RE: Attempt at a Schema

[James Juniper <James.Juniper@xxxxxxxxxxxx>]

	Dear Goncalo,

	I agree entirely with you're assessment of Keynes as an objectivist and
his response to Ramsey. However, in terms of modern finance theory,
Arrow-Debreu prices represent risk-neutral probabilities that are, in
equilibrium, independent of individual subjective utilities. In a multi-period
context, these risk-neutral probabilities are martingales associated with the
transformation of the stochastic process for discounted stock prices (after
ignoring or re-investing dividend proceeds). This martingale transformation can
be interpreted in two ways: utility theoretic (reflecting the intertemporal
marginal utility of consumption); or based on non-arbitrage (the latter assumed
to be an ontological property of equilibrium, possessing much the same status
as Keynes' Chapter 17 description of asset market equilibrium: although in
Keynes' analysis the latter is broadened to encompass liquidity premia and not
just risk-premia). Thus Arrow-Debreu prices can be veiwed as an objective
manifestation of the workings of the law of one price within financial markets.
Of course, as Paul Davidson emphasizes, problems arise for Arrow-Debreu pricing
when markets are incomplete (e.g. due to stochastic risk-free interest rates,
stochastic volatility, or discrete rather than continuous rebalancing of
portfolios, or finally, due to non-ergodicity).

> On lumping Keynes and Lucas together: I absolutely insist on this.  Keynes
> and Lucas have effectively the SAME theory about how probability assessments
> are made.  They both believe that if people share the same information, they
> make the same probability estimates. The difference between them lies in
> their justification of this (structural model-uniformity for Lucas,
> I-don't-quite-know-what for Keynes) and in the assumptions of the
> information available to people (all info will "come out" for Lucas, most
> info does not exist, for Keynes).
>
	The distinction between Keynes and the new Knightian uncertainty
theorists like Gilboa and Schmeidler, Epstein and Wang etc. is much harder to
establish. In my view it pertains to your later comments (see below) about how
information is processed and for what purpose. In incomplete markets there is
an infinity of potential martingale measures. For example, in pricing options
in incomplete markets (ie. establishing bounds over the gap between buyer and
seller prices) some theorists (Stutzer, 1989) use minimum cross entropy methods
based on plausible axioms of statistical inference while, for delta hedging
purposes, other theorists (Schwiezer, 1992,1993) use minimum martingale methods
(which are related to minimum variance hedging). Others recommend the
application of plausible bounds over the gain-loss ratio  (Bernardo ands
Ledoit, 2000) or over the Sharpe ratio (Cochrane and Saa-Requiro's good-deal
bounds, 2000). Nevertheless, I would argue that these stipulated bounds would
also fluctuate due to variations in uncertainty aversion (liquidity
preference), and not just due to variations in transaction costs, the market
price of risk, or the volatility of the underlying stochastic process for
interest rates or asset prices.

	However, I also think that an understanding of the distinction between
Keynes and the Knightians requires a deeper criticism of representative agent
and pure exchange assumptions in macroeconomic/financial modeling. Once
decisions about physical investment are separated from decisions about
consumption/savings and about financial investment this opens the door for the
sometimes independent influence of specific types of liquidity preference over
each these different long-term economic decisions. Moreover, it exposes the
economy to the possibility of what could loosely be called coordination
failure.
	
> Personally, I think subjective beliefs are the ultimate guides to action,
> but I also think that these beliefs ought to be "consistent" with the
> information and data available.   So, for me, the true source of the problem
> is perhaps not how complicated the world is (i.e. the information
> available), but how this information is processed differently by people and
> the consequences of this. The same stock market data has led economists to
> believe it is a bubble, and many practitioners to believe a "new economy" is
> in the offering.  Keynes's liquidity preference theory has aspects of this.
> Same data, different beliefs -- a dangerous combination for the stability of
> the economy.
>
>