Estimation of the Behavioral Equilibrium Real Exchange Rate of the Czech Koruna

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1 Esimaion of he Behavioral Equilibrium Real Exchange Rae of he Czech Koruna Absrac Ví Poša Purpose of he aricle The paper examines he behavior of he real exchange rae in he Czech Republic. I focuses on he analysis of is driving forces wih he emphasis on he urbulences which have been laely seen in he financial and real secor of he economy. Mehodology/mehods Real equilibrium exchange rae can be esimaed using various approaches ranging from purely saisical o fully srucural models. In his paper i is esimaed using he BEER mehodology, i.e. behavioral equilibrium exchange rae. The BEER approach as applied here ress on building vecor error correcion models which relae he behavior of he acual real exchange rae o various economic fundamenals from boh he real and financial secor of he economy. Scienific aim The esimaed behavioral equilibrium exchange rae serves as a benchmark o which he acual behavior of real exchange rae is compared. The paper also poins o various problems ha are faced when esimaing he real equilibrium exchange rae in a posransiive economy. Findings Three varians of he model, which differ in he respecive fundamenal variables inluded in he esimaion, are esimaed in he paper. The gap beween he esimaed real equilibrium exchange rae and real exchange rae as well as he key deerminans of he real equilibrium exchange rae are analyzed and compared. The models show ha he misalignmen beween he real exchange rae and fundamenals have narrowed in he recession and pos recession period. The key drivers of he real equilibrium exchange rae are he produciviy differenial, real ineres rae differenial and ne foreign asses. Conclusions (limis, implicaions ec) The relaively shor ime series for he Czech economy, especially for some of he variables, do no enable o make reliable esimaion of models which would include all of he variables discussed in his paper. This paper is a par of a research projec financed by IGA Universiy of Economics, Prague Keywords: BEER, equilibrium real exchange rae, produciviy differenial, real exchange rae, VEC JEL Classificaion: E44, F3, F37 48

2 Inroducion The world economy has been going hrough severe urbulences over he las few years and so have he pos-ransiive economies of he Middle and Easern Europe. The behavior of real exchange rae can bear some impornan informaion on he sae of he economy; in he curren conex i is especially he informaion wheher or no i has gone off is rails. There is a vas amoun of boh purely heoreical and empirical lieraure focused on he analysis and esimaion of some equilibrium value of exchange rae. Rogoff (996) and Taylor and Taylor (2004) presen an overview of he behavior of exchange rae especially wih respec o purchasing power pariy condiion where hey also hin a he Balassa-Samuelson effec which is pu o use in some of he models for he esimaion of real equlibrium exchange rae as i is shown furher on. Dornbusch (989) and Sarno (2002), among ohers, pain a broader picure of heoreical approaches aken o exchange rae modelling, he laer covering dynamic ineremporal models. However, he approaches presened in hose papers deal radiionally wih he modelling and analysis of nominal exchange raes. The analysis of real exchange rae and, especially, he esimaion of real equilibrium exchange rae have gained populariy since he 90 s. Driver and Wesaway (2004) give a full axanomy of he various real equilibrium exchange rae models. The fac is ha he mos frequen modelling sraegies include behavioral equilibrium exchange rae (BEER), fundamenal equilibrium exchange rae (FEER), Smidkova (998) presens one of he earlies esimaes of real equilibrium exchange raes in a pos-ransiive economy using his modelling sraegy, and naural real exchange rae (NA- TREX). Eger and Halpern (2005) give an exhausive accoun of he respecive modelling sraegies and discuss heir implemenaion in deail. This paper explois he BEER approach o modelling he real equilibrium exchange rae. This approach has one clear seback which is ha i is no a srucural model which would be expliciely buil on derived relaionships among he included variables, le alone microfundaions as do he modern ineremporal models. The NATREX approach, see Sein (200) and Belloc (2007) for he speacial reamen of he res of he world par of he model, is he one wih clear srucural feaures, however, i is ofen esimaed in reduced form using vecor auoregression mehods which wipes ou almos all he posiive feaures of he srucural approach. Deken (200) comes up wih a mixure of srucural and VAR approaches. On he oher hand, he BEER approach has one advanage over he oher wo modelling sraegies: i is he leas sensiive o shorer ime series which is a fac ha mus be aken ino accoun considering he economy which will be used in he anlysis. Komárek and Melecký (2005) presen a BEER esimae of he equilibrium exchange rae for he Czech economy. The esimaion of real equilibrium exchange rae serves wo basic purposes regarding he case of pos-ransiive economies and curren sae of he world economy. Firs, i can deec possible fundamenal misalignmens wihin he economy and second i can be used o analyse he process of nominal convergence. The paper is divided ino five pars. The firs par presens some basic facs on nominal convergence in he Czech Republic. The second par gives he sandard derivaion of he BEER approach and presens some examples of is usage. The hird par describes he daa used for he esimaion and he fourh par presens boh he esimaes of he behavioral exchange rae and also heir analysis. The final par concludes. Some sylized facs The Czech Republic enered he EU in 2004 and ranks among he mos prosperous counries in he region of he Middle and Easern Europe. This is also refleced by real convergence of he economy. In 200 GDP per capia in Purchasing Power Sandards (EU-27 = 00) reached 70,2 while in 2008 i amouned o 80,4. Figure presens quarerly changes in real exchange rae (RER) of he Czech Koruna o euro (amoun of domesic currency per uni of euro) ogeher wih he conribuions of nominal exchange rae, domesic price level and foreign (eurozone) price level. The average quarerly change from 200 o he fourh quarer of 2009 in RER is negaive: - 0,87 %, ha is, i appreciaed on average. The key conribuion comes from he change in nominal exchange rae: - 0,84 per- 49

3 cenage poin. The conribuion of domesic price level is also negaive while he conribuion of eurozone price level is posiive. One can readily observe ha he conribuions of price levels almos cancel hemselves ou. There was a srong real appreciaion beween he hird quarer of 2007 and he hird quarer of 2008 followed by a sharp real depreciaion in he las quarer of 2008 and he firs quarer of The srong appreciaion was boosed by nominal appreciaion and rapidly increasing domesic price level while he sharp real depreciaion was driven by he behavior of nominal exchange rae. where IR denoes ineres rae, S denoes spo exchange rae, E denoes he expecaion operaor and superscrips D and F refer o domesic and foreign, respecively. Taking logarihms of boh sides of (), he condiion may be expressed in more familiar erms: D F E ( s+ s ) = IR IR, (2) which means ha he expeced change in he spo exchange rae equals he ineres rae differenial. Subsracing inflaion differenial from boh sides of (2): 2 The BEER Following MacDonald (997), he BEER approach may be derived as follows. The model buils on he uncovered ineres rae pariy condiion, which saes ha he reurn on domesic asses mus equal he expeced reurn on foreign asses measured in he unis of domesic currency: D S+ F + IR = E ( + IR ) S, () D F D F D F ( s s ) E ( π π ) = IR IR E ( π π ) E where π refers o inflaion rae, one obains: RER D F ( RER ) ( R R ), (3) = E +, (4) where RER denoes real exchange rae and R refers o real ineres rae. Wihin he BEER approach he expecaion of real exchange rae is considered o be he real equilibrium exchange rae which depends upon he fundamenals. Thus i can be 50

4 concluded ha real exchange rae depends on real equilibrium exchange rae (REER) and real ineres rae differenial: RER = REER D F ( R R ). (5) The key quesion is: which fundamenals should be considered as deerminans of he real equilibrium exchange rae? There is no single way o approach his ask and he acual models differ in his respec. Clark (2000) considers jus wo deerminans of he real equilibrium exchange rae: he relaive price of raded and nonraded goods which should, according o Balassa-Samuelson hypohesis, be an imporan facor especially in he cases of converging economies and ne foreign asses which are considered as a general measure of he economy s risk higher ne foreign deb means ha invesors require higher reurns which can be achieved, given he ineres rae differenial, hrough depreciaion. However, he role of ne foreign asses is ambiguous. Firs, as Eger and Halpern (2005) poin ou he effec may be quie he opposie in ransiive economies. The reason is ha, especially ransiive economies, which suffer from low sock of domesic savings, may have a negaive argeed sock of ne foreign asses. While hey converge oward ha level, he addiional inflows of foreign direc invesmen, which ypically finances he negaive foreign asses, end o appreciae he real exchange rae. When he sock ges beyond he opimal (negaive) level of ne foreign asses, addiional curren accoun deficis will depreciae he real exchange rae. Second, Rogoff (996) saes ha he supposed correlaion beween ne foreign asses and real exchange rae ends o be deeced a he lags beween 5 0 years. However, he ime series for he ransiive economies may be oo shor o reveal such relaionship when he mehod used does no esimae ime-varying coefficiens. As a resul, an appreciaing affec of larger negaive sock of ne foreign asses should no come as a surprise. According o Balassa-Samuelson hypohesis he increase in domesic produciviy should appreciae he real exchange rae as well as he rise of ne foreign asses. The increase in real ineres rae differenial should depreciae he real exchange rae. MacDonald (997) uses a broader se of deerminans of he real equilibrium exchange rae. Beside he facors jus menioned, many oher deerminans are included. He inroduces he role of governmen spending in he sense ha a larger share of governmen spending in oal spending may induce faser increase in nonradable prices as governmen spending is ofen channelled ino his secor. This may amplify he role of privae secor in a growing economy when he income elasiciy of demand for nonradable goods exceeds one. Besides ne foreign asses he also includes oher measures of balances, namely: fiscal balance and personal savings. Higher fiscal surplus and personal savings should appreciae he real exchange rae. He also adds an imporan deerminan of erms of rade for small open economies, which is he real price of oil. Considering an imporing economy, an increase in real price of oil should depreciae he real exchange rae. Maeso e al (200) consider a broader inerpreaion of governmen spending as hey realize ha in longer erm higher governmen spending may be accompanied by various disoring effecs pushing down he economic growh and leading o depreciaion. In his paper I consider a basic model which consiss of only produciviy, ne foreign asses and he real ineres rae differenial. This model is furher exended by including he effec of real price of oil, governmen spending and governmen deb. The esimaion procedure ress on using vecor error correcion models. Shor inroducion is presened below. The principle of coinegraion lies in he fac ha a saionary linear combinaion of nonsaionary series may exis, which is perceived as a long-run equilibrium owards which he dependen vecor of series ends o reurn. A necessary condiion for using coinegraion echnique is ha he analyzed series have o be inegraed of he same order. I is herefore necessary o es for he uni roo in he levels of he series and check wheher he same order of differencing saionarizes hem. Several ess o check for uni roo behavior have been developed. I is imporan o noe ha esing he uni roo behavior ress even in he simples approaches on several choices: i has o be decided wheher a consan 5

5 or linear rend will be included or boh and he lag of he regressor mus be chosen. Also, he problem of low power of uni roo ess is repored in he exchange rae lieraure, for example in Rogoff (996). In his paper augmened Dickey Fuller (ADF) es is used. The following regression is run o check for uni roo behavior: y = α y x + δ + β y + β y β y + ε 2 2 p p,(6) where y is he examined series, x represens he exogenous facors (consan, linear rend or nohing). The null hypohesis of uni roo and he alernaive one are saed as follows: H H 0 : α = 0 : α < 0. If he series mee he condiion of being inegraed of he same order, he coinagraion es may be run o check for long-run relaionships among he series. In his paper Johansen approach oward coinagraion analysis is used. Firs VAR model is se up for each problem: y + = A y A py p + c ε, (7) where y is he vecor of endogenous variables, A is a marix of coefficiens, c is a vecor of consans and ε is a vecor of innovaions. An imporan ask is how o se he lag order of VAR model. A number of informaion crieria may be used, however, as noed in Lukepohl (2007) when he ou-of-sample forecasing is no he prime goal of he model, a direc aenion should be urned o he behavior of residuals. The lag should be chosen so ha residuals do no display serial correlaion or remaining heeroskedasiciy a an accepable saisical level of significance and follow normal disribuion. This is a common pracice when using coinegraion in economic papers focused on exchange raes, for example Hwang (200) or Bjorland (2006) and will be adoped in his paper as well. The lag chosen amouns up o 3 in case of monhly daa in hese papers. Two widespread ess are used: pormoneau auocorrelaion es which is based on Ljung-Box Q-saisic and Breusch-Godfrey (LM) es. When he number of lags a which he residuals are esed is relaively small, Breusch-Godfrey es is preferrable, see Lukepohl (2007). Afer a VAR model is se up, he vecor of endogenous variables may be checked for presence of coinegraion. Two saisic crieria were used o es he presence and number of coinegraing vecors: LR race = T LR k i= r+ log ( λ ) ( λ ) λ max = T log r+, where T is he number of observaions, λi is he i-h larges eigenvalue of marix Π (furher below) and k is he number of endogenous variables. The firs saisic ess he null of r coinegraing vecors agains an alernaive of he number of coinegraing vecors being equal he number of endogenous variables. The second saisic ess he null of r coinegraing vecors agains an alernaive of r+ coinegraing vecors. Wih he known number of coinegraing vecors, a vecor error corecion model is se up: p Γ i y i + Πy i= y = + c + ε,(8) where Γ Π í = p = i= p j= i+ A j, i A i I. The Π marix may be divided ino wo marices: α and β so ha Π = α* β. Each column of marix β represens one coinegraion vecor while he coefficiens of marix α represen he adjusmen coefficiens (how fas he sysem moves oward equilibrium wih respec o he paricular variables). 3 Daa Daa were drawn from eurosa daabase. The variables menioned above are defined as follows. The real exchange rae is based on nominal exchange rae expressed as number of unis of he Koruna per one uni of foreign currency (euro). The nominal exchange rae is hen muliplied by a raio of foreign (eurozone) and domesic price level., 52

6 The real ineres rae differenial (DIFF) was consruced by deducing he inflaion differenial based on average inflaion raes from nominal ineres rae differenials beween he Czech economy and eurozone based on bond yields which are used as convergence crierion. The Balassa-Samuelson effec (PROD) was expressed as he raio of he price level measured by CPI o he price level measured by PPI and his raio was furher relaed o he corresponding raio for eurozone. This approach was applied in mos of he papers menioned above. The real price of oil (OIL) was obained by convering he price of Bren oil measured in euro ino he Koruna and deflaing i by PPI. Daa on curren accoun deficis and nominal GDP were rerieved from he daabase. Ne foreign asses are compued cumulaing curren accoun deficis. The share of ne foreign asses in nominal GDP was compued and he raio of he share of he Czech economy o he share of eurozone was calculaed. This serves as a measure of ne foreign asses (NFA). For he upcoming par of he paper i should be noed ha ne foreign asses are negaive hroughou he sample for he Czech economy and eurozone. This means ha increase in he raio represens a relaively higher foreign indebness of he Czech economy. The same approach was aken in he case of he variable of governmen spending (GOV). The share of governmen spending in nominal GDP was compued and a raio of he share for he Czech economy o he one of eurozone was expressed. The shares of oal deb in GDP (DEBT) were direcly rerieved from he daabase. Raio of he Czech economy and eurozone shares was compued. 53

7 Even hough some of he series have a longer hisory, he beginning of 2000 was se as a saring poin for he esimaion. Quarerly daa were used. For he use of VAR and VEC modelling, i is imporan o check he uni roo behavior of he series. Excep he real ineres rae differenials, he series are in logs. The analysis of he uni roo behavior is presened in he Appendix. 4 Esimaes of REER I presen hree esimaed models in Table. The esimaed coefficiens of he respecive coinegraing vecors are given as well as he key characerisics of he esimaed vecor error correcion models. In all hree cases VARs wih 4 lags were chosen so ha he residuals passed sandard auocorrelaion, heeroskedasiciy and normaliy ess. The firs model is he base model which includes only produciviy and ne foreign asses variables in he coinegraing vecor. Real ineres rae differenial is also used bu is ouside he coinegraing vecor. All he esimaed coefficiens have he expeced or possible signs: increase in produciviy facor appreciaes he real exchange rae, increase in real ineres rae differenial depreciaes he real exchange rae and increase in ne foreign asses (increase in relaive foreign indebedness) appreciaes he real exchange rae. The second model includes he real price of oil in he coinegraing vecor and he esimaed coefficien is posiive, which, as expeced, means ha increase in real price of oil depreciaes he real exchange rae. The hird model includes governmen spending in he coinegraing vecor. The esimaed coefficien is negaive, which, as oulined above, means ha increase in governmen spending leads o real appreciaion. Nex I will focus on he esimaed error correcion models. The firs model (model ) explains approximaely 58 % of he variabiliy of real exchange rae and he esimaed adjusmen coefficien is negaive, which means he model shows sabiliy in he sense ha real exchange rae ends o reurn owards is equilibrium as given by he coinegraing vecor. According o he esimaed adjusmen coefficien, he half-life of a shock o he equilibrium is lile less han one quarer. The second model explains approximaely 76 % of he variabiliy of real exchange rae. Regarding he esimaed adjusmen coefficien, he half-life of a shock is lile less han one quarer (and slighly higher han in he case of model ). The hird model explains abou 76 % of he variabiliy of 54

8 real exchange rae and he half-life of a shock is lile over one quarer. However, as one can see from he able he significance of governmen spending is no high (acceped a 0 % level of significance) and he significance of real price of oil is lower han in he case of model 2. The variable of governmen deb did no ener significanly any of he models. The esimaes of real equilibrium exchange (REER) raes ogeher wih real exchange rae (RER) are capured in Figure 2. The esimaes run from he firs quarer of 200 up o he fourh quarer of The esimaes show he real exxhange rae was a lile overappreciaed on average. The exen of overappreciaion depends on he model. The esimaed equilibrium exchange rae appreciaed from 2004 o app (second quarer). Mos of his period produciviy variable conribued o REER appreciaion as well as ne foreign asses. Ne foreign asses dropped in 2008 which conribued o REER depreciaion. Also real price of oil conribued o emporary and mild REER depreciaion in he second half of 2006 and hen o rapid depreciaion in 2008 (second half). Real ineres rae differenial conribued o REER appreciaion in 2007 and in he beginning of 2008 (i had appreciaing effecs in he second half of 2008 References Belloc, M., Federici, D. (2007) A Two-Counry NATREX Model for he Euro/Dollar. MPRA Paper no oo). I can be seen ha he period of urbulences in he economy lead real exchange rae oward is equilibrium. This is even more apparen in Figure 3 where he misalignmens (differences beween RER abd REERs) are given. Conclusions The esimaed models of real equilibrium exchange rae show ha real exchange rae of he Koruna was more or less overappreciaed in he sample, he exen of which depends on he esimaed model. The esimaed real equilibrium exchange rae shows appreciaing endency from 2004 o he second quarer of Main drivers of he real equilibrium appreciaion are relaive produciviy, ne foreign asses and real ineres rae differenial. While he sharp appreciaion of nominal and real exchange rae oward he end of 2007 pushed real exchange rae furher from he equilibrium, he following adjusmens of nominal and real exchange rae narrowed he gap beween he esimaed equilibrium given by he fundamenals and acual real exchange rae. All in all he urbulences in he financial markes (and real economy) brough real exchange rae closer o he equilibrium. Bjorland, H.C., Hungnes, H. (2006) The Imporance of Ineres Raes for Forecasing he Exchange Rae. Journal of Forecasing. 25, pp

9 Clark, P.B., MacDonald, R.(2000) Filering he BEER: A Permanen and Transiory Decomposiion. IMF Working Paper WP/00/44. Deken, C., Marinez, C.M. (200) The Effecive Euro Equilibrium Exchange Rae Since he 70 s: A Srucural NATREX Esimaion. ECB WP. Dornbusch, R. (989) Real Exchange Raes and Macroeconomics: A Selecive Survey, Scandinavian Journal of Economics, 2, pp Driver, L.R., Wesaway, P.F. (2004) Conceps of Equilibrium Exchange Raes. BE WP no Eger, B., Halpern, L. (2005) Equilibrium Exchange Raes in Cenral and Easern Europe: A Mea- Regression Analysis. BOFIT Discussion Paper No. 4/2005. Hwang, J.K. (200) Dynamic Forecasing of Moneary Exchange Rae Models: Evidence from Coinegraion. Inernaional Advances in Economic Research., pp Komárek, L., Melecký, M. (2005) The Behavioural Equilibrum Exchange Rae of he Czech Koruna. CNB WP 5/2005. Lukepohl, H. (2007) New Inroducion o Muliple Time Series Analysis. Springer, Appendix MacDonald (997) Wha Deermines Real Exchange Raes? The Long and Shor of I. IMF Working Paper WP/97/2. Maeso-Fernandez, F., Osba, C., Schnaz, B. (200) Deerminans of he Euro Real Effecive Exchange Rae: A BEER/PEER Approach. ECB Working Paper no. 85. Rogoff, K. (996) The Purchasing Power Pariy Puzzle. Journal of Economic Lieraure. 2, pp Sarno, L., Taylor, M.P. (2002) The Economics of Exchange Raes. Cambridge Universiy Press, ISBN Smidkova, K. (998) Esimaing he FEER for he Czech Economy. CNB WP 87. Sein, J.L. (200) The Equilibrium Value of he Euro/US Exchange Rae: an Evaluaion of Research. CESifo Working Paper no Taylor, A.M., Taylor, M.P. (2004) The Purchasing Power Pariy Debae. Journal of Economic Perspecives, 4, pp Auhor (s) conac (s) Ing. Ví Poša, Ph.D. Universiy of Economics, Prague, Dp. of Microeconomics Minisry of Finance, Dp. of Macroeconomic Analyses posav@vse.cz Doručeno redakci: Recenzováno: Schváleno k publikování: