A tale of two tails: Do Power Law and Lognormal models fit firm-size distributions in the mid-Victorian era?
Physica A: Statistical Mechanics and its Applications
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Montebruno, P., Bennett, R., Van Lieshout, C., & Smith, H. (2019). A tale of two tails: Do Power Law and Lognormal models fit firm-size distributions in the mid-Victorian era?. Physica A: Statistical Mechanics and its Applications, 523 858-875. https://doi.org/10.1016/j.physa.2019.02.054
The paper explores the frequency and size distributions of firm-size in a novel dataset for the mid-Victorian era from a recent extraction of the England and Wales population censuses of 1851, 1861, 1871, and 1881. The paper contrasts the hypothesis of the Power Laws against the Lognormal model for the tails of the distributions using maximum likelihood estimation, log likelihood ratio, clipped sample coefficient of variation UMPU-Wilks test, Kolmogorov-Smirnov statistic, among other state-of-the-art statistical methods. Our results show that the Power Law hypothesis is accepted for the size distribution for the years 1851 and 1861, while 1871 is marginally non-significant, but for 1881 the test is inconclusive. The paper discusses the process that generates these distributions citing recent literature that shows how after adding an i.i.d. noise to the Gibrat's multiplicative model one can recreate a Power Law behaviour. Overall, the paper provides, describes and statistically tests for the very first time a unique historical dataset confirming that the tails of the distributions at least for 1851 and 1861 follow a Pareto model and that the Lognormal model is firmly rejected.
This research has been supported by the ESRC under project grant ES/M010953: `Drivers of Entrepreneurship and Small Businesses'. Piloting of the research for 1881 draws from Leverhulme Trust grant RG66385: `The long-term evolution of Small and Medium-Sized Enterprises (SMEs)' . Additional support for the coding the 1871 census data was supported by the Isaac Newton Trust research grant 17.07(d):`Business Employers in 1871'.
Isaac Newton Trust (17.07(d))
External DOI: https://doi.org/10.1016/j.physa.2019.02.054
This record's URL: https://www.repository.cam.ac.uk/handle/1810/290062