1 THE INTENSIVE MARGIN IN TRADE

# **1. Introduction**

Across trading partners, exports can vary along the extensive margin (number of exporting firms) and along the intensive margin (average exports per exporting firm). The classic Krugman (1980) model predicts all export variation will be on the intensive margin because all firms export to every destination. Melitz (2003) brings the extensive margin to life with fixed costs of exporting, and emphasizes the importance of selection of firms into exporting.

In this paper we document the importance of the two margins empirically and then study the implications of our findings for quantitative trade theory. Exploiting data on a much larger set of exporting countries than in the existing literature,<sup>1</sup> we find that the intensive margin is at least as important as the extensive margin in driving bilateral trade flows. The importance of the intensive margin is at odds with the Melitz model if one assumes that firm productivity is distributed Pareto, as is customary in the quantitative trade literature. In the benchmark Melitz-Pareto model, the extensive margin is dominant. In contrast, a lognormal distribution of productivities allows the Melitz model to successfully match the empirical prominence of the intensive margin. We finish by examining whether moving from a Pareto to a lognormal firm productivity distribution alters how trade costs affect trade flows and welfare.

To elaborate, we use the World Bank’s _Exporter Dynamics Database_ (hereafter EDD) to systematically examine the importance of the extensive and intensive margins. The EDD covers firm-level exports from 59 (mostly developing) countries to all destination countries in most years from 2003 to 2013. For 49 of the countries, every exporting firm’s exports to each destination in a given year can be broken down into HS 6-digit products.<sup>2</sup> We add China to the 49 EDD countries to arrive at 50 countries for our analysis. Having many origin and destination countries enables us to study the role of the intensive and extensive margins while allowing for origin-year and destination-year fixed effects that control for differences in population, wages, and other country characteristics that affect firm entry into exporting and exports per firm.

We find that between 40 and 60 percent of the variation in overall exports across origindestination pairs is accounted for by the intensive margin, with the rest accounted for by the extensive margin. For reasons that will become clear in Section 2, we refer to these two shares as the intensive margin and extensive margin elasticities. This breakdown into the intensive and extensive margin elasticities is robust to using different country samples or sets of fixed effects,

> 1Most firm-level empirical trade studies have only one or at most a few exporting countries. Bernard, Jensen, Redding and Schott (2007) decompose exports from the U.S. to other countries. Eaton, Eslava, Kugler and Tybout (2008) analyze firm-level exports for Colombia, Eaton, Kortum and Kramarz (2011) do so for France, Eaton et al. (2012a) for Denmark and France, Manova and Zhang (2012) for China, and Arkolakis and Muendler (2013) for Brazil, Chile, Denmark and Norway.

> 2See Fernandes, Freund and Pierola (2016) for a detailed description of the dataset.