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Unemployment Insurance with Hidden Savings

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Abstract
This paper studies the design of unemployment insurance when neither the searching effort nor the savings of an unemployed agent can be monitored. If the principal could monitor the savings, the optimal policy would leave the agent savings-constrained. With a constant absolute risk-aversion (CARA) utility function, we obtain a closed form solution of the optimal contract. Under the optimal contract, the agent is neither saving nor borrowing constrained. Counter-intuitively, his consumption declines faster than implied by Hopenhayn and Nicolini [4]. The efficient allocation can be implemented by an increasing benefit during unemployment and a constant tax during employment.

Suggested Citation

  • Mitchell, Matthew & Zhang, Yuzhe, 2010. "Unemployment Insurance with Hidden Savings," MPRA Paper 23214, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:23214
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    File URL: https://mpra.ub.uni-muenchen.de/23214/1/MPRA_paper_23214.pdf
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    References listed on IDEAS

    as
    1. Robert Shimer & Ivan Werning, 2008. "Liquidity and Insurance for the Unemployed," American Economic Review, American Economic Association, vol. 98(5), pages 1922-1942, December.
    2. Shavell, Steven & Weiss, Laurence, 1979. "The Optimal Payment of Unemployment Insurance Benefits over Time," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1347-1362, December.
    3. Abraham, Arpad & Pavoni, Nicola, 2004. "Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending," Working Papers 04-05, Duke University, Department of Economics.
    4. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
    5. David Card & Raj Chetty & Andrea Weber, 2007. "Cash-on-Hand and Competing Models of Intertemporal Behavior: New Evidence from the Labor Market," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(4), pages 1511-1560.
    6. 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.
    7. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    8. Árpád Ábrahám & Nicola Pavoni, 2008. "Optimal Income Taxation and Hidden Borrowing and Lending: The First-Order Approach in Two Periods," Carlo Alberto Notebooks 102, Collegio Carlo Alberto.
    9. 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.
    10. 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.
    Full references (including those not matched with items on IDEAS)

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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Unemployment Insurance with Hidden Savings
      by Christian Zimmermann in NEP-DGE blog on 2010-06-23 12:09:58

    Citations

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    Cited by:

    1. Miyazaki, Koichi, 2019. "Optimal paid job-protected leave policy," MPRA Paper 96223, University Library of Munich, Germany.
    2. Joseph, Gilles & Maingé, Paul-Emile, 2023. "Characterization of optimal durations of unemployment benefits in a nonstationary job search model," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 76-93.
    3. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
    4. Fuller, David L., 2014. "Adverse selection and moral hazard: Quantitative implications for unemployment insurance," Journal of Monetary Economics, Elsevier, vol. 62(C), pages 108-122.
    5. Francesc Dilmé & Daniel F. Garrett, 2023. "Relational Contracts: Public versus Private Savings," Econometrica, Econometric Society, vol. 91(3), pages 1025-1075, May.
    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. Shan, Yaping, 2019. "Incentives for research agents and performance-vested equity-based compensation," Journal of Economic Dynamics and Control, Elsevier, vol. 102(C), pages 44-69.
    8. Miyazaki, Koichi, 2021. "A theory of optimal paid parental leave policies," MPRA Paper 109035, University Library of Munich, Germany.
    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. Tomoyuki Nakajima, 2021. "Principal-Agent Problems with Hidden Savings in Continuous Time," CIRJE F-Series CIRJE-F-1182, CIRJE, Faculty of Economics, University of Tokyo.
    11. Williams, Noah, 2015. "A solvable continuous time dynamic principal–agent model," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 989-1015.
    12. Parsons, Donald O., 2014. "Job Displacement Insurance: An Overview," IZA Discussion Papers 8223, Institute of Labor Economics (IZA).
    13. Gilles Joseph & Paul-Emile Maingé, 2018. "The Optimal Duration of Unemployment Benefits ," Working Papers hal-01722116, HAL.
    14. Park, Jaevin, 2023. "Rights to retrade, free-riding and insurance requirement," Economics Letters, Elsevier, vol. 225(C).

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    More about this item

    Keywords

    hidden savings; hidden wealth; repeated moral hazard; unemployment insurance.;
    All these keywords.

    JEL classification:

    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • J65 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment Insurance; Severance Pay; Plant Closings
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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