Re: [Gretl-users] Discrepancy between R and Gretl in Johansen cointegration
Am 01.02.2019 um 17:51 schrieb Allin Cottrell:
On Fri, 1 Feb 2019, Sven Schreiber wrote:
> Both Stata and urca claim to use Osterwald-Lenum. Unfortunately I
> haven't been able to quickly grab a copy of that paper, so I couldn't
> check.
I've looked at Osterwald-Lenum. The Stata critical values are taken from
Table 1 on page 468 which pertains to "Case 1" (unrestricted constant).
The urca ones are from Table 1.1* on page 472. This applies to a special
extension of the five Johansen cases considered in Johansen and Juselius
(Oxford Bulletin, 1990) where "the statistical model allows for an
unrestricted intercept in the differenced form representation ... but
the DGP only included a restricted intercept." That description is from
Osterwald-Lenum (p. 465).
So it looks as if urca picked the wrong table.
Thanks, interesting. However, I don't think that it is necessarily
wrong per se. This is exactly the problem why the people from Copenhagen
and Oxford tried to promote only the usage of the cases where the tests
are (asymptotically) "similar" (terminus technicus here). And the
unrestricted constant case is not, it depends on whether a trend is
actually in the data or not.
(I hope I'm not misrepresenting their opinions.)
So one could interpret the urca choice as trying to be on the safe side,
at the cost of having a conservative test (asymptotically). Another
question is whether that was done consciously.
So that would settle the issue. Maybe I'm going to tell the statsmodels
people (linked earlier in this thread) about those insights.
cheers,
sven