IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v685y2026ics0378437126000221.html

Productivity dispersion and allocation of labor among firms in economics

Author

Listed:
  • Fujiwara, Yoshi
  • Aoyama, Hideaki

Abstract

Inequalities are ubiquitous in economics. In this paper, we investigate productivity dispersion and the allocation of workers among different levels of productivity and output, by using a large dataset for small and medium-sized companies at a nationwide scale. Focusing on the manufacturing sector and small and medium levels of productivity, where more workers are distributed among higher levels of productivity, we first observe that the productivity dispersion can be characterized by a power-law distribution. We then have new empirical findings in a pivotal role of workers’ allocation among different levels of output as a key to understand their allocation among different levels of productivity. We also propose a stochastic process, mathematically a jump Markov process, in which workers are allocated to firms of differing output and productivity, interrupted by transitions to unemployment, where transitions are coupled with growth and shrink of firms output that relate with fluctuations of demand.

Suggested Citation

  • Fujiwara, Yoshi & Aoyama, Hideaki, 2026. "Productivity dispersion and allocation of labor among firms in economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 685(C).
    • Handle: RePEc:eee:phsmap:v:685:y:2026:i:c:s0378437126000221
    DOI: 10.1016/j.physa.2026.131286
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437126000221
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2026.131286?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Ikeda, Yuichi & Fujiwara, Yoshi & Aoyama, Hideaki & Iyetomi, Hiroshi & Souma, Wataru, 2009. "Superstatistics of Labour Productivity in Manufacturing and Nonmanufacturing Sectors," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy, vol. 3, pages 1-17.
    2. Masanao Aoki & Hiroshi Yoshikawa, 2012. "Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(1), pages 1-22, May.
    3. Hideaki Aoyama & Yoshi Fujiwara & Mauro Gallegati, 2015. "Micro-macro relation of production: double scaling law for statistical physics of economy," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 67-78, April.
    4. Albaek, Karsten & Sorensen, Bent E, 1998. "Worker Flows and Job Flows in Danish Manufacturing, 1980-91," Economic Journal, Royal Economic Society, vol. 108(451), pages 1750-1771, November.
    5. Hiroshi Yoshikawa, 2022. "Reconstruction of Macroeconomics: Methods of Statistical Physics, and Keynes' Principle of Effective Demand," Advances in Japanese Business and Economics, Springer, number 978-981-19-5264-7, December.
    6. Hideaki Aoyama & Hiroshi Yoshikawa & Hiroshi Iyetomi & Yoshi Fujiwara, 2010. "Productivity dispersion: facts, theory, and implications," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 5(1), pages 27-54, June.
    7. Chakrabarti,Bikas K. & Chakraborti,Anirban & Chakravarty,Satya R. & Chatterjee,Arnab, 2013. "Econophysics of Income and Wealth Distributions," Cambridge Books, Cambridge University Press, number 9781107013445.
    8. Alexis Toda, 2010. "Existence of a statistical equilibrium for an economy with endogenous offer sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(3), pages 379-415, December.
    9. Hideaki Aoyama & Yoshi Fujiwara & Yuichi Ikeda & Hiroshi Iyetomi & Wataru Souma, 2009. "Superstatistics of Labour Productivity in Manufacturing and Nonmanufacturing Sectors," Papers 0901.1500, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2021. "Why does production function take the Cobb–Douglas form?," Evolutionary and Institutional Economics Review, Springer, vol. 18(1), pages 79-102, April.
    2. Hideaki AOYAMA & Hiroshi IYETOMI & Hiroshi YOSHIKAWA, 2012. "Equilibrium Distribution of Labor Productivity," Discussion papers 12041, Research Institute of Economy, Trade and Industry (RIETI).
    3. Hideaki Aoyama & Hiroshi Iyetomi & Hiroshi Yoshikawa, 2012. "Equilibrium Distribution of Labor Productivity: A Theoretical Model," Papers 1205.2470, arXiv.org.
    4. Hideaki Aoyama & Hiroshi Iyetomi & Hiroshi Yoshikawa, 2015. "Equilibrium distribution of labor productivity: a theoretical model," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 57-66, April.
    5. Aoki, Masanao & Hawkins, Raymond J., 2010. "Non-self-averaging and the statistical mechanics of endogenous macroeconomic fluctuations," Economic Modelling, Elsevier, vol. 27(6), pages 1543-1546, November.
    6. Souma, Wataru & Ikeda, Yuichi & Iyetomi, Hiroshi & Fujiwara, Yoshi, 2009. "Distribution of Labour Productivity in Japan over the Period 1996--2006," Economics Discussion Papers 2009-2, Kiel Institute for the World Economy.
    7. Hawkins, Raymond J. & Aoki, Masanao & Roy Frieden, B., 2010. "Asymmetric information and macroeconomic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3565-3571.
    8. Kiran Sharma & Subhradeep Das & Anirban Chakraborti, 2017. "Global Income Inequality and Savings: A Data Science Perspective," Papers 1801.00253, arXiv.org, revised Aug 2018.
    9. Costas Efthimiou & Adam Wearne, 2016. "Household Income Distribution in the USA," Papers 1602.06234, arXiv.org.
    10. Hutzler, S. & Sommer, C. & Richmond, P., 2016. "On the relationship between income, fertility rates and the state of democracy in society," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 9-18.
    11. Venkatasubramanian, Venkat & Luo, Yu & Sethuraman, Jay, 2015. "How much inequality in income is fair? A microeconomic game theoretic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 120-138.
    12. Campolieti, Michele, 2018. "Heavy-tailed distributions and the distribution of wealth: Evidence from rich lists in Canada, 1999–2017," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 263-272.
    13. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    14. Yashiv, Eran, 2007. "Labor search and matching in macroeconomics," European Economic Review, Elsevier, vol. 51(8), pages 1859-1895, November.
    15. Thitithep Sitthiyot & Kanyarat Holasut, 2024. "Income distribution in Thailand is scale-invariant," Papers 2402.01141, arXiv.org.
    16. Hiroshi YOSHIKAWA, 2013. "Stochastic Macro-equilibrium and Microfoundations for Keynesian Economics," Discussion papers 13039, Research Institute of Economy, Trade and Industry (RIETI).
    17. Kerim Eser Afc{s}ar & Mehmet Ozyi~git & Yusuf Yuksel & Umit Ak{i}nc{i}, 2021. "Testing the Goodwin Growth Cycles with Econophysics Approach in 2002-2019 Period in Turkey," Papers 2106.02546, arXiv.org.
    18. Maia, Adriano & Matsushita, Raul & Demarcus, Antonio & Da Silva, Sergio, 2023. "Scalability in a two-class interoccupational earnings distribution model," SocArXiv 23brg, Center for Open Science.
    19. Marcelo B. Ribeiro, 2025. "Modeling Income Distribution with the Gause-Witt Population Ecology System," Papers 2506.20881, arXiv.org.
    20. Caticha, Ariel & Golan, Amos, 2014. "An entropic framework for modeling economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 149-163.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:685:y:2026:i:c:s0378437126000221. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.