Kooma

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Kooma is a dynamic economic model used by the Ministry of Finance of Finland. The model is described here (original published code as pdf(!))

+ Show code- Hide code %% Kooma-model file. % Valtiovarainministeriö % Kansantalousosasto % Mika Kuismanen & Mikko Sariola & % Samuli Pietiläinen September 2013 %---------------------------------- % Meri Obstbaum November 2013 % adds frictional labour market %linear !transition_variables %Households 'Private consumption' cp 'Transitory UIP shock process (risk premium)' i_e % Ricardian Households 'Consumption of forward looking households' cp_fl 'Marginal utility of consumption' muc 'Shadow value of consumption' iso_lambda 'Capital-labour ratio in production' k 'Effective capital' K 'Physical capital' Kp 'Capacity utilisation rate' nu 'Investment' ip 'Rental rate on capital k' yint_roc 'Real value of installed capital - Tobin Q' tobin_q 'Nominal interest rate' i 'Price of domestic wholesale good' pyint 'Consumer price' p 'CPI inflation' pie_p 'Producer price inflation' pie_yint 'Real price of K-L product' preal_kl 'Price of K-L product in terms of the CPI' pyint_kl 'Marginal productivity of capital' mpk 'Shock process of household consumption' cp_fl_e 'Shock process of investment adjustment costs' eps_ip 'Shock process of Tobin Q ' eps_tobin_q 'Process of TFP shock' yint_z 'Operating surplus / dividents' D % Rule of thumb households 'Consumption of hand-to-mouth households' cp_lc % Labour Market matching % PRODUCTION 'Output of labour and capital intermediate' yint_kl 'Aggregate output n*yint_kl' yint % LABOUR MARKET 'number of matches' match 'unemployment' u 'Employment, number of workers' n 'Working hours, per person' h 'Total hours =n*h' total_h 'Vacancies' v 'job destruction rate' rhohat 'firms vacancy-filling probability' qf 'workers job-finding probability' qw 'labour market tightness' theta 'Shock process of labour shock' n_e % Wage bargaining 'Firm surplus' J 'Worker surplus' H 'Marginal Productivity of Labour' mpl 'Contract wage' w_contract 'Nominal wage' w 'Employers social contribution' tau_sc 'Marginal rate of substitution btw consumption and labour' mrs 'Workers tax on earned income' tau_w 'Value added tax' tau_cp 'Bargaining strenght of workers' etahat % Job creation and determination of hours worked (per person) 'Vacancy posting cost' kappahat %Marginal cost of wholesale firm 'price mark-up domestic market' yint_phi % RETAILERS, final goods producers %Retailer of investment good 'price of composite investment good' pip 'demand of domestic intermediate investment good' iph 'imported investment good' mi %Importer price setting: consumption good 'pcp price of imported consumption good' pmc_pcp % PCP pri- ce equation for imported intermediate input ($) 'lcp price of imported consumption good' pmc_lcp % LCP pri- ce equation for imported intermediate input (€) 'price of imported consumption good' pmc % aggregate import price equation of consumption good %Retailer of consumption good 'price of composite consumption good' pcp 'imported consumption good' mc %'price of domestic intermediate good' pcph 'demand of domestic intermediate consumption good' cph %Retailer of export good 'demand for imports used in exports' mex 'demand for domestic goods used in exports' hex %Importer price setting: export good 'PCP price of imported intermediate good used in exports ($)' pmex_pcp 'LCP price of imported intermediate good used in exports (€)' pmex_lcp 'price of composite import good used in exports' pmex % EXTERNAL SECTOR: Exports, imports %Total imports 'imports' m 'import price' pm %%Importer price setting: investment good 'PCP price equation for imported intermediate input ($)' pmi_pcp 'LCP price equation for imported intermediate input (€)' pmi_lcp 'aggregate import price equation of investment good' pmi % Exports 'marginal cost of exports' mcex 'export market size' xd 'aggregate export price level' px 'LCP export price' px_lcp 'PCP export price' px_pcp 'aggregate exports' x 'LCP export volume' x_lcp 'PCP export volume' x_pcp 'Foreign price level ($) competing with finnish exporters' f_pex % one foreign price level, $ equal to f_pim % Some general variables 'exchange rate' e 'foreign price level ($) competing with finnish importers' f_pim % foreign price level 'Trade balance' tb; 'Foreign bond' BF; 'Foreign interest rate' istar % Shock processes to imports and exports 'Transitory price shock process to imported consumption goods' pmc_e 'Transitory price shock process to mc of exports' mcex_e 'Transitory price shock process to imported investment goods' pmi_e 'Transitory price shock process to imported goods used in exports' pmex_e 'Transitory shock process to imported consumption goods' mc_e 'Transitory shock process to imported investment goods' mi_e 'Transitory shock process to imported goods used in exports' mex_e % Public sector / General government 'General government bonds' BH 'Tax on dividents' tau_d 'Tax on investment/ investment tax credit' tau_ip 'Tax on capital' tau_k 'general government consumption (real)' cg 'transfers to households' ott % Some reporting variables 'General government income' GG_income 'General government income, VAT' GG_income_VAT 'General government income, tau_W+tau_SC' GG_income_W_SC 'General government income, tau_W' GG_income_W 'General government income, tau_SC' GG_income_SC 'General government income, tau_D' GG_income_D 'price of oil, $' poil 'export price aggegation' px_e 'general government investment (real)' ig !transition_shocks 'UIP shock (risk premium)' e_i_e 'Transitory shock to investments' e_ip 'Transitory shock to Tobin q' e_eps_q 'Transitory household consumption preference shock' e_cp_fl 'Transitory shock in productivity' e_yint_z 'Labour shock' e_n 'Shock to job destruction rate' e_rhohat 'Shock to vacancy costs' e_kappahat 'Shock to workers negotiation weight' e_etahat 'Shock to average wage process' e_w 'Shock to unemployment rate'e_u 'Price markup shock of intermediate firm' e_yint_phi 'exchange rate shock' e_e 'foreign price shock' e_f_pim 'export demand shock' e_xd 'Price shock to imported consumption goods' e_pmc 'Price shock to MC of exports' e_mcex 'Price shock to imported investment goods' e_pmi 'Price shock to imported goods used in exports' e_pmex 'Shock to aggregate imports' e_m_e 'Shock to imported consumption goods' e_mc_e 'Shock to imported investment goods' e_mi_e 'Shock to imported consumption goods used in exports' e_mex_e 'Shock to wage tax parameter' e_tau_w 'Shock to VAT tax parameter' e_tau_cp 'Shock to capital tax' e_tau_k 'Shock to employers social contributions' e_tau_sc 'Shock to dividend tax' e_tau_d 'Shock to investment tax or subsidy if minus sign' e_tau_ip 'Shock to government transfers' e_ott 'Shock to government consumption' e_cg 'Shock to government investment' e_ig 'Shock to oil price' e_poil 'shock to export price aggregation' e_px % !parameters omega_lc % share of liquidity constrained households, set =0 with matching istar_ss % SS foreign interest rate gamma_sastar % debt elastic interest rate penalty parame- ter rho_i_e % AR-coefficient of UIP shock process tau_cp_ss % SS VAT on consumption sigma_cp % household risk aversion varkappa % habit persistence rho_cp_fl_e % AR coefficient of consumption shock beta % discount factor cp_ss % SS consumption cp_lc_ss % SS consumption of liquidity constraint hou- seholds cp_fl_ss % SS consumption of forward-looking house- holds ott_ss % SS transfers to households % Investment and capital %----------------------- kappa_i % investment adjustment cost parameter rho_ip % AR coefficient of investment shock delta_k % depreciation of capital gamma_yint % share of capital in intermediate goods pro- duction eta_nu % capital utilization rate yint_roc_ss % SS return on capital rho_tobin_q % AR coefficient of equity premium shock rho_z % AR coefficient of transitory technology shock % Labour market matching and wage bargaining %------------------------------------------- sigma_M % elasticity of matches w.r.t. unemployment rho % SS job destruction rate match_ss % SS matches n_ss % SS employment u_ss % SS unemployment pyint_kl_ss % SS price of K-L good, = preal_kl_ss mpl_ss % SS marginal productivity of labour h_ss % SS hours worked per person J_ss % SS firm surplus w_ss % SS wage b % unemployment benefit tau_sc_ss % SS employer's social contribution k_ss % SS operative capital tau_w_ss % SS worker's tax on earned income H_ss % SS worker surplus mrs_ss % SS marginal rate of substitution sigma_n % Frish elasticity of labour qw_ss % SS job-finding probability eta % SS bargaining power omega_w % Weight of contract wage rho_n_e % AR of labour supply shock rho_rhohat % AR of job destruction shock rho_kappahat % AR of vacancy cost shock rho_etahat % AR of shock to workers' negotiation weight % Wholesale firm %--------------- rho_yint_phi % AR-coeff. of markup shock% pyint_ksi % probability of taking the price as given (calvo) pyint_ss % SS price of domestic intermediate input SAMULI yint_ss % SS production of intermediate firm %----------------------------------- f_pim_ss % foreign SS price level ($) for intermediate import input market. rhoe % ar coefficient in exchange rate shock rho_f_pim % ar coefficient in foreign price shock i_ss % SS nominal interest rate % importer price setting: investment good %---------------------------------------- omegai % share of LCP importing firms. (1-omegai) is the share of pcp firms gammai_lcp % calvo parameter, share of LCP import firms that are NOT allowed to change price at period t gammai_pcp % calvo parameter, share of PCP import firms that are NOT allowed to change price at period t % retailer of investment good thetaip % demand elasticity for domestic and foreign interme- diate investment good omegaip % share of domestic intermediate investment good in production of composite investment good % Importer price setting: consumption good %---------------------------------------- omegac % share of LCP importing firms. (1-omegac) is the share of pcp firms gammac_lcp % calvo parameter, share of LCP import firms that are NOT allowed to change price at period t gammac_pcp % calvo parameter, share of PCP import firms that are NOT allowed to change price at period t %Retailer of consumption good thetacp % demand elasticity for domestic and foreign interme- diate consumption good omegacp % share of domestic intermediate consumtion good in production of composite consumption good %Exporter %------------ gammax_pcp % calvo parameter, share of PCP firms that are NOT allowed to change price at period t, gammax_lcp % calvo parameter, share of LCP firms that are NOT allowed to change price at period t omegax % share of LCP firms in exports thetax % price elasticity of demand for the export product. Determined by rhox x_ss % SS of exports rhoxd % ar-parameter of foreign market shock rhostar thetaex deltaex mex_ss %Importer price setting: export good %----------------------------------- mcex_ss % SS marginal cost of exports pmex_ss % aggregate steady state import price level for goods used in export production(€) omegaex % share of LCP importing firms. (1-omegaex) is the share of pcp firms gammaex_lcp % calvo parameter, share of LCP import firms that are NOT allowed to change price at period t gammaex_pcp % calvo parameter, share of PCP import firms that are NOT allowed to change price at period t m_ss % SS imports mc_ss % SS imported C goods share of total imports mi_ss % SS imported I goods share of total imports rho_pmc_e % ar coefficient in imported consumption good price shock rho_mcex_e % ar coefficient in mc of exports shock rho_pmi_e % ar coefficient in imported investment good price shock rho_pmex_e % ar coefficient in imported goods used in exports price shock rho_mc_e % the following 3 are ar's of import volume shocks rho_mi_e rho_mex_e % Public sector %-------------- BH_ss % General government bonds in SS tau_d_ss % Tax on dividents in SS tau_k_ss % Tax on effective capital in SS tau_ip_ss % Tax on investments in SS rho_cg % AR of public spending shock rho_ig % AR of public investment shock rho_ott % AR-coeff of transfers to households (ott_e) shock rho_tau_w rho_tau_cp rho_tau_k rho_tau_sc rho_tau_d rho_tau_ip rho_poil % Closing the model %------------------ ip_ss % Investment in SS cg_ss % Government consumption ig_ss % Government investment v_ss % Vacancies in SS kappa % Vacancy posting cost in SS K_ss % Effective capital in SS rho_istar % AR coefficient of foreign interest D_ss % Dividends in SS total_h_ss % Total hours worked in SS % shock magnitude parameters std_e_rhohat % std error of job destruction shock std_e_kappahat % std error of vacancy cost shock std_e_etahat % std error of shock to negotiation weight std_e_pmc % st. error of the shock std_e_mcex % st. error of the shock std_e_pmi % st. error of the shock std_e_pmex % st. error of the shock std_e_m_e std_e_mc_e std_e_mi_e std_e_mex_e std_e_e % st. error of the shock std_e_f_pim % st. error of the shock std_e_i_e % st. error of the shock std_e_xd % st. error of the shock std_e_px std_e_n std_e_ott % St. error of transfers to households (ott_e) shock std_e_tau_w std_e_tau_k std_e_tau_cp std_e_tau_sc std_e_tau_d std_e_tau_ip std_e_cg !transition_equations %% Debt-elastic interest rate i=istar-gamma_sastar*(BF-yint-pyint)+i_e; i_e=rho_i_e*i_e{-1}+e_i_e; poil = rho_poil*poil{-1}+e_poil; %% Ricardian Households % Consumption iso_lambda = iso_lambda{+1}+i-(p{+1}-p); % Euler equation iso_lambda = muc-(tau_cp_ss)/(1+tau_cp_ss)*tau_cp; % Marginal uti- lity of wealth muc = -((sigma_cp)/(1-varkappa))*(cp_fl-varkappa*cp_fl{-1})+cp_fl_e; % where muc is marginal utility of consumption % Investment and capital accumulation nu = eta_nu*yint_roc; % Capital utili- zation rate ip = (1/(1+beta))*ip{- 1}+(beta/(1+beta))*ip{+1}+(1/(1+beta))*(1/kappa_i)*tobin_q- (1/(1+beta))*(beta*eps_ip{+1}-eps_ip); % Investment Kp = (1-delta_k)*Kp{-1}+delta_k*ip{-1}; % (physical) Capital accumulation equation K = nu+Kp{-1}; % Effective ca- pital tobin_q = -(i-(p{+1}-p))+((1-delta_k)/(1- delta_k+yint_roc_ss))*tobin_q{+1}+((yint_roc_ss)/(1- delta_k+yint_roc_ss))*yint_roc{+1}+eps_tobin_q; % Real value of capital, Tobin Q yint_roc = pyint_kl+mpk; % Rental rate for capital pyint_kl = pyint-p+preal_kl; mpk = (1-gamma_yint)*(h-k)+yint_z; k = K-n; % Capital-Labour ratio % shocks cp_fl_e=rho_cp_fl_e*cp_fl_e{-1}+e_cp_fl; % AR consumption shock process eps_ip=rho_ip*eps_ip{-1}+e_ip; % Investment AR1-Shock eps_tobin_q = rho_tobin_q*eps_tobin_q{-1}+e_eps_q; % yint_z=rho_z*yint_z{-1}+e_yint_z; % Technology shock %% Rule of thumb households %Liquidity constrained households consume all their income cp_lc = ((n_ss*w_ss*h_ss*(1- tau_w_ss))/((1+tau_cp_ss)*cp_lc_ss))*(w+h) + ((n_ss*(w_ss*h_ss*(1- tau_w_ss)-b))/((1+tau_cp_ss)*cp_lc_ss))*n + (ott_ss/((1+tau_cp_ss)*cp_lc_ss))*ott - (1-((b*(1-n_ss))/((1+tau_cp_ss)*cp_lc_ss)))*p - (tau_cp_ss/(1+tau_cp_ss))*tau_cp - ((n_ss*w_ss*h_ss*tau_w_ss)/((1+tau_cp_ss)*cp_lc_ss))*tau_w; % Aggregate consumption cp = ((omega_lc*cp_lc_ss)/cp_ss)*cp_lc + (((1- omega_lc)*cp_fl_ss)/cp_ss)*cp_fl; %% Labour Market matching % On intermediate firms: % Matching and employment dynamics match = sigma_M*u+(1-sigma_M)*v ; % Nr of new mat- ches in each period n = (1-rho)*n{-1}+(match_ss/n_ss)*match{-1}-rho*rhohat ; % Total nr of matches that enter each period = employment u = -((1-u_ss)/u_ss)*n + e_u ; % unem- ployment, e_u added to be able to exogenise in conditional forecast qf = match-v ; % vacancy- filling probability qw = match-u ; % job- finding probability theta = v-u ; % labour market tightness rhohat = rho_rhohat*rhohat{-1}+e_rhohat ; % Shock to job destruction rate %rhohat = -7.79*yint_z+e_rhohat ; %% Wage bargaining % % Firm surplus J = ((pyint_kl_ss*mpl_ss*h_ss)/((1- gamma_yint)*J_ss))*(pyint_kl+mpl+h)- ((w_ss*h_ss*(1+tau_sc_ss))/J_ss)*(w+h-p) -((w_ss*h_ss*tau_sc_ss)/J_ss)*tau_sc- (((yint_roc_ss)*k_ss)/J_ss)*(yint_roc+k)+(beta*(1- rho))*(J{+1}+iso_lambda{+1}-iso_lambda) -(beta*rho)*(rhohat{+1}); % where the marginal productivity of labour is % mpl = gamma_yint*(k-h)+yint_z mpl = gamma_yint*(k-h)+yint_z ; % Worker surplus H = ((w_ss*h_ss*(1-tau_w_ss))/H_ss)*(w+h-p)- ((w_ss*h_ss*tau_w_ss)/H_ss)*tau_w- ((mrs_ss*h_ss*(1+tau_cp_ss))/((1+sigma_n)*H_ss))*(mrs+h) -((mrs_ss*h_ss*tau_cp_ss)/((1+sigma_n)*H_ss))*tau_cp+(beta*(1-rho- qw_ss))*(H{+1}+iso_lambda{+1}-iso_lambda)-(beta*rho)*rhohat{+1}- (beta*qw_ss)*qw; % where the marginal rate of substitution is mrs = sigma_n*h+(1-sigma_n)*n_e-muc; % Negotiated wage w_contract = ((eta*pyint_kl_ss*mpl_ss)/((1+tau_sc_ss)*(1- gamma_yint)*w_ss))*(pyint_kl+mpl)- ((eta*yint_roc_ss*k_ss)/(w_ss*h_ss*(1+tau_sc_ss)))*(yint_roc+k) +(((1-eta)*H_ss*beta*qw_ss)/(w_ss*h_ss*(1- tau_w_ss)))*(H{+1}+iso_lambda{+1}-iso_lambda+qw)+(((1- eta)*mrs_ss*(1+tau_cp_ss))/((1-tau_w_ss)*(1+sigma_n)*w_ss))*mrs -(1-((eta*pyint_kl_ss*mpl_ss)/((1+tau_sc_ss)*(1-gamma_yint)*w_ss))-(((1- eta)*mrs_ss*(1+tau_cp_ss))/((1-tau_w_ss)*(1+sigma_n)*w_ss)))*h +((((1-eta)*tau_w_ss)/(1-tau_w_ss))*(1-(H_ss/(w_ss*h_ss*(1- tau_w_ss)))))*tau_w +((((1-eta)*tau_w_ss)/(1-tau_w_ss))*((H_ss*beta*(1-rho))/(w_ss*h_ss*(1- tau_w_ss))))*tau_w{+1} - (((eta*tau_sc_ss)/(1+tau_sc_ss))*(1+(J_ss/(w_ss*h_ss*(1+tau_sc_ss)))))*ta u_sc +(((eta*tau_sc_ss)/(1+tau_sc_ss))*((J_ss*beta*(1- rho))/(w_ss*h_ss*(1+tau_sc_ss))))*tau_sc{+1} +(((1-eta)*mrs_ss*tau_cp_ss)/((1-tau_w_ss)*(1+sigma_n)*w_ss))*tau_cp +(1/(1-eta))*etahat-((H_ss*beta*(1-rho))/(w_ss*h_ss*(1- tau_w_ss)))*etahat{+1}+p; % Average wage w = omega_w*w_contract + (1-omega_w)*w{-1} + e_w; % Shock to workers' negotiation weight etahat = rho_etahat*etahat{-1}+e_etahat; % Hours supply shock process n_e=rho_n_e*n_e{-1}+e_n; %% Job creation and determination of hours worked (per person) %-------------------------- % % Comments here % Vacancy posting / job creation condition (analogous to labour de- mand in conventional models kappahat-qf = J{+1}+iso_lambda{+1}-iso_lambda; % Hours worked xmpl(1-tau_w)=mrs(1+tau_sc)(1+tau_cp) pyint_kl+mpl = mrs+(tau_w_ss/(1- tau_w_ss))*tau_w+(tau_sc_ss/(1+tau_sc_ss))*tau_sc+(tau_cp_ss/(1+tau_cp_ss ))*tau_cp; % Shock to vacancy costs kappahat = rho_kappahat*kappahat{-1}+e_kappahat; % %% Wholesale firm, price setting %------------------------------- % New Keynesian Phillips curve pie_yint = (((1-pyint_ksi)*(1- (pyint_ksi*beta)))/pyint_ksi)*(preal_kl+yint_phi)+beta*pie_yint{1}; pie_yint = pyint-pyint{-1}; yint_phi = rho_yint_phi*yint_phi{-1}+e_yint_phi; %% External sector: Imports, Exports % % Comments here % % Aggregate imports m = (mex_ss/m_ss)*mex+(mc_ss/m_ss)*mc+(mi_ss/m_ss)*mi+e_m_e; pm = (mex_ss/m_ss)*pmex+(mc_ss/m_ss)*pmc+(mi_ss/m_ss)*pmi; % Importer price setting: INVESTMENT good pmi = omegai*pmi_lcp - omegai*e +(1-omegai)*pmi_pcp + pmi_e; % aggre- gate pmi_lcp - pmi_lcp{-1} = (1/(1+beta))*(pmi_lcp{-1} - pmi_lcp{-2}) + (((1-gammai_lcp)*(1-beta*gammai_lcp))/((1+beta)*gammai_lcp))*(f_pim-e- pmi_lcp)+(beta/(1+beta))*(pmi_lcp{+1}-pmi_lcp); %LCP pmi_pcp - pmi_pcp{-1} = (1/(1+beta))*(pmi_pcp{-1} - pmi_pcp{-2}) + (((1-gammai_pcp)*(1-beta*gammai_pcp))/((1+beta)*gammai_pcp))*(f_pim- pmi_pcp)+(beta/(1+beta))*(pmi_pcp{+1}-pmi_pcp); %PCP pmi_e = rho_pmi_e*pmi_e{-1} + e_pmi; % Importer price setting: CONSUMPTION good pmc = omegac*pmc_lcp - omegac*e +(1-omegac)*pmc_pcp +0.0463*poil + pmc_e; pmc_lcp - pmc_lcp{-1} = (1/(1+beta))*(pmc_lcp{-1} - pmc_lcp{- 2}) + (((1-gammac_lcp)*(1- beta*gammac_lcp))/((1+beta)*gammac_lcp))*(f_pim-e- pmc_lcp)+(beta/(1+beta))*(pmc_lcp{+1}-pmc_lcp); %LCP pmc_pcp - pmc_pcp{-1} = (1/(1+beta))*(pmc_pcp{-1} - pmc_pcp{- 2}) + (((1-gammac_pcp)*(1- beta*gammac_pcp))/((1+beta)*gammac_pcp))*(f_pim- pmc_pcp)+(beta/(1+beta))*(pmc_pcp{+1}-pmc_pcp); %PCP pmc_e = rho_pmc_e*pmc_e{-1} + e_pmc; % Importer price setting: EXPORT good pmex = omegaex*pmex_lcp - omegaex*e +(1-omegaex)*pmex_pcp +0.1043*poil + pmex_e; % aggregate import price equation that com- bines PCP and LCP price levels pmex_lcp - pmex_lcp{-1} = (1/(1+beta))*(pmex_lcp{-1} - pmex_lcp{-2}) + (((1-gammaex_lcp)*(1-beta*gammaex_lcp))/((1+beta)*gammaex_lcp))*(f_pim- e-pmex_lcp)+(beta/(1+beta))*(pmex_lcp{+1}-pmex_lcp); pmex_pcp - pmex_pcp{-1} = (1/(1+beta))*(pmex_pcp{-1} - pmex_pcp{-2}) + (((1-gammaex_pcp)*(1-beta*gammaex_pcp))/((1+beta)*gammaex_pcp))*(f_pim- pmex_pcp)+(beta/(1+beta))*(pmex_pcp{+1}-pmex_pcp); pmex_e = rho_pmex_e*pmex_e{-1} + e_pmex; % price shock AR to imported good used in exports % Export price setting px = omegax*px_lcp - omegax*e+(1-omegax)*px_pcp + px_e; px_lcp - px_lcp{-1} = (1/(1+beta))*(px_lcp{-1} - px_lcp{-2}) + (((1- gammax_lcp)*(1-beta*gammax_lcp))/((1+beta)*gammax_lcp))*(mcex -e - px_lcp)+(beta/(1+beta))*(px_lcp{+1}-px_lcp); px_pcp - px_pcp{-1} = (1/(1+beta))*(px_pcp{-1} - px_pcp{-2}) + (((1- gammax_pcp)*(1-beta*gammax_pcp))/((1+beta)*gammax_pcp))*(mcex- px_pcp)+(beta/(1+beta))*(px_pcp{+1}-px_pcp); %px = omegax*px_lcp +(1-omegax)*px_pcp; % aggregate export price equation that combines PCP and LCP price levels px_e = rho_pmex_e*px_e{-1} + e_px; % Exchange rate shock e = rhoe*e{-1}+e_e; f_pim = rho_f_pim*f_pim{-1}+e_f_pim; % foreign price shock f_pex = f_pim; % %% Final goods producers % % Comments here % The public consumption-good is in the section on the public sector % Investment good retailer iph = thetaip*(pip-pyint)+ip; % demand for domestic intermediate good in investment-good production mi = thetaip*(pip-pmi)+ip + mi_e; % demand for foreign intermediate good in investment-good production mi_e= rho_mi_e*mi_e{-1} + e_mi_e; % shock to the volume of imported investment good pip = omegaip*pyint+(1-omegaip)*pmi; % price of composite investment good % Consumption good retailer cph = thetacp*(pcp-pyint)+cp; % demand for domestic intermediate good mc = thetacp*(pcp-pmc)+cp+mc_e; % demand for foreign intermediate good mc_e= rho_mc_e*mc_e{-1} + e_mc_e; % shock to the volume of imported consumption good pcp = omegacp*pyint+(1-omegacp)*pmc; % price of composite consumption good = CPI % Export good retailer: volumes hex = thetaex*(mcex-pyint)+x; % demand for domes- tic intermediate good used in exports mex = thetaex*(mcex-pmex)+x+mex_e; % demand for impor- ted foreign goods used in export-good production mex_e= rho_mex_e*mex_e{-1} + e_mex_e; % shock to the volume of imported export good % Export good retailer: marginal costs mcex = ((delta- ex^thetaex)*(pyint_ss/mcex_ss)^(rhostar/(rhostar+1)))*pyint + (((1- deltaex)^thetaex)*(pmex_ss/mcex_ss)^(rhostar/(rhostar+1)))*pmex + mcex_e ;% mcex of exports mcex_e = rho_mcex_e*mcex_e{-1} + e_mcex; % Price shock to mar- ginal costs of exports % Export volumes x_lcp = thetax*(f_pex-px_lcp)+xd; % LCP export demand equation x_pcp = thetax*(f_pex-px_pcp-e)+xd; % PCP export demand equation % CHECK THESE % aggr. export demand = aggr. export supply, i.e. the aggregator! x = omegax*x_lcp+(1-omegax)*x_pcp; % aggregate export demand, assumes linear combination xd = rhoxd*xd{-1}+e_xd; % Export demand / foreign market AR %% Public sector % % General government % Government budget constraint / Evolution of gvmt REAL debt BH = i_ss*(BH{-1}+i-pie_p) + (cg_ss/BH_ss)*(pyint+cg) + ((b*u_ss*u)/BH_ss) + ((-cg_ss-ig_ss-ott_ss)/BH_ss)*p + (ig_ss/BH_ss)*(pyint+ig) + (ott_ss/BH_ss)*ott - (((n_ss*w_ss*h_ss)*(tau_w_ss+tau_sc_ss))/BH_ss)*(n+w+h) - ((n_ss*w_ss*h_ss*tau_w_ss)/BH_ss)*tau_w - ((n_ss*w_ss*h_ss*tau_sc_ss)/BH_ss)*tau_sc - ((tau_cp_ss*cp_ss)/BH_ss)*(tau_cp+cp) - ((tau_d_ss*D_ss)/BH_ss)*(tau_d+D) - ((yint_roc_ss*tau_k_ss*K_ss)/BH_ss)*(yint_roc+tau_k+K); % where dividends to domestic households (D_ss/yint_ss)*D = yint - (((1+tau_sc_ss)*w_ss*total_h_ss)/(yint_ss))*(w+total_h) - ((tau_sc_ss*w_ss*total_h_ss)/(yint_ss))*(tau_sc) -(yint_roc_ss*K_ss/yint_ss)*(yint_roc+K)+(1- (kappa*v_ss/yint_ss))*pyint_kl-(kappa*v_ss/yint_ss)*(kappahat+v) +(x_ss/yint_ss)*px-(mcex_ss*x_ss/yint_ss)*mcex+((1- mcex_ss)*x_ss/yint_ss)*x+(m_ss/yint_ss)*pm- (f_pim_ss*m_ss/yint_ss)*f_pim+(1-f_pim_ss/yint_ss)*m_ss*m; % For reporting purposes: General government income GG_income= (tau_cp_ss*cp_ss)*(tau_cp+p+cp) + (tau_ip_ss*ip_ss)*(tau_ip+pip+ip) + (n_ss*w_ss*h_ss*tau_sc_ss)*(tau_sc+n+w+h) + (n_ss*w_ss*h_ss*tau_w_ss)*(tau_w+n+w+h) + (yint_roc_ss*tau_k_ss*K_ss)*(yint_roc+tau_k+K) + (D_ss*tau_d_ss)*(tau_d+D); GG_income_VAT = (tau_cp_ss*cp_ss)*(tau_cp+p+cp); GG_income_W_SC = (n_ss*w_ss*h_ss*tau_sc_ss)*(tau_sc+n+w+h) + (n_ss*w_ss*h_ss*tau_w_ss)*(tau_w+n+w+h); GG_income_W = (n_ss*w_ss*h_ss*tau_w_ss)*(tau_w+n+w+h); GG_income_SC = (n_ss*w_ss*h_ss*tau_sc_ss)*(tau_sc+n+w+h); GG_income_D = (D_ss*tau_d_ss)*(tau_d+D); % Expenditure ott = rho_ott*ott{-1}+e_ott; cg = rho_cg*cg{-1}+e_cg; % Revenue ig = rho_ig*ig{-1}+e_ig; tau_w = rho_tau_w*tau_w{-1} + e_tau_w; tau_cp = rho_tau_cp*tau_cp{-1} + e_tau_cp; tau_k = rho_tau_k*tau_k{-1} + e_tau_k; tau_sc = rho_tau_sc*tau_sc{-1} + e_tau_sc; tau_d = rho_tau_d*tau_d{-1} + e_tau_d; tau_ip = rho_tau_ip*tau_ip{-1} + e_tau_ip; %% Closing the model % % Comments here % % Trade Balance tb = yint - cp_ss*cp - ip_ss*ip - cg_ss*cg + ((1-mcex_ss)*x_ss)*x + ((1-f_pim_ss)*m_ss)*m + x_ss*px - (mcex_ss*x_ss)*mcex + m_ss*pm - (f_pim_ss*m_ss)*f_pim - cp_ss*p - ip_ss*pip + (1-cg_ss- (kappa*v_ss))*pyint -(kappa*v_ss)*(kappahat+v) - (yint_roc_ss*K_ss)*nu; BF = tb + i_ss*istar{-1}+i_ss*(1-gamma_sastar)*BF{-1} + i_ss*gamma_sastar*f_pim{-1} + i_ss*gamma_sastar*yint{-1}; istar=rho_istar*istar{-1}+i_e; % Economy wide resource constraint yint = (omegacp*cp_ss)*cp + (omegacp*cp_ss*thetacp)*p + (ome- gaip*ip_ss)*ip + (omegaip*ip_ss*thetaip)*pip + (omegaex*x_ss)*x + (omega- ex*x_ss*thetaex)*px + cg_ss*cg - (ome- gacp*cp_ss*thetacp+omegaip*ip_ss*thetaip+omegaex*x_ss*thetaex)*pyint; %Production yint_kl = gamma_yint*k+(1-gamma_yint)*h+yint_z; yint = n+yint_kl; total_h=n + h; p = pcp; pie_p = p-p{-1}; %% Measurement / Data % % Comments here % !measurement_variables 'Consumption' cp_ 'Output' yint_ 'Imports' m_ 'Exports' x_ 'Private investment' ip_ 'Interest rate' i_ 'Nominal wage' w_ 'Exchange rate' e_ 'Consumption good price level' pcp_ 'Labour force, total hours' total_h_ 'Unemployment' u_ 'Operating surplus / Dividents (nominal)' D_ 'Import price level' pm_ %%%hankala 'Export price level' px_ %%%hankala 'price of composite investment good' pip_ 'Foreign price level ($) competing with finnish importers' f_pim_ %%%hankala 'Foreign price level ($) competing with finnish exporters' f_pex_ %% 'External demand' xd_ 'Price of imported consumption good' pmc_ 'Price of imported investment good' pmi_ 'Price of imported good used in exports' pmex_ 'General government consumption (real)' cg_ 'Price of oil' poil_ !measurement_shocks 'measurement error on foreign prices competing with importers' m_f_pim 'measurement error on foreign prices competing with exporter' m_f_pex 'measurement error on price of imported consumption good' m_pmc 'measurement error on price of imported investment good' m_pmi 'measurement error on price of imported good used in exports' m_pmex 'measurement error on external demand' m_xd 'measurement error on output' m_yint !measurement_equations cp_ = cp; yint_ = yint; m_ = m; x_ = x; ip_ = ip; e_ = e; i_ = i; w_ = w; pcp_ = pcp; total_h_ = total_h; u_ = u; D_ = D; %osv cg_ = cg; pm_ = pm; px_ = px; pip_ = pip; % f_pim_ = f_pim+m_f_pim; f_pex_ = f_pex +m_f_pex; % xd_ = xd+m_xd; % pmc_ = pmc + m_pmc; % pmi_ = pmi+ m_pmi; % pmex_ = pmex+ m_pmex ; % poil_ = poil; %% %% Set parameters omega_lc = 0.2 ; % share of liquidity constrained households i_ss=0.03/4 ; % SS nominal interest rate istar_ss = i_ss ; % SS foreign interest rate gamma_sastar = 0.01 ; % debt elastic interest rate penalty parameter rho_i_e = 0.8; % AR-coefficient of UIP shock process tau_cp_s = 0.11; % " SS VAT on consumption" sigma_cp = 1.6; % household risk aversion varkappa = 0.6; % habit persistence rho_cp_fl_e = 0.8; % AR coefficient of consumption shock beta = 0.99; % discount factor BH_ss = 0.6; % SS gvmt debt % Investment and capital % ----------------------- kappa_i = 6.617; % investment adjustment cost parameter rho_ip= 0.485; % AR coefficient of investment shock delta_k= 0.025; % depreciation of capital gamma_yint = 0.33; % share of capital in intermediate goods production eta_nu = 0.43; % capital utilization rate yint_roc_ss = i_ss+delta_k; % SS return on capital rho_tobin_q = 0.3; % AR coefficient of equity premium shock rho_z = 0.9 ; % AR coefficient of transitory techno- logy shock tau_ip_ss = 0.1; % check this value tau_k_ss = 0.1; % check this value tau_d_ss = 0.1; % check this value % Labour market matching and wage bargaining % ------------------------------------------- sigma_n = 10; % Frish elasticity of labour eta = 0.5; % SS bargaining power b = 0.3; % unemployment benefit tau_w_ss = 0.15; % SS worker's tax on earned income 0.30 tau_sc_ss = 0.12; % sotut/palkkasumma, keskiarvo v. 2010-2013. SS employer's social contribution 0.23 tau_cp_ss = 0.11; % SS Consumption tax omega_w = 0.3; %0.5 % Ad hoc wage rigidity parameter sigma_M = 0.6; % Elasticity of mat- ching w.r.t unemployment (exponent of Cobb-Douglas matching function rho = 0.06; % SS job destruction rate qf_ss = 0.7; % Steady state vacancy filling rate u_ss = 0.1; % Steady state unem- ployment, keskiarvo 1994-2010 = 10.2 n_ss = 1-u_ss; % Steady state emplo- yment rate match_ss = rho*n_ss; % Steady state matches are equal to ss separations v_ss = match_ss/qf_ss; % Steady state vacancies theta_ss = v_ss/u_ss; % Labour market tightness; vacancies per unemployed searching workers eff_match = match_ss/((u_ss^sigma_M)*(v_ss^(1-sigma_M))); % Efficiency of matching qw_ss = match_ss/u_ss; % Steady state job finding rate, 1994-2010 datan keskiarvo = 0.28 h_ss = 0.33; % SS hours worked per person preal_kl_ss = (5-1)/5; % =1/markup => implies a markup of 20 % pyint_kl_ss = P.preal_kl_ss; % SS price of K-L good, = preal_kl_ss. Equal to marginal cost of wholesale firm mpk_ss = yint_roc_ss/pyint_kl_ss; % SS marginal producti- vity of capital k_ss = gamma_yint*(1/(n_ss*mpk_ss)); % SS capital-labour ratio in the firm-level production function K_ss = k_ss*n_ss; % SS aggregate capital yint_z_ss = 1/((K_ss^(gamma_yint))*((n_ss*h_ss)^(1-gamma_yint))); % Technology yint_kl_ss=P.yint_z_ss*(k_ss)^(gamma_yint)*(h_ss)^(1-gamma_yint); % SS output of K-L good mpl_ss = yint_z_ss*(1-gamma_yint)*k_ss^(gamma_yint)*(h_ss)^(-gamma_yint); % SS marginal productivity of labour mrs_ss = ((1-tau_w_ss)/((1+tau_sc_ss)*(1+tau_cp_ss)))*preal_kl_ss*mpl_ss; % SS marginal rate of substitution w_ss = 1.5849; kappa = 0.0976; % The resulting Firm and Worker surpluses are H_ss = (1/1-beta*(1-rho-qw_ss))*(w_ss*h_ss*(1-tau_w_ss)- (mrs_ss*h_ss*(1+tau_cp_ss))/(1+sigma_n)-b); % SS worker surplus J_ss = (1/(1-beta*(1-rho)))*(pyint_kl_ss*yint_kl_ss - (1+tau_sc_ss)*w_ss*h_ss - yint_roc_ss*k_ss); % SS firm surplus R_rate = b/(w_ss*h_ss*(1-tau_w_ss)); % Fiscal policy rule parameters tau_share = 0.5; w_para = 1; %% Closing the model %------------------ ip_ss = 0.172; % Investment in SS cg_ss = 0.28; % Government consumption ig_ss = 0.04; % Government investment yint_ss = yint_kl_ss*n_ss; % Aggregate SS production of intermediate firm cp_ss = yint_ss-ip_ss-cg_ss-kappa*v_ss ; % SS consumption cp_lc_ss = 0.2*cp_ss; % SS consumption of liquidity constrained households cp_fl_ss = 0.8*cp_ss; % SS consumption of forward-looking hou- seholds D_ss = yint_kl_ss - ((1+tau_sc_ss)*n_ss*w_ss*h_ss) - (yint_roc_ss*K_ss) - (kappa*v_ss); ott_ss = (tau_cp_ss*cp_ss) + (tau_ip_ss*ip_ss) + ((tau_w_ss+tau_sc_ss)*n_ss*w_ss*h_ss) + (tau_k_ss*yint_roc_ss*K_ss) + (tau_d_ss*D_ss) - cg_ss - (1-n_ss)*b - (1-i_ss)*BH_ss; total_h_ss = n_ss*h_ss; % Total hours worked in SS %% % parameter values rho_istar=0.95; % AR coefficient of foreign interest rho_n_e=0.37; % AR of labour supply shock rho_rhohat=0.75; % AR of job destruction shock rho_kappahat=0.75; % AR of vacancy cost shock rho_etahat=0.75; % AR of shock to workers' negotiation weight % Wholesale firm %--------------- rho_yint_phi=0.80; % AR-coeff. of markup shock pyint_ksi= 0.75; % probability of taking the price as given (cal- vo) pyint_ss=5; % SS price of domestic intermediate input % These needed to calculate ss prices %----------------------------------- f_pim_ss= 1 ; % foreign SS price level ($) for intermediate import input market. rhoe= 0.4; % ar coefficient in exchange rate shock rho_f_pim=0.4 ; % ar coefficient in foreign price shock rho_f_pex=0.4 ; % ar coefficient in foreign price shock % importer price setting: investment good %---------------------------------------- omegai= 0.15; %0.8 ; % share of LCP importing firms. (1- omegai) is the share of pcp firms gammai_lcp= 0.4; %0.5 ; % calvo parameter, share of LCP import firms that are NOT allowed to change price at period t gammai_pcp=0.5 ; % calvo parameter, share of PCP import firms that are NOT allowed to change price at period t % % retailer of investment good thetaip=0.22; % demand elasticity for domestic and foreign intermediate investment good, previously 2.2 omegaip=0.67; % share of domestic intermediate investment good in production of composite investment good % Importer price setting: consumption good %---------------------------------------- omegac=0.15; %0.8; %" share of LCP importing firms. (1- omegac) is the share of pcp firms gammac_lcp=0.4; %0.5; %" calvo parameter, share of LCP import firms that are NOT allowed to change price at period t gammac_pcp=0.5; %" calvo parameter, share of PCP import firms that are NOT allowed to change price at period t %Retailer of consumption good thetacp=0.45; % demand elasticity for domestic and foreign intermediate consumption good, previously 4.5 omegacp=0.65; % share of domestic intermediate consumtion good in production of composite consumption good % Exporter %------------ gammax_pcp=0.65; %0.5; % calvo parameter, share of PCP firms that are NOT allowed to change price at period t, gammax_lcp=0.65; %0.5; % calvo parameter, share of LCP firms that are NOT allowed to change price at period t omegax=0.1; %0.5; % share of LCP firms in exports thetax=0.5882; % price elasticity of demand for the export product. Determined by rhox x_ss=0.39; % SS of exports rhoxd=0.7346; % ar-parameter of foreign market shock rhostar=1; thetaex=0.4545; % phi deltaex=0.8; % delta mex_ss=0.22; % SS imports used in export production % % Importer price setting: export good %----------------------------------- mcex_ss=1; % SS marginal cost of exports pmex_ss=1; % aggregate steady state import price level for goods used in export production(€) omegaex=0.15; % share of LCP importing firms. (1-omegaex) is the share of pcp firms gammaex_lcp=0.4; % calvo parameter, share of LCP import firms that are NOT allowed to change price at period t gammaex_pcp=0.5; % calvo parameter, share of PCP import firms that are NOT allowed to change price at period t % m_ss=0.39; % SS imports mc_ss=0.09; % SS imported C goods share of total imports mi_ss=0.08; % SS imported I goods share of total imports % rho_pmc_e=0.7; % ar coefficient in imported consumption good price shock rho_mcex_e=0.4; % ar coefficient in mc of exports shock rho_pmi_e=0.7; % ar coefficient in imported investment good price shock rho_pmex_e=0.7; % ar coefficient in imported goods used in ex- ports price shock rho_mc_e=0.7; % rho_mi_e=0.7; % rho_mex_e=0.7; % % % Public sector %-------------- rho_cg= 0.9; % AR of public spending shock rho_ig= 0.9; % AR of public investment shock rho_ott=0.9; % AR-coeff of transfers to households (ott_e) shock rho_tau_w=0.9; rho_tau_cp=0.9; rho_tau_k=0.9; rho_tau_sc=0.9; rho_tau_d=0.9; rho_tau_ip=0.9; rho_poil=0.6; std_e_tau_w= 0.01; std_e_tau_cp= 0.01; std_e_tau_k= 0.01; std_e_tau_sc= 0.01; std_e_tau_d= 0.01; std_e_tau_ip= 0.01; std_e_ott= 0.01; std_e_cg= 0.01;