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Production functions and distributions of unit factor productivities: Uncovering the link

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  • Growiec, Jakub

Abstract

We derive a reversible "endogenous technology choice transform," according to which firm-level production functions and distributions of unit factor productivities are two sides of the same coin. The Cobb-Douglas function relates to Pareto distributions, and the CES to Weibull distributions.

Suggested Citation

  • Growiec, Jakub, 2008. "Production functions and distributions of unit factor productivities: Uncovering the link," Economics Letters, Elsevier, vol. 101(1), pages 87-90, October.
    • Handle: RePEc:eee:ecolet:v:101:y:2008:i:1:p:87-90
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    References listed on IDEAS

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    1. Samuel S. Kortum, 1997. "Research, Patenting, and Technological Change," Econometrica, Econometric Society, vol. 65(6), pages 1389-1420, November.
    2. Charles I. Jones, 2005. "The Shape of Production Functions and the Direction of Technical Change," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(2), pages 517-549.
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    Cited by:

    1. Paul, Saumik, 2019. "Labor Income Share Dynamics with Variable Elasticity of Substitution," IZA Discussion Papers 12418, Institute of Labor Economics (IZA).
    2. McAdam, Peter & Willman, Alpo, 2008. "Medium run redux: technical change, factor shares and frictions in the euro area," Working Paper Series 915, European Central Bank.
    3. Robert S. Chirinko & Debdulal Mallick, 2014. "The Substitution Elasticity, Factor Shares, Long-Run Growth, and the Low-Frequency Panel Model," CESifo Working Paper Series 4895, CESifo.
    4. Growiec, Jakub, 2018. "Factor-specific technology choice," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 1-14.
    5. Growiec, Jakub, 2013. "Factor-augmenting technology choice and monopolistic competition," Journal of Macroeconomics, Elsevier, vol. 38(PA), pages 86-94.
    6. Miguel A León-Ledesma & Peter McAdam & Alpo Willman, 2012. "Non-Balanced Growth and Production Technology Estimation," Studies in Economics 1204, School of Economics, University of Kent.
    7. Michael Knoblach & Fabian Stöckl, 2020. "What Determines The Elasticity Of Substitution Between Capital And Labor? A Literature Review," Journal of Economic Surveys, Wiley Blackwell, vol. 34(4), pages 847-875, September.
    8. Growiec, Jakub & McAdam, Peter & Mućk, Jakub, 2018. "Endogenous labor share cycles: Theory and evidence," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 74-93.
    9. Growiec, Jakub & Mućk, Jakub, 2020. "Isoelastic Elasticity Of Substitution Production Functions," Macroeconomic Dynamics, Cambridge University Press, vol. 24(7), pages 1597-1634, October.
    10. Dariusz Kotlewski, 2022. "Przesłanki za wykorzystaniem rachunkowości wzrostu gospodarczego w badaniu specjalizacji regionalnych," Ekonomista, Polskie Towarzystwo Ekonomiczne, issue 2, pages 235-258.
    11. Mangin, Sephorah, 2017. "A theory of production, matching, and distribution," Journal of Economic Theory, Elsevier, vol. 172(C), pages 376-409.
    12. Growiec, Jakub, 2013. "A microfoundation for normalized CES production functions with factor-augmenting technical change," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2336-2350.
    13. Mariusz & Mirosław Błażej, 2020. "A control function approach to measuring the total factor productivity of enterprises in Poland," Bank i Kredyt, Narodowy Bank Polski, vol. 51(3), pages 293-316.
    14. Growiec, Jakub, 2015. "On the modeling of size distributions when technologies are complex," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 1-8.
    15. Miguel A. León-Ledesma & Peter McAdam & Alpo Willman, 2015. "Production Technology Estimates and Balanced Growth," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 40-65, February.
    16. Rainer Klump & Peter McAdam & Alpo Willman, 2012. "The Normalized Ces Production Function: Theory And Empirics," Journal of Economic Surveys, Wiley Blackwell, vol. 26(5), pages 769-799, December.
    17. Матвеенко В.Д. & Бронштейн Е.М., 2016. "О Свойствах Производственных Ces-Функций В Модели Производства С Промежуточными Товарами," Журнал Экономика и математические методы (ЭММ), Центральный Экономико-Математический Институт (ЦЭМИ), vol. 52(2), pages 91-102, апрель.
    18. Kemnitz, Alexander & Knoblach, Michael, 2020. "Endogenous sigma-augmenting technological change: An R&D-based approach," CEPIE Working Papers 02/20, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    19. Armando Sánchez-Vargas & José Manuel Márquez-Estrada & Eric Hernández-Ramírez, 2023. "Uncovering the Link Between the Theoretical and Probabilistic Models of the Global Production Function: A Copula Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(2), pages 289-315, June.
    20. Temple, Jonathan, 2012. "The calibration of CES production functions," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 294-303.
    21. Alina Szewc-Rogalska & Tomasz Jakiel, 2021. "Zmiany strukturalne a wydajność pracy w krajach Europy Środkowej," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 3, pages 63-96.
    22. McAdam, Peter & Willman, Alpo, 2013. "Medium Run Redux," Macroeconomic Dynamics, Cambridge University Press, vol. 17(4), pages 695-727, June.

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