Financial accelerator mechanism in a small open economy: DSGE model of the Czech economy

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1 Financial acceleraor mechanism in a small open economy: DSGE model of he Czech economy 1 Inroducion Sanislav Tvrz 1, Jaromír Tonner 2, Osvald Vašíček 3 Absrac. Our research is moivaed by curren experience of worldwide economic difficulies ha suggess ha i could be he banking secor ha can o a cerain exen cause and exacerbae economic recessions. In his paper we focus on he effecs of financial acceleraor mechanism in he Czech economy in recen period of unsable financial secor and he deb crisis in he EU. In order o be able o assess he imporance of he financial fricions in his paricular economy, a DSGE model of a small open economy is esimaed. Model framework conaining financial acceleraor mechanism proposed by Bernanke, Gerler and Gilchris (1999) is used for he analysis. The original model specificaion is slighly alered by adding a shock in enrepreneurial ne-worh. Also, we decided o model he foreign secor as a VAR block, which enables us o impose more srucure on foreign variables han independen AR processes. Quarerly daa from period 1999 o 2011 are used for he esimaion. Model parameers are esimaed wih he use of Bayesian echniques. A mehod of shock decomposiion is used o analyze hisorical developmen of endogenous variables and o evaluae paricular effecs of individual exogenous shocks. Keywords: DSGE model, financial fricions, financial acceleraor, Bayesian mehods, variance decomposiion, shock decomposiion. JEL classificaion: E44, E32 AMS classificaion: 91B64 In he afermah of he global financial crisis of ha provoked subsequen global economic slowdown and recenly in some European counries even a deb crisis, he economiss around he world realize ha here exis imporan relaions beween he financial secor and he real economy. In fac, curren experience of worldwide economic difficulies shows ha he macro-financial linkages can o a cerain exen influence he aggregae flucuaions. Thanks o high capializaion, liquidiy and renabiliy of he Czech banking sysem, he Czech economy was exposed o he subprime crises only marginally. Neverheless, he global economic economic crisis hi he Czech economy in he las quarer of The developmen of he domesic economy during he global crisis was influenced predominanly by he downurn of foreign demand. Despie he fac ha he impacs of he crisis on he domesic financial secor were relaively mild, he ineres rae spreads increased subsanially. During he period of economic boom of he ineres rae spreads declined slighly. Wih he ouburs of he global economic crisis he difference beween he commercial ineres raes and he policy ineres rae increased sharply, which significanly reduced he efficiency of moneary policy in his period. The cenral bank sared lowering he policy ineres rae in However, much of is effecs were counered by he growing spread. Apparenly, here can be imes when he developmen of he policy ineres rae differ significanly from he developmen of commercial ineres raes ha he households and firms in he economy acually face. The idea of a fricionless banking secor seems, herefore, no longer enable. Several financial 1 Masaryk Universiy, Deparmen of Economics, Lipová 41a, Brno, olorin@mail.muni.cz 2 Masaryk Universiy, Deparmen of Economics, Lipová 41a, Brno and Macroeconomic Forecasing Division, Czech Naional Bank, Na Příkopě 28, Praha, Jaromir.Tonner@cnb.cz 3 Masaryk Universiy, Deparmen of Economics, Lipová 41a, Brno, osvald@mail.muni.cz The views expressed here are hose of he auhors, and do no necessarily reflec he posiion of he Czech Naional Bank

2 fricions mechanisms were considered in academia as well as in he cenral banks in pas years ha would enhance curren workhorse DSGE macroeconomic models wih mechanisms ha could explain wha we observe. In our paper we use he model framework developed by Shaari [6] ha includes financial acceleraor mechanism proposed by Bernanke e al. [2]. We inroduce a ne worh shock ino he original model and redefine he foreign secor as a VAR(1) block. This appropriaely complex medium-sized model of a small open economy incorporaes imporan real as well as nominal rigidiies and allows us o describe he Czech economy in a reasonable deail. Using he esimaed DSGE model, we employ a mehod of shock decomposiion in his paper o analyse hisorical developmen of real oupu and o evaluae paricular effecs of individual exogenous shocks wih special aenion given o he shocks in he enrepreneurial ne worh. 2 The model The model framework follows Shaari [6]. Overall srucure of he model is based on Galí and Monacelli [4] and i is modified o incorporae he financial acceleraor mechanism in line wih Bernanke e al. [2]. The model conains households, enrepreneurs, reailers, cenral bank and foreign secor. The households receive wages for supplied labour, governmen ransfers, profis made by reailers and domesic and foreign bonds reurns. Domesic bonds pay fixed nominal reurn in domesic currency while foreign non-coningen bonds give a risk adjused nominal reurn denominaed in foreign currency. The definiion of deb-elasic risk premium follows Adolfson e al. [1] and i conains exogenous AR(1) componen of risk-premium or uncovered ineres pariy shock (A UIP ). The households hen spend heir earnings on consumpion and domesic and foreign bonds acquisiion. The enrepreneurs play wo imporan roles in he model. They run wholesale goods producing firms and hey produce and own he capial. Marke of inermediae goods as well as capial goods marke is assumed o be compeiive. The wholesale goods producion is affeced by domesic produciviy AR(1) shock (A Y ) and he capial goods producion is subjec o capial adjusmen coss. Enrepreneurs finance he producion and ownership of capial by heir ne-worh N and borrowed funds F. The cos of borrowed funds is influenced by borrower s leverage raio via exernal finance premium, EF P = ( N Q 1 K ) χ, (1) where Q is real price of capial or Tobin s Q and χ is financial acceleraor parameer. To maximize profi he enrepreneurs choose he level of capial K +1 and he level of borrowed funds F +1 in accordance wih following opimaliy condiion, [ ( ) ] χ N+1 P E (R K,+1 ) = E R, (2) Q K +1 P +1 where R K,+1 is marginal reurn from capial invesmen, R is nominal ineres rae, P is price level and E is expecaions operaor. The enrepreneurial equiy develops according o [ ( ) ] χ N P 1 V = R K, Q 1 K R 1 F. (3) Q 1 K P Each urn a proporion (1 A NW ransfered o households in a form of ransfers. A NW ς) of enrepreneurs leaves he marke and heir equiy (1 A NW ς)v is is a shock in enrepreneurial ne worh. I influences he developmen of ne worh by changing he effecive survival rae of enrepreneurs. Is logarihmic deviaion from seady sae is assumed o evolve according o AR(1) process. Enrepreneurs also receive wage W E, for he labour hey supply o he producion of domesic inermediae goods. Enrepreneurial ne-worh is hen given by N +1 = ςa NW V + W E,. (4) Nex, here are wo ypes of reailers in he model. Home goods reailers and foreign goods reailers. Boh ypes of reailers are assumed o operae in condiions of monopolisic compeiion. Home good

3 reailers buy domesic inermediae goods a wholesale price and sell he final home goods o he consumers. Foreign good reailers buy goods from foreign producers a he wholesale price and resell he he foreign goods o he domesic consumers. The difference beween foreign wholesale price expressed in domesic currency and final foreign goods price, i.e. deviaion from law of one price is deermined by exogenous AR(1) shock (A LOP ). By Calvo-ype price seing and inflaion indexaion of he reailers he nominal rigidiies are inroduced ino he model. The cenral bank deermines he nominal ineres rae in accordance wih forward-looking Taylor ype ineres rae rule. Deviaions of ineres rae from he ineres rae rule are explained as moneary policy iid shocks (ε MP ). Following Chrisiano e al. [3], he foreign economy variables - real oupu, CPI inflaion and nominal ineres rae, are modelled using a VAR(1) model of his form, y π r ρ y y ρ y π ρ y r = ρ π y ρ π π ρ π r ρ r y ρ r π ρ r r y 1 π 1 r σ π y 1 0 σ r y σ r π 1 ε y ε π ε r, (5) where ε y iid(0, σy 2 ), επ iid(0, σπ 2 ) and εr iid(0, σr 2 ). Auocorrelaion coefficiens saisfy ρ y y, ρ π π, ρ r r 0, 1. Remaining coefficiens are no consrained. Compared o foreign variables modelled as independen AR(1) processes his approach should capure he relaions beween foreign variables more closely. 3 Esimaion The model parameers were esimaed using Random Walk Meropolis-Hasings algorihm as implemened in Dynare oolbox for Malab. Two parallel chains of draws each were generaed during he esimaion. Firs 75 % of draws were discarded as burn-in sample. The scale parameer was se o achieve he accepance raes around 30 %. 3.1 Daa Quarerly ime series of eigh observables were used for he purposes of esimaion. These ime series cover he period beween he firs quarer of 1999 and he fourh quarer of 2011 and conain 52 observaions each. For he domesic economy, ime series of real aggregae produc, consumer price index (CPI), 3-monh PRIBOR and Prague sock exchange (PSE) PX index are used. These seasonally adjused ime series were obained from he daabase of Czech Saisical Office and PSE. The foreign economy is represened by eleven founding counries of he Euro area plus Greece ha joined he moneary union in For hese welve economies, he seasonally adjused ime series of real aggregae produc, CPI index and 3-monh EURIBOR are used. Also, ime series of CZK/EUR real exchange rae is used. These daa were obained from he Eurosa daabase. The ime series of PX index is used as a proxy for he enrepreneurial ne worh. Changes in he value of he companies raded on he PSE are expressed in a condensed form in he PX index. We assume ha all he companies in he economy are affeced by he same evens as he companies raded on he PSE and ha hey are affeced in a similar way. Therefore, we come o a conclusion ha he developmen of he PX index should o a reasonable exen capure also he changes in he aggregae value of all he companies in he economy and herefore also he aggregae enrepreneurial ne worh. The original ime series were ransformed prior o esimaion so as o express he logarihmic deviaions from seady sae. Log values of he CPI indices were aken and heir firs differences were calculaed. Obained ime series were demeaned and idenified as he logarihmic deviaions of he domesic and foreign CPI inflaion from seady sae. The logarihmic deviaions of remaining observables from heir seady sae were calculaed wih he use of Hodrick-Presco filer (HP filer). Since we are working wih quarerly ime series in his paper, HP filer wih parameer λ = 1600 was used o find he approximaion of heir seady sae

4 3.2 Priors and poseriors The DSGE model was successfully esimaed on hisorical daa of he Czech economy in he period Prior and poserior disribuions of he srucural parameers are described in able 1. Obained esimaes are similar o he resuls repored in he lieraure. The parameer of he financial acceleraor is esimaed a a value of , which is a slighly higher value ha he esimae of repored by Tonner and Vašíček [7]. The parameer Γ is esimaed a he value of , which is below he prior mean of 2. Our resul is quie close o Bernanke e al. [2] who sugges calibraion of his parameer o 2. The enrepreneurs survival rae ς is esimaed somewha below he prior mean a he value of , which implies average enrepreneurs business lifespan of nearly 4 years. Tonner and Vašíček [7] calibrae his parameer o he value of , which would imply he business lifespan of almos 10 years. Ineres rae smoohing parameer of he Taylor rule is esimaed a he value of Similar value of is repored by Tonner and Vašíček [7]. The poserior mean of parameer β π suggess a value of inflaion weigh in he Taylor rule of This resul is in accordance wih Ryšánek e al. [5] who found a value of The weigh of oupu gap in he Taylor rule Θ y is esimaed a , which is close o he resul of repored by Tonner and Vašíček [7]. Prior Poserior Parameer Disribuion Mean Sd Mean 95% HPDI Υ habi persisence Bea Ψ inverse elas. of labour supply Gamma ψ B elas. of deb-elasic risk prem. Gamma η home/foreign goods elas. subs. Gamma κ price indexaion Bea γ preference bias o foreign goods Bea θ H home goods Calvo parameer Bea θ F foreign goods Calvo paremeer Bea ψ I capial adjusmen coss Gamma Financial fricions Γ s-s. capial/ne worh raio Gamma ς enrepreneurs survival rae Bea χ financial acceleraor Gamma Taylor rule ρ ineres rae smoohing Bea β π inflaion weigh Gamma Θ y oupu gap weigh Gamma Shifed gamma disribuion is used for hese parameers, because hey are assumed o ake values from inerval 1, ). Table 1 Esimaed srucural parameers 3.3 Variance decomposiion The able 2 conains asympoic variance decomposiion of model variables. The variance of he model variables is decomposed ino he conribuions of exogenous shocks based on a simulaion wih infinie horizon. Obviously, he ne worh shock is a one of he driving forces of his model in he long run. More han half of he variance of real oupu, consumpion, nominal ineres rae and inflaion is explained by his shock. Nearly 75 % of he variance of he real reurn o capial invesmen and over 85 % of he real invesmen, real price of capial and capial sock is explained by he ne worh shock. The variance of enrepreneurial ne worh and exernal finance premium is explained predominanly by his shock. In general, we can say ha he shocks in enrepreneurial ne worh, domesic produciviy, law of one price gap and foreign oupu explain predominan par of he variance of he model variables. The remaining shocks play only marginal role in he long run

5 Variable NW Y MP UIP LOP r π y y real oupu c real consumpion inv real invesmen k capial sock r nominal ineres rae rer real exchange rae π CPI inflaion z ne foreign asses posiion l H households labour supply w H households wages w E enrepreneurs wages r G gross renal rae of capial r K gross reurn on capial inves q real price of capial mc marginal coss n enrepreneurial ne worh efp exernal finance premium r foreign ineres rae π foreign CPI inflaion y foreign oupu Table 2 Variance decomposiion (in percen) 3.4 Shock decomposiion In he following secion, we discuss he shock decomposiion of he real oupu gap, ha is depiced in figure 1 and is expressed in percen of he poenial oupu. The insrumen of shock decomposiion allows us o see he effecs of paricular exogenous shocks on his smoohed variable in ime. Figure 1 Shock decomposiion of real oupu gap According o he model, he foreign oupu shock played imporan role in he economic upswing of Growing foreign oupu in his period boosed he foreign demand and ne expors. Posiive shock in he enrepreneurial ne worh played is role as well, especially in Raher low nominal ineres rae in his period also suppored he economic growh. In he second half of 2007, he debelasic risk premium shock and he shock in he law of one price gap furher simulaed he growh of real oupu

6 In he las quarer of 2008, he foreign demand sared o subside. Togeher wih he exogenous decline in enrepreneurial ne worh and relaively high nominal ineres rae his caused a swif decline of he real oupu in his period. In he beginning of 2009, he shock in he law of one price gap caused a quick depreciaion of he real exchange rae and furher acceleraed he decline of he real oupu. Low foreign demand affeced he domesic real oupu mainly in he 2009 and in he beginning of The exogenous reducion of he enrepreneurial ne worh ook he bigges effec in he beginning of 2009, when i conribued around 0.75 percenage poins o he negaive real oupu gap. During 2010, he negaive effecs of he majoriy of exogenous shocks diminished and he real oupu reurned o he neighbourhood of is poenial. 4 Conclusion I was a goal of his paper o evaluae he imporance of financial fricions in he Czech economy during he period of global financial and economic crisis. A DSGE model framework proposed by Shaari [6] was chosen for his purpose. This model of a small open economy conains he financial acceleraor mechanism inroduced by Bernanke e al. [2] and i also includes imporan real and nominal rigidiies. Original model was slighly modified by inroducing exogenous shock in he enrepreneurial ne worh ino he model. Furhermore, he foreign secor was redefined as a VAR(1) block. According o he variance decomposiion, he shock in enrepreneurial ne worh is one of he driving forces of he model economy. Togeher wih he shock in domesic produciviy, law of one price gap and he foreign oupu, i explains predominan par of he variance in he long run. The shock decomposiion of he real oupu showed considerable effecs of he shock in he ne worh during he period of economic boom of and also in he early phase of he economic crisis. Even hough he developmen of he Czech economy in he period was mainly affeced by he siuaion abroad and especially by he developmen of foreign demand, he resuls of his model sugges relaively significan effecs of he financial fricions as well. Acknowledgemens This work is suppored by funding of specific research a Faculy of Economics and Adminisraion, projec MUNI/A/0780/2011. References [1] Adolfson, M., Laséen, S., and Villani, M.: Bayesian Esimaion of an Open Economy DSGE wih Incomplee Pass-Through. Journal of Inernaional Economics, vol. 72, 2008, [2] Bernanke, B.S., Gerler, M., and Gilchris, S.: The Financial Acceleraor in a Quaniaive Business Cycle Framework. In: Taylor, J.B., Woodford, M (eds.) Handbook of Macroeconomics, vol. 1, Elsevier, Amserdam, 1999, [3] Chrisiano, L. J., Traband, M., and Walenin, K.: Inroducing financial fricions and unemploymen ino a small open economy model. Journal of Economic Dynamics and Conrol, vol. 35, Issue 12 (December), 2011, [4] Galí, J., and Monacelli, T.: Opimal Moneary and Fiscal Policy in a Currency Union. Economics Working Papers 909. Universia Pompeu Fabra: Deparmen of Economics and Business, [5] Ryšánek, J., Tonner, J., and Vašíček, O.: Moneary Policy Implicaions of Financial Fricions in he Czech Republic. CNB Working paper series, Czech naional bank, Prague, [6] Shaari, M. H.: Analysing Bank Negara Malaysia s Behaviour in Formulaing Moneary Policy: An Empirical Approach. Docoral hesis, College of Business and Economics, The Ausralian Naional Universiy, [7] Tonner, J., and Vašíček, O.: Financial Fricions Relevance during he Crisis: Czech Case. In: Advances in Applied Economics, Business and Developmen, vol. 209, Springer, Dalian, 2011,