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Persistent Private Information

  • Noah Williams

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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File URL: http://www.nber.org/papers/w13894.pdf
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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
Note: EFG
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  1. 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.
  2. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
  3. Biais, Bruno & Mariotti, Thomas & Plantin, Guillaume & Rochet, Jean-Charles, 2004. "Dynamic Security Design," CEPR Discussion Papers 4753, C.E.P.R. Discussion Papers.
  4. Mikhail Golosov & Aleh Tsyvinski, 2004. "Designing Optimal Disability Insurance: A Case for Asset Testing," NBER Working Papers 10792, National Bureau of Economic Research, Inc.
  5. Narayana R Kocherlakota & Luigi Pistaferri, 2005. "Asset Pricing Implications of Pareto Optimality with Private Information," Levine's Bibliography 784828000000000507, UCLA Department of Economics.
  6. Stefania Albanesi & Christopher Sleet, 2004. "Dynamic optimal taxation with private information," Discussion Paper / Institute for Empirical Macroeconomics 140, Federal Reserve Bank of Minneapolis.
  7. 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.
  8. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2001. "Optimal indirect and capital taxation," Staff Report 293, Federal Reserve Bank of Minneapolis.
  9. Atkeson, Andrew & Lucas, Robert E, Jr, 1992. "On Efficient Distribution with Private Information," Review of Economic Studies, Wiley Blackwell, vol. 59(3), pages 427-53, July.
  10. 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.
  11. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Marco Battaglini, 2005. "Long-Term Contracting with Markovian Consumers," American Economic Review, American Economic Association, vol. 95(3), pages 637-658, June.
  17. Meghir, Costas & Pistaferri, Luigi, 2002. "Income Variance Dynamics and Heterogeneity," CEPR Discussion Papers 3632, C.E.P.R. Discussion Papers.
  18. 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.
  19. Abraham, Arpad & Pavoni, Nicola, 2004. "Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending," Working Papers 04-05, Duke University, Department of Economics.
  20. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-67, November.
  21. 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.
  22. Dilip Abreu & David Pearce & Ennio Stacchetti, 1997. "Optimal Cartel Equilibria with Imperfect monitoring," Levine's Working Paper Archive 632, David K. Levine.
  23. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
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