# **1 Introduction**

In 2018 and 2019, the US and China engaged in a trade war, mutually escalating tariffs that ultimately covered approximately $450 billion in trade flows. These policies upended a decades-long trend toward lower global trade barriers and, unsurprisingly, reduced trade between the US and China, with escalated tariffs persisting until today.<sup>1</sup> While the US-China trade war can be seen as a turning point in the globalization era, it has also presented “bystander” countries with the opportunity to grow exports to the world’s biggest economies.

Did other countries take over the US and Chinese markets? Did they reallocate exports away from the rest of the world? Affirmative answers would be consistent with substitution elasticities across exporters above one and with standard upward-sloping export supply curves. However, importers in the US and China may perceive products from certain origins as substitutes to Chinese or US varieties, respectively, and others as complements; in parallel, greater demand from the US or China could have raised global exports for bystander countries if supply curves slope downward. In addition, countries specialized in sectors with more elastic supplies may have responded more strongly. The trade war provides an opportunity to inspect the importance of these forces.

We first develop a simple framework to estimate countries’ export responses to third-country tariffs. The empirical analysis is guided by a Ricardian-Armington trade model allowing substitution elasticities to be country-pair specific and above or below one; and for country- and sector-specific supply elasticities that may be downward sloping. Our first proposition derives, from a first-order approximation around an arbitrary equilibrium, an estimating equation that shows how a bystander’s product-level exports to the US (China) and the rest of the world change with the US (Chinese) tariffs. Our second proposition shows that the estimated tariff elasticities of exports jointly identify: i) whether a country’s exports substitute or complement the US or China; and ii) whether it operates along downward- or upward-sloping supply curves.

We implement the empirical analysis on global bilateral HS6-level trade data. We first estimate product-level export responses from exporters other than the US or China assuming common tariff elasticities across countries.<sup>2</sup> The first takeaway is that, on average, bystanders increased their exports to the US, barely changed their exports to China, and _increased_ their exports to the rest of the world in products with higher US-China tariffs. So, while the US and China taxed each other, the average country increased its global exports in targeted products relative to untargeted products. Therefore, the trade war created net trade opportunities rather than simply shifting trade across destinations.

This initial approach assumes common tariff elasticities across countries, but these elasticities may vary by exporter, importer, sector, and size of the trade flow, as implied by the model.

> 1See Amiti et al. (2019), Cavallo et al. (2021), Fajgelbaum et al. (2020), Flaaen et al. (2020), Flaaen and Pierce (2019), and Waugh (2019), among others. Fajgelbaum and Khandelwal (2021) review the research that has examined the economic impacts of the trade war.

> 2Consistent with other findings in the literature, we find that the US and China reduced bilateral exports in products with larger tariff increases.

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