Re: Letter form Bob Solow

["Lonnie K. Stevans" <acslks@xxxxxxxxxxxxxxxxx>]

If you do not believe in the existence of Type II errors, then under what scientific basis did
they run the experiment?  Did not Yaglam and the graduate students use some kind of
significance testing to detect unit roots?  You are obviously accepting the hypothesis
that the noise data contains a unit root, but keep in mind that the simulation is done
under the alternative hypothesis of no unit root--so there is no way of getting around
the probability of a Type II error.

A similar argument can be made concerning the finding of cointegration.
Whether you like it or not, finding in favor of cointegration when there is
none is rejecting the null hypothesis of no cointegration when the null is true
(assuming the residual-based tests were used).  This is obviously a Type I
error, whose probabilty is set prior to doing the test.

You cannot have it both ways--if significance tests are being performed then
there are Type I and II errors and the probability of these errors can be
observed through Monte Carlo simulation.

Lonnie K. Stevans
acslks@xxxxxxxxxxx

Unfortunately for you -- Yaglom did repeat the experiment -- and if fact so
did others that I have requested assign graduate students to do.  The results
are always the same -- by the n-th difference-- usually no more than the third
difference --, there appears to be something of statistical significance.

But Lonnie-- think before you pay lip service to type II errors to rationalize
any kind of nonsense.  If we know that two columns of data are merely random
numbers then there should be no relationship between the original columns or
any nth-difference of these columns.  Otherwise what do you mean by random
numbers?

When I tell these results to pure statisticians, and ask them how come, the
first question they ask is "Are you sure that the random number generatdr
really generates random numbers?" Only if the original data in the two columns
are in some sense nonrandom can you expect to find a statistical significance,
if not inthe original data, then in some nth difference.

Paul

Paul Davidson
Editor, Journal of Post Keynesian Economics
University of Tennessee
SMC 523
Knoxville, Tennessee 37996-0550
phone # (865)974-4221; fax #(561)737-8262;
email pdavidson@xxxxxxx
http://econ.bus.utk.edu/davidsonextra/Davidson.html