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Measuring firm size distribution with semi-nonparametric densities

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  • Lina Cortés
  • Andrés Mora-Valencia
  • Javier Perote

Abstract

In this article, we propose a new methodology based on a (log) semi-nonparametric (log- SNP) distribution that nests the lognormal and enables better fits in the upper tail of the distribution through the introduction of new parameters. We test the performance of the lognormal and log-SNP distributions capturing firm size, measured through a sample of US firms in 2004-2015. Taking different levels of aggregation by type of economic activity, our study shows that the log-SNP provides a better fit of the firm size distribution. We also formally introduce the multivariate log-SNP distribution, which encompasses the multivariate lognormal, to analyze the estimation of the joint distribution of the value of the firm’s assets and sales. The results suggest that sales are a better firm size measure, as indicated by other studies in the literature.

Suggested Citation

  • Lina Cortés & Andrés Mora-Valencia & Javier Perote, 2017. "Measuring firm size distribution with semi-nonparametric densities," Documentos de Trabajo de Valor Público 15300, Universidad EAFIT.
    • Handle: RePEc:col:000122:015300
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    Cited by:

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    2. 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.
    3. Lina M. Cortés & Javier Perote & Andrés Mora-Valencia, 2017. "Implicit probability distribution for WTI options: The Black Scholes vs. the semi-nonparametric approach," Documentos de Trabajo de Valor Público 15923, Universidad EAFIT.
    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. Chamay Kruger & Willem Daniel Schutte & Tanja Verster, 2021. "Using Model Performance to Assess the Representativeness of Data for Model Development and Calibration in Financial Institutions," Risks, MDPI, vol. 9(11), pages 1-26, November.
    6. Alfredo Trespalacios & Lina M. Cortés & Javier Perote, 2021. "Modeling Electricity Price and Quantity Uncertainty: An Application for Hedging with Forward Contracts," Energies, MDPI, vol. 14(11), pages 1-26, June.
    7. Shouji Fujimoto & Takayuki Mizuno & Atushi Ishikawa, 2022. "Interpolation of non-random missing values in financial statements’ big data using CatBoost," Journal of Computational Social Science, Springer, vol. 5(2), pages 1281-1301, November.
    8. Trespalacios, Alfredo & Cortés, Lina M. & Perote, Javier, 2020. "Uncertainty in electricity markets from a semi-nonparametric approach," Energy Policy, Elsevier, vol. 137(C).
    9. Arturo Ramos & Till Massing & Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2023. "Composite distributions in the social sciences: A comparative empirical study of firms' sales distribution for France, Germany, Italy, Japan, South Korea, and Spain," Papers 2301.09438, arXiv.org.
    10. Francesca Greselin & Fabio Piacenza & Ričardas Zitikis, 2019. "Practice Oriented and Monte Carlo Based Estimation of the Value-at-Risk for Operational Risk Measurement," Risks, MDPI, vol. 7(2), pages 1-20, May.
    11. Cortés, Lina M. & Mora-Valencia, Andrés & Perote, Javier, 2020. "Retrieving the implicit risk neutral density of WTI options with a semi-nonparametric approach," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    12. Tomaschitz, Roman, 2020. "Multiply broken power-law densities as survival functions: An alternative to Pareto and lognormal fits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

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    More about this item

    Keywords

    Firms size distribution; Heavy tail distributions; Semi-nonparametric modeling; Bivariate distributions.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

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