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The Nash Bargaining Two-tier Stochastic Frontier Model

In: Essays in Honor of Subal Kumbhakar

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  • Alecos Papadopoulos

Abstract

The author develops a bilateral Nash bargaining model under value uncertainty and private/asymmetric information, combining ideas from axiomatic and strategic bargaining theory. The solution to the model leads organically to a two-tier stochastic frontier (2TSF) setup with intra-error dependence. The author presents two different statistical specifications to estimate the model, one that accounts for regressor endogeneity using copulas, the other able to identify separately the bargaining power from the private information effects at the individual level. An empirical application using a matched employer–employee data set (MEEDS) from Zambia and a second using another one from Ghana showcase the applied potential of the approach.

Suggested Citation

  • Alecos Papadopoulos, 2024. "The Nash Bargaining Two-tier Stochastic Frontier Model," Advances in Econometrics, in: Essays in Honor of Subal Kumbhakar, volume 46, pages 439-476, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-905320240000046015
    DOI: 10.1108/S0731-905320240000046015
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    References listed on IDEAS

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    1. Das, Tirthatanmoy & Polachek, Solomon W., 2017. "Estimating labor force joiners and leavers using a heterogeneity augmented two-tier stochastic frontier," Journal of Econometrics, Elsevier, vol. 199(2), pages 156-172.
    2. repec:eee:labchp:v:3:y:1999:i:pb:p:2629-2710 is not listed on IDEAS
    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. Subal Kumbhakar & Christopher Parmeter, 2010. "Estimation of hedonic price functions with incomplete information," Empirical Economics, Springer, vol. 39(1), pages 1-25, August.
    5. Daniel Keniston & Bradley J. Larsen & Shengwu Li & J.J. Prescott & Bernardo S. Silveira & Chuan Yu, 2021. "Fairness in Incomplete Information Bargaining: Theory and Widespread Evidence from the Field," NBER Working Papers 29111, National Bureau of Economic Research, Inc.
    6. Peter X.-K. Song & Mingyao Li & Ying Yuan, 2009. "Joint Regression Analysis of Correlated Data Using Gaussian Copulas," Biometrics, The International Biometric Society, vol. 65(1), pages 60-68, March.
    7. Polachek, Solomon W & Yoon, Bong Joon, 1987. "A Two-tiered Earnings Frontier Estimation of Employer and Employee Information in the Labor Market," The Review of Economics and Statistics, MIT Press, vol. 69(2), pages 296-302, May.
    8. Robert E. Hall & Paul R. Milgrom, 2008. "The Limited Influence of Unemployment on the Wage Bargain," American Economic Review, American Economic Association, vol. 98(4), pages 1653-1674, September.
    9. Ana María Iregui & Ligia Alba Melo & María Teresa Ramírez, 2014. "Wage‐setting Decisions on Newly Hired Employees: Survey Evidence from Colombian Firms," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 35(3), pages 231-246, April.
    10. Alecos Papadopoulos, 2021. "Stochastic frontier models using the Generalized Exponential distribution," Journal of Productivity Analysis, Springer, vol. 55(1), pages 15-29, February.
    11. Paul H. Jensen, 2010. "Exploring the Uses of Matched Employer–Employee Datasets," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 43(2), pages 209-216, June.
    12. Subal Kumbhakar & Christopher Parmeter, 2009. "The effects of match uncertainty and bargaining on labor market outcomes: evidence from firm and worker specific estimates," Journal of Productivity Analysis, Springer, vol. 31(1), pages 1-14, February.
    13. John P. Harding & Stuart S. Rosenthal & C. F. Sirmans, 2003. "Estimating Bargaining Power in the Market for Existing Homes," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 178-188, February.
    14. Groot, Wim & van den Brink, Henriette Maassen, 2007. "Optimism, pessimism and the compensating income variation of cardiovascular disease: A two-tiered quality of life stochastic frontier model," Social Science & Medicine, Elsevier, vol. 65(7), pages 1479-1489, October.
    15. Alecos Papadopoulos, 2015. "The half-normal specification for the two-tier stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 43(2), pages 225-230, April.
    16. Tran, Kien C. & Tsionas, Efthymios G., 2015. "Endogeneity in stochastic frontier models: Copula approach without external instruments," Economics Letters, Elsevier, vol. 133(C), pages 85-88.
    17. Alecos Papadopoulos & Christopher F. Parmeter & Subal C. Kumbhakar, 2021. "Modeling dependence in two-tier stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 56(2), pages 85-101, December.
    18. Anders Forslund & Nils Gottfries & Andreas Westermark, 2008. "Prices, Productivity and Wage Bargaining in Open Economies," Scandinavian Journal of Economics, Wiley Blackwell, vol. 110(1), pages 169-195, March.
    19. Christopher F. Parmeter, 2018. "Estimation of the two-tiered stochastic frontier model with the scaling property," Journal of Productivity Analysis, Springer, vol. 49(1), pages 37-47, February.
    20. Polachek, Solomon W & Yoon, Bong Joon, 1996. "Panel Estimates of a Two-Tiered Earnings Frontier," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(2), pages 169-178, March-Apr.
    21. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
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    More about this item

    Keywords

    Nash bargaining; asymmetric information; two-tier stochastic frontier; copula; matched employer–employee data set; identification; J30; C78; D82; C21;
    All these keywords.

    JEL classification:

    • J30 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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