Steady state is found but other problems occur

Stochastic simulations
1

ModeloConTransfer.mod (5.1 KB)

Hi. I have coded my model with Dynare and it works perfectly. Now I want to extend my model by adding an equation to this model that transforms the interest rate r* from a parameter to an endogenous variable. This way, the interest rate is forced to depend on the savings from the consumer’s budget constraint. It could be any equation, I tried to use the relation r*= savings^kappa, kappa is a constant. I got steady state results. However, I got the following error: Error using print_info (line 51) The Jacobian matrix evaluated at the steady state contains elements that are not real or are infinite.
Also, if I run model_diagnostics(M_,options_,oo_), it says

MODEL_DIAGNOSTICS: The Jacobian of the dynamic model contains imaginary parts. The problem arises from:

Derivative of Equation 21 with respect to Variable sav (initial value of sav: -1.14818)

MODEL_DIAGNOSTICS: The problem most often occurs, because a variable with
MODEL_DIAGNOSTICS: exponent smaller than 1 has been initialized to 0. Taking the derivative
MODEL_DIAGNOSTICS: and evaluating it at the steady state then results in a division by 0.
MODEL_DIAGNOSTICS: If you are using model-local variables (# operator), check their values as well.

Could you advice me how to solve this problem?

2

You have

rstar = sav^kappa;

where sav is negative in steady state and kappa is a fraction. So you are taking a root of a negative number, which is not allowed.

3

Thank you very much. It was very helpful.

4

Dear Jpfeifer

Sorry for disturbing you again. I changed the previous equation of the interest rate to r* = (1/beta)(Savings(+1)/Savings)^kappa and the program works correctly. In order to have a more logical equation of the interest rate I would like to use a very similar equation to the one mentioned above which is: 1+r (rather than r*) equalized to (1/beta)(Savings(+1)/Savings)^kappa, i.e., 1+r = (1/beta)*(Savings(+1)/Savings)^kappa. But in this case I get the following error:

Blanchard Kahn conditions are not satisfied: indeterminacy.

Also, if I run model_diagnostics(M_,options_,oo_), it says

MODEL_DIAGNOSTICS: The singularity seems to be (partly) caused by the presence of a unit root

MODEL_DIAGNOSTICS: as the absolute value of one eigenvalue is in the range of ±1e-6 to 1.

MODEL_DIAGNOSTICS: If the model is actually supposed to feature unit root behavior, such a warning is expected,

MODEL_DIAGNOSTICS: but you should nevertheless check whether there is an additional singularity problem.

MODEL_DIAGNOSTICS: The presence of a singularity problem typically indicates that there is one

MODEL_DIAGNOSTICS: redundant equation entered in the model block, while another non-redundant equation

MODEL_DIAGNOSTICS: is missing. The problem often derives from Walras Law.

My question is why it works with the former equation and it doesn’t work with the latter one?

ModeloRCrediticia.mod (5.1 KB)

5

You did not explain the difference between r and r*

6

Sorry, I meant 1+r* = (1/beta)(Savings(+1)/Savings)^kappa.

i.e., no difference between r and r* in my previous message.

7

You need to check your model. Maybe there is still a timing problem somewhere.