The Return to Protectionism^*

Abstract

I. Introduction

After more than a half-century of leading efforts to lower international trade barriers, in 2018 the United States enacted several waves of tariff increases on specific products and countries. Import tariffs increased from 2.6% to 16.6% on 12,043 products covering $303 billion (12.7%) of annual U.S. imports. In response, trade partners imposed retaliatory tariffs on U.S. exports. These countermeasures increased tariffs from 7.3% to 20.4% on 8,073 export products covering $127 billion (8.2%) of annual U.S. exports.

This return to protection is unprecedented in the postwar era because of the sizes of the countries involved, the magnitudes of the tariff increases, and the breadth of tariffs across sectors. What were the short-run effects on the U.S. economy? Classical trade theory dictates that the effects depend on the incidence of tariffs. Consumers and firms who buy foreign products lose from higher tariffs. Reallocations of expenditures into or away from domestic products induced by the United States and retaliatory tariffs may lead to changes in U.S. export prices relative to import prices—that is, terms-of-trade effects—and generate tariff revenue. The trade war may have distributional consequences across sectors and thus across regions with different patterns of specialization.

Very little is known about tariff incidence, despite its central role in policy analysis. In this article, we estimate the impacts of tariffs on U.S. trade quantities and prices. We estimate a U.S. demand system that accommodates reallocations across imported varieties (defined as country-product pairs), across imported products (defined as 10-digit Harmonized System product codes), and between imported and domestic products within a sector (defined as a 4-digit NAICS industry code). We combine this system with foreign export supply curves for each variety. The estimation leverages the property that if changes in tariffs are uncorrelated with demand and supply shocks, then a tariff can be used to simultaneously instrument both the import demand and foreign export supply curves.¹ We exploit panel variation at the variety level and aggregate tariffs to construct instruments that identify elasticities of substitution at the product and sector levels. Tests for preexisting trends, tariff anticipation, and an event-study framework validate using tariffs as a source of identification.

We find large declines in imports when the tariffs were implemented. Imports of varieties targeted by U.S. tariffs fell on average 31.7%; imports of targeted products fell 2.5%; and imports in targeted sectors fell 0.2%. The event study reveals no differential change in before-duty import prices between targeted and untargeted source countries exporting the same product. These results imply that we cannot reject horizontal foreign export supply curves. We estimate elasticities of substitution across origins (i.e., varieties) within a product, across imported products, and between domestic goods and imports within a sector of 2.53, 1.53, and 1.19, respectively.

On the export side, we find that retaliatory tariffs resulted in a 9.9% decline in U.S. exports within products. We estimate a roughly unitary elastic foreign demand for U.S. varieties (1.04) and also find complete pass-through of retaliatory tariffs to foreign consumers. As with the import side, we demonstrate that these elasticities are not confounded by preexisting trends or anticipation of the retaliations.

The findings imply complete pass-through of tariffs to duty-inclusive import prices, a finding that is systematic across products with heterogeneous characteristics. The resulting real income loss to U.S. consumers and firms that buy imports can be computed as the product of the import share of value added (⁠|$15\%$|⁠), the fraction of U.S. imports targeted by tariff increases (⁠|$13\%$|⁠), and the average increase in tariffs among targeted varieties (⁠|$14\%$|⁠). This decline is $51 billion, or 0.27% of GDP.

These results have two important caveats. First, our analysis considers short-run effects, but relative prices could change over longer horizons. Second, our estimation controls for country-time and product-time effects and therefore is unable to capture import price declines from relative wage changes across countries or sectors.² In other words, the results do not imply that the United States is a small open economy unable to affect world prices, as terms-of-trade effects could have occurred through wage adjustments at the country-sector level.

We combine the previously estimated parameters with a supply-side model of the U.S. economy to gauge some of these effects. The model imposes upward-sloping industry supply curves in the United States and predicts changes in sector-level prices because of demand reallocation induced by tariffs. We impose perfect competition, flexible prices, and flexible adjustment of intermediate inputs. To assess regional effects, we assume immobile labor and calibrate the model to match specialization patterns across U.S. counties.³ In the model, U.S. tariffs reallocate domestic demand onto U.S. goods, raising total demand and therefore U.S. export prices, while retaliatory tariffs have the opposite effect. These price changes are qualitatively consistent with suggestive evidence that U.S. tariffs led to increases in the PPI and that sector-level export prices fell with retaliatory tariffs.

We obtain a ballpark estimate of the aggregate and regional effects of the 2018 tariff waves. We estimate producer gains of $9.4 billion, or 0.05% of GDP. Adding up these gains, tariffs revenue, and the losses from higher import costs yields a short-run loss of the 2018 tariffs on aggregate real income of $7.2 billion, or 0.04% of GDP. Hence, we find substantial redistribution from buyers of foreign goods to U.S. producers and the government, but a small net loss for the U.S. economy as a whole (which is not statistically significant at conventional levels after accounting for the parameters’ standard errors). Although we cannot reject the null hypothesis that the aggregate losses are 0, the results strongly indicate large consumer losses from the trade war. If trade partners had not retaliated, the economy would have experienced a modest (and also not statistically significant) gain of $0.5 billion.

The small net effect also masks heterogeneous impacts across regions driven by patterns of specialization across sectors. If capital and labor are regionally immobile—a reasonable assumption over this short time horizon—sectoral heterogeneity in U.S. and foreign tariffs generates unequal regional effects. Our counterfactuals imply that all counties experienced reductions in tradeable real wages. Using the model, we find a standard deviation of real wages in the tradeable sectors across counties of 0.5%, relative to an average decline of 1.0%.

We show that U.S. import protection was biased toward products made in electorally competitive counties, as measured by their 2016 presidential vote share, suggesting a potential ex ante electoral rationale for the pattern of tariffs increases. This structure of U.S. protection is consistent with the view that trade policies determined by electoral competition tend to favor voters who are likely to be closer to an indifference point between candidates (Mayer 1984; Dixit and Londregan 1996; Grossman and Helpman 2005). In contrast, retaliations disproportionately targeted agricultural sectors, which tend to be concentrated in Republican-leaning counties. The model-based results suggest that tradeable sector workers in heavily Republican counties were the most negatively affected because of this pattern of tariff retaliations.

A large literature studies the effects of changes in trade costs or foreign shocks through empirical and quantitative methods (e.g., Eaton and Kortum 2002; Arkolakis, Costinot, and Rodríguez-Clare 2012; Autor, Dorn, and Hanson 2013). We focus instead on trade policy, and tariffs in particular, because they are the primary policy instrument of the 2018 trade war.

One approach to studying the impacts of trade policy uses ex post variation in tariffs across sectors to assess effects on sectors (e.g., Attanasio, Goldberg, and Pavcnik 2004), regions (e.g., Topalova 2010; Kovak 2013; Dix-Carneiro and Kovak 2017), firms (e.g., Amiti and Konings 2007; Goldberg et al. 2010; Bustos 2011), or workers (e.g., Autor et al. 2014; McCaig and Pavcnik 2018). A complementary approach uses quantitative models to simulate aggregate effects of tariffs, such as the Nash equilibrium of a global trade war (Ossa 2014) or regional trade liberalizations (e.g., Caliendo and Parro 2015; Caliendo et al. 2015).⁴

A key challenge in the empirical literature is to address the potential endogeneity of tariff changes, and we devote significant attention to these concerns in our analysis. In quantitative models, the parameterization of how trade volumes change with trade policy plays a key role, and we use the observed changes in tariffs to estimate these trade elasticities.⁵

Finally, our finding of complete pass-through deserves some discussion.⁶Amiti, Redding, and Weinstein (2019) and Cavallo et al. (2019) also find complete tariff pass-through to border prices in this trade war, and Flaaen, Hortaçsu, and Tintelnot (2019) estimate high tariff pass-through to retail prices for washing machines. Yet a large body of literature has estimated incomplete pass-through, in particular for exchange rates (e.g., Goldberg and Knetter 1997). An exception is Feenstra (1989), who finds symmetry in the pass-through between tariffs and exchange rate movements. Several hypotheses could reconcile our findings with the exchange rate pass-through literature. The persistence of the tariff shocks may cause before-duty import prices to eventually decline as time elapses. Our results are also consistent with incomplete exchange rate pass-through if import prices are sticky and denominated in dollars (Gopinath, Itskhoki, and Rigobon 2010). Inspecting the precise mechanism underlying the complete tariff pass-through finding deserves further exploration in future research.

The remainder of the article is structured as follows. Section II summarizes the data used for the analysis. Section III outlines the demand-side framework that guides the estimation of the elasticities and discusses the identification strategy. Section IV presents the empirical results. Section V presents the model-based aggregate and distributional effects. Section VI concludes.

II. Data and Timeline

This section describes the data, provides a timeline of key events, and presents an event study of the impact of tariffs. The details about the data set construction are available in Online Appendix A.

II.A. Data

We build a monthly panel data set of U.S. statutory import tariffs using public schedules from the U.S. International Trade Commission (USITC). Prior to 2018, the USITC released annual “baseline” tariff schedules in January and a revised schedule in July. In 2018, by contrast, the USITC issued 14 schedule revisions, reflecting a rapid series of tariff increases. These ad valorem tariff increases were predominantly set at the eight-digit Harmonized System (HS) level and were swiftly implemented within three weeks following a press release by the Office of the U.S. Trade Representative.⁷ Because we work with monthly data and the tariffs were implemented in the middle of months, we scale the tariff increases by the number of days of the month they were in effect.

We compile retaliatory tariffs on U.S. exports from official documents released by the Ministry of Finance of China, the Department of Finance of Canada, the Office of the President of Mexico, and the World Trade Organization (covering the EU, Russia, and Turkey). These tariffs were entirely ad valorem and went into effect shortly after the announcement dates. To construct the retaliatory tariffs, we use the annual WTO database of Most Favored Nation (MFN) tariff rates and compute the retaliatory tariff rate for each country-product as the sum of the MFN rate and the announced tariff rate change. We measure export tariffs at the HS-6 level, because HS-8 codes are not directly comparable across countries. As with the import tariffs, we scale the retaliations based on the day of the month they go into effect.

We use publicly available monthly administrative U.S. import and export data from the U.S. Census Bureau that record values and quantities of trade flows at the HS-10 level, which we refer to as products.⁸ Country-product pairs are referred to as varieties. Our sample period covers 2017:1 to 2019:4, and covers the universe of HS-10 codes and countries. For imports, we directly observe the value of duties collected. Unit values are constructed as the ratio of values to quantities, and duty-inclusive unit values are constructed as |$\frac{(\text{value}\, +\, \text{duties})}{\text{quantity}}$|⁠. We do not observe the duties collected by foreign governments on U.S. exports, so we construct duty-inclusive unit values for exports as the unit value multiplied by (1 plus) the ad valorem retaliatory statutory rate.

We define sectors as NAICS-4 codes. We use the Federal Reserve G17 Industrial Production Index as a measure of domestic sector output, and the BLS PPI, MPI, and XPI indices of producer prices, import prices, and export prices, respectively. These sector-level panels are available at a monthly frequency. We use the 2016 Bureau of Economic Analysis (BEA) annual “use” tables from the national input-output (I-O) accounts to construct I-O linkages between sectors.

To analyze regional exposure, we use the Census County Business Patterns (CBP) database, which provides annual industry employment and wage data at the county-by-sector level for all nonfarm sectors. For county-level data covering the farm sector, we use the BEA Local Area Personal Income and Employment database. From both data sources, we use 2016 data to compute the industry employment share of each county. Finally, we obtain county-level demographic statistics from the 2016 five-year American Community Survey and county-level voting data from the U.S. Federal Election Commission.

II.B. Timeline

Table I provides a timeline of events, and Figure I plots the tariff increases. Table I, Panel A reports the total scope of affected imports and shows that U.S. import tariffs targeted 12,043 distinct HS-10 products. In 2017, these imports were valued at $303 billion, or 12.7% of imports. The average statutory tariff rate increased from 2.6% to 16.6%. An important feature of these tariffs is that they were discriminatory across countries, which allows us to exploit variation in tariff changes across varieties within products.⁹

The first wave of tariff increases began in February 2018, when the United States increased tariffs on $8 billion of solar panel and washing machine imports. A second wave of tariffs, implemented in March 2018, targeted iron, aluminum, and steel products. The largest tranches of import tariffs targeted approximately $247 billion worth of imports from China. In March 2018 the United States implemented tariffs on approximately $50 billion of Chinese imports, and the scope and value of targeted Chinese products expanded with subsequent tariff waves implemented in July and September. Rows 5–7 indicate that tariffs on China targeted 11,207 imported products worth $247 billion, and increased tariffs, on average, from 3.0% to 15.5%. A total of 48.8% of imports from China were targeted with tariff increases.

Table I, Panel B reports the retaliatory tariffs imposed on U.S. exports by trade partners. Canada, China, Mexico, Russia, Turkey, and the EU enacted retaliatory tariffs against the United States, and collectively these retaliations covered $127 billion (8.2%) of annual U.S. exports across 7,763 products. The average statutory tariff rate on these exports increased from 7.3% to 20.4%.

II.C. Structure of Protection across Sectors

Table II reports summary statistics for targeted import and export varieties across NAICS-3 codes. For imports, we report the number of targeted HS-10 products and varieties and the means and standard deviations of tariff increases across targeted varieties within NAICS-3 codes. In sectors where only China was targeted, the number of targeted products equals the number of targeted varieties. The table also reports the corresponding statistics for the retaliatory tariffs on U.S. exports.

The table conveys three facts. First, U.S. sectors that receive the most protection are primary metals, machinery, computer products, and electrical equipment and appliances. These sectors contain a large share of intermediate inputs, make up a large share of targeted varieties and products, and saw steep tariff increases relative to most other sectors.¹⁰ Second, U.S. trade partners concentrated retaliatory tariffs on different sets of products and sectors; the sector-level correlation between import and retaliatory tariffs is 0.46. For example, retaliatory tariff increases on U.S. agriculture exports are on average more than double the U.S. tariff increases in the crop, fishing, and beverage and tobacco sectors. Third, column (5) shows that the mean tariff increases on targeted import varieties are similar across sectors, and column (6) shows that the standard deviation of U.S. tariff changes within sectors is low (and most often 0).

Since Johnson (1953), an extensive literature on optimal tariffs has argued that governments can maximize national income by setting higher tariffs on sectors with more inelastic foreign export supply, and Broda, Limão, and Weinstein (2008) offer empirical support. However, the tariff changes observed in the 2018 trade war are highly similar across sectors. Online Appendix Figure A.1 illustrates this point by plotting the distribution of tariff changes for targeted varieties. The left panel shows that during the trade war, the United States applied only five tariff rate changes to targeted varieties: 10%, 20%, 25%, 30%, and 50%. Virtually all varieties (99.8%) were hit with either 10% or 25% tariff changes. The right panel shows that most of the retaliatory rate increases were concentrated at 10% or 25% as well. These patterns suggest that neither the United States nor retaliating countries were likely driven by a terms-of-trade rationale, because in that case we would expect tariff changes to vary across sectors. Online Appendix Figure A.2 plots average 2018 sector-level tariff rates against the foreign export supply elasticities estimated by Broda, Limão, and Weinstein (2008) and reveals a negative (and statistically insignificant) relationship (the correlation is −0.10).

This lack of variation across sectors also suggests that the tariff changes are unlikely to have been driven by sector-specific interest groups. Explanations in this tradition argue that sectors make political campaign contributions and engage in costly lobbying activities to secure import protection from policy makers (Grossman and Helpman 1994; Goldberg and Maggi 1999). However, these explanations also rely on variation in protection across sectors. Online Appendix Figure A.3 plots financial campaign contributions made to candidates for the U.S. House of Representatives in the 2016 election against tariff changes at the sector level and reveals a negative, rather than a positive, correlation. Although this evidence is only suggestive, it appears unlikely that campaign contributions were the main determinant of the U.S. tariff structure in the trade war.

II.D. Event Study

This specification includes variety (α_ig), country-time (α_it), and product-month (α_gt) fixed effects. Varieties targeted by tariffs are captured by the target_ig dummy. The inclusion of α_gt fixed effects implies that the β_1j coefficients are identified using variation between targeted and nontargeted varieties in product-time. The event time coefficients are captured by the indicator variables. In these specifications, we assign the event date of targeted varieties to be the nearest full month to the actual event date, using the 15th of the month as the cutoff date.¹¹ Nontargeted varieties in the same HS-10 product as a targeted variety are assigned the earliest event date within that product code. For all other nontargeted varieties, we assign the event date to be the earliest month of a targeted variety within the same NAICS-4 sector. If a nontargeted variety does not share the same NAICS-4 as any targeted varieties, we sequentially use NAICS-3 and NAICS-2 codes and otherwise assign the event month to be the earliest month of the trade war (February 2018 for imports and April 2018 for exports). We bin event times ≥6 together and exclude event time ≤−7. For import outcomes, standard errors are clustered by country and HS-8, because these are generally the levels at which the tariffs are set.¹² For export outcomes, standard errors are clustered by HS-6 and country; here, we use HS-6 because that is the finest level at which product codes are comparable across countries and the level at which we code the retaliatory tariffs. We plot the β_1j dummies that capture the relative trends of targeted varieties.

Figure II reports the impacts on imported varieties. The top two panels trace the impact of tariffs on import values and quantities, and the bottom panels show the effects on unit values, exclusive and inclusive of duties. On impact, we detect large declines in imports. Import values decline on average by 20% and quantities decline by 23%.¹³ In the bottom left panel, before-duty unit values do not change. However, duty-inclusive unit values increase sharply for targeted varieties. These two panels provide initial evidence of complete pass-through of the tariffs to import prices at the variety level.

Figure I

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Trade War Timeline

Figure shows the unweighted average tariff rate of targeted import and export varieties for each tariff wave before and after they are targeted. Import tariffs are constructed from U.S. International Trade Commission (USITC) documents, and retaliatory tariffs are constructed using official documents from foreign finance and trade ministries.

Figure II

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Variety Event Study: Imports

Figure plots event time dummies for targeted varieties relative to untargeted varieties. Regressions include country-product, product-time, and country-time fixed effects. Standard errors are clustered by country and HS-8. Event periods before −6 are dropped, and event periods ≥ 6 are binned. Error bars show 95% confidence intervals. In Online Appendix B we provide evidence that the temporary surge in imports during event period 2 reflects an anticipation response to additional tariff threats on a subset of Chinese varieties. Sample: monthly variety-level import data are from U.S. Census. The sample period is 2017:1 to 2019:4.

The event study also addresses concerns of tariff anticipation that would complicate the elasticity estimates. The figure reveals anticipatory effects occurring before the tariff changes, but they are quantitatively small. Hence, the concern that importers shifted forward their purchases to avoid paying tariffs is mild. Below, we further assess tariff anticipation through dynamic specifications.

Figure III reports the impacts of the retaliatory tariffs on U.S. exports. The patterns are similar to what we observe for imports. We find that at the month of implementation, export values decline on average by 24% and quantities fall by 25%. Again, we observe no change in the before-duty unit values, suggesting complete pass-through of the retaliatory tariffs to foreigners’ imports of U.S. varieties. We also observe no clear pattern of anticipation for U.S. exports.

Figure III

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Variety Event Study: Exports

Figure plots event time dummies for targeted varieties relative to untargeted varieties. Regressions include country-product, product-time, and country-time fixed effects. Standard errors are clustered by country and HS-6. Event periods before −6 are dropped, and event periods ≥ 6 are binned. Error bars show 95% confidence intervals. Sample: monthly variety-level export data are from U.S. Census. The sample period is 2017:1 to 2019:4.

III. Trade Framework and Identification

Here we describe the trade framework that guides the estimation. We defer supply-side and general-equilibrium assumptions to Section V.

III.A. U.S. Import Demand

There are S traded sectors corresponding to four-digit NAICS sectors (collected in the set |$\mathcal {S}$| and indexed by s). Within each traded sector, aggregate demand (from producers and consumers) is structured according to a three-tier CES demand system. In the upper nest there is differentiation between domestic and imported goods. Within each of these two nests of sector s there are G_s products (collected in the set |$\mathcal {G}_{s}$| and indexed by product g) corresponding to an HS-10 level of aggregation. Within the nest of imported products, varieties are differentiated by country of origin. The United States trades with I countries (collected in the set |$\mathcal {I}$| and indexed by country i).

The previous demand equations depend on three elasticities: across imported varieties within product (σ), across products (η), and between imports and domestic products within a sector (κ).¹⁴

III.B. Foreign Export Supply and Import Demand

III.C. Identification

This section discusses the identification strategy for the elasticities and its potential threats.

1. U.S. Import and Foreign Export Variety Elasticities (σ, ω*)

We use variation in U.S. import tariffs to estimate the variety import demand and export supply elasticities simultaneously. The strategy of identifying two elasticities with one instrument was applied by Romalis (2007) in a trade context and studied by Zoutman, Gavrilova, and Hopland (2018) in the context of applications to public finance. Intuitively, tariffs create a wedge between what the importer pays and what the exporter receives. A tariff shifts down the demand curve for any given price received by the exporter, tracing the supply curve. Similarly, a tariff shifts up the supply curve for any given price paid by the consumer, tracing the demand curve. Hence, data on changes in prices, tariffs, and quantities is sufficient to trace both the demand and supply curves simultaneously.

2. Product Elasticity (η)

3. Import Elasticity (κ)

4. Foreign Import and U.S. Export Variety Elasticities (σ*, ω)

5. Threats to Identification

There are three main identification threats when using tariffs to estimate the elasticities.

First, the simultaneous identification of demand and supply requires that the tariff affects importers’ willingness to pay. If importers can evade the tariff or do not base their demand on duty-inclusive prices, the tariffs will not cause inward shifts of the import demand curve. In our setting, we do not believe either concern is of first order. Although sales taxes may not be salient to consumers because retail prices are quoted in before-tax prices (e.g., Chetty, Looney, and Kroft 2009), tariffs are paid at the border, and importers observe the after-tariff prices. Tariff evasion is a larger concern in developing countries (e.g., Sequeira 2016).

Second, as previously mentioned, we require that tariff changes are uncorrelated with unobserved import demand and export supply shocks. The system of equations is estimated in first differences and controls flexibly for unobserved demand and supply shocks at each step, which mitigates this concern. The event study figures suggest that targeted import and export varieties were not on statistically different trends prior to the war. In the next section, we implement additional checks for pretrends that support this key identification assumption.

Third, importers may have anticipated looming tariffs in the months before implementation. If they shifted their imports forward, this could bias the elasticities because of a mismatch in the timing of imports and tariff changes.¹⁷ The event study suggests that tariff anticipation is not a concern, and in the next section we implement dynamic specifications that allow lags and leads of tariffs to test formally for anticipation effects.

The identification strategy is not threatened if the tariff changes reflect differences in preferences for redistribution toward specific sectors between the policy makers elected in 2016 and the previous policy makers. Rather, the identification only requires those changes in preferences to be uncorrelated with unobserved shocks to demand and supply over the time period in which the tariff changes take place.

IV. Estimation

This section addresses threats to identification, presents the elasticity estimates, and examines the robustness of the results.

IV.A. Preexisting Trends

To identify the elasticities, tariff changes must be uncorrelated with import demand and export supply shocks. The event studies suggest that targeted varieties were not on different trends prior to the trade war. We further assess concerns about pretrends by correlating import and export outcomes before the 2018 trade war—values, quantities, unit values, and duty-inclusive unit values—with the subsequent tariff changes.

These regressions control for HS-10 product (α_g) and country-sector (α_is) fixed effects, because the estimating equations derived in Section III.C.1 exploit tariff variation controlling for these fixed effects. Standard errors are clustered by country and HS-8 (for imports) or HS-6 (for exports).

The top panel of Table III reports the pretrend tests for imports. We do not observe any statistically significant relationship across import outcomes, suggesting that targeted import varieties were not on differential trends prior to the war. The bottom panel reports the analogous results for U.S. export outcomes and show a similar pattern: prewar export trends are uncorrelated with retaliatory tariffs.

IV.B. U.S. Imports and Foreign Exports at the Variety Level

This subsection estimates the elasticity of variety import demand and foreign export supply following the approach described in Section III.C.1.

Table IV reports the responses of U.S. imports to the tariff changes. Columns (1)–(4) report the results of regressing the four outcomes—values (p*m), quantities (m), unit values (p*), and duty-inclusive unit values (p)—on the tariffs. Each specification is run in first differences and includes fixed effects for product-time, country-time, and country-sector pairs. The specification exploits variation in variety-level tariffs over time to identify the elasticities while controlling for seasonality, time-varying country factors (such as exchange rates), and country-sector time trends. Standard errors are two-way clustered by country and HS-8.

Column (1) shows that import values drop sharply with tariff increases. Column (2) shows that the decline in import values is closely matched by a commensurate decline in quantities.

Column (3) indicates no impact of tariff increases on before-duty unit values. This is the key result providing evidence that the incidence of import tariffs is borne by the U.S. economy, which is consistent with the event study in Figure II.¹⁹ The reduced-form regressions suggest a complete pass-through of tariffs to duty-inclusive import prices.

IV.C. Product-Level Imports

Table V presents estimates of the product elasticity (η) from equation (10), following the steps described in Section III.C.2. The procedure aggregates the import data to the product-time level, and the regressions are run in first differences controlling for sector-time pair fixed effects, as dictated by the model. Standard errors are clustered at the HS-8 level. We construct the price index from equation (11) using |$\hat{\sigma }=2.53$| and the demand shocks from the import variety demand equation from Table IV, column (6). We build the instrument Δln Z_gMt using equation (12).

Column (1) regresses the change in product shares, Δln (s_Mgt), on the instrument Δln Z_Mgt (i.e., the reduced form). Higher product-level tariffs lower the product import share. Column (2) reports the first stage, a regression of the duty-inclusive product-level price index Δln (p_Mgt) on the instrument. The sign is consistent with higher tariffs raising the product price index. Column (3) reports the IV estimate, which regresses the change in product shares on the change in the instrumented price index. The estimate implies |$\hat{\eta }=1.53$| (std. err. = 0.27). The bootstrapped confidence interval for η, which accounts for the variance of |$\hat{\sigma }$| and the demand shocks from the lowest tier, is [1.15, 1.89].

The reduction in imports of targeted products implies that imports from untargeted origins did not fully offset import declines from targeted origins. Hence, rerouting of imports or reallocation of producers to untargeted countries does not seem to be a first-order force over the time horizon that we consider. We also find that import tariffs did not lower before-tariff product-level prices. We construct the before-duty product-level price index using (11) but excluding duties. This before-duty product-level price index includes a Feenstra variety correction, so it accounts for reallocations towards new source countries. Regressing that index against the tariff instrument Δln Z_gMt with sector-time fixed effects yields a positive coefficient of 0.91 (std. err. = 0.40).

We complement this product-level analysis with a reduced-form approach that does not rely on the CES nesting structure. Online Appendix Table A.8 regresses the product-time fixed effects from the variety-level regressions on the product-time component of variety-level tariffs. Consistent with the previous results, we find a decline in product-level imports of targeted products, suggesting that rerouting is not an important concern, and no statistically significant decline in the before-duty import price, suggesting complete pass-through at the product level.²⁰

Using this elasticity and the average change in product-level statutory import tariffs, these estimates imply that import values for targeted products within imported sectors fell, on average, 2.5% across targeted products. This number is the average change in import values for targeted products obtained from |$\Delta \ln p_{Mgt}m_{gt}=-\left(\hat{\eta }-1\right)\Delta \ln Z_{gMt}$|⁠, where |$\hat{\eta }=1.53$| and |$\overline{\Delta \ln Z_{gMt}}=4.7$|%.

IV.D. Sector-Level Imports

Table VI reports estimates of the sector elasticity (κ) following the steps described in Section III.C.3. The regressions control for sector and time fixed effects, and cluster standard errors at the sector level. As shown in equation(13), estimating this elasticity requires data on changes in imports and domestic expenditures at the sectoral level.

The monthly change in U.S. expenditures on domestically produced goods, Δln (P_DstD_st), is not directly observed. We measure it as the difference between the changes in sectoral production and exports. We also need data on the price index of domestically produced goods, Δln (P_Dst). We assume that the change in the price index of domestically produced goods equals the change in PPI, Δln p_st, plus a mean-0 shock: |$\Delta \ln P_{Dst}=\Delta \ln p_{st}+\Delta \ln \varepsilon _{st}^{P}$|⁠.²¹ Then we can implement equation (13) using the PPI instead of the consumer price index of domestically produced goods, which we do not observe. Hence, our specification uses |$\Delta \ln (\frac{P_{Mst}}{p_{st}})$| instead of |$\Delta \ln (\frac{P_{Mst}}{P_{Dst}})$| in equation(13). The change in the price index, Δln P_Mst, is constructed from equation(14) using the estimated |$\hat{\sigma }$| and |$\hat{\eta }$| from the previous two steps, and the demand shocks are constructed from these regressions.

Column (1) is the reduced-form specification that projects relative imports on the instrument, column (2) is the first stage, and column (3) is the IV estimate. The coefficient is negative, suggesting that price propagation of the tariff through input-output linkages is strong and causes the domestic PPI to increase but is noisy. The estimate implies a statistically significant |$\hat{\kappa }=1.19$| (std. err. = 0.49). The bootstrapped confidence interval for |$\hat{\kappa }$|⁠, which takes into account the estimated |$\left\lbrace \hat{\sigma },\hat{\eta }\right\rbrace$| and demand shocks from the previous stages, is [0.89, 1.71].

Using this elasticity and the average change in sector-level statutory import tariffs, these estimates imply that import values across targeted sectors fell, on average, 0.2%. This number is the average change in import values for targeted sectors obtained from |$\Delta \ln \left(\frac{P_{Mst}M_{st}}{P_{Dst}D_{st}}\right)=\left(1-\hat{\kappa }\right)\Delta \ln Z_{Mst}^{stat}$|⁠, where |$\hat{\kappa }=1.19$| and |$\overline{\Delta \ln Z_{gMt}}=1.0$|%.

IV.E. U.S. Exports at the Variety Level

This subsection implements the analysis in Section III.C.A. These regressions examine the change in U.S. export outcomes at the variety level in response to changes in retaliatory tariffs. The regressions include product-time, destination-time, and destination-sector fixed effects and cluster standard errors by destination country and HS-6.

We first report regressions of the four export outcomes on the retaliatory tariffs in Table VII, columns (1)–(4). We observe a statistically significant decline in both export values and quantities. In column (3) we find no evidence that the retaliatory tariffs, on average, caused U.S. exporters to lower (before-duty) product-level unit values. Rather, column (4) implies that the duty-inclusive export price rises approximately one-for-one with the tariff.

Column (5) reports the IV regression that estimates the U.S. export supply curve at the variety level. This is the analog to the variety-level supply curve in equation (6) on the export side. The first stage is column (2). The estimate is imprecisely measured, and we cannot reject the null that foreigners face a horizontal U.S. export supply curve. Column (6) reports the IV estimate of equation (16). The first stage is column (4). We estimate |$\hat{\sigma }^{*}=1.04$| (std. err. = 0.32). The bootstrapped confidence interval is [0.73, 1.39].

Using the estimated elasticity and the average change in retaliatory tariffs, these estimates imply that U.S. export values for varieties targeted by trade partners fell, on average, 9.9%. This number is the average change in export values for targeted varieties obtained from |$\overline{\Delta \ln (p_{igt}^{X}x_{igt})}=-\hat{\sigma }^{*}\overline{\Delta \ln (1+\tau _{igt}^{*})}$| where |$\overline{\Delta \ln (1+\tau _{igt}^{*})}=9.5$|%.

IV.F. Robustness Checks

This section explores the robustness of the results. We first assess concerns that underlying trends or tariff anticipation bias the estimates. We also explore heterogeneity across sectors, compare the pass-through of tariffs to unit values at different time horizons, and examine how the results change with alternative sets of fixed effects.

1. Trends and Dynamic Specifications

Section IV.A documents that preexisting trends and anticipation effects are unlikely to threaten our identification. In this section, we provide further evidence that the elasticities are not sensitive to concerns over preexisting trends or anticipation effects.

The first robustness check controls for trends through panel fixed effects. We reestimate the variety-level specifications to include variety fixed effects and report the analog to Table IV in Online Appendix Table A.4 and the analog to Table VII in Online Appendix Table A.6. We assess long-run trends by reestimating the specifications with variety fixed effects using data from 2013:1 to 2019:4 in Online Appendix Tables A.5 and A.7. The results are essentially unchanged and remain consistent with the prior evidence that preexisting trends are unlikely to be confounding factors.

Figure IV reports the cumulative estimated coefficients for import values, quantities, unit values, and duty-inclusive unit values. The results reveal no quantitatively large patterns of tariff anticipation. In addition, the results show no evidence of before-duty price declines occurring after the tariffs are implemented. Finally, the cumulative magnitudes displayed in the figure are quantitatively similar to the reduced-form estimates from the static regressions. These results reassure us that the elasticities are not biased due to anticipation effects and that the variety-level pass-through findings are robust.

Figure IV

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Dynamic Specification

Figure IV. Figures plot cumulative sum of β coefficients from the regression

$$\begin{eqnarray*} \Delta \ln y_{igt}=\alpha _{gt}+\alpha _{it}+\alpha _{is}+\sum _{m=-6}^{m=6}\beta _{m}^{y}\left[\ln \left(1+\tau _{ig,t-m}\right)-\ln \left(1+\tau _{ig,t-1-m}\right)\right]+\epsilon _{igt},\end{eqnarray*}$$

where i denotes countries, g denotes products, and t denotes time. Standard errors are clustered by country and HS-8 for imports and by country and HS-6 for exports. Error bands show 95% confidence intervals. Monthly variety-level import and export data are from U.S. Census. The sample period is 2017:1 to 2019:4.

The bottom panel of Figure IV reports the results for exported varieties. In this specification, we find some evidence of tariff anticipation as U.S. export values increase in the month before tariffs change; however, we do not observe this pattern for export quantities. We also do not observe cumulative declines in before-duty export prices occurring as time elapses after the retaliations are implemented.

2. Heterogeneity

The baseline specifications impose common elasticities across sectors. However, these specifications potentially mask variation in the tariff pass-through result. For example, we may expect more differentiated products or less competitive sectors to exhibit less than complete pass-through. We may also expect demand elasticities to depend on inventories and whether goods are durable, which may allow buyers to postpone sales more easily. Other product characteristics, such as variation in price stickiness or stocks of inventories, could induce heterogeneous pass-through.

In this subsection, we explore this potential heterogeneity by focusing on the complete pass-through finding at the variety level. To do so, we implement reduced-form specifications that regress changes in the import (export) unit values on changes in import (retaliatory) tariffs, controlling for product-time, country-time, and country-sector fixed effects. Each specification interacts the tariff change with different measures of product or sector characteristics that have been used widely in the literature.

Online Appendix Table A.9 reports results from interacting the tariff changes with three different classifications of final versus intermediate goods. The top panel examines the pass-through of the import tariffs to import unit values, and the bottom panel examines pass-through of the retaliatory tariffs to U.S. export unit values. Column (1) uses the Broad Economic Categories (BEC) classification that categorizes sectors according to their end use. Column (2) uses an indicator for whether the HS product matches an entry line item in the BLS Consumer Price Index (CPI). Column (3) uses an indicator for whether each HS-10 product description contains the word “part” or “component.” Although each classification is imperfect, the results do not show statistical differences between final and intermediate goods.

Online Appendix Table A.10 examines interactions across 11 different measures of product or sector characteristics that have been used in the literature: (i) quality ladders from Khandelwal (2010); (ii) markups estimated by De Loecker, Eeckhout, and Unger (forthcoming); (iii) the coefficient of price variation; (iv) elasticities of substitution estimated by Broda and Weinstein (2006); (v) trade elasticities estimated by Caliendo and Parro (2015); (vi) contract intensity measured by Nunn (2007); (vii) inverse frequency of price adjustments from micro-data tabulated by Nakamura and Steinsson (2008) (a higher value indicates less frequent price adjustments); (viii) measures of industry upstreamness by Antràs et al. (2012); (ix) inventory to sales ratios constructed from Census data; (x) differentiation developed by Rauch (1999); and (xi) an indicator for durable goods using the BEC classifications. The top panel reports the results for imports. The pattern across the 11 different metrics, along with the previous table, suggests that there is no meaningful heterogeneity in the complete pass-through result, at least with respect to the characteristics we have examined. Online Appendix Table A.11 reports the results for export unit values. Again we find no systematic evidence of heterogeneity with respect to observable characteristics.

3. Horizons

The variety-level complete pass-through results may be a short-run phenomenon. We assess the incidence of the tariffs at different time horizons by aggregating the data to the two-month, three-month, and four-month levels, taking first differences, and reimplementing the reduced-form regression specifications. The results for before-duty import and export unit values are reported in Online Appendix Table A.12, with the baseline estimates from the monthly data replicated in column (1) of each panel. Even at these medium-term frequencies, we do not observe downward pressure on before-duty unit values in response to the tariff changes.

4. Alternative Fixed Effects

Our baseline set of fixed effects—that is, product-time, country-time, and country-sector fixed effects—control for potentially confounding import demand and export supply shocks. However, if the trade war induces global or country-specific general-equilibrium responses to wages, these fixed effects may mask tariff pass-through effects in our regressions. Online Appendix Table A.13 reports the elasticity of before-duty unit values against the tariff changes controlling for different sets of fixed effects to explore this possibility. The top panel reports the import results and the bottom panel reports the export results, and column (1) of each panel reports the baseline estimates to facilitate comparisons across the alternate specifications. We do not observe any effect of the tariff on before-duty unit values across eight different sets of fixed effects, some of which exclude country-time or product-time fixed effects, in both the import and export data. We also extract the country-time α_it fixed effects in the baseline specification and regress them against monthly exchange rates, and do not find a statistically significant relationship (estimate is 0.11, std. err. = 0.19). We also do not find a relationship between the country-time fixed effects and exchange rate changes for China (estimate is 0.04, std. err. = 0.04).

V. Aggregate and Regional Impacts

Before turning to the full model in the next section, it is instructive to perform a few back-of the-envelope calculations using the estimated parameters to gauge the magnitude of the aggregate impacts of the trade war.

First, given complete tariff pass-through, the first-order approximation to the impact on U.S. consumer surplus is the product of three terms: the import share of value added (⁠|$15\%$|⁠), the fraction of U.S. imports targeted by tariff increases (⁠|$13\%$|⁠), and the average import price increase among targeted varieties (⁠|$14\%$|⁠). This calculation implies buyers of imports lost in aggregate 0.27% of GDP, or $50.8 billion at a 2016 annual basis.

Second, under some assumptions the elasticities can be used to compute the impact on aggregate real income. Specifically, in the absence of changes in U.S. import and export prices, starting from free trade, and provided the environment satisfies neoclassical assumptions, the (second-order) approximation to the aggregate equivalent variation is |$\frac{1}{2}\left(\Delta \mathbf {m}\right)^{\prime }\Delta \tau$|⁠, where |$\Delta \mathbf {m}$| is the change in the vector of imports and Δt is the change in per unit import tariffs. Using the estimates for the changes in variety-level imports estimated in Section IV.B, and assuming that the fixed effects in those regressions are unresponsive to the tariffs, this calculation yields a real GDP loss of $11 billion, or 0.059% of GDP.²³

These approximations are computed assuming complete tariff pass-through. However, our empirical analysis at the variety level does not rule out terms-of-trade effects through changes in prices at the country or sector levels. Also, these calculations do not consider the impacts of retaliatory tariffs. We now combine the previously estimated parameters with a supply side of the U.S. economy. The model imposes upward-sloping industry curves and predicts changes in sector-level prices in the United States due to the demand reallocation induced by import and retaliatory tariffs. Through this channel, it generates additional aggregate and regional effects not captured by the previous measurements.

V.A. General-Equilibrium Structure

We use a static general-equilibrium model of the United States, imposing strong assumptions such as perfect competition, flexible prices, and an input-output structure with unitary elasticities. We implement counterfactuals that keep constant the wages in foreign countries.