4:52 p.m.
Thank you for explaining your view on this.
Den 12/11/2011 kl. 20.14 skrev Sven Schreiber:
First of all let me state that I am fully aware of the similarity
issues
in that context, which you already briefly alluded to. I also heard the
recommendations you are following, and for some time I even tried to
follow them. And there are cases where I fully agree, for example when I
have to model the German unification break.
To take the example of the unrestricted constant term, however, in the
end I think there is often not a real problem. That is, if you have data
which beyond any doubt have linear trend terms, and you are not ready to
accept any long-run equilibrium which is trend stationary instead of
mean stationary. (Because after all, how do you really interpret
economically an equilibrium which is diverging?)
I agree on the interpretation. Diverging equilibria are not something you want to end up
with but that is an economics issue.
Well then you say: no problem, just kick the trend term out of the CI
space after determining the rank. However with typical small-sample data
often this just doesn't work; in my real-world experience first you
often get quite strange rank test results when you allow for linear
trends in the CI space, and secondly afterwards often the restriction
test wouldn't allow you to set the trend coefficient to zero. The
alternative is to not allow the trend terms right from the start,
because you really have no use for them.
Statistically things are different and wether or not there is a trend in the cointegration
space is a matter of a statistical testing. If your model class is too restrictive from
the outset your model misspecified. If the trend cannot be excluded I would take it as a
problem of something different, say unmodelled structural breaks in either the economy or
data or maybe I(2) variables.
That's what we often do in econometrics: we make some specification
assumptions to gain efficiency, power and so on. And sure there is the
danger that those assumptions could be wrong, and so you really have to
think hard about them. But I don't see why a fixed rule like "thou shalt
not test for cointegration with unrestricted deterministic terms" would
be the best solution of the dilemma.
My argument here is just that it is an unnecessary assumption to make and both theory and
simulations tell us that statistical problems exist when allowing the deterministic terms
to vary unrestricted. Of course there are small sample problems in these models but
personally I think that the larger problem is to work within too narrow a model class.
BTW, it could be argued that since I am holding small sample sizes
responsible for the dilemma, we should always use the newly available
small-sample tools like bootstrapping and Bartlett corrections. I have
some experience with that and indeed, maybe that would resolve some of
the otherwise strange test results. This may be a case to push for these
tools to be more widely available.
I agree. As said the small sample problems are there and we should try to handle them as
well as possible. The Bartlett corrections would definitely be good to have in Gretl but
they are a bit messy to program, I think, but I would be happy to test them against the
results in CATS if they were programmed by someone.
A more feasible approach is the bootstrap (but I guess Bartlett corrections could be
combined with the bootstrap also). I have done a very preliminary first attempt on the
writing the bootstrapped trace test and would be happy to hear your comments. It was also
a great opportunity to try out the excellent package facility so please have a look at the
coint2boot package. It builds on Cavaliere, Rahbek and Taylor, forthcoming in
Econometrica. The algorithm is only valid for the Cases 1, 2 and 4 so here, at least, I
get it as I want it.:-)
A final question to Allin and a general Gretl question. It would make my function more
useful if there existed a --quiet flag on the vecm and var commands. Is it possible to
add? I need to save some matrices as series to use them in vecm and var. Is there a way to
save a Txp dimensional matrix as p series. My way of doing it right now is not elegant.
Best
Andreas
--
Andreas Noack Jensen
Ph.d.-stipendiat
Økonomisk Institut andreas.noack.jensen(a)econ.ku.dk
Københavns Universitet http://www.econ.ku.dk/phdstudent/noack/
Øster Farimagsgade 5, bygning 26 Tlf.: 353 23094
1353 København K