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On the first-order approach in principal-agent models with hidden borrowing and lending

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  • Ábrahám, Árpád
  • Koehne, Sebastian
  • Pavoni, Nicola

Abstract

We provide sufficient conditions for the validity of the first-order approach for two-period dynamic moral hazard problems where the agent can save and borrow secretly. The first-order approach is valid if the following conditions hold: (i) the agent has non-increasing absolute risk aversion utility (NIARA), (ii) the output technology has monotone likelihood ratios (MLR), and (iii) the distribution function of output is log-convex in effort (LCDF). Moreover, under these three conditions, the optimal contract is monotone in output. We also investigate a few possibilities of relaxing these requirements.

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  • Ábrahám, Árpád & Koehne, Sebastian & Pavoni, Nicola, 2011. "On the first-order approach in principal-agent models with hidden borrowing and lending," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1331-1361, July.
    • Handle: RePEc:eee:jetheo:v:146:y:2011:i:4:p:1331-1361
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    1. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    2. Narayana R. Kocherlakota, 2005. "Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Econometrica, Econometric Society, vol. 73(5), pages 1587-1621, September.
    3. Chiappori, Pierre-Andre & Macho, Ines & Rey, Patrick & Salanie, Bernard, 1994. "Repeated moral hazard: The role of memory, commitment, and the access to credit markets," European Economic Review, Elsevier, vol. 38(8), pages 1527-1553, October.
    4. Atkeson, Andrew, 1991. "International Lending with Moral Hazard and Risk of Repudiation," Econometrica, Econometric Society, vol. 59(4), pages 1069-1089, July.
    5. David Domeij & Martin Floden, 2006. "The Labor-Supply Elasticity and Borrowing Constraints: Why Estimates are Biased," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(2), pages 242-262, April.
    6. hector chade, 2009. "moral hazard with unobservable wealth and a continuum of actions," 2009 Meeting Papers 848, Society for Economic Dynamics.
    7. Harold L. Cole & Narayana R. Kocherlakota, 2001. "Efficient Allocations with Hidden Income and Hidden Storage," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 523-542.
    8. Luigi Guiso & Monica Paiella, 2008. "Risk Aversion, Wealth, and Background Risk," Journal of the European Economic Association, MIT Press, vol. 6(6), pages 1109-1150, December.
    9. Sebastian Koehne & Nicola Pavoni & Arpad Abraham, 2011. "Optimal Income Taxation with Asset Accumulation," 2011 Meeting Papers 1161, Society for Economic Dynamics.
    10. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    11. Allen, Franklin, 1985. "Repeated principal-agent relationships with lending and borrowing," Economics Letters, Elsevier, vol. 17(1-2), pages 27-31.
    12. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    13. Hopenhayn, Hugo A & Nicolini, Juan Pablo, 1997. "Optimal Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 412-438, April.
    14. Arpad Abraham & Nicola Pavoni, 2008. "Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending: A Recursive Formulation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(4), pages 781-803, October.
    15. Bengt Holmstrom, 1979. "Moral Hazard and Observability," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 74-91, Spring.
    16. Alberto Bisin & Adriano Rampini, 2006. "Exclusive contracts and the institution of bankruptcy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 277-304, January.
    17. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    18. Bizer, David S. & DeMarzo, Peter M., 1999. "Optimal Incentive Contracts When Agents Can Save, Borrow, and Default," Journal of Financial Intermediation, Elsevier, vol. 8(4), pages 241-269, October.
    19. Narayana Kocherlakota, 2004. "Figuring out the Impact of Hidden Savings on Optimal Unemployment Insurance," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(3), pages 541-554, July.
    20. Mitchell, Matthew & Zhang, Yuzhe, 2010. "Unemployment insurance with hidden savings," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2078-2107, November.
    21. In-Uck Park, 2004. "Moral Hazard Contracting and Private Credit Markets," Econometrica, Econometric Society, vol. 72(3), pages 701-746, May.
    22. University of Venice & Nicola Pavoni & Piero Gottardi, 2008. "Ramsey Asset Taxation under Asymmetric Information," 2008 Meeting Papers 309, Society for Economic Dynamics.
    23. Schattler, Heinz & Sung, Jaeyoung, 1997. "On optimal sharing rules in discrete-and continuous-time principal-agent problems with exponential utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 551-574.
    24. J. A. Mirrlees, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 3-21.
    25. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    26. John R. Conlon, 2009. "Two New Conditions Supporting the First-Order Approach to Multisignal Principal-Agent Problems," Econometrica, Econometric Society, vol. 77(1), pages 249-278, January.
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    4. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    5. Fagart, Marie-Cécile & Fluet, Claude, 2013. "The first-order approach when the cost of effort is money," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 7-16.
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    7. René Kirkegaard, 2020. "Contracting with private rewards," RAND Journal of Economics, RAND Corporation, vol. 51(2), pages 589-612, June.
    8. Krebs, Tom & Scheffel, Martin, 2022. "Optimal Allocations in Growth Models with Private Information," IZA Discussion Papers 15650, Institute of Labor Economics (IZA).
    9. Árpád Ábrahám & Sarolta Laczó, 2018. "Efficient Risk Sharing with Limited Commitment and Storage," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1389-1424.
    10. Ales, Laurence & Maziero, Pricila, 2016. "Non-exclusive dynamic contracts, competition, and the limits of insurance," Journal of Economic Theory, Elsevier, vol. 166(C), pages 362-395.
    11. Giuseppe Bertola & Winfried Koeniger, 2015. "Hidden insurance in a moral-hazard economy," RAND Journal of Economics, RAND Corporation, vol. 46(4), pages 777-790, October.
    12. Sebastian Koehne & Nicola Pavoni & Arpad Abraham, 2011. "Optimal Income Taxation with Asset Accumulation," 2011 Meeting Papers 1161, Society for Economic Dynamics.
    13. Bertola, Giuseppe & Koeniger, Winfried, 2010. "Public and Private Insurance with Costly Transactions," CEPR Discussion Papers 8062, C.E.P.R. Discussion Papers.
    14. Francesc Dilmé & Daniel F. Garrett, 2023. "Relational Contracts: Public versus Private Savings," Econometrica, Econometric Society, vol. 91(3), pages 1025-1075, May.
    15. Gabaix, Xavier & Sannikov, Yuliy & Edmans, Alex & Sadzik, Tomasz, 2009. "Dynamic Incentive Accounts," CEPR Discussion Papers 7497, C.E.P.R. Discussion Papers.
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    17. Ábrahám, Árpád & Koehne, Sebastian & Pavoni, Nicola, 2016. "Optimal income taxation when asset taxation is limited," Journal of Public Economics, Elsevier, vol. 136(C), pages 14-29.
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    19. Sebastian Koehne, 2018. "On The Taxation Of Durable Goods," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(2), pages 825-857, May.
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    21. Arpad Abraham & Nicola Pavoni, 2008. "Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending: A Recursive Formulation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(4), pages 781-803, October.
    22. Bertola, Giuseppe & Koeniger, Winfried, 2014. "On the validity of the first-order approach with moral hazard and hidden assets," Economics Letters, Elsevier, vol. 124(3), pages 402-405.

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