A questions about inverse gamma distribution in Dynare

Dynare help (legacy posts)
1

Dear all,

I have a question regarding inverse gamma distribution in Dynare. I will greatly appreciate it if you could provide me some clarifications.

Specifically, I am confused by the treatment of inverse gamma distribution in Dynare. For standard deviations, inverse gamma 1 is used in Dynare, which is explained in details on page 5-11 in the attached file written by STEPHANE ADJEMIAN. I assume Dynare treats inverse gamma 1 in the same way as specified in the file. But it seems that inverse gamma 1 in the file is inconsistent with the textbook version such as the appendix of Zellner’s “An Introduction to Bayesian Inference in Econometrics”. Besides, Lubik and Schorfheide (2004, AER) specify the inverse gamma distribution for standard deviation on page 204, which is in the same way as Zellner. Could any of you give me some clarification on why Dynare has a different specification for inverse gamma?

Thank you!

Best,

Bing
DynareDistributions.pdf (293 KB)

2

Hi, could you be more precise what you think the difference is?

3

Hi, please compare the specification of inverse gamma distribution in the two attached files. I found them different, for example the probability density function. As an example, I attached the priors in Lubik and Schorfheide (2004, AER), which are consistent with the specification in the file “Inverse Gamma Distribution.pdf” but not consistent with “DynareDistribution.pdf”. Please take a look and any clarifications are highly appreciated.

Best,

Bing
(Lubik and Schorfheide) 2004 AER Page 16.pdf (105 KB)
DynareDistributions.pdf (293 KB)
Inverse Gamma Distribution.pdf (103 KB)

4

Dear Johannes,

Do you have any idea on the question I posted a few days ago? I would appreciate it very much if you could please shed some light on it for me.

Thanks a lot!

Best,

Bing

5

As far as I can see, the difference is that the document by Stephane Adjemian follows Bauwens, Lubrano, and Richard (1999) in using Gamma 1 and Gamma 2 distributions to set up the Inverse Gamma 1 and 2 distributions. This involves redefining the parameters of the gamma distribution and should explain the difference to the other two sources you cite, which use the conventional Gamma distribution parameterization.

6

Thank you very much for the clarifications, Johannes.