IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/23108.html
   My bibliography  Save this paper

Dynamic Contracting with Persistent Shocks

Author

Listed:
  • Zhang, Yuzhe

Abstract

In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. We characterize the optimal contract as the solution to a system of ordinary differential equations and show that, under this contract, the agent's utility converges to its lower bound|immiserization occurs. Unlike under risk-neutrality, the wedge between the marginal rate of transformation and a low-productivity agent's marginal rate of substitution between consumption and leisure will not vanish permanently at her first high-productivity report; also, the wedge increases with the duration of a low-productivity report. We apply the methods to numerically solve the Mirrleesian dynamic taxation model, and find that the wedge is significantly larger than that in the independently and identically distributed (i.i.d.) shock case.

Suggested Citation

  • Zhang, Yuzhe, 2009. "Dynamic Contracting with Persistent Shocks," MPRA Paper 23108, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:23108
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/23108/1/MPRA_paper_23108.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Holmstrom, Bengt & Milgrom, Paul, 1990. "Short-term contracts and long-term agency relationships," Journal of Economic Theory, Elsevier, vol. 51(1), pages 1-31, June.
    2. Klaus Walde, 2008. "Applied Intertemporal Optimization," Books, Business School - Economics, University of Glasgow, number econ1.
    3. Battaglini, Marco & Coate, Stephen, 2008. "Pareto efficient income taxation with stochastic abilities," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 844-868, April.
    4. Narayana R. Kocherlakota, 2005. "Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Econometrica, Econometric Society, vol. 73(5), pages 1587-1621, September.
    5. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
    6. Andrew Atkeson & Robert E. Lucas, 1992. "On Efficient Distribution With Private Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 427-453.
    7. Emmanuel Farhi & Iván Werning, 2007. "Inequality and Social Discounting," Journal of Political Economy, University of Chicago Press, vol. 115(3), pages 365-402.
    8. Albanesi, Stefania, 2006. "Optimal Taxation of Entrepreneurial Capital with Private Information," CEPR Discussion Papers 5647, C.E.P.R. Discussion Papers.
    9. Yuliy Sannikov, 2007. "Games with Imperfectly Observable Actions in Continuous Time," Econometrica, Econometric Society, vol. 75(5), pages 1285-1329, September.
    10. Stefania Albanesi & Christopher Sleet, 2006. "Dynamic Optimal Taxation with Private Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(1), pages 1-30.
    11. Marek Kapicka, 2006. "Optimal Income Taxation with Human Capital Accumulation and Limited Record Keeping," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(4), pages 612-639, October.
    12. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    13. Mikhail Golosov & Aleh Tsyvinski, 2006. "Designing Optimal Disability Insurance: A Case for Asset Testing," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 257-279, April.
    14. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    15. Mikhail Golosov & Aleh Tsyvinski, 2007. "Optimal Taxation with Endogenous Insurance Markets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(2), pages 487-534.
    16. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2003. "Optimal Indirect and Capital Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(3), pages 569-587.
    17. Schattler Heinz & Sung Jaeyoung, 1993. "The First-Order Approach to the Continuous-Time Principal-Agent Problem with Exponential Utility," Journal of Economic Theory, Elsevier, vol. 61(2), pages 331-371, December.
    18. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    19. Yuzhe Zhang, 2005. "Dynamic contracting, persistent shocks and optimal taxation," Working Papers 640, Federal Reserve Bank of Minneapolis.
    20. Fernandes, Ana & Phelan, Christopher, 2000. "A Recursive Formulation for Repeated Agency with History Dependence," Journal of Economic Theory, Elsevier, vol. 91(2), pages 223-247, April.
    21. 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.
    22. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 2000. "Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?," Econometrica, Econometric Society, vol. 68(5), pages 1151-1180, September.
    23. Cvitanic Jaksa & Wan Xuhu & Zhang Jianfeng, 2008. "Principal-Agent Problems with Exit Options," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-43, October.
    24. Marek Kapicka, 2013. "Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(3), pages 1027-1054.
    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. Mikhail Golosov & Maxim Troshkin & Aleh Tsyvinski, 2011. "Optimal Taxation: Merging Micro and Macro Approaches," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43, pages 147-174, August.
    3. Grochulski, Borys & Piskorski, Tomasz, 2010. "Risky human capital and deferred capital income taxation," Journal of Economic Theory, Elsevier, vol. 145(3), pages 908-943, May.
    4. Yuzhe Zhang, 2005. "Dynamic contracting, persistent shocks and optimal taxation," Working Papers 640, Federal Reserve Bank of Minneapolis.
    5. Julien Prat & Boyan Jovanovic, 2010. "Dynamic Incentive Contracts Under Parameter Uncertainty," NBER Working Papers 16649, National Bureau of Economic Research, Inc.
    6. da Costa, Carlos E. & Severo, Tiago, 2008. "Education, preferences for leisure and the optimal income tax schedule," Journal of Public Economics, Elsevier, vol. 92(1-2), pages 113-138, February.
    7. Maxim Troshkin & Aleh Tsyvinski & Mikhail Golosov, 2010. "Optimal Dynamic Taxes," 2010 Meeting Papers 320, Society for Economic Dynamics.
    8. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    9. Roozbeh Hosseini & Larry E. Jones & Ali Shourideh, 2009. "Risk Sharing, Inequality and Fertility," NBER Working Papers 15111, National Bureau of Economic Research, Inc.
    10. , & ,, 2014. "Dynamic contracts when agent's quality is unknown," Theoretical Economics, Econometric Society, vol. 9(3), September.
    11. Xi Chen & Yu Chen & Xuhu Wan, 2018. "Delegated Project Search," Graz Economics Papers 2018-11, University of Graz, Department of Economics.
    12. J. C. Parra & M. Huggett, 2005. "Quantifying the Inefficiency of the US Social Security System," Computing in Economics and Finance 2005 70, Society for Computational Economics.
    13. Guo, Lu & Yan, Chong, 2021. "Optimal Taxation in the Endogenous Growth Framework with the Private Information," MPRA Paper 109548, University Library of Munich, Germany.
    14. Hosseini, Roozbeh & Jones, Larry E. & Shourideh, Ali, 2013. "Optimal contracting with dynastic altruism: Family size and per capita consumption," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1806-1840.
    15. Stefania Albanesi & Roc Armenter, 2012. "Intertemporal Distortions in the Second Best," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(4), pages 1271-1307.
    16. Winfried Koeniger & Julien Prat, 2018. "Human Capital and Optimal Redistribution," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 27, pages 1-26, January.
    17. Narayana R Kocherlakota, 2005. "Advances in Dynamic Optimal Taxation," Levine's Bibliography 784828000000000518, UCLA Department of Economics.
    18. Abdoulaye Ndiaye, 2017. "Flexible Retirement and Optimal Taxation," Working Paper Series WP-2018-18, Federal Reserve Bank of Chicago.
    19. Borys Grochulski, 2007. "Optimal Personal Bankruptcy Design: A Mirrlees Approach," 2007 Meeting Papers 1008, Society for Economic Dynamics.
    20. Williams, Noah, 2015. "A solvable continuous time dynamic principal–agent model," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 989-1015.

    More about this item

    Keywords

    Persistent Information; Principal-agent Problem; Private Information; Optimal Taxation;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination

    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:pra:mprapa:23108. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.