Specification of a Stochastic Simulation Model for Assessing Debt Sustainability in Emerging Market Economies

Transcription

1 WP/06/68 Specificaion of a Sochasic Simulaion Model for Assessing Deb Susainabiliy in Emerging Marke Economies Doug Hosland and Philippe Karam

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3 006 Inernaional Moneary Fund WP/06/68 IMF Working Paper IMF Insiue Specificaion of a Sochasic Simulaion Model for Assessing Deb Susainabiliy in Emerging Marke Economies Prepared by Doug Hosland and Philippe Karam 1 Auhorized for disribuion by Ralph Chami December 006 Absrac This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. This paper documens he specificaion of a model ha was consruced o assess deb susainabiliy in emerging marke economies. Key feaures of he model include exernal and fiscal secors, which allow assessmen of exernal and public deb in a unified framework; public and exernal deb, which boh have an explici mauriy srucure along wih a disincion beween denominaion in domesic versus foreign currency o faciliae deb managemen analysis; moneary and fiscal policy, which are endogenous and specified using explici forward-looking policy rules; an endogenous risk premium on public and exernal deb; and a mechanism for invoking a sudden sop in privae capial flows. The paper provides an overview of he basic srucure of he model, oulines he mehodology used o calibrae he parameers, and illusraes he key properies of he model wih reference o dynamic responses of seleced variables o shocks of ineres. JEL Classificaion Numbers: C15, C61, H6, H63 Keywords: Deb susainabiliy, dynamic analysis, Mone Carlo simulaions. Auhor s Address: dhosland@worldbank.org, pkaram@imf.org 1 This is a companion paper o a previously issued IMF Working Paper 05/6, Assessing Deb Susainabiliy in Emerging Marke Economies Using Sochasic Simulaion Mehods, by he same auhors. Doug Hosland is a Senior Economis in he Developmen Economics Vice Presidency of he World Bank; Philippe Karam is an economis a he IMF Insiue. We hank Ms. Lei Lei Myaing and Ms. Pinn Siraprapasiri for providing research assisance, and Ms. Asmahan Bedri and Ms. Yasmina Zinbi for heir ediorial help.

4 - - Conens Page I. Overview...3 II. Model Srucure...4 A. The Foreign Secor...5 B. The Domesic Secor...8 C. The Fiscal Secor...1 D. The Exernal Secor...14 III. Calibraion Mehodology...16 A. Calibraion of he Parameers...17 IV. Model Properies...0 A. The Benchmark Specificaion...0 B. Alernaive Fiscal Policy Rules...1 C. Alernaive Moneary Policy Rules... D. Foreign-Currency-Denominaed Deb... E. Endogenous Defaul Premium...3 F. Exchange Rae Response o he Exernal Deb Burden...3 V. Conclusions...3 References...3 Tables Table 1: Volailiy of Simulaed Variables...18 Figures Figure 1. Dynamic Response o Adverse Aggregae Demand Shock-Benchmark Scenario...5 Figure. Dynamic Response wih Alernaive Fiscal Policy Rules...7 Figure 3. Dynamic Response wih Less Aggressive Moneary Policy Rule...8 Figure 4. Dynamic Response wih Foreign Currency Denominaed Deb...9 Figure 5. Dynamic Response wih Endogenous Risk Premium...30

5 - 3 - I. OVERVIEW Deb susainabiliy plays a cenral role in economic policy analysis in emerging marke economies. The sandard framework used by he IMF and he World Bank o assess deb susainabiliy basically enails conducing sress ess wih reference o a baseline projecion scenario. The framework largely consiss of accouning ideniies, wih few economic (behavioral) relaionships. The sress ess are herefore difficul o inerpre from an economic perspecive. A number of recen sudies have addressed his shorcoming by applying sochasic simulaion mehods o economic models (noably, Barnhill and Kopis, 003; Garcia and Rigobon, 004, and Mendoza and Oviedo, 003). This approach generaes explici probabiliy measures ha ake ino accoun ineracion among key economic variables, which provides insigh ino he likelihood ha he deb burden will rise over he projecion period. Our companion paper (Hosland and Karam, 005) exended his line of research by invesigaing how various modeling specificaion issues affec probabiliy measures generaed using sochasic simulaion mehods. Four feaures were found o have a major influence: (1) moneary and fiscal policy; () financial fragiliy (reliance on shor-erm, foreign currency borrowing); (3) an endogenous defaul premium; and (4) sudden sops in privae capial flows. This paper documens he specificaion of a sochasic simulaion model ha incorporaes each of hese feaures. Moneary and fiscal policy have ofen been major conribuing facors o financial crises in emerging marke economies over he pas few decades and, hence, play a cenral role in our analysis. Moneary and fiscal policy are endogenous in he model, implemened using forward-looking policy rules. Our previous research (Hosland and Karam, 005) has shown how a well-designed fiscal planning sraegy can be used o help manage he risks surrounding deb susainabiliy over he medium erm. The curren paper illusraes ha he response of moneary policy o shocks also has a significan impac on public and exernal deb burdens. Moneary and fiscal policies are herefore an inegral elemen in assessing deb susainabiliy in our modeling framework. Deb managemen also plays a prominen role in our analysis. Exernal and public deb have explici mauriy srucures and include a disincion beween deb denominaed in foreign versus domesic currency, enabling one o vary he degree of financial fragiliy. In addiion, he cos of issuing (exernal and public) deb includes a defaul premium, which responds endogenously o changes in he deb burden. The inuiion here is ha lenders are concerned abou borrowers willingness o repay ; a higher deb burden is herefore perceived o increase he risk of deb defaul. The defaul premium canno rise above a hreshold level, above which deb defaul is perceived as being imminen. This invokes a sudden sop in This is documened in IMF (00 and 003). A similar framework has been adoped by he IMF and World Bank (004a and 004b) o assess deb susainabiliy in low-income counries.

6 - 4 - privae capial flows. We believe ha hese feaures play a prominen role in assessing deb susainabiliy in emerging marke economies. The macroeconomic core model consiss of a few reduced-form equaions for aggregae demand/supply dynamics and he inflaion process. Our preference for a small, aggregae model is largely driven by compuaional requiremens of sochasic simulaion mehods. In addiion, such a (reduced-form) specificaion enables us o focus on key parameers of ineres and grealy faciliaes calibraion of he model and sensiiviy analysis. Some equaions in he model are specified based on heoreical grounds. For example, he exchange rae is deermined by he uncovered ineres pariy condiion, and he erm srucure of ineres raes is modeled using he expecaions hypohesis. Expecaions are formed by combining backward- and forward-looking componens, so as o encompass purely adapive and raional (model-consisen) mechanisms as wo exremes. The parameers of he model are calibraed o mach seleced ime-series properies of he daa. This enails seing parameers o values such ha he variables simulaed by he model have variances and auocorrelaions ha correspond as close as possible o hose observed in he daa. For insance, he forward- and backward-looking componens of expecaions are combined such ha he variance and auocorrelaion of he exchange rae and ineres raes simulaed by he model mach hose observed in he daa. A fair amoun of judgmen is also added o he calibraion exercise. The nex secion of he paper describes he basic srucure of he model. Secion III discusses he calibraion of he model, secion IV illusraes some of he model s key simulaion properies, and Secion V offers conclusions. II. MODEL STRUCTURE The model has foreign and domesic secors, allowing an impac in foreign economic developmens and erms of rade o affec a (generic) domesic open economy. Real oupu and real ineres raes are decomposed ino ransiory and permanen componens. The permanen componens have a sochasic rend. The ransiory componens are inerpreed as deviaions from equilibrium levels. All variables converge o heir respecive equilibrium levels (he permanen componens) in he long run. This ensures ha he cyclical componens are saionary. The moneary and fiscal auhoriies in he model can disinguish beween he ransiory and permanen componens. Hence, here is no uncerainy abou he source or persisence of he shocks encounered. The model can be simulaed, however, such ha policymakers canno immediaely ascerain wheher observed changes o oupu and real ineres raes are ransiory or permanen. We will presen he foreign and domesic secors of he model, each in urn.

7 - 5 - A. The Foreign Secor The foreign secor of he model comprises five sochasic equaions along wih several ideniies. Aggregae Supply/Demand Dynamics The cyclical componen of foreign real oupu using he following reduced-form equaion: c yf (he foreign oupu gap ) is modeled yf = α yf + α E yf + α rf + ε f, ( F.1 ) c c c c c where rf is he cyclical componen of he foreign real cos of funds and ε f1 (0, σ f1) is a c random error erm. Oupu dynamics are deermined by an auoregressive componen yf 1 c and a forward-looking componen Eyf + 1, generaed in a model-consisen manner. Oupu (and inflaion) exhibi persisence in he model. This reflecs he view ha various fricions associaed wih price and wage seing preven produc markes from clearing insananeously. The cyclical componen of he real cos of funds is defined as a weighed average of real yields on shor- and long-erm bonds, given by: rf = υrf + (1 υ) rf, c 1c 40c 1c 40c where rf and rf represen he cyclical componens of he real yield on 1-period and 40-1c period bonds. The model is specified a he quarerly frequency so ha rf corresponds o 40c he yield on 3-monh reasury bills and rf corresponds o he real yield on 10-year discoun bonds. The Inflaion Process The foreign inflaion rae pf is deermined by simulaneous ineracion beween he reacion of he moneary auhoriy o economic developmens and he formaion of inflaion expecaions: pf = β ( yf + yf ) + β pf + β pf + β pf + εf, ( F. ) c c e ess

8 - 6 - where pf 1 is he inflaion rae in he previous quarer, pf e + 4 is he expeced inflaion rae ess over he coming year, pf is he expeced seady-sae inflaion rae, and ε f (0, σ f ) ess is a random error erm. The expeced seady-sae rae pf is deermined by he modelconsisen projecion of he inflaion rae in en years ( E pf + 40). Nominal rigidiies do no have explici micro-foundaions. The amoun of persisence underlying he inflaion process is deermined by ineracion among moneary policy, expecaions, and inrinsic facors. The parameer β capures he degree o which curren inflaion pf is influenced by pas inflaion pf 1. This capures persisence from inrinsic sources (wage conracs or menu-cos pricing), as well as backward-looking (adapive) expecaions. β3 and β 4 capure he degree o which inflaion is influenced by expeced inflaion over he coming year pf e + 4 and in he long run. The resricion β4 = (1 β β3) ensures ha inflaion converges o he arge rae pf * in seady sae, condiional on an inflaion (forecas-based) argeing rule (o be discussed laer). Inflaion expecaions are deermined by equaions of he general form: i e + i ψ ( 1 ) + j (1 ψ) j= 1 pf = i E pf + pf where E pf + j represens he model-consisen forecas of inflaion in period j. ψ combines backward-looking and forward-looking elemens of inflaion expecaions. This ness adapive expecaions (ψ = 0) and raional (model-consisen) expecaions (ψ = 1) as special cases. Ineres Raes The Fisher ideniy is used o decompose nominal ineres raes ino real and expeced inflaion componens: i i e if = rf + pf + i, i i where if and rf represen he nominal and real yield on an i-period bond, respecively, e and pf + iis he expeced inflaion rae over he coming i-periods. Real ineres raes are decomposed ino cyclical and permanen componens: rf = rf + κ + rf, i 1p i ic i ic 1p where rf is he real yield on an i-period bond, rf is he cyclical componen, and rf is he permanen componen of he real yield on a one-period bond. Real yields on bonds wih

9 - 7 - i differen mauriies differ by a consan erm premium κ, which ranges from 5 basis poins κ = 1.0. a one year ( κ = ) o 100 basis poins a en years ( ) The permanen componen of he one-period real ineres rae evolves sochasically over ime as a random walk: rf = rf + ε f, ( F.3 ) 1p 1p 1 3 whereε f (0, σ ) is a random error erm. The cyclical componen is deermined by 3 f 3 moneary policy. Moneary Policy Moneary policy is se each period using a forward-looking policy rule: 3 ( ) 1 c * c 1c rf = γ 1 E pf+ 3 pf 1 pf + γyf + γ3rf 1+ ε f4, ( F.4 ) whereγ 1 capures he moneary auhoriy s response o he expeced deviaion in he inflaion * rae over he coming year E( pf+ 3 pf 1) from he inflaion arge pf ; γ capures he response o he oupu gap; and γ 3 capures he ineres rae smoohing aspec of moneary policy, which is ofen moivaed by he need o preserve orderly financial markes by limiing ineres rae and exchange rae volailiy. 4 The random error erm ε f4 (0, σ f 4) reflecs he idea ha he moneary auhoriy canno conrol shor-erm ineres raes wih cerainy. The moneary policy rule (F.4) is a general specificaion ha encompasses a number of special cases, noably a Taylor rule and an Inflaion Forecas Based (IFB) rule. 5 Rewriing he erm 3 1c Alhough he moneary policy rule (F.4) is specified wih reference o he shor-erm real ineres rae rf, 1c one can inerpre he shor-erm nominal ineres rae if as he insrumen of moneary policy. This simply 1 1 e enails subsiuing he Fisher ideniy if = rf + pf + ino he reacion funcion (F.4). 1 4 High values of γ 3 dampen volailiy in shor-erm ineres raes, bu delays he moneary policy response o shocks. See Taylor (1999b) and Sack and Wieland (1999). 5 The firs rule is referred o as he Taylor rule, following Taylor (1993) in which a simple ineres rae reacion funcion depended on conemporaneous values for inflaion and oupu gap. A second ype of moneary rule, an IFB rule, is a more forward-looking version of he Taylor rule where a shor-erm policy rae responds o a forecas of fuure inflaion raher han he conemporaneous level of inflaion. See Svensson (003) for a criique of hese rules.

10 - 8 - * above E( pf+ 3 pf 1) pf, as ( ) * E pf+ τ pf+ τ 4 pf + τ, where ( pf ) + τ pf+ τ 4 is he year-on-year gross CPI inflaion rae τ quarers ino he fuure, (F.4) becomes he original Taylor (1993) when γ1 = γ = 0.5, and γ 3 and τ are se o zero where no ineria is allowed. By conras, when τ > 0, we refer o he rule as an IFB rule. The Term Srucure of Ineres Raes The erm srucure of ineres raes is modeled using he expecaions hypohesis: where i j i i rfi = ϕ ( 1 i) E ( rf1 + j ) + κ + ( 1 ϕ) rfi 1+ υ ε f4 + ( 1 υ ) ε f5, ( F.5 ) j= 1 E rf + is he rf i is he expeced real yield on an i-period discoun bond, ( 1 j) expeced real yield on one-period bonds j-periods in he fuure and ε f (0, σ ) and 5 f 5 4 f 4 ε f (0, σ ) are random error erms.ϕ combines forward- and backward-looking componens of expecaions (as in he case of inflaion expecaions). In he case where ϕ = 1, he expeced real yield on an i-period bond is deermined by model-consisen i forecass of fuure yields on he one-period bond plus a consan erm premium κ. In he case where 0 E rf = rf. The wo random error erms ϕ =, expecaions are saic ( ) 1+ j 1 1 ε f 4 and ε f5 enable us o calibrae he model o be consisen wih he empirical finding ha long-erm ineres raes flucuae by more han wha is prediced by he expecaions hypohesis wih raional expecaions. Noe ha he formaion of inflaion expecaions used o define real ineres raes can differ from hose used in he inflaion equaions. This enables us o consider he possibiliy ha inflaion expecaions in financial markes are more (or less) forward-looking han hose underlying he wage/price seing process. B. The Domesic Secor Aggregae Supply/Demand Dynamics The domesic secor of he model is essenially an open-economy version of he foreign secor. The cyclical componen of oupu y (he oupu gap ) is influenced by cyclical movemens in real ineres raes, he real exchange rae, he sance of fiscal policy and foreign aggregae demand condiions: 3 c c c c c = α1 1+ α + 1+ α3 + α4 τ j j + α5 + α6 + α7 + ε1 j= 0 y y E y r q yf pbal r, ( 1 )

11 - 9 - where c r is he cyclical componen of he real cos of funds, q is he real exchange rae, pbal is he primary budge balance as a percenage of GDP, r is he erms of rade ( ) c yf is he cyclical componen of he foreign oupu, px p m wih he expor and impor prices modeled below using an error correcion specificaion, and ε1 (0, σ 1) is a random error c erm. The cyclical componen of he real cos of funds r is deermined by a combinaion of shor- and long-erm ineres raes: ( 1 υ) r = υr + r, c 1c 40c 1c 40c where r and r represen he cyclical componens of he real yield on one-period and 40- period (10-year) discoun bonds, respecively. p The rend componen of oupu y (poenial oupu) evolves over ime as a random walk wih a ime-varying drif componen µ : y = µ + ε ( ) p µ =+ ε, ( 3 ) 3 where ε (0, σ ) and ε (0, σ ) are random error erms. The Inflaion Process 3 3 Inflaion is deermined in he same manner as in he foreign secor, wih he addiion of impor prices: 3 1( c c 1) e ess β β 1 β3 + 4 β4 β5 τ j j ε4 j= 0 p = y + y + p + p + p + rpm +, ( 4 ) where rpm is he relaive price of impors (he influence of his variable reflecs he open economy s saus of he domesic secor), and changes influence inflaion wih lags. ε (0, σ ) is a random error erm. 4 4 Inflaion expecaions are generaed along he same lines as in he foreign secor: i e + i ψ ( 1 ) + j (1 ψ) j= 1 p = i E p + p.

12 The expeced seady-sae inflaion rae projecion of inflaion rae in en years ( ) Ineres Raes ess p is deermined by he model-consisen E p +. Ineres raes are deermined along he same lines as in he foreign secor, wih he addiion of a ime-varying risk premium on exernal and public deb. The Fisher condiion decomposes nominal ineres raes ino real and expeced inflaion componens: 40 ( 4 )( ) i = r + E i p p. i i + i Real ineres raes are decomposed ino permanen and cyclical componens: r = r + κ + r, i 1p i ic i ic 1p where r is he real yield on an i-period bond, r is is cyclical componen, r is he i permanen componen of he real yield on one-period bonds and κ is a consan erm 1p premium. The permanen componen of he real yield on one-period bonds r differs from 1p ed is foreign counerpar rf by a ime-varying risk premium χ : r = rf + χ, 1p 1p ed Where ed denoes exernal deb and ed χ evolves over ime according o: χ = χ + a ( edeb edeb ) + b a ( pdeb pdeb ). ( 5 ) ed ss * * 1 1 On he oher hand, a ime-varying risk premium relaed o public deb pd is wrien as: χ = χ + a ( pdeb pdeb ) + b a ( edeb edeb ), ( 6 ) pd ss * * 1 where χ ss is he seady sae level of he risk premium on exernal deb; χ is he risk premium on public deb. b 1 is he porion of exernal deb issued by he public secor; and b is he porion of public deb issued abroad. The inuiion underlying equaions (5) and (6) is as follows: The risk premium on he privae secor porion of exernal deb (1 b1 ) increases ss * as he exernal deb burden rises above is iniial level: χ + a ( ) 1 edeb edeb, where a 1 represens foreign invesors subjecive percepion of he defaul risk. Similarly, he risk premium on he domesic porion of public deb (1 b ) increases as he public deb burden pd

13 * rises above is iniial level: a ( ) pdeb pdeb, where a represens domesic invesors subjecive percepion of he defaul risk. The risk premium on he foreign porion of public deb ( b 1) includes boh of he erms lised above: ss * * χ + a1( edeb edeb ) + a( pdeb pdeb ), combining domesic and foreign invesors subjecive percepion of he defaul risk. Moneary Policy The moneary policy rule in he domesic secor is he same as in he foreign secor: ( ) 1 c * c 1c r = γ 1 E p+ 3 p 1 p + γy + γ3r 1+ ε5, ( 7 ) where ε (0, σ ) is he random error erm. 5 5 The Term Srucure of Ineres Raes The erm srucure of ineres raes is modeled using he expecaions hypohesis wih consan erm premia: ( 1 ) i j i i ( 1 + ) (1 ) 1 5 (1 ) 6 ( 0 1) ri = ϕ E r j r i + κ + ϕ i + υ ε + υ ε ϕ, ( 8 ) j= 1 where i E r 1 + j is he modelconsisen forecas of he real yield on one-period bonds j-periods in he fuure, and ε5 (0, σ 5) and ε 6 (0, σ 6) are (muually independen) random error erms. These las erms are inroduced o make he model more consisen wih he empirical finding ha longerm ineres raes flucuae by more han wha is prediced by he expecaions hypohesis wih raional expecaions. r is he expeced real yield on an i-period discoun bond, ( ) The Exchange Rae The expeced change in he real exchange rae q e + 1 is deermined by: 6 6 To clarify, q represens he (log of he) price of foreign exchange (expressed in real erms) so ha an increase in q implies a real exchange rae depreciaion. The real exchange rae q equals ( s p + pf ), where p and p f are he (log of he) domesic and foreign price levels and s denoes he (log of he ) nominal exchange rae expressed as domesic currency per uni of foreign currency.

14 - 1 - where ( r 1 1 ed rf χ ) ( 1 1 ed χ ) 4 θ( * ) q = r rf + E edeb edeb, ( 9 ) e is he domesic-foreign real ineres rae differenial ha akes ino accoun a risk premium on exernal deb ed * χ, and ( Eedeb+ 1 edeb ) is he expeced deviaion in he exernal deb burden from is iniial level. Expecaions are modeled using a combinaion of backward- and forward-looking componens: = ϕ + ( 1 ϕ) ( 0 ϕ 1) q Eq q e , where Eq + 1 is he model-consisen forecas of he real exchange rae in he coming period and q 1 is he lagged value. In he case where he exernal deb burden is expeced o be a * is iniial level ( Eedeb+ 1 edeb ) e 1 1 ed pariy condiion: q+ 1 ( r rf χ ) 4 * above is iniial level ( Eedeb+ 1 edeb ) =, equaion (9) collapses o he uncovered ineres rae =. When he exernal deb burden is expeced o rise >, he real exchange rae is expeced o depreciae. The exchange rae depreciaion improves he curren accoun, reducing he deviaion in he exernal deb burden from he iniial level. This mechanism serves o limi he amoun of volailiy in he curren accoun and exernal deb burden (discussed laer in he paper). C. The Fiscal Secor Deb Service Deb service paymens are defined wih reference o he implici ineres rae on public deb i and he sock of public deb D : d d DS = i * D. In order o capure he exac relaionship beween movemens in ineres raes, he sock of deb and deb service coss, one would have o keep rack of yields on all financial asses and liabiliies held by he governmen a each poin in ime. We make a number of simplifying assumpions o reduce he compuaional burden. We absrac from ineres-earning asses held by he governmen o equae ne and gross public deb. The mauriy srucure of public deb is held consan so ha he implici ineres rae can be calculaed as a weighed average of curren and lagged ineres raes on governmen securiies wih differen mauriy daes. The weighs reflec wo facors. Firs, new deb issues are financed by bonds wih differen mauriies. Second, ineres rae paymens are made on ousanding bonds ha were issued a differen daes in he pas. We approximae he mauriy srucure by focusing on five mauriy caegories ranging from one quarer (90-day reasury bills) o 0 years. The implici ineres rae can be hen approximaed by:

15 where weighs 8 d = ω1 + ω4( 14)( ) + ω8( 18) j+ 1 j = ω0 ( 10) i j+ 1 + ω40 ( 140 ) i j+ 1, j= 1 j= 1 i i i i i i i k i represens he (when issued) yield on a k-period bond issued in period and he ω i represen he proporion of ousanding bonds of each mauriyi. The inuiion underlying he above equaion is as follows: One-period bonds maure each period so ha he implici ineres rae on one-period bonds is simply he curren shor-erm ineres rae i 1. One-quarer of he one-year bonds maure each quarer so ha he implici ineres rae is given by he average yield on one-year bonds issued in he curren period and in he previous hree quarers. Primary Fiscal Balance The primary fiscal balance, pbal, has a discreionary and a nondiscreionary componen: pbal = pbal + pbal. d c c The cyclical componen pbal moves in a counercyclical manner o capure he auomaic sabilizaion properies of various ax and spending programs: pbal c = ς y. c d The discreionary componen pbal is deermined by a fiscal policy rule. The fiscal auhoriy aims o keep he deb-o-gdp raio from rising over he medium erm in he presence of uncerainy abou fuure economic and fiscal developmens. This is implemened using a forward-looking reacion funcion: d ss where ( pbal pbal ) d ss * ( pbal pbal ) λ ( Epdeb+ 1 pdeb ) =, ( 10 ) represens he deviaion of he discreionary componen of he primary balance from is seady sae level (expressed as proporions of GDP) and * E pdeb pdeb represens he expeced deviaion of he deb-o-gdp raio from is ( + 1 ) iniial level in he coming quarer. The seady sae level of he primary balance deermined by: ss pbal is

16 pbal r g g pdeb ss ss ss ss * = ( ) (1 + ), ss ss where r and g represen he seady-sae real ineres rae and real growh rae. The fiscal policy rule (10) can be hough of as a conrol mechanism for aaining a deb arge over he long run. D. The Exernal Secor In Hosland and Karam (005), we find ha he pricing of raded goods had a significan influence on he susainabiliy of exernal deb. An exchange rae depreciaion can resul in a rapid improvemen in he rade balance in our model mainly when raded goods are priced in foreign currency. The adjusmen largely occurs hrough rade prices, no volumes. In he case where expors are priced in domesic currency, he adjusmen largely occurs hrough rade volumes. The empirical evidence indicaes ha rade volumes adjus more slowly han rade prices. This makes he rade balance respond more gradually o exchange rae changes. We illusrae he imporance of rade pricing by comparing simulaions wih expors priced in foreign versus domesic currency (Hosland and Karam, 005, Table 3, p.4, simulaions 6 and 6a, respecively). The simulaion resuls indicae ha pricing expors in domesic raher han foreign currency raises he amoun of variabiliy in he rade balance significanly. When expors are priced in domesic currency, he response of he rade balance o he exchange rae is sensiive o he rade price elasiciy. The elasiciy mus be large enough so ha an exchange rae depreciaion improves he curren accoun, oherwise he solvency condiion will be violaed. 7 To summarize, an exchange rae depreciaion affecs he rade balance hrough he following channels: rade volumes, rade prices, and consumer prices. The laer ineracs wih he role ha he moneary policy plays in allowing an impac of an exchange rae depreciaion on wages and consumer prices, where a greaer pass-hrough ono prices will induce less exernal adjusmen and greaer rade balance volailiy. Trade Volumes The dynamic adjusmens of impor and expor volumes (m and x) are specified in logarihmic form using an error correcion specificaion (recall, all lower case variables are measured in logs scaled by a facor of 100, wih he excepion of a few variables such as he ineres rae and he growh rae of GDP) : 7 This can be hough of in erms of he exended Marshall-Lerner Condiions (MLC) as in Hosland and Schembri (005).

17 ( ) m = α y + α rpm λ m β y η rpm + ε ( 11a ) 11 d 1 1 m 1 m 1 7 ( ) x = α y + α rpx λ x β yf η rpx + ε, ( 11b ) 1 d 1 x 1 m 1 8 where y d and y f are domesic and foreign income and ε 7 (0, σ 7) and ε8 (0, σ 8) are he random error erms. The variables rp m and rp x represen he relaive price of impors and expors defined by: rpm = pm pd ( 1a ) rpx = px e p f, ( 1b ) where p m is he price of impors, proxy price of impor subsiues a home, foreign counry poin of view), e is he nominal exchange rae and, p d is he price of he domesic consumpion baske a px is he price of expors (in domesic currency: a p f is he price of he foreign consumpion baske (in foreign currency). The error correcion dynamics underlying equaions (11a) and (11b) are calibraed o mach he empirical evidence which indicaes ha rade volumes respond gradually o changes in relaive prices ( m and x) Marshall-Lerner Condiion) and income ( β and β ). Trade Prices m x η η (as per he Impor and expor prices are also modeled using an error correcion specificaion o capure slow adjusmen: p = p ρ( p φ e ) ( 13a ) ess m m 1 m p = pf ρ( p φ e ), ( 13b ) ess x x 1 x ess ess where p and pf represen he domesic and foreign seady-sae inflaion rae, respecively, which are assumed o be exogenous, and ρ represens he dynamic error correcion coefficien. The parameers ( φm and φx) deermine he long-run effec of exchange rae changes on impor and expor prices. Seing ( φm = φx = 1) implies ha expors and impors are priced in foreign currency (he small open economy assumpion.) I implies ha all exchange rae movemens are ulimaely passed-hrough ino he domesic prices of raded

18 goods, or in oher words, exchange rae movemens have no effec on he erms of rade ( px p m). Seing ( φ m = 1) and ( φ x = 0) implies producer currency pricing for expors only (as is he case under he classic MLC). In his case, exchange rae changes affec impor prices (here is full exchange rae pass-hough), bu no expor prices (boh measured in erms of he domesic currency). The error correcion dynamics underlying equaions (13a) and (13b) are calibraed so ha he prices of raded goods respond gradually o exchange rae changes. The adjusmen can be hough of in erms of saggered conracs for impors and expors in which prices are fixed for he duraion of each conrac. The saggered naure of he conracs implies ha a proporion of conracs erminae in each period and he dynamic adjusmen of impor and expor prices is herefore deermined by he average conrac lengh. Empirical observaions guide us in he calibraion of he error-correcion parameer ρ such ha a cerain percenage (95%) of he adjusmen is compleed wihin a year. Consumer Prices The inflaion rae based on domesic consumpion baske p d is given by: p = (1 δ ) p + δ p, ( 14 ) d n m where δ and ( 1 δ ) represen he shares of impored goods and nonraded goods in he consumer price index. Thus, he direc effec of an exchange rae depreciaion on he inflaion rae depends on wo facors: he impac on he price of impors (he degree of exchange rae pass-hrough, φ m parameer above) and he share of impored goods in he consumpion baske (δ parameer). III. CALIBRATION METHODOLOGY The sochasic simulaion framework ness a number of feaures ha make emerging marke economies vulnerable o adverse shocks. The benchmark specificaion of he model is calibraed o mach empirical regulariies observed in advanced counries. We hen sequenially add feaures o he model (increased oupu volailiy, foreign-currencydenominaed deb, endogenous risk premium, sudden sops in capial flows, rade pricing and exchange rae adjusmen mechanism, and increased public deb burden) o show how each in urn influences deb susainabiliy. We begin by seing he implici ineres rae of deb (r) equal o he economic growh rae (g) in he benchmark specificaion (r=g=3%, and r-g=0). This resuls in a seady sae growh rae equilibrium where he rade balance and primary fiscal balance are boh zero. The advanced counry does no pay a risk premium on exernal or public deb. All of exernal and public deb is denominaed in domesic currency. Each of hese assumpions will be relaxed laer when we examine simulaions for emerging marke economies.

19 The exernal deb burden in middle-income counries (World Bank, Global Developmen Finance, GDF, daa) is se o abou 38% of GNI in 003 and 3% in 004 (esimae). Exernal deb is abou 99% of expors in 003 wih an esimae of 80% in 004. Public and publicly guaraneed deb reached $1,094 billion in 003, which is 65% of oal long-erm deb. For emerging marke economies, r = 8%, g = 4%, and (r-g) = 4% (consan risk premium). There has been a major swing in he curren accoun from a balanced posiion in 1999 o a surplus equal o 1.5% of GDP in 003, well above an average defici a 1.% of GDP over he period There is, however, a concern ha public deb burdens have risen in some emerging marke economies over he pas few years, spurred by he developmen of domesic deb markes (World Bank, 005, pp ). Our calculaions indicae ha he public deb burden in 31 emerging marke economies increased from an average level of 54% of GDP in 000 o 59% in 003, before declining slighly o 56% in In Hosland and Karam (005), we explore how he increase in public deb burdens in some emerging marke economies has affeced heir vulnerabiliy o adverse shocks. The model is calibraed such ha 38% of public deb is issued exernally (denominaed in foreign currency), while anoher 1% is issued domesically (denominaed in local currency), bu indexed o he exchange rae. 9 Term premia range from 5 basis poins for yield on a one-year bond o 100 basis poins for yield on a en-year bond, relaive o he benchmark yield on hree-monh reasury bills. In he equaion on real ineres raes, real yields on bonds wih differen mauriies differ by a i consan erm premium ( κ = 0, 0.5, 0.50, 0.75, 1 for i=1, 4, 8, 0, 40 quarers, respecively). The mauriy srucure of public deb is much shorer han ha for exernal deb, making he public deb service paymens more sensiive o ineres rae flucuaions. Mauriy srucure of exernal deb is such ha 18% of ousanding issues comes due wihin one year wih an average duraion of 10 years. Daa in Global Developmen Finance (GDF) shows he average erms of new commimens (made o privae crediors) for middle income counries equal o 10 years in 003. For public deb, 90% come due wihin one year, wih an average duraion of 10 monhs. A. Calibraion of he Parameers The calibraion approach in essence ries o avoid complicaions associaed wih esimaing equaions for emerging marke economies where he quaniy of daa is limied (consider for insance he lack of moneary policy rules and fiscal planning sraegies in place over 8 Daa compiled as per IMF, World Economic Oulook (Sepember, 005). 9 IMF (005, p. 17) esimaes ha he proporion of public deb denominaed in foreign currency has declined from 55% a end-00 o under half a end-005. This proporion varies grealy across emerging marke economies and over ime. For insance, in he case of Brazil, he proporion of domesic federal deb held by he public ha is indexed o he exchange rae declined from 3% in December 1999 o almos 4% in May 005.

20 hisorical periods) and he daa qualiy is poor. While mos sochasic simulaion models are calibraed wih reference o hisorical daa, we ake he IMF (003, p. 1) warning ino accoun which argues ha his can be a major drawback because of he lack of sufficien daa or sable ime series for many counries, and address his concern by adoping a calibraion mehodology ha is less suscepible o poor daa qualiy. Raher han relying on esimaes specific o a paricular counry, our model is calibraed o mach broad, sylized facs ha are common across a large se of emerging marke economies. 10 The parameers of he model are calibraed such ha seleced ime series properies of he variables simulaed by he model mach hose observed in he daa. The momen maching exercise is applied using a fair amoun of judgmen. For insance, he model is calibraed such ha he amoun of volailiy in inflaion is consisen wih he moneary policy rule (equaion 7). This enails making he volailiy of inflaion generaed by he model mach ha observed in he advanced counries during he low and sable inflaionary environmen ha emerged in he 1990s. To illusrae, we consider wo versions of he model: one calibraed o mach seleced sylized facs of major (G-7) advanced counries; he oher o mach seleced sylized facs of emerging marke economies. Volailiies of (seleced) simulaed variables in comparison o hisorical volailiies are repored in Table 1. Table 1: Volailiy of Simulaed Variables (Sandard deviaions) Major Advanced Counries Emerging Marke Economy Daa¹ Simulaion Daa² Simulaion GDP Inflaion Real ineres raes: shor-erm long-erm: Real exchange rae Curren accoun/gdp ¹Average across G-7 counries over he period ²Average across sample of 31 EM economies over he period The analysis can be ailored o he characerisics of individual counries, where we recalibrae he exising model for, say, counry-specific values of he public and exernal deb burdens, he mauriy srucure of public and exernal deb, he porion of exernal and public deb denominaed in foreign currency, and more. Modifying he behavioral parameers o mach he srucural characerisics of individual counries requires a closer familiariy wih he economy under consideraion, as he exercise is no mechanical. For a more deailed discussion of esimaion versus calibraion approaches o specifying macro models, see Berg, Karam, and Laxon (006) and he references herein.

21 The advanced economy version of he model generaes an inflaion process ha has a sandard deviaion of 0.55, which is somewha less han he average value (0.67) observed for he major (G-7) advanced counries over he period and significanly lower han he value (4.17) observed over he period As a consequence, he sochasic simulaion resuls should be inerpreed as being condiional on a credible inflaion argeing regime. We relax he assumpions underlying he benchmark advanced economy when we examine simulaions for emerging marke economies. Emerging marke economies exhibi higher oupu volailiy. The sandard deviaion of GDP growh in he major (G-7) advanced counries is.% over he hisorical period , compared o an average value of 4. for a sample of 31 emerging marke economies over he same period. Firs, he model is recalibraed o generae a higher amoun of volailiy in oupu o mach hese sylized facs: SD of 1.9% for advanced counry version, compared o 3.8% for EM economy version (Hosland and Karam, 005, Table, p.18, simulaion.). Real ineres raes are difficul o measure in emerging marke economies, due o daa limiaions and he effecs of hyperinflaion. In advanced economies, he shor-erm and longerm ineres raes are calibraed o mach he daa over hisorical periods. An emerging marke economy version of he model generaes more volaile real ineres raes. Real exchange raes are also much more volaile in emerging marke economies, parly due o currency crises. We calibrae he advanced economy version of model o mach daa over hisorical periods and come up shor here (7.4% versus 9.5%). A calibraed emerging marke economy version of he model generaes a more volaile real exchange rae bu canno come close o he observed hisorical daa average of 39%. The calibraion of he parameer θ in he exchange rae equaion (9) deserves special aenion because i plays an imporan role in sabilizing he exernal secor. The parameer θ is calibraed such ha he benchmark advanced-economy specificaion of he model generaes a 10% probabiliy ha he exernal deb burden increases by 9.5 percenage poins or more over a five-year period, which is equal o he average oucome for he major advanced counries over he period Finally, he volailiy of he curren accoun-o-gdp raio generaed by he benchmark specificaion of he model is comparable o ha observed in he daa for advanced economies. Again, a calibraed emerging marke economy version of he model generaes a more volaile curren accoun raio bu falls shor of maching he observed hisorical daa. We don induce mechanically a larger volailiy o mach he daa because we recognize ha imporan feaures in he deerminaion of he exchange rae and curren accoun are missing from he model in is curren specificaion. 11 Discussed in deail by Hosland and Karam (005). This calculaion uses daa on ne inernaional invesmen posiions compiled by Lane and Milesi-Ferrei (005).

22 - 0 - IV. MODEL PROPERTIES To illusrae some of he main properies of he model, we examine he dynamic response of key variables o seleced shocks of ineres. For presenaion purposes, we firs examine he properies of a benchmark model specified wih exernal deb denominaed in domesic currency, a consan defaul premium, and he exchange rae deermined by he uncovered ineres rae pariy condiion. We hen examine he following model specificaion issues sequenially: (i) alernaive fiscal policy rules; (ii) alernaive moneary policy rule; (iii) exernal deb denominaed in foreign currency; (iv) endogenous defaul premium; and (v) exchange rae response o he exernal deb burden. A. The Benchmark Specificaion We begin wih an adverse aggregae demand shock. This is implemened by reducing he error erm ε 1 in he aggregae demand equaion (1) by one percenage poin for one quarer. The dynamic responses of some of he key variables in he model are illusraed in Figure 1. The decline in aggregae demand causes inflaion o fall abou half of a percenage poin below he arge level (4%) in he firs year. The moneary auhoriy reacs o he projeced deviaion of inflaion below he arge level by reducing he shor-erm real ineres rae by almos 50 basis poins insananeously. The ransiory naure of he moneary policy response implies ha long-erm ineres raes decline by much less. The implici real ineres rae on exernal deb (measured as a weighed average of ineres raes across he erm srucure) declines by only 0 basis poins iniially. The decline in ineres raes causes he real exchange rae o depreciae iniially, reflecing he uncovered ineres rae pariy condiion. The real exchange rae converges gradually o is equilibrium level, which is unchanged from is iniial level given he ransiory naure of he shock. There is, however, a permanen effec on he nominal exchange rae. The ransiory decline in inflaion implies a lower price level. An appreciaion of he nominal exchange rae is required o in he long run o bring he real exchange rae back o is iniial (equilibrium) level. The real exchange rae depreciaion, ogeher wih he decline in aggregae demand, ac o improve he curren accoun (hrough he rade balance), which reduces he exernal deb burden over ime. Noe ha exernal deb iniially increases as a percen of GDP, because of he decline in GDP (he denominaor). Exernal deb declines, however, when aken as a percen of poenial GDP (which adjuss he denominaor for he aggregae demand shock). The overall fiscal balance (he primary budge balance less deb service paymens) improves over he medium erm. This is he resul of wo opposing forces. The decline in aggregae demand worsens he primary budge balance (by 0.13% of poenial GDP afer one year), due o he auomaic sabilizaion properies of he ax and ransfer sysem. However, his is more

23 - 1 - han offse by a decline in deb service paymens (by 0.39% of poenial GDP afer one year), due o lower ineres raes. A relaively small increase in he discreionary componen of he primary balance is required o bring he public deb burden back o is iniial level over he long erm. 1 In oher words, he fiscal auhoriy responds o he conracion in aggregae demand by reducing fiscal expendiures by a small amoun over several years. 13 This forward-looking approach o fiscal planning enables he fiscal auhoriy o srike a balance beween is deb conrol objecive ensuring ha he deb burden revers o is iniial level over he medium erm and is policy-smoohing and economic sabilizaion objecives avoiding abrup pro-cyclical changes in discreionary spending or axes. 14 B. Alernaive Fiscal Policy Rules One can gain a beer undersanding of he fiscal policy rule (10) by examining alernaive approaches o fiscal planning. We consider wo exreme approaches: a sric deb arge and a budge balance arge. Under a cyclically-adjused deb arge, he fiscal auhoriy responds o shocks by making he discreionary changes required o keep he projeced deb o GDP raio a he arge level each period. This provides a high degree of deb conrol a he expense of is policy smoohing and economic sabilizaion objecives. Under a budge balance arge, he fiscal auhoriy makes discreionary changes o keep he projeced overall budge balance o GDP raio a is arge level each period. This approach o fiscal planning accenuaes he policy smoohing and economic sabilizaion objecives, bu does no provide a feedback mechanism required o preven he deb burden from diverging from is arge over he long erm. In boh cases, arge levels are defined wih reference o he poenial level of GDP. In oher words he fiscal auhoriy adjuss he arge levels for he cyclical componen of oupu. Figure compares he responses of he model o he ransiory decline in aggregae demand under he hree alernaive fiscal planning sraegies. Under he flexible deb rule (used in he benchmark specificaion), he fiscal auhoriy reduces discreionary spending by a small amoun over several years, which gradually brings he public deb burden back o is arge level. Under he sric deb arge, an abrup cu in discreionary spending is required o preven he deb burden from rising above he arge level. The primary budge balance worsens despie he cu in discreionary spending due o he auomaic sabilizaion properies of he fiscal secor. Under he flexible deb arge, he fiscal auhoriy raises discreionary 1 The public deb burden increases even hough he overall budge balance improves. This seemingly conradicory resul is due o he effec of disinflaion on he denominaor nominal GDP. The decline in inflaion implies a lower price level, which has a greaer effec on he public deb o GDP raio han on he budge balance o GDP raio. 13 For presenaion purposes, changes in he discreionary componen of he primary balance are referred o as changes in discreionary spending. In pracice, he fiscal auhoriy may elec o make discreionary ax changes. Given ha he economic impac of changes in fiscal spending and axes are equivalen in he model, his is merely a maer of inerpreaion. 14 For a more deailed discussion of he rade-off beween fiscal policy objecives, see Hosland and Maier (001); Hemming and Perie (00); and Perry (004).

24 - - spending o offse he lower deb service coss resuling from he decline in ineres raes. The deb o GDP raio rises abou half of one percenage poin above is iniial level, where i remains hroughou he en-year projecion horizon. C. Alernaive Moneary Policy Rules To illusrae he role of moneary policy in he model, we consider a case where he moneary auhoriy responds less aggressively o flucuaions in inflaion and oupu. This enails reducing he parameers on he oupu gap and inflaion ( γ1and γ ) in moneary policy rule (7). Figure 3 compares he response of seleced variables in he model under wo parameer seings: he benchmark specificaion ( γ1 =0.5 and γ = 0.5) ; versus a less aggressive policy response ( γ1 = 0.5 and γ = 0.5). Under he less aggressive policy response, he real ineres rae iniially decreases by 5 basis poins, compared o 50 basis poins under he benchmark specificaion. Inflaion, oupu and he real ineres rae all adjus more gradually under he less aggressive policy response. A less aggressive moneary policy has relaively minor implicaions for he curren accoun and he overall budge balance, bu has imporan implicaions for he exernal burden and public deb burden. A less aggressive moneary policy response curbs he appreciaion of he real exchange rae, which leads o a smaller curren accoun response and hence, less of a decline in he exernal deb. In conras, a less aggressive moneary policy response acs o accenuae movemens in he public deb burden. These simulaions reveal ha moneary policy has an imporan influence on he exernal and public deb burden. D. Foreign-Currency-Denominaed Deb Exernal deb is denominaed in domesic currency in he benchmark specificaion. Figure 4 shows he implicaions of having exernal deb denominaed in foreign currency. 15 The exernal deb burden iniially increases due o he valuaion effec he nominal exchange rae depreciaion increases he value of exernal deb measured in domesic currency. Afer abou he firs year, however, he nominal exchange rae begins o appreciae (Figure 1). A his poin, he valuaion effec acs in he opposie direcion he nominal exchange rae appreciaion decreases he value of exernal deb measured in domesic currency. Exchange rae changes have a similar effec on he public deb burden. However, he fiscal auhoriy in he model reacs o ensure ha he public deb burden revers o he arge level over he medium erm. Denominaing public deb in domesic versus foreign currency herefore affecs he profile of discreionary spending. 15 We also specify ha half of he public deb is denominaed in foreign currency. This reflecs he fac ha a porion of he public deb is issued exernally and anoher porion issued domesically is indexed o he exchange rae.

25 - 3 - E. Endogenous Defaul Premium Figure 5 illusraes he implicaions of inroducing an endogenous defaul premium ino he model. The defaul premium amplifies he decline in he exernal deb burden. The lower deb service coss improve he curren accoun balance. There is, however, lile effec on he public deb burden. This is because of he forward-looking naure of he fiscal policy rule. The decline in he exernal deb burden reduces he defaul premium on he porion of he public deb ha is issued exernally. The lower deb service coss enable he fiscal auhoriy o increase discreionary spending permanenly wihou sacrificing is deb conrol objecive. F. Exchange Rae Response o he Exernal Deb Burden The benchmark specificaion of he model generaes excess volailiy in he exernal deb burden and he curren accoun. This calibraion issue is addressed by having he real exchange rae adjus o changes in he exernal deb burden. 16 An increase in he exernal deb burden above is iniial level leads o a real exchange rae depreciaion, which aenuaes he increase. Figure 6 illusraes he implicaions of inroducing such an exchange rae response ino he model. In he benchmark specificaion, he exernal deb o GDP raio declines from an iniial level of 3% o almos 9.5% over a en-year projecion horizon, a.5 percenage poin decline. The exchange rae response limis he decline o around one percenage poin. V. CONCLUSIONS This paper documens he specificaion of a model ha was consruced o assess deb susainabiliy in emerging marke economies using sochasic simulaion mehods. The model akes ino accoun ineracions beween key economic variables o generae probabiliy measures ha have a well-defined economic inerpreaion. This can provide imporan insighs ino he sress ess used by he IMF and he World Bank o assess deb susainabiliy in middle-income counries. In paricular, sochasic simulaion mehods provide analyss and policy makers wih quaniaive measures of risk surrounding projecions of he deb burden. Moreover, he modeling framework documened in his paper can be used o examine how various policy opions can manage he risks. For insance, he model can be used o analyze he role of deb managemen by invesigaing how issuing less shor-erm foreign currency denominaed deb affecs he probabiliy ha he deb burden rises over he projecion period. The simple reduced-form macroeconomic srucure underlying our analysis faciliaes calibraion of he model and eases he compuaional burden of sochasic simulaion mehods. We view his as he firs sage of a longer-erm research agenda on model developmen. Two avenues of research are of paricular ineres. 16 Specifically, he parameer θ in equaion (9) is calibraed such ha he amoun of variaion in he exernal deb burden generaed by he model maches ha observed in he daa for advanced counries.