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Size distribution of Portuguese firms between 2006 and 2012

Author

Listed:
  • Pascoal, Rui
  • Augusto, Mário
  • Monteiro, A.M.

Abstract

This study aims to describe the size distribution of Portuguese firms, as measured by annual sales and total assets, between 2006 and 2012, giving an economic interpretation for the evolution of the distribution along the time. Three distributions are fitted to data: the lognormal, the Pareto (and as a particular case Zipf) and the Simplified Canonical Law (SCL). We present the main arguments found in literature to justify the use of distributions and emphasize the interpretation of SCL coefficients. Methods of estimation include Maximum Likelihood, modified Ordinary Least Squares in log–log scale and Nonlinear Least Squares considering the Levenberg–Marquardt algorithm. When applying these approaches to Portuguese’s firms data, we analyze if the evolution of estimated parameters in both lognormal power and SCL is in accordance with the known existence of a recession period after 2008. This is confirmed for sales but not for assets, leading to the conclusion that the first variable is a best proxy for firm size.

Suggested Citation

  • Pascoal, Rui & Augusto, Mário & Monteiro, A.M., 2016. "Size distribution of Portuguese firms between 2006 and 2012," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 342-355.
    • Handle: RePEc:eee:phsmap:v:458:y:2016:i:c:p:342-355
    DOI: 10.1016/j.physa.2016.04.010
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    Cited by:

    1. Lina Cortés & Juan M. Lozada & Javier Perote, 2019. "Firm size and concentration inequality: A flexible extension of Gibrat’s law," Documentos de Trabajo de Valor Público 17205, Universidad EAFIT.
    2. Petra Štamfestová & Lukáš Sobíšek & Jiří Hnilica, 2023. "Firm Size Distribution in the Central European Context," Central European Business Review, Prague University of Economics and Business, vol. 2023(5), pages 151-175.
    3. Lina M Cortés & Juan M Lozada & Javier Perote, 2021. "Firm size and economic concentration: An analysis from a lognormal expansion," PLOS ONE, Public Library of Science, vol. 16(7), pages 1-21, July.
    4. Da Silva, Sergio & Matsushita, Raul & Giglio, Ricardo & Massena, Gunther, 2018. "Granularity of the top 1,000 Brazilian companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 68-73.
    5. Cortés, Lina M. & Mora-Valencia, Andrés & Perote, Javier, 2017. "Measuring firm size distribution with semi-nonparametric densities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 35-47.
    6. Montebruno, Piero & Bennett, Robert J. & van Lieshout, Carry & Smith, Harry, 2019. "A tale of two tails: Do Power Law and Lognormal models fit firm-size distributions in the mid-Victorian era?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 858-875.
    7. Jan Schulz & Daniel M. Mayerhoffer, 2021. "Equal chances, unequal outcomes? Network-based evolutionary learning and the industrial dynamics of superstar firms," Journal of Business Economics, Springer, vol. 91(9), pages 1357-1385, November.

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    More about this item

    Keywords

    Firms size; Lognormal law; Zipf’s law; Simplified canonical law; Shannon entropy;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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