Re: Attempt at a Schema

["Goncalo Fonseca" <fonseca@xxxxxxxxxxxxxxxxxx>]

Barkley (& Colin),

Well, you won't find me in disagreement with the content of what you say.  I
suppose it's your emphasis I dispute.

(1) On Bayesians:  I was dividing theorists by their conception of
probability.  You are absolutely correct that many Bayesians work on the
idea that their are "objective" probabilities to be discovered.  That puts
them in the I.1 "Classical" class, not the II. informational one. Similarly,
many Classical probability theorists also embrace the central limit theorem,
which talks about the convergence of empirical frequency distributions to
objective probabilities, but that doesn't make them "relative frequentists"
because they are not DEFINING probability as that
limit.

So, the only people who I am placing under category II (informational)
category are actually those who define probability as a measure of
"unknowledge" and not something "real". Frank Knight certainly falls under
this (which is one of the reasons that Lawson's article troubled me). I am
not sure about Dale Poirier.  He would certainly not be in category I, but
could fall under either II or III, depending on his attitude towards
information vs. belief.

(2) On Keynes:

I agree that his attitude may be hard to pin down.  But I don't think he was
ambivalent.  He did write a Treatise on this stuff in 1921, so he must have
had some strong views.

I am not quite persuaded by your claim that he allowed objective randomness.
The magic of the die ("risk") versus calculating "interest rates twenty
years hence" ("uncertainty") lies in the kind of information you have.  The
die provides clear and simple information that permits you to calculate
probabilities with precision.  But to conclude that the probability of a
particlar face on a die is 1/6 does not imply "objectivity". It simply means
that one has not bothered to calculate how the strength of your hand, the
position of the die, the angle of the throw, the friction in the air, etc.
will affect the outcome.  But still, on the basis of the information that
you DO have, you can calculate that probability is 1/6.

On the "interest rate twenty years hence", you have none of the necessary
information to mathematically derive a single probability estimate.  You
might be able, in some circumstances, to derive upper and lower bounds
within which the
probability should lie.  This is how I am reading the quote you provide:

>       "...it [the market valuation] cannot be uniquely correct, since
> our existing knowledge does not provide a sufficient basis for
> a calculated mathematical expectation."

Notice how carefully he uses his words.  He always does this.  Whenever he
talks about the "impossibility" of deriving a precise probability, he always
precedes that remark with "on the basis of existing knowledge" or something
to that effect.  He never simply comes out and says simply "it is unknown".

Which brings me to Colin Danby's query about the 1937 QJE paper.  Its been a
while since I've gone through it carefully, but I don't recall being struck
by "very clear ontological argument about future events". The "interest rate
twenty years hence" is not a random event.  If we had all the relevant
information (assuming this information was obtainable), then it would not be
random.  Keynes conditions his statement here too, e.g.

".About these matters there is no scientific basis on which to form any
calculable probability whatever. We simply do not know.".

where if he is not using the term "scientific" to mean "my 1921
informational theory", then I have  no idea how to interpret this remark.

Also, back to Barkley's point, Ramsey himself also accepted the idea that
his theory was purely "as if".  Indeed, that is the very strength of
Ramsey's theory.  I don't think he was aiming for "usefulness".

So, in sum, I believe you (Barkley) are correct in saying Keynes "was
neither strictly a subjectivist nor an objectivist".  But I believe you are
stretching it when you say "he accepted both".  I would say "he accepted
neither".  He was an informationalist.

(3) On Lucas:

Lucas's claim that people's probability assessments "converge" to an
"objectively true" probability is pure bluster on his part.  With rational
expectations, they converge to the probabilities the economist builds into
the structural model -- which may be a correct or incorrect representation
of the economy. So that's not quite "objective" probability.     It's an
assumption Keynes would have disputed vehemently.  So point taken.

If it helps take the stain off my remark, then let me say I prefer Roy
Radner's formulation of "rational expectations" which is altogether cleaner
and blusterless. Radner does not assume the structural model is "true", but
simply believed by all agents.  So if the structural model is stupid and
wrong, rational expectations would argue that  information and expectations
would converge to collective stupidity -- and that's all it says.

Be that as it may, in the schema I laid out, I was categorizing theories on
the basis of how they viewed the assessment of probability (i.e.
objectively, informationally or subjectively).  In that sense (and in that
sense only) might Keynes and Lucas (OK, Radner) fall under the same
category.  On all other points (e.g. structural knowledge), I would be happy
for them to part ways.

Goncalo