Division of Labor and Extent of the Market: 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. I propose a theoretical model in which this relationship 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, by reducing the costs associated with greater division of labor. The model embeds a theory of firms’ choice of the optimal division of labor in a spatial equilibrium model. Structural estimates derived from the model show that division of labor accounts for 16% 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 city size. The theory also generates a set of auxiliary predictions of firms’ responses to a reduction in the cost of division of labor. Exploiting a quasi-experiment that changes the cost of division of labor within cities—the gradual rollout of broadband internet infrastructure—I find causal empirical support for these predictions, validating the model. Finally, the quasi-experiment also provides validation for the structural estimation. The estimated model predicts changes in the average division of labor within different cities in response to the new broadband internet infrastructure, which I find are similar to the actual changes. ∗I am very grateful to Donald Davis, Jonathan Vogel, Réka Juhász, Jonas Hjort and David Weinstein for their invaluable guidance and continued support. I thank Nate Baum-Snow, Lorenzo Caliendo, Davin Chor, Rebecca Diamond, Cecilia Fieler, François Gerard, Yang Jiao, Amit Khandelwal, Nandita Krishnaswamy, Ildikó Magyari, Dávid Nagy, Stephen Redding, Tobias Salz, Rodrigo Soares, Meredith Startz, Adrian Tang, Danna Thomas, Sharon Traiberman, Eric Verhoogen, Mike Waugh, ShangJin Wei, Scott Weiner, Yue Yu, Ding Yuan, Jing Zhou, and International Trade, Applied Microeconomics and Development Colloquia participants at Columbia University for helpful discussions and comments. All errors are mine. †Department of Economics, 420 W. 118th St., New York, NY 10027. Email: [email protected]. 1