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Recursive Contracts, Lotteries and Weakly Concave Pareto Sets

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  • Felix Kubler

    (University of Zurich)

  • Harold L. Cole

    (University of Pennsylvania)

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 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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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2011 Meeting Papers with number 59.

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Date of creation: 2011
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Handle: RePEc:red:sed011:59

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References

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  1. Albert Marcet & Ramon Marimon, 1992. "Communication, commitment, and growth," Discussion Paper / Institute for Empirical Macroeconomics, Federal Reserve Bank of Minneapolis 74, Federal Reserve Bank of Minneapolis.
  2. Matthias Messner & Nicola Pavoni, 2004. "On the Recursive Saddle Point Method," Working Papers 255, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  3. Aubhik Khan & Robert G. King & Alexander L. Wolman, 2001. "Optimal monetary policy," Working Papers 01-5, Federal Reserve Bank of Philadelphia.
  4. Yili Chien & Harold Cole & Hanno Lustig, 2011. "A Multiplier Approach to Understanding the Macro Implications of Household Finance," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 199-234.
  5. Thomas Cooley & Ramon Marimon & Vincenzo Quadrini, 2003. "Aggregate Consequences of Limited Contract Enforceability," Working Papers 1, Barcelona Graduate School of Economics.
  6. 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.
  7. Patrick J. Kehoe & Fabrizio Perri, 2002. "International Business Cycles with Endogenous Incomplete Markets," Econometrica, Econometric Society, Econometric Society, vol. 70(3), pages 907-928, May.
  8. Prescott, Edward C & Townsend, Robert M, 1984. "General Competitive Analysis in an Economy with Private Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 1-20, February.
  9. Edward C Prescott & Robert M Townsend, 2010. "Pareto Optima and Competitive Equilibria With Adverse Selection and Moral Hazard," Levine's Working Paper Archive 2069, David K. Levine.
  10. Rustichini, A., 1998. "Lagrange multipliers in incentive-constrained problems," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 365-380, May.
  11. 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.
  12. 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.
  13. Matthias Messner & Nicola Pavoni & Christopher Sleet, 2011. "Recursive methods for incentive problems," Working Papers 381, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  14. Harold L. Cole & Edward C. Prescott, 1996. "Valuation equilibria with clubs," Staff Report, Federal Reserve Bank of Minneapolis 174, Federal Reserve Bank of Minneapolis.
  15. 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.
  16. Richard Rogerson, 2010. "Indivisible Labor, Lotteries and Equilibrium," Levine's Working Paper Archive 250, David K. Levine.
  17. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262100711, December.
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Cited by:
  1. Marcet, A. & Marimon, R., 1998. "Recursive Contracts," Economics Working Papers, European University Institute eco98/37, European University Institute.
  2. 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.
  3. 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.
  4. 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.
  5. Antonio Mele, 2008. "Repeated Moral Hazard and Recursive Lagrangeans," 2008 Meeting Papers 482, Society for Economic Dynamics.
  6. 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.
  7. Matthias Messner & Nicola Pavoni & Christopher Sleet, 2011. "On the Dual Approach to Recursive Optimization," Working Papers 423, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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