Markets and the non-monotonic relation between productivity and establishment size


  • This document reports the results of research and analysis undertaken by the U.S. Census Bureau staff. It has undergone a Census Bureau review more limited in scope than that given to official Census Bureau publications. This document is released to inform interested parties of research and to encourage discussion. This research is a part of the U.S. Census Bureau’s Longitudinal Employer-Household Dynamics Program (LEHD), which is partially supported by the National Science Foundation Grants SES-9978093 and SES-0427889 to Cornell University (Cornell Institute for Social and Economic Research), the National Institute on Aging Grant R01 AG018854-02, and the Alfred P. Sloan Foundation. The views expressed on statistical issues are those of the author and not necessarily those of the U.S. Census Bureau, its program sponsors, or data providers. Some or all of the data used in this paper are confidential data from the LEHD Program. The U.S. Census Bureau supports external researchers’ use of these data through the Research Data Centers (see For other questions regarding the data, please contact Jeremy S. Wu, Program Manager, U.S. Census Bureau, LEHD Program, Room 6H141, 4600 Silver Hill Road, Suitland, MD 20746, USA (, The author thanks Hyowook Chiang for providing the data. The author gratefully acknowledges John Haltiwanger, John Shea, Daniel Vincent, Arghya Ghosh, Kevin Fox, Shiko Maruyama, Chris Edmond, Craig Burnside and the two anonymous referees for very helpful comments. Email:


Abstract A model of monopolistic competition is presented in which the relation between the productivity and input size of producers is non-monotonic and bell-shaped. The model predicts that markets matter and the average size of the producers is directly scaled by the size of the market. An indirect effect increases the cutoff productivity, making the bell narrower in larger markets or when the transportation cost falls. Empirical evidence from the concrete industry and a few other 4-digit industries supports the model’s predictions. The bell-shaped relation has especially important implications on how size distributions are formed across localized versus globalized market industries.


On présente un modèle de concurrence monopolistique dans lequel la relation entre la productivité et la taille de l’établissement de production mesurée par les intrants n’est pas monotone mais en forme de cloche. Le modèle prédit que la taille du marché est importante: la taille moyenne des producteurs dépend directement de la taille du marché. Un effet indirect accroît la taille minimale requise (celle du producteur le moins efficient qui reste viable): ce qui fait que la cloche est plus étroite dans les grands marchés ou quand les coûts de transport chutent. Des résultats empiriques pour l’industrie du ciment et quelques autres industries (code à quatre chiffres) supportent les prédictions du modèle. La relation en forme de cloche a des implications particulièrement importantes sur la façon dont se forment les distributions de la taille des établissements dans les industries dont le marché est local par opposition à global.