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Default in a General Equilibrium Model with Incomplete Markets

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Abstract

We extend the standard model of general equilibrium with incomplete markets (GEI) to allow for default. The equilibrating variables include aggregate default levels, as well as prices of assets and commodities. Default can be either strategic, or due to ill-fortune. It can be caused by events directly affecting the borrower, or indirectly as part of a chain reaction in which a borrower cannot repay because he himself has not been repaid. Each asset is defined by its promises A, the penalties lambda for default, and the limitations Q on its sale. The model is thus named GE(A,lambda,Q). Each asset is regarded as a pool of promises. Different sellers will often exercise their default options differently, while each buyer of an asset receives the same pro rata share of all deliveries. This model of assets represents for example the securitized mortgage market and the securitized credit card market. Given any collection of assets, we prove that equilibrium exists under conditions similar to those necessary to guarantee the existence of GEI equilibrium. We argue that default is thus reasonably modeled as an equilibrium phenomenon. Moreover, we show that more lenient lambda which encourage default may be Pareto improving because they allow for better risk spreading. Our definition of equilibrium includes a condition on expected deliveries for untraded assets that is similar to the trembling hand refinements used in game theory. Using this condition, we argue that the possibility of default is an important factor in explaining which assets are traded in equilibrium. Asset promises, default penalties, and quantity constraints can all be thought of as determined endogenously by the forces of supply and demand. Our model encompasses a broad range of moral hazard, adverse selection, and signalling phenomena (including the Akerlof lemons model and Rothschild-Stiglitz insurance model) in a general equilibrium framework. Many authors (including Akerlof , Rothschild and Stiglitz) have suggested that equilibrium may not exist in the presence of adverse selection. But our existence theorem shows that it must. The problem is the inefficiency of the resulting equilibrium, not its nonexistence. The power of perfect competition simplifies many of the complications attending the finite player, game theoretic analyses of the same topics. The Modigliani-Miller theorem typically fails to hold when there is the possibility that the firm or one of its investors might default.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1247.

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Length: 68 pages
Date of creation: Jan 2000
Date of revision:
Handle: RePEc:cwl:cwldpp:1247

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Default; incomplete markets; adverse selection; moral hazard; equilibrium refinement; endogenous assets;

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References

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  1. Hellwig, Martin F, 1981. "Bankruptcy, Limited Liability, and the Modigliani-Miller Theorem," American Economic Review, American Economic Association, vol. 71(1), pages 155-70, March.
  2. Hellwig,Martin, 1986. "Some recent developments in the theory of competition in markets with adverse selection," Discussion Paper Serie A 82, University of Bonn, Germany.
  3. Franklin Allen & Douglas Gale, . "Optimal Security Design," Rodney L. White Center for Financial Research Working Papers 26-87, Wharton School Rodney L. White Center for Financial Research.
  4. Franklin Allen & Douglas Gale, . "Arbitrage, Short Sales and Financial Innovation," Rodney L. White Center for Financial Research Working Papers 10-89, Wharton School Rodney L. White Center for Financial Research.
  5. Stiglitz, Joseph E & Weiss, Andrew, 1981. "Credit Rationing in Markets with Imperfect Information," American Economic Review, American Economic Association, vol. 71(3), pages 393-410, June.
  6. Prescott, Edward C & Townsend, Robert M, 1984. "Pareto Optima and Competitive Equilibria with Adverse Selection and Moral Hazard," Econometrica, Econometric Society, vol. 52(1), pages 21-45, January.
  7. Smith, Vernon L, 1972. "Default Risk, Scale, and the Homemade Leverage Theorem," American Economic Review, American Economic Association, vol. 62(1), pages 66-76, March.
  8. Rothschild, Michael & Stiglitz, Joseph E, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, MIT Press, vol. 90(4), pages 630-49, November.
  9. Akerlof, George A, 1970. "The Market for 'Lemons': Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, MIT Press, vol. 84(3), pages 488-500, August.
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