Corporate growth and industrial dynamics: evidence from French manufacturing

Abstract

This work explores basic properties of the size and growth rates distributions of firms at the aggregate and disaggregate levels. Using an extensive dataset on French manufacturing firms, we investigate which properties of firm size distributions and growth dynamics characterize the aggregate dynamics and are, at the same time, robust under disaggregation. Our analysis is based on nonlinear robust regression methods which have never been applied before to this kind of data. The growth rates distributions we observe are well described by a Subbotin distribution with a shape parameter significantly lower than 1, suggesting a noticeable departure from the Laplace behaviour reported in previous works on Italian and the US data. At the same time, the variance of growth rates depends negatively on size and the relationship does not seem to be linear, with larger firms possibly displaying lower variability in their growth dynamics. At the disaggregate level, we observe significant heterogeneity in the firm size distributions across sectors, while the shape of the sectoral growth rates density displays a surprising degree of homogeneity.

Acknowledgements

We thank Giovanni Dosi and two anonymous referees for helpful comments. This work would not have been possible without data provided by INSEE. Precious help from Daniele Bastide at SESSI is gratefully acknowledged. Some of the research that has led to this work has been undertaken as part of the activities of the DIME Network of Excellence, sponsored by the European Union. The usual caveat applies.

Notes

¹ When the normality assumption seems untenable more flexible probability distributions can be adopted to account for heavy tails. The Subbotin is one of these probability models. An attractive feature of using such flexible distribution is that it offers the possibility of checking the assumption of normality through formal test on a single parameter. Details on the statistical properties of the Subbotin distributions are in Section ‘Growth process’.

² The EAE databank has been made available to Nadia Jacoby and Alex Coad under the mandatory condition of censorship of any individual information.

³ The French classification of industrial activities (Nomenclature des Activités Française, NAF) matches with the standard European one (Nomenclature General des Activités Économiques dans les Communautés Européennes, NACE) and with the International Standard Industrial Classification (ISIC).

⁴ 22 319, 22 231, 22 305, 22 085, 21 966, 22 053, and 21 855 firms, respectively

⁵ Results of these analysis are available from authors upon request.

⁶ These estimates are built following Silverman (1986).

⁷ Throughout this article the kernel function will always be the Gaussian density. The use of different kernels, such as the Epanechnikov or the Triangular, does not change our results noticeably. Where not specified otherwise, the bandwidth h has been chosen according to Silverman (1986, Section 3.4).

⁸ In estimating Equation 5 we checked for possible autocorrelation in the error term u(t), but we did not find any. Had it been present, such autocorrelation would have given us unreliable results.

⁹ Usual caveats should apply in interpreting statistical significance when the sample size has the dimension of the database we use.

¹⁰ For a more detailed analysis of growth rates autocorrelation, see Coad (2007b).

¹¹ We do not find any firms from sector 37 ‘Recycling’ that meet the balanced panel construction requirements.

¹² The result has been proved for a small family of kernels of which the Gaussian kernel is a member. See Silverman (1981).

¹³ Indeed our dataset excludes firms with less than 20 employees.