Unbounded density


I use the Dynare 4.5.5 to estimate my DSGE model. There are warnings about unbounded density. However, I am confused that those unbounded densities are all following beta distribution. To my knowledge, beta distribution is bounded between 0 and 1, right?
How can I deal with this problem? Or I just need to change to another distribution, then which distribution is better?


You are talking about the support of the beta distribution. But the density is the “probability” of the value x occurring. If you look at the prior plots, you will see that there is an asymptote at 0 or 1 where the density/likelihood goes to infinity.

Thanks for letting me know this.
Could you please give me a hint on how to deal with this problem. Shall I change a prior or anything else?


Yes, you need to change your prior. Given your prior mean, the prior variance is too big, putting mass into an asymptote.

Dear Prof. Pfeiper,

I read the following comments form your previous post:

“Yes, you need to change your prior. Given your prior mean, the prior variance is too big, putting mass into an asymptote.”

And I change the variance to a small number. But, there was an error immediately. Before I change the variance, the code could run about half and hour, and then showed up an error.The error was:

“Error using chol
Matrix must be positive definite.”

I am confused that why the erroe happended so fast after I changed the variance to a smaller number?

Thank you,

You need to have a look at the mode_check-plots. Maybe the optimizer failed to proceed. Did you try mode_compute=5?

I tried it, but it still does not work. However, Thank you for your advice.

Did you look at the mode_check-plots?

Thank you Prof. Pfeifer for your reply. I read the latest dynare menual about the mode_check. And i wrote the following command:
estimation(optim= (‘MaxIter’,3000),datafile=BayesianData3,xls_sheet=Sheet1,xls_range=B1:K216,mode_compute=6,first_obs=1, presample=4,lik_init=2,prefilter=0,mh_replic=10000,mh_nblocks=2,mh_jscale=0.50,mode_check_symmetric_plots=1,mh_drop=0.2);

But I did not see any plot. Could you tell me if the command that I wrote is correct or not? if not, what is the correct way to write the command?

Thank you,

You only need to add mode_check.

Thank you Prof. Peifer for your reply. I added it to my code, but there was nothing generated. I guess that the code needs to run to a certain point before the command mode_check starts to work. My code ran about half an hour and then stopped due to an error. I am not sure if my guess is correct. I look forward to your reply. Thank you Prof. Pfeifer.

Always provide the entire error message. But the plots should appear before an error can be triggered.

Thank you Prof. Pfeifer. I figured this out. Another question is what the diffrences are when we use different values for mode_compute. What should we consider When we pick the value of mode_compure? Or, the value does not matter as long as the estimation works.

You may find the following slides useful:

Thank you very much for answering my question. Another question is What should we consider when we pick the value of mh_replic. The biggre, the better?

Your only constraint is time. You want to be certain that you are properly sampling from the ergodic distribution. That’s why we check convergence diagnostics.

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Thank you Prof. Pfeifer for answering my question.

Thank you Prof. Pfeifer for providing your slides. It seems mode_compute=6 is a separate catogory. Can we say the value of 6 is the weakest (worst) one for estimation? and the value of 5 is the best one?

When I change the value of mh_replic, the IRFs will also change. Sometimes, a small value, like 10000, will make the IRFs look better (consistent with the intuition), however, a bigger mh_replic makes the IRFs look worse (not consistent with the intuition. Can I just choose the smaller value? Or, why does this happen?

  1. No, you cannot say that. It’s very context dependent and each optimizer has its strengths and weaknesses. mode_compute=6 tends to be slow and inefficient, but rather robust.
  2. That suggests your MCMC has not yet converged and you need more draws.