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Box-Cox quantile regression and the distribution of firm sizes

Author

Listed:
  • 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)

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.

Suggested Citation

  • 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

    as
    1. Mills, David E & Schumann, Laurence, 1985. "Industry Structure with Fluctuating Demand," American Economic Review, American Economic Association, vol. 75(4), pages 758-767, September.
    2. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
    3. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    4. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, January.
    5. 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.
    6. 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, December.
    7. Evans, David S, 1987. "Tests of Alternative Theories of Firm Growth," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 657-674, August.
    8. Wooldridge, Jeffrey M, 1992. "Some Alternatives to the Box-Cox Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(4), pages 935-955, November.
    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.
    10. 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.
    11. Brown, Charles & Medoff, James, 1989. "The Employer Size-Wage Effect," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1027-1059, October.
    12. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, January.
    13. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905, January.
    14. 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.
    15. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    16. 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.
    17. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    18. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318, January.
    19. repec:bla:econom:v:47:y:1980:i:185:p:19-34 is not listed on IDEAS
    20. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(1), pages 105-121, February.
    21. R. Schmalensee & R. Willig (ed.), 1989. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 2, number 2, May.
    22. Gort, Michael & Klepper, Steven, 1982. "Time Paths in the Diffusion of Product Innovations," Economic Journal, Royal Economic Society, vol. 92(367), pages 630-653, September.
    23. R. Schmalensee & R. Willig (ed.), 1989. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 1, number 1, May.
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