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Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral

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Author Info
Felix Kubler
Karl Schmedders

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Abstract

We consider an infinite-horizon exchange economy with incomplete markets and collateral constraints. As in the two-period model of Geanakoplos and Zame (2002), households can default on their liabilities at any time, and financial securities are only traded if the promises associated with these securities are backed by collateral. We examine an economy with a single perishable consumption good, where the only collateral available consists of productive assets. In this model, competitive equilibria always exist and we show that, under the assumption that all exogenous variables follow a Markov chain, there also exist stationary equilibria. These equilibria can be characterized by a mapping from the exogenous shock and the current distribution of financial wealth to prices and portfolio choices. We develop an algorithm to approximate this mapping numerically and discuss ways to implement the algorithm in practice. A computational example demonstrates the performance of the algorithm and shows some quantitative features of equilibria in a model with collateral and default. Copyright The Econometric Society 2003.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 71 (2003)
Issue (Month): 6 (November)
Pages: 1767-1793
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Handle: RePEc:ecm:emetrp:v:71:y:2003:i:6:p:1767-1793

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  1. Heaton, John & Lucas, Deborah J, 1996. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 443-87, June. [Downloadable!] (restricted)
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  2. David K. Levine & William Zame, 1996. "Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets," Levine's Working Paper Archive 1954, David K. Levine. [Downloadable!]
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  3. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July. [Downloadable!] (restricted)
  4. Kiyotaki, Nobuhiro & Moore, John, 1997. "Credit Cycles," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 211-48, April.
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  5. Jesus Fernandez-Villaverde & Dirk Krueger, 2004. "Consumption and Saving over the Life Cycle: How Important are Consumer Durables?," 2004 Meeting Papers 357b, Society for Economic Dynamics.
  6. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November. [Downloadable!] (restricted)
  7. Shleifer, Andrei & Vishny, Robert W, 1992. " Liquidation Values and Debt Capacity: A Market Equilibrium Approach," Journal of Finance, American Finance Association, vol. 47(4), pages 1343-66, September. [Downloadable!] (restricted)
  8. Pradeep Dubey & John Geanakoplos & Martin Shubik, 2000. "Default in a General Equilibrium Model with Incomplete Markets," Cowles Foundation Discussion Papers 1247, Cowles Foundation, Yale University. [Downloadable!]
  9. Magill, Michael & Quinzii, Martine, 1996. "Incomplete markets over an infinite horizon: Long-lived securities and speculative bubbles," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 133-170. [Downloadable!] (restricted)
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  10. Timothy J Kehoe & David K Levine, 1993. "Debt Constrained Asset Markets," Levine's Working Paper Archive 1276, David K. Levine. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Hanno Lustig, 2001. "The Market Price of Aggregate Risk and the Wealth Distribution," Finance 0111004, EconWPA, revised 16 Nov 2001. [Downloadable!]
    Other versions:
  2. K.Schmedders & F.Kubler, 2004. "Approximate Versus Exact Equilibria," Computing in Economics and Finance 2004 46, Society for Computational Economics. [Downloadable!]
    Other versions:
  3. Hanno Lustig & Stijn Van Nieuwerburgh, 2004. "A Theory of Housing Collateral, Consumption Insurance and Risk Premia," NBER Working Papers 10955, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  4. Bernard Dumas & Andrew Lyasoff, 2008. "Incomplete-Market Equilibria Solved Recursively on an Event Tree," NBER Working Papers 14629, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Aloisio Araujo & Mario Rui Pascoa & Juan Pablo Torres-Martinez, 2007. "Long-lived collateralized assets and bubbles," Textos para discussão 542, Department of Economics PUC-Rio (Brazil). [Downloadable!]
  6. Martins-da-Rocha, V. F. & Vailakis, Yiannis, 2008. "Collateral, default penalties and almost finite-time solvency," Economics Working Papers (Ensaios Economicos da EPGE) 670, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
    Other versions:
  7. Abdelkrim Seghir & Juan Torres-Martínez, 2008. "Wealth transfers and the role of collateral when lifetimes are uncertain," Economic Theory, Springer, vol. 36(3), pages 471-502, September. [Downloadable!] (restricted)
    Other versions:
  8. Hanno Lustig & Stijn Van Nieuwerburgh, 2006. "Can Housing Collateral Explain Long-Run Swings in Asset Returns?," NBER Working Papers 12766, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  9. Hanno Lustig, . "Exploring the Link between Housing and the Value Premium (joint with Stijn Van Nieuwerburgh)," UCLA Economics Online Papers 389, UCLA Department of Economics. [Downloadable!]
  10. Dumas, Bernard J & Lyasoff, Andrew, 2009. "Incomplete-Market Equilibria Solved Recursively on an Event Tree," CEPR Discussion Papers 7138, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  11. Thiago Revil & Juan Pablo Torres-Martínez, 2007. "Does Collateral Avoid Ponzi Schemes?," Levine's Bibliography 843644000000000339, UCLA Department of Economics. [Downloadable!]
  12. Manjira Datta & Leonard J. Mirman & Olivier F. Morand & Kevin L. Reffett, 2005. "Markovian Equilibrium in Infinite Horizon Economies with Incomplete Markets and Public Policy," Tinbergen Institute Discussion Papers 05-013/2, Tinbergen Institute. [Downloadable!]
    Other versions:
  13. Timothy J. Kehoe & David K. Levine, 2006. "Bankruptcy and Collateral in Debt Constrained Markets," NBER Working Papers 12656, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  14. Zhigang Feng & Jianjun Miao & Adrian Peralta-Alva & Manual Santos, 2009. "Numerical Simulation of Nonoptimal Dynamic Equilibrium Models," Working Papers 0912, University of Miami, Department of Economics. [Downloadable!]
    Other versions:
  15. Hanno Lustig, 2004. "Can Housing Collateral Explain Long-Run Swings in Asset Returns? (joint with Stijn Van Nieuwerburgh)," UCLA Economics Online Papers 322, UCLA Department of Economics. [Downloadable!]
  16. Junjian Miao & Manuel Santos, 2005. "Numerical Solution of Dynamic Non-Optimal Economies," Boston University - Department of Economics - Working Papers Series WP2005-003, Boston University - Department of Economics. [Downloadable!]
    Other versions:
  17. Marques, Luis B, 2007. "Welfare Implications of Exchange Rate Changes," MPRA Paper 5721, University Library of Munich, Germany. [Downloadable!]
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