Dear Dynare users,

I would really appreciate your help on the following issue. Let me tell you in advance that I have tried to follow and understand a couple of threads on this point, but I have not succeeded: I am not sure that I can use them for the problem that I am trying to solve.

This is the question briefly exposed: a model of tax evasion in which tax payers face a positive probability of being audited at time t+1. If they are audited, their tax returns for the income declared at time t will be revised. And, in case of tax fraud, tax payers will suffer a penalty which will be a function of the evaded income/taxes. In short: at time t individuals form expectations about a random variable realized at time t+1

i) which can take only two possible outcomes, and

ii) which in turn depend on the choice previously made at time t.

I am perfectly aware that this deviates from the standard macro models usually solved with Dynare. Still, can Dynare be used to deal with this kind of set-up? If so, how?

Thanks in advance,

Cruz

Without knowing the details, it is hard to tell. But a priori it sounds not possible without using some tricks. You seem to be interested in stochastics. Dynare’s stoch_simul command approximates shock distributions using mean and variance, essentially turning them into normal distributions.

The second issue seems to be state dependence in the form of a discrete indicator variable. This again results in problems with continuous Taylor approximations.

The third issue may be keeping track of the distribution of who got audited. Unless you have some law of large numbers kicking in, you need to keep track of the distribution, requiring something like Krusell/Smith.

Dear Johannes,

First of all, thanks a lot for your immediate response. Actually I was expecting it: you seem to be deeply committed with Dynare forum; and, by the way, also with the resources that you post on your web page. Unfortunately, your response seems to bring bad news. I will try to fully understand your reply. In the meantime, if you still were willing to rethink about it, I would be willing to send you (or post) an attachment: I do not know which is most convenient option. If not, that would be fine. I would perfectly understand it and try to seek a solution in some other direction.

Once again, thanks.

Cruz

You can send it to me per email, but I cannot promise I will find time to look at it considering other commitments I have.