Discussion Paper

No. 2008-42 | December 17, 2008
Superstatistics of Labour Productivity in Manufacturing and Nonmanufacturing Sectors


Labour productivity distribution (dispersion) is studied both theoretically and empirically. Superstatistics is presented as a natural theoretical framework for productivity. The demand index κ is proposed within this framework as a new business index. Japanese productivity data covering small-to-medium to large firms from 1996 to 2006 is analyzed and the power-law for both firms and workers is established. The demand index κ is evaluated in the manufacturing sector. A new discovery is reported for the nonmanufacturing (service) sector, which calls for expansion of the super¬statistics framework to negative temperature range.

Paper submitted to the special issue “Reconstructing Macroeconomics

JEL Classification:

E10, E30, O40


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Cite As

Hideaki Aoyama, Yoshi Fujiwara, Yuichi Ikeda, Hiroshi Iyetomi, and Wataru Souma (2008). Superstatistics of Labour Productivity in Manufacturing and Nonmanufacturing Sectors. Economics Discussion Papers, No 2008-42, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2008-42

Comments and Questions

Anonymous - Referee Report
January 12, 2009 - 09:45

The following report refers to a related, but different paper, the third paper in the reference:

In this paper, the authors investigate empiritical data of the distribution of productivity (from NIKKE-NEEDS) for three levels of aggregation, namely, business sectors, firms and workers. It turns out that the distributions ...[more]

... obey the Pareto law (power-law). This law is shown to be deduced from a Jump Markov process where the transition rates are power functions of the productivity. If one assume the demand to be an external constant giving rise to a constraint to economy, the most-likelihood distribution is given by the Maxwell-Boltzmann type (Yoshikawa(2002),Aoki-Yoshikawa(2007)). Thus the Pareto law cannot be explained under the assumption. The authors argue that the global equilibrium of the demand to be replaced by local ones and consider the probability distribution of the demand i.e. the statistics of the Boltzmann factor (superstatistics). The Pareto law of the productivity distributions can be deduced if the superstatistics obeys a power law as in formula (58)(65).

I think that the empirical data used here is creditable and the observation of the Pareto law of productivity distributions is important. Also the model based on superstatistics seems to have applications to similar problems in economics. Thus I recommend this paper to be published in the journal.

I have a few remarks:
1. To use the formula (20), one needs to identify the output $Y$. It would be better to give some additional description of the definition of "output" in the NIKKEI-NEEDS data. The description in Appendix A is insufficient for readers.

2. A principle or a model behinds the power law for superstatistics i.e. the formulae (58)(65) is missing.

Hideaki Aoyoma - Revised Version as Response to the Referee Report
January 14, 2009 - 10:07

see attached file