multimodal posterior density

[Vermandel]

Hello,
I've got something strange regarding posterior distributions of parameters. I estimate a 2 country model with cross border loans under different scenario. One of the scenario has some quite strange results concerning the productivity shock as you can see in the picture. I run 350k MH iterations and neglict the 1st half of the sample. I solved this by reeastimating from scratch the model but by curiosity i'd to know why this kind of multimodal posterior density comes up.

[jpfeifer]

It looks like you chain has not converged yet. Plot the draws and see whether you see a trend. If yes, put more effort into the mode computation.

[reubenpjacob]

Yes, finding a well-behaved hessian at the mode will definitely alleviate the problem. you also probably noticed that the acceptance ratio is not very stable during your MCMC?
Reuben

[Vermandel]

thanks you for your responses jpfeifer and reubenpjacob.

Yes reubenpjacob you're right, the acceptance ratio is not stable at all during MCMC.

I'd like to know how this can be solved up. There shouldnt be a trend in my data (i used a linear trend and variables are per capitae). From your advices jpfeifer, I run a diagnostic Brooks Gelman MCMC diagnoctics and there some problem convergence (see the picture). I suppose to solve this I need to change the value of mh_jscale=0.20 to an higher value (a value of 0.6 solves it). In dynare manual it's written that the default value (0.2) is rarely satisfactory. This option must be tuned to obtain, ideally, an acceptation rate of 25% in the Metropolis-Hastings algorithm. Is there any way to get a kind of optimal value of mh_jscale (or get close to this optimal value) ?

[jpfeifer]

You could try a very intensive run of mode_compute=6. Alternatively, try using mode_compute=9.

[reubenpjacob]

yes, mode_compute= 8 or 9 usually gives good estimates of the Hessian at the mode.
reuben