Specifying a process (Bernoulli Trial and normal)


I am finding trouble to specify a process that evolves like a Bernoulli trial where:

z = z(-1) with probability p and z = s with probability 1-p, given that s ~ N(0, var_s)

Does anyone know how to deal with it?

Thanks in advance


I am afraid this won’t work in Dynare. At time t, there is seems to be a discontinuity here, depending on the realization of z. Hence, you most probably cannot rely on a continuous approximation to z.

My aim is to simulate the IRF with shocks that follow the process mentioned above.

I think that maybe one possible implementation would be to generate a series of such process and then ask Dynare to simulate the model for each observation.

How can this be done since it seems that shock definition is restricted to std dev from a normal distribution?

thanks in advance

I am not entirely understanding what your suggested approach is, but I will try to provide a few comments. You can simulate the model solution of the linearized standard model using the simult_ function, see e.g. [Normal AND Non-Normal Random Variables)
What you have to ask yourself is whether your model solution from the linearized model is correct. First of all, the model needs to be differentiable. If that is the case, Dynare approximates any shock distribution by the first two moments, i.e. effectively a normal distribution. However, at first order, we have certainty equivalence. Thus, the variance of the shock process does not matter (as do higher order moments). Rather, only the mean matters. Thus, you can basically use any shock distribution, but you need to be aware that by construction, the higher order moments will not affect the solution.