I was wondering how I might go about specifying non-normal distributions for my shocks. For example, some of the variables in the model are financial returns and I’d like for the distributions of the shocks to these variables to have excess kurtosis.

I think that you have a good idea, thank you for that! In order to get another distribution than normal, you can use the following transformation:

You want to simulate the variable x. First, define the exogenous variable y with std = 1. That means, y ~ N(0,1). Let U(y) be the cumulate distribution of N(0,1) and let F(x) be your desired cumulative distribution. We want to generate x using the variable y. Thus we have

F(x) = U(y),

or equivalently

x = F^{-1} ( U(y) ),
x = (F^(-1) o U) (y).

The function U can be find in Matlab, only you need to know is the inverse cumulative distribution of your variable x.

Regards,

Pavel

PS. Can you introduce me little bit into what you are working on?