On firm size distribution: statistical models, mechanisms, and empirical evidence
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On firm size distribution: statistical models, mechanisms, and empirical evidence Anna Maria Fiori1 Accepted: 14 July 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
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. Keywords Stochastic differential equation · Gibrat’s Law · Generalized beta distribution of the second kind · Dagum distribution · Firm growth
1 Introduction Understanding the statistical distribution of firm size and the mechanisms through which it is determined is crucial to studies into industrial organization, business structure and policy regulation. Research promoted by the European Commission has recently recognized that small and medium-sized enterprises (SMEs) are ‘the backbone of the European economy’ (Eurostat 2009). Public policies have been designed to encourage the growth of these firms, which is thought to have a beneficial effect in generating new employment and stimulating entrepreneurial talent. In contrast, the
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Anna Maria Fiori [email protected] Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milan, Italy
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growth of large businesses has been put in a bad light as it raises questions of unfair competition and market power (Coad 2009). Nevertheless, larger firms are frequently in a better position to take full advantage of innovative technologies, fostering productivity and creating relatively stable job positions (Pagano and Schivardi 2003). The question of how firm size affects growth has a long history in statistical, econometric and economic literature. The pioneering work of Gibrat (1931) opened the debate about the determinants of growth and their relationship to shapes of the Firm Size Distribution (FSD) observed in real world circumstances. After nearly one century and an impressive body of theoretical and empirical work, the debate is still going on. A frequent message that has emerged from these studies is that the empirical FSD is far from being the ‘optimal firm size’ theorized
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