Deviation form steady state

Stochastic simulations
1

Dear Prof. Jpfeifer,
I would like to plot “percentage deviation from steady state” for the IRFs. I have reviewed other posts but I got very confused. I used order 1 : stoch_simul(periods=2100,irf = 100,order =1); percentage deviation from steady state is which one?:
1: 100* oo_.irfs.c_P_epsilon_Eps/oo_.steady_state(7);
or
2: log( oo_.irfs.c_P_epsilon_Eps);
or
3: log(oo_.irfs.c_P_epsilon_Eps/oo_.steady_state(7));

and I have a determisitic model with :
perfect_foresight_setup(periods=203);
options_.simul.robust_lin_solve=1;
perfect_foresight_solver(stack_solve_algo =0);

Is “percentage deviation from steady state” :
100*(oo_.endo_simul(39,:)-oo_.endo_simul(39,1))/oo_.endo_simul(39,1);

I am looking forward to hearing from you
Leo

2

Hello,
I am still waiting for the answer, IS there anybody who knows the answer?
Thnaks

3

That depends on your variable definition. If you defined your variable in logs, the IRF is already in percentage deviations. If the variable is in levels, things are different. Options 2 and 3 are wrong, because the numerator will have a mean of 0 and you cannot take the log of 0. Option 1 is correct, unless your variable has a steady state of 0. To see that option 1 is correct, consider that

X_IRF=X_with_shock-steadystate(X)

Therefore, with option 1 you have

(X_with_shock-steadystate(X))/steadystate(X)

which is the exact definition of a percentage definition.

4

Thank you very much for your time and consideration.
And what about deterministic model? is it percentage derivation of steady state? (All my variables are in level)

100*(oo_.endo_simul(39,:)-oo_.endo_simul(39,1))/oo_.endo_simul(39,1);
5

If you start at the steady state with your simulation, that would be correct. Otherwise, it will be a percentage deviation from the initial point.

6

Thank you so much for your great comment. Yes, I start from the steady state, so there is no problem.
Sincerely,