IDEAS home Printed from https://ideas.repec.org/p/upf/upfgen/337.html
   My bibliography  Save this paper

Recursive contracts

Author

Listed:
  • Albert Marcet
  • Ramon Marimon

Abstract

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).

Suggested Citation

  • Albert Marcet & Ramon Marimon, 1994. "Recursive contracts," Economics Working Papers 337, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 1998.
    • Handle: RePEc:upf:upfgen:337
    as

    Download full text from publisher

    File URL: https://econ-papers.upf.edu/papers/337.pdf
    File Function: Whole Paper
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Davide Debortoli & Ricardo Nunes, 2007. "Loose commitment," International Finance Discussion Papers 916, Board of Governors of the Federal Reserve System (U.S.).
    2. 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.
    3. Albert Marcet & Ramon Marimon, 2019. "Recursive Contracts," Econometrica, Econometric Society, vol. 87(5), pages 1589-1631, September.
    4. Marcet, Albert & Marimon, Ramon, 1992. "Communication, commitment, and growth," Journal of Economic Theory, Elsevier, vol. 58(2), pages 219-249, December.
    5. Andrés Velasco & Jess Benhabib & Aldo Rustichini, 2001. "Public spending and optimal taxes without commitment," Review of Economic Design, Springer;Society for Economic Design, vol. 6(3), pages 371-396.
    6. Benhabib, Jess & Rustichini, Aldo, 1997. "Optimal Taxes without Commitment," Journal of Economic Theory, Elsevier, vol. 77(2), pages 231-259, December.
    7. Acemoglu, Daron & Golosov, Mikhail & Tsyvinski, Aleh, 2011. "Power fluctuations and political economy," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1009-1041, May.
    8. Christopher Phelan & Ennio Stacchetti, 2001. "Sequential Equilibria in a Ramsey Tax Model," Econometrica, Econometric Society, vol. 69(6), pages 1491-1518, November.
    9. 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.
    10. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    11. 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.
    12. Roberto Chang, 1996. "Credible monetary policy with long-lived agents: recursive approaches," FRB Atlanta Working Paper 96-20, Federal Reserve Bank of Atlanta.
    13. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    14. Marimon, Ramon & Quadrini, Vincenzo, 2011. "Competition, human capital and income inequality with limited commitment," Journal of Economic Theory, Elsevier, vol. 146(3), pages 976-1008, May.
    15. 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.
    16. 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.
    17. Patrick J. Kehoe & Fabrizio Perri, 2002. "International Business Cycles with Endogenous Incomplete Markets," Econometrica, Econometric Society, vol. 70(3), pages 907-928, May.
    18. Matthias Messner & Nicola Pavoni, 2004. "On the Recursive Saddle Point Method," Working Papers 255, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    19. 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.
    20. 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 745-775, August.
    21. Debortoli, Davide & Nunes, Ricardo, 2010. "Fiscal policy under loose commitment," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1005-1032, May.
    22. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    23. Kletzer, Kenneth M. & Wright, Brian D., 1998. "Sovereign Debt as Intertemporal Barter," Santa Cruz Department of Economics, Working Paper Series qt4qg3c42v, Department of Economics, UC Santa Cruz.
    24. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    25. Lars E. O. Svensson & Noah Williams, 2008. "Optimal monetary policy under uncertainty: a Markov jump-linear-quadratic approach," Review, Federal Reserve Bank of St. Louis, vol. 90(Jul), pages 275-294.
    26. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    27. 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.
    28. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
    29. 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.
    30. Eva Carceles-Poveda & Albert Marcet & Alexis Anagnostopoulos, 2008. "Equity Financing," 2008 Meeting Papers 954, Society for Economic Dynamics.
    31. Narayana R. Kocherlakota, 1996. "Implications of Efficient Risk Sharing without Commitment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 595-609.
    32. 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 473-491, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Miao, Jianjun & Zhang, Yuzhe, 2015. "A duality approach to continuous-time contracting problems with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 929-988.
    3. 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.
    4. Zhigang Feng, 2015. "Time‐consistent optimal fiscal policy over the business cycle," Quantitative Economics, Econometric Society, vol. 6(1), pages 189-221, March.
    5. Bauducco, Sofia & Caprioli, Francesco, 2014. "Optimal fiscal policy in a small open economy with limited commitment," Journal of International Economics, Elsevier, vol. 93(2), pages 302-315.
    6. Catarina Reis, 2013. "Taxation without commitment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(2), pages 565-588, March.
    7. Brendon, Charles & Ellison, Martin, 2018. "Time-consistently undominated policies," LSE Research Online Documents on Economics 87176, London School of Economics and Political Science, LSE Library.
    8. Marimon, Ramon & Werner, Jan, 2021. "The envelope theorem, Euler and Bellman equations, without differentiability," Journal of Economic Theory, Elsevier, vol. 196(C).
    9. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    10. 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.
    11. Almuth Scholl, 2002. "Limited Enforceable International Loans, International Risk Sharing and Trade," SFB 649 Discussion Papers SFB649DP2005-055, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2005.
    12. Matthias Messner & Nicola Pavoni, 2004. "On the Recursive Saddle Point Method," Working Papers 255, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    13. Patrick J. Kehoe & Fabrizio Perri, 2002. "International Business Cycles with Endogenous Incomplete Markets," Econometrica, Econometric Society, vol. 70(3), pages 907-928, May.
    14. 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.
    15. Zhigang Feng & Jianjun Miao & Adrian Peralta‐Alva & Manuel S. Santos, 2014. "Numerical Simulation Of Nonoptimal Dynamic Equilibrium Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(1), pages 83-110, February.
    16. Vasilev, Aleksandar, 2013. "Essays on Real Business Cycle Modeling and the Public Sector," EconStor Theses, ZBW - Leibniz Information Centre for Economics, number 130522, March.
    17. Debortoli, Davide & Maih, Junior & Nunes, Ricardo, 2014. "Loose Commitment In Medium-Scale Macroeconomic Models: Theory And Applications," Macroeconomic Dynamics, Cambridge University Press, vol. 18(1), pages 175-198, January.
    18. Almuth Scholl, 2009. "Aid Effectiveness and Limited Enforceable Conditionality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(2), pages 377-391, April.
    19. Patrick Bolton & Neng Wang & Jinqiang Yang, 2016. "Liquidity and Risk Management: Coordinating Investment and Compensation Policies," 2016 Meeting Papers 1703, Society for Economic Dynamics.
    20. Kurozumi, Takushi, 2008. "Optimal sustainable monetary policy," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1277-1289, October.

    More about this item

    Keywords

    Time inconsistency; recursive formulation; dynamic programming; Ramsey equilibrium; participation constraint; recursive saddle points;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Lists

    This item is featured on the following reading lists, Wikipedia, or ReplicationWiki pages:
    1. Recursive Macroeconomic Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:upf:upfgen:337. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.upf.edu/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.