Indeterminacy,rank condition and BK condition

Stochastic simulations
1

Hi,

  1. What is the relationship between the rank condition and the BK condition?

  2. Does indeterminacy mean both rank condition and BK condition do not satisfy? or either one of them can cause indeterminate model?

  3. In the literature of Sunspot equillibria, “indeterminacy” mean BK condition fail or rank condition fail.

Thanks

2

The BK conditions, as formulated in Dynare, is explained in these slides. Indeterminacy means that you have more stable eigenvalues than state variables. In this case, there is no unique choice for the decision variables (hence the name).

Best,
Stéphane.

3

Thanks for your quick reply.

My model includes externalities. I analytically solve the condition for determinacy of my model.

However, when I want to check my analytical condition for determinacy with dynare, they do not match.

For example, my analytical result shows for given parameter values, externalities need to be greater than 3 to have determinacy of the model.

However, when I ran the program in dynare, for externalities greater than 3.9 the model run.

Also, For the value of 2.7-3.8 it shows error that the steady state can not find ( not all residuals are zero).
For less than 2.7 it shows indeterminate (though steady states are calculated ).
For greater than 3.9 model runs good.

I am not sure what is the problem. Can you give some advice where the problem may come from?

4

Without knowing the details of the model, it is difficult to help. I don’t understand what you mean by externality greater than 3. Also I suppose that if you are able to establish such condition, you should have a closed form solution for the steady state, but from what you say I have the impression that you do not use this information. If the numerical solver finds another steady state than the one you had in mind, this may explain the difference between the results you expected and the results you find with Dynare. Obviously we can think of more trivial explanations (an error in the coding of the model in Dynare, or an error in your maths).

Best regards,
Stéphane.

5

By externalities, I mean a parameter. From my analytical result, I know this parameter “externalities” need to be greater than 3 for determinacy.

But when I run the model in dynare, it shows for “externalities”>3.9 , the model is determinant.

I use the closed form solution for steady state in dynare.

For "externalities " between “2.7-3.8”, it can not solve the steady state. But above 3.9 it does.

Does it mean I type the model wrong? If I do, why the model gives good result after 3.9 cut-off points?

6

Yes , it probably means that your coding of the model in Dynare or that your analytical results about indeterminacy/determinacy conditions are wrong. Cannot say more.

Best regards,
Stéphane.

7

Thank you. I will recheck my code agian