% ----------------------------------- % A Financial accelerator model % % with ZLB? % ------ Non Linear Version ----- % ----------------------------------- var lambda, c, R, pip, rreal, lh, w, piw, y, l, k, s, we, z, Q1, Q2, Pstar, il, Q1w, Q2w, Wstar, lomegatilde, clag, Fome, Fnome, omegatilde, SIG, muG, ffome, deltau, deltauu, adji, adjii, nw, i, ktilde, b, xx, q, rk, rr, LAM, v, ce, SIGp, muGp, gammat, pref, em, techno, chil, g, sigome, a; varexo eps_gamma ; //varexo_det eps_em; 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; load_params_and_steady_state(ParamMatrix); model; // ---- Household's Preferences lambda = pref*(c-bc*c(-1))^(-1/sigmac) - betaa*bc*pref(1)*(c(1)-bc*c)^(-1/sigmac); (1/R) = betaa*(lambda(1)/lambda)*(1/(pip(1))); rreal = R/pip(1); clag = c(-1); // ---- Wage Setting //chil*lh^(sigmal) = lambda*w; piw = (w*pip)/w(-1); Q1w = chilbar*lh^(sigmal) + alphaw*betaa*Q1w(1); Q2w = (1+eps_taxw)*lambda + alphaw*betaa*Q2w(1); Wstar = muww*(Q1w/Q2w); //Q1w = 0; //Q2w = 0; //Wstar = 0; 1 = (1-alphaw)*(Wstar/w)^(1-tetaw) + alphaw*(pip(-1)^(gammaw*(1-tetaw)))*(piw^(tetaw-1)); // ---- Production Sector y = techno*((l)^(1-alpha))*(k^(alpha)); l = lh^(Omega); w = s*Omega*(1-alpha)*(y/lh); we = s*(1-Omega)*(1-alpha)*y; z = s*alpha*(y/k); // ---- Price Setting Q1 = y*s + alphap*betaa*Q1(1); Q2 = (1+eps_tax)*y + alphap*betaa*Q2(1); Pstar = mup*Q1/Q2; 1 = (1-alphap)*Pstar^(1-tetap) + alphap*(pip(-1)^(gammap*(1-tetap)))*(pip^(tetap-1)); // ---- Financial Accelerator: Definitions lomegatilde = log(omegatilde); Fome = normcdf(lomegatilde,muW,sigmaWbar); ffome = exp(-0.5 * ((log(omegatilde) - muW)/sigmaWbar)^2) / (omegatilde * sqrt(2*3.14) * sigmaWbar); Fnome = 1 - exp(muW+sigome*sigome/2)*normcdf(((muW - lomegatilde)/sigome)+sigome,0,1); SIG = omegatilde*(1-Fome) + Fnome; muG = mu*Fnome; SIGp = 1 - Fome; muGp = mu*omegatilde*ffome; il = i(-1); deltau = delta; deltauu = 0; adji = (kapai/2)*(i/i(-1) - 1)^2; adjii = (kapai)*(i/i(-1))*(i/i(-1) - 1); b = q(-1)*ktilde(-1) - nw(-1); xx = q(-1)*ktilde(-1)/nw(-1); rr = rk(1)/rreal; // ---- Financial Accelerator Contract LAM(1) = (rk(1)/rreal)*(1 - SIG(1) + LAM(1)*(SIG(1) - muG(1))); SIGp = LAM*(SIGp - muGp); a*(xx - 1) = (rk/rreal(-1))*xx*(SIG - muG); // ---- Financial Intermediate Sector rk = (z + (1-deltau)*q)/q(-1); nw = gammat*v + we; v = rk*q(-1)*ktilde(-1) - rreal(-1)*q(-1)*ktilde(-1) + rreal(-1)*nw(-1) - muG*rk*q(-1)*ktilde(-1); ce = (1-gammat)*varrho*v; // ---- Capital Producer Sector ktilde = (1-deltau)*ktilde(-1) + (1-adji)*i; 1/q = 1 - adji - adjii + betaa*(q(1)/q)*(lambda(1)/lambda)*pip(1)*adjii(1)*(i(1)/i); k = ktilde(-1); // ---- Resource Constraint & Monetary Policy y = c + i + g + ce + muG*rk*q(-1)*ktilde(-1); //(R)/(R) = ((((R(-1))/(Rbar))^(rhoi))*((pip/pipbar)^((1-rhoi)*ap))*((y/ybar)^((1-rhoi)*ay)))+ (1-eps_em)*1; //(R)/(R) = ((((R(-1))/(Rbar))^(rhoi))*((pip/pipbar)^((1-rhoi)*ap))*((y/ybar)^((1-rhoi)*ay))) ; // ---- Shocks (gammat/gammabar) - ((gammat(-1)/gammabar)^rhoGamma)*exp((sigmaGamma)*eps_gamma); pref = prefbar; techno = technobar; chil = chilbar; g = gbar; sigome = sigmaWbar; a = abar; em = embar; end; initval; lambda = lambdabar; c = cbar; clag = cbar; R = Rbar; pip = pipbar; rreal = rrealbar; lh = lhbar; w = wbar; piw = piwbar; y = ybar; l = lbar; k = kbar; s = sbar; we = webar; z = zbar; Q1 = Q1bar; Q2 = Q2bar; Pstar = Pstarbar; Q1w = Q1wbar; Q2w = Q2wbar; Wstar = Wstarbar; Fome = Fomebar; Fnome = Fnomebar; omegatilde = omebar; lomegatilde = lomebar; SIG = SIGbar; SIGp = SIGpbar; muG = muGbar; muGp = muGpbar; ffome = ffomebar; deltau = deltaubar; deltauu = deltauubar; adji = adjibar; adjii = adjiibar; nw = nwbar; i = ibar; il = ibar; ktilde = ktildebar; b = bbar; xx = xxbar; q = qbar; rk = rkbar; rr = rrbar; LAM = LAMbar; v = vbar; ce = cebar; gammat = gammabar; pref = prefbar; em = embar; techno = technobar; chil = chilbar; g = gbar; sigome = sigmaWbar; a = abar; //eps_em = 1; end; shocks; var eps_gamma=1; //stderr 0.01; //var eps_em; //periods 0:10 11:21; //values 1 0; //var eps_pref = 0; //var eps_em = 1; //var eps_techno = 0; //var eps_chil = 0; //var eps_gv = 0; //var eps_SIG = 0; //var eps_av = 0; end; //resid(1); //steady(solve_algo=2); //resid(1); //check; //planner_objective((sigmac/(sigmac-1))*(c-bc*clag)^((sigmac-1)/sigmac) - (1/(1+sigmal))*lh^(1+sigmal)); planner_objective(ln(c-bc*clag) - (1/(1+sigmal))*lh^(1+sigmal)); ramsey_policy(planner_discount=1,order=1,irf=30) y R c pip; //options_.pruning = 1; //stoch_simul(order=1,irf=30) y R c pip; //stoch_simul(dr_algo=0,ar=0,nocorr, order=1, irf=0, drop=0); //forecast(periods=310) R pip; //conditional_forecast_paths; //var y; //periods 1; //values 1; //end; //conditional_forecast(parameter_set = ParamMatrix, controlled_varexo=(eps_gamma), replic=3000);