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On the modeling of size distributions when technologies are complex

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  • Growiec, Jakub

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 qualitatively thinner than the Pareto (power law) one. We also numerically assess the rate of convergence of the true technological productivity distribution to the theoretical limit with n as fast in the body but slow in the tail.

Suggested Citation

  • Growiec, Jakub, 2015. "On the modeling of size distributions when technologies are complex," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 1-8.
  • Handle: RePEc:eee:mateco:v:60:y:2015:i:c:p:1-8
    DOI: 10.1016/j.jmateco.2015.06.004
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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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    More about this item

    Keywords

    Technological productivity distribution; Stochastic R&D; CES; Weibull distribution; Lognormal distribution; Power law;

    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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