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Dynamic Optimal Insurance and Lack of Commitment

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Abstract

We analyze the role of commitment in a dynamic principal-agent model of optimal insurance with hidden effort and observable but non-contractible savings. We argue that the optimal contract under full commitment is time-inconsistent. Consequently, we analyze the optimal time-consistent Markov-perfect insurance contract when both the agent and the principal cannot commit for longer than one period and contrast our results with the full commitment case from the existing literature. We find that the optimal contract under lack of commitment provides additional insurance relative to the autarky allocation and features non-degenerate long-run asset and consumption distributions. Furthermore, the no-commitment contract differs significantly from the commitment contract in the time profiles of consumption, savings, and welfare. We solve for the optimal insurance contracts in several environments featuring different degrees of market incompleteness and find that the welfare loss due to lack of commitment can be very high relative to the welfare costs of moral hazard or savings non-contractibility.

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  • Alexander K. Karaivanov & Fernando M. Martin, 2007. "Dynamic Optimal Insurance and Lack of Commitment," Discussion Papers dp07-22, Department of Economics, Simon Fraser University.
    • Handle: RePEc:sfu:sfudps:dp07-22
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    1. Sleet, Christopher & Yeltekin, Sevin, 2008. "Politically credible social insurance," Journal of Monetary Economics, Elsevier, vol. 55(1), pages 129-151, January.
    2. Daron Acemoglu & Michael Golosov & Aleh Tsyvinski, 2006. "Markets Versus Governments: Political Economy of Mechanisms," Levine's Bibliography 321307000000000032, UCLA Department of Economics.
    3. Ethan Ligon & Jonathan P. Thomas & Tim Worrall, 2002. "Informal Insurance Arrangements with Limited Commitment: Theory and Evidence from Village Economies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(1), pages 209-244.
    4. Jonathan Thomas & Tim Worrall, 1994. "Foreign Direct Investment and the Risk of Expropriation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 81-108.
    5. Krueger, Dirk & Uhlig, Harald, 2006. "Competitive risk sharing contracts with one-sided commitment," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1661-1691, October.
    6. 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.
    7. Gary Chamberlain & Charles A. Wilson, 2000. "Optimal Intertemporal Consumption Under Uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 365-395, July.
    8. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    9. Daron Acemoglu & Michael Golosov & Aleh Tsyvinski, 2008. "Political Economy of Mechanisms," Econometrica, Econometric Society, vol. 76(3), pages 619-641, May.
    10. Bester, Helmut & Strausz, Roland, 2001. "Contracting with Imperfect Commitment and the Revelation Principle: The Single Agent Case," Econometrica, Econometric Society, vol. 69(4), pages 1077-1098, July.
    11. Per Krusell & Anthony A. Smith, Jr., 2003. "Consumption--Savings Decisions with Quasi--Geometric Discounting," Econometrica, Econometric Society, vol. 71(1), pages 365-375, January.
    12. 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.
    13. 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.
    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. Natalia Kovrijnykh, 2013. "Debt Contracts with Partial Commitment," American Economic Review, American Economic Association, vol. 103(7), pages 2848-2874, December.
    16. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    17. 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.
    18. Karaivanov, Alexander, 2012. "Financial constraints and occupational choice in Thai villages," Journal of Development Economics, Elsevier, vol. 97(2), pages 201-220.
    19. Allen, Franklin, 1985. "Repeated principal-agent relationships with lending and borrowing," Economics Letters, Elsevier, vol. 17(1-2), pages 27-31.
    20. 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.
    21. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    22. 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.
    23. Abraham Arpad & Nicola Pavoni, 2004. "Efficient Allocations, with Moral Hazard and Hidden Borrowing and Lending," Levine's Bibliography 122247000000000138, UCLA Department of Economics.
    24. Fernando Martin, 2009. "A Positive Theory of Government Debt," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(4), pages 608-631, October.
    25. de Oliveira Sotomayor, Marilda A., 1984. "On income fluctuations and capital gains," Journal of Economic Theory, Elsevier, vol. 32(1), pages 14-35, February.
    26. 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.
    27. 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.
    28. Bisin, Alberto & Rampini, Adriano A., 2006. "Markets as beneficial constraints on the government," Journal of Public Economics, Elsevier, vol. 90(4-5), pages 601-629, May.
    29. Helmut Bester & Roland Strausz, "undated". "Imperfect Commitment and the Revelation Principle," Papers 004, Departmental Working Papers.
    30. Christopher Sleet & Sevin Yeltekin, 2006. "Credibility and endogenous societal discounting," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(3), pages 410-437, July.
    31. 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.
    32. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    33. Liebhafsky, H H, 1969. "New Thoughts About Inferior Goods," American Economic Review, American Economic Association, vol. 59(5), pages 931-934, December.
    34. 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.
    35. Phelan Christopher, 1995. "Repeated Moral Hazard and One-Sided Commitment," Journal of Economic Theory, Elsevier, vol. 66(2), pages 488-506, August.
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    Cited by:

    1. 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.
    2. Oikonomou Rigas, 2018. "Unemployment insurance with limited commitment wage contracts and savings," The B.E. Journal of Macroeconomics, De Gruyter, vol. 18(1), pages 1-21, January.
    3. Alexander K. Karaivanov & Fernando M. Martin, 2016. "Market Power and Asset Contractibility in Dynamic Insurance Contracts," Review, Federal Reserve Bank of St. Louis, vol. 98(2).
    4. Yanyan Liu & Robert J. Myers, 2016. "The Dynamics Of Microinsurance Demand In Developing Countries Under Liquidity Constraints And Insurer Default Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(1), pages 121-138, January.
    5. Oikonomou, Rigas, 2013. "Optimal Unemployment Insurance with Private Insurance," MPRA Paper 55726, University Library of Munich, Germany.
    6. Alexander Karaivanov, 2021. "Blockchains, Collateral and Financial Contracts," Discussion Papers dp21-03, Department of Economics, Simon Fraser University.
    7. Nguyen Phuc Canh & Udomsak Wongchoti & Su Dinh Thanh, 2021. "Does economic policy uncertainty matter for insurance development? Evidence from 16 OECD countries," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 46(4), pages 614-648, October.

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    More about this item

    Keywords

    optimal insurance; time consistency; moral hazard;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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