IDEAS home Printed from https://ideas.repec.org/a/spr/decfin/v44y2021i1d10.1007_s10203-021-00326-x.html
   My bibliography  Save this article

Wage bargaining as an optimal control problem: a dynamic version of the efficient bargaining model

Author

Listed:
  • Marco Guerrazzi

    (University of Genoa)

Abstract

In this paper, I develop a dynamic version of the efficient bargaining model grounded on optimal control in which a firm and a union bargain over the wage in a continuous-time environment under the supervision of an infinitely lived mediator. Overturning the findings achieved by means of a companion right-to-manage framework, I demonstrate that when employment is assumed to adjust itself with some attrition in the direction of the contract curve implied by the preferences of the two bargainers, increases in the bargaining power of the firm (union) accelerate (delay) the speed of convergence towards the stationary solution. In addition, confirming the reversal of the results obtained when employment moves over time towards the firm’s labour demand, I show that the dynamic negotiation of wages tends to penalize unionized workers and favour the firm with respect to the bargaining outcomes retrieved with a similar static wage-setting model.

Suggested Citation

  • Marco Guerrazzi, 2021. "Wage bargaining as an optimal control problem: a dynamic version of the efficient bargaining model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 359-374, June.
    • Handle: RePEc:spr:decfin:v:44:y:2021:i:1:d:10.1007_s10203-021-00326-x
    DOI: 10.1007/s10203-021-00326-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10203-021-00326-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10203-021-00326-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Morten O. Ravn & Saverio Simonelli, 2007. "Labor Market Dynamics and the Business Cycle: Structural Evidence for the United States," Scandinavian Journal of Economics, Wiley Blackwell, vol. 109(4), pages 743-777, December.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    4. Richard Layard & Stephen Nickell, 1990. "Is Unemployment Lower if Unions Bargain over Employment?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(3), pages 773-787.
    5. Lars A. Stole & Jeffrey Zwiebel, 1996. "Intra-firm Bargaining under Non-binding Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 375-410.
    6. Strand, Jon, 1989. "Monopoly unions versus efficient bargaining : A repeated game approach," European Journal of Political Economy, Elsevier, vol. 5(4), pages 473-486.
    7. Robert Shimer, 2004. "The Consequences of Rigid Wages in Search Models," Journal of the European Economic Association, MIT Press, vol. 2(2-3), pages 469-479, 04/05.
    8. Johnson, George E, 1990. "Work Rules, Featherbedding, and Pareto-optimal Union-Management Bargaining," Journal of Labor Economics, University of Chicago Press, vol. 8(1), pages 237-259, January.
    9. McDonald, Ian M & Solow, Robert M, 1981. "Wage Bargaining and Employment," American Economic Review, American Economic Association, vol. 71(5), pages 896-908, December.
    10. Jonathan Thomas & Tim Worrall, 1988. "Self-Enforcing Wage Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 541-554.
    11. Attila Ambrus & Shih En Lu, 2015. "A Continuous-Time Model of Multilateral Bargaining," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 208-249, February.
    12. Marco Guerrazzi, 2007. "Wage Bargaining in an Optimal Control Framework: A Dynamic Version of the Right-to-Manage Model," Open Discussion Papers in Economics 61, The Open University, Faculty of Social Sciences, Department of Economics.
    13. William Fellner, 1947. "Prices and Wages under Bilateral Monopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 61(4), pages 503-532.
    14. de la Croix, David & Palm, Franz C. & Pfann, Gerard A., 1996. "A dynamic contracting model for wages and employment in three European economies," European Economic Review, Elsevier, vol. 40(2), pages 429-448, February.
    15. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475.
    16. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    17. Petrakis, Emmanuel & Vlassis, Minas, 2000. "Endogenous scope of bargaining in a union-oligopoly model: when will firms and unions bargain over employment?," Labour Economics, Elsevier, vol. 7(3), pages 261-281, May.
    18. Gerber, Anke & Upmann, Thorsten, 2006. "Bargaining solutions at work: Qualitative differences in policy implications," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 162-175, September.
    19. Lockwood, Ben & Manning, Alan, 1989. "Dynamic Wage-Employment Bargaining with Employment Adjustment Costs," Economic Journal, Royal Economic Society, vol. 99(398), pages 1143-1158, December.
    20. Maria Paz Espinosa & Changyong Rhee, 1989. "Efficient Wage Bargaining as a Repeated Game," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(3), pages 565-588.
    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. Marco Guerrazzi & Pier Giuseppe Giribone, 2022. "The dynamics of working hours and wages under implicit contracts," Bulletin of Economic Research, Wiley Blackwell, vol. 74(4), pages 1075-1094, October.
    2. Marco Guerrazzi & Pier Giuseppe Giribone, 2021. "Dynamic wage bargaining and labour market fluctuations: the role of productivity shocks," SN Business & Economics, Springer, vol. 1(8), pages 1-20, August.

    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. Marco Guerrazzi & Pier Giuseppe Giribone, 2021. "Dynamic wage bargaining and labour market fluctuations: the role of productivity shocks," SN Business & Economics, Springer, vol. 1(8), pages 1-20, August.
    2. Claus-Jochen Haake & Thorsten Upmann & Papatya Duman, 2019. "The Decomposability of the Nash Bargaining Solution in Labor Markets," Working Papers CIE 128, Paderborn University, CIE Center for International Economics.
    3. Claus-Jochen Haake & Thorsten Upmann & Papatya Duman, 2020. "Wage Bargaining and Employment Revisited: Separability and Efficiency in Collective Bargaining," CESifo Working Paper Series 8422, CESifo.
    4. Nicholas Lawson, 2011. "Is Collective Bargaining Pareto Efficient? A Survey of the Literature," Journal of Labor Research, Springer, vol. 32(3), pages 282-304, September.
    5. Fuest, Clemens & Thum, Marcel, 2001. "Immigration and skill formation in unionised labour markets," European Journal of Political Economy, Elsevier, vol. 17(3), pages 557-573, September.
    6. Claus‐Jochen Haake & Thorsten Upmann & Papatya Duman, 2023. "Wage bargaining and employment revisited: separability and efficiency in collective bargaining," Scandinavian Journal of Economics, Wiley Blackwell, vol. 125(2), pages 403-440, April.
    7. Björn Brügemann & Pieter Gautier & Guido Menzio, 2019. "Intra Firm Bargaining and Shapley Values," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(2), pages 564-592.
    8. Bas, Maria & Carluccio, Juan, 2009. "Wage bargaining and the boundaries of the multinational firm," LSE Research Online Documents on Economics 28700, London School of Economics and Political Science, LSE Library.
    9. Hanato, Shunsuke, 2019. "Simultaneous-offers bargaining with a mediator," Games and Economic Behavior, Elsevier, vol. 117(C), pages 361-379.
    10. l'Haridon, Olivier & Malherbet, Franck & Pérez-Duarte, Sébastien, 2013. "Does bargaining matter in the small firms matching model?," Labour Economics, Elsevier, vol. 21(C), pages 42-58.
    11. Thorsten Bayindir-Upmann & Anke Gerber, 2003. "The Kalai-Smorodinsky Solution in Labor-Market Negotiations," CESifo Working Paper Series 941, CESifo.
    12. Adriana Breccia, 2006. "Sequential Bargaining in a Stochastic Environment," Discussion Papers 06/07, Department of Economics, University of York.
    13. repec:pri:indrel:dsp01cc08hf62w is not listed on IDEAS
    14. Spulber, Daniel F., 2016. "Patent licensing and bargaining with innovative complements and substitutes," Research in Economics, Elsevier, vol. 70(4), pages 693-713.
    15. Samir Amine & Sylvain Baumann & Pedro Lages Dos Santos, 2018. "Bargaining Solutions and Public Policies in Matching Models," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 4, pages 3-14.
    16. Marcus Dittrich, 2010. "Minimum Wages and Unemployment Benefits in a Unionized Economy: A Game-Theoretic Approach," Annals of Economics and Finance, Society for AEF, vol. 11(2), pages 209-229, November.
    17. Ahmet Ozkardas & Agnieszka Rusinowska, 2012. "Wage bargaining with discount rates varying in time under exogenous strike decisions," Post-Print halshs-00674033, HAL.
    18. Cheng-Zhong Qin & Shuzhong Shi & Guofu Tan, 2015. "Nash bargaining for log-convex problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(3), pages 413-440, April.
    19. Zhong, Feimin & Zhou, Zhongbao & Leng, Mingming, 2021. "Negotiation-sequence, pricing, and ordering decisions in a three-echelon supply chain: A coopetitive-game analysis," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1096-1107.
    20. Falch, Torberg, 2001. "Collective bargaining in the public sector and the role of budget determination," European Journal of Political Economy, Elsevier, vol. 17(1), pages 75-99, March.
    21. Papatya Duman & Walter Trockel, 2016. "On non-cooperative foundation and implementation of the Nash solution in subgame perfect equilibrium via Rubinstein's game," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 83-107, December.

    More about this item

    Keywords

    Wage–employment bargaining; Optimal control; Local dynamics;
    All these keywords.

    JEL classification:

    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • J52 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - Dispute Resolution: Strikes, Arbitration, and Mediation

    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:spr:decfin:v:44:y:2021:i:1:d:10.1007_s10203-021-00326-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.