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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36609.

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Date of creation: 01 Jan 2011
Date of revision: 12 Feb 2012
Handle: RePEc:pra:mprapa:36609

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Related research

Keywords: rational bubbles; endogenous debt limits; not-too-tight constraints; self-enforcing debt; limited enforcement;

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References

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  1. Azariadis, Costas & Kaas, Leo, 2013. "Endogenous credit limits with small default costs," Journal of Economic Theory, Elsevier, vol. 148(2), pages 806-824.
  2. Kehoe, Timothy J & Levine, David K, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 865-88, October.
  3. Fernando Alvarez & Urban J. Jermann, 1999. "Quantitative Asset Pricing Implications of Endogenous Solvency Constraints," NBER Working Papers 6953, National Bureau of Economic Research, Inc.
  4. Bloise, Gaetano & Reichlin, Pietro, 2008. "Asset Prices, Debt Constraints and Inefficiency," CEPR Discussion Papers 6779, C.E.P.R. Discussion Papers.
  5. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-98, May.
  6. Kevin X.D. Huang & Jan Werner, 2000. "Asset price bubbles in Arrow-Debreu and sequential equilibrium," Economic Theory, Springer, vol. 15(2), pages 253-278.
  7. Woodford, Michael, 1990. "Public Debt as Private Liquidity," American Economic Review, American Economic Association, vol. 80(2), pages 382-88, May.
  8. 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.
  9. Narayana Kocherlakota, 2010. "Implications of Efficient Risk Sharing Without Commitment," Levine's Working Paper Archive 2053, David K. Levine.
  10. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
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Cited by:
  1. 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.
  2. 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.
  3. Jan Werner, 2012. "Rational Asset Pricing Bubbles Revisited," 2012 Meeting Papers 1165, Society for Economic Dynamics.
  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.

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