Engle Granger cointegration testing

[Christoph_EU]

Hello all,

we have an internal discussion about the difference of:

(1) using the EViews integrated Engle-Granger test on cointegration or
(2) estimating an FMOLS regression and then manually plugging the residuals into an ADF test (using MacKinnon critical values).

Outcomes differ for the series analysed. With approach (1) we reject cointegration, with approach (2) cointegration is present.
Could anyone shortly elaborate what is the difference in the two approaches? Help much appreciated.

Best regards
Christoph

[Christoph_EU]

Hello all,

I have found the following two threads on the topic:
http://forums.eviews.com/viewtopic.php?f=18&t=7467
http://forums.eviews.com/viewtopic.php?f=4&t=176

As I understand the critical values used in the ADF tests are not the same as those used in the Engle-Granger (EG) test. What is puzzeling me is that both the ADF test as well as the EG test are relying on critical values of MacKinnon (e.g. http://akson.sgh.waw.pl/~ewams/MacKinno ... p_1227.pdf) ADF test on MacKinnon (1996) and EG MacKinnon (2010) - what is to my understanding an update of the 1996 values.

Could anyone explain the difference in the two sets of critical values of MacKinnon? Potentially also quoting the relevant passage that is indicating this set of critical values is for ADF tests and that for EG tests?

Any help much appreciated!

Best regards
Christoph

[EViews Glenn]

The asymptotic distributions are different when there is a first stage long-run regression to obtain the presumably stationary residuals as opposed to when you are testing directly for a unit root in a series. The distribution of the former depends on the number of estimated coefficients in the cointegrating vector as described in MacKinnon 1996, p. 603. There are different response surface simulations for the various cases.

[Christoph_EU]

Thank you Glenn for your explanation! I think I better understand the issue, now.

In a nutshell - ADF critical values are derived assuming only one (N=1) integrated series while for the EG tests the exact number of N coefficients is taken into account. So Eviews uses the N=1 row data to calculate the ADF critical values. The EG test explicitly accounts for a different 'N' value. Actually no other difference exists between ADF and EG critical values from MacKinnon. Is that correct?

BR
Christoph

[EViews Glenn]

I'm not sure what you mean by your penultimate sentence, but the rest sounds correct.

[Christoph_EU]

Hello Glenn,

I meant that the ADF test and also the cointegration critical values are derived from the same tables - only the "N" differs. In consequence different rows for the lookup are used. However, there is no totally different equation used when deriving the critical values.

Thanks a lot!

Best regards
Christoph