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Martingale properties of self-enforcing debt

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  • Bidian, Florin
  • Bejan, Camelia

Abstract

Not-too-tight (NTT) debt limits are endogenous restrictions on debt that prevent agents from defaulting and opting for a specified continuation utility, while allowing for maximal credit expansion (Alvarez and Jermann, 2000). For an agent facing some fixed prices for the Arrow securities, we prove that discounted NTT debt limits must differ by a martingale. Discounted debt limits are submartingales/martingales under an interdiction to trade/borrow, and can be supermartingales under a temporary interdiction to trade. With high interest rates and borrowing limited by the agent's ability to repay debt out of his future endowments, nonpositive NTT debt limits are unique. With low interest rates, bubbles limited by the size of the total martingale components in debt limits can be sustained in equilibrium. Bubbles arise in response to debt limits more restrictive (at the prevailing interest rates) than the total amount of self-enforcing debt allowed by the underlying enforcement limitations.

Suggested Citation

  • Bidian, Florin & Bejan, Camelia, 2011. "Martingale properties of self-enforcing debt," MPRA Paper 36609, University Library of Munich, Germany, revised 12 Feb 2012.
    • Handle: RePEc:pra:mprapa:36609
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    References listed on IDEAS

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    1. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
    2. Bejan, Camelia & Bidian, Florin, 2014. "Bubbles and trading in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 137-144.
    3. Koeppl, Thorsten V., 2007. "Optimal dynamic risk sharing when enforcement is a decision variable," Journal of Economic Theory, Elsevier, vol. 134(1), pages 34-60, May.
    4. Kocherlakota, Narayana R., 1992. "Bubbles and constraints on debt accumulation," Journal of Economic Theory, Elsevier, vol. 57(1), pages 245-256.
    5. Alvarez, Fernando & Jermann, Urban J, 2001. "Quantitative Asset Pricing Implications of Endogenous Solvency Constraints," The Review of Financial Studies, Society for Financial Studies, vol. 14(4), pages 1117-1151.
    6. David Croix & Philippe Michel, 2007. "Education and growth with endogenous debt constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 509-530, December.
    7. Bulow, Jeremy & Rogoff, Kenneth, 1989. "Sovereign Debt: Is to Forgive to Forget?," American Economic Review, American Economic Association, vol. 79(1), pages 43-50, March.
    8. Azariadis, Costas & Kaas, Leo, 2013. "Endogenous credit limits with small default costs," Journal of Economic Theory, Elsevier, vol. 148(2), pages 806-824.
    9. Xavier Mateos-Planas & Giulio Seccia, 2013. "Consumer Default with Complete Markets: Default-based Pricing and Finite Punishment," Working Papers 711, Queen Mary University of London, School of Economics and Finance.
    10. Timothy J. Kehoe & David K. Levine, 1993. "Debt-Constrained Asset Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 865-888.
    11. Jürgen Eichberger & Klaus Rheinberger & Martin Summer, 2014. "Credit risk in general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 407-435, October.
    12. Dirk Krueger & Fabrizio Perri, 2006. "Does Income Inequality Lead to Consumption Inequality? Evidence and Theory -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(1), pages 163-193.
    13. Fernando Alvarez & Urban J. Jermann, 2000. "Efficiency, Equilibrium, and Asset Pricing with Risk of Default," Econometrica, Econometric Society, vol. 68(4), pages 775-798, July.
    14. Bloise, Gaetano & Reichlin, Pietro, 2011. "Asset prices, debt constraints and inefficiency," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1520-1546, July.
    15. Bidian, Florin & Bejan, Camelia, 2011. "Supplement to ``Martingale properties of self-enforcing debt''," MPRA Paper 36610, University Library of Munich, Germany, revised 12 Feb 2012.
    16. Christian Hellwig & Guido Lorenzoni, 2009. "Bubbles and Self-Enforcing Debt," Econometrica, Econometric Society, vol. 77(4), pages 1137-1164, July.
    17. Florin Bidian & Camelia Bejan, 2015. "Martingale properties of self-enforcing debt," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 35-57, September.
    18. Min Wang, 2014. "Optimal education policies under endogenous borrowing constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 135-159, January.
    19. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120, February.
    20. Gaetano Antinolfi & Costas Azariadis & James B. Bullard, 2007. "Monetary policy as equilibrium selection," Review, Federal Reserve Bank of St. Louis, vol. 89(Jul), pages 331-342.
    21. Kocherlakota, Narayana, 2008. "Injecting rational bubbles," Journal of Economic Theory, Elsevier, vol. 142(1), pages 218-232, September.
    22. Kevin X.D. Huang & Jan Werner, 2000. "Asset price bubbles in Arrow-Debreu and sequential equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 253-278.
    23. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-598, May.
    24. Gaetano Bloise & Pietro Reichlin & Mario Tirelli, 2013. "Fragility of Competitive Equilibrium with Risk of Default," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 16(2), pages 271-295, April.
    25. Woodford, Michael, 1990. "Public Debt as Private Liquidity," American Economic Review, American Economic Association, vol. 80(2), pages 382-388, May.
    26. Bejan, Camelia & Bidian, Florin, 2010. "Limited enforcement, bubbles and trading in incomplete markets," MPRA Paper 36819, University Library of Munich, Germany, revised 20 Feb 2012.
    27. Xavier Mateos-Planas & Giulio Seccia, 2013. "Consumer Default with Complete Markets: Default-based Pricing and Finite Punishment," Working Papers 711, Queen Mary University of London, School of Economics and Finance.
    28. Weerachart Kilenthong, 2011. "Collateral premia and risk sharing under limited commitment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 475-501, April.
    29. Narayana R. Kocherlakota, 1996. "Implications of Efficient Risk Sharing without Commitment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 595-609.
    30. Thorsten Koeppl & Cyril Monnet & Erwan Quintin, 2014. "Efficient contract enforcement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 161-183, January.
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    Citations

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    Cited by:

    1. Bidian, Florin, 2016. "Robust bubbles with mild penalties for default," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 141-153.
    2. Victor Filipe Martins da Rocha & Yiannis Vailakis, 2015. "Constrained Efficiency Without Commitment," Working Papers hal-01097121, HAL.
    3. Bidian, Florin & Bejan, Camelia, 2011. "Supplement to ``Martingale properties of self-enforcing debt''," MPRA Paper 36610, University Library of Munich, Germany, revised 12 Feb 2012.
    4. Gaetano Bloise & Pietro Reichlin & Mario Tirelli, 2013. "Fragility of Competitive Equilibrium with Risk of Default," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 16(2), pages 271-295, April.
    5. Bejan, Camelia & Bidian, Florin, 2010. "Limited enforcement, bubbles and trading in incomplete markets," MPRA Paper 36819, University Library of Munich, Germany, revised 20 Feb 2012.
    6. Nicolas Houy & Frédéric Jouneau & François Le Grand, 2020. "Defaulting firms and systemic risks in financial networks: a normative approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 503-526, September.
    7. Bloise, Gaetano & Polemarchakis, Herakles & Vailakis, Yiannis, 2017. "Sovereign debt and incentives to default with uninsurable risks," Theoretical Economics, Econometric Society, vol. 12(3), September.
    8. Bejan, Camelia & Bidian, Florin, 2014. "Bubbles and trading in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 137-144.
    9. Victor Filipe Martins da Rocha & Yiannis Vailakis, 2014. "Self-enforcing Debt, Reputation, and the Role of Interest Rates," Working Papers hal-01097114, HAL.
    10. Florin Bidian & Camelia Bejan, 2015. "Martingale properties of self-enforcing debt," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 35-57, September.
    11. Neus Herranz & Stefan Krasa & Anne P. Villamil, 2015. "Entrepreneurs, Risk Aversion, and Dynamic Firms," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 1133-1176.
    12. Victor Filipe Martins da Rocha & Toan Phan & Yiannis Vailakis, 2019. "Debt Limits and Credit Bubbles in General Equilibrium," Post-Print hal-02429759, HAL.
    13. Victor Filipe Martins da Rocha & Yiannis Vailakis, 2015. "On the Sovereign Debt Paradox," Working Papers hal-01097118, HAL.
    14. Filipe Martins da Rocha & Yiannis Vailakis, 2017. "Borrowing in Excess of Natural Ability to Repay," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 23, pages 42-59, January.
    15. Jan Werner, 2012. "Rational Asset Pricing Bubbles Revisited," 2012 Meeting Papers 1165, Society for Economic Dynamics.
    16. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2017. "On the sovereign debt paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(4), pages 825-846, December.
    17. Bidian, Florin, 2015. "Portfolio constraints, differences in beliefs and bubbles," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 317-326.
    18. Werner, Jan, 2014. "Rational asset pricing bubbles and debt constraints," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 145-152.

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    More about this item

    Keywords

    rational bubbles; endogenous debt limits; not-too-tight constraints; self-enforcing debt; limited enforcement;
    All these keywords.

    JEL classification:

    • E0 - Macroeconomics and Monetary Economics - - General
    • G0 - Financial Economics - - General

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