Extended DSGE Model of the Czech Economy

Zbyněk Štork Božena Bobková Ilkin Aliyev Moderní nástroje pro finanční analýzu a modelování 5. 6. 214

Outline 1 Extended DSGE model 2 3 Simulation 4

DSGE Modelling in General... Forecast model scenario for quarterly Macroeconomic Forecast Simulations for strategic documents (Convergence Programme, Fiscal Outlook) and ad hoc analysis HUBERT - Dynamic Stochastic General Equilibrium model. We began from a small simple model (households, firms, government, central bank, foreign sector) two extensions were made: 1 households and fiscal block 2 domestic demand (consumption and investments) net export (exports and imports)

Outline 1 Extended DSGE model 2 3 Simulation 4

Building Blocks of the Model Households Infinitely lived agents; Habit formation for smoother consumption; Savers and Spenders. Governmental authorities Monetary policy: Taylor rule; Fiscal policy: aggregated revenues and expenditures, fiscal rule focused on debt stability. Firms Cobb-Douglas production function, CES aggregation ; Price takers assumption; Calvo pricing. Foreign sector Approximated by EA aggregate; simple AR processes; imports and exports based on domestic and foreign demand and price differentials.

Building Blocks of the Model Households Infinitely lived agents; Habit formation for smoother consumption; Savers and Spenders. Firms Cobb-Douglas production function, CES aggregation ; Price takers assumption; Calvo pricing. Households - main equations: Governmental authorities Monetary policy: Taylor rule; Fiscal policy: aggregated revenues (1 + τt c )PC t Cand j,t R + PI expenditures, t I j,t + P t a(u j,t )K s fiscal rule focused on debt stability. Foreign sector E t β n U j,t+n = E t β n ( log C R ) j,t+n H j,t+n (NR j,t+n )1+ψ N (1) 1 + ψ n= n= N j,t + R 1 B j,t+1 + 1 t R t S +ζ t B t j,t+1 = = B j,t + S t Bj,t + (1 τ t k )[Rt k u j,t Kj,t s + Q t ] + (1 τt w Approximated by EA aggregate; simple AR processes; imports and exports based on )W domestic t N R (2) j,t and foreign demand and price differentials. (1 + τ c t )PC t C N j,t = (1 τ w t )W t N N j,t + τ b t W b(n N j,t LN j,t ) + TR t (3)

Building Blocks of the Model Households Infinitely lived agents; Habit formation for smoother consumption; Savers and Spenders. Firms Cobb-Douglas production function, CES aggregation ; Price takers assumption; Calvo pricing. Firms - main equations: Governmental authorities Monetary policy: Taylor t rule; it Fiscal policy: aggregated Y t = it revenues and expenditures, P 1 θ t = ξ pp 1 θ t 1 fiscal rule focused on debt stability. Foreign sector Y it = z 1 η K η it L1 η Approximated by EA aggregate; (1a) [ 1 θ/(θ 1) Y di] (θ 1)/θ (1b) simple AR processes; + ( ) ( 1 ξ p P new ) 1 θ t (1c) (W t ) 1 θ W = α R [ξ w ( Wt 1 ) 1 θw + (1 ξw ) imports and exports based on domestic ( and foreign demand W and new ) ] 1 θw t price differentials. + (1 α R ) ( W t 1 ) 1 θw (1d)

Building Blocks of the Model Governmental authorities - main equations: Households Infinitely lived agents; Habit formation for smoother consumption; Savers and Spenders. Firms GR t = τ c t (P C ) t C t + G t + τ w t W t L t + τ k t (R k ) t K t + Q t Cobb-Douglas production function, CES aggregation ; Price takers assumption; Calvo pricing. (1a) GE t = G C t + τ b t W t L t + G O t (1b) GE t GR t = 1 R t B t+1 B t (1c) ˆR t = (1 φ r )[λ π ˆπ t + λ y ŷ t ] + φ r ˆRt 1 (1d) Governmental authorities Monetary policy: Taylor rule; Fiscal policy: aggregated revenues and expenditures, fiscal rule focused on debt stability. Foreign sector Approximated by EA aggregate; simple AR processes; imports and exports based on domestic and foreign demand and price differentials.

Building Blocks of the Model Households Foreign sector - main equations: Infinitely lived agents; Habit formation for smoother consumption; Savers and Spenders. Firms M t = C m t + I m t (1a) X t = C m t + I m t Cobb-Douglas production function, CES aggregation ; Price takers assumption; F t = Φ F t 1 + ɛ t, wheref t = [C m t, I m t, P t, R t ]. (1c) Calvo pricing. (1b) Governmental authorities Monetary policy: Taylor rule; Fiscal policy: aggregated revenues and expenditures, fiscal rule focused on debt stability. Foreign sector Approximated by EA aggregate; simple AR processes; imports and exports based on domestic and foreign demand and price differentials.

Outline 1 Extended DSGE model 2 3 Simulation 4

Model parameters Initial values of selected parameters Parameters Value Calibrated Estimated from data regression ss α r, s R.32, 1.55 β.99 δ.1 η.53 θ c, θ c, θ i, θ i.2.3 κ 11 µ cm, µ im.22,.32 µ z 1.5 ξ p, ξ w.9,.2 φ r, λ π, λ y.5,1.5,.5 ω rkz 12.72

Outline 1 Extended DSGE model 2 3 Simulation 4

Preliminary estimation results of selected parameters Parameters Prior Prior Posterior distribution mean mean h r habit formation beta.65.8 θ c domestic good e.s. beta.4.13 θ w labor good e.s. uniform 2. 1.15 θ i investment good e.s. beta.2.2 κ inv. adjustment cost normal 8. 2.39 δ depreciation rate beta.1.1 ξ p Calvo prices uniform.5.2 ξ w Calvo wages uniform.5.46 ψ n Frisch elasticity invgamma 1.55 3.99

Prior and posterior distribution of selected parameters

Multivariate convergence diagnostics

Simulation Outline 1 Extended DSGE model 2 3 Simulation 4

Simulation Macroeconomic shocks Foreign demand shock 1 y* y.5 y* c.5 y* i 1 y* x.5.5 1 1 2 3 4 y* m.1 1 2 3 4 y* P.5.1 1 2 3 4 y* R 1.5 1 2 3 4 y* N 1 1.1 1 2 3 4 y* L.4 1 2 3 4 y* w.1.4.5 1 2 3 4 1 2 3 4 y* gr 1 x y* ge 1 3.2.2 1 1 2 3 4.2 1 2 3 4 y* s 1 1 2 3 4 y* y* 1 1 2 3 4.5.2 1 2 3 4 1 2 3 4

Simulation Fiscal shocks Tax rate on consumption shock.2 τ c y 1 τ c c.2 τ c i.2 τ c x.2.5 1 2 3 4 τ c m 1 1 2 3 4 1 x τ c P 1 3.2.5 1 2 3 4 τ c R.2.2 1 2 3 4 τ c N.5.2 1 2 3 4 τ c L 1.5 1 2 3 4 τ c w 5.2 1 2 3 4 1 2 3 4 τ c gr 5 x τ c ge 1 4.1.2.2 1 2 3 4.1 1 2 3 4 τ c s 5 1 1 2 3 4 τ c τ c 5 1 2 3 4.5.1 1 2 3 4 1 2 3 4

Summary Started from a simple model......necessary extensions driven by demand. Recently focusing on estimations. Next steps Not any further enlargements......focus on improving outputs; case studies. Solve labor market issues.

Thank you for your attention... Zbyněk Štork and Božena Bobková (zbynek.stork@mfcr.cz, bozena.bobkova@mfcr.cz) Aliyev, I. Bobková, B. Štork, Z. (214) Extended DSGE model of the Czech economy. Ministry of Finance of the Czech Republic, Working Paper, 1/214.