Re: [Gretl-users] Discrepancy between R and Gretl in Johansen cointegration
On Fri, 1 Feb 2019, Sven Schreiber wrote:
Am 01.02.2019 um 09:30 schrieb Sven Schreiber:
>
> urca:
> test 10pct 5pct 1pct
> r <= 1 | 5.67 6.50 8.18 11.65
> r = 0 | 26.35 15.66 17.95 23.52
>
> So that's the differing conclusions from the OP, and Gretl and tsDyn again
> agree, urca doesn't.
OK, got it.
Some further evidence from Stata's documentation, see
https://www.stata.com/manuals14/tsvecrank.pdf.
There are some critical values for the trace stat printed in the examples.
Note: They have a 3-equation system, whereas in our (Reynaldo's) example we
have 2 equations (2 endogenous). For the distribution (critical values) what
matters is N - r_0 under H0, the number of I(1) trends under the null. You
must not compare their r=0 case with our r=0 directly. This can be confusing
here, but I hope I got it right.
With this in mind, Stata has (Examples 2 and 1):
20.04 where urca has 23.52 (N - r_0 = 2 at 1%)
6.65 where urca has 11.65 (N - r_0 = 1 at 1%)
15.41 where urca has 17.95 (N - r_0 = 2 at 5%)
3.76 where urca has 8.18 (N - r_0 = 1 at 5%)
Notice that with Stata's critical values the test conclusions from Reynaldo's
example would agree with gretl (and tsDyn).
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.
Allin