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Persistent Private Information

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  • Noah Williams

Abstract

This paper studies the design of optimal contracts in dynamic environments where agents' private information is persistent. In particular, I focus on a continuous time version of an insurance problem similar to Green (1987) and Thomas and Worall (1990), where a risk averse agent would like to borrow from a risk neutral lender to stabilize his income stream. The income stream is private information to the borrower and is persistent. I show that a first order approach to contracting applies, and this allows me to characterize the optimal contract.
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Suggested Citation

  • Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
  • Handle: RePEc:ecm:emetrp:v:79:y:2011:i:4:p:1233-1275
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    References listed on IDEAS

    as
    1. Costas Meghir & Luigi Pistaferri, 2004. "Income Variance Dynamics and Heterogeneity," Econometrica, Econometric Society, vol. 72(1), pages 1-32, January.
    2. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
    3. 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.
    4. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    5. Stefania Albanesi & Christopher Sleet, 2006. "Dynamic Optimal Taxation with Private Information," Review of Economic Studies, Oxford University Press, vol. 73(1), pages 1-30.
    6. 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.
    7. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2003. "Optimal Indirect and Capital Taxation," Review of Economic Studies, Oxford University Press, vol. 70(3), pages 569-587.
    8. 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.
    9. Narayana Kocherlakota & Luigi Pistaferri, 2009. "Asset Pricing Implications of Pareto Optimality with Private Information," Journal of Political Economy, University of Chicago Press, vol. 117(3), pages 555-590, June.
    10. Abraham, Arpad & Pavoni, Nicola, 2004. "Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending," Working Papers 04-05, Duke University, Department of Economics.
    11. PETER M. DeMARZO & YULIY SANNIKOV, 2006. "Optimal Security Design and Dynamic Capital Structure in a Continuous-Time Agency Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2681-2724, December.
    12. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
    13. Bruno Biais & Thomas Mariotti & Guillaume Plantin & Jean-Charles Rochet, 2007. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 345-390.
    14. Kjetil Storesletten & Chris I. Telmer & Amir Yaron, 2004. "Cyclical Dynamics in Idiosyncratic Labor Market Risk," Journal of Political Economy, University of Chicago Press, vol. 112(3), pages 695-717, June.
    15. 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.
    16. 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.
    17. Marco Battaglini, 2005. "Long-Term Contracting with Markovian Consumers," American Economic Review, American Economic Association, vol. 95(3), pages 637-658, June.
    18. 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.
    19. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
    20. Marek Kapicka, 2013. "Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach," Review of Economic Studies, Oxford University Press, vol. 80(3), pages 1027-1054.
    21. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. repec:spr:joptap:v::y::i::d:10.1007_s10957-018-1230-8 is not listed on IDEAS
    2. Giat, Yahel & Subramanian, Ajay, 2013. "Dynamic contracting under imperfect public information and asymmetric beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2833-2861.
    3. Jovanovic, Boyan & Prat, Julien, 2014. "Dynamic contracts when agent's quality is unknown," Theoretical Economics, Econometric Society, vol. 9(3), September.
    4. Messa, Alexandre, 2015. "Security design and capital structure of business groups," The Quarterly Review of Economics and Finance, Elsevier, vol. 58(C), pages 163-179.
    5. Arie, Guy, 2016. "Dynamic costs and moral hazard: A duality-based approach," Journal of Economic Theory, Elsevier, vol. 166(C), pages 1-50.
    6. Zhiguo He & Bin Wei & Jianfeng Yu & Feng Gao, 2017. "Optimal Long-Term Contracting with Learning," Review of Financial Studies, Society for Financial Studies, vol. 30(6), pages 2006-2065.
    7. Noah Williams & Rui Li, 2014. "Optimal Unemployment Insurance and Cyclical Fluctuations," 2014 Meeting Papers 804, Society for Economic Dynamics.
    8. Williams, Noah, 2015. "A solvable continuous time dynamic principal–agent model," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 989-1015.
    9. Bergemann, Dirk & Pavan, Alessandro, 2015. "Introduction to Symposium on Dynamic Contracts and Mechanism Design," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 679-701.
    10. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
    11. repec:eee:macchp:v2-725 is not listed on IDEAS
    12. Miao, Jianjun & Zhang, Yuzhe, 2015. "A duality approach to continuous-time contracting problems with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 929-988.
    13. Vasama, Suvi, 2017. "Contracting with long-term consequences," Research Discussion Papers 14/2017, Bank of Finland.
    14. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, Elsevier.
    15. Piskorski, Tomasz & Westerfield, Mark M., 2016. "Optimal dynamic contracts with moral hazard and costly monitoring," Journal of Economic Theory, Elsevier, vol. 166(C), pages 242-281.
    16. repec:spr:finsto:v:21:y:2017:i:3:d:10.1007_s00780-017-0323-9 is not listed on IDEAS
    17. Vasama, Suvi, 2017. "On moral hazard and persistent private information," Research Discussion Papers 15/2017, Bank of Finland.
    18. repec:cuf:journl:y:2018:v:19:i:1:li is not listed on IDEAS
    19. Hengjie Ai & Rui Li, 2012. "Moral hazard, investment, and firm dynamics," FRB Atlanta CQER Working Paper 2012-01, Federal Reserve Bank of Atlanta.

    More about this item

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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