Labour Market in the Czech Republic: DSGE Approach

Železník, Martin Article Labour Market in the Czech Republic: DSGE Approach Review of Economic Perspectives Provided in Cooperation with: Masaryk University, Faculty of Economics and Administration Suggested Citation: Železník, Martin (2018) : Labour Market in the Czech Republic: DSGE Approach, Review of Economic Perspectives, ISSN 1804-1663, De Gruyter, Warsaw, Vol. 18, Iss. 3, pp. 225-259, https://doi.org/10.2478/revecp-2018-0011 This Version is available at: https://hdl.handle.net/10419/194194 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/ Review of Economic Perspectives – Národohospodářský obzor Vol. 18, Issue 3, 2018, pp. 225–259, DOI: 10.2478/revecp-2018-0011 © 2018 by the authors; licensee Review of Economic Perspectives / Národohospodářský obzor, Masaryk University, Faculty of Economics and Administration, Brno, Czech Republic. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 3.0 license, Attribution – Non Commercial – No Derivatives. Labour Market in the Czech Republic: DSGE Approach Martin Železník 1 Abstract: This paper deals with the comparison of two versions of the DSGE model, supplemented with labour market frictions, based on different data used. One of the data sets has been pre-filtered with the HP filter (lambda set to 1) to get rid of any noise and the other with the original data series with measurement errors allowed. I compare the models with the following tools: parameters estimation, impulse response analysis, standard deviation and cross-correlations and recursive forecast. I also present the historical shock decomposition of the labour market variables to provide the explanation of the development in the Czech labour market, which is considered the most efficient labour market in Europe of the last couple of years with the lowest unemployment rate. Key words: DSGE models, labour market, search and matching JEL Classification: E32, E44, E58, J01 Received: 18 March 2018 / Accepted: 24 May 2018 / Sent for Publication: 3 September 2018 Introduction A good model can be devalued by the application of various transformations of the data, producing different results. Thus, I provide an analysis that presents the results using two different data sets in the estimation of the same model. The model is designed to describe the labour market in the Czech economy as it plays an important role in the functioning and understanding of the economy. This topic is of interest to the policy makers who can influence the labour market in the economy by setting law boundaries in which the agents, households, workers and firms exist. Policy makers should also understand the driving forces of the labour market in order to prevent the high volatility of the key labour market variables. The aim of the paper is to compare the two versions of the model with a set of tools that can provide valuable information about the functioning of the model. Another, more empirical part of the paper is the identification of the main factors that can explain the 1 National Bank of Slovakia, Economic and Monetary Analyses Department, Section of forecasting, Modelling and International Economy Analyses, Imricha Karvaša 1, 813 25 Bratislava, Slovak Republic, [email protected]. Review of Economic Perspectives 226 development of the labour market in the Czech Republic especially in the last decade. I have used data from the 2000q1 − 2017q2 period. To achieve the objective of the paper, the model approach is used. The dynamic stochastic general equilibrium (DSGE) models belong among the main tools of a macroeconomic modelling used in many central banks and institutions as policy advice. The basic version of this model without an elaborate labour market is used in the National Bank of Slovakia (Výškrabka, Tvrz and Železník (2018), to be published). Model Since we focus on the labour market development, a DSGE model with an elaborate labour market and search and matching frictions is used for the analysis. We use a model much like the one used by the Czech National Bank developed by Andrle et al. (2009) but supplemented with labour market as designed by Christoffel et al. (2009) and Trigari (2006). Similar work can be found in Tonner et al. (2015), where they use different versions of the possible incorporation of the labour market and test the model for a forecast. The structure of the model is quite standard; therefore, we only describe its most important features. The domestic economy has been modelled using the following representative economic agents: households, intermediate firms, importers, final goods producers, government and central bank. Firms The monopolistically competitive intermediate firms combine capital and labour to produce domestic intermediate goods similar to the ones described by Christoffel et al. (2008). Homogenous bundles of the intermediate goods together with homogenous bundles of imported goods are then used by the final goods producers. There are four different final production sectors that produce consumption goods, investment goods, government consumption goods and export goods. Each sector is comprised of infinite number of firms which combine domestic intermediate and imported goods to produce final goods similar to Gomes et al. (2010). Each firm produces distinct goods which allows them to charge a price that may differ from the prices charged by its competitors. Nevertheless, firms are not allowed to re-optimize prices every period. They follow the Calvo (1983) pricing mechanism, where only a fraction of firms can re-optimize their prices in a given period. All of the remaining firms adjust their prices according to the past and steady-state inflation. Moreover, firms producing export goods set prices in foreign currency (local currency pricing), which prevents the immediate transmission of exchange rate movements to prices. Capital is a homogeneous production factor which is rented by the firms on a perfectly competitive market. On the other hand, there are infinitely many different types of labour and imported goods. All firms also pay taxes levied on their wage cost (social security). Households Households are Ricardian – they consume, own capital (invest), own firms, have access to financial markets (both domestic and international), supply labour and negotiate the price of their labour service. They also receive transfers from government and pay consumption (VAT), labour and dividend income taxes. The household members maximize Volume 18, Issue 3, 2018 227 the given expected lifetime utility similar to the one described by Christoffel et al. (2008). Monetary authority The monetary authority sets the nominal interest rates according to the modified Taylor (1993) rule: 𝑅 𝑡 4= 𝜌𝑅𝑅 𝑡−1 4+(1−𝜌𝑅)(𝜙𝜋(𝜋𝑡−1 4−𝜋𝑡 4)+𝜙𝐶𝐶𝑡 + 𝜙𝑆Δ𝑆 󰆹𝑡+1)+𝜀𝑡 𝑅. Current value of nominal interest rate deviation from its steady state 𝑅 𝑡 4 depends on its previous value 𝑅 𝑡−1 4, on the deviation of previous inflation 𝜋𝑡−1 4 from its steady-state 𝜋𝑡 4, on real consumption gap 𝐶𝑡  – which is here because the GDP variable does not exist in the model and consumption works as the approximation of GDP – and on deviation of expected nominal exchange rate Δ𝑆 󰆹𝑡+1. The parameter 𝜌𝑅 represents the smoothing parameter, 𝜙𝜋weight parameter of lagged inflation 𝜋𝑡−1 4 , 𝜙𝐶 weight on consumption gap, and 𝜙𝑆weight on expected nominal exchange rate. Deviations of interest rate from the interest rate rule are explained as monetary policy i.i.d. shock 𝜀𝑡 𝑅. Fiscal authority The government collects taxes (both distortionary and lump-sum) paid by households and firms. It unproductively consumes part of its income and pays the rest in a form of transfers to households. The difference between revenues and expenditures is financed by issuing bonds. Financial markets Financial markets are incomplete, which means that households are unable to perfectly insure against unexpected shocks. This structure leads to the UIP condition, which links together the domestic interest rates, foreign interest rates and expected changes in the exchange rate. Foreign sector The foreign sector is comprised of interest rates, prices and the demand for domestic export goods. This sector is exogenous, reflecting the negligible size of the domestic economy. Similarly to the Taylor rule, the foreign inflation 𝜋𝑡 𝐼𝑀∗is defined as the deviation from its steady state. In this paper’s set up, the foreign inflation is only influenced by the foreign monetary policy 𝑅𝑡 ∗ that corresponds with the ECB. The foreign output 𝑌𝑡𝐼𝑀∗, which determines the foreign demand for the domestic economy exports, is defined in similar fashion. The monetary policy in the foreign economy, in this case the Eurozone, is again defined via the Taylor rule, where the deviation of current nominal interest rate from its steady state 𝑅𝑡 ∗ is influenced by foreign inflation 𝜋𝑡 𝐼𝑀∗ and foreign output 𝑌𝑡𝐼𝑀∗ with their representative weight parameters 𝜅𝑅∗𝜋𝐼𝑀∗ and 𝜅𝑅∗𝑌∗. Each equation includes i.i.d. shocks and a straightforward explanation. Labour Market In this section the focus is on labour market, the main interest of the study. This model contains a labour market block with the search and matching frictions (S&M) and right- Review of Economic Perspectives 228 to-manage bargaining (RTM). Christoffel et al. (2009) and Trigari (2006) are the main consulted sources. In this alternative setup, an additional economic agent is introduced to the model - the employment agencies 2 . They act as the middleman between households that supply their labour and the intermediate firms which buy the labour as an input in their production. The labour agencies negotiate with the workers their wage and set the optimal amount of hours worked per employee according to the RTM concept. Under the RTM, the workers and the firms only negotiate the hourly wage rate and the firm then chooses the employment along the intensive margin 3 . This would imply a direct channel from the wages to inflation, so that the level of hourly wages and their stickiness play a direct role in inflation dynamics. This wage channel is in line with much of the New Keynesian modelling tradition, as seen in e.g. Christiano et al., (2005) and Smets and Wouters (2003). First, I build on Trigari's RTM framework to allow for a direct channel from wages to inflation. Second, once the firm and the worker meet, they bargain over the hourly wage rate, but in an infrequent way, where the staggering of the wage-setting process is modelled according to Calvo (1983). I assume there is a continuum (normalized to one) of perfectly competitive employment agencies, each employing only one worker. The production function of j-th employment agency is: 𝑁𝑡𝑂𝑈𝑇(𝑗) = 𝑧𝐿𝑀𝑁𝑡𝐼𝑁(𝑗)𝛼𝐿𝑀, where zLM is a scale parameter and 𝛼𝐿𝑀 is elasticity of the production function. The employment agency pays workers for NtIN(j) hours of work and sells NtOUT(j) hours of work to the intermediate firms. Due to perfect competition and the homogeneity of workers, the aggregate production of employment agencies is: 𝑁𝑡=∫𝑁𝑡𝑂𝑈𝑇 𝑛𝑡 0(𝑗)d𝑗 = 𝑛𝑡𝑁𝑡(𝑗), ∀𝑗, where 𝑛𝑡 is the number of employed workers in the population. The employment evolves according to the following law of motion 𝑛𝑡=(1−𝜌𝐿𝑀)𝑛𝑡−1 +𝑚𝑡−1, where 𝜌𝐿𝑀 is exogenous separation rate that determines how many job-worker pairs are destroyed each period, and 𝑚𝑡−1 is the number of new matches formed in the previous period. Since the labour force 4 is normalized to one (the labour force is not modelled in this paper), the unemployment rate is expressed as 1-nt at the beginning of the period. However, it is assumed that the workers that have lost employment start searching for a new job within that same period. Therefore, the pool of unemployed workers available for hire evolves according to 𝑢𝑡= 1−(1−𝜌𝐿𝑀)𝑛𝑡. 2 In reality, one could link the theoretical concept of employment agencies to the human resources department of the intermediate firms 3 Intensive margin represents the hours worked. 4 Labour force is defined as a sum of employment and unemployment. Volume 18, Issue 3, 2018 229 We assume that the search and matching process follow a standard matching function 𝑚𝑡= 𝜒𝑡 𝐿𝑀𝑢𝑡 𝜈𝐿𝑀𝑣𝑡 1−𝜈𝐿𝑀, where 𝜒𝑡 𝐿𝑀 is matching efficiency shock, 𝑣𝑡 is the number of vacant jobs and 𝜈𝐿𝑀 is the elasticity of matching function w.r.t. unemployment. The matching efficiency shock develops according to 𝜒𝑡 𝐿𝑀 = 𝜌𝜒𝜒𝑡−1 𝐿𝑀 +(1−𝜌𝜒)𝜒𝑆𝑆 𝐿𝑀 +𝜀𝑡 𝜒, where 𝜀𝑡 𝜒∼ 𝑁(0,𝜎𝜒). To be able to describe the behaviour of workers and employment agencies, we now need to define their respective value functions. The Bellman equation for employed workers 𝒲𝑡(𝑗) that take part in wage bargaining captures the trade-off between labour income and disutility of work 𝒲𝑡(𝑗)=(1−𝜏𝑡 𝑤)𝑊𝑡∗𝑁𝑡𝐼𝑁(𝑗)−𝜅𝐿𝑁𝑡 𝐼𝑁(𝑗)1+𝜓 (1+𝜓)Λ𝑡 𝐼+ 𝐸𝑡{𝛽𝑡,𝑡+1 [(1−𝜌𝐿𝑀)(𝜔𝑤𝒲𝑡+1(𝑗)+(1−𝜔𝑤𝒲∗𝑡+1(𝑗)))+𝜌𝐿𝑀𝒰𝑡+1(𝑗)]}, where 𝛽𝑡,𝑡+1 = 𝛽Λ𝑡+1 𝐼 Λ𝐼𝑡 is a stochastic discount factor, Λ𝑡 𝐼 is marginal utility, 𝑊𝑡∗ is the newly bargained wage, 𝜏𝑡 𝑤 is the income tax payed by the workers, 𝜔𝑤 is wage Calvo parameter and 𝒰𝑡(𝑗) is the value function of unemployed workers. The value of a worker in employment 𝒲𝑡(𝑗) depends on his wage income, which is determined by the product of nominal wage rate 𝑊𝑡∗ and the hours worked 𝑁𝑡𝐼𝑁(𝑗), which is then taxed. Second term in the first row represents the loss of utility from working. In the next period, an employee retains his job with the probability (1−𝜌𝐿𝑀). If he stays employed in t+1, with the probability 𝜔𝑤 he will not be able to re-negotiate the nominal wage. In this case the nominal wage is partially indexed to inflation and the employee’s value to the family is 𝒲𝑡+1(𝑗). If the employee manages to re-negotiate after all, it leads to the optimal re-negotiated wage in t+1 and his value to the family is 𝒲∗𝑡+1(𝑗). With the probability 𝜌𝐿𝑀 he will be unemployed the next period. The value of an unemployed family member to the family is given by 𝒰𝑡(𝑗) = 𝑏𝑡 𝐿𝑀 +𝐸𝑡{𝛽𝑡,𝑡+1[𝑠𝑡(1−𝜌𝐿𝑀)(𝜔𝑤𝒲𝑡+1(𝑗)+ (1−𝜔𝑤)𝒲∗𝑡+1(𝑗))+(1−𝑠𝑡(1−𝜌𝐿𝑀))𝒰𝑡+1(𝑗)]} , where 𝑏𝑡 𝐿𝑀 = 𝛽𝑏(1−𝜏𝑤)𝑊𝑁𝐼𝑁 are unemployment benefits that are given as 𝛽𝑏 fraction of steady-state wage income and 𝑠𝑡 is job-finding rate defined as 𝑚𝑡𝑢𝑡 ⁄. Therefore, both the employed and unemployed workers that find a new job have the same chance of being able to take part in wage negotiations the next period, which is defined as 1−𝜔𝑤. In such a case they will have the value function 𝒲∗𝑡+1. Otherwise, they keep the average wage from the previous period and only index it to inflation. The value function in the next period is then 𝒲𝑡+1. Full indexation to inflation is assumed. The value functions of employed and unemployed worker can be added up to express the worker’s surplus Δ𝑡 𝑊(𝑗)= 𝒲𝑡(𝑗)−𝒰𝑡(𝑗), which denotes the family's surplus from an employed family member at wage Wt(j) rather than having him unemployed: Review of Economic Perspectives 230 Δ𝑡 𝑊(𝑗) = (1−𝜏𝑡 𝑤)𝑊𝑡∗𝑁𝑡𝐼𝑁(𝑗)−𝑏𝐿𝑀 −𝜅𝐿𝑁𝑡 𝐼𝑁(𝑗)1+𝜓 (1+𝜓)Λ𝑡 𝐼+ 𝐸𝑡{𝛽𝑡,𝑡+1(1−𝜌𝐿𝑀)(1−𝑠𝑡 𝐿𝑀)[𝜔𝑤Δ𝑡+1 𝑊(𝑗)+(1−𝜔𝑤)Δ𝑡+1 𝑊∗ (𝑗)]}. Because there is a free entry in the vacancy posting market, firms are economically worthless in equilibrium if separated from a worker. The market value of a labour firm 𝐽𝑡(𝑗) matched to a worker who receives the nominal wage Wt(j) is given by 𝐽𝑡(𝑗) = 𝑥𝑡𝑧𝐿𝑀𝑁𝑡𝐼𝑁(𝑗)𝛼𝐿𝑀 −(1+𝜏𝑛)𝑊𝑡∗𝑁𝑡𝐼𝑁(𝑗)−𝑓𝑐𝐿𝑀 + (1−𝜌𝐿𝑀)𝐸𝑡{𝛽𝑡,𝑡+1[𝜔𝑤𝐽𝑡+1(𝑗)+(1−𝜔𝑤)𝐽𝑡+1 ∗(𝑗)]}, where 𝑥𝑡 is the competitive price the intermediate firms pay to the labour agencies for the supplied labour 𝑁𝑡𝐼𝑁(𝑗), 𝜏𝑛 is labour tax payed by the employer, and 𝑓𝑐𝐿𝑀 is the fixed cost 5 of production. The first row represents the real per-period profits of the firm when the nominal wage rate is Wt(j). 𝑁𝑡𝐼𝑁(𝑗) is the firm's labour input. The value function of the employment agencies in the next period is either 𝐽𝑡+1(𝑗) with the probability 𝜔𝑤 or 𝐽𝑡+1 ∗(𝑗) with the probability1−𝜔𝑤. In the first case, the average wage from the last period is only indexed to inflation, while in the other case the wage is re-negotiated to a new optimum. Vacancy posting is a costly process in this model, just as it is in the reality. We can write down the value of vacancy opening to the firm as follows: 𝑉𝑡(𝑗) = −𝜅𝑉 Λ𝑡 𝐼+𝐸𝑡{𝛽𝑡,𝑡+1[𝑞𝑡(1−𝜌𝐿𝑀)[𝜔𝑤𝐽𝑡+1(𝑗)+(1−𝜔𝑤)𝐽𝑡+1 ∗(𝑗)] + (1 −𝑞𝑡)𝑉𝑡+1)]} where 𝜅𝑉 is the vacancy posting cost parameter and 𝑞𝑡= 𝑚𝑡𝑣𝑡 ⁄ is the job-filling rate. The value of an open vacancy 𝑉𝑡(𝑗) depends negatively on fixed costs 𝜅𝑉, expressed in terms of marginal utility, and positively on the value of the labour firm matched to the worker 𝐽𝑡+1(𝑗) with the probability 𝑞𝑡, as the firm only gains the value 𝐽𝑡+1(𝑗) if the vacancy is filled. The free-entry condition implies that the firm would open new vacancies whenever 𝑉𝑡(𝑗)> 0. Thus, in equilibrium 𝑉𝑡= 0, ∀t and the vacancy posting condition is 𝜅𝑉 Λ𝑡 𝐼= 𝐸𝑡{𝛽𝑡,𝑡+1𝑞𝑡(1−𝜌𝐿𝑀)[𝜔𝑤𝐽𝑡+1(𝑗)+(1−𝜔𝑤)𝐽𝑡+1 ∗(𝑗)]}. Under right-to-manage bargaining the labour agencies and workers first negotiate a real wage and then the labour agencies unilaterally choose the optimal number of hours worked according to their optimality condition, i.e. equating the return from marginal product of labour to the marginal cost, which is the wage plus the labour taxes that pay 5 Job-related fixed costs are costs that are independent of the actual hours worked per employee, but not of the number of employees. In practice, such job-related fixed costs arise both on the labour and the capital side. On the labour side some employer benefits are not linked to the actual input of hours worked. An example of this can be a fixed entitlement of paid leave per quarter. Volume 18, Issue 3, 2018 231 the firm: x𝑡∗𝑀𝑃𝐿𝑡= 𝑊𝑡 (1+𝜏𝑁). MPLt from production function of employment agencies is equal to 𝑀𝑃𝐿𝑡= 𝑧𝐿𝑀𝛼𝐿𝑀𝑁𝑡𝐼𝑁𝛼𝐿𝑀−1. This step is anticipated and internalized during the wage bargaining. Since both the labour agencies and the workers alike know how the change in wage will influence the choice of hours worked (let us denote this change by 𝑑𝑁𝑊,𝑡), they take this effect into account. 𝑑𝑁𝑊,𝑡 can be derived from production function of employment agencies. Considering the RTM condition x𝑡∗𝑀𝑃𝐿𝑡= 𝑊𝑡(1+𝜏𝑁) , the optimal wage 𝑊𝑡∗ is negotiated via Nash bargaining, i.e. the total match surplus is divided between workers and employment agencies according to their negotiating power that is captured by the parameter 𝜂 (negotiating power of workers). The wage negotiation can then be described as optimization problem of the following equation: 𝑚𝑎𝑥 𝑊𝑡∗(Δ𝑡 𝑊)𝜂𝐽𝑡 1−𝜂. This yields the following first-order condition: 𝜂𝐽𝑡𝛿𝑡 𝑊=(1−𝜂)Δ𝑡 𝑊𝛿𝑡 𝐽 The average wage 𝑊𝑡 evolves according to 𝑊𝑡= 𝜔𝑤𝑊𝑡−1𝜋(1−𝛾𝑤)𝜋𝑡−1 𝛾𝑤+(1−𝜔𝑤)𝑊∗ Balanced growth path The model structure incorporates multiple stochastic trends that are used for stationarization of the input data within the model. This means that all the input time series are stationarized simultaneously while taking their mutual relationships as assumed by the DSGE model into account. As Andrle, M. (2009) argues, there is a need to investigate any trend behaviour in emerging countries because permanent shocks may potentially influence business cycle frequencies. He states: "The point is that the stationary DSGE model then may be unable to explain co-movements of filtered time series since it cannot explain the dynamics induced by permanent shocks in the de-trended variables." That is the reason why we employ the stochastic permanent trend shocks that can help investigate the data. Next, we shall have a look at the individual sources of these permanent shocks. The real part of the growth at the BGP is driven by a set of nonstationary shocks: • labour augmenting shock in the production process, ξtA – the main driving force of growth, grows at the rate gξA • willingness to work shock, ξtN – introduces non-stationarity to hours worked, grows at the rate gξN • investment specific shock, ξtI – allows relative prices to trend in steady state, grows at the rate gξI • trade productivity shock, ξtX – allows imports and exports to grow faster than output in a steady state, grows at the rate gξX , Review of Economic Perspectives 232 • exports quality shock, ξtQ – allows for a higher growth rate of domestic exports relative to the foreign demand proxy in a steady state, grows at rate gξQ . Apart from these five real nonstationary shocks, there is also a nominal trend assumed in the model: • consumer price index, PtC – grows at the BGP at the predetermined rate πC . Some details are shown in the section Stationarization of the appendix. Trade openness Further transformation of data is applied to trade variables – specifically exports, imports and world demand. Balanced growth path would indicate that nominal expenditure share of exports and imports in value added is constant. For treating the model trend behaviour consistently, we introduce an openness technology shock ξOt to include the notion of the growing trend in nominal expenditure share of trade in value added. It is defined in measurement equations of these variables, which means that agents perceive trade variables as already deflated by the openness shock. Thus, the observed time series exhibit the following trend: 𝐸𝑋𝑡 𝑜𝑏𝑠 = 𝐼𝑀𝑡 𝑜𝑏𝑠 = 𝑌𝑡∗𝑜𝑏𝑠 = 𝑔ξ𝐴𝑔𝜉𝑁𝑔𝜉𝐼(1−𝛼 𝛼)𝑔𝜉𝑋𝑔𝜉𝑂 Data Quarterly time series of 19 observables were used for the estimation. These data are consistent with ESA 2010 and cover the period between the first quarter of 2000 and the second quarter of 2017. Figures with the observed time series can be found in Figure 5 presented as quarter-on-quarter growths in percent except for interest rates that are in level and trade balance defined as net export on nominal GDP. I have used seasonally adjusted time series of real private consumption (C), gross fixed capital formation (I), government consumption (G), exports (goods and services) (EX), trade balance (goods and services) (TB), and their respective deflators – private consumption deflator (Pc), gross fixed capital formation deflator (Pi), government consumption deflator (Pg), export deflator (goods and services) (Px), import deflator (goods and services) (Pm); then also employment in hours worked (N), compensation per hour (W), unemployment rate (UR), nominal interest rate (R), nominal exchange rate 6 (S), and for the foreign environment foreign demand (WD), foreign interest rates (R*, EURIBOR), competitors’ price on the import side (pf) and competitors’ prices on the export side (pimf). The time series were obtained from the databases of Eurostat and Czech National Bank. The data I have used are usually revised in time, which brings certain level of uncertainty. These revisions can be quite substantial. This is the motivation behind this paper: to investigate whether the different use of the data changes the results of the model. Thus, not only do I estimate the parameters of the model, but I also estimate the model with different data sets. First, I use the original data set, which allows the model to use the measurement errors to estimate and then filter out the part of the data that the model 6 of CZK/EUR Volume 18, Issue 3, 2018 239 Figure 1. IRF: Matching efficiency shock (HP vs ORIG, deviation from ss, qoq, in pp) Source: the author´s own calculations. Simulated Moments In this section, a different tool is used to analyse the results of the models. Comparing the model-implied standard deviations and correlations with the observed data shows us how the model can fit the data. In Table 3 we can see the standard deviations of the key macroeconomic variables with their 90 % HPDI intervals for the two estimated models. In Table 4 the cross-correlations are presented. 00 01 02 03 04 0 0.05 0.1 Price of Labour Agency product (x_t) 00 01 02 03 04 0 0.05 0.1 0.15 Matches (m_t) 00 01 02 03 04 0 0.05 0.1 0.15 0.2 Employment (n_t) 00 01 02 03 04 -0.2 -0.15 -0.1 -0.05 0Unemployment (u_t) 00 01 02 03 04 0 0.1 0.2 0.3 Vacancies (v_t) 00 01 02 03 04 0.5 1 1.5 2 2.5 Job finding rate (s_t) 00 01 02 03 04 0 0.1 0.2 0.3 0.4 Job filling rate (q_t) 00 01 02 03 04 0 0.2 0.4 Value of a match to firm (J_t) 00 01 02 03 04 -0.2 -0.1 0 Hours worked per employee (N^IN_t) 00 01 02 03 04 -0.05 0 0.05 0.1 Wage inflation 00 01 02 03 04 -2 -1 0 1 x 10-3 Consumer inflation estimated HP estimated ORIG Review of Economic Perspectives 240 Looking at labour market variables, specifically wage inflation standard deviation (W), we can see that the version estimated using the HP data performs well, 1.01 vs 0.87 in the data. The next model is less successful, 1.06 in the model vs 1.69 in the data. Hours worked (HW, in equations 𝑁𝑡𝑂𝑈𝑇) are less volatile in the HP-filtered data and a model that uses this data is not able to fit this low volatility. However, looking at the model estimated with the original data (the column ‘Std (orig model)’), the model is very successful as opposed to the original data and implies almost the same standard deviation as in the data: 1.41 in the model and 1.43 in the data. Employment of persons (E) brings quite the opposite result. The less volatile data, estimated with the HP data model, fits this standard deviation very well: 0.64 in the model versus 0.48 in the data. The second model has a twice as high standard deviation. A great interest here is the unemployment rate (UR, in the model ut), where both models fit the data on a satisfactory level. Table 3. Standard deviations: data vs. model vars Std (orig data) Std (orig model) (90% HPDI) Std (HP data) Std (HP model) (90% HPDI) C 0.72 0.61 (0.55-0.66) 0.46 2.13 (1.93-2.31) Pc 0.58 0.33 (0.29-0.36) 0.37 0.20 (0.32-0.41) W 1.69 1.06 (1.00-1.16) 0.87 1.01 (0.95-1.04) HW 1.43 1.41 (1.35-1.46) 0.51 1.64 (1.41-1.67) E 0.49 0.95 (0.87-0.99) 0.48 0.64 (0.59-0.69) UR 1.64 1.81 (1.23-2.29) 1.64 1.21 (0.89-1.21) Source: the author’s own calculations. The following table presents the cross-correlations of the variables. The results are quite reasonable – for example, the correlation of unemployment (UR) with wages (W) is 0.22 in the data and 0.12 in the model. Correlations of the vacancies are less satisfactory: for example, for the unemployment rate the correlation is -0.96 in the data, but in the model it is only -0.04. The correlations of the labour market variables with real part of the economy, in this case with consumption, are good. The results of the original version of the model are shown in the appendix in Table 7. Table 4. Cross-correlations: data vs. model (HP) DATA C Pc W HW UR V MODEL C Pc W HW UR V C 1.00 0.06 0.56 0.29 -0.10 0.69 C 1.00 0.27 0.28 0.61 -0.05 0.32 Pc 0.06 1.00 0.46 -0.10 -0.05 0.42 Pc 0.27 1.00 0.20 0.00 0.04 -0.19 W 0.56 0.46 1.00 -0.38 0.22 0.40 W 0.28 0.20 1.00 0.31 0.12 0.09 HW 0.29 -0.10 -0.38 1.00 -0.27 0.47 HW 0.61 0.00 0.31 1.00 -0.06 0.22 UR -0.10 -0.05 0.22 -0.27 1.00 -0.96 UR -0.05 0.04 0.12 -0.06 1.00 -0.04 V 0.69 0.42 0.40 0.47 -0.96 1.00 V 0.32 -0.19 0.09 0.22 -0.04 1.00 Source: the author’s own calculations. Volume 18, Issue 3, 2018 241 Recursive Forecasts Figure 2 shows the recursive forecast for every quarter of the examined period. The forecast covers 8 quarters as these kinds of models are usually used for medium-term forecasting, which in many central banks is 2 years. The model tends to come back to its steady state as all shocks are on this trajectory during the unconditional forecast. ‘Unconditional forecast’ means that in any forecast for any period we do not impose any values to innovations of shocks on the forecast horizon, and just let them follow their respective shock processes instead. The steady state value for the Czech Republic is set close to its historical average of 6%. For the 2010-2014 period, when the unemployment rate was around its steady state value, the model predicts the unemployment rate well; but from 2014 on, when the unemployment rate in the Czech Republic began to fall and widely opened the unemployment rate gap, the model fails to predict this development. Figure 2. Recursive forecast: unemployment rate (unconditional, HP model) Source: the author’s own calculations. In the appendix, I have enclosed the unconditional recursive forecast for consumer price inflation for both versions of the model. In Figure 7 and Figure 8 we can see that the model did not predict the inflation drop during the crises, but performs well after the crisis during the years 2010-2012. It did not capture the drop in inflation at the end of 2012, but from then on the model seems to predict adequately. Historical shock decomposition In this part, I have applied the shock decomposition to identify the shocks behind the evolution of the examined variables. The outcome is presented in groups of shocks to make the results more transparent. I have divided the shocks into the following categories: technology shocks (trend shocks that mainly govern the labour productivity), demand shocks (shocks that capture preferences in individual sectors of the model), foreign shocks (shocks regarding a foreign environment), markups (shocks that are linked 2001:1 2003:1 2005:1 2007:1 2009:1 2011:1 2013:1 2015:1 2017:1 3 4 5 6 7 8 9 Review of Economic Perspectives 242 to profit margins in individual sectors), and, finally, labour market group (match efficiency shocks). One of the key macroeconomic variables linked to labour market is wage (in our case, compensation per hour). Figure 3 presents the results. We can see that the growth of wages is mainly influenced by the technology group that includes shocks regarding the labour productivity: the growth was high before the crisis and fell down in 2009 and so it also stayed (under its steady state growth) until 2016 when it started to pull the wage growth up again. There are some periods when it has produced a positive effect on wages, for example 2011 or 2016. Another interesting effect can be found in domestic demand shocks (horizontal line bars), which include the domestic monetary policy shock. There is a positive effect of the monetary policy in the second half of 2012, where the Czech National Bank lowered the interest rates from 1.21 in 2012q2 to 0.87 in 2012q3 and to 0.5 in 2012q4. From then on, the interest rates very slowly decreased to 0.29 at the end of 2015 with no effect on wages. Following the interest rates as a standard monetary policy tool, the Czech National Bank decided to implement a non-standard measure of fixing the exchange rate of CZK/EUR. This policy took place in November 2013 and the analysis shows a positive impact of this policy on wages in the 2013q4 and 2014q1. This effect is hidden in the foreign group of shocks (forward slash bars) thanks to the UIP shock that captures the exchange rate movements. In the first half of 2017, we can again see a positive effect of monetary policy that stems from the setting of interest rates. In the last quarter, 2017q2, the positive effect on wages (in demand bars) is of one third due to the loose monetary policy. The Czech National Bank must have registered the same effect as they started to increase the interest rates in 2017q3. The same effects can be observed in the Czech domestic inflation. The next variable to discuss is the hours worked presented in the Figure 11. The effect of technology shocks in this variable is mainly driven by the temporary TFP shock together with the willingness to work shock. Before the crisis hit the economy, the total factor productivity was quite high between 2007 - 2009. After the crisis, the technology shocks development was very volatile, but most of the time it shows a negative impact on the growth of hours worked, just as at the end of the observed period. On the other hand, the foreign environment influences the hours worked positively after the crisis, which is mainly assigned to the foreign demand shock as it takes place at the end of the 2017q2. In the group of demand shocks can be again seen the effect of domestic monetary policy at the end of 2012, but it is slightly negated by the domestic preference shocks. In the first half of 2017, there is, again, a positive effect of monetary policy together with preference shock raising the demand, which increases the hours worked needed. Markups have a very volatile influence on the hours worked, whereas the labour market shock has a surprisingly small influence. It exhibits a negative influence after the crisis, but from 2014 on it started to affect the growth of hours worked in a positive manner. Lastly, the unemployment rate variable. The results are shown in Figure 12, where we can see that the main effect comes from the labour market shock. Before the crisis, the Volume 18, Issue 3, 2018 243 labour market shock together with a high demand for employment caused the fall of the unemployment rate. Right after the crisis, in 2009, the effect of labour market shock changed dramatically and stands behind the rise of the unemployment rate. From 2011 on, the technology group of shocks shows a positive effect on the decrease in the unemployment rate; mainly the productivity shock that grew slowly under its steady state level, which was slowing down the increase of the productivity, and thus more employment was needed. The foreign shocks exhibit the opposite effect. This is mainly driven by the development of the foreign interest rates. The ECBs interest rates are lower almost the whole time after the crisis, which produces a contractionary effect on the Czech economy. Therefore, it increases the unemployment rate. The demand shocks have only a small influence after the crisis, but at the end of the period they show a positive effect on the decrease in unemployment. The effects on the unemployment rate in these kinds of models can vary quite significantly. A good example of the different model approaches to the labour market and how they can affect the progress of the unemployment rate can be found in Tonner et al. (2015). Conclusion In this paper, I have applied the DSGE model to a small open economy of the Czech Republic with search and matching frictions in the labour market. Firstly, I have calibrated the model to match the average growth in the individual sectors according to the data using various permanent shocks, which allowed for modelling of the BGP with different steady-state growths in the individual sectors of the economy examined in the model. Secondly, I have adjusted the import content of the individual sectors to match the data. Two sets of data have been used for the estimation. The first set consists of data filtered with the Hodrick-Prescott filter with a very volatile trend (lambda set to 1) to get rid of any noise that could influence the estimation, while the second set contains the original data. For both versions of the model the Random Walk Metropolis-Hastings algorithm has been used. The posterior means of the model parameters, which represent the structure of the economies, have been compared. The estimated parameters in both versions are quite similar with some expected differences, for example in the price rigidities or in the persistence of the markup shocks, which in both cases stems from the differences in the data used. The more volatile the data used, the less persistent markup shocks and the less rigid prices are produced. The results of the labour market parameters’ estimation are quite similar for the two versions of the model. The negotiation power of workers is lower than the power of firms, which is a likely situation for the Czech economy. It could be interesting to estimate this parameter in a few years to see whether this result changes. The reason behind the change in the negotiation power can come from the fact that the Czech labour market nowadays lacks the available work force as the unemployment rate is the lowest in the whole of European Union and firms here have to fight over job candidates – and a possible tool to do that is to offer them higher wages. Review of Economic Perspectives 244 Figure 3. Shock decomposition, wages (qoq, deviation from the steady state, in p.p., HP model) Source: the author’s own calculations. Volume 18, Issue 3, 2018 245 As a next step, we have compared the reactions of the two versions of the model to the same shocks using the impulse response functions to see any differences between the different sets of data used for the estimation. It turns out that the reactions of the prices are quite similar, but the main differences are in the reaction of the real part of the economy, where the model estimated using the HP-filtered data suggests that the real variables would react more on the monetary policy shock. The same result can be observed concerning the labour market variables, where the unemployment rate reacts at least twice as strongly in the model using the HP data than in the model using the original data. Another tool to check how the model fits the data has been the comparison of the standard deviations and cross-correlations of variables that are produces by the two versions of the model and data. Both models fit the respective data quite well, with some room for improvement. The main tool for the investigation of the development of the labour market variables has been the historical shock decomposition, showing us that the wage inflation is mainly driven by the labour productivity (long term or temporary, technology shocks) with significant effects of domestic demand shocks. In the demand shocks group, an inflationary effect of the domestic monetary policy has been revealed, resulting from the setting of the interest rates. Moreover, in the foreign group of shocks, a positive (inflationary) effect of the non-standard monetary policy measure has been found as the Czech National Bank fixed the CZK/EUR exchange rate in 2013 on a higher depreciated level than would be set on the market. At the end of the observed period, inflationary pressures coming from the interest rate setting has been uncovered, suggesting that the monetary policy started being expansionary in the 2017. The decomposition of hours worked has shown that they are mainly influenced by quite volatile temporary shocks. The analysis has revealed that the foreign environment influenced the hours worked positively after the crisis. A positive effect of domestic monetary policy has been found in the increase of hours worked in 2012 as well as at the end of the observed period, in 2017q2. The decomposition of unemployment rate has revealed a major influence of the labour market shocks explaining most of the unemployment rate volatility. In addition, it turns out that the slow increase of labour productivity after the crisis led to a lower unemployment rate with the opposite effect of the foreign environment. Considering the results obtained using different techniques to compare the usefulness of the different versions of the model for forecasting and the identification of the development of the labour market variables, I prefer the model with the HP-filtered data as the original data are very volatile for the Czech Republic (the same for the identified shocks), and it is hard to disentangle the relevant information for policy makers. The estimation results and the behaviour of the economy based on the IRFs have not proven the big difference between the two versions. The fit of the two versions of the model is quite satisfactory too. Therefore, it can be concluded that for forecasting and policy analysis, the HP-filtered version is indeed more suitable. Disclosure statement: No potential conflict of interest was reported by the author. Review of Economic Perspectives 246 References ANDRLE, M. (2009): The Role of Trends and Detrending in DSGE Models - Emerging Countries Need "Trendy" Models, Munich Personal RePec Archive Paper No. 13289 ANDRLE, M., HLÉDIK T., KAMENÍK O., VLČEK J. (2009): Implementing the New Structural Model of the Czech National Bank, Working paper series 2/2009 http://www.cnb.cz/en/research/research_publications/cnb_wp/download/cnbwp_2009_0 2.pdf CALVO, G. A. (1983). Staggered Prices in a Utility Maximizing Framework, Journal of Monetary Economics, Vol. 12, Issue 3, Pages 383-398. DOI: 10.1016/0304- 3932(83)90060-0 GOMES, S., JACQUINOT, P. and PISANI, M. (2010). The EAGLE: a Model for Policy Analysis of Macroeconomic Interdependence in the Euro Area, European Central Bank Working Paper No. 1195 CHRISTIANO, L.J., EICHENBAUM, M. and EVANS, CH.L. (2005). Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy, Journal of Political Economy, Vol. 113(1). DOI: 10.1086/426038 CHRISTOFFEL, K., COENEN, G. and WARNE, A. (2008). The New Area-wide Model of the Euro Area: A Micro-Founded Open-Economy Model for Forecasting and Policy Analysis, European Central Bank Working Paper No. 944 CHRISTOFFEL, K., KUESTER, K. and LINZERT, T (2009). The role of labor markets for euro area monetary policy. European Central Bank Working Paper No. 1035 PÁPAI, A. (2017). Modelling Labour Market Rigidities, dissertation thesis, Masaryk University, Faculty of Economics and Administration, Department of Economics SMETS, F. and WOUTERS, R. (2003). An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area, Journal of the European Economic Association, Vol. 1(5). DOI: 10.1162/154247603770383415 TAYLOR, J. B. (1993): Discretion Versus Policy Rules in Practice. Carnegie-Rochester Conference Series on Public Policy, 39(1). pp. 195–214. DOI: 10.1016/0167- 2231(93)90009-L TONNER, J., TVRZ, S., VAŠÍČEK, O. (2015).: Labour Market Modelling within a DSGE Approach , Working paper series, 6/2015 TRIGARI, A. (2006). The Role of Search Frictions and Bargaining for Inflation Dynamics, IGIER Working Paper No. 304 VÝŠKRABKA, M., TVRZ, S. and ŽELEZNÍK, M. (2018): Prediction model of Integrated Slovak economy (PreMISE), National Bank of Slovakia, (to be published) Volume 18, Issue 3, 2018 247 Appendix Stationarization To present how permanent shocks influence the behaviour of the economy, this paper expresses the notion that there is a common real trend growth in all production sectors, and that is the combination of shocks: 𝑔𝑌𝑘𝑙 = 𝑔𝐴𝑔𝜉𝑁(𝑔𝜉𝐼)(1−𝛼 𝛼) which is also the real growth of the intermediate sector. The growth of the final production sectors in the economy should also be established. The consumption sector 𝑌𝑡𝐶 exhibits the same growth as the domestic intermediate production. However, the investment sector 𝑌𝑡𝐼 is enriched with another trend shock ξtI which allows the real investment in a steady state grow faster than the consumption sector. The same investment specific trend shock is responsible for the different growth of inflation in the investment sector πtI which is lower in the data than in the consumption sector. The growth of inflation in the consumption sector πtC is defined through the parameter πC that captures the steady-state growth of inflation according to BGP. Thus, the inflation in the investment sector is defined as 𝜋𝐼=𝜋𝐶 𝑔𝜉𝐼 Another example of how the model has been constructed is the definition and stationarization of the growth of real consumption through a combination of real shocks: 𝑑𝐶𝐼𝑡=𝐶𝐼𝑡 𝐶𝐼𝑡−1 𝑔ξ𝐴𝑔𝜉𝑁𝑔𝜉𝐼(1−𝛼 𝛼) The rest of the variables are stationarized in accordance with their respective trends. The setting of the growths of individual trend shocks in a steady state is defined in the calibration section. Review of Economic Perspectives 248 Figure 4. Exchange rate CZK/EUR ( original vs HP-filtered, qoq) 1999:1 2001:1 2003:1 2005:1 2007:1 2009:1 2011:1 2013:1 2015:1 2017:1 -6 -4 -2 0 2 4 6 8 Original HP,lambda=1600 Volume 18, Issue 3, 2018 255 Table 7. Cross-correlations: data vs. model (ORIG) DATA C Pc W HW U V MODEL C Pc W HW U V C 1.00 -0.33 0.12 0.12 -0.11 0.50 C 1.00 0.08 0.23 0.15 0.06 -0.07 Pc -0.33 1.00 0.39 -0.21 -0.01 0.28 Pc 0.08 1.00 0.23 0.08 0.18 -0.39 W 0.12 0.39 1.00 -0.77 0.11 0.15 W 0.23 0.23 1.00 0.20 0.07 -0.05 HW 0.12 -0.21 -0.77 1.00 -0.11 0.14 HW 0.15 0.08 0.20 1.00 -0.04 0.03 UR -0.11 -0.01 0.11 -0.11 1.00 -0.96 UR 0.06 0.18 0.07 -0.04 1.00 -0.16 V 0.50 0.28 0.15 0.14 -0.96 1.00 V -0.07 -0.39 -0.05 0.03 -0.16 1.00 Review of Economic Perspectives 256 Figure 11. Shock decomposition, hours worked (qoq, deviation from the steady state, in p.p., HP model) Source: the author’s own calculations. Volume 18, Issue 3, 2018 257 Figure 12. Shock Decomposition, Unemployment Rate (level, deviation from steady state, in p.p., HP model) Source: the author’s own calculations. Review of Economic Perspectives 258 Table 8. Parameter legend Param Description Para m Description ρχ AR parameter of matching efficiency shock σχLM std of matching efficiency shock νLM elasticity of matching function wrt unemployment σξIprem std of investment demand shock η bargaining power of workers σξgovy std of government shock Foreign Std ρπIM* AR parameter of foreign competitors prices on the export side σπIM* std of foreign competitors prices on the export side shock ρY* AR parameter of foreign demand σY* std of foreign demand shock ρπEX* AR parameter of foreign competitors prices on the import side σπEX* std of foreign competitors prices on the import side shock ρR* AR parameter of foreign Taylor Rule σR* std of foreign monetary policy shock Markup s Std ρθYkl AR parameter of intermediate good sector markup shock σθYkl std of intermediate good sector markup shock ρθC AR parameter of final good consumption sector markup shock σθC std of final good consumption sector markup shock ρθI AR parameter of final good investment sector markup shock σθI std of final good investment sector markup shock ρθG AR parameter of final good government sector markup shock σθG std of final good government sector markup shock ρθEX AR parameter of final good export sector markup shock σθEX std of final good export sector markup shock ρθIM AR parameter of final good import sector markup shock σθIM std of final good import sector markup shock Trends Std ρξI AR parameter of investment specific shock σξI std of investment specific shock ρξX AR parameter of export specific shock σξX std of export specific shock ρξQ AR parameter of quality shock σξQ std of quality specific shock ρξA AR parameter of labour augmented shock σξA std of labour augmented shock ρξO AR parameter of opennes shock σξO std of opennes shock MP MP ρR AR parameter in domestic Taylor Rule κR*πIM* weight of foreign inflation in foreign Taylor Rule φπ weight of lagged inflation in domestic Taylor Rule κR*Y* weight of foreign output in foreign Taylor Rule φC weight of consumption gap in domestic Taylor Rule φS weight of exchange rate in domestic Taylor Rule Calvo Index ωW Calvo parameter in wages γW Indexation parameter in wages Volume 18, Issue 3, 2018 259 ωYkl Calvo parameter in intermediate good sector γYkl Indexation parameter in intermediate good sector ωC Calvo parameter in final good consumption sector γC Indexation parameter in final good consumption sector ωI Calvo parameter in final good investment sector γI Indexation parameter in final good investment sector ωG Calvo parameter in final good government sector γG Indexation parameter in final good government sector ωEX Calvo parameter in final good export sector γEX Indexation parameter in final good export sector ωIM Calvo parameter in final good import sector γIM Indexation parameter in final good import sector Other Std ρθTFP AR parameter in total factor productivity shock σθTFP std of total factor productivity shock ρξC AR parameter in consumption preference shock σξC std of consumption preference shock ρξRP AR parameter in domestic risk premium shock σξRP std of domestic risk premium shock