2 FERNANDES-KLENOW-MELESHCHUK-PIEROLA-RODR ́ıGUEZ-CLARE excluding country pairs with few exporters or tiny exporters, and looking within industries.

We interpret the finding that up to 60 percent of the variation in bilateral trade flows are explained by the extensive margin as providing support for the Melitz (2003) model. But the finding that at least 40 percent of that variation is explained by the intensive margin — even while allowing for origin-year and destination-year fixed effects — contradicts an important special case of the Melitz model, namely the one with Pareto-distributed firm productivity and fixed trade costs that vary only because of separate origin and destination components. In this case all variation in exports across trading partners should occur through the number of exporters (the extensive margin). Lower variable trade costs should stimulate sales of a given exporting firm, but draw in marginal exporting firms to the point that average exports per exporter (the intensive margin) is unchanged. This exact offset is a special property of the Pareto distribution.<sup>3</sup> We explore several potential explanations for the prominent intensive margin in the EDD data while retaining a Melitz-Pareto core. We do this because Melitz-Pareto has become an important benchmark model in international trade. It is consistent with many firm-level facts (Eaton et al., 2011), generates a gravity equation (Chaney, 2008), and yields a simple summary statistic for the welfare gains from trade (Arkolakis, Costinot and Rodr ́ıguez-Clare, 2012). We want to make sure our empirical finding cannot be made compatible with Melitz-Pareto before exploring an alternative productivity distribution.

First, we consider the possibility that fixed trade costs vary by origin-destination pair. Higher fixed trade costs raise average exports per exporter, but _lower_ total exports. For average exports to be increasing in total exports, therefore, one needs variable trade costs to be very negatively correlated with fixed trade costs. A corollary is that, whereas variable trade costs rise decisively with distance between trade partners, fixed trade costs would need to fall with distance. We find this rather implausible. More importantly, this model would imply that the intensive margin elasticity should be equally important among the smallest and largest exporting firms; in the data, the intensive margin elasticity rises steadily with exporting firm size when we put exporting firms into size percentiles.

Second, we explore the role of multi-product firms. If the typical firm exports a higher number of products to destinations with larger overall exports, this could account for the importance of the intensive margin for exports. We find that the number of HS 6-digit products per exporting firm does indeed account for about 12 percent of the variation in overall exports, or about

> 3This property of the Melitz-Pareto model extends to environments with demand and fixed costs that are idiosyncratic to firm-destinations (Eaton et al., 2011); convex marketing costs (Arkolakis, 2010); non-CES preferences (Arkolakis, Costinot, Donaldson and Rodr ́ıguez-Clare, 2015); non-monopolistic competition (Bernard, Eaton, Jensen and Kortum, 2003), and multinational production (Arkolakis, Ramondo, Rodr ́ıguez-Clare and Yeaple, 2014).