%Model Description+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
This is Chris Sims' simple RBC model used to test his second order approximation code.


%Model Information+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Name = Chris Sims' RBC model;


%Parameters++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
betta     = 0.95;
delta     = 0.0;
alpha     = 0.3;
rho       = 0.0;
gamma     = 2.0;
z_bar     = 1.0;
sigma_eps = 1.0; 


%Variable Vectors+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[1]  k(t):capital{endo}[log,hp]
[2]  c(t):consumption{con}[log,hp]
[3]  z(t):eps(t):productivity{exo}[log,hp]
[4]  @y(t):output[log,hp]


%Boundary Conditions++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
None


%Variable Substitution Non-Linear System++++++++++++++++++++++++++++++++++++++++++++++++
[1]  @y(t)   = z(t-1)*k(t-1)**alpha;
[2]  @F(t)   = z(t-1)*k(t-1)**alpha;
[3]  @inv(t) = k(t)-delta*k(t-1);


%Non-Linear First-Order Conditions++++++++++++++++++++++++++++++++++++++++++++++++++++++
# Insert here the non-linear FOCs in format g(x)=0
[1]  c(t)**(-gamma)-betta*E(t)|c(t+1)**(-gamma)*...
     (alpha*z(t)*k(t)**(alpha-1)+delta) = 0;
[2]  c(t)+@inv(t)-@F(t) = 0;
[3]  LOG(z(t))-rho*LOG(z(t-1)) = 0;


%Manual entry of sstate non-linear system++++++++++++++++++++++++++++++++++++++++++++++++
None


%Steady States [Closed Form]++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
k_bar = (alpha*betta/(1-betta*delta))**(1/(1-alpha));
c_bar = k_bar**alpha-(1-delta)*k_bar;

%Steady State Non-Linear System [Manual]+++++++++++++++++++++++++++++++++++++++++++++++++
None

%Log-Linearized Model Equations++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
None


%Variance-Covariance Matrix++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sigma = [sigma_eps**2];


%End Of Model File+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
