%Model Description+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
This is the 1998 Urban Jermann asset pricing model.


%Model Information+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Name = Jermann RBC model;


%Parameters++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
alpha      = 0.36;
chi        = 0.819;
xi         = 1.0/4.3;
g          = 0.005;
tau        = 5.0;
betta      = 1.014;
bettaa     = betta*(1+g)**(-tau);
delta      = 0.025;
rho        = 0.95;
a1         = (g+delta)**(1.0/xi);
a2         = (g+delta)/(1.0-xi);
z_bar      = 1.0;
sigma_eps  = 0.01;


%Variable Vectors+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[1]   k(t):capital{endo}[log,cf]
[2]   c(t):consumption{con}[log,cf]
[3]   inv(t):investment{con}[log,cf]
[4]   mu(t):mwealth{con}[log,cf]
[5]   z(t):eps(t):productivity{exo}[log,cf]

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


%Variable Substitution Non-Linear System++++++++++++++++++++++++++++++++++++++++++++++++
# Utility function derivative
[1]   @MUcg(t)     = (c(t)-chi*(1+g)**(-1)*c(t-1))**(-tau)-bettaa*chi*((1+g)*E(t)|c(t+1)-chi*c(t))**(-tau);
# Goods production function
[3]   @Fg(t)       = z(t-1)*(1+g)**(-alpha)*k(t-1)**alpha;
[4]   @Fkg(t)      = alpha*z(t-1)*(1+g)**(1-alpha)*k(t-1)**(alpha-1);
[5]   @Fkg(t+1)    = FF_1{@Fkg(t)};
# Investment adjustment cost function
[6]   @IKC(t)     = a1/(1-(1/xi))*((1+g)*inv(t)/k(t-1))**(1-(1/xi))+a2;
[7]   @IKC(t+1)   = FF_1{@IKC(t)};
[8]   @IKCa(t)    = a1*((1+g)*inv(t)/k(t-1))**(-1/xi);
[9]   @IKCa(t+1)  = FF_1{@IKCa(t)};
# Rates of return
[10]  @rf(t)      = 1/(bettaa*(E(t)|mu(t+1)/mu(t)));
[11]  @r(t)       = @IKCa(t)*(@Fkg(t+1)+(1+@IKC(t+1)-delta)/@IKCa(t+1)-(1+g)*(E(t)|inv(t+1)/k(t)));



%Non-Linear First-Order Conditions++++++++++++++++++++++++++++++++++++++++++++++++++++++
# Insert here the non-linear FOCs in format g(x)=0

[1]   mu(t) - @MUcg(t) = 0;

[2]   mu(t) - bettaa*E(t)|mu(t+1) * @r(t) = 0;

[3]   @Fg(t) - c(t) - inv(t) = 0;

[4]   (1+g) * k(t) - (1 + @IKC(t) - delta) * k(t-1) = 0;

[5]   LOG(z(t)) - rho * LOG(z(t-1)) - eps(t) = 0;


%Steady States [Closed Form]+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
None


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


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


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


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