Re: [Gretl-devel] VECM experts ahoy!
On Wed, 6 Apr 2011, Sven Schreiber wrote:
Am 05.04.2011 23:01, schrieb Allin Cottrell:
> I think I now understand this better: the test statistic is indeed
> just the standard one, but PSS refer it to a different
> distribution from Johansen. I've written up a note on this, by way
> of response to a 2009 piece in the Journal of Applied Econometrics
> by Paul Turner, which I think gets it wrong. My note is at
> http://www.wfu.edu/~cottrell/tmp/coint_model.pdf
> Comments, criticisms welcome.
Hm, I took a look at your note and also some further look at the PSS
paper (still without a proper reading though, so take everything with
grains of salt). I understand why they want to work with their framework
where the lag polynomial is applied to the de-trended levels (X_t - \mu
- \gamma t). IIRC the Saikkonen&Lütkepohl-type approach does it in a
similar way (including dummies for shifts). But then I don't understand
why they have their Case III at all, where the corresponding restriction
is "ignored". Your table 4 seems to show exactly the problems with that
"ignorance", if I understand correctly.
Thanks for following upon this. I agree: it seems to me there's
something faintly bogus about PSS Case III: they calculate the
statistic "ignoring" the restriction implied by their VAR
formulation, but then refer it to a distribution that is
constructed on the assumption that the restriction holds.
Also, the way you describe the Turner exercise, it seems that he
pointed
out that the trace test is not "similar" (in the statistical jargon
sense) in the famous unrestricted constant case. But that had been well
known for a long time. Or am I missing something here (haven't looked at
the Turner paper myself)?
I don't think you're missing anything here. In fact I'm surprised
that the Turner paper made it into JAE. He says, "Look, the
Johansen Case 1 test over-rejects!" and backs this up by feeding
it data that by construction belong in Johansen Case 0.
Anyway, in many applications the presence of deterministic trend
components in the data is pretty obvious IMHO. And at the same time we
don't really want to "explain" long-run connections between variables
with exogenous deterministic terms. I mean we want long-run forcing
variables, elasticities, and all that! So the famous unrestricted
constant case remains highly relevant, despite the statistical
drawbacks. (Not that I think that you were doubting that...)
Well, I don't _think_ I was doubting that ;-) But this is a pretty
subtle area.
Allin