//********************************************************* /* Endo. Variables */ var mcf zcapf rkf kf pkf muf cf invef yf labf pinff wf pf emplf rrf effortf rf mc zcap rk k pk mu c inve y lab pinf w p empl ww effort pinf4 r dr pinfLAG1 pinfLAG2 ygap a as b g ls qs ps ms scons sinv sy slab spinf sw kpf habf kp hab one //********************************************************* // Modelbase Variables interest interestq inflation outputgap output; //********************************************************* //* Exo. Variables */ varexo ea eb y_ els eqs eps eas econs einv ey elab epinf ew em //********************************************************* // Modelbase Shocks interest_ fiscal_; //********************************************************* //* IDENTIFICATION OF MODEL PARAMETERS*/ parameters calfa ctou cbeta chab ccs cinvs crelwage chabw clabeff chlab csadjcost csigma chabb cprobw clandaw csigl cprobp cindw cindp cfc cinvdyn czcap csadjlab crpi crdpi crr cry crdy crhoa crhoas crhob crhog crhols crhoqs crhops crhoms crhoy crhocons crhoinv crhopinf crhow crholab cscaleea cscaleeas cscaleeb cscaleeg cscaleels cscaleeqs cscaleeps cscaleem cscaleecons cscaleeinv cscaleey cscaleelab cscaleepinf cscaleew //********************************************************* //* Modelbase Parameters cofintintb1 cofintintb2 cofintintb3 cofintintb4 cofintinf0 cofintinfb1 cofintinfb2 cofintinfb3 cofintinfb4 cofintinff1 cofintinff2 cofintinff3 cofintinff4 cofintout cofintoutb1 cofintoutb2 cofintoutb3 cofintoutb4 cofintoutf1 cofintoutf2 cofintoutf3 cofintoutf4 std_r_ std_r_quart; //******************************************************* // load Modelbase Monetary Policy Parameters //* Policy Rule cofintintb1 = 0.87^3; cofintintb2 = 0; cofintintb3 = 0; cofintintb4 = 0; cofintinf0 = (1-0.87^3)*1.93; cofintinfb1 = 0; cofintinfb2 = 0; cofintinfb3 = 0; cofintinfb4 = 0; cofintinff1 = 0; cofintinff2 = 0; cofintinff3 = 0; cofintinff4 = 0; cofintout = (1-0.87^3)*0.28; cofintoutb1 = 0; cofintoutb2 = 0; cofintoutb3 = 0; cofintoutb4 = 0; cofintoutf1 = 0; cofintoutf2 = 0; cofintoutf3 = 0; cofintoutf4 = 0; std_r_ = 1; //1.0124*1.0238; std_r_quart = 0.0808*.25*4*3.1479; //********************************************************* /*The parameter values ??were taken from the following sources: J.P Medina and Claudio Soto (2007) Raphael Bergoeing et al. 2001, cuentas Nacionales Chilenas, Michael Kumhof and Douglas Laxton (2009)*/ calfa = 0.47; //labor share in production ctou = 0.058; //depreciation rate cbeta = 0.99; //discount factor chab = 0; ccs = 0.6;// steady state consumption in output cinvs = 0.22;//steady state investment crelwage = 0; chabw = 0; clabeff = 0; chlab = 0; csadjcost = 6.7711; //investment adjustment cost csigma = 1.3533; // elasticity of intertemporal substitution chabb = 0.5732; // habit persistence cprobw = 0.7367;//calvo parameter labor market clandaw = 1.5; // SS markup labor market csigl = 2.3995;// inverse of the elasticity of labor supply cprobp = 0.9082;//calvo parameter goods market cindw = 0.7627;//indexation labor market cindp = 0.4694;//indexation goods market cfc = 1.4077; cinvdyn = 1; czcap = 0.1690; //capital utilization csadjlab = 0.5990; // reaction function crpi = 1.6841; //Taylor rule reaction to inflation crdpi = 0.1398; crr = 0.9613;//Taylor rule interest rate cry = 0.0988;//Taylor rule long run reaction to output gap crdy = 0.1586;//Taylor rule short run reaction to output gap // AR(1) shocks - To simulate Shocks crhoa = 0.8232;/* productivity shock/* crhoas = 0.9238; crhob = 0.8545; /*cons. preference shock*/ crhog = 0.9493; /*government spending shock*/ crhols = 0.8894; /*labor supply shock*/ crhoqs = 0.9273; crhops = 0; crhoms = 0; crhoy = 0; crhocons = 0; crhoinv = 0; crhopinf = 0; crhow = 0; crholab = 0; // scaling factor of the innovations cscaleea = 0.5978; /* productivity/* cscaleeas = 0.0165; cscaleeb = 0.3361; /*cons. preference*/ cscaleeg = 0.3247; /*government spending*/ cscaleels = 3.5197; /*labor supply*/ cscaleeqs = 0.0851; cscaleeps = 0; cscaleem = 0.0808; cscaleecons = 0; cscaleeinv = 0.6043; /*investment*/ cscaleey = 0; cscaleelab = 0; cscaleepinf = 0.1602; /*inflation*/ cscaleew = 0.2892; /*wage*/ //********************************************************* // Model Definition model(linear); //********************************************************* // Modelbase Variables interest = interestq * 4; interestq = r; inflation = pinf4; outputgap = ygap; output = y; // Monetary Policy Rule interestq = cofintintb1*interestq(-1) + cofintintb2*interestq(-2) + cofintintb3*interestq(-3) + cofintintb4*interestq(-4) + cofintinf0/4*inflation + cofintinfb1/4*inflation(-1) + cofintinfb2/4*inflation(-2) + cofintinfb3/4*inflation(-3) + cofintinfb4/4*inflation(-4) + cofintinff1/4*inflation(+1) + cofintinff2/4*inflation(+2) + cofintinff3/4*inflation(+3) + cofintinff4/4*inflation(+4) + cofintout/4*outputgap + cofintoutb1/4*outputgap(-1) + cofintoutb2/4*outputgap(-2) + cofintoutb3/4*outputgap(-3) + cofintoutb4/4*outputgap(-4) + cofintoutf1/4*outputgap(+1) + cofintoutf2/4*outputgap(+2) + cofintoutf3/4*outputgap(+3) + cofintoutf4/4*outputgap(+4) + std_r_quart * interest_; //********************************************************* // Original Model Code: // Original monetary policy rule (Smets and Wouters, 2003) // r = crr*r(-1) + (1-crr)*(crpi*pinf+cry*ygap)+crdpi*(pinf-pinf(-1))+crdy*(ygap-ygap(-1))+interest_ // //************** Flexible Economy mcf = calfa*rkf + (1-calfa)*wf - a; zcapf = (1/czcap)*rkf; rkf = wf + labf - kf; kf = kpf(-1) + zcapf; //************** Investment Euler Equation invef = (1/(1+cinvdyn*cbeta))*((cinvdyn*invef(-1) + cbeta*invef(+1)) + (1/csadjcost)*pkf) + 0*sinv; pkf = - muf - 1*b + muf(+1) + (1-cbeta*(1-ctou))*rkf(+1) + 0*(1-cbeta*(1-ctou))*zcapf(+1) + cbeta*(1-ctou)*pkf(+1) + qs; muf = muf(+1) + rf - pinff(+1) - b; muf = - csigma*((1-chab)/(1-chab-chabb))*cf + csigma*(chabb/(1-chab-chabb))*habf; // ************* Aggregate Resource constraint yf = ccs*cf + cinvs*invef + g; // ************* Aggregate Production function yf = cfc*(calfa*kf + (1-calfa)*labf + a); mcf = - 0*ps - 0*(1+cbeta*cindp)*(1/((1-cprobp)*(1-cbeta*cprobp)/(cprobp)))*spinf; wf = - 1*muf - 1*ls + csigl*labf; pf = 0*pf(-1) + pinff; emplf = emplf(-1) + 1*emplf(+1)- 1*emplf + ((1-csadjlab)*(1-csadjlab)/csadjlab)*effortf; rrf = rf - pinff(+1); effortf = labf - emplf; pinff = 0; //************ Sticky Price - wage economy //************ Marginal Cost mc = calfa*rk+(1-calfa)*w - a - slab; //************ Capital Utilization zcap = (1/czcap)*rk - 0*(1/czcap)*pk; //************ Rental Rate of Capital rk = w + lab - k; //************ Capital installed used one period later in production k = kp(-1) + zcap; //************ Investment Euler equation inve = (1/(1+cinvdyn*cbeta))*((cinvdyn*inve(-1) + cbeta*inve(+1)) + (1/csadjcost)*pk) + 1*sinv; //************ Arbitrage equation for Value of Capital pk = - mu - 1*b - 0*(1-crhols)*ls - 0*scons+mu(+1) + 0*b(+1) + (1-cbeta*(1-ctou))*rk(+1) + 0*(1-cbeta*(1-ctou))*zcap(+1) + cbeta*(1-ctou)*pk(+1) + qs + 0*sinv; mu = mu(+1) + r - pinf(+1) - b + 0*b(+1) - scons - 0*(1-crhols)*ls; mu = - csigma*((1-chab)/(1-chab-chabb))*c + csigma*(chabb/(1-chab-chabb))*hab; y = ccs*c + cinvs*inve + g + sy; //************ Aggregate Production function y = cfc*(calfa*k + (1-calfa)*lab + a + slab); //************ Phillips Curve pinf = 0*as + (1/(1+cbeta*cindp))*((cbeta)*(pinf(+1) - 0*as(+1)) + (cindp)*(pinf(-1) - 0*as(-1)) + ((1-cprobp)*(1-cbeta*cprobp)/(cprobp))*(mc+ps) + 0*0.1*ps)+ spinf; w = ((1/(((1+cbeta)*cprobw*((clandaw/(1-clandaw))*csigl-1+crelwage)/(1-cprobw))+crelwage+crelwage*cprobw*cbeta*(chabw-1)))) *(((cprobw*((clandaw/(1-clandaw))*csigl-1+crelwage))/(1-cprobw)+crelwage+crelwage*(chabw-1))*w(-1) + (cbeta)*((cprobw*((clandaw/(1-clandaw))*csigl-1+crelwage))/(1-cprobw))*w(+1) + (cindw)*(cprobw/(1-cprobw))*((clandaw/(1-clandaw))*csigl-1+crelwage)*(pinf(-1)-0*as(-1)) - (cindw*cbeta*cprobw*(cprobw/(1-cprobw))*((clandaw/(1-clandaw))*csigl-1+crelwage) + (cprobw/(1-cprobw))*((clandaw/(1-clandaw))*csigl-1+crelwage) + cprobw*cbeta*cindw*((clandaw/(1-clandaw))*csigl-1))*(pinf - 0*as) + (cbeta*cprobw)*(((cprobw/(1-cprobw))*((clandaw/(1-clandaw))*csigl-1+crelwage)) + ((clandaw/(1-clandaw))*csigl-1))*(pinf(+1) - 0*as(+1)) + (1-cbeta*cprobw)*(w + 1*mu + 1*ls - clabeff*effort - csigl*(1/(1-chlab))*lab + csigl*(chlab/(1-chlab))*lab(-1))) + 0*(1/(1+cbeta))*1*ls + 1*sw; p = 0*p(-1) + pinf; empl = empl(-1) + 1*empl(+1) - 1*empl - 0*r + 0*pinf(+1) + 0*csadjlab*effort + ((1-csadjlab)*(1-csadjlab)/csadjlab)*effort + 0.0*(a(-1) + cbeta*a(+1) - (1+cbeta)*a); ww = w + 0*(lab - empl); effort = lab - empl; dr = r - r(-1); pinfLAG1 = pinf(-1); pinfLAG2 = pinfLAG1(-1); pinf4 = pinf + pinfLAG1 + pinfLAG2 + pinfLAG2(-1); ygap = y - yf; a = crhoa*a(-1) + cscaleea*ea; as = crhoas*as(-1) + cscaleeas*eas; b = crhob*b(-1) + cscaleeb*eb; //g = crhog*g(-1) + cscaleeg*fiscal_; //************ exogenous spending (also including net exports) g = crhog*g(-1) + fiscal_; qs = crhoqs*qs(-1) + cscaleeqs*eqs; ms = crhoms*ms(-1) + cscaleem*em; ls = crhols*ls(-1) + cscaleels*els; ps = crhops*ps(-1) + cscaleeps*eps; scons = crhocons*scons(-1) + cscaleecons*econs; sinv = crhoinv*sinv(-1) + cscaleeinv*einv; sy = crhoy*sy(-1) + cscaleey*ey; slab = crholab*slab(-1) + cscaleelab*elab; //cost push shock spinf = crhopinf*spinf(-1) + cscaleepinf*epinf; sw = crhow*sw(-1) + cscaleew*ew; //************ Accumulation of installed capital kpf = (1-ctou)*kpf(-1) + ctou*invef(-1); habf = chab*habf(-1) + (1-chab)*cf(-1); //************ accumulation of installed capital kp = (1-ctou)*kp(-1) + ctou*inve(-1); hab = chab*hab(-1) + (1-chab)*c(-1); one = 0*one(-1); end; shocks; //************ productivity shock var ea = 1; var eas = 1; //************ wedge between FFR and return on assets var eb = 1; var fiscal_ = 1; //eg var interest_ = 1; // set equal to one for IRF var els = 1; //************ investment specific technology var eqs = 1; //************ monetary policy shock var em = 1; var econs = 1; var einv = 1; var ey = 1; var elab = 1; var epinf = 1; var ew = 1; end; check; steady; //*********************************************************** //* stoch_simul (irf = 200, ar=0, nograph, noprint); //* //*stoch_simul (irf = 200, ar=0, nograph, noprint) inflation outputgap interest;//* //************************************************************ // BAYESIAN ESTIMATION // estimated_params; csigl, inv_gamma_pdf, 1, 3; chabb, beta_pdf, 0.5, 0.25; cprobw, beta_pdf, 0.75, 0.2; cindw, beta_pdf, 0.5, 0.25; cprobp, beta_pdf, 0.75, 0.2; cindp, beta_pdf, 0.5, 0.25; stderr eb, inv_gamma_pdf, 1, 3; stderr fiscal_, inv_gamma_pdf, 1, 3; stderr els, inv_gamma_pdf, 1, 3; stderr epinf, inv_gamma_pdf, 1, 3; stderr einv, inv_gamma_pdf, 1, 3; end; estimated_params_init; csigl, 0.5; chabb, 0.5; cprobw, 0.5; cindw, 0.5; cprobp, 0.5; cindp, 0.5; stderr eb, 0.1; stderr fiscal_, 0.1; stderr els, 0.1; stderr epinf, 0.1; stderr einv,0.1; end; varobs ygap inve cf w; identification; dynare_sensitivity(identification=1); estimation(datafile=Input7,mode_check, first_obs=2,nobs=69,mode_compute=4,mh_replic=3000, mh_jscale=1.5,mh_nblocks=1,bayesian_irf,irf=24, forecast=12) ygap inve cf w interestq pinf empl; /**********************************************************************************/