IDEAS home Printed from https://ideas.repec.org/p/hhs/nierwp/0050.html
   My bibliography  Save this paper

Hierarchical Assignments: Stability and Fairness

Author

Listed:
  • Eriksson, Kimmo

    (Stockholm University)

  • Karlander, Johan

    (Royal Institute of Technology)

  • Öller, Lars-Erik

    () (National Institute of Economic Research)

Abstract

We study a simple assigning workers to employers, where each pair of a worker and an employer has a potential joint productivity, and the complete information about the market is contained in the matrix of potential productivities. Under certain conditions that we specify, the market is hierarchical, in the sense that both workers and employers can be ordered according to ability, and the Pareto optimal assignment in terms of maximal total productivity is achieved by matching the top worker with the top employer and so on. In other words, we describe a market situation in which the above simple matching procedure is optimal. Some further properties of hierarchies are presented. We can state explicit values for the earnings in the worker optimal and employer optimal solutions. We further show that our hierarchy concept is descrete analogue to the Ricardian differential rent model of Sattinger (1979), and that the latter one can easily be derived from our model. We discuss the compatibility problems between fairness and stability of earnings and assignments. In particular, two notions of fairness that seem sensible in general fail to be stable in hierarchical markets. First, pairwise sharing the Pareto optimal product using a fixed sharing rule generates stable assignments only under a very restrictive assumption. Second, distributing the same amount to all workers preserves stability only in the extreme situation of an equal distribution of ability among workers. A uniform distribution of ability will always generate a smaller overall production than an uneaven distribution in Pareto optimum. we argue for another notion of fairness that turns out to be stable: an average between the worker optimal and employer otimal solutions. The model can be used to illustrate imperfect competition, economic growth and corruption.

Suggested Citation

  • Eriksson, Kimmo & Karlander, Johan & Öller, Lars-Erik, 1996. "Hierarchical Assignments: Stability and Fairness," Working Papers 50, National Institute of Economic Research.
  • Handle: RePEc:hhs:nierwp:0050
    as

    Download full text from publisher

    File URL: http://www.konj.se/download/18.42684e214e71a39d0723aad/1436518524148/Working-Paper-50-Hierarchical-+Assignments%3A-Stability-and-Fairness.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Michael Kremer, 1993. "The O-Ring Theory of Economic Development," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 551-575.
    2. Lindbeck, Assar & Snower, Dennis J, 1996. "Reorganization of Firms and Labor-Market Inequality," American Economic Review, American Economic Association, vol. 86(2), pages 315-321, May.
    3. Sattinger, Michael, 1993. "Assignment Models of the Distribution of Earnings," Journal of Economic Literature, American Economic Association, vol. 31(2), pages 831-880, June.
    4. Bloch, Francis & Ryder, Harl, 2000. "Two-Sided Search, Marriages, and Matchmakers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 93-115, February.
    5. Feldman, Allan M & Kirman, Alan, 1974. "Fairness and Envy," American Economic Review, American Economic Association, vol. 64(6), pages 995-1005, December.
    6. Tjalling C. Koopmans & Martin J. Beckmann, 1955. "Assignment Problems and the Location of Economic Activities," Cowles Foundation Discussion Papers 4, Cowles Foundation for Research in Economics, Yale University.
    7. Sattinger, Michael, 1979. "Differential Rents and the Distribution of Earnings," Oxford Economic Papers, Oxford University Press, vol. 31(1), pages 60-71, March.
    8. Ken Burdett & Melvyn G. Coles, 1997. "Marriage and Class," The Quarterly Journal of Economics, Oxford University Press, vol. 112(1), pages 141-168.
    9. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    10. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    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. Marcus Mossfeldt & Par Osterholm, 2011. "The persistent labour-market effects of the financial crisis," Applied Economics Letters, Taylor & Francis Journals, vol. 18(7), pages 637-642.
    2. Lindén, Johan, 2004. "The Labor Market in KIMOD," Working Papers 89, National Institute of Economic Research.
    3. P�r Österholm, 2014. "Survey data and short-term forecasts of Swedish GDP growth," Applied Economics Letters, Taylor & Francis Journals, vol. 21(2), pages 135-139, January.
    4. Österholm, Pär, 2013. "Forecasting Business Investment in the Short Term Using Survey Data," Working Papers 131, National Institute of Economic Research.
    5. Gren, Ing-Marie, 2003. "Monetary Green Accounting and Ecosystem Services," Working Papers 86, National Institute of Economic Research.
    6. Lindström, Tomas, 2003. "The Role of High-Tech Capital Formation for Swedish Productivity Growth," Working Papers 83, National Institute of Economic Research.
    7. Forslund, Johanna & Samakovlis, Eva & Vredin Johansson, Maria, 2006. "Matters Risk? The Allocation of Government Subsidies for Remediation of Contaminated Sites under the Local Investment Programme," Working Papers 94, National Institute of Economic Research.
    8. Jan-Erik Antipin & Farid Jimmy Boumediene & Pär Österholm, 2014. "On the Usefulness of Constant Gain Least Squares when Forecasting the Unemployment Rate," Applied Economics Quarterly (formerly: Konjunkturpolitik), Duncker & Humblot GmbH, Berlin, vol. 60(4), pages 315-336.
    9. Boman, Mattias & Huhtala, Anni & Nilsson, Charlotte & Alroth, Sofia & Bostedt, Göran & Mattssson, Leif & Gong, Peichen, 2003. "Applying the Contingent Valuation Method in Resource Accounting: A Bold Proposal," Working Papers 85, National Institute of Economic Research.
    10. Vartiainen, Juhana, 2010. "Interpreting Wage Bargaining Norms," Working Papers 116, National Institute of Economic Research.
    11. Meredith Beechey & Pär Österholm, 2014. "Central Bank Forecasts of Policy Interest Rates: An Evaluation of the First Years," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 43(1), pages 63-78, February.
    12. Östblom, Göran & Ljunggren Söderman, Maria & Sjöström, Magnus, 2010. "Analysing future solid waste generation - Soft linking a model of waste management with a CGE-model for Sweden," Working Papers 118, National Institute of Economic Research.

    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. Eriksson, Kimmo & Karlander, Johan & Oller, Lars-Erik, 2000. "Becker's assortative assignments: stability and fairness," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 109-118, March.
    2. Ramya Sundaram, 2000. "Multiple Traits in the Marriage Market: Does Diversity Sometimes Win?," Econometric Society World Congress 2000 Contributed Papers 1666, Econometric Society.
    3. Wing Suen, 2007. "The comparative statics of differential rents in two-sided matching markets," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(2), pages 149-158, August.
    4. Simeon D. Alder, 2016. "In the Wrong Hands: Complementarities, Resource Allocation, and TFP," American Economic Journal: Macroeconomics, American Economic Association, vol. 8(1), pages 199-241, January.
    5. Burgess, Simon & Lane, Julia & Stevens, David, 1997. "Jobs, Workers and Changes in Earnings Dispersion," CEPR Discussion Papers 1714, C.E.P.R. Discussion Papers.
    6. E. M. Parilina & A. Tampieri, 2013. "Marriage Formation with Assortative Meeting as a Two-Sided Optimal Stopping Problem," Working Papers wp886, Dipartimento Scienze Economiche, Universita' di Bologna.
    7. Heidrun C. Hoppe & Benny Moldovanu & Aner Sela, 2009. "The Theory of Assortative Matching Based on Costly Signals," Review of Economic Studies, Oxford University Press, vol. 76(1), pages 253-281.
    8. Linda Y. Wong, 2003. "Structural Estimation of Marriage Models," Journal of Labor Economics, University of Chicago Press, vol. 21(3), pages 699-728, July.
    9. Patrick Legros & Andrew F. Newman, 2002. "Monotone Matching in Perfect and Imperfect Worlds," Review of Economic Studies, Oxford University Press, vol. 69(4), pages 925-942.
    10. Robert M. Costrell & Glenn C. Loury, 2004. "Distribution of Ability and Earnings in a Hierarchical Job Assignment Model," Journal of Political Economy, University of Chicago Press, vol. 112(6), pages 1322-1363, December.
    11. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    12. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    13. Simon Burgess & Julia Lane & Kevin McKinney, 2009. "Matching, Reallocation and Changes in Earnings Dispersion," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(1), pages 91-110, February.
    14. Rui Baptista & Francisco Lima & Miguel Preto, 2013. "Entrepreneurial skills and workers’ wages in small firms," Small Business Economics, Springer, vol. 40(2), pages 309-323, February.
    15. Antonio Falato & Dan Li & Todd Milbourn, 2015. "Which Skills Matter in the Market for CEOs? Evidence from Pay for CEO Credentials," Management Science, INFORMS, vol. 61(12), pages 2845-2869, December.
    16. Ángel Gavilán, 2006. "Wage inequality, segregation by skill and the price of capital in an assignment model," Working Papers 0613, Banco de España;Working Papers Homepage.
    17. Luis Garicano & Thomas N. Hubbard, 2016. "The Returns to Knowledge Hierarchies," Journal of Law, Economics, and Organization, Oxford University Press, vol. 32(4), pages 653-684.
    18. Lones Smith & Axel Anderson, 2002. "Assortative Matching, Reputation, and the Beatles Break-Up," Game Theory and Information 0201002, University Library of Munich, Germany.
    19. Herrenbrueck, Lucas & Xia, Xiaoyu & Eastwick, Paul & Hui, Chin Ming, 2018. "Smart-dating in speed-dating: How a simple Search model can explain matching decisions," European Economic Review, Elsevier, vol. 106(C), pages 54-76.
    20. Ran Abramitzky & Adeline Delavande & Luis Vasconcelos, 2011. "Marrying Up: The Role of Sex Ratio in Assortative Matching," American Economic Journal: Applied Economics, American Economic Association, vol. 3(3), pages 124-157, July.

    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:hhs:nierwp:0050. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sarah Hegardt Grant). General contact details of provider: http://edirc.repec.org/data/kongvse.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.