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Piece-Rates, Principal-Agent, and Productivity Profiles: Parametric and Semi-Parametric Evidence


  • Bruce S. Shearer


This paper exploits the natural link between observed wages and productivity that is inherent in piece-rate wage data to estimate worker productivity profiles. Piece-rate wages are functions of the parameters of the compensation system and worker effort. Identifying productivity from such data requires separating out these effects. This can be accomplished by explicitly modelling the principal-agent relationship between the worker and the firm and deriving optimal decision rules for worker effort. This approach is applied to historical payroll data collected from a British Columbia copper mine. The salient aspects of the mine's production process are incorporated into the model, namely, asymmetric information, team production and heterogeneous workers. Solving the model for equilibrium worker effort implies a censored wage distribution which is estimated both parametrically and semi-parametrically. Methods to control for unobserved heterogeneity among workers are also used. Productivity profiles are then constructed from the resulting parameter estimates. Results suggest that productivity profiles were increasing concave functions of worker tenure. Cette étude utilise le lien naturel qui existe entre les salaire observés et la productivité des travailleurs lorsque les travailleurs sont payés à la pièce afin d'estimer les profils de productivité des travailleurs. Quand les travailleurs sont payés à la pièce, les salaires observés sont une fonction des paramètres du système de compensation et du niveau d'effort des travailleurs. L'identification de la productivité des travailleurs nécessite la séparation de ces deux effets dans les données. Ceci peut être accompli en modélisant la relation principal-agent qui existe entre la firme et le travailleur tout en trouvant les règles de comportement optimal de l'effort du travailleur. Cette approche est appliquée à des données de salaires historiques, colligées à partir des archives d'une mine en Colombie-Britannique. Les aspects importants de la technologie de la mine sont incorporés dans le modèle, ie. l'asymétrie d'information qui existe entre la firme et les travailleurs, la production en équipe et les travailleurs hétérogènes. Le modèle est résolu pour le niveau d'effort du travailleur en équilibre. Celui-ci implique une distribution de salaires censorés qui est estimée de façon paramétrique et semi-paramétrique tout en contrôlant pour l'hétérogénéité inobservable des travailleurs. Les profils de productivité sont construits à partir des paramètres estimés. Les résultats suggèrent que les profils de productivité étaient des fonctions croissantes et concaves de l'ancienneté du travai

Suggested Citation

  • Bruce S. Shearer, 1994. "Piece-Rates, Principal-Agent, and Productivity Profiles: Parametric and Semi-Parametric Evidence," CIRANO Working Papers 94s-16, CIRANO.
  • Handle: RePEc:cir:cirwor:94s-16

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    References listed on IDEAS

    1. Christensen, Bent Jesper & Kiefer, Nicholas M., 1991. "The Exact Likelihood Function for an Empirical Job Search Model," Econometric Theory, Cambridge University Press, vol. 7(04), pages 464-486, December.
    2. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-1460, November.
    3. Jovanovic, Boyan, 1979. "Job Matching and the Theory of Turnover," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 972-990, October.
    4. Lazear, Edward P, 1979. "Why Is There Mandatory Retirement?," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1261-1284, December.
    5. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    6. repec:cup:etheor:v:7:y:1991:i:4:p:464-86 is not listed on IDEAS
    7. Oliver Hart & Bengt Holmstrom, 1986. "The Theory of Contracts," Working papers 418, Massachusetts Institute of Technology (MIT), Department of Economics.
    8. Lazear, Edward P, 1986. "Salaries and Piece Rates," The Journal of Business, University of Chicago Press, vol. 59(3), pages 405-431, July.
    9. Joanne Salop & Steven Salop, 1976. "Self-Selection and Turnover in the Labor Market," The Quarterly Journal of Economics, Oxford University Press, vol. 90(4), pages 619-627.
    10. Gunderson, Morley, 1975. "Male-Female Wage Differentials and the Impact of Equal Pay Legislation," The Review of Economics and Statistics, MIT Press, vol. 57(4), pages 462-469, November.
    11. Flinn, C. & Heckman, J., 1982. "New methods for analyzing structural models of labor force dynamics," Journal of Econometrics, Elsevier, vol. 18(1), pages 115-168, January.
    12. Joanne Salop & Steven C. Salop, 1976. "Self-selection and turnover in the labor market," Special Studies Papers 80, Board of Governors of the Federal Reserve System (U.S.).
    13. Donald, Stephen G & Paarsch, Harry J, 1993. "Piecewise Pseudo-maximum Likelihood Estimation in Empirical Models of Auctions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 121-148, February.
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    More about this item


    ; Modèle du principal-agent ; Productivité de travail; Système de prime; Modèle de régression censorée ; Estimations semi-paramétriques;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials


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