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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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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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  1. Kocherlakota, Narayana R. & Pistaferri, Luigi, 2005. "Asset pricing implications of Pareto optimality with private information," Discussion Paper Series 1: Economic Studies 2005,29, Deutsche Bundesbank, Research Centre.
  2. Albanesi, Stefania & Sleet, Christopher, 2003. "Dynamic Optimal Taxation with Private Information," CEPR Discussion Papers 4006, C.E.P.R. Discussion Papers.
  3. Abraham Arpad & Nicola Pavoni, 2004. "Efficient Allocations, with Moral Hazard and Hidden Borrowing and Lending," Levine's Bibliography 122247000000000138, UCLA Department of Economics.
  4. Zhang, Yuzhe, 2009. "Dynamic Contracting with Persistent Shocks," MPRA Paper 23108, University Library of Munich, Germany.
  5. Ana Fernandes & Christopher Phelan, 1999. "A recursive formulation for repeated agency with history dependence," Staff Report 259, Federal Reserve Bank of Minneapolis.
  6. Mikhail Golosov & Narayana R. Kocherlakota & Aleh Tsyvinski, 2001. "Optimal indirect and capital taxation," Working Papers 615, Federal Reserve Bank of Minneapolis.
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  9. 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.
  10. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
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  15. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
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  17. 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.
  18. Costas Meghir & Luigi Pistaferri, 2001. "Income variance dynamics and heterogenity," IFS Working Papers W01/07, Institute for Fiscal Studies.
  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.
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  23. Dilip Abreu & David Pearce & Ennio Stacchetti, 1997. "Optimal Cartel Equilibria with Imperfect monitoring," Levine's Working Paper Archive 632, David K. Levine.
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