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DEFAULT PENALTY AS A DISCIPLINARY AND SELECTION MECHANISM IN PRESENCE OF MULTIPLE EQUILIBRIA. Shyam Sunder (From the joint work of Juergen Huber, Martin Shubik and Shyam Sunder) Workshop on Experimental Social Sciences Mumbai Vidyapeeth December 28-29, 2009.
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DEFAULT PENALTY AS A DISCIPLINARY AND SELECTION MECHANISM IN PRESENCE OF MULTIPLE EQUILIBRIA Shyam Sunder (From the joint work of Juergen Huber, Martin Shubik and Shyam Sunder) Workshop on Experimental Social Sciences Mumbai Vidyapeeth December 28-29, 2009
A basic question and several solutions • In the microeconomic theory of the price system it is possible that several equilibria may be present. • Macro economists tend to ignore this possibility as essentially irrelevant • Are they right? Does this represent a gap between macro practice and micro theory? • Is there a satisfactory solution, and does it matter?
A Summary of Experimental Evidence • Default penalties and bankruptcy laws needed to implement general equilibrium as a playable game and to mitigate strategic defaults can also provide conditions for uniqueness • Assignment of default penalty on fiat money economy goes to selected equilibrium • Role of accounting/bankruptcy aspects of social mechanisms in resolving mathematically intractable multiplicity problem
The general equilibrium proof of the existence of a competitive price system was both a triumph and a disaster • It provided a deep mathematization for the existence of equilibrium conditions for efficient prices that cut out time and uncertainty
A whole school of mathematical economics was born with considerable sophistication but little connection with the context and realities of the ongoing economy
The work of Arrow, Debreu and Mckenzie proved the existence of efficient prices but did nothing about their evolution or their fairness. This can be seen easily when we observe that an economy may have many equilibria
One of the tasks of extreme mathematical difficulty is what necessary and sufficient conditions are required for a unique competitive equilibrium to exist? We believe that the answer that society gives to both uniqueness and fairness lies in extending the model to embed it an a dynamic model of society that permits default and requires default laws.
Our program involves both theory and experimentation. • We utilize an example of an exchange economy with three equilibrium points constructed by Shapley and Shubik. This is illustrated in the next slide
Figure 1: An Exchange Economy with Two Goods and Three Competitive Equilibria
We observe that it has three equilibrium points the two extreme ones favoring either traders of type a or b. • The middle is more equitable (and is not stable under Walrasian dynamics)
When this exchange economy is remodeled as a playable strategic market game, if borrowing is permitted default rules must be specified to take care of every possibility in the system. But these rules will entail some action of negative worth to the defaulter and are denominated in money. Thus they link money to the individual’s utility
Technically if the penalties are set equal to or above the Lagrangian multipliers of the related general equilibrium model this will be sufficient to prevent strategic bankruptcy. Thus by selecting the penalties we can select the equilibrium point to be chosen.
In selecting the penalties associated with the middle equilibrium the society resolves its “fairness” problem but from the viewpoint of finance it does not select the minimal cash flow equilibrium. This is shown in the next slide
In higher dimensions it is always straightforward to select the minimum cash flow equilibrium, but this is not true for the selection of “fair” as well as efficient equilibrium • In fact government selects the penalties more or less blindly and in the course of the application of legal and political pressures they are adjusted
There is a considerable literature on multiple equilibria as is summarized by Morris and shin(2000) • They deal primarily with Bayesian equilibria with noise • Our approach here is different from, but complementary with, this literature. We stress the laws of society as providing direct strong coordinating and coercive devices for the economy
Treatment 1: Conjectures • In Treatment 1 the process fails to converge to any of the three competitive equilibria. • In Treatment 1 the middle CE is favored. • In Treatment 1 the choice of the medium of exchange or numeraire does not influence the outcomes (prices and distribution of goods).
Treatment 1 • No clear convergence to any of the three CEs. • It does not matter which of the two goods in this exchange economy is chosen as the numeraire. • Efficiency in all markets is high, demonstrating that such simple markets serve well as coordination mechanisms.
Treatment 2: Conjectures • 4. In Treatment 2 the system converges and can be made to converge to any of the three equilibria guided by the selection of parameter μ(default penalty). • 5. In Treatment 2 net money holdings will be equal to the equilibrium level of zero.
Treatment 2 • These results of T2 and T2-R broadly confirm the results from T1—the introduction of a money allows convergence to the unique equilibrium that is defined by the value/default penalty associated with the money.
Treatment 3: Conjectures • 6. In Treatment 3 the unique equilibrium defined by the default penalties μ1 and μ2 is approached.
Treatment 3 • The unique equilibrium defined by the chosen penalty is approached in Treatment 3.
Conclusions • Treatment 1: Empirical support for theoretical indeterminacy. • Treatment 2: Salvage value/default penalty of a fiat money can be chosen to achieve any of the competitive equilibria of the economy. • Other penalties generate specific equilibrium outcomes (not necessarily economize on use of money) • Institutional arrangements in a society provide the means to resolve the possibility of multiple equilibria in an economy. • Empirical support for the attitudes of macroeconomists who do not regard the non-uniqueness of competitive equilibria as a major applied problem.
