Behavioral New Keynesian Model

[Elle211]

Dear all,
I'm new in Dynare and I'm currently trying to simulate a personal behavioral model.
The model is totally backward looking since I have written simply heuristics for any expectations.
The problem is that any utility function Z,V and U has always calculated equal 0.
This happens for each one, apart from V which is the only one that doesn't include past values.
For this reason, I'm sure that the problem concernes past values of pi, g and a, but I don't understand why Dynare works out, for example:
g(-1)-g(-2)=0,
when g(-1) should be the value of g one period ago, and g(-2) should be a value of g two periods ago, and hence different values.
Moreover, it seems very strange to me that the weights of forecasters could be negative when they are calculated as a ratio between exponential functions.
I have attached my file.mod.
I hope in your answer and I thank you.
Best,
Alessandro

[jpfeifer]

You need to try to better understand your model and what is going on in it.
Consider

Code: Select all

[code]U_ext_g=varrho*U_ext_g(-1)-(1-varrho)*(g(-1)-g(-2))^2;                                   // 31. Utilità estrapolatori spesa pubblica     
[/code]

The term that is supposed to change utility is the last one. The first order Taylor approximation around the steady state is
(1-varrho)*2*(bar g -bar g)*(ghat1+ghat2)
The second bracket evaluates to 0 so there is no first order effect of g on utility. I presume this is what drives the results.

[Elle211]

Dear jpfeifer,
thank you so much for your answer.
I agree with your point of view and what you describe is exactly what happens when I try to simulate my model.
According to me, the problem is that the behavioral model shouldn't be linearized by Dynare in order to work effectively, but I suspect that it is impossible, it isn't?
Trying to solve such a issue, I have added a very small constant in each utility function, in this way they are always different by zero. In your opinion, is it a good solution?
Anyway, the fact that Dynare linearizes equations with exponential function, cause me to sometimes obtain negative values for the weights of the forecasters, and a similar result is totally a nonsense.
So far, I haven't been able to work out this problem.
I hope you will help me.
Thank you.
Best regards,
Alessandro

[jpfeifer]

You need to understand the economic reasons behind this result. It is well known that first order approximations to the welfare function are not sufficient (see linear-quadratic control problems). But your problem seems to be deeper as even a second order approximation does not help.