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Journal of Economic Interaction and Coordination

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26-03-2015 | Regular Article

Is the service sector different in size heterogeneity?

Authors: Junho Na, Jeong-dong Lee, Chulwoo Baek

Published in: Journal of Economic Interaction and Coordination | Issue 1/2017

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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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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”.

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”.

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 \(x\).

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.

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Title: Is the service sector different in size heterogeneity?
Authors: Junho Na
Jeong-dong Lee
Chulwoo Baek
Publication date: 26-03-2015
Publisher: Springer Berlin Heidelberg
Published in: Journal of Economic Interaction and Coordination / Issue 1/2017
Print ISSN: 1860-711X
Electronic ISSN: 1860-7128
DOI: https://doi.org/10.1007/s11403-015-0152-x

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