Modelling Czech and Slovak labour markets: A DSGE model with labour frictions Daniel Němec Faculty of Economics and Administrations Masaryk University Brno, Czech Republic nemecd@econ.muni.cz ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 1 / 44
Content 1 Model 2 Estimation results 3 Model evaluation 4 Conclusion ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 2 / 44
Motivation DSGE models with labour market rigidities: models with wage bargaining mechanism, models with search and matching functions. An alternative to the perfectly competitive Walrasian labour market model integration into standard macroeconomic models. Description of employment flows in the economy influence on business cycles. Revealing some structural properties of the labour market. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 3 / 44
Labour markets properties Slovak labour market: wages relative flexible, overall wage flexibility only poorly influenced by the institutional arrangements. Czech labour market: losing its flexibility due to high reservation wage and due to the obstacles connected with the necessary layoffs, decreasing flows of workers among industries and problem with long-term unemloyment. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 4 / 44
Model 1 Model 2 Estimation results 3 Model evaluation 4 Conclusion ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 5 / 44
Model Introduction Log-linear version of Lubik (29): Estimating a Search and Matching Model of the Aggregate Labor Market. Simple search and matching model: labour market subject to frictions. -consuming search process for workers and firms. Cost of finding a job/worker shared rents. Wages as an outcome of a bargaining process. Simple general equilibrium framework key labour market features. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 6 / 44
Model Households Intertemporal utility of a representative household: E t j=1 [ C 1 σ ] β j t j 1 χ j n j, 1 σ C aggregate consumption, n [, 1] fraction of employed household members (determined in the matching market), β (, 1) discount factor, σ coefficient of relative risk aversion, χ t exogenous stochastic process (labour shock). Budget constraint: C t + T t = w t n t + (1 n t )b + Π t, b unemployment benefits (financed by a lump-sum tax T t ), Π t profits from ownership of the firms, w wage. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 7 / 44
Households (cont.) Model No explicit labour supply (outcome of the matching process) F.O.C.: C σ t = λ t, λ t Lagrange multiplier on the budget constraint. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 8 / 44
Model Labour Market Search frictions: m(u t, v t ) = µ t u ξ t ν 1 ξ t, u t unemployed job seekers, ν t vacancies, m(u t, ν t ) matching rate, < ξ < 1 match elasticity of the unemployed, µ t efficiency of the matching process. Aggregate probability of filling a vacancy: θ t = νt u t labour market tightness. q(θ t ) = m(u t, ν t )/ν t, ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 9 / 44
Model Labour Market (cont.) Assumption: one period for new matches to be productive; old and new matches destroyed at a constant rate. Evolution of employment (n t = 1 u t ): n t = (1 ρ) [n t 1 + ν t 1 q(θ t 1 )], < ρ < 1 constant separation rate (inflows into unemployment). ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 1 / 44
Model Firms Monopolistic competition (deviation from standard S&M framework). Demand function of a firm: y t = ( pt P t ) 1 ɛ Y t, y t firm s production (its demand), Y t aggregate output, p t price set by the firm, P t aggregate price index, ɛ demand elasticity. Production function: y t = A t n α t, A t aggregate technology process, < α 1 curvature in production ( fixed and firm-specific capital). ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 11 / 44
Model Firms (cont.) Maximizing intertemporal profit function (n t, v t, p t ): E t β j t λ j j=1 p j ( pj P j ) (1+ɛ) Y j w j n j κ ψ νψ j subject to the employment accumulation equation and production function equation. Profits evaluated in terms of marginal utility λ j. Cost of vacancy posting κ ψ v ψ t, κ >, ψ > ( < ψ < 1, posting costs exhibit decreasing returns, ψ > 1 costs are increasing, ψ = 1 fixed vacancy costs)., ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 12 / 44
Firms (cont.) Model First-order conditions: τ t = α y t ɛ n t 1 + ɛ w t + (1 ρ)e t β t+1 τ t+1, κνt ψ 1 = (1 ρ)q(θ t )E t β t+1 τ t+1, β t+1 = β λ t+1 λ t stochastic discount factor, τ t Lagrange multiplier for employment constraint (current-period marginal value of a job). ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 13 / 44
Wage Determination Model Bilateral bargaining process wage rates to maximize the joint surplus from employment relationship: ( 1 S t λt W t (n t ) n t ) η ( ) Jt (n t ) 1 η, η [, 1] bargaining power of workers, Wt(nt) n t marginal value of a worker to the household s welfare, Jt(nt) n t marginal value of a worker to the firm. J t(n t) n t n t = τ t (F.O.C. for the firms with respect to the employment). ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 14 / 44
Model Wage Determination (cont.) Recursive representation for Wt(nt) n t : W t (n t ) n t = λ t w t λ t b χ t + βe t W t+1 (n t+1 ) n t+1 n t+1 n t. Using employment equation: n t+1 n t = (1 ρ)[1 θ t q(θ t )]. Real payments valued at the marginal utility λ t. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 15 / 44
Model Wage Determination (cont.) Standard optimality condition for wages: (1 η) 1 λ t W t (n t ) n t = η J t(n t ) n t. After some intuitive algebra: [ w t = η α y ] t ɛ n t 1 + ɛ + κνψ 1 t θ t + (1 η) [b + χ t Ct σ ]. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 16 / 44
Model Closing the model Lump-sum taxes T + balanced budget: T t = (1 n t )b. Social resource constraint: C t + κ ψ νψ t = Y t. Law of motion for aggregate employment: [ n t = (1 ρ) n t 1 + µ t 1 u ξ t 1 ν1 ξ t 1 Shocks: technology A t, labour χ t, matching µ t independent AR(1) processes (in logs) with coefficients ρ i, i (A, ξ, µ). Innovations ɛ i t N(, σ 2 i ). ]. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 17 / 44
Estimation results 1 Model 2 Estimation results 3 Model evaluation 4 Conclusion ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 18 / 44
Estimation results Data and estimation techniques Quarterly data: 1st quarter 1999 4th quarter 21: GDP at purchaser prices, constant prices 2, s.a., CZSO, millions of CZK; GDP at purchaser prices, constant prices 2, s.a., SOSR, millions of EUR; Index of hourly earnings (manufacturing), 25=1, s.a., OECD; Registered unemployment rate, s.a., OECD; Unfilled job vacancies, level (transformed to ratio of unfilled vacancies to labour force), s.a., OECD and SAFSR. Bayesian techniques combined with Kalman filtering procedures (all computations performed using Dynare toolbox for Matlab). ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 19 / 44
Estimation results Figure source data SVK 9.5 9.4 HP filter log(y) logged real GDP 4.8 HP filter log(w) logged wage 9.3 9.2 9.1 4.6 4.4 9 4.2 8.9.18.16.14.12.1.8 mean unemployment unemployment rate x 1 3 1 8 6 4 2 mean vacany rate vacancy rate ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 2 / 44
Estimation results Figure source data CZE 13.6 13.5 HP filter log(y) logged real GDP 4.8 HP filter log(w) logged wage 13.4 4.6 13.3 4.4 13.2 4.2.11.1.9.8 unemployment rate.3.25.2 mean vacany rate vacancy rate.7.15.6.5 mean unemployment.1 ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 21 / 44
Estimation results Figure model data SVK.8.6.4 output gap filtered Y using HP filter.5.4.3.2 wage gap filtered W using HP filter.2.1.2.4.1.2 unemployment gap vacancy gap.6.2.4.2.2.2.4.4 demeaned log(u).6.8 demeaned log(v) ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 22 / 44
Estimation results Figure model data CZE.4.3.2.1.1 output gap filtered Y using HP filter.5.4.3.2.1 wage gap filtered W using HP filter.2.1.3.2.2.1 unemployment gap 1 demeaned log(v) vacancy gap.5.1.2.3.4 demeaned log(u).5 ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 23 / 44
Estimation results Parameters description and prior densities Description Parameter Density Priors SVK Priors CZE Mean Std. Dev Mean Std. Dev Discount factor β.99.99 Labor elasticity α.67.67 Demand elasticity ɛ 1 1 Relative risk aversion σ G 1..5 1..5 Match elasticity ξ G.7.1.7.1 Separation rate ρ G.1.5.1.5 Bargaining power of the workers η U.5.3.5.3 Unemployment benefits b B.2.15.2.15 Elasticity of vacancy creation cost ψ G 1..5 1..5 Scaling factor on vacancy creation cost κ G.1.5.1.5 AR coefficients of shocks ρ {χ,a,µ,y } B.8.2.8.2 Standard deviation of shocks σ {χ,a,µ } IG.1 1.1 1 Standard deviation of shocks σ {Y } IG.5 1.5 1 ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 24 / 44
Parameter estimates Estimation results SVK CZE Posterior mean 9% HPDI Posterior mean 9% HPDI σ.2843.1319.4248.4517.2989.5648 ξ.8196.7645.8782.7758.7229.8316 ρ.677.185.1259.75.563.843 η.46..99.22..5 b.1566.1.2988.4557.483.552 ψ 2.2769 1.787 2.744 1.9257 1.8313 2.563 κ.1245.811.1759.875.524.1259 ρ χ.2514.616.4554.7347.6994.7641 ρ A.9449.8785 1..9851.982.9914 ρ µ.9563.9188.9998.8222.7211.884 ρ Y.879.6948.9267.9184.8632.986 σ χ.17.141.199.85.71.99 σ A.563.13.8161.3181.2429.3981 σ µ.64.531.743.666.551.767 σ Y.168.142.194.97.82.112 ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 25 / 44
Comments Estimation results Bargaining power of workers, η almost for both countries the firms are willing to create vacancies. Separation rate, ρ considerably lower than the one estimated for U.S. economy less flexible Czech and Slovak labour market with limited ability to destroy old and new matches (restricted flows of the workers among industries). Vacancy posting elasticity, ψ shifted away from the prior mean the vacancy creation is more costly because of increasing marginal posting costs. The estimate of parameter b remarkably high value of.46 for the Czech economy (in accordance with the real unemployment benefits) lower value of.16 for the Slovak economy supports the view of lower reservation wage for this country. Matching function parameter, ξ in accordance with the common values in literature. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 26 / 44
Estimation results Trajectories of selected (smoothed) variables SVK (1/3) unemployment rate (u) vacancy rate (v) 2 5 u 2 4 v 5 6 4 wage rate (w) 8 6 aggregate output (Y) w 2 Y 4 2 2 2 ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 27 / 44
Estimation results Trajectories of selected (smoothed) variables CZE (1/3) 2 unemployment rate (u) 1 vacancy rate (v) 5 u 2 v 4 5 wage rate (w) aggregate output (Y) 4 4 w 2 2 Y 2 2 ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 28 / 44
Estimation results Trajectories of selected (smoothed) variables SVK (2/3) 8 consumption (C) 1 employment rate (n) 6 4 5 C 2 n 2 matching rate (m) 5 probability filling a vacancy (q) m 1 1 q 5 2 5 ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 29 / 44
Estimation results Trajectories of selected (smoothed) variables CZE (2/3) C 4 2 2 2 1 consumption (C) matching rate (m) n 4 3 2 1 1 2 5 employment rate (n) probability filling a vacancy (q) m 1 q 2 3 5 1 ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 3 / 44
Estimation results Trajectories of selected (smoothed) variables SVK (3/3) labour market tightness (θ) labour shock (χ) 1 5 6 4 θ χ 2 5 1 4 efficiency shock (µ) 2 3 2 technological shock (A) µ 2 A 1 2 1 2 ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 31 / 44
Estimation results Trajectories of selected (smoothed) variables CZE (3/3) θ 15 1 5 5 3 2 labour market tightness (θ) efficiency shock (µ) χ 4 3 2 1 1 2 1 labour shock (χ) technological shock (A) µ 1 A 1 1 2 ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 32 / 44
Estimation results Comments Relative sharp decline in the development of variable q (probability of filling a vacancy) at the end of the year 26 the role of an obvious lack of employees in the Czech economy. Similar results for the Slovak economy. Downturn of both economies influenced a fall of the matching rates m below their steady-state values. The starting recession has reestablished the equilibrium on both labour markets (see the trajectories of employment rate and labour market tightness). The improvement of labour market institutions (trajectory of efficiency shock, µ) remarkable changes on the Czech and Slovak labour markets started at the end of 24 and at the beginning of the 26 respectively. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 33 / 44
Estimation results IRFs and historical shocks decomposition. Except the responses on technology shocks (which is too persistent), the rest of IRFs in accordance with the standard economic theory. Similar dynamics of both economies. The persistent response of the technology and output shocks in accordance with hysteresis hypothesis (hysteresis of unemployment)? Similar historical shocks decomposition in both economies + important role of the technology (more important in the Czech economy) and matching shocks. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 34 / 44
Model evaluation 1 Model 2 Estimation results 3 Model evaluation 4 Conclusion ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 35 / 44
Model evaluation Sample moments and autocorrelation coefficients (SVK) Sample moments Lags for autocorrelation coefficients Mean Std. dev. 1 2 3 4 u data..9.91.71.45.16 model..1.88.7.51.35 9% HPDI (.1,.1) (.7,.14) (.79,.94) (.48,.83) (.11,.72) (.8,.62) ν data..4.91.71.45.17 model..8.72.54.4.29 9% HPDI (.1,.1) (.6,.11) (.55,.87) (.25,.8) (.8,.73) (.9,.67) w data..14.8.53.29.14 model..54.72.52.36.24 9% HPDI (.4,.4) (.41,.71) (.57,.84) (.3,.72) (.6,.61) (.9,.57) Y data..2.91.74.54.33 model..17.79.62.47.36 9% HPDI (.1,.1) (.12,.24) (.64,.88) (.33,.77) (.9,.7) (.1,.63) ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 36 / 44
Model evaluation Correlation matrix (SVK) Data Model (9% HPDI) u ν w Y u ν w Y u 1..75.25.5 1..29.4.1 (1., 1.) (.82,.48) (.31,.41) (.48,.54) ν.75 1..9.38.29 1..15.2 (.82,.48) (1., 1.) (.47,.17) (.58,.51) w.25.9 1..28.4.15 1..4 (.31,.41) (.47,.17) (1., 1.) (.15,.63) Y.5.38.28 1..1.2.4 1. (.48,.54) (.58,.51) (.15,.63) (1., 1.) ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 37 / 44
Model evaluation Sample moments and autocorrelation coefficients (CZE) Sample moments Lags for autocorrelation coefficients Mean Std. dev. 1 2 3 4 u data.1.17.95.84.69.52 model..134.88.71.55.4 9% HPDI (.2,.2) (.81,.24) (.76,.95) (.5,.87) (.27,.79) (.4,.71) ν data.11.456.95.83.67.5 model..31.83.69.57.47 9% HPDI (.88,.88) (.17,.517) (.65,.93) (.37,.87) (.22,.81) (.9,.74) w data..14.84.6.37.19 model..1.72.52.37.26 9% HPDI (.1,.1) (.7,.13) (.5,.86) (.25,.73) (.7,.63) (.6,.54) Y data..2.92.78.61.43 model..2.81.65.51.4 9% HPDI (.3,.3) (.13,.31) (.63,.93) (.4,.86) (.22,.78) (.2,.74) ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 38 / 44
Model evaluation Correlation matrix (CZE) Data Model (9% HPDI) u ν w Y u ν w Y u 1..85.75.78 1..41.5.2 (1., 1.) (.81,.16) (.55,.44) (.65,.56) ν.85 1..76.82.41 1..3.1 (.81,.16) (1., 1.) (.53,.46) (.63,.52) w.75.76 1..7.5.3 1..61 (.55,.44) (.53,.46) (1., 1.) (.31,.84) Y.78.82.7 1..2.1.61 1. (.65,.56) (.63,.52) (.31,.84) (1., 1.) ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 39 / 44
Model evaluation Comments The model is very successful in matching sample moments and autocorrelation coefficients (not typical for such a small-scale model!). Results are in accordance with the authors arguing that the model with search and matching frictions in the labour market is able to generate negative correlation between vacancies and unemployment. Cross-correlation coefficients not sufficient for the correlations of unemployment and the rest of observable variables (similar experience for U.S. labour market) presence of matching shock (acting as a residual in employment and wage equations). ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 4 / 44
Conclusion 1 Model 2 Estimation results 3 Model evaluation 4 Conclusion ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 41 / 44
Conclusion Conclusion Good ability to identify most structural parameters. Plausible description of labour market dynamics and properties of the Czech and Slovak labour market. Convincing evidence that wage bargaining process is determined mainly by the power of the firms. The structural properties of both markets do not differ too much from the properties of the U.S. labour market. Flexible wage environment in both economies the firms are confronted by the increasing vacancy posting costs that limit vacancies creation + the lower separation as an evidence of reduced mobility of the workers. ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 42 / 44
Conclusion Further research Robustness check based on estimation using the information provided by a variety of filters or by direct linking of the observable data to the DSGE model. Model comparison based on various wage bargaining settings. Inclusion of price rigidities and monetary policy (monetary rule) to analyse implications of wages and labor market shocks on inflation process. Incorporating labour market rigidities into an open economy model (the direct effects of labour market shocks should become more obvious). ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 43 / 44
Conclusion Thank you for your attention. Comments? Suggestions? ESF MU (Brno) Search and matching DSGE model Humusoft, May 25, 212 44 / 44