at destination and export less – a selection effect of deep trade agreements. On average, the inclusion of an additional legally enforceable provision in RTAs stimulates the exports of large firms by 0.4%-0.6%, while it reduces the exports of small firms by 0.5%-0.6%.<sup>3</sup> Interestingly, high-productivity firms participating in Global Value Chains (GVC), i.e. firms that export and import to/from the same country, benefit the most from the signature of deep RTAs. For these firms, an additional legally enforceable provision in RTAs stimulates exports by 0.8%. The selection effect of deep trade agreements shows that using firm-level data is key to understand the welfare implications of RTAs. Specifically, by favoring exports of large and high-productivity firms and reducing exports of small and less productive firms, deep RTAs promote a reallocation of resources from the latter to the first which entails adjustment costs but also leads to an overall increase in the average productivity of firms.

We next investigate how deep trade agreements affect the margin of trade at the firm level. Deep RTAs could reduce both the variable and the fixed trade costs between member countries. This in turn impacts on the margin of trade that is affected. Previous work by Baier et al. (2014) uses aggregate trade data to study how different types of RTAs affect the intensive and the extensive margin of trade. Here, we use a decomposition approach à la Berman et al. (2012), to disentangle the average export sales effect of deep RTAs into intensive _versus_ extensive (firm-based) margin component. Namely, we use the firm-specific export behavior to impute the extensive _versus_ intensive margin effect of deep RTAs. We show that the extensive margin channel has only a slightly larger contribution (60%) than the intensive margin channel (40%). This evidence, in light of the theoretical predictions in Chaney (2008), suggests that indeed deep RTAs represent a reduction in both the fixed and the variable export cost components. This is the second contribution of this paper which provides novel firm-level evidence on the channel through which deep RTAs boost aggregate exports.

Finally, we study the dynamic effects of deep trade agreements on firms’ exports. The positive effect of _bilateral_ deep RTAs may vanish over time because of the worldwide increase in RTAs and their depth and the inclusion in RTAs of non-discriminatory provisions that _de facto_ can reduce trade costs for exporters in third countries (Lee et al., 2019). By adopting an event study approach in the vein of Fajgelbaum et al. (2020), we show that a _change_ in the depth of RTAs makes firms export more during the two years after the shock. The effect of the change in depth of RTAs vanishes afterwards. The event study approach also shows the validity of the

> 3This finding is the average effect of deep trade agreements on firms’ exports. It is still possible that individual provisions in DTAs have effects that are more favorable to small firms. For instance, Fernades et al. (2021) find that for a sample of Latin American countries firms’ exports increase significantly in destination markets with RTAs that promote regulatory cooperation and that the effect is stronger for smaller firms. They find that this effect is driven by entry into new product markets and increases in export quality of smaller firms.

3