# 1st order vs. 2nd order Bayes estimation

Hi,

I’ve got complicated model that I would like to estimate using 2nd order approximation but it seems that it is not very possible as in order to get steady state values I need to solve quadratic equation (I’ve also done it, but I am not sure whether it is possible to “put” this into MATLAB as .m file as one root is complex number).

I was wondering if I estimate the model using 1st order approximation (I’ve done it) and get the parameter estimates, can I use those parameter estimates for the 2nd order approximation of the model and, let’s say, obtain impulse responses, variance decomposition etc.
How different are the parameter estimates for 1st order and 2nd order approximations of the model?

Cheers,

Sigitas

Hi Sigitas,

With Dynare it is not (yet) possible to estimate a DSGE model considering a second order approximation. The Kalman filter used to evaluate the likelihood (posterior kernel) is for linear(ized) models. So to estimate a 2nd (or k, with k>1) order we would need to rewrite a more general kalman filter routine (the problem is not related to the deterministic steady state which does not depend on the order of approximation).

Obviously you can estimate the (deep) parameters of a model with a first order approximation and compute IRFs associated with the second order approximation. If you write:

``stoch_simul(order=2,irf=20) Y C I ;``

after the estimation command you will obtain IRFs with the second order approximation of the model, where the deep parameters are set at the posterior mode or the posterior mean (if you did not use the option mh_replic=0 in the estimation command). Note however that if the variance of the shocks are too big, the IRFs may diverge with the second order approximation.

We do not know, a priori, the difference between the estimates obtained with a first order approximation and the etimates we would obtain with a second order approximation. We can think of examples where some parameters cannot be identified with a first order approximation but where these parameters can be identified with a k>1 order approximation. So the difference can be important.

Best,
Stéphane.