# Shock equations for model written in their non-linear form

Dear dynare users,

I have a question regarding the shock equations for model written in their non-linear form (so that dynare does the linearization job).
I have downloaded the Adolfson et al. 2005 code written in dynare by Schmidt (already in its linearized form). I have tried to replicate the same model on my own but this time by writing the equation in their non-linear form and ask dynare to make the first order approximation. I then compared the results for both models. I think I have everything correct except that the size of some shock does not correspond. When I look at IRF of the non-linearized model, some correspond exactly to the linear one while some other correspond in shape, but not in size.
My conclusion is that I failed to write the shock equation. I take the consumption preference shock to illustrate. What the original code does is
ZETA_C=rho_zetac*ZETA_C(-1)+epsilon_zetac;

While in my code I have tried
ZETA_C = rho_zetac*ZETA_C(-1) + (1-rho_zetac)*zeta_c + epsilon_zetac;

As well as
log(ZETA_C) = rho_zetac*log(ZETA_C(-1)) + (1-rho_zetac)*log(zeta_c) + epsilon_zetac;

where zeta_c is steady sate of ZETA_C.

And we both define the shock as
var epsilon_zetac;
stderr 0.157;

But we end up with different IRF (same shape, different size). I’m doing something wrong?

With best regards,
Jolan

Without seeing how those variables enter the actual equations, it is hard to tell. One general question: did you write down the model for linearization or log-linearization (putting everything in exp())? If not, the latter may explain the different sizes.

Thank you for your answer. I did not use the exp. In particular, the FOC in the households’ problem w.r.t consumption reads

ZETA_C/(C-bC(-1)/MU_Z) - betabZETA_C(+1)/(C(+1)MU_Z(+1) - bC) - PSI_ZGAMMA_CD*(1+TAU_C) = 0;

Does it mean that my model is written for linearization? And how should i interpret my shock size in this case?
With best regards,
Jolan

Yes, your model is written for linearization. Thus, your IRFs are the absolute deviations from steady state, not the percentage deviations. E.g. if the SS of C is 2 and the IRF is 0.2 in period 1, this is a 0.2/2=0.1=10% deviation from steady state. If you put

as an additional line to your model, log_C will give you the IRF in percentage deviations.

Thank you for your reply. I have updated my dynare file following your advice and now I think I have the percentage deviations from steady state. But there are still some shocks that give IRFs with different scales and I can’t find why. Here I have posted the 2 mod files (as well as the m files calling them and making the plots of the IRFs) because I could have forgot to mention something worth. With best regards,
Jolan