-1- episodes elsewhere (see Helpman and Razin (1987), Kiguel and Liviatan (1992), and Végh (1992)).

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3 -1-1. Inroducion The devaluaion of he Mexican peso in December of 1994 marked he collapse of an aggressive sabilizaion plan inroduced six years earlier under he name of El Paco de Solidaridad Economica (The Pac for Economic Solidariy). El Paco was a varian of an exchange-rae-based sabilizaion plan which pracically fixed he peso-dollar exchange rae while ighening sharply boh fiscal and moneary policies. Four significan sylized facs were observed during he period ha his sabilizaion plan was in place: he real exchange rae appreciaed sharply and a a varying speed, he economy boomed iniially and hen fell ino recession, exernal imbalances widened markedly, and he velociy of circulaion of money plummeed. Srikingly similar phenomena preceded he devaluaions of he Mexican peso in 194, 1976 and 1982, and have also been documened for a large lis of exchange-rae-based sabilizaion episodes elsewhere (see Helpman and Razin (1987), Kiguel and Liviaan (1992), and Végh (1992)). Exchange-rae-based sabilizaions hus seem o exhibi a syndrome defined by hese sylized facs. The sudy of his syndrome has been he focus of an exensive research program seeking o undersand he naure of he moneary ransmission mechanism behind i. This paper proposes a ransmission mechanism in which he syndrome is a feaure of he compeiive equilibrium of a moneary economy wih incomplee insurance markes, disored by he risk of collapse of a currency peg. The ransmission mechanism operaes by allowing devaluaion risk o aler he nominal ineres rae and money velociy, in an environmen in which changes in velociy affec he real secor of he economy because money balances help agens economize ransacions coss. The probabiliy of collapse of he peg creaes a sae-coningen differenial beween domesic and world ineres raes, and his devaluaion-risk premium inroduces sochasic disorions on money demand, saving, invesmen, and labor supply. Marke incompleeness adds endogenous sae-coningen wealh effecs o hese disorions via subopimal invesmen decisions and fiscal cus induced by he imevarian paern of he inflaion ax. Numerical simulaions of he model calibraed o he Mexican experience of produce macroeconomic dynamics ha are roughly consisen wih key feaures of he daa. The exising lieraure has produced o dae four compeing heories for explaining he syndrome of exchange-rae-based sabilizaions. Dornbusch (1982) and Rodriguez (1982) argued ha a fixed

4 -2- exchange rae lowers he real ineres rae and causes an economic boom because prices are sicky and expecaions of inflaion adjus slowly. The real ineres rae falls because ineres pariy forces he nominal ineres rae o fall, while expecaions of inflaion remain high. Calvo (1986) proposed he perfec-foresigh credibiliy framework, in which agens anicipae a devaluaion and reurn o high inflaion wih full cerainy. Ineremporal subsiuion leads consumpion o jump o a higher consan level for he duraion of he plan, before collapsing in anoher discree jump o a lower consan level when he plan fails. 1 Helpman and Razin (1987) and Drazen and Helpman (1987) examined models in which fiscal policy is no ighened as required by he solvency consrains ha deermine he susainabiliy of a peg. They showed ha he syndrome can be caused by wealh effecs resuling from he iming of changes in he inflaion ax or in governmen expendiures. Finally, Roldós (199) and Uribe (1997) proposed he supply-side hypohesis. They argued ha, even under perfec credibiliy and price flexibiliy, a permanen decline in he rae of depreciaion of he currency can induce a gradual real appreciaion, a boom in domesic absorpion, and a deerioraion of he curren accoun because i reduces inflaion-induced disorions on he relaive price of capial and oher durable goods. These heories fi well some elemens of he counry experiences of he 197s and 198s, bu hey seem a sharply odds wih recen experiences. The syndrome of exchange-rae-based sabilizaions affeced Argenina and Mexico despie sharp declines in price ineria and large fiscal cus in boh counries. Moreover, even hough he qualiaive predicions of exising heories are consisen wih some of he sylized facs, heir quaniaive performance has been very mixed. They canno accoun for he magniude of observed macroeconomic flucuaions, hey fail o explain he high correlaion beween he real exchange rae and expendiures and he periods of sable real exchange raes in beween large appreciaions, and hey produce real appreciaions ha are roughly 1/8 of wha is observed in he daa (see Rebelo and Végh (1996)). 2 Recen heoreical work sheds ligh on he origins of some of hese empirical shorcomings. Firs, Calvo and Drazen (1998) showed in a parial-equilibrium seing ha uncerainy abou he duraion 1 Furher research added nonraded goods and saggered prices o show ha lack of credibiliy could also rigger gradual real appreciaions (see Chapers 1-18 in Calvo (1996)). 2 Uribe (1997) is an excepion ha yields a large real appreciaion and a large spending boom using a model in which inflaion acs as a ax on purchases of inermediae maerials as well as on final ransacions.

5 -3- of policy changes and incomplee conigen-claims markes, boh issues generally absraced from in he exising lieraure, are required in order o accoun for he observed gradual consumpion booms. If Calvo s (1986) model is alered so ha he dae of a policy reversal is uncerain, producing a gradual consumpion boom requires wealh effecs resuling from incomplee markes and he unproducive use of governmen revenue. Sill, he Calvo-Drazen framework canno accoun for he observed cyclical dynamics because consumpion is always nondecreasing, regardless of he ime pah of he probabiliy of reversal. Second, Uribe (1998a) showed ha mos of he exising models ha sudy exchange-rae-based sabilizaions belong o a large class ha feaures he "price-consumpion puzzle." This puzzle implies ha he observed high correlaion beween consumpion and he real exchange rae canno be a propery of he equilibrium of models in ha class. Along he equilibrium pah of hese models, he real exchange rae appreciaes only if consumpion declines. In his paper we sudy a sochasic environmen similar o he Calvo-Drazen model. There is a major difference, however, because in he framework ha we sudy he currency risk premium esablishes an endogenous link beween he uncerain duraion of he policy regime (i.e., he currency peg) and he variable ha drives he disorions on he real economy (i.e., he nominal ineres rae). In conras, he Calvo-Drazen model deals wih a rade reform of uncerain duraion in which he value of impor ariffs while he reform is in place is no affeced by he probabiliy of reversal of he rade reform. Our analysis also differs in ha we sudy policy uncerainy in a general-equilibrium conex and wih he emphasis on he model s quaniaive predicions. We assess wheher he quaniaive feaures of he syndrome of exchange-rae-based sabilizaions can be raionalized as feaures of equilibrium dynamics in a seing in which agens face devaluaion risk. The numerical analysis applied o he Mexican case shows ha he model can accoun for he price-consumpion puzzle, booms followed by recessions ha pre-dae devaluaions, and periods of realexchange-rae sabiliy in beween sharp appreciaions. The real appreciaions we produced are sill smaller han measured in he daa, bu hey are imes larger han hose produced by exising models, and hey are also in line wih he fracion of he real appreciaions ha he daa sugges can be aribued o currency risk. Moreover, he welfare coss of devaluaion risk largely exceed he negligible coss of lack of policy credibiliy obained in perfec-foresigh sudies (see Calvo (1988)).

6 -4- The res of he paper is organized as follows. Secion 2 documens empirical regulariies of Mexico s sabilizaion plan. Secion 3 describes he model and he soluion mehod. Secion 4 presens he resuls of he quaniaive analysis. Secion concludes. 2. Mexico s Exchange-Rae-Based Sabilizaion Plan The syndrome of exchange-rae-based sabilizaions is described by four sylized facs: (1) A large appreciaion of he real exchange rae ha may occur wih periods of sabiliy in beween rapid appreciaions, and is highly correlaed wih an expansion in privae expendiures. (2) Booms of producion and privae expendiures, followed by recessions ha ofen predae he collapse of he plans. (3) A widening of exernal imbalances ha is reversed by he ime of he collapse. (4) A fall in he velociy of circulaion of money, followed by a surge around he ime of he collapse. This secion documens he above empirical regulariies for he Mexican sabilizaion plan of Mendoza and Uribe (1997) documened similar sylized facs before he devaluaions of he peso in 194, 1976, and The secion also provides evidence on oher elemens of he Mexican daa ha are imporan for he ransmission mechanism of he model proposed in Secion 3. Daa on naional accouns are from he Banco de Información Económica del Insiuo Nacional de Esadísica, Geografía e Informáica, and daa on consumer prices, moneary aggregaes, ineres raes and he exchange rae are from Indicadores Económicos del Banco de México. A deailed daa appendix is available from he auhors on reques Exchange Raes and Consumer Prices Figure 1 plos he monhly evoluion of Mexico s real and nominal exchange raes during The nominal exchange rae in he lef scale is in pesos per dollar, so i increases as he peso depreciaes. The real exchange rae index, in he righ scale, follows he IMF s convenion and is measured as he raio of Mexico s consumer price index (CPI) over he exchange-rae-adjused CPI of he Unied Saes. An increase in his index indicaes a real appreciaion of he peso. As Figure 1 shows, Mexico fixed he peso-dollar exchange rae in February of 1988 and kep if fixed for he remainder of ha year. This was done joinly wih oher sabilizaion measures announced wih El Paco in December

7 -- of 1987, which preceded he economic reforms of he early 199s. 3 Afer 1988 he exchange rae followed a slow-crawling peg sysem ha wen hrough several adjusmens. The resul was in effec a nearly-fixed exchange rae unil he collapse of he peso in December of The real exchange rae index is ploed in Figure 1 wih February 1988=1, so ha he base dae coincides wih he fixing of he nominal exchange rae. The peso had depreciaed sharply in real erms in , so he currency peg sared from a low real exchange rae from a hisorical perspecive. The peso appreciaed sharply, by abou 1 percen, during 1988, and hen remained relaively sable during The appreciaion re-emerged in 1991 and coninued unil i peaked a abou percen in March, Measured from he beginning of he peg o he end (i.e., February, 1988 o December, 1994), he peso appreciaed by 4 percen in real erms. A he quarerly frequency consisen wih he model we sudy laer, he real appreciaion beween he firs quarer of 1988 and he las quarer of 1994 was 41. percen. Since during he period in quesion boh U.S. CPI inflaion and changes in he nominal exchange rae were negligible, compared o Mexico s CPI inflaion,, a closer analysis of he Mexican CPI provides key informaion for undersanding he real appreciaion of he peso. Figure 2 shows ha he real appreciaion was driven by a large increase in he domesic relaive price of nonradable goods o radable goods. 4 The inflaion rae for radables converged rapidly o inernaional levels, bu he one for nonradables fell very slowly. This paern conrass sharply wih evidence from indusrial counries showing ha real-exchange-rae flucuaions are unrelaed o movemens in he relaive price of nonraded goods (see Engel (199)). Figure 3 illusraes he high correlaion beween privae expendiures and he real exchange rae a a quarerly frequency. The cyclical componens of privae consumpion and invesmen moved ogeher wih he real exchange rae from he beginning of he sabilizaion plan and unil expendiures slowed down in 1993, while he real appreciaion coninued. The correlaion coefficien for eiher consumpion or invesmen and he real exchange rae is abou.7, excluding he daa from he second quarer of 1993 unil he collapse of he plan. 3 Aspe (1993) provides a deailed descripion of he sabilizaion plan and he economic reforms. 4 The CPI for radables corresponds o durable goods and he one for nonradables corresponds o services. This is roughly consisen wih he definiions based on secoral rade-o-gdp raios inroduced laer.

8 -6- The fac ha he real exchange rae and expendiures increased ogeher for 3/4 of he duraion of he plan generaes he "price-consumpion puzzle" idenified by Uribe (1998a). This puzzle emerges because along he ineremporal equilibrium pah of a cerain class of models, which includes he majoriy of models in he lieraure on exchange-rae-based sabilizaions, he real exchange rae and consumpion canno increase ogeher. The models in his class are hose ha feaure perfec foresigh, perfec capial mobiliy, an exogenous world real ineres rae equal o he rae of ime preference, and a sandard ime-separable uiliy funcion defined in erms of a linearly homogeneous, concave aggregaor of raded and nonraded goods. These feaures imply ha in a fixed-exchange-rae equilibrium he following wo condiions mus hold: (a) he relaive price of nonradables is increasing in he raio of consumpion of radables o consumpion of nonradables, and (b) he marginal uiliy of consumpion of radables equals he marginal uiliy of wealh imes he moneary disorion (if he model feaures one). Since perfec foresigh and ineres pariy imply ha he marginal uiliy of wealh and he moneary disorion are consan, condiions (a) and (b) imply ha consumpion and he real exchange rae move in opposie direcions along he equilibrium pah Producion, Privae Expendiures and Ne Expors The lieraure on sabilizaion in high-inflaion counries ypically measures booms and recessions using he overall growh of oupu or consumpion beween he daes of inroducion and abandonmen of sabilizaion plans. We adoped insead he approach of business cycle heory and focused only on he cyclical componens of he daa. This is imporan because our model is a model of business cycles, and hence should be assessed using daa ha excludes long-run rends. In addiion, recen sabilizaion plans have been accompanied by exensive programs of economic reform, as was he case in Mexico. Hence, focusing on raw daa can bias he analysis by picking up effecs due o he ransiional dynamics of economic reforms, as hose sudied by Fernandez de Córdoba and Kehoe (1999). Figure 4 plos cyclical componens of GDP, privae consumpion, fixed invesmen, and he raio of ne expors o GDP using quarerly daa for he period 1983:1-1994:4. Given he shor sample, he daa were filered using a quadraic rend, esing o confirm ha i produced saionary cyclical componens. In Mendoza and Uribe (1997) we show ha he main feaures of hese cyclical componens are robus o he choice of filers.

9 -7- Invesmen, GDP, and consumpion experienced significan booms during he firs five years of he program, bu in 1993 all hree fell in recession. Thus, his was a ypical sabilizaion plan in which recession predaed currency collapse. Measuring from he firs quarer of 1988 o he peak of he cycle in 1992, GDP and consumpion increased by 4- percenage poins, and invesmen by more han 1 percenage poins. The rade balance as a share of GDP worsened from virual balance in 1988 o a defici of 6 percen of GDP by 1992, and remained around ha level unil i was suddenly reversed ino a surplus in he firs quarer afer he devaluaion. I is imporan o acknowledge ha while in our model devaluaion risk drives he business cycle, he Mexican business cycle is clearly influenced by oher facors -- such as shocks o produciviy or he erms of rade -- ha may also inerac wih devaluaion risk. Hence, i is worhwhile o ry o measure he fracion of Mexican business cycles ha can be aribued o devaluaion risk alone, and o consider his fracion in assessing he performance of he model. We measured devaluaion risk using he nominal ineres rae differenial beween Mexico s peso-denominaed reasury cerificaes CETES and U.S. T- bills, and gauged is conribuion o explain Mexico s business cycles using variance decomposiions of he VAR model proposed by Calvo and Mendoza (1996). The ineres rae differenial explains abou 4 percen of he variabiliy of each of he endogenous variables over 24 quarers. Thus, hese resuls sugges ha devaluaion risk considered in isolaion may explain real appreciaions of up o 2 percen Secoral Feaures of he Daa Microeconomic heory predics ha a large change in domesic relaive prices as he one documened earlier needs o be accompanied by large shifs in secoral marginal raes of subsiuion in consumpion and producion. Assuming convenional linear-homogeneous funcions o represen preferences and echnology, hese shifs require in urn secoral shifs in capial-labor raios and in consumpion. Evidence of hese shifs is difficul o documen because of serious limiaions regarding secoral daa. A consisen secoral breakdown of value added, gross oupu, invesmen and consumpion is only available a an annual frequency and saring in This shor sample does no allow us o isolae cyclical componens, and hence we canno deermine he exen o which changes in Noe, however, ha he CETE rae was influenced by exensive serilized inervenion during Thus, he CETE- T-bill differenial is a bes a noisy measure of marke expecaions of devaluaion.

10 -8- secoral daa may have refleced srucural changes in response o economic reforms. Moreover, daa on secoral capial socks are no available and secoral labor allocaions are repored only in number of employees per secor. Neverheless, he available daa do show evidence of secoral shifs in he direcion he heory predics. We define he radables and nonradables secors following he convenional pracice of examining he raios of oal rade o gross oupu in he nine indusrial secors in which oal producion is divided in he naional income accouns. The nonradables secor is composed of he indusries for which oal rade is less han percen of gross oupu a curren prices. Taking averages over , he nonradables secor includes: (1) consrucion, (2) uiliies, (3) reailing, resaurans and hoels, (4) financial services and real esae, and () social and personal services. The radables secor consiss of (1) agriculure, (2) mining, (3) manufacuring, and (4) ransporaion, sorage and communicaions. The raio of radables-o-nonradables oupu a consan prices was nearly unchanged over he period , and averaged.89. The raio of value added across secors also remained approximaely consan a an average near.6. In conras, labor produciviy (i.e., oupu a consan prices per paid employee) in he radables secor relaive o ha in he nonradables secor increased from.9 in 1988 o.68 in 1994, while he raio of employmen in he radables secor relaive o he nonradables secor fell from.81 o.67 in he same period. Hence, here was roughly no change in relaive value added across secors because he reallocaion of employmen from radables o nonradables was offse by an increase in relaive labor produciviy in favor of he radables secor. Moreover, since furher evidence from secoral daa documened in Secion 3 favors modeling secoral producion funcions as Cobb-Douglas echnologies, we conjecure from he efficiency condiions equaing secoral marginal raes of ransformaion in he Cobb-Douglas case ha: (a) he reallocaion of labor from radables o nonradables should have been accompanied by a secoral reallocaion of capial in he same direcion, and (b) for he raio of secoral GDP o have remained consan, while boh capial and labor were being reallocaed o he nonradables secor, here mus have been an offseing increase in oal facor produciviy in he radables secor. Secoral consumpion daa a 1993 prices, indicae ha radables consumpion grew faser han nonradables consumpion during he early sages of he plan. Tradables consumpion grew 8. and 6.6

11 -9- percen in 1989 and 199 respecively, compared o.2 and 4.9 percen in he nonradables secor. Surprisingly, however, radables consumpion slowed down more sharply during he cyclical downurn. Tradables consumpion grew only.3 percen in 1993, compared o growh of 3.9 percen in nonradables consumpion, and consumpion of manufacures acually declined. For he period, radables consumpion increased 33.4 percen, compared o 3.3 percen for nonradables. This reallocaion of consumpion in favor of radables is qualiaively in line wih he movemen required for he marginal rae of subsiuion in consumpion o mach he increase in he relaive price of nonradables Expendiure Velociy and he Rae of Ineres The ransmission mechanism ha drives he model examined in Secion 3 operaes hrough he effec of devaluaion risk on he nominal ineres rae and he velociy of circulaion of money. Figure plos he cyclical componen of he expendiure velociy of M2 (i.e., consumpion plus invesmen over M2 money balances), which is he relevan measure for money balances used in ransacions in Mexico. Velociy followed he U-shaped paern ypical of exchange-rae-based sabilizaions during he period Measured from he maximum in early 1989 o he minimum reached in 1993, velociy fell by nearly 4 percenage poins. Evidence on he link beween devaluaion risk and he ineres rae can be documened by examining again he CETES-Tbill ineres rae differenial. This indicaor suggess ha devaluaion risk was high, a near 6 percen, a he beginning of he program and hen declined gradually unil he end of 1991, when i sabilized around 1 percen unil he devaluaion of he peso. However, here is a puzzle in ha his indicaor refleced only a sligh increase in devaluaion risk in he monhs before he devaluaion, as he CETE rae did no increase sharply. Oher benchmark money-marke raes did increase sharply -- he differenial beween he Mexican inerbank ineres rae and he CETE rae widened by 1 percenage poins before he crisis. Calvo and Mendoza (1996) and Kumhof (1999) proposed models ha ry o accoun for his anomaly by modelling banking fragiliy and cenral bank serilizaion of capial ouflows. 2.. Fiscal Policy The sance of fiscal policy is anoher key ingredien of he model sudied in Secion 3. In paricular, he model requires emporary reducions in unproducive governmen expendiures ha las for

12 -1- he duraion of a currency peg. In his accoun, he Mexican experience is sriking. The overall public defici shifed by nearly 17 percenage poins of GDP beween 1987 and 1993, going from a defici of 16 percen of GDP o a surplus of.7 percen of GDP. This sharp fiscal conracion refleced in par a marked decline in public deb service ha resuled from he decline in he CETE rae afer 1988, bu i was also suppored by a series of large cus in governmen absorpion ha sared in Real governmen absorpion (defined as wages and salaries, goods purchases, federal remiances o sae governmens, and subsidies o public enerprises) declined by 32 percen beween 1986 and 1988 (or he equivalen of 6 percenage poins of GDP). Sill, hese figures underesimae he wealh effecs of he fiscal consolidaion because hey do no capure he efficiency gains ha resuled from he exensive program of liquidaion and privaizaion of public enerprises. Through his program, over 4 public enerprises were closed and several ohers sold. Subsidies o public enerprises fell from a peak of near 4 percen of GDP in 198 o 1 percen of GDP in The above figures also reflec poorly he emporariness of he fiscal adjusmen because hey exclude large expenses incurred o suppor he banking sysem since Adding financial inermediaion by he governmen, he fiscal posiion swiched from virual balance o a defici of 4. percen of GDP beween 1993 and By 1998, he fiscal cos of he programs implemened o suppor he commercial banks since 199 had escalaed o 17 percen of GDP and was sill rising. 3. A Business Cycle Model Driven by Devaluaion Risk 3.1. Preferences and Technology Households are infiniely-lived and maximize he following expeced uiliy funcion: 4 E j ' C 1!L 1& 1! (1) C ' (C T ) & µ % (1! )(C N ) & µ 1 & µ (2) Households consume a raded good (C T ) and a nonraded good (C N ). They supply labor L and demand leisure R given he normalized ime consrain R = 1-L. The expecaions operaor E o applies o he probabiliy of devaluaion of he currency, as defined below. Equaion (2) characerizes preferences beween C T and C N by an isoelasic aggregaor, where 1/1+µ is he elasiciy of subsiuion beween

13 -11- radables and nonradables. Uiliy from C and R is also represened by an isoelasic funcion, wih 1/ denoing he ineremporal elasiciy of subsiuion in consumpion and deermining he ineremporal elasiciy of subsiuion in leisure for a given value of. is he sandard discoun facor. Households maximize uiliy subjec o he following consrains: 1%S(V ) C T %p N C N % I ' r K % w L % m!1!m 1%e & B % 1%r ( %1 B % T (3) K %1 ' (1! )K % I K K, (4) V ' C T % p N C N % I () m lim 64 E B %1 (1%r() '. (6) Equaion (3) is he budge consrain in unis of he raded good. The lef-hand side of (3) represens oal expendiures in consumpion and invesmen, I, wih p N defining he relaive price of nonradables, or he real exchange rae. Following Greenwood (1983) and Kimbrough (1986), we assume ha real balances m are held because hey help economize ransacion coss. Specifically, he uniary ransacion cos is assumed o be an increasing funcion S of he expendiure velociy of money V. The uni ransacion cos funcion is assumed o ake he form S=AV, where A and are nonnegaive parameers. 6 The righ-hand-side of (3) represens he sources of income: facor paymens o labor and capial, K, a he renal raes w and r respecively, plus changes in he real value of money holdings, minus he ne accumulaion of real, one-period foreign bonds B ha pay he ime-invarian real ineres rae r*, plus lump-sum governmen ransfers T. Since world asse rading is limied o nonconingen bonds, markes of coningen claims are incomplee. PPP in radable goods holds and foreign prices are assumed o be consan, so ha e represens boh he inflaion rae of radables and he rae of depreciaion of he currency. Real nominal balances are eroded by inflaion a he rae e. Equaion (4) is he law of moion of he capial sock which embodies capial-adjusmen coss as 6 The exponenial form of S belongs o he class ha yields implicaions of he ransacions coss framework equivalen o hose of models wih money in he uiliy funcion enering in log-separable form (see Feensra (1986)).

14 -12- deermined by he concave funcion (.). Adjusmen coss are inroduced so as o differeniae capial and foreign asses as vehicles of saving and hus avoid he excessive invesmen variabiliy ha would resul oherwise (see Mendoza (199)). To avoid ransacion coss in he seady sae, we assume ha ( )= and ha ( )=1. Equaion () is he definiion of expendiure velociy. Equaion (6) rules ou Ponzi games in foreign deb accumulaion. Oupu of radable and nonradable goods is produced by compeiive, profi-maximizing indusries using sandard Cobb-Douglas echnologies: Y i = A i (K i ) i (L i ) 1- i for i=t,n. This assumpion is consisen wih srong evidence of consan facor income shares in each of he nine indusries ha compose he raded and nonraded secors (as documened laer in he calibraion exercise). Since facor markes are compeiive, facors of producion earn heir marginal producs and he secoral zero-profis condiions simplify o: w L % r K ' A T (K T ) T (L T ) 1& T % p N A N (K N ) N (L N ) 1& N (7) The equilibrium secoral allocaion of producion and he relaive price of nonradables will be deermined a he angency poin beween he producion possibiliies fronier (PPF) of Y T and Y N and he corresponding isorevenue curve. A equilibrium, he slope of he PPF equals p N and is he key deerminan of is ime-series variaion. I is well-known, however, ha if facors of producion are homogeneous, and hus can be freely allocaed across secors, he Cobb-Douglas echnologies ha we assumed produce he Balassa-Samuelson resul: p N reflecs shifs in secoral facor produciviies and is ime-series variaion is limied o a fracion of he shif in secoral capial-labor raios (he fracion deermined by he difference T- N). Given ha, as we documen laer, T and N differ by a small margin in he Mexican daa, and lacking evidence of he massive produciviy changes needed o produce large changes in p N under hese condiions, we deviae from he Balassa-Samuelson resul by adoping a varian of he specific-facors models developed in he rade lieraure. These models use ransformaion curves o represen feasible secoral facor allocaions, considering ha facors of producion are specific o each secor. For simpliciy, we adop Mussa's (1978) specificaion, in which capial is secor-specific bu labor remains an homogeneous facor. The facor ransformaion curves are: K ' (K T, K N ) and L ' L T % L N (8)

15 Equilibrium and Numerical Soluion Mehod The firs-order condiions of he maximizaion problems of households and firms can be combined in he following se of opimaliy condiions: C T h(i ) ' C & 1 % µ C & 1&L N &L T (1& ) (9) p N ' 1 & C N C T & 1%µ (1) C T % p N C N h(i ) (1 & L N & L T ) ' (1& T) A T K T L T T (11) 1 & S ) (V )V 2 ' E % 1 1 % e % 1 (12) ' E % 1 (1%r() (13) ) h(i ) I ' E % 1 TA T 1 (K T %1,K N %1 ) K T %1 L T %1 & (1& T) % ) h(i %1 ) I %1 (1& ) % I %1 K %1 & ) I %1 K %1 I %1 K %1 (14) K K %1 (1 & T)A K T T L T T ' (1& N)A N K N L N N p N (1) TA T K T L T & (1& T) ' NA K N N L N & (1& N) p N 1 (K T,K N ) 2 (K T,K N ) (16) In hese expressions, h(i )/1+V(i )+V(i )S (V(i )) denoes he marginal ransacions cos of privae expendiures, where 1+i is he gross, risk-free domesic nominal ineres rae (i.e., he reciprocal of he period- price of a nominal bond ha pays 1 uni of domesic currency in +1). We refer o h(i ) as he model s moneary disorion. V is expressed as a funcion of i because i follows from (12) and (13) ha in equilibrium he following condiion holds: S ) (V )V 2 ' i (1 % i ) (17)

16 -14- Given he convexiy of S, i is sraighforward o show ha boh V and h are increasing in i. The opimaliy condiions are easy o inerpre. Equaion (9) deermines he marginal uiliy of wealh. Equaion (1) equaes he marginal rae of subsiuion beween C T and C N o p n. 7 Equaion (11) represens he opimal consumpion-leisure radeoff. Equaions (12)-(14) are Euler equaions for real balances, foreign asses, and aggregae capial respecively. Equaions (1)-(16) reflec he equaliy of secoral marginal producs of L and K respecively. The governmen issues money, from which i collecs seigniorage, makes unproducive purchases of G unis of raded goods, and makes ransfer paymens o households. We assume ha a fracion of he inflaion ax revenue is allocaed o G, and he res of he governmen revenue is rebaed as a lump sum ransfer. Hence he governmen budge consrain is: G % T ' m! m!1 1%e, wih G ' e 1%e m &1, # #1. (18) This consrain induces an endogenous ighening of fiscal policy afer an exchange-rae-based sabilizaion plan begins because of he sharp decline in seigniorage ha follows. Noe in paricular ha, for as long as he plan is in place, he inflaion ax is eliminaed leading o a sharp cu in governmen expendiures. The emporariness of he fiscal adjusmen is also endogenous, since a devaluaion implies a sudden surge in seigniorage and a reurn o permanenly-higher inflaion. This endogenous, saeconingen fiscal adjusmen is analogous o he one inroduced by Calvo and Drazen (1998). The marke-clearing condiions of each secor are he following: C N ' A N (K N ) N (L N ) 1& N (19) C T % I % G ' A T (K T ) T (L T ) 1& T & B %1 % 1 % r ( B! m V S(V ) (2) We examine he equilibrium dynamics of his model for a policy experimen in which he governmen implemens an exchange-rae-based sabilizaion plan a dae bu agens aach some posiive probabiliy o he even ha he plan may be abandoned. Specifically, a = he governmen ses e o = and announces he sabilizaion plan. Agens aach a ime-dependen, condiional probabiliy 7 Uribe (1998a) derived he price-consumpion puzzle from expressions like (9)-(1), assuming perfec-foresigh and a fixed exchange rae. In his case, and i are ime-invarian, so he righ-hand-side of (9) is consan, and by (1) p n is increasing in C T /C N. These resuls, and he fac ha C is linear-homogenous in (C T,C N ) imply ha C is decreasing in p n.

17 -1- z =Pr[e +1 > e =], defined by he hazard rae funcion Z(), o he devaluaion of he currency. As in Calvo and Drazen (1998), Z is exogenous and he reversal of he sabilizaion plan is an absorben sae (i.e., Pr[e +1 > e >]=1). We also adop heir assumpion ha he policy variable has only wo saes. Hence, he depreciaion rae is eiher e = or e =e>, wih e he same regardless of he dae in which he devaluaion occurs. The pos-collapse value of e is idenical o is pre-sabilizaion value, which is he sandard assumpion of he credibiliy models of exchange-rae-based sabilizaion. Moreover, a some fuure dae J#4 policy uncerainy is resolved, so if he sabilizaion plan is in place a dae J-1, hen a J he plan eiher fails permanenly wih probabiliy or succeeds permanenly wih probabiliy 1-. The compeiive equilibrium of he model is given by he sequences of sae-coningen 4 allocaions and prices {C T, C N,, L T, L N, K T, K N, K +1, I, m, i, V, p N, G, B +1 } = such ha equaions (3)-(2) hold for =,...4. Since he sae e > is absorben, each period he economy can eiher: (a) follow he opimal pah corresponding o he sae in which e = a, wih z governing he probabiliy ha e +1 =e, or (b) if e =e a here is a once-and-for-all swich o a perfec-foresigh pah corresponding o ha consan rae of depreciaion. The soluion mehod draws on Uribe (1998b) and i is a log-linear adapaion of he near-exac soluion mehod used in he working paper version of his paper (see he appendix o Mendoza and Uribe, (1997)). In ha paper, we developed a near-exac soluion mehod for a model ha feaured perfec-foresigh equilibria wih consan depreciaion raes in which he rajecories for consumpion and leisure were consan. This propery was a consequence of he assumpion ha he nonraded secor employed only labor and he raded secor employed only capial. In conras, in he model we sudy here boh secors use capial and labor. As a resul, all endogenous variables, excep for he marginal uiliy of consumpion, display ime-dependen pahs under perfecforesigh. The mehod we use also keeps rack of he sae-coningen evoluion of wealh by aking advanage of he wo-sae absorben Markovian specificaion of uncerainy, and addresses he dependency on iniial condiions of he model s deerminisic saionary equilibrium (which is ypical of open-economy models wih nonconingen bonds and sandard preferences) Calibraion 8 If capial were homogenous across secors, he dependency on iniial condiions can be addressed by solving direcly he wo-poin boundary problem. Wih secor-specific capial, however, i is more efficien o circumven he problem by allowing r* o be a funcion of he sock of foreign deb wih a negligible elasiciy.

18 -16- We propose below benchmark parameer values for he numerical analysis. The values of mos parameers are deermined using Mexican daa, bu here are a few key parameers, on which here is limied empirical evidence. The implicaions of varying hese paramaeres will be illusraed laer by conducing sensiiviy analysis. a) Velociy and Money demand: Given S=AV, equaion (17) implies: V =(i /1+i ) 1/(1+ ) ( A) -1/(1+ ). Since V/(C+I)/m, i follows herefore ha he model predics a log-linear relaionship beween money demand, expendiures, and i/(1+i). The elasiciy of money demand wih respec o is opporuniy cos is -1/(1+ ) and he elasiciy wih respec o expendiure equals one. These predicions are srongly suppored by he findings of recen economeric sudies of he demand for M2 in Mexico before he 1994 crash (see Kamin and Rogers (1996) and Calvo and Mendoza (1996)). These sudies used GDP, insead of privae expendiures, as an explanaory variable of money demand bu we examined he performance of similar economeric models replacing GDP wih (C+I). We found ha he exising resuls are generally robus o his change. In paricular, we obained he same ineres elasiciy of money demand, -.16 (wih a sandard error of.27), and we found srong evidence of a long-run, uniary expendiures elasiciy as well as a coinegraing relaionship beween real M2, i/(1+i), and expendiures. 9 Our esimae of he ineres elasiciy implies ha 1/(1+ ) = -.16 so we se =.2. We hen se A=.48 by solving from V =(i /1+i ) 1/(1+ ) ( A) -1/(1+ ) seing V=.374/4, which is he quarerly equivalen of he 1987 raio (C+I)/M2 in he Mexican daa, and seing i o 3 percen per quarer. The laer was deermined by seing r*=.6 per year and by aking Mexico s observed radables inflaion rae of 17 percen per year (an average of annual inflaion raes for he hree-monh period ending in February, 1988, when he exchange rae was fixed), and combining hese figures wih he assumpions of perfec capial mobiliy, PPP in radables, and ineres rae pariy. b) Preferences: The risk aversion coefficien,, is se a, which is he median of exising esimaes for developing economies ha range beween 1.2 and 1 (see Reinhar and Vegh (199)). = is also he lower-bound of esimaes obained for Mexico by Reinhar and Vegh (1994). The elasiciy of subsiuion beween C T and C N is se o 1/(1+µ)=.76, reflecing he developing-counry esimaes 9 This implies ha he money demand regression can be efficienly esimaed using as independen variables he logarihms of i/(1+i) and lagged V, he annual change in i/(1+i), and seasonal dummies (see Kamin and Rogers (1996)).

19 -17- produced by Osry and Reinhar (1992). For simpliciy, he rae of ime preference is assumed o be idenical o r*, so ha =(1+r * ) -1. The parameer is se a a value such ha, given he unis in which each of he wo goods are measured, he seady-sae share of consumpion of nonradables in GDP is.6. The leisure exponen in uiliy is se imposing he sandard real-business-cycle resricion ha in seady sae households spend 2 percen of heir ime working. This implies = c) Technology: Values of echnology parameers were deermined using naional accouns daa on secoral facor paymens and value added. The shares of labor income in value added were se o 1- T =.26 and 1- N =.36, which are averages over he period for which daa are currenly available ( ). 1 The labor income shares of each of he 9 indusries in which GDP is decomposed flucuaed very lile over he sample period, suggesing ha he Cobb-Douglas represenaion of secoral value added is a reasonable approximaion. The quarerly rae of depreciaion of he capial sock,, was se a 1 percen, which, ogeher wih he oher parameers of he model implies a seady-sae share of gross invesmen in GDP of 18 percen, consisen wih Mexican daa. This approach o calibrae o mimic he observed invesmen rae follows he calibraion guidelines of Cooley and Presco (199). The remaining echnology parameers involve capial adjusmen coss and he secoral capial ransformaion curve. Since hese parameers canno be direcly relaed o Mexican daa or exising economeric sudies, we produced benchmark parameers aiming o mach hose feaures of he daa ha hese parameers are likely o affec mos direcly. Wih regard o he capial-adjusmen-cos funcion, he simulaions require a value for he elasiciy of invesmen wih respec o Tobin s Q, which is given by -1/[ O( )]. We se his elasiciy so ha he invesmen boom in he model is roughly consisen wih Mexican daa. The implied value is 1/3. For he capial ransformaion curve, we se he elasiciy of subsiuion beween K T and K N, /( 12 )/( 1 2 )#, equal o -.1, so as o mach he observed increase in p n ha according o he variance decomposiion of he daa could be aribued o devaluaion risk (a mos 2 percen). d) Policy variables: The fracion of he inflaion ax assigned o governmen purchases,, is se o 2/3 so 1 The fac ha he labor shares are abou 1/2 hose in indusrial counries raises doub abou he accuracy of Mexican daa, alhough Mendoza (199) shows ha several developing counries repor similar figures. We also argue below ha for our key resuls, he relaive values of he shares is more imporan han heir absolue values. Developing and indusrial counry daa are consisen in ha labor shares do no differ sharply across secors (see Mendoza (199)).

20 -18- as o roughly mach he observed share of governmen absorpion in GDP (as defined in Secion 2) a he end of 1987 (i.e., 18. percen). The rae of depreciaion of he currency o which he economy swiches when he program fails is se so ha a he ime of he collapse he inflaion rae of radables reurns o is pre-sabilizaion peak of 17 percen per annum. e) Hazard rae funcion: The sochasic process driving devaluaion probabiliies is reaed as analogous o he exogenous disurbances ha drive a real-business-cycle model. Thus, we calibrae Z o he exising empirical evidence on he ime pah of devaluaion probabiliies. Several sudies provide srong evidence indicaing ha devaluaion probabiliies follow a J-shaped ime pah, boh in Mexico and in many fixedexchange-rae regimes across developing counries. Blanco and Garber (1986) esimaed J-shaped devaluaion probabiliies for he Mexican peso before he devaluaions of 1976 and 1982 using a Krugman-syle model of balance-of-paymens crises. The probabiliy of collapse was.2 early in 1977, declining o near zero in abou a year, rising slowly in , and rising rapidly o abou.4 before he 1982 devaluaion. Goldberg (1994) exended he Blanco-Garber analysis o he period and found ha he probabiliy of collapse in early 1982 was in excess of.9. Klein and Marion (1997) used logi analysis o idenify facors ha influence he duraion of currency pegs in a panel of monhly daa for 17 counries over he period. They found srong evidence showing ha sharp real appreciaions predae devaluaions and ha devaluaion probabiliies are J-shaped. Probabiliies of collapse one monh before a devaluaion are as high as.89, wih 1/1 of he esimaes higher han.. In ligh of his evidence, we adoped a J-shaped hazard rae se below. when he program begins, falling o zero, and rising o abou.8 prior o he collapse. We also se J=24, in line wih he six-year duraion of Mexican currency pegs observed since 197 and assume as a benchmark case ha if he program survives unil period J-1, hen in period J i is abandoned for sure, ha is, =1. 4. Quaniaive Implicaions of he Model 4.1 Inuiion of The Model s Transmission Mechanism We develop some inuiion for undersanding he model s moneary ransmission mechanism before examining he resuls of he numerical simulaions. The key disorion ha devaluaion risk inroduces in he model can be illusraed by rewriing equaion (17) as follows: S ) (V L )(V L ) 2 ' r ( (1 % r ( ) % H %1 E [ %1 e '] z e (1%e)(1%r ( ) (21)

21 -19- This equaion is he equilibrium condiion for he choice of m from he perspecive of any dae in which he sabilizaion plan is in place, and hence he depreciaion rae is a is low sae e L = wih he corresponding sae-coningen choice for velociy V L. In equilibrium, he marginal benefi of holding an exra uni of real balances, in he lef-hand-side of (21), equals he opporuniy cos of holding money in he righ-hand-side. Thus, he erm in he righ-hand-side is also he nominal ineres rae facor i /(1+i ). Equaion (21) shows ha he domesic nominal ineres rae differs from he world ineres rae because of he presence of currency risk in holding domesic money (recall ha world inflaion is assumed o be zero, so r* in (21) denoes boh he real and nominal world ineres raes). In paricular, he ineres rae differenial reflecs a disorion ha akes he form of a risk-adjused covered ineres pariy condiion. The second erm in he righ-hand-side of (21) shows ha he ime pah of his disorion is governed by wo effecs: (a) changes in he expeced rae of depreciaion of he currency z e and (b) flucuaions in he marginal uiliy of wealh in he high-depreciaion-rae sae +1H relaive o is condiional mean E [ +1 e =]. The firs effec is exogenous o he model and corresponds o he sandard expeced-depreciaion premium under risk neuraliy. The second effec, in conras, is endogenous and reflecs he risk-averse naure of households and he incompleeness of insurance markes (wihou eiher of hese assumpions +1H /E [ +1 e =]=1). Moreover, we can also infer ha he wealh effec enlarges he ineres rae differenial (i.e., +1H /E [ +1 e =]>1) because a reurn o high inflaion and high unproducive governmen purchases reduces wealh (which increases ). The ineres rae disorion affecs he real secor via he moneary disorion h(i), which has a direc effec on he margins of decision-making ha deermine saving, invesmen, and labor supply. By combining equaions (9) and (13), using he assumpion ha (1+r*)=1, we can show ha h(i) acs as a sochasic saving ax by alering he ineremporal relaive price of C T : U C T(C T,C N,R ) ' E U C T(C T %1,C N %1,R %1 ) h(i ) h(i %1 ) (22) Since h(i) is increasing in i and i increases wih he condiional probabiliy of devaluaion, he effecive ax on saving (in erms of unis of C T ) rises (falls) when he probabiliy of devaluaion rises (falls). Thus, an increasing (decreasing) probabiliy of devaluaion induces an ineremporal subsiuion effec ha favors a decreasing (increasing) radables consumpion pah.

22 -2- The fac ha devaluaion risk drives a wedge beween i and i* while he exchange rae is fixed is an imporan feaure ha disinguishes his model from he perfec-foresigh credibiliy models based on Calvo (1986). Consumpion booms in hese models resul from an ineremporal subsiuion effec refleced in he perfec-foresigh varian of condiion (22) ha holds only beween he las period of a currency peg and he firs pos-collapse period. Beween any wo periods and +1 in which he exchange rae is fixed here is no subsiuion effec because under perfec foresigh i.r*, and hence he ineremporal relaive price of consumpion equals 1. Moreover, he size of he subsiuion effec ha his a he dae of he collapse is also differen because, while he pos-collapse nominal ineres rae in our model is he same as in he perfec foresigh models (i.e. he ineres rae jumps o i. r*+e when a devaluaion occurs), he pre-collapse ineres rae in our model is sae-coningen and depends on z. Devaluaion risk also inroduces sae-coningen wealh effecs because of he assumed marke incompleeness. The wealh and subsiuion effecs operae joinly in a similar fashion as in Calvo and Drazen (1998). If he inflaion ax were fully rebaed o households, he disorions affecing he model would be limied o ineremporal subsiuion effecs. For as long as i lass, a currency peg represens a sequence of favorable relaive price shocks. A each dae in he fixed-exchange-rae period, agens aach a cerain probabiliy o he scenario ha prices a +1 will rise wih a devaluaion, and hence have an incenive o over-consume. As +1 arrives hey realize hey over-consumed and adjus consumpion accordingly. In conras, when he inflaion ax finances G, he ineremporal subsiuion effec can be offse by a wealh effec. Each period ha he peg survives, permanen income rises by he amoun of he foregone unproducive expendiures. If he elasiciy of ineremporal subsiuion is sufficienly low, he wealh effec dominaes and consumpion rises over ime. The model s opimaliy condiions can be re-arranged o show ha devaluaion risk also imposes sochasic axes on invesmen and labor supply via he moneary disorion: U C T(C T,C N,R ) ) I K &1 ' E U C T(C T %1,C N %1,R ) %1 h(i ) %1 TA T 1 (K T %1,K N %1 ) K T %1 L T %1 & (1& T) % ) h(i %1 ) I %1 (1& ) % I %1 K %1 & ) I %1 K %1 I %1 K %1 (23) K %1

23 -21- U R (C T,C N,R ) U C T(C T,C N,R ) ' (1& T)A T h(i ) K T L T T (24) The moneary disorion axes he marginal produc of newly insalled capial a a rae of 1/h(i +1 ) and he marginal produc of curren labor supply a a rae of 1/h(i ). Equaions (23) and (24) also embody he so-called supply side disorions induced by he ransacion coss seup under perfec foresigh (see Uribe (1997) and Lahiri (1996)). These disorions affec boh ransiional dynamics and he seady sae because a once-and-for-all disinflaion under perfec foresigh would cu ransacion coss permanenly, hereby releasing resources o finance a permanenly higher capial sock and reducing permanenly he wedge beween he real wage and he marginal rae of subsiuion beween consumpion and leisure. The inuiion for he behavior of he real exchange rae can be derived by combining equaions (1) and (16) o solve for p N as he slope of he PPF of radables and nonradables and aking logs of he resuling expression (assuming for simpliciy ha (K T,K N )=[(K T ) - +(K N ) - ] -1/, where =1/(1+ ) and #): Ln (p N ) ' Ln 1& T 1& N 1& T T N T A T A N % ( T& N) Ln K N L N & T Ln K N K T (2) This expression illusraes how secor-specific capial alers he deerminaion of p N relaive o he Balassa-Samuelson resul. The Balassa-Samuelson resul is he erm in square brackes and shows ha he ime series variaion of p N can be expressed as he fracion T- N of he change in he capial-labor raio of he nonradables secor. Secor-specific capial modifies his resul by inroducing changes in p N as a resul of secoral re-allocaions of capial, even if capial-labor raios remain consan or if T= N. The elasiciy of he real exchange rae wih respec o K N /K T is given by - T/, which is non-negaive because # T#1 and #. Noe, however, ha (2) is no a closed-form soluion, bu only a condiion ha reflecs efficien facor allocaion. I is also imporan o noe ha he moneary disorion is buil no o affec direcly he slope of he PPF in he righ-hand-side of (2), or he marginal rae of subsiuion beween C T and C N in he lefhand-side of (1). Hence, he real exchange rae is influenced by he moneary disorion only indirecly

24 -22- hrough is effecs on he capial accumulaion process, labor supply, and he secoral allocaion of capial, labor and consumpion. 4.2 Benchmark Simulaion Figure 6 plos he sae-coningen equilibrium dynamics for he benchmark simulaion as percen deviaions from he pre-sabilizaion seady sae, ogeher wih he hazard rae funcion. The coninuous lines represen equilibrium pahs for he sae of naure in which he exchange rae remains fixed. The doed lines indicae allocaions o which he model jumps on impac when a devaluaion occurs on he corresponding dae in he horizonal axis. The benchmark simulaion produces cyclical dynamics for GDP, velociy, ne expors, aggregae and secoral consumpion, he real exchange rae, invesmen, and labor. 11 These dynamics are roughly in line wih several of he sylized facs documened in Secion 2: (1) The model produces boom-recession cycles in GDP, consumpion, and invesmen wih recessions ha pre-dae he devaluaion. The magniude of he booms in GDP and nonradables consumpion are roughly consisen wih he empirical evidence. The invesmen boom is also consisen wih he daa bu his resul reflecs he crierion used o calibrae he invesmen elasiciy of Tobin s Q. (2) Consumpion and he real exchange rae are highly, bu no perfecly, correlaed. This resul shows ha he price-consumpion puzzle can be solved by inroducing uncerainy and incomplee markes. These feaures make boh he moneary disorion and he marginal uiliy of wealh coningen on he sae of naure, allowing currency risk o yield equilibrium dynamics in which he relaive price of nonradables and consumpion increase a he same ime. There is a sharp real appreciaion of abou 18 percen in he firs wo years of he program. The real exchange rae hen sabilizes and begins o depreciae gradually, bu sill ends appreciaed by abou 13 percen even if he sabilizaion plan lass is maximum duraion of 6 years. (3) The rade balance worsens markedly on impac, coninues o decline for he firs wo years of he program and hen displays a gradual recovery. Sill, even if he plan does no collapse unil i reaches is maximum duraion, ne expors remain 12 percen below he pre-sabilizaion level. (4) Velociy falls sharply in a sudden jump of 1 percen when he program begins, and coninues o fall 11 Ne expors exclude public absorpion, which remains consan for he duraion of he currency peg.