Re: Son [or DAUGHTER] of unit roots

[ecwfm@xxxxxxxxxxxxxxxxxxx (bill mitchell)]

JMC Here are some brief answers:

>Three questions for the unit root and cointegration crowd:
>
>1) Is it appropriate to take differences in an I(1) series and compare it
>with an undifferenced I(0) series? For example, share prices are I(1) but
>interest rates, which are regularly cited as a determinant of share value
>(based on theoretical although usually not empirical justifications), are
>I(0). Don't you then have a comparison of differences and levels, and isn't
>this wrong? Moreover, if you take differences on interest rates, haven't you
>then distorted the key attribute of the series (its stationarity) to the
>point of meaninglessness?
>
Yes it is okay. It is called integration accounting. I am not agreeing that
the series you designate I(1) or (0) or (d) are indeed that, and I caution
you in your use of low power ADF and DF tests. There are other tests which
take the TS as the null and which will give opposite conclusions to the ADF
over the same data and sample space. So we proceed with caution on all these
tests. But given that, you can run a regression in this genre as long as
both sides of the regression add up so to speak. In other words, the linear
combination of a series of variables will take the highest order of
integration of the series. So if they are all I(0) by level or difference
then the residuals (the linear combination) will be I(0). For an application
of just this issue and how it can make economic sense to do it, see a paper
i wrote with Martin Watts in Applied Economics in 1991 on Okuns Law.


>2) In the short-run dynamic equation, provided you have no lagged dependent
>variables on the right side, what qualifies as an "acceptable" r-squared? If
>you're in the range of 0.25-0.35, and all other tests (DW, chi2, maximized
>partial r-squared's, etc.), are acceptable, is it reasonable to stop there?
>
The maximisation of R2 went out with the arc. it is only one guide to a good
regression, and a fairly low priority one. the tests rather should be on the
residuals and whether they betray the basic assumptions on which your
inference is based. Also stability and post-sample forecasting is a big
thing. leverage, and other matters are also useful to look at.


>3) Is it okay to *delete* from the short-run dynamic equation a variable
>that was used in the long-run static equation?

well if you are running a CI model, then there is only one Error correcting
levels term in your short run dynamic model and that is the lagged residuals
from the long-run static regression. Some people use an informal cross test
on the implied long run surface by individually putting the level terms in
lagged to the degree of the lagged residuals term but it only to solve the
lr model and see if it looks like the CI long run model. So i would not be
deleting anything like this.


Hope this helps. Maybe someone else from the UR-CI crowd can add more.

kind regards
bill
(no academic qualifications listed in signature, a sometime reader of non
academic articles, and forced by ci cumstance (my work) to connect from an
.edu server)
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