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On firm size distribution: statistical models, mechanisms, and empirical evidence. (English) Zbl 1458.62284

Summary: 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.

MSC:

62P20 Applications of statistics to economics
62E15 Exact distribution theory in statistics
60E05 Probability distributions: general theory
60G12 General second-order stochastic processes

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[1] Alfarano, S.; Milaković, M.; Irle, A.; Kauschke, J., A statistical equilibrium model of competitive firms, J Econ Dyn Control, 36, 1, 136-149 (2012) · Zbl 1241.91070
[2] Axtell, RL, Zipf distribution of us firm sizes, Science, 293, 5536, 1818-1820 (2001)
[3] Bee, M.; Riccaboni, M.; Schiavo, S., Where Gibrat meets Zipf: Scale and scope of French firms, Physica A: Stat Mech Appl, 481, 265-275 (2017)
[4] Borgan Ø, Liestøl K (1990) A note on confidence intervals and bands for the survival function based on transformations. Scand J Statist pp 35-41
[5] Cabral, L.; Mata, J., On the evolution of the firm size distribution: Facts and theory, Am Econ Rev, 93, 4, 1075-1090 (2003)
[6] Champernowne, D., The theory of income distribution, Econometrica, 5, 4, 379-381 (1937)
[7] Champernowne, DG, The graduation of income distributions, Econometrica, 20, 4, 591-615 (1952) · Zbl 0048.12802
[8] Cirillo, P., An analysis of the size distribution of Italian firms by age, Physica A: Stat Mech Appl, 389, 3, 459-466 (2010)
[9] Cirillo, P.; Hüsler, J., On the upper tail of Italian firms’ size distribution, Physica A: Stat Mech Appl, 388, 8, 1546-1554 (2009)
[10] Coad A (2009) The growth of firms: A survey of theories and empirical evidence. Edward Elgar Publishing
[11] Crosato, L.; Ganugi, P., Statistical regularity of firm size distribution: the Pareto IV and truncated Yule for Italian SCI manufacturing, Stat Meth & Appl, 16, 1, 85-115 (2007) · Zbl 1157.62558
[12] Crosato L, Destefanis S, Ganugi P (2014) Firm size distribution and returns to scale. Innovation, Globalization and Firm Dynamics: Lessons for Enterprise Policy, pp 71-94
[13] D’Agostino, RB; Stephens, MA, Goodness-of-Fit Techniques (1986), New York: Marcel Dekker Inc., New York · Zbl 0597.62030
[14] Dagum, C., A new model of personal income distribution: Specification and estimation, Economie appliquée, 30, 3, 413-437 (1977)
[15] Dagum C, Lemmi A (1987) A contribution to the analysis of income distribution and income inequality, and a case study: Italy. In: Slottje DJ (ed) Research on Economic Inequality. JAI Press, Greenwich, CN, pp 123-157
[16] De Wit, G., Firm size distributions: An overview of steady-state distributions resulting from firm dynamics models, Int J Ind Organ, 23, 5, 423-450 (2005)
[17] Domma, F.; Perri, PF, Some developments on the log-Dagum distribution, Stat Meth & Appl, 18, 2, 205-220 (2009) · Zbl 1405.62023
[18] Erlingsson EJ, Alfarano S, Raberto M, Stefánsson H (2013) On the distributional properties of size, profit and growth of Icelandic firms. J Econ Interact Coord pp 1-18
[19] Eurostat (2008) NACE Rev. 2-Statistical classification of economic activities in the European Community. Official Publications of the European Community, Luxemburg
[20] Eurostat (2009) SMEs were the main drivers of economic growth between 2004 and 2006. Statistics in Focus 71:1-8
[21] Fattorini, L.; Lemmi, A., Proposta di un modello alternativo per l’analisi della distribuzione personale del reddito, Atti Giornate di Lavoro AIRO, 28, 89-117 (1979)
[22] Fattorini, L.; Lemmi, A., The stochastic interpretation of the Dagum personal income distribution: a tale, Statistica, 66, 3, 325-329 (2006) · Zbl 1188.62362
[23] Feller W (1968) An introduction to probability theory and its applications, vol 1. John Wiley & Sons, · Zbl 0155.23101
[24] Fiori, AM; Zenga, M., Karl Pearson and the origin of kurtosis, Int Stat Rev, 77, 1, 40-50 (2009)
[25] Fisk, PR, The graduation of income distributions, Econometrica, 29, 2, 171-185 (1961) · Zbl 0104.38702
[26] Gabaix, X., Power laws in economics and finance, Ann Rev Econ, 1, 1, 255-294 (2009)
[27] Ganugi, P.; Grossi, L.; Crosato, L., Firm size distributions and stochastic growth models: a comparison between ICT and mechanical Italian companies, Stat Meth & Appl, 12, 3, 391-414 (2004) · Zbl 1090.91556
[28] Ganugi, P.; Grossi, L.; Gozzi, G., Testing Gibrat’s law in Italian macro-regions: analysis on a panel of mechanical companies, Stat Meth & Appl, 14, 1, 101-126 (2005) · Zbl 1089.62147
[29] Gibrat R (1931) Les inégalités économiques. Librairie du Recueil Sirey · JFM 57.0635.06
[30] Hastie, T.; Tibshirani, R.; Friedman, J., The elements of statistical learning: data mining, inference, and prediction (2009), New York, NY: Springer, New York, NY · Zbl 1273.62005
[31] Johnson, N.; Kotz, S.; Balakrishnan, N., Continuous Univariate Distributions (1994), New York: Wiley, New York · Zbl 0811.62001
[32] Kalecki, M., On the Gibrat distribution, Econometrica, 13, 2, 161-170 (1945) · Zbl 0063.03111
[33] Karlin S, Taylor HE (1981) A second course in stochastic processes. Elsevier · Zbl 0469.60001
[34] Kleiber, C., Dagum vs. Singh-Maddala income distributions, Econ Lett, 53, 3, 265-268 (1996) · Zbl 0897.90060
[35] Kleiber C (2008) A guide to the Dagum distribution. Modeling Income Distributions and Lorenz Curves Series: Economic Studies in Inequality, Social Exclusion and Well-Being, vol 5. Springer, New York, pp 97-117 · Zbl 1151.91704
[36] Kleiber, C.; Kotz, S., Statistical size distributions in economics and actuarial sciences (2003), Hoboken, New Jersey: John Wiley & Sons, Hoboken, New Jersey · Zbl 1044.62014
[37] Lyons, B., A new measure of minimum efficient plant size in uk manufacturing industry, Economica, 47, 185, 19-34 (1980)
[38] Ord K (1975) Statistical models for personal income distributions. In: A Modern Course on Statistical Distributions in Scientific Work, Springer, pp 151-158
[39] Pagano, P.; Schivardi, F., Firm size distribution and growth, Scand J Econ, 105, 2, 255-274 (2003)
[40] Shapiro, SS; Wilk, MB; Chen, HJ, A comparative study of various tests for normality, J Am Stat Assoc, 63, 324, 1343-1372 (1968)
[41] Steindl J (1965) Random processes and the growth of firms: A study of the Pareto law, vol 18. Hafner Pub. Co
[42] Stuart A, Ord JK, Arnold S (1999) Kendall’s advanced theory of statistics. Vol. 2A: Classical inference and the linear model. Wiley
[43] Sutton, J., Gibrat’s legacy, J Econ Lit, 35, 1, 40-59 (1997)
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