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Recursive contracts

  • Albert Marcet
  • Ramon Marimon

We obtain a recursive formulation for a general class of contracting problems involving incentive constraints. Under these constraints, the corresponding maximization (sup) problems fails to have a recursive solution. Our approach consists of studying the Lagrangian. We show that, under standard assumptions, the solution to the Lagrangian is characterized by a recursive saddle point (infsup) functional equation, analogous to Bellman's equation. Our approach applies to a large class of contractual problems. As examples, we study the optimal policy in a model with intertemporal participation constraints (which arise in models of default) and intertemporal competitive constraints (which arise in Ramsey equilibria).

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 337.

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Date of creation: Sep 1994
Date of revision: Oct 1998
Handle: RePEc:upf:upfgen:337
Contact details of provider: Web page: http://www.econ.upf.edu/

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  1. Antonio Mele, 2008. "Repeated Moral Hazard and Recursive Lagrangeans," 2008 Meeting Papers 482, Society for Economic Dynamics.
  2. Eva Carceles-Poveda & Albert Marcet & Alexis Anagnostopoulos, 2008. "Equity Financing," 2008 Meeting Papers 954, Society for Economic Dynamics.
  3. Andrés Velasco & Jess Benhabib & Aldo Rustichini, 2001. "Public spending and optimal taxes without commitment," Review of Economic Design, Springer, vol. 6(3), pages 371-396.
  4. Harold Cole & Felix Kubler, 2010. "Recursive Contracts, Lotteries and Weakly Concave Pareto Sets," PIER Working Paper Archive 10-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-91, June.
  6. Brian D. Wright & Kenneth M. Kletzer, 2000. "Sovereign Debt as Intertemporal Barter," American Economic Review, American Economic Association, vol. 90(3), pages 621-639, June.
  7. Narayana Kocherlakota, 2010. "Implications of Efficient Risk Sharing Without Commitment," Levine's Working Paper Archive 2053, David K. Levine.
  8. Patrick J. Kehoe & Fabrizio Perri, 2000. "International Business Cycles with Endogenous Incomplete Markets," NBER Working Papers 7870, National Bureau of Economic Research, Inc.
  9. S. Rao Aiyagari & Albert Marcet & Thomas J. Sargent & Juha Seppala, 2002. "Optimal Taxation without State-Contingent Debt," Journal of Political Economy, University of Chicago Press, vol. 110(6), pages 1220-1254, December.
  10. Árpád Ábrahám & Nicola Pavoni, 2005. "The Efficient Allocation of Consumption under Moral Hazard and Hidden Access to the Credit Market," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 370-381, 04/05.
  11. Nicola Pavoni & Ramon Marimon & Matthias Messner, 2005. "On the Recursive Saddle Point Method," 2005 Meeting Papers 294, Society for Economic Dynamics.
  12. 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.
  13. Levine, Paul & Currie, David, 1987. "The design of feedback rules in linear stochastic rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 11(1), pages 1-28, March.
  14. Davide Debortoli & Ricardo Nunes, 2007. "Loose commitment," International Finance Discussion Papers 916, Board of Governors of the Federal Reserve System (U.S.).
  15. Backus, David K & Kehoe, Patrick J & Kydland, Finn E, 1992. "International Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 100(4), pages 745-75, August.
  16. Daron Acemoglu & Mikhail Golosov & Aleh Tsyvinski, 2009. "Power Fluctuations and Political Economy," NBER Working Papers 15400, National Bureau of Economic Research, Inc.
  17. 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.
  18. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-63, September.
  19. Christopher Phelan & Ennio Stacchetti, 2001. "Sequential Equilibria in a Ramsey Tax Model," Econometrica, Econometric Society, vol. 69(6), pages 1491-1518, November.
  20. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
  21. Roberto Chang, 1996. "Credible monetary policy with long-lived agents: recursive approaches," Working Paper 96-20, Federal Reserve Bank of Atlanta.
  22. German Rojas, 1993. "Optimal taxation in a stochastic growth model with public capital: Crowding-in effects and stabilization policy," Economics Working Papers 62, Department of Economics and Business, Universitat Pompeu Fabra.
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