Small Business Economics

, Volume 41, Issue 3, pp 609–632 | Cite as

Reconciling quantile autoregressions of firm size and variance–size scaling

  • Marco Capasso
  • Elena CefisEmail author
  • Alessandro Sapio


The aim of this paper is to understand what economic mechanisms may cause the Law of Proportionate Effect to break down for fast-growing and shrinking firms. Recent evidence has highlighted that the first-order coefficients of quantile auto-regression of firm size decline across quantiles. Our theoretical results show that negative variance–size scaling is sufficient to yield a decline in quantile auto-regression coefficients if firm log-size is Laplace-distributed, conditional on size one period ahead. However, it is sufficient only for declining auto-regression coefficients for fast-growing firms under Asymmetric Laplace conditional log-size if skewness is decreasing with size. In other words, if the growth of large firms is less dispersed and more left-skewed, size is a disadvantage for the growth of fast-growers, but not necessarily an advantage for fast-decliners. Thus, size-related determinants of negative growth skewness, such as diseconomies of growth, market power, and managerial attention issues, impact on how the LPE is violated. Using data on Dutch manufacturing companies from the Business Register of Enterprises observed between 1994 and 2004, our empirical estimates of quantile regression models confirm the evidence of declining quantile regression coefficients for small–medium firms (20–199 employees) mainly in the right-most quantiles, and for the same subsample, we find that growth rates variance and skewness are decreasing with size. The theoretical propositions of the paper are thus corroborated.


Firm growth Law of Proportionate Effect Quantile regression Variance–size scaling Skewness 

JEL Classifications

L11 L25 L26 L60 



The authors would like to thank Koen Frenken, Michael Fritsch (the Associate Editor), Federico Tamagni, two anonymous referees, and the participants at 7th European Meeting on Applied Evolutionary Economics (EMAEE), Pisa, 2011, for helpful comments and suggestions. The empirical analysis in this research has been carried out at the Centre for Research of Economic Microdata at Statistics Netherlands (CBS). The views expressed in this paper are those of the authors and do not necessarily reflect the policies of Statistics Netherlands. The authors thank the on-site and the remote-access staff of CBS for their collaboration. This work was supported by Utrecht University [High Potential Grant (HIPO) to E. Cefis and K. Frenken]; and the University of Bergamo (Grant ex. 60 %, no. 60CEFI10, Department of Economics, to E. Cefis).


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Copyright information

© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  • Marco Capasso
    • 1
    • 2
  • Elena Cefis
    • 3
    • 4
    Email author
  • Alessandro Sapio
    • 5
    • 6
  1. 1.School of Business and EconomicsMaastricht UniversityMaastrichtThe Netherlands
  2. 2.UNU-MERITMaastrichtThe Netherlands
  3. 3.Economics DepartmentUniversity of BergamoBergamoItaly
  4. 4.Urban and Regional Research Centre Utrecht (URU)Utrecht UniversityThe Netherlands
  5. 5.Department of Economic StudiesUniversity of Napoli ParthenopeNaplesItaly
  6. 6.LEM, Sant’Anna School of Advanced StudiesPisaItaly

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