## Multivariate Granger Causality

Questions and discussions on Vector Autoregressions

### Re: Questions about Multivariate Granger Causality

bok1234 wrote:Dear Mr.Doan,

Let me ask you 2 things about multivariate Granger Sims causality test(Multi-GS test), especially focusing on varcause.rpf.

[Question 1] On Sat Apr 21, 2007, you replied as follows; "The test is whether the nominal variables enter the real equations. The null is that they don't, which means that the real variables don't respond to nominal shocks - they form an exogenous block."

I guess that the 2nd 'they' in the last sentence means 'real variables.' Therefore, according to the result of varcause.rpf, a block of real variables do not secure exogeneity. This means that 'a bundle of nominal variables' DO GRANGER CAUSE 'a bundle of real variables'. And finally, this is "the one-side test(nominal variables -> real variables)", not including a test of 'real variables->nominal variables' Am I right?

Correct. The test in VARCAUSE is whether the real variables are exogenous (are not caused by the nominal variables) and that is rejected. It does not include a test of the other direction.

bok1234 wrote:[Question 2] In your reply Fri Jul 16, 2010. You referred that unit root could result in some problems. If differenced data series does not have unit root anymore and they get to input into the VAR system(varcause.rpf, for example), the probable problems that you referred would be solved. Is this right?

The problem with unit roots is that, while the test statistic is calculated the same way, it has a non-standard asymptotic distribution. If the model is properly specified in first differences (that is, there was no cointegration), then the block exogeneity test on the differences has the standard asymptotics.
TomDoan

Posts: 2761
Joined: Wed Nov 01, 2006 5:36 pm

### Re: Optimal Time Lag for Multivariate Granger Causality

Would you mind if I ask you a bit more?

I tested optimal time lag according to the example of p.55 in "RATS Programming Manual(Walter Enders)."
My VAR model is composed of 17 variables and each has 100 observations.
Therefore, I can test AIC and SBC upto 4 lags. I attached the result. Please see the graph.
The result is a little ambiguous.
Will you let me know which time lag is optimal?
And if lag T is optimal, should I input lag "T-1" or just "T" for the Multivariate Granger Causality?
It will be helpful if you answer these questions and explain why.

Sincerely,

Seung
Attachments
optimal time lag selection.xls
bok1234

Posts: 6
Joined: Tue Jan 11, 2011 9:14 pm

### Re: Multivariate Granger Causality

With 17 variables and 100 observations, 4 is way too many lags to even consider. Even 2 is bordering on clearly being overparameterized (which seems apparent from the SBC).

If you're going to run in differences, pick the lag length based on the differenced data and use the full number that you choose.
TomDoan

Posts: 2761
Joined: Wed Nov 01, 2006 5:36 pm

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