Bayesian VAR _Minnesota Prior Mean

[Tristan]

Dear Eviews Users,

I have a question on the specification of the prior mean in the Bayesian VAR specification. The Eviews manual advises that: “the prior mean is likely to have most or all of its elements set to zero to lessen the risk of over-fitting, and this implies that should be close to zero”. This is fine, but in the traditional Litterman / Minnesota application, the first lag of the dependent variable in each equation should have a prior mean of 1.0. This centers the prior around a random walk process. The other coefficients, as is rightly stated, gets a prior mean of 0. I am not sure if this is being done in Eviews: do all coefficients get a prior mean of 0? Or do the first lag of the dependent variable get a prior mean of 1, as originally specified by Litterman?

The question I have, is what if the model is run in first differences? Then the prior mean of 1.0 on the first lag of the dependent variable will be inconsistent with the random walk assumption, and should be adjusted towards zero accordingly. How can this be done in Eviews? In the applications of BVARs in the manual, I notice that the example on page 312 in Lutkepohl (2007) was not done – in this case, the VAR is specified in levels (preserving any integration properties of the data) and Lutkepohl runs a traditional Litterman / Minnesota prior, placing a prior of 1 on the first lag of the dependent variables in each equation, 0 on everything else.


This may sound like semantics, but it is very important: if the VAR is run in levels, then the traditional Litterman / Minnesota prior of mean zero on all coefficients except the first lag of the dependent variable is warranted. If the VAR is run in first differences, then all coefficients should be adjusted towards zero, including the first lag of the dependent variable.

Many thanks!

[EViews Gareth]

You can set the hyper-parameters to whatever you want... We use 1 as the default value, but if you think it should be a different value, feel free to change it.

[Tristan]

Thank you very much Gareth. I take this to mean that the default in Eviews is set up exactly as how Litterman described it: a prior mean of zero on all coefficients except the first lag of the dependent variable in each equation, which gets a prior mean of 1.0.

Best wishes,

Tristan

[EViews Gareth]

Yep.