Decision Rules in Dynare++ and Normal Disturbances

[amfasolo]

Hey all,

I have a question about the transition rule computed by Dynare++. On page 9 of the tutorial, there is a claim that Dynare++ assumes that exogenous shocks (u_t) are serially independent and Normally distributed: u_t ~ N (0, SIGMA). However, it doesn't seem that the literature, when presenting perturbation methods, assume that shocks are Gaussian. As an example, Schmitt-Grohé and Uribe (2004) (link: http://www.columbia.edu/~mu2166/2nd_order/2nd_order.pdf), page 758, claim that the disturbance must "have a bounded support and to be independently and identically distributed, with mean zero and variance/covariance matrix I." It does not imply Normal shocks, but only iid disturbances.

I would like to know where, exactly, in the transition rule computed by Dynare++ the assumption of Gaussian errors kicks in, and how the transition rule would change if Non-Gaussian disturbances were assumed.

Thanks in advance,

Angelo

[SébastienVillemot]

It makes a difference for higher order approximations (i.e. at order 3 and above). Basically the point is that when you make an approximation to order n, you need to know the moments of the shocks distribution up to order n.

By assuming that shocks are normal, Dynare++ makes a simplifying assumption for all moments. As far as I know, Dynare++ does not exploit the specific shape of the Gaussian distribution, just its moments at order 3 and above (since variance is directly given by the user).

An alternative design of Dynare++ would have been to require the user to input all moments up to order n when requesting a approximation at order n, but this was deemed to complicated an approach.

[amfasolo]

Hi Sebastien,

Back to the same topic, and given your reply (thanks for that, I really appreciated it), is it possible to assume that shocks have an independent iid Student-t distribution (skewness = 0 for 3 or more degrees of freedom) and use Dynare++ in a 3rd order approximation? In this case, third moments seems to be the same as assuming the model with Gaussian shocks.

Thanks in advance,

Angelo

[SébastienVillemot]

If the first, second and third moments of that distribution are the same than for the standard Gaussian (I did not check) then the answer is yes.

[amfasolo]

Thanks for the reply, Sebastien!

Best,

Angelo