%------------------------------------------------------------------------------------------%
% MODELO de Economia Abierta
%------------------------------------------------------------------------------------------%
% PUCP
% Tópicos de Econometría
% Junio 2013
%------------------------------------------------------------------------------------------%
% Jose Carlos Gonzales Tanaka                                                                          
%------------------------------------------------------------------------------------------%
%===========================================================================================

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

% VARIABLES (9)                                                                        
%------------------------------------------------------------------------------------------%

var
y %product
c %consumption
k %capital
h %labor
m %money
b %internation assets
p %domestic prices
e %exchange rate
r %rental of capital
w %real wage
rf %return on international assets
x %net exports

pf %foreign prices
prod %productivity
g %gross growth of money
;

varexo e1, e2, e3;

%------------------------------------------------------------------------------------------%
% PARAMETERS ()                                                                         
%------------------------------------------------------------------------------------------%
parameters

r_ast
beta
delta
theta
a % derivative of international return with respect to international assets
kappa

A
ho
gamma_prod
gamma_g
gamma_pf

sigma1 %Shocks Variances
sigma2
sigma3

B

y_ss 
c_ss 
k_ss
h_ss
m_ss
b_ss
p_ss
e_ss
r_ss
w_ss
rf_ss
x_ss

prod_ss
g_ss
pf_ss
;

%------------------------------------------------------------------------------------------%
% CALIBRATION                                                                      
%------------------------------------------------------------------------------------------%
%1)PREFERENCES
%--------------
A = 1.72;
ho = 0.53;
beta = 0.99;
delta = 0.025;
B = (A*log(1-ho))/ho;

%2)FIRMS
%--------------
theta = 0.36;
kappa = 0.2;   %parametro de ajuste del capital

%3)OPEN ECONOMY
%--------------
a = 0.01; %Derivada de la tasa de interes internacional con respecto a los
          %activos internacionales
r_ast = 0.03;
         
%4)SHOCKS
%--------------
gamma_prod = 0.95;
gamma_g = 0.95;
gamma_pf = 0.95;

sigma1 = 0.00712;
sigma2 = 0.00712;
sigma3 = 0.00712;

%------------------------------------------------------------------------------------------%
% STEADY STATE                                                                   
%------------------------------------------------------------------------------------------%
prod_ss = 1;
g_ss = 1;
pf_ss = 1;
p_ss = 1;
pi = 1;


r_ss = 1/beta - (1 - delta);
rf_ss = 1/beta - 1;
b_ss = (r_ast + 1 - (1/beta))/a;
x_ss = -(rf_ss*b_ss);
w_ss = (1 - theta)*(theta/r_ss)^(theta/(1 - theta));
c_ss = (beta*w_ss)/(-B*pi);
m_ss = p_ss*c_ss;
k_ss = theta*((m_ss/p_ss) - rf_ss*b_ss)/(r_ss - theta*delta);
h_ss = (r_ss*(1 - theta))*k_ss/(w_ss*theta);
y_ss = c_ss + delta*k_ss + x_ss;
e_ss = p_ss;

%================================
% MODEL
%================================
model;
%================================
% Families 
%================================
%%%   p*c = m(-1) + (g - 1)*m(-1);
e/(p(+1)*c(+1)) = beta*(e(+1)*(1 + rf))/(p(+2)*c(+2));
(p/(p(+1)*c(+1)))*(1 + kappa*(k - k(-1))) = beta*(p(+1)/(p(+2)*c(+2)))*(r(+1) + (1 - delta) + kappa*(k(+1) - k));
B/w = -beta*(p/(p(+1)*c(+1)));
p*c = m;
m/p + (e*b)/p + k + (kappa/2)*((k - k(-1))^2) = w*h + r*k(-1) + (1 - delta)*k(-1) + (e*(1 + rf(-1))*b(-1))/p;

%================================
% Firms
%================================
w = (1-theta)*k(-1)^(theta)*h^(-theta);
r = theta*k(-1)^(theta - 1)*h^(1 - theta);

%================================
% Open economy conditions
%================================
pf*x = b - (1 + rf(-1))*b(-1);
rf = r_ast - (a*b)/pf;
e = p/pf;

%================================
% Money condition
%================================
m = g*m(-1);  

%================================
% Market clearing 
%================================
prod*((k(-1))^theta)*h^(1-theta) = c + k - (1 - delta)*k(-1) + x;  
%================================
% Uncertainty laws of motion 
%================================
ln(prod) = (gamma_prod)*ln(prod(-1)) + e1;
ln(g) = (gamma_g)*ln(g(-1)) + e2;
ln(pf) = (gamma_pf)*ln(pf(-1)) + e3;

end;
%------------------------------------------------------------------------------------------%
% VALORES INICIALES
%------------------------------------------------------------------------------------------%
initval;
c = c_ss;
k = k_ss;
h = h_ss;
m = m_ss;
b = b_ss;
p = p_ss;
e = e_ss;
y = y_ss;
r = r_ss;
w = w_ss;
rf = rf_ss; 
x = x_ss;

prod = prod_ss;
g = g_ss;
pf = pf_ss;

end;

resid(1);
steady;

%------------------------------------------------------------------------------------------%
% SHOCKS                                                                         
%------------------------------------------------------------------------------------------%
shocks;
var e1 = (sigma1)^2;
var e2 = (sigma2)^2;
var e3 = (sigma3)^2;
end;

check;