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  • Noah Williams

Abstract

This paper studies the design of optimal contracts in dynamic environments where agents have private information that is persistent. In particular, I focus on a continuous time version of a benchmark insurance problem 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 find that the optimal contract conditions on the agent's reported endowment as well as two additional state variables: the agent's utility and marginal utility under the contract. I show how persistence alters the nature of the contract, and consider an exponential utility example which can be solved in closed form. Unlike the previous discrete time models with i.i.d. private information, the agent's consumption under the contract may grow over time. Furthermore, in my setting the efficiency losses due to private information increase with the persistence of the endowment, and the distortions vanish as I approximate an i.i.d. endowment.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 79 (2011)
Issue (Month): 4 (07)
Pages: 1233-1275

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Handle: RePEc:ecm:emetrp:v:79:y:2011:i:4:p:1233-1275

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References

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  1. Biais, Bruno & Mariotti, Thomas & Plantin, Guillaume & Rochet, Jean-Charles, 2004. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," IDEI Working Papers 312, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2006.
  2. Costas Meghir & Luigi Pistaferri, 2001. "Income variance dynamics and heterogenity," IFS Working Papers W01/07, Institute for Fiscal Studies.
  3. 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.
  4. Mikhail Golosov & Aleh Tsyvinski, 2005. "Designing Optimal Disability Insurance: A Case for Asset Testing," Levine's Bibliography 784828000000000450, UCLA Department of Economics.
  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. 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.
  7. Mikhail Golosov & Narayana R. Kocherlakota & Aleh Tsyvinski, 2001. "Optimal indirect and capital taxation," Working Papers 615, Federal Reserve Bank of Minneapolis.
  8. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
  9. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
  10. 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.
  11. 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.
  12. Biais, Bruno & Mariotti, Thomas & Plantin, Guillaume & Rochet, Jean Charles, 2004. "Dynamic Security Design," CEPR Discussion Papers 4753, C.E.P.R. Discussion Papers.
  13. Andrew Atkeson & Robert E Lucas, 2010. "On Efficient Distribution with Private Information," Levine's Working Paper Archive 2179, David K. Levine.
  14. Abraham, Arpad & Pavoni, Nicola, 2004. "Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending," Working Papers 04-05, Duke University, Department of Economics.
  15. 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.
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  17. Dilip Abreu & David Pearce & Ennio Stacchetti, 1997. "Optimal Cartel Equilibria with Imperfect monitoring," Levine's Working Paper Archive 632, David K. Levine.
  18. 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, 06.
  19. Spear, Stephen E & Srivastava, Sanjay, 1987. "On Repeated Moral Hazard with Discounting," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 599-617, October.
  20. 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.
  21. Marco Battaglini, 2003. "Long-Term Contracting with Markovian Consumers," Theory workshop papers 505798000000000048, UCLA Department of Economics.
  22. 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.
  23. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
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Citations

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Cited by:
  1. Prat, Julien & Jovanovic, Boyan, 2010. "Dynamic Incentive Contracts under Parameter Uncertainty," IZA Discussion Papers 5323, Institute for the Study of Labor (IZA).
  2. Hengjie Ai & Rui Li, 2012. "Moral hazard, investment, and firm dynamics," CQER Working Paper 2012-01, Federal Reserve Bank of Atlanta.
  3. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
  4. 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.
  5. Jovanovic, Boyan & Prat, Julien, 0. "Dynamic contracts when agent'’s quality is unknown," Theoretical Economics, Econometric Society.

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