Smets_Wouters_2007.mod 8.57 KB
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// --+ options: json=compute +--
path(['..' filesep 'ols'], path);

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/*
 * This file provides replication files for 
 * Smets, Frank and Wouters, Rafael (2007): "Shocks and Frictions in US Business Cycles: A Bayesian
 * DSGE Approach", American Economic Review, 97(3), 586-606, that are compatible with Dynare 4.2.5 onwards
 *
 * To replicate the full results, you have to get back to the original replication files available at
 * https://www.aeaweb.org/articles.php?doi=10.1257/aer.97.3.586 and include the respective estimation commands and mode-files.
 *
 * Notes: Please see the header to the Smets_Wouters_2007_45.mod for more details and a fully documented version.
 *
 * This file was originally written by Frank Smets and Rafeal Wouters and has been updated by
 * Johannes Pfeifer. 
 *
 * Please note that the following copyright notice only applies to this Dynare 
 * implementation of the model
 */

/*
 * Copyright (C) 2007-2013 Frank Smets and Raf Wouters
 * Copyright (C) 2013-15 Johannes Pfeifer
 *
 * This is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This file is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You can receive a copy of the GNU General Public License
 * at <http://www.gnu.org/licenses/>.
 */

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var labobs robs pinfobs dy dc dinve dw ewma epinfma zcapf rkf kf pkf cf
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    invef yf labf wf rrf mc zcap rk k pk c inve y lab pinf w r a b g qs
    spinf sw kpf kp ygap;
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varexo ea eb eg eqs ms epinf ew;
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parameters curvw cgy curvp constelab constepinf constebeta cmaw cmap calfa
           czcap csadjcost ctou csigma chabb ccs cinvs cfc
           cindw cprobw cindp cprobp csigl clandaw
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           crdpi crdy crr crpiMcrpiXcrr cryMcryXcrr
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           crhoa crhoas crhob crhog crhols crhoqs crhoms crhopinf crhow
           ctrend cg;
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// fixed parameters
ctou=.025;
clandaw=1.5;
cg=0.18;
curvp=10;
curvw=10;

// estimated parameters initialisation
calfa=.24;
cbeta=.9995;
csigma=1.5;
cfc=1.5;
cgy=0.51;

csadjcost= 6.0144;
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chabb=    0.6361;
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cprobw=   0.8087;
csigl=    1.9423;
cprobp=   0.6;
cindw=    0.3243;
cindp=    0.47;
czcap=    0.2696;
crr=      0.8762;
crdy=     0.2347;
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crpiMcrpiXcrr = 0.1842;
cryMcryXcrr   = 0.0073;
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crhoa=    0.9977;
crhob=    0.5799;
crhog=    0.9957;
crhols=   0.9928;
crhoqs=   0.7165;
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crhoas=1;
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crhoms=0;
crhopinf=0;
crhow=0;
cmap = 0;
cmaw  = 0;

constelab=0;

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model(linear);
//deal with parameter dependencies; taken from usmodel_stst.mod
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#cpie=1+constepinf/100;
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#cgamma=1+ctrend/100;
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#cbeta=1/(1+constebeta/100);

#clandap=cfc;
#cbetabar=cbeta*cgamma^(-csigma);
#cr=cpie/(cbeta*cgamma^(-csigma));
#crk=(cbeta^(-1))*(cgamma^csigma) - (1-ctou);
#cw = (calfa^calfa*(1-calfa)^(1-calfa)/(clandap*crk^calfa))^(1/(1-calfa));
#cikbar=(1-(1-ctou)/cgamma);
#cik=(1-(1-ctou)/cgamma)*cgamma;
#clk=((1-calfa)/calfa)*(crk/cw);
#cky=cfc*(clk)^(calfa-1);
#ciy=cik*cky;
#ccy=1-cg-cik*cky;
#crkky=crk*cky;
#cwhlc=(1/clandaw)*(1-calfa)/calfa*crk*cky/ccy;
#cwly=1-crk*cky;

#conster=(cr-1)*100;

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    // flexible economy
    0*(1-calfa)*a + 1*a = calfa*rkf+(1-calfa)*(wf);
    zcapf = (1/(czcap/(1-czcap)))* rkf;
    rkf = (wf)+labf-kf;
    kf = kpf(-1)+zcapf;
    invef = (1/(1+cbetabar*cgamma))* (  invef(-1) + cbetabar*cgamma*invef(1)+(1/(cgamma^2*csadjcost))*pkf ) +qs;
    pkf = -rrf-0*b+(1/((1-chabb/cgamma)/(csigma*(1+chabb/cgamma))))*b +(crk/(crk+(1-ctou)))*rkf(1) +  ((1-ctou)/(crk+(1-ctou)))*pkf(1);
    cf = (chabb/cgamma)/(1+chabb/cgamma)*cf(-1) + (1/(1+chabb/cgamma))*cf(+1) +((csigma-1)*cwhlc/(csigma*(1+chabb/cgamma)))*(labf-labf(+1)) - (1-chabb/cgamma)/(csigma*(1+chabb/cgamma))*(rrf+0*b) + b;
    yf = ccy*cf+ciy*invef+g  +  crkky*zcapf;
    yf = cfc*( calfa*kf+(1-calfa)*labf +a );
    wf = csigl*labf   +(1/(1-chabb/cgamma))*cf - (chabb/cgamma)/(1-chabb/cgamma)*cf(-1);
    kpf = (1-cikbar)*kpf(-1)+(cikbar)*invef + (cikbar)*(cgamma^2*csadjcost)*qs;

    // sticky price - wage economy
    mc = calfa*rk+(1-calfa)*(w) - 1*a - 0*(1-calfa)*a;
    zcap = (1/(czcap/(1-czcap)))* rk;
    rk = w+lab-k;
    k = kp(-1)+zcap;
    inve = (1/(1+cbetabar*cgamma))* (  inve(-1) + cbetabar*cgamma*inve(1)+(1/(cgamma^2*csadjcost))*pk ) +qs;
    pk = -r+pinf(1)-0*b +(1/((1-chabb/cgamma)/(csigma*(1+chabb/cgamma))))*b + (crk/(crk+(1-ctou)))*rk(1) +  ((1-ctou)/(crk+(1-ctou)))*pk(1);
    c = (chabb/cgamma)/(1+chabb/cgamma)*c(-1) + (1/(1+chabb/cgamma))*c(+1) +((csigma-1)*cwhlc/(csigma*(1+chabb/cgamma)))*(lab-lab(+1)) - (1-chabb/cgamma)/(csigma*(1+chabb/cgamma))*(r-pinf(+1) + 0*b) +b;
    y = ccy*c+ciy*inve+g  +  1*crkky*zcap;
    y = cfc*( calfa*k+(1-calfa)*lab +a );
    pinf = (1/(1+cbetabar*cgamma*cindp)) * ( cbetabar*cgamma*pinf(1) +cindp*pinf(-1)+((1-cprobp)*(1-cbetabar*cgamma*cprobp)/cprobp)/((cfc-1)*curvp+1)*(mc)  )  + spinf;
    w = (1/(1+cbetabar*cgamma))*w(-1)+(cbetabar*cgamma/(1+cbetabar*cgamma))*w(1)+(cindw/(1+cbetabar*cgamma))*pinf(-1)-(1+cbetabar*cgamma*cindw)/(1+cbetabar*cgamma)*pinf+(cbetabar*cgamma)/(1+cbetabar*cgamma)*pinf(1)+(1-cprobw)*(1-cbetabar*cgamma*cprobw)/((1+cbetabar*cgamma)*cprobw)*(1/((clandaw-1)*curvw+1))*(csigl*lab + (1/(1-chabb/cgamma))*c - ((chabb/cgamma)/(1-chabb/cgamma))*c(-1) -w)+ 1*sw;
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    [name='taylor_rule']
    r = crpiMcrpiXcrr*pinf + cryMcryXcrr*ygap + crdy*diff(ygap) + crr*r(-1) + ms;
    ygap = y - yf;
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    a = crhoa*a(-1)  + ea;
    b = crhob*b(-1) + eb;
    g = crhog*(g(-1)) + eg + cgy*ea;
    qs = crhoqs*qs(-1) + eqs;
    spinf = crhopinf*spinf(-1) + epinfma - cmap*epinfma(-1);
    epinfma=epinf;
    sw = crhow*sw(-1) + ewma - cmaw*ewma(-1);
    ewma = ew;
    kp = (1-cikbar)*kp(-1)+cikbar*inve + cikbar*cgamma^2*csadjcost*qs;

    // measurment equations
    dy = y-y(-1)+ctrend;
    dc = c-c(-1)+ctrend;
    dinve = inve-inve(-1)+ctrend;
    dw = w-w(-1)+ctrend;
    pinfobs = 1*(pinf) + constepinf;
    robs = 1*(r) + conster;
    labobs = lab + constelab;
end;
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steady_state_model;
dy=ctrend;
dc=ctrend;
dinve=ctrend;
dw=ctrend;
pinfobs = constepinf;
robs = (((1+constepinf/100)/((1/(1+constebeta/100))*(1+ctrend/100)^(-csigma)))-1)*100;
labobs = constelab;
end;

shocks;
var ea;
stderr 0.4618;
var eb;
stderr 1.8513;
var eg;
stderr 0.6090;
var eqs;
stderr 0.6017;
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var ms;
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stderr 0.2397;
var epinf;
stderr 0.1455;
var ew;
stderr 0.2089;
end;

estimated_params;
// PARAM NAME, INITVAL, LB, UB, PRIOR_SHAPE, PRIOR_P1, PRIOR_P2, PRIOR_P3, PRIOR_P4, JSCALE
// PRIOR_SHAPE: BETA_PDF, GAMMA_PDF, NORMAL_PDF, INV_GAMMA_PDF
stderr ea,0.4618,0.01,3,INV_GAMMA_PDF,0.1,2;
stderr eb,0.1818513,0.025,5,INV_GAMMA_PDF,0.1,2;
stderr eg,0.6090,0.01,3,INV_GAMMA_PDF,0.1,2;
stderr eqs,0.46017,0.01,3,INV_GAMMA_PDF,0.1,2;
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stderr ms,0.2397,0.01,3,INV_GAMMA_PDF,0.1,2;
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stderr epinf,0.1455,0.01,3,INV_GAMMA_PDF,0.1,2;
stderr ew,0.2089,0.01,3,INV_GAMMA_PDF,0.1,2;
crhoa,.9676 ,.01,.9999,BETA_PDF,0.5,0.20;
crhob,.2703,.01,.9999,BETA_PDF,0.5,0.20;
crhog,.9930,.01,.9999,BETA_PDF,0.5,0.20;
crhoqs,.5724,.01,.9999,BETA_PDF,0.5,0.20;
crhoms,.3,.01,.9999,BETA_PDF,0.5,0.20;
crhopinf,.8692,.01,.9999,BETA_PDF,0.5,0.20;
crhow,.9546,.001,.9999,BETA_PDF,0.5,0.20;
cmap,.7652,0.01,.9999,BETA_PDF,0.5,0.2;
cmaw,.8936,0.01,.9999,BETA_PDF,0.5,0.2;
csadjcost,6.3325,2,15,NORMAL_PDF,4,1.5;
csigma,1.2312,0.25,3,NORMAL_PDF,1.50,0.375;
chabb,0.7205,0.001,0.99,BETA_PDF,0.7,0.1;
cprobw,0.7937,0.3,0.95,BETA_PDF,0.5,0.1;
csigl,2.8401,0.25,10,NORMAL_PDF,2,0.75;
cprobp,0.7813,0.5,0.95,BETA_PDF,0.5,0.10;
cindw,0.4425,0.01,0.99,BETA_PDF,0.5,0.15;
cindp,0.3291,0.01,0.99,BETA_PDF,0.5,0.15;
czcap,0.2648,0.01,1,BETA_PDF,0.5,0.15;
cfc,1.4672,1.0,3,NORMAL_PDF,1.25,0.125;
crr,0.8258,0.5,0.975,BETA_PDF,0.75,0.10;
crdy,0.2239,0.001,0.5,NORMAL_PDF,0.125,0.05;
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crpiMcrpiXcrr,0.1842,0.01,2,NORMAL_PDF,1.5,0.25;
cryMcryXcrr,0.0073,0.001,0.975,NORMAL_PDF,0.125,0.05;
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constepinf,0.7,0.1,2.0,GAMMA_PDF,0.625,0.1;//20;
constebeta,0.7420,0.01,2.0,GAMMA_PDF,0.25,0.1;//0.20;
constelab,1.2918,-10.0,10.0,NORMAL_PDF,0.0,2.0;
ctrend,0.3982,0.1,0.8,NORMAL_PDF,0.4,0.10;
cgy,0.05,0.01,2.0,NORMAL_PDF,0.5,0.25;
calfa,0.24,0.01,1.0,NORMAL_PDF,0.3,0.05;
end;

varobs dy dc dinve labobs pinfobs dw robs;

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ds = dseries('usmodel_dseries.csv');
ds.ygap = ds.y.detrend(1);
dyn_ols(ds, {}, {'taylor_rule'});
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crr           = 0.8762;
crdy          = 0.2347;
crpiMcrpiXcrr = 0.1842;
cryMcryXcrr   = 0.0073;

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estimation(optim=('MaxIter',200),datafile=usmodel_data,mode_compute=4,first_obs=1, presample=4,lik_init=2,prefilter=0,mh_replic=0,mh_nblocks=2,mh_jscale=0.20,mh_drop=0.2, nograph, nodiagnostic, tex, filtered_vars);
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shock_decomposition y;