Model simulation with unit root

[Zhirong]

Dear SébastienVillemot/Michael,

I have searching in the forum for posts about dealing with unit root process in a normal DSGE model, but I was a bit confused:

I understand the most appropriate way is to stationarize the model; but it seems putting eg x=x(-1)+iid directly in the model block will also work? Am I right?

If so, can i see that a unit root without drift is a special case which dynare can solve without stationarizing the model?
I also notice dynare will always give the same steady state though in theory it should change given the unit root process, but My purpose is just to use .ghx and .ghu for simulation so i guess i shall be fine?

Thanks in advance.

Zhirong

[jpfeifer]

Hi,
you are referring to a borderline case in the Blanchard-Kahn conditions. Dynare is able to solve the model and correctly generates the IRFs. However, all IRFs are relative to the old steady state around which the model was linearized. This does in no way imply that this is also the new steady state.

[jojokre]

Dear J. Pfeifer,

I'm working with two-country models with incomplete markets. As I understand, these models generally have a unit root. And, as I also understand, generally, these models have many steady states. Basically, any international debt level yields another steady state. This is also what Schmitt-Grohe and Uribe (2003) stated in their famous paper with respect to the small open economy: "The small open economy model with incomplete asset markets features a steady-state that depends on initial conditions and equilibrium dynamics that possess a random walk component".

So now I wonder what you mean if you say that when variables remain at a new level after a shock, that this does "in no way imply that this is also the new steady state"? I also included a very small example of a two-country endowment model with one international bond. After a positive shock to home endowment, home agents will borrow to foreign agents which takes debt to a new level on which it remains untill a further shock. Home consumption will remain at a slightly higher and foreign consumption at a slightly lower level than before due to interest payments. I would interpret that as a new steady state. Am I mistaken?

Best regards and thanks in advance,
Johanna

[jpfeifer]

My initial statement seems to be ambiguous. I meant to say that the theoretical steady state usually changes, in your case in the asset position. You cannot assume that this new steady state is identical to the one around which Dynare originally approximated the model. Thus, using the decision rule computed around the old steady state is invalid for simulation as the new steady state will wander arbitrarily far away from the old steady state.