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On the modeling of size distributions when technologies are complex

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  • Jakub Growiec

Abstract

The study considers a stochastic R&D process where the invented production technologies consist of a large number n of complementary components. The degree of complementarity is captured by the elasticity of substitution of the CES aggregator function. Drawing from the Central Limit Theorem and the Extreme Value Theory we find, under very general assumptions, that the cross-sectional distributions of technological productivity are well-approximated either by the lognormal, Weibull, or a novel “CES/Normal” distribution, depending on the underlying elasticity of substitution between technology components. We find the tail of the “CES/Normal” distribution to be fatter than the Weibull tail but thinner than the Pareto (power law) one. We numerically assess the rate of convergence of the true technological productivity distribution to the theoretical limit with n.

Suggested Citation

  • Jakub Growiec, 2015. "On the modeling of size distributions when technologies are complex," NBP Working Papers 195, Narodowy Bank Polski.
    • Handle: RePEc:nbp:nbpmis:195
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    References listed on IDEAS

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    1. Dongfeng Fu & Fabio Pammolli & S. V. Buldyrev & Massimo Riccaboni & Kaushik Matia & Kazuko Yamasaki & H. E. Stanley, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," Papers physics/0512005, arXiv.org.
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    3. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    4. Growiec, Jakub & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2008. "On the size distribution of business firms," Economics Letters, Elsevier, vol. 98(2), pages 207-212, February.
    5. Chang-Tai Hsieh & Peter J. Klenow, 2009. "Misallocation and Manufacturing TFP in China and India," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(4), pages 1403-1448.
    6. 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.
    7. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
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    9. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    10. Growiec, Jakub, 2008. "Production functions and distributions of unit factor productivities: Uncovering the link," Economics Letters, Elsevier, vol. 101(1), pages 87-90, October.
    11. 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.
    12. 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.
    13. Jakub Growiec, 2008. "A new class of production functions and an argument against purely labor‐augmenting technical change," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 483-502, December.
    14. Charles I. Jones, 2011. "Intermediate Goods and Weak Links in the Theory of Economic Development," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(2), pages 1-28, April.
    15. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2013. "The size distribution of US cities: Not Pareto, even in the tail," Economics Letters, Elsevier, vol. 120(2), pages 232-237.
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    Cited by:

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    2. Sequeira, Tiago Neves & Gil, Pedro Mazeda & Afonso, Oscar, 2018. "Endogenous growth and entropy," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 100-120.

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    More about this item

    Keywords

    technological productivity distribution; stochastic R&D; CES; Weibull distribution; lognormal distribution; limiting distribution;
    All these keywords.

    JEL classification:

    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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