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

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  • 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
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    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. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475, October.
    5. 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.
    6. 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.
    7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    8. 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.
    9. 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.
    10. 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.
    11. Strand, Jon, 1989. "Monopoly unions versus efficient bargaining : A repeated game approach," European Journal of Political Economy, Elsevier, vol. 5(4), pages 473-486.
    12. 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.
    13. McDonald, Ian M & Solow, Robert M, 1981. "Wage Bargaining and Employment," American Economic Review, American Economic Association, vol. 71(5), pages 896-908, December.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
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    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.

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    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

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