure ismodelled in mukip!icative form inthe momentary utility function,with pgoverning the elasticity of substitution k laborsupply. Utility from Cand t isrepresented also by an isoelasticfunction,where l/u isthe intertemporal elasticity ofsubstitution. 13isthe discount factor.

-7- Households maximize (1) subjectto the following budgetconstraint and lawof motion for capital: B- (l+r”p, +(ctT+p,Nc: )+~,- 1.1 (3) #’(~,~)l”qL y~ +J q - - mtv~(v) +~ m - ,. m l t+Tt t It =K,,; - (l- b)KtT (4) The budgetconstraint (3) has implicitthe characterization of productiontechnologies and financial marketsofthe model. International financial markets are incomplete. In particular, world assettrading islimitedto one-period bondsBpaying thetime-invariant rater* inunitsofthe traded good. Usesof household income inthe left-hand-side of(3) includeprivateabsorption ( i.e. purchases oftraded and nontraded goods forconsumption and investment,with#’ definingthe relative price of nontradables or the realexchange rate) and changes inbond holdingsnetof interest(which finance the current account). The sources of household income inthe right-hand-sideof(3) includecapital and labor income from industriesproducing traded and nontraded goods,netofcapital-adjustment costs,transaction costs, changes inreal money balances, and nettransfers from government. Production technologies are Cobb- Douglas,with capital inelastically suppliedto thenontraded sectoratthe levelKN,assuming thatKNhasa zero depreciation rate.4 K“isassumed to beatraded good. Traded- and nontraded-sector industriesare perfectlycompetitive, soproduction isexhausted inpayingfactor incomes--hence production functions enter intothe households’budgetconstraint without lossof generality. Capital-adjustment costs distinguish financial assets from physicalassetsto preventexcessive investment variability (see Mendoza(1995)). Realmoney balances menterthe modelasameanstoeconomize transaction costs. Following Greenwood (1983), transactions costs perunitof privateabsorption aregiven byS’,which isaconvex 4Mendoza(1995) and Rebelo and V6gh (1995) assume similar production environments in which labor (capital) isinelastically supplied inthetraded (nontraded) sector.

-8functionofexpenditure velocity V=(Cr+@CN+l)/m. Thus, mVS(19represents totaltransaction costs. Realmoney balances carried over from earlier periods depreciates atthe rate e. IfPPP intradable goods holdsand foreign prices are constant, erepresents boththe inflationandthe depreciation rates. Tisa lump-sum transfer from the government. The government i m a u T rebateto households fractions n~and ~,$of,seignorage and transaction costs; q~=q~=Oisa case inwhich revenuefinances unproductive expenditures G.s The government budgetconstraints are: G, +T, - m, - ~ +m~VfS(V,) ( l+e, [ ‘l-1 Tt - qm m,-— +11~(m,J’p(J’’J)> o~nm,fl# I ( 1+et The policy experiment referred to asacurrency peg of uncertain duration isthe following. At t=Othegovernment announces and implementsthe policy e.=0. Agents attach a time-dependent, conditional probability z,=Pr[e,+l>Ole,=O],defined bythe hazard rate function Z(t), t a ofthe peg. As inCaivo and Drazen (1993), the abandonment ofthepeg isan absorbent state, so ifatany date/>0 the rate of devaluation ispositive, itisassumed to remain positive forever w f c (Pr[el+,~O\e,>OJ=I). EquilibriumandNumericalSolutionMethod The first-order conditions ofthe households’optimization problem a t f ~t ( “ - At = (J [J (7) 1+s(v)+ v)’(v) T -(l.~ ) 1-(AICfN PtN - — — (8) (A) ctT [: 5Underfullrebates,theassumptionthattransactioncostsarerebated to households by government can also be interpretedas assuming that households own the banking systemand they collect itsnet profits.

-9- 1~N1l C~-”p(l-LtN-L‘) @(*-o}l). A,aN At — PtN (9) LtN ( (11) wt.-: S(v,) + v}’(v) + L 1l .- I . I UT (12) T pE, A , (l-aT)A,, T , ~ ‘LI +( +NV,,,)+V + -‘t.;) [1 (*1 Equation(7) isthe marginal utilityofweahh, usingCras the numeraire. Equation (8) reflects optimal sectoralallocation ofconsumer demand byequating themarginal rateof substitution between CTa’nd CV tothecorresponding relative price. Equation(9) reflectstheoptimal leisure-consumption decision by equatingthe marginal disutility of laborinthe nontradablessectorto itsmarginal product. Itfollows from(8)and (9)thatthe real exchange rate inthis model isdriven bysupplyand demand effects, in contrastwith theconventional Balassa-Samuelson model inwhich perfect sectoral labormobility implies that@ issupply-determined bythe ratioof sectoral laborproductivities. Equations (10)-(12) are standard Eulerequations that equate the marginal costsand benefitsofaccumulating foreign assets, real balances,and physicalcapital. Equation (11) iscrucial forunderstanding the intertemporalsubstitution effects triggered by uncertain duration. Define AHand L[-asthe marginal utilityofCTunderequilibrium allocations forhigh and lowinflation respectively. It followsthat (11)can berewritten as:

- (13) It isclear from (13) that the devaluation rate e,+,isatax on real balances carried over from the past. The probabilityofdevaluation z,plays a very similar role. A higherz, increasesthe effective tax rate onreal balancesbyattaching a higher probability to the devaluation scenario. Thus, uncertain duration can be interpretedasacase ofrandom taxation, which explainswhy credibility and policy temporariness are treated assynonymous. Note, however, that under uncertain duration the probability of reversal of the policy(z,)isseparated from the policy instrument(e,+,)itself. Throughthe transaction costs technology, thedistortions inducedby uncertain duration on real balancesaretransmitted intothe real sectorofthe economy. Ifseignorage and transaction costs are fully rebated, thedistortions are limited to intertemporal substitution effects.b Under complete markets the experiment reduces to a fully anticipated price increase.Consumption istemporarily higher ata constant levelinthe low-price period, and collapsesto a lowerconstant level inthe high-price period. Under incompletemarkets, incontrast, a long-lastingcurrency peg represents a sequence of favorable relative price shockswith non-insurable incomeeffects. These effects are magnified ifseignorage and transaction costsare notrebated. Each quarter that apeg survives inducesapositive shock to permanent income, which risesbythe amount of seignorage and transaction coststhat would have been collected underhigh inflation.The impact oneconomic dynamics resulting from allthese effects depends critically onthe shapeofthe hazard rate function, as we show later. Inequilibrium, conditions (7)-(12) holdjointly with market-clearing conditions: ctN=At~(K~)1-~(L,N)~ (14) bNote that equations (9) and (12) introducethe so-called supply-side effects (see Rold6s (1995), Lahiri (1995), andUribe (1995)), viathe capital accumulation and leisure-consumption choices.

-11- @ ‘Kr)z CtT+Gt +1,+B,,,- Bt(l.r.) . A,T(KtT)l-=r‘()Lar- ( # , The equilibrium stochastic processes ofthe modelare given bysequences of state-contingent allocationsandprices suchthat (7)-(12) and (14)-(15)h f O S a d t>Othere are two possiblerealizationsof e, and sincethe state e,>Oisabsorben~ ineach date macroeconomic aggregatescan either: (a) follow the optimal path corresponding tothe state inwhich e,=Oat twithz, governingthe probabilitythate,+,>O,or(b) ife,>Oat tthey switch tothe path corresponding to that rate ofdevaluation with perfect-foresight. The benchmark versionofthemodel issolved by assuming thatat somefuturedateJthe c c w p t Z a s exogenously afunctionZto determine z,fort=O,..,J-2. Thisprovideswell-defined state-transition probabilitiesandterminal conditions, sothat paths (a) and(b)can besolvedby backward-recursion followingthe intuitionfromthetwo-period analysis inCalvoand Mendoza(1994). The multi-period analysishasthecomplication thatthe netforeign assetpositionsetasterminal condition atthetime of thecollapsemustbeconsistent with the initialnet foreignassetpositionatthe time the currency peg starts. This isachieved byconstructing ashooting routinewhich undertakessuccessive iterations onthe terminal conditions. Detailsare provided inthe Appendix. The benchmark version of the model isparametrized foraquarterly frequency asfollows. a)FinancialSector: The transaction coststechnology adoptsthe formS(V)=A VT,sothat the first-order conditions implyan implicitmoney demand function V,=(i\]+i)’’(’+yJ(yA)-]’(]+Yw),here iisthe nominal interestrate.Thisfunction iscalibrated to M2 money demand inM6xico,given strong empirical evidence infavorofthe log-linear relationship between mand i/l+i that itproduces.’ The exponent y is setto r[limicthe interestelasticity of money demand estimated at-0.15,sothat y=5.66. A isset so~ ~t 7Kaminand Rogers(1996)foundthatfortheperiod 1988-94thereisastable,error-correction specification ofthe demand forreal M2 inMexico asafunction of iand V. They alsoprovide evidence ofa strong cointegratingrelationship between these two variables.

-12the high-inflation, pre-stabilization steady statemimics the M2/GDP ratio (31.8percent on an annual basis) and nominal interest rate (177 percent annually) atend-1987, when the lastMexican ERBS program started. M2/GDP rose gradually to 35.5 percent in 1994,and collapsed in 1995.With allthis in mind, the steady-statemoney demand equation can be solvedforA(A=O.19). b)Preferences, TechnologyandRebates: The values p =0.786,ti=O.5, ~=-O.218, a=2.61, aT=O.42, cN=O.34 and 6=0.1, aretaken from the developing country, small open economy model calibrated in Mendoza (1995). P and a reflect estimates fromeconometric studies fordeveloping economies, pisset sothat householdsallocate 75percent oftheirtime to leisureinamodel without money, and aT and a~ reflect long-runaverages computed with sectoralGDP data.@O.06 issetto mimic the standard deviation ofMexican investment inan RBC model. Also,we assume that p=(l+r’’)-’w r 6 percent perannum,so that there isnodebtaccumulation resulting from agents aiming to attain atarget levelof wealth, and q~=q.$‘O, reflecting the assumption that fiscaldiscipline isrestored during the currency peg(i.e. G=O). c)Hazardrafefunction: The hazardratetakes aJ-shaped form consistent with theeconometric studies by Garber and Blanco(1986), Goldberg (1994),and Kleinand Marion (1994). Garber and Blanco’s estimates arederived from a model of balance-of-payment crisesapplied to the Mexicandevaluationsof 1976and 1982. Inthe lattercase, the authors estimate a probabilityof collapse at 0.2 early in 1977, declining tonearzero inabout ayear, rising slowly in 1978-79,and rising rapidly to about 0.3 before the collapse. Goldberg applied a similar approach to data for 1980-86,although after 1982Mexico did not followan ERBSplan. Shefindsthat probabilities ofcollapse oscillate between lowand high andthat before the 1982collapsethe probability ofdevaluation was roughly 1. Klein and Marion use Iogit analysis to identifyfactors that influence the duration ofcurrency pegs, without requiring a specific model ofcurrency crises, ina panel of monthly data for 17countries overthe 1957-91period. They found strongevidence showing that real appreciation isakeydeterminant o~”theprobability of devaluation andthatthis probability isJ-shaped. Probabilitiesofcollapse onemonth prior to the

-13devaluation areashigh as 0.89, with 1/10ofthe estimates higherthan0.55.8Thus, these studies suggest aJ-shaped hazard rate setbelow 0.5 when the program begins, fallingto zero and rising to about0.8 priortothe collapse. We also set ex-postduration atJ=24 quarters, inlinewith the six-year duration of currency pegsobserved inMexico since 1970(see Section 4). 3. Model Simulations: Does Uncertain Duration Explain the Syndrome? This sectionexamines the quantitative implications ofuncertainduration. First we quanti~ the demand-side, uncertain-duration effects identified by Calvo andDrazen (1993). Inthe second stagewe simulatethe general equilibrium model and examine itswelfare implications. Uncertain-DurationEflectsintheCalvo-Drazen TradeReform The model isreduced to represent an endowment, exchangeeconomy inwhich consumer goods are importedpayingatariff ~set at percent. The government announcesand implements the abolition oftariffs (~=0) atdatet=O,but agents interpretthis as areform of uncertainduration. Thus, z,denotes the probabilitythat ~=0.2 atdate t given that r=0 atdate/. Considerthethree specifications ofz, plotted inFigure2: (a)the perfect foresight case (z,is always zero, exceptatdate~),(b) the flat hazard rate(z,issomepositiveconstant, say 0.5, untildateJ in which itrisesto 1),and (c)the J-shaped hazard rate. Figure3 plotsthecorresponding state-contingent equilibrium pathsforconsumption underalternative specificationsofrebates and values of a. The continuous (dotted) linesrepresent allocations undertheassumptionthattrade reform continues (ends). The perfect-foresight case reproduces the predictionsderived byCalvo (1988). Consumption “booms”when thetariffs are abolished at O,and remains high untilitcollapses atdateJ. AsCalvoand Mendoza(1994) show, for u>] consumption collapses to apoint below(above) the pre-reform equilibrium iftariff revenue is(is not)rebated. If u=I, consumptioncollapses exactly to the levelithad priorto thetrade reform. Under full rebates, thetemporary tariff inducesapure substitution effe~” %ote howeverthatthe Klein-Marion estimates make useofallthewithin-sample information to generate the ex-post probability of devaluation, whereas the Blanco-Garber and Goldberg studies are based on comparing a:’shadow”exchange rate(i.e. aperiod-ahead forecast) totheactualprevailing peg.

-14against savings(since future prices are expected to risepermanently atJ), and hence the consumption profile istilted toward the present for agiven lifetimewealth. Withoutthe rebate and o>], thetrade reform inducesapositive income effect inaddition to the substitution effect, and hence the less pronounced collapseat dateJ. The uncertain duration e with aflat hazard ratefunction confirms Proposition 1inCalvo and Drazen (1993). Under incomplete markets and a>], consumption first booms and then gradually falls(rises) beforethe finalcollapse iftariff revenue is-(isnot)rebated. The intuition forthis result follows from the incomeeffects introduced by market incompletenessdiscussed earlier. Without rebates, there issomeprobability thattariffs will return between dates OandJ, and thus at every date in . this intervalthatfreetrade continues households are “pleasantly”surprised with a gain inpermanent incomebytheamountofthe nonrebated tariff revenue foregone. Consumption increases gradually asa result, untildateJar-rives, when there isa sudden fall inconsumption since forever after the probability oftariffs returning isexactly 1. Inthe case with rebatesthese “pleasant”surprises do not exist. In contrast, the probabilityof policy r an incentiveto over-consume relative to a perfect foresight case (noticethatthe impacteffect on consumption isstrongerthan underperfect foresight). If pricesdo not rise, householdsrealize they over-consumed, and hence depleted their wealth too much, andthusthe incentiveto reduceconsumption. Note also thatwith the flat, linear hazard rate function consumption dynamics areapproximately linear. The resultsforthe J-shaped hazard rate illustratetherich dynamics thatthe uncertain duration framework can produce. With rebates, the initialboom isfollowed byaquick fall intoaplateau ofhigh consumption that lastsuntilthe collapse arrives. Similarly, without rebatesthere isa boom on impact, followed byanaccelerated boom to ahigh consumption plateauthat collapsesat date J. In both cases there isa higherdegree ofnonlinearity inconsumption dynamics relative tothe case of the linearhazard rate. Thus,the shapeofmacroeconomic dynamics depends critically onthe shapeofthe hazard rate function defining the probability of policy reversal.

-15- UncertainDurationE#ects ina ModelofExchange-Rate-BasedStabilizations Consider nextthebenchmark general equilibrium model. Figure4 plots state-contingent equilibrium dynamicsaspercent deviations from thepre-stabilization steady state. The J-shaped hazard rateproducesJ-shaped dynamics invelocity and netexports, and invertedJ-shaped (i.e. concave) dynamics inGDP, consumption, investment, laborsupply,andthe realexchange rate. These concave dynamics arevery importantto produce given theobservation that boom-recession cycles, with recessionsattimes pre-dating devaluations, are typicalof ERBS syndrome (see Rebelo and V6gh (1995) andthe casestudyfor Mexico inSection 4). Itisstraightforward to show,given (13)and ~=(l+r*)-’, that ifz,reachesOatthe minimum ofthe hazard rate function (as itdoes inFigure 4),then the equality of intertemporalmarginal utilitiesofCTwill likely induceconcave dynamics. In factthis isa necessary condition inaone-good model with endowments. Inour model, however,z,>Oatthe minimum ofthe hazard rate functionstillyields similar concave dynamics asthez,=Ocase. What isrequired forthe concavity result isthatthehazard rate function bestrictlyconvex. z,=0 isnotrequired because ofthe supply-side effectsthatderive from laborsupply elasticity andthepresence of investmentexpenditures inthetransaction coststechnology. These effects addto the steady-state supply-side effects of permanentdisinflation examined inrecent studies. The sensitivity analysis undertaken below shows in additionthatthesupply-sideeffects implythat a strictlyconvex hazard rate, while necessa~, isnot suflcienf to ensureconcave dynamics. The sharpdecline invelocity shown in Figure4 isconsistentwith the observation that liquidity risesmuch fasterthan output inthe early stages ofa currency peg. Thisaccelerated expansion of monetary aggregates has inturn been linkedto banking fragility, andbothbanking fragility and the collapseof money demand that occurs at date J havebeen attributed akeyrole ingenerating balance-ofpaymentscrises (see Calvo and Mendoza (1996)). Thetrade balanceasa shareofGDP worsens markedly on impact,fromasurplus of about 5percentofGDP to adeficitof similar magnitude, and then itfollows aJ-curve pattern similar to thatof the hazard rate, reaching almost 10percent of GDP bythe

-16- 8thquarter afterthe plan starts. The booms inGDP, consumption and investmentare also in linewith ERBS syndrome,althoughthe investment boom seems excessive. Investment risesmore than consumption andGDP inthe early stagesofthe program, and, more importantly,allthree b decline beforethepegc T b m a g as r a a 6p t f year ofthe program. Theappreciation continues atamore moderate rateto reach 15percent bythe IOth quarter, andthen itstopsand actually reverses to about 10percent bythe date ofthe collapse. The real exchange rate isdetermined bythe interaction of demand and supplyfeatures, particularly theelasticity of substitution c t a n g l t e l a t share of laborincome inproduction ofnontradables, dl. Thev ~ u i e ( of 1.28,thus making c~and CNgross substitutes. @ ( f t w b a booming(falling), causingthe rise (fall) inp””.Note also thatthe boom inCNcanonly beaccomplished attheexpense ofreducing leisure, a LNr t w t c b Next wecompare the results ofthe uncertain-duration m w t o p foresightstudies. Considerfirst the m R a V ( R a V s consumption “ g o t d n i r t e duration of stabilizationplans, and e e a u t c s f consumption inaone-good,endowment e m w m e v t c They foundthat forthe model to predict increases inconsumption similarto those observed inthedata, the fall in interestrates needsto besubstantial (in excess 1 b p M t perfect-foresight m c j i t s b a r c until itcollapseswhen the program isabandoned. Rebelo andVegh (199S)undertake a similar analysis but inthe context ofatwo-sector, ge e~s!equilibrium framework inwhich the credibility effect onthe demand side isaugmented by supply-side effects. They simulated atemporary currency peg knownwith fullcertainty to collapse in 10quarters

-17and found thatthetemporariness hypothesis underestimates significantlythe magnitude ofthe consumption boomsand realappreciations. The real exchangerate appreciates byabout 5percent ata nearly constant rate, consumptionoftradables (nontradables) rises on impact also byabout 5percent and then itrises(falls) gradually until itcollapses when devaluation arrives. Investment and real balances jump by 75and 50percent respectively on impact and remain constant untilthey collapsetogether with the currency. The Rebelo-Vegh simulations produce “smooth”consumption dynamics, insteadofdiscrete jumps, despitetheperfect-foresight nature oftheir model, because ofthe combination of(a) the slow adjustment ofthecapital stockresulting fromadjustment costs,(b)the introduction of investment inthe transaction coststechnology,(c) the perfect substitutability of laboracross sectors with Cobb-Douglas technologies, and(d) the useofthe utility function proposedby Greenwood, Hercowitz and Huffman (1988), inwhich the marginalrate of substitution between consumption and leisure is independentof consumption, effectively eliminating the wealth effect on laborsupply.9 The model proposed here shares features (a) and(b), andyetthe perfect-foresight simulation examined below yieldsthe discrete consumptionjumps typicalofperfect-foresight credibility models. Moreover, even with allfour assumptions, investmentandreal balances intheir model stilldisplay the suddenjumps typical of perfect-foresight models. Incontrast, inthe benchmark modelwith aJ-shaped hazard rate smooth business cycles resultonly fromuncertain duration. The 15percent realappreciation inour model ismore than 3 times largerthan those produced with perfect-foresight models,without requiring exogenous price rigidities. Differences across models on the magnitude of real appreciations depend critically onassumptions regarding sectoral labor mobility. If labor isperfectly mobile, as inRebelo andV6gh(1995), the real exchange rate is 9Rebe!oand Vegh (1995) also examined the implications of an isoelasticutility function likethe TICwe postulated, but found that laborSUpplyexhibited a counter-factual decline. Note also that intheir model government rebates seignorage, butthe resources losttotransaction costsare a pureexcess burden. ‘“Alternatively,Uribe(1995)showsthatshiftsinnontradables investmentdemand, driven by time-to-build effects,canproducegradualandsizablerealappreciationregardlessoflabormobilityandcredibilityeffects.

govemed bythe Balassa-Samuelson condition--changes infl must reflect sectoral laborproductivity c ar l l re p s a r g l r ap s t as tr c b p t a no m r E a f t B m a s c l evidenceshowingitscounter-factualimplications(see AseaandMendoza(1994)). One al a t af e n w r t o e w t r e r de t v p ( t c m G ( a F a R ( a l e a t o a h w l s m l b d n e as r t n s C t a r r l t t s s s d N a t l r a ourmodelalsorequireincomplete markets and thewealth effects ofnonrebated seignorage andtransaction costs. SensitivityAnalysis Figure5providesc s t r e s a P f d t r e r t t b r a c a in a p f a m s T f o r t b m a the restare forthe following experiments: (1) flathazard rate, setat 28 percent to reflect the same unconditional expectationsofdevaluation asthe J-shaped hazard rate, (2) petiect-foresight (z,=O for Os[<Jand z forJ=24), (3) fullrebates of seignorage andtransaction costs (q~=~~=~), (4) inelastic laborsupply(P=O),(5)unitaryelasticity of substitution between traded and nontraded goods (P=O),(6) reduced intertemporalelasticity of substitution (l/u fallsfrom 1/2.6to 1/5),(7) extended time horizon (the program failsafter 9years,J=36), (8) calibration ofmoney demand based on Ml velocity, and (9) non-zero long-runprobabilitiesof success ofthe stabilization program (the long-run probability of continuation ofthe peg atJ issetat 10and 50percent). The shootingroutine ensures that allthe

-19si a b t c f a c w t s i f a p t b t c p T f h r c e t r t C m t g eq m w m am e t c a s t me F u i m r a u as u d l i c i f ag b p t c S al h r p n m dynamics. The perfect-foresight simulation confirms that, t a u d the model behaves asthetypical credibility model,despite adjustment costsand the strengthened non-neutralities of money inducedby supply-sideeffects. Consumption, investment andthe real exchange ratejump on impactto higherconstant levelsastheprogram begins, and collapse when the program ends. The model with fullrebatesproducesdynamics qualitatively similarto thoseofthe benchmark model. Quantitatively, however, the modelwith fullrebates produces small booms inconsumption and the real exchange rate, anda largefall innetexports. With rebates, onlythetax-like distortion of uncertain duration onrelative prices, acting via inter-temporalsubstitution, isatwork. Thus,the comparison ofthe benchmark and full-rebatescases showsthatthe wealth effects allowed bymarket incompleteness and norebatesare critical inenabling the mode]to produce largeboomsand real appreciations. Ina similarvein, Uribe(1995) showsthat the permanent-income effect oftransactioncosts rebates rises from 2to 15percentof GDP as monthly inflationrisesfrom 1to 50 percent.Note also that under no rebatesthere isatransitory cut inG forthe durationofthe currency peg, which is reminiscent ofthe fiscal-induced wealth effects used by Helpman and Razin(1987) and Drazen and Helpman (1988) to explainthe realeffects ofdisinflation. The preference parameters uand p playa crucial role. Inelastic laborsupply altersthe shapeof consumption and real-exchange-rate dynamics sothatan initialboom isfollowed byaperiod of stability inboth, prior to acontinuationof the boom, insteadofthe gradual decline observed inthe benchmark

model. Here, strictconvexity ofthe hazard rate function failsto yield concave consumption dynamics. Ifthe intertemporal elasticity of substitution falls to 1/5,real exchange rate dynamics are altered inthe sameway as inthe case of inelasticlabor,but consumption dynamics are not significantly different from those inthe benchmark model. Thedifference results fromthe supplyresponse inthe nontradables sectorthat ispresent with reduced intertemporal elasticity of substitution,and absent with inelastic labor. Incontrast to u and p,P andJdo notalterthe outcome ofthe simulations significantly--except forthe factthatJ=36 produces a largerand more sustained real appreciation than the benchmark model. The moveto (1/l+@ =1 isnotaradicaldeparture from the 1.28elasticity inthe benchmark. However, this elasticity hasthe potential foraffecting significantly sectoral consumption allocations and the behavior ofthe real exchange rate if itisallowedto vary more widely, asevident from equilibrium condition (10). The model calibrated to Ml, rather than M2, is intendedto controlfor the fact that while M2 isa good proxy formoney balances used intransactions, it includesinterest-bearing deposits on which seignorage iscollected ataratesmaller than the rate of inflation(or devaluation). Thus, the M2 specification approximates welltransaction costs, but exaggerates seignorage, while the Ml specification isbetterat measuring seignoragebutunderestimates transaction costs. The results show that transaction costs rebates play acrucial role inthe benchmark model’sability toproduce largebooms and largereal appreciations. The assumption thatthe program fails with probability 1afler6years isnotcrucial forthe positivepredictions ofthe benchmark model. Ifthe eventual probabilityof currency collapse after 6 years is 1,0.9,oreven 0.5,thedynamics before the 20th quarter are nearly identical inthe three experiments, although afterthat datethey differ markedly. Thisresultshows alsothat ERBS syndrome occurs regardless ofthe long-runprobability of success oftheprogram. The normative predictions ofthe model can, however, be significantlyaffected bythe potentially largedifferences inmacroeconomic dynamics after the 20th quarter.

-21- One additional element thatmay alterthe results isthe fact thatthe probability ofd may be updated given thestateofthe economy. ERBS syndrome is likelyto influence t p which agents form their expectations onthesustainability ofthe currency peg, leadingthem to grow pessimistic about itsprospectsasthe stabilization program progresses. Indeed, Klein and Marion (1994), Frenkeland Rose (1996),and Kaminsky and Reinhart (1996) showthat realappreciations provide useful informationto anticipate currency crashes. Thus, insteadofmodelling an exogenous hazard rate function,one should consideran endogenous hazard rateand compute arational expectations equilibrium inwhich thedynamics oftherealexchange rate, and other determinants ofcurrency collapse, influencethe probabilityof devaluation. Weanalyze this inaseparate paper, which considers a probabilityofcollapse thatdepends onthedegree of realappreciation relative to the pre-stabilization levelofthe real exchange rate.ll Preliminary results suggestthatthe J-shaped hazard rate function can bean endogenous outcome ofthe model. WelfareandPolicy Implications Ifuncertain duration causes ERBSsyndrome, policy-makers face a serious challenge. On the one hand,the high-inflation equilibrium embodies thedistortion on money balances and itsspillover into transaction costs and realactivity, which makedisinflation policy desirable. On the other hand,a lessthan-full>-credible stabilization program introducesnewdistortions, which make disinflation policy undesirable. Inthe classic caseof the perfect-foresight credibility literature, without supply-sideeffects and with fullrebates (i.e. Calvo (1988)),lackofcredibility isalways costly because it isidenticalto a temporary tax on savings with the proceedings rebatedto households. But inmodels liketheone studied here, severaldistortions areatwork, andwelfare assessments are more complex. The previousanalysis ‘iThe solution of the model is complicated by the fact that we need to compute a sequence of the real exchange rate yielding a hazard rate function that supports the same real exchange rate dynamics. This requiresextendingthealgorithmtoadditerationsoverhazardratefunctions. Webeginwithaguessforthi; function, and solve equilibrium dynamics as before using the resulting path of the real exchange rate to update the hazard rate. We have found numerical solutions for this problem, but cannot prove that the solutionsalways exist andare unique.

thus needsto beextended to (a) provideaquantitative assessment ofthewelfare implications ofdifferent strategies (no stabilization, credible and incredible disinflations), and (b) if the first step suggests that stabilization isdesirable, consider policiesto counteract the distortions induced by uncertain duration. Quanti&ing the welfare implicationsof uncertain duration isastraightforward extension ofthe simulations conducted earlier. Wecomputed welfare effects asa function ofthe exposf duration ofthe currency peg underalternative hazard rate functions for the cases with and without rebates. These welfare effects, plotted inFigure 6,were computed asfollows. Consider apolicy-maker atany date />0, ator afterthe beginningofastabilizationplan, that assesses the welfare effect ofthe currency peggiven thatthe stabilization program has lastedupto date /. He pondersthe benefits of stabilization by comparing the familiar compensating variations inconsumption (see Lucas(1987)) that capture the change inexpected lifetime utilitythatrenders agents indifferent between the allocations implied by an ERBS of uncertain duration andthe continuation ofthe high-inflation statusquo. These calculations take intoaccount the state-contingent allocationsof consumption and leisure,and the associated probabilities. Forthewelfare effect at/, uncertainty uptodate / has been resolved, sothe realizations of Cand Ithat enter intothe computation ofexpected lifetime utility fromdates Oto tare known, and expectations are usedonly fordates fromt+] toJ. Thus,the vertical interceptsofthe curves plotted inFigure 6(listed in Table 1)measure the exanlewelfare effects that evaluate the disinflation program atthe outset. The welfare effects forthe 24thquarter, incontrast, measures theexposf welfare effect ofthe policy assuming thatthe program infact lasted6years. In between the two, thewelfare effects assess the value of a currency pegthat has lastedtperiodsand may or may notfail untilthe24th quarter. The exanle measures tell usaboutthe desirability ofdisinflation ingeneral, whilethe rest illustratehow uncertain duration affects welfare calculations.

-23- The first important feature ofthe welfare analysis isthe factthat temporary programs always producea welfare gain.12Thisdeviates from perfect-foresight credibility modelswith rebates and no supply-side features, inwhich lackofcredibility isatemporary, welfare-reducing tax. Indeed, fora perfect-foresight incredibletrade reform inanendowment economy with rebates to yield the same ex ante lifetime utilityasthe pre-reform steady statewith tariffs, consumption would need to rise by 0.14 percent inevery period (i.e. thewelfare cost is0.14 percent ). T compares to anegative welfare cost of-0.33 (i.e. awelfare gain of0.33) percent inthe perfect-foresight, general-equilibrium model ofERBS programs with rebates. Thus, itfollowsthatcurrency pegs,even iftemporary, are betterthan continued high inflation becauseofthe supply-side effectscaused byelastic labor supplyand capital accumulation. The second key resultofwelfare calculations isthat uncertain duration embodies much larger welfare coststhan the standard perfect-foresight credibility problem, particularly ifthe policiesare compared atthetime the currency peg is introduced. These exantecomparisons showthat uncertain duration entails welfare gainsthat are equivalentto 1/4to 1/6those produced under perfect foresight, with orwithout rebates and regardless ofthecurvature ofthehazard rate function. Thus, while temporary programsare beneficial, uncertainduration induces largeadditional distortionswith marked adverse effects oneconomic behavior. Aswelfare assessments are corrected forthe resolution of uncertainty (i.e. for highervaluesof/), welfare gainsunderuncertain duration rise and almostconverge to those obtained under perfect foresight. This isbecauseforevery date thatthe program lasts,the computations consider as “accrued”the realizationsofconsumption and leisure inthe “good”stateof nature inwhich thecurrency pegcontinued, anddo notweightthem bythe complement cf the probability ofdevaluation. Figure7plotsthe state-contingent dynamics of consumption and leisure underthe different policy regimes thathelpto clari~ this argument. The “speedof convergence” depends onthe curvature ofthe hazard rate function. With aflat hazard rate,welfare risesata nearly ‘2Uribe(1996)obtainsasimilarresultbyshowing that in the presence ofcurrencysubstitutiontemporary programs can generate welfare gainseven underfullrebate of seignorage income.

constantrate, reflecting the quasi-linear dynamicsthat itproduces. The J-shaped hazard rateyields a highlynonlinear welfare path. Welfare atfirstrisesfaster than with the flat hazard rate, butthen it remains nearly unchanged for abouttwo years before starting to rise again. Thus,these results showthat uncertainduration isvery costly, andthat underaconvex hazard rate there may beperiodsduring which the program may continue without any benefitto socialwelfare. Our analysis does not rule out,however, thepossibility thatthe welfare pathmay beupward sloping(at least locally)for somenonlinear hazard ratefunction. Moreover, this analysis ofthe resolutionof uncertainty isof little usefor the policymaker, who decides whether to startan ERBS programatdate t=Ousing only the exantewelfare costs. Comparing the exantewelfare effects inTable 1,ittranspires thatthe wealth effects under no rebatesand incomplete markets have significantwelfare implications. The welfare gains oftemporary stabilizations range between 0.05and 0.33 percentunder full rebates, and thus are much smaller than thoseobtained inthe absence ofrebates, which range from 1.1to 7.4percent. Note, however, that the pr~portionby which welfare gainsunderperfect foresightexceed those of uncertain duration isnearly thesame with and without rebates. Table 1alsosuggeststhat, forwelfare analysis, the supply-side effect introduced by laborsupplyelasticity is lessimportantthan thatdueto capital accumulation. This is conjectured on the basisthatwelfare gains foramodelwith inelastic laborare similar tothose forthe benchmark model. The exantewelfare gain underthe convex hazard rate function is0.07(1.44)percent with inelastic laborand with (without) rebates, compared to 0.08 (1.57) percent inthe benchmark model Following Calvo and Mendoza (1994), itisalso importantto notethatonce one breaks away fromthe basiccredibility model, comparing welfare under atemporary program with welfare undera fully-credible program isimportant. This comparison istrivial inthe basicmodel because in itthe allocations underthe status quoanda fully-credible policy reform are identical. Inthe benchmark model, incontrast, theexantewelfare effect ofuncertain duration isequivalent to a 1.57percent gain in permanent consumption relative tothe pre-stabilization equilibrium, butthat welfare gain is22 percentage points smaller thanthe 23.7 percent gainproduced byafully-credible stabilization. Thus,

-25credible disinflation programs are stillsignificantly moredesirable than temporary programs. We concludewith somecomments onpolicy alternatives. First, ifall policies are equally incredible, the policymessage issimple:exchange-rate-based disinflation, even if incredible, are still worth implementing because the neteffect ofcredibility distortions ismeasured to besmaller than the high-inflation distortion. Second. ifsome policiesarecredible, they maybe useful incountering the adverse effects of lackofcredibility and hencemake disinflation programs even more beneficial. For example, a policyrecommendation that emerges fromour analysis isthat iftax policy iscredible, a properly-chosen consumption tax can bevery effective incontrolling credibility-induced business cycles. Inthe basic case inwhich temporary reform isalwajfssocially costly, onecan construct a sequence of consumption taxesthat completely eliminates thecredibility problem yielding the Pareto optimal equilibrium. Note, however, that inpractice optimaltax design would require information on how incredible the stabilization policy is(i.e. an estimate ofz,),andthat assessing how pervasive isthe lack ofcredibility usingmacroeconomic data may bevery difficultgiven the effects ofother sources of business cycles (seeCalvo and Mendoza (1994)). 4.A Case Study: The Mexican Experience inthePost-War Period and the 1994Crash This sectionexamines the empirical regularitiesthatcharacterize ERBS syndrome inMexico fromthe perspective ofthe uncertain duration model. Theanalysis ofthe Mexican case isan interesting addition to the comprehensive cross-country studiesby Kigueland Liviatan (1992) and V6gh(1992)for three reasons. First,Mexico’scurrency collapsesco-existed with a solidpolitical structure, incontrast with the major politicalcrisesthat oilen accompany economic crises inother developing countries. Thus, in Mexico lackofcredibility did not reflect uncertaintyonthe duration of political institutions, but mainly uncertainty aboutthe future course of economicpolicies. Second,the analysisof Mexico’sERBS episodes highlightscertain aspects ofthe process, suchasthevarying duration of currency pegsand varying speed ofeconomic expansion and realappreciation, on which the uncertain duration framework sheds some light.Third, insteadof conducting across-country analysis, we focus on Mexico’ssix

e E s s 1 T t u c b c a t analyses applies. Note, however, that our objective isnotto obtain the best possible match to Mexican data,asthat would require adding other major sources ofbusiness cyclesthat would make it impossible toexamine uncertain-duration effects in isolation. The first part ofthe empirical analysis covers 1945-94using annual da~ and the second part usesquarterly data forthe lastERBS episode(1988-94). The analysis ofthe 1988-94episode isuseful becausereforms implemented inthis period brought M4xicocloser to the environment ofopenness to globalmarkets and flexibleprices assumed inthe model, insharp contrast to the expansionary policies andexcessive government intervention ofthe past. Also,the quarterly data allow usto usetime-series methodsto isolatethe potential contribution ofcredibility to business cycles. Data on prices and exchangerates were obtained from the I ZnfernationalFinancialStatistics, a n a d w r f In Economics ofBanco de M6xico.The real exchange rate (RER) in the 1945-94sample isabilateral CPI-based indexwith 1970=100and defined as P/EP*, where Pand P* areend-of-period Mexican and U.S. CPIS respectively, and E isthe nominal exchange rate interms of nuevospesos per U.S. dollar. RER inthequarterly sample isthe IMF’smeasure ofthe trade-weighted, CPI-based real effective exchange rate. Figure 8plots the evolution of annualexchange rates.The logarithmofthe nominal exchange rate ISinthe lefl scale, and the RER index is inthe rightscale. Figure 8shows sharp real appreciations during fixed-exchange-rate regimes, typical ofERBS syndrome, priorto largereal depreciations that coincidedwith the collapses ofthe currency in 1949,1954,1976, 1982,and 1994.13The real appreciations occurred rapidly, over 2to 4years, and intwo instances periods ofreal-exchange-rate stabilityexisted inbetween sharp appreciations--in the 1960’sera ofthe so-called “stabilizing development” and in 1989-90.14 ‘31987isan exception inwhich the peso collapsewas notpreceded by exchange-rate-based stabilization. ‘4It is also interesting to notethat Mexican inflation was closerto U.S. inflation under the high levelsof protection of the.1960sthan underthe substantially more open regime ofthe 1990s.

-27- This “eye-of-the-hurricane” feature ofthe realappreciation posesa serious challenge for models of ERBS syndrome. If realappreciation followed from conventional price inertia inducing persistent inflation,the real exchange rate should appreciate ata sustainedrate. Calvo and Mendoza (1996) and Aspe (1993) argue a t M r a w n j ac g p i b w d as d i nontmdablesgoods p a b Mexico’ss p b b i p a r l d s r wages. Al l c u p f m c w t c ofthe real appreciation, the real exchange rate shoulddisplaydiscretejumps around the dates of adoption and abandonment ofcurrency p s F c t s t b m s t uncertain duration, usingac h r f c w empirical evidence basedon Mexican data(e.g. Blancoand Garber (1986)), provides an explanation for temporary stability ofthe real exchange rate. Dependingon preference parameters, itisalso possible to obtain either a real exchange rate thatcontinues to appreciate orthat depreciates slightlyafler the period of stability. Consider nextthe cyclical behaviorofreal GDP percapita and itsexpenditure components. Figure9 plots the logarithmof real per-capita GDP andtwo conventional estimates of itslong-run trend; the cubic time trend (T3)andthe random-walk (RW) trend. Bothtrends show a large structural break in Mexico’sgrowth after 1980that raises important issues,someofwhich go beyond the scope ofthis study. Forinstance, the protracted recession intowhich M6xicofell intheaftermath ofthe debtcrisis, and from which ithasyetto recover, isan issueforwhich noclear explanation exists.15Roughly the same structural break isidentified usingeitherthe Hodrick-Prescott (HP) filter orthe Baxter-King bandpass (BP) filter. ‘sThisphenomenon iscommonto othercountriesthatexperiencedlargeandpersistentadverseshocksto the world interest rate and theterms oftrade inthe 1980s. These shockscan cause protracted recessions and reduce Iong-run,growth ineconomies dependenton internationaltrade (see Mendoza (1995) and (1996)).

-28- 1 M&xico’s“longgreat depression” also raises importantissues forthe choice of filter usedto define business cycles, which inturn playsa key role indefining ER13Ssyndrome. The BP filter, designed hereto isolate information contained infrequencies between 2and 8years, and the RW filter track more closely the structural break than the T3and HP filters, and hence produce smaller cycles.ls Thecyclical components ofthe four filtersare stationary.}’ Thus, these filters define business cycles as relatively low-frequency (T3 and HP filters), mid-frequency (BP filter), or high-frequency (RW filter) componentsofthe data, while maintaining the conditi~nthatcyclical components are stationary. Since there isnoclear “best”filter, the cyclical components ofthe four filters are examined. Figures 10plots business cycles of key macroeconomic aggregates and Table 2 reports cyclical co-movements. The qualitative features of Mexico’scyclesare similar to those observed inother developingcountries (see Mendoza (1995)). Fixed investment(I) and the netexports-GDP ratio (h/X/Y) aresignificantly more volatile than GDP, while privateconsumption (C) isonly slightly more volatile.]8 Cand Iare procyclical and countercyclical, and allfourvariables (GDP, C, I,andNX/Y) exhibitpositive persistence]9 Business cycle volatility,measured interms of percent standard deviations, ishigherthe lower the frequency ofthe filter used. However,the standard deviations ofCand IreZafive toGDP are similal for the BP, HP, and T3filters, while forthe RW filterthe relative variability ofC is largerand thatof I issmaller than with the other filters.Thus,as a first approximation, the lowerfrequency filters produce larger, more persistent, andmore correlated business cycles, butthe differences acrossfilters are not substantial. . . I%e T3filterandthe HPfilterwith the smoothingparameter setat 100produce highly correlated cyclical components forGDP, C, and I. The correlations exceed 0.91 inall cases. “The BPandHPfiltersexclude unit roots bydesign,and forthe RW and T3filters ADF tests rejected unit rootsatthe l-percent confidence levelwith 3 lags. 1*Cincludesdurables, which often results in largerconsumption fluctuations relative to GDP. 19ADFtestsrejectedthehypothesesthatNX/Y andRER contain unit roots, and hence it isunclear whether they should be filtered. Co-movements for NX/Y and RER in the BP and T3columns of Table 2 were computedinlevels,whileNX/Y andRERwere filtered inthe HPand RWcolumns. The Table showsthat cyclical indicators are nottoo dependent onwhether thesevariables are filtered or not.

I - Table 2also shows thatthe variability ofRER ismuch largerthan that ofthe othervariables-relative toGDP the fluctuations of RER are at least6.7times largerthan those of the other variables. There islittleevidence that real appreciations are correlated with G f w N a R d s n c T r a c a w aw t i r G r as p c b r a a d ab T f E s r t u d m F 6s t u d g p an r b R a t GDP share ofnetexports. Thisdiscussion ofcyclical co-movements isintendedasageneral description of Mexican businesscycles, rather than asthe foundationof a “moment-matching”exercise typical of RBC analysis, because thequantitative experiments conducted inSection3 focuson simulated time-series paths rather than on cyclical co-movements. Initialconditions were setto mimic roughly those prevailing before ERBSprograms start, with the intentto examine whether simulatedmacroeconomic dynamics resemble thoseobserved inthe data. Thisapproach seems adequate intheMexican case because thedata show that Mexico goesthrough the complete expansionary phaseofthecycle during each fixed-exchange-rate regime (except inthe long-lastingcurrency peg covering 1955-76),sothatthe size of the boomsand real appreciations associated with ERBS episodescan be identifiedbyexamining Figures 8and 10. A typical example isthe 1976-82episode. Between 1976and 1981,RERappreciated by 38 percent, deviations fromtrend inIwidened by 30percentage points andthose forCand GDP widened by 8 percentage points(according to the BP filter), and NX/Y changed fromvirtualbalance to an 8percent deficit. Figure 11plots cyclical components of quarterly data forthe period 1983:1-1994:4. The chart forthe trade-weighted RER showsthat, afier a sharp initialappreciation inthe first semester of 1988, following the beginning ofthe currency peg inFebruary, RERremained almost constant until 1990:4. In 1991:1the real appreciation started again, sothat bythe December 1994devaluation the real exchange rateappreciated by 35.4 percent relative to 1988:1. By end-1993therealappreciation infact reached

- 46.&rcqnt, soRER fell byabout 10percentage points intheyear before to the devaluation. Similarly, v’ the de - ionsfromtrend inI,GDP, and C widened considerably between 1988and 1992,but in 1993all + three cyclical indicators fellbelow trend.zo Interestingly,the sizeofthe booms inGDP, expenditures, andthe real appreciation are very similar to thoseobserved inthe 1976-82episode. In assessingthe m p a t a b c a c b s f a l c such asthecollapse ofoil prices and the rise inworld interestratesthathit M6xico in 1982. Thus.we do notexpectuncertain duration to explain infull Mexican businesscycles and real appreciations. and ask insteadwhafjkzction ofthem can itexplain. .4 findingthata largefraction can beexplained byuncertain duration favors the model, without rejecting the hypothesisthat other sources of business cycles are relevant. Ifonly a negligible share of observed fluctuationscan beexplained bythe model, however, one shouldconclude that credibility isof little relevance. Another reasonable strategy isto gaugethe contributionof lackof credibility to explain ERBS syndrome inthe data by isolating the potentialcontributionofcredibility effects from the effects of other sourcesof business cycles using VAR methods(see Schmitt-Grohe (1995)). Wecomputed variance decompositions ofaparsimonious VAR systemthat usesthe interest-rate spread between Mexican and U.S.treasury b am t probabilityofdevaluation and default. GDP, NX/Y, RER, and real M2enter asendogenous andtheterms oftrade are exogenous.21The exercise uses2 lags suggested bymaximization ofthe Akaike Information Criterion. The results showthat the interest differential explainsabout 40 percent of the variabilityof RER,GDP, NX/Y, and real M2 over 24 quarters. Unfortunately, because the interestdifferential isalmost perfectly correlated with the Mexican interestrate, andthe latter was influenced by sterilized interventionof largecapital flows during 1990- 94,the differential isat besta noisy measure ofthe “market”expectations ofthe sustainability ofthepeg. ‘“Sincetheperiodexamined hereexcludesthesharpstructuralbreakinGDP notedearlier, a~;adratic trend producesstationarycyclicalcomponents. ADFtestsshowthatthese components do not include unit roots. **ThisVAR analysis borrows h f as e C a M ( . i.

-31- Given theoverall size of ERBS boomsand realappreciationsdocumented for Mexico, andthe estimate ofthecredibility component provided bytheV c t u model that produces an 18percent realappreciation, consumption andGDP booms inexcess of2 percent. and investment booms inexcess of 5percent would be inlinewith the most recent Mexican experience. The 15percent real appreciation produced bythebenchmark model is lessthan 1/2the real appreciation observed in Mexico during 1988-94or 1976-82,but iscloseto the 18percent credibilityinducedreal appreciation measured usingt V T m a m t d t RER is stable inthe middle ofthe program and depreciates slightlypriortothecollapse. The fluctuations in GDP andthetrade deficit are also consistent with Mexican dat~ as isthefact that recessions may start priortothe collapse of the currency. Incontrast, and contrary to thefindingsof perfect-foresight studies, the booms intradables consumption and investment seemlargerthanthoseobserved inthe data. IIIaddition to the roleof sources of business cycles ignoredbythe model, the match between the modeland the datacan beaffected bythe structure of parameters set inthecalibration. As shown inthe sensitivit}analysis. assumptions on the sizeof rebates (which ultimatelyreflect the stance of fiscal polic>’),the shapeof the hazard rate function,theelasticities of intertemporalsubstitution and labor suppl}’,and the nature of financial assetsthatconform transaction balances,are key forthe performance ofthe model. 5.Concluding Remarks This paper shows that uncertain duration ofan exchange-rate-based stabilization produces boomrecession cycles, worsening external deficits, and sharp real appreciationssimilar inmagnitude tothose thataffect chronically countries that adoptdisinflation programsbasedon fixed exchange rates. The analysis isconducted by simulating numerically the equilibriumdynamicsofa general equilibrium modelof atwo-sector, small open economy with incompletemarkets. Devaluation ismodelled asan eventto which agents assign an exogenous probability ofoccurrence, insteadofbeing fully-anticipated as inthe traditional credibility literature, and abackward-recursion algorithm isused to compute

equilibrium dynamics a f f p r s a t c T experience ofM&xicointhe post-war period, which includessixfixed-exchange rate regimes, is examined asacase study. Thisapproach to model lackof credibility asaproblem of uncertain duration has been shown in theory to alterthe predictionsofconventional perfect-foresigh~ partial-equilibrium credibility models. However, the quantitative im t a a i p a n p ina general equilibrium settingwere unexplored. Our results suggestthat uncertain duration may help to explain theactuai experience of countries where, as in Mexico in 1994,currency pegs fail under the pressure of largeexternaldeficits and overvalued exchange ratesdespitesuccessful efforts to dismantle indexationand reduce fiscal deficits. The model explains key features ofthe syndrome of exchange-ratebased stabilizations withoutprice orwage rigidities, orborrowing constraints. The obsewation thatdevaluation probabilities are “J-shaped,”borrowed from the empirical literatureonbalance-of-payments crises, iscritical forthequantitative successofthe uncertain duration framework. The shapeof macroeconomic dynamics during acurrency peg isheavily influenced bythe shape ofthehazard rate function that governs devaluation probabilities. Linear hazard rates yield quasi- Iineardynamics, while strictly convex hazard rates area necessary (though not sufficient) condition to producethe concave dynamics observed inprivate expenditures and realappreciations. The “J-shaped” hazard ratealso allowsthe model to mimic periods oftemporary real-exchange-rate stability inbetween periodsof sharp real appreciation, and recessions thatpre-date currency collapses. Wealtheffects introduced by the incompleteness of financialmarkets, underthe assumption that seignorage and transaction costs are not fully rebated, are alsocrucial forthe model’sperformance. This isreminiscent oftheoretical work on the real effects ofdisinflationthatemphasizes wealth effects resulting from inconsistencies between fiscal and exchange-rate policies. Because ofthe wealth effects, uncertain duration entails iargewelfare costs compared to thenegligiblewelfare costs ofcredibility obtained underperfect foresight.

-33- The general equilibrium natureofthe model impliesthatuncertainduration, which acts likea random tax on savings, affects boththe supplyand demand sectorsofthe economy. As a result, supply- -sideeffects that have been examinedfor fully-credible disinflation plans,which operate via the leisureconsumption margin andthe capital accumulation choice, also influencemarkedly the dynamics of uncertain duration models. Because ofthese effects, particularly the investmenteffect, exchange-ratebased stabilizations of uncertain duration are generally welfare-improving, relative to an initialhighinflationequilibrium. These stabilizations are stillvery inferiorto fully-credible stabilizations, and hence policies aimed atenhancing the credibility ofcurrency pegs,orat lesseningthe impact ofthe tax- Iikedistortion dueto uncertain duration aredesirable. Our results also show that, despitethe eventual successorfailureof stabilization plans, and even inenvironments of perfect capital mobility, flexible prices, and fiscaland monetary discipline, stabilizations go through difficult stages inwhich the exchange rate ishighlyovervalued and the current account deficit islargebecause agents doubtthe intentionsofpolicy-makers. Policy lessons mustthen bedrawn carefully, asdevaluation by itself isnot apermanent solutionforreal overvaluation and large trade deficits. Beforeconcluding, it isworth notingthat while uncertain duration may helpto explain Mexican macroeconomic dynamics between 1988and 1994,itseems insufficientto explain the violence ofthe financial collapse and economic recession that hit Mexico in 1995. Asnoted inthe August, 1996 symposium issueoftheJourna~ofInternationalEconomics,several researchers sharethe viewthat Mexico-style crises are magnified byelements of self-fulfilling crisesand “herding”behavior inglobal markets, which inMexico ledto massive runs ona largestockofdollar-denominated public debt.

-34- References Asea, Patrick, and Enrique G. Mendoza (1994), “TheBalassa-Samuelson Model:A General Equilibrium Appraisal,”ReviewofInternationalEconomics,vol. 2, pp.244-267. Aspe, Pedro (1993),EconomicTransformation:77reMexican W~, MITPress,Cambridge: MA. Blanco, Herminio, and Peter M.G ( “ D a S A t M P JournalofPolitical Economy,V.94, p. 148-166. Calve, Guillermo A.(1986), “Temporary Stabilization: Predetermined Exchange Rates,”Journalof PoliticalEconomy,v. 94, pp.1319-1329. , (1988), “CostlyTrade Liberalizations: Durable Goods and CapitalMobility,” I.FStaflPapers, v. 35, 461-473. and AlIanDrazen, (1993) “Uncertain Duration of Reform: Dynamic Implications,” Working Papers ii International EconomicsNo. WP4, Department of Economics, Center for International Economics, University ofMaryland atCollege Park. and EnriqueG. Mendoza(1994), “TradeReforms ofUncertain Duration and Real Uncertainty: A First~pproximation,” ]&f..StaflPapers, vol. 41, pp.555-586. and EnriqueG. Mendoza (1996), “Mexico’sBalance-of-Payments Crisis: A Chronicle of a Death F~retold,”forthcoming,JournalofInternationalEconomics. Dornbusch, Rudiger(1982),“Stabilization Policies inDeveloping Countries: What havewe Learned?” Wor/dDevelopment,VOI.10,pp.701-708. (1983),“RealInterest Rates, Home Goods, and Optimal External Borrowing,”Journalof Po[itica[Econom~.v. 91, pp. 141-153. Drazen. AlIanand Elhanan Helpman, (1988), “Stabilizationwith Exchange RateManagement under Uncertainty,” in E.Helpman, A. Razin, and E. Sadka eds.EconomicEflectsoftheGovernmentBudget, MIT Press. Cambridge:MA, pp.310-327. Edwards, Sebastian(1993), “Exchange RatesasNominal Anchors,”Reviewof WorldEconomics,VOI 1~9.no.l, Kiel Institute of World Economics, Pp. 1-32. (1996), “TheMexican Crisis inHistorical Perspective,” forthcomingAmericanEconomic Review:Papers andProceedings. Femandez, RoqueB.(1985), “The Expectation Management Approach to Stabilization inArgentina, 1976-82”,WorMDevelopment, August, v.13, pp. 871-92. Frankel, Jeffrey andAndrew K. Rose,(1996), “Currency Crises inEmerging Markets: An Empirical Treatment,” forthcoming,JournalofInternationalEconomics.

-35- Frenkel, Jacob A.and Assaf Razin (,1987),~iscaIPoIiciesinthe WorldEconomy,M P Ca Goldberg, Linda S.(1994), “Predicting Exchange Rate Crises: M&xicoRevisited,”Journalof InternationalEconomics,v. 36,p 4 Go A (1 1 P Monetariay FiscaldeJ4Zxico:LaExperienciadesde la Posguerra, 1946-1976,F C E M C M -. Greenwood, Jeremy (1983), “E t E R a t C A Journalof MonetaryEconomics,vol. 12,pp. 543-569.0 , (1984), “Non-traded Goods, the Trade Balance, andthe Balance of Payments,” Canadian JournalofEconomics,vol. 17,pp. 806-823 ,Z Hercowitz, and”Gregory Huffman, (1988), “Investment,Capacity Utilization, andthe Real BusinessCycle,”AmericanEconomicReview, vol. 87,pp.402-417. Helpman, Elhanan and Assaf R“hzir(i1987), “Exchange RateManagement: Intertemporal Tradeoffs,” AmericanEconomicReview, vol. 77, pp.107-123. Kaminsky, Graciela and Carmen M. Reinhart (1995), “TheTwin Crises: TheCauses ofBanking and Balance-of-Payments Problems,” mimeo, Board of Governors ofthe FederalReserve System. Kamin, Steven andJohn H. Rogers(1996),“Monetary Policy inthe End-Game to Exchange-Rate-Based Stabilizations: TheCase of Mexico,” forthcoming,JournalofZnternationa/Economics. Kiguel, MiguelandNissan L ( “ B C A w E R B St WorldBankEconomicReview, vol. 6.,pp.279-305. Klein,Michael W. andNancy P.Marion, (1994) “Explainingthe Duration of Exchange-Rate Pegs,” unpublished manuscript, Department of Economics, Dartmouth College. Lahiri, Amartya (1995), “Exchange-Rate-Based Stabilization Under RealFrictions:The Roleof Endogenous Labor Supply,”mimeo, Department of Economics, UCLA. .. LucasJr., Robert E.(1987), ModelsofBusinessCyc2es,Basil-Blackwell, New York. Mendoza, EnriqueG. (1995), “TheTerms of Trade, the RealExchange Rateand Economic Fluctuations,”InternationalEconomicReview,vol. 36, pp. 101-137. ,(1996), “Terms-of-Trade Uncertainty and Economic Growth: Are RiskIndicators Significant in Growth Regressions,” forthcoming, JournalofDevelopmentEconomics. Rebelo, Sergioand Carlos A. Vegh, (1995), “RealEffects of Exchange-Rate-Based Stabilization: An Analysis ofCompeting Theories,” NBERMacroAnnual,National Bureau ofEconomic Research, Cambridge: MA.

- R C a C V ( “ S C I Countries: T E E m R D I M FUWL (1995), “NominalInterest Rates, Consumption B a LackofC AQ Ex JournalofDevelopmentEconomics,f Ro C ( “ A S P D 2 W D v p 8 R J ( “S D P I V 4 p 1 Sc S ( ) I T E F E U B C t C E Financea E D S N 9 B G t F R S W D 2 U M ( “E I S t I R E C P I N 5 B G t F R S W D (1996), “Comparing the Welfme C a t I D A T Stabilization Policies,”IFDPNo. 539, Board G t F R S W DC. V C ( “ H I A O J V 3 P 6

-37- 000+ 1 t=

-38- I u 1+ .-— I g : u

-39- F H F 1 I I i I n 0.9 J —. f o c \——— —— —— 0 n n n n A n n n w n n n n A n n 0 5

- Figure 3: C DYNAMICS UNDER A TEMPORARY TARIFF CUT (endowment economy case) Perfect foresight 1 1 1 T 0 0 1 ‘. \ 0.9 - ‘“- 0 0 40 0 0 Rebateanda = 2.61 rebate anda = 2.61 Norebateanda = 1 Uncertain Duration: flat hazard function 1 1 0 0 I I / / / / / 0 ~ 0 0 40 0 Rebateanda = 2.61 Norebate anda = 2.61 Norebateanda = 1 Uncertain Duration: non-linear hazard rate 1 I I 0 0 1 ~ ~ 0 o 40 0 40 0 rebateanda = 2.61 Norebate anda = 2.61 Norebateanda = 1 ------ before the policy switch ---- at and after the policy switch

-41- Figure 4: MACROECONOMIC DYNAMICS OF AN EXCHANGE-R.4TE BASED STABILIZATION OF UNCERTAIN DURATION* GDP velocity tradebalance ————--—-- OF 6 - 4‘ - 2 / v & K&l~abg 6 / 5 / 2 -- .- o- ———————— 0 OL- I , d r $rossl$ve!$ne$” 80‘ 60 / ‘ / ‘ / / o- - o- — ‘ 5 10 15 20 5 10 15 20 5 10 15 20 0.8 d 0.6 0 0 0 5 10 15 20 hazardfunction *AHvariables,except NX~/y~, are expressedin percentage deviationsfromtheir pre-stabilizationsteadj’state. Solid linesdenote pre-collapsevaluesand brokenlinesat-collapsevalues.

-42- Figure 5: SENSITIVITY ANALYSIS* The Benchmark Model -- ——- 80 &#45;&#45;&#45; 15 15 5- 60 10 0 10 5 5 / .“ -- -10: 0 nL ‘- n - 4 u 5 10 15 20 5 10 15 20 u 5 10 15 20 5 10 15 20 NXt /Y; I, P? Flat Hazard Rate -_- —- ——-- 15‘ 60; 5- 15 40 10‘ 10 0 5 -5 ~ I 5 / / / / / / . 2 o 0 - ---— --— 0 0- “ “ 5 10 15 20 5 10 15 20 5 10 15 20 It Pi” Perfect Foresight 10r --- _---– 80 15 60 0 10 40 20 -10 5 -- -- I --- 0 ---- --— 0 5 10 15 20 5 10 15 20 - 5 10 15 20 5 10 15 20 NX,lY, c, I, P: Full Rebate (q. = q~ = 1) 4“ 10 ‘n 80 -15 60 2 -20 5 40 o- -. . -25 20 \ \ \ ‘ -30 0 ----- --- 0 ---- -. 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 NX,l Y, et I* P7 *Allvariables,except NXt /Y~,are expressedin percentage deviationsfromtheir pre-stabilizationsteadystate. Solidlinesdenote pre-collapsevaluesand brokenlinesat-collapsevalues.

-43- Figure 5: (continued) SENSITIVITY ANALYSIS Inelastic Labor supply (p= o) -. —-- 8‘ 80‘ _-” % 5 6 60 4 20 o- —--- ‘ -5 L 0- ‘ 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 It Piv Low Intertemporal Elasticity of Substitution (a = 5) ‘ — - 5‘ 0 k / / ‘ / / 0 ‘ H 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 . / Cobb-Douglas Aggregator Function (p = O) -- —-. 80 5 / / 0 :M - / 0 —-— o ‘ I 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 NA-, /Yt It Extended Time Horizon (J = 36) --—- 80‘ 4 5 60 0 20 5 o- ---- - -— 0 0 10 20 30 10 20 30 10 20 30 10 20 30 NX,/Y, It P?

-44- Figure 5: (continued) SENSITIVITY\’ AX,+l.}’SI$ High SteadJ7State }Ioney J;elocity (1‘t] = 15.4 per )’{~~ir~ 4 .—————--- 10 -lo 2 - 5 / / I / / - , --- — o~ 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 I, Non-zero Probability of Long-Run Success = H, L and j >1 J 80~ 15 60 10 5 . / / / / 20‘ o- ---o- ‘“- - 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 I, . ~/) ~ f,J= (JHICJ-l = CL )= ..5and P?’(eJ+j = d IC’J= et) = 1 for i = H,L and j >1 4 --- -- ——-. 80 5- 60 0 40 ,- 20 .- -- -- --- .- o- ---- - 0 ----- 0 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 N.3-,/}; c, I, P:

-45- R o! I I , J 1 —— I , \ f \ —--- perfect f ___------------- ——---------- ——---- —-- —---—----— —--_--- —--——--——--- I I I I 1 ; 0 5 t F R J -0.1 —— f I -—-—p f $ - \ \ \ \ \ - \ -.- —----------- —----- ———-———-——-—---- —--------- _->~_____-–.–– –-. I ———— ~ I I I ! J 5 10

-46- Figure 7: Co and Labor S A U A H R REBATE Co pr L p 3 1 3 .-l , / t t 3 ‘ .,~’ I 0 ., 3 I ‘ 3(3~ (3.15~ o 1 20 30 o 1 20 30 Co po L p 3 i 1 0 1 / 30.5 / / / 0 \ ‘ / \ 30 / \ / / 0 \ \ 29.5 /’ \ \ 29/ ~ 0 :\ \ \ \ \\ : I 2 0 -? \ I o 1 20 30 o 1 20 30 FULLREBATE Co pr L p 4 0 4 0 - - _ 4 I 0 - - , t t 1 3 t 0 f I I 3 I 0 ~‘ ~ ‘ ~ 3 0 0 1 2 3 0 1 20 30 Co po L p 3 I 37.8 . ‘ . . 0 “ . . / 37.6 \ \ . / 0 / \ : 0 , 0 / 37.4 0 37.2 0 ‘ 0 1 2 3 0 1 2 3 J - f ...p f

-47- F 8 M R N E R 2 m 0 n e r — r e i ( s ( s N r e r index is P w P M CPI. E is the n e r n p d is the” U C b index is I .. F 9 M c T E . 8 IIIIIrI1II1I11III11III?III81vIIIII II 45 50 55 60 65 70 75 80 8I5 I I I I9I0I — actual - c time trend ––– first-difference trend

-48- Figure10 Post-warMexkanBusinessCycles Fixedcapitalformation Privateconsumption 0.4 I ‘0.loj. ~ -. ----’ 0 0 I -0.2 -0.10 . . . - -0.4 -,....1.1..1. 1 1. 5I0 5 I 5 6 I 0 65 70 75 80 85 90 45 50 55 60 65 70 75 80 85 90 band-pasfislter---- wbictrendfilter‘ -- fi=t-dlfferef’=filter — ba f - c t f ‘ - fi f — Netexports/ GDPr Grossdomesticproduct 0.08- ; t I I .1, , 1, 1, # I I , ! -0 {, , ,, , ,, , I -0.08 ,. ‘“1”’’”1”””’1’”’ v, v, 45 50 55 60 65 70 75 80 85 90 45 50 55 60 65 70 75 80 85 90 ba f - Cu f - fi f — level --- firstdifference

-49- Figure 11 Mexican Business Cycles: 1983:1-1994:4 (percent deviations from quadratic trend, except RER) Investment 0.06 0 0.04 0 0.02 0.00 0 -0.02 - -0.04 006 8 ? 3 r 1 84 T , 1 8 , 5 , I 86 1 I 8 1 7 r I 8 r 8 , I 8 r 9 , , I 9 , 0 , 1 I 9 , 1 , 1 9 r 2 r , I 9 , 3 1 1 9 * 4 f - ‘ )3 1,, I 8 , 4 , , 1 8 , 5 , , 1 8 , 6 , , I 8 , 7 , , I 8 , 8 , 1 I 8 , 9 , i 9 a 0 r , I 9 v 1 , , i 9 I 2 , r i 9 1 3 , 1 I 9 , 4 i Real exchange rate Private consumption (log effective exchange rate, 1 O 5 004 5 0 0.00 4 0 4 3 ) } rI ,, I , , , r , I , I , vI , , 1, 1, I , I , , , I , , I * I , s 4 t,, I , , , 1, , 1 I f , , 1, , 1, , nI , r I , r , I , , #I r , I , , , I , i 83 84 85 86 87 88 89 90 91 92 93 94 83 84 85 86 87 88 89 90 91 92 93 94

- A S M Computing equilibrium dynamics for models ofincomplete markets isa complex task in general because of difficulties involved in tracing the optimal state-contingent evolution of wealth. In the case ofsmall open economy models, with perfect capital mobility and conventional utility functions, this problem is compounded by the fact that stationary equilibria, when they exist, are determined by initial conditions. In ]ig~l~O! t dii%cuities. we developed an algorithm that obtains a nearexact solution for equilibrium dynamics. The equilibrium stochastic processes’that characterize macroeconomic dynamics are computed by backward recursion on the general equilibrium system defined by equations (.5)-(12) and (14)- (15). The method exploits the assumptions that (a) the date ofcollapse of the program is a random variable with finite support ([1,J]) and (b) that the collapse of the program is an absorbent state. Thus, there is a distant future date in which policy uncertainty is resol~’ed. This imposes w“elldefineclterminal conditions on consumption, leisure and money velocity, all of which jump to their corresponding high-inflation stationary equilibria on the date of the collapse. The current account and in~’estrnent take some time to reach their steady state equilibria because of the inertia incluced b}’capital adjustment costs. but their post-collapse dynamics are easily determined b}’solt”inga linearized \-ersion of the Euler equatior-ifor capital accumulation. The algorithm begins by guessing period-J values for the state variables (capital ~[ld boil(ls) and uses intertemporid Euler equations and the budget constraint to compute the vaiuw taken b}” these variables in periods t = .J– 1 J– ...0. Solutions for the control and co-state variables are pro~idecl by atemporal optimality and market-clearing conditions. A shooting algorithm is then introduced to ensure that the period-J guess is consistent with the initial conditions for the capital stock axldI)ond holdings. Notation: let XHt denote t assumedby X if ‘~ =e H and et–l = e‘, and x: the \.alue assumed b~ x~if et = e~’.The exception to this notation is the capital stock. ~~~1. fi;~}~del~otes the \’alue assumed by 1;~+l if et = e~ and et-l = eL, and 1{~+1the value assumed b!- ~~~~1if L e~= f . Initial conditions are given for the capital stock, A-OT, the stock of red financial wealth. ~– 1+ 11–~~/(1+ eG). Since et = eH is an absorbent state, it followsfrom the equiilb U c i t in t e~’entconsumption and money velocity are constant. In particular money velocity solves 1-- S’(I’”H = +eH) (see equation (1l)). Given this value for money velocity, it follows froln {12) that l;~~+J,.i Z 1follows a second order differential equation with a unique stead?’ state. 1~~,gi~’enby (1– ~T)(~{~/LT)-U~ = (~+ fi)(l + S(VH) + S“(V}{)\.TH), Equilibrium dynamics are computed in the following way. S i g for ~~~!-l. C;fl anti {T& }::; ‘- this last guess is necessary onl~’if the go~wrnment does not fully rebate seignorage income (q~ < 1). (1) Period .J– 1 In this period all variables except 1i~ reach their steady state. since ti~~ exchange rate uncertainty is removed. (1.1) Given C~~l, find C’~-Ll,p~~l, L~Xl and AJL–l b}’solving the intra-te:c.p”crt}i~,lli~l.~.~(1 tions (7)-(9) and the market clearing condition (13). (1.2) Compute an approximate solution for ~i$’-l+~,.~> ] bysolving a linearized ~wrsionof(12).

-51- (I.3) Find B~ * by solving (14) forward, using m$-z and (5)-(6’)to eliminate GJ-1 and ~J-1. (1.4) Use I?.L1-2- and rn$-2 to solve equations (.5)-(9)and (13)-(14) for c$~l ~c~-~~ PNJ_Hl, LNJH_l ~~]- ~. ~;~-l and T~-l. (2) Periods t = .] – 2,...o (2.1) Given V/+l, Jj+l, i = L, H, Kfi:, j = 1,2, and fi’~~, solve the intertemporal Euler ~~quations(10)-(12) for VtL,~~?and ~P~~TL. NL (2.2) Given ~L and A;, solve (7)-(9) and (13) for @L, CtNL,p a L . (2.3) Use B:, m~–l and the values obtained in (2.2) to solve (5)-(6) and (14) for l?~-l, and T;. (2.4) B: ~and m: ~ can then be used to solve (7)-(9), (13) and (14) (forward) for ~~, C p~’H,-and Ljvll.- (2.5) Use a linearized version of (12) to solve for K~.. (3) Steps (1)-(2) yield a new vector of real balances {rn~-l}~-~ = {(C’fl- + p~~c~~)~~l}~~~. If this vector differs from the one guessed, use it as the new guess and repeat steps (l)-(2). (4) If li~ differs from the desired initial condition for the capital stock, change the guess for ~(~!~land re~~eatsteps (1)-(3). (Ii; is increasing in l (5) if D-l + m-l /(1 + LO)differs from the desired initial condition for the stock of financial W-ea.ltll.change the guess for ~~~’1and repeat steps (I)-(4). (l?–I + m–1/( 1+ eo) is i i C .)

-52h F D P IFDP Number I Author(s) 1996 548 The Syndrome of Exchange-Rate-Based Enrique G. Mendoza Stabilization and the Uncertain Duration of Martin Uribe Currency Pegs 547 German Unification: What Have We Learned Joseph E. Gagnon from Milti-Country Models? Paul R. Masson Warwick J. McKibbin 546 Returns to Scale in U.S. Production: Estimates S B and Implications J F 545 Mexico’s Balance-of-Payments Crisis: A Chronicle Guillermo A. Calvo of Death Foretold Enrique G. Mendoza 544 The Twin Crises: The Causes of Banking and Graciela L. Kaminsky Baiance-of-Payments Problems Carmen M. Reinhart 543 High Real Interest Rates in the Afiermath of Graciela L. Kaminsky Disinflation: Is it a Lack of Credibility? Leonardo Leiderman 542 Precautionary Portfolio Behavior from a Life-Cycle Carol C. Bertaut Perspective Michael Haliassos 541 Using Options Prices to Infer PDF’sfor Asset Prices: William R. Melick An Application to Oil Prices During the Gulf Crisis Charles P. Thomas 540 Monetary Policy in the End-Game to Exchange-Rate Steven B. Kamin Based Stabilizations: The Case of Mexico John H. Rogers 539 Comparing the Welfare Costs and the Initial Dynamics Martin Uribe of Alternative Temporary Stabilization Policies 538 Long Memory in Inflation Expectations: Evidence Joseph E. Gagnon from International Financial Markets 537 Using Measures of Expectations to Identi& the AlIan D. Brunner Effects of a Monetary Policy Shock 536 Regime Switching in the Dynamic Relationship Chan Huh between the Federal Funds Rate and Innovations in Nonborrowed Reserves Please address requests for copies to International Finance Discussion Papers, Division ot International Finance, Stop 24, Board of Governors of the Federal Reserve System, Washington, D.C. 20551.

-53- In F D P IFDP 535 T R a I E F Edwin M. Truman Shocks: Lessons from Mexico 534 Currency Crashes in Emerging Markets: An Jeffrey A. Frankel Empirical Treatment Andrew K. Rose 533 Regional Patterns in the Law of One Price: Charles Engel The Roles of Geography vs. Currencies John H. Rogers 95 532 Aggregate Productivity and the Productivity Susanto Basu of Aggregates John G. Femald 531 A C of Trade Elasticities for Canada, Japan, J M and the United States 530 Modelling Inflation in Australia Gordon de Brouwer Neil R. Ericsson 529 Hyperinflation and Stabilisation: Cagan Marcus Miller Revisited Lei Zhang 528 On the Inverse of the Covariance Matrix in Guy V.G. Stevens Portfolio Analysis 526 Uncertainty, Instrument Choice, and the Uniqueness Dale W’.Henderson of Nash Equilibrium: Macroeconomic and Ning S. Zhu Macroeconomic Examples 5’)5 Targeting Inflation in the 1990s: Recent Challenges Richard T. Freeman Jonathan L. Willis 524 Economic Development and Intergenerational Murat F. Iyigun Economic Mobility 523 Human Capital Accumulation, Fertility and Murat F. Iyigun Growth: A Re-Analysis 522 Excess Returns and Risk at the Long End of the AlIan D. Brunner Treasury Market: An EGARCH-M Approach David P. Simon 521 The Money Transmission Mechanism in Mexico Martina Copelman Alejandro M. Werner