Re: Reply to B. Mitchell, P. Davidson

[ACSLKS@xxxxxxxxxxxxxxxx id <01HN06BNGLF48Y71XE@xxxxxxxxxxxxxxxx>; Mon, 13 Feb 1995 15:56:24 -0400 (EDT)]

> FROM:  Paul Davidson
> "      Holly Chair of Excellence in Political Economy
> "      University of Tennessee, Knoxville, Tn. 37996-0550
> Dear Lonnie Stevens: Don't read cointegration textbooks -- read books by people
>
> who are mathematicans and statisticans developing the theory of stochastic
> processes, e.g., Diggle, Yaglom, Billingsley, etc. Textbook authors wantto
> sell books-- they will appeal to anything plausible (or even impulse0 rational
> possible.
>     Read Hicks (e.g.,CAUSALITY IN ECONOMICS, P. 121) "the usefulness of 'statis
> tical' or 'stochastic' methods in economics is a good deal less than is now con
> ventionally supposed. We have no business to turn to them automatically;
> we should always ask ourselves before we apply them whether they are
> appropriate to the problem at hand. very often they are not". it is my
> contention thjat most economic times series do not meet the criteria of
> statistical control if the dat run any significant length of calendar time
> --and as Christiano and Eichenbaum  explain "Simply put it is hard to believe a
>  mere 40 years contain much evidence on the only experiement that is relevant"
> (p.8) and "To see why suppose we actually knew a particular random variable was
> difference stationary. Indeed assume that we actually knew the univarite, diffe
> rence stationary, Wold representation of the randon variable. For each such
> respresentation, the variable can be decomposed into permanent and temporary co
> mponents in an infinite number of ways (Quah, 1988). While each decomposition
> embodies different assumptions about the relative importance of permanent andte
> mporary shocks to the variable. Simply knowing the univariate time series
> representation of a random variable provides no information about which of the
> infinite decompositions agents may be observing and responding to...Agreeing
> on the presence of a unit root in the law of motion for some variable, or even
> the variable's univariate time series representation, imposes almost no restric
> tion on one's views of this issue, since there always exists a decomposition wh
> ich makes the permanent component arbitrarily small!"
>
> Remember when at my request Bill Mitchell generated 2 columns of
> random numbers and then found that 5 times in 20 the first differences
> of these columns were cointegrated? Tell me Lonnie what "relationship"   --
> equilibrium or otherwise-- "bunds" these two columns of variables. Moreover, o
> I am sure that if Bill Mitchell on the other 15 times when the first
> differences didn't cointegrate, tried the n-th difference he would have
> found close to 20 out of 20 times a cointegrated relationship!
>
> Have a good day! Paul
> email address: PB108928@xxxxxxxxxxxxxx
> fax# (615)974-1686
> phone# (615)974-4221

Regarding your last paragraph, why would anyone determine if differences of
series were cointegrated??  It is the levels of the series that one tests for
presence of cointegration.  By first differencing and then testing, it is quite
obvious that both series become I(0) or stationary and hence cointegrated.  I
do not know what models B. Mitchell used to generate the series, but maybe in
the remaining cases, some data required higher differences (I did not get the
PKT message regarding the test).  In any event, it is not meaningful to
"cointegrate" differenced series.

As I have mentioned in past messages, this technique with its resulting model
specification is an improvement over the past where "spurious" relationships
were the rule rather than the exception (like the case you mentioned above).
Given the potential for misuse, as you make crystal clear, without these tools
we would be stuck in a discipline with nothing but untestable hypotheses--much
like the way physics was (and still is, to a certain extent).

By the way, not all of what I read are textbooks.  In fact, I recommend a
number of articles on this subject by Granger, Engle, and Phillips.

Lonnie K. Stevans