PINIGØ STUDIJOS MONETARY STUDIES

Transcription

1 PINIGØ STUDIJOS MONETARY STUDIES Birþelis / June VILNIUS

2 REDAKTORIØ KOLEGIJA / EDITORIAL BOARD Vyriausiasis redaktorius Editor-in-Chief Redaktorius Editor Redaktoriaus pavaduotoas Associate Editor Nariai Members Jonas ÈIÈINSKAS Profesorius, habilituotas daktaras (ekonomika 04 S), Vilniaus universitetas, Tarptautiniø santykiø ir politikos mokslø institutas Vaidievutis GERALAVIÈIUS Profesorius, habilituotas daktaras (ekonomika 04 S, matematika 01 P), Lietuvos bankas Tomas RAMANAUSKAS Daktaras (ekonomika 04 S), Lietuvos bankas Serge A. AIVAZIAN Profesorius, PhD (matematika 01 P), RMA Centrinis ekonomikos ir matematikos institutas, Maskvos valstybinis M. V. Lomonosovo vardo universitetas, Nauosios ekonomikos mokykla (Maskva) Anders Åslund Profesorius, PhD (ekonomika 04 S), Georgetown universitetas, Peter G. Peterson tarptautinës ekonomikos institutas Juozas BIVAINIS Profesorius, habilituotas daktaras (ekonomika 04 S), Vilniaus Gedimino technikos universitetas Raimondas KUODIS Daktaras (ekonomika 04 S), Vilniaus universitetas, Lietuvos bankas Virmantas KVEDARAS Docentas, daktaras (ekonomika 04 S), Vilniaus universitetas, Vilniaus vadybos aukštoi mokykla Remigius LEIPUS Profesorius, habilituotas daktaras (matematika 01 P), Vilniaus universiteto Matematikos ir informatikos institutas Gitanas NAUSËDA Daktaras (ekonomika 04 S), AB SEB bankas Rimantas RUDZKIS Profesorius, habilituotas daktaras (matematika 01 P), Vilniaus universiteto Matematikos ir informatikos institutas Timo TERÄSVIRTA Profesorius, PhD (matematika 01 P), Orhuso universitetas, Stokholmo ekonomikos mokykla, Vidurio Europos universitetas (Budapeštas), Švedios ekonomikos mokykla (Helsinkis) REDAKCIJA / Editorial office Tomas Ramanauskas kontaktinis asmuo (contact person), tel , el. p. tramanauskas@lb.lt Ramunė Vaskelaitė kalbos redaktorė (language editor), tel , el. p. rvaskelaite@lb.lt Lietuvos bankas, Gedimino pr. 6, LT Vilnius, Lietuva. Tel , el. p. vgeralavicius@lb.lt Interneto svetainės adresas: NUORODOS / REFERENCES Mokslinis leidinys Pinigø studios skelbiamas EBSCO Publishing, Inc. duomenø bazëe Business Source Complete: Leidþiamas nuo 1997 m., iðeina du kartus per metus, platinamas nemokamai. Leidëas Lietuvos bankas. Leidinye Pinigø studios spausdinamø mokslo darbø autoriø nuomonë gali ir nesutapti su oficialia Lietuvos banko pozicia. Academic ournal Monetary Studies is available online at EBSCO Publishing, Inc., Business Source Complete: First issued in 1997, Monetary Studies are published biannually by the Bank of Lithuania and distributed free of charge. The views expressed in the Journal are those of the authors and do not necessarily reflect the official position of the Bank of Lithuania. ISSN (Print) ISSN (Online) Lietuvos bankas, 2013

3 PINIGØ STUDIJOS ŠEŠIOLIKTIEJI metai Nr Birželis M o k s l i n i a i s t r a i p s n i a i EKONOMIKOS TEORIJA IR PRAKTIKA Aurelia Proškutė BUSINESS CYCLE DRIVERS IN LITHUANIA / 5 Jaunius Karmelavičius, Violeta Klyvienė BALTIJOS ŠALIŲ MAKROEKONOMINIŲ RODIKLIŲ ATSAKO Į FISKALINĖS POLITIKOS POKYČIUS ANALIZĖ / 30 Julius Stakėnas GENERATING SHORT-TERM FORECASTS OF THE LITHUANIAN GDP USING FACTOR MODELS / 49 MATEMATINĖ EKONOMIKA Virmantas Kvedaras, Remigius Leipus, Jonas Šiaulys ESTIMATION OF THE GENERALIZED STOCHASTIC CLAIMS RESERVING MODEL AND THE CHAIN-LADDER METHOD / 68 K i t o s p u b l i k a c i o s NOBELIO 2010 M. EKONOMIKOS MOKSLŲ PREMIJOS LAUREATŲ DARBAI / 91

4 MONETARY STUDIES Volume XVI Number 1 une 2012 R e s e a r c h P a p e r s THEORY AND PRACTICE OF ECONOMICs Aurelia Proškutė BUSINESS CYCLE DRIVERS IN LITHUANIA / 5 Jaunius Karmelavičius, Violeta Klyvienė ANALYSIS OF RESPONSE OF MACROECONOMIC INDICATORS TO FISCAL POLICY SHOCKS: THE CASE OF THE BALTIC STATES / 30 Julius Stakėnas GENERATING SHORT-TERM FORECASTS OF THE LITHUANIAN GDP USING FACTOR MODELS / 49 MATHEMATICAL ECONOMICS Virmantas Kvedaras, Remigius Leipus, Jonas Šiaulys ESTIMATION OF THE GENERALIZED STOCHASTIC CLAIMS RESERVING MODEL AND THE CHAIN-LADDER METHOD / 68 O t h e r P u b l i c a t i o n s WORKS OF THE 2010 NOBEL PRIZE IN ECONOMICS LAUREATES / 91

5 BUSINESS CYCLE DRIVERS IN LITHUANIA Aurelia Proškutė Vilniaus universitetas, Ekonomikos fakultetas Saulėtekio al Vilnius auretaure@yahoo.com The paper attempts to answer the question of what drives the business cycle in Lithuania. For that purpose an augmented real business cycle model is constructed. Structural permanent and transitory productivity shocks, preference, interest rate premium and public spending shocks are included in the system that aims at explaining the dynamics of aggregate demand components in Lithuania over the period of The model is estimated using Bayesian techniques. It shows that a non-stationary productivity shock to trend is the main source of variation in output; investment is driven mostly by exogenous interest rate premium shocks, while the dynamics of consumption and trade-balance-tooutput ratio is mostly affected by stochastic preference shocks. The model s results for Lithuania are then compared with the findings in other emerging economies. Keywords: real business cycle, permanent productivity shocks, financial frictions, Bayesian estimation, small open economies. A. Proškutė Business Cycle Drivers in Lithuania 5 Introduction The motivation for this paper comes from a simple question: what drives the business cycle in Lithuania? With this goal in mind, we attempt at building a general equilibrium model of a small open economy which would be capable of replicating the dynamics of aggregate demand components over the business cycle in Lithuania and would reveal the importance of the underlying forces (structural shocks) responsible for variable movements around the steady-state of the economy. The main obective of this task is to understand what happening on in the past, i.e. what shocks, and to what extent, influenced the dynamics of the selected macroeconomic variables in Lithuania over the period of 1995 to Lithuanian economy exhibits a number of emerging economy features observed and documented as stylized facts of small open emerging economies (Neumeyer, Perri 2005; Aguiar, Gopinath 2007a; Uribe 2012). These include procyclical private final consumption, highly procyclical investment, countercyclical trade-balance-to-output ratio (the latter is more evident in annual than quarterly Lithuanian data), large standard deviations of output and its components. The mentioned stylized facts represent specific features of the emerging economies that distinguish them from the developed ones. For this reason a specific business cycle model is required; the approaches used to explain business cycle fluctuations in developed economies require some specific adustments to be able to account for emerging small open economy dynamics. On a global scale business cycle analysis of small open economies started with Mendoza s (1991) canonical model explaining selected stylized facts of the economy. Since then Mendoza s model has been extended in a number of dimensions and adusted to account for stylized facts in small open emerging economies, yet there is still no consensus about the main driving forces of business cycles in this type of economies. Two competing strands of empirical literature dominate. The first one finds evidence that business cycle dynamics is mostly resulting from the shocks to long-term growth trend (Aguiar, Gopinath 2007a), while the second one supports the view that business cycles are to a large extent driven by interest rate and transitory productivity shocks that are Aurelia Proškutė is a doctoral student at Vilnius University, Department of Quantitative Methods and Modelling, Faculty of Economics. Areas of activity: business cycles, emerging economies, dynamic stochastic general equilibrium models.

6 Pinigø studios 2012/1 Ekonomikos teoria ir praktika 6 propagated through the presence of financial frictions (Neumeyer, Perri 2005; Uribe, Yue 2006; Garcia-Cicco et al. 2010). Some studies find the mixed evidence of the importance of both channels (Aguiar, Gopinath 2007b; Chang, Fernandez 2010). The variety of the results from the existing empirical studies of small open emerging economies urges us to employ the combined approach and to consider both potential sources of typical emerging market fluctuations for the Lithuanian business cycle model. Thus we include both non-stationary productivity shocks and interest rate shocks coupled with financial frictions into the model. In this framework the results of our study add another piece of evidence to the ongoing debate. There are only a few distantly related general equilibrium studies of the Lithuanian business cycle (Vetlov 2004; Karpavičius 2008; Ramanauskas 2011). The existing works reveal the importance of interest rate and foreign demand shocks on output dynamics of the country at business cycle frequency. Yet the lack of microfoundations and short time series used in estimation of the models may have affected the stability and robustness of the main results, especially under regime changes like the switch of the reference currency in the currency board regime in 2002, oining the European Union (EU) in 2004 or economic policy effects under global financial crisis impact. We build a micro-founded macroeconomic model that is robust to policy changes in the economy. Besides we take the natural advantage of having longer statistical data series for our estimations. The model we present is the first estimated rather than calibrated Dynamic Stochastic General Equilibrium (DSGE) model of Lithuania. The model that we choose to describe the dynamics of the Lithuanian macroeconomic variables is an extended Real Business Cycle (RBC) model as the one employed by Garcia- Cicco et al. (2010). The model contains five structural shocks hitting the system; besides the above-mentioned permanent productivity and interest rate shocks it also contains transitory productivity shocks together with preference shocks that allow replicating procyclical consumption patterns observed in real data and domestic spending shocks representing a simplified government purchases shocks in the economy. The model is estimated with the quarterly data for Lithuania over the period from 1995 Q1 to 2011 Q2. The remainder of the paper is organized as follows. In Section 1 we describe the data used in the model and highlight typical features of emerging economies and respective characteristics of Lithuanian data that we attempt to explain with the selected model. Theoretical foundations of the model and its assumptions are outlined in Section 2. Section 3 contains the description of the parameter calibration and Bayesian estimation procedures. Estimated model s results including parameter estimates discussion, impulse response functions of the observables, variance decomposition of aggregate demand and its components are presented in Section Stylised facts and data In this section we show the main features of the Lithuanian business cycle and its resemblance to other emerging economies. All the data in this section and the data used in model estimation are taken from Statistics Lithuania. During the historic period of Lithuania experienced two economic downturns: the effects of the Russian financial crisis in and the recent global financial crisis in The HP-filtered output series presented in Figure 1 reveal the two periods of economic recession that are also detected in other empirical studies using alternative data-filtering methods (Kučinskas 2011). The composition of the Lithuanian aggregate demand is presented in Table 1. It shows the average shares of chain-linked volume measures of aggregate demand components over the period from 1995 Q1 to 2011 Q2. Large foreign trade shares reveal a high degree of the openness of the economy. This feature gets a special attention in the modelling process: among other robustness checks the model s ability to reproduce a downward sloping autocorrelation function of trade-balance-to-output ratio and its correlations with aggregate demand components are tracked closely. Large foreign trade deficits are

7 associated with high foreign borrowing and public debt of the economy; these features are also taken into consideration when building and calibrating the model. Figure 1. Lithuanian chain-linked volume GDP series + A. Proškutė Business Cycle Drivers in Lithuania Note: + seasonally and working days adusted measure. Source: Statistics Lithuania; the author s calculations. 7 Table 1 Average shares of real GDP components in Lithuania (per cent) Private final consumption Government consumption Gross capital formation Exports Imports (negative) Foreign trade balance Source: Statistics Lithuania; the author s calculations. Table 2 Large standard deviations of output growth, even higher volatility of procyclical consumption patterns, largely volatile and highly procyclical investment growth rate and large trade-balance-to-output ratio movements are typical features of most emerging countries documented as stylized facts by Aguiar and Gopinath (2007a), Neumeyer and Perri (2005), Uribe (2012). The empirical volatilities of aggregate demand components for developed, emerging and poor countries are presented in Table 2. Standard deviations of the growth rates of aggregate demand components (percentage points) Variable All countries Developed countries Emerging countries Poor countries Lithuania gy gc gi gexp gimp tby Sources: Heston et al. (2011), Uribe (2012), Statistics Lithuania; the author s calculations. In Table 2 economies are divided into developed, emerging and poor countries based on their average annual Gross Domestic Product (GDP) per capita measured at Purchasing Power Parity (PPP) over the period The thresholds for country division into

8 Pinigø studios 2012/1 Ekonomikos teoria ir praktika 8 the three groups are more than 25,000, from 3,000 to 25,000 and less than 3,000 international USD per capita respectively. Group statistics are calculated as weighted averages from individual country statistics using population weights. 24 developed, 73 emerging and 54 poor countries are included in the calculations. Calculations are based on annual data sample. Lithuania is not included in the group s statistics due to its short time series. Analogous statistics of the Lithuanian economy are calculated on an annual data sample Exact data sources are presented in Table 1 in the Appendix and variable descriptions are presented in Table 2 in the Appendix. As can be seen in Table 2, the empirical volatilities of Lithuanian aggregate demand components and the output itself match well their counterparts of other emerging economies. 2. Theoretical framework The theoretical model that we employ to account for high volatilities of the aggregate demand variables and other specific features of the Lithuanian economy is the neoclassical growth model with additional preference, interest rate shocks, debt-elastic interest rate and domestic spending shocks as in the augmented business cycle model by Garcia-Cicco et al. (2010). The origins of the model can be traced back to the small open economy representation built by Mendoza (1991) and Correia et al. (1995). It also contains permanent productivity shocks as in the model by Aguiar and Gopinath (2007a); a debtelastic interest-rate premium is introduced to induce the stationarity of the model as proposed by Schmitt-Grohe and Uribe (2003). The model s economy is populated by an infinite number of identical households that supply their labour for the production of a single asset that can be consumed immediately, invested or traded with the rest of the world. The government is included implicitly into the model and has a limited role in the economy: public spending is financed with lump-sum taxes, government expenditure is assumed to be proportional to output with some stochastic domestic spending shocks. As there is no specific government institution in the model, stochastic domestic spending is included directly in the household budget equation. The interest rate that households have to pay over the accu mulated public debt depends on the size of the debt. Domestic output is produced combining labour and physical capital inputs in a standard Cobb-Douglas production function: α 1 α t t t t t Y = a K ( X h ), where Y t denotes gross domestic output, K t is the capital stock used in the production process and h t stands for the number of hours supplied by households. Parameter a shows the output elasticity of capital. The production function contains two types of productivity shocks: a stationary productivity shock a t and a stochastic trend X t. A stationary productivity shock is described as an AR(1) process: lna a t+ 1 a t t+ 1 a = ρ lna + ε, ε ~ N 0, σ 2. t ( a ) Here r and s denote persistence and size parameters of a structural shock. If the gross growth rate of non-stationary productivity shock X t is denoted as g t X t / X, the dynamics of the process is given by: g t+ 1 g t t + 1 ln( g / g) = ρ ln( g / g) + ε, ε ~ N, σ, g t ( 0 2 g ) where g signifies growth rate of the economy in its steady state. The law of motion of capital is given by: ( ) + Kt+ 1 = 1 δ Kt It. It shows how the stock of capital evolves over time given the depreciation rate of capital d and gross investment I t.

9 The instantaneous utility function of a representative household is of the form: u t 1 ω 1 γ [ Ct θω Xt 1h t ] = 1 γ 1, where C t is the consumption in period t, and h t is the number of working hours. Parameter g shapes the curvature of the utility function; parameters q and w influence the labour supply elasticity. As in Aguiar and Gopinath (2007a), a representative household s utility is normalized by previous period s productivity levels to ensure that productivity changes are fully realised by the households and they enter its information set when making decisions in period t. Yet, as the authors notice, the solution to the model is invariant to the choice of normalisation variable (Aguiar, Gopinath 2007a: 11). The functional forms of the instantaneous utility function imply that the marginal rate of ω substitution between consumption and leisure depends only on labour, MRS = θ Xt h 1 1 t. A household s lifetime utility function is given by: U = E 0 t = 0 1 ω 1 γ t [ Ct θω Xt 1h t ] νβ t 1 γ 1, where E 0 is the expectations operator, b is a subective discount factor and n t stands for stochastic preference shocks which are modelled as first-order autoregressive processes: ν lnνt+ 1 = ρν lnνt + εt + 1, ε t ~ N( 0, σ 2 ν ). ν A. Proškutė Business Cycle Drivers in Lithuania 9 Trade balance is the difference between domestic output and domestic absorption: TB = Y C I Φ( K 1, K ) S, t t t t t+ t t where F( ) is the capital adustment cost function dependent on the change in capital stock (net investment). S t stands for exogenous stochastic domestic spending shocks, which could be interpreted as a reduced-form government consumption patterns. It is included in the system as an autoregressive process. Adding a notation s t S t / X t 1 and denoting the steady-state spending level as share_s, the stochastic spending shock is modelled as: s t+ 1 s t t+ 1 ln( s / share _ s) = ρ ln ( s / share_ s) + ε, ε ~ N, σ. s t ( 0 2 s ) In each period, households have the ability to borrow or lend in a risk-free real bond that pays an interest rate. The evolution of the debt position D t of the representative household is given by: Dt+ = ( rt ) ( Dt TBt), where r t denotes the interest rate that households have to pay over the accumulated debt between two consecutive periods. The change in the level of debt (D t+1 D t ) has two sources: the interest paid on previously acquired debt and the value of the trade imbalance; if households spend, invest and consume more than their domestic output, the debt increases. Domestic agents are assumed to face an interest rate r t that is increasing in the country s aggregate detrended level of net foreign debt D t : * Dt+ Xt d t rt = r + ψ( e 1/ µ 1 1)+ e 1. The domestic interest rate is the sum of the global interest rate r * (assumed to be constant over time) and interest rate premium. The latter depends positively on the level of external aggregate debt D t (the second term in the interest rate equation) and is controlled by the constant parameter d guaranteeing the unique existence of steadystate in the economy. This parameter also governs the steady-state level of the foreign debt. As households are assumed to be identical in the model, in equilibrium aggregate debt per capita equals individual debt:

10 D t = D. t Pinigø studios 2012/1 Ekonomikos teoria ir praktika 10 Finally, the parameter y shows the sensitivity of interest rate premium to the total level of external debt. In the steady state domestic interest rate equals the world interest rate and the risk premium equals zero. The last term in interest rate equation is the stochastic interest rate shock m t that follows a stationary AR(1) process and captures interest rate fluctuations independent of domestic conditions: µ ( µ ) µ lnµ t+ 1 = ρ µ lnµ t + εt + 1, ε ~ N 0, σ 2. t Combining all of the above, we get the household s period-by-period budget constraint: Dt + 1 ϕ Kt + = Dt Yt + Ct + St + It + ( 1 g ) 2 Kt. 1+ r 2 K t t The last term in the budget constraint expression denotes the capital adustment costs: the additional expenses required to adust the stock of capital to the desired level. Inclusion of capital adustment costs is rather a technical way to fix the excessive investment volatility in response to variations in the foreign interest rate in small open economy models (Schmitt-Grohe, Uribe 2003). Representative household maximizes its lifetime utility by choosing output, consumption, working hours, capital, investment and debt levels given the initial conditions D 0 and K 1 and subect to its budget constraint, law-of-motion of capital, production function, and a restriction of no Ponzi-game written as: lim E t Dt+ ( r ) s= 0 s The last condition ensures that the future debt dynamics is not explosive and the expected net present value of the future debt is negative or equals zero. In other words, household debt should be expected to grow at a lower rate than interest rate. This limitation does not allow the household to engage in an infinitely-running scheme of financing the interest payments with further borrowing and never paying their initial debt. The model set-up is complete now. There are five stochastic structural shocks introduced to the system: permanent and transitory productivity shocks, preference shocks affecting the marginal utility of consumption, shocks to interest rate and domestic spending shocks. They are forced to compete for explaining business cycles in emerging countries (Uribe 2012: 188). In addition to the structural disturbances, there are four measurement errors added to the system which are also allowed to participate in the explanation of the business cycle dynamics in Lithuania. Log-linearization of the system around its steady-state results in a system of linear rational expectation equations that are solved using Klein s method (Klein 2000). The model brought to the estimation stage consists of ten state variables (including five structural shocks) and five control variables* among which there are four observable macroeconomic aggregates of our interest: growth rates of output, consumption and investment and the trade-balance-to-output ratio. The state-space system is estimated with four measurement errors of the observed variables. 3. Estimation of parameters State variables are y t, c t, i t, k t, d t, h t, m t, s t, g t, a t. Control variables are gy t, gc t, gi t, tby t, h t. The behaviour of the system is governed by structural (deep) parameters. A number of the parameters are calibrated to match the properties and certain characteristics of the Lithuanian quarterly data over the period from 1995 Q1 to 2011 Q2. The remaining parameters are estimated using Bayesian estimation techniques. The details of the parameterization and Bayesian estimation procedures are explained in two subsections below.

11 *Alternative parameter values of 0.05 and 0.1 do not have any maor impact on model s main results Parameterization In the calibration task we target the properties of the Lithuanian quarterly data over the period from 1995 Q1 to 2011 Q2 or rely on other studies that used similar structural parameters for the models of Lithuanian economy. In the case when no evidence for Lithuanian economy exists, we rely on the values of the parameters used in other emerging economy studies. The parameter of output elasticity of capital a in the production function measures the share of capital income in the economy. The parameter is set at 0.32, equal to the average share of fixed capital consumption and half of operating surplus and mixed income in Lithuania over the period. The ratio is in line with the standard values of the parameter in DSGE literature, where it varies from 0.3 to 0.4 and also the values of a used in previous studies of the Lithuanian economy that vary in the range [0.297, 0.36] in earlier economic models (Vetlov 2004; Karpavičius 2008). Quarterly capital depreciation rate d takes a standard value of (2.5%) and is equal to annual capital depreciation rate of 10 per cent used in most macroeconomic models. Parameter share_s indicates the steady-state share of public spending in total output. For the analysed period share of public spending in GDP of Lithuania is equal to approximately 20 per cent on average, thus share_s is set at 0.2 in the model. A subective quarterly discount factor which shows a relative importance of consumption in the current period to consumption in the following period b is set at 0.99 a standard value in DSGE literature. Parameter w governs the labour supply elasticity in the model. The value of it is a debatable one, as macroeconomists in the business cycle studies estimate the labour supply elasticity being higher than that suggested by microevidence (Smets, Wouters 2003; Fiorito, Zanella 2008). As there is no unique consensus about the standard values of labour supply elasticity in the economy, we specify the middle value in the range of known literature for emerging economies. The value of w is set at 1.6 to attain the labour supply elasticity of 1.7 in the economy. The parameter is slightly higher than the calibrated values of (Mendoza 1991; Schmitt-Grohe, Uribe 2003), is equal to the one used in the studies by Neumeyer and Perri (2005), Aguiar and Gopinath (2007a), Garcia-Cicco et al. (2010) and is slightly lower than the value of 1.7 assumed by Correia et al. (1995). The parameter q is assigned the value of 4.4 to obtain a standard share of household s working time allocated to the labour market equal the standard 20 per cent in the steady state. Utility function curvature is defined by the value of g, which is set at 2.0, following a vast maority of business cycle literature. Parameter d signifies the steady-state foreign debt level of the economy at which risk premium is equal to zero. It is subectively set at 0.2*. This parameter value is associated with a small steady-state trade balance-to-output ratio of about 0.7 per cent. The calibrated small positive trade balance ratio is different from the period s average seen in the data of Lithuania (which is equal to 9%). Yet as the negative trade-balance-to-output ratio is incompatible with the steady-state of the economy having foreign debt in its steady-state, the values of trade-balance-to-output ratio need to be adusted to ensure the sustainability of the debt. The values of all calibrated parameters are reported in Table 3. A. Proškutė Business Cycle Drivers in Lithuania 11 Table 3 Model s calibrated parameters Parameter Description Value a Capital income share 0.32 d Capital depreciation rate share_s Share of public spending in total output 0.2 b Subective discount rate 0.99 q Labour supply elasticity parameter 4.4 w Labour supply elasticity parameter 1.6 g Curvature of the utility function 2.0 d Parameter associated with steady-state trade-balance-to-output ratio 0.2

12 Pinigø studios 2012/1 Ekonomikos teoria ir praktika 12 Table 4 The values of calibrated parameters guarantee that average consumption share of the Lithuanian economy in the steady state is around 59 per cent, which is close to the period s average of 65 per cent observed in Lithuania. In the steady state investmentto-output ratio is approximately 21 per cent, which is in line with the average share of gross capital formation in total output of Lithuania of 22 per cent. The calibrated steadystate of the Lithuanian economy assumes slightly lower consumption share and a very small but positive trade-balance-to-output ratio in order to guarantee the sustainability of the foreign debt and the convergence of the economy to the balanced growth path Bayesian estimation The model s parameter estimation in a Bayesian framework is conducted in several steps. The first step is to impose prior distributions on model s parameters. In our case non-informative priors (uniform distributions) are chosen (see Table 4). Prior and posterior distributions of model parameters + Parameter Prior distributions Bayesian posterior percentiles Distribution Min Max 5% Median Mean 95% s g Uniform s a Uniform s n Uniform s s Uniform s μ Uniform G Uniform r g Uniform r a Uniform r n Uniform r s Uniform r μ Uniform Uniform y Uniform std(mey) Uniform std(mec) Uniform std(mei) Uniform std(metby) Uniform Note: + std (MEy), std(mec), std(mei), std(metby) stand for the standard deviations of measurement errors of output, consumption, investment and trade-balance-to-output ratio respectively. *Posterior mode values are computed by directly maximizing the posterior distribution using the quasi-newton BFGS method using the csminwel.m algorithm by C. A. Sims (2012). The first three columns in Table 4 give the prior uniform distribution ranges for each parameter estimated. The upper bound of the prior distributions for measurement errors of aggregate demand components are set at 25 per cent of the standard deviations of the corresponding empirical data series. The following procedures of estimation are conducted as suggested by Juillard et al. (2006), An and Schorfheide (2007), Levine et al. (2010). Firstly, a chain of 1,000 random draws of parameter values is run and 10 sets of estimates with the highest log-likelihood function realisation are selected. These 10 draws with the highest log-likelihood function values are then taken as starting points for quasi-newton BFGSI optimisation algorithm. The BFGSI algorithm is a numerical optimization procedure that finds the mode of the posterior distribution and the approximation of the Hessian-inverse at the mode that gives the variances of the umping distribution. The third step consists of selecting a starting point for the Metropolis-Hastings algorithm among the number of posterior modes obtained from running BFGSI optimization procedure*. A common practice is to select the parameter values having the highest occurrence among the results of numerical optimization procedure as the initial draw for Bayesian estimation procedure. Before

13 running the Metropolis-Hastings algorithm, a scaling constant is calibrated to achieve the acceptance rate of per cent. Finally, a Markov chain of 800,000 iterations is run; the first 400,000 draws are discarded as a burn-in phase to eliminate the dependency of the chain on its starting values. The likelihood function is then combined with diffuse prior distributions to compute the posterior densities of the model s structural parameters. The resulting statistics of posterior distributions of the structural parameters are presented in Table 4. Full posterior distributions of the parameter estimates are depicted in Figure 1 in the Appendix. They reveal several features that are important for the model s results. The permanent technology shock, domestic spending and interest rate shocks are well identified as their autoregressive and standard deviation parameters are dispersed in relatively narrow ranges. The autoregressive parameter estimate of a preference shock process is distributed in a very narrow range, yet the shock s variance measure is weakly identified. Thus the size of the shock and its impact on the observable variables may be quite dispersed. Posterior distribution estimates display the highest incertitude about the transitory productivity shock s persistence. The 90 per cent probability interval for the shock s autoregressive parameter takes almost the entire prior range thus making it is uncertain how fast the shock effects die out in the economy. On the contrary, the size of a transitory productivity shock represented by its standard deviation parameter is estimated to be in a narrow range, thus the immediate impact of the shock in the economy is evaluated rather precisely. The debt elasticity parameter is estimated to be small and defined in a narrow range, supporting the interest rate premium insensitivity finding. A. Proškutė Business Cycle Drivers in Lithuania Results The estimated model delivers a number of results. In the following subsections we discuss the parameter estimates and their influence on the model s results. We also show the model s fit to actual data to check the robustness of the estimated model. Finally, we present impulse response functions and variance decomposition of main macroeconomic variables in response to structural shocks of the system. This gives the intuition of the structural shock transmission mechanism in the economy and the relative importance of each of the shocks on the dynamics of the selected macroeconomic variables in Lithuania Parameter estimates In the estimated model all the structural shocks can be analysed in terms of their size and persistence. Among the two productivity shocks permanent shock is much larger and persistent than the transitory shock. Preference shock is estimated to be the largest disturbance with the longest-lasting effects among the structural shocks in the system. Domestic spending shocks are estimated to be relatively large but their effects die out quickly. On the contrary, interest rate shocks are rather small but their effects are longlasting. High persistence of permanent productivity, preference and interest rate shocks, the distribution means of which lie between 0.70 and 0.99, are in line with other studies of small open economies. Comparing these shock characteristics to analogous shocks investigated by Karpavičius (2008) in Lithuania we can see a number of concurrences. A non-stationary productivity shock was calibrated at 0.85 (following Smets and Wouters 2003) and our estimated mean value of the parameter is The mean of interest rate shock persistence is estimated to be 0.85 in our model versus the calibrated value of 0.88 by Karpavičius (2008). Preference shock is estimated to be slightly more persistent (the value of 0.96) compared to discount rate shock of 0.85 assumed in Karpavičius (2008). Preference and interest rate premium shocks exhibit similar very high degrees of persistence in Lithuania as the findings by Garcia-Cicco et al. (2010) for Argentina. On the other hand, the inertia of a domestic spending shock is smaller in both surveys.

14 Pinigø studios 2012/1 Ekonomikos teoria ir praktika 14 There is no consensus in the economic literature about the importance of transitory productivity shock effects on the business cycle. In our estimated model transitory productivity shock is found to be of a small size and thus of a limited impact on the dynamics of economics. High persistence of permanent productivity shock is needed to achieve the observed volatility of output and consumption and the variable cross-correlations with output at the levels of the empirical dataset. An alternative parameter r g value of 0.5 lowers considerably the cross-correlations with output and reduces standard deviations of all variables. Similarly, lower size of the permanent productivity shock reduces the volatilities of all observables. The reduction of the interest rate shock persistence (parameter r μ ) lowers the volatility of investment; the dynamics of output and investment then are closer to each other, as a result of which their cross-correlation increases deviating from the respective statistics in the empirical data. Artificially larger interest rate shock boosts the volatility of investment and weakens its procyclical behaviour patterns. Modifications of the discount rate shock s autoregressive parameter lead to an excessive volatility of consumption and the reduction in consumption-output correlation. Finally, only several times higher size and persistence of the domestic spending shock would have more significant effects on the economy. The mean of risk premium elasticity is estimated to be 0.02 in our model. The small para meter value is in line with the value of used by Karpavičius (2008), especially taking into consideration the width of the prior range considered for the parameter s prior distribution. The estimated parameter value implies a moderate reaction of the interest rates to net foreign debt changes; it also suggests that the main movements in domestic interest rates come from stochastic interest rate shocks not associated with the level of indebtedness of the Lithuanian economy. This model s result is supported by the evidence provided by Lithuanian sovereign debt and interest rate data analysis (see Figure 2). Figure 2. Lithuanian public foreign debt and interest rate spreads of long-term government bonds (Lithuania vs. Germany) Sources: European Central Bank, Statistics Lithuania; the author s calculations. Even though the rapid foreign debt-accumulation period in Lithuania coincides with the episode of higher interest rate spreads of Lithuanian long-term government bonds denominated in Euros against the interest rate of German government bonds, it is clearly detached from the level of foreign public debt. The interest rate spreads started shrinking earlier than the actual accumulation of the Lithuania s public foreign debt slowed down; moreover, in 2011 they are at their long-term average, while the foreign public debt is at its highest-ever level. Thus the hike of the interest rate spreads cannot be explained by the level of Lithuanian public foreign debt; rather it is attributable to other economic

15 events unrelated to the domestic economy (global financial crisis and overall uncertainty in financial markets) Model fit Table 5 Conducting a moment matching task is a common macroeconomic model s robustness evaluation procedure. The comparison of simulated and empirical moments of the analyzed economic variables gives an evaluation of a model s fit. Comparing the empirical data statistics calculated from the actual quarterly data sample for Lithuania from 1995 Q1 to 2011 Q2 and our model s simulated moments in Table 5 we can see that the model fits well the observed volatility of output, consumption and investment. The implemented model structure replicates a higher volatility of consumption compared to that one of output and a largely more volatile investment seen in the actual data. The model slightly overestimates the volatility of trade-balance-to-output ratio. Possibly this is stemming from the assumption made during the calibration procedure during which the steady-state trade-balance-to-output ratio was defined at a different level than seen in the empirical averages of the Lithuanian data. Statistical moments of Lithuanian data, and model s simulated results A. Proškutė Business Cycle Drivers in Lithuania 15 Moments Source gy gc gi tby Standard deviation, p. p. Data (st. dev.) 2.26 (0.33) 3.03 (0.49) 9.47 (1.37) 5.87 (1.43) Model Correlation with gy Data (st. dev.) 1.00 (-) 0.56 (0.11) 0.49 (0.11) (0.13) Model Correlation with tby Data (st. dev.) (0.13) (0.13) 0.07 (0.13) 1.00 (-) Model First-order autocorrelation Data (st. dev.) 0.32 (0.12) 0.24 (0.12) 0.06 (0.13) 0.82 (0.07) Model Source: Lithuanian Statistics; author s calculations. The model mimics reasonably well the correlation of the growth rates of consumption, investment and trade-balance-to-output ratio with the output growth sequence. As the empirical correlations of the observable variables with the trade-balance-to-output ratio in the data sample are highly insignificant thus exhibiting a high uncertainty about the actual correlations in the population, the model gives satisfactory results in replicating these. The model simulates correctly the highest first-order autocorrelation function value of the trade-balance-to-output ratio compared to other variables under consideration. For other variables the estimated first-order correlations are lower than in the actual data, yet they still fit into two-standard deviations intervals of their respective empirical counterparts. The autocorrelation function of the trade-balance-to-output ratio is slighty flatter than exhibited in the actual quarterly data sample (1995 Q Q2), yet it still falls into two standard deviations interval of the actual data (see Figure 3). The reason for the mismatch between the empirical moments and model s estimates of the autocorrelation function lies in the small estimated parameter of risk premium elasticity to foreign debt levels accumulated by the country. The slope of the curve increases with the parameter y as shown by Uribe (2012). However, the model s posterior distribution of the parameter embeds it into low-sensitivity region. Artificially imposing higher values of the debt elasticity parameter would distort the correlations between output and other variables and would unreasonably strengthen the correlation between trade-balance-to-output ratio and the remaining variables.

16 Figure 3. Autocorrelation function of trade-balanceto-output ratio in Lithuania Pinigø studios 2012/1 Ekonomikos teoria ir praktika 16 Moreover, reducing the model specification to the basic RBC model without preference, interest rate and domestic spending shocks and financial frictions significantly worsen the performance of the model. The basic model fails to predict not only the downward sloping autocorrelation function of trade-balance-to-output ratio but also has problems in capturing the standard deviations of the aggregate demand variables and their crosscorrelations*. Thus the basic RBC model is not considered as the alternative for Lithuanian business cycle description Impulse response functions *The results of a basic model are available from the author upon request. Model s impulse response functions are presented in Figures 2 6 in the Appendix. They offer an additional look into the structural shocks dynamic effects on the macroeconomic variables of interest. Variables notations in impulse response function figures are presented in Table 2 of the Appendix. Figure 2 of the Appendix shows the effects of a positive preference shock affecting the inter-temporal substitution of households and thus making current consumption more attractive than future consumption. This produces an immediate rise in consumption with a crowding-out effect on investment; the latter reduces capital stock over a number of consecutive periods. The increase in domestic consumption is supported by increasing imports, as a results of which trade-balance-to-output ratio deteriorates (imports increase and exports go down). High persistence of a preference shock keeps the economy away from its balanced growth path for a relatively long period. As a result of an increase in interest rates (see Figure 3 of the Appendix) investment drops down temporarily. This affects the stock of capital negatively, which further translates into a temporary decrease in output. Decreasing stock of capital raises the marginal product of capital which in turn influences negatively the hours of work that further dampens the output of the country. Lower output affects the consumption negatively which in turn depresses imports to the country and produce a positive temporary effect on trade-balance-to-output ratio. Domestic spending shock (see Figure 4 of the Appendix) has a negative effect on a trade-balance-to-output ratio implying that most of government purchases are directed to the consumption of imported production. Increase in imported production partially crowds out local production, which then results in the reduction of labour hired and capital utilisation in the production process. This is followed by a reduction in consumption and investment. The combination of public spending shock s negative effects on output, number of hours of work, investment and capital accumulation together with a drop in the trade-balance-to-output ratio make external debt of the country rise (increasing public spending is financed by additional borrowing and increase in the external debt).

17 The effects of a positive non-stationary productivity shock are depicted in Figure 5 of the Appendix. The shock raises the growth rate of output permanently. Households attempt to smooth their consumption over time thus they increase their consumption by a larger amount than the actual output growth. In other words, current income growth is lower than the current consumption increase resulting in a worsening trade balance of the country and gradually increasing foreign debt. Consumption smoothing also crowds out investment, which harms the initially assumed long-run output growth. A positive transitory productivity shock (see Figure 6 of the Appendix) leads to a temporary increase in output and consumption. Households understand that the change in income growth is not permanent, thus they try to smooth consumption in time not spending all the additional income immediately. Higher saving leads to higher capital stock, yet at a smaller rate than an increase in saving due to the presence of capital adustment costs. Labour supply responds positively to all the changes. Higher labour and capital produce an additional positive effect on output. Exports grow as a result of productivity advancements, imports also increase in response to a higher do mestic demand. Yet, the growth in exports exceeds that one of imports leading to an overall increase in the trade-balance-to-output ratio. All of the factors contribute to a lower foreign debt of the country. The next period higher consumption and investment growth cannot be supported as productivity is not increasing anymore. Therefore growth rates of the respective variables start gradually decreasing which results in decelerating labour supply, capital accumulation rates and trade-balance-to-output ratio. The economy converges back to its steady-state. A. Proškutė Business Cycle Drivers in Lithuania Variance decomposition The question about the driving forces of the business cycle in Lithuania can be best answered by looking into variance decomposition of four observed macroeconomic variables into the percentage shares of all model shocks presented in Table 6. Table 6 Variance decomposition of aggregate demand components in Lithuania (per cent) gy gc gi tby Preference shock Country premium shock Domestic spending shock Permanent productivity shock Transitory productivity shock Measurement errors Table 6 shows that the growth of output is mostly affected by non-stationary productivity shocks. The same shock affects the consumption dynamics, yet to a smaller extent, around 25 per cent of its total variance. The most influential sources of consumption fluctuations are shifts in the marginal utility of consumption (preference shocks). Preference shocks are also most important factor of trade-balance-to-output ratio dynamics implying a close relationship between consumption and net exports in the economy, which is most likely stemming from imported goods consumption by the households. Thus shifts in the marginal utility of consumption (preference shocks) have a strong impact on trade balance movements as well. Country premium shocks are the most important sources of investment growth dynamics. Non-stationary productivity disturbances play a smaller role in explaining the movements in investment. Some of the above-mentioned results differ from findings in other emerging countries: among the two productivity shocks permanent productivity shock is more important in driving the output in Lithuania; this result is in line with the findings of Aguiar and Gopinath (2007a, b) but contradict to the results of Garcia-Cicco et al. (2010) where transitory productivity shock is found to have the highest effect on the variance of output