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Modeling Firm-Size Distribution Using Box-Cox Heteroscedastic Regression


  • Zhenlin Yang

    () (School of Economics and Social Sciences, Singapore Management University)

  • Yiu Kuen Tse

    () (School of Economics and Social Sciences, Singapore Management University)


Using the Box-Cox regression model with heteroscedasticity, we examine the size distribution of firms. Analyzing the data set of Portuguese manufacturing firms as in Machado and Mata (2000), we show that our approach compares favorably against the Box-Cox quantile regression method. In particular, we are able to answer the key questions addressed by Machado and Mata, with the additional advantage that our empirical quantile functions are monotonic. Furthermore, confidence intervals of the regression quantiles are easy to compute, and the estimation of the Box-Cox heteroscedastic regression model is straightforward.

Suggested Citation

  • Zhenlin Yang & Yiu Kuen Tse, 2004. "Modeling Firm-Size Distribution Using Box-Cox Heteroscedastic Regression," Working Papers 10-2004, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:10-2004

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    References listed on IDEAS

    1. Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
    2. Buchinsky, Moshe, 1995. "Quantile regression, Box-Cox transformation model, and the U.S. wage structure, 1963-1987," Journal of Econometrics, Elsevier, vol. 65(1), pages 109-154, January.
    3. 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.
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    More about this item


    Box-Cox transformation; Firm-size distribution; Quantile regression.;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms


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