Division of Labor and Productivity Advantage of Cities: Theory and Evidence from Brazil

Firms are more productive in larger cities. This paper investigates a potential explanation that was first proposed by Adam Smith: Larger cities facilitate greater division of labor within firms. Using a dataset of Brazilian firms, I first document that division of labor is indeed robustly correlated with city size, controlling for firm size. To quantify the importance of division of labor in explaining productivity advantages of cities, I propose and estimate a quantitative model that embeds a theory of firms' choice of the optimal division of labor in a spatial equilibrium framework. In the model, the observed positive correlation between firm's division of labor and city size is generated by both a selection effect -firms endogenously sort across space, choosing different extents of division of labor-and a treatment effect-larger cities increase division of labor for all firms, possibly by reducing costs associated with greater division of labor. Structural estimates derived from the model show that division of labor accounts for 17% of the productivity advantage of larger cities in Brazil, half of which is due to firm sorting and the other half to the treatment effect of larger city size. The theory also generates a set of auxiliary predictions of firms' responses to an exogenous shock to division of labor. Exploiting a quasi-experiment - the gradual roll-out of broadband internet infrastructure - I find causal empirical support for these predictions. Finally, the quasi-experiment also provides out-of-sample validation for the structural estimation: The model is successful in predicting the heterogeneous impacts of the new infrastructure across Brazilian cities.