% Modèle non linéraisé:

%Déclaration des variables ( endogenes et exogenes):

var y, c, n, k, b, i, lamda, mu, tb, z, r, g, trf ;
varexo e1, e2, e3, e4 ;

%Calibration et définitions des parametres:

parameters beta, alpha, delta, psi, nu, sigma, rhoz, rhor, rhotrf, rhog, sg, strf, phi, phi_prima ;

beta  = 0.988;
alpha = 0.68;
delta = 0.025;
nu    = 0.455;
psi   = 0.002;
sigma = 0.001;
rhoz   =  0.95;
sg    = 0.51;
strf  = 0.45;
rhor   = 0.70;
rhog = 0.30;
rhotrf  = 0.10;
phi = delta;
phi_prima = 1;



%  Les équations du Modele:

model;
lamda = (c-psi*n^nu)^(-sigma);
n^nu  = (alpha*(1- sg + strf)/(psi*nu))*y;
lamda =  mu *(phi_prima*(i/k));
mu  = beta * (lamda (+1)*(1- sg + strf)* (1-alpha)*(y(+1)/k(+1)) + mu (+1)*((1-delta)+ (phi*(i(+1)/k(+1)))-(i(+1)/k(+1))*((phi_prima*(i(+1)/k(+1))))));
lamda = beta * (lamda (+1)*(1+ r(+1)));
k(+1) = (1-delta)*k + (phi*(i/k))*k ;
b(+1)= (1+r)*b + tb + trf;
y = c + g + i + tb;
y = z*k^(1-alpha)*n^alpha;
z  =  rhoz*z(-1)+ e1;
r  = rhor*r(-1)+ e2;
g    = rhog* g(-1)+ e3;
trf  = rhotrf*trf(-1)+ e4;
 
end;

initval;
tb = 0;    
c = 0.000002081 ;
n =  0.000000981 ;
y = 0.00000267;
k = 0.000017;
lamda = 0.0089;
mu= 0.0089;
z = 0.80;
r = 0;
g = 0;
trf = 0.80 ;
i = 0.000000428;
end;
steady;
stoch_simul;