IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v146y2011i4p1331-1361.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053111000214
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Sebastian Koehne & Nicola Pavoni & Arpad Abraham, 2011. "Optimal Income Taxation with Asset Accumulation," 2011 Meeting Papers 1161, Society for Economic Dynamics.
    3. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    4. 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.
    5. 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.
    6. 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.
    7. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    8. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    9. 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.
    10. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    11. 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.
    12. 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.
    13. Allen, Franklin, 1985. "Repeated principal-agent relationships with lending and borrowing," Economics Letters, Elsevier, vol. 17(1-2), pages 27-31.
    14. Atkeson, Andrew, 1991. "International Lending with Moral Hazard and Risk of Repudiation," Econometrica, Econometric Society, vol. 59(4), pages 1069-1089, July.
    15. 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.
    16. Mitchell, Matthew & Zhang, Yuzhe, 2010. "Unemployment insurance with hidden savings," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2078-2107, November.
    17. In-Uck Park, 2004. "Moral Hazard Contracting and Private Credit Markets," Econometrica, Econometric Society, vol. 72(3), pages 701-746, May.
    18. hector chade, 2009. "moral hazard with unobservable wealth and a continuum of actions," 2009 Meeting Papers 848, Society for Economic Dynamics.
    19. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    20. 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.
    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. Bengt Holmstrom, 1979. "Moral Hazard and Observability," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 74-91, Spring.
    23. 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.
    24. 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.
    25. University of Venice & Nicola Pavoni & Piero Gottardi, 2008. "Ramsey Asset Taxation under Asymmetric Information," 2008 Meeting Papers 309, Society for Economic Dynamics.
    26. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Raith, Michael, 2012. "Optimal incentives and the time dimension of performance measurement," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2158-2189.
    2. Stefanie Stantcheva, 2020. "Dynamic Taxation," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 801-831, August.
    3. Tom Krebs & Martin Scheffel, 2016. "Labor Market Institutions and the Cost of Recessions," CESifo Working Paper Series 6262, CESifo.
    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.
    6. Ethan Ligon & Laura Schechter, 2020. "Structural Experimentation to Distinguish between Models of Risk Sharing with Frictions in Rural Paraguay," Economic Development and Cultural Change, University of Chicago Press, vol. 69(1), pages 1-50.
    7. René Kirkegaard, 2020. "Contracting with private rewards," RAND Journal of Economics, RAND Corporation, vol. 51(2), pages 589-612, June.
    8. Tom Krebs & Martin Scheffel, 2024. "Optimal allocations in growth models with private information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(1), pages 125-154, August.
    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.
    16. Arie, Guy, 2016. "Dynamic costs and moral hazard: A duality-based approach," Journal of Economic Theory, Elsevier, vol. 166(C), pages 1-50.
    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.
    18. Sarolta Laczo & Arpad Abraham, 2012. "Efficient Risk Sharing with Limited Commitment and Hidden Saving," 2012 Meeting Papers 680, Society for Economic Dynamics.
    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.
    20. Wataru Nozawa, 2016. "Failure of the first-order approach in an insurance problem with no commitment and hidden savings," Economics Bulletin, AccessEcon, vol. 36(4), pages 2422-2429.
    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.
    23. Pietrobon, Davide, 2024. "The dual role of insurance in input use: Mitigating risk versus curtailing incentives," Journal of Development Economics, Elsevier, vol. 166(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Abraham Arpad & Nicola Pavoni, 2004. "Efficient Allocations, with Moral Hazard and Hidden Borrowing and Lending," Levine's Bibliography 122247000000000138, UCLA Department of Economics.
    3. Raith, Michael, 2012. "Optimal incentives and the time dimension of performance measurement," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2158-2189.
    4. Alberto Bisin & Piero Gottardi & Adriano A. Rampini, 2008. "Managerial Hedging and Portfolio Monitoring," Journal of the European Economic Association, MIT Press, vol. 6(1), pages 158-209, March.
    5. Williams, Noah, 2015. "A solvable continuous time dynamic principal–agent model," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 989-1015.
    6. Sebastian Koehne & Nicola Pavoni & Arpad Abraham, 2011. "Optimal Income Taxation with Asset Accumulation," 2011 Meeting Papers 1161, Society for Economic Dynamics.
    7. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    8. 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.
    9. Jarque, Arantxa, 2010. "Repeated moral hazard with effort persistence," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2412-2423, November.
    10. Karaivanov, Alexander K. & Martin, Fernando M., 2018. "Markov-perfect risk sharing, moral hazard and limited commitment," Journal of Economic Dynamics and Control, Elsevier, vol. 94(C), pages 1-23.
    11. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
    12. Nicola Pavoni & G. L. Violante, 2007. "Optimal Welfare-to-Work Programs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(1), pages 283-318.
    13. Dionne, Georges & Vanasse, Charles, 1997. "Une évaluation empirique de la nouvelle tarification de l’assurance automobile (1992) au Québec," L'Actualité Economique, Société Canadienne de Science Economique, vol. 73(1), pages 47-80, mars-juin.
    14. Hugo Hopenhayn & Arantxa Jarque, 2010. "Unobservable Persistent Productivity and Long Term Contracts," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(2), pages 333-349, April.
    15. Balmaceda, Felipe & Balseiro, Santiago R. & Correa, José R. & Stier-Moses, Nicolás E., 2016. "Bounds on the welfare loss from moral hazard with limited liability," Games and Economic Behavior, Elsevier, vol. 95(C), pages 137-155.
    16. Kadan, Ohad & Swinkels, Jeroen M., 2013. "On the moral hazard problem without the first-order approach," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2313-2343.
    17. Daron Acemoglu & Alp Simsek, 2010. "Moral Hazard and Efficiency in General Equilibrium with Anonymous Trading," Levine's Working Paper Archive 661465000000000232, David K. Levine.
    18. 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.
    19. Li, Zhaolin, 2020. "Robust Moral Hazard with Distributional Ambiguity," Working Papers BAWP-2020-03, University of Sydney Business School, Discipline of Business Analytics.
    20. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:146:y:2011:i:4:p:1331-1361. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.