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Is the service sector different in size heterogeneity?

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Abstract

We examined whether significant differences in size heterogeneity exist between the service and the manufacturing industries by using PL exponents as the proxy for intra-industry size heterogeneity. For the purpose, we analyzed firm size distribution (FSD) and estimated the PL exponents, on the right tails of FSD, of the service and manufacturing industries in Korea for the period 2008–2012 using the Business Activity Survey dataset created by the Korean National Statistical Office As a result, we observed that the estimates of the PL exponents for the service industry are lower than those for the manufacturing industry (\(\upalpha _\mathrm{Service}<\upalpha _\mathrm{Manufacturing}\)) regardless of size variable, year, and dataset. This relationship may be related to the weaker negative relationship between the size and growth of the service industry, which made the slope of the PL distribution in the right tail of the FSD smoother. This finding implies that size heterogeneity may be more distinctive in the service industry than in the manufacturing industry. In addition, the PL exponents of sales were larger than those of assets and smaller than those of employees (\(\upalpha _\mathrm{Asset}<\upalpha _\mathrm{Sales}<\upalpha _\mathrm{Employee}\)) regardless of industry, year, and dataset. We also observed the PL exponents in the survived-firm dataset to decrease, compared to those in the all-firm dataset.

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Notes

  1. A comparison of the results requires careful consideration since the estimates of the exponents might differ, depending on which distribution model is used. For comparison, we may consider the relationship between the exponents of each distribution: \(\upalpha =\upmu + 1\) and \(\hbox {b} = 1/\upmu \), where \(\upalpha \) indicates the PL exponents of PDF, \(\mu \) denotes the Pareto exponent of counter-CDF, and b indicates the Zipf exponents of the Zipf distribution (Adamic 2000; Aoyama et al. 2010). The illustration for transformational relations of exponents are presented in “Appendix”.

  2. The variant of Zipf exponents were used in those studies. We transformed the results and showed in the form of PL exponents using the relationship of Zipf exponent and PL exponent, which are presented in “Appendix”.

  3. Pareto (1897) actually used \(N=\frac{A}{(x+b)^{\alpha }}\) instead of Eq. (8). \(N\) denotes the number of people whose income is higher than \(x\).

  4. Cobb-Douglas production function (\(Y=AL^{\gamma }K^{\delta }\)) may give clues to the question why the PL exponents of sales were found between those of assets and labor (Fujimoto et al. 2011; Takayuki et al. 2011). In this function, \(Y\) denotes output, \(A\) denotes productivity, \(L\) denotes labor, \(K\) denotes capital, and \(\gamma \) and \(\delta \) are positive numbers smaller than one. This equation implies that the output of an industry or a firm is determined by the input—labor and capital—and its productivity. Considering the Cobb–Douglas function with Eqs. (11) and (13), the PL exponent of the output is deduced as \(\alpha _Y =\min \left( {\frac{\alpha _L }{\gamma },\frac{\alpha _K }{\delta }} \right) \). For example, \(\upalpha _{\mathrm{Asset}}\) was 1.63, \(\upalpha _{\mathrm{Sales}}\) was 1.74, and \(\upalpha _{\mathrm{Employee}}\) was 2.08 for the service industry for the all-firm dataset in 2008. The equation is satisfied when \(\upgamma =0.065, \updelta =0.935\). However, it is merely a theoretical illustration in that the assumptions of the Cobb-Douglas function are not always satisfied in reality and the empirical values for \(\upgamma \) and \(\updelta \) are far from the above.

References

  • Adamic LA (2000) Zipf, power-laws, and pareto-a ranking tutorial. Xerox Palo Alto Research Center, Palo Alto, CA. http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html

  • Almus M (2000) Testing “Gibrat’s Law” for young firms–empirical results for West Germany. Small Bus Econ 15(1):1–12

    Article  Google Scholar 

  • Andriani P, McKelvey B (2009) Perspective—from Gaussian to Paretian thinking: causes and implications of power laws in organizations. Organ Sci 20(6):1053–1071

    Article  Google Scholar 

  • Aoyama H, Fujiwara Y, Ikeda Y (2010) Econophysics and companies: statistical life and death in complex business networks. Cambridge Univ Press, Cambridge

    Book  Google Scholar 

  • Aoyama H, Grüne L, Semmler W, Fujiwara Y, Souma W (2011) Fluctuation of firm size in the long-run and bimodal distribution. Adv Oper Res 2011:21. doi:10.1155/2011/269239

  • Audretsch DB, Klomp L, Santarelli E, Thurik AR (2004) Gibrat’s law: are the services different? Rev Ind Organ 24(3):301–324

    Article  Google Scholar 

  • Audretsch DB, Santarelli E, Vivarelli M (1999) Start-up size and industrial dynamics: some evidence from Italian manufacturing. Int J Ind Organ 17(7):965–983

    Article  Google Scholar 

  • Axtell RL (2001) Zipf distribution of US firm sizes. Science 293(5536):1818–1820

    Article  Google Scholar 

  • Bak P (1996) How nature works: the science of self-organized criticality, vol 212. Copernicus, New York

    Book  Google Scholar 

  • Barron DN, West E, Hannan MT (1994) A time to grow and a time to die: growth and mortality of credit unions in New York City, 1914–1990. Am J Sociol 100:381–421

  • Bauke H (2007) Parameter estimation for power-law distributions by maximum likelihood methods. Eur Phys J B 58(2):167–173

    Article  Google Scholar 

  • Baum JA, Singh JV (1994) Organizational niches and the dynamics of organizational mortality. Am J Sociol 100:346–380

  • Beinhocker ED (2007) The origin of wealth: evolution, complexity, and the radical remaking of economics. Random House

  • Blau PM (1977) Inequality and heterogeneity: a primitive theory of social structure. Free Press, New York

    Google Scholar 

  • Bottazzi G (2009) On the irreconcilability of Pareto and Gibrat laws. Phys A Stat Mech Appl 388(7):1133–1136

    Article  Google Scholar 

  • Breschi S, Malerba F, Orsenigo L (2000) Technological regimes and Schumpeterian patterns of innovation. Econ J 110(463):388–410

    Google Scholar 

  • Brzezinski M (2014) Do wealth distributions follow power laws? Evidence from ‘rich lists’. Phys A Stat Mech Appl 406:155–162

    Article  Google Scholar 

  • Cabral LMB, Mata J (2003) On the evolution of the firm size distribution: facts and theory. Am Econ Rev 93(4):1075–1090

    Article  Google Scholar 

  • Carrizosa MT (2007) Firm growth, persistence and multiplicity of equilibria: an analysis of Spanish manufacturing and service industries. Universitat Rovira i Virgili

  • Carroll GR (1993) A sociological view on why firms differ. Strateg Manag J 14(4):237–249

    Article  Google Scholar 

  • Cefis E, Marsili O, Schenk H (2009) The effects of mergers and acquisitions on the firm size distribution. J Evol Econ 19(1):1–20

    Article  Google Scholar 

  • Chakrabarti BK, Chakraborti A, Chatterjee A (2007) Econophysics and sociophysics: trends and perspectives. Wiley-VCH, Weinheim

    Google Scholar 

  • Champernowne DG (1974) A comparison of measures of inequality of income distribution. Econ J 84:787–816

  • Chatterjee A, Yarlagadda S, Chakrabarti BK (2005) Econophysics of Wealth Distributions: Econophys-Kolkata I. Recherche 67:02

    Google Scholar 

  • Cirillo P (2010) An analysis of the size distribution of Italian firms by age. Phys A Stat Mech Appl 389(3):459–466

    Article  Google Scholar 

  • Clauset A, Shalizi CR, Newman ME (2009) Power-law distributions in empirical data. SIAM Rev 51(4):661–703

    Article  Google Scholar 

  • Coad A (2009) The growth of firms: a survey of theories and empirical evidence. Edward Elgar Publishing, Cheltenham

    Book  Google Scholar 

  • Coad A, Segarra A, Teruel M (2010) Like milk or wine: Does firm performance improve with age? Papers on Economics and Evolution

  • Crosato L, Ganugi P (2007) Statistical regularity of firm size distribution: the Pareto IV and truncated Yule for Italian SCI manufacturing. Stat Methods Appl 16(1):85–115

    Article  Google Scholar 

  • Daunfeldt S-O, Elert N (2010) When is Gibrat’s law a law? Small Bus Econ 41:1–15

  • De Wit G (2005) Firm size distributions: an overview of steady-state distributions resulting from firm dynamics models. Int J Ind Organ 23(5):423–450

    Article  Google Scholar 

  • Delli Gatti D, Gaffeo E, Gallegati M, Giulioni G, Palestrini A (2008) Emergent macroeconomics: an agent-based approach to business fluctuations. Springer Milan, Milano

    Google Scholar 

  • Dosi G (2007) Statistical regularities in the evolution of industries. A guide through some evidence and challenges for the theory. In: Brusoni S, Malerba F (eds) Perspectives on innovation. Cambridge University Press, Cambridge

  • Dosi G, Lechevalier S, Secchi A (2010) Introduction: interfirm heterogeneity—nature, sources and consequences for industrial dynamics. Ind Corp Change 19(6):1867–1890

    Article  Google Scholar 

  • Dunne T, Roberts MJ, Samuelson L (1989) The growth and failure of US manufacturing plants. Q J Econ 104(4):671–698

    Article  Google Scholar 

  • Evans DS (1987) The relationship between firm growth, size, and age: estimates for 100 manufacturing industries. J Ind Econ 567–581

  • Frank RH, Cook PJ (1995) The winner takes-all society. Simon and Schuster, Free Press, Martin Kessler Books, New York; London and Toronto

    Google Scholar 

  • Fujimoto S, Ishikawa A, Mizuno T, Watanabe T (2011) A new method for measuring tail exponents of firm size distributions. Econ Open-Access, Open-Assess E-J 5:2011–2020

  • Fujiwara Y, Aoyama H, Di Guilmi C, Souma W, Gallegati M (2004) Gibrat and Pareto-Zipf revisited with European firms. Phys A Stat Mech Appl 344(1):112–116

    Article  Google Scholar 

  • Gabaix X (2008) Power laws in economics and finance. National Bureau of Economic Research

  • Gabaix X, Ibragimov R (2011) Rank-1/2: a simple way to improve the OLS estimation of tail exponents. J Bus Econ Stat 29(1):24–39

    Article  Google Scholar 

  • Gaffeo E, Gallegati M, Palestrini A (2003) On the size distribution of firms: additional evidence from the G7 countries. Phys A Stat Mech Appl 324(1):117–123

    Article  Google Scholar 

  • Ganugi P, Grossi L, Crosato L (2004) Firm size distributions and stochastic growth models: a comparison between ICT and Mechanical Italian Companies. Stat Methods Appl 12(3):391–414

    Google Scholar 

  • Geroski PA (1995) What do we know about entry? Int J Ind Organ 13(4):421–440

    Article  Google Scholar 

  • Goldstein ML, Morris SA, Yen GG (2004) Problems with fitting to the power-law distribution. Eur Phys J B Condens Matter Complex Syst 41(2):255–258

    Article  Google Scholar 

  • Growiec J, Pammolli F, Riccaboni M, Stanley HE (2008) On the size distribution of business firms. Econ Lett 98(2):207–212

    Article  Google Scholar 

  • Guilmi CD, Gallegati M, Ormerod P (2004) Scaling invariant distributions of firms’ exit in OECD countries. Phys A Stat Mech Appl 334(1):267–273

    Article  Google Scholar 

  • Guo J, Huang J, Chen Q, Wang Y (2010) Notice of retraction mobility of top 500 Chinese firms. In: 2010 international conference on E-business and E-government (ICEE). IEEE, pp 5207–5210

  • Hall BH (1986) The relationship between firm size and firm growth in the US manufacturing sector. National Bureau of Economic Research, Cambridge

    Book  Google Scholar 

  • Hannan MT, Freeman J (1977) The population ecology of organizations. Am J Sociol 82(5):929–964

  • Hart PE, Oulton N (1997) Zipf and the size distribution of firms. Appl Econ Lett 4(4):205–206

    Article  Google Scholar 

  • Hart PE, Prais SJ (1956) The analysis of business concentration: a statistical approach. J R Stat Soc Ser A (Gen) 119(2):150–191

    Article  Google Scholar 

  • Helfat CE, Peteraf MA (2003) The dynamic resource-based view: capability lifecycles. Strat Manag J 24(10):997–1010

    Article  Google Scholar 

  • Hernández-Pérez R, Angulo-Brown F, Tun D (2006) Company size distribution for developing countries. Phys A Stat Mech Appl 359:607–618

    Article  Google Scholar 

  • Hodgson GM (2002) A modern reader in institutional and evolutionary economics: key concepts. Edward Elgar Pub, Cheltenham

    Book  Google Scholar 

  • Hoopes DG, Madsen TL (2008) A capability-based view of competitive heterogeneity. Ind Corp Change 17(3):393–426

    Article  Google Scholar 

  • Ijiri Y, Simon HA (1977) Skew distributions and the sizes of business firms. North-Holland Publishing Company, New York

    Google Scholar 

  • Ishikawa A (2006) Pareto index induced from the scale of companies. Phys A Stat Mech Appl 363(2):367–376

    Article  Google Scholar 

  • Ishikawa A (2007) The uniqueness of firm size distribution function from tent-shaped growth rate distribution. Phys A Stat Mech Appl 383(1):79–84

    Article  Google Scholar 

  • Ishikawa A (2009) Power-law and log-normal distributions in temporal changes of firm-size variables. Econ Open Access, Open Assess E-J 3:1–25

  • Jessen AH, Mikosch T (2006) Regularly varying functions. University of Copenhagen, Laboratory of Actuarial Mathematics

  • Johnson P, Conway C, Kattuman P (1999) Small business growth in the short run. Small Bus Econ 12(2):103–112

    Article  Google Scholar 

  • Kauffman S (1995) At home in the universe: the search for the laws of self-organization and complexity. Oxford University Press, Oxford

    Google Scholar 

  • Lotti F, Santarelli E, Vivarelli M (2004) Gibrat’s law and market selection. Papers on entrepreneurship, growth and public policy

  • Luttmer EG (2011) On the mechanics of firm growth. Rev Econ Stud 78(3):1042–1068

    Article  Google Scholar 

  • Malerba F, Orsenigo L (1997) Technological regimes and sectoral patterns of innovative activities. Ind Corp Change 6(1):83–118

    Article  Google Scholar 

  • Marsili O (2005) Technology and the size distribution of firms: evidence from Dutch manufacturing. Rev Ind Organ 27(4):303–328

    Article  Google Scholar 

  • Marsili O (2006) Stability and turbulence in the size distribution of firms: evidence from Dutch manufacturing. Int Rev Appl Econ 20(02):255–272

    Article  Google Scholar 

  • McKelvey B, Andriani P (2005) Why Gaussian statistics are mostly wrong for strategic organization. Strat Organ 3(2):219–228

    Article  Google Scholar 

  • Mizuno T, Katori M, Takayasu H, Takayasu M (2003) Statistical laws in the income of Japanese companies. arXiv preprint cond-mat/0308365

  • Nelson RR (1991) Why do firms differ, and how does it matter? Strat Manag J 12(S2):61–74

    Article  Google Scholar 

  • Nelson RR (1994) The role of firm differences in an evolutionary theory of technical advance. In: Magnusson L (ed) Evolutionary and neo-Schumpeterian approaches to economics. Kluwer Academic, Boston, pp 231–242

  • Newman MEJ (2005) Power laws, Pareto distributions and Zipf’s law. Contemp Phys 46(5):323–351

    Article  Google Scholar 

  • Noda T, Collis DJ (2001) The evolution of intraindustry firm heterogeneity: insights from a process study. Acad Manag J 44(4):897–925

    Article  Google Scholar 

  • Okuyama K, Takayasu M, Takayasu H (1999) Zipf’s law in income distribution of companies. Phys A Stat Mech Appl 269(1):125–131

    Article  Google Scholar 

  • Oliveira B, Fortunato A (2008) The dynamics of the growth of firms: evidence from the services sector. Empirica 35(3):293–312

    Article  Google Scholar 

  • Pareto V (1897) The new theories of economics. J Polit Econ 5(4):485–502

    Article  Google Scholar 

  • Pavitt K (1987) The objectives of technology policy. Sci Public Policy 14(4):182–188

    Google Scholar 

  • Peteraf MA (1993) The cornerstones of competitive advantage: a resource-based view. Strat Manag J 14(3):179–191

    Article  Google Scholar 

  • Ramsden J, Kiss-Haypal G (2000) Company size distribution in different countries. Phys A Stat Mech Appl 277(1):220–227

    Article  Google Scholar 

  • Rumelt RP (1991) How much does industry matter? Strat Manag J 12(3):167–185

    Article  Google Scholar 

  • Saichev A, Malevergne Y, Sornette D (2009) Theory of Zipf’s law and beyond, vol 632. Springer, New York

    Google Scholar 

  • Santarelli E, Klomp L, Thurik AR (2006) Gibrat’s Law: an overview of the empirical literature. In: Santarelli E (ed) Entrepreneurship, growth, and innovation: the dynamics of firms and industries. Springer, New York, pp 41–73

  • Saviotti PP (1994) Variety, economic and technological development. In: Shionoya Y, Perlman M (eds) Innovation in technology, industries, and institutions: studies in Schumpeterian perspectives. The University of Michigan Press, Ann Arbor, pp 27–48

  • Singh A, Whittington G (1975) The size and growth of firms. Rev Econ Stud 42(1):15–26

    Article  Google Scholar 

  • Stanley MHR, Buldyrev SV, Havlin S, Mantegna RN, Salinger MA, Eugene Stanley H (1995) Zipf plots and the size distribution of firms. Econ Lett 49(4):453–457

    Article  Google Scholar 

  • Steindl J (1965) Random processes and the growth of firms: a study of the Pareto law. Griffin, London

    Google Scholar 

  • Sutton J (1997) Gibrat’s legacy. J Econ Lit 35(1):40–59

    Google Scholar 

  • Takayuki M, Atushi I, Shouji F, Tsutomu W (2011) Power Laws in Firm Productivity. Center for Interfirm Network, Institute of Economic Research, Hitotsubashi University Working Paper Series

  • Wagner J (2011) From estimation results to stylized facts twelve recommendations for empirical research in international activities of heterogeneous firms. De Econ 159(4):389–412

    Google Scholar 

  • Weiss CR (1998) Size, growth, and survival in the upper Austrian farm sector. Small Bus Econ 10(4):305–312

    Article  Google Scholar 

  • Wernerfelt B (1995) The resource-based view of the firm: ten years after. Strat Manag J 16(3):171–174

    Article  Google Scholar 

  • Winter SG (2005) Developing evolutionary theory for economics and management. In: Smith KG, Hitt MA (eds) Great minds in management. Oxford University Press, Oxford, UK, pp 509–546

  • Zhang J, Chen Q, Wang Y (2009) Zipf distribution in top Chinese firms and an economic explanation. Phys A Stat Mech Appl 388(10):2020–2024

    Article  Google Scholar 

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Authors and Affiliations

  1. LG Economic Research Institute, Seoul, Korea

    Junho Na

  2. Technology, Management, Economics and Policy Program, Seoul National University, Seoul, Korea

    Jeong-dong Lee

  3. Department of International Trade, Duksung Women’s University, 33, Samyangro 144-Gil, Dobong-gu, Seoul, 132-714, Korea

    Chulwoo Baek

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  1. Junho Na
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Correspondence to Chulwoo Baek.

Appendix: Illustrations of transformation among power, Pareto, Zipf exponents

Appendix: Illustrations of transformation among power, Pareto, Zipf exponents

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Na, J., Lee, Jd. & Baek, C. Is the service sector different in size heterogeneity?. J Econ Interact Coord 12, 95–120 (2017). https://doi.org/10.1007/s11403-015-0152-x

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