Dear Johannes,

Many thanks for this. I think that I finalized the codes with your help. Does this model gives me non-stationary log-level variables to use in VAR? I think the answer is yes but I just want to confirm with you

that I defined the variables correctly in below.

var c k y B h A y_h i w r g_A g_B log_y log_h log_y_h;

varexo eps_a eps_b;

parameters delta psi alpha beta ;

% Parameter Values

beta = 0.95;

psi = 0.33;

alpha = 0.68;

delta = 0.07;

Model;

y = k(-1)^(1-alpha)*exp(eps_a+eps_b)^(alpha-1)**h^alpha;*

g_A=eps_a;

g_B=eps_b;

log(A)=log(A(-1)) + eps_a;

log(B)=log(B(-1)) + eps_b;

r = (1-alpha)(y/k(-1))*exp(eps_a+eps_b);*

w= alpha(y/(hB)); %7

c^(-1)= exp(eps_a(+1)*eps_b(+1))^(-1)**beta*c(+1)^(-1)(1+r(+1)-delta);

h^(1/psi)*B^(-1) = c^(-1)*w; %9*

y_h = y/(hB); %10

c + k = y + (1-delta)*k(-1)*exp(eps_a+eps_b)^(-1);

i = y-c;

// use logarithm to get variables in percentage deviations

log_y=log(y);

log_h=log(h);

log_y_h=log(y_h);

end;

steady_state_model;

A=1;

B=1;

r=(1/beta)-(1-delta);

y_k=r/(1-alpha);

k_y=(1-alpha)/r;

i_y=(1/y_k)*delta;*

c_y=1-i_y;

h= (alpha1/c_y)^(psi/(1+psi));

k=((h^alpha)/y_k)^(1/alpha);

y=k^(1-alpha)*h^alpha;*

c=c_yy;

i=i_y*y;*

y_h =y/h;

w=alpha(y_h);

log_y=log(y);

log_h=log(h);

log_y_h=log(y_h);

end;

shocks;

var eps_a; stderr 0.01;

var eps_b; stderr 0.01;

end;

resid(1);

steady;

check;

stoch_simul(order=1, periods=1000,drop=960) y h y_h;

// Rebuild non-stationary time series by remultiplying with A_{t} and B_{t}

log_A_0=0; //Initialize Level of Technology at t=0;

log_B_0=0; //Initialize Level of Technology at t=0;

log_A(1,1)=log_A_0 ; //Level of Tech. after shock in period 1

log_B(1,1)=log_B_0; //Level of Tech. after shock in period 1

// reaccumulate the non-stationary level series

for ii=1:options_.periods

```
log_A(ii+1,1)=log_A(ii,1)+g_A(ii,1);
log_B(ii+1,1)=log_B(ii,1)+g_B(ii,1);
log_y_nonstationary(ii+1,1)=exp(log_y(ii,1)+log_A(ii,1)+log_B(ii,1));
log_h_nonstationary(ii+1,1)=exp(log_h(ii,1)+log_B(ii,1));
log_y_h_nonstationary(ii+1,1)=exp(log_y_h(ii,1)+log_A(ii,1)+log_B(ii,1));
```

end

Many thanks,