metadata: authors: 0: author: Fajgelbaum,Pablo David
1: author: Goldberg,Pinelopi Koujianou
2: author: Kennedy,Patrick
3: author: Khandelwal,Amit Kumar
4: author: Taglioni,Daria
count: United States,China
docna: 0: docna: The US-China Trade War and Global Reallocations
docty: Policy Research Working Paper
subtopic: International Trade and Trade Rules,Armed Conflict,Transport Services,Food Security,Energy and Mining
teratopic: International Economics and Trade,Conflict and Development,Transport,Energy,Agriculture
abstracts: cdata!: How did the US-China trade war affect
            global trade? Surprisingly, exports of products taxed by US
            or China increased from &#x201c;bystander&#x201d;
            countries to the rest of world (excluding US and China).
            Hence, the trade war created trade opportunities rather than
            simply shifting trade across destinations. There was large
            cross-country variation in export growth of tariff-exposed
            products, explained mostly by country-specific components of
            tariff elasticities rather than by specialization patterns.
            Through a standard trade model, the signs of the tariff
            elasticities identify if a country complements or
            substitutes the US or China, and the slope of its supply
            curve. Countries that operate along downward-sloping
            supplies whose exports substitute (complement) US and China
            are among the larger (smaller) beneficiaries of the trade war.
geo_reg_key: 119228,119225,517198,517191
repnme: repnme: The US-China Trade War and Global Reallocations
display_title: The US-China Trade War and Global Reallocations
listing_relative_url: /research/2022/01/33698601/us-china-trade-war-global-reallocations
topicv3: Agriculture and Food Security m1326205 435,Transport m1326661 135,Trade m1326924 698,Political Violence and War m1327310 2462,Iron m1503514 2931
publishtoextweb_dt: 2022-01-06T00:00:00Z
dois: 10.1596/1813-9450-9894
historic_topic: International Economics and Trade,Conflict and Development,Transport,Energy,Agriculture
origu: DECRG: Trade & Intl. Integration (DECTI)
no_of_pages: 30
author_keys: 0: author_key: 1611801
1: author_key: 1513476
2: author_key: NA
3: author_key: 744856
4: author_key: 1155075
model_extractions: Policy Research Working Paper 9894 The US-China Trade War and Global Reallocations _Pablo Fajgelbaum Pinelopi Goldberg Patrick Kennedy Amit Khandelwal Daria Taglioni_ Development Economics Development Research Group January 2022
Policy Research Working Paper 9894

# **Abstract**

How did the US-China trade war affect global trade? Surprisingly, exports of products taxed by US or China increased from “bystander” countries to the rest of world (excluding US and China). Hence, the trade war created trade opportunities rather than simply shifting trade across destinations. There was large cross-country variation in export growth of tariff-exposed products, explained mostly by country-specific components of tariff elasticities rather than by specialization patterns. Through a standard trade model, the signs of the tariff elasticities identify if a country complements or substitutes the US or China, and the slope of its supply curve. Countries that operate along downward-sloping supplies whose exports substitute (complement) US and China are among the larger (smaller) beneficiaries of the trade war.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at pfajgelb@princeton.edu, penny.goldberg@yale.edu, patrick.kennedy@berkeley.edu, ak2796@columbia.edu, and dtaglioni@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **The US-China Trade War and Global Reallocations**<sup>*</sup>

Pablo Fajgelbaum Pinelopi Goldberg Patrick Kennedy UCLA and NBER Yale and NBER Berkeley Amit Khandelwal Daria Taglioni Yale and NBER World Bank Originally published in the Policy Research Working Paper Series on _January 2022._ This version is updated on _February 2023._ To obtain the originally published version, please email prwp@worldbank.org.

> *Maximilian Schwarz provided excellent research assistance. E-mail: pfajgelbaum@ucla.edu, penny.goldberg@yale.edu, patrick.kennedy@berkeley.edu, amit.khandelwal@yale.edu, dtaglioni@worldbank.org. We thank Veronica Rappaport and Irene Brambilla for their conference discussions of the paper; Juan Carlos Hallak and Ahmad Lashkaripour for helpful comments; and seminar participants at Australasian Meeting of the Econometric Society, ERWIT, Bank of Portugal, Barcelona Summer Workshop, CEU Vienna, China Meeting of Econometric Society, Federal Reserve Board, HKU, Harvard/MIT, Indiana, LACEA/LAMES, LACEA TIGN, NBER ITI, Penn State, Princeton, Purdue, SMU, Tsinghua, World Bank, and UCSD for comments.
# **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.

1
Our main estimation allows for this flexibility. Aggregating the predicted product-level export responses using pre-trade war export shares, we obtain, for each country, the predicted export growth in targeted products compared to non-targeted ones.

This flexible specification reveals a second takeaway: there is substantial cross-country heterogeneity in export growth in targeted products compared to non-targeted products. Moreover, this heterogeneity is largely driven by countries’ export responses to the rest of world. Some countries such as Vietnam, Thailand, Korea, and Mexico were among the largest export “winners”, in the sense that they better exploited trade opportunities in product markets with declining US or Chinese participation. The average export growth in taxed products across countries is 6.7% with a standard deviation across countries of 6.3% (compared to a standard deviation of just 1.3% implied by a specification with homogeneous tariff elasticities).

These cross-country differences in export growth in targeted products result from i) tariff elasticities that differ by country; and ii) tariff elasticities that differ by sector and size of the trade flow, combined with pre-war specialization patterns across products. Our third key takeaway is that the country-specific component explains the bulk – 82.8% – of the cross-country variation in export growth in targeted products. The combination of pre-war specialization and size-dependent or sector-specific tariff elasticities explains the remaining variation.

Having isolated the country-specific component as the key driver of heterogeneous export growth, we exploit our theoretical proposition to identify supply- and demand- channels. We find a subset of countries where the pattern of country-specific components across destinations suggests downward-sloping supplies. Moreover, many countries responded as complements to US and Chinese production, while others responded as substitutes. Importantly, the interaction of demand and supply heterogeneity in the elasticities matters: due to different patterns of demand substitution, countries operating along downward-sloping supplies can be found among those with the strongest and the weakest export growth. For example, Mexico, Thailand, Colombia, and Ukraine operate along downward sloping supplies; however, the former two are strong beneficiaries of the war because, as revealed by our estimates, they export products that substitute China in the US, while the latter are not because their products complement US or Chinese exports.

Our first result–that the average country increases global exports in products taxed by US or China–suggests an interdependency across export destinations. We rationalize this finding through downward-sloping supply curves at the product level. Morales, Sheu, and Zahler (2019) and Alfaro, Castro-Vincenzi, Fanelli, and Morales (2023) provide firm-level evidence consistent with complementarities via trade costs, such that exporting to a destination lowers the costs of exporting to similar destinations. Almunia, Antràs, Lopez Rodriguez, and Morales (2018) show that Spanish firms export more when the domestic market shrinks. Mau (2017) and Albornoz, Brambilla, and Ornelas (2021) show third-market effects after tariff reforms faced by Chinese and Argentinean firms, respectively. The result is also consistent with reallocations of supply chains. Flaaen et al. (2020) show that, for washing machines, product-specific capital migrates from China to other countries serving as export platform to the US. Our result suggests that export platforms 2
also increase exports to the rest of the world.

Our subsequent results –substantial cross-country heterogeneity in export growth consistent with country-specific demand and supply elasticities– is surprising given that trade or scale elasticities are typically assumed to vary across sectors rather than across countries. On the demand side, standard gravity models such as Anderson and Van Wincoop (2003) and Eaton and Kortum (2002), and multi-sector models such as Costinot, Donaldson, and Komunjer (2012) or Caliendo and Parro (2015), impose elasticities of substitution between imports from different origins that may be sector-specific but common across country-pairs, with typical estimates revealing substitution greater than one. In contrast, our trade-war responses are consistent with exporter-specific substitution elasticities with US or China that may be above or below one. Therefore, the results are broadly consistent with trade frameworks adopting flexible substitution patterns, such as Adao, Costinot, and Donaldson (2017) and Lind and Ramondo (2018).<sup>3</sup> On the supply side, identifying scale economies has been a focus of empirical research; see Antweiler and Trefler (2002) and, more recently, Costinot, Donaldson, Kyle, and Williams (2019).<sup>4</sup> In standard applications, these scale elasticities vary by sector but not across countries, providing a rationale for industrial policies (Bartelme, Costinot, Donaldson, and Rodriguez-Clare, 2019; Lashkaripour and Lugovskyy, 2022).<sup>5</sup> We show that, in addition, a country-specific and often downward-sloping component of supply curves plays an important role, providing an additional basis for potentially country-varying optimal subsidies. Computing these subsidies would require the exact parameters values and modeling additional general-equilibrium aspects. These steps would be interesting for future research but lie outside our scope of analysis.

# **2 Framework**

This section presents the framework that guides the empirical analysis.

## **2.1 Environment**

**Demand** There is a set _I_ of countries (indexed by _i_ for exporters and _n_ for importers) and a set Ω<sup>_j_</sup> of products (indexed by _ω_ ) in sector _j_ = 1, ..., _J_ . Each product _ω_ , in turn, is differentiated by origin _i_ ; a variety is _iω_ . We let _piω_ be the price received by competitive producers of product _ω_

> 3Our empirical results are not inconsistent with general-equilibrium responses under particular input-output structures. For example, increasing exports to the rest of the world could reflect supply chains of some HS6 products becoming more dispersed across countries, as long as product-level input-output matrixes are heavy on the diagonal. Reyes-Heroles et al. (2020) shows that a trade framework with capital accumulation and input-output linkages predicts heterogeneous impacts of trade barriers across countries and sectors depending on factor intensities.

> 4Like Costinot et al. (2019), we do not quantitatively pin down the scale parameters, but rather propose a signs test for whether supplies are downward sloping. They show that the elasticities of exports to domestic and foreign demand reveal the slope of supply relative to the own-price demand elasticity. We show that the elasticity of exports to the country imposing a tariff and to the rest of the world identify the slope signs of supply and of the cross-price demand elasticity with respect to the country imposing tariffs.

> 5Other recent estimates of sector-specific supply elasticities with scale economies using a variety of approaches include Farrokhi and Soderbery (2020), and Breinlich et al. (2021).

3
in country _i_ . In each country, imported and domestic varieties are aggregated, through a translog aggregator, into a non-traded good used either as input or for consumption. Hence, in destination _n_ , the share of (tariff-inclusive) spending in product _ω ∈_ Ω<sup>_j_</sup> imported from origin _i_ is: where _p_<sup>_n_</sup> _iω_<sup>is the tariff-inclusive price in country</sup><sup>_n_.</sup> The parameter _a_<sup>_n_</sup> _iω_<sup>capturesanidiosyncraticdemandofcountry</sup><sup>_n_forthevariety</sup><sup>_iω_.The</sup> semi-elasticities _σi_<sup>_j′_</sup> _i_<sup>arecommonacrossimportingcountriesandcapturethesubstitutability</sup> between products from _i_ and _i_<sup>_′_</sup> . When _σi_<sup>_j′_</sup> _i_<sup>_>_0(</sup><sup>_σ_</sup> _i_<sup>_j′_</sup> _i_<sup>_<_0),varieties</sup><sup>_i_and</sup><sup>_i′_=</sup><sup>_i_aresubstitutes</sup> (complements) within sector _j_ , in the sense that an increase in the price of goods from _i_ leads to increase (reduction) in the expenditure share (and quantity) purchased in goods from _i_<sup>_′_</sup> .<sup>6</sup> As we will only observe tariff variation imposed by US or China, we impose a common substitution elasticities within the sector: _σii_<sup>_j′_=</sup><sup>_σ_</sup> _RW_<sup>_j_for</sup><sup>_i′_=</sup><sup>_i_and</sup><sup>_i_,</sup><sup>_i′_=</sup><sup>_US_,</sup><sup>_CH_.</sup> A key feature of this demand system is that Chinese and American goods command country-specific substitution patterns. Goods from a given exporter _i_ can substitute Chinese goods and complement American goods ( _σi_ , _CH >_ 0 and _σi_ , _US <_ 0); while the opposite may be true for goods from another exporter.<sup>7</sup>

**Supply** Due to trade costs, _τiω_<sup>_n_unitsofvariety</sup><sup>_iω_mustbeshippedto</sup><sup>_n_foroneunittoarrive.</sup> Also, country _n_ imposes ad-valorem tariffs _t_<sup>_n_</sup> _iω_<sup>on imports of good</sup><sup>_ω_from</sup><sup>_i_.Letting</sup><sup>_piω≡pi_</sup> _iω_<sup>be</sup> the domestic price of variety _i_ and assuming competitive pricing, the tariff-inclusive prices faced by consumers in country _n_ are

where _Tiω_<sup>_n≡_1 +</sup><sup>_tn_</sup> _iω_<sup>is one plus the ad-valorem tariff.Total sales of</sup><sup>_ω_in sector</sup><sup>_j_from country</sup><sup>_i_are:</sup> where _b_<sup>_j_</sup> _i_<sup>the inverse supply elasticity defined as the elasticity of price of total sales and</sup><sup>_piω_be the</sup> domestic price of variety _i_ . The supply shifters are partitioned into an endogenous country-sector component _Aij_ and an exogenous cost shifter _Ziω_ . The former captures factor and input prices common across products within a sector. Changes in these costs due to tariffs are absorbed by fixed effects in our estimation. The supply curve is potentially downward sloping ( _b_<sup>_j_</sup> _i_<sup>_<_0);Appendix</sup> B.1 shows a standard micro-foundation where _b_<sup>_j_</sup> _i_<sup>combinesreturnstoscaleandanelasticityof</sup> factor mobility across products and sectors.<sup>8</sup>

> 6The elasticity of quantity to price is<sup>_σ_</sup> _s_<sup>_<u>n</u>_</sup> _iωi′i_<sup>.</sup> Additivity and symmetry of the substitution matrix require that ∑<sup>_N_</sup> _i_ =1<sup>_an_</sup> _iω_<sup>= 1 for all</sup><sup>_n_and</sup><sup>_ω_, as well as</sup><sup>_σ_</sup> _i_<sup>_j′_</sup> _i_<sup>=</sup><sup>_σ_</sup> _ii_<sup>_j′_for all</sup><sup>_i_,</sup><sup>_i′_,</sup><sup>_j_and ∑</sup><sup>_i′∈Iσ_</sup> _ii_<sup>_j′_= 0 for all</sup><sup>_i_,</sup><sup>_j_.</sup> 7 Most studies using a translog or almost-ideal demand system assume symmetric substitution elasticities (e.g., Novy 2012, Kee et al. 2008, Fajgelbaum and Khandelwal 2016, and Feenstra and Weinstein 2017).

> 8Other microfoundations include increasing returns with monopolistic competition as in Krugman (1980), reorganization (Caliendo and Rossi-Hansberg, 2012) or division of labor (Chaney and Ossa, 2013). The micro-foundation for factor mobility is standard (e.g., see Burstein et al. 2019 or Galle et al. (2023)).

4
**Equilibrium** The price of variety _iω_ in importer _n_ is _p_<sup>_n_</sup> _iω_<sup>=(1 +</sup><sup>_τ n_</sup> _iω_<sup>)</sup><sup>_tn_</sup> _iω_<sup>_piω_,where</sup><sup>_τ n_</sup> _iω_<sup>isthe</sup> ad-valorem tariff and _t_<sup>_n_</sup> _iω_<sup>isthetradecost.Aworldequilibriumisgivenbyprices</sup><sup>_{piω}_such</sup> that markets clear; i.e., the aggregate sales _Xiω_ given by (3) must equal aggregate expenditures:

where _Eω_<sup>_n_are country-</sup><sup>_n_expenditures in product</sup><sup>_ω_.</sup> To complete the description of a fully-specified general equilibrium model, we would to determine the country-sector supply shifters _Aij_ and the product-sector demand shifters _Eω_<sup>_n_.</sup> However, we do not impose additional restrictions for the empirical analysis. The empirical specifications control for importer-exporter-sector fixed effects and for model-implied measures of the size of the trade flows. As a result, our analysis is consistent with a range of assumptions about internal and international factor reallocation.

# **2.2 Impact of US-China Tariffs on Bystanders’ Exports**

The following proposition summarizes how tariff changes imposed by the US or China impact exports to each destination:

**Proposition 1.** _Around an arbitrary initial equilibrium, to a first order approximation, exports Xiω_<sup>_nof_</sup> _product ω from exporter i to importer n change according to:_<sup>9</sup>

_where, letting Eω ≡_ ∑ _n′ Eω_<sup>_n′be world expenditures in product ω,_</sup> _β_ 2<sup>_n_</sup> _iω_<sup>_to β_</sup> 6<sup>_n_</sup> _iω_<sup>_are given by_(B.33)</sup><sup>_-_(B.37)</sup><sup>_in the Appendix,_</sup> Each _βkiω_<sup>_n_in(5)isthetariffelasticityofexportsofvariety</sup><sup>_iω_toimporter</sup><sup>_n_,givenaggregates</sup> that enter in the last term, _ηiω_<sup>_n_.Theseaggregatesinclude:expenditurechangesbyimporterand</sup> product, cost changes by exporter and sector, and the average prices of competing varieties. In the empirical analysis we implement equation (5) to estimate the _β_ ’s using across-product variation in export responses. We include all the terms suggested by (5), but our focus is on the first two coefficients, _β_ 1<sup>_n_</sup> _iω_<sup>and</sup><sup>_β_</sup> 2<sup>_n_</sup> _iω_<sup>, showing the response of exports from country</sup><sup>_i_to each destination</sup> as a function of the tariffs set by the US and China on each other. Equation (6) shows the expression for _β_ 1<sup>_n_</sup> _iω_<sup>, the elasticity of variety</sup><sup>_iω_exports to destination</sup><sup>_n_in response to US tariffs (with a similar</sup>

> 9∆ ln ( _Y_ ) _≡_ ln <u>�</u> _Y_<sup>_′_</sup><sup><u>�</u></sup> _−_ ln ( _Y_ ) is the log-difference in _Y_ after the change in tariffs.

5
expression for _β_ 2<sup>_n_</sup> _iω_<sup>,correspondingtoChinesetariffs,in(B.33)).Thetariffelasticitiesmayvary</sup> by exporter and sector due to heterogeneity in substitution elasticities _σCHi_<sup>_j_orintheproductof</sup> the scale and own-demand elasticities, _b_<sup>_j_</sup> _i_<sup>_σ_</sup> _ii_<sup>_j_.Duetosizedependence,thetariffelasticityisalso</sup> _variety-specific_ (decreasing with the export flow’s size and increasing with the size of US or China as buyers of the taxed product).

Naturally, higher substitution or scale elasticities imply stronger responses. The next proposition shows that the tariff elasticities of variety _iω_ to the US and to the rest of the world (RW) jointly identify the signs of _σCHi_<sup>_j_and</sup><sup>_b_</sup> _i_<sup>_jσ_</sup> _ii_<sup>_j_.</sup>

**Proposition 2.** _When the US imposes a tariff on China in product ω, then:_

- _(i) if σCHi_<sup>_j>_0</sup><sup>_(σ_</sup> _CHi_<sup>_j<_0</sup><sup>_),exportsfromitotheUSincrease(decrease)iff_</sup> _Xbiω_<sup>_j_</sup> _<u>i</u>_<sup>_σ_</sup> / _<u>ii</u>_<sup>_j_</sup> _Eω_<sup>_∈_(</sup><sup>_−∞_, 1]</sup><sup>_∪_</sup> <u>1</u>

- [ 1 _−Eω_<sup>_US_</sup> / _Eω_<sup>,</sup><sup>_∞_)</sup><sup>_; and_</sup> _(ii) assuming σii_<sup>_j<_0</sup><sup>_:if σ_</sup> _CHi_<sup>_j>_0</sup><sup>_and exports increase (decrease) from i to the rest of the world, then_</sup>

- _b_<sup>_j_</sup> _i_<sup>_<_0</sup> _b_<sup>_j_</sup> _i_<sup>_>_0</sup> _; while if σCHi_<sup>_j<_0</sup><sup>_andexportsincrease(decrease)fromitotherestoftheworld,then_</sup> � �

- _b_<sup>_j_</sup> _b_<sup>_j_</sup> _. i_<sup>_>_0</sup> _i_<sup>_<_0</sup> � �

The proposition implies that, when the US taxes China, the responses of a bystander’s exports to the US and to the RW reveal both the sign of the substitutability between that country’s products and Chinese varieties _and_ the sign of the supply curve slope. Table 1 shows the possible cases. A downward-sloping supply ( _b_<sup>_j_</sup> _i_<sup>_<_0) is consistent with observing export responses with equal sign</sup> to both the US and the rest of the world. Conversely, upward-sloping supply ( _b_<sup>_j_</sup> _i_<sup>_<_0) is consistent</sup> with observing export responses with opposite sign to the two destinations. While the proposition describes the results using a US tariff on Chinese products, the same logic applies for Chinese tariffs on US imports.

For example, consider the China-substitutes case on the right column. As implied by part (i) of the proposition, this column corresponds to estimating _β_ 1<sup>_US_</sup> _iω_<sup>_>_0(anincreaseinvariety</sup><sup>_iω_</sup> exports to US in response to the US tariff on China).<sup>10</sup> As implied by part (ii), given negatively sloped demand, further estimating an increase in exports to countries other than US ( _β_ 1<sup>_RW_</sup> _iω >_ 0) reveals a downward-sloping supply ( _b_<sup>_j_</sup> _i_<sup>_<_0).Inthiscase,thegaininscaleduetoincreased</sup> US demand leads to an increase in exports to the rest of the world.<sup>11</sup> Conversely, on the right column, a reduction in exports to RW would be consistent with upward-sloping supply, so that higher demand in one destination reallocates sales away from other. By this logic, in the China-complements case of the first column, the downward-sloping supply is revealed by a reduction in exports to RW.

> 10Part (i) holds for a range of values of the parameters, and it is guaranteed to hold as the number of countries grows large or if the US does not command a very large share of the global market of product _ω_ .

> 11 _j_ As shown in Proposition 2 (ii), this statement holds assuming _σii_<sup>_<_0.Otherwise,anincreaseinexportswould</sup> reveal a pathological case where inverse demand is positively sloped, and even more so than a positively sloped supply.

6
# **3 Data and Summary Statistics**

We use UN Comtrade data that record bilateral exports in 5203 HS6 products. We aggregate into biennial (24-month) intervals (2014/2015; 2016/17; 2018/19), and refer to each 24-month period by its ending year. We restrict our sample to the top 50 exporting countries, excluding oil exporters. The resulting sample covers 95.9% of global trade (or 70.5% excluding US and China). We analyze exports from each of these countries to three destinations: the United States ( _US_ ), China ( _CH_ ), and the aggregate of all destinations except the US and China ( _RW_ ). We classify products into nine sectors: agriculture, apparel, chemicals, materials, machinery, metals, minerals, transport, and miscellaneous. Figure A.1 reports countries’ export shares by sector prior to the trade war.

We consider four sets of tariff changes as part of the US-China trade war: i) imposed by the US on China (the “US tariffs”), denoted as _TCH_<sup>_US_</sup> , _ω_<sup>, where</sup><sup>_ω_denotes an HS6 product code; ii) imposed</sup> by China on the US, _TUS_<sup>_CH_</sup> , _ω_<sup>(the “China tariffs”); iii) imposed by the US on each country</sup><sup>_i_other than</sup> China, _Ti_<sup>_US_</sup> , _ω_<sup>(e.g.,steeltariffsonMexico);andiv)most-favored-nation(MFN)tariffsimposedby</sup> China on all countries but the US, _Ti_<sup>_CH_</sup> , _ω_<sup>.Bown et al. (2019) argue that China’s MFN tariff cuts were</sup> likely influenced by the trade war with the US, so we include them in our analysis. The first three sets of tariffs are taken from Fajgelbaum et al. (2020) and extended through the end of 2019, and the last set is from Bown et al. (2019). We scale tariff changes in proportion to their duration within each 24-month interval. This scaling generates variation in tariff changes across products due to both the timing and magnitude of rate changes.

Figure A.2 illustrates the tariff variation. The US substantially raised tariffs on China, but except for two sectors (machinery and metals) it did not significantly raise tariffs on other partners. Panel B shows that China’s tariffs increased across all sectors on the US and decreased for non-US partners. For both the US and China, we observe substantial variation within sectors.

# **4 Average Export Responses**

Figure 1 presents binscatters that examine the exports of the 48 bystander countries to _US_ , _CH_ , and _RW_ against the US-China tariffs. Panel A shows the binscatter of exports to the US against the US tariffs: ∆ ln _Xiω_<sup>_US_</sup> = _α_ + _β_ ∆ ln _TCH_<sup>_US_+</sup><sup>_ε_</sup> _i_<sup>_US_</sup> . Panel B shows exports to China against the Chinese tariffs: ∆ ln _Xiω_<sup>_CH_</sup> = _α_ + _β_ ∆ ln _TUS_<sup>_CH_+</sup><sup>_ε_</sup> _i_<sup>_CH_</sup> . Panels C and D report exports to _RW_ against the US and China tariffs, respectively.<sup>12</sup> Panel A reveals that, on average, bystanders increased exports to the US in products with high US tariffs on China, with an elasticity of 0.31 (se 0.10). This growth rate is statistically distinct from the pre-war export growth rate from 2015 to 2017 (elasticity -0.19 and se -0.19). Panel B shows that, on average, countries did not reallocate exports into China in response to China’s tariffs on the US. Panels C and D show that exports to _RW_ increased with both tariffs, with an elasticity of 0.20 (se 0.08) for the US tariffs (Panel C), and of 0.29 (se 0.08) for the China tariffs (Panel D).

> 12Each binscatter includes exports from every country in our dataset, except for US and China. Figure A.3 confirms, as others have found, that the Chinese tariffs reduced US exports to China, and vice versa.

7
These results suggest that the trade war created net trade opportunities on average rather than merely prompting reallocations: joint exports to US and China in tariff-exposed products increased, and so did exports to the rest of the world. However, this average response masks large heterogeneity across countries. For example, the average country is revealed to neither complement nor substitute China, but this null average response may hide that some countries substitute and others complement China. We examine heterogeneity next.<sup>13</sup>

# **5 Heterogeneous Tariff Responses**

To explore heterogeneity in tariff elasticities, we implement a specification motivated by (5). We now discuss a few aspects of the implementation.

First, the tariff elasticities _βziω_<sup>_n_in (5) vary by importer,exporter,and measures of variety size.</sup> We flexibly capture this dependence by imposing: where _SIZEziω_ is a set of theory-driven set of observables that determine the tariff elasticity.<sup>14</sup> So, for each of the 4 tariffs ( _z_ = 1, .., 4), variation in tariff elasticities across exporters _i_ is captured by _βzi_<sup>_n_;variationacrosssectors</sup><sup>_j_iscapturedby</sup><sup>_β_</sup> _zj_<sup>_n_</sup> ( _ω_ )<sup>(where</sup><sup>_j_(</sup><sup>_ω_)isthesectorofproduct</sup><sup>_ω_);and</sup> variation across varieties is driven by _SIZEziω_ .

Second, the regressions include exporter-sector-destination fixed effects ( _αij_<sup>_n_)anddirect</sup> controls for size, _SIZEziω_ , to control for _ηiω_<sup>_n_defined in (7).15</sup> Third, we set _β_ 5<sup>_n_</sup> _i_<sup>and</sup><sup>_β_</sup> 6<sup>_n_</sup> _i_<sup>inequation(5)tozero.</sup> While theoretically justified, the tariff summation terms that identify these coefficients are highly correlated with the underlying bilateral tariffs from which they are constructed.<sup>16</sup> The identifying assumption underlying this empirical strategy is that, within country-sectors, potential export growth across products would have been the same in the absence of the trade war tariffs. We assess the plausibility of this parallel trends assumption by testing for differential trends in export growth in the years prior to the trade war. Figure 1 shows that bystander countries’ pre-war export growth is largely uncorrelated with the future changes in tariffs. To further mitigate

> 13Figure A.4 shows that the patterns, including the sharp response to RW, are robust to controlling for country-by-sector fixed effects. We also find that the patterns are robust to including all four tariffs and lagged export growth.

> 14For _β_ 1 _nω_<sup>,condition(6)fromProposition1indicatesthatthese(pre-war)variablesare:</sup> _EEω_<sup>_US_</sup> _ω_ (the share US _ω_ expenditures in global expenditures in product), and _s_<sup>_n_</sup> _iω_<sup>(the share of variety</sup><sup>_iω_in destination</sup> _ω_<sup>_n_</sup> ),<sup>expenditures).</sup><sup>_<u>X</u>_</sup> _E_<sup>_<u>iω</u>_</sup> _ω_<sup>(the share of exporterConditions (</sup><sup>_i_B.33 sales in global expenditures in product) to (B.37) in the Appendix show the</sup> corresponding variables for the remaining regressions. We proxy global expenditures with global imports.

> 15Conditional on the importer, exporter, and sector fixed effects, _ηiωn_<sup>vanishesassumingi)weaksubstitutionacross</sup> from RW ( _σRW →_ 0); ii) small differences in US and Chinese price changes within sector( ˆ _piω ≈ p_ ˆ _iω′_ for _ω_ , _ω_<sup>_′_</sup> _∈_ Ω<sup>_j_</sup> for _i_ = _CH_ , _US_ ); and iii) Cobb-Douglas preferences across products.

> 16This is because China changed tariffs on an MFN basis to third countries, so the ∑ _i′_ = _CH_ , _US_ , _i_ ∆ ln _Ti CH_<sup>_′_</sup> , _ω_<sup>termis</sup> ∆ ln _Ti_<sup>_CH_</sup> , _ω_ times the number of exporters (excluding US, China, and exporter _i_ ) in product _ω_ . The correlation between US changed tariff rates on third countries, it often did so by a similar amount across trade partners.∑ _i′_ = _CH_ , _US_ , _i_ ∆ ln _Ti_<sup>_CH′_</sup> , _ω_<sup>and∆ln</sup><sup>_T_</sup> _i_<sup>_CH_</sup> , _ω_ is 0.997. A similar issue arises for the corresponding US term because when the

8
concerns of pre-existing trends, we include lagged export growth.

The resulting specification is run separately to each destination, _n_ = _US_ , _CH_ , _RW_ : where _λ_<sup>_n_</sup> _iω_<sup>istheshareofvariety</sup><sup>_iω_tocountry</sup><sup>_n_intotalexportsofcountry</sup><sup>_i_.The</sup><sup>_λn_</sup> _iω_<sup>sharesare</sup> defined as the (pre-war) export values for continuing products divided by total country exports.

# **5.1 Heterogeneous Export Growth in Targeted Products**

The analysis reveals two key takeaways: i) substantial cross-country heterogeneity in export growth in targeted products compared to non-targeted products; and ii) a central role for the country-specific component of the tariff elasticities, rather than any other component, in explaining of this heterogeneity.

Figure 2 plots the export growth defined in (10) across countries.<sup>17</sup> By export growth, we specifically mean the growth of products taxed by US or China relative to other products within each exporter, importer, and sector. Hence, the figure indicates the countries that better exploited global export opportunities in products targeted by the trade-war tariffs.

On average, countries’ exports in targeted products increase by 6.7%, with a standard deviation just as large at 6.3%. For example, the increases in exports of targeted relative to untargeted products in Thailand and Mexico are 14.5% (se 4.9%) and 10.9% (se 6.4%), respectively, while Ukraine’s exports fall 12.1% (se 8.7%) and Canada’s export growth is just 2.1% (se 5.4%).<sup>18</sup> Through the lens of our model, the heterogeneity is expected. By construction of (10), it may be due to the country-specific demand or supply parameters, or due to differences in specialization across products with different tariff changes or with different supply elasticities elasticities. We find that the bulk of the cross-country variation in Figure 2 comes from the country-specific component of the tariff elasticities (the _βzi_<sup>_n_in (8)), and not from specialization (</sup><sup>_λn_</sup> _iω_<sup>), sectoral tariff</sup> elasticities ( _βzj_<sup>_n_</sup> ( _ω_ )<sup>), or size-specific tariff elasticities (Γ</sup> _z_<sup>_n_).</sup>

> 17We report bootstrapped confidence intervals for ∆ ln� _Xi_<sup>_W D_</sup> . We construct bootstrapped standard errors to each aggregate response by cluster bootstrapping specifications (9). We sample with replacement within products, estimate the specifications in (18We correlate ∆ ln�9 _X_ ), construct the aggregate predicted exports to the each estimation using ( _i_<sup>_W D_</sup> with _i_ ’s characteristics: size, distance to the US and China; the share of exports covered by10), and repeat 50 times. “deep” trade agreements (Mattoo et al., 2020); and 2017 FDI stock (Financial Times FDI Markets Database and Refinitiv). These descriptive relationships suggest that greater predicted exports for countries that are larger, further from the US, and with more exports covered by trade agreements. This is consistent with Alfaro et al. (2023), who find that trade agreements result in cross-country export complementarities for firms.

9
To see this, Figure 3 re-computes the export growth in (10) for different configurations of these components and plots each case against the case with full heterogeneity from Figure 2. First, assuming a homogenous tariff elasticity ( _β_<sup>�</sup> _ziω_<sup>_n_=</sup> _β_<sup>�</sup> _z_<sup>_n_</sup> in (9)), the variation only comes from _λ_<sup>_n_</sup> _iω_ pre-war specialization patterns. The grey series reveals virtually no variation across countries and the standard deviation is just 1.3%. Next, the red series re-computes export growth only allowing for sectoral heterogeneity: _β_<sup>�</sup> _ziω_<sup>_n_=</sup> _β_<sup>�</sup> _zj_<sup>_n_</sup> ( _ω_ )<sup>;the standard deviation is now 2.2%,and the correlation</sup> with the full heterogeneity case is just 0.50. Similarly, the green series next constructs predicted growth using only the estimated size component, _β_<sup>�</sup> _ziω_<sup>_n_=</sup> Γ<sup>�</sup><sup>_n_</sup> _z SIZEziω_ , which also yields a low correlation of -0.01 with the full heterogeneity benchmark. Finally, the blue series allows for just the country component, _β_<sup>�</sup> _ziω_<sup>_n_=</sup> _β_<sup>�</sup> _i_<sup>_n_. The standard deviation across countries’ response is now 5.5%,</sup> and the correlation with the benchmark rises to 0.95.

A formal decomposition of relative export growth into the three components reveals that country-specific responses explain 82.8% of the variation, while the sector and size component explains 17.3% and -0.2%, respectively.

The importance of the country-specific component of tariff elasticities, even after allowing the estimated elasticities to vary by sector and size of the trade flow, is surprising given that trade or scale elasticities are typically assumed to vary across sectors rather than across countries. We explore this point next.

# **5.2 Supply and Demand Forces**

Table 1 provides a taxonomy to understand the underlying demand and supply forces driving countries’ exports from the trade war. We construct an empirical analog to the table by aggregating the variety-level tariff elasticities to the country level: Panel A of Figure 4 shows the export elasticities to the US and RW in response to the US tariff ( _β_<sup>�</sup> 1<sup>_US_</sup> _i_<sup>, �</sup> _β_ 1<sup>_RW_</sup> _i_ ), revealing the substitutability/complementarity with Chinese varieties and the slope of supply curves. Panel B reports ( _β_<sup>�</sup> 2<sup>_CH_</sup> _i_<sup>, �</sup> _β_ 2<sup>_RW_</sup> _i_ ), revealing substitutability/complementarity with American varieties and upward/downward sloping supplies.

The figure shows that there is considerable variation across countries in the underlying supply 2. and demand forces that drive export responses in Figure To highlight a few examples, consider first the set of countries that lie in the same quadrant in both panels (highlighted in blue). Ukraine and Colombia lie in the SW quadrants, indicating that they exports varieties that complement Chinese and American varieties, and that their exports operate along downward sloping supply curves. These patterns provide a rationale for why Ukraine’s and Colombia’s global exports fell in response to the trade war, as illustrated in Figure 2: the tariffs reduced exports to the US and China (because they are complements); and because of the downward-sloped supply, the lower scale led exports to RW to decline. In contrast, Thailand, Taiwan, UK, Bulgaria and Finland are the 10
countries whose export responses lay in the NE quadrant of both panels. This reveals that their exports substitute for the US and China. As they operate on downward supplies, the expansion into the US and China led to expanding exports to RW, and to an increase in global exports of 2. targeted products, as confirmed by Figure For countries that lie in different quadrants of Panels A and B, it is not possible to immediately sign the direction of their global export changes since it depends on the importance of the US and Chinese destinations in their export basket. However, the figure does reveal the underlying forces to each market. Countries that lie in the NE and SW quadrants (in red) of both panels operate along downward supplies. Mexico, Malaysia, and the Czech Republic lie in the NE quadrant in Panel A and the SW quadrant of Panel B. These countries export varieties that substitute China and complement the US, and operate along downward supplies. The countries highlighted in green lie in the NE and SW quadrants of both panels, suggesting that they operate along upward supplies.

Finally, the grey countries flip the diagonal between panels. Their responses suggest a downward-sloping export supply in response to one tariff and an upward-sloping export supply to the other. Our model would require an additional source of heterogeneity to accommodate these cases. Supply elasticities operating at bilateral level, as in Lind and Ramondo (2018), or bilateral complementarities through trade costs, as in Alfaro et al. (2023), are possible explanations.

The downward sloping supplies could reflect that some countries identified the trade war early as an opportunity and invested in new plants, trade infrastructure, or facilitation, with these investments benefiting exports to all destinations. Or that some countries were already well integrated in the global trading system and could take advantage of the new exporting opportunities across multiple sectors. Our data do not allow us to measure these potential explanations, but we view this as an area for future research.

# **6 Conclusion**

The US-China trade war was seen as a major turning point in the globalization era. Our results do not support this view, at least for the time horizon we analyze: we find that several countries increased global exports in products with higher US-China tariffs, relative to non-taxed products.

We also find cross-country heterogeneity in this export growth in targeted products, and that a country-specific component of the tariff elasticities explains the bulk of the variation. Through the lens of a standard trade model, the export responses suggest negatively-sloped supply curves for several countries as well as differences across countries in terms of whether their exports substitute or complement China. These results contrast with trade models where trade or scale elasticities are typically assumed to vary across sectors rather than across countries.

While product-level global trade data can uncover broad reallocation patterns, firm-level data can unpack the factors driving the country-specific elasticities —whether they consist of increasing returns to scale, trade-war-induced investments in new plants, or participation in trade agreements. We anticipate further research on these mechanisms as the data becomes available.

11
# **References**

- Adao, R., A. Costinot, and D. Donaldson (2017). Nonparametric counterfactual predictions in neoclassical models of international trade. _American Economic Review 107_ (3), 633–89.

- Albornoz, F., I. Brambilla, and E. Ornelas (2021). Firm export responses to tariff hikes.

- Alfaro, A., J. Castro-Vincenzi, S. Fanelli, and E. Morales (2023). Firm export dynamics in interdependent markets.

- Almunia, M., P. Antràs, D. Lopez Rodriguez, and E. Morales (2018). Venting out: Exports during a domestic slump.

- Amiti, M., S. J. Redding, and D. E. Weinstein (2019). The impact of the 2018 tariffs on prices and welfare. _Journal of Economic Perspectives 33_ (4), 187–210.

- Anderson, J. E. and E. Van Wincoop (2003). Gravity with gravitas: A solution to the border puzzle. _The American Economic Review 93_ (1), 170–192.

- Antweiler, W. and D. Trefler (2002). Increasing returns and all that: A view from trade. _American Economic Review 92_ (1), 93–119.

- Bartelme, D. G., A. Costinot, D. Donaldson, and A. Rodriguez-Clare (2019). The textbook case for industrial policy: Theory meets data. Technical report, National Bureau of Economic Research.

- Bown, C., E. Jung, and E. Zhang (2019). Trump Has Gotten China to Lower Its Tariffs. Just Toward Everyone Else.

- Breinlich, H., E. Leromain, D. Novy, and T. Sampson (2021). Import liberalization as export destruction? evidence from the united states.

- Burstein, A., E. Morales, and J. Vogel (2019). Changes in between-group inequality: computers, occupations, and international trade. _American Economic Journal: Macroeconomics 11_ (2), 348–400.

- Caliendo, L. and F. Parro (2015). Estimates of the trade and welfare effects of nafta. _The Review of Economic Studies 82_ (1), 1–44.

- Caliendo, L. and E. Rossi-Hansberg (2012). The impact of trade on organization and productivity. _The quarterly journal of economics 127_ (3), 1393–1467.

- Cavallo, A., G. Gopinath, B. Neiman, and J. Tang (2021). Tariff pass-through at the border and at the store: Evidence from us trade policy. _American Economic Review: Insights 3_ (1), 19–34.

- Chaney, T. and R. Ossa (2013). Market size, division of labor, and firm productivity. _Journal of International Economics 90_ (1), 177–180.

- Costinot, A., D. Donaldson, and I. Komunjer (2012). What goods do countries trade? a quantitative exploration of ricardo’s ideas. _The Review of Economic Studies 79_ (2), 581–608.

- Costinot, A., D. Donaldson, M. Kyle, and H. Williams (2019). The more we die, the more we sell? a simple test of the home-market effect. _The quarterly journal of economics 134_ (2), 843–894.

- Eaton, J. and S. Kortum (2002). Technology, geography, and trade. _Econometrica 70_ (5), 1741–1779.

12
- Fajgelbaum, P. and A. K. Khandelwal (2021). The economic impacts of the us-china trade war. _Annual Review of Economics, Forthcoming_ .

- Fajgelbaum, P. D., P. K. Goldberg, P. J. Kennedy, and A. K. Khandelwal (2020). The return to protectionism. _The Quarterly Journal of Economics 135_ (1), 1–55.

- Fajgelbaum, P. D. and A. K. Khandelwal (2016). Measuring the unequal gains from trade. _The Quarterly Journal of Economics 131_ (3), 1113–1180.

- Farrokhi, F. and A. Soderbery (2020). Trade elasticities in general equilibrium.

- Feenstra, R. C. and D. E. Weinstein (2017). Globalization, markups, and us welfare. _Journal of Political Economy 125_ (4), 1040–1074.

- Flaaen, A., A. Hortaçsu, and F. Tintelnot (2020). The production relocation and price effects of us trade policy: the case of washing machines. _American Economic Review 110_ (7), 2103–27.

- Flaaen, A. and J. R. Pierce (2019). Disentangling the effects of the 2018-2019 tariffs on a globally connected us manufacturing sector.

- Galle, S., A. Rodríguez-Clare, and M. Yi (2023). Slicing the pie: Quantifying the aggregate and distributional effects of trade. _The Review of Economic Studies 90_ (1), 331–375.

- Kee, H. L., A. Nicita, and M. Olarreaga (2008). Import demand elasticities and trade distortions. _The Review of Economics and Statistics 90_ (4), 666–682.

- Krugman, P. (1980). Scale economies, product differentiation, and the pattern of trade. _The American Economic Review 70_ (5), 950–959.

- Lashkaripour, A. and V. Lugovskyy (2022). Profits, scale economies, and the gains from trade and industrial policy. Technical report, Center for Applied Economics and Policy Research, Department of Economics.

- Lind, N. and N. Ramondo (2018). Trade with correlation. Technical report, National Bureau of Economic Research.

- Mattoo, A., N. Rocha, and M. Ruta (2020). Handbook of deep trade agreements. _World Bank_ .

- Mau, K. (2017). Us policy spillover (?)–china accession to the wto and rising exports to the eu. _European Economic Review 98_ , 169–188.

- Morales, E., G. Sheu, and A. Zahler (2019). Extended gravity. _The Review of Economic Studies 86_ (6), 2668–2712.

- Novy, D. (2012). International trade without ces: Estimating translog gravity. _Journal of International Economics 89_ (2), 271–282.

- Reyes-Heroles, R., S. Traiberman, and E. Van Leemput (2020). Emerging markets and the new geography of trade: The effects of rising trade barriers. _IMF Economic Review 68_ , 456–508.

- Waugh, M. E. (2019). The consumption response to trade shocks: Evidence from the us-china trade war. Technical report, National Bureau of Economic Research.

13
**TABLE 1: PARAMETER REGIONS IMPLIED BY EXPORT RESPONSES TO US TARIFFS ON CHINA**

|||Country_i_’s Expor|t Response to US|
|---|---|---|---|
|||Decrease|Increase|
|Country_i_<sup>_′_</sup>_s_<br>Export|Increase|China Complement<br>Upward-Sloping Supply<br>_σCHi <_0;_bi >_0|China Substitute<br>Downward-Sloping Supply<br>_σCHi >_0;_bi <_0|
|Response||||
|to RW|Decrease|China Complement<br>Downward- Sloping Supply<br>_σCHi <_0;_bi <_0|China Substitute<br>Upward-Sloping Supply<br>_σCHi >_0;_bi >_0|

Notes: Table shows the parameter regions implied by the export response of country to the US and to the rest of the world (RW) when the US increases tariffs on China. A similar taxonomy applies for China’s tariffs on the US, in which case the responses would reveal substitutability with the US ( _σUSi_ instead of _σCHi_ ).

14
# **FIGURE 1: TRADE WAR TARIFFS AND EXPORT GROWTH**

<!-- Start of picture text --> Panel A Panel B<br>Bystanders' Export Value to US Bystanders' Export Value to China<br>2015-17 2017-19 2015-17 2017-19<br>.2 .3<br>.2<br>.1<br>.1<br>0<br>0<br>-.1 -.1<br>0 .05 .1 .15 .2 0 .05 .1 .15 .2<br>∆ ln T(US,CH) ∆ ln T(CH,US)<br>Pre-period: β =-0.19 (0.10). Post-period: β =0.31 (0.10). Pre-period: β =0.07 (0.18). Post-period: β =0.01 (0.19).<br>Panel C Panel D<br>Bystanders' Export Value to RW Bystanders' Export Value to RW<br>2015-17 2017-19 2015-17 2017-19<br>.2 .2<br>.1 .1<br>0 0<br>-.1 -.1<br>-.2 -.2<br>0 .05 .1 .15 .2 0 .1 .2 .3<br>∆ ln T(US,CH) ∆ ln T(CH,US)<br>Pre-period: β =-0.14 (0.08). Post-period: β =0.20 (0.08). Pre-period: β =0.11 (0.08). Post-period: β =0.29 (0.08).<br>ln X(i,US) ln X(i,CH)<br>∆ ∆<br>ln X(i,RW) ln X(i,RW)<br>∆ ∆<br><!-- End of picture text --> Notes: The panels show binscatter plots of bystanders’ export growth (on the y-axes) against changes in tariffs due to the trade war (on the x-axes). Panel A is the regression: ∆ ln _Xiω_<sup>_US_</sup> = _α_ + _β_ ∆ ln _TCH_<sup>_US_+</sup><sup>_ε_</sup> _iω_<sup>_US_.Panel B is the regression:</sup> ∆ ln _Xiω_<sup>_CH_</sup> = _α_ + _β_ ∆ ln _TUS_<sup>_CH_+</sup><sup>_ε_</sup> _iω_<sup>_CH_.PanelCistheregression:∆ln</sup><sup>_X_</sup> _iω_<sup>_RW_</sup> = _α_ + _β_ ∆ ln _TCH_<sup>_US_+</sup><sup>_ε_</sup> _iω_<sup>_RW_</sup> . Panel D is the regression: ∆ ln _Xiω_<sup>_RW_</sup> = _α_ + _β_ ∆ ln _TUS_<sup>_CH_+</sup><sup>_ε_</sup> _iω_<sup>_RW_</sup> . Also reported are regressions with exports prior to the trade war from 2015-17. Below each panel are OLS coefficients (standard errors clustered by product).

15
**FIGURE 2: RELATIVE EXPORT GROWTH IN TARGETED PRODUCTS ACROSS COUNTRIES**

<!-- Start of picture text --> .35<br>.3<br>.25<br>.2<br>.15<br>.1<br>.05<br>0<br>-.05<br>-.1<br>-.15<br>-.2<br>-.25<br>-.3<br>-.35<br>Log Change<br>UKR EGY ISR COL IRL DNK GRC POL CAN BRA SVN HKG ITA IND PER ARG ESP AUS BGD AUT BGR TWN BEL JPNMYS DEU PRT SWE NLD SGP CHE PHL HUN NZL CHL MEX IDN SVK ZAF GBR CZE FIN FRA KOR THA VNM TUR ROU<br><!-- End of picture text --> Notes: The figure plots changes in predicted exports to the world. Bootstrapped error bars denote 90% confidence intervals. These bands are constructed by implementing (9) on 50 bootstrap samples and calculating countries’ predicted exports from (10).

16
**FIGURE 3: DECOMPOSING RELATIVE EXPORTS BY HETEROGENOUS RESPONSE TYPE**

<!-- Start of picture text --> Homogenous Response Sector Component Only Size Component Only Country Component Only<br>.3<br>.2<br>.1<br>0<br>-.1<br>-.1 0 .1 .2 .3<br>∆ X(i), Full Heterogeneity<br>(ziw)<br>∆β<br> X(i), Alternative Configurations of<br>∆<br><!-- End of picture text --> Notes: Figure reports alternative predicted exports to _WD_ from (10) derived under alternative configurations of the tariff responses. The first series (grey) constructs predicted exports assuming a homogenous response to the tariffs across countries. The next three series emphasize each of the three components of the full heterogenous response: sectoral ( _β_<sup>�</sup> _ziω_<sup>_n_=</sup> _β_<sup>�</sup> _zj_<sup>_n_</sup> ( _ω_ )<sup>), size (</sup> _β_<sup>�</sup> _ziω_<sup>_n_=</sup> Γ<sup>�</sup><sup>_n_</sup> _z SIZEziω_ ), and country ( _β_<sup>�</sup> _ziω_<sup>_n_=</sup> _β_<sup>�</sup> _i_<sup>_n_).The 45-degree line (black) is the benchmark full</sup> heterogeneity series.
# **FIGURE 4: SUPPLY AND DEMAND FORCES**

<!-- Start of picture text -->
1.5<br>VNM<br>PHL<br>upward supply, CH complement downward supply, CH substitute<br>1 ROU<br>IND<br>CZE<br>.5 NZL ISR BEL BGRFRA TWN MEX MYS<br>ZAFGRC EGY PERPRTHUNNLD GBR ITAKORFIN<br>IDN DEU THA<br>JPN<br>HKG TUR SGP BRA POL<br>0<br>DNK<br>SWEIRL SVK CHE AUT<br>ESPCAN<br>COL<br>-.5<br>AUS<br>UKR SVN CHL BGD<br>ARG<br>-1<br>downward supply, CH complement upward supply, CH substitute<br>-1.5<br>-2 -1.5 -1 -.5 0 .5 1 1.5 2<br>β (US,1i)<br>1.5<br>TUR<br>upward supply, US complementVNM downward supply, US substituteTHA<br>1 ROU<br>IDN<br>PHL ZAF JPNKOR SGPCAN<br>ARG FIN<br>HUNSWE AUSGBR<br>PER AUT<br>.5<br>PRTNLD CHENZL<br>SVK<br>BGDFRA IRL SVN<br>DEU IND TWN BGRESP CHLHKG<br>0 CZE GRCDNK BEL<br>COL UKR MYSPOL ITA<br>BRA<br>-.5<br>MEX<br>-1 EGY<br>downward supply, US complement ISR upward supply, US substitute<br>-1.5<br>-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -.5 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5<br>β (CH,2i)<br>(RW,1i)<br>β<br>(RW,2i)<br>β<br><!-- End of picture text -->

Notes: The figure plots the tariff responses to the US-China tariffs, _β_<sup>�</sup> _iω_<sup>_n_=∑</sup> _ω_<sup>_λn_</sup> _Xiωβ_<sup>�</sup> _ziω_<sup>_n_using the taxonomy in Table 1.</sup> Panel A plots ( _β_<sup>�</sup> 1<sup>_US_</sup> _i_<sup>,</sup> _β_<sup>�</sup> 1<sup>_RW_</sup> _i_ ). Panel B plots ( _β_<sup>�</sup> 2<sup>_CH_</sup> _i_ , _β_<sup>�</sup> 2<sup>_RW_</sup> _i_ ). Countries noted in blue operate in the same quadrant in both figures. Countries in red operate along downward-sloping supplies in both figures. Countries in green operate along upward-sloping supplies in both figures.
# **A Appendix Figures and Tables**

## **FIGURE A.1: PRE-WAR EXPORT BASKETS**

<!-- Start of picture text --> Agriculture Apparel Chemicals Machinery Materials Metals Minerals Misc Transport<br>1<br>.8<br>.6<br>.4<br>.2<br>0<br>1<br>.8<br>.6<br>.4<br>.2<br>0<br>ARG AUS AUT BEL BGD BGR BRA CAN CHE CHL CHN COL CZE DEU DNK EGY ESP FIN FRA GBR GRC HKG HUN IDN IND<br>IND IRL ISR ITA JPN KOR MEX MYS NLD NZL PER PHL POL PRT ROU SGP SVK SVN SWE THA TUR TWN UKR USA VNM ZAF<br><!-- End of picture text --> Notes: Figure reports countries’ pre-war export shares by sector. Agriculture includes products in HS code chapters 1-24; Apparel includes chapters 41-43 and 50-67; Chemicals includes chapters 28-38; Machinery includes chapters 84-85; Materials includes chapters 39-40, 44-49, and 68-71; Metals includes chapters 72-83; Minerals includes chapters 25-27; Transport includes chapters 86-89; and Miscellaneous includes chapters 90-99.
# **FIGURE A.2: TARIFF CHANGES**

**Panel A: US Tariff Changes**

<!-- Start of picture text --> ∆ T(US,CH)<br>Agriculture ∆ T(US,i)<br>Apparel<br>Chemicals<br>Machinery<br>Materials<br>Metals<br>Minerals<br>Miscellaneous<br>Transport<br>-.3 -.2 -.1 0 .1 .2 .3<br>Panel B: China Tariff Changes<br>∆ T(CH,US)<br>Agriculture ∆ T(CH,i)<br>Apparel<br>Chemicals<br>Machinery<br>Materials<br>Metals<br>Minerals<br>Miscellaneous<br>Transport<br>-.3 -.2 -.1 0 .1 .2 .3<br><!-- End of picture text --> Notes: Figure reports the set of tariff changes imposed by the US (Panel A) and China (Panel B), by sector. The tariff changes are scaled by total time in effect over the two year window. For example, if the US raised tariffs on a product from China in September 2018 by 10%, the scaled tariff change over the two year window would be 6.66% = (16/24) _∗_ 10%. If the tariff of a product went up 25% in September 2019, the scaled tariff change would be 4.16% (= (4/24) _∗_ 25%). The black dots indicate the median tariff increase, the boxes denote the 25th and 75th percentiles, and whiskers show the 10th and 90th percentiles.
# **FIGURE A.3: TRADE WAR TARIFFS AND EXPORT CHANGES FOR USA AND CHN**

<!-- Start of picture text --> Panel A Panel B<br>China's Export Value to US US Export Value to China<br>2015-17 2017-19 2015-17 2017-19<br>.2 1<br>.5<br>0<br>0<br>-.2<br>-.5<br>-.4<br>-1<br>0 .05 .1 .15 .2 0 .05 .1 .15 .2<br>∆ ln T(US,CH) ∆ ln T(CH,US)<br>Pre-period: β =-0.12 (0.29). Post-period: β =-1.34 (0.27). Pre-period: β =1.87 (0.46). Post-period: β =-2.98 (0.42).<br>ln X(CH,US) ln X(US,CH)<br>∆ ∆<br><!-- End of picture text --> Notes: The panels show binscatter plots of USA and China’s export change (on the y-axes) against changes in tariffs due to the trade war (on the x-axes), Panel A is the regression: ∆ ln _XCHN_<sup>_US_</sup> , _ω_<sup>=</sup><sup>_α_+</sup><sup>_β_∆ln</sup><sup>_T_</sup> _CH_<sup>_US_+</sup><sup>_εUS_</sup> _CHN_ , _ω_<sup>.Panel B is the</sup> from 2015-17.regression: ∆ lnBelow each panel are OLS coefficients. _XUSA_<sup>_CH_</sup> , _ω_<sup>=</sup><sup>_α_+</sup><sup>_β_∆ln</sup><sup>_T_</sup> _US_<sup>_CH_+</sup><sup>_εCH_</sup> _USA_ , _ω_<sup>.Also reported are regressions with exports prior to the trade war</sup>
**FIGURE A.4: TRADE WAR TARIFFS AND EXPORT CHANGES, WITH FIXED EFFECTS**

<!-- Start of picture text --> Panel A Panel B<br>Bystanders' Export Value to US Bystanders' Export Value to China<br>2015-17 2017-19 2015-17 2017-19<br>.2 .3<br>.15 .2<br>.1 .1<br>.05 0<br>0 -.1<br>0 .05 .1 .15 .2 0 .05 .1 .15 .2<br>∆ ln T(US,CH) ∆ ln T(CH,US)<br>Pre-period: β =-0.12 (0.11). Post-period: β =0.20 (0.11). Pre-period: β =-0.01 (0.18). Post-period: β =-0.06 (0.20).<br>Panel C Panel D<br>Bystanders' Export Value to RW Bystanders' Export Value to RW<br>2015-17 2017-19 2015-17 2017-19<br>.1<br>.1<br>.05<br>.05<br>0<br>0<br>-.05<br>-.05<br>-.1<br>-.1<br>0 .05 .1 .15 .2 0 .05 .1 .15 .2<br>∆ ln T(US,CH) ∆ ln T(CH,US)<br>Pre-period: β =-0.00 (0.09). Post-period: β =0.15 (0.09). Pre-period: β =0.12 (0.08). Post-period: β =0.30 (0.08).<br>ln X(i,US) ln X(i,CH)<br>∆ ∆<br>ln X(i,RW) ln X(i,RW)<br>∆ ∆<br><!-- End of picture text --> Notes: The panels show binscatter plots of bystanders’ export growth (on the y-axes) against changes in tariffs due to the trade war (on the x-axes), controlling for country-by-sector fixed effects. Panel A is the regression: ∆ ln _Xiω_<sup>_US_</sup> = _αi_<sup>_US_</sup> , _j_ ( _ω_ )<sup>+</sup><sup>_β_∆ln</sup><sup>_T_</sup> _CH_<sup>_US_+</sup><sup>_ε_</sup> _iω_<sup>_US_. Panel B is the regression: ∆ln</sup><sup>_X_</sup> _iω_<sup>_CH_</sup> = _αi_<sup>_CH_</sup> , _j_ ( _ω_ )<sup>+</sup><sup>_β_∆ln</sup><sup>_T_</sup> _US_<sup>_CH_+</sup><sup>_ε_</sup> _iω_<sup>_CH_. Panel C is the regression:</sup> ∆ ln _Xiω_<sup>_RW_</sup> = _αi_<sup>_RW_</sup> , _j_ ( _ω_ )<sup>+</sup><sup>_β_∆ln</sup><sup>_T_</sup> _CH_<sup>_US_+</sup><sup>_ε_</sup> _iω_<sup>_RW_</sup> . Panel D is the regression: ∆ ln _Xiω_<sup>_RW_</sup> = _ααi_<sup>_RW_</sup> , _j_ ( _ω_ )<sup>+</sup><sup>_β_∆ln</sup><sup>_T_</sup> _US_<sup>_CH_+</sup><sup>_ε_</sup> _iω_<sup>_RW_</sup> . Also reported are regressions with exports prior to the trade war from 2015-17. Below each panel are OLS coefficients (standard errors clustered by product).
# **B Model Appendix**

## **B.1 Microfoundation of the Supply Side**

We present a microfoundation for the supply curve in (3). We assume that, in country _i_ and sector _j_ , a quantity _KTi_<sup>_j_of a bundle of inputs and primary factors is used to produce tradeable goods in</sup> sector _j_ This sector-specific input supply could be determined endogenously through domestic or international mobility or be taken as given under the assumption of no factor mobility; however, we do not need to take a stand for our empirical analysis.

This factor supply consists of a continuum of heterogeneous units, with each unit _k_ having productivity _ziω_<sup>0</sup><sup>_e_</sup> _ω_<sup>_k_.</sup> The term _ziω_<sup>0iscommontoallinputsin</sup><sup>_ω_.</sup> It depends on an exogenous country-product specific component of productivity _Ziω_ and, through scale economies, on the amount of inputs _Kiω_ allocated to the product: where _γi_<sup>_j_is a country-sector specific scale elasticity. In turn, the term</sup><sup>_e_</sup> _ω_<sup>_k_is specific to each unit with</sup> CDF from an iid Frechet distribution: where the parameter _ε_<sup>_j_</sup> _i_<sup>is also country-specific and determines factor mobility across products in</sup> response to changes in factor returns. Each unit of factors _k_ in sector _j_ chooses a product _ω_ in that sector and, conditional on the product, a bundle of intermediate inputs _x_ with sector-specific intensity _αj_<sup>_I_andunitcost</sup><sup>_cI_</sup> _ij_<sup>,to</sup> maximize its returns _πi_<sup>_k_:</sup> where _piω_ is the price received by producers of _ω_ in country _i_ . The input bundle used by each product combines output from other sectors. For our empirical analysis, we impose that _c_<sup>_I_</sup> _ijω_<sup>does</sup> not vary across products within a sector, but may vary across sectors. This corresponds to the standard assumption of sector-level input-output matrixes. Maximizing out inputs _x_ , the problem in (B.14) is equivalent to: _α_<sup>_I_</sup> _<u>j</u>_ where _ziω ≡_ � _c_<sup>_I_</sup> _ij_<sup>/</sup><sup>_α_</sup> _j_<sup>_I_</sup> � _α_<sup>_I_</sup> _j_<sup>_−_1</sup> _ziω_<sup>0capturesproductivityandinputcostsofproduct</sup><sup>_ω_.</sup> From the solution to (B.15), the supply of inputs to product _ω_ in sector _j_ of country _i_ is where _rTi_<sup>_j_aretheaveragefactorreturnsinsector</sup><sup>_j_ofcountry</sup><sup>_i_.Thedistributionalassumption</sup> in (B.13) implies that the average factor return by product is equalized across products within a sector, and therefore the total sales _Xiω_ vary within a sector only with the size of each product:
_Xiω_ = _rTi_<sup>_jKiω_.Combining this property with (B.12) and (B.16) we obtain (3) in the text, where the</sup> inverse supply elasticity (defined as the elasticity of price of total sales) is the supply shifter is and the exogenous component of productivity is _Ziω_ = � _Ziω_<sup>0</sup> � _b_<sup><u>1</u></sup><sup>_<u>j</u>_</sup> _i_ . The supply curve is upward-sloping as long as scale economies are not too strong ( _γi_<sup>_jεj_</sup> _i_<sup>_<_1).The average returns to</sup> inputs in the sector _rTi_<sup>_j_must be such that the factor market clears within each sector, ∑</sup> _ω∈_ Ω<sup>_j Kiω_=</sup> _K_<sup>_j_</sup> _Ti_<sup>, implying:</sup> Combining (B.12), (B.16), and (B.19), we obtain a function _rTi_<sup>_j_as an implicit function of the goods</sup> prices _{piω}ω∈_ Ω _j_ and the aggregate factor supply _KTi_<sup>_j_in sector</sup><sup>_j_.</sup>

# **B.2 Proof of Proposition 1**

As a preliminary step, we derive some equilibrium equations in changes. In what follows, let ˆ <u>∆</u> _<u>X</u> X ≡_<sup>theinfinitesimalchangeinthelogofvariable</sup><sup>_X_,where∆</sup><sup>_X_=</sup><sup>_X′ −X_isthe</sup> _X_<sup>denote</sup> difference in the value of _X_ between a counterfactual and an initial equilibrium. Given tariff shocks � _T_ ˆ _niω_ �, to a first order approximation, the equilibrium consists of changes in tradeable prices _{_ ˆ _piω}_ such that i) from (3), price changes are given by ii) from (4), the changes in total sales are consistent with goods market clearing, where _λ_<sup>_n_</sup> _iω_<sup>_≡_</sup> _X_<sup>_X_</sup> _iωiω_<sup>_n_is the share of sales to</sup><sup>_n_in total sales of product</sup><sup>_ω_from</sup><sup>_i_, and where from (1) and</sup> (2), the changes in expenditure shares are Take exporter _i_ = _US_ , _CH_ and suppose that the US and China impose tariffs on each other and on other countries. From the market clearing condition (B.21) and the definition of expenditure
( ) I )

| oo ! ~~<u>Fo)</u> eee~~ e ~~ee e~~ r
<!-- Start of picture text --> fy<br>(| ——)- ( —)-<br>(©)<br>(—)-,<br>(——)-,<br>-<br><!-- End of picture text -->
<!-- Start of picture text --> a<br>fo (—)<br>( i ——<br><!-- End of picture text -->