IDEAS home Printed from https://ideas.repec.org/p/nwu/cmsems/1543.html
   My bibliography  Save this paper

Ambiguity in Dynamic Contracts

Author

Listed:
  • Martin Szydlowski

Abstract

I study a dynamic principal agent model in which the effort cost of the agent is unknown to the principal. The principal is ambiguity averse, and designs a contract which is robust to the worst case effort cost process. Ambiguity divides the contract into two regions. After sufficiently high performance, the agent reaches the over-compensation region, where he receives excessive benefits compared to the contract without ambiguity, while after low performance, he enters the under-compensation region. Ambiguity also causes a disconnect between the current effort cost and the strength of incentives. That is, even when the agent is under-compensated, his incentives are as strong as in the over-compensation region, since the principal fears the agent might shirk otherwise. Under ambiguity, the agent’s true effort cost does not need to equal the worst-case. I analyze the agent’s incentives for this case, and show that the possibility of firing is detrimental to the agent’s incentives. I study several extensions concerning the timing structure and the nature of the principal’s ambiguity aversion. JEL Code: D82, D86, M52

Suggested Citation

  • Martin Szydlowski, 2012. "Ambiguity in Dynamic Contracts," Discussion Papers 1543, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1543
    as

    Download full text from publisher

    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1543.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 49-100.
    2. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    3. Bose, Subir & Daripa, Arup, 2009. "A dynamic mechanism and surplus extraction under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2084-2114, September.
    4. Tomasz Piskorski & Alexei Tchistyi, 2011. "Stochastic House Appreciation and Optimal Mortgage Lending," The Review of Financial Studies, Society for Financial Studies, vol. 24(5), pages 1407-1446.
    5. Brian J. Hall & Kevin J. Murphy, 2003. "The Trouble with Stock Options," Journal of Economic Perspectives, American Economic Association, vol. 17(3), pages 49-70, Summer.
    6. Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & StÈphane Villeneuve, 2010. "Large Risks, Limited Liability, and Dynamic Moral Hazard," Econometrica, Econometric Society, vol. 78(1), pages 73-118, January.
    7. Alfredo Di Tillio & Nenad Kos & Matthias Messner, 2012. "The Design of Ambiguous Mechanisms," Working Papers 446, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    8. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    9. Bruno Strulovici & Martin Szydlowski, 2012. "On the Smoothness of Value Functions," Discussion Papers 1542, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Spear, Stephen E. & Wang, Cheng, 2005. "When to fire a CEO: optimal termination in dynamic contracts," Journal of Economic Theory, Elsevier, vol. 120(2), pages 239-256, February.
    11. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    12. Dirk Bergemann & Karl H. Schlag, 2012. "Pricing Without Priors," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 12, pages 405-415, World Scientific Publishing Co. Pte. Ltd..
    13. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    14. 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.
    15. Daniel F. Garrett & Alessandro Pavan, 2012. "Managerial Turnover in a Changing World," Journal of Political Economy, University of Chicago Press, vol. 120(5), pages 879-925.
    16. Peter M. Demarzo & Michael J. Fishman & Zhiguo He & Neng Wang, 2012. "Dynamic Agency and the q Theory of Investment," Journal of Finance, American Finance Association, vol. 67(6), pages 2295-2340, December.
    17. Oyer, Paul & Schaefer, Scott, 2011. "Personnel Economics: Hiring and Incentives," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 20, pages 1769-1823, Elsevier.
    18. repec:oup:restud:v:84:y::i:1:p:237-276. is not listed on IDEAS
    19. PETER M. DeMARZO & YULIY SANNIKOV, 2006. "Optimal Security Design and Dynamic Capital Structure in a Continuous‐Time Agency Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2681-2724, December.
    20. Daniel Garrett & Alessandro Pavan, 2014. "Dynamic Managerial Compensation: On the Optimality of Seniority-based Schemes," Discussion Papers 1579, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    21. repec:nwu:cmsems:1542 is not listed on IDEAS
    22. Brian J. Hall & Kevin J. Murphy, 2003. "The Trouble with Stock Options," NBER Working Papers 9784, National Bureau of Economic Research, Inc.
    23. Zhiguo He, 2009. "Optimal Executive Compensation when Firm Size Follows Geometric Brownian Motion," The Review of Financial Studies, Society for Financial Studies, vol. 22(2), pages 859-892, February.
    24. Yahel Giat & Steve T. Hackman & Ajay Subramanian, 2010. "Investment under Uncertainty, Heterogeneous Beliefs, and Agency Conflicts," The Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1360-1404, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Cheng, 2011. "Termination of dynamic contracts in an equilibrium labor market model," Journal of Economic Theory, Elsevier, vol. 146(1), pages 74-110, January.
    2. Thibaut Mastrolia & Dylan Possamaï, 2018. "Moral Hazard Under Ambiguity," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 452-500, November.
    3. Jianjun Miao & Alejandro Rivera, 2016. "Robust Contracts in Continuous Time," Econometrica, Econometric Society, vol. 84, pages 1405-1440, July.
    4. Hansen, Peter G., 2022. "New formulations of ambiguous volatility with an application to optimal dynamic contracting," Journal of Economic Theory, Elsevier, vol. 199(C).
    5. Jaeyoung Sung, 2022. "Optimal contracting under mean-volatility joint ambiguity uncertainties," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 593-642, September.
    6. Peter G. Hansen, 2021. "New Formulations of Ambiguous Volatility with an Application to Optimal Dynamic Contracting," Papers 2101.12306, arXiv.org.
    7. Swagata Bhattacharjee, 2019. "Dynamic Contracting for Innovation Under Ambiguity," Working Papers 1022, Ashoka University, Department of Economics, revised Aug 2019.
    8. Bhattacharjee, Swagata, 2022. "Dynamic contracting for innovation under ambiguity," Games and Economic Behavior, Elsevier, vol. 132(C), pages 534-552.
    9. Spear, Stephen E. & Wang, Cheng, 2005. "When to fire a CEO: optimal termination in dynamic contracts," Journal of Economic Theory, Elsevier, vol. 120(2), pages 239-256, February.
    10. Li, Rui, 2017. "Dynamic agency with persistent observable shocks," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 74-91.
    11. Martin Dumav, 2021. "Moral Hazard, Dynamic Incentives, and Ambiguous Perceptions," Papers 2110.15229, arXiv.org.
    12. Yaoyao Wu & Jinqiang Yang & Zhentao Zou, 2018. "Ambiguity sharing and the lack of relative performance evaluation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 141-157, July.
    13. Szydlowski, Martin & Yoon, Ji Hee, 2022. "Ambiguity in dynamic contracts," Journal of Economic Theory, Elsevier, vol. 199(C).
    14. Qi Liu & Lei Lu & Bo Sun, 2018. "Incentive contracting under ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 929-950, December.

    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. Szydlowski, Martin & Yoon, Ji Hee, 2022. "Ambiguity in dynamic contracts," Journal of Economic Theory, Elsevier, vol. 199(C).
    2. Jianjun Miao & Alejandro Rivera, 2016. "Robust Contracts in Continuous Time," Econometrica, Econometric Society, vol. 84, pages 1405-1440, July.
    3. Ronald Anderson & Cecilia Bustamante & Stéphane Guibaud & Mihail Zervos, 2018. "Agency, Firm Growth, and Managerial Turnover," Post-Print hal-03391936, HAL.
    4. Ronald Anderson & Cecilia Bustamante & Stéphane Guibaud & Mihail Zervos, 2018. "Agency, Firm Growth, and Managerial Turnover," Sciences Po publications info:hdl:2441/2iclr3ojhv9, Sciences Po.
    5. repec:hal:spmain:info:hdl:2441/2iclr3ojhv9ko9ord4mpg9odaj is not listed on IDEAS
    6. Hiroshi Osano & Keiichi Hori, 2015. "A Dynamic Agency Theory of Investment and Managerial Replacement," KIER Working Papers 921, Kyoto University, Institute of Economic Research.
    7. Anderson, Ronald W. & Bustamante, Maria Cecilia & Guibaud, Stéphane & Zervos, Mihail, 2018. "Agency, firm growth, and managerial turnover," LSE Research Online Documents on Economics 68784, London School of Economics and Political Science, LSE Library.
    8. Rui Li & Dana Kiku & Hengjie Ai, 2014. "A Mechanism Design Model of Firm Dynamics: The Case of Limited Commitment," 2014 Meeting Papers 855, Society for Economic Dynamics.
    9. Szydlowski, Martin, 2019. "Incentives, project choice, and dynamic multitasking," Theoretical Economics, Econometric Society, vol. 14(3), July.
    10. Ronald Anderson & Cecilia Bustamante & Stéphane Guibaud & Mihail Zervos, 2018. "Agency, Firm Growth, and Managerial Turnover," SciencePo Working papers Main hal-03391936, HAL.
    11. Chang-Koo Chi & Kyoung Jin Choi, 2017. "The impact of firm size on dynamic incentives and investment," RAND Journal of Economics, RAND Corporation, vol. 48(1), pages 147-177, March.
    12. Alex Edmans & Xavier Gabaix, 2016. "Executive Compensation: A Modern Primer," Journal of Economic Literature, American Economic Association, vol. 54(4), pages 1232-1287, December.
    13. Wuming Fu & Qian Qi, 2023. "Artificial Intelligence and Dual Contract," Papers 2303.12350, arXiv.org.
    14. Ronald Anderson & Cecilia Bustamante & Stéphane Guibaud & Mihail Zervos, 2018. "Agency, Firm Growth, and Managerial Turnover," SciencePo Working papers hal-03391936, HAL.
    15. Giat, Yahel & Subramanian, Ajay, 2013. "Dynamic contracting under imperfect public information and asymmetric beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2833-2861.
    16. Ales, Laurence & Maziero, Pricila & Yared, Pierre, 2014. "A theory of political and economic cycles," Journal of Economic Theory, Elsevier, vol. 153(C), pages 224-251.
    17. Nenad Kos & Matthias Messner, 2015. "Selling to the mean," Working Papers 551, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    18. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    19. Mayer, Simon, 2022. "Financing breakthroughs under failure risk," Journal of Financial Economics, Elsevier, vol. 144(3), pages 807-848.
    20. Gryglewicz, Sebastian & Mayer, Simon & Morellec, Erwan, 2020. "Agency conflicts and short- versus long-termism in corporate policies," Journal of Financial Economics, Elsevier, vol. 136(3), pages 718-742.
    21. 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.

    More about this item

    Keywords

    Dynamic contract; principal-agent model; ambiguity aversion; continuous time JEL Classification Numbers: 1543;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • M52 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Compensation and Compensation Methods and Their Effects

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:nwu:cmsems:1543. 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: Fran Walker (email available below). General contact details of provider: https://edirc.repec.org/data/cmnwuus.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.