// Model: CA_LS07 // Further references: // Lubik, T.A. and Schorfheide, F. (2007): "Do central banks respond to exchange rate movements? // A structural investigation", Journal of Monetary Economics 54. 1069-1087. // small open economy model; a simplified version of the Gali and Monacelli (2005) model // Last edited: 22/08/11 by M.Jancokova var y R pi z deltaq deltay_star y_bar y_star deltae pi_star tau g b ;//ajout de tau g b varexo epsR epsq epspi_star epsz epsy_star epsg epstau;// ajout de epsg epstau //declaration of the deep parameters parameters omega alfa rhoz beta kappa rhoR rpi ry psi3 rhoq rhoy_star rhopi_star rss rhog rhotau tauy taub cbar bbar sigmaR sigmaq sigmaz sigmay_star sigmapi_star sigmag sigmatau gy gb;// ajout de rhog rhotau tauy taub cbar bbar sigmaR sigmaq sigmaz sigmay_star sigmapi_star sigmag sigmatau gy gb omega =0.31; //intertemporal substition elasticity alfa=0.11; //import share gy= 0; // ajouté gb= -0.05; //ajouté rss=2.52; //steady state real interest rate beta=0.9937 ; //discount factor beta=exp(-rss/400); kappa=0.32; //slope coef. of the Phillips curve; function of underlying structural parameters rpi=1.3; //policy coefficient w.r.t. inflation ry=0.23; //policy coefficient w.r.t. output psi3=0.14; //policy coefficient w.r.t. nom. exch.rate diff. rhoR=0.69; //persistence in nom.int.rate; smoothing termu rhoz= 0.42; //persistence in the technology growth rate rhoq=0.31; //persistence in TOT growth rate rhoy_star=0.97; //persistence in exogenous world output rhopi_star=0.46; //persistence in world inflation shock rhog= 0.45; // ajouté rhotau=0.47; //ajouté cbar = 0.7; // ajouté bbar =0.37; // ajouté tauy=0.18; //ajouté taub=0.02; // ajouté sigmaR = 0.36; // ajouté sigmaq = 1.25;// ajouté sigmaz = 0.84;// ajouté sigmay_star = 1.29;// ajouté sigmapi_star = 2;// ajouté sigmag = 2;// ajouté sigmatau = 1;// ajouté model(linear); //1.open economy IS curve y=y(+1)-(omega+alfa*(2-alfa)*(1-omega))*(R-pi(+1))-rhoz*z-alfa*(omega+alfa*(2-alfa)*(1-omega))*deltaq(+1)+alfa*(2-alfa)*((1-omega)/omega)*deltay_star(+1); deltay_star=y_star-y_star(-1); //3.open economy Phillips curve (ne pas changer) pi=beta*pi(+1)+alfa*beta*deltaq(+1)-alfa*deltaq+kappa/(omega+alfa*(2-alfa)*(1-omega))*(y-y_bar); //4.potential output in absence of nominal rigidities y_bar=-alfa*(2-alfa)*(1-omega)/omega*y_star; //5.CPI pi=deltae+(1-alfa)*deltaq+pi_star; //6.MP rule (psi 1 et 2 changéen rpi et ry )et ajout de (y-ybar) et de sigmaR R=rhoR*R(-1)+(1-rhoR)*(rpi*pi+ry*y+psi3*deltae)+ sigmaR * epsR; // 7.8 et 9 Fiscal policy (ajouté) g=rhog*g(-1)+(1-rhog)*(gy*(y(-1)-y_bar(-1))+gb*b)+ epsg; //fiscal rule for government spending tau=rhotau*tau(-1)+(1-rhotau)*(tauy*(y(-1)-y_bar(-1))+taub*b)+ epstau;//fiscal rule for tax b=R+(1/beta)*(b-pi+(1-beta)*(R-y)+(cbar/bbar)*(g-tau));//The government solvency constraint (b au lieu de b(+1) //10.law of motion for the TOT growth rate(ajut de sigmaq) deltaq= rhoq*deltaq(-1)+ sigmaq*epsq; // 11.AR(1) process of the growth rate of an underlying technology process (ajout de sigmaz) z=rhoz*z(-1)+sigmaz*epsz; //12.AR(1) processes for y_star ; introducing TOT shocks (ajout de sigmay_star) y_star=rhoy_star*y_star(-1)+sigmay_star*epsy_star; //13.AR(1) processes for pi_star (ajout de sigmapi_star) pi_star =rhopi_star*pi_star(-1)+sigmapi_star*epspi_star; end; initval;//ajouté deltae = 0; pi = 0; pi_star = 0; deltaq = 0; R = 0; y = 0; y_bar = 0; y_star = 0; z = 0; end; shocks; //shocks IN TERMS OF VARIANCE var epsR = 0.36^2; var epsq=1.25^2; var epsz=0.84^2; var epsy_star=1.29^2; var epspi_star=2.00^2; var epsg =0.4^2;//ajouté var epstau=0.5^2;//ajouté end; steady(solve_algo=3, maxit=100); resid(1); check(qz_zero_threshold=1e-7); stoch_simul (irf = 200,order=1,ar=1); varobs pi deltaq R y deltae g b ;// ajout de pi deltaq R y deltae g b % Estimated parameters from DSGE model(ajouté) estimated_params; tauy,normal_pdf,0,0.05; taub,normal_pdf,0.03,0.01; rpi,gamma_pdf,1.5, 0.5; ry,gamma_pdf,0.25,0.13; psi3,gamma_pdf,0.25,0.13; rss,gamma_pdf,2.5,1; gy,normal_pdf,0,0.05; gb,normal_pdf,-0.03,0.02; alfa,beta_pdf,0.2,0.05; kappa,gamma_pdf,0.5,0.25; tau,beta_pdf,0.5,0.2; rhoR,beta_pdf,0.5,0.2; rhoq,beta_pdf,0.4,0.2; rhoz,beta_pdf,0.2,0.05; rhoy_star,beta_pdf,0.9,0.05; rhopi_star,beta_pdf,0.8,0.1; rhog, beta_pdf, 0.5,0.15; rhotau, beta_pdf,0.5,0.15; omega, beta_pdf, 0.50, 0.20; sigmaR,inv_gamma_pdf, 0.5, 4; sigmaq,inv_gamma_pdf,1.5, 4; sigmaz,inv_gamma_pdf,1, 4; sigmay_star,inv_gamma_pdf, 1.5, 4; sigmapi_star,inv_gamma_pdf,0.55,4; sigmag,inv_gamma_pdf,1, 4; sigmatau,inv_gamma_pdf, 0.5,4; dsge_prior_weight, uniform_pdf,,,0,2;//ajouté end; options_.gradient_method = 3; estimation(datafile = data2, mh_nblocks = 2, dsge_var,dsge_varlag=4,mh_replic = 20000, mh_drop = 0.5, mode_compute = 6,mh_jscale=0.2, bayesian_irf,irf=40,conf_sig = 0.90,optim=('NumgradAlgorithm',3),nobs=128,first_obs=50,nograph) ;