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.