The ''new'' Geithner plan

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Forse Giulio si riferiva a cose come questa?

Econometrica, January 2005 - Volume 73 Issue 1 Page 203 - 243


Uncertainty and Risk in Financial Markets

Luca Rigotti
Chris Shannon


This paper considers a general equilibrium model in which the distinction between uncertainty and risk is formalized by assuming agents have incomplete preferences over state-contingent consumption bundles, as in Bewley (1986). Without completeness, individual decision making depends on a set of probability distributions over the state space. A bundle is preferred to another if and only if it has larger expected utility for all probabilities in this set. When preferences are complete this set is a singleton, and the model reduces to standard expected utility. In this setting, we characterize Pareto optima and equilibria, and show that the presence of uncertainty generates robust indeterminacies in equilibrium prices and allocations for any specification of initial endowments. We derive comparative statics results linking the degree of uncertainty with changes in equilibria. Despite the presence of robust indeterminacies, we show that equilibrium prices and allocations vary continuously with underlying fundamentals. Equilibria in a standard risk economy are thus robust to adding small degrees of uncertainty. Finally, we give conditions under which some assets are not traded due to uncertainty aversion.

Thanks Valter, this is in fact a very interesting reference. I think Giulio summarized the matter well. If the lack of trade is due to the fact that bank managers have no idea of what the toxic assets are worth then we want at least to know that. Right now they are not saying that they have no idea, or they have multiple priors or any other fancy decision-theoretic statement. They are claiming that the assets are really, really worth more, much more, than what the market is willing to pay, because the mortgagors are mostly going to pay their debts. But there is no reason why we should believe those statements. Quite simply, they are not incentive compatible.

Asking them to put their money where their mouth is the elementary thing to do in these cases. If they really believe what they claim they should have no problem in betting their own money, as opposed to taxpayers' money. It is true that if they refuse we may not learn the true reason: it may be because they have pessimistic information or because they have no information and are simply confused. But, at the end of the day, this is not really important. We would still learn that they do not have any optimistic information, and that's what really matters.

This is close to home, so I feel I have to say something. The post mentions (in different words) willingness to sell and willigness to buy (or what is sometimes called a bid-ask spread). The fact that bank managers are willing to sell at 60, does not necessarily imply they know what the asset is worth. In fact, they may think the asset is worth anywhere between 30 and 60, and yet not be willing to sell for less than 60. In an enviroment like the one we described in the paper, when the range of probabilities used to evaluate the assets is very large no-trade results exactly because sellers ask for too high a price relative to what buyers are willing to pay for. I am not sure this is exactly what is happening with the toxic assets (I'm a poor micro theorist), but I suspect (Knightian) uncertainty could be one of the explanations.

Luca: serious question. In what sense "ambiguity" fits the observations better than the plain idea that those who have the info believes this stuff is worth nothing? I understand that under ambiguity if someone follows, say, a α-MEU rule (as in Ghirardato, Maccheroni, Marinacci) one tends to invest less (in fact, see Paolo&Co on this).

My issue is: is there a way to tell the two things apart? That one knows better than the other versus both being in an "ambiguous" situation?

Molto interessante, Valter.

Lungi da me fare il filologo, ma credo che 'ambiguity' abbia prevalso su 'uncertainty' perche' la distinzione tra quest'ultima e 'risk' e' pian piano svanita.

Ecco qui una sintesi "enciclopedica": formalizzare uncertainty come incompletezza delle preferenze o, diciamo cosi', incompletezza delle aspettative e' equivalente.

Non c'e' dubbio che il meccanismo suggerito da Sandro e' in grado, quantomeno, di rivelare se questo e' il caso.

Io credo tu abbia ragione, Giulio. La maggioranza degli economisti hanno sempre usato "risk" e "uncertainty" come sinonimi ed e' difficile cambiare abitudine. Ambiguity, termine usato originariamente da Ellsberg, e' un vocabolo relativamente nuovo per la professione ed ha vita piu' facile. Questo con buona pace di Knight che, nel 1921, fu il primo a distinguere tra uncertainty e risk.

Qui un articolo che rende esplicita la connessione tra il modello mio e di Chris e il problema della valutazione dei toxic assets.