Re: Attempt at a Schema

["J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>]

     Let me begin by saying that I second the useful
remarks by both Ted Winslow and James Juniper
on this that they have just made.
     With regard to Keynes' views, he argued that probability
ultimately involves "logical relations," a view that I think
he got from Moore.  The Treatise certainly contains strong
views, but it also exhibits a wide range of positions.  Keynes
clearly distinguished different cases and how they should be
viewed, with dice rolling at one extreme and the cases where
"no probability exists" at the other, which he later seems to
have identified with long run economic forecasts where free
will and social interactions and expectations about others'
expectations all come to mess things up totally.
      Of course the dice rolling case is a central one.  Your
remarks regarding the factors determining the outcomes
show something closer to the pure subjectivist view.  There
are no objective probability distributions, even for dice rolling,
and what happens depends on the details of the dice, how
they are thrown, etc. etc.  Clearly Keynes is not that strong of
a Bayesian subjectivist, although he seems to be much more
of a subjectivist than a classical in general.  It is more that he
reserves a narrow zone for classical frequentism.
     BTW, the whole issue of determinism and ontology and
epistemology can be seen through the example of dice rolling.
Thus, the Einseinian determinist (who said that God does not
roll dice) could say that God (or the super computing, infinitely
knowledgeable, hypothetical being) will know with absolute
certainty the outcome of each roll of the dice because this
being will know all those details of the dice, the throw of the
hand, the details of the surface they land on, any wind currents
that are passing by, etc. etc.  But, we fall back on probabilities
to give our answers because of our lack of information.
       I would note that Keynes here would (probably) note
the issue of logical relations and cite these as the basis for
the calculation of those probabilities.  The only valid basis for
disbelieving such probabilities would be the case of a loaded
die.  But then, how does one determine that one is dealing with
a loaded die....   ?  (back to the Bayesian problem)
         As regards Lucas, I am pleased that you agree to back
off your original claims.  I would accept that Radner's formulation
looks a lot more "Keynesian."  Indeed, this is the basis for the
whole theory of sunspot equilibria (which Paul Davidson does
not like), in which multiple equilibria arise because of mutliple
possible self-fulfillling prophecies about each others' expectations.
Certainly the developers of that theory saw it as inspired by and
directly deriving from Keynes.  I agree with that. We really do live
in a world of beauty contests, and to the nth degree and higher...
       With regard to Lucas, let me pound the point in even harder.
You accurately describe as "pure bluster" Lucas' claim that
agents are converging on reality in their expectations.  You
accurately note that what they are converging on is a structural
model.  But, drawing on Muth's original characterization that I
have never seen Lucas disavow anywhere, the model that it is
assumed that they are converging on is, in fact, the true model
of reality, or at least one that accurately describes and forecasts
reality.  Allow me to quote Muth directly from his very first
presentation of the idea of rational expectations (1961,
Econometrica, pp. 315-316):
     "...expectations, since they are informed predictions of
future events, are essentially the same as predictions of the
relevant economic theory.
     ...expectations of firms (or, more generally, the subjective
probability distribution of outcomes) tend to be distributed,
for the same information set, about the prediction of the theory
(or, the "objective" probability distribution of outcomes)."
      Despite the caveats about the information set and the " "
about "objective," it is clear that the expectations are based
on a ("the relevant") theory that actually forecasts the future
on average. Lucas fully buys into this, as near as I can tell.
But, this is very far from Keynes, very far indeed.
Barkley Rosser

-----Original Message-----
From: Goncalo Fonseca <fonseca@xxxxxxxxxxxxxxxxxx>
To: J. Barkley Rosser, Jr. <rosserjb@xxxxxxx>
Cc: Colin Danby <danbyc@xxxxxxx>; pkt <pkt@xxxxxxxxxxxxxxxx>
Date: Wednesday, December 20, 2000 9:29 AM
Subject: Re: Attempt at a Schema


>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
>
>