IRFs do converge, but not to the steady state

Dear all,

I tried a model with money. I assume that the government control the growth rate of nominal bond purchasing by printing money. The BK condition is satisfied. Though the IRFs converge, they does not converge back to the steady state, but back to some other level. What does this imply? Something wrong or multiple steady state?

Thanks in advance.

Check whether your model has a unit root. Use

to see if there is a unit eigenvalue. If yes, you need to think about the economic intuition why this happens.

Thank you professor,

Yes, there is indeed an engenavlue equal to 1. Attached is the mod. What does this mean? Does it mean that the steady state is unstable? Or the results are wrong? How to fix or avoid it? Is there any paper or book discusses this problem?

I think the problem comes from the money growth rule or bond growth rule that I use. Since the nominal money or nominal bond does not have steady state, the government can only control the growth rate of the nominal variable, i.e.
g_t=log(nominal M_t)-log(nominal M_{t-1})=log(real M_t)-log(real M_{t-1})+log(inflation_t), by rearranging, we have
log(real M_t)=log(real M_{t-1})-log(inflation_t)+g_t,
which is a unit root process.

Is this money supply rule standard in the literature? If so, then this problem should be popular. Could you please correct me?

allowtax_steady_state_helper.m (414 Bytes)
tran.mod (4.12 KB)

That may well be the reason. It is well known that the price level in many monetary models features a unit root, i.e. while inflation is uniquely determined, the same is not true for the price level and thereby nominal bonds. This is an economic feature of the model.