THE US-CHINA TRADE WAR AND GLOBAL REALLOCATIONS

The US-China trade war created net export opportunities rather than simply shifting trade across destinations. Many “bystander” countries grew their exports of taxed products into the rest of the world (excluding US and China). Country-specific components of tariff elasticities, rather than specialization patterns, drove large cross-country variation in export growth of tariff-exposed products. The elasticities of exports to US-China tariffs identify whether a country’s exports complement or substitute US or China and its supply curve’s slope. Countries that operate along downward-sloping supplies whose exports substitute (complement) US and China are among the larger (smaller) beneficiaries of the trade war


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. 1 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 and, potentially, among themselves.
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 these forces.
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, a formula for the reduced-form elasticity of a bystander's product-level exports (to the US, China, and the rest of the world) to US and Chinese tariffs.This elasticity captures the effects of demand shifts due to tariff changes, conditioning on indirect demand and supply shifters through general equilibrium adjustments.
Our second proposition shows that, properly controlling for these indirect effects, 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.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. 2his initial approach assumes common tariff elasticities across countries, but these elasticities 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 the US or China-suggests an interdependency across export destinations.We rationalize this finding through downward-sloping supply curves at the product level.Mau (2017) and Albornoz, Brambilla, and Ornelas (2021) both show third-market effects after tariff reforms faced by Chinese and Argentinean firms, respectively, that are consistent with scale effects.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.The result is also consistent with reallocations of supply chains under particular input-output structures. 3Flaaen   et al. (2020) show that, for washing machines, product-specific capital migrates from China to other countries serving as export platforms to the US in order to avoid the tariffs.Our result suggests that these export platforms may also increase exports to the rest of the world.
Our subsequent results, which reveal substantial cross-country heterogeneity in export growth consistent with country-specific demand and supply elasticities, are 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.These empirical results are also broadly consistent, and could be explained, by frameworks that feature flexible patterns of substitution across imports, such as Adao, Costinot, and Donaldson (2017) and Lind and Ramondo (2023). 4  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), Farrokhi and Soderbery (2020), with whom we share an identical supply-side structure, and ?. 5 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).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, which could be a path for future research.

Framework
This section presents the framework that guides the empirical analysis.

Environment
Demand There is a set I of countries (indexed by i for exporters and n for importers) and a set Ω j of products (indexed by ω) in sector j = 1, ..., J.Each product ω is differentiated by origin i; a variety is iω.We let p iω be the price received by competitive producers of the variety.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 j imported from origin i is: where p n iω is the tariff-inclusive price in country n.The parameter a n iω captures an idiosyncratic demand of country n for the variety iω.The semi-elasticities σ j i i are common across importing countries and capture the substitutability between products from i and i .When σ j i i > 0 (σ j i i < 0), varieties i and i = i are substitutes (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 . 6We impose a common substitution elasticity within the sector: 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 (σ i,CH > 0 and σ i,U S < 0) while the opposite may be true for goods from another exporter. 7 Supply Due to trade costs, τ n iω units of variety iω must be shipped to n for one unit to arrive.Also, country n imposes ad-valorem tariffs t n iω on imports of good ω from i. Letting p iω ≡ p i iω be the domestic price of variety i and assuming competitive pricing, the tariff-inclusive prices faced by consumers in country n are where T n iω ≡ 1 + t n iω is one plus the ad-valorem tariff.Total sales of ω in sector j from country i are: where b j i the inverse supply elasticity defined as the elasticity of price of total sales and p iω be the domestic price of variety i.The supply shifters are partitioned into an endogenous country-sector component A j i and an exogenous cost shifter Z iω .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 j i < 0).
6 Additivity and symmetry of the substitution matrix require that ∑ N i=1 a n iω = 1 for all n and ω, as well as σ j i i = σ j ii for all i, i , j and ∑ i ∈I σ j ii = 0 for all i, j. 7 Studies using a translog or almost-ideal demand system with symmetric substitution elasticities include Novy (2012), Kee et al. (2008), Fajgelbaum andKhandelwal (2016), andFeenstra andWeinstein (2017).
Appendix B.1 shows a micro-foundation where b j i combines returns to scale and an elasticity of factor mobility across products and sectors. 8In particular, b j i = 1 , where ε j i ≥ 1 is a factor supply elasticity and γ j i captures returns to scale.Although we do not attempt to separately identify the components of b j i , within this framework, b j i < 0 implies γ j i > 0. At the same time, the more flexible is factor substitution across products (the higher is ε j i ) the more likely it is to observe b j i < 0.
Equilibrium The price of variety iω in importer n is p n iω = (1 + τ n iω ) t n iω p iω , where τ n iω is the ad-valorem tariff and t n iω is the trade cost.A world equilibrium is given by prices {p iω } such that markets clear; i.e., the aggregate sales X iω given by (3) must equal aggregate expenditures: where E n ω ≡ ζ n ω E n are country n's expenditure in product ω, which is a constant share ζ n ω of national expenditure E n .To complete the description of the general equilibrium model, we need additional assumptions to determine the country-sector supply shifters A j i and the country expenditures E n .Rather than imposing additional model structure, we flexibly control for importer-exporter-sector fixed effects and for model-implied measures of the size of the trade flows in our empirical specifications.

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 X n iω of product ω from exporter i to importer n change according to: where, letting E ω ≡ ∑ n E n ω be world expenditures in product ω, β n 2iω to β n 6iω are given by (B.31)-(B.35) in the Appendix, and where p−iω ≡ ∑ i =i σ j i i pi ω .
Equation ( 5) partitions the total change in sales of product ω from country i to destination n into two distinct components.The first two lines, an inner product β∆T of elasticities and tariff changes, captures the demand shocks from tariffs such that the price of variety iω changes to clear its global market.The last line, the term η n iω defined in (7), captures the indirect effects of tariffs through endogenous demand shifters for each buying country (national expenditure shares, Ên , and average price changes of competing varieties, p−iω ), and of supply shifters for the exporter (endogenous changes in sector-level factor prices Âj i ).We will implement equation ( 5) to estimate tariff elasticities 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 n 1iω and β n 2iω .Equation ( 6) shows the expression for β n 1iω , the elasticity of variety iω exports to destination n in response to US tariffs (with a similar expression for β n 2iω , corresponding to Chinese tariffs, in (B.31)).The tariff elasticities may vary by exporter i and sector j due to heterogeneous σ j CHi or b j i σ j ii .Due to size dependence, the tariff elasticity is also variety-specific, decreasing with the export flow's size and increasing with the size of US or China as buyers.
Naturally, higher substitution or scale elasticities imply stronger responses.The next proposition shows that the tariff elasticities β of variety iω to the US and to the rest of the world, as defined in (5), jointly identify the signs of σ j CHi and b j i σ j ii .
Proposition 2. When the US imposes a tariff on China in product ω, then: CHi > 0 and exports increase (decrease) from i to the rest of the world, then b j i < 0 b j i > 0 ; while if σ j CHi < 0 and exports increase (decrease) from i to the rest of the world, then 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 A.1 shows the possible cases.A downward-sloping supply (b j i < 0) is consistent with observing export responses with equal sign to both the US and the rest of the world.Conversely, upward-sloping supply (b j i < 0) is consistent with observing export responses with opposite sign to the two destinations.The same logic applies for Chinese tariffs on US imports.
For example, consider the China-substitutes case in the right column.As implied by part (i) of the proposition, this column corresponds to estimating β U S 1iω > 0 (an increase in variety iω exports to US in response to the US tariff on China).10As implied by part (ii), given negatively sloped demand, further estimating an increase in exports to countries other than US (β RW 1iω > 0) reveals a downward-sloping supply (b j i < 0).In this case, the gain in scale due to increased US demand leads to an increase in exports to the rest of the world.11Conversely, estimating β RW 1iω < 0 would be consistent with upward-sloping supply, so that higher demand in one destination reallocates sales away from others.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.

Data and Summary Statistics
We use ?data recording bilateral exports in 5203 HS6 products.We aggregate into 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 (U S), 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.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 T U S CH,ω , where ω denotes an HS6 product code; ii) imposed by China on the US, T CH U S,ω (the "China tariffs"); iii) imposed by the US on each country i other than China, T U S i,ω (e.g., steel tariffs on Mexico); and iv) most-favored-nation (MFN) tariffs imposed by China on all countries but the US, T CH i,ω .Bown et al. (2019b) argue that China's MFN tariff cuts were 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. (2020b) and extended through the end of 2019, and the last set is from Bown et al. (2019b).We compute averages of tariffs at the HS6 level, and 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.

Average Export Responses
Figure 1 presents binscatters that examine the exports of the 48 bystander countries to U S, CH, and RW against the US-China tariffs.Each panel plots linear relationships of the form Panel A shows the binscatter of exports of bystander i to the US (X U S iω ) against the US tariffs (T U S CH,ω ).12 Panel B shows i's exports to China (X U S iω ) against the Chinese tariffs (T CH U S,ω ).Panels C and D report exports to RW (X RW iω ) against the US (T U S CH,ω ) and China (T CH U S,ω ) tariffs, respectively.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 , se -0.19).Panel B shows that, on average, countries did not reallocate exports to 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 0.29 (se 0.08) for the China tariffs (Panel D).
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, as 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.13

Heterogeneous Export Responses
To explore heterogeneity in tariff elasticities, we implement a specification motivated by Proposition (1).We now discuss the implementation.
First, we set β n 5i and β n 6i in equation ( 5) to zero.While theoretically justified, the tariff summation terms that identify these coefficients are highly correlated with the bilateral tariffs from which they are constructed. 14econd, the tariff elasticities β n ziω vary by importer, exporter, and measures of variety size according to Proposition 1.For example, from (6), the elasticity β n 1iω to US tariffs is a non-linear function of observable variables SIZE n 1iω that capture the (pre-war) relative size of the variety's trade flow, exporter-sector components (b j i σ j ii and σ j CHi ), and an importer component (the indicator . 15 We capture this heterogeneity by imposing a linear structure: For each of the four tariffs (z = 1, .., 4), variation in tariff elasticities across exporters i is captured by the exporter-importer component β n zi ; variation across sectors j is captured by importer-sector component β n zj(ω) (where j (ω) is the sector of product ω); and, variation across varieties within an exporter-importer-sector cell is due to SIZE n ziω .Third, the term η n iω in (5) is not directly observed and may, in principle, correlate with tariffs.In that case, our estimated tariff elasticities would still be unbiased estimators of the response of exports to tariffs under the parallel trend assumptions discussed below, but the interpretation of each of the β's would include the sum of the corresponding direct effects in (B.30)-(B.33)and the correlations between η n iω and the respective tariffs.We mitigate this concern by controlling for η n iω by origin-destination-sector fixed effects (α n ij ), and the SIZE n ziω variables. 16Finally, the regressions also include an error term ε n iω capturing the reduced-form impact of non-tariff shocks (e.g., variety level shocks to preferences or productivity) on X n iω .We control for these unobserved shocks with the fixed effects and pre-trends.
We define the structural and reduced-form residuals as follows, The resulting specification is run separately to each destination, n = U S, CH, RW and takes the form: where β n ziω for z = 1, .., 4 is defined in (9).The identifying assumption underlying this empirical strategy is that, within origin-destination-sector, potential export growth across products would have been similar in the absence of the tariff shocks.We assess the plausibility of this 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 broadly uncorrelated with the future changes in tariffs.To further mitigate concerns of pre-existing trends, we control for lagged export growth.
Having estimated β n ziω , we predict the growth of variety iω to the world (relative to 15 For Eω (the share US expenditures in global expenditures of product ω), Xiω Eω (the share of exporter i sales in global expenditures of ω), and s n iω (the share of variety iω in destination n expenditures).Equations (B.31)-(B.33)show the corresponding variables SIZE n ziω for the remaining β's in the specification. 16Variation in η n iω comes from two sources.The first is exporter-sector factor costs, importer-sector expenditures, and sizes of variety-level trade flows, which we control for through fixed effects and size variables.The second is the sum of price changes of product ω in countries other than i, p−iω et al. (2020b) find that prices of US and Chinese varieties do not respond to tariffs, so the US and Chinese entries in this sum are small.Moreover, a takeaway below is that the tariff elasticities are heterogeneous.Thus, export prices would likely decrease for some countries and increase for others, without necessarily covarying with tariffs in a systematic way.We checked for systematic patterns between average price changes of each country's competitors and the tariffs.From country-by-country regressions on the four tariffs and sector fixed effects, we cannot reject that either US or Chinese tariffs have no impact on i s competitors' average price changes, ∑ i ∈RW ,i =i pRW i ω , in any of the bystanders.
non-targeted varieties) using the four tariffs: where λ n iω is the share of variety iω to country n in total exports of country i.The λ n iω shares are defined as the (pre-war) export values for continuing products divided by total country exports.

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 this heterogeneity.
Figure 2 plots the export growth defined in (11) across countries. 17By 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 6.5%, with a standard deviation just as large at 6.1%.For example, the increases in exports of targeted relative to untargeted products in Thailand and Mexico are 14.1% (se 4.8%) and 12.0% (se 6.5%), respectively, while Ukraine's exports fall 11.7% (se 8.3%) and Canada's export growth is just 2.6% (se 5.3%). 18  Through the lens of the model, heterogeneity is expected.By construction of (11), 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 the bulk of the cross-country variation in Figure 2 comes from the country-specific component of the tariff elasticities (the β n zi in (9)), and not from specialization (λ n iω ), sectoral tariff elasticities (β n zj(ω) ), or size-specific tariff elasticities (Γ n z ).To see this, Figure 3 re-computes the export growth in (11) 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 n ziω = β n z in (10)), the variation only comes from λ n iω pre-war specialization patterns.The grey series reveals virtually no variation across countries and the standard deviation is just 1.4%.Next, the red series re-computes export growth only allowing for sectoral heterogeneity: ; the standard deviation is now 3.3%, and the correlation with the full heterogeneity case is just 0.39.Similarly, the green series next constructs predicted 17 We report bootstrapped confidence intervals for ∆ ln X W D i .We construct bootstrapped standard errors through a cluster bootstrap of specifications (10): we sample with replacement within products, estimate the specifications in (10), construct the aggregate predicted exports for each estimation using (11), and repeat 50 times. 18We correlate ∆ ln X W D i with i's characteristics: GDP (World Bank 2022), distance to the US and China (?); the share of exports covered by "deep" trade agreements (Mattoo et al., 2020b); and 2017 FDI stock (UNCTAD (2022)).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.growth using only the estimated size component, β n ziω = Γ n z SIZE ziω , which also yields a low correlation of -0.03 with the full heterogeneity benchmark.Finally, the blue series allows for just the country component, β n ziω = β n i .The standard deviation across countries' response is now 5.9%, and the correlation with the benchmark rises to 0.84.
A formal decomposition of relative export growth into the three components reveals that country-specific responses explain 80.5% of the variation, while the sector and size component explains 20.6% and -1.1%, respectively.
The importance of the country-specific component of the 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.

Supply and Demand Forces
Table A.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 U S 1i , β RW 1i ), revealing the substitutability/complementarity with Chinese varieties and the slope of supply curves.Panel B reports ( β CH 2i , β RW 2i ), 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 and demand forces that drive export responses in Figure 2. 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 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 targeted products, as confirmed by Figure 2.
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 the bilateral level, as in Lind and Ramondo (2023), 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 with 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 this as an area for future research.

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: several countries increased global exports in products with higher US-China tariffs, relative to non-taxed products.
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.Our reduced-form tariff elasticities could also be used to target moments and identify parameters in estimated general equilibrium models.

Panel D Bystanders' Export Value to RW
Notes: The panels show binscatter plots of the regression in (8), ∆ ln X = α + β∆ ln T + ε.This is a regression of bystanders' export growth (on the y-axes) against changes in tariffs due to the trade war (on the x-axes).Panel A is bystanders' exports to the US (X U S iω ) against the US tariffs (T Notes: The figure plots changes in predicted exports to the world in taxed relative to untaxed products using (11): .
The β's are estimated from the specification (10): Notes: Figure reports alternative predictions for exports to the world constructed using (11):

FIGURE 3: DECOMPOSING RELATIVE EXPORTS BY HETEROGENOUS RESPONSE TYPE
where the β's are estimated under alternative configurations of the heterogeneity in 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 n ziω = β n zj(ω) ), size ( β n ziω = Γ n z SIZE ziω ), and country ( β n ziω = β n i ).The 45-degree line (black) is the benchmark full heterogeneity series.
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.

Online Appendix: The US-China Trade War and Global Reallocations
Pablo Fajgelbaum, Pinelopi Goldberg, Patrick Kennedy, Amit Khandelwal, Daria Taglioni FIGURE A 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%).

Panel B US Export Value to China
Notes: The panels show binscatter plots of the regression in (8), ∆ ln X = α + β∆ ln T + ε, for US and China exports.Panel A is China's exports to the US (X U S CH,ω ) against the US tariffs (T U S CH,ω ).Panel B is US exports to China (X CH U S,ω ) against the China tariffs (T CH U S,ω ).Also shown are the binscatters of the regressions with exports prior to the trade war from 2015-17.Below each panel are OLS coefficients.Pre-period: β=0.12 (0.08).Post-period: β=0.30 (0.08).

Panel D Bystanders' Export Value to RW
Notes: The panels show binscatter plots of the regression in (8), ∆ ln X = α ij + β∆ ln T + ε.This is a regression of bystanders' export growth (on the y-axes) against changes in tariffs due to the trade war (on the x-axes), controlling for country-sector fixed effects.Panel A is bystanders' exports to the US (X U S iω ) against the US tariffs (T U S CH,ω ).Panels B is bystanders' exports to China (X CH iω ) against the China tariffs (T CH U S,ω ).Panels C and D show bystanders' exports to RW (X RW iω ) against the US (T U S CH,ω ) and China tariffs (T CH U S,ω ), respectively.Also shown are the binscatters of the regressions with exports prior to the trade war from 2015-17.Below each panel are OLS coefficients (standard errors clustered by product).Panels C and D of Table A.2 report the regression coefficients.Panel C: Pre-Period, With Controls

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 K j T i of a bundle of inputs and primary factors is used to produce tradeable goods in 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 z 0 iω e k ω .The term z 0 iω is common to all inputs in ω.It depends on an exogenous country-product specific component of productivity Z iω and, through scale economies, on the amount of inputs K iω allocated to the product: where γ j i is a country-sector specific scale elasticity.In turn, the term e k ω is specific to each unit with CDF from an iid Frechet distribution: where the parameter ε j i is also country-specific and determines factor mobility across products in 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 α I j and unit cost c I ij , to maximize its returns π k i : where p iω 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 I ijω does 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.15) is equivalent to: B.16) where z iω ≡ c I ij /α I j α I j α I j −1 z 0 iω captures productivity and input costs of product ω.From the solution to (B.16), the supply of inputs to product ω in sector j of country i is where r j T i are the average factor returns in sector j of country i.The distributional assumption in (B.14) implies that the average factor return by product is equalized across products within a sector, and therefore the total sales X iω vary within a sector only with the size of each product: Combining this property with (B.13) and (B.17) we obtain (3) in the text, where the inverse supply elasticity (defined as the elasticity of price with respect to total sales) is the supply shifter is and the exogenous component of productivity is The supply curve is upward-sloping as long as scale economies are not too strong (γ j i ε j i < 1).The average returns to inputs in the sector r j T i must be such that the factor market clears within each sector, ∑ ω∈Ω j K iω = K j T i , implying: Combining (B.13), (B.17), and (B.20), we obtain a function r j T i as an implicit function of the goods prices {p iω } ω∈Ω j and the aggregate factor supply K j T i in sector j.

B.2 Proof of Proposition 1
As a preliminary step, we derive some equilibrium equations in changes.In what follows, let X ≡ ∆X X denote the infinitesimal change in the log of variable X, where ∆X = X − X is the difference in the value of X between a counterfactual and an initial equilibrium.Given tariff shocks T n iω , to a first order approximation, the equilibrium consists of changes in tradeable prices { piω } such that i) from ( 3 where we have imposed the restriction that σ j RW = σ j i i for i , i = U S, CH and i = i and where, to shorten notation, we have defined λn The two terms in the first line of (B.24) capture the direct impact of US and Chinese tariffs country i's exports these two markets.For example, the first of these terms says that a bigger Chinese tariff on the US reallocates Chinese demand to country i if country i and the US are substitutes (σ U Si > 0); in percentage, this reallocation is larger the bigger is Chinese expenditure in product ω (a larger E CH ω ) or the smaller are the initial sales of ω from i (a smaller X iω ).The second line of (B.24) is the change in sales due to the change in variety iω's price.and where η n iω is given by (7).

A. 1
reports countries' export shares by sector prior to the trade war.

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

FIGURE
FIGURE 4: SUPPLY AND DEMAND FORCES

FIGURE
FIGURE A.3: TRADE WAR TARIFFS AND EXPORT CHANGES FOR USA AND CHN Notes: Panels A and B report the regression output corresponding to Figure 1, and Panels C and D report the regression output corresponding to Figure A.4.Standard errors clustered by product shown in parentheses.

X
iω is the share of sales to n in total sales of product ω from i, and where from (1) and (2), the changes in expenditure shares are ŝn iω = pi ω .(B.23) Take exporter i = U S, CH and suppose that the US and China impose tariffs on each other and on other countries.From the market clearing condition (B.22) and the definition of expenditure shares (B.23), the total sales of ω from i change around an initial equilibrium according to Xiω Finally, in the third line of (B.24), T other iω captures the impact on country i of US and China tariffs imposed on countries other than each other, in the third line capture changes in prices of other varieties and in aggregate expenditures.Combining (B.24) with the inverse supply (B.21) and solving for piω we obtain the price change of variety iω: change in sales from i to a specific destination n: Xn iω = Ên + ŝn iω − T n iω .iω is defined in (7) in the main text.Using (B.25) and rearranging terms in (B.28) we obtain Xn iω = 1 n=U S +

FIGURE 2: RELATIVE EXPORT GROWTH IN TARGETED PRODUCTS ACROSS COUNTRIES
Also shown are the binscatters of the regressions with exports prior to the trade war from 2015-17.Below each panel are OLS coefficients, with standard errors clustered by product shown in parentheses.Panels A and B of Table A.2 report the corresponding regression tables.
U S  CH,ω).Panels B is bystanders' exports to China (X CH iω ) against the China tariffs (T CH U S,ω ).Panels C and D show bystanders' exports to RW (X RW iω ) against the US (T U S CH,ω ) and China tariffs (T CH U S,ω ), respectively.

TABLE A .1: PARAMETER REGIONS IMPLIED BY EXPORT RESPONSES TO US TARIFFS ON CHINA
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.σ CHi represents the demand substitution between Chinese and country i's goods, while b i represents the inverse supply elasticity in country i.A similar taxonomy applies for China's tariffs on the US, in which case the responses would reveal substitutability with the US (σ U Si instead of σ CHi ).