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Hello,

I have a question about Granger causality tests on a VECM. Are the adjustment and cointegrating parameters taken into account in the tests? They would have to be (with respect to a VAR), but I don't know if they are in Eviews. Can someboby help me?

With usual notations, gammas are the VAR parameters and alphas and betas are the adjustment and cointegrating parameters. With a VAR, only the gammas are taken into account in the hypothesis tests for Granger causality (since alphas and betas do not exist in this case). When we are in a VECM setting, alphas and betas need to be taken into consideration in addition to the gammas. Are they taken into account in Eviews?

Thank you.

Vincent

I think you're right.

The Granger causality tests being quoted on VECMs in EViews are just Wald style exclusion tests on the lagged difference terms. This leaves open the possibility of the first lag on another variable feeding into the variable through the cointegrating vector. So if you fail the test we quote, you can reject the hypothesis of no granger causality, but if you pass the exclusion test, there may still be granger causality that we're not testing for coming in through the cointegrating vector.

I tried to think through whether I could run the complete test by adding restrictions on the cointegrating coefficients during estimation, but I couldn't figure out any way to do that. Restricting beta knocks out the variable from the cointegrating vector for all variables, while restricting alpha knocks out any effect of any variable on this variable via the cointegrating vector. Both of these are more of a restriction than you need.

Do you know of a reference for the test that you'd like us to perform? Lutkepohl has some discussion of this in his book 'Introduction to Multiple Time Series Analysis', but (based on a quick reading) he seems to be talking about using the Wald test from the unrestricted levels VAR where he points out that you can run into issues due to the coefficient covariance matrix having reduced rank (asymptotically).

Thanks,

Chris

I think two interesting references for you are:

Lutkepohl and Kratzig , Applied Time Series Econometrics (2004),
and
Mosconi and Giannini, Non-causality in cointegrated systems: representation, estimation and testing (1992, Oxford bulletin of economics and statistics).

In page 146 of Lutkepohl and Kratzig (2004) there is short presentation, but there is no detail on how to test this hypothesis. However, they quote a paper that seems to deal with this issue: Mosconi and Giannini (1992). Maybe it can help you.


For your suggestion to do Granger tests with Wald tests for a VECM, I join you my Eviews file (“Granger on vecm”). I have first estimated my VECM (called “vecm_03”) with ML using the system called “vecm03_maxlik”. Next I tried to test the hypothesis “lpg does not granger cause lspp2” with a Wald test. Results are in the table called “lpg_on_lspp2”. If Wald test can be used in this case (with what you quote from Lutkepohl with the covariance matrix), is it a proper way to test Granger causality with my VECM ?


I have also a question on consequences of heteroscedasticity for inference. Maybe you can help me. With ols, estimators are unbiased and consistent, but not BLUE. Consequently they do not have minimum variances so that the standard errors can be biased and hence inference could be misleading. What about ML? Many papers quote a reference (Gonzalo J,1994, Five alternative methods of estimating long-run equilibrium relationships, Journal of Econometrics) that explains that maximum likelihood estimates in a cointegration analysis are still consistent even with heteroscedasticity. What about inference in this context? Can you help me?

Thank you,

Vincent

I've just forgotten to upload my eviews file in my last post... Here it is:

How to run Granger causality in VECM using Eviews? I really need this info urgently. Thank you.