TEXTO PARA DISCUSSÃO. No A Risk Management Approach to Emerging Market s Sovereign Debt Sustainability with an application to Brazilian data

Transcription

1 TEXTO PARA DISCUSSÃO No. 484 A Risk Managemen Approach o Emerging Marke s Sovereign Deb Susainabiliy wih an applicaion o Brazilian daa Márcio Garcia Robero Rigobon DEPARTAMENTO DE ECONOMIA

2 DEPARTAMENTO DE ECONOMIA PUC-RIO TEXTO PARA DISCUSSÃO N o. 484 A RISK MANAGEMENT APPROACH TO EMERGING MARKET S SOVEREIGN DEBT SUSTAINABILITY WITH AN APPLICATION TO BRAZILIAN DATA MÁRCIO GARCIA ROBERTO RIGOBON MARÇO 2004

3 A Risk Managemen Approach o Emerging Marke s Sovereign Deb Susainabiliy wih an applicaion o Brazilian daa Márcio Garcia PUC-Rio Robero Rigobon MIT Absrac In his paper we sudy he quesion of deb susainabiliy from a risk managemen perspecive. The deb accumulaion equaion for any counry involves variables ha are sochasic and closely inerwined. When hese aspecs are aken ino consideraion he noion of deb susainabiliy is expanded o sudying he sochasic properies of he deb dynamics. We illusrae he mehodology by sudying he Brazilian case. We find ha even hough he deb could be susainable in he absence of risk, here are pahs in which i is clearly unsusainable. Furhermore, we show ha properies of he deb dynamics are closely relaed o he spreads on sovereign dollar denominaed deb. Wednesday, March 17, 2004 Keywords: Public Deb, Deb Susainabiliy, Counry Risk, Brazil JEL classificaion: F34, F37, G15 We hank Ilan Goldfajn and paricipans of he seminar Inflaion argeing and deb: he case of Brazil (Rio de Janeiro, December 2003) for commens. Fernanda Lima and Rafael Vasconcellos provided invaluable research assisance. All remaining erros are ours.

4 I. Inroducion There are several ways o assess deb susainabiliy. A widely used crierion is he gap beween he acual primary budge defici and he one required o keep he deb GDP raio sable (he deb sabilizing primary balance ). 1 This measure has several drawbacks: since he purpose of having deb in he firs place is o smooh consumpion, why would a counry wan o keep he deb o GDP raio consan? Or, if a counry is excessively heavily indebed, o keep he deb o GDP raio would no be susainable. Oher measures have been proposed. IMF (2003) esimaes he fiscal reacion funcion. The idea is similar o esimae he coefficien of he expeced inflaion in a Taylor rule, and check wheher i exceeds one, as required for he rule o provide a saionary inflaion. In he fiscal reacion funcion, he aim is o esimae how he primary balance reacs o increases in he deb o GDP raio. Anoher measure is o compue a raio beween he acual deb level and a benchmark level equal o he presen value of fuure primary surpluses compued under conservaive assumpions. If he raio exceeds one, he counry would be over borrowing (IMF 2003). Risk based measures of fiscal susainabiliy have been borrowed from he financial lieraure. One of hem is he very famous Value-a-Risk (V@R). Oher susainabiliy measures include sress esing hrough Mone Carlo simulaions. 2 Here we propose a relaed measure ha akes very seriously he realizaion ha he deb accumulaion equaion for any counry involves variables ha are sochasic and closely inerwined. By aking hese aspecs ino consideraion, he noion of deb susainabiliy is expanded o sudying he sochasic properies of he deb dynamics. We propose a VAR (Vecor Auo Regression) o esimae he correlaion paern of he macro variables and use i o implemen Mone Carlo simulaions. These simulaions allow us o compue risk probabiliies, i.e., probabiliies ha he simulaed Deb o GDP raio exceeds a given hreshold deemed risky (say, 75% of GDP). 3 The ime-series of such probabiliies is hen used o invesigae wheher or no i is correlaed wih he marke risk assessmen, measured by he spread on sovereign dollar denominaed deb. The applicaion of our mehodology for Brazil shows ha even hough he deb could be susainable in he absence of risk, here are pahs in which i is clearly unsusainable. Furhermore, we show ha properies of he deb dynamics are closely relaed o he EMBI+ Brazil spread. Nex Secion describes he daa used and performs a few deb decomposiion exercises. Secion III presens he core mehodology and he applicaion o Brazilian daa. Secion IV concludes. 1 2 See IMF (2003), p. 124, for references. Garcia (2002) compues a V@R for he Brazilian deb and performs Mone Carlo simulaions o implemen a CF@R (cash-flow a risk). 3 For a financial insiuion, his probabiliy would be analogous o he probabiliy of wiping ou he ne worh.

5 II. Brazilian Sovereign Deb A. Daa Descripion The simulaion of he deb dynamics requires he compaibiliy of many saisics ha are produced in differen places. Bevilaqua and Garcia (2002) performed a decomposiion exercise of he growh sources of he domesic bonded deb in Brazil. The domesic bonded deb is he componen of he ne public deb ha grew he mos: from 11.81% of GDP in December, 1994 o 48.95% of GDP in Sepember, Here, we use a similar framework o decompose he sources of growh of he Brazilian ne deb. To pu ogeher he daa was no a sraighforward ask, and i ook us a few monhs and many ineracions wih he Brazilian Cenral saff o clean he daa and adap hem o he forma required in he simulaions. 4 Currenly, hese daa are all available a he Brazilian Cenral Bank web page ( We now briefly describe he daa. We use deb socks (domesic, foreign; gross and ne) monhly series. These socks are convered o raios of GDP using he valorized GDP, 5 which are used o compue all raios of GDP ha we use in his paper. The PSBR (public secor borrowing requiremens) are compued in hree differen conceps: primary, operaional and nominal. We favor he use of he operaional and primary conceps, which miigae he effecs of high inflaion, because our sample conains he immediae afermah of he Real plan, when he inflaion came down from almos 50% per monh. Massive disorions (see Figure 2 A) show up in he nominal defici figures immediaely succeeding he Real plan saring poin (July 1, 1994) because we use welve-monhmoving averages o provide comparabiliy and avoid excessive flucuaion. 6 Wih he moving averages, unil a full year had elapsed, he disorionary effecs of he hyperinflaion sill conaminaed he nominal defici figures. 7 Two main adjusmens have o be aken ino consideraion in order o make he deb saisics compaible wih he PSBR s. Firs, privaizaion revenues have he (accouning) effec of reducing he deb, bu are no compued as fiscal revenues for purposes of calculaing he PSBR. Second, many expendiures incurred in he presen are resuls of 4 Box 3.1 (Daa on Public Deb in Emerging Marke Economies) of he las World Economic Oulook (IMF 2003) describes he many difficulies involved in gahering such daa. 5 The valorized GDP is a beer measure han he nominal GDP because, even under moderae inflaion, he simple addiion of he GDP flow wihin a welve-monh period disors he saisic. For example, for a 10% yearly inflaion, each uni of domesic currency of he las monh will be worh 1.1 unis of domesic currency of he firs monh included in he sample. The valorizaion procedure miigaes his disorion. Under zero inflaion, he valorizaion procedure revers o usual addiion of monhly GDP flows. Box 3.1 of he World Economic Oulook (IMF 2003) commens on he effecs of such procedure, grossly exaggeraing hem. 6 Since he deficis are so imporan o deermine deb susainabiliy, we oped o use welve-monhmoving averages insead of monhly figures. This is because he laer series is very volaile, ofen changing signs. For example, if some expenses were concenraed in a given monh, he monhly series would show a large defici among many surpluses, while he moving average would beer reflec he fiscal sance. 7 See Figure 2.

6 previous coningen liabiliies ha evenually maerialized. These skeleons have he (accouning) effec of increasing he deb, bu are no compued as fiscal oulays for purposes of calculaing he PSBR. 8 The remaining daa used are sandard. Inflaion is measured hrough he CPI (IPCA) and WPI (IGP-M) 9 indices. Domesic ineres raes are measured by he Selic rae. 10 The counry risk is measured hrough he EMBI and EMBI + Brazil indices produced by JP Morgan. Exchange raes are he monh-end PTAX. B. Decomposiion of deb shocks Figure 1 displays he evoluion of he ne deb o GDP raio since A few monhs afer he sar of he Real Plan, he ne deb o GDP raio sared o grow almos monoonically from he 30% level, reaching levels above 60% during he 2002 financial and poliical crisis, and currenly hovering around 58%. This very fas growh is deemed he mos imporan fragiliy in Brazilian macroeconomic indicaors. To be sure, alhough some conend ha he level of he ne deb could be high given invesors collecive behavior, 11 he ne deb o GDP raio in Brazil is no paricularly high among naions. The oal (probably gross) deb averages 70% of GDP for emerging marke economies (IMF 2003, p. 116). However, he speed i increased (doubled from 30% o 60% in eigh years), i.e., he deb velociy, is unambiguously very concerning. The fiscal siuaion ha generaed such remendous growh in he ne deb o GDP raio is displayed in Figure 2 A. The operaional and primary defici measures clearly show he fiscal sance deerioraion afer he firs quarer of As explained earlier, he nominal defici canno be used o make any inference during he firs year of he Real plan because i is sill heavily conaminaed by he previous very large inflaion raes. I is only afer Ocober, ha he fiscal sance improves. 8 Oher minor adjusmens have o be performed in order o make he debs saisics compaible wih he PSBR s, as explained in Bevilaqua and Garcia (2001). 9 The IGP-M is in fac an index ha mixes a WPI (60%) a CPI (30%) and a consrucion cos index (10%) 10 The equivalen of he US Fed funds rae. 11 For he deb inolerance phenomenon, see Reinhar, Rogoff and Savasano (2003) and IMF (2003). 12 Alhough correlaion does no imply causaion, he change in he fiscal sance was simulaneous o he agreemen wih he IMF.

7 FIGURE 1 BRAZILIAN PUBLIC NET DEBT (%GDP) 65,00% 60,00% 55,00% 50,00% 45,00% 40,00% 35,00% 30,00% 25,00% jan/94 abr/94 jul/94 ou/94 jan/95 abr/95 jul/95 ou/95 jan/96 abr/96 jul/96 ou/96 jan/97 abr/97 jul/97 ou/97 jan/98 abr/98 jul/98 ou/98 jan/99 abr/99 jul/99 ou/99 jan/00 abr/00 jul/00 ou/00 jan/01 abr/01 jul/01 ou/01 jan/02 abr/02 jul/02 ou/02 jan/03 abr/03 jul/03 Toal Ne Deb Hypoheical Ne Deb wihou Skeleons Hypoheical Ne Deb wihou Skeleons and Privaizaion Hypoheical Ne Deb wihou Skeleons, Privaizaion and Exchange-Rae Devaluaions FIGURE 2 A PSBR - Nominal, Primary and Operaional Deficis (% of GDP) 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% -2.00% -4.00% Jan-94 Apr-94 Jul-94 Oc-94 Jan-95 Apr-95 Jul-95 Oc-95 Jan-96 Apr-96 Jul-96 Oc-96 Jan-97 Apr-97 Jul-97 Oc-97 Jan-98 Apr-98 Jul-98 Oc-98 Jan-99 Apr-99 Jul-99 Oc-99 Jan-00 Apr-00 Jul-00 Oc-00 Jan-01 Apr-01 Jul-01 Oc-01 Jan-02 Apr-02 Jul-02 Oc-02 Jan-03 Apr-03 Jul % -8.00% PSBR - nominal defici (% GDP) PSBR - nominal defici (valorized) (% GDP) PSBR - primary defici (% GDP) PSBR - primary defici (valorized) (%GDP) PSBR - operaional defici (% GDP) PSBR - operaional resul (valorized) (% GDP) However bad during he period , he fiscal sance is no he sole responsible for he doubling of he ne deb o GDP raio. Many oher facors influenced he behavior of he deb. Bevilaqua and Garcia (2001), analyzing he increase in he bonded public deb during he period , poined ou ha exremely high ineres paymens were he

8 main culpris of he deb explosion. 13 I has been a maer of grea discussion in Brazil how much of he high ineres raes were endogenously deermined by he weak fiscal sance. On one corner, he economiss a Cenral Bank during he firs erm of Presiden Fernando Henrique Cardoso argued ha o keep inflaion a bay hey had o mainain a very high real ineres rae given he weak fiscal sance. On he opposie corner, oher economiss argued ha ineres raes were kep ha high only o mainain he (overvalued) exchange rae. One inerpreaion is ha during good imes (beween he Mexican crisis and he Asian crisis, and for a few monhs beween he end of he Asian crisis and he sar of he Russian crisis), ineres raes were kep above wha was required by covered ineres pariy o figh inflaion. Figure 2 B displays he behavior of wo measures of counry (Brazil) risk, one consruced wih exernal deb yield (C-Bond yield minus he yield of he T-bill of equivalen duraion) and he oher consruced wih he domesic one-year ineres rae (he covered ineres pariy differenial). 14 In hose ranquil periods before he floaaion of he real (January 1999), o avoid he inconsisen riniy, conrols on capial inflows were pu in place so ha he resricive moneary policy could be underaken. 15 In bad imes, i.e., periods of high risk aversion in inernaional financial markes, ineres raes were raised even higher o avoid capial ouflows which would kill he exchange-rae peg. In any case, i is only reasonable o assume ha a ougher fiscal sance would have allowed a smaller real ineres rae. On he oher hand, had he peg ended before 1999, probably a lower real rae would have been paid during he inervening years. Therefore, when analyzing he deb decomposiion exercises presened below, one has o bear in mind he sochasic relaions beween he variables, which lie a he hear of he simulaion procedures presened in Secion III. Besides high ineres paymens, he so-called skeleons (coningen liabiliies ha urned sour) conribued significanly o he deb increase. Figure 1 shows he evoluion of a hypoheical deb o GDP raio had he skeleons no exised. The ne deb o GDP raio would have fallen by more han 6 p.p. of GDP had he skeleons no exised. On he oher hand, had he governmen no privaized, he deb would have increased. The ne effec of boh privaizaions and skeleons is negligible, as displayed in Figure 1 by he series Hypoheical Ne Deb wihou Skeleons and Privaizaions. Noe ha his a mere accouning exercise, no a counerfacual one Here, we use he primary defici as a measure of he fiscal sance, according o he usual pracice of successful sabilizaion programs (see Missale, Giavazzi and Benigno 2000). This is because he nominal (and, in lesser measure, real) ineres paymens are deermined by many facors and may hinder he acual changes in he fiscal sance. 14 Noe ha here are many differences beween he domesic and he exernal bond whose yields are used o compue he wo counry risk measures, among hem he much longer duraion of he C-Bond. Neverheless, he regulariy poined ou remains valid. For deails, see Garcia and Didier (2003). 15 A descripion and an evaluaion of he effeciveness of he capial conrols on inflows is done in Garcia and Valpassos (2000). See also Cardoso and Goldfajn (1998). 16 For a counerfacual exercise, see Goldfajn and Guardia (2003).

9 FIGURE 2 B Two Measures of Brazil Risk: Domesic and Exernal Deb 35% 30% 25% 20% 15% 10% 5% 0% jan/95 mai/95 se/95 jan/96 mai/96 se/96 jan/97 mai/97 se/97 jan/98 mai/98 se/98 jan/99 mai/99 se/99 jan/00 mai/00 se/00 jan/01 mai/01 se/01 jan/02 mai/02 se/02 jan/03 mai/03 Covered-Ineres-Pariy Differenial C-Bond Spread The effec of he devaluaions can be seen in he series Hypoheical Ne Deb wihou Skeleons, Privaizaions and Exchange-Rae Devaluaions. Again, since his is no a counerfacual exercise, he series has a downward bias. This is because lower ineres raes accrued on public bonds denominaed or indexed in US$ (vis-à-vis he non indexed ones) because of he forecased devaluaion and he currency risk. A flexible exchange rae regime would probably have required higher dollar raes, leading o higher ne deb o GDP raios along he counerfacual pah. Despie hese flaws, his series shows ha he ne deb o GDP raio would hover around 37% by Augus 2003 had skeleons and privaizaions being ou of he picure, and he nominal exchange rae remained (à la chinoise) a par wih he US$. The simulaion procedure of Secion III, among several uses, may also be used o perform a complee counerfacual exercise. For example, given he srucures of correlaions esimaed by he VAR, by hypohesizing a differen pah for he primary defici, one would also change he (endogenously deermined) ineres raes, affecing he deb boh direcly (hrough he primary defici) and indirecly (hrough he ineres paymens) We will perform such full-blown counerfacual exercises in a fuure version.

10 III. Risk Managemen Approach In his secion we evaluae he deb susainabiliy quesion from a risk managemen perspecive. Mos of he deb susainabiliy lieraure concenraes on he deb accumulaion equaion ( + r g ) d f d 1 + (1) = 1 where d is he deb o GDP raio, r is he real ineres rae paid, g is he growh rae of GDP, and f is he primary defici. The idea in his equaion is o deermine he primary defici or growh rae of GDP ha would mainain he deb a cerain level. This lieraure has been remendously imporan in offering insighs on he imporance and iming of sabilizaion programs, as well as deb resrucuring. 18 In his paper we recognize ha he variables enering his equaion are sochasic, and perhaps, correlaed. Furhermore, we also consider he possibiliy ha here are oher exernal variables (such as he exchange rae and inflaion rae) ha could generae comovemen in he variables enering he deb accumulaion equaion. In paricular, we assume ha d ( + ~ r g~ ) = 1 d 1 { ~ ~ r, g~, f, ε ~, ~ s, π~ } ~ N( µ, Σ ) ~ + f + ε ~ r (2) where ~ r, g~ ~, f, ε ~ ~, s, and π~ are he sochasic real ineres rae, GDP growh rae, primary defici, deb shocks (skeleons (+) and privaizaions (-)), he real exchange rae, and he inflaion rae. We also assume ha hey are disribued mulinomial 19 wih condiional mean µ r, and condiional covariance marix Σ. The risk managemen approach o deb susainabiliy is simply he characerizaion of he evoluion of all he relevan sochasic variables and he calculaion of he differen deb pahs. The idea is o esimae he condiional means and variances from he daa and simulae he differen pahs of he deb from hose pahs, we can compue he probabiliy he deb will reach some level wihin some ime and measure risk accordingly. The properies of he covariance marix are imporan o deb susainabiliy. For example, in developed economies recessions (lower growh) are usually accompanied by a decrease in he ineres rae (expansionary moneary policy). If his is he case, hen he 18 For a review of he possible crieria o deermine deb susainabiliy, see Chaper III of he Sepember, 2003 World Economic Oulook (IMF 2003). 19 We are assuming ha he variables are normally disribued, even hough some of hem canno be negaive. This is a simplificaion ha can be easily correced in he Mone Carlo exercise. Here i is made mainly for exposiional purposes.

11 recession and he deerioraion of he primary defici which are huring he deb susainabiliy comes wih a reducion in he ineres rae which is helping deb susainabiliy. There is an auomaic sabilizer in he equaion. On he oher hand, in emerging marke economies, usually a recession deerioraes he fiscal accouns, increases he real ineres rae, induces inflaion and depreciaes he exchange rae. If he sovereign deb is in dollars (which is usually he case), hen all he variables are making he deb dynamics worse. Therefore, for emerging economies, he risk (covariance) par of deb susainabiliy becomes predominan, and simulaions ha posulae independen pahs for he relevan variables badly miss his key feaure. A. Mehodology In his secion we briefly discuss he procedure used o compue he deb dynamics. The variables considered are he following: real growh of GDP, real ineres rae, he primary defici measured as a share of GDP, he skeleons derived from he deb dynamics equaion, he real exchange rae compued as he nominal depreciaion minus inflaion, and he inflaion rae. All he daa are monhly. To compue he deb shocks, or skeleons, we ake he acual deb daa and realizaions of he growh rae and ineres raes and compue ~ ε ~ d (3) ( 1+ ~ r g~ ) d 1 f = We hen compue a VAR using he macro variables. One problem ha migh arise from using a VAR is ha if he variables are non-saionary bu coinegraed we should run a error correcion model. Unforunaely he daa we have is exremely shor, and here is lile hope ha he sandard ess are srong enough o produce a definie answer. Because we know ha even in near uni roo seups VAR s produce consisen esimaes (see Rohenberg and Sock (1997)) we decided o pursue his alernaive. Therefore, he macrovariables are given by X X ν = c + B ~ N ( L) ( ~ r ~, g~, f, ε ~, ~ s, π~ )' ( 0, Ω) X + ν (4) where ν are he reduced form residuals disribued mulinomial wih mean zero and covariance marix Ω, and B ( L) are he coefficiens of he lags. Using he Choleski decomposiion of he reduced form residuals we generae several pahs of he shocks and using he coefficiens from he VAR we can compue he pah of he variables in X - which can be used o esimae he pah of he deb. This simple procedure uses Mone Carlo o deermine several pahs of he deb. I has several advanages: Firs, because we are no ineresed in esimaing he

12 conemporaneous causaliy beween he macro variables, he VAR is used only o produce he bes predicor on he join dynamics of he macro variables. In oher words, mos applicaions on moneary policy are ineresed in compuing impulse responses and idenifying srucural shocks from he reduced form. In his paper his is no our objecive, alhough in Secion III.D below we will compue some impulse responses. However, o undersand he dynamics of he macro variables or beer said o describe i, he only requiremen is o produce he conemporaneous correlaion as he resul of some Choleski decomposiion. Indeed, any Choleski decomposiion (meaning any ordering of he variables in he VAR) will produce he same reduced form covariance marix which explains why for risk managemen applicaions he ordering is irrelevan. 20 Second, he procedure can be used o esimae rolling regressions ha will be used o assess he predicive power of he model and perform ou of sample ess. This also allows us o esimae he model using he mos recen condiions o compue differen deb dynamics. Finally, his allows us o compare how differen exchange rae regimes migh impac he deb susainabiliy by concenraing only on he correlaion srucure. Third, variables and shocks ha are no par of he deb accumulaion equaion sill can have an impac on he deb dynamics. For example, he exchange rae, he erms of rade, and inflaion can be included as variables in he VAR and analyze heir impac on he deb. Finally, even if variables are no included, i is possible ha he VAR could summarize heir effec. For example, if erms of rade is no included bu heir impac on he deb dynamic is going o show up eiher as oupu, inflaion or a real exchange rae depreciaion, hen he fac ha i has been excluded from he VAR does no mean ha is effec is no included or summarized in he variance covariance marix of he reduced form residuals. B. Deb susainabiliy In his secion we presen he resuls from esimaing he procedure described previously o he case of Brazil. There are several aspecs ha are imporan in he esimaion - such as he choice of he relevan ineres rae ha are discussed in deail. Furhermore, we sudied he sensiiviy of he resuls o changes in some of he assumpions. The variables we included are: (i) oal ne deb; (ii) GDP and GDP growh which were compued from he 12 monhs valorized GDP; (iii) he real ineres rae was compued as he Selic rae minus he inflaion in he WPI; (iv) he primary defici is he valorized defici divided by he valorized GDP; (v) he real exchange rae change was compued 20 The inuiion is ha he covariance marix of he reduced form can have several riangular facorizaions which in he VAR language i means ha hey have differen orderings. There are as many riangular facorizaions as he facorial of he number of variables (or columns of he marix), which corresponds o he number of differen permuaions of he variables. Each facorizaion recovers by definiion he original marix bu implies differen Choleski decomposiions.

13 as he change in he nominal Real US Dollar exchange rae minus he inflaion rae (WPI); 21 (vi) and finally, he inflaion rae used is he monhly WPI. 22 The firs sep is o compue he skeleons and esimae he VAR using he six variables. The poin esimaes of he VAR are of lile ineres, so no shown here, he covariance of he reduced form residuals, on he oher hand, deserves special aenion. Table 1 Covariance and correlaion marix Real Real Real Exchange Nominal Ineres Growh Primary Deb Rae Inflaion Rae Rae Defici Shocks Depreciaion (WPI) Real Ineres Rae Real Growh Rae 35.2% Primary Defici 17.8% 18.2% Deb Shocks -25.5% -7.0% -77.7% Real Exchange Rae Depreciaion -1.0% 28.6% 9.3% -8.3% Nominal Inflaion (WPI) 34.8% -22.8% -10.5% -4.0% -17.8% In Table 1, we show he covariance marix of he reduced form residuals on he upper riangular, and on he lower riangular we show he correlaions (highlighed). Some paerns of correlaion are worh emphasizing. Firs, he primary defici is posiively associaed wih he real ineres rae and he growh rae. These correlaions are compaible wih he sandard Keynesian fiscal muliplier effecs. Second, he inflaion rae is posiively correlaed wih he real ineres rae, and negaively correlaed wih he growh rae. As we menioned before, in emerging markes i is common ha inflaion scares are recessionary and increase he real ineres raes. Furhermore, noice ha he inflaion rae is negaively correlaed wih he real exchange rae bu he pass hrough is less han one o one given ha he correlaion is quie small. Third, a real exchange rae depreciaion is associaed wih an increase in he fiscal defici (he correlaion is small bu posiive), bu an increase in growh. Remember ha hese correlaions reflec parial correlaions and herefore in his discussion, he real exchange rae depreciaion is assumed o have happened wihou inflaion. In oher words, his is a rue real exchange rae depreciaion and herefore expansionary in erms of oupu. On he oher hand, mos of he acual depreciaions we observe in Brazil are accompanied by boh he change in he real exchange rae and an increase in he inflaion rae. In his case, he firs movemen increases oupu, while he second one would reduce i. The final effec has o be compued by looking a impulse responses. See Secion III.D below. Before concenraing on impulse responses, which are sensiive o he ordering of he variables in he VAR, we sudy he implicaions of he correlaion srucure on he deb. To compue he deb pah we need o deermine he iniial condiions, i.e. wha is he 21 Since he US inflaion has very low variance in he sample, we exclude i from he real exchange rae calculaion. In our framework, he consan erm in he regression akes care of he effec of he US inflaion on he real exchange rae. 22 We also compued he model using he CPI and no difference on he main message was found.

14 iniial primary defici, ineres rae, growh rae, ec? To simplify he analysis we have decided o use he average of hese variables he previous 9 monhs. We esimaed he same pah using only 6 monhs, and exending o 12 and 24 monhs. The resuls are almos unalered by his assumpion hence we use 9 monhs o deermine he iniial condiions and all he daa available up o ha poin o esimae he VAR and he covariance marix. In Figure 3, we presen he deb pah using he iniial condiions compued a he end of Sepember of In oher words, we compue he deb accumulaion equaion using he inflaion rae, ineres rae, primary defici, growh rae of he previous 9 monhs, and he final deb, he pah of fuure deb assuming hose variables remain consan is depiced in Figure 3. This is he pah for he following 30 monhs. 0.8 Figure 3 Deb susainabiliy in he absence of risk mean Noice ha saring from almos 60 percen deb, he deb would gradually fall o jus above 50 percen of GDP 30 monhs hence. I is possible o conclude from his exercise ha he deb in Brazil given he value of he curren macroeconomic variables is susainable. However, his would be he wrong conclusion. Indeed, we perform he Mone Carlo exercise and show in Figure 4 he pah of he deb, he maximum and minimum deb, he 95 and 5 percen bands, and he sandard deviaion of he deb o GDP raio are shown.

15 Figure 4 Deb susainabiliy wih risk mean max min band 97.5% band 2.5% sd 0 The sandard deviaion of he deb o GDP raio is measured in he righ hand side scale, while all he oher variables are measured on he lef hand. 23 There are several imporan poins ha can be exraced from Figures 3 and 4. Firs, i is he case ha he deb on average is falling, as he sandard deb susainabiliy exercise would imply. Second, here is a non-rivial proporion of realizaions in which he deb increases o more han 70 percen a level of deb ha would be considered exremely large for an emerging marke. 24 Remember ha he horizon of sudy is only wo and a half years and he deb o GDP reaching 80 percen in ha period reflecs a very fas accumulaion when we consider we are saring from less han 60 percen and he means of he sochasic variables is poining o a deb reducion. Third, he volailiy of he deb o GDP raio is increasing hrough ime. I is easy o show ha he deb o GDP raio has a variance ha is increasing faser han he one implied from a random walk. In oher words, he variance T periods ahead is larger han T imes he variance of one period ahead. In oher words, he variance is increasing no only because simulaion period is longer, bu because he covariance marix is such ha he opposie of a diversificaion effec arises. This is he opposie of he auomaic sabilizer effec ha exiss in developed economies, as menioned earlier. In Figure 5 we presen he sandard deviaion of he deb adjused by he horizon. Here we presen he simulaions for he nex 4 years. As can be seen, afer one year, he volailiy increases more han proporionally o ime. This is he resul found in several of he simulaions; he real ineres rae in some of hem is larger han he growh rae of oupu generaing an exploding deb pah The shocks are zero he firs wo periods because he VAR was esimaed using 2 lags. See Reinhar, Rogoff and Savasano (2003).

16 Figure 5 Adjused Variance by Horizon C. Deb susainabiliy and sovereign spreads In he previous secion we sudied he properies of he deb 30 monhs afer he curren siuaion. In his secion, we repea his exercise for each monh saring in January of The idea is o compue he VAR wih he available daa up o monh, and compue he pah of he deb aferwards for 10 years. Using hose pahs we can compue an saisic on he deb les say he probabiliy ha he deb o GDP raio is larger han 75 percen. Then we can repea he exercise for monh +1. This rolling exercise produces a pah for several saisics of he deb. In Figure 6 we presen he resuls for he probabiliies of reaching a deb larger han 66, 75, 85, 95 and 100 percen of GDP in he following 10 years. The inerpreaion of his is he following. For example, assume ha we are esimaing hese probabiliies for June of Using all he daa unil May of 2002 we esimae he VAR, he covariance marix of he shocks, and generae he Mone Carlo simulaions (500 replicaions of 120 monhs). Wih he simulaed pahs we compue he deb for each of hem using he deb accumulaion equaion and he esimaes from he VAR. Then we compue he number of imes he deb reaches some hreshold (say, 75 percen of GDP) in any monh of he nex 10 years. Hence, for June of 2002, given he iniial condiions a ha ime, he real ineres rae and he covariance marix esimaed unil he previous monh, he probabiliy of a deb o GDP raio larger han 75 percen is 79 percen, while i has a 59 percen chance of being larger han 100 percen of GDP. In oher words, a ha ime i is clear ha he siuaion exising in Brazil implies a very risky pah of he deb. In oher imes, such as in May or June of 2003, hese probabiliies are much smaller. The exercise performed here is akin o a sress es.

17 Figure 6 Probabiliy of deb o GDP raio reaching more han hreshold in following en years P(>0.67) P(>0.75) P(>0.85) P(>0.95) P(>1.00) I is imporan o menion ha in order o consruc hese pahs we are using only informaion from he pas. Hence his is an ou-of-sample exercise. The idea is o compare one of hese pahs wih he he EMBI+ yield. Figure 7 shows he resuls. Figure 7 Probabiliy of oal deb o be larger han 75 percen of GDP a any ime in he following 10 years, and he EMBI+ spread Correlaion Level= Correlaion Change= Embi P(>0.75) As can be seen in Figure 7, he probabiliy and he spread on he EMBI are closely relaed. Firs, our procedure is ou-of-sample in he sense ha o compue he probabiliy in monh, we use only informaion unil ime -1, and we compare he probabiliy wih he average ineres rae on he EMBI on monh.

18 The correlaion beween hese wo series is 54 percen on levels and 33 percen in changes. A simple regression analysis shows ha our variable has srong predicive power on he fuure EMBI+ spreads. A simple AR(2) model produces s = s s p p where s is he change in he EMBI+ spread, and p is he probabiliy ha he deb reaches some hreshold in our Mone Carlo exercises. As can be seen he probabiliies are significan even hough hey have been compued wih daa before he monh where he change in he EMBI is aking place. The R square of he regression is economically imporan: 56 percen. In fac, he AR(2) wihou he probabiliy measures has only one of coefficien significan ( s 1 ) and an R square of 38 percen. Indeed, he simple F ess show ha he p-value of he significance of he lagged changes in he EMBI+ spread is 8.9 percen (H0: he coefficiens on he wo lagged changes in he EMBI+ spread are zero), and 2.2 percen for he probabiliies lags (H0: he coefficiens on he wo lagged probabiliies are zero). We inerpre hese resuls as a srong corroboraion ha our mehodology capures he bulk of marke percepion of he defaul risk in Brazilian sovereign deb, and ha such risk measure is largely correlaed wih he Brazilian risk spread. We herefore hink ha heses probabiliies consiue an alernaive, very effecive, mehod o assess deb susainabiliy. D. Impulse responses One of he advanages of he previous procedure evaluaing he pah of he deb is ha we do no have o commi ourselves o a paricular srucural model or disribuion of he residuals. This is crucial in counries such as Brazil because he sandard riangular assumpion imposed in moneary economies is rarely saisfied. I is hardly he case ha decisions of moneary policy in a paricular monh do no affec prices, oupu, or exchange raes conemporaneously. The previous analysis, by concenraing on he conemporaneous covariance of he residuals, allows us o sudy he pah of he deb o he ypical mixure of shocks ha have hi he Brazilian economy. The only propery imposed is ha hey have o saisfy he covariance marix compued in he sample. However, looking a he mixure of shocks does no always provide he bes descripion. For example quesions such as wha is he impac of a depreciaion of he exchange rae on he pah of he deb canno be answered. In his secion, we will impose a riangular decomposiion of he reduced form shocks, even hough we believe ha i may be a poor descripion of wha really akes place in he Brazilian economy. Neverheless, his

19 exercise will provide some inuiion abou he behavior of he deb, bu i is always subjec o he criique ha i depends crucially on he idenificaion assumpions. This is an imporan limiaion bu unforunaely his is he bes we can do wih he available daa. In paricular, we will assume ha he ordering of he equaions is as follows: real ineres rae, GDP growh rae, primary fiscal defici, skeleons, real exchange rae, and inflaion. This order implies ha inflaion affecs all he variables conemporaneously, while he real ineres rae only acs wih a lag. Figure 8.1 Impulse response o an increase in he ineres rae Deb in growh prim def deb shock rer inflaion In Figure 8.1 o 8.6 we presen he impulse responses of all he shocks plus he implied deb accumulaion. The impulse response of each of he shocks is compued using he Choleski decomposiion and he esimaes from he VAR. The impulse response of he deb accumulaion is calculaed using he response of each of he shocks, he iniial condiions a he end of he sample, and he deb accumulaion equaion. In Figure 8.1 he impulse response o a one sandard deviaion increase in he real ineres rae is depiced. As can be seen, he increase in he real ineres rae is quie persisen and i lass around 10 monhs. Noice ha he increase in he real ineres rae depreciaes he real exchange rae and reduces he inflaion rae. I has a small impac on he growh rae and he primary defici. The ne effec on he deb pah is ha an increase in he real ineres rae increases he deb o GDP raio, and according o our simulaion and he given iniial condiions, he deb keeps on growing for a long period of ime even afer he variables have reurned o seady sae.

20 Figure 8.2 Impulse response o an increase in he growh rae of monhly oupu Deb in growh prim def deb shock rer inflaion In Figure 8.2, he impulse response o a one sandard deviaion increase on he growh rae of oupu is depiced. As can be seen, he increase in he growh rae is associaed wih a conemporaneous increase in he real ineres rae bu subsequen reducions, a reducion in inflaion rae, and a small real exchange rae appreciaion. In he end, he pah of he deb reflecs a permanen improvemen. Noice ha even when he variables are close o he seady sae, he deb is almos consan a a lower level. One surprising resul, a leas o us, is he fac ha he primary defici is almos unaffeced by he oupu increase. I is possible ha his is he resul of he bad idenificaion, bu also i could reflec ha in he sample oupu increases are associaed wih expansionary fiscal policy. Figure 8.3 looks a he impulse response afer an increase in he primary defici. In his case, he increase in he primary defici is associaed wih a depreciaion of he real exchange rae, an increase in he inflaion rae, an increase in he ineres rae, and a ransiory increase in he growh rae. The shock and he firs hree reacions should deeriorae he deb o GDP raio, bu he increase in growh should improve i. In he end, our simulaions show ha he negaive effecs ou-weigh he posiive ones and he deb o GDP raio increases. In fac, in comparison o he previous wo shocks, clearly he innovaions o he primary defici have he larges impac. These hree impulse responses confirm quie well our inuiion abou he impac of hese shocks on he pah of he deb. We should expec ha increases in he real ineres rae and deerioraions of he primary defici end o increase he deb, while increases in he growh rae end o improve i. I is no appropriae o judge he idenificaion of shocks by heir impulse responses, bu a leas he resuls are no conradicing i.

21 Figure 8.3 Impulse response o an increase in he primary defici Deb in growh prim def deb shock rer inflaion Figure 8.4 Impulse response o an increase in he skeleons Deb in growh prim def deb shock rer inflaion In Figure 8.4 we sudy he impac of an increase in he skeleons. Our simulaions show ha here is a ransiory increase in he deb o GDP raio followed by a decline. This impulse response is hard o reconcile wih inuiion. Indeed, from all our responses his is he mos inconsisen one. In Figure 8.5 we depiced he impulse response o a real exchange rae depreciaion. Before drawing any conclusions is imporan o remember ha given our idenificaion

22 assumpion his is a very paricular form of depreciaion. This is an exchange rae depreciaion ha is no accompanied by an increase in he inflaion rae. In oher words, his is a rue real exchange rae depreciaion. Increases in inflaion rae, ha could also cause a depreciaion of he real exchange rae is he nex shock. In oher words, we can hink of his shocks as he good par of he depreciaion, and he nex shocks as he bad par. Figure 8.5 Impulse response o an increase in he real exchange rae (depreciaion) Deb in growh prim def deb shock rer inflaion Noice ha in line wih our good depreciaion inerpreaion an increase in he real exchange rae is accompanied by an increase in he growh rae, a moderae increase in he ineres rae (smaller han he growh rae), and a large improvemen in he primary defici. This is exacly he implicaions of a real depreciaion rae ha is expansionary. Because he increase in he growh rae is higher han he increase in he real ineres rae in he end he deb o GDP raio improves permanenly. The final exercise is shown in Figure 8.6. In his case we sudy he impulse response o an increase in he inflaion rae. Given he idenificaion assumpion i is possible o inerpre his shock as a nominal shock ha depreciaes he exchange rae and increases he inflaion rae a he same ime. Indeed, in he impulse response i can be seen ha he increase in inflaion also depreciaes he real exchange rae very significanly. Furhermore, he real ineres rae increases on impac while he growh rae declines, and he primary defici deerioraes. The movemen of all he variables poins ou o a clear increase in he deb o GDP raio, which in fac akes place.

23 I is imporan o remember ha comparing he previous impulse responses he increase in he primary defici and he increase in he inflaion rae are he wo mos imporan ones quaniaively speaking Figure 8.6 Impulse response o an increase in he inflaion rae Deb in growh prim def deb shock rer inflaion In his secion we have made a big deal abou he impulse responses and how he impac he pah of he deb. I is imporan o reierae wha was menioned in he inroducion. The resuls in his secion depend crucially on idenificaion assumpions ha are unlikely o be rue in he daa. Wih his cavea in mind, we sill believe ha somehing can be learned from he exercise. Firs, he comovemen observed in he variables of ineres and he deb dynamics are close o wha our inuiion would have prediced 25 which is reassuring. Second, he magniudes involved show ha he mos imporan shocks regarding he sensiiviy of he deb o GDP raio o he shock are innovaions o he primary defici and he inflaion rae, where we have inerpreed he innovaions of he inflaion rae as nominal shocks or bad exchange rae depreciaions. 25 Excep for he skeleons.

24 IV. Conclusions The main conribuion of his paper is o propose a risk based measure o assess deb susainabiliy. The main insigh ha lead o his measure is ha deb in emerging marke economies is quie risky. An increasingly larger number of models and body of empirical evidence show ha emerging marke economies lack he naural sabilizing feaures ha allow and make counercyclical policies effecive. For example, during a recession, real ineres raes end o fall in developed economies, which makes room for larger primary expendiures given he reducion in ineres paymens. In emerging marke economies, ofen he reverse happens: real ineres rae rises, governmen revenues fall and governmen oulays increase, hereby negaively leveraging he deb impac. The proposed measure is consruced from a framework ha combines a saisical model o uncover he sochasic relaions among he variables ha direcly or indirecly influence he deb accumulaion wih a simulaion engine ha compues fuure pahs for he deb o GDP raios. The Mone Carlo simulaions allow us o compue risk probabiliies, i.e., probabiliies ha he simulaed Deb o GDP raio exceeds a given hreshold deemed risky (say, 75% of GDP). The ime-series of such probabiliies is hen used o invesigae wheher or no i is correlaed wih he marke risk assessmen, measured by he spread on sovereign dollar denominaed deb. The applicaion of our mehodology for Brazil shows ha even hough he deb could be susainable in he absence of risk, here are many pahs in which i is clearly unsusainable. I.e., alhough on average he Brazilian deb is susainable, he correlaion srucure under which he Brazilian economy operaes poses a huge quesion mark on he deb susainabiliy. We also show ha properies of he deb dynamics are closely relaed o he EMBI+ Brazil spread. This is quie a remarkable resul, since our mehodology uses ou-ofsample simulaions, and does no use regressors relaed o he risk aversion of inernaional invesors, as he high-yield spread in he US, which are deemed very imporan in he deerminaion of he EMBI+ spread. Thus, our measures consiue an alernaive, very effecive, mehod o assess deb susainabiliy.

25 V. References Bevilaqua, A. and M. Garcia. Deb Managemen in Brazil: Evaluaion of he Real Plan and Challenges Ahead, Inernaional Journal of Finance and Economics, January Cardoso, E. and I. Goldfajn, "Capial Flows o Brazil -The Endogeneiy of Capial Conrols", IMF Saff Papers, v. 45, n.1, 1998 (also as IMF Working Paper, 97/115, 1997). Garcia, M. PUBLIC DEBT MANAGEMENT, MONETARY POLICY AND FINANCIAL INSTITUTIONS, PUC-Rio working paper, July Garcia, M. and T. Didier, Very High Ineres Raes and he Cousin Risks: Brazil During he Real Plan in José González and Anne O. Krueger, eds., Macroeconomic Reforms: The Second Generaion, The Universiy of Chicago Press, Garcia, M. and M. Valpassos,, Capial Flows, Capial Conrols and Currency Crisis: The Case of Brazil in he Nineies in Felipe Larrain, ed., Capial Flows, Capial Conrols, and Currency Crises: Lain America in he 1990s, Universiy of Michigan Press, Goldfajn, I.and E. Guardia, Fiscal Rules and Deb Susainabiliy in Brazil, forhcoming in a book edied by Kopviz, George, IMF, 2003 (available a hp:// IMF, World Economic Oulook, Sepember Missale, A., F. Giavazzi and P. Benigno. How is Deb Managed: Learning from Fiscal Sabilizaions, RePEc:igi:igierp:174, Sepember Reinhar, C., K. Rogoff and M. Savasano. Deb Inolerance, Brookings Papers on Economic Aciviy, Rohenberg, T. and J. Sock. Inference in a Nearly Inegraed Auoregressive Model wih Nonnormal Innovaions, Journal of Economerics, 80 (1997),

26 Deparameno de Economia PUC-Rio Ponifícia Universidade Caólica do Rio de Janeiro Rua Marques de Sâo Vicene Rio de Janeiro , RJ Tel.(21) Fax (21) flavia@econ.puc-rio.br