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Recursive Contracts, Lotteries and Weakly Concave Pareto Sets

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  • Harold L. Cole
  • Felix Kubler

Abstract

Marcet and Marimon (1994, revised 1998, revised 2011) 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 flat 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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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 17064.

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Date of creation: May 2011
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Publication status: published as Harold Cole & Felix Kubler, 2012. "Recursive Contracts, Lotteries and Weakly Concave Pareto Sets," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(4), pages 479-500, October.
Handle: RePEc:nbr:nberwo:17064

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  1. Marcet, Albert & Marimon, Ramon, 1992. "Communication, commitment, and growth," Journal of Economic Theory, Elsevier, vol. 58(2), pages 219-249, December.
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  8. Thomas Cooley & Ramon Marimon & Vincenzo Quadrini, 2003. "Aggregate Consequences of Limited Contract Enforceability," Working Papers 1, Barcelona Graduate School of Economics.
  9. Matthias Messner & Nicola Pavoni & Christopher Sleet, 2012. "Recursive Methods for Incentive Problems," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(4), pages 501-525, October.
  10. Matthias Messner & Nicola Pavoni, 2004. "On the Recursive Saddle Point Method," Levine's Bibliography 122247000000000050, UCLA Department of Economics.
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Cited by:
  1. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
  2. Matthias Messner & Nicola Pavoni & Christopher Sleet, 2012. "Contractive Dual Methods for Incentive Problems," Working Papers 466, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  3. 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.
  4. Marcet, A. & Marimon, R., 1998. "Recursive Contracts," Economics Working Papers eco98/37, European University Institute.
  5. 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.
  6. Chien, YiLi & Cole, Harold L. & Lustig, Hanno, 2014. "Implications of heterogeneity in preferences, beliefs and asset trading technologies for the macroeconomy," Working Papers 2014-14, Federal Reserve Bank of St. Louis.
  7. Matthias Messner & Nicola Pavoni & Christopher Sleet, 2012. "Recursive Methods for Incentive Problems," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(4), pages 501-525, October.

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