Parameter setting of Bayesian prior distribution

Ask everyone. I encountered some confusion in learning Bayesian estimation. How to set the prior distribution parameters of Bayes, such as prior mean and variance. Is that a guess? There’s some quantitative studies that need to be done. Parameter estimation Are the parameter values that need to be guessed before estimation written in the parameter block? After the parameters are estimated, then rewrite the parameters into the mod file? Do the impulse response again? Thank you for the teacher’s advice, I am a beginner, more confused.

Hi heroluotao,

is this a technical question regarding how to enter prior mean, variance, etc. into Dynare or a theoretical one on how to find these terms? I will try to answer them both.

I start with the theoretical one. Following the wording of prior distribution we already see that this is something that we as researchers should/could have prior knowledge about. That could for instance be the domain of a parameter and where we believe the parameter will be. This stems from the definition of Bayes’ rule on which Bayesian estimation is built, I recommend looking up those terms in a textbook. That we are able to include prior knowledge into our estimation routine, through choosing particular prior distributions is one of the major distinctions of using Bayesian methods over frequentis ones like OLS and GMM.
Thus, you can put in your prior knowledge by choosing a particular prior distribution. There is, of course, literature on what distributions (Beta, Normal, Inv. Gamma) to use on which parameters, but in general it is up to you.

For Dynare, before you try to do estimation you should make sure your model runs in calibrated form. Only then you can start thinking about estimation, because there is a lot that can go wrong, starting from data treatment, observational equations, and mode finding to what exact algorithm to use.
But let’s give an example on how to include a parameter to be estimated into Dynare. Assume that you think that the parameter that governs the central banks reaction to output growth is called phi_y and your prior knowledge, based on theory and data, is that is follows roughly a normal around 0.1 with some variance (in the following case 0.15). Then, under estiamted_params you enter

phi_y , normal_pdf , 0.1, 0.15 ;

But again, you should do a lot of reading before approaching estimation. A good book is Bayesian Estimation of DSGE Models by Herbst and Schorfheide. Before writing too much, which maybe you are familiar with, I end it here and feel free to ask follow up questions.

But let me quote Prof. Pfeifer’s usual response here that he already posted in one of your other topics:
You are not supposed to work on estimation without intense supervision or sufficient prior training. I have seen too many cases like this miserably fail. Most of the time, the goals set are too unrealistic given the prior training and the time frame envisioned.

Dear DoubleBass, thank you so much for answering, I feel very productive

See also

Thank you professor Jpfeifer