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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.

Suggested Citation

  • Pradeep Dubey & John Geanakoplos & Martin Shubik, 2000. "Default in a General Equilibrium Model with Incomplete Markets," Cowles Foundation Discussion Papers 1247, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1247
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    1. Allen, Franklin & Gale, Douglas, 1991. "Arbitrage, Short Sales, and Financial Innovation," Econometrica, Econometric Society, vol. 59(4), pages 1041-1068, July.
    2. Franklin Allen, Douglas Gale, 1988. "Optimal Security Design," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 229-263.
    3. Pradeep Dubey & John Geanakoplos & Martin Shubik, 1988. "Default and Efficiency in a General Equilibrium Model with Incomplete Markets," Cowles Foundation Discussion Papers 879R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1989.
    4. 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.
    5. Hellwig, Martin F, 1981. "Bankruptcy, Limited Liability, and the Modigliani-Miller Theorem," American Economic Review, American Economic Association, vol. 71(1), pages 155-170, March.
    6. Hellwig, Martin, 1987. "Some recent developments in the theory of competition in markets with adverse selection ," European Economic Review, Elsevier, vol. 31(1-2), pages 319-325.
    7. 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.
    8. 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.
    9. George A. Akerlof, 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, Oxford University Press, vol. 84(3), pages 488-500.
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    Cited by:

    1. Eva Catarineu-Rabell & Patricia Jackson & Dimitrios Tsomocos, 2005. "Procyclicality and the new Basel Accord - banks’ choice of loan rating system," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 537-557, October.
    2. Charles A. E. Goodhart, 2005. "What Can Academics Contribute to the Study of Financial Stability?," The Economic and Social Review, Economic and Social Studies, vol. 36(3), pages 189-203.
    3. Martin Summer, 2003. "Banking Regulation and Systemic Risk," Open Economies Review, Springer, vol. 14(1), pages 43-70, January.
    4. Tsomocos, Dimitrios P., 2003. "Equilibrium analysis, banking, contagion and financial fragility," LSE Research Online Documents on Economics 24826, London School of Economics and Political Science, LSE Library.
    5. Goodhart, Charles A. E. & Sunirand, Pojanart & Tsomocos, Dimitrios P., 2004. "A model to analyse financial fragility: applications," Journal of Financial Stability, Elsevier, vol. 1(1), pages 1-30, September.
    6. Igor Livshits & James MacGee & Michèle Tertilt, 2007. "Consumer Bankruptcy: A Fresh Start," American Economic Review, American Economic Association, vol. 97(1), pages 402-418, March.
    7. Tsomocos, Dimitrios P., 2003. "Equilibrium analysis, banking and financial instability," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 619-655, July.
    8. Athreya, Kartik, 2006. "Fresh start or head start? Uniform bankruptcy exemptions and welfare," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 2051-2079, November.
    9. Athreya, Kartik B., 2002. "Welfare implications of the Bankruptcy Reform Act of 1999," Journal of Monetary Economics, Elsevier, vol. 49(8), pages 1567-1595, November.
    10. Kartik B. Athreya, 2003. "Unemployment insurance and personal bankruptcy," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 33-53.
    11. Dubey, Pradeep & Geanakoplos, John, 2003. "Monetary equilibrium with missing markets," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 585-618, July.
    12. Goetz von Peter, 2003. "A Unified Approach to Credit Crunches, Financial Instability, and Banking Crises," Macroeconomics 0312006, University Library of Munich, Germany.
    13. Felix Kubler & Karl Schmedders, 2003. "Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral," Econometrica, Econometric Society, vol. 71(6), pages 1767-1793, November.
    14. M. Shubik & D. Tsomocos, 1992. "A strategic market game with a mutual bank with fractional reserves and redemption in gold," Journal of Economics, Springer, vol. 55(2), pages 123-150, June.
    15. Pradeep Dubey & John Geanakoplos, 2001. "Signalling and Default: Rothschild-Stiglitz Reconsidered," Cowles Foundation Discussion Papers 1305, Cowles Foundation for Research in Economics, Yale University.
    16. Pavan, Marina, 2008. "Consumer durables and risky borrowing: The effects of bankruptcy protection," Journal of Monetary Economics, Elsevier, vol. 55(8), pages 1441-1456, November.
    17. Kartik B. Athreya, 2001. "The growth of unsecured credit : are we better off?," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 11-33.
    18. Kannai, Yakar & Rosenmüller, Joachim, 2010. "Strategic behavior in financial markets," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 148-162, March.
    19. Jose S. Penalva Zuasti, 2008. "A Study of the Interaction of Insurance and Financial Markets: Efficiency and Full Insurance Coverage," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 313-342.
    20. Eduardo Siandra, 2002. "The Economics of financial Matching," Documentos de Trabajo (working papers) 1002, Department of Economics - dECON.
    21. Paul Tucker, 2009. "Money And Credit, Twelve Months On," Manchester School, University of Manchester, vol. 77(s1), pages 1-20, September.
    22. Martin Shubik & Shontan Yao, 1990. "Gold, liquidity and secured loans in a multistage economy," Journal of Economics, Springer, vol. 52(1), pages 1-23, February.

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    Keywords

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

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