How to set up the Jeffreys Prior for VECM?

[dennis0125hk]

In RATS User's Guide, Jeffreys Prior is introduced for VAR (P.493) for computation of Impulse Response. However, how can I set up the Jeffreys Prior for VECM? For me, I first transformed the VECM to VAR, and then set up the Jeffreys Prior for the transformed VAR. Is it appropriate to do that? If not, how can I set up the Jeffreys Prior for VECM?

Thanks for attention...

[TomDoan]

It would be the same prior. Note that (in either case), this is the Jeffreys' prior treating the RHS variables as fixed. A true Jeffreys' prior taking into account the endogeneity of the RHS variables doesn't really have a closed form.

[dennis0125hk]

If I choose not to transform VECM into VAR, how can I set the Jeffreys Prior for VECM given the cointegrating vector has to be estimated?

The Jeffreys Prior can be set easily for VECM by using the commands introduced in P.497-498 in User Guide if the cointegrating vector is fixed. In this case, xx is the matrix of cross product of regressors in VECM. But can I do so if the cointegrating vector has to be estimated? I tried to replicate IRF of two-variable VECM in Beaudry and Portier 'Stock Price, News, and Economic Fluctuation' (2006) and if I set the Jeffrey's Prior by using commands introduced in P.497-498 in User Guide, I can get the similar estimates as the one in paper. However, if I transform the VECM into VAR and set the Jeffrey's Prior for transformed VAR, I notice that there are differences in the result.

Thanks for attention...

[TomDoan]

You're focusing too much on the Jeffreys' prior, which is only a minor issue, as it determines only the degrees of freedom of the Wishart from which the covariance matrix is drawn. A more important issue is how to do Monte Carlo integration in a VECM. That's not a trivial issue. The paper that you're citing is showing the RATS manual as the source for the method used, but the "MonteVAR" process can only be applied in the case of a VECM if the cointegrating vector is treated as fixed. You might want to clarify what procedure was used for that with the authors.

[MC128]

Dear Tom,

Following your earlier discussion on this topic, may I ask:

1. If I first estimate the co-integreation relations
2. then Insert the co-integration relations in the following way (using the example in the User Guide p.376):

system(model=ectmodel)
variables ftbs3 ftb12 fcm7
lags 1 to 6
ect ecteq
end(system)

3. then use the montevar.src to generate the error band for the impulse response.

Do you think there will be any problem? May I also ask whether it is better to use bootstrapping to generate the error bands for a VECM in general?


Many thanks for your kind attention.

MC

[TomDoan]

Yes. You can use the stock montevar.src procedure after estimating a VAR with an ECT term or terms. It will do the simulations treating the cointegration vector(s) as fixed.