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Size Distribution of Portuguese Firms between 2006 and 2012

Author

Listed:
  • Mário Augusto

    (Faculty of Economics, University of Coimbra, Portugal)

  • Rui Pascoal

    (Faculty of Economics, University of Coimbra, Portugal)

  • Ana Margarida Monteiro

    (Faculty of Economics, University of Coimbra and GEMF, Portugal)

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, emphasizing the interpretation of SCL coefficients and its analogy with thermodynamics. Methods of estimation include Maximum Likelihood, modified Ordinary Least Squares in log-log scale and Nonlinear Least Squares considering the Levenberg-Marquardt algorithm. We apply these approaches to Portuguese firm data. In the sales case, the evolution of estimated parameters in both lognormal and SCL reflects the existence of a recession period more pronounced after 2008.

Suggested Citation

  • Mário Augusto & Rui Pascoal & Ana Margarida Monteiro, 2015. "Size Distribution of Portuguese Firms between 2006 and 2012," GEMF Working Papers 2015-04, GEMF, Faculty of Economics, University of Coimbra.
    • Handle: RePEc:gmf:wpaper:2015-04
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    References listed on IDEAS

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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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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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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