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Box-Cox quantile regression and the distribution of firm sizes


  • Jose A. F. Machado

    (Faculdade de Economia, Universidade Nova de Lisboa, Travessa Estevão Pinto, 1099-032 Lisboa, Portugal)

  • Jose Mata

    (Instituto Superior Tecnico and CEPR, Portugal)


Using the Box-Cox quantile regression model, we analyse the size distribution of firms in Portuguese manufacturing during the 1980s. Specifically, we estimate the effect of selected industry attributes on the location, scale, skewness and kurtosis of the conditional size distributions of firms. We find that industry attributes affect the size of firms in the same direction across the distribution, but the effects of these variables are typically much greater at the largest quantiles. Over time the distribution shifted towards smaller firms, due mainly to the way the economy responds to industry characteristics rather than to changes of the level of these characteristics. The prediction of lognormality, implied by Gibrat's Law, is soundly rejected by the observed distribution of firm sizes. However, we found that, at least in 1983, lognormality is a reasonable description of the conditional size distribution. Copyright © 2000 John Wiley & Sons, Ltd.

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  • Jose A. F. Machado & Jose Mata, 2000. "Box-Cox quantile regression and the distribution of firm sizes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(3), pages 253-274.
  • Handle: RePEc:jae:japmet:v:15:y:2000:i:3:p:253-274

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    References listed on IDEAS

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    Cited by:

    1. Bartelsman, Eric & Dobbelaere, Sabien & Peters, Bettina, 2013. "Allocation of Human Capital and Innovation at the Frontier: Firm-Level Evidence on Germany and the Netherlands," IZA Discussion Papers 7540, Institute for the Study of Labor (IZA).
    2. Elke Lüdemann & Ralf Wilke & Xuan Zhang, 2006. "Censored quantile regressions and the length of unemployment periods in West Germany," Empirical Economics, Springer, vol. 31(4), pages 1003-1024, November.
    3. D.B. Audretsch & L. Klomp & E. Santarelli & A.R. Thurik, 2004. "Gibrat's Law: Are the Services Different?," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 24(3), pages 301-324, May.
    4. Cosimo Abbate & Alessandro Sapio, 2016. "Gazelles and muppets in the City: Stock market listing, risk sharing, and firm growth quantiles," LEM Papers Series 2016/33, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    5. Francesca Lotti & Enrico Santarelli, 2004. "Industry Dynamics and the Distribution of Firm Sizes: A Nonparametric Approach," Southern Economic Journal, Southern Economic Association, vol. 70(3), pages 443-466, January.
    6. Marco Capasso & Elena Cefis & Alessandro Sapio, 2013. "Reconciling quantile autoregressions of firm size and variance–size scaling," Small Business Economics, Springer, vol. 41(3), pages 609-632, October.
    7. Fitzenberger, Bernd & Wilke, Ralf A., 2007. "New insights on unemployment duration and post unemployment earnings in Germany: censored Box-Cox quantile regression at work," ZEW Discussion Papers 07-007, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    8. Halkos, George & Polemis, Michael, 2018. "Does market structure trigger efficiency? Evidence for the USA before and after the financial crisis," MPRA Paper 84511, University Library of Munich, Germany.
    9. Wilke, Ralf A. & Fitzenberger, Bernd & Zhang, Xuan, 2004. "A Note on Implementing Box-Cox Quantile Regression," ZEW Discussion Papers 04-61, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    10. Josep-Maria Arauzo-Carod & Agustí Segarra-Blasco, 2005. "The Determinants of Entry are not Independent of Start-up Size: Some Evidence from Spanish Manufacturing," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 27(2), pages 147-165, September.
    11. Christopher A Laincz & Ana Sofia Domingues Rodrigues, "undated". "A Theoretical Foundation for Understanding Firm Size Distributions and Gibrat's Law," Discussion Papers 05/34, Department of Economics, University of York.
    12. Cheung, Cherry & Coucke, Kristien & Neicu, Daniel, 2011. "A Decision Tree as a Quick Scan for Effective Market Functioning," Working Papers 2011/06, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    13. Y. K. Tse & Z. L. Yang, 2006. "Modelling firm-size distribution using Box-Cox heteroscedastic regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 641-653.
    14. Muriel Meunier, 2006. "Fonctions de production éducationnelle: le cas de la Suisse," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 142(IV), pages 579-615, December.
    15. Ana Sofia Domingues Rodrigues & Christopher A. Laincz, 2004. "Understanding the Variations in Gibrat's Law with a Markov-Perfect Dynamic Industry Model," Computing in Economics and Finance 2004 173, Society for Computational Economics.
    16. Grace Hong, Hyokyoung, 2013. "A quantile approach to the power transformed location–scale model," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 50-62.
    17. Insik Min & Inchul Kim, 2004. "A Monte Carlo comparison of parametric and nonparametric quantile regressions," Applied Economics Letters, Taylor & Francis Journals, vol. 11(2), pages 71-74.
    18. Bernd Fitzenberger & Ralf A. Wilke, 2010. "New Insights into Unemployment Duration and Post Unemployment Earnings in Germany," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(6), pages 794-826, December.
    19. Hadi Esfahani & Seyed Karimi, 2014. "The Distributional Consequences of Economic Growth and Public Spending Programs in Iran," Working Papers 891, Economic Research Forum, revised Dec 2014.
    20. Bernd Fitzenberger & Ralf A. Wilke & Xuan Zhang, 2010. "Implementing Box-Cox Quantile Regression," Econometric Reviews, Taylor & Francis Journals, vol. 29(2), pages 158-181, April.
    21. Distante, Roberta & Petrella, Ivan & Santoro, Emiliano, 2017. "Gibrat's Law and Quantile Regressions: an Application to Firm Growth," EMF Research Papers 16, Economic Modelling and Forecasting Group.
    22. Roberta Distante & Ivan Petrella & Emiliano Santoro, 2014. "Size, Age and the Growth of Firms: New Evidence from Quantile Regressions," Working Papers 2014.69, Fondazione Eni Enrico Mattei.
    23. Carlos Lamarche & Alberto Porto & Walter Sosa Escudero, 1998. "Aspectos Regionales del Desempleo en la Argentina," Department of Economics, Working Papers 008, Departamento de Economía, Facultad de Ciencias Económicas, Universidad Nacional de La Plata.
    24. Mercedes Teruel & Agustí Segarra, 2011. "Productivity and R&D sources in manufacturing and service firms in Catalonia: a regional approach," ERSA conference papers ersa11p1860, European Regional Science Association.
    25. repec:sbe:breart:v:27:y:2007:i:2:a:1525 is not listed on IDEAS

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