Steady State transition from initial values

Perfect foresight simulations
1

Hi, I have the following mod code and want to see the transition from the initial values to the steady state. Any suggestions on how to do this? Thank you very much in advance!!

var y c k i l y l w r ;

varexo z;

parameters beta psi delta alpha sigma epsilon;

alpha = 0.33;

beta = 0.99;

delta = 0.023;

psi = 1.75;

sigma = (0.007/(1-alpha));

epsilon = 10;

model;

(1/c) = beta*(1/c(+1))*(1+r(+1)-delta);

psi*c/(1-l) = w;

c+i = y;

y = (k(-1)^alpha)*(exp(z)*l)^(1-alpha);

w = y*((epsilon-1)/epsilon)*(1-alpha)/l;

r = y*((epsilon-1)/epsilon)*alpha/k(-1);

i = k-(1-delta)*k(-1);

//yl = y/l;

end;

   

initval;

k = 9;

c = 0.7;

l = 0.3;

w = 2.0;

r = 0;

z = 0;

end;

steady;

check;

   

simul(periods=2100);
2

If you put steady after initval, you will start at an initial steady state. Given that no shock happens subsequently, there is no transition. See https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Solow_model/Solow_SS_transition.mod for a proper transition exercise.

3

Thank you for the response! I have carried on with my model. The code is the following. I get that the rank condition ISN’t verified. Why can this be?

var c k h u ;

varexo N0;

parameters lambda A kappa beta s v gamma sigma bhat delta;

 

lambda= 1.013;

kappa= 1.014;

beta= 0.25;

s= 0.1;

v= 1.009;

gamma= (log(kappa)/log(v))*(1-beta)-(1-beta);

sigma= 2;

b=(s*kappa^sigma)/(beta*(kappa*lambda-1)+s);

bhat=lambda*b*kappa^(1-sigma);

delta= (1/lambda)*(1/((b/kappa^sigma)^(1-beta+gamma)*kappa^(beta*(1-beta+gamma))*kappa^((-beta+gamma)*(1-beta)))^(1/(1-beta+gamma)))-1;

A=1;

 

model;

(1/(kappa*lambda))*(1+A*k^(beta-1)*(u(+1)*h*N0)^(1-beta)*h^gamma) = (1/bhat)*(c(+1)/c)^sigma;

 

//(1/(k(-1)^beta*(1-beta)*h(-1)^(-beta)*u^(-beta)*(v/delta)))*(k^beta*u(+1)^(1-beta)*(1-beta+gamma)*h^(-beta+gamma)+k^beta*(1-beta)*u(+1)^(-beta)*h^(-beta)*(v/delta)*(1+delta*(1-u(+1)))/v)=(1/bhat)*(c(+1)/c)^sigma;

 

(1/(k(-1)^beta*h(-1)^(-beta)*u^(-beta)*(v/delta)))*(k^beta*u(+1)^(1-beta)*h^(-beta+gamma)+k^beta*u(+1)^(-beta)*h^(-beta)*(v/delta)*(1+delta*(1-u(+1)))/v)=(1/bhat)*(c(+1)/c)^sigma;

N0*c+k*kappa*lambda-k(-1)=A*k(-1)^beta*(u*h(-1)*N0)^(1-beta)*h(-1)^gamma;

 

h=(h(-1)/v)*(1+delta*(1-u));

 

end;

  

initval;

k = 25;

c = 1;

h = 0.89;

u = 0.81;

N0=1;

   

end;

steady;

check;

simul(periods=2100);
4

I can only recommend to recheck all equations, particularly with respect to the timing.

5

Thank you very much!