CAPITAL CONTROLS ON INFLOWS, EXCHANGE RATE VOLATILITY AND EXTERNAL VULNERABILITY * SEBASTIAN EDWARDS Universiy of California, Los Angeles Naional Bureau of Economic Research and ROBERTO RIGOBON Massachuses Insiue of Technology Naional Bureau of Economic Research Revised: March, 2009, ABSTRACT We use high frequency daa and a new economeric approach o evaluae he effeciveness of conrols on capial inflows. We focus on Chile s experience during he 1990s, and invesigae wheher conrols on capial inflows reduced Chile s vulnerabiliy o exernal shocks. We recognize ha changes in he conrols will affec he way in which differen macro variables relae o each oher. In paricular, we consider he case where conrols co-exis wih an exchange rae band aimed a managing he nominal exchange rae. We develop a mehodology o deal explicily wih he ineracion beween hese wo policies. The main findings may be summarized as follows: (a) A ighening of capial conrols on inflows depreciaes he exchange rae. And (b), we find ha a ighening of capial conrols increases he uncondiional volailiy of he exchange rae, bu makes i less sensiive o exernal shocks. JEL Classificaion No: F30, F32 Keywords: Capial conrols, capial mobiliy, capial inflows, exchange rae volailiy, Chile. * We hank Simon Johnson, Aar Kraay and Vincen Reinhar for excellen commens and suggesions on an earlier draf. Par of his research was done while Robero Rigobon was visiing he Research Deparmen a he World Bank. We are graeful o wo referees and o one of he co-ediors for very helpful commens and suggesions. Correspondence should be sen o sebasian.edwards@anderson.ucla.edu or rigobon@mi.edu.
1 I. Inroducion During he las few years he economics profession has made imporan progress in undersanding he deerminans of currency crises. This research has helped reshape he way in which moneary and fiscal policies are conduced in emerging and ransiion naions. Scholars and policy makers, however, coninue o disagree on some imporan aspecs of macroeconomic policy. One of he key opics of debae refers o he role of capial conrols and he adequae degree of financial inegraion of emerging markes o he res of he world. 1 According o some auhors, limiing he exen of financial inegraion reduces speculaion, and helps counries wihsand exernal shocks and avoid exreme exchange rae flucuaions (Bhagwai 1998, Krugman 1999, Sigliz 2000 and 2002, Rodrik 2006). 2 Auhors ha suppor resricing capial mobiliy have menioned Chile s experience wih marke-based conrols on capial inflows beween 1991 and 1998 as an example worhwhile emulaing. 3 In lae 2006 Thailand s economic auhoriies jusified he imposiion of conrols on shor erm capial inflows, by referring o Chile s experience during he 1990s. 4 In 2007, Colombia imposed shor erm capial inflows in an effor o reduce he exen of (nominal) exchange rae appreciaion; in raionalizing his policy he auhoriies also referred o Chile s experience wih conrols on inflows. 5 Auhors such as Sigliz (2002), Eichengreen (2000), Eichengreen and Hausmann (1999), Sallings (2007) and Williamson (2003) have argued ha Chile-syle conrols on inflows have hree imporan effecs: (a) hey reduce he degree of vulnerabiliy o exernal shocks; (b) hey resul in lower exchange rae volailiy; and (c) hey help avoid he exen of currency appreciaion during episodes of capial inflows. 1 See, for example, he papers colleced in Edwards (2007). 2 The IMF seems o suppor a very gradual lifing of resricions o capial mobiliy in emerging economies. See, for example Prasad, Rogoff, Wei, and Kose (2003). 3 For a deailed discussion of Chile s experience wih capial conrols on inflows see Cowan and De Gregorio (2007). 4 On Thailand s 2006 imposiion of conrols on inflows, see hp://www.imf.org/exernal/np/sec/pn/2007/pn0739.hm 5 On Colombia s 2007 conrols on inflows, see, hp://www.rgemonior.com/blog/economonior/196421
2 According o hese auhors, conrolling shor erm inflows were one of he keys o Chile s economic success during he 1990s. Calvo and Mendoza (1999), however, have argued ha Chile s success during he 1990s was mosly he resul of favorable exernal condiions, including very posiive erms of rade. In heir view, macroeconomic policies including he conrols on inflows had lile o do wih he noable accomplishmens of he Chilean economy. 6 The empirical lieraure on Chile s conrols has ended o suppor Calvo and Mendoza (1999); mos works on he subjec have found ha Chile s conrols had limied macroeconomic effecs. De Gregorio e al (2000), for example, found ha during he 1990s conrols on inflows alered he composiion of capial flows, wih shor erm flows declining and longer erm flows increasing. Conrols, however, failed o sop currency appreciaion or o increase he Cenral Bank s abiliy o conrol moneary aggregaes over he medium or long run. Similar resuls were found by Edwards (1999) and Valdes-Prieo and Soo (1998). Forbes (2003, 2005) uses firm-level daa o invesigae wheher Chile s conrols had microeconomics effecs. Her resuls indicae ha by resricing access o exernal funding, he conrols increased he cos of capial o small and mid size firms (See, also, Ulan 2000). Alhough he resuls repored by hese early papers are useful, hey are subjec o some limiaions and poenial economeric problems. In paricular, hese works have ignored he fac ha conrols on capial inflows were only one componen of Chile s exernal macroeconomic policy, and of he auhoriies effors o avoid excessive nominal exchange rae flucuaions and, in paricular, currency appreciaion. A second key elemen of his policy was a band of varying widh ha consrained he movemen of he nominal exchange rae. Ignoring his exchange rae band can inroduce an imporan bias in he esimaion of equaions ha aemp o assess he effecs of he conrols on key macroeconomic daa, such as he exchange rae (nominal or real). The reason for his is ha he conrols hemselves affeced he widh and realignmen of he band, and he exisence of he band affeced he behavior of macroeconomic variables such as ineres raes and he exchange rae. The purpose of his paper is o develop a new mehodology ha allows us o evaluae he effecs of capial conrols on inflows in counries ha inervene in he foreign exchange marke. In paricular, his 6 In a differen paper Calvo and Mendoza (2000) poin ou ha capial conrols on inflows may be jusified if he coss of conagion are high. See also Edwards (2007).
3 new approach allows us o invesigae wheher resricing capial inflows will reduce nominal exchange rae changes and volailiy. We do his by using a wo-seps esimaion echnique ha incorporaes he concep of shadow or equilibrium exchange rae developed by Berola and Caballero (1992). In he firs sep, we use daa on exchange rae fundamenals and on he naure of he foreign exchange rae inervenion policy (or, if appropriae, he exchange rae band) o esimae he shadow exchange rae. 7 In he second sep, we use an augmened GARCH approach o evaluae wheher changes in he resriciveness of capial conrols affeced he level and volailiy of he nominal exchange rae. In he empirical secion we use high frequency daily daa for Chile for 1991-1998; in some of he esimaes, and in order o invesigae he robusness of our esimaes, we use monhly daa. The mehodology and resuls presened in his paper go beyond he hisorical inerpreaion of Chile s economic performance, and are useful o evaluae fuure iniiaives aimed a resricing capial mobiliy in counries ha pursue an acive exchange rae managemen policy. This exchange rae inervenion policy may ake place hrough an explici band, as in Chile, or hrough implici feedback rules ha rely on more implici inervenion hresholds. As poined ou above, boh Thailand and Colombia recenly imposed conrols on inflows as a way o avoid nominal exchange rae appreciaion. Our analysis differs from previous work on he subjec in, a leas, four respecs: Firs, we use high frequency (daily) daa o analyze he effecs of conrols on capial inflows on he nominal exchange rae. Previous work, in conras, has used relaively low frequency daa (monhly or quarerly) o analyze real exchange rae behavior. Second, we explicily ake ino accoun he fac ha an acive exchange rae policy affecs he evaluaion of capial conrols. All previous papers on he subjec ha we are aware of ignored his imporan fac. Indeed, one of he key objecives of inroducing capial conrols is o allow he moneary auhoriy o exercise some conrol over exchange raes. As we explain in deail in Secion III, we do his by esimaing a shadow exchange rae, which capures he response of he exchange rae o changes in fundamenals in he absence of he exchange rae band. Third, we focus on he effecs of he conrols on he level and volailiy of he nominal exchange rae. In conras, mos previous research deals wih he 7 See Kearns and Rigobon (2005) for a discussion on idenificaion and esimaion of cenral bank exchange rae inervenion rules.
4 impac of conrols on he level of he exchange rae only. And fourh, we use a wo-sep augmened ARCH and GARCH, while mos previous analyses have relied on VARs and/or sandard regressions. I is also imporan o clarify a he ouse wha our paper doesn do: we don provide a complee cos-benefi analysis of Chilean syle capial conrols. In paricular, we don deal wih he poenial efficiency (and oher) coss of resricing capial mobiliy. Also, his paper doesn deal wih he effecs of capial conrols on he probabiliy of a currency crisis, or heir effecs on ineres raes and foreign deb mauriies. These are imporan issues, bu hey are beyond he scope of he presen paper. 8 The main findings from our analysis may be summarized as follows. Firs, a ighening of capial conrols resuls in a depreciaion of he domesic currency. This level effec on he nominal exchange rae should have been expeced, given ha igher capial conrols reduce capial inflows, and cause a deerioraion in he balance of paymens. 9 To reurn o equilibrium, hen, an improvemen in he curren accoun is required, and hence a real exchange rae depreciaion should ake place; his real exchange rae change akes mosly place hrough changes in he nominal exchange rae. Surprisingly, mos of he papers ha have sudied he Chilean experience have no found significan effecs of he conrols on he real exchange rae. 10 We believe ha his is because early sudies on he subjec ignored he endogenous response of he exchange rae o moneary policy. Second, we find ha he vulnerabiliy of he nominal exchange rae o exernal facors decreases wih a ighening of he capial conrols. More specifically, we find ha Chile s conrols on capial inflows were effecive in (parially) isolaing he nominal exchange rae from exernal shocks o impor and expor prices and inernaional ineres raes. Third, we find ha a ighening of capial conrols increases he uncondiional volailiy of he exchange rae. This effec can be explained by he fac ha igher conrols are likely o have segmened he Chilean foreign exchange marke furher. On he oher hand, isolaing he foreign exchange marke conemporaneously means ha, in he end, exchange rae volailiy is larger in he following periods. Capial conrols inroduce a radeoff 8 For an analysis of (some of) he coss of Chile s experience wih conrols on inflows, see Forbes (2003, 2005). Edwards (2007) addresses he effecs of conrols on he probabiliy of a crisis; De Gregorio e al (2000) analyze he effecs on ineres raes and deb mauriy. 9 Mos emerging markes ha have underaken modernizing reforms have been subjec o massive capial inflows ha have generaed forces oward currency appreciaion. See, for example, Calvo e. al. (1993). 10 See, for example, De Gregorio e. al. (2000).
5 sabilizing conemporaneous exchange raes (in erms of exernal shocks), bu desabilizing fuure nominal raes. The res of he paper is organized as follows: In Secion II we discuss he funcioning of Chile s conrols on inflows, and we review he empirical lieraure on he subjec. Secion III is he core of he paper: we presen our model, and we discuss a wo-sage sraegy for esimaing he effecs of conrols on inflows on he level and volailiy of he exchange rae. In his Secion we compare he resuls obained using a shadow exchange rae and he observed exchange rae. In Secion IV we presen some robusness ess and we discuss issues for fuure research. Finally, Secion V is he conclusions. II. Conrols on Capial Inflows: Chile s Experience during he 1990s A. The Mechanisms for Conrolling Capial Inflows ino Chile Chile inroduced marke-based conrols on capial inflows in June 1991. 11 Originally all porfolio inflows were subjec o a 20% reserve deposi ha earned no ineres. If he inflow had a mauriy of less han a year, he deposi applied for he enire duraion of he inflow. For longer mauriies, he reserve deposi was for one year. In July 1992 he rae of he reserve requiremen was raised o 30%, and is holding period was se a one year, independenly of he lengh of he mauriy of he inflow. Also, a ha ime rade credis and loans relaed o foreign direc invesmen became subjec o he unremuneraed reserve requiremen (URR). New changes o his policy were inroduced in 1995, when he reserve requiremen coverage was exended o include Chilean socks raded in he New York Sock Exchange (ADRs), financial foreign direc invesmen (FDI), and bond issues. In June of 1998, and as a resul of he sudden slowdown of capial inflows associaed wih he Eas Asian currency crises, he rae of he reserve requiremen was lowered o 10%, and in Sepember of ha year he deposi rae was reduced o zero. Throughou his period Chile also regulaed foreign direc invesmen: unil 1992, FDI was subjec o 11 For a deailed discussion on he adminisraive deails of Chile s conrols on inflows, see Ulan (2000), and De Gregorio and Cowan (2007). Chile also implemened conrols on inflows during he 1980s. Tha earlier episode is discussed in Edwards (1998).
6 a hree years minimum say in he counry; a ha ime he minimum say was reduced o one year. There were no resricions on he repariaion of profis from FDI. In 1991, when capial conrols on inflows were inroduced, he auhoriies had four goals in mind: 12 Firs, o slow down he volume of capial flowing ino he counry, and o il is composiion owards longer mauriies; second, o reduce he degree of nominal (and real) exchange rae volailiy; hird, o reduce (or, a leas, delay) he real exchange rae appreciaion ha semmed from hese inflows; and fourh, o allow he Cenral Bank o implemen an independen moneary policy, and o mainain high domesic (real) ineres raes (De Gregorio e al 2000, Massad 1998). Chile s sysem of unremuneraed reserve requiremens was equivalen o a ax on capial inflows. Wha made his policy paricularly ineresing was ha he rae of he ax was no consan; in fac, i varied consanly. This was because he rae of he ax depended boh on he period of ime during which he funds sayed in he counry, as well as on he opporuniy cos of hese funds (i.e. he world rae of ineres). As shown by Valdés-Prieo and Soo (1998) and De Gregorio e al (2000), he ax equivalen for funds ha sayed in he counry for k monhs, is given by he following expression: where τ ( k) * r λ ρ =, (1) 1 λ k * r is an inernaional ineres rae ha capures he opporuniy cos of he reserve requiremen, λ is he proporion of he funds ha has o be deposied a he Cenral Bank, and ρ is he period of ime (measured in monhs) ha he deposi has o be kep in he Cenral Bank. Figure 1 conains esimaes of his ax-equivalen for hree values of k: six monhs, one year and hree years. Three aspecs of his figure are paricularly ineresing: firs, he rae of he ax is inversely relaed o he lengh of say of he funds in he counry. Thiswas exacly he inen of he policy, as he auhoriies waned o discourage shor-erm inflows. Second, he rae of he ax is quie high even for a hree year period. During 1997, for example, he average ax for 3 year-funds was 80 basis poins. And hird, he ax equivalen varied hrough ime, boh because he rae of he required deposi was alered and because he opporuniy cos of he unremuneraed deposis changed. 12 Magud and Reinhar (2006) refer o hese four objecives as he four macroeconomic fears of emerging and ransiion economies.
7 Beween 1988 and 1998 shorer-erm flows ino Chile - ha is, flows wih less han a one year mauriy-- declined seeply relaive o longer erm capial. Liabiliies in hands of foreigners mauring wihin a year also declined in he period following he imposiion of conrols (De Gregorio e al 2000). By lae 1996 Chile had a lower percenage of shor-erm deb (relaive o oal deb) o G-10 banks han any of he Eas Asian counries, wih he excepion of Malaysia (Edwards 1998b). A radiional shorcoming of capial conrols (eiher on ouflows or inflows) is ha i is relaively easy for invesors o avoid hem. Valdés-Prieo and Soo (1998), for example, have argued ha in spie of he auhoriies effors o close loopholes, Chile s conrols were subjec o considerable evasion. Cowan and De Gregorio (1998) acknowledged his fac, and consruced an index of he power of he conrols. This index akes a value of one if here is no (or very lile) evasion, and akes a value of zero if here is complee evasion. According o hem his index reached is lowes value during he second quarer of 1995. B. A Selecive Review of he Empirical Lieraure Mos previous works on he macroeconomic effecs of Chile s conrols on capial inflows have relied on wo alernaive empirical mehodologies: single equaion esimaion or vecor auo regressions (VARs). In addiion, a few papers used GARCH echniques o invesigae he effec of conrols on he second momens of key macroeconomic daa. The vas majoriy of hese works have focused on real exchange raes, ineres raes and he mauriies of flows. As far as we know, however, none of hem has deal wih he effecs of conrols on he nominal exchange rae. In addiion no sudy has incorporaed he exisence of an acive exchange rae managemen policy. Some of he single regression works include Soo and Valdes-Prieo (1998, 2000), who concluded ha, alhough he conrols changed he composiion of capial inflows, hey did no affec he exchange rae level. Eyzaguirre and Schmid-Hebbel (1997) found ha he URR increased he cenral bank s abiliy o engage in independen moneary policy, and had a small and emporary effec on he exchange rae. Afer esimaing a series of rolling regressions on ineres rae differenials, Edwards (1998) concluded ha he capial conrols increased he degree of moneary policy effeciveness in he shor run. Cardoso and Laurens (1998) also esimaed ineres rae differenial equaions, and found ha he conrols had no significan effecs on he macroeconomic variables of ineres. Laban e al (2000) used a nonlinear swiching regimes model for capial flows of differen mauriies. They found ha while shor erm flows
8 declined afer he URR was adoped, long erm flows were no affeced. Gallegos e al (2002) esimaed a series of nonlinear equaions and error correcion models, and concluded ha during he URR period he cenral bank had a somewha greaer abiliy o pursue independen moneary policy objecives. However, he capial conrols did no affec he exchange rae level. 13 A number of auhors have ried o accoun for he simulaneous deerminaion of differen macroeconomic variables by esimaing vecor auo regressions. Soo (1997) and Edwards (1999) concluded ha he conrols on inflows were effecive in helping avoid an appreciaion of he currency in he shor run. Edwards (2000) used muli-counry sysems VARs o analyze wheher he capial conrols were able o isolae Chile from conagion semming from aboard. He concluded ha conagion was no reduced by he conrols. De Gregorio e al (2000) esimaed a series of VARs using monhly daa and found ha heir effecs on ineres raes and he exchange rae were (very) shor lived. The effecs on he composiion of capial inflows, on he oher hand, were longer. Magud and Reinhar (2006) provide an in deph review of some of hese sudies, and compares hem o sudies for oher counries. These sudies have provided some ligh on he funcioning of capial conrols on inflows, and have helped evaluae he effeciveness of his policy. None of hese works, however, have aken explicily ino accoun he exisence of an exchange rae band ha resriced nominal exchange rae movemens. As we show in Secion III of his paper, ignoring his band will inroduce serious biases in he esimaion. In Secion III we also propose a specific mehodology for evaluaing he effecs of capial conrols on inflows in counries ha pursue an acive exchange rae managemen policy. III. Esimaing he Effecs of Capial Conrols on he Nominal Exchange Rae A serious difficuly in evaluaing wheher Chile s policy on capial conrols was successful in reducing macroeconomic volailiy and in paricular, in reducing exchange rae volailiy -- is ha i was implemened a he same ime as he counry had a (credible) arge-zone exchange rae regime. The coexisence of hese wo policies conrols on inflows and a arge zone make i difficul o deermine if 13 These resuls are consisen wih Moniel and Reinhar (1999).
9 changes in exchange rae volailiy are he resul of he conrols, or if hey respond o he fac ha hroughou mos of he period he acual exchange rae was very close o one of he bands. This resuls in an idenificaion problem from he moneary policy choice o he observed exchange rae. There also exiss an effec ha goes from capial conrols o he way a arge zone works. As i is well known, a credible arge zone regime implies a mapping from a fundamenal exchange rae o an observed exchange rae ha depends on he sochasic process of such fundamenals. Therefore, if he capial conrols are effecive, when he conrols are ighened, hey should reduce he volailiy of he fundamenals ha drive he exchange rae. Tha is, effecive conrols aler he mapping from he fundamenals o he observed exchange rae. From he policy poin of view, i is no surprising ha here is a link beween nominal exchange raes managemen and capial conrols. Indeed, mos counries implemen capial resricions because hey are hoping o have some conrol over he nominal exchange rae. In his paper we develop a mehodology o disenangle hese effecs. We ake seriously he exchange rae bands announced by he Chilean Cenral Bank, and we esimae he implied fundamenals deermining he observed exchange rae his is equivalen o esimaing a shadow exchange rae ha would have prevailed in he absence of he inervenion implied by he arge-zone exchange rae regime. Once he shadow exchange rae has been compued in he firs sage of he analysis, we can hen evaluae he effeciveness of he capial conrols by measuring he pass hrough from exernal shocks o he shadow exchange rae, under alernaive inensiies of capial conrols. We carry ou his second sage by esimaing a series of GARCH regressions on he condiional variance of he shadow exchange rae. A. Daa The daa are daily and are aken from Daasream and he Cenral Bank of Chile. Exchange rae daa correspond o he daily exchange rae, he cenral pariy and he arge-zone bands. We also use daily daa on domesic peso denominaed ineres raes on 30-day deposis, and on he equivalen ax rae implied by he conrols compued according o equaion (1). Finally, we used alernaive sources of exernal shocks changes in U.S. ineres raes (30-day deposi raes), and he JP Morgan EMBI+ index ha excludes Chile. We also colleced he price of oil and copper (Chile s main impors and expors,
10 respecively) for he same period. 14 The sample corresponds o he period in which he arge zone regime was in place saring in January 1991 unil Sepember 2 nd, 1999. (Daily domesic ineres raes were only available from January 1 s 1994, however.) B. Esimaion: Model and Mehodology In order o esimae he shadow exchange rae or exchange rae ha would have prevailed in he absence of inervenion (arge zone) -- we assume ha he announcemen of he arge zone regime is credible while in place; however, we allow for he possibiliy of a bands realignmen, somehing ha indeed happened in Chile during his period. Condiional on modeling he Cenral Bank acions, he mapping from he shadow exchange rae o he observed nominal exchange rae is uniquely deermined by he bands and by he sochasic properies of he exchange rae process. We assume ha he mean of he shadow exchange rae is consan across ime; he variance, on he oher hand, is assumed o be ime dependen. 15 This means ha a each insan, he mapping from he shadow o he observed exchange rae will shif. This assumpion is required because our purpose is o evaluae how capial conrols have changed he sochasic properies of he fundamenals deermining he exchange rae. Therefore, given ha he degree of ighness of he capial conrols changes hrough ime -- recall equaion (1) --, and ha he shocks are characerized by condiional heeroskedasiciy, we should also expec he shadow exchange rae o have condiional heeroskedasiciy. To derive he shadow exchange rae as a funcion of he observed exchange rae we follow Berola and Caballero (1992) closely, where he possibiliy of realignmen is exogenously specified. 16 I is imporan o recognize ha our mehodology does no assume a connecion beween he capial conrols and possible sources of crises. For insance, assume ha capial conrols allow he fiscal auhoriy o raise is 14 Ideally we would have used indexes for he price of impors and expors, or he erms of rade. These daa, however, are no available a daily inervals. This is he reason why, as suggesed by one of he referees, we concenrae on he prices of copper and oil (Chile s main impor). 15 We can allow he mean o change and makes no difference in he esimaion. Means, however, are very badly esimaed when he process follows a random walk. We faced he exac same esimaion issues in our procedure. Neverheless, we were encouraged by he fac ha allowing he rend o vary or o force i o be he same produced (qualiaively) very similar resuls. 16 See Garber and Svensson (1995) for a deailed survey of he lieraure.
11 fiscal defici (by lowering he domesic cos of financing) and ulimaely cause an exchange rae crisis. This connecion beween he capial conrols and he exchange rae is missing in our mehodology we concenrae exclusively on he endogeneiy ha exiss beween moneary policy managemen and capial conrols and absrac from all oher feedback effecs. As in he sandard arge zone model, assume ha money demand in each counry is given by (where sandard noaion has been used): m p * * = αi * m p = αi (2) Assume furher ha boh purchasing power pariy (PPP) and uncovered ineres pariy (UIP) hold. This implies ha he exchange rae is: [ de ] * E e = m m + α d, (3) where we have subsiued he money demands in he PPP equaion and use he fac ha he ineres rae differenial is equal o he expeced exchange rae depreciaion. In his equaion he changes in money supplies are he fundamenals or shadow exchange rae ha govern he exchange rae dynamics. We assume ha he fundamenals are given by: f = μ d + σ dz (4) where he mean is consan and he variance is ime shifing. Using Io s lemma i is easy o show ha he exchange rae saisfies he following differenial equaion: The soluion o he differenial equaion is: where λ 1 and λ 2 saisfy e 2 e e + + 1 α μ 2 σ. f f = f 2 ( f ) αμ + f + A exp( λ f ) + B ( λ f ) e 1 exp 2 =, (5) 2 μ μ 2 λ = ± + 2 2 σ σ. (6) ασ
12 To pin-down he coefficiens in he homogeneous soluion o he differenial equaion we require boundary condiions. These are specified by he bands of he arge zone and he credibiliy of he exchange rae regime. The exchange rae bands in Chile moved frequenly see Figure 2. In his figure we presen he nominal exchange rae (he hick line in) and he upper and lower bands (he hinner lines). A sizeable proporion of his movemen is predicable in he sense ha i depended on how he cenral pariy is compued. Throughou he period under consideraion he Cenral Bank se he cenral pariy as a weighed average of pas realizaions which means ha he bands can be compued according o he informaion available a ime. 17 Indeed, during our sample here are only 5 band alignmens (See Figure 2): (a) On January 2 nd 1991 he bands are se o +/-5 percen of he cenral pariy; (b) On January 23 rd 1992 he bands are expanded o +/-10 percen; (c) On January 21 s 1997 he bands are furher expanded o +/-12.5 percen of he cenral pariy; (d) On June 26 h 1998 he bands are heavily ighened o an upper band of only 2 percen and a lower band of 3.5 percen; and (e) On Sepember 17 h 1998 boh bands are se o +/-3.5 percen, and he bands are progressively increased every day unil hey become almos 12 percen in Sepember 2 nd 1999 when he regime was abandoned. I is reasonable o assume ha he probabiliy ha he bands are realigned increases when he exchange rae is close o he band. The realignmen model of Berola and Caballero needs an esimae of his probabiliy or realignmen which is usually assumed o be fixed or exogenous. In our esimaion, we compued he probabiliy of realignmen as he number of realignmens ha occurred in he sample divided by he number of observaions in which he exchange rae was closer han 0.5 percen of he band. 18 A each poin in ime we have he following boundary condiions: 17 For deails on exchange rae policy during his period see, for example, Cowan and De Gregorio (2007) 18 The mehodology only deals wih exogenous realignmens, and herefore, we decided o allow for a relaively large probabiliy of realignmen. In fac, he larger his probabiliy is, he closer he shadow and he acual exchange raes are going o be. In oher words, if he probabiliy of realignmen is one, he arge zone regime is irrelevan and he shadow and acual exchange raes are idenical. When we performed he esimaion we ried wih differen probabiliies of realignmen and he resuls remain unchanged. Indeed, he resuls seing he probabiliy equal o zero are almos idenical o he ones we presen.
13 f [ f, f ] e = αμ + f e = αμ + f + A exp + A exp ( λ1 f ) + B exp( λ2 f ) ( λ f ) + B exp( λ f ), 1 2 (7) where f and f represen he lower and upper implied shadow exchange rae bands. These boundary condiions are known as he value maching condiions. The smooh pasing condiions ake ino accoun he fac ha he bands are ime varying and incorporae he probabiliy of realignmen, as well as he prediced changes in he cenral pariy. As may be seen in Figure 2, mos of he changes in he cenral pariy and he widh of he band are relaively small and follow he predicable process described above. We compue he expeced change in each of he bands, and wrie he smooh pasing condiions as follows: eˆ = 1+ A λ exp 1 1 ( λ1 f ) + Bλ2 exp( λ2 f ) ( λ1 f ) + Bλ2 exp( λ2 f eˆ = 1+ A λ exp ) Our daa se includes he following informaion: he acual (observed) exchange rae ( (8) e ), he bands ( e and e ), and he probabiliy of realignmen (refleced in he fac ha he smooh pasing condiions are no equaed o zero). We also have knowledge on he backward looking rule used by he cenral bank o deermine he cenral pariy. Our objecive is o esimae he shadow exchange rae ( f [ f, ] ), he bands f, he coefficiens A and B, and he ime varying momens describing he fundamenals process: μ and σ. This is a highly complex non-linear problem: here are as many sochasic differenial equaions as observaions. The mapping from he fundamenal or he shadow exchange rae o observed exchange rae changes wih he condiional mean and variance. If capial conrols are effecive and change he volailiy of he fundamenal, or he pass hrough from exernal shocks o he fundamenals, he mapping beween he shadow and he observed will change as well. We ake ino accoun hese changes in our esimaion. C. Compuing he Shadow Exchange Rae We assume ha he variance of he shadow exchange rae moves smoohly and ha i can be approximaed by a moving average. This assumpion is required for idenificaion reasons. We have a limied number of momens a each poin in ime, and smoohness allows us o esimae condiional
14 variances on he acual exchange raes, and use hem in he esimaion. 19 Under his assumpion, he condiional variance a some ime is given by he variance of he previous n observaions. This mehod allows us a very flexible specificaion, where we do no have o commi o a paricular paramerizaion of he variance process we only need ha he variance process is approximaed relaively well by a moving average. We did some sensiiviy analysis on hese assumpions ha is discussed below. The procedure of esimaion is by ieraion, and involves he following seps: 0 a) Iniialize he shadow exchange rae equal o he observed exchange rae: f =. This is he firs ieraion. i b) A ieraion i we have an iniial guess denoed as f. e c) Compue he mean reurn in he fundamenals (we are assuming ha he mean reurn is consan hroughou he whole sample) and he rolling variance of he fundamenals ( σ i i = var( f n : f 1) ). For some n ha represens a reasonable window (we used 5, 10, 20 and 60 days and he resuls are very similar. All he resuls we show are hose from he 5 days) d) Using he mean reurn and he rolling variance, compue he series of λ 1 and λ 2 ha prevails a each ime. 20 e) Using he observed bands [ ] e e,, he λ 1 and expeced changes in he bands [ e, ˆ ] λ2 previously compued, and he ˆ e we compue ( A B, f, f, ) using equaions (7) and (8). Noe ha a each ime, equaions (7) and (8) form a sysem of four equaions in four unknowns hence, for each observaion we solve he sysem of equaions. 19 If he variances where o be compleely random wih no paern whasoever, we canno esimae he model. The reason is ha here are far oo many unknowns a every poin in ime: he fundamenal, he bands, and he volailiy. The smoohness on he variance implies ha he volailiy of he shadow exchange rae is explained by a process ha can be approximaed (reasonably well) by a moving average. For insance, a GARCH or ARCH model. 20 In fac, all he variaion in hese variables is due o he change in he volailiy.
15 f) Using equaions (5) and (6) we solve for he implied fundamenal ha explains he exchange rae. This provides an esimae of he shadow exchange rae i+1 f for every ime. i+1 f g) We compare he esimaed fundamenal ( ) wih he iniial guess ( ). h) Jump o sep (c) and coninue ieraing unil convergence has been achieved in he shadow exchange rae. i f Because he mapping is unique, coninuous and differeniable beween [ f, f ], he ieraion has a fixed poin. In he end, we esimae he shadow exchange rae, he implied shadow exchange rae s bands, and he condiional variance of he shadow exchange rae ha is consisen wih he observed exchange rae and he bands. Noice ha in developing his procedure we have made several imporan assumpions: Firs, we have assumed ha he mean reurns are consan. This is mainly for convenience. I is well known ha mean reurns are poorly esimaed when he ime horizon is shor. In our case, he (daily) daa runs from he beginning of he 90 s o he end of he 90 s. If we were o esimae a yearly mean reurn we would inroduce a noisy esimae in he procedure. However, when we allowed he rend o change, he shadow exchange rae was almos idenical o he one we esimaed forcing he rend o be consan. Thus, we view his resricion as innocuous. Second, we have assumed ha he cenral bank only inervenes when he exchange rae is close o he band, following precisely wha a arge zone exchange rae regime implies. We made his assumpion because here are no daa on daily inervenions for he period under sudy. 21 We were only able o compile monhly inervenions; when we re-esimae he esimae a his lower frequency, he resuls are quie similar o hose obained under our assumpion ha inervenion only akes place in he neighborhood of he bands, bu he sandard errors became large. Finally, alhough we allow for exchange rae bands realignmens we assume ha he exchange rae regime as a whole is credible. In oher words, i is fully credible up o he realignmen. For insance, assume ha a drop in he price of copper migh imply a lower 21 We hank Rodrigo Valdes from he Cenral Bank of Chile for confirming his o us.
16 credibiliy in he arge zone. This connecion is missing in our esimaes given ha he probabiliy of realignmen has been fixed. The resuls from he esimaion of he shadow exchange rae are shown in Figure 3, where in order o avoid cluer we have no shown he cenral pariy. The hick line corresponds o he esimaed fundamenal, he op and boom lines are he esimaed bands, and he dashed line is he difference beween he fundamenal and he acual exchange rae. The bands and he fundamenals are measured on he lef axis, while he difference is measured on he righ hand side axis. Noice ha when he cenral pariy shifs are removed, he bands are much sable han hose shown in Figure 2. Indeed, his is he case jus in he raw daa. This is no a feaure from he esimaion. Second, as may be seen in Figure 3, he shadow and acual exchange raes are fairly close o each oher. The differences are, however, in line wih wha we would have expeced. From he heory we know ha when he exchange rae is below he cenral pariy he observed exchange rae is larger han he shadow exchange rae. The opposie occurs when he exchange rae is above he cenral pariy. 22 Noice ha indeed his is he relaionship beween he exchange rae and he shadow exchange rae. A he beginning of he sample he exchange rae is usually below he pariy and he difference o he shadow one are always negaive. The opposie happens when he exchange rae is posiive. Furhermore, he heory also implies ha he closer he exchange rae is o he band, he larger he deviaions should be (ceeris paribus). Our shadow exchange rae follows exacly such prescripion. Third, in order o highligh he differences even furher, in Figure 4 we presen he demeaned and de-rended acual and shadow exchange raes. The hick line is he acual exchange rae, and he dashed line is he shadow exchange rae (or fundamenal). Noice ha he differences can be appreciaed much beer in his case; he differences are more meaningful a he beginning of he sample han a he end. This is indeed a characerisic of he Chilean exchange rae regime ha prevailed a he ime. The credibiliy of he exchange rae regime sared o be severely affeced a he end of he sample, and his is shown by he fac ha he shadow and he acual exchange raes are almos idenical. 22 This is a sandard resul in he arge zone lieraure. In our seup, he slope of he mapping a he cenral pariy is one and i goes o zero when he exchange rae approaches he bands.
17 D. Exernal Vulnerabiliy and Capial Conrols Afer he shadow exchange rae has been compued, he second sep is o esimae a GARCH model o evaluae he imporance (and role) of capial conrols in he propagaion of exernal shocks. As menioned earlier, we measure he degree of capial conrol ighness by he ax equivalen pressure. We have hree measures depending on he horizon, and because hey are mulicollinear, we decided o use he shorer mauriy (180 days). 23 In Figure 5 we presen he acual exchange rae, ogeher wih he bands and he equivalen ax from he conrols. We assume ha changes in he exen of he conrols are exogenous o he exchange rae. This is a reasonable assumpion, since changes in he ax equivalence of capial conrols ax rae are no associaed wih realignmens in he band, bu wih changes in he inernaional ineres rae. Indeed, hese wo variables are only relaed when he conrols are abandoned in 1998 and he band is widened. We esimae he following GARCH specificaion: f = c0 + β 0 x + β1τ + β 2 x τ + ε ε ~ N(0, h ) (9) h = η + η h + η ε + η x + η τ + η x τ 0 1 2 1 2 1 3 4 5 where f is he shadow exchange rae compued in he firs sep, x is he vecor of exernal shocks, τ is he equivalen ax rae on capial inflows, x τ is a erm ha ineracs he exernal shocks and he ax rae implied by he capial conrols, and ε is he heeroskedasic residual. All variables have been demeaned and normalized by heir sandard deviaions. We presens he resuls in differences and in levels. In equaion (9), x is a vecor of exernal shocks. We inroduced a measure of he erms of rade (he price of copper minus he price of oil), and he EMBI+ (excluding Chile); his las variable is compued as he change in JP Morgan s EMBI+ spread for Lain America, excluding Chile. Our main ineres is o undersand how he exernal shock affecs he shadow exchange rae and is condiional variance, for differen levels of he ax equivalence of he capial conrols. We esimae he model wih no lags, and wih 23 The resuls are virually idenical (excep for normalizaion) if we use any of he oher measures of capial conrols. If he implied axes were much differen han he ones we have, a weighed esimaor would have proven very useful. In our case, because he measures are idenical, such esimaor makes very lile difference.
18 one lag; and we also esimaed only he ARCH model. We also inroduced he US ineres rae, bu because i was insignifican and he esimaes of he oher coefficiens were invarian o is inroducion we decided no o presen hen in he resuls. All he resuls are presened in Tables 1 and 2. We esimaed he same regression for he acual and he shadow exchange raes. This will allow us o analyze he way in which he resuls are affeced when he shadow exchange rae is used in he analysis. Table 1 presens he resuls of he level s regression, while Table 2 shows he resuls for he regressions in firs differences. The model is esimaed by maximum likelihood. Several esimaions are presened in Table 1. The firs column represens our preferred specificaion; a ARCH (1,1). The second are he GARCH (1,1) resuls. The firs wo columns are he esimaes for he shadow exchange rae, while he esimaes in he second se of columns are he resuls for he spo exchange rae. Table 2 is organized in he same way and we presen he esimaes for he firs differences. For each esimae he firs coefficien indicaes he poin esimae, and he T-sas are presened nex. 24 For he exogenous variables, EMBI is he EMBI Lain America excluding Chile; TOT is he daily price of copper in inernaional markes relaive o he daily WTI price of oil. This is a rough measure of he erms of rade affecing Chile. TAX is he measure of capial conrols used assuming a lengh of say of 180 days. 25 The ineracions should be clearly undersood by heir labels. 1. The Mean Equaion In discussing he resuls, we firs concenrae on he esimaion of he shadow exchange rae and compare hem o he esimaion using nominal (observed) exchange raes. The purpose of his comparison is o highligh he differences ha arise due o our esimaion procedure, raher han repeaing he resuls ha are common o boh specificaions. We sar wih he regressions in levels. We discuss he resuls for he in-differences specificaion in he nex sub-secion. 24 Jus o clarify purposes, when he exchange rae moves up is a depreciaion; his is because he exchange rae in Chile is measured as number of pesos for one dollar. 25 When oher mauriy lenghs were used, or a weighed average of mauriies was used, he resuls were very similar.
19 The direc effecs of he exogenous variables on he shadow exchange rae are in line wih economic inuiion: an increase in he emerging marke risk premium (EMBI), and a deerioraion of he erms of rade (TOT) produce a depreciaion of he shadow exchange rae. These coefficiens are all saisically significan. All variables were normalized by heir sandard deviaions; hence, he inerpreaion is as follows: a one sandard deviaion increase in he EMBI depreciaes he exchange rae by 0.5374 of is sandard deviaion. While he improvemen in he erms of rade by one sandard deviaion appreciaes he exchange rae by 0.57 percen of is sandard deviaion. As can be seen in column 2, hese resuls are robus o he GARCH specificaion. The message is he same, and he esimaed coefficiens are very similar. We now focus on he capial conrols variable TAX. As may be seen, an increase in he exen of capial conrols depreciaes he shadow exchange rae. The effec is saisically significan and has he expeced sign. A higher ax equivalence of he conrols makes domesic securiies less aracive, and resuls in a decline in he volume of capial flowing ino he counry. Hence, o reurn o equilibrium an improvemen in he curren accoun is needed which requires a depreciaion of he exchange rae. I is insrucive, a his ime, o compare he resuls wih he esimaes using he observed or acual nominal exchange rae, as opposed o he shadow exchange rae. Firs, he direc effecs are all consisen wih he ones esimaed using he shadow exchange rae consisen in erms of heir signs and someimes significances. The poin esimaes, however, change. If we ake he esimaes from he shadow as he correc ones, he regression using (observed) nominal raes exacerbaes he imporance of TAX and underesimaes he imporance of he TOT. When hinking abou moneary policy, hese resuls make sense. The Cenral Bank is more likely o inervene when pressures in he marke are forcing i o move he capial conrols. In fac, as shown below, mos of he capial conrol changes occurred when he exchange rae was closed o he bands This is he ime when expeced Cenral Bank inervenions is a is highes, and indeed he differences beween shadow and spo are he bigges. In oher words, here is an auomaic response of he cenral bank o he shocks ha is cleaned ou in he esimaion of he shadow exchange rae. Le us urn our aenion now o he ineracion erms, boh in he shadow and nominal exchange rae specificaions. As can be seen, all he ineracion erms have he opposie sign o he direc effecs, and hey are all saisically significan. This means ha he capial conrols are effecively reducing he impac of foreign shocks o he shadow exchange rae. Imporanly, his is a measure of he effeciveness of he
20 conrols. The esimaed coefficiens of he variables ineraced wih TAX run from a minimum of 0 o a maximum of 0.2, which means ha he economic effec for some of hem is small. For insance, in he case of he TOT, he oal effec goes from -0.46 o -0.40 when he ax equivalen of he conrols is increased from he minimum o he maximum. The effec of he EMBI, on he oher hand, declines from 0.54 o 0.45. Moving o he esimaes ha use he (observed) nominal exchange rae i can be seen ha he sabilizing effec of he capial conrols is also presen for he EMBI, bu no for he TOT. In summary, he mean equaions have wo imporan messages. An increase in he equivalen ax rae of he capial conrols depreciaes he exchange rae, and makes he fundamenal exchange rae less sensiive o exernal shocks. Alhough he firs resul could have been inferred from esimaing he regression on he observed exchange rae, he second one is mosly found when he proper (shadow) exchange rae is used. 2. The Variance Equaion We now urn our aenion o he variance equaion, which we presen in he lower panels. As may be seen, when he ax rae equivalen of he capial conrols increases, he exchange rae condiional volailiy decreases. In all specificaions he coefficiens are negaive, alhough hey are only saisically significan when he shadow exchange rae is used and he ARCH model is esimaed. This resul should be expeced because usually he capial conrols in Chile where changed when he nominal exchange rae was close o a band. Tha means ha he observed exchange rae had very lile variance, while he shadow exchange rae migh be more volaile. Hence, he reducion in variance is more likely o be observed in he shadow han in he nominal exchange rae. Movemens in he erms of rade and EMBI increase he condiional volailiy of he shadow exchange rae. All hese resuls are very srong in he ARCH esimaion, bu are weakened when he GARCH model is esimaed. In fac, he effecs become saisically insignifican. Ineresingly, he resuls for he spo exchange rae reflec no paerns whasoever even in he esimaion of he ARCH. One poin we have made repeaedly in his discussion has been relaed o he iming of he capial conrols changes. In Figure 6 we presen he relaionship beween he prediced variance of he shadow exchange rae and he ax rae. The ax rae is measured on he righ hand axis and he variance is measured on he lef-hand side. Noe ha in he earlier periods in he sample ha is before 1996 increases in he
21 equivalen ax rae were associaed wih significan reducions in he condiional volailiy; which is in line wih he regression resuls we have shown. This implies ha he effeciveness of he capial conrols is no he same along he whole sample. Afer 1997, changes in he ax rae seem o have no effec on he variance of he shadow exchange rae. This indicaes ha capial conrols experienced a reducion in heir degree of effeciveness afer mid-1997, a period when capial flows o all emerging markes plunged severely. No surprisingly, hen, in he absence of capial inflows, marke-based capial conrols on he inflows, by consrucion, should be ineffecive. Our evidence suggess ha indeed he changes in he policy were unable o affec he sabiliy of he exchange rae in he laer par of he sample; hey were effecive, however, during he earlier period. E. Sensiiviy Analysis and Fuure Research We performed several sensiiviy analyses in order o deermine he robusness of our findings. In his Secion we presen he main resuls, and we discuss some open issues ha, in our opinion, should be addressed by fuure research. We firs, checked he esimaion of he shadow exchange rae by changing he rolling window used o compue he variance. The resuls presened above are for a 5-day window; in he robusness analysis we esed 10, 20 and 60-day windows. The resuls are qualiaively very similar. The only difference is he magniude of he coefficiens in he second sep (ARCH/GARCH), bu no heir significance, nor heir signs. In general, he longer he window is, he larger he coefficiens in he regression. We also allowed he rend o shif hrough ime. The resuling shadow exchange rae is almos idenical o he one used in he regressions repored in he preceding secions. Addiionally, we esimaed he model assuming ha no exchange rae realignmen was possible, i.e. ha he bands were fully credible. Once again, he shadow exchange rae compued was almos idenical o he one in our preferred specificaion. As a second sep in our robusness analysis, we evaluaed he sensiiviy of he resuls in he ARCH/GARCH specificaion. We ried specificaions in firs differences, and wih more lags. The resuls for he firs differences are shown in Table 2. 26 As can be seen, he esimaes in he second sage are somewha weakened when he regression is esimaed in firs differences (for all variables). For he ARCH 26 We hank he edior and he referee for poining ou o us he imporance of hese resuls.
22 specificaion using he Shadow Exchange Rae, sill an increase in he EMBI and a deerioraion of he erms of rade generae an exchange rae depreciaion. These effecs are saisically significan and have he correc signs. The GARCH specificaion conserves he EMBI effec, while he TOT one becomes insignifican. Noice ha he regression using he spo exchange rae have almos no significan coefficiens, and he ones ha are significan have he incorrec sign. Having poined ou o he direc effecs, he ineracion erms are all insignifican. The variance equaion exhibis a similar paern. The TOT effec is posiive and is ineracion erm has he same sign as he level equaion. The impac of axes and he EMBI are insignifican, hough. The regression on he spo exchange rae has eiher he wrong sign or coefficiens are insignifican. Taking he resuls in he level equaion and he firs differences ogeher implies ha we should moderae somewha of our previous claims. Clearly here seems o be a benefi of esimaing he regressions on he shadow exchange rae, bu he resuls ha were significanly clean in he levels equaion are weakened in he in-differences specificaion. An imporan cavea is ha he model assumes ha inervenions only occurred close o he bands. This was no always he case for Chile. Unforunaely we did no have informaion abou daily inervenions. For he period under consideraion we were only able o collec bi-weekly inervenion daa. As a way of dealing wih his issue we re-esimaed he model using bi-weekly daa. However, he amoun of informaion los is remendous, and in he end mos esimaes were no saisically differen from zero (excep for he level effecs in he mean and he variance equaion). Three addiional issues are worh menioning. Firs, we have obviaed he issue of evasion and assumed ha capial conrols were effecive. However, here is evidence ha his was no he case in Chile. Taking evasion ino accoun should make our resuls sronger no weaker. 27 Second, we have assumed ha oher policies are no endogenous o capial conrols such as fiscal policy and foreign borrowing. Fuure research should incorporae hese issues in order o undersand fully he consequences of capial conrols on macroeconomic vulnerabiliy. Third, we have aken he cenral bank announcemens wih respec o he exchange rae sysem o be fully credible. We have assumed ha he managed exchange rae 27 In oher words, he evasion implies ha he effec of he capial conrols on he exchange rae are smaller in pracice han he heoreical ones. Hence, our esimaes should reflec he coefficiens assuming evasion which means ha all he rue effecs are larger han he ones shown here.