BK condition, rank condition

Hi Professor Pfeifer,

I apologize that I’ll bring out an old problem “Blanchard Kahn conditions are not satisfied: indeterminacy due to rank failure”, but i still not sure how to fix the attached code after reading the forum archives.

The rank is deficient. Since the model has an unit root, the “model_diagnostics(M_,options_,oo_)” always detects collinearity.

Thanks very much!
test.mod (2.94 KB)

It could be a problem with the two bond stocks. See [Timing of capital in two sector economy)

Thanks professor Pfeifer!

I haven’t found a problem for the bond stocks. I’ll keep an eye on it.

  1. I find the BK condition and rank condition are very sensitive to the value of phi_T and z in the .mod file I posted. The large phi_T and z will lead to both BK and rank failure. Small phi_T and z will lead to BK ok but rank failure.

  2. I wonder if it’s possible to write down the matrix by hand and look at how the coefficients are related to the rank deficiency. If so, do you have any materials about how to write down the matrix? The original paper by BK? Thanks!

  1. This suggests that there is a fundamental modeling problem present. It seems (at least) two of the variables in your model are only jointly determined, but not separately. You need to find out which ones. Are you for example sure that consumption of the two agents is uniquely determined in your setup? It could be that the aggregate movements of the variables are unique, but not their split.

  2. That is usually impractical, because the mapping from these matrices back to the model economics are intractable.

[quote=“jpfeifer”]1. This suggests that there is a fundamental modeling problem present. It seems (at least) two of the variables in your model are only jointly determined, but not separately. You need to find out which ones. Are you for example sure that consumption of the two agents is uniquely determined in your setup? It could be that the aggregate movements of the variables are unique, but not their split.

  1. That is usually impractical, because the mapping from these matrices back to the model economics are intractable.[/quote]

  2. I think that consumption variables are pinned down, at least in the steady state. I’ve assigned the C_ratio between the two agents’ consumption in steady state, and the Y_ss is fixed and unrelated to the C_ratio. This will pin down the steady state consumption and labor (because of the real wage decision) for each type.

  3. A separate question. If I cannot calibrate the model, will it work that I give the prior of some parameters and estimate the model? Is the calibration success necessary for the success of Bayesian estimation of the linearized model?

Thanks!

[quote=“jpfeifer”]1. This suggests that there is a fundamental modeling problem present. It seems (at least) two of the variables in your model are only jointly determined, but not separately. You need to find out which ones. Are you for example sure that consumption of the two agents is uniquely determined in your setup? It could be that the aggregate movements of the variables are unique, but not their split.

  1. That is usually impractical, because the mapping from these matrices back to the model economics are intractable.[/quote]

  2. I think that consumption variables are pinned down, at least in the steady state. I’ve assigned the C_ratio between the two agents’ consumption in steady state, and the Y_ss is fixed and unrelated to the C_ratio. This will pin down the steady state consumption and labor (because of the real wage decision) for each type. If the spilt is undetermined, then the steady states will be undetermined. Not sure this argument is reasonable or not.

  3. A separate question. If I cannot calibrate the model, will it work that I give the prior of some parameters and estimate the model? Is the calibration success necessary for the success of Bayesian estimation of the linearized model?

Thanks!

  1. Indeterminacy is not about the steady state, but about the dynamics around this steady state. Having C determined in steady state is necessary but not sufficient.
  2. If you are not able to find a calibrated version of the model that works, estimation will typically not work as well as it introduces additional complications.

[quote=“jpfeifer”]1. Indeterminacy is not about the steady state, but about the dynamics around this steady state. Having C determined in steady state is necessary but not sufficient.
2. If you are not able to find a calibrated version of the model that works, estimation will typically not work as well as it introduces additional complications.[/quote]

1.The .mod attached in previous posts is wrong because I assigned the ratio of each type’s steady state consumption instead of calibration. I recalculate the equations. I find that the steady state of each type’s consumption isn’t determined, nor are the dynamics. Furthermore, the indeterminacy holds for any parameterization. I need to rewrite the model.

  1. I see. Thanks!

Actually, I was wrong as well. Having determinacy of the steady state is not required. In case of a unit root, the steady state will not be unique, but you can get unique dynamics around any steady state you pick.

Sorry, I’m confused with "In case of a unit root, the steady state will not be unique, but you can get unique dynamics around any steady state you pick."
Does it mean that the mod file attached in the first post is workable if I pin down a steady state?

No, not necessarily. All I was saying is that there are cases where due to a unit root, you need to select one of the infinitely many steady states and then dynamics around this steady state will be determinate. But there can be cases where that is not true. There is indeterminacy in both the steady state and the dynamics. Your problem seems to fall into the latter category (but I am not 100% sure).