The relationship between labor productivity and number of operating firms

This paper constructs a theoretical model matching empirically observed relationships between average labor productivity and the number of operating firms. The models in the related literature which utilize CES utility function find no relationship between average labor productivity and the number of operating firms in the economy (Melitz, Marc J. [2003. “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity.” Econometrica 71 (6): 1695–1725] and many versions of this model). Moreover, the models which utilize non-homothetic preferences with a numeraire good find a positive relationship between average labor productivity and the number of operating firms (Melitz, Marc, and Gianmarco I. P. Ottaviano [2008. “Market Size, Trade, and Productivity.” Review of Economic Studies 75: 295–316] and many versions of this model). However, the model developed in this paper provides a single theoretical framework that depending on the source, a rise in the average labor productivity may lead to an increase or a decrease in the number of operating firms. In line with our results, we provide empirical evidence from ten European countries for the 2008–2016 period, which shows that the correlation between these two variables is positive for some of the countries, while negative for the others.