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Unobservable Persistent Productivity and Long Term Contracts


  • Hugo Hopenhayn


  • Arantxa Jarque

    (Universidad Carlos III de Madrid)


We study the problem of a firm that faces asymmetric information about the persistent productivity of its potential workers. In our framework, a worker's productivity is either assigned by nature at birth, or determined by an unobservable initial action of the worker that has persistent effects over time. We provide a characterization of the optimal dynamic compensation scheme that attracts only high productivity workers: consumption -- regardless of time period -- is ranked according to likelihood ratios of output histories, and the inverse of the marginal utility of consumption satisfies the martingale property derived in Rogerson (1985). However, in the case of i.i.d. output and square root utility we show that, contrary to the features of the optimal contract for a repeated moral hazard problem, the level and the variance of consumption are negatively correlated, due to the influence of early luck into future compensation. Moreover, in this example long-term inequality is lower under persistent private information. (Copyright: Elsevier)

Suggested Citation

  • Hugo Hopenhayn & Arantxa Jarque, 2010. "Unobservable Persistent Productivity and Long Term Contracts," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(2), pages 333-349, April.
  • Handle: RePEc:red:issued:07-192
    DOI: 10.1016/

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    References listed on IDEAS

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    Cited by:

    1. Jacek Rothert, 2015. "Monitoring, moral hazard, and turnover," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 355-374, February.
    2. Roman Inderst & Marcus Opp & Florian Hoffmann, 2016. "Deferred compensation and risk-taking incentives," 2016 Meeting Papers 674, Society for Economic Dynamics.
    3. Jin, Yu, 2012. "Essays on financial institutions and instability," ISU General Staff Papers 201201010800003361, Iowa State University, Department of Economics.
    4. Moritz Kuhn & Sebastian Koehne, 2013. "Optimal capital taxation for time-nonseparable preferences," 2013 Meeting Papers 322, Society for Economic Dynamics.

    More about this item


    Mechanism design; Moral hazard; Persistence;

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design


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