% -------------------------------------- % Parameters' Declaration % -------------------------------------- parameters bc sigmac betaa alpha Omega alphap tetap mup gammap muW mu varrho rhoi ap ay eps_tax delta d kapai sigmal sigmaWbar eps_taxw muww alphaw tetaw gammaw Q1wbar Q2wbar Wstarbar lomebar muGpbar pi SEome lambdabar cbar Rbar pipbar rrealbar lhbar wbar piwbar ybar lbar kbar sbar webar zbar Q1bar Q2bar Pstarbar Fomebar abar rhoA sigmaA Fnomebar omebar SIGbar muGbar SIGpbar ffomebar deltaubar deltauubar adjibar adjiibar nwbar ibar ubar gbar chilbar rhoChil rhoG ktildebar bbar xxbar qbar rkbar rrbar LAMbar vbar cebar gammabar deltatild rhoGamma rhoPref rhoEm rhoTechno prefbar embar technobar sigmaGamma sigmaPref sigmaTechno sigmaEm sigmaChil sigmaG sigmaSIG rhoSIG; % ---- Preference and production parameters betaa = 0.99; % discount factor bc = 0; % habits sigmac = 1; % Intert. elasticity of substitution sigmal = 1; % alpha = 0.35; % capital share Omega = 0.9846; % Proportion of Houshold labor on aggregate labor composite, Omega = 1 - .01/(1-alpha), where .01 is entrepreneurs' labor income share delta = 0.025; tau = 0; % tax (does not appear in .mod) kapai = 5.86; % investment adjustment cost alphap = 0.67; % calvo price gammap = 0.75; % indexation price tetap = 11; % elasticity of subst. demand mup = tetap/(tetap-1); % mark up SNbar = 1/mup; alphaw = 0.75; gammaw = 0.75; tetaw = 11; muww = tetaw/(tetaw-1); kappap = (1-alphap)*(1-alphap*betaa)/(alphap); kappaw = ((1-alphaw)*(1-betaa*alphaw)/(alphaw*(1+sigmal*tetaw))); xbar = 2; % = ktildebar/nbar rrbar = 1.02^(1/4); % = rkbar/rbar Rbar = 1/betaa; % risk free interest rate rkbar = rrbar*Rbar; % return of capital gammabar = 0.9728; % entrepr default proba -- BGG varrho = 0.01; % (1-varrho) = tranfers from entrepreneur to HH Eome = 1; % mean of omegabar -- BGG omebar0 = 1; % Initial value of omegabar SEome0 = 0.28; % s.e of omegabar -- BGG gamma0 = 0.9; mu0 = 0.1; paramm0 = [omebar0 SEome0 gamma0 mu0]; paramc = [tau betaa delta alpha Omega tetap xbar rrbar Eome]; options = optimset('Display','iter'); [x,Fval,exitflag] = fsolve('funx2',paramm0,options,paramc); % what value of omebar such that: logncdf(omebar,muW,sigmaW) = PHI; omebar = x(1); SEome = x(2); gammabar = x(3); mu = x(4); % ---------- Compute SIGMA(omebar) and G(omebar) % ---------------------------------------------- sigmaWbar = sqrt(log(1 + (SEome^2)/(Eome^2))); muW = log(Eome) - 0.5*sigmaWbar^2; tbar = (muW - log(omebar))/sigmaWbar; lomebar = log(omebar); Fomebar = normcdf(lomebar,muW,sigmaWbar); % F(omebar) aa = exp(-0.5 * ((log(omebar) - muW)/sigmaWbar)^2) / (omebar * sqrt(2*3.14) * sigmaWbar); ffomebar = aa; //Fomebar = logncdf(omebar,muW,sigmaWbar); % F(omebar) //ffomebar = lognpdf(omebar,muW,sigmaWbar); % f(omebar) ffomep = -(ffomebar/omebar)*(1 - (muW-log(omebar))/(sigmaWbar*sigmaWbar)); Fnomebar = Eome - exp(muW+sigmaWbar*sigmaWbar/2)*normcdf(tbar+sigmaWbar,0,1); SIGbar = omebar*(1-Fomebar) + Fnomebar; % SIGMA(omebar) SIGpbar = 1 - Fomebar; % SIGMA'(omebar) muGbar = mu*Fnomebar; % mu*G(omebar) muGpbar = mu*omebar*ffomebar; % mu*G'(omebar) SIGppbar = - ffomebar; % SIGMA''(omebar) muGbar = mu*Fnomebar; % mu*G(omebar) muGpbar = mu*omebar*ffomebar; % mu*G'(omebar) muGppbar = mu*(ffomebar + omebar*ffomep); % mu*G''(omebar) % --------------------------------------------------------- % ---------- Numerical computations of sigome derivatices % --------------------------------------------------------- vareps = 1e-15; SEome1 = SEome + vareps; % ---------- Compute derivative of SIGMA(omebar) and G(omebar) sigmaW1 = sqrt(log(1 + (SEome1^2)/(Eome^2))); muW1 = log(Eome) - 0.5*sigmaWbar^2; sigmaW = sigmaW1; muW = muW1; tbar1 = (muW1 - log(omebar))/sigmaW1; //Fome1 = normcdf(lomebar,muW1,sigmaW1); % F(omebar) //fome1 = normcdf(lomebar,muW1,sigmaW1); % f(omebar) //fomep1 = -(fome1/omebar)*(1 - (muW1-log(omebar))/(sigmaW1*sigmaW1)); % f'(omebar) Fome1 = logncdf(omebar,muW1,sigmaW1); % F(omebar) fome1 = lognpdf(omebar,muW1,sigmaW1); % f(omebar) fomep1 = -(fome1/omebar)*(1 - (muW1-log(omebar))/(sigmaW1*sigmaW1)); % f'(omebar) Fnome1 = Eome - exp(muW1+sigmaW1*sigmaW1/2)*normcdf(tbar1+sigmaW1,0,1); % Fnormal(omebar) % Gamma SIG1 = omebar*(1-Fome1) + Fnome1; % SIGMA(omebar) SIGp1 = 1 - Fome1; % SIGMA'(omebar) SIGpp1 = - fome1; % SIGMA''(omebar) muG1 = mu*Fnome1; % mu*G(omebar) muGp1 = mu*omebar*fome1; % mu*G'(omebar) muGpp1 = mu*(fome1 + omebar*fomep1); % mu*G''(omebar) % ---------------------------------------------------------- SIGsbar = (SIG1-SIGbar)/vareps; SIGpsbar = (SIGp1-SIGpbar)/vareps; muGsbar = (muG1-muGbar)/vareps; muGpsbar = (muGp1-muGpbar)/vareps; % ---------------------------------------------------------- % ---------- Steady State variables %------------------------------------ % ------- Ratios GbarY = 0.19; eps_tax = 1/(tetap-1); eps_taxw = 1/(tetaw-1); Pstarbar = ((1-alphap)/(1-alphap))^(1/(1-tetap)); sbar = (1+eps_tax)*Pstarbar/mup; % rmc zbar = (rkbar - (1-delta)); % rental price of capital YbarK = zbar/(sbar*alpha); IbarY = delta*(1/YbarK); CebarK = varrho*(1-gammabar)*(rkbar - Rbar*(1-1/xbar) - muGbar*rkbar); CebarY = CebarK/YbarK; CbarY = 1 - IbarY - CebarY - GbarY - muGbar*rkbar*(1/YbarK) ; WebarK = sbar*(1-Omega)*(1-alpha)*YbarK; VbarN = rkbar*xbar - Rbar*(xbar - 1) - muGbar*rkbar*xbar; CebarN = (1-gammabar)*varrho*VbarN; LbarK = (YbarK)^(1/(1-alpha)); % ------- Variables ybar = 1; piwbar = 1; pipbar = 1; rrealbar = Rbar; ubar = 0; qbar = 1; kbar = 1/(YbarK*(1/ybar)); ktildebar = kbar; ibar = IbarY*ybar; cebar = CebarY*ybar; cbar = CbarY*ybar; gbar = GbarY*ybar; nwbar = kbar/xbar; vbar = VbarN*nwbar; lambdabar = (1-betaa*bc)*(cbar*(1-bc))^(-1/sigmac); lbar = LbarK*kbar; lhbar = lbar^(1/Omega); webar = WebarK*kbar; wbar = sbar*Omega*(1-alpha)*ybar/lhbar; Wstarbar = wbar; % chilbar = wbar*lambdabar*lhbar^(-sigmal) chilbar = (1+eps_taxw)*Wstarbar*lambdabar*lhbar^(-sigmal)/muww; bbar = ktildebar - nwbar; xxbar = ktildebar/nwbar; LAMbar = SIGpbar/(SIGpbar - muGpbar); abar = ((rkbar/rrealbar)*xxbar*(SIGbar - muGbar))/(xxbar - 1); deltatild = zbar; d = deltatild/delta; Q1bar = (ybar*sbar)/(1-alphap*betaa); Q2bar = (1+eps_tax)*ybar/(1-alphap*betaa); Q1wbar = (chilbar*lhbar^(sigmal))/(1-alphaw*betaa); Q2wbar = ((1+eps_taxw)*lambdabar)/(1-alphaw*betaa); deltaubar = delta; deltauubar = 0;%deltatild; adjibar = 0; adjiibar = 0; prefbar = 1; embar = 1; technobar = 1; % ----- Monetary policy rule and shocks % -------------------------------------- rhoi = 0.878; % Monetary policy rule ap = 1.852; % CMR(2009) - US ay = 0.313/4; % CMR(2009) - US aq = 0; rhoGamma = 0.561; %% CMR(2009) - US rhoPref = 0.903; rhoTechno = 0.945; rhoEm = 0; rhoChil = 0.2; rhoG = 0.6; rhoSIG = 0.98; rhoA = 0.5; sigmaGamma = 0.01^2; sigmaPref = 0.01^2; sigmaTechno = 0.01^2; sigmaEm = 0.01^2; sigmaChil = 0.01^2; sigmaG = 0.01^2; sigmaSIG = 0.01^2; sigmaA = 0.01^2; save_params_and_steady_state(ParamMatrix);