solve and estimate model with "infinite steady states"

[ZBCPA]

Dear Johannes Pfeifer,

Could I ask if dynare can solve and estimate global indeterminacy model with "infinite steady states"?

Thanks in advance,
Huan

[jpfeifer]

What exactly do you have in mind? A model with a unit root is one with infinitely many steady states, but Dynare can handle them.

[ZBCPA]

What exactly do you have in mind? A model with a unit root is one with infinitely many steady states, but Dynare can handle them.

Many thanks for your reply.

I just saw a JET 2008 paper "Imperfect competition and indeterminacy of aggregate output".

The global indeterminate benchmark model has a continuum of steady states determined by the value of the marginal cost. When I tried to replicate the irf figures ,Dynare shows "Impossible to find the steady state. Either the model doesn't have a steady state, there are an infinity of steady states,or the guess values are too far from the solution". I have no idea how to handle it . Could you please give me some hints?

Kind regards,
Huan

[jpfeifer]

In models with an infinity of steady states, you cannot obviously not use the numerical solver to solve for the steady state as it cannot be endogenously determined. You need to use a steady state file to select one.

[ZBCPA]

In models with an infinity of steady states, you cannot obviously not use the numerical solver to solve for the steady state as it cannot be endogenously determined. You need to use a steady state file to select one.

Many thanks.

I log-linearized the model using pencil and paper then use steady_state_model block where I set each variable =0; then the result shows that Blanchard Kahn conditions are not satisfied: indeterminacy.I am not sure if this is right since the model is indeed a global indeterminate model. Unless using Farmer's JEDC 2015 paper's method to define a new sunspot, such model can not be solved.

Could you please give me some hints?

Kind regards,
Huan

[jpfeifer]

I am not sure I am following. Are you talking about a replication of Wang/Wen (2008): "Imperfect competition and indeterminacy of aggregate output"? In that paper, the sunspot introduced seems to assure "determinacy" of the model (but not determinacy of the endogenous variables of the model as you need to introduce and extraneous shock to determine them).

[ZBCPA]

I am not sure I am following. Are you talking about a replication of Wang/Wen (2008): "Imperfect competition and indeterminacy of aggregate output"? In that paper, the sunspot introduced seems to assure "determinacy" of the model (but not determinacy of the endogenous variables of the model as you need to introduce and extraneous shock to determine them).

Really appreciated!

Yes, I am replicating that paper, especially the impulse responses to a sunspot shock (fig 1 in the paper) but get stuck since the Blanchard Kahn conditions are not satisfied: indeterminacy.

Could I ask the difference between "determinacy of the model" and "determinacy of the endogenous variables of the model" ?

I also attached the code for benchmark model. At least the model block and calibrations in this code are all right. Could you please give me some hints on the right way to replicate the irf in the paper ?

Kind regards,
Huan

[jpfeifer]

You should work with the nonlinear model in equations (23)-(30) of the paper. I don't have time to check your linearizations and steady state computations.