IDEAS home Printed from https://ideas.repec.org/p/duk/dukeec/04-05.html
   My bibliography  Save this paper

Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending

Author

Listed:
  • Abraham, Arpad
  • Pavoni, Nicola

Abstract

We analyze a dynamic moral hazard setting, in which agents can borrow and lend and their decisions about effort, consumption and savings are private information. In contrast with previous findings, we show that as long as agents do not have perfect control over publicly observable outcomes, the efficient allocation is welfare improving with respect to the case where the agents can self insure only through borrowing and lending. We identify the main sources of welfare improvement, and we compute substantial efficiency gains. We provide a tractable recursive framework to study the optimal allocation in this setting. The dynamic programming formulation is based on a generalized first order approach, whose validity is verified ex post, using a parsimonious numerical procedure based on the recursive formulation itself.

Suggested Citation

  • Abraham, Arpad & Pavoni, Nicola, 2004. "Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending," Working Papers 04-05, Duke University, Department of Economics.
    • Handle: RePEc:duk:dukeec:04-05
    as

    Download full text from publisher

    File URL: http://www.econ.duke.edu/Papers/Abstracts04/abstract.04.05.html
    File Function: main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Holmstrom, Bengt & Milgrom, Paul, 1990. "Short-term contracts and long-term agency relationships," Journal of Economic Theory, Elsevier, vol. 51(1), pages 1-31, June.
    2. Cole, Harold L. & Kocherlakota, Narayana, 2001. "Dynamic Games with Hidden Actions and Hidden States," Journal of Economic Theory, Elsevier, vol. 98(1), pages 114-126, May.
    3. Christopher Phelan & Robert M. Townsend, 1991. "Computing Multi-Period, Information-Constrained Optima," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(5), pages 853-881.
    4. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    5. Cronshaw, Mark B, 1997. "Algorithms for Finding Repeated Game Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 10(2), pages 139-168, May.
    6. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    7. Albert Marcet & Ramon Marimon, 2019. "Recursive Contracts," Econometrica, Econometric Society, vol. 87(5), pages 1589-1631, September.
    8. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    9. Hansen, Gary D & Imrohoroglu, Ayse, 1992. "The Role of Unemployment Insurance in an Economy with Liquidity Constraints and Moral Hazard," Journal of Political Economy, University of Chicago Press, vol. 100(1), pages 118-142, February.
    10. Doepke, Matthias & Townsend, Robert M., 2006. "Dynamic mechanism design with hidden income and hidden actions," Journal of Economic Theory, Elsevier, vol. 126(1), pages 235-285, January.
    11. 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.
    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. Attanasio, Orazio & Davis, Steven J, 1996. "Relative Wage Movements and the Distribution of Consumption," Journal of Political Economy, University of Chicago Press, vol. 104(6), pages 1227-1262, December.
    14. Atkeson, Andrew, 1991. "International Lending with Moral Hazard and Risk of Repudiation," Econometrica, Econometric Society, vol. 59(4), pages 1069-1089, July.
    15. Townsend, Robert M, 1994. "Risk and Insurance in Village India," Econometrica, Econometric Society, vol. 62(3), pages 539-591, May.
    16. 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.
    17. Ethan Ligon, 1998. "Risk Sharing and Information in Village Economies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(4), pages 847-864.
    18. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    19. Nicola Pavoni, 2009. "Optimal Unemployment Insurance, With Human Capital Depreciation, And Duration Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(2), pages 323-362, May.
    20. Mace, Barbara J, 1991. "Full Insurance in the Presence of Aggregate Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 928-956, October.
    21. Christopher Phelan & Ennio Stacchetti, 2001. "Sequential Equilibria in a Ramsey Tax Model," Econometrica, Econometric Society, vol. 69(6), pages 1491-1518, November.
    22. Pavoni, Nicola, 2007. "On optimal unemployment compensation," Journal of Monetary Economics, Elsevier, vol. 54(6), pages 1612-1630, September.
    23. 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.
    24. Fernandes, Ana & Phelan, Christopher, 2000. "A Recursive Formulation for Repeated Agency with History Dependence," Journal of Economic Theory, Elsevier, vol. 91(2), pages 223-247, April.
    25. 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.
    26. 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.
    27. 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.
    28. Kydland, Finn E. & Prescott, Edward C., 1980. "Dynamic optimal taxation, rational expectations and optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 79-91, May.
    29. Rustichini, Aldo, 1998. "Dynamic Programming Solution of Incentive Constrained Problems," Journal of Economic Theory, Elsevier, vol. 78(2), pages 329-354, February.
    30. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    31. Allen, Franklin, 1985. "Repeated principal-agent relationships with lending and borrowing," Economics Letters, Elsevier, vol. 17(1-2), pages 27-31.
    32. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    33. Hayashi, Fumio & Altonji, Joseph & Kotlikoff, Laurence, 1996. "Risk-Sharing between and within Families," Econometrica, Econometric Society, vol. 64(2), pages 261-294, March.
    34. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    35. 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.
    36. Cochrane, John H, 1991. "A Simple Test of Consumption Insurance," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 957-976, October.
    37. Chang, Roberto, 1998. "Credible Monetary Policy in an Infinite Horizon Model: Recursive Approaches," Journal of Economic Theory, Elsevier, vol. 81(2), pages 431-461, August.
    38. Atila Abdulkadiroglu & Burhanettin Kuruscu & Aysegul Sahin, 2002. "Unemployment Insurance and the Role of Self-Insurance," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 5(3), pages 681-703, July.
    39. 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.
    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. Setty, Ofer, 2011. "Unemployment Accounts," Foerder Institute for Economic Research Working Papers 275748, Tel-Aviv University > Foerder Institute for Economic Research.
    2. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
    3. Orazio P. Attanasio & Nicola Pavoni, 2011. "Risk Sharing in Private Information Models With Asset Accumulation: Explaining the Excess Smoothness of Consumption," Econometrica, Econometric Society, vol. 79(4), pages 1027-1068, July.
    4. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    5. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    6. Yuzhe Zhang & Matthew Mitchell, 2007. "Optimal Unemployment Insurance with Hidden Trade," 2007 Meeting Papers 1023, Society for Economic Dynamics.
    7. Álvarez-Parra, Fernando & Sánchez, Juan M., 2009. "Unemployment insurance with a hidden labor market," Journal of Monetary Economics, Elsevier, vol. 56(7), pages 954-967, October.
    8. 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.
    9. Mikhail Golosov & Aleh Tsyvinski, 2007. "Optimal Taxation with Endogenous Insurance Markets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(2), pages 487-534.
    10. Orazio P. Attanasio & Guglielmo Weber, 2010. "Consumption and Saving: Models of Intertemporal Allocation and Their Implications for Public Policy," Journal of Economic Literature, American Economic Association, vol. 48(3), pages 693-751, September.
    11. Jarque, Arantxa, 2010. "Repeated moral hazard with effort persistence," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2412-2423, November.
    12. Costa, Carlos Eugênio da & Maestri, Lucas Jóver, 2005. "The interaction between unemployment insurance and human capital policies," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 595, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    13. Matthias Messner & Nicola Pavoni, 2004. "On the Recursive Saddle Point Method," Levine's Bibliography 122247000000000050, UCLA Department of Economics.
    14. 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.
    15. Emilio Espino & Julian Kozlowski & Juan M. Sanchez, 2013. "Too big to cheat: Efficiency and Investment in Partnerships," Working Papers 2013-001, Federal Reserve Bank of St. Louis.
    16. Mitchell, Matthew & Zhang, Yuzhe, 2010. "Unemployment insurance with hidden savings," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2078-2107, November.
    17. Josepa Miquel-Florensa, 2013. "Dynamic contractual incentives in the face of a Samaritans’s dilemma," Theory and Decision, Springer, vol. 74(1), pages 151-166, January.
    18. Marek Kapicka, 2006. "Optimal Income Taxation with Human Capital Accumulation and Limited Record Keeping," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(4), pages 612-639, October.
    19. 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.
    20. 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.
    21. Hassler, John & Rodriguez Mora, José V., 2002. "Should UI Benefits Really Fall Over Time?," IZA Discussion Papers 622, Institute of Labor Economics (IZA).
    22. Mikhail Golosov & Aleh Tsyvinski, 2003. "Designing optimal disability insurance," Working Papers 628, Federal Reserve Bank of Minneapolis.
    23. Mikhail Golosov & Aleh Tsyvinski, 2006. "Designing Optimal Disability Insurance: A Case for Asset Testing," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 257-279, April.
    24. 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.

    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. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    3. Zhao, Rui R., 2007. "Dynamic risk-sharing with two-sided moral hazard," Journal of Economic Theory, Elsevier, vol. 136(1), pages 601-640, September.
    4. 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.
    5. 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.
    6. 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.
    7. Doepke, Matthias & Townsend, Robert M., 2006. "Dynamic mechanism design with hidden income and hidden actions," Journal of Economic Theory, Elsevier, vol. 126(1), pages 235-285, January.
    8. 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.
    9. Kam, Timothy & Stauber, Ronald, 2016. "Solving dynamic public insurance games with endogenous agent distributions: Theory and computational approximation," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 77-98.
    10. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, April.
    11. 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.
    12. Hagedorn, Marcus & Kaul, Ashok & Mennel, Tim, 2010. "An adverse selection model of optimal unemployment insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 490-502, March.
    13. 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.
    14. Muhammet Fatih Guvenen, 2000. "Does Stockholding Provide Perfect Risk Sharing?," GSIA Working Papers 2000-E48, Carnegie Mellon University, Tepper School of Business.
    15. Espino, Emilio, 2005. "On Ramsey's conjecture: efficient allocations in the neoclassical growth model with private information," Journal of Economic Theory, Elsevier, vol. 121(2), pages 192-213, April.
    16. Zhigang Feng & Jianjun Miao & Adrian Peralta‐Alva & Manuel S. Santos, 2014. "Numerical Simulation Of Nonoptimal Dynamic Equilibrium Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(1), pages 83-110, February.
    17. Robert Shimer & Ivan Werning, 2008. "Liquidity and Insurance for the Unemployed," American Economic Review, American Economic Association, vol. 98(5), pages 1922-1942, December.
    18. Jarque, Arantxa, 2010. "Repeated moral hazard with effort persistence," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2412-2423, November.
    19. 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.
    20. Laurence Ales & Maziero Pricila, "undated". "Accounting for Private Information," GSIA Working Papers 2010-E58, Carnegie Mellon University, Tepper School of Business.

    More about this item

    Keywords

    Moral hazard; hidden savings; social insurance; first order approach; recursive contracts; ex-post verification;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:duk:dukeec:04-05. 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: Department of Economics Webmaster (email available below). General contact details of provider: http://econ.duke.edu/ .

    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.