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Box-Cox quantile regression and the distribution of firm sizes

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Author Info
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)

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Abstract

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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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 15 (2000)
Issue (Month): 3 ()
Pages: 253-274
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Handle: RePEc:jae:japmet:v:15:y:2000:i:3:p:253-274

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  1. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
  2. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January. [Downloadable!] (restricted)
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  4. Luís M B Cabral & José Mata, 2003. "On the Evolution of the Firm Size Distribution: Facts and Theory," American Economic Review, American Economic Association, vol. 93(4), pages 1075-1090, September. [Downloadable!]
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  5. Mata, Jose & Machado, Jose A. F., 1996. "Firm start-up size: A conditional quantile approach," European Economic Review, Elsevier, vol. 40(6), pages 1305-1323, June. [Downloadable!] (restricted)
  6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
  7. Wooldridge, J.M., 1989. "Some Aleternative To The Box-Cox Regression Model," Working papers 534, Massachusetts Institute of Technology (MIT), Department of Economics.
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  8. Gort, Michael & Klepper, Steven, 1982. "Time Paths in the Diffusion of Product Innovations," Economic Journal, Royal Economic Society, vol. 92(367), pages 630-53, September. [Downloadable!] (restricted)
  9. White, Lawrence J, 1982. "The Determinants of the Relative Importance of Small Business," The Review of Economics and Statistics, MIT Press, vol. 64(1), pages 42-49, February. [Downloadable!] (restricted)
  10. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March. [Downloadable!] (restricted)
  11. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(01), pages 105-121, February. [Downloadable!]
  12. Schmalensee, Richard, 1989. "Inter-industry studies of structure and performance," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 2, chapter 16, pages 951-1009 Elsevier. [Downloadable!] (restricted)
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  13. Fitzenberger, Bernd, 1998. "The moving blocks bootstrap and robust inference for linear least squares and quantile regressions," Journal of Econometrics, Elsevier, vol. 82(2), pages 235-287, February. [Downloadable!] (restricted)
  14. Steven J. Davis & John C. Haltiwanger & Scott Schuh, 1998. "Job Creation and Destruction," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262540932.
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  1. Bernd Fitzenberger & Ralf A. Wilke, 2007. "New Insights on Unemployment Duration and Post Unemployment Earnings in Germany: Censored Box-Cox Quantile Regression at Work," IZA Discussion Papers 2609, Institute for the Study of Labor (IZA). [Downloadable!]
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  2. Insik Min & Inchul Kim, 2004. "A Monte Carlo comparison of parametric and nonparametric quantile regressions," Applied Economics Letters, Taylor and Francis Journals, vol. 11(2), pages 71-74, February. [Downloadable!] (restricted)
  3. 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. [Downloadable!]
    Other versions:
  4. 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. [Downloadable!]
  5. Francesca Lotti & Enrico Santarelli, 2001. "Industry Dynamics and the Distribution of Firm Sizes: A Non-Parametric Approach," LEM Papers Series 2001/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy. [Downloadable!]
    Other versions:
  6. 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. [Downloadable!] (restricted)
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  7. Christopher A Laincz & Ana Sofia Domingues Rodrigues, . "A Theoretical Foundation for Understanding Firm Size Distributions and Gibrat's Law," Discussion Papers 05/34, Department of Economics, University of York. [Downloadable!]
  8. 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. [Downloadable!]
  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. [Downloadable!]
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  10. Roy Thurik & Enrico Santarelli & David Audretsch & Luuk Klomp, 2002. "Gibrat's Law: Are the Services Different?," Scales Research Reports H200201, EIM Business and Policy Research. [Downloadable!]
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  11. Orietta Marsili, 2006. "Stability and Turbulence in the Size Distribution of Firms: Evidence from Dutch Manufacturing," International Review of Applied Economics, Taylor and Francis Journals, vol. 20(2), pages 255-272, April. [Downloadable!] (restricted)
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