%----------------------------------------------------------------
% 0. Housekeeping (close all graphic windows)
%----------------------------------------------------------------

close all;

%----------------------------------------------------------------
% 1. Defining variables
%----------------------------------------------------------------

var y c k inv m r i pi x g;
varexo u;

parameters a b alpha beta delta rho;

%----------------------------------------------------------------
% 2. Calibration
%----------------------------------------------------------------

a=.5;
b=1.5;
alpha   = 0.36;
beta    = 0.99;
delta   = 0.025;
rho     = 0.95;

%----------------------------------------------------------------
% 3. Model
%----------------------------------------------------------------

model; 
  (1/b)*((a*c^b+(1-a)*m^b)^((1/b)-1))*(a*b*c^(b-1)) = beta*(1/b)*(((a*(c(+1))^b)+(1-a)*(m(+1))^b)^((1/b)-1))*(a*b*(c(+1))^(b-1))*(alpha*((k)^(alpha-1))+1-delta);
  ((1-a)/a)*((c/m)^(1-b)) = i;
  r = alpha*(k(-1)^(alpha-1))-delta;
  i = r + pi;
  m=((1+x)/(1+pi(-1)))*m(-1);  
  c+inv = y;
  y = (k(-1)^alpha);
  inv= k-(1-delta)*k(-1);
  x = exp(g)-1;
  g=u;  
end;




%----------------------------------------------------------------
% 4. Computation
%----------------------------------------------------------------

initval;
  k = 2;
  c = 0.76; 
  m=2.83;
  i=.0101;
  g=0;
  u = 0;
end;

shocks;
var u = 1;
end;

steady;

stoch_simul(hp_filter = 1600, order = 1);

%----------------------------------------------------------------
% 5. Some Results
%----------------------------------------------------------------

statistic1 = 100*sqrt(diag(oo_.var(1:6,1:6)))./oo_.mean(1:6);
table('Relative standard deviations in %',strvcat('VARIABLE','REL. S.D.'),lgy_(1:6,:),statistic1,10,8,4);