Question on MCMC and MDD

[fuyangzhao]

Hi Professor,

We know that Dynare is sometimes inefficient in estimating posterior modes of parameters by Bayesian method. Now I have some accurate posterior modes in hand, can I skip the estimation stage and directly use the accurate posterior modes for MCMC and to get marginal data density or log data density?

Thanks and best wishes!

[jpfeifer]

What do you mean with

inefficient in estimating posterior modes

Either you found a mode or not. If you have information on the mode, you can actually provide that mode as starting values for the MCMC (e.g. using an estimated_params_init-block) and then use

Code: Select all

mode_compute=0

to avoid triggering another round of mode-finding (although that might be a good check on your provided mode)

[fuyangzhao]

What do you mean with

inefficient in estimating posterior modes

Either you found a mode or not. If you have information on the mode, you can actually provide that mode as starting values for the MCMC (e.g. using an estimated_params_init-block) and then use

Code: Select all

mode_compute=0

to avoid triggering another round of mode-finding (although that might be a good check on your provided mode)

Thanks Professor!
In the paper Land-price dynamics and macroeconomic fluctuations, the author has aruged that dynare fails to find the posterior mode with its various built-in optimizing methods. So I said "inefficient".

And I have other questions. One is that after estimation, in which method does dynare compute log data density? In the paper Land Price and Unemployment, the authors gave MDD by three different methods (see the attachment

MDD_jme_LMZ.pdf

(261.75 KiB) Downloaded 46 times

), SWZ, Mueller, and Bridge. Which does dynare uses?

Another question is that, in Table 3 of the same attachment, does the "mode" means the value of object functions?
Thanks for your help!

[jpfeifer]

1. Since they wrote the paper, some powerful mod-finders have been added to Dynare. Particularly,

Code: Select all

mode_compute=9

works really well even in the presence of local modes. But of course, finding global modes is hard.

2. Dynare will report both the Laplace approximation and the Geweke modified harmonic mean estimator. The ones used in that paper are not supported (yet)

3. Yes, mode here means the value of the objective function (i.e. the posterior density) at the mode.