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The Design of Optimal Collateralized Contracts

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Abstract

This paper presents a two-period optimal contracting model of collateral. A borrower values a capital good and a composite non-capital good. He privately observes an income shock in the composite good in the second period. Collateralization of both goods occurs in the optimal contract, whereas it does not under full information. Relative to full information, the capital good in the optimal contract is over-consumed in the initial loan period and under-consumed in the repayment period. The relation between forfeiture of assets and contractual distortion is summarized by a formula showing higher distortions associated with larger increases in forfeited collateral. Forfeiture is decreasing in income at the tails of the income distribution, and low income types forfeit more than high income types. We obtain a closed form solution in a parameterized model. Forfeited collateral is globally decreasing in income with pooling at the bottom when the borrower's initial assets are low.

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  • Dan Cao & Roger Lagunoff, 2016. "The Design of Optimal Collateralized Contracts," Working Papers gueconwpa~16-16-01, Georgetown University, Department of Economics, revised 01 Jun 2017.
    • Handle: RePEc:geo:guwopa:gueconwpa~16-16-01
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    1. Hellwig, Martin F., 2007. "A contribution to the theory of optimal utilitarian income taxation," Journal of Public Economics, Elsevier, vol. 91(7-8), pages 1449-1477, August.
    2. Jeffrey Lacker, 2001. "Collateralized Debt as the Optimal Contract," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(4), pages 842-859, October.
    3. Rampini, Adriano A. & Viswanathan, S., 2013. "Collateral and capital structure," Journal of Financial Economics, Elsevier, vol. 109(2), pages 466-492.
    4. Noldeke, Georg & Samuelson, Larry, 2007. "Optimal bunching without optimal control," Journal of Economic Theory, Elsevier, vol. 134(1), pages 405-420, May.
    5. Piazzesi, Monika & Schneider, Martin & Tuzel, Selale, 2007. "Housing, consumption and asset pricing," Journal of Financial Economics, Elsevier, vol. 83(3), pages 531-569, March.
    6. Lollivier, Stefan & Rochet, Jean-Charles, 1983. "Bunching and second-order conditions: A note on optimal tax theory," Journal of Economic Theory, Elsevier, vol. 31(2), pages 392-400, December.
    7. Casey Rothschild & Florian Scheuer, 2016. "Optimal Taxation with Rent-Seeking," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(3), pages 1225-1262.
    8. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    9. John Y. Campbell & João F. Cocco, 2015. "A Model of Mortgage Default," Journal of Finance, American Finance Association, vol. 70(4), pages 1495-1554, August.
    10. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2003. "Optimal Indirect and Capital Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(3), pages 569-587.
    11. Besanko, David & Thakor, Anjan V, 1987. "Collateral and Rationing: Sorting Equilibria in Monopolistic and Competitive Credit Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 671-689, October.
    12. Dixit, Avinash & Seade, Jesus, 1979. "Utilitarian versus egalitarian redistributions," Economics Letters, Elsevier, vol. 4(2), pages 121-124.
    13. Andrea L. Eisfeldt & Adriano A. Rampini, 2009. "Leasing, Ability to Repossess, and Debt Capacity," The Review of Financial Studies, Society for Financial Studies, vol. 22(4), pages 1621-1657, April.
    14. Jullien, Bruno, 2000. "Participation Constraints in Adverse Selection Models," Journal of Economic Theory, Elsevier, vol. 93(1), pages 1-47, July.
    15. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    16. Emmanuel Farhi & Iván Werning, 2012. "Capital Taxation: Quantitative Explorations of the Inverse Euler Equation," Journal of Political Economy, University of Chicago Press, vol. 120(3), pages 000.
    17. Jesus Seade, 1982. "On the Sign of the Optimum Marginal Income Tax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(4), pages 637-643.
    18. John Geanakoplos & Ana Fostel, 2008. "Leverage Cycles and the Anxious Economy," American Economic Review, American Economic Association, vol. 98(4), pages 1211-1244, September.
    19. Manove, Michael & Padilla, A Jorge & Pagano, Marco, 2001. "Collateral versus Project Screening: A Model of Lazy Banks," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 726-744, Winter.
    20. Diamond, Peter A, 1998. "Optimal Income Taxation: An Example with a U-Shaped Pattern of Optimal Marginal Tax Rates," American Economic Review, American Economic Association, vol. 88(1), pages 83-95, March.
    21. Casey Rothschild & Florian Scheuer, 2013. "Redistributive Taxation in the Roy Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 623-668.
    22. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
    23. Jeffrey Lacker, 2001. "Collateralized Debt as the Optimal Contract," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(4), pages 842-859, October.
    24. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    25. A. Rampini, Adriano, 2005. "Default and aggregate income," Journal of Economic Theory, Elsevier, vol. 122(2), pages 225-253, June.
    26. 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.
    27. Barro, Robert J, 1976. "The Loan Market, Collateral, and Rates of Interest," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 8(4), pages 439-456, November.
    28. Alp Simsek, 2013. "Belief Disagreements and Collateral Constraints," Econometrica, Econometric Society, vol. 81(1), pages 1-53, January.
    29. Bester, Helmut, 1985. "Screening vs. Rationing in Credit Markets with Imperfect Information," American Economic Review, American Economic Association, vol. 75(4), pages 850-855, September.
    30. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    31. Townsend, Robert M, 1982. "Optimal Multiperiod Contracts and the Gain from Enduring Relationships under Private Information," Journal of Political Economy, University of Chicago Press, vol. 90(6), pages 1166-1186, December.
    32. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    33. Chan, Yuk-Shee & Kanatas, George, 1985. "Asymmetric Valuations and the Role of Collateral in Loan Agreements," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 17(1), pages 84-95, February.
    34. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
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    More about this item

    Keywords

    Optimal contract; asymmetric information; collateral; forfeiture; collateralized contract.;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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