to export to a given foreign market is shaped by a comparison of the potential operating profit obtained in that foreign market with the fixed costs associated with distributing products in that market.

Although the canonical model in this firm-level approach to international trade was written in a setting in which international trade involves the exchange of only final goods, as in traditional conceptualizations of trade, an active literature has adopted similar ideas to understand the rise of GVCs. In the presence of fixed costs of engaging in global sourcing (i.e., of importing intermediate inputs), one would expect that the use of imported inputs in production will demand that importers attain a minimum effi cient scale of production, with smaller and less productive firms in an industry being excluded from GVC participation (see Antràs and Helpman, 2004, Halpern, Koren, and Szeidl, 2015, Gopinath and Neiman, 2014, Antràs, Fort and Tintelnot, 2017). The combination of scale economies and fixed costs of importing and exporting also provides a natural explanation for the fact that firms that are large enough to be able to amortize the fixed costs associated with importing will also tend to be large enough to find exporting successful. Selection into importing thus naturally is associated with firms engaged in backward GVC participation according to the definition developed in our broad conceptualization of GVCs (i.e., the use of foreign value added in exporting). Similarly, firms exporting intermediate inputs, are likely to engage in forward GVC participation, as the firms importing their products are likely to be exporters themselves.

When adopting a firm-level approach one can also distinguish global value chains that are organized by a lead firm, which incurs the bulk of the fixed costs associated with setting up the network of producers in a given production process, and global value chains that are more decentralized in nature, with individual producers incurring costs to set up links upstream and downstream from them (see Bernard, Moxnes, and Ulltveit-Moe, 2018, Antràs and de Gortari, 2019).

# 3.1 Measurement

Firm-level datasets containing information on the import and export transactions of firms can be fruitfully used to construct measures of GVC participation similar in nature to those discussed above based on the country- industry information in global Input-Output tables. More specifically, transaction-level customs datasets of the type available from the World Bank’s Export Dynamics Database can be used to identify the set of firms in a country that participate in trade, further distinguishing firms that export, firms that import and firms that both export and import. When a given firm in a given country both imports and exports, it is natural to conclude that this firm participates in GVCs.

To map this definition more precisely to the definition of backward GVC participation developed in country-industry studies, one would ideally also resort to product-level information to verify that the goods imported by an exporting firm are indeed intermediate inputs (rather than final goods), so that one can more comfortably conclude that this firm is indeed using foreign value-added in their production destined for exports. Without linking customs-level data across countries, it is much harder to come up with analogous firm-level measures of forward GVC participation. The 15