% Foreign aid and its volatility
%__________________________________________________________________________
%1. Defining variables
%__________________________________________________________________________

% List of endogenous variables
var yt yn Y Ct Cn C Kt Kn K  Lt L i x pn eps1 eps2 eps3;
% List of exogenuous variables
varexo e1 e2 e3;

parameters beta omega mu sigma alpha eta delta nu At An sigma1 sigma2 sigma3  X psi11 psi12 psi13 psi21 psi22 psi23 psi31 psi32 psi33;

%__________________________________________________________________________
% 2. Calibration
%__________________________________________________________________________

beta  = 0.95;
omega = 0.26;
mu = 0.3157;
delta =  0.05;
alpha = 0.3;
eta   = 0.5;
sigma = 5.00;
nu= -10.09;
At    = 1;
An    = 1.52;
sigma1 = 0.74;
sigma2= 0.11;
sigma3= 0.11;
X     = 1.32;
psi11 = 0.95;
psi12 = 0;
psi13 = 0;
psi21 = 0.95;
psi22 = 0;
psi23 = 0;
psi31 = 0.95;
psi32 = 0;
psi33 = 0;



klt=((1-beta+beta*delta)/(alpha*beta*At))^(1/(alpha-1));                        %Kt/Lt
kln=((1-alpha)/(1-eta))*(eta/alpha)*(klt);                                      %Kn/Ln

ky_t= (beta*alpha)/(1+beta*delta-beta);                                         %Kt/yt
kpy_n= (eta*beta)/(1+beta*delta-beta);                                          %Kn/pn*yn
knkt=1/(1+nu);                                                                  %Kn/Kt


                     

%__________________________________________________________________________
% 3. Model
%__________________________________________________________________________
model;
%households:

(C^(-sigma))/Ct^(mu+1)=beta*(C(+1)^(-sigma))/(Ct(+1)^(mu+1))*(alpha*At*exp(eps3(+1))*((Kt(+1)/Lt(+1))^(alpha-1)) + 1- delta) ;     % Euler equation

pn = ((1-omega)/omega)*(Cn/Ct)^(-(1+eta));                                     % Marginal rate of substitution between consumptin of tradable and non-tradable goods


%Firms:

pn*An*exp(eps2)*eta*(Kn/L)^(eta-1)=At*exp(eps3)*alpha*(Kt/Lt)^(alpha-1);       % Marginal productivity of capital/The rate of return
pn*An*exp(eps2)*(1-eta)*(Kn/L)^eta =At*exp(eps3)*(1-alpha)*(Kt/Lt)^alpha ;     % Marginal productivity of labor/ The wage rate 



%Market Clearing/Resource constrains

yt=At*exp(eps3)*(Kt^alpha)*Lt^(1-alpha);                                      % Output in tradable sector
yn=An*exp(eps2)*(Kn^eta)*L^(1-eta);                                           % Output in non-tradable sector
Y= pn*yn+yt;                                                                  % GDP

K= i+ (1-delta)*K(-1);                                                         % Capital Accumulation
K=(Kt^(-nu)+Kn^(-nu))^(-1/nu);                                                 % Capital sector specifiation

Ct+i = yt + x ;                                                              % Maret clearing condition in the sector of tradable goods
Cn = An*(Kn^eta)*L^(1-eta);                                                  % Market clearing condition in the sector of non-tradable goods

C=((1-omega)*(Ct)^(-mu)+omega*(Cn)^(-mu))^(-1/mu);                           % Total consumption

Lt+L=1;                                                                      % Labor Market, market clearing condition

x=X*exp(eps1) ;                                                              % Aid        

log(eps1)=psi11*log(eps1(-1)) + psi12*log(eps2(-1))+psi13*log(eps3(-1))+e1;   %Aid shock
log(eps2)=psi21*log(eps2(-1)) + psi22*log(eps1(-1))+psi23*log(eps3(-1))+e2;  %non-tradable sector productivity shock
log(eps3)=psi31*log(eps3(-1)) + psi32*log(eps1(-1))+psi33*log(eps3(-1))+e3;  %tradable sector productivity shock


end;

%__________________________________________________________________________
%4.Computation
%__________________________________________________________________________

initval;

pn=((1-alpha)/(1-eta))*(At/An)*((klt)^alpha)*(kln)^(-eta);                      %marginal rate of substitution between consumption of tradable and non-tradable secotrs
Lt=1/(1+((1-eta)*alpha/((1-alpha)*eta))*knkt);
L=1-Lt;

yt=At*((klt)^alpha)*Lt;
yn=An*((kln)^eta)*L;
Y=yt+pn*yn;

Ct=yn*(pn*omega/(1-omega))^(1/1+eta);
Cn=yn;
C=((1-omega)*(Cn)^(-mu)+omega*(Ct)^(-mu))^(-1/mu);

Kt=yt*ky_t;
Kn=yn*pn*kpy_n;
K=(Kt^(-nu)+Kn^(-nu))^(-1/nu);

i=delta*K;
x=X;



e1=0;
e2=0;
e3=0;
eps1=1;
eps2=1;
eps3=1;

end;

shocks;
var e1=sigma1^2;
var e2=sigma2^2;
var e3=sigma3^2;
var e1,e2=0.4*sigma1*sigma2;
var e1,e3=0.4*sigma1*sigma3;
var e2,e3=0.4*sigma2*sigma3;
end;

steady;

stoch_simul(hp_filter = 1600, order = 1);                                    % calculates the theoretical moments. HP-filtering before.