independent Normal-Wishart prior

[AhmedSahlool]

Dear Tom,

I hope this finds you well,

I would like to know if there is a code for independent Normal - Wishart prior.

Thank you

Ahmed Sahloul

[TomDoan]

Have you looked at Section 16.4 in the User's Guide? The Normal-inverse Wishart is the standard form of prior for a VAR.

[AhmedSahlool]

I don't know if I can explain clearly what I want " I have recently started working with BVAR models.

I see that in the paper "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics" there are six different priors, of which the Independent Normal-Wishart Prior, where different equations in the VAR are allowed to have different explanatory variables, VAR coefficients and the error covariance being independent of one another, necessitating therefore Gibbs sampler.

So I would like to know if there is a code for this prior?

In section 16.4 in the User Guide, the Normal-inverse Wishart is used for Sigma in the Jefferys Prior, where different equations in the VAR are not allowed to have different explanatory variables.

[TomDoan]

Please do not repeat a question.

Near-VAR's (of modest size) can be handled using the SURGibbsSetup procedure and routines related to that. Whether there's a prior or not really doesn't matter much. See the discussion about the prior at http://www.estima.com/forum/viewtopic.php?f=8&t=1582. The point about their construction of the model is that once you have a prior which is informative and isn't in conjugate form, there is no longer any computational advantage in being a full VAR---the calculation is basically the "SUR" model whether the VAR is full or not.

[AhmedSahlool]

Hi Tom,

And What do you recommend as a prior when estimating using SURGibbsSetup procedure?

I need also to compute the variance decomposition and use the model for forecasting, Could you kindly indicate the code used with Bayesian VAR estimated with the preceding procedure.

Thank you very much for your help.

Best regards

Ahmed

[TomDoan]

A Minnesota prior would certainly be the most common. The use of Gibbs sampling in a BVAR is covered in detail in the Bayesian Econometrics e-course.

[AhmedSahlool]

I got the Bayesian Econometrics e-course where it's mentioned that the most used prior for Near BVAR model is the non informative one, Page 75.

However, it's not mentioned how to compute the variance decomposition and to use the model for forecasting, would you kindly indicate me where to find this code in the course manual.

Thank you and best regards.

[TomDoan]

Did you check out the Cushman-Zha replicationthat was posted recently? Is that the type of model that you want? It would be helpful if you would explain what you're trying to do, rather than giving a reference to a remark in a paper.

[AhmedSahlool]

Thank you for your quick reply.

I went through the attached program, but I can't see the relevant code for variance decomposition and forecasting. It's mostly focused on the impulse responses for Near SVAR model.

would kindly tell me if this is included somewhere in this program.

Thank you

[TomDoan]

Though I'm not a great fan of trying to do error bands for FEVD's, you can do that using @FEVDTABLE after the loop that does the impulse responses. The "bookkeeping" for the forecasts is identical for a near VAR as for a VAR; once you have the model with the draw for the coefficients, you can just do a FORECAST and save the results as is done in the example for the full BVAR in the Bayesian Econometrics course.

[AhmedSahlool]

Thank you for your reply.

I would like to ask you a general question.

I am confused about the selection of the prior; informative or uninformative?

What is the most performing uninformative prior?

You replied before that "once you have a prior which is informative and isn't in conjugate form, there is no longer any computational advantage in being a full VAR---the calculation is basically the "SUR" model whether the VAR is full or not"

Thus, when shifting to a SUR estimation, I use informative or uninformative prior?

What is the most performing uninformative prior with SUR,

And Does the estimation using SUR increases the performance of an uninformative prior?

Thank you for your help

[TomDoan]

Thank you for your reply.

I would like to ask you a general question.

I am confused about the selection of the prior; informative or uninformative?

What is the most performing uninformative prior?

The standard uninformative prior is diffuse on the lag coefficients and Jeffrey's on the covariance matrix.

You replied before that "once you have a prior which is informative and isn't in conjugate form, there is no longer any computational advantage in being a full VAR---the calculation is basically the "SUR" model whether the VAR is full or not"

Thus, when shifting to a SUR estimation, I use informative or uninformative prior?

You might want to go back over section 5.4 in the Bayesian Econometrics course. When you knock variables out of the model to form a near-VAR, you are using a very informative prior.

What is the most performing uninformative prior with SUR,

The standard uninformative prior is again diffuse on the lag coefficients and Jeffrey's on the covariance matrix.

And Does the estimation using SUR increases the performance of an uninformative prior?

If the restriction is reasonable, it will give better results to use the restricted model rather than the unrestricted one.

[AhmedSahlool]

Thank you for your reply,

did you read this paper "Noninformative Priors and Frequentist Risks of Bayesian Estimators of Vector-Autoregressive Models"

http://economics.missouri.edu/working-p ... 210_ni.pdf

They discuss the Rats uninformative prior; diffuse on the lag coefficients and Jeffrey's on the covariance matrix.

[TomDoan]

The "RATS" prior that they are talking about is a close relative of the Jeffrey's prior for the covariance matrix which added back the degrees of freedom lost to the regressors. Beginning with RATS v6, we changed the coding and the description to the standard prior. The differences, in practice, are quite small. However, since they were doing simulations with often very small data set sizes (T=20??, seriously?) the difference there could be more substantial.

Their shrinkage prior for the coefficients is certainly doable, since it just requires, as part of the Gibbs sampler, one added step of drawing a single gamma variate. The problem is that it treats all variables the same regardless of magnitude. If you have a bivariate X, Y and rescale Y upwards by 100, the effect of the prior would be to largely eliminate the effect of X on Y relative to the same model with unscaled Y.

[AhmedSahlool]

Hi,

Thank you for this comment, since yesterday I am searching for the most performing non-informative prior, that gives proper posterior distribution.

Could you kindly tell me if the standard prior, actually implemented with Winrats, results in proper posterior distribution.

Is there other non-informative priors implemented with Winrats.

and another naive question, once I apply flat prior, like the example 5.4 and 6.2 in Bayesian course book, am I applying the standard non-informative prior?

Thank you for your help and I regret that I did not assist the course with you, don't you intend repeat it again.