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On the Recursive Saddle Point Method

Author

Listed:
  • Nicola Pavoni
  • Ramon Marimon

    (Economics Bocconi University)

  • Matthias Messner
Abstract
In this paper a simple dynamic optimization problem is solved with the help of the recursive saddle point method developed by Marcet and Marimon (1999). According to Marcet and Marimon, their technique should yield a full characterization of the set of solutions for this problem. We show though, that while their method allows us to calculate the true value of the optimization program, not all solutions which it admits are correct. Indeed, some of the policies which it generates as solutions to our problem, are either suboptimal or do not even satisfy feasibility. We identify the reasons underlying this failure and discuss its implications for the numerous existing applications.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Nicola Pavoni & Ramon Marimon & Matthias Messner, 2005. "On the Recursive Saddle Point Method," 2005 Meeting Papers 294, Society for Economic Dynamics.
  • Handle: RePEc:red:sed005:294
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    References listed on IDEAS

    as
    1. Thomas Cooley & Ramon Marimon & Vincenzo Quadrini, 2004. "Aggregate Consequences of Limited Contract Enforceability," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 817-847, August.
    2. Christopher Phelan & Robert M. Townsend, 1991. "Computing Multi-Period, Information-Constrained Optima," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(5), pages 853-881.
    3. Aubhik Khan & Robert G. King & Alexander L. Wolman, 2003. "Optimal Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(4), pages 825-860.
    4. Ezra Friedman, 1998. "Risk Sharing and the Dynamics of Inequality," Discussion Papers 1235, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Albert Marcet & Ramon Marimon, 2019. "Recursive Contracts," Econometrica, Econometric Society, vol. 87(5), pages 1589-1631, September.
    6. Marcet, Albert & Marimon, Ramon, 1992. "Communication, commitment, and growth," Journal of Economic Theory, Elsevier, vol. 58(2), pages 219-249, December.
    7. Paul Klein & JosÈ-VÌctor RÌos-Rull, 2003. "Time-consistent optimal fiscal policy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(4), pages 1217-1245, November.
    8. Rui Albuquerque & Hugo Hopenhayn, 2002. "Optimal Lending Contracts and Firm Dynamics," RCER Working Papers 493, University of Rochester - Center for Economic Research (RCER).
    9. Christopher Phelan & Ennio Stacchetti, 2001. "Sequential Equilibria in a Ramsey Tax Model," Econometrica, Econometric Society, vol. 69(6), pages 1491-1518, November.
    10. Gian Luca Clementi & Hugo Hopenhayn, "undated". "A Theory of Financing Constraints and Firm Dynamics," GSIA Working Papers 2002-E9, Carnegie Mellon University, Tepper School of Business.
    11. Abraham Arpad & Nicola Pavoni, 2004. "Efficient Allocations, with Moral Hazard and Hidden Borrowing and Lending," Levine's Bibliography 122247000000000138, UCLA Department of Economics.
    12. Patrick J. Kehoe & Fabrizio Perri, 2002. "International Business Cycles with Endogenous Incomplete Markets," Econometrica, Econometric Society, vol. 70(3), pages 907-928, May.
    13. Attanasio, Orazio & Rios-Rull, Jose-Victor, 2000. "Consumption smoothing in island economies: Can public insurance reduce welfare?," European Economic Review, Elsevier, vol. 44(7), pages 1225-1258, June.
    14. Ethan Ligon & Jonathan P. Thomas & Tim Worrall, 2000. "Mutual Insurance, Individual Savings and Limited Commitment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 216-246, April.
    15. Lucas, Robert Jr. & Stokey, Nancy L., 1983. "Optimal fiscal and monetary policy in an economy without capital," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 55-93.
    16. Hanno Lustig & Stijn Van Nieuwerburgh, 2002. "Housing Collateral, Consumption Insurance and Risk Premia," Macroeconomics 0211008, University Library of Munich, Germany.
    17. Stephen E. Spear & Sanjay Srivastava, 1987. "On Repeated Moral Hazard with Discounting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 599-617.
    18. 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.
    19. Chang, Roberto, 1998. "Credible Monetary Policy in an Infinite Horizon Model: Recursive Approaches," Journal of Economic Theory, Elsevier, vol. 81(2), pages 431-461, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. Martin Bodenstein, 2008. "International Asset Markets and Real Exchange Rate Volatility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 688-705, July.
    3. Messner Matthias & Pavoni Nicola & Sleet Christopher, "undated". "Recursive Methods for Dynamic Incentive Problems," GSIA Working Papers 2012-E13, Carnegie Mellon University, Tepper School of Business.
    4. Marimon, Ramon & Werner, Jan, 2021. "The envelope theorem, Euler and Bellman equations, without differentiability," Journal of Economic Theory, Elsevier, vol. 196(C).
    5. Albert Marcet & Ramon Marimon, 2019. "Recursive Contracts," Econometrica, Econometric Society, vol. 87(5), pages 1589-1631, September.
    6. Messner Matthias & Pavoni Nicola & Sleet Christopher, "undated". "On the Dual Approach to Recursive Optimization," GSIA Working Papers 2012-E12, Carnegie Mellon University, Tepper School of Business.
    7. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    8. 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.
    9. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 725-841, Elsevier.
    10. Matthias Messner & Nicola Pavoni & Christopher Sleet, "undated". "Contractive Dual Methods for Incentive Problems," GSIA Working Papers 2012-E26, Carnegie Mellon University, Tepper School of Business.
    11. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2015. "Time consistent Markov policies in dynamic economies with quasi-hyperbolic consumers," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 83-112, February.
    12. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2013. "A constructive geometrical approach to the uniqueness of Markov stationary equilibrium in stochastic games of intergenerational altruism," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1019-1039.

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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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