Using empirical probability distribution for exogenous variables

[skumar]

Hello,
I am working with a income fluctuation problem where I have inflation as one of the exogenous variable.

1. I wish to use an empirical probability distribution for inflation instead of an AR(1) setup with normal random errors. Is there a way to implement this in dynare?
2. Is it at all possible to have random values follow a non-normal distribution?

Thanks for the help!

[jpfeifer]

See

Stochastic Simulation based on Non-Normal Shocks

The problem is not really that Dynare does only support normally distributed shocks but that perturbation is used to solve the models and up to first order, only the mean and the variance of the shock distribution play a role. Thus, even a beta distribution is effectively approximated with a normal distribution for computing the model solution, because the distribution is fully characterized by its first two moments. A limitation of Dynare currently is that it does not allow for skewed distribut…

Drawing from non-normal distributions(uniform)in simulation

At first order, you have to change line 83 of the simult.m in the Dynare/matlab folder, which reads DynareResults.exo_simul(:,i_exo_var) = randn(nxs,DynareOptions.periods)'*chol_S; to something like DynareResults.exo_simul(:,i_exo_var) = 2*(rand(nxs,DynareOptions.periods)-0.5); Due to certainty equivalence, it does not matter that the shocks you are drawing now have a different standard deviation than is used for computing the decision rules. At higher order, this approach …

[skumar]

Thanks for your reply. My understanding from following the threads is that by changing the simult.m file non normal shocks can be incorporated in Dynare. However you talk about how this approach would be not correct at higher order. https://forum.dynare.org/t/drawing-from-non-normal-distributions-uniform-in-simulation/4966?u=skumar
I am currently using third order perturbation to solve my model. All the shocks in my models are independent of each other. Could you elaborate on the issues or the correct way to go for third order models?

Thanks again.

[jpfeifer]

The computation of the decision rules in Dynare is based on the moments of the distribution of exogenous shocks. At second order, what matters are the mean and variance, at third order also the skewness. Dynare takes the mean and skewness of the distribution to be 0 and you specify the second moments, the variance in the shocks-block. Using a normal distribution for your shocks with the specified variance is obviously consistent with these moments. If you now use a different shock distribution, you still need to stay consistent this these specifications. For example, using a skewed shock distribution would be wrong.

[skumar]

Thank you for the clarification.