% PB Model with Monopolistic Competion. 






%----------------------------------------------------------------


% 0. Housekeeping


%----------------------------------------------------------------





close all





%----------------------------------------------------------------


% 1. Defining variables


%----------------------------------------------------------------





var ub C taoc R ul L taol q Y K taok v I ui GI GC B Z ua uZ uk uL uc uGC SS A KG;


varexo eZ ek eL ec eGC eb el ei ea eA;





parameters gamma h taocbar kappa taolbar beta taokbar alpha YtoK delta1 delta0 delta2 spiepie CtoY GCtoY GItoY ItoY BtoY ZtoY alphaGbar psiZ gammaZ psik gammak psil gammal gammaGC rhoZ rhok rhoL rhoc rhoGC rhob rhol rhoi rhoa rhoaA AtoGI alphaG deltaG;





%----------------------------------------------------------------


% 2. Calibration


%----------------------------------------------------------------


gamma=3.46;

h=0.31;

taocbar=0.095;

kappa=1.89;

taolbar=0.214;

beta=0.99;

taokbar=0.384;

alpha=0.36;

YtoK=0.158;
%!!!!!!!!!!!!!computed

delta1=0.035;

delta0=0.025;

delta2=0.067;

spiepie=5.21;

CtoY=0.66;
%!!!!!!!!!!!!!computed

GCtoY=0.144;

GItoY=0.038;

ItoY=0.158;
%!!!!!!!!!!!!!computed

BtoY=0.381;

ZtoY=0.1;

alphaGbar=0.05;
%This value can change to 0.1

psiZ=0.23;

gammaZ=0.15;

psik=1.2;

gammak=0.095;

psil=0.53;

gammal=0.051;

gammaGC=0.072;

rhoZ=0.96;

rhok=0.89;

rhoL=0.99;

rhoc=0.88;

rhoGC=0.95;

rhob=0.78;

rhol=0.99;

rhoi=0.24;

rhoa=0.95;

rhoaA=0.94;

AtoGI=1;

alphaG=0.05;

deltaG=0.02;


















%----------------------------------------------------------------


% 3. Model


%----------------------------------------------------------------





model(linear);

ub-gamma*(1+h)*C/(1-h)+gamma*h*C(-1)/(1-h)-taocbar*taoc/(1+taocbar)=R-taocbar*taoc(+1)/(1+taocbar)+ub(+1)-gamma*C(+1)/(1-h);

ul+(1+kappa)*L+taocbar*taoc/(1+taocbar)=Y-taolbar*taol/(1-taolbar)-gamma*C/(1-h)+gamma*h*C(-1)/(1-h);

q=ub(+1)-gamma*C(+1)/(1-h)+gamma*(1+h)*C/(1-h)-taocbar*taoc(+1)/(1+taocbar)-ub-gamma*h*C(-1)/(1-h)+taocbar*taoc/(1+taocbar)+beta*(1-taokbar)*alpha*Y(+1)*YtoK-beta*(1-taokbar)*alpha*K(-1)*YtoK-beta*taokbar*alpha*taok(+1)*YtoK-beta*delta1*v(+1)+beta*(1-delta0)*q(+1);

Y-taokbar*taok/(1-taokbar)-K(-2)=q+(1+delta2/delta1)*v;

q/spiepie-(1+beta)*I+I(-1)+beta*I(+1)-ui+beta*ui(+1)=0;

Y=CtoY*C+GCtoY*GC+GItoY*GI+ItoY*I;

K(-1)=(1-delta0)*K(-2)-delta1*v+delta0*I;

BtoY*B+taokbar*alpha*(taok+Y)+taolbar*(1-alpha)*(taol+Y)+taocbar*CtoY*(taoc+C)=BtoY*R(-1)/beta+BtoY*B(-1)/beta+GItoY*GI+GCtoY*GC+ZtoY*Z;

Y=ua+alpha*v+alpha*K(-2)+(1-alpha)*L+(1-alphaG)*KG(-2);

GI=A*AtoGI;

KG(-2)=(1-deltaG)*KG(-3)+deltaG*A(-1);


%Goverment Finance Equation

Z=-psiZ*Y-gammaZ*SS(-8)+uZ;

taok=psik*Y-gammak*SS(-8)+ui;

taol=psil*Y-gammal*SS(-8)+uL;

taoc=uc;

GC=-gammaGC*SS(-8)+uGC;

SS=B-Y;


%Shock Equation

uZ=rhoZ*uZ(-1)+eZ;

uk=rhok*uk(-1)+ek;

uL=rhoL*uL(-1)+eL;

uc=rhoc*uc(-1)+ec;

uGC=rhoGC*uGC(-1)+eGC;

ub=rhob*ub(-1)+eb;

ul=rhol*ul(-1)+el;

ui=rhoi*ui(-1)+ei;

ua=rhoa*ua(-1)+ea;

A=rhoaA*A(-1)+eA;


end;





%----------------------------------------------------------------


% 4. Computation


%----------------------------------------------------------------





initval;

ub=0;

C=0;

R=0;

ul=0;

L=0;

taoc=0;

taol=0;

q=0;

Y=0;

K=0;

taok=0;

v=0;

I=0;

ui=0;

GI=0;

GC=0;

B=0;

Z=0;

ua=0;

uZ=0;

uk=0;

uL=0;

uc=0;

uGC=0;

SS=0;

A=0;

KG=0;


end;





shocks;


var eZ=4.46^2;

var ek=2.60^2;

var eL=2.91^2;

var ec=1.25^2;

var eGC=2.04^2;

var eb=2.35^2;

var el=2.82^2;

var ei=4.59^2;

var ea=0.63^2;

var eA=3.17^2;


end;



steady;




stoch_simul;