STOCHASTIC APPROACH TO DEBT SUSTAINABILITY ANALYSIS APPLIED TO SERBIA

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1 Aleksandar Zdravković Universiy of Ljubljana, Faculy of Economics, Ljubljana, Slovenia STOCHASTIC APPROACH TO DEBT SUSTAINABILITY ANALYSIS APPLIED TO SERBIA ABSTRACT This paper examines he public deb susainabiliy of Serbia, based on inegraion of financial gap analysis approach and sochasic modeling and forecasing of relevan macroeconomic and fiscal variables. Wihin his analyical framework, susainabiliy is inerpreed as wheher underlying policies can be susained under plausible macroeconomic condiions wihou endangering solvency (Debrun, Celasun and Osry, 2006). Convenional deb susainabiliy analysis is conduced as a simple accouning exercise, based on deerminisic forecass of variables ha are included ino deb accumulaion equaion and arbirary scheduled bound ess. However, because deb susainabiliy is a forward-looking concep, i canno be assessed wih cerainy (Wyplosz, 2011). Sochasic approach o deb susainabiliy as an alernaive o convenional deb analysis akes ino accoun he high degree of uncerainy surrounding medium-erm deb rajecories, which canno be capured by simple bound ess as hese are limied in number (ECB, 2012). The recen research in his area (Garcia and Rigobon, 2004; Debrun e al., 2006; Kawakami and Romeu, 2011) mainly uses a Vecor Auoregression (VAR) modeling as a basic framework for economeric esimaion of he relaionships among ineres and exchange raes, inflaion and primary balance and heir forecasing and simulaion. In addiion, impulse response analysis is based on calibraed shocks obained by Cholesky decomposiion of variance-covariance marix of he regression residuals. We apply sochasic approach o Serbian monhly daa, run simulaions of deb-o- GDP raio and compare he resuls wih IMF and Serbian Governmen mid-erm projecions. Our projecions of deb-o-gdp raio in wo years ahead based on VAR approach gives he similar forecas relaive o hose given by IMF, while projecions based on AR(1) approach seem o overesimae deb-o-gdp raio wih increase of forecas horizon. Ye, our forecass srongly sugges ha projecion of Serbian governmen of deb-o-gdp raio is oo low and consequenly misleading. Keywords: deb susainabiliy assessmen, deb-o-gdp forecas, Vecor Auoregression model, sochasic simulaions, Serbia JEL classificaion: H63, H68 662

2 1. INTRODUCTION The financial crisis and subsequen recession have led o rapid deerioraion of governmen finances in many European counries, which has caused ineres raes o rise srongly in some of hem. Self-reinforcing effec on he deficis, he higher ineres raes and declines in he crediworhiness of sovereign issuers have reduced he susainabiliy of fuure deb dynamics. The escalaing yield spreads in he euro area in 2010 have underlined how suddenly hese mechanisms can cu off a sovereign borrower from he capial markes. Threa of sovereign deb crisis in curren worldwide economic circumsances clearly increases imporance of proper deb managemen and deb susainabiliy analysis. Convenional deb susainabiliy analysis is conduced as a simple accouning exercise, based on deerminisic forecass of variables ha are included ino deb accumulaion equaion and arbirary scheduled bound ess. However, because deb susainabiliy is a forward-looking concep, i canno be assessed wih cerainy (Wyplosz, 2011). Sochasic approach o deb susainabiliy as an alernaive o convenional deb analysis akes ino accoun he high degree of uncerainy surrounding medium-erm deb rajecories, which canno be capured by simple bound ess as hese are limied in number (ECB, 2012). The recen research in his area (Garcia and Rigobon, 2004; Debrun e al., 2006; Kawakami and Romeu, 2011) mainly uses a Vecor Auoregression (VAR) modeling as a basic framework for economeric esimaion of he relaionships among ineres and exchange raes, inflaion and primary balance and heir forecasing and simulaion. In addiion, impulse response analysis is based on calibraed shocks obained by Cholesky decomposiion of variance-covariance marix of he regression residuals. In his work we analyze sochasic approach o deb susainabiliy assessmen. Secion 2 is dealing wih framework of convenional deb analysis and is shorcomings. Secion 3 inroduces mehodology of sochasic approach o public deb susainabiliy and provides empirical evidence on is applicaion o forecasing of Serbian deb-o- GDP raio. 2. CONVENTIONAL APPROACH TO PUBLIC DEBT SUSTAINABILITY ANALYSIS Convenional deb susainabiliy analysis is a simple accouning exercise, based on he sandard deb accumulaion equaion (ECB, 2012): i g d = d + pb + dda 1 1+ g (2.1) where: 663

3 i g d is he ineres-growh differenial, which capures he impac of he 1 1+ g deb raio-increasing ineres rae as well as he impac of he deb raio-reducing GDP growh rae pb is he primary defici dda is he defici-deb adjusmen The defici-deb adjusmen relaes o ha par of he change in he deb-o-gdp raio which is no refleced in he defici. Probably he mos used convenional approach in pracice is IMF Deb Susainabiliy Assessmen framework (DSA). Basically, DSA mehodology imposes assessmen of deb susainabiliy as he medium-erm simulaions of he deb-o-gdp raio given specific macroeconomic forecass and fiscal policy assumpions. Wihin his analyical framework, susainabiliy is inerpreed as wheher underlying policies can be susained under plausible macroeconomic condiions wihou endangering solvency (Debrun, Celasun and Osry, 2006). IMF counry eams impose rouinely his framework and publish he resuls as he par of repor on Aricle IV Consulaions 3. According o he DSA, change in public deb could be decomposed ino he regular par, comprised of idenified deb-creaing flows and irregular, comprised of unidenified residuals and change of asse. Idenified par is furher decomposed o auomaic deb dynamics, i.e. conribuion of ineres rae, real GDP growh and change of exchange rae, hen primary balance conribuion and oher idenified flows, manly privaizaion receips and recogniion of coningen liabiliies. Decomposiion of public deb, according o his mehodology allows sensiiviy analysis of public deb under differen scenarios of economic policies and macroeconomic developmen and sress esing of deb dynamic assuming some arbirary marke or fiscal shocks (so-called bound ess), as i is shown in Figure 1. 3 The IMF consuls annually wih each member governmen. Through hese conacs, known as Aricle IV Consulaions, he IMF aemps o assess each counry s economic healh and o foresall fuure financial problems. 664

4 Figure 1: Example of bound ess of Serbian governmen deb according o IMF DSA mehodology Source: IMF Counry Repor No. 11/311 (2011) However, use of such convenional approach like DSA suffers from several shorcomings: i neglecs counry-specific correlaion beween main drivers of public deb and does no include hese correlaion paerns in forecasing (deerminisic scenarios do no consider he effecs of correlaion); i neglecs counry specific shocks ha affec he public deb drivers and does no use hem o produce simulaions; insead, i applies arbirary selecion of shocks ha migh no be suppored by empirical facs a all; i produces single poin forecas insead of giving disribuion of possible forecasing oucomes. Consequenly, hese shorcomings could reflec in poor forecasing power of convenional deb analysis, as i is illusraed in case of Serbia, based on five IMF counry repors, where DSA forecas of he deb-o-gdp (gross governmen deb) underesimaes acual values for more han 8% on average. 665

5 Table 1: Comparison of DSA baseline projecions and acual values of deb-o GDP for Serbia Reporing year February May April July Ocober Acual Values Forecas errors Projecions of deb-o-gdp in % Average Average Source: IMF counry repors for Serbia and IMF World Oulook daabase 3. STOCHASTIC APPROACH TO PUBLIC DEBT SUSTAINABILITY ANALYSIS Applicaion of sochasic approach o public deb susainabiliy as a specific issue of cos-risk analysis of public deb emerged around 2003, rigged by he one of he shorcomings of radiional fiscal susainabiliy analysis which ofen does no ake ino accoun he effecs of uncerainy (Burnside, 2004). In regard o he exising lieraure, sochasic approach o deb susainabiliy is mainly based on numerical approach and uses he common risk managemen ools (sochasic simulaions, scenario analysis, sress esing); i is primarily subjeced o sress esing and sensiiviy analysis of public deb dynamics under he differen scenarios of governmen economic policy or possible exogenous shocks. Ferruci and Penalver (2003) and Garcia and Rigobon (2004) works became he basis for he mos persisen line in furher research as hey inroduced sochasic modeling o he convenional Deb Susainabiliy Assessmen framework. Relaed work in his field also includes Debrun, Celasun and Osry (2006), Penalver and Thwaies (2005), Tanner and Samake (2006), Di Bella (2008), Gray e al. (2008), Giovanni and Gardner (2008) and Kawakami and Romeu (2011) Mehodology Saring poin of he mehodology is deb accumulaion equaion which operaes wih real variables, under addiional assumpion ha real ineres rae on domesic and 666

6 foreign deb is he same. Thus, deb accumulaion equaion in relaive erms could be simply rewrien as: d = (1 + r g ) d + pb, (3.1) 1 where d is raio of real 4 public deb o real GDP and pb is real primary defici o real GDP, while r and g now represen real ineres rae and real growh of GDP. In addiion, as he lef and righ side of his equaion in pracice would never be equal due o deb-defici adjusmens, equaion 3.1 could be furher exended wih new erm which represens public deb skeleons, or simply said deb shocks, denoed as s. d = (1 + r g ) d + pb + s. (3.2) 1 I has o be emphasized ha wihin he sochasic framework all variables in equaion 3.2 apar from public deb are considered o be sochasic by naure and herefore hey represen he possible sources of riskiness of public deb unexpeced changes. We considered o approaches in sochasic modeling of risk variables, one based on Vecor Auoregression (VAR) esimaion and one based on univariae auoregression (AR) esimaion VAR approach In his work we exended ou previous research (Zdravkovic, Bradic-Marinovic, 2012) based on Garcia and Rigobon (2004) wih approach of Debrun, Celasun and Osry (2006). Inflaion rae π and real exchange rae depreciaion e are added as he addiional risk facors ou of equaion 3.2. By aking ino he consideraion ha all of hese risk variables are mos probably correlaed o cerain degree, we could assume ha hey follow mulinomial normal disribuion wih condiional mean μ and condiional variance-covariance marix { r, g, e,, pb, s } N (, ) Σ π μ Σ. Under he assumpion of join disribuion, dynamic of hese variables could be modeled by he sandard reduced-form VAR models. In his case, VAR model in vecor erms is given as: p { π } x = c+ Ax +, = r,,,,, i 1 g e pb s = i -i v x (3.3) 4 Terms real deb and primary balance here denoe inflaion-free value of deb and primary balance. 667

7 where { } i (, ) v N 0 Σ, v A are marices of lag coefficiens up o p lags and Σ v is variancecovariance marix of reduced-form residuals. However, as he reduced-form residuals are linear combinaion of srucural shocks, hey are no suiable o perform impulse response analysis of innovaions in risk variables dynamic which requires srucural VAR models. Of course, he main problem wih srucural VAR models is idenificaion of he model. As we do no impose some specific heory abou he conemporaneous relaions srucure, we use recursive ordering approach by arbirary proposed exogeneiy of variables and se simple AB specificaion of srucural VAR model: Av = Bu, (3.4) where A is he marix defining conemporaneous relaions, u represen srucural shocks and B is he marix of srucural form parameers. Srucural model is idenified wih orhogonalizaion of reduced-form residuals o obain marix B by Cholesky decomposiion (Sims, 1981), Σv = BB', while marix A is assumed o be ideniy marix. As marix B is upper riangular marix, he las variable will be he mos exogenous and hus is innovaion will have conemporaneous effecs on all variables, while innovaion in he firs variable will affec only iself. Afer he esimaion, model's parameers can be used for deerminisic projecion of muual pah of all risk variables using he las known values of risk variables. In addiion, using he variance-covariance marix of esimaed residuals i is possible o produce Mone Carlo simulaions in order o obain full sochasic forecas of hese variables wih simulaed disribuion of heir probabiliies. Forecased values of relevan variables are plugged in deb accumulaion equaion in order o produce forecas of possible public deb pahs. Thus, mehodology described could be summarized in he following seps. Based on hisorical daa, parameers of reduced-form VAR(2) model 5 are esimaed p x = c+ Ax +, = 1 { r, g, e, π, pb, s i= i -i v x } ; Marix B, which represens mahemaically how combinaion of all (srucural) shocks of risk variables u affecs paricular values of risk variables, is esimaed; Based on esimaed coefficiens from hisorical daa, values of risk variables are forecased k periods ahead, which is acually baseline (and deerminisic) forecas p x+ k = c+ Ax, 1 k { r, g, e, π, pb, s i= i + -i x = } ; (3.5) 5 Order of lag is resriced o 2 due o he limied number of observaions in daa sample and large number of parameers for esimaion 668

8 Based on esimaed values of marix B, simulaions of reduced-form shocks (linear combinaion of srucural shocks) are generaed by running he simulaions of srucural shocks randomized from sandardized normal disribuion, v + k = Bu + k, u N(0,1) ; (3.6) Simulaions of risk variables are produced by adding he simulaed reduced-form shocks v + k o deerminisic projecions of x + k ; Simulaed forecass of risk variables are plugged ino deb accumulaion equaion o simulae deb-o-gdp raio pahs AR(1) approach Our AR(1) approach o sochasic modeling is loosely relaed o Bergsrom e al. (2002) work, which is primarily concerned wih Cos a Risk modeling of public deb. Their model consiss of wo building blocks, macroeconomic model based on AR(1) modeling of risk variables and sraegies simulaion par. Mehodology of AR(1) simulaions is described by he following seps. I is assumed ha each risk facor follows a univariae AR(1) process of he form: 2 x = α + ρx + ε, ε IIDN 0, σ (3.7) 1 ( ) Based on hisorical daa, he parameers of AR(1) process are esimaed for each of he risk facors and esimae processes, as well as he error erms, using ordinary leas squares or maximum likelihood esimaor. x = α /1 ρ and he (uncondiional) variance of he error Mean of each series ( ) 2 erms, σ = Var ( ε ) are calculaed Differen pahs for x are simulaed using he following dynamics implied by he AR(1) process: x + = ( 1 ρ)( x x) + σ * e + (3.8) where is he ime sep in he simulaion, while e + is a random variable drawn from he sandard normal disribuion. Finally, we plugged simulaions of risk variables ino deb accumulaion equaion in order o produce sochasic simulaions of deb pahs Daa In regard o he poliical and economic changes ha Serbia has passed during he recen decades, consisen series of monhly daa do no exis for longer periods; herefore implemenaion of proposed mehodology requires use of daa wih higher frequency for he empirical esimaion of he model. We use he annualized monhly daa o provide sufficien daa se regarding he possible large number of parameers o be 669

9 esimaed by VAR model. This limis scope of daa o period January 2008 Sepember 2012, for which exiss consisen monhly daa series of public deb and primary balance in nominal values. I is also imporan o emphasize ha public deb in his analysis comprise only he deb of cenral governmen. Addiional problem o analysis is lack of monhly daa on GDP, which is measured only on quarerly basis. In order o end up wih approximaed monhly daa on GDP, we use mehodology of Zaman and Markovic (2011) based on quarerly real GDP values weighed by weighs obained from index of indusrial producion, which is usually highly correlaed wih GDP dynamic. We used daa on chain-linked values of GDP (in 2005 relaive prices) as real GDP measure, as i is usual in saisical offices. Furher, in order o obain real values of public deb and primary balances, we used CPI base index as denominaor. Daa for public deb, primary balance and GDP are annualized as he rolling sum of monhly daa for previous welve monhs. As he Serbian public deb porfolio is composed from loans and securiies which very differ in mauriies and currencies, we have o use some approximaions of ineres raes and exchange rae depreciaion o mee he parsimonious daa requiremens of he model. Hence, we use he daa on weighed average ineres rae on governmen deb insrumens which are provided by Naional Bank of Serbia as an approximaion of aggregae ineres rae. Real ineres rae is obained as a difference beween nominal ineres raes and inflaion raes. Aggregae exchange rae is approximaed wih EUR/RSD exchange rae, in regard o currency srucure of deb porfolio were euro-indexed deb dominaes, as well as srong correlaion beween EUR/RSD and exchange raes of oher insrumens indexed in foreign currency (mosly USD and CHF). Real depreciaion is calculaed as a difference beween nominal depreciaion and inflaion rae. Deb shocks are calculaed based on equaion 3.2, as a difference beween righ and lef side of he equaion Resuls A firs, we esimaed VAR model for he period January 2008 Sepember The esimaion of he VAR parameers is of lile ineres and no shown here, insead he marix B is presened in order o give insigh how srucural shocks in one risk variable influence oher variables (posiively or negaively). 670

10 Table 2: Marix B of esimaed VAR model Real ineres rae Real GDP growh Primary defici Deb shocks Real exchange rae dep. Inflaion rae Real ineres rae Real GDP growh Primary defici Deb shocks Real exchange rae dep. Inflaion rae Source: auhor s calculaions Following char presen he dispersion of simulaed deb pahs over forecasing ime (Ocober 2012 December 2014), based on 1000 simulaions: Figure 2: Simulaed deb-o-gdp pahs, VAR approach Source: auhor s calculaions This char demonsraes imporan advanage of sochasic approach in regard o convenional approach; insead of single poin forecas of deb-o-gdp raio over ime, sochasic approach provides a range of possible deb-o-gdp raios wih assigned probabiliies of heir realizaion a any poin in ime. Following char gives he range of possible values of deb-o-gdp raio in June 2014 wih probabiliy disribuion of heir realizaion: 671

11 Figure 3: Probabiliy disribuion of forecased deb-o-gdp raio in June 2014 Source: auhor s calculaions In addiion, a any poin in ime i is possible o calculae probabiliy ha deb-o-gdp will exceed some hreshold value. For example, if hreshold value of deb-o-gdp raio is se o 70%, by dividing number of simulaions exceeding 70% wih oal number of simulaions we end up wih probabiliy of 12.4% ha deb-o-gdp will exceed 70%. This calculaion could be done also in reverse manner - i is possible o deermine criical value of deb-o-gdp ha will be no exceeded for given probabiliy, e.g. for probabiliy level of 95%, criical value is 70.73%. I means ha here is 95% chance ha deb-o-gdp will no exceed value of 70.73%. We also apply AR(1) approach as a benchmark and run separae regression o esimae parameers of he AR(1) process for real ineres rae, GDP real growh and primary defici. Following char presen he dispersion of simulaed deb pahs over forecasing ime (Ocober 2012 December 2014), based on 1000 simulaions: 672

12 Figure 4 Simulaed deb-o-gdp pahs, AR(1) approach Source: auhor s calculaions Evenually, we compare four differen ypes of projecion: wo obained by convenional deb susainabiliy analysis (IMF recen projecion and official projecion of Serbian Governmen) 6 and wo obained by sochasic approach o deb susainabiliy analysis ha we applied in his paper: Table 3: Comparison of deb-o-gdp forecas VAR 61.27% 66.02% AR(1) 61.43% 69.86% IMF 64.68% 66.53% Serbian Governmen 60.60% 53.30% Source: auhor s calculaions, IMF World Oulook Daabase, Sraegy of Serbian Public Den Managemen (2012) Annual projecions of deb-o-gdp for VAR and AR(1) approach are obained by averaging simulaions for given year. Our projecions of deb-o-gdp raio in wo years ahead based on VAR approach gives he similar forecas relaive o hose given by IMF, while projecions based on AR(1) approach seem o overesimae deb-o-gdp raio wih increase of forecas horizon. Ye, our forecass srongly sugges ha projecion of Serbian governmen of deb-o-gdp raio is oo low and consequenly misleading. 6 IMF projecion is relaed o level of gross governmen deb, hus i is no direcly comparable o our projecions which are relaed o deb of cenral governmen. However, hisorical daa shows ha cenral governmen deb paricipaes wih more han 95% in gross deb. Also, projecion of Serbian Governmen is approximaion of cenral governmen deb obained by reducing gross governmen deb for deb of lower level of governmen. 673

13 4. CONCLUSIONS There were several advances in recen years oward he improvemens of he key shorcomings of convenional deb susainabiliy analysis, mainly lack of sochasic ools in applicaion and lack of counry specific calibraion of shocks. In his work we analyze sochasic approach o deb susainabiliy assessmen. Two approaches are proposed, firs one based on muual modelling of risk variables using he VAR esimaion and second one based on separae esimaion of auoregression process for each risk variable enering he deb accumulaion equaion. We apply sochasic approach o Serbian monhly daa, run simulaions of deb-o-gdp raio and compare he resuls wih IMF and Serbian Governmen mid-erm projecions. Our projecions of deb-o-gdp raio in wo years ahead based on VAR approach gives he similar forecas relaive o hose given by IMF, while projecion based on AR(1) approach seems o overesimae deb-o-gdp raio wih increase of forecas horizon. Ye, our forecass srongly sugges ha projecion of Serbian governmen of deb-o- GDP raio is oo low and consequenly misleading in making policy decisions. Unforunaely, due o daa unavailabiliy for he longer period of ime, i is no possible o conduc serious ou-of-sample analysis. Use of such parsimonious model for deb susainabiliy analysis like he one proposed in his research has is obvious advanages: lower daa requiremens (in sense of number of variables enering he model), ease of applicaion, endogenous forecasing and capuring of counry specific facors. Furhermore, we poin imporan advanage of sochasic approach in regard o convenional approach; insead of single poin forecas of deb-o-gdp raio over ime, sochasic approach provides a range of possible deb-o-gdp raios wih assigned probabiliies of heir realizaion a any poin in ime. In addiion, applicaion of sochasic approach allows calculaing probabiliy ha deb-o-gdp will exceed some hreshold value. REFERENCES Debrun, X., Celasun O. and Osry, J. (2006). Primary surplus behavior and risks o fiscal susainabiliy in emerging marke counries: a "fan-char" approach, IMF Working Papers 06/67 Di Bella, G. (2008). A sochasic framework for public deb susainabiliy analysis. IMF Working Paper Series European Cenral Bank. (2012). Analysing governmen deb susainabiliy in he euro area. Monhly Bullein April 2012 Ferrucci, G. and Penalver, A. (2003). Assessing sovereign deb under uncerainy. Financial Sabiliy Review. 15, , Bank of England. Gapen a al. (2008). Measuring and analyzing sovereign risk wih coningen claims. IMF Saff Papers 55 Garcia, M. and Rigobon R. (2004). A risk managemen approach o emerging marke s sovereign deb susainabiliy wih an applicaion o Brazilian daa, NBER Working Papers Series Giovanni, J. and Gardner, E. (2008). A simple sochasic approach o deb susainabiliy applied o Lebanon. IMF Working Paper Series 674

14 Hosland, D. and Karam, P. (2006). Assessing deb susainabiliy in emerging marke economies using sochasic simulaion mehods. IMF Working Papers Series Inernaional Moneary Fund. Counry repors for Serbia Kawakami, K. and and Romeu, R. (2011). Idenifying fiscal policy ransmission in sochasic deb forecass, IMF Working Paper Series Penalver A. and Thwaies, G. (2005). Fiscal rules for deb susainabiliy in emerging markes: he impac of volailiy and defaul risk. Bank of England Working Paper no. 307 Sims, C. (1980). Macroeconomics and realiy, Economerica 48,1 48. Tanner E. and Samake, I. (2006). Probabilisic susainabiliy of public deb: a vecor auoregression approach for Brazil, Mexico, and Turkey. IMF Working Paper WP/06/295 Wyplosz, C. (2011). Deb susainabiliy assessmen: mission impossible. Review of Economics and Insiuions, Universià di Perugia, Diparimeno Economia, Finanza e Saisica, vol. 2(3). Zdravkovic, A. and Bradic-Marinovc, A. (2012). Public deb susainabiliy in Wesern Balkan counries. European inegraion process in Wesern Balkan counries. Universiy of Coimbra. 675