Abstract
In this work we explain the size distribution of business firms using a stochastic growth process that reproduces the main stylized facts documented in empirical studies. The steady state solution of this process is a three-parameter Dagum distribution, which possibly combines strong unimodality with a Paretian upper tail. Thanks to its flexibility, the proposed distribution is able to fit the whole range of firm size data, in contrast with traditional models that typically focus on large businesses only. An empirical application to Italian firms illustrates the practical merits of the Dagum distribution. Our findings go beyond goodness-of-fit per se, and shed light on possible connections between stochastic elements that influence firm growth and the meaning of parameters that appear in the steady state distribution of firm size. These results are ultimately relevant for studies into industrial organization and for policy interventions aimed at promoting sustainable growth and monitoring industrial concentration phenomena.
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Notes
This mechanism has a simple economic interpretation: if firms in a given industry decline below the minimum size, they exit and are replaced by new firms with starting size \(x_0\), so the overall number of operating entities remains constant (De Wit 2005).
This result holds true essentially under the regularity conditions necessary to establish the asymptotic normality of maximum likelihood estimators (Stuart et al. 1999). The conditions are satisfied as long as the SLI parameters do not tend to their boundary values (Kleiber 2008) and our ML estimation results are compatible with this requirement.
The plots observed for all years were very similar.
Goodness-of-fit tests were replicated at each step of the sensitivity analysis, and the SLI distribution was never rejected by either the KS or the AD test statistic (additional details are available upon request).
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Acknowledgements
A number of people have greatly helped me with this research. I would like to thank, in particular, Angiola Pollastri, Simone Alfarano, Anna Motta and Lisa Crosato for sharing their experience with me and for providing highly valuable comments and suggestions. I also thank the Editors and two anonymous Reviewers for careful reading and constructive remarks, which have contributed to improve the manuscript considerably.
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Fiori, A.M. On firm size distribution: statistical models, mechanisms, and empirical evidence. Stat Methods Appl 29, 447–482 (2020). https://doi.org/10.1007/s10260-019-00485-7
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DOI: https://doi.org/10.1007/s10260-019-00485-7