Self-fulfilling risk predictions: an application to speculative attacks

Transcription

1 Journal of Inernaional Economics 50 (2000) locae/ econbase Self-fulfilling risk predicions: an applicaion o speculaive aacks a b, * Rober P. Flood, Nancy P. Marion a Inernaional Moneary Fund, h Sree, N.W. IS Washingon, D.C , USA b Darmouh College Deparmen of Economics, Hanover, NH 03755, USA Received 13 Sepember 1996; received in revised form 17 February 1998; acceped 27 April 1998 Absrac We show ha changing marke beliefs abou currency risk can generae a self-fulfilling speculaive aack on a fixed exchange rae. The aack does no require a laer change in policies o make i profiable. We illusrae his poin by inroducing an endogenous risk premium ino a firs-generaion model of a speculaive aack. The model is furher modified o ake accoun of serilizaion, deb-financed fiscal deficis and anicipaory price-seing behavior. We use he model o inerpre he 1994 Mexican peso crisis Elsevier Science B.V. All righs reserved. Keywords: Currency crisis; Devaluaion; Risk premium; Mexico JEL classificaion: F3; F4 1. Inroducion Currency crises in Europe and Mexico, as well as hose unfolding in Asia, have renewed effors o undersand and conrol he forces underlying speculaive aacks on fixed exchange raes. Unil he European crises in , here was general agreemen abou he underlying cause of speculaive aacks. A counry would ulimaely face an aack if i ran macroeconomic policies inconsisen in he longer erm wih he fixed exchange rae. For example, if a governmen moneized * Corresponding auhor. Tel.: ; fax: address: nancy.p.marion@darmouh.edu (N.P. Marion) / 00/ $ see fron maer 2000 Elsevier Science B.V. All righs reserved. PII: S (98)

2 246 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) a large fiscal defici, excessive money growh would cause is inernaional reserve holdings o decline and evenually rigger an aack by speculaors. The governmen would be forced o abandon he fixed exchange rae and le he currency depreciae. The view ha deerioraing fundamenals led o currency crises was 1 formalized in a se of firs-generaion crisis models. The European experience and he 1994 Mexican peso crisis forced economiss o rehink he cause of speculaive aacks. Many of he European counries, and laer Mexico, were running fairly disciplined macroeconomic policies when heir currencies were aacked. If inconsisen macroeconomic policies were no in place o push an economy owards a currency crisis, wha could cause an aack? Some economiss have suggesed ha aack-condiional policy expansion can pull a counry off a fixed exchange rae even if he counry follows appropriae policies beforehand. The aack is self-fulfilling because posaack policy expansion validaes speculaors prior beliefs ha he currency will depreciae. Muliple equilibria are possible when policy responds endogenously o an aack. The economy can find iself in a no-aack equilibrium, where he governmen mainains he fixed exchange rae and appropriae domesic policies, or he economy can suddenly face an aack equilibrium, where ex-pos policy changes jusify he speculaive behavior. This alernaive view of currency crises has been formalized in se of second- 2 generaion models. While hese models are o be credied wih expanding our ideas abou he causes of currency crises, heir requiremen ha posaack policies become more expansionary is problemaic. Empirical suppor for such a policy 3 response is far from overwhelming (Eichengreen e al., 1995). This paper argues ha currency crises may resul from self-fulfilling shifs in speculaive opinion abou exchange-marke risk raher han posaack policy expansion. To illusrae his poin, we incorporae an endogenous risk premium ino asse reurns. The risk premium inroduces a nonlineariy ino asse markes and provides a mechanism hrough which muliple equilibria can occur even when policy is invarian o an aack. Indeed, muliple equilibria are obained enirely 1 A noable example is Krugman (1979), whose work was inspired by Salan and Henderson (1978) and simplified by Flood and Garber (1984a). A survey of hese models is provided in Agenor e al. (1992). 2 See, for example, Obsfeld (1986) and Eichengreen and Wyplosz (1993). These models build on an idea suggesed by Sephen Salan in privae correspondence and formalized by Flood and Garber (1984b). Second-generaion models wih differen feaures can be found in Obsfeld (1994), (1997); Calvo (1995); Jeanne (1997); Bensaid and Jeanne (1995) and Sachs e al. (1996). See Flood and Marion (1997) for an overview. 3 I migh be argued ha he posaack depreciaion iself is he relevan expansionary policy. Tha argumen requires eiher ha he real exchange rae be misaligned prior o he depreciaion, which would be a fundamenals problem, or ha domesic prices be increased afer he depreciaion, which would show up as a posaack policy validaion.

3 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) hrough privae speculaive behavior and do no depend on he governmen s reacion o privae behavior. We embed he endogenous risk premium in a model ha reains key feaures of he firs-generaion model bu also depars from i in several ways. We herefore consider our model o be a modified firs-generaion model. We adop he firs-generaion model s focus on speculaors and he profis available o hem. Currency crises do no occur if here is no profi for speculaors. Once profi opporuniies appear, speculaors pounce. In he model, speculaion is profiable if he exchange rae ha would prevail afer an aack he shadow exchange rae is greaer han he fixed exchange rae. We depar from he sandard firs-generaion model in four ways. The firs deparure allows us o inroduce he possibiliy of muliple equilibria. The oher hree help us replicae he Mexican experience. Our firs deparure is he inroducion of a sochasic, ime-varying risk premium in he ineres pariy condiion. The risk premium reflecs he risk aached by he foreign invesor o domesic-currency asses. If hese agens suddenly perceive more posaack risk, i can increase he chance of a speculaive aack. This is because he amoun of perceived risk affecs he value of he shadow rae used o deermine he profiabiliy of an aack. If agens come o expec increased exchange-rae variance in a posaack environmen, he change in expecaions magnifies he variance of he underlying sochasic disurbance and hereby increases he acual exchange-rae variance of he shadow exchange rae. Moreover, because of volaile beliefs abou currency risk, he relaionship beween he 4 aack and fundamenals is no uniquely deermined. Our second deparure involves recognizing ha he moneary auhoriy may be consrained from underaking a srong defense of he fixed exchange rae by oher domesic consideraions. We model hese consrains by assuming he moneary auhoriy coninually serilizes he effecs of inernaional reserve changes on he moneary base. Consequenly, here is no decline in he moneary base during a speculaive aack and no change in he money growh rae afer he aack. Such 5 serilizaion operaions accord well wih acual evens in Mexico. 4 Driskill and McCaffery (1980) were among he firs o noe he implicaions of incorporaing a risk premium in asse reurns. 5 This poin is discussed furher in Secion 4. When serilizaion is incorporaed ino he sandard firs-generaion model, i makes a fixed exchange rae exremely precarious regardless of he amoun of inernaional reserves available o he auhoriies or he behavior of oher economic fundamenals. For example, Flood e al. (1996) show ha in he radiional firs-generaion model where domesiccurrency bonds and foreign-currency bonds are perfec subsiues, if he public knows an aack on he fixed exchange rae regime will be serilized compleely, he fixed rae regime will be sillborn regardless of he exchange rae chosen for fixing and he size of he finie reserve sock commied o preserving he fixed exchange rae. Consequenly, we allow for imperfec subsiuabiliy beween domesic and foreign-currency bonds when he cenral bank serilizes fully.

4 248 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) Our hird deparure relaes o he financing of he fiscal defici. While we reain he assumpion ha he counry runs a fiscal defici, we depar from he sandard firs-generaion model by having he fiscal defici be bond-financed raher han moneized. More imporanly, he amoun of bond financing need no be so large as o make a currency crisis ineviable. Our choice of financing sraegy can make he economy increasingly vulnerable o an aack and seems appropriae for Mexico. Our fourh deparure is o relax he assumpion of purchasing power pariy. Insead, we assume ha goods prices are se a period in advance a a level ha is expeced o clear he marke. This price-seing behavior grealy simplifies our risk premium derivaion since porfolio holders can ignore goods-price variance and concenrae on exchange-rae variance. In addiion, since prices can rise before an aack in anicipaion of fuure currency depreciaion, he model mimics boh he appreciaion of he real exchange rae and he increase in he domesic ineres rae ha precede a currency crisis like he one in Mexico. The res of he paper is organized as follows. In Secion 2, we describe he model in more deail. We specify he economy s asse markes and goods markes and he assumpions abou governmen policy. In Secion 3, we idenify he condiions under which a speculaive aack akes place. To do so, we solve for he shadow exchange rae and find ha i has muliple soluions. Muliple soluions give rise o he possibiliy of self-fulfilling speculaive aacks driven by changing percepions abou risk. In Secion 4, we examine how well our model capures some feaures of he 1994 Mexican currency crisis. 2. The model The model is a sochasic, discree-ime model of an open economy wih a fixed exchange rae. Agens have raional expecaions and know he fixed exchange rae 6 will be abandoned should he cenral bank run ou of reserves. There is uncerainy abou fundamenals, and his uncerainy influences asse reurns and price-seing behavior. We now urn o he specificaion of he asse markes Asse marke srucure The principal equaions of he model are:. m 2 p 52ai 1 d ; a. 0, d] 0 (1), i5 i* 1 E (s11 2 s ) 1u (c 1 b2 b* 2 s ) (2) 6 Wih a bi more srucure we could have he aack end in devaluaion.

5 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) Eq. (1) describes he domesic money marke, where m is he log of he domesic high-powered money supply, p is he log of he domesic price level, and he demand for real money balances depends negaively on he domesic ineres rae, 7 i. Money demand is also influenced by a real shock,. Eq. (2) is he ineres pariy condiion. Le s be he log of he exchange rae, quoed as he domesic-currency price of foreign exchange. Then he domesic ineres rae deviaes from he foreign ineres rae, i *, by he expeced rae of change of he exchange rae, E (s11 2s ), plus a ime-varying risk premium, u (...). The risk premium is influenced by he relaive privae holdings of domesic and foreign governmen securiies, agens aiudes owards risk, and uncerainy abou he fuure exchange rae. The erm (b2b* 2s ) describes he worldwide relaive privae holdings of governmen securiies, where b is he log of worldwide privae holdings of domesic governmen securiies and b* 1s is he log of worldwide privae holdings of foreign governmen securiies expressed in domesic-currency 8 erms. The erm u summarizes how desired asse holdings are influenced by ases oward risk and uncerainy abou reurns. In he example developed below, u5zv (s 11), where z is proporional o a measure of risk aversion and V is he 9 variance operaor condiional on informaion available a ime. u (...) is a racable log approximaion of elemens ha may influence aiudes oward asse risk. I has he following properies: (1) in a world of cerainy (V (.)50) or risk neuraliy (z50), he risk premium is zero; (2) he consan c is sufficienly large o ensure ha a bigger u increases he risk premium; and (3) neiher aggregae world wealh nor counry shares in world wealh are imporan deerminans of he risk premium Goods marke srucure Households consume boh domesically-produced goods and impored goods. We assume p, he domesic price of domesically-produced goods, is se a ime 7 Nohing subsanive is alered by using domesic prices as he deflaor for nominal money balances raher han he weighed average of domesic prices and he domesic-currency value of foreign prices. Using he home goods price level as he deflaor corresponds o Dornbusch (1976). 8 The assumpion ha he risk premium responds o relaive supplies of governmen deb is familiar from he porfolio-balance models of Tobin (1969) and Branson (1968) and was esed by Frankel (1984); Black and Salemi (1988) and ohers. The assumpion has no found much empirical suppor. Werner (1996), however, has found such a risk premium works well for Mexico during he period. 9 Our risk premium is based on a model where he foreign invesor maximizes expeced welfare ha depends posiively on expeced fuure wealh and negaively on he variance of fuure wealh relaive o curren wealh. Since he variance of fuure wealh depends on he variance of he fuure exchange rae, he risk premium is affeced by expeced exchange-rae variance. For deails of he derivaion of he risk premium, see Appendix A.

6 250 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) a a value ha is expeced o clear he marke for home goods a ime. Ifhe excess demand for home goods depends on relaive prices and he foreign price level and oher influences on excess demand are normalized o zero in logs, he expeced marke clearing price for home goods is: p5 E21s. (3) The price of domesically-produced goods will change only if agens anicipae a change in he exchange rae Asse accouning We now urn o he governmen s balance shees. Before a speculaive aack, he domesic high-powered money supply is equal o domesic credi plus he book value of inernaional reserves held by he cenral bank. An aack causes inernaional reserves o fall o heir lower bound, which we se a zero for 10 simpliciy. Afer he aack, he high-powered money supply is simply equal o domesic credi. I is useful o specify he bond marke firs in levels of he variables and hen move o he appropriae log-linearizaion. The ousanding supply of domesiccurrency governmen bonds is denoed by H. Worldwide privae holdings of hese bonds are B and he domesic moneary auhoriy s holdings of hese bonds are denoed as domesic credi, D. Leing h 5log H, b 5log B, and d 5log D, he log-linearizaion of he bond marke is: b 5gh 1(12g )d, where g.1 is he raio H /B a he poin of linearizaion. Afer a successful aack on he currency, d 5m in he bond-marke equaion. One final piece of srucure involves he underlying exogenous process driving he economy. We assume real governmen expendiure is financed parly by issuing nominal governmen bonds and parly by levying axes. Taxes increase wih he sock of ousanding governmen bonds so ha he defici does no grow wihou bound and ransversaliy condiions apply. Recalling ha h is he log of ousanding ineres-paying nominal claims on he domesic governmen, le hese bonds follow he process: h 5 m 1 rh 1 ; u. 0, 0, r, 1, (4) 21 where m/(12r) is he seady sae sock of domesic bonds, r is he degree of auocorrelaion in he bond process, and is he shock o he bond process. The shock can signify one of several disurbances. For example, a negaive produciviy shock ha reduces ax revenues will cause bond financing o increase unexpecedly, and his disurbance permanenly feeds ino he bond process o 10 Buier (1987) endogenizes his lower bound, as do Flood and Marion (1997).

7 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) cover nex period s unexpecedly higher ineres paymens. The negaive produciviy shock also reduces he demand for money, so in his example he parameer d in he money demand funcion is negaive. The shock o he bond process can also arise from an unexpeced increase in governmen expendiures ha is financed in par by bond sales. In his case, he disurbance increases he demand for money, so he parameer d in he money demand funcion is posiive. 11 Noice ha is he only sochasic elemen in he model. The precise disribuion of will urn ou o be crucial, bu we will urn o ha laer Governmen policy We posulae lexicographic governmen preferences concerning he fiscal defici, moneary policy and he fixed exchange rae. The fixed rae, s, ges he lowes prioriy. When inernaional reserves hi heir lower limi, he governmen decides agains borrowing reserves or changing domesic ineres raes. Insead, he fixed 12 rae is abandoned and he exchange rae is allowed o floa freely hereafer. The moneary auhoriy alers is holdings of governmen securiies o keep he domesic high-powered money supply consan. This policy requires full serilizaion of inernaional reserves prior o he aack. The policy is mainained even if 13 here is a speculaive aack. Thus m5m boh before and afer an aack. Alhough having policy become more expansionary afer a speculaive aack is an essenial feaure of second-generaion models, Eichengreen e al. (1995), Eichengreen e al. (1996) find no consisen paern in a cross-secion of counry experiences. Consequenly, while he governmen les he exchange rae floa freely afer a successful aack, we assume oher governmen policies are invarian o he aack. 3. Wha riggers an aack? If domesic bond expansion exceeds foreign bond expansion, hen over he longer run i will become increasingly difficul o mainain a fixed exchange rae since porfolio reallocaion by he privae secor will drain inernaional reserves. The crucial quesion, of course, is when will he fixed exchange rae break down? The simple answer is ha i will break down whenever i is worhwhile for 11 We could incorporae many differen ypes of shocks, bu doing so would increase he dimensionaliy of he problem and make i impossible o graph our resuls. 12 In our model, foreign bond expansion is zero and he domesic bond supply reaches a seady-sae level ha may or may no make an aack ineviable. Recall ha he lower limi on he reserve level is se a zero. Endogenizing he lower limi need no affec he main resuls. 13 This feaure differs from Flood e al. (1996) in which he aack iself is serilized, bu he aack resuls in a discree expansionary shif in moneary policy. In many real-world episodes, however, moneary policy is invarian o he aack and here is no policy expansion afer he aack.

8 252 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) speculaors o aack he currency, and ha will happen when speculaors believe he foreign exchange hey buy from he cenral bank a a fixed price can immediaely be resold a a higher price. Following Flood and Garber (1984a), define he shadow exchange rae, s, obe he rae ha would prevail a ime if he fixed exchange rae were aacked, inernaional reserves were driven o heir lower bound, and he exchange rae were allowed o floa freely hereafer. The condiion for an aack is ha he shadow rae exceed he fixed rae (s.s ). We mus herefore solve he model for he shadow exchange rae and deermine when i exceeds he fixed rae. Since he domesic price level is ied o beliefs abou he exchange rae ha were formed in he previous period, i follows from Eq. (3) ha: p 5 (1 2 p )s 1 p E (s us. s ), (5) where p21 is he probabiliy a ime 21 ha an aack will ake place a ime and E 21 (s us.s ) is he 21 expecaion of nex period s (flexible) exchange rae, condiional on he exchange rae exceeding s so he aack occurs. The probabiliy esimae and he condiional expecaion of he exchange rae change wih he sae of he economy. To aid in soluion of he shadow rae, we linearize he cumulaive disribuion for he sochasic variable e by assuming e has a uniform disribuion cenered on zero wih upper bound w and lower bound 2w. Formally, if f( ) is he probabiliy densiy associaed wih he oucome e, hen f( ) 5 0;,2w,. w f( ) 5 1/(2w); 2 w # # w (6) 3.1. Solving for he shadow rae Since he model is linear in he posaack period, we propose a linear soluion 14 for he shadow exchange rae of he form: s 5 l 1 l h 1 l. (7) The soluion mehod is described in Appendix A. I explois he assumpion ha he sochasic variable has a uniform disribuion. The soluion for he shadow rae in (7) is: l 5 a consan erm (see appendix) (8) 0 14 Posaack, exchange-rae variance is consan. There is sill a sligh ransiion-relaed nonlineariy, bu we approximae i in Eq. (A.16) of Appendix A.

9 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) ar[ug 1 b 1] l1 5 ]]]]]]] $0 (9) p 1 Fa(1 1u ) 1] 1] G 2 4 d gu 2] 1b a 1 l2 5]]]] (1 1u ) (10) where b1 is he unknown variable in a fifh-order polynomial and is discussed more fully in Appendix A. Ignoring values for l1 and l2 ha are imaginary and hence are no economically sensible leaves he possibiliy of hree soluions for he shadow exchange rae for a range of parameer configuraions. Nohing seems o preclude any of hese 15 soluions. The mos imporan nonlineariy ha produces hese muliple soluions involves he disurbance erm. The disurbance erm eners money demand wih coefficien d and i eners he risk premium wih he coefficien ug. The composie disurbance is herefore (d 2aug ). Since u is proporional o exchange-rae variance, an increase in perceived variance (a bigger u ) can magnify shocks and increase acual exchange-rae variance. In he special case where he disurbance o he bond process is uncorrelaed wih money demand (d 50), he money marke is nonsochasic. The disurbance does no ener money demand addiively nor does i ener hrough he risk premium, since when d 50, u 50 as well. When d is zero, one of he hree values for he shadow exchange rae is a consan. We refer o his soluion as he marke fundamenals soluion. Depending on parameer values, his marke fundamenals soluion may be less han he fixed exchange rae, in which case an aack never occurs, or i may be above he fixed exchange rae, so ha he aack occurs righ away. The oher wo shadow-rae soluions can be classified as second-momen bubbles. These bubbles involve self-fulfilling beliefs abou exchange-rae variance and are no o be confused wih he more familiar firs-momen bubbles ha come abou when he exchange rae oday depends on he expeced fuure exchange rae. Sandard firs-momen bubbles are excluded by assumpion. In conras o firs-momen bubbles, hese second-momen ones have no explosive ineremporal dimension and do no violae ransversaliy condiions. Because he model yields hree soluions for he shadow exchange rae, here is he poenial for muliple equilibria even hough governmen macroeconomic policies remain invarian o he speculaive aack. If agens expec more currency 15 In Appendix A, we describe in more deail hese hree soluions for he shadow exchange rae. All hree soluions are raional expecaions equilibria. Tha is, hey are soluions for which beliefs abou exchange-rae variance and acual exchange-rae variance coincide.

10 254 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) variabiliy, i affecs he domesic ineres rae hrough he ineres pariy relaion and feeds ino he asse markes in a way ha will make he exchange rae more variable should he fixed rae be abandoned. Tha, in urn, alers he shadow exchange rae used o deermined wheher an aack is profiable o underake A numerical example Obaining soluions for he shadow rae involves solving a consan-coefficien polynomial of order five. Since such a polynomial generally does no have explici reduced-form soluions for he roos in erms of he consan coefficiens, we resor 16 o numerical mehods. Suppose he shocks o money demand and bond supply are negaively 17 correlaed. Le d and se a 51 (he semielasiciy of money demand wih respec o he ineres rae) r 50.9 (auoregressive coefficien in he bond supply process) m 51 (The seady sae sock of domesic governmen bonds is m/(12r)) g 51.1 (implying ha domesic credi held by he cenral bank accouns for abou 10 percen of he deb issued by he domesic governmen) z52 (risk aversion parameer) w52 (he bound of he uniform shock disribuion) 2 w 2 ] 3 s 5 (he variance of he shock ha is uniform on (2w, w)). The example is picured in Fig. 1. The figure summarizes he mos imporan aspecs of a hree-dimensional figure drawn in (s, h 21, ) space. The hree- dimensional picure (no drawn) consiss of four planes. Wih s as he verical axis, he firs plane is fla a he heigh s 5s. Call his he s plane. The oher hree planes are found by ploing Eq. (7) for he hree differen real values of he l i s. These planes are upward-sloping wih respec o boh h and. Call hese planes he s 21 planes. The ableop recangle in Fig. 1 is he view obained from looking down on he s plane, where he horizonal axis on he s plane is cenered on zero and measures 2w in lengh o conform wih he uniform disribuion of. The hree lines on he ableop indicae where he hree s planes cu hrough he s plane; ha is, he poins in (h 21, e ) space where he hree shadow exchange raes equal he fixed exchange rae. Line (a) is he locus of poins where he low-variance shadow-rae soluion equals he fixed exchange rae, while line (c) is where he 16 The parameers are se o esablish an example of he exisence of viable muliple equilibria. They are no proposed as esimaes from any paricular daa se. 17 In addiion o he parameers lised below, variables such as i*, s, b*, and m mus be se in order o deermine he consan erm (l o) in he shadow rae Eq. (7). The variable b* is reaed as a consan because i is assumed ha cenral bank sales of foreign securiies o agens speculaing agains he domesic currency are small relaive o he worldwide holdings of hese securiies. The Gauss program used o exrac he roos and draw he shadow-rae soluions in Fig. 1 is available from he auhors.

11 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) Fig. 1. Tableop picure of shadow raes crossing fixed rae. highes-variance shadow-rae soluion equals he fixed rae. Noe ha when d,0, he hree lines on he s plane have differen negaive slopes. The key poin illusraed by Fig. 1 is ha a s plane can cu he s plane in one of hree places. If he economy s sae (deermined by h and ) is below all hree lines, hen here can be no aack because none of he s planes has ye cu hrough he s plane. If he sae is above all hree lines, hen here mus be an aack because all of he s planes are above he s plane. Suppose agens expec he low-variance shadow-rae soluion represened by line (a) and ha he sae is somewhere in he region bordered by lines (a) and (c), having cu hrough he s plane a line (c). Here we have he possibiliy of muliple equilibria. The economy can mainain he fixed exchange rae as long as agens coninue o expec a low-variance shadow rae. Bu if agens suddenly come o expec he high-variance shadow rae, here would be an immediae and successful aack since he high-variance shadow exchange rae already exceeds he fixed exchange rae. Thus if agens suddenly revise heir expecaions because hey believe he foreign-exchange marke has become riskier, he fixed exchange rae can collapse, producing afer he collapse he risk anicipaed by he agens. I should be clear, however, ha his possibiliy of a self-fulfilling collapse can only occur for cerain saes of he economy. For insance, if he economy s fundamenals are very sound, so ha he sae is in he no-aack zone below he s plane, hen even if agens suddenly come o believe he world is riskier, he fixed exchange rae will no collapse. Only if he economy s fundamenals deeriorae sufficienly o pu he

12 256 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) sae in he possible aack zone (above line (c) bu no ye above lines (a) and 18,19 (b)) could a sudden adverse shif in expecaions abou risk rigger an aack. Noe also ha in his possible aack zone he collapse is iniiaed by a change in agens beliefs abou risk and does no require an ex-pos change in governmen sabilizaion policies. To summarize, he exisence and relevance of muliple equilibria depend on (1) having he appropriae parameer values o give muliple real values for l, (2) 2 having agens adop he low-variance shadow rae soluion a he sar, and (3) having he sae ake on a value such ha he economy finds iself in he possible aack zone. Muliple equilibria can be excluded if (1) he parameers of he model do no give muliple relevan soluions for he shadow rae, or (2) if he preaack sae is no in he possible aack zone. For example, in his model if u is consan, hen here are no muliple equilibria. In his framework, a speculaive aack can be caused by poor fundamenals because he sae pus he economy ino he aack zone. Alernaively, he aack can be caused by a self-fulfilling shif in expecaions because he sae pus he economy ino he fragile possible aack zone and agens suddenly shif from he low-variance shadow rae soluion o a higher-variance one. I is no he case ha any fixed exchange rae regime is subjec o successful aack. 20 Fundamenals mus pu he economy in he fragile zone. 4. The Mexican experience In his secion, we consider how well some aspecs of he Mexican experience 18 See Velasco (1997) for anoher model where muliple equilibria can occur only for some range of fundamenals. 19 Our linearizaion of he bond marke is a igh (calculus) argumen only in an infiniesimal neighborhood of he poin of linearizaion, ye we consider he possibiliy ha bonds issued by he domesic governmen, h, may change enough o move he economy from a no-aack zone o an aack zone. If he change in h is a big change alhough i migh equally well be very small he linearizaion may no be appropriae. Moreover, he aack iself may resul in a large change in privae versus governmen holdings of domesic bonds. Hence linearizaion a he beginning of he crisis may be quie differen from linearizaion once he crisis has run is course. To address his issue wihou underaking a complee simulaion, we re-solved he model s crucial polynomial for a range of values of he parameer, g, ha is consrained o be above one in he linearizaion of he bond marke. For g beween 1.05 and 1.5, he fifh-order polynomial sill had hree real roo soluions. We repor resuls for g 51.1 in he ex. 20 In principle, he framework someimes permis us o disinguish beween an acual aack caused by fundamenals and one caused by a self-fulfilling shif in expecaions. If we use daa o esimae he lambdas and find ha he economy was a he low-variance shadow-rae soluion a he aack ime, hen he speculaive aack was due o fundamenals. If he esimaed lambdas indicae ha he economy was a he high-variance shadow-rae soluion, hen he aack could have been brough on by fundamenals or by a sudden shif from he low-variance shadow-rae soluion.

13 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) are capured by our model. We focus on five areas: serilizaion policy, ineres 21 raes, real exchange raes, inernaional reserves and muliple equilibria Serilizaion policy The sandard firs-generaion model assumes ha he ne domesic credi componen of he moneary base is exogenous and unaffeced by aciviy in he foreign-exchange marke. Inernaional reserves are merely he residual ha balances he domesic money marke a he fixed exchange rae. A he ime of he aack, here is a discree drop in he money supply ha reflecs he sudden depleion of reserves. The Mexican sory was differen in he period. Boh before and during he exchange-rae crisis, he auhoriies serilized reserve losses, keeping he moneary base on a relaively smooh rend. (See Fig. 2.) Our model capures his policy sance by assuming he moneary auhoriy serilizes fully o keep he moneary base a he desired level before, during and afer he speculaive aack. The serilizaion policy also ses he sage for he aack by ying he hands of policymakers. Afer he Colosio assassinaion, he Mexican auhoriies could have defended he peso by ighening moneary policy or passively allowing he loss of inernaional reserves o conrac he moneary base. The governmen resised moneary conracion in par because higher ineres raes would have srained an Fig. 2. Mexico: Base money by componen, January 1992 Sepember 1997 (in billions of new pesos). 21 Our descripion of he sylized facs draws heavily on Inernaional Moneary Fund (1995).

14 258 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) already vulnerable banking sysem and confliced wih he goal of promoing economic aciviy in an elecion year. We capure hese domesic consrains in a general way by requiring he cenral bank o keep he moneary base consan even as reserves decline Ineres raes In he radiional firs-generaion model wih perfec foresigh, he nominal domesic ineres rae is consan unil he momen of aack. Wih uncerainy, he domesic ineres rae rises wih he approach of he aack because he condiional expeced rae of change of he exchange rae rises as reserves are depleed. The behavior of Mexican ineres raes prior o he aack follows an ineresing paern. Fig. 3 presens hree-monh raes on cees, Tesobonos, and U.S. reasury bills. Cees are peso-denominaed Mexican governmen securiies, while Tesobonos are peso-denominaed Mexican governmen securiies wih he principal indexed o he U.S. dollar exchange rae. In early 1994, cees ineres raes were around 10 percen. They moved up o he percen range in April, increasing he spread over Tesobono raes and U.S. reasury bill raes. However, hese ineres differenials narrowed somewha in he second half of 1994 before shooing up a he ime of he aack in December. The ineres-rae differenial beween Tesobonos and U.S. reasury bills also widened afer he Colosio assassinaion in March, 1994, narrowed afer Zedillo was eleced presiden in Augus, and sho up again a he aack ime in December. The ineresing feaure of ineres-rae behavior is ha he marke did no demand a very large premium Fig. 3. Yields on Mexican and U.S. Governmen Securiies, January 1994 January 1997 (in percen).

15 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) for peso lending in he second half of Some observers have aken his paern o mean ha he currency crisis was unexpeced by he markes. In our model, he spread beween he ineres rae on domesic-currency asses and he risk-free foreign ineres rae is accouned for no only by he expeced rae of depreciaion of he exchange rae, bu by a ime-varying sochasic risk premium. The risk premium depends in par on he relaive supplies of ineresbearing domesic and foreign securiies in he porfolios of he privae secor. Suppose ha in he period leading up o he speculaive aack, privae invesors come o expec a depreciaion of he domesic currency. By iself, ha will raise domesic ineres raes above he risk-free foreign ineres rae as privae invesors sell domesic securiies and purchase foreign securiies. Bu since his porfolio reallocaion enails a loss of inernaional reserves, he cenral bank serilizes he reserve loss by purchasing domesic securiies. Consequenly, he ousanding sock of domesic securiies held by he privae secor declines and one componen of he risk premium falls. Thus, on ne, he ineres rae on domesic-currency asses migh rise very lile. Privae invesors also seemed o moderae heir views abou an expeced depreciaion of he peso in he summer of 1994, as evidenced by he narrowing spread beween raes on cees and Tesobonos in July. Since he model incorporaes a ime-varying probabiliy of collapse ha is influenced by invesors percepions of risk, i can allow for an adjusmen in expecaions ha gives lesser weigh o he chance of a devaluaion The real exchange rae In he sandard firs-generaion aack model, he counry experiencing an aack is a price aker and is real exchange rae, he domesic price level divided by he produc of is rading parner s price level and he fixed exchange rae, is presumed o be fixed. In Mexico, a large movemen occurred in he real exchange rae afer fixing he nominal rae because domesic inflaion, while declining, exceeded inflaion in is major rading parner(s). Fig. 4 shows ha Mexico s real effecive exchange rae appreciaed significanly afer he peso was conrolled in Our model ges he real appreciaion in he preaack period, bu no hrough inflaionary moneary policy. By allowing home-goods prices o be se a period in advance, domesic prices can rise prior o he aack if agens come o expec a depreciaion of he home currency. Real exchange-rae appreciaion via inflaionary moneary policy can ake place if we relax he assumpion of a consan moneary base and insead allow he moneary base o grow faser han is foreign counerpar. Such a modificaion is a sraighforward exension bu is no explored here for simpliciy Inernaional reserves The firs-generaion aack model shows ha inernaional reserves decline in he period leading up o he currency crisis and fall precipiously a he ime of aack

16 260 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) Fig. 4. Mexico: Real effecive exchange rae, January 1979 November 1997 ( ). as he cenral bank makes a las-dich effor o defend he fixed exchange rae. The underlying reason for he reserve loss is he excess supply of money produced by moneizaion of he fiscal defici. Fig. 5 shows gross and ne Mexican inernaional reserves since Ne Fig. 5. Mexico: Inernaional Reserves, January 1990 Ocober 1997 (in billions of U.S. dollars).

17 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) reserves buil up over he period, reaching a peak of US$25 billion in February, Subsequenly, here was a dramaic decline. More han US$3 billion in reserves was los in March; more han US$8 billion in April. Afer a lull, US$4.5 billion was los in November and finally US$6.5 billion in December. Our model capures he decline in reserves in he period leading up o he aack even hough here is no moneizaion of he fiscal defici. Insead, he governmen s bond-financing leads privae invesors o reallocae heir porfolios. When privae invesors sell domesic securiies for foreign securiies, he cenral bank mus exchange reserves for domesic currency a he fixed exchange rae. Consequenly, he cenral bank s invenory of inernaional reserves declines. If he cenral bank also serilizes his reserve loss, he domesic ineres rae may no rise sufficienly o coax privae invesors o hold he ousanding sock of domesic securiies. As a resul, porfolio reallocaion effors may coninue, furher draining reserves. The governmen s deb financing also generaes expecaions of a fuure currency depreciaion ha simulaes porfolio reallocaion and drains reserves. If speculaive opinion suddenly shifs, wih invesors perceiving more risk, here will be a massive porfolio reallocaion ha exhauss reserves and ends he cenral bank s abiliy or desire o defend he fixed exchange rae Muliple equilibria We have developed a model in which we can observe shifs in exchange-rae volailiy even hough here is no change in he underlying process driving fundamenals. In he model, i is possible ha he mere percepion of increased currency risk can aler behavior in a way ha validaes he percepion. During a fixed exchange-rae period, surprising volailiy in he (unobserved) shadow exchange rae ranslaes ino insabiliy of he fixed-rae regime. More generally, volaile beliefs abou exchange-rae risk may help explain why empirical models of exchange-rae deerminaion have difficuly esablishing a reliable relaionship beween he exchange rae and underlying fundamenals. The economy can be a he marke fundamenals soluion for he exchange rae, or changes in speculaive opinion can shif he economy o anoher exchange-rae soluion. Were self-fulfilling risk predicions parly responsible for he Mexican crisis? Many aspecs of he model jus recouned mach up wih daa reasonably well. Cerainly here was a large shif in speculaive opinion abou he riskiness of Mexican invesmens. Tha shif coincided wih an aack on he fixed-rae pariy. While i seems possible ha Mexico faced a self-fulfilling aack due o changed risk percepions, producing a complee answer will require careful empirical 22 work. 22 See e.g. Jeanne (1997) empirical ess for muliple equilibria relaed o he European crises.

18 262 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) Conclusion The firs-generaion model of currency crises relies on deerioraing fundamenals as he underlying cause of speculaive aacks. I emphasizes ha speculaors rigger he aack in anicipaion of large capial gains. I also pus reserve movemens cener sage, capuring heir seady decline prior o an aack and heir sudden depleion during an aack. Our modified firs-generaion model mainains his focus on he profi opporuniies of speculaors and he role of inernaional reserves. For he Mexican case, hese feaures were clearly imporan. To capure oher feaures of he Mexican experience, we have modified he sandard firs-generaion model under uncerainy in several ways. We have no made he crisis ineviable by assuming ongoing moneizaion of he fiscal defici. We have aken ino accoun he moneary auhoriy s pracice of serilizing he effecs of reserve changes on he moneary base. We have also modeled priceseing behavior ha allows he real exchange rae o appreciae and he domesic ineres rae o rise in he period leading up o he aack and simplifies our reamen of he risk premium. Since he domesic ineres rae depends on a ime-varying sochasic risk premium as well as he condiional expeced rae of change of he exchange rae, i may no rise much prior o an aack. The ime-varying sochasic risk premium inroduces a nonlineariy ino he asse markes. This nonlineariy gives rise o he possibiliy of self-fulfilling risk predicions for some range of he fundamenals. Muliple equilibria are generaed solely by privae secor behavior and do no require a change in governmen policy ex pos o validae he aack. If privae invesors suddenly come o believe here is increased risk, ha alone can lead o a self-fulfilling speculaive aack if he economy s fundamenals have deerioraed sufficienly. While he risk-premium channel need no be he only source of nonlineariies, i is a sensible and convenien way o focus on self-fulfilling speculaive aacks arising solely from privae-secor behavior. Acknowledgemens ` We would like o hank Maurice Obsfeld, Helene Rey, Andres Velasco, wo anonymous referees and paricipans a a CEPR-sponsored conference on Speculaive Aacks in Sesimbra, Porugal (April, 1997) and a IMF and Federal Reserve Board research seminars for helpful commens. An earlier version of his paper was processed as NBER Working Paper No under he ile Speculaive Aacks: Fundamenals and Self-Fulfilling Prophecies.

19 Appendix A R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) Derivaion of he risk premium The risk premium is calculaed from he perspecive of he foreign invesor. The foreign invesor holds he mix of domesic and foreign bonds ha maximizes expeced welfare, which depends posiively on fuure real wealh and negaively on he variance of fuure real wealh relaive o curren wealh. The foreign invesor s problem is: H gv [W * 11 /P 11 * ] MaxBE [W 11 * /P* 11 ] 2 ]]]]] (A.1) [W */P*] subjec o he consrain W * 5 B* 1 XB (A.2) where upper-case leers are levels, * signifies he asses are foreign-currency denominaed (he foreign currency is he invesor s own currency), X is he exchange rae quoed as foreign currency/ domesic currency, and g is a measure of risk aversion. Prices are se a period in advance in he foreign invesor s currency. The opimizaion yields he following risk premium on domesic bonds before linearizaion: 2 X S ]] 11 X D 2g(1 1 i ) V XB ]]]]]]] (A.3) (1 1 p *)W * We adop he following linearizaions/ convenions: X 2 * S]] 11 X D z952g(1 1 i )/(11 p ); V 5V (x ) 5V (s ); XB ]] 5 a01 a 1(b2 b* 2 s ) 5 a 1(c 1 b2 b* 2 s ) (A.4) * W where lower-case leers b, b*, x and s are logs, he average domesic ineres rae i and he average foreign inflaion rae p * are aken as consans in he linearizaion, s is he log exchange rae quoed as domesic currency/ foreign currency, he coefficien a1 is he share of domesic bonds in foreign wealh, and c is a consan equal o a 0/a 1. In he ex, u5zv (s 11), where z5a1z9. Agens residing in he domesic and foreign counries are assumed o hold proporionaely idenical porfolios. J

20 264 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) The shadow exchange rae We describe here our soluion echnique for obaining he shadow exchange rae. Because prices are se a period in advance, he shadow rae a aack ime, s, is no he same as he flexible exchange rae in he following period, s 11. Since we need an expression for he expeced depreciaion of he exchange rae beween ime and ime 11 o solve for s, we also mus also solve for s 11. Le he shadow exchange rae a ime and he flexible exchange rae a ime 11 ake he forms: s 5 l 1 l h 1 l (A.5) s 5 b 1 b h 1 b (A.6) The flexible exchange rae s 11 equilibraes he posaack money marke: m 2 p 52a[i* 1 E (s 2 s ) 1u (c 1 b 2 b* 2 s )] d (A.7) 11 Three observaions abou (A.7) are in order. Firs, since he moneary auhoriy s policy is o keep he high-powered money base consan a all imes, m115m in (A.7). Second, o obain he expression for b11 in (A.7), we recall he log- linearizaion of he bond marke: b 5 gh 1 (1 2 g )d ; g. 1 (A.8) where privae holdings of domesic-currency bonds (b) are equal o he oal supply (h) ne of he holdings of he domesic moneary auhoriy (d). Posaack, he domesic bonds held by he cenral bank equal he high-powered money base since he cenral bank s inernaional reserve holdings are compleely depleed. Hence d 5 m 5 m and (A.8) becomes: b 5 gh 1 (1 2 g )m. (A.9) Third, b* is reaed as a consan in (A.7) on he assumpion ha cenral bank sales of foreign securiies o agens speculaing agains he domesic currency are small relaive o he worldwide holdings of hese securiies. Given he assumpions above, he assumpion ha p11 is se a a value expeced o clear nex period s goods marke ( p 5Es 11 11), and he process specified for h11 in he ex, we subsiue (A.6) and (A.9) ino (A.7) and solve for he shadow rae s 11 using he mehod of undeermined coefficiens. The soluion for s has he following coefficiens: 11

21 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) m[1 1 au (1 2 g )] 1 ai* 1 amb1 1 au [c 1 gm 2 b *] b 0 5]]]]]]]]]]]]]]] (1 1 au ) agru ab1 1 aug 2 d b15 ]]]]]] $0 b25]]]]] [1 1 a(1 1u ) 2 ar] a(1 1u ) (A.10) where u ;zv (s ). Since V (s ) is he variance of he shadow rae a ime 11 if here is a speculaive aack a ime, V (s ) 5 E (s 2 Es ) 5 b s (A.11) so ha u ;zb s. For laer reference, noe ha in (A.11), s is he variance of he sochasic elemen ha has a uniform disribuion cenered on zero wih he range [2w, w]. Thus w w s 5E ]( ) d 5 ]. (A.12) 2w 3 2w 2 2 Leing u ;zb2 s in (A.10) and manipulaing erms, we find ha b2 saisfies he fifh-order polynomial: c 1 c b 1 c b 1 c b 1 c b 1 c b 5 0 where 1 c 5 d 1 1] 2r F 0 a c a(1 2 r) 1 G 2 c 52zs [g h1 1 a(1 2 r)j 2 d 1 agr] 2 2 c 5 zs [1 1 a 1 a(1 2 r)] c4 52gaz (s ) c5 5 az (s ) (A.13) For each of he five possible values of b 2, here is a corresponding value for b1 and b0 in (A.10). Examining he c i, we noe ha if he money-demand parameer d equals zero, hen c050 and one value for b2 is zero. When b250, u 50 and b 50, so one soluion for s 1 11 is deerminisic. We call his soluion he marke fundamenals soluion. We are now ready o solve he model for s, he shadow rae a aack ime. The shadow rae s equilibraes he money marke a ime : m 2 p 52a[i* 1 E (s 2 s ) 1u (c 1 b 2 b* 2 s )] 1 de (A.14) 11

22 266 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) where p 5 E s 5 (1 2 p )s 1 p E (s us. s ) (A.15) using Eqs. (3) and (5) in he ex. We linearize he las erm in (A.15) as follows: p E (s us. s ) 52ps ˆ1 pe (s us. s ) 1 sp ˆ, (A.16) where p is he average probabiliy of aack nex period and sˆ is he average expecaion of nex period s exchange rae, condiional on an aack nex period. We obain an expression for p21 in erms of he sae. Recall ha p21 is he probabiliy of an aack in period based on ime 21 informaion: p 5 prhs 2 s. 0j (A.17) 21 Given he expression for he shadow exchange rae in (A.5), (A.17) can be rewrien as: p215 prhl01 l1h211 l 2 2 s. 0j 5 prh. k21j (A.18) where k215(s2( l01l1h 21)) /l 2.0.Since he shock is assumed o have a uniform disribuion (2w, w) cenered on zero, p 5 prh. k j 5 (w 2 k )/2w. (A.19) Subsiuing ino (A.19) our expression for k 21 gives: p 5 e 1 eh, (A.20) where e05(wl21l02s )/2wl2 and e15l 1/2wl 2. Nex we obain an expression for E 21(sus.s ) in (A.15). Given he proposed form for he shadow rae in (A.5), E 21(sus.s )5l01l1h211l 2(E 21 us.s ). Since he disribuion of is uniform, he ime 21 expeced value of he shock a ime, condiional on being in he posaack regime a, is E ( us. s ) 5 k 1 (w 2 k )/2. (A.21) Subsiuing ino (A.21) he expression for k 21 yields: E ( us. s ) 5 f 1 fh (A.22) where f05(s 2 l01 wl 2)/2l2 and f152l 1/2l 2. Finally, we use (A.5) and (A.6) o derive an expression for he expeced depreciaion of he exchange rae beween ime and ime 11 if here is an aack a ime : E (s 2 s ) 5 b 1 b (m 1 rh 1 ) 2 (l 1 l h 1 l ) (A.23) where he b are given in (A.10). i Subsiuing (A.5), (A.15), (A.16), (A.20), (A.22) and (A.23) ino (A.14), we

23 R.P. Flood, N.P. Marion / Journal of Inernaional Economics 50 (2000) solve for s using he mehod of undeermined coefficiens. The shadow rae soluion is described in he ex by Eqs. (7) (10), where he acual expression for he consan erm in (8) is p 1 21 ps 3 l w F ] ] G ] ] ]] 2 * l0 5 a(1 1u ) 1 1 hm 1 2 s 2 1ai au [c 1 gm 1 (1 2 g )m 2 b *] 1 ab01 ab1mj (A.24) l 2 w i ˆ ] ˆ 2 The l coefficiens reflec he fac ha s 5 s 1, where s is he expeced value of he shadow rae condiional on having a shock large enough o pu he economy ino he aack range. In he numerical example in he ex, we ake advanage of he informaion in (A.10) (A.13) and se he average probabiliy of an aack a p since he economy is considered o be in he aack range. References Agenor, P.-R., Jagdeep, B., Flood, R., Speculaive aacks and models of balance-of-paymens crises. Inernaional Moneary Fund Saff Papers 39, Bensaid, B., Jeanne, O., The insabiliy of fixed exchange rae sysems when raising he nominal ineres rae is cosly. Mimeo. Branson, W., Financial Capial Flows in he U.S. Balance-of-Paymens. Norh-Holland, Amserdam. Calvo, G., Varieies of capial-marke crises. Working paper, Universiy of Maryland. Black, S., Salemi, M., FIML esimaion of he Dollar Deuschmark risk premium in a porfolio model. Journal of Inernaional Economics 25 (3/ 4), Buier, W., Borrowing o defend he exchange rae and he iming and magniude of speculaive aacks. Journal of Inernaional Economics 23, Dornbusch, R., Expecaions and exchange rae dynamics. Journal of Poliical Economy 84, Driskill, R., McCaffery, S., Speculaion, raional expecaions and sabiliy of he foreign exchange marke. Journal of Inernaional Economics 10 (1), Eichengreen, B., Wyplosz, C., The unsable EMS. Brookings Papers on Economic Aciviy 1, Eichengreen, B., Rose, A., Wyplosz, C., Exchange marke mayhem: he anecedens and afermah of speculaive aacks. Economic Policy 21, Eichengreen, B., Rose, A., Wyplosz, C., Speculaive aacks on pegged exchange raes: an empirical exploraion wih special reference o he European Moneary Sysem. In: Canzoneri, M., Masson, P., Grilli, V. (Eds.), Transalanic Economic Issues. Cambridge Universiy Press, Cambridge, UK. Flood, R., Garber, P., Collapsing exchange-rae regimes: some linear examples. Journal of Inernaional Economics 17, Flood, R., Garber, P., Gold moneizaion and gold discipline. Journal of Poliical Economy 92 (1), Flood, R., Garber, P., Kramer, C., Collapsing exchange rae regimes: anoher linear example. Journal of Inernaional Economics 41 (3/ 4),