A Unified Theory of Firm Selection and Growth *

Abstract

This paper develops an analytical framework to study firm and exporter growth and provides a dynamic foundation for a standard general equilibrium trade model.Firm-level growth is the result of idiosyncratic productivity improvements and there is continuous arrival of new potential producers. A firm enters a market if it is profitable to incur the marginal cost to reach the first consumer and pays an increasing marketing cost to reach additional consumers. I calibrate the model using data on the cross section of firm sales and bilateral trade, as well as the rate of incumbent firm exit. The calibrated model predicts that a firm's growth is inversely related to its initial size and that the distribution of growth rates of small firms is heavily skewed to the right. These predictions are confirmed by looking at the growth of sales of US firms and Brazilian exporters to the US. I use this model to study the impact of cross-firm reallocations on economic activity and measured productivity. JEL codes: F12, L11, M31, D92. * I am grateful to Timothy Kehoe, Samuel Kortum, Cristina Arellano, Jonathan Eaton as well as Giuseppe Moscarini for their insightful comments and discussions on this topic. I am also indebted to Marc Muendler for providing me with moments from the Brazilian data, and Jose Mata for providing me with the estimates for Portuguese firms. For their suggestions and comments, I would also like to thank Andy Atkeson,

Price, Product Quality, and Exporter Dynamics: Evidence From China

“…Finally, our work relates to studies of exporter dynamics and, particularly, the mechanisms by which successful entrants grow into large, stable exporters. As such, our work closely relates to that of Costantini and Melitz (), Atkeson and Burstein (), and Arkolakis (). Like these papers, we allow for differences in productivity across firms, but, unlike these papers, the key source of firm‐level dynamics is not due to firm decisions that influence the evolution of productivity.…”

“…An alternative mechanism would be to allow sales to grow through continual productivity improvements (e.g., Arkolakis, ) or learning‐by‐doing (Bastos et al., ). We do not suggest that these mechanisms may not be important, particularly in the Chinese context.…”

Learning, prices and firm dynamics

“…Models of firm dynamics that introduce idiosyncratic productivity shocks into Melitz (), including Luttmer (), Impullitti et al. () and Arkolakis (), would have difficulty predicting the age dependence of various firms’ life cycle patterns. In these models, productivity dynamics follows a Brownian motion process.…”

Financial Frictions and New Exporter Dynamics

“…They argue that the low but increasing probability of continuing to export arises from initial uncertainty about the idiosyncratic profitability of exporting. Arkolakis () investigates the role of marketing costs and customer capital in explaining increasing export volumes. We present evidence in support of our mechanism and view these alternative explanations as complementary to ours.…”