# 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!

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.