Little question about Bayesian Estimation

[marco_dp]

Hi all,

I have 2 little questions about Bayesian estimation on dynare:

1) I am trying to estimate a large scale model (similar to QUEST III or NEMO): often, in this class of models, it is very difficult to compute the mode and the Hessian is close to be singular and cannot be inverted. My question is: using a larger set of observable variables can help dynare in computing the mode and solving the error on Hessian inversion?

2) In order to avoid stochastic singularity it is required to have a number of shocks at least equal to the number of observable used to perform the estimation. What happen if I need to estimate a number of shocks larger than the observable set? Are the parameters estimated robust?

Thanks in advance for the answers and suggestions.

[jpfeifer]

There are no general answers for your questions.

1) It depends. If more observation provide the likelihood with a better shape, the answer might be yes. But there is no guarantee that this will help. Rather, if your data is measured with a lot of noise or you add a data series for which the model is misspecified, it might even increase your problems.

2) Having more shocks than observables is no problem as long as the parameters you are estimating (including shock variances) are still identified. Concerning robustness, I would tend to say no. Only when adding shocks with true variance 0 should the estimates be unaltered. To see this, consider a data-generating process with TFP and government spending shocks. Estimating a model without allowing for government spending shocks means estimating a misspecified model. That misspecification will influence your parameter estimates. How big the problem is cannot be answered in general.

[marco_dp]

Dear jpfeifer, thanks a lot for your useful comments!!!