The firm size distribution: evidence from Belgium

ABSTRACT

The firm size distribution (FSD) is one of the most well-known economic empirical regularity in market economies. Its functional form, postulated in macroeconomic models with heterogeneous firms, can be approximated by a parametric distribution. However, the parametric approximations proposed in the literature have long been contested due to the lack of unbiased databases and robust statistical methods. This paper addresses these shortcomings. First, a robust estimation method is proposed to test the fit of parametric distributions and to determine the one offering the best fit at different truncation thresholds. Then, by applying it to a comprehensive database of Belgian firms for the period 2006–2012, the results show that the lognormal distribution is a better approximation of the empirical FSD than the Pareto distribution. These results hold true at the aggregate, sectoral and regional levels establishing that the shape of the aggregate distribution is not an aggregation artefact arising from the potential distributional heterogeneity of sectoral or regional subsets. This empirical evidence is essential information for tracing the root causes of a plausible underlying stochastic model explaining firm dynamics.

KEYWORDS:

• Firm size distribution
• Gibrat’s law
• lognormal
• Pareto
• power law
• Zipf

JEL CLASSIFICATION:

• C13
• L11
• L25

Acknowledgement

The authors acknowledge the financial support of BELSPO.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ See, for instance: Antras and Helpman (2004), Helpman, Melitz, and Yeaple (2004), Luttmer (2007), Rossi-Hansberg and Wright (2007), Chaney (2008); Gabaix and Landier (2008), Eaton, Kortum, and Kramarz (2011). In the trade literature, see among others: Arkolakis et al. (2008), Helpman, Melitz, and Rubinstein (2008), Melitz and Ottaviano (2008) and Melitz and Redding (2015).

² A lognormal distribution with a high enough value of its variance relative to its mean can look like a straight line in a log-log plot. For an example involving lognormal, Pareto, and exponential distributions, see Figure 5a in Clauset, Shalizi, and Newman (2009).

³ For the list and description of the 2008 NACE sectors in the European Union, see Appendix A.

⁴ Gibrat’s model is a Markov chain and Champernowne’s model is a Markov chain with a reflecting barrier.

⁵ Champernowne (1953) proposed such a model to account for the distribution of incomes and, therefore, assumed a minimum income. However, his model can also be applied to other asymmetric empirical distributions such as the firm size distribution to fit their upper tail.

⁶ The estimation results are available on request.

⁷ The results are available on request.

⁸ Results not presented in this paper are available upon request.

⁹ We repeated the exercise for all the years available in the database and found similar results which are available on request.

Additional information

Funding

The work was supported by the Belspo [BR/132/A4/BEL-Ageing].