Re: Reply to B. Mitchell, P. Davidson

[ACSLKS@xxxxxxxxxxxxxxxx id <01HN0IM1KI468Y7115@xxxxxxxxxxxxxxxx>; Mon, 13 Feb 1995 21:21:50 -0400 (EDT)]

> To Lonnie K. Stevans:
>      The original question was whether it is OK to CI
> level and first differenced series and Bill Mitchell
> correctly answered "yes."  Your statement regarding the
> inappropriateness of CI'ing first differenced series
> only applies if levels are CI'ed.  If not, it is
> perfectly legitimate to search for the lowest levels of
> respective differencing which will CI.  Such a finding
> naturally implies something different than finding a
> CI for levels.
>      Of course, the real issue here which has been raised
> by Ebert, Davidson, et al, is what does finding (or not
> finding) any CI mean?  The answer may be that it is more
> useful (Popperianly) for _rejecting_ hypothesized equilibrium
> or other linking relationships if no CI at any difference can
> be found.  It is not at all clear that finding a CI "proves"
> anything anymore than finding nice values for various
> statistics in an OLS regression "proves" anything.  Why
> are CI findings any less likely to be "spurious"?  Correlation
> is still not necessarily causation, in spite of Granger's
> highly misleading use of the term "causality."
>      To get at "causation," one must have theory, of one
> sort or another, both deductive and inductive (yes, Paul,
> I agree with you on that one).
> Barkley Rosser
> James Madison University

On your first point, of course you can cointegrate differenced series.  One can
also look for causality between liquor sales and the number of ordained
ministers.  My point is that it is meaningless to do so.  Cointegrating levels
of variables allows for long-run deviations from an equilibrium relationship
to be included in a dynamic model. Using differences allows for short-run
deviations.  Not "equilibrium" in the sense of market clearing, but in
terms of a hypothesized relationship:  y = f(x).  If a cointegration
relationship is found, then it is included as an adjustment to a deviation from
equilibrium in a dynamic model that also contains short-run deviations or
differences of the variables used.  That is its meaning.

The "findings" of an error correction model are less likely to be spurious,
because each variable is stationary or I(0).  Try a simple experiment.
Generate two independent random walks and then regress one upon the other.  The
statistical results rejecting independence imply a spurious relationship.
However, if you were to first difference each and then run a regression on
differences and the error correction you will get the correct results.

I agree on having the theory--although I have seen times when GIGO (garbage-in,
garbage-out) has been appropriate.

Lonnie K. Stevans