%% Script to compute steady state of the model: function [ys,check] = oilpol_steadystate(ys,exo) % function [ys,check] = NK_baseline_steadystate(ys,exo) % computes the steady state for the NK_baseline.mod and uses a numerical % solver to do so % Inputs: % - ys [vector] vector of initial values for the steady state of % the endogenous variables % - exo [vector] vector of values for the exogenous variables % % Output: % - ys [vector] vector of steady state values fpr the the endogenous variables % - check [scalar] set to 0 if steady state computation worked and to % 1 of not (allows to impos restriction on parameters) global M_ % read out parameters to access them with their name NumberOfParameters = M_.param_nbr; for ii = 1:NumberOfParameters paramname = deblank(M_.param_names(ii,:)); eval([ paramname ' = M_.params(' int2str(ii) ');']); end % initialize indicator check = 0; %% Enter model equations here %tic % CALIBRATION: Numsec = 2; % # of industries betta = 0.99; % Time discount factor sigma = 1; % Inverse of IES varphi = 2; % Inverse of Frisch phi = [0.60,0.40]; % CD-production materials Home phiF = [0.60,0.40]; % CD-production materials Foreign psi = 1 - phi; % CD-production labor Home psiF = 1 - phiF; % CD-production labor Foreign xi = [0.35,0.65]; % SS Consumption share (of total consumption) Home xiF = [0.35,0.65]; % SS Consumption share (of total consumption) Foreign zeta = [0.70, 0.30; % SS Material share (of total material) Home (Note: each column sums to one) 0.30, 0.70]; zetaF = [0.70, 0.30; % SS Material share (of total material) Foreign (Note: each column sums to one) 0.30, 0.70]; gammaex = [0.60, 0.15]; % SS export-GDP ratio gammaim = [0.60, 0.15]; % SS import-GDP ratio L = 1/3; % Normalization of hours Home eps_p = 0.2; % Markup goods markets eps_w = 0.2; % Markup labor markets theta_pj = [0.25, 0.75]; % Oil sector: gammao = 0.2; % Oil share of total GDP alphao = 0.2; % Non-land share of oil output phio = 0.7;%.16; % Use of mainland intermediates psio = 1 - phio; % Use of mainland labor Oilshare_ss = gammao/(1 - gammao); % Oil share of mainland GDP. zetao = [0.4, 0.6]; % Oil input shares from goods and services. if length(zeta) ~= Numsec error('Error: Input-output matrix must be square and of size equal to # sectors!'); end SS_INF = 1.000; %% Recursive steady state solution: % REST OF THE WORLD: RF = SS_INF/betta; BarPrjF = ((1 - theta_pj)./(1 - theta_pj*SS_INF^(1/eps_p))).^eps_p; VjF = (1 - theta_pj).*BarPrjF.^(-(1 + eps_p)/eps_p)./(1 - theta_pj*SS_INF^((1 + eps_p)/eps_p)); RMCjF = (BarPrjF/(1 + eps_p)) .* (1 - betta*theta_pj*SS_INF^((1 + eps_p)/eps_p)) ./ (1 - betta*theta_pj*SS_INF^(1/eps_p)); % Normalization CF = 1; % C_j = xi_j*C CjF = xiF*CF; % Y_j = C_j + M_{j1} + ... + M_{jJ} iomatrixF = [zetaF(1,1)*phiF(1), zetaF(1,2)*phiF(2); zetaF(2,1)*phiF(1), zetaF(2,2)*phiF(2)]; XjF = ((eye(Numsec) - iomatrixF)\CjF')'; YjF = XjF.*VjF; % 1 + eps_p = 1 + Phi_j/Y_j PhijF = (1./RMCjF - VjF).*XjF;%eps_p*YjF; % M_j/Y_j = phi_j MjF = phiF.*XjF;%phiF.*YjF; MjjF = bsxfun(@times, zetaF, MjF); % GDP = Omega*L OmegaF = CF/L; % Omega = (1 + eps_w)*MRS chi_NF = OmegaF/((L^varphi)*(CF^sigma)*(1 + eps_w)); % RMC_j = Z_j^(-1) * (1/phi_j)^(phi_j) * (Omega/psi_j)^(psi_j) ZjF = (1./RMCjF) .* (1./phiF).^(phiF) .* (OmegaF./psiF).^(psiF); % Omega*N_j/Y_j = psi_j NjF = psiF.*XjF/OmegaF;%psiF.*YjF/OmegaF; % L = N_j/mu_j mujF = NjF/L; % Value added GDPjF = (1 - phiF).*XjF;%YjF - MjF; GDPF = sum(GDPjF); LambdaF = CF^(-sigma); G1F = LambdaF*XjF.*RMCjF./(1 - betta*theta_pj*SS_INF^((1 + eps_p)/eps_p)); G2F = LambdaF*XjF.*BarPrjF./(1 - betta*theta_pj*SS_INF^(1/eps_p)); TildeG1F = SS_INF^((1 + eps_p)/eps_p)*G1F; TildeG2F = SS_INF^(1/eps_p)*G2F; gdpF = log(GDPF); vaF = log(CF); cF = log(CF); lambdaF = log(LambdaF); lambdaauxF = log(LambdaF/betta); picF = log(SS_INF); rrF = log(1/betta); rF = log(RF); nF = log(L); rwF = log(OmegaF); Consumption = CF; Hours = L; UtilityF = log(CF) - chi_NF*(L)^(1 + varphi)/(1 + varphi); WelfareF = UtilityF/(1 - betta); for i=1:Numsec % Variables evalc(sprintf('c%dF = log(CjF(i))', i)); evalc(sprintf('gdp%dF = log(GDPjF(i))', i)); evalc(sprintf('y%dF = log(YjF(i))', i)); evalc(sprintf('x%dF = log(XjF(i))', i)); evalc(sprintf('m1%dF = log(MjjF(1,i))', i)); evalc(sprintf('m2%dF = log(MjjF(2,i))', i)); evalc(sprintf('m%dF = log(MjF(i))', i)); evalc(sprintf('n%dF = log(mujF(i)*L)', i)); evalc(sprintf('l%dF = log(L)', i)); evalc(sprintf('mrs%dF = log(OmegaF/(1 + eps_w))', i)); evalc(sprintf('piw%dF = log(SS_INF)', i)); evalc(sprintf('rw%dF = log(OmegaF)', i)); evalc(sprintf('pip%dF = log(SS_INF)', i)); evalc(sprintf('pr%dF = log(1)', i)); evalc(sprintf('barpr%dF = log(BarPrjF(i))', i)); evalc(sprintf('g1%dF = log(G1F(i))', i)); evalc(sprintf('tildeg1%dF = log(TildeG1F(i))', i)); evalc(sprintf('g2%dF = log(G2F(i))', i)); evalc(sprintf('tildeg2%dF = log(TildeG2F(i))', i)); evalc(sprintf('v%dF = log(VjF(i))', i)); evalc(sprintf('prm%dF = log(1)', i)); evalc(sprintf('rmc%dF = log(RMCjF(i))', i)); evalc(sprintf('z%dF = log(ZjF(i))', i)); % Parameters evalc(sprintf('theta_p%d = theta_pj(i)', i)); evalc(sprintf('Phi%dF = PhijF(i)', i)); evalc(sprintf('phi%dF = phiF(i)', i)); evalc(sprintf('psi%dF = 1 - phiF(i)', i)); evalc(sprintf('xi%dF = xiF(i)', i)); evalc(sprintf('mu%dF = mujF(i)', i)); evalc(sprintf('zeta1%dF = zetaF(1,i)', i)); evalc(sprintf('zeta2%dF = zetaF(2,i)', i)); end % CHECK SOLUTION: if abs(sum(mujF) - 1) >= 1e-10 warning('Warning: Employment shares in labor markets do not add up to total labor force'); end if any(sum(zetaF,1)) ~= 1 warning('Warning: Material shares do not sum to 1'); end %% end own model equations for iter = 1:length(M_.params) %update parameters set in the file eval([ 'M_.params(' num2str(iter) ') = ' M_.param_names(iter,:) ';' ]) end NumberOfEndogenousVariables = M_.orig_endo_nbr; %auxiliary variables are set automatically for ii = 1:NumberOfEndogenousVariables varname = deblank(M_.endo_names(ii,:)); eval(['ys(' int2str(ii) ') = ' varname ';']); end