# Re: The macro value of information

From: John Conover <john@email.johncon.com>
Subject: Re: The macro value of information
Date: 14 Jun 2001 20:15:49 GMT

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The duration and magnitude of expansions and contractions in the US
GDP seem to follow a Bachelier/Samuelson/Black/Scholes/Merton
scenario:

http://www.johncon.com/john/correspondence/990215192020.29398.html
http://www.johncon.com/john/correspondence/990905134341.23530.html

where the probability of an expansion, or contraction, lasting at
least n many years, (or any other time scale for that matter-which is
a difficult concept to grasp,) is proportional to erf (1 / sqrt (n)),
and its magnitude proportional to the sqrt (n). Expansion, or
contraction, is defined as whether the growth in GDP is greater, or
less, than its average value.

This would mean that the median, (the mean is not defined,) business
"cycle" is about 4.3 years, since half of the "cycles" would have a
duration that is longer, and half less; there would be significant
variability in the durations since the tail of the erf (1 / sqrt (n))
distribution decreases rapidly for short durations, then very
sluggishly for longer durations.

I suppose, (depending on who is telling the story, of course,) that
such knowledge can be turned into some use with information theory.
For example, in 2000, the chances of the expansion that started in
1991 continuing would have been about erf (1 / sqrt (9)) which is
about 1 / sqrt (9) for n >> 1, or about 1 in 3, which is not a viable
wager, (since it has less than a 50/50 chance of success.)

However, in 1992 the chances of the GDP expansion continuing was about
1 / sqrt (2), or about 70.7%, so one would have put 2 * 0.707 - 1 =
41.4% of one's wealth at risk on the probability, (assuming Shannon's
binary symmetric channel paradigm.)

So, there would have had about 40% at risk in 1992 invested to make
money, but by 2000, 0%.

John

Don Libby writes:
> _Al wrote:
> >
> > On 10 Jun 2001 19:00:56 GMT, chasna1@aol.com (Chasna1) wrote:
> >
> > >>I get the impression that I've said something terriblly
> > >>foolish, but what I had in mind was a global decade-scale
> > >>recession during the 1930's, and Japan during the 1990's.
> > >>
> > >>-dl
> > >
> > >I don't know if it's foolish, but the decade-scale recession terminology kine
> > >of threw me. There are texts on the business cycle which distinguish the
> > >recovery stage from the expansionary stage and that seems reasonable, but the
> > >time duration of one decade for a recovery as some sort of average threw me.
> > >
> > >I should also add that I don't believe in business cycle averages and
> > >periodicities.
> >
> > There are all sorts of cycles in business and the economy.  Economic
> > downturns are caused by weather, changes in government tax or spending
> > policies or other such macro phenomena.  I sure would like to see
> > these conservatives prove JMK wrong by cutting government spending by
> > 10%.
> > _Al
>
> I should add that I wasn't using "decade-scale recession" as
> "some kind of average", rather, as an extreme outlier that
> most would consider rather undesireable.
>
> What I was getting at was that if a business cycle can be
> approximated by some sort of sinusoidal fluctuation (perhaps
> with a variable period) then on average, other things equal,
> faster more comprehensive information flow between demanders
> and suppliers should shorten the lag between recession and
> recovery.
>
> If so, then the risk of very long lags of arbitrary length
> (say 10 years for example) ought to diminish.
>
> Faster "switching times" may make for a bumpier ride along
> the way, but the bumps come in the form of short, sharp,
> shocks, rather than long drawn-out episodes of severe
> depression, so to speak.
>
> -dl
>

--

John Conover, john@email.johncon.com, http://www.johncon.com/

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Copyright © 2001 John Conover, john@email.johncon.com. All Rights Reserved.
Last modified: Thu Jun 14 21:23:27 PDT 2001 \$Id: 010614132342.5729.html,v 1.0 2001/11/17 23:05:50 conover Exp \$