%


var

k_t  %Capital

x_t  %Investment

q_t  % q_t 

y_t  %Output

Ci_t %CI 

Ck_t %Ck 

C_t % Adjustment cost

ky_t % Capital to GDP

xy_t % Investment to GDP

div_t %% Dividendos

divy_t %%Dividends as percentage of GDP
z_t %%Productivity

;

varexo

tiva
trent
tdiv
tpat
sh_z_t

;

predetermined_variables k_t z_t;

parameters
z_bar
r
delta
alpha
theta
kappa
Phi
rho_z
betta
ky_bar 
xy_bar
;
%Valor de los parámetros

r=0.0101000000000000000000; 
rho_z=0.8000000000000000400000; 
kappa=5.0000000000000000000000; 
Phi=0.0000000000000000000000; 
ky_bar=9.9390000000000001000000; 
xy_bar=0.2419999999999999900000; 
betta=0.9900009900009899600000; 
z_bar=0.2643910419647027600000; 
delta=0.0243485260086527750000; 
alpha=0.4207073766666666900000; 






%Initial Steady State

tdivss = 0.0;
tivass = 0.16;
trentss = 0.40;
tpatss = 0.00475;

Ciss   = 0;
Ckss   = 0;
Css    = 0;
qss    = log((1-tdivss)*(1+tivass*(1-Phi*trentss)));
zss    = log(z_bar);
kss    = log((((1-trentss)*(1-alpha)*exp(zss))/(((r+delta)*(1+tivass*(1-(trentss*Phi))))+tpatss-(trentss*delta)))^(1/alpha));
xss    = log(delta*exp(kss));
yss   = log(exp(zss)*exp(kss)^(1-alpha));
kyss   = kss-yss;
xyss   = xss-yss;
divss  = log(exp(yss)-exp(xss)-(trentss)*(exp(yss)-delta*exp(kss)-Phi*tivass*exp(xss))-tivass*exp(xss)-tpatss*exp(kss));
divyss = divss-yss;



model;

% % % Adjustment cost Equation 1
C_t = (kappa/2)*(((exp(x_t)/exp(k_t))-delta)^2)*exp(k_t);

% % % Derivada con respecto a C to I Equation 2
Ci_t = kappa*((exp(x_t)/exp(k_t))-delta);

% % % Derivada con respecto a K(t+1) Equation 3
Ck_t = ((kappa/2)*((exp(x_t)/exp(k_t))-delta)^2)-kappa*((exp(x_t)/exp(k_t))-delta)*(exp(x_t)/exp(k_t));

% % % Law motion of capital+ adjustment cost Equation 4
exp(k_t(+1)) = exp(x_t)+(1-delta)*exp(k_t);


% % % Output Equation 5
exp(y_t)=exp(z_t)*(exp(k_t)^(1-alpha));


% % % F.O.C with respect to investment Equation 6

exp(q_t) =(1-tdiv)*(1+(tiva*(1-Phi*trent))+Ci_t);


% % % law motion of the capital CPO Equation 7

% exp(q_t)=(1/(1+r))*((1-tdiv)*((1-trent)*exp(z_t)*(1-alpha)*(exp(k_t(-1))^(-alpha))+(trent*delta)-tpat-Ck_t(+1))+(1-delta)*exp(q_t(+1)));
exp(q_t)=(1/(1+r))*(((1-tdiv)*((1-trent)*(1-alpha)*exp(z_t(+1))*(exp(k_t(+1))^(-alpha))+(trent*delta)-tpat-Ck_t(+1)))+(1-delta)*exp(q_t(+1)));

% % % Capital to GDP Equation 8
exp(ky_t) = exp(k_t)/exp(y_t);


% % % Investment to GDP Equation 9
exp(xy_t) = exp(x_t)/exp(y_t);


% % % Dividends Equation 10
exp(div_t) =exp(y_t)-exp(x_t)-(trent*(exp(y_t)-(delta*exp(k_t))-Phi*tiva*exp(x_t)))-tiva*exp(x_t)-tpat*exp(k_t)-C_t;

% % % Dividends como porcentaje de PIB Equation 11
exp(divy_t)=exp(div_t)/exp(y_t);


% % % Productivity shock. Equation 12
z_t = rho_z*z_t(-1)+(1-rho_z)*log(z_bar)+sh_z_t;

end;

initval;



% % Steady state

q_t      = qss;
k_t      = kss;
x_t      = xss;
y_t      = yss;
C_t      = 0;
Ci_t     = 0;
Ck_t     = 0;
tiva     = tivass;
trent    = trentss;
tdiv     = tdivss;
tpat     = tpatss;
ky_t     = kyss;
xy_t     = xyss;
div_t    = divss;
divy_t   = divyss;
z_t      = zss;

end;


resid;
steady ;
check;

endval;

%% New Steady state



tiva =     0.16;
trent =    0.33;
tdiv =     0.0;
tpat =     0.00;

Ci_t   = 0;
Ck_t   = 0;
C_t    = 0;
q_t    = log((1-tdiv)*(1+tiva*(1-Phi*trent)));
z_t    = log(z_bar);
k_t    = log((((1-trent)*(1-alpha)*exp(z_t))/(((r+delta)*(1+tiva*(1-(trent*Phi))))+tpat-(trent*delta)))^(1/alpha));
x_t    = log(delta*exp(k_t));
y_t    = log(exp(z_t)*exp(k_t)^(1-alpha));
ky_t   = k_t-y_t;
xy_t   = x_t-y_t;
div_t  = log(exp(y_t)-exp(x_t)-(trent)*(exp(y_t)-delta*exp(k_t)-Phi*tiva*exp(x_t))-tiva*exp(x_t)-tpat*exp(k_t));
divy_t = div_t-y_t;





end;

resid;
steady ;
% check;

simul(periods=1000);