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Recursive Contracts, Lotteries and Weakly Concave Pareto Sets

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  • Harold Cole

    ()
    (Department of Economics, University of Pennsylvania)

  • Felix Kubler

    ()
    (University of Zurich and Swiss Finance Institute)

Abstract

Marcet and Marimon (1994, revised 1998) developed a recursive saddle point method which can be used to solve dynamic contracting problems that include participation, enforcement and incentive constraints. Their method uses a recursive multiplier to capture implicit prior promises to the agent(s) that were made in order to satisfy earlier instances of these constraints. As a result, their method relies on the invertibility of the derivative of the Pareto frontier and cannot be applied to problems for which this frontier is not strictly concave. In this paper we show how one can extend their method to a weakly concave Pareto frontier by expanding the state space to include the realizations of an end of period lottery over the extreme points of a .at region of the Pareto frontier. With this expansion the basic insight of Marcet and Marimon goes through .one can make the problem recursive in the Lagrangian multiplier which yields significant computational advantages over the conventional approach of using utility as the state variable. The case of a weakly concave Pareto frontier arises naturally in applications where the principal’s choice set is not convex but where randomization is possible.

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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 10-038.

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Length: 31 pages
Date of creation: 10 Dec 2010
Date of revision:
Handle: RePEc:pen:papers:10-038

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Keywords: Recursive Contracting; Recursive Multipliers; Lotteries;

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References

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  1. Nicola Pavoni & Ramon Marimon & Matthias Messner, 2005. "On the Recursive Saddle Point Method," 2005 Meeting Papers, Society for Economic Dynamics 294, Society for Economic Dynamics.
  2. Thomas Cooley & Ramon Marimon & Vincenzo Quadrini, 2004. "Aggregate Consequences of Limited Contract Enforceability," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 112(4), pages 817-847, August.
  3. Aubhik Khan & Robert G. King & Alexander L. Wolman, 2000. "Optimal monetary policy," Working Paper, Federal Reserve Bank of Richmond 00-10, Federal Reserve Bank of Richmond.
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  5. Spear, Stephen E & Srivastava, Sanjay, 1987. "On Repeated Moral Hazard with Discounting," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 54(4), pages 599-617, October.
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  7. Patrick J. Kehoe & Fabrizio Perri, 2000. "International Business Cycles with Endogenous Incomplete Markets," NBER Working Papers 7870, National Bureau of Economic Research, Inc.
  8. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262100711, December.
  9. Richard Rogerson, 2010. "Indivisible Labor, Lotteries and Equilibrium," Levine's Working Paper Archive 250, David K. Levine.
  10. Harold L Cole & Edward C Prescott, 1997. "Valuation equilibrium with Clubs," Levine's Working Paper Archive 912, David K. Levine.
  11. Prescott, Edward C & Townsend, Robert M, 1984. "Pareto Optima and Competitive Equilibria with Adverse Selection and Moral Hazard," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 21-45, January.
  12. Matthias Messner & Nicola Pavoni & Christopher Sleet, 2011. "Recursive methods for incentive problems," Working Papers, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University 381, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  13. Dechert, W. D., 1982. "Lagrange multipliers in infinite horizon discrete time optimal control models," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 285-302, March.
  14. Albert Marcet & Ramon Marimon, 1991. "Communication, commitment and growth," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 1, Department of Economics and Business, Universitat Pompeu Fabra.
  15. Yongyang Cai & Kenneth L. Judd, 2010. "Stable and Efficient Computational Methods for Dynamic Programming," Journal of the European Economic Association, MIT Press, MIT Press, vol. 8(2-3), pages 626-634, 04-05.
  16. Attanasio, Orazio & Rios-Rull, Jose-Victor, 2000. "Consumption smoothing in island economies: Can public insurance reduce welfare?," European Economic Review, Elsevier, Elsevier, vol. 44(7), pages 1225-1258, June.
  17. YiLi Chien & Harold Cole & Hanno Lustig, 2007. "A Multiplier Approach to Understanding the Macro Implications of Household Finance," NBER Working Papers 13555, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. Albert Marcet & Ramon Marimon, 2011. "Recursive Contracts," Economics Working Papers, European University Institute ECO2011/15, European University Institute.
  2. Matthias Messner & Nicola Pavoni & Sleet Christopher, 2011. "On the Dual Approach to Recursive Optimization," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 2012-E8, Carnegie Mellon University, Tepper School of Business.
  3. Mele, Antonio, 2011. "Repeated moral hazard and recursive Lagrangeans," MPRA Paper 30310, University Library of Munich, Germany.
  4. Matthias Messner & Nicola Pavoni & Christopher Sleet, 2011. "Recursive methods for incentive problems," Working Papers, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University 381, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  5. Chien, YiLi & Cole, Harold L. & Lustig, Hanno, 2014. "Implications of heterogeneity in preferences, beliefs and asset trading technologies for the macroeconomy," Working Papers, Federal Reserve Bank of St. Louis 2014-14, Federal Reserve Bank of St. Louis.
  6. Matthias Messner & Nicola Pavoni & Christopher Sleet, . "Contractive Dual Methods for Incentive Problems," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 2012-E26, Carnegie Mellon University, Tepper School of Business.
  7. Messner Matthias & Pavoni Nicola & Sleet Christopher, . "Recursive Methods for Dynamic Incentive Problems," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 2012-E13, Carnegie Mellon University, Tepper School of Business.

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