% endogenous variables

var yt kt nt ct it gt nut xt mt ut vt qt st kpt et

Gammat rt pit rkt qkt pwt at wt chit mut wot

bt fyt thetat e_wt e_bt e_it e_zt e_etat e_pt e_rt

e_gt 

% observables

dy dinve dc dw labobs pinfobs robs;



% exogenous variables

varexo innovation_bt innovation_it innovation_zt 

innovation_etat innovation_pt innovation_rt

innovation_gt ;



parameters alpha beta delta sigma rho yg s csi psinu etak h bb eta lambda lambdap gamma
epsilonp epsilong  rpi ry rhos gammaz rhob rhoi rhoz rhoeta rhop rhor rhog sigmab sigmai sigmaz 
sigmaeta sigmap sigmar sigmag rk x n u qk k a y i g mu e chi pw kappa w b c Gamma yc yi ynu yx 
htilda etanu betatilda kappaa kappaw kappalambda phia psi tau H phis phix phib phichi phieta taup
smallcp pi gammap fip iotaf iotao iotab G tau1 tau2 smallc fi gammab gammao gammaf ;


alpha = 0.33;
beta = 0.99;
delta = 0.025;
sigma = 0.5;
rho = 0.895;
yg= 0.2;
s = 0.95;
csi = 10;
%-----------------------estimated parameters
psinu = 0.5;
etak = 4;
h = 0.5;
bb = 0.5;
eta = 0.5;
lambda = 0.75;
lambdap = 0.66;
gamma = 0.5;
epsilonp = 1.15;
%to make it consistent with 0.2 ss gov't share
epsilong = 1.25;
rpi = 1.7;
ry = 0.125;
rhos = 0.75;
gammaz = 1.025;
rhob = 0.5;
rhoi = 0.5;
rhoz = 0.5;
rhoeta = 0.5;
rhop = 0.5;
rhor = 0.5;
rhog = 0.5;
sigmab = 0.15;
sigmai = 0.15;
sigmaz = 0.15;
sigmaeta = 0.15;
sigmap = 0.15;
sigmar = 0.15;
sigmag = 0.15;





% model equations

model(linear);

% technology
yt=alpha*kt+(1-alpha)*nt;

% resource constraint 
yt=yc*ct+yi*it+yg*gt+ynu*nut+yx*(2*xt+nt(-1));

% matching
mt=sigma*ut+(1-sigma)*vt;

% employment dynamics
nt=nt(-1)+(1-rho)*xt;

% transition probabilities
qt=mt-vt;
st=mt-ut;

% unemployment
ut=-(n/u)*nt(-1);

% effective capital
kt+e_zt=nut+kpt(-1);

% physical capital dynamics
kpt=(1-delta)/gammaz*(kpt(-1)-e_zt)+(1-(1-delta)/gammaz)*(it+e_it);

% aggregate vacancies
xt=qt+vt-nt(-1);

% consumption-saving
0=Gammat(+1)+(rt-pit(+1))-e_zt(+1);

% marginal utility
%(1-htilda)*(1-beta*htilda)lambdat=htilda*(ct(-1)-e_zt)-(1+beta*htilda^2)*ct+beta*htilda*(ct(+1)+e_zt(+1))+(1-htilda)*(e_bt-beta*htilda*e_bt(+1));
%Gammat=lambdat/lambdat(-1);

Gammat = (htilda*(ct(-1)-e_zt)-(1+beta*htilda^2)*ct+beta*htilda*(ct(+1)+e_zt(+1))+(1-htilda)*(e_bt-beta*htilda*e_bt(+1)))/((1-htilda)*(1-beta*htilda))-(htilda*(ct(-2)-e_zt(-1))-(1+beta*htilda^2)*ct(-1)+beta*htilda*(ct+e_zt)+(1-htilda)*(e_bt(-1)-beta*htilda*e_bt))/((1-htilda)*(1-beta*htilda));

% capital utilization
nut=etanu*rkt;

% investment
it=1/(1+beta)*(it(-1)-e_zt)+1/(etak*gammaz^2)*1/(1+beta)*(qkt+e_it)+beta/(1+beta)*(it(+1)+e_zt(+1));

% capital renting
pwt+yt-kt=rkt;

% tobin's q    
qkt=betatilda*(1-delta)*qkt(+1)+(1-betatilda*(1-delta))*rkt(+1)-(rt-pit(+1));

% aggregate hiring rate  
xt=kappaa*(pwt+at)-kappaw*wt+kappalambda*Gammat(+1)+beta*xt(+1);

% marginal product of labor
at=yt-nt;

% weight in Nash bargaining
chit=-(1-chi)*(mut-et);
et=(rho*lambda*beta)*(Gammat(+1)-pit(+1)+gamma*pit+et(+1)-e_zt(+1));
mut=(x*lambda*beta)*xt(+1)-(x*lambda*beta)*(kappaw*mu)*mu*(wt+gamma*pit-pit(+1)-e_zt(+1)-wt(+1))+(lambda*beta)*(mut(+1)+Gammat(+1)+gamma*pit-pit(+1)-e_zt(+1));

% spillover free target wage
wot=phia*(pwt+at)+(phis+phix)*xt(+1)+phis*st(+1)+phib*bt+(phis+phix/2)*Gammat(+1)+phix*(chit-(rho-s)*beta*chit(+1))+e_wt;
e_wt = phieta*(1-(rho-s)*beta*rhoeta)*e_etat;

% aggregate wage
wt=gammab*(wt(-1)-pit+gamma*pit(-1)-e_zt)+gammao*wot+gammaf*(wt(+1)+pit(+1)-gamma*pit+e_zt(+1));

% Philips curve
pit=iotab*pit(-1)+iotao*(pwt+e_pt)+iotaf*pit(+1);

% Taylor rule
rt=rhos*rt(-1)+(1-rhos)*(rpi*pit+ry*(yt-fyt))+e_rt;

% government spending
gt=yt+(1-yg)/yg*e_gt;

% market tightness 
thetat=vt-ut;

% benefits
bt=kpt;


% FLEX ECONOMY   30
fyt = 0;    

%------------------- shocks

% preferences
e_bt=rhob*e_bt(-1)+innovation_bt;

% investment 
e_it=rhoi*e_it(-1)+innovation_it;

% labour productivity    33
e_zt=rhoz*e_zt(-1)+innovation_zt;

% bargaining power
e_etat=rhoeta*e_etat(-1)+innovation_etat;

% markup   35
e_pt=rhop*e_pt(-1)+innovation_pt;

% monetary policy
e_rt=rhor*e_rt(-1)+innovation_rt;

% govenrment spendings     37
e_gt=rhog*e_gt(-1)+innovation_gt;


% ------------ observation equations

% 100*(gammaz-1)


dy=100*(gammaz-1)+yt-yt(-1)+e_zt;

dc=100*(gammaz-1)+ct-ct(-1)+e_zt;

dinve=100*(gammaz-1)+it-it(-1)+e_zt;

dw=100*(gammaz-1)+wt-wt(-1)+e_zt;

labobs=nt;

pinfobs=pit;

robs=rt;


end;





varobs  dy dc dinve dw labobs pinfobs robs;




%%%%%%%%%%%%%%%%%%%%%%%%%%% ESTIMATION
 
estimated_params;

rhoz, beta_pdf, 0.5, 0.2;
rhob, beta_pdf, 0.5, 0.2;
rhoi, beta_pdf, 0.5, 0.2;
rhop, beta_pdf, 0.5, 0.2;
rhoeta, beta_pdf, 0.5, 0.2;
rhog, beta_pdf, 0.5, 0.2;
rhor, beta_pdf, 0.5, 0.2;

stderr innovation_zt, inv_gamma_pdf, 0.15, 0.15;
stderr innovation_bt, inv_gamma_pdf, 0.15, 0.15;
stderr innovation_it, inv_gamma_pdf, 0.15, 0.15;
stderr innovation_pt, inv_gamma_pdf, 0.15, 0.15;
stderr innovation_etat, inv_gamma_pdf, 0.15, 0.15;
stderr innovation_gt, inv_gamma_pdf, 0.15, 0.15;
stderr innovation_rt, inv_gamma_pdf, 0.15, 0.15;

psinu, beta_pdf, 0.5, 0.1;
etak, normal_pdf, 4, 1.5;
h, beta_pdf, 0.5, 0.1;
eta, beta_pdf, 0.5, 0.1;
bb, beta_pdf, 0.5, 0.1;
lambda, beta_pdf, 0.75, 0.1;
lambdap, beta_pdf, 0.66, 0.1;
gamma, uniform_pdf, , , 0, 1;
epsilonp, normal_pdf, 1.15, 0.05;
rpi, normal_pdf, 1.7, 0.3;
ry, gamma_pdf, 0.125, 0.1;
rhos, beta_pdf, 0.75, 0.1;
gammaz, uniform_pdf, , , 1, 1.5;


end;


check;
resid(1);
steady;


estimation(order=1,datafile=trigari_dataUS, plot_priors=0, mh_jscale=0.3, mh_nblocks=2, mode_compute=6);