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Abstract
Okubo T. and Tomiura E. Skew productivity distributions and agglomeration: evidence from plant-level data, Regional Studies. This paper empirically examines how the shapes of plant productivity distributions vary across regions based on Japan's manufacturing census. It focuses on the skewness to examine the asymmetry by estimating the gamma distribution at the plant level. By linking the estimated shape parameters with economic geography variables, it is found that the productivity distribution tends to be significantly left skewed, especially in cores, regions with diversified industrial compositions, regions with weak market potential and in agglomerated industries. These findings suggest that agglomeration economies are likely to accommodate heterogeneous plants with wide ranges of productivities.
Okubo T. and Tomiura E. 偏斜的生产力分布与集群：来自工厂层级资料的证据，区域研究。本文根据日本的制造业统计数据，经验性地检视工厂的生产力分布形式如何因区域而异。本文透过评估工厂层级的伽玛分布（gamma distribution)，聚焦于偏斜以检视不对称性。本研究透过将估计的形状参数连结至经济地理变项，发现生产力分布显著地向左偏斜，特别是在核心、具有多样化工业元素的区域、具有微弱市场潜力的区域，以及集群的产业之中。这些研究发现指出，集群经济或可容纳多元异质且具有各式生产力的工厂。
Okubo T. et Tomiura E. Les distributions de la productivité asymétriques et l'agglomération: des preuves provenant des données recueillies au niveau des usines, Regional Studies. À partir du recensement des entreprises au Japon, cet article examine empiriquement comment les formes des distributions de la productivité des usines varient suivant les régions. On en examine l'asymétrie en estimant la distribution gamma au niveau de l'usine. En reliant les paramètres de forme estimés aux variables de l'économie géographique, il s'avère que la distribution de la productivité a tendance à se désaxer vers la gauche, surtout dans les centres, les régions où la structure industrielle est diversifiée, les régions dont le potentiel commercial est faible et dans les industries agglomérées. Les résultats laissent supposer que les économies d'agglomération sont susceptibles de prendre en compte des usines hétérogènes dont la gamme des productivités est large.
Okubo T. und Tomiura E. Schiefe Produktivitätsverteilung und Agglomeration: Belege von Daten auf Werksebene, Regional Studies. In diesem Beitrag wird anhand der japanischen Erhebung über die produzierende Industrie auf empirische Weise untersucht, wie die Formen der Verteilung der Werksproduktivität von Region zu Region unterschiedlich ausfallen. Wir konzentrieren uns auf die Schiefe, um die Asymmetrie durch eine Schätzung der Gammaverteilung auf Werksebene zu untersuchen. Durch eine Verknüpfung der geschätzten Formparameter mit wirtschaftsgeografischen Variablen stellen wir fest, dass die Produktivitätsverteilung vor allem in Kernregionen, Regionen mit diversifizierter Branchenzusammensetzung, Regionen mit schwachem Marktpotenzial sowie in Branchenagglomerationen zu einer signifikanten Linksschiefe tendiert. Aus den Ergebnissen geht hervor, dass sich Agglomerationswirtschaften häufiger durch heterogene Werke mit einem breiten Spektrum von Produktivitätsstufen auszeichnen.
Okubo T. y Tomiura E. Distribuciones de productividad y aglomeración sesgadas: ejemplo de los datos de empresas, Regional Studies. En este artículo examinamos empíricamente cómo varían las formas de las distribuciones de productividad de las empresas en las diferentes regiones en función del censo manufacturero en Japón. Prestamos atención a los sesgos para analizar la asimetría al calcular la distribución gamma en un ámbito empresarial. Al vincular los parámetros de forma calculados con las variables económicas y geográficas, observamos que la distribución de productividad tiende a tener una asimetría izquierda significativa, especialmente en zonas centrales, regiones con composiciones industriales diversificadas, regiones con un potencial de mercado débil y en industrias aglomeradas. Estos resultados indican que es probable que las economías de aglomeración se ajusten a las empresas heterogéneas con amplias variaciones de productividad.
Acknowledgements
Earlier versions of this paper were circulated under the title ‘Productivity distribution, firm heterogeneity, and agglomeration: evidence from firm-level data’ in discussion paper forms. The authors acknowledge the insightful comments from the Editor and two anonymous referees of this journal; as well as Anthony Venables and Masahisa Fujita. This research was partly financed by Grant-in-Aid for Scientific Research (Grant Number 22530218) and the Research Institute of Economy, Trade, and Industry (RIETI). The access to micro-data was arranged by RIETI.
Notes
Okubo et al. Citation(2010) considered only two levels (high or low) of productivity levels without assuming any firm productivity distributions.
Syverson Citation(2004b) compared 443 US manufacturing industries and found lower dispersion in industries with higher substitutability, which is proxied by the value/weight ratio or shipped distance.
Cabral and Mata Citation(2003) also reported that the distribution becomes closer to log-normal as firms get older, but Angelini and Generale Citation(2008) found no significant impact of financial constraints on this evolution of distributions in Organisation for Economic Co-operation and Development (OECD) data.
Combes et al. Citation(2010) also considered the case that agglomeration dilates the distribution and they applied their method to French establishment-level data.
Furthermore, as reported in the fourth section, the selection appears not to be critical in the comparison of Japanese prefectures, while Combes et al. Citation(2010) analysed French cities.
Henderson Citation(2003) studied Marshallian externality based on the US Census of Manufacturers.
The results are unlikely to be qualitatively affected by the choice of productivity measures (for example, Bernard and Jones, Citation1996).
The Greater Tokyo Area (the nation capital area, or shuto-ken in Japanese) is defined here as Tokyo and its neighbouring prefectures: Kanagawa, Chiba and Saitama. The Greater Osaka Area (the Kyoto–Osaka–Kobe Area, or Keihanshin in Japanese) is defined here as Osaka and the neighbouring Kyoto and Hyogo prefectures.
The test statistics are available from the authors upon request.
Holmes and Stevens Citation(2002) showed the strong connection between firm size and industry concentration.
Comparable graphs for all other two-digit industries are shown in the discussion paper version (Okubo and Tomiura, 2010).
Employment size, labour to output ratio, material to output ratio, and sector dummies are used in the first-stage regression for PSM, as the data on capital are unavailable for many small-sized plants. The average productivity in the core is still higher than in the periphery by 4.00% after PSM, though the differential becomes smaller than 4.65% based on the simple mean comparison without plant matching. The gap is statistically significant at any conventional significance level. The detailed PSM results are available from the authors upon request.
Frequency histograms before kernel smoothing are available from the authors upon request. Prefectures in Japan are compared herein, while Combes et al. Citation(2010) compared cities in France.
Graphs for different years are shown in the discussion paper version (Okubo and Tomiura, 2010) and are available from the authors upon request.
Fig. A1 shows the comparisons with log-normal distribution.
Both Cabral and Mata Citation(2003) and Barrios et al. Citation(2005) estimated the distribution of firm size, not of plant productivity.
Note that the skewness statistics are negative (the density is called negatively skewed) when κ of the gamma distribution is positive.
The estimated gamma parameters for all forty-seven prefectures are reported in the discussion paper version (Okubo and Tomiura, 2010) and are available from the authors upon request.
The estimated κ for each industry is omitted but is available from the authors upon request.
Soo Citation(2005) estimated a similar regression with the country's Pareto exponent of city size distribution as the dependent variable.
In the sample, the correlations between the moments actually turn out to be low. Related with this issue, Huber and Pfaffermayr Citation(2010) investigated the second and third moments of firm size distribution separately and demonstrated that Gibrat's law ‘may be compatible with both an increase and a decrease in the skewness’ (p. 649).
When m = r, the internal distance is calculated by:
where Area denotes the area of the prefecture r (Combes and Overman, Citation2004).
A densely inhabited district is defined by the district in which population density is more than 4000 people per km2 and population in an adjacent area is more than 5000 people per km2. The data are taken from the Population Census.
The prefecture data for gross domestic product (GDP), population and infrastructure are taken from Fukao and Yue's (2000) data set.
Regressions shown in Table A1 in Appendix A use the estimated result from Otsuka and Yamano Citation(2008) of the contribution of TFP to growth over 1980–2002 for each prefecture. The regressions of Otsuka and Yamano also included population density and market access index.
Marsili Citation(2005) estimated a similar sectoral regression with Pareto cumulative distribution function as the dependent variable.
Regressions shown in Table A2 in Appendix A use the K-density of Japanese industries estimated by Nakajima et al. Citation(2012). For details, see Appendix A.
Trade share at 1990 is included into the regressions after it is interacted with year dummies, as the authors cannot trace sectoral trade data back to the 1970s on a consistent basis.
All input–output tables' data were derived from Japan Industrial Productivity database. Both variables were included into the regressions after being interacted with year dummies.
Okubo and Tomiura Citation(2012) found that policies for relocating plants out of cores affected the shapes of productivity distributions in Japan.
As this index barely varies over time, it was included after being interacted with year dummies.
Even if one replaces the EG index by K-density in Table A2 in Appendix A, the sign of the coefficient on foreign trade remains mostly negative though statistically insignificant.
As a related result, Marsili Citation(2005) found that increased mobility of firms across sizes makes distributions less skewed towards small firms by estimating the impacts of technology variables.