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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 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

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 13894.

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Date of creation: Mar 2008
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Publication status: published as Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, 07.
Handle: RePEc:nbr:nberwo:13894

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References

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  1. 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.
  2. 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.
  3. 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.
  4. Ana Fernandes & Christopher Phelan, 1999. "A recursive formulation for repeated agency with history dependence," Staff Report 259, Federal Reserve Bank of Minneapolis.
  5. 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.
  6. Guillaume Plantin & Bruno Biais & Thomas Mariotti & Jean-Charles Rochet, 2004. "Dynamic Security Design," GSIA Working Papers 2005-E5, Carnegie Mellon University, Tepper School of Business.
  7. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
  8. Narayana R. Kocherlakota & Luigi Pistaferri, 2007. "Asset Pricing Implications of Pareto Optimality with Private Information," Levine's Bibliography 321307000000000701, UCLA Department of Economics.
  9. Andrew Atkeson & Robert E Lucas, 2010. "On Efficient Distribution with Private Information," Levine's Working Paper Archive 2179, David K. Levine.
  10. 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.
  11. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
  12. Abraham Arpad & Nicola Pavoni, 2004. "Efficient Allocations, with Moral Hazard and Hidden Borrowing and Lending," Levine's Bibliography 122247000000000138, UCLA Department of Economics.
  13. Meghir, Costas & Pistaferri, Luigi, 2002. "Income Variance Dynamics and Heterogeneity," CEPR Discussion Papers 3632, C.E.P.R. Discussion Papers.
  14. Marco Battaglini, 2005. "Long-Term Contracting with Markovian Consumers," American Economic Review, American Economic Association, vol. 95(3), pages 637-658, June.
  15. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
  16. Mikhail Golosov & Aleh Tsyvinski, 2004. "Designing Optimal Disability Insurance: A Case for Asset Testing," NBER Working Papers 10792, National Bureau of Economic Research, Inc.
  17. Dilip Abreu & David Pearce & Ennio Stacchetti, 1997. "Optimal Cartel Equilibria with Imperfect monitoring," Levine's Working Paper Archive 632, David K. Levine.
  18. Stefania Albanesi & Christopher Sleet, 2006. "Dynamic Optimal Taxation with Private Information," Review of Economic Studies, Oxford University Press, vol. 73(1), pages 1-30.
  19. 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.
  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. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-67, November.
  22. 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.
  23. 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.
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Cited by:
  1. Zhang, Yuzhe, 2009. "Dynamic Contracting with Persistent Shocks," MPRA Paper 23108, University Library of Munich, Germany.
  2. Julien Prat & Boyan Jovanovic, 2010. "Dynamic Incentive Contracts Under Parameter Uncertainty," NBER Working Papers 16649, National Bureau of Economic Research, Inc.
  3. Hengjie Ai & Rui Li, 2012. "Moral hazard, investment, and firm dynamics," CQER Working Paper 2012-01, Federal Reserve Bank of Atlanta.
  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.

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