IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-16-00250.html
   My bibliography  Save this article

Failure of the first-order approach in an insurance problem with no commitment and hidden savings

Author

Listed:
  • Wataru Nozawa

    (Kyushu University)

Abstract

Efficient insurance contracts in environments with various frictions have been characterized in the literature (see, for example, Thomas and Worrall (1988)). In some environments, the first-order approach suggested by Rogerson (1985) is useful in their characterization. This paper shows that the first-order approach is not valid in an environment with one-sided no commitment and hidden savings under the assumption that the utility function is CRRA or CARA and the return on savings is equal to the inverse of the agent's discount factor. The result complements the numerical result by à brahám and Laczó (2014), which suggests that the first-order approach is valid when the return on savings is low.

Suggested Citation

  • 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.
    • Handle: RePEc:ebl:ecbull:eb-16-00250
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/Pubs/EB/2016/Volume36/EB-16-V36-I4-P234.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    2. 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.
    3. Jonathan Thomas & Tim Worrall, 1988. "Self-Enforcing Wage Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 541-554.
    4. Thomas, Jonathan & Worrall, Tim, 1990. "Income fluctuation and asymmetric information: An example of a repeated principal-agent problem," Journal of Economic Theory, Elsevier, vol. 51(2), pages 367-390, August.
    5. 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.
    6. 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.
    7. 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.
    8. Ethan Ligon & Jonathan P. Thomas & Tim Worrall, 2000. "Mutual Insurance, Individual Savings and Limited Commitment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 216-246, April.
    9. 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.
    10. 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.
    11. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, April.
    12. Stephen E. Spear & Sanjay Srivastava, 1987. "On Repeated Moral Hazard with Discounting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 599-617.
    13. Narayana R. Kocherlakota, 1996. "Implications of Efficient Risk Sharing without Commitment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 595-609.
    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. 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.

    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. 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.
    2. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 725-841, Elsevier.
    3. 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.
    4. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    5. Alexander Karaivanov & Fernando Martin, 2015. "Dynamic Optimal Insurance and Lack of Commitment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(2), pages 287-305, April.
    6. Zhao, Rui R., 2007. "Dynamic risk-sharing with two-sided moral hazard," Journal of Economic Theory, Elsevier, vol. 136(1), pages 601-640, September.
    7. Francesc Dilmé & Daniel F. Garrett, 2023. "Relational Contracts: Public versus Private Savings," Econometrica, Econometric Society, vol. 91(3), pages 1025-1075, May.
    8. Abraham Arpad & Nicola Pavoni, 2004. "Efficient Allocations, with Moral Hazard and Hidden Borrowing and Lending," Levine's Bibliography 122247000000000138, UCLA Department of Economics.
    9. Pierre Dubois & Bruno Jullien & Thierry Magnac, 2008. "Formal and Informal Risk Sharing in LDCs: Theory and Empirical Evidence," Econometrica, Econometric Society, vol. 76(4), pages 679-725, July.
    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. 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.
    12. Jarque, Arantxa, 2010. "Repeated moral hazard with effort persistence," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2412-2423, November.
    13. 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.
    14. Wahhaj, Zaki, 2010. "Social norms and individual savings in the context of informal insurance," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 511-530, December.
    15. Shiv Dixit, 2023. "Contract Enforcement and Preventive Healthcare: Theory and Evidence," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 51, pages 1048-1094, December.
    16. Alexander Karaivanov & Robert M. Townsend, 2014. "Dynamic Financial Constraints: Distinguishing Mechanism Design From Exogenously Incomplete Regimes," Econometrica, Econometric Society, vol. 82(3), pages 887-959, May.
    17. Jean Guillaume Forand & Jan Zapal, 2017. "The Demand and Supply of Favours in Dynamic Relationships," Working Papers 1705, University of Waterloo, Department of Economics, revised Sep 2017.
    18. Dubois, Pierre, 2002. "Consommation, partage de risque et assurance informelle : développements théoriques et tests empiriques récents," L'Actualité Economique, Société Canadienne de Science Economique, vol. 78(1), pages 115-149, Mars.
    19. 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.
    20. Balke, Neele & Lamadon, Thibaut, 2021. "Productivity shocks, long-term contracts and earnings dynamics," Working Paper Series 2021:19, IFAU - Institute for Evaluation of Labour Market and Education Policy.

    More about this item

    Keywords

    dynamic contract; risk sharing; default; first-order approach;
    All these keywords.

    JEL classification:

    • G0 - Financial Economics - - General
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment

    Statistics

    Access and download statistics

    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:ebl:ecbull:eb-16-00250. 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: John P. Conley (email available below). General contact details of provider: .

    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.