// stephane [DOT] adjemian [AT] ens [DOT] fr /* ** MACROs */ // Add an efficient block (without nominal rigidities), used to define the output gap. @#define efficient_block = 1 @#define NumberOfShocks = 0 @#define ar_variance_decrease = "1.0" @#define ExogenousVariables_vnames = ["ProductionEfficiencyGrowth"] @#define ExogenousVariables_inames = ["EfficiencyGrowthInnovation"] @#define ExogenousVariables_pnames = ["production_efficiency_growth"] @#define ExogenousVariables_nblags = [1] @#define ExogenousVariables_acorr1_mode = [".3919"] @#define ExogenousVariables_acorr1_std = [".02"] @#define ExogenousVariables_vtexnames = ["A_T"] @#define ExogenousVariables_sstexnames = ["\overline A_T"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["ProductionEfficiencyCycle"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["EfficiencyCycleInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["production_efficiency"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".6001"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".10"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["A_C"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\overline A_C"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["ConsumptionTax"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["ConsumptionTaxInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["consumption_tax"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".0000"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".10"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\tau_C"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar \tau_C"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["LabourIncomeTax"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["LabourIncomeTaxInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["labour_income_tax"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".0000"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".02"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\tau_W"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar \tau_W"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["IncomeTax"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["IncomeTaxInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["income_tax"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".0000"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".02"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\tau_R"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar \tau_R"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["RiskPremium"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["RiskPremiumInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["risk_premium"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".9090"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".10"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\varepsilon_B"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar\varepsilon_B"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["LabourSupplyShock"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["LabourSupplyInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["labour_supply"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".7035"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".10"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\varepsilon_L"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\widetilde L"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["InvestmentRelativePrice"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["InvestmentRelativePriceInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["investment_relative_price"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".6223"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".02"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["p_I"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar p_I"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["InvestmentEfficiencyShock"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["InvestmentEfficiencyInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["investment_efficiency"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".6289"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".10"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\varepsilon_I"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar\varepsilon_I"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["LabourTax"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["LabourTaxInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["labour_tax"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".0000"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".02"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\tau_L"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar\tau_L"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["PriceMarkUpShock"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["PriceMarkUpInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["price_mark_up"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".8050"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".10"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\varepsilon_y"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar\varepsilon_y"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["WageMarkUpShock"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["WageMarkUpInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["wage_mark_up"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".7400"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".05"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\varepsilon_l"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar\varepsilon_l"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["InflationTarget"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["InflationTargetInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["inflation_target"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".0000"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".10"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\bar\pi"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar\pi"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["TaylorShock"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["TaylorInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["taylor"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".6388"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".10"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\varepsilon_R"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar\varepsilon_R"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["PublicSpendingShare"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["PublicSpendingShareInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["public_spending"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".7135"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".02"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\varepsilon_g"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar\varepsilon_g"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["HabitShock"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["HabitInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["habit"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".98"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".02"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\eta^s"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar\eta^s"] @#define NumberOfShocks = NumberOfShocks + 1 @#define ExogenousVariables_vnames = ExogenousVariables_vnames + ["PreferenceShock"] @#define ExogenousVariables_inames = ExogenousVariables_inames + ["PreferenceInnovation"] @#define ExogenousVariables_pnames = ExogenousVariables_pnames + ["preference"] @#define ExogenousVariables_nblags = ExogenousVariables_nblags + [1] @#define ExogenousVariables_acorr1_mode = ExogenousVariables_acorr1_mode + [".9000"] @#define ExogenousVariables_acorr1_std = ExogenousVariables_acorr1_std + [".02"] @#define ExogenousVariables_vtexnames = ExogenousVariables_vtexnames + ["\varsigma"] @#define ExogenousVariables_sstexnames = ExogenousVariables_sstexnames + ["\bar\varsigma"] @#define NumberOfShocks = NumberOfShocks + 1 // AutoregressiveProcesses(i,1) [string] Name of the variable. // AutoregressiveProcesses(i,2) [string] Generic name of the autoregressive parameters // AutoregressiveProcesses(i,3) [integer] Number of lags. global AutoregressiveProcesses; % Needed in the steady state file, where we have to update parameters related to the exogenous variables. AutoregressiveProcesses = cell(@{NumberOfShocks},3); @#for shock in 1:NumberOfShocks AutoregressiveProcesses(@{shock},1) = {'@{ExogenousVariables_vnames[shock]}'} ; AutoregressiveProcesses(@{shock},2) = {'@{ExogenousVariables_pnames[shock]}'} ; AutoregressiveProcesses(@{shock},3) = { @{ExogenousVariables_nblags[shock]} } ; @#endfor /* ** MOD FILE CORE */ /* 84 Endogenous variables (if efficient_block is equal to 1) */ var /* Households */ Consumption HouseholdLabourSupply HouseholdLagrangeMultiplier Investment CapitalStock DepreciationRate dDepreciationRate InvestmentCost dInvestmentCost CapacityUtilizationFactor CapitalReturnRate HouseholdRealWage TobinQ /* Prices */ RealGrossWage LabourDemand CapitalDemand RealMarginalCost OptimalRelativePrice Z1 Z2 Z3 GDP FinalGoodLagrangeMultiplier NonOptimizingFirmsPriceGrowth AveragedRelativePrices PriceDistorsion NablaPrice InflationFactor /* Wages */ RealWageGrowthFactor AveragedRelativeWages OptimalRelativeRealWage H1 H2 H3 EmploymentAgencyLagrangeMultiplier EmploymentAgencyLabourSupply NonOptimizingUnionsWageGrowth WageDistorsion NablaWage /* Monetary authority and Government */ NominalInterestFactor OutputGap PublicSpending /* Efficient variables (model without nominal rigidities) */ @#if (efficient_block==1) EfficientConsumption EfficientHouseholdLabourSupply EfficientHouseholdLagrangeMultiplier EfficientInvestment EfficientCapitalStock EfficientDepreciationRate dEfficientDepreciationRate EfficientInvestmentCost dEfficientInvestmentCost EfficientCapacityUtilizationFactor EfficientCapitalReturnRate EfficientHouseholdRealWage EfficientTobinQ EfficientRealInterestFactor EfficientLabourDemand EfficientRealMarginalCost EfficientGDP EfficientCapitalDemand EfficientRealGrossWage @#endif /* Shocks */ @#for shock in 1:NumberOfShocks @{ExogenousVariables_vnames[shock]} @#endfor ; /* 15 Exogenous variables */ varexo @#for shock in 1:NumberOfShocks @{ExogenousVariables_inames[shock]} @#endfor ; parameters /* ** Household */ sigmac $\sigma_c$ sigmal $\sigma_l$ eta $\eta$ beta $\beta$ investment_cost_size $\psi$ capacity_utilization_factor_ss $\bar z$ depreciation_rate_ss $\bar \delta$ first_derivate_depreciation_rate_ss $\bar \delta''$ household_labour_supply_ss $\overline L$ steady_state_investment_ratio $\frac{I}{Y}$ /* ** Prices */ alpha $\alpha$ thetaf $\theta_f$ psif $\psi_f$ xip $\xi_p$ price_contract_length $\frac{1}{1-\xi_p}$ gammap $\gamma_p$ steady_state_mark_up_f $\mu_f$ steady_state_labour_share $\frac{wL}{Y}$ kimball_curvature_f $\epsilon_f$ /* ** Wages */ psis $\psi_s$ thetas $\theta_s$ xiw $\xi_w$ wage_contract_length $\frac{1}{1-\xi_w}$ gammaw $\gamma_w$ steady_state_mark_up_s $\mu_s$ kimball_curvature_s $\epsilon_f$ /* ** Monetary authority */ @#if (efficient_block==0) ssGDP $\bar Y$ @#endif steady_state_nominal_interest_factor $\bar R$ steady_state_real_interest_factor $\bar r$ nominal_interest_rate_smoothing $\rho_R$ elasticity_of_nominal_interest_rate_to_inflation $r_{\pi}$ elasticity_of_nominal_interest_rate_to_output_gap $r_y$ elasticity_of_nominal_interest_rate_to_inflation_growth $r_{\Delta \pi}$ elasticity_of_nominal_interest_rate_to_output_gap_growth $r_{\Delta y}$ /* ** Parameters related to exogenous processes */ @#for shock in 1:NumberOfShocks @#if (ExogenousVariables_nblags[shock]>0) @#for lag in 1:ExogenousVariables_nblags[shock] @{ExogenousVariables_pnames[shock]}_ar@{lag} $\rho_{@{ExogenousVariables_vtexnames[shock]},@{lag}}$ @{ExogenousVariables_pnames[shock]}_rho@{lag} $\rho_{@{ExogenousVariables_vtexnames[shock]}}(@{lag})$ @#endfor @#endif @{ExogenousVariables_pnames[shock]}_i_std @{ExogenousVariables_pnames[shock]}_std $\sqrt{\mathbb V[@{ExogenousVariables_vtexnames[shock]}]}$ @{ExogenousVariables_pnames[shock]}_ss $ @{ExogenousVariables_sstexnames[shock]} $ @#endfor Epsilon // This is not a parameter of the model. ; /* ** ??talonnage des param??tres */ beta = 0.9975 ; sigmac = 0.8514 ; sigmal = 1.7180 ; eta = 0.1836 ; price_contract_length = 1.6824; // quarters wage_contract_length = 4.6296; // quarters gammap = 0.2079 ; gammaw = 0.2757 ; // Is this parameter needed? --> steady_state_investment_ratio = 0.2094; steady_state_mark_up_f = 1.1931 ; steady_state_mark_up_s = 1.2027 ; production_efficiency_growth_ss = 0.0031 ; production_efficiency_ss = 1.0000 ; inflation_target_ss = 1.0050 ; steady_state_nominal_interest_factor = 1.0100 ; steady_state_real_interest_factor = steady_state_nominal_interest_factor / inflation_target_ss ; consumption_tax_ss = 1.0000 ;//1.1106 ; income_tax_ss = 1.0000 ;//0.8814 ; labour_income_tax_ss = 1.0000 ;//0.8730 ; labour_tax_ss = 1.0000 ; preference_ss = 1.0000 ; investment_relative_price_ss = 1.0000 ; investment_efficiency_ss = 1.0000 ; risk_premium_ss = 1.0000 ; labour_supply_ss = 1.0000 ;//0.1800 ; taylor_ss = 1.0000 ; public_spending_ss = 0.2500 ;//0.2181 ; wage_mark_up_ss = 1.0000 ; price_mark_up_ss = 1.0000 ; investment_cost_size = 0.2361 ; habit_ss = 1.0000 ; capacity_utilization_factor_ss = 0.8012 ; depreciation_rate_ss = 0.0250 ;//0.0200 ; steady_state_labour_share = (1-0.3030)/(labour_tax_ss*steady_state_mark_up_f);//0.3914 ; kimball_curvature_f = -(-4.8380)*steady_state_mark_up_f/(steady_state_mark_up_f-1);//10.3333; kimball_curvature_s = -(-5.5056)*steady_state_mark_up_s/(steady_state_mark_up_s-1);//*10.3333; household_labour_supply_ss = 0.2712; nominal_interest_rate_smoothing = 0.5807 ;//0.8400 ; elasticity_of_nominal_interest_rate_to_inflation = 1.4290 ;//1.5000 ; elasticity_of_nominal_interest_rate_to_output_gap = 1.7418 ;//0.1400 ; elasticity_of_nominal_interest_rate_to_inflation_growth = 0.0000 ; elasticity_of_nominal_interest_rate_to_output_gap_growth = 0.0000 ; production_efficiency_growth_rho1 = .3919 ; production_efficiency_rho1 = .6001 ; consumption_tax_rho1 = .0000 ; labour_income_tax_rho1 = .0000 ; income_tax_rho1 = .0000 ; risk_premium_rho1 = .9090 ; labour_supply_rho1 = .7035 ; investment_relative_price_rho1 = .6223 ; investment_efficiency_rho1 = .6289 ; labour_tax_rho1 = .0000 ; price_mark_up_rho1 = .8050 ; wage_mark_up_rho1 = .7400 ; inflation_target_rho1 = .0000 ; taylor_rho1 = .6388 ; public_spending_rho1 = .7135 ; habit_rho1 = .9800; preference_rho1 = .9000; production_efficiency_growth_std = sqrt(0.0058^2/(1-production_efficiency_growth_rho1^2)); production_efficiency_std = sqrt(0.0209^2/(1-production_efficiency_rho1^2)); risk_premium_std = sqrt(0.0048^2/(1-risk_premium_rho1^2)); consumption_tax_std = 0.0000; labour_income_tax_std = 0.0000; income_tax_std = 0.0000; labour_supply_std = sqrt(0.0077^2/(1-labour_supply_rho1^2)); investment_relative_price_std = sqrt(0.0055^2/(1-investment_relative_price_rho1^2)); investment_efficiency_std = sqrt(0.0061^2/(1-investment_efficiency_rho1^2)); labour_tax_std = 0.0000; price_mark_up_std = sqrt(0.0042^2/(1-price_mark_up_rho1^2)); wage_mark_up_std = sqrt(0.0040^2/(1-wage_mark_up_rho1^2)); inflation_target_std = sqrt(1.0000^2/(1-inflation_target_rho1^2)); taylor_std = sqrt(0.0049^2/(1-taylor_rho1^2)); public_spending_std = sqrt(0.0055^2/(1-public_spending_rho1^2)); habit_std = sqrt(1.0000^2/(1-habit_rho1^2)); preference_std = sqrt(1.0000^2/(1-preference_rho1^2)); @#for shock in 1:NumberOfShocks @{ExogenousVariables_pnames[shock]}_i_std = 1.000 ; // Useless. Will be updated in the steady state file! @#if (ExogenousVariables_nblags[shock]>0) @#for lag in 1:ExogenousVariables_nblags[shock] @{ExogenousVariables_pnames[shock]}_ar@{lag} = 0.0000 ; // Useless. Will be updated in the steady state file! @{ExogenousVariables_pnames[shock]}_rho@{lag} = @{ExogenousVariables_acorr1_mode[shock]}^@{lag}; @#endfor @#endif @#endfor FinalGoodLagrangeMultiplier_ss = 1 ; AveragedRelativePrices_ss = 1 ; PriceDistorsion_ss = 1 ; NablaPrice_ss = 1 ; OptimalRelativePrice_ss = 1 ; EmploymentAgencyLagrangeMultiplier_ss = 1 ; RealWageGrowthFactor_ss = 1; AveragedRelativeWages_ss = 1 ; OptimalRelativeRealWage_ss = 1 ; WageDistorsion_ss = 1 ; NablaWage_ss = 1 ; TobinQ_ss = 1; OutputGap_ss = 1 ; InvestmentCost_ss = 0; dInvestmentCost_ss = 0; EfficientInvestmentCost_ss = 0; dEfficientInvestmentCost_ss = 0; RealMarginalCost_ss = 1/steady_state_mark_up_f ; NonOptimizingFirmsPriceGrowth_ss = inflation_target_ss ; InflationFactor_ss = inflation_target_ss ; NonOptimizingUnionsWageGrowth_ss = inflation_target_ss ; ssratio_HouseholdRealWage_RealGrossWage = 1/steady_state_mark_up_s ; NominalInterestFactor_ss = steady_state_nominal_interest_factor ; beta = inflation_target_ss/(risk_premium_ss*NominalInterestFactor_ss)*(1+production_efficiency_growth_ss)^(sigmac); RealInterestFactor_ss = NominalInterestFactor_ss / inflation_target_ss ; CapacityUtilizationFactor_ss = capacity_utilization_factor_ss ; DepreciationRate_ss = depreciation_rate_ss; CapitalReturnRate_ss = ((1+production_efficiency_growth_ss)^sigmac-beta*(1-depreciation_rate_ss))/(beta*income_tax_ss*capacity_utilization_factor_ss); dDepreciationRate_ss = CapitalReturnRate_ss*income_tax_ss; first_derivate_depreciation_rate_ss = dDepreciationRate_ss; alpha = 1 - labour_tax_ss*steady_state_mark_up_f*steady_state_labour_share; RealGrossWage_ss = (RealMarginalCost_ss*(alpha/CapitalReturnRate_ss)^alpha)^(1/(1-alpha))*(1-alpha)/labour_tax_ss*production_efficiency_ss; HouseholdRealWage_ss = ssratio_HouseholdRealWage_RealGrossWage * RealGrossWage_ss; ssratio_CapitalDemand_HouseholdLabourSupply = labour_tax_ss*RealGrossWage_ss/CapitalReturnRate_ss*alpha/(1-alpha) ; ssratio_GDP_HouseholdLabourSupply = ssratio_CapitalDemand_HouseholdLabourSupply^alpha * production_efficiency_ss^(1-alpha) ; ssratio_Investment_GDP = (production_efficiency_growth_ss + depreciation_rate_ss)/capacity_utilization_factor_ss*ssratio_CapitalDemand_HouseholdLabourSupply^(1-alpha)/production_efficiency_ss^(1-alpha) ; ssratio_Consumption_GDP = 1 - public_spending_ss - ssratio_Investment_GDP; labour_supply_ss = HouseholdRealWage_ss/(ssratio_Consumption_GDP*ssratio_GDP_HouseholdLabourSupply) * income_tax_ss * labour_income_tax_ss / consumption_tax_ss /(1-eta/(1+production_efficiency_growth_ss)); HouseholdLabourSupply_ss = household_labour_supply_ss; LabourDemand_ss = HouseholdLabourSupply_ss; EmploymentAgencyLabourSupply_ss = HouseholdLabourSupply_ss; GDP_ss = ssratio_GDP_HouseholdLabourSupply * HouseholdLabourSupply_ss ; Consumption_ss = ssratio_Consumption_GDP * GDP_ss ; Investment_ss = ssratio_Investment_GDP * GDP_ss ; HouseholdLagrangeMultiplier_ss = (1/consumption_tax_ss)*(Consumption_ss*(1-eta/(1+production_efficiency_growth_ss)))^(-sigmac) * exp(labour_supply_ss*(sigmac-1)/(1+sigmal)); CapitalDemand_ss = ssratio_CapitalDemand_HouseholdLabourSupply * HouseholdLabourSupply_ss ; CapitalStock_ss = (1+production_efficiency_growth_ss)/(production_efficiency_growth_ss+depreciation_rate_ss)*Investment_ss ; psif = - kimball_curvature_f / thetaf ; psis = - kimball_curvature_s / thetas ; xip = (price_contract_length - 1)/price_contract_length ; xiw = (wage_contract_length - 1)/wage_contract_length ; Z1_ss = RealMarginalCost_ss*HouseholdLagrangeMultiplier_ss*GDP_ss /(1-beta*xip*(1+production_efficiency_growth_ss)^(1-sigmac)) ; Z2_ss = Z1_ss/RealMarginalCost_ss ; Z3_ss = Z2_ss ; H1_ss = HouseholdRealWage_ss*HouseholdLagrangeMultiplier_ss*EmploymentAgencyLabourSupply_ss /(1-beta*xiw*(1+production_efficiency_growth_ss)^(1-sigmac)) ; H2_ss = H1_ss/ssratio_HouseholdRealWage_RealGrossWage ; H3_ss = H2_ss ; ProductionEfficiencyGrowth_ss = (1+production_efficiency_growth_ss) ; ProductionEfficiencyCycle_ss = production_efficiency_ss ; ConsumptionTax_ss = consumption_tax_ss ; LabourIncomeTax_ss = labour_income_tax_ss ; IncomeTax_ss = income_tax_ss ; RiskPremium_ss = risk_premium_ss ; LabourSupplyShock_ss = labour_supply_ss ; InvestmentRelativePrice_ss = investment_relative_price_ss ; InvestmentEfficiencyShock_ss = investment_efficiency_ss ; LabourTax_ss = labour_tax_ss ; PriceMarkUpShock_ss = price_mark_up_ss ; WageMarkUpShock_ss = wage_mark_up_ss ; InflationTarget_ss = inflation_target_ss ; TaylorShock_ss = taylor_ss ; PublicSpendingShare_ss = public_spending_ss ; PublicSpending_ss = GDP_ss * PublicSpendingShare_ss ; HabitShock_ss = 1.0000; PreferenceShock_ss = 1.0000; EfficientConsumption_ss = Consumption_ss ; EfficientHouseholdLabourSupply_ss = HouseholdLabourSupply_ss ; EfficientHouseholdLagrangeMultiplier_ss = HouseholdLagrangeMultiplier_ss ; EfficientInvestment_ss = Investment_ss; EfficientCapitalStock_ss = CapitalStock_ss; EfficientDepreciationRate_ss = DepreciationRate_ss; dEfficientDepreciationRate_ss = dDepreciationRate_ss; EfficientCapacityUtilizationFactor_ss = CapacityUtilizationFactor_ss; EfficientCapitalReturnRate_ss = CapitalReturnRate_ss; EfficientHouseholdRealWage_ss = HouseholdRealWage_ss; EfficientTobinQ_ss = TobinQ_ss; EfficientRealInterestFactor_ss = RealInterestFactor_ss; EfficientLabourDemand_ss = LabourDemand_ss; EfficientRealMarginalCost_ss = RealMarginalCost_ss; EfficientGDP_ss = GDP_ss; EfficientCapitalDemand_ss = CapitalDemand_ss; EfficientRealGrossWage_ss = RealGrossWage_ss; model; /* ** HOUSEHOLDS. */ /* Equation:1:: Household Consumption FOC */ (Consumption - eta*HabitShock*Consumption(-1)/ProductionEfficiencyGrowth+log(PreferenceShock))^(-sigmac) *exp(LabourSupplyShock*(sigmac-1)/(1+sigmal)*(HouseholdLabourSupply/household_labour_supply_ss)^(1+sigmal)) - ConsumptionTax*HouseholdLagrangeMultiplier ; /* Equation:2:: Household Euler equation */ beta*RiskPremium*NominalInterestFactor*ProductionEfficiencyGrowth(1)^(-sigmac) *HouseholdLagrangeMultiplier(1)*IncomeTax(1)/InflationFactor(1) - HouseholdLagrangeMultiplier*IncomeTax; /* Equation:3:: Household Labour FOC */ (Consumption - eta*HabitShock*Consumption(-1)/ProductionEfficiencyGrowth+log(PreferenceShock))^(1-sigmac) *(LabourSupplyShock/household_labour_supply_ss) *exp(LabourSupplyShock*(sigmac-1)/(1+sigmal)*(HouseholdLabourSupply/household_labour_supply_ss)^(1+sigmal)) *(HouseholdLabourSupply/household_labour_supply_ss)^sigmal -HouseholdLagrangeMultiplier*IncomeTax*LabourIncomeTax*HouseholdRealWage; /* Equation:4:: Household Investment FOC */ TobinQ*(1-InvestmentCost-Investment/Investment(-1)*ProductionEfficiencyGrowth*dInvestmentCost) +beta*HouseholdLagrangeMultiplier(1)/HouseholdLagrangeMultiplier *ProductionEfficiencyGrowth(1)^(-sigmac)*TobinQ(1)*InvestmentEfficiencyShock(1)/InvestmentEfficiencyShock *(Investment(1)/Investment*ProductionEfficiencyGrowth(1))^2 *dInvestmentCost(1) -InvestmentRelativePrice/InvestmentEfficiencyShock; /* Equation:5:: Depreciation rate */ depreciation_rate_ss *exp((CapacityUtilizationFactor-capacity_utilization_factor_ss)*first_derivate_depreciation_rate_ss/depreciation_rate_ss) -DepreciationRate; /* Equation:6:: First derivate of the depreciation rate */ first_derivate_depreciation_rate_ss *exp((CapacityUtilizationFactor-capacity_utilization_factor_ss)*first_derivate_depreciation_rate_ss/depreciation_rate_ss) -dDepreciationRate; /* Equation:7:: Household Capacity utilization rate */ IncomeTax*CapitalReturnRate-TobinQ*dDepreciationRate; /* Equation:8:: Household Physical capital FOC */ beta*HouseholdLagrangeMultiplier(1)/HouseholdLagrangeMultiplier *ProductionEfficiencyGrowth(1)^(-sigmac) *(TobinQ(1)*(1-DepreciationRate(1))+IncomeTax(1)*CapitalReturnRate(1)*CapacityUtilizationFactor(1)) -TobinQ; /*Equation:9:: Physical capital stock law of motion */ (1-DepreciationRate)*CapitalStock(-1)/ProductionEfficiencyGrowth +InvestmentEfficiencyShock*(1-InvestmentCost)*Investment-CapitalStock; /*Equation:10:: Investment cost */ InvestmentCost = .5*investment_cost_size*(1+production_efficiency_growth_ss)*(1+production_efficiency_growth_ss) *(Investment/Investment(-1)*ProductionEfficiencyGrowth/(1+production_efficiency_growth_ss)-1)^2; /*Equation:11:: First derivate of the investment cost */ dInvestmentCost = (Investment/Investment(-1)*ProductionEfficiencyGrowth/(1+production_efficiency_growth_ss)-1) *(1+production_efficiency_growth_ss)*investment_cost_size; /* ** PRICES. */ /*Equation:12:: Price growth factor for non optimizing intermediate firms */ InflationTarget^(1-gammap) *InflationFactor(-1)^gammap -NonOptimizingFirmsPriceGrowth; /*Equation:13:: Factor Price Frontier */ LabourTax*RealGrossWage*LabourDemand/(CapitalReturnRate*CapitalDemand) - (1-alpha)/alpha; /*Equation:14:: Marginal cost */ ProductionEfficiencyCycle^(alpha-1) *(CapitalReturnRate/alpha)^alpha *(LabourTax*RealGrossWage/(1-alpha))^(1-alpha) -RealMarginalCost; /*Equation:15:: Relative price of an optimizing intermediate firm */ thetaf*(1+psif)/(thetaf*(1+psif)-1)*(Z1/Z2) +psif/(thetaf*(1+psif)-1)*OptimalRelativePrice^(1+(1+psif)*thetaf)*Z3/Z2 -OptimalRelativePrice; /*Equation:16:: Lagrange multiplier associated to technological constraint of the final good representative firm */ (1-xip)*OptimalRelativePrice^(1-thetaf*(1+psif)) +xip*(NonOptimizingFirmsPriceGrowth/InflationFactor)^(1-thetaf*(1+psif)) *FinalGoodLagrangeMultiplier(-1)^(1-thetaf*(1+psif)) -FinalGoodLagrangeMultiplier^(1-thetaf*(1+psif)); /*Equation:17:: Z1 (relative price equation) */ HouseholdLagrangeMultiplier*RealMarginalCost*FinalGoodLagrangeMultiplier^(thetaf*(1+psif))*GDP +beta*xip*ProductionEfficiencyGrowth(1)^(1-sigmac) *(InflationFactor(1)/NonOptimizingFirmsPriceGrowth)^((1+psif)*thetaf)*Z1(1) -Z1; /*Equation:18:: Z2 (relative price equation) */ HouseholdLagrangeMultiplier*PriceMarkUpShock*FinalGoodLagrangeMultiplier^(thetaf*(1+psif))*GDP +beta*xip*ProductionEfficiencyGrowth(1)^(1-sigmac) *(InflationFactor(1)/NonOptimizingFirmsPriceGrowth)^((1+psif)*thetaf-1)*Z2(1) -Z2; /*Equation:19:: Z3 (relative price equation) */ HouseholdLagrangeMultiplier*PriceMarkUpShock*GDP +beta*xip*ProductionEfficiencyGrowth(1)^(1-sigmac) *NonOptimizingFirmsPriceGrowth/InflationFactor(1)*Z3(1) -Z3; /*Equation:20:: Average of relative prices */ (1-xip)*OptimalRelativePrice +xip*NonOptimizingFirmsPriceGrowth/InflationFactor*AveragedRelativePrices(-1) -AveragedRelativePrices; /*Equation:21:: Agregate price */ psif*AveragedRelativePrices/(1+psif) +FinalGoodLagrangeMultiplier/(1+psif) -1; /*Equation:22:: Price Distorsion */ psif/(1+psif) +NablaPrice/(1+psif)*FinalGoodLagrangeMultiplier^(thetaf*(1+psif)) -PriceDistorsion; /*Equation:23:: nabla (recursive latent variable used in price distorsion equation) */ (1-xip)*OptimalRelativePrice^(-(1+psif)*thetaf) +xip*NablaPrice(-1)*(NonOptimizingFirmsPriceGrowth/InflationFactor)^(-thetaf*(1+psif)) -NablaPrice; /* ** WAGES. */ /*Equation:24:: Wage growth factor of the non optimizing firms */ InflationFactor^gammaw*InflationTarget^(1-gammaw) -NonOptimizingUnionsWageGrowth; /*Equation:25:: Real wage inflation factor */ RealGrossWage/RealGrossWage(-1)-RealWageGrowthFactor; /*Equation:26:: Relative wage of an optimizing union */ thetas*(1+psis)/(thetas*(1+psis)-1)*H1/H2 +psis/(thetas*(1+psis)-1)*OptimalRelativeRealWage^(1+(1+psis)*thetas)*H3/H2 -OptimalRelativeRealWage; /*Equation:27:: Lagrange multiplier associated to the employment agency */ (1-xiw)*OptimalRelativeRealWage^(1-thetas*(1+psis)) +xiw*(NonOptimizingUnionsWageGrowth/(RealWageGrowthFactor*InflationFactor))^(1-thetas*(1+psis)) *EmploymentAgencyLagrangeMultiplier(-1)^(1-thetas*(1+psis)) -EmploymentAgencyLagrangeMultiplier^(1-thetas*(1+psis)); /*Equation:28:: H1 (relative wage equation) */ HouseholdLagrangeMultiplier*HouseholdRealWage*EmploymentAgencyLagrangeMultiplier^(thetas*(1+psis))*EmploymentAgencyLabourSupply +beta*xiw*ProductionEfficiencyGrowth(1)^(1-sigmac) *(RealWageGrowthFactor(1)*InflationFactor(1)/NonOptimizingUnionsWageGrowth)^((1+psis)*thetas)*H1(1) -H1; /*Equation:29:: H2 (relative wage equation) */ HouseholdLagrangeMultiplier*WageMarkUpShock*RealGrossWage *EmploymentAgencyLagrangeMultiplier^(thetas*(1+psis))*EmploymentAgencyLabourSupply +beta*xiw*ProductionEfficiencyGrowth(1)^(1-sigmac) *(RealWageGrowthFactor(1)*InflationFactor(1)/NonOptimizingUnionsWageGrowth)^((1+psis)*thetas-1)*H2(1) -H2; /*Equation:30:: H3 (relative wage equation) */ HouseholdLagrangeMultiplier*WageMarkUpShock*RealGrossWage*EmploymentAgencyLabourSupply +beta*xiw*ProductionEfficiencyGrowth(1)^(1-sigmac) *NonOptimizingUnionsWageGrowth/(InflationFactor(1)*RealWageGrowthFactor(1))*H3(1) -H3; /*Equation:31:: Average of relative wages */ (1-xiw)*OptimalRelativeRealWage +xiw*NonOptimizingUnionsWageGrowth/(RealWageGrowthFactor*InflationFactor)*AveragedRelativeWages(-1) -AveragedRelativeWages; /*Equation:32:: Agregate Wage */ psis*AveragedRelativeWages/(1+psis) +EmploymentAgencyLagrangeMultiplier/(1+psis) -1; /*Equation:33:: Wage Distorsion */ psis/(1+psis) +NablaWage/(1+psis)*EmploymentAgencyLagrangeMultiplier^(thetas*(1+psis)) -WageDistorsion; /*Equation:34:: nabla (recursive latent variable used in wage distorsion equation) */ (1-xiw)*OptimalRelativeRealWage^(-(1+psis)*thetas) +xiw*NablaWage(-1)*(NonOptimizingUnionsWageGrowth/(RealWageGrowthFactor*InflationFactor))^(-thetas*(1+psis)) -NablaWage; /* ** MONETARY AUTHORITY & GOVERNMENT */ /*Equation:35:: Taylor rule */ NominalInterestFactor(-1)^nominal_interest_rate_smoothing *( steady_state_nominal_interest_factor *(InflationFactor(-1)/InflationTarget)^elasticity_of_nominal_interest_rate_to_inflation *OutputGap^elasticity_of_nominal_interest_rate_to_output_gap *(InflationFactor/InflationTarget*InflationTarget(-1)/InflationFactor(-1))^elasticity_of_nominal_interest_rate_to_inflation_growth *(OutputGap/OutputGap(-1))^elasticity_of_nominal_interest_rate_to_output_gap_growth )^(1-nominal_interest_rate_smoothing) *TaylorShock - NominalInterestFactor; /*Equation:36:: Output gap */ @#if (efficient_block==1) GDP/EfficientGDP -OutputGap; @#endif @#if (efficient_block==0) GDP/ssGDP -OutputGap; @#endif /*Equation:37:: Public Spending */ PublicSpendingShare * GDP - PublicSpending; /* ** MARKETS */ /*Equation:38:: Physical capital market equilibrium */ CapacityUtilizationFactor*CapitalStock(-1)/ProductionEfficiencyGrowth - CapitalDemand ; /*Equation:39:: Relation between household labour supply and employment agency labour supply */ HouseholdLabourSupply/WageDistorsion - EmploymentAgencyLabourSupply; /*Equation:40:: Labour market equilibrium */ EmploymentAgencyLabourSupply - LabourDemand; /*Equation:41:: Relation between GDP and the sum of produced intermediate goods */ CapitalDemand^alpha * (ProductionEfficiencyCycle*LabourDemand)^(1-alpha) / PriceDistorsion - GDP; /*Equation:42:: Final good market equilibrium */ PublicSpending + Consumption + InvestmentRelativePrice*Investment - PriceMarkUpShock*GDP - (1-WageMarkUpShock)*RealGrossWage*LabourDemand; /* ** EQUATIONS FOR THE SHOCKS (Equations 43 to 57). */ @#for shock in 1:NumberOfShocks exp(@{ExogenousVariables_pnames[shock]}_i_std*@{ExogenousVariables_inames[shock]}) @#if (shock==1) @#if (ExogenousVariables_nblags[shock]>0) @#for lag in 1:ExogenousVariables_nblags[shock] * (@{ExogenousVariables_vnames[shock]}(-@{lag})/(1+@{ExogenousVariables_pnames[shock]}_ss))^@{ExogenousVariables_pnames[shock]}_ar@{lag} @#endfor @#endif @#else @#if (ExogenousVariables_nblags[shock]>0) @#for lag in 1:ExogenousVariables_nblags[shock] * (@{ExogenousVariables_vnames[shock]}(-@{lag})/@{ExogenousVariables_pnames[shock]}_ss)^@{ExogenousVariables_pnames[shock]}_ar@{lag} @#endfor @#endif @#endif @#if (shock==1) - @{ExogenousVariables_vnames[shock]}/(1+@{ExogenousVariables_pnames[shock]}_ss) @#else - @{ExogenousVariables_vnames[shock]}/@{ExogenousVariables_pnames[shock]}_ss @#endif ; @#endfor @#if (efficient_block==1) /* ** EQUATIONS FOR THE EFFICIENT VARIABLES. */ /* Equation:58:: (Efficient) Household Consumption FOC */ (EfficientConsumption - eta*HabitShock*EfficientConsumption(-1)/ProductionEfficiencyGrowth+log(PreferenceShock))^(-sigmac) *exp(LabourSupplyShock*(sigmac-1)/(1+sigmal)*(EfficientHouseholdLabourSupply/household_labour_supply_ss)^(1+sigmal)) - ConsumptionTax*EfficientHouseholdLagrangeMultiplier ; /* Equation:59:: (Efficient) Household Euler equation */ beta*RiskPremium*EfficientRealInterestFactor*ProductionEfficiencyGrowth(1)^(-sigmac) *EfficientHouseholdLagrangeMultiplier(1)*IncomeTax(1) - EfficientHouseholdLagrangeMultiplier*IncomeTax; /* Equation:60:: (Efficient) Household Labour FOC */ (EfficientConsumption - eta*HabitShock*EfficientConsumption(-1)/ProductionEfficiencyGrowth+log(PreferenceShock))^(1-sigmac) *(LabourSupplyShock/household_labour_supply_ss) *exp(LabourSupplyShock*(sigmac-1)/(1+sigmal)*(EfficientHouseholdLabourSupply/household_labour_supply_ss)^(1+sigmal)) *(EfficientHouseholdLabourSupply/household_labour_supply_ss)^sigmal -EfficientHouseholdLagrangeMultiplier*IncomeTax*LabourIncomeTax*EfficientHouseholdRealWage; /* Equation:61:: (Efficient) Household Investment FOC */ EfficientTobinQ*(1-EfficientInvestmentCost-EfficientInvestment/EfficientInvestment(-1)*ProductionEfficiencyGrowth*dEfficientInvestmentCost) +beta*EfficientHouseholdLagrangeMultiplier(1)/EfficientHouseholdLagrangeMultiplier *ProductionEfficiencyGrowth(1)^(-sigmac)*EfficientTobinQ(1)*InvestmentEfficiencyShock(1)/InvestmentEfficiencyShock *(EfficientInvestment(1)/EfficientInvestment*ProductionEfficiencyGrowth(1))^2 *dEfficientInvestmentCost(1)-InvestmentRelativePrice/InvestmentEfficiencyShock; /* Equation:62:: (Efficient) Depreciation rate */ depreciation_rate_ss *exp((EfficientCapacityUtilizationFactor-capacity_utilization_factor_ss)*first_derivate_depreciation_rate_ss/depreciation_rate_ss) -EfficientDepreciationRate; /* Equation:63:: (Efficient) First derivate of the depreciation rate */ first_derivate_depreciation_rate_ss *exp((EfficientCapacityUtilizationFactor-capacity_utilization_factor_ss)*first_derivate_depreciation_rate_ss/depreciation_rate_ss) -dEfficientDepreciationRate; /* Equation:64:: (Efficient) Household Capacity utilization rate */ IncomeTax*EfficientCapitalReturnRate-EfficientTobinQ*dEfficientDepreciationRate; /* Equation:65:: (Efficient) Household Physical capital FOC */ beta*EfficientHouseholdLagrangeMultiplier(1)/EfficientHouseholdLagrangeMultiplier *ProductionEfficiencyGrowth(1)^(-sigmac) *(EfficientTobinQ(1)*(1-EfficientDepreciationRate(1))+IncomeTax(1)*EfficientCapitalReturnRate(1)*EfficientCapacityUtilizationFactor(1)) -EfficientTobinQ; /*Equation:66:: (Efficient) Physical capital stock law of motion */ (1-EfficientDepreciationRate)*EfficientCapitalStock(-1)/ProductionEfficiencyGrowth +InvestmentEfficiencyShock*(1-EfficientInvestmentCost)*EfficientInvestment -EfficientCapitalStock; /*Equation:67:: (Efficient) Factor Price Frontier */ LabourTax*EfficientRealGrossWage*EfficientLabourDemand/(EfficientCapitalReturnRate*EfficientCapitalDemand) - (1-alpha)/alpha; /*Equation:68:: (Efficient) Marginal cost */ ProductionEfficiencyCycle^(alpha-1) *(EfficientCapitalReturnRate/alpha)^alpha *(LabourTax*EfficientRealGrossWage/(1-alpha))^(1-alpha) -EfficientRealMarginalCost; /*Equation:69:: (Efficient) Price decision */ thetaf*(1+psif)/(thetaf*(1+psif)-1)*EfficientRealMarginalCost +psif/(thetaf*(1+psif)-1) -1; /*Equation:70:: (Efficient) Wage decision */ thetas*(1+psis)/(thetas*(1+psis)-1)*EfficientHouseholdRealWage/EfficientRealGrossWage +psis/(thetas*(1+psis)-1) -1; /*Equation:71:: (Efficient) Labour market equilibrium */ EfficientLabourDemand - EfficientHouseholdLabourSupply; /*Equation:72:: (Efficient) Physical capital market equilibrium */ EfficientCapacityUtilizationFactor*EfficientCapitalStock(-1)/ProductionEfficiencyGrowth - EfficientCapitalDemand ; /*Equation:73:: (Efficient) Final good market equilibrium */ EfficientConsumption + InvestmentRelativePrice*EfficientInvestment - (1-PublicSpendingShare)*EfficientGDP; /*Equation:74:: (Efficient) Relation between GDP and the sum of produced intermediate goods */ EfficientCapitalDemand^alpha * (ProductionEfficiencyCycle*EfficientLabourDemand)^(1-alpha) - EfficientGDP; /*Equation:75:: (Efficient) Investment cost */ .5*investment_cost_size*(1+production_efficiency_growth_ss)*(1+production_efficiency_growth_ss) *(EfficientInvestment/EfficientInvestment(-1)*ProductionEfficiencyGrowth/(1+production_efficiency_growth_ss)-1)^2 -EfficientInvestmentCost; /*Equation:76:: (Efficient) First derivate of the investment cost */ (EfficientInvestment/EfficientInvestment(-1)*ProductionEfficiencyGrowth/(1+production_efficiency_growth_ss)-1) *(1+production_efficiency_growth_ss)*investment_cost_size - dEfficientInvestmentCost; @#endif end; initval; /* Households */ Consumption = Consumption_ss; HouseholdLabourSupply = HouseholdLabourSupply_ss; HouseholdLagrangeMultiplier = HouseholdLagrangeMultiplier_ss; Investment = Investment_ss; CapitalStock = CapitalStock_ss; DepreciationRate = DepreciationRate_ss; dDepreciationRate = dDepreciationRate_ss; InvestmentCost = InvestmentCost_ss; dInvestmentCost = dInvestmentCost_ss; CapacityUtilizationFactor = CapacityUtilizationFactor_ss; CapitalReturnRate = CapitalReturnRate_ss; HouseholdRealWage = HouseholdRealWage_ss; TobinQ = TobinQ_ss; /* Prices */ RealGrossWage = RealGrossWage_ss; LabourDemand = LabourDemand_ss; CapitalDemand = CapitalDemand_ss; RealMarginalCost = RealMarginalCost_ss; OptimalRelativePrice = OptimalRelativePrice_ss; Z1 = Z1_ss; Z2 = Z2_ss; Z3 = Z3_ss; GDP = GDP_ss; FinalGoodLagrangeMultiplier = FinalGoodLagrangeMultiplier_ss; NonOptimizingFirmsPriceGrowth = NonOptimizingFirmsPriceGrowth_ss; AveragedRelativePrices = AveragedRelativePrices_ss; PriceDistorsion = PriceDistorsion_ss; NablaPrice = NablaPrice_ss; InflationFactor = InflationFactor_ss; /* Wages */ RealWageGrowthFactor = RealWageGrowthFactor_ss; AveragedRelativeWages = AveragedRelativeWages_ss; OptimalRelativeRealWage = OptimalRelativeRealWage_ss; H1 = H1_ss; H2 = H2_ss; H3 = H3_ss; EmploymentAgencyLagrangeMultiplier = EmploymentAgencyLagrangeMultiplier_ss; EmploymentAgencyLabourSupply = EmploymentAgencyLabourSupply_ss; NonOptimizingUnionsWageGrowth = NonOptimizingUnionsWageGrowth_ss; WageDistorsion = WageDistorsion_ss; NablaWage = NablaWage_ss; /* Monetary authority and Government */ NominalInterestFactor = NominalInterestFactor_ss; OutputGap = OutputGap_ss; PublicSpending = PublicSpending_ss; /* Efficient variables (model without nominal rigidities) */ @#if (efficient_block==1) EfficientConsumption = EfficientConsumption_ss; EfficientHouseholdLabourSupply = EfficientHouseholdLabourSupply_ss; EfficientHouseholdLagrangeMultiplier = EfficientHouseholdLagrangeMultiplier_ss; EfficientInvestment = EfficientInvestment_ss; EfficientCapitalStock = EfficientCapitalStock_ss; EfficientDepreciationRate = EfficientDepreciationRate_ss; dEfficientDepreciationRate = dEfficientDepreciationRate_ss; EfficientInvestmentCost = EfficientInvestmentCost_ss; dEfficientInvestmentCost = dEfficientInvestmentCost_ss; EfficientCapacityUtilizationFactor = EfficientCapacityUtilizationFactor_ss; EfficientCapitalReturnRate = EfficientCapitalReturnRate_ss; EfficientHouseholdRealWage = EfficientHouseholdRealWage_ss; EfficientTobinQ = EfficientTobinQ_ss; EfficientRealInterestFactor = EfficientRealInterestFactor_ss; EfficientLabourDemand = EfficientLabourDemand_ss; EfficientRealMarginalCost = EfficientRealMarginalCost_ss; EfficientGDP = EfficientGDP_ss; EfficientCapitalDemand = EfficientCapitalDemand_ss; EfficientRealGrossWage = EfficientRealGrossWage_ss; @#endif /* Shocks */ @#for shock in 1:NumberOfShocks @{ExogenousVariables_inames[shock]} = 0.0; @#endfor @{ExogenousVariables_vnames[shock]} = 1+@{ExogenousVariables_pnames[shock]}_ss ; @#for shock in 2:NumberOfShocks @{ExogenousVariables_vnames[shock]} = @{ExogenousVariables_pnames[shock]}_ss; @#endfor end; steady; resid(1); check; shocks; var EfficiencyGrowthInnovation = .001; var EfficiencyCycleInnovation = .005; var RiskPremiumInnovation = .003; /* var ConsumptionTaxInnovation = .0000001; var LabourIncomeTaxInnovation = .0000001; var IncomeTaxInnovation = .0000001; var LabourSupplyInnovation = .0000001; var InvestmentRelativePriceInnovation = .0000001; var InvestmentEfficiencyInnovation = .0000001; var LabourTaxInnovation = .0000001; var PriceMarkUpInnovation = .0000001; var WageMarkUpInnovation = .0000001; var InflationTargetInnovation = .0000001; var TaylorInnovation = .0000001; var PublicSpendingShareInnovation = .0000001; var HabitInnovation = .0000001; var PreferenceInnovation = .0000001; */ end; stoch_simul(order=1,irf=0,noprint,periods=2000); plot(OutputGap);