Nominal rigidities and wage-price dynamics in DSGE model of open economy: application for the Czech Republic

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1 Nominal rigidities and wage-price dynamics in DSGE model of open economy: application for the Czech Republic Miroslav Hloušek Masaryk University, Faculty of Economics and Administration, Department of Economics Lipová 41a, 62 Brno ÐÓÙ ÓÒºÑÙÒ ºÞ Abstract The goal of this paper is to examine importance of nominal rigidities especially of wages and prices in the Czech economy. As a tool, DSGE model of open economy with nominal rigidities is used. The model is estimated on data of the Czech economy using Bayesian techniques. The dynamical properties of the model are studied using impulse responses with emphasis on wage-price dynamics. Next, the relative importance of nominal rigidities is examined using sensitivity analysis. The conclusion is that nominal rigidities as such are important feature of the model economy. The model specification without nominal rigidities has the worst fit to data. Next conclusion is that wages are more rigid than prices. Estimated Calvo parameters showed that wage contracts last longer than price contracts and assumption of flexible nominal wages does not correspond to data well. Model with flexible domestic prices showed best performance on data. Rigidities in import prices are also quite important while export prices stickiness is not so significant. These results should be taken into consideration for forming of monetary policy by the central bank and for modelling of behaviour of the Czech economy. 1 Introduction 1.1 Motivation New Keynesian economics is mainstream in present macroeconomics. Methodologically, this theory builds on Real Business Cycle theory but introduces new aspects such as monopolistic competition and nominal rigidities which give rise to short run non-neutrality of monetary policy. Monetary factors thus play significant role; central bank can influence the real interest rate (through controlling nominal interest rate) and subsequently other real variables. But in the long run, all prices and wages adjust and 1

2 economy returns to its natural equilibrium. New Keynesian models are not only in the center of academic research, but they are also widely used in central banks and other institutions for forming and evaluating of economic policy. Nominal rigidities play important role in New Keynesian models because they also help to match some features of data such as persistence of inflation, correlation between real and nominal variables or slow passthrough from exchange rate movements into prices. Nominal rigidities have also important effects for optimal monetary policy. As Erceg et al. (2) show in their model, if both prices and wages are sticky the natural equilibrium can not be attained by means of monetary policy. The policy that focuses exclusively on stabilizing price inflation, as most central banks do, is suboptimal. The central bank should aim at appropriate weighted average of price and wage inflation to mitigate welfare losses relative to the first best optimum. These weights are functions of structural parameters that describe preferences and technologies in the model economy. And some of the structural parameters relates to degree of price or wage stickiness. Thus the importance of nominal rigidities, especially of wages and prices, has significant impact for pursuance of monetary policy and its stabilization effects. There is number of empirical studies on relative importance of price and wage stickiness, for various countries using various estimation techniques. The results show quite mixed picture and suggest that this issue can be country specific. E.g. Ambler et al. (23) combine GMM and SMM 1 for estimation of DSGE model for Canada. Their model assumes Calvo (1983) pricing mechanism for domestic prices, import prices and wages and the results of estimation indicate that wage contracts last longer than price contracts. Smets and Wouters (23) estimate DSGE model for Euro area using Bayesian techniques. Relative importance of nominal rigidities says in favour of price stickiness. Adolfson et al. (27) use richer model with more nominal (and real) rigidities and estimate it also on Euro data using Bayesian methods. Their results confirm findings of Smets and Wouters. Christiano et al. (25) estimate DSGE model for US economy by minimizing a measure of the distance between the model and empirical impulse response functions. The length of Calvo contracts were quite similar but subsequent quantitative analysis shows that sticky wages play a crucial role in the model s performance while sticky prices play only limited role for good fit of the model. Del Negro and Schorfheide (28) argue that some degree of price rigidity is needed to describe US data but the whole issue is much more complex and the results may be 1 Generalized method of moments (GMM) and Simulated method of moments (SMM). 2

3 influenced by the choice of priors for parameters and by data sets. Maih (25) found out for Norwegian economy that wage contracts last longer than price contracts but adjustment to stochastic shocks is faster for wages than for prices. 1.2 Czech data evidence and the research question What can we say about rigidity of wages and prices in the Czech economy? First, we can look at raw data. Figure 1 depicts y-on-y growth rate of the real wage and y-on-y inflation rate of CPI. When there is a change in inflation the real wages reacts in opposite direction. This behaviour is consistent with the view that nominal wages are more rigid than prices. Figure 1: Inflation and real wages growth rate.12 CPI inflation Real wages growth rate Looking at data can give some qualitative answer about the source of rigidity. To get some quantitative answer, e.g. how much are wages more rigid than prices, two main approaches are available. The first approach uses microeconomic data. Babecký et al. (28) report results from the survey made among Czech firms. There is clear evidence that wage contracts last more than price contracts. The second approach how to assess degree of rigidity relies on aggregate data. Babecký (28) or Babecký and Dybczak (28) use various 3

4 methods such as time varying Phillips curve, cointegration of the macroeconomic series or structural vector-error correction framework on Czech data. Their findings confirm the fact that wage rigidity prevails on the Czech labour market. Alternative way that uses aggregate data is model approach. It is widely used by many researchers as number of papers cited above shows. And this is the approach that I have chosen. I want to verify facts about the source of nominal rigidities on macro level using model approach. To use the model is convenient because it can capture many other factors such as various types of shocks, transmission mechanisms, openness of the economy and also mutual relationship between wages and prices. The first research question of the paper is to find out whether wages are more sticky than prices. The second question is wider and asks which type of nominal rigidities is the most important for modelling of the Czech economy. To provide answers to these questions, the DSGE model of open economy with nominal rigidities on various markets is used. The model is estimated on Czech data using Bayesian techniques. The behaviour of the model is studied along several dimensions including impulse responses, variance decomposition or sensitivity analysis. The emphasis is put on relative importance of wage and price stickiness and on their joint dynamics. There already exist some DSGE models that are estimated on Czech data using Bayesian approach, e.g. Musil (28) or Remo and Vašíček (29). However, they do not assume rigidity in wages. Other models that include wage rigidities and are applied on Czech economy use calibration instead of estimation. For example, Vlček (27) uses Calvo setup for rigidities in prices and wages and he assumes higher rigidity in wages than in prices. The reasoning is stylized fact of acyclical real wage behaviour during business cycle in the Czech economy. Similarly, Andrle et al. (29) have cascade of nominal and real rigidities in calibrated policy model for the Czech economy. They also assume that wages are more rigid than consumer prices with reference to stylized facts of the Czech economy. 2 The Model The model is borrowed from Maih (25), it is slightly extended (especially by rigidities on export market) and adjusted for Czech economy conditions. Detailed description of the model can be found in Hloušek (28). The model economy consists of the following agents: households, firms and aggregators, government, central bank and foreign sector that is modelled exogenously. There is monopolistic competition on the markets 4

5 of various goods and on the labour market. This market structure implies that goods and services are imperfect substitutes and the firms (households) have certain market power and they can set price of their goods (wages). This allows existence of frictions which are modelled in the form of Calvo (1983) contracts with indexation. Specifically, there are rigidities in the following sectors: labour market, market of domestic intermediate goods and market of imported and exported intermediate goods. The optimization problem of agents results in Phillips curve, which has following form (here for prices of imported goods; similarly for other prices/wages) ˆπ f t = β 1 + β E t ˆπ f t β ˆπ f t 1 + (1 δ f)(1 βδ f ) δ f (1 + βδ f ) The hybrid Phillips curve shows that contemporary inflation (of imported intermediate goods) depends on both lagged and expected future inflation and on the gap of the real marginal cost. Parameter β is subjective discount factor, β (, 1), and δ f is Calvo parameter that expresses the degree of nominal rigidity, δ f [, 1). This parameter is quite crucial in our analysis; it says how often the contracts are reset. Average length of contract can be calculated using formula: 1 1 δ f. 2 Similar Phillips curves characterize behaviour of inflation in all sectors with monopolistically competitive markets. The production structure of the model is illustrated in Figure 2. Nominal rigidities in price setting are depicted by dashed line. Domestic intermediate firms use labour and final goods that are not consumed as factors of production. Part of domestic intermediate goods is exported and the other part, together with imported intermediate goods, is used for production of final goods. Final goods are either consumed by households and government or used as input in production of intermediate goods. The model also includes one type of real rigidity that is expressed by habit in consumption. Thus the benchmark model contains four types of nominal rigidities and one real rigidity. The model is rather complex, there are 47 sequences of variables and thus 47 equations are needed to solve the system. The model does not have an analytical solution; it is possible to get only approximate numerical solution. First, the variables are transformed into stationary form and the steady state of the model is computed. Then the model is log-linearized around the steady state and the system of equations is transferred into state-space form. Blanchard and Kahn (198) procedure or its modification outlined in Klein (2) can be used for deriving of numerical solution of 2 If δ f =.75, contract is not changed for 4 quarters mc f t 5

6 Figure 2: Production side of the economy Labor h t (i,j) [W t (i)] Aggregator Imported intermediates Y F,t (j ) [P F,t (j )] Domestic intermediates Y H,t (j) [P H,t (j)] h t (., j) [W t ] Aggregator Y F,t [P F,t ] Y H,t [P H,t ] Y X,t [P X,t ] Exported intermediates Y d H,t Y [P t ] Aggregator G Government spend. C Consumption (Y G C) Investment 6

7 the system. The log-linearized system consists of 41 equations. 3 There are 28 endogenous variables and 13 exogenous shocks. Some of the structural parameters were calibrated and 31 parameters remain to be estimated. 3 Estimation methodology For the estimation of model parameters I used Bayesian methods. It combines maximum likelihood with some prior information on the distribution of the parameters to form the posterior density function of those parameters. All the computations are done using Dynare toolbox in Matlab software. 4 The joint posterior distribution of the vector of parameters is obtained in two steps using numerical algorithms. In the first step, the posterior mode and the Hessian matrix evaluated at the mode are computed by standard numerical optimization routines. The likelihood function is computed first by solving the model and then by using the Kalman filter. In the second step, Random Walk Chain Metropolis-Hastings algorithm is used for generating of samples from joint posterior distribution to carry out Bayesian inferences. The algorithm starts from the mode and generates 1,, draws from the posterior distribution. 5 % of replications are discarded so as to avoid influence of the initial conditions. The moments of the posterior distribution are computed through Monte-Carlo averaging of the remaining draws. Markov Chain Monte Carlo diagnostics were used for convergence verification of the algorithm. The prior values of the estimated parameters were set following the literature, other empirical studies or according to great ratios calculated from data. The data used for estimation are quarterly, spanning period from 1996:Q1 to 27:Q4. Time series are obtained from databases of the Czech Statistical Office, the Czech National Bank and the European Central Bank. The model variables and their empirical counterparts that enter the estimation are worked hours (h t ), the growth rate of consumption (π ct ), the growth rate of output (π yht ), the real exchange rate (rer t ), wage inflation (π wt ), inflation of domestic prices (π ht ), inflation of import prices (π f t ), the CPI inflation and nominal interest rate (R t ). Processes and corresponding variables that are estimated exogenously are government 3 Some of the variables and equations are not important in equilibrium and therefore were dropped. 4 Dynare is a free software for solving and simulation of (non-)linear models with forward looking variables. It can be also used for estimation of model parameters either by maximum likelihood or using a Bayesian approach. See ØØÔ»»ÛÛÛº ÝÒ Ö ºÓÖ» for more details. 7

8 spendings (g t ), foreign output (y t ), foreign inflation (π t ) and foreign interest rate (R t ).5 Government spendings are estimated as AR(1) process, foreign sector as SVAR model. OLS method was used for estimation of these processes. 4 Results of estimation Table 1 shows the results from the Bayesian estimation. The structural parameters and their domain are presented in the first and second column. The third up to the fifth column summarizes moments of the prior distribution. The mode and the standard deviation of the posterior maximization are reported in the sixth and seventh column. The eighth column shows the posterior mean together with the 5th and 95th percentile of the posterior distribution (ninth and tenth column). The last two columns thus constitute the 9 % confidence interval. Let us start interpretation of the results with the parameters describing degree of nominal rigidity Calvo parameters (δ f, δ h, δ w, δ x ). The average duration of wage contracts is nearly 7 quarters and that of domestic price contracts is only 1.7 quarters. 6 It indicates that wages adjust more sluggishly than domestic prices. More importantly, according to this measure, wages are the most rigid and domestic prices are the most flexible nominal prices. Calvo parameters (and contracts duration) for other nominal variables lie between these two values. Average duration of price contracts for imported intermediates is 4 quarters and for exported intermediates 2.7 quarters. The point estimate of Calvo parameter for domestic prices deviated from the prior value more than three times the standard deviation. However, this result turned out to be robust outcome of the estimation procedure. Next two parameters describe preferences of households. The habit formation (hab) seems not so important, its posterior mean is.6937, lower than the prior value. The mean of the Frisch labor supply elasticity (inverse of υ) is which indicates that labour adjust quite slowly to the real wage movements. However, this estimated value should be taken with care because time series of hours worked was found nonstationary and enter the estimation with measurement error. Parameter γ expresses openness of the economy. More precisely (1 γ) should capture share of imports to output. Posterior mean of γ is.1629 which indicates much higher openness than the prior value. Labour share in the production function, parameter ψ, was estimated to It is 5 Foreign economy is represented by Euroarea that includes twelve countries. 6 Average duration of contract is calculated using formula 1 1 δ. 8

9 Table 1: Bayesian estimation results Prior distribution Posterior max Posterior distribution Par. Dom. Dens. Mean S.D. Mode S.D. Mean 5 % 95 % Nominal rigidities δ f [,1) beta δ h [,1) beta δ w [,1) beta δ x [,1) beta Preferences hab [,1) beta υ R + gamm Miscellaneous (CPI index, risk premium) γ [,1) beta ϕ [,1) invg.5 Inf Monetary policy reaction function α [,1) beta ω π R + norm ω yh R + norm Production and export function ψ [,1) beta θ x R + gamm Shock persistence ρ π T [,1) beta ρ θh [,1) beta ρ θw [,1) beta ρ θ f [,1) beta ρ zc [,1) beta ρ zy [,1) beta ρ zrp [,1) beta Standard deviation of shocks σ Zc R + invg.1 Inf σ Zls R + invg.1 Inf σ Zmp R + invg.1 Inf σ π T R + invg.1 Inf σ Zy R + invg.1 Inf σ Zrp R + invg.1 Inf σ θh R + invg.1 Inf σ θw R + invg.1 Inf σ θ f R + invg.1 Inf Standard deviation of measurement errors π ht R + invg.1 Inf h t R + invg.1 Inf

10 quite reasonable value, as the capital share 7 is usually calibrated to one third. The monetary policy reaction function shows very high interest rate smoothing. Mean of the parameter corresponding to the lagged interest rate, α, is This value seems to be too high in comparison with rhetoric of the Czech National Bank about inflation targeting as the main strategy. Weights on inflation and output in the reaction function, ω π and ω yh, are very similar to the priors; emphasis on inflation targeting is sixteen times higher than on output stabilization. However, these two parameters were not properly identified from the data; the difference between the prior and the posterior distribution was negligible which indicates that the parameters are rather calibrated than estimated. The price elasticity of export function, θ x, is rather high compared to the prior mean. Risk premium parameter was estimated to.192 showing lower response of risk premium to foreign debt. Looking at the autoregressive parameters of the shocks, the most persistent shock is the risk premium shock (ρ zrp =.5719). On the other hand, the least persistent are the shocks to price markup of imported intermediates (ρ θ f =.175) and markup of domestic intermediates (ρ θh =.3151). Other autoregressive shock processes exhibit inertia not far from the prior value. Looking at the volatility of the shocks, labor supply shock and shock to price markup of imported intermediates are the most volatile (σ Zls =.1415, σ θ f =.1321.) Quite substantial is also wage markup shock σ θw. Productivity shock, σ Zy, and monetary policy shock, σ Zmp are the least volatile. The measurement error of output growth is relatively small, measurement error of hours worked is more substantial but still acceptable. Their impact on the overall fit of the model could be considered as negligible. After the estimation, the model fit to data was assessed in three dimensions. Firstly, the fitted series were visually compared with the observed series. Secondly, the volatility and the autocorrelations implied by the model were compared with the statistics calculated from the data. And thirdly, estimated unobserved shocks were interpreted from the point of view of Czech economy history. For more details, see Hloušek (28). Overall assessment of the model in replicating the data can be considered as satisfactory. Next, the dynamical properties of the model were studied using variance decomposition and impulse responses. 8 Variance decomposition im- 7 Complement to one, (1 ψ). 8 Again see Hloušek (28) for full description. 1

11 plies that shock to import prices markup is the most important. It has substantial effect not only for nominal but also for real variables. Second most important shock is wage markup shock. Impulse responses offer interpretable behaviour of the model variables in reaction to various types of shocks. 4.1 Implications for wage-price dynamics The point estimates of Calvo parameters indicates how often the contracts change, but they do not say anything about the dynamics of wages and prices. Wages and prices are endogenous variables which means that they do not affect each other directly and they are subject to many other influences. Figure 3 shows impulse responses of wages (solid line) and consumer price index (dashed line) in reaction to exogenous shocks. The results show that behaviour of the variables depends on the type of shock and considered time horizon. Wages and prices behave almost identically in case of monetary policy and inflation target shock. The prices change quicker (lead) than wages for most of the shocks. 9 However, wages are significantly more volatile than prices for labour supply, wage markup and technology shocks. It is intuitive, because these shocks influence the process of wage setting directly. Wages and prices do not need to move in the same direction in the short run. Examples of such behaviour are responses to price markup shock and technology shock. In the case of technology shock, prices and wages diverge even in the long run (wages come to higher and prices to lower level than before the shock). At long run horizon wages and prices do not converge to the qualitatively and quantitatively same level for many shocks. The reasoning can stem from high openness of the Czech economy. Wages are the main component of domestic prices, but large part of CPI is composed of import prices and they are determined on different markets. 5 Sensitivity analysis This section focuses on assessment of relative importance of nominal rigidities in the model. Special attention is devoted to wage and price rigidity. The subject of interest is comparison of competing models in terms how they fit the data. These competing models assume flexibility in some of the prices or combinations of them. Quantitative measure of data fit provides marginal likelihood calculated from Bayesian estimation. The Bayesian estimation overcomes maximum likelihood estimation because it takes into 9 Leading behaviour is very subtle but is noticeable. 11

12 Figure 3: Wage-price dynamics 5 x Consumption pref. x 1 3 Technology x 1 3 Labor supply 4 x 1 3 Monetary policy 6 x 1 3 Inflation target 6 x 1 3 Risk premium x 1 3 Domestic prices markup.2 Import prices markup 5 x 1 3 Wage markup x 1 4 Foreign interest rate 3 x 1 3 Foreign output 6 x 1 4 Foreign inflation x 1 3 Government spending 1.5 W P 12

13 account the uncertainty that comes from the models or the estimates of shocks and parameters. Because the priors play key role in Bayesian estimation and can influence results in important way, it is necessary to set the priors of all estimated parameters for all models to their initial values. It is exceptionally important for the sensitivity analysis. 1 The competing models are derived from the benchmark model (with all rigidities) and assume flexible prices in particular sector(s). The term flexibility (or no habit persistence) means that corresponding parameter is set to The analysis considers following specifications: the benchmark model (BM), the model with flexible import prices (FIP), the model with flexible domestic prices (FDP), the model with flexible wages (FW) and the model with flexible export prices (FEP). Then some combinations with rigidities in two or more sectors are: the model with flexible domestic and export prices (FDEP), the model with flexible domestic, import prices and no habit formation (FDIPH) and model without nominal rigidities (FWDIEP). 12 Table 2 presents estimated parameters of competing models together with Laplace approximation of the log data density. The models are ordered according to the value of log data density which measures fit of the data. Table 3 shows computed posterior odds ratios of competing models. Posterior odd (PO) shows how many times one model specification is more probable compared to other. The range of this ratio is from zero to infinity. DeJong and Dave (27) with reference to Jeffreys (1961) interpret the weight of evidence provided by data in favour of model A against model B as follows. 13 Posterior odds between 1:1 3:1 constitute very slight evidence in favor of model A, between 3:1 1:1 slight evidence, between 1:1 1:1 strong to very strong evidence and values above 1:1 indicate decisive evidence. 14 As the models are ordered according to the value of log data density, the posterior odds ratio is always calcu- 1 However, Del Negro and Schorfheide (28) point out that standard setting of priors, macro time series and derived marginal likelihoods of data need not be the right guide for discrimination among different theories and can be even misleading in driving the conclusion in model comparison. They suggest alternative approach for choosing the priors that is based on quasi-likelihood function with the aim of levelling the playing field. However, I believe that this new approach does not have substantial qualitative influence for the results presented here. Nevertheless it could be interesting topic for further research if and how the results are quantitatively different. 11 It means that the contract is changed once in 1.25 quarters. 12 Some other specifications such as the models with flexible domestic and import prices (FDIP) plus flexible export prices (FDIEP) were also analyzed. Their performance to fit the data is not significantly different from FDIPH model, so they are not presented here. 13 See page 242 in DeJong and Dave (27). 14 However, these rules must be taken with reservation as the influence of uninformative priors may matter. 13

14 lated for two neighbouring model specifications. The table also reports posterior odds ratios for some other selected models. The results of the analysis are quite surprising. The model with flexible domestic prices fits the data better than the richer benchmark model. Also model with assumption of flexible domestic and export prices overtook the benchmark model. According to posterior odds ratios the FDP model is much better specification (PO FDP/BM = ) but FDEP is better only to smaller extent (PO FDEP/BM = 42.11). 15 With focus on relative importance between price and wage stickiness it is obvious that wage rigidity is more important than price rigidity. It is confirmed both by triumph of FDP model and by poor fit of FW model. 16 These results correspond to estimated values of Calvo parameters as already showed. Average length of wage contracts is the highest while domestic prices contracts last the shortest time. The second most important rigidity is of import prices as implied by Calvo parameter. And it is confirmed by the fact that flexible import prices model do not fit data well. Next, the results indicate that extension of the model by rigidities in export market (compared to Maih s (25) original model) has only small effect. Difference between benchmark model and that with flexible export prices is not so large. 17 The model without nominal rigidities and with only real rigidity (habit in consumption) has the worst fit of all models. It suggests that nominal stickiness as such is important phenomenon. Interesting fact is how the model parameters compensate the lack of rigidity in particular sector (compared to the benchmark model). The most striking difference is in estimates of Frisch elasticity of labor supply ( 1 1 υ ) which decreases from for the benchmark model to for the flexible wage model. It implies that labour supply is more unresponsive to changes in the real wage. In other words, the nominal rigidity in wages is transferred to rigidity in labour supply. Another structural parameter that is highly volatile for different specifications is γ. It expresses openness of the economy; more precisely (1 γ) should capture share of imports to output. However, γ also regards to the price index, it expresses weight of domestic prices in the CPI. Because the nominal time series (inflation of domestic prices, import prices and CPI) are used for estimation this influence is probably more important for the results. Value of γ fluctuates from.1629 for the benchmark model (very open economy) up to.5128 for flexible import prices model (smaller 15 I made also sensitivity analysis with different setting of priors for Calvo parameters (δ =.5 and δ =.25) but the results did not qualitatively changed, only posterior odds were slightly lower. 16 PO FDP/FW = 6.84E PO BM/FEP =

15 Table 2: Comparison of the models Par. Prior FDP FDEP BM FEP FDIPH FIP FW FWDIEP Nominal rigidities δ f [.2] [.2].7571 [.2] δ h.75 [.2] [.2] [.2] [.2] δ w [.2] [.2] δ x [.2].6329 [.2] [.2] Preferences hab [.2] υ Miscellaneous (CPI index, risk premium) γ ϕ Monetary policy reaction function α ω π ω yh Production and export function ψ xp Shock persistence ρ π T ρ θh ρ θw ρ θ f ρ zc ρ zy ρ zrp Standard deviation of shocks σ Zc σ Zls σ Zmp σ π T σ Zy σ Zrp σ θh σ θw σ θ f Standard deviation of measurement errors π yt π t Data density

16 Table 3: Posterior odd ratios Model specifications Posterior odd FDP vs FDEP 7.7 FDEP vs BM BM vs FEP 3. FEP vs FDIPH 5.7E+8 FDIPH vs FIP 5.5 FIP vs FW 2.25E+5 FW vs FWDIEP 9.51E+14 FDP vs BM FDP vs FW 6.84E+18 BM vs FIP 9.43e+1 openness). The domestic prices thus increased their ability in explaining (rigid) behaviour of CPI index. Low value of.94 for flexible wage model shows extreme openness to trade. This result is quite puzzle and can stem from mutual influence of more parameters for this specification. Finally, the question whether wage and price rigidity is interchangeable was examined. 18 This was done by comparison of impulse responses for different model specification, i.e. with different assumption about nominal rigidity and also by vector autocorrelations. Impulse responses for alternative models illustrated that the source of nominal rigidity had important impact for behaviour of several variables, especially in the short horizon. It was also confirmed by vector autocorrelation functions. The price rigidity is thus distinguishable from wage rigidity. 6 Conclusion This paper examined importance of nominal rigidities in DSGE model of the Czech economy with emphasis on wage-price dynamics. Results of estimation revealed quite clear conclusion. Estimated Calvo parameters show that wage contracts last much longer than price. The model approach allowed us to investigate the dynamics of wages and prices in more detail. The impulse response function show that adjustment of domestic prices is faster than of wages for many stochastic shocks. Next, prices and wages need not move in the same direction and can converge to different levels. Their joint dynamics depends on type of the shock and considered time horizon. Sensitivity analysis show that assumption of flexible nominal wages is flawed feature of the model and does not fit 18 See Hloušek (28) for details. 16

17 data well. On the other hand, model specification with flexible domestic prices is in accordance with the data. It means that rigidity in wages is more important than in prices. Regarding other types of nominal rigidities, the length of contracts for import and export prices are somewhere between the length of contracts for wages and domestic prices. Rigidity in import prices is also quite important while sticky export prices do not contribute much to model performance on data. The main message of the paper is that nominal rigidities as such are important characteristic of the model of the Czech economy. More importantly, monetary models for the Czech economy should include sticky wages, otherwise they miss an important feature of this economy. The paper confirmed results from microstudies among Czech firms and analysis of raw data that wages are more rigid than prices. Several topics for further research on both theoretical and empirical have arisen. The export/import side of the model economy could be more elaborated to better reflect the Czech economy. It includes e.g. dividing of the production into tradable and nontradable goods and/or incorporating of imports and exports of consumption and investment goods. The model can be extended by several real rigidities such as investment adjustment cost, variable capital utilization and working capital channel as in Adolfson et al. (27). Hot topic in recent times is incorporating of credit market frictions and financial accelerator into DSGE models as suggested by Bernanke et al. (1999). Interesting issue is also optimal monetary policy and its impacts for welfare as made e.g. by Vlček (27) or Remo and Vašíček (29) for Czech economy. On the empirical level, the sensitivity analysis can be carried out using Global Sensitivity Analysis (GSA) techniques propagated by Ratto (28). This approach can more effectively show possible weaknesses of estimation process or relationship between data series and parameters or between structural parameters and parameters of the reduced form. Next, the setting of priors for Bayesian estimation in the form of quasi-likelihood based priors as suggested DelNegro and Schorfheide (28) can have some quantitative impacts for the result. They are worth to be examined. References [1] Andrle, M. Hlédik, T. Kameník, O. Vlček, J. (29) Implementing the New Structural Model of the Czech National Bank, CNB Working paper series, 2/29. 17

18 [2] Adolfson, M. Laseen, S. Linde, J. Villani, M. (27), Bayesian estimation of an open economy DSGE model with incomplete passthrough, Journal of International Economics 72, [3] Ambler, S. Dib, A. Rebei, N. (23) Nominal rigidities and exchange rate pass-through in a structural model of a small open economy, Working Paper 23-29, Bank of Canada. [4] Babecký, J. (28) Aggregate Wage Flexibility in New EU Member States, Czech Economic Review, 37(2), [5] Babecký, J. Dybczak, K. Galuščák, K. (28) Survey on Wage and Price Formation of Czech Firms, CNB Working paper series, 12/28. [6] Babecký, J. Dybczak, K. (28) Real Wage Flexibility in the Enlarged EU: Evidence from a Structural VAR National Institute Economic Review, 24, [7] Bernanke, B. S. Gertler, M. Gilchrist, S. (1999) The Financial Accelerator in a quantitative business cycle framework. In Handbook of Macroeconomics, Vol. 1, editors: J. B. Taylor and M. Woodford. [8] Blanchard, O. J. and Kahn, C. M. (198) The solution of linear difference models under rational expectations, Econometrica 48(5), [9] Calvo, G. (1983) Staggered prices in a utility-maximizing framework, Journal of Monetary Economics 12, [1] Christiano, L. J. Eichenbaum, M. Evans, C. (25) Nominal rigidities and the dynamic effects of a shock to monetary policy, Journal of Political Economy 113(1), [11] DeJong, D. N. Dave, C. (27) Structural macroeconometrics, Princeton: Princeton University Press. [12] Del Negro, M. Schorfheide, F. (28) Forming Priors for DSGE Models (and How It affects the Assessment of Nominal Rigidities), Journal of Monetary Economics 55, [13] Erceg C. J. Henderson, D. W. Levin, A. T. (2) Optimal monetary policy with staggered wage and price contracts, Journal of Monetary Economics, 46, [14] Gali, J. (28) Monetary policy, inflation, and the business cycle: An Introduction to the New Keynesian framework. Princeton: Princeton University Press. 18

19 [15] Hloušek, M.: (28) Nominal rigidities in DSGE model with imperfect exchange rate pass-through, Working Paper, 28/28, Brno: ESF MU, CVKSČE, Available from: ØØÔ»» ºÑÙÒ ºÞ» Ó»½» ÓÙ ÓÖÝ»Ó Ð Ò» ÒØÖÙÑ»Ô Ô Ö» ÛÔ¾¼¼ ¹¾ ºÔ. [16] Jeffreys, H. (1961) Theory of probability, 3rd ed., Oxford: Clarendon Press, 447 p. [17] Juillard, M. (24) Dynare manual, Dynare Toolbox, latest version 4.1., CEPREMAP, Available from: ØØÔ»»ÛÛÛº ÝÒ Ö ºÓÖ. [18] Klein, P. (2) Using the generalized schur form to solve a multivariate linear rational expectations model, Journal of Economic Dynamics and Control 24(1), [19] Koop, G. (23) Bayesian Econometrics. Chichester: Wiley. [2] Maih, J. (25) Asymmetric Trade and Nominal Rigidities in a DSGE Perspective: Implications for the Transmission of Shocks and Real Exchange Rate Dynamics, PhD thesis, The University of Oslo. [21] Maih, J. (26) A Bayesian Investigation of Wage-Price Dynamics in a DSGE Model with Imperfect Exchange Rate Pass- Through, Discussion paper, Dynare conference, Available at: ØØÔ»»ÛÛÛº ÔÖ Ñ ÔºÒÖ º Ö» Ù ÐÐ Ö»Ô Ö ¼». [22] Musil, K. (28) International Growth Rule Model: New Approach to the Foreign Sector of the Open Economy PhD Thesis, Brno: Masaryk University. [23] Ratto, M. (28) Analysing DSGE Models with Global Sensitivity Analysis. Computational Economics Springer Netherlands, Vol. 31, No. 2. [24] Remo, A. Vašíček. O. (29) Estimate of the Czech National Bank s Preferences in NOEM DSGE model, Bulletin of the Czech Econometric Society. Vol. 16, No. 26. [25] Smets, F. Wouters, R. (23) An estimated dynamic stochastic general equilibrium model of the euro area, Journal of the European Economic Association 1(5), [26] Vlček, J. (27) Monetary Policy and its Stabilization Role. PhD thesis, Brno: Masaryk University, 14 p. 19