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Dynamic risk-sharing with two-sided moral hazard

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  • Zhao, Rui R.

Abstract

In this paper I study a class of repeated two-sided moral hazard problems with discounting. I consider two agents who are involved in multiperiod, and possibly infinite-horizon, contractual relationships. In every period, the agents simultaneously take hidden actions, each of which independently affects the distribution of a separate random public signal. The realizations of the public signals jointly determine the output of a perishable final good, which the agents consume. This abstract framework can be used to analyze contractual relations within a variety of institutions, such as partnership firms, households, or cooperatives, in which bilateral moral hazard is an essential feature. I examine the nature of Pareto optimal contracts in this environment that respect both technological and informational constraints. After establishing the existence of optimal contracts, I show that every continuation contract of an optimal contract is itself optimal. Using this recursive property, next I derive a partial, but fairly general, characterization of optimal consumption allocations. It is an equation that links the ratio of marginal utilities of the agents in the current period to the same ratio in the next period. Moreover, optimal contracts imply that the sequence of ratios of marginal utilities in each period is a submartingale. I provide sufficient conditions for the submartingale to converge. Finally, using this result, I identify conditions under which one agent receives all surplus in the long run.
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  • Zhao, Rui R., 2007. "Dynamic risk-sharing with two-sided moral hazard," Journal of Economic Theory, Elsevier, vol. 136(1), pages 601-640, September.
  • Handle: RePEc:eee:jetheo:v:136:y:2007:i:1:p:601-640
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    as
    1. Jonathan Thomas & Tim Worrall, 1988. "Self-Enforcing Wage Contracts," Review of Economic Studies, Oxford University Press, vol. 55(4), pages 541-554.
    2. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    3. 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.
    4. Phelan, Christopher, 1998. "On the Long Run Implications of Repeated Moral Hazard," Journal of Economic Theory, Elsevier, vol. 79(2), pages 174-191, April.
    5. Zhao, Rui R., 2006. "Renegotiation-proof contract in repeated agency," Journal of Economic Theory, Elsevier, vol. 131(1), pages 263-281, November.
    6. Christopher Phelan & Robert M. Townsend, 1991. "Computing Multi-Period, Information-Constrained Optima," Review of Economic Studies, Oxford University Press, vol. 58(5), pages 853-881.
    7. Townsend, Robert M, 1994. "Risk and Insurance in Village India," Econometrica, Econometric Society, vol. 62(3), pages 539-591, May.
    8. Stephen E. Spear & Sanjay Srivastava, 1987. "On Repeated Moral Hazard with Discounting," Review of Economic Studies, Oxford University Press, vol. 54(4), pages 599-617.
    9. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    10. Jonathan Thomas & Tim Worrall, 1994. "Foreign Direct Investment and the Risk of Expropriation," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 81-108.
    11. Cheng Wang, 2000. "Renegotiation-Proof Dynamic Contracts with Private Information," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 396-422, July.
    12. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
    13. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    14. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    15. Srabana Gupta & Richard E. Romano, 1998. "Monitoring the Principal with Multiple Agents," RAND Journal of Economics, The RAND Corporation, vol. 29(2), pages 427-442, Summer.
    16. Demski, Joel S. & Sappington, David, 1984. "Optimal incentive contracts with multiple agents," Journal of Economic Theory, Elsevier, vol. 33(1), pages 152-171, June.
    17. Christopher Phelan, 1994. "Incentives and Aggregate Shocks," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 681-700.
    18. Sugato Bhattacharyya & Francine Lafontaine, 1995. "Double-Sided Moral Hazard and the Nature of Share Contracts," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 761-781, Winter.
    19. Cheng Wang, 1995. "Dynamic Insurance with Private Information and Balanced Budgets," Review of Economic Studies, Oxford University Press, vol. 62(4), pages 577-595.
    20. Fudenberg, Drew & Tirole, Jean, 1990. "Moral Hazard and Renegotiation in Agency Contracts," Econometrica, Econometric Society, vol. 58(6), pages 1279-1319, November.
    21. Dilip Abreu & David Pearce & Ennio Stacchetti, 2010. "Towards a Theory of Discounted Repeated Games with Imperfect Monitoring," Levine's Working Paper Archive 199, David K. Levine.
    22. Andrew Atkeson & Robert E. Lucas, 1992. "On Efficient Distribution With Private Information," Review of Economic Studies, Oxford University Press, vol. 59(3), pages 427-453.
    23. Diamond, P. A. & Mirrlees, J. A., 1978. "A model of social insurance with variable retirement," Journal of Public Economics, Elsevier, vol. 10(3), pages 295-336, December.
    24. Atkeson, Andrew, 1991. "International Lending with Moral Hazard and Risk of Repudiation," Econometrica, Econometric Society, vol. 59(4), pages 1069-1089, July.
    25. Atkeson Andrew & Lucas Jr. , Robert E., 1995. "Efficiency and Equality in a Simple Model of Efficient Unemployment Insurance," Journal of Economic Theory, Elsevier, vol. 66(1), pages 64-88, June.
    26. Legros, Patrick & Matsushima, Hitoshi, 1991. "Efficiency in partnerships," Journal of Economic Theory, Elsevier, vol. 55(2), pages 296-322, December.
    27. 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.
    28. Patrick Legros & Steven A. Matthews, 1993. "Efficient and Nearly-Efficient Partnerships," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 599-611.
    29. Ethan Ligon, 1998. "Risk Sharing and Information in Village Economies," Review of Economic Studies, Oxford University Press, vol. 65(4), pages 847-864.
    30. 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.
    31. Debraj Ray, 2002. "The Time Structure of Self-Enforcing Agreements," Econometrica, Econometric Society, vol. 70(2), pages 547-582, March.
    32. Gian Luca Clementi & Hugo A. Hopenhayn, 2006. "A Theory of Financing Constraints and Firm Dynamics," The Quarterly Journal of Economics, Oxford University Press, vol. 121(1), pages 229-265.
    33. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    34. Dilip Mookherjee, 1984. "Optimal Incentive Schemes with Many Agents," Review of Economic Studies, Oxford University Press, vol. 51(3), pages 433-446.
    35. Ching-To Ma, 1988. "Unique Implementation of Incentive Contracts with Many Agents," Review of Economic Studies, Oxford University Press, vol. 55(4), pages 555-572.
    36. 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.
    37. Narayana R. Kocherlakota, 1996. "Implications of Efficient Risk Sharing without Commitment," Review of Economic Studies, Oxford University Press, vol. 63(4), pages 595-609.
    38. Kim, Son Ku & Wang, Susheng, 1998. "Linear Contracts and the Double Moral-Hazard," Journal of Economic Theory, Elsevier, vol. 82(2), pages 342-378, October.
    39. Phelan Christopher, 1995. "Repeated Moral Hazard and One-Sided Commitment," Journal of Economic Theory, Elsevier, vol. 66(2), pages 488-506, August.
    40. Harold L. Cole & Narayana R. Kocherlakota, 2001. "Efficient Allocations with Hidden Income and Hidden Storage," Review of Economic Studies, Oxford University Press, vol. 68(3), pages 523-542.
    41. Al-Najjar, Nabil I., 1997. "Incentive Contracts in Two-Sided Moral Hazards with Multiple Agents," Journal of Economic Theory, Elsevier, vol. 74(1), pages 174-195, May.
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    2. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    3. Karel Janda, 2006. "Lender and Borrower as Principal and Agent," Working Papers IES 2006/24, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jul 2006.
    4. Michail Anthropelos, 2012. "The Effect of Market Power on Risk-Sharing," Papers 1206.0384, arXiv.org, revised May 2016.
    5. Karel Janda, 2006. "Agency Theory Approach to the Contracting between Lender and Borrower [Smluvní vztah mezi věřitelem a dlužníkem z hlediska přístupu teorie zastoupení]," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2006(3), pages 34-47.
    6. Philipp Renner & Karl Schmedders, 2017. "Dynamic Principal–Agent Models," Working Papers 203620456, Lancaster University Management School, Economics Department.
    7. Carrasco, Vinicius & Fuchs, William & Fukuda, Satoshi, 2019. "From equals to despots: The dynamics of repeated decision making in partnerships with private information," Journal of Economic Theory, Elsevier, vol. 182(C), pages 402-432.

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