Tariff Rate Uncertainty and the Structure of Supply Chains

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1389 April 2024 Tariff Rate Uncertainty and the Structure of Supply Chains Sebastian Heise, Justin R. Pierce, Georg Schaur, and Peter K. Schott Please cite this paper as: Heise, Sebastian, Justin R. Pierce, Georg Schaur, and Peter K. Schott (2024). “Tariff Rate Uncertainty and the Structure of Supply Chains,” International Finance Discussion Papers 1389. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2024.1389. NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Tariff Rate Uncertainty and the Structure of Supply Chains∗ Sebastian Heise † Justin R. Pierce ‡ Georg Schaur § Peter K. Schott ¶ April 2, 2024 Abstract We show that reducing the probability of a trade war promotes long-term importerexporter relationships that ensure provision of high-quality inputs via incentive premia. Empirically, we introduce a method for distinguishing between these long-term relationships—which the literature has termed “Japanese” due to their introduction byJapanesefirms—fromspot-marketrelationshipsincustomsdata. Weshowthatthe use of “Japanese” relationships varies intuitively across trading partners and products andfindthattheuseofsuchrelationshipsincreasesafterareductioninthepossibility of a trade war. Extending the standard general equilibrium trade model to encompass potentialtradewarsandrelationalcontracts,weestimatethateliminating“Japanese” procurement reduces welfare about a third as much as moving to autarky. Keywords: supply chain, uncertainty, trade war, procurement JEL Codes: F13, F14, F15, F23 ∗Schott and Heise thank the National Science Foundation (SES-1427027) for research support. We thank George Alessandria, Davin Chor, Kerem Cosar, Teresa Fort, Virgiliu Midrigan, Dan Trefler, and seminar participants at the Bank of Canada, the Barcelona Summer Forum, ERWIT, Indiana,theInter-AmericanDevelopmentBank,Mannheim,theNBERFallITIMeeting,theNBER Japan Conference, Oregon, Toronto, the US International Trade Commission, and the Yale Cowles Conference for helpful comments. The views and opinions expressed in this work do not necessarily represent the views of the Federal Reserve Bank of New York, the Census Bureau, the Board of Governors, or its research staff. The Census Bureau has reviewed this data product to ensure appropriate access, use, and disclosure avoidance protection of the confidential source data used to produce this product. This research was performed at a Federal Statistical Research Data Center under FSRDC Project Number 1883 (CBDRB-FY21-P1883-R9019, CBDRB-FY22-P1883-R9643). †Federal Reserve Bank of New York; sebastian.heise@ny.frb.org. ‡Board of Governors of the Federal Reserve System; justin.r.pierce@frb.gov §University of Tennessee; gschaur@utk.edu ¶Yale School of Management & CEPR & NBER; peter.schott@yale.edu 1

1 Introduction Since the early 1990s, the rapid expansion of global value chains has promoted a substantial increase in world trade, boosted aggregate productivity, and supported an unprecedented convergence in rich and poor country incomes (Johnson, 2018; World Bank, 2020; Antras and Chor, 2022). For much of this time, the international spread of production networks was bolstered by trade liberalization and policy stability. Risingprotectionismin recent years, however, hasdampenedfirms’enthusiasmforglobal supply chains, threatening the welfare gains of previous decades.1 In this paper, we demonstrate that the trade and welfare effects of an increase in the probability of trade restrictions depend on firms’ use of different types of procurement systems. We develop a model of global sourcing that builds upon the partial-equilibrium framework for domestic supply chains introduced by Taylor and Wiggins (1997). In that framework, buyers choose an optimal order pattern, payments, and inspections to procure inputs from sellers that benefit from evading quality standards. Buyers’ costminimizing strategy is one of two systems. Under the “Japanese” system, buyers motivate a seller to maintain high input quality by committing to smaller, more frequent purchases at a price above cost over a long-term relationship. In the opposing “American” system, buyers choose larger, less frequent purchases from a parade of lowest-cost sellers in the spot market. Costly inspections and enforceable contracts deter cheating. Lower inspection costs favor the “American” system, while factors supporting firms’ ability to form long-term relationships favor the “Japanese” system. We hereafter refer to the “Japanese” and “American” systems as J and A. Inthefirstpartofthepaper,weextendTaylorandWiggins(1997)tointernational procurement by linking domestic importers’ ability to maintain long-term relationships with foreign sellers to changes in the probability of a trade war. In equilibrium, eachbuyerprocuresanddistributesitsproductusingthesystemthatminimizescosts. We show that increases in the probability of a trade war reduce the likelihood that buyers choose J procurement because it shortens the expected length of buyer-seller relationships, thereby raising the premia buyers must pay sellers to incentivize high quality under the J system. In the second part of the paper, we document the prevalence of J sourcing among US importers using transaction-level US import data that record both the number of 1See,forexample,Amitietal.(2019),Fajgelbaumetal.(2019),FlaaenandPierce(2019),Flaaen et al. (2020), and Bown et al. (2021). 2

foreign exporters with which US importers trade as well as the values and quantities (and therefore the unit values) associated with each shipment. Guided by our model, we classify importers as using either J or A procurement based on the number of foreign suppliers from which they purchase a particular product from each country over the 1992 to 2016 sample period. A lower ratio of suppliers to the number of shipments indicates more repeat purchases from the same seller, hence a higher likelihood of the J system. Intuitively, we find that J importing is most prevalent from Japan and Mexico, for products classified as transportation and machinery, and for imports obtained by manufacturing versus service firms. We then show, consistent with the model, that buyers with a lower ratio of suppliers to shipments do indeed receive smaller, more frequent shipments at a higher price than A buyers of the same product. J buyers also tend to be larger, pay higher wages, and have lower inventory to sales ratios. These results provide the first systematic empirical evidence of the J and A procurement patterns as highlighted by Taylor and Wiggins (1997).2 In the third part of the paper, we provide evidence of a switch towards J procurement among US importers and Chinese exporters after a 2001 change in US trade policy that substantially reduced the probability of a trade war between the two counties. Our triple difference-in-differences specification, which asks whether US importers’ procurement patterns change after the policy is implemented (first difference), for imports from China relative to other countries (second difference), in products with greater relative exposure to the policy (third difference), provides support for the model along two dimensions. First, we show that imports by importers of more-exposed products from China become relatively smaller, more frequent, and increase in unit value after the change in policy, consistent with a shift to J. A one standard deviation increase in exposure to the policy is associated with a relative decline in shipment size of 4.5 percent and a relative increase in shipment frequency and shipment unit value of 3.9 percent and 2.1 percent, respectively. Second, we find that US importers of more-exposed products exhibit a relative reduction in sellers per shipment. Both results indicate a shift from A to J procurement among the products that benefit most from the elimination of future tariff threats. 2Citing an earlier version of this paper, Cajal-Grossi et al. (2023) use the sellers per shipment measure we propose and find further support for its relevance when examining markups in the Bangladeshi garment market. Macchiavello and Morjaria (2020) examine the use of relational contracts in the Rwanda coffee industry but do not aim to provide evidence for Taylor and Wiggins (1997). 3

In the final part of the paper, motivated by recent events such as Brexit and US-China “de-risking”, we embed our procurement framework in an Eaton and Kortum (2002) model of trade to provide the first assessment of the impact of trade policy uncertainty on relational contracting, i.e., repeated transactions between buyers and sellers under an informal agreement. In our setup, sourcing is governed by bilateral trade war arrival rates in addition to standard cross-country differences in productivity, as they affect the relative costs of procurement under the two systems. Quantitative simulations of the model reveal that an increase in the probability of a trade war that is sufficient to eliminate J-style procurement reduces US welfare about one third as much as placing the US in autarky. Literature Our analysis makes contributions to several literatures. First, we add to the growing body of research on trade wars and trade policy uncertainty (Ossa, 2014; Handley, 2014; Handley and Lim˜ao, 2017; Alessandria et al., 2024; Handley and Lima˜o, 2022) by identifying procurement systems as a new channel through which uncertainty can influence trade patterns and welfare. Our finding of a relationship between procurement system switching and unit values highlights a novel source of price variation in response to changes in trade policy that goes beyond the quality premiums and markups studied in the existing literature (Schott, 2004; Verhoogen, 2008; Khandelwal, 2010; Hallak and Schott, 2011; Kugler and Verhoogen, 2012; Antoniades, 2015; Manova and Yu, 2017). Our model also demonstrates that the distributional implications of changes in policy uncertainty depend on firms’ procurement strategies, with firms choosing to enter relational contracts being more sensitive to increases in the probability of a trade war than firms that rely on the spot market. Second, we contribute to greater understanding of the organization of global value chains (Antra`s et al., 2017; Antra`s and Chor, 2018; Antras and Chor, 2022), as well as a larger literature on incomplete contracts, imperfect contract enforcement, and information asymmetries (Antra`s, 2003; Antra`s, 2005; Grossman and Helpman, 2004; Spencer, 2005; Feenstra and Hanson, 2005; Antr`as and Helpman, 2008; Kukharskyy and Pflu¨ger, 2010). In contrast to much of the research in this area, we consider choice of procurement system rather than firm integration as a solution to firms’ quality-control problem. This path is particularly relevant for understanding sourcing in settings where integration is difficult, for example in China, where foreign firms 4

face numerous formal and informal restrictions regarding ownership of domestic assets. Our work builds upon the literature on relational contracting as an alternative to integration (Defever et al., 2016; Kukharskyy, 2016), where the pattern of trade between buyers and sellers is usually governed by idiosyncratic time preferences. In our model, by contrast, discount rates are common and firms choose between procurement systems based on inspection costs and policy stability. As a result, our model links shipment patterns to policy in a manner amenable to empirical inquiry using transaction-level trade data. Third, our results relate to analyses of importer-exporter trade flows demonstratingthathighfixedper-shipmenttradecostsreduceshippingfrequency,therebyraising inventories in a manner that influences firms’ adjustment to trade shocks (Alessandria et al., 2010; Alessandria et al., 2011; Kropf and Saur´e, 2014; Hornok and Koren, 2015a; Hornok and Koren, 2015b; B´ek´es et al., 2017). Here, we document that firms that source under the A system have higher inventories, and show that trade policy uncertainty can be an important barrier to firms’ efforts to reduce inventory costs, as it discourages use of the leaner J system. We estimate inspection costs of 0.4 percent of the transaction value for the average import transaction, about one tenth of our estimated average fixed cost per shipment. Finally, we examine the consequences of optimal procurement in general equilibrium by extending Eaton and Kortum (2002) along two dimensions. First, we have product prices depending on the probability of a trade war as well as supplier productivity. Second, we have increasing returns to scale in procurement costs due to fixed logistics fees. Quantification exercises reveal that reducing buyers’ ability to form J relationships due to a higher trade war probability reallocates trade towards source countries that rely more on A procurement and lowers welfare by raising prices, akin to an adverse productivity shock. While we focus on changes in the probability of a trade war, our mechanism applies to any factor that undermines sellers’ beliefs about the viability of long-term relationships with buyers, e.g., uncertainty about shipment arrival due to corruption, pandemics, or port disruptions. We examine J sourcing theoretically and empirically in Sections 2 through 4. Sections 5 through 7 extend our model to general equilibrium and perform counterfactuals. Section 8 concludes. An appendix provides additional detail and results. 5

2 Extending Taylor and Wiggins, 1997 Quality control and incomplete contracts are a common problem in firms’ procurement decisions. Taylor and Wiggins (1997) provide a framework that focuses on an arm’s-length solution to these challenges.3 In their theory, a buyer repeatedly seeks to obtain high-quality inputs from a supplier whose effort is unobservable.4 Their solution to this problem is one of two optimal contracts. Under the A system, buyers use competitive bidding to select the lowest-cost supplier for each shipment of inputs, and use the threat of inspection to deter provision of low-quality goods. Under the J system, by contrast, buyers offer sellers a price premium over a long-term relationship as an incentive to deter cheating. The Taylor and Wiggins (1997) framework is particularly suitable to our context because it broadly characterizes typical procurement strategies (Helper and Sako, 1995) and, linking incentive premia to potential trade wars, allows us to examine the effect of trade policy stability on international shipping patterns and welfare. 2.1 The Procurement Problem The Seller’s Problem: There is a country populated by a continuum of homogeneous sellers able to produce the same good.5 To complete a production run (i.e., produce one shipment) a seller hires labor l at wage w = 1 to produce and deliver output x = Υl, where Υ is a seller’s productivity and θ represents her product’s level of θ quality. The unit input requirement, θ, allows for variation in quality, giving rise to a Υ (cid:8) (cid:9) “quality control” problem.6 Sellers choose between discrete quality levels, θ ∈ θ,θ , where lower quality is less costly to produce. To complete the shipment, the seller absorbs f units of labor for per-shipment logistics services, including transport costs.7 The seller’s total costs for each production and delivery cycle are therefore xθ +f. Υ The Buyer’s Problem: Homogeneous buyers with complete bargaining power procure 3Firmintegrationisanotherbutpotentiallyverycostlymeansofaddressingtheseissues(Antr`as, 2003; Antr`as, 2005; Antr`as and Helpman, 2008). China, for example, requires foreign ventures to include a domestic partner, while the United States (and other developed countries) mandate national security reviews. 4Thisproblemfallsintotheclassofrepeatedgameswithincompleteinformation(Kandori,2002). 5We extend the model to multiple products and sellers in multiple countries in Section 5. 6See, for example, “Poorly Made,” The Economist, May 14th, 2009. 7Recentevidenceemphasizesper-unitand-shipmentspecificdeliverycosts(HummelsandSkiba, 2004; Martin, 2012; Kropf and Saur´e, 2014; Hornok and Koren, 2015a; Hornok and Koren, 2015b). 6

Figure 1: Timing Notes: Thetotalquantityshippedoveranordercycleisq. Ordercyclesrepeatindefinitelyandareindexedby o={1,2,...}. Thereares={1,2,...,q/x}shipmentsduringanordercycle,arrivingeveryx/q unitsoftimeapart. a seller’s output and distribute it to consumers. Conditional on desired quality, θ, consumer demand arrives continuously. Let t denote continuous time and consider (cid:82)1 time periods ∆t = 1dt = 1, e.g., 1 year. To supply the consumer market over one 0 time period, a buyer procures total quantity, q, in a series of discrete, equally sized, symmetric shipments of size x. We take q as fixed in this section, but solve for it in equilibrium in Section 5. Consequently, there are q/x shipments during each period. Figure 1 summarizes the shipment and consumption pattern. If quality is less than desirable, then no demand arrives and buyers must dispose of the obsolete shipment without recompense. Following Taylor and Wiggins (1997), the buyer seeks to ensure the desired level of quality using either an A or a J procurement system. In the A system, buyers inspect each shipment, and inspections reveal product quality with certainty.8 Inspection costs m for each shipment are fixed.9 Given an A orderofsizex placedwithaseller,thebuyersetsthepershipmentpricev (x ,θ)/x A A A A to allow the seller to exactly break even and participate, where θ v (x ,θ) = f + x . (1) A A A Υ 8TaylorandWiggins(1997)allowforprobabilisticinspectionsandderivelimittheoremsforsmall discount rates. Our simplification facilitates analytical tractability when we extend discount rates for the possibility of trade wars. 9“[I]tcoststhesametohave20palletsinspectedasitdoesjustone.”See“WhataYearofBrexit Brought UK Companies: Higher Costs and Endless Forms,” New York Times, December 29, 2021. 7

Due to the fixed cost, the buyers’ average procurement costs are decreasing in order size, and therefore each buyer optimally places each order with a single seller. Since the sellers are homogeneous and all willing to supply at the same price, we assume that for a given buyer the winning seller is chosen randomly for each order. Inclusive of inspection costs, the buyer’s total procurement expense equals v (x ,θ)+m . A A A J procurement motivates the production of high quality via an incentive premium and the value of a long-term relationship. This value depends upon the relationship’s longevity. Let trade policy shocks that break buyer-seller relationships, e.g. tariff escalation to prohibitive levels, arrive at a constant rate, ρ.10 Then, relationships survive over a shipment cycle with probability e−ρ q x .11 Our focus is on trade policy but other shocks including natural disasters may have similar consequences (Boehm et al., 2019). Ife−ρ q x < 1, thenfirmsareuncertainaboutwhetherfuturetradepolicywillsustain relationships and a greater arrival rate of trade wars, ρ, increases the separation probability.12 Let r be the per-period interest rate and v (x ,θ) be the payment the J J buyer sets under the J system for each shipment. With continuous compounding, the expected discounted value of the relationship is then vJ(xJ,θ¯) .13 1−e−(r+ρ)xs/q If the buyer does not observe product quality until the shipment is received and the payment is made, then, to guarantee desired quality, he sets a per-shipment payment such that the seller’s net present value of the continued relationship exceeds the one-time profit from cheating on quality, vJ(xJ,θ¯)−f− Υ θ¯ xJ ≥ v (x ,θ ¯ ) − f − θx . 1−e−(r+ρ)xJ/q J J Υ J Rearranging, buyers under the J system set the per-shipment payment 1 1 v (x ,θ ¯ ) = f +θ ¯ x + (cid:2) e(r+ρ)xJ/q −1 (cid:3) (θ ¯ −θ) x . (2) J J J J Υ Υ 1 The per-unit premium (cid:2) e(r+ρ)xJ/q −1 (cid:3) (θ ¯ −θ) incentivizes quality. A key feature of Υ the J system is that more stable trade relationships (i.e., a lower ρ) with repeated smaller shipments, x , sent more frequently reduce the premium necessary to guar- J 10In a potential trade war average tariffs are estimated at 63 percent worldwide (Ossa, 2014). 11Relationships thus break with probability F(t)=1−e−ρt over interval t (Wooldridge, 2002, p. 688). At the product level, ρ reflects both the probability of a trade war (which is the same for all products) and the magnitude of the subsequent rise in tariffs (which might vary across products). 12Handley and Lim˜ao (2017) consider trade policy where tariffs may either go up or down. In our case, the uncertainty is w.r.t. greater tariffs that break relationships. (cid:16) (cid:17)N 13The discount rate over a shipping cycle is lim N→∞ 1+r 1 x/N =e−r q x . q 8

antee desired quality. Long-term relationships are optimal in the Japanese system because they increase the incentive to provide quality. Buyers choose between the A and J system by comparing long-term expected revenues and costs taking into account that trade wars will result in a loss of profits. At a given market price p, long-term expected profits in the two procurement systems are then given by (cid:34) (cid:35) (cid:90) xs/q (cid:2) (cid:3) πb = e−rtpq dt−v (x ,θ)−m / 1−e−(r+ρ)xs/q s∈{J,A} (3) s s s s 0 where discounted revenues per shipment cycle are (cid:82)xs/q e−rtpq dt and m = 0. 0 J 2.2 Market Equilibrium and Optimal Procurement Choice We now determine the optimal procurement system. In equilibrium, buyers’ profits equal zero (see Section 5). Therefore, the market price must equal average costs, AC (x ,q), and employing (3) set equal to zero we obtain s s (cid:18) (cid:19) ¯ r v (x ,θ)+m s s s p = AC (x ,q) = s∈{J,A}. (4) s s s q [1−e−rxs/q] Buyerschooseashipmentsizetominimizeaverageprocurementcostswithineachprocurement system. Taking first order conditions (FOC ) for each system and setting s them to zero we obtain, v s (cid:48)(x s ,θ ¯ ) = (cid:2) v s (x s ,θ ¯ )+m s (cid:3) q re−rxs/q s∈{J,A}. (5) 1−e−rxs/q (1−e−rxs/q) 2 The firm optimally procures x∗ such that the discounted value of higher costs ass sociated with a small increase in order size (left-hand side) equals the savings from an increased discount factor due to spacing these larger orders further apart in time (right-hand side).14 Thebuyercomparesaverageprocurementcostsevaluatedattheoptimum,AC (x∗,q), s s ¯ to determine the cost-minimizing procurement system. If θ−θ = 0 and with m = 0, A then there is no incentive problem and costs in both systems are identical. Com- 14Supplemental Appendix J.1 shows that an interior solution to the first order condition is a unique cost minimizer for 0 < rx/q < 1. The Supplemental Appendix is available on the authors’ websites. It is not for publication and provides additional results not central for the argument. 9

pared to this benchmark case, differentiating equation (4) under the J system with respect to θ and ρ using the envelope theorem shows that average procurement costs in the J system increase with the arrival rate of trade wars, ρ, and with the range ¯ of potential qualities, θ − θ, due to the greater incentive premia they necessitate, ∂ACJ (x∗ J ,q) ≤ 0 and ∂ACJ (x∗ J ,q) ≥ 0.15 In the A system, differentiating (4) with re- ∂θ ∂ρ spect to m shows that average costs increase with inspection costs m. Importantly, as m → ∞, we have AC (x∗,q) → ∞ because average costs grow without bound, A A ∂ACA (x∗ A ,q) = 1 > 1. We obtain the following proposition. ∂m rx∗ 1−e− q A Proposition 2.1. For θ ¯ −θ > 0 and ρ > 0, there is always a threshold value m∗ ∈ (0,∞) for inspection costs such that average procurement costs in both systems are the same. This point is the cut-off at which the buyer switches systems: the American system is chosen for m < m∗, and the J system is chosen for m > m∗. Proof. See Appendix A.2. This proposition highlights that the arrival rate of trade wars affects the average procurement cost under the J system and buyers’ endogenous choice of the procurement system. Starting at a level of inspection cost m slightly below m∗, a reduction in ρ lowers average costs under the J system and reduces the threshold inspection cost m∗ at which procurement costs under both system are the same, causing the buyer to switch from the A to the J system if m∗ falls below m.16 To map the choice of procurement system into observable trade flows, we examine how order size, frequency, and unit values differ across the two systems. We restrict our attention to a setting where buyers make a purchase at least once per period, x∗ ≤ q, and where discount rates are bounded, i.e., 0 < rxs < 1. q Proposition 2.2. An increase in the probability of a trade war, which increases ρ, raises the unit value per shipment and reduces the size of shipments (i.e., raises shipment frequency) in the J system. An increase in the inspection cost m lowers the unit value per shipment and raises the size of shipments (i.e, reduces shipment frequency) in the A system. 15See Appendix Section A.1 below for the proof. 16Existing theories of relational contracts in trade rely on exogenous heterogeneity in discount rates to determine relationship-based transactions (Kamal and Tang, 2015; Defever et al., 2016; Kukharskyy, 2016). In our framework, buyers endogenously determine the effective discount rate of rx /q by choosing the optimal procurement system and order size in response to inspection costs s and the probability of a future trade conflict. 10

Proof. See Appendix A.3. Under the J procurement system an increase in ρ raises the incentive premium. As a result, variable procurement costs increase and buyers re-optimize by lowering shipment sizes (i.e., raising shipping frequency). Unit values increase because fixed per-shipment costs are spread over smaller shipment sizes. Instead, an increase in the inspection cost m raises fixed per-shipment costs under the A system, and buyers reoptimize by increasing per-shipment quantities (i.e., decreasing shipping frequency). The unit value paid to the seller must decrease in the A system since the fixed cost f is spread over more units. We can now rank shipping frequencies and unit values across the two systems. If ¯ θ − θ = 0 and m = 0, then the A and J procurement systems are identical. An A ¯ increase in θ−θ raises variable shipment costs under the J system, leading buyers to increase their shipping frequency by lowering the shipment size. Unit values increase because fixed costs are spread over fewer units. Under the A system, Proposition 2.2 showsthatanincreaseininspectioncostsraisestheshipmentsize, andhenceshipping ¯ frequency and unit values decrease. Therefore, if θ−θ > 0 and m ≥ 0, then shipping sizes are greater in the A system and unit values are greater in the J system. This reasoning forms the basis of our third proposition. Proposition 2.3. Batch sizes in the A system are greater than in the J system, x∗ > x∗, and therefore time between shipments is greater under the A system, x∗/q > A J A x∗/q. Unit values in the J system are greater than in the A system, v (x ,θ ¯ )/x > J J J J ¯ v (x ,θ)/x . A A A Proof. See Appendix A.4. Figure 2 illustrates the predictions of a lower likelihood of trade war (a decrease in ρ) according to Proposition 2.2 and 2.3. The effect depends on whether the adjustment takes place within the J system or via a switch from the A to the J system. Within the J system, unit values fall, shipment sizes increase, and shipping frequency declines. Within the A system we expect no impact on prices, quantities, or frequencies. If a lower trade war arrival rate triggers a switch from A to J procurement, then we predict a decrease in shipment sizes and an increase in the unit value. In Section 3, we show that the frequency of US importing from China under the J system is relatively low in the first part of our sample period, but that it rises 11

Figure 2: Impact of A Decline in the Probability of Trade Conflict (ρ) Notes: Figureillustratestheimpactofachangeinthearrivalrateofatradewar,ρonshipmentunitvalues(uv) andquantities(x)underbothsystemswhere,e.g.,∆uv<0indicatesadeclineinunitvalue. over time. Consistent with this finding, Section 4 shows that a plausibly exogenous reduction in ρ vis `a vis China primarily results in A to J switching. 3 Data on J Importers We use the US Census Bureau’s Longitudinal Foreign Trade Transaction Database (LFTTD) to identify J importers and to examine the predictions of the model introduced above. Our dataset tracks every US import transaction from 1992 to 2016 and includes: the dates the shipment left the exporting country and arrived in the United States; identifiers for the US and foreign firm conducting the trade; the shipment’s value and quantity; a ten-digit Harmonized System (HS10) code classifying the product traded; the country of origin of the exporter; and the mode of transport.17 We perform standard data cleaning and use the concordance developed by Pierce and Schott (2012) to create time-consistent HS codes. Given our focus on arm’s-length trade, we drop all related-party transactions. Since shipments of the same product between the same buyer and seller spread over multiple containers are recorded as separate transactions, we aggregate the dataset to the weekly level. For more detail on our data preparation, see Appendix Section B. Our analysis below focuses on “buyer quadruples” that group shipments of a tendigit HS product (h) imported by a US importer (m) from origin country (c) shipped 17We focus on vessel, rail, road, and air, dropping the small fraction of transactions that are transported by other means, e.g., hand-carried by passengers. See Bernard et al. (2009) for further information on the LFTTD and Kamal and Monarch (2018) for more detail on the foreign firm identifier. 12

via mode of transportation (z).18 Since our theory requires that we observe repeated shipments to learn about the procurement system, we exclude buyer quadruples with fewer than five shipments in our analysis.19 Our sample represents more than 80 percent of all arm’s length trade and contains almost 3 million mhcz quadruples between 1992 and 2016. There are nearly 22 million “buyer-seller relationships” associated with these bins, i.e., the number of mxhcz quintuples, where x denotes the exporter. Table A.1 in Appendix B provides an overview.20 Table 1 summarizes the mhcz quadruples, which are the focus of our study in the next section. The first four rows of the table reveal that from 1992 to 2016, the average mhcz bin traded 1.9 million dollars (in 2009 units), lasted for 304 weeks and encompassed 39 shipments across 7 sellers. Rows 5 through 7 highlight “procurement patterns,” showing that average value per shipment (VPS ), weeks between mhcz shipments (WBS ), and buyer-seller relationship length across the relationships mhcz within a quadruple (length ) averaged 36 thousand dollars, 24 weeks and 181 mhcz weeks, respectively.21 3.1 Sellers per Shipment (SPS ) mhcz A key characteristic of J buyers in the model developed in Section 2 is that they trade with just one seller. Guided by this insight, we use the ratio of the number of sellers to the number of shipments (SPS) within importer-product-country-mode 18Includingmodeoftransportinthesebinsmitigatestheinfluenceofspurioussourcesofvariation like product quality that might differ across product varieties shipped using different methods. 19Quadruples with fewer than five shipments might also represent importers trying out a new productorotheridiosyncrasies. InSupplementalAppendixK,weprovidesomestatisticscomparing oursampleagainstthebroadersampleofallarm’s-lengthquadrupleswithatleasttwotransactions. Weneedatleasttwotransactionstobeabletocomputesomeofourvariables,suchasweeksbetween shipments(WBS ). Asexpected,theexcludedquadrupleswithfewerthanfivetransactionstend mhcz to be relatively small and trade more rarely. 20Referringto“mhcz quadruples”and“mxhcz quintuples”isawkwardbutprecise. Inthedata,a given seller (i.e., exporter) may supply a particular HS code to multiple buyers (i.e., importers). To match theory and data, we interpret this behavior as sellers producing different varieties within HS codes for each buyer without any costs to the buyer or seller beyond those described in Section 2. Moreover,weassumethatAbuyerscanprocuretheirvarietyfromdifferentsellersovertime,andthat different buyers procuring the same product from the same seller might use different procurement systems because inspection costs can vary by variety within a product. 21Appendix C provides more details on how all variables are constructed. While below we also analyze quantity per shipment (QPS ) and unit value per shipment (UV ), they are not mhcz mhcz summarized here due to differences in quantity units across products. Relationship lengths can be subjecttobothleftandrightcensoringatthebeginningandendofour1992to2016sampleperiod. 13

Table 1: Attributes of mhcz Quadruples Standard Mean Deviation Total Value Traded ($) 1,914,000 36,300,000 Length Between Buyer’s First and Last Shipment (Weeks) 304.3 266 Total Shipments 38.6 157.9 Number of Sellers (x) 7.3 25.5 Value per Shipment (VPS), ($) 35,910 386,100 Weeks Between Shipments (WBS) 23.5 28.5 Average Relationship Length in Weeks (length) 180.8 154.7 Ratio of Sellers to Shipments (SPS) 0.334 0.241 Source: LFTTD and authors’ calculations. Table reports the mean and standard deviation across importer (m) by country (c) by ten-digit Harmonized System category (h) by mode of transport (z) quadruples during our 1992 to 2016sampleperiod. Importvaluesareinreal2009dollars. Observationsarerestrictedtoquadrupleswithatleastfive transactions. Observation counts are rounded to the nearest thousand per US Census Bureau disclosure guidelines. (mhcz) quadruples, Sellers mhcz SPS = , (6) mhcz Shipments mhcz as an observable metric of J sourcing. This variable has an upper bound of one, i.e., a different supplier for every shipment, and approaches a lower bound of zero in the case of many transactions sourced from a single seller. Buyers that use fewer sellers relative to the number of shipments (i.e., those with lower values of SPS ) mhcz are more likely to be engaged in repeated transactions, and hence in J procurement. While A buyers might in theory also transact with few sellers if they repeatedly offer the lowest price, introducing noise into our measure, we find below that SPS is mhcz indeed correlated with procurement patterns in a manner consistent with the model. The distribution of SPS across buyer quadruples with at least five transacmhcz tions from 1992 to 2016 is displayed in the kernel density reported in Figure 3. As indicated in the figure, most buyer quadruples have a relatively small ratio of sellers to shipments. Observations in the right tail approach a value of 1, i.e., a different seller for each shipment. As reported in the final row of Table 1, the mean ratio of sellers to shipments across buyer quadruples is 0.33, with standard deviation 0.24. The first two columns of Table 2 report the weighted average of SPS for buyer mhcz quadruples trading with the noted countries, using the quadruples’ total imports as weights. These means are reported for the two five-year time periods used in our regression analysis in Section 4. For the first time period, we find that the 14

Figure 3: Sellers Per Shipment (SPS) Across Relationships, 1992 to 2016 Source: LFTTDandauthor’scalculations. Figuredisplaysthedistributionofsellerspershipment(SPS ) mhcz acrossallbuyerquadrupleswithatleastfivetransactionsbetween1992and2016. Thefigurewascreatedaccording toCensusBureauguidelinesandomitsobservationsbelowthe5thpercentileandabovethe95thpercentile. averageSPS islowestforUSimportsfromMexicoandJapan, consistentwiththe mhcz prevalence of J sourcing in the automobile industry—a key industry in US trade with these countries—including among large Japanese multinationals like Toyota (Boehm et al., 2020). Results in the second column reveal that, over time, average SPS mhcz generally falls. The largest decreases exhibited, both in levels and percent growth, are for Mexico, China and Brazil. The relatively large drop for Mexico may be related to increasingly close supply-chain integration with US producers as a result of NAFTA. In Section 4, we examine whether the decline in SPS for China is related to the mhcz US granting Permanent Normal Trade Relations (PNTR) in 2001. In subsequent analysis, we will also consider an indicator variable for J importers that takes the value 1 when SPS falls in the first quartile of its distribution mhcz computed within a given bin k in the first period, 1995-2000, Jk . For our crossmhcz country comparison, we compute the SPS distribution within product-mode bins, but across countries (k = hz). This choice implies that the share of J imports can vary between countries even though, worldwide, 25 percent of quadruples fall into the first quartile by construction. We define analogous dummies for the later time period, also with respect to the distribution of SPS in the first time period, to mhcz capture changes with respect to the initial distribution. The final two columns of Table 2 report the share of imports from each country in each time period accounted for by buyer quadruples for which Jhz = 1. While the 25th percentile cutoff used in mhcz this procedure is arbitrary, it provides a rough indication of variation in J importing across source countries. Consistent with the raw SPS measure, J import value mhcz 15

Table 2: J Relationships by Country Jhz =1 Mean SPS mhcz Share of Import Value (1) (2) (3) (4) Country 1995-2000 2002-2007 1995-2000 2002-2007 Mexico 0.095 0.068 0.750 0.869 Japan 0.107 0.123 0.756 0.725 Taiwan 0.132 0.114 0.711 0.743 Canada 0.141 0.120 0.602 0.667 United Kingdom 0.146 0.225 0.717 0.519 South Korea 0.156 0.135 0.656 0.724 France 0.177 0.158 0.627 0.667 Rest of the World 0.180 0.156 0.625 0.678 Germany 0.184 0.163 0.582 0.606 China 0.185 0.147 0.582 0.693 Brazil 0.190 0.151 0.576 0.706 Source: LFTTDandauthors’calculations. Columns(1)and(2)reporttheweightedaveragesellerspershipment (SPS )acrossbuyerquadrupleswithatleastfivetransactionsbycountryandperiod,whereimportvaluesare mhcz usedasweights. Columns(3)and(4)reporttheshareofthevalueofUSimportsaccountedforbyquadrupleswith SPS inthefirstquartileofthedistributionofSPS withinproduct-modeinthefirstperiod. Rowsofthe mhcz mhcz tablearesortedbycolumn(1). shares increase over time, overall, and most strongly for Brazil, China, and Mexico. Appendix B presents further breakdowns of how SPS varies across groups of mhcz ten-digit HS codes and 6-digit NAICS industries of importing firms. We find that J sourcing is most prevalent for transportation equipment, machinery, and plastics, and that manufacturers are the most likely to use J sourcing, consistent with these firms obtaining relatively customized inputs for their production processes. 3.2 SPS and Procurement Attributes mhcz We now evaluate the link between SPS and procurement patterns via an mhczmhcz level OLS regression, ln(Y ) = β ln(SPS )+β ln(QPW )+β beg +β end +λ +(cid:15) . mhcz 1 mhcz 2 mhcz 3 mhcz 4 mhcz hcz mhcz (7) Guided by our theory, the dependent variable, Y , represents the key dimensions mhcz by which the A and the J systems differ: average quantity per shipment (QPS ), mhcz weeks between shipments (WBS ), and unit value (UV ) across all transacmhcz mhcz 16

Table 3: SPS and Procurement Attributes mhcz (1) (2) (3) (4) (5) (6) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) ln(QPS ) ln(WBS ) ln(UV ) mhcz mhcz mhcz mhcz mhcz mhcz ln(SPS ) 0.418∗∗∗ 0.452∗∗∗ −0.123∗∗∗ mhcz 0.017 0.017 0.021 1{SPS =Q2} 0.328∗∗∗ 0.350∗∗∗ −0.117∗∗∗ mhcz 0.014 0.015 0.014 1{SPS =Q3} 0.552∗∗∗ 0.591∗∗∗ −0.179∗∗∗ mhcz 0.024 0.024 0.023 1{SPS =Q4} 0.792∗∗∗ 0.856∗∗∗ −0.226∗∗∗ mhcz 0.034 0.035 0.038 ln(QPW ) 0.701∗∗∗ −0.308∗∗∗ −0.287∗∗∗ 0.687∗∗∗ −0.323∗∗∗ −0.282∗∗∗ mhcz 0.014 0.014 0.020 0.013 0.014 0.019 Observations 2,966,000 2,966,000 2,966,000 2,966,000 2,966,000 2,966,000 Fixedeffects hcz hcz hcz hcz hcz hcz R-squared 0.947 0.674 0.845 0.945 0.661 0.845 Controls beg,end beg,end beg,end beg,end beg,end beg,end Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingnotedattributesofimporterbyproductbycountrybymodeoftransport(mhcz)binsonbins’sellerspershipment(SPS ),sellerspershipmentquarmhcz tiledummies,andtotalquantityshippedperweek(QPW ). (QPS ),(WBS ),and(UV )areaverage mhcz mhcz mhcz mhcz quantitypershipment,averageweeksbetweenshipment,andaverageunitvalue. Allregressionsincludeproductby countrybymodeoftransport(hcz)fixedeffects,controlforthebeginningandendweekofthequadruple,andexclude quadrupleswithlessthanfiveshipments. Standarderrors,adjustedforclusteringbycountry(c)andproduct(h)are reportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percentlevels. tions within the mhcz quadruple. In line with holding quantity fixed in Section 2, we condition on buyers’ total order “flow” by controlling for the quantity imported by a buyer quadruple over its entire lifetime divided by its overall length in weeks, QPW .22 We control for quadruples’ first and last weeks of trade, beg and mhcz mhcz end , to capture effects of trading in a specific time period—such as a particumhcz lar stage in the business cycle—and duration effects.23 Our regression also includes product by country by mode of transportation fixed effects (λ ), which capture hcz time-invariant characteristics of trade along these dimensions such as distance, transit time, or level of transportation infrastructure. The sample period is 1992 to 2016, and standard errors are two-way clustered at the country and product level.24 Results for specification (7) are reported in Table 3. In the first three columns, we find that quadruples with higher SPS , i.e., those that are more A, receive mhcz 22This variable also controls for the possibility that overall order flow could lead to variation in averageshipmentsizesorunitvaluesforreasonsunrelatedtotheprocurementsystem. Wenormalize the total quantity traded by the number of weeks since it is straightforward to implement in our weekly dataset. An alternative would be to use the annual quantity traded. 23beg andend arecontinuousvariablesindicatingtheweeknumbersthattherelationship mhcz mhcz commences and ceases. 24As before, we only use quadruples with at least five shipments over the entire sample period. In Appendix D, we show that results are qualitatively identical for a cutoff of 10 shipments. We describe the construction of all variables in detail in Appendix C. 17

shipments for a given total order flow that are larger, less frequent, and lower in price, consistent with Proposition 2.3. Furthermore, the coefficient estimates for our quantity control, QPW , are in line with Proposition 5.1, discussed below, where mhcz an increase in the total quantity procured leads to an increase in shipment size and reductions in the number of weeks between shipments and unit value. Coefficient estimates for SPS indicate that increasing sellers per shipment by one standard mhcz deviation from its mean (from 0.33 to 0.58) is associated with a 23 log point rise in quantity per shipment, a 25 log point increase in weeks between shipments, and a 7 log point decline in price.25 In the final three columns of Table 3, we consider a related specification that relaxes the restriction of a linear relationship between procurement attributes and sellerspershipmentbyreplacingSPS withaseriesofdummyvariablesindicating mhcz the quartile into which buyer quadruples fall. We compute these quartiles separately for each hcz bucket using the entire sample period. The first quartile, 1{SPS = mhcz Q1}, is the left-out category. This specification further justifies the use of SPS as mhcz a metric of J sourcing, as coefficient estimates for SPS rise or fall monotonically mhcz from quartile 1 to quartile 4 in a manner consistent with the quartiles representing increasingly A quadruples.26 3.3 SPS and Other Characteristics mhcz Relationship Length: Buyers under the J system rely on repeat purchases from the same seller, while buyers under the A system choose potentially different lowest-cost suppliers for each transaction. An implication of these choices is that J buyers have longer relationships with their suppliers. We investigate this prediction using the variable length , which tracks the average length of the mx buyer-seller relationmhcz 25Our analysis computes SPS at the level of buyer quadruples (mhcz). One concern with this definition might be that buyers obtain shipments across multiple modes of transportation, and therefore procurement systems – and hence SPS – should be better defined at the mhc level. Analogously, SPS could be defined at at an even more aggregated mh level. In Appendix D, we re-runspecification(7)wherewecomputeSPSusingtheratioofsellerstotransactionswithinbuyerproduct-country triples (SPS ) and buyer-product doubles (SPS ), and find similar results. mhc mh 26In Appendix Section D we show that the relationships displayed above are robust to analyzing procurement patterns separately by mode of transport, i.e., vessel versus air. In Supplemental Appendix L, on the authors’ websites, we show that the results are similar when we examine procurement patterns within mxhcz buyer-seller relationships, and that the results hold separately within each sector, such as manufacturing or retail. We also show that procurement patterns for differentiated products based on Rauch (1999) are more J compared to commodities. 18

Table 4: SPS and Relationship Length mhcz (1) (2) Dep. var. ln(length ) ln(length ) mhcz mhcz ln(SPS ) −0.576∗∗∗ mhcz 0.015 (SPS =Q2) −0.383∗∗∗ mhcz 0.015 (SPS =Q3) −0.683∗∗∗ mhcz 0.027 (SPS =Q4) −1.139∗∗∗ mhcz 0.047 ln(QPW ) −0.147∗∗∗ −0.130∗∗∗ mhcz 0.006 0.005 Observations 2,966,000 2,966,000 R-squared 0.431 0.413 Fixedeffects hcz hcz Controls beg,end beg,end Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingtheaveragebuyer-sellerquadruple relationshiplength(length )onquadruples’sellerspershipment(SPS ),sellerspershipmentquartile mhcz mhcz dummiesandtotalquantityshippedperweek(QPW ). Theregressionsincludeproductbycountrybymodeof mhcz transport(hcz)fixedeffects. Allregressionscontrolforthebeginningandendweekofthequadruple,andexclude quadrupleswithlessthan5shipments. Standarderrors,adjustedforclusteringbycountry(c)andproduct(h)bin arereportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percent levels. ships associated with mhcz buyer quadruples. This variable is constructed in two steps. First, for each mxhcz quintuple, we compute the total number of weeks passed between the first and the last transaction of any product by any mode between the buyer m and seller x, i.e., their total relationship length. Second, for each mhcz buyer quadruple, we take the average of these numbers of weeks across all mxhcz quintuples within the quadruple. This average allows for the possibility that buyers already sourcing one product from a given supplier, or already using a different mode of transportation with that seller, add products over time. We use the same specification outlined in equation (7) but using length as mhcz the dependent variable. The results, reported in Table 4, show that mhcz buyer quadruples with lower ratios of SPS tend to have longer relationships. In column mhcz (1), we find that a one standard deviation increase of sellers per shipment from its mean is associated with a 31 log point decrease in average relationship length. In column (2), the average relationship length for quadruples in the fourth quartile (most A) is about 114 log points lower than that in the first quartile (most J).27 27In Appendix section D and Supplemental Appendix L, we show that all our robustness checks alsogothroughforthelengthvariable. InSupplementalAppendixL,wealsoconsideranalternative definitionofrelationshiplengthwherewetreateachquintupleasaseparaterelationship,ratherthan using the overall importer-supplier pair, and show that our results still hold. 19

Table 5: SPS and Firm Characteristics m (1) (2) (3) (4) Dep. var. ln(sales ) ln(pay ) ln(wage ) (inv/sales) m m m m ln(SPS ) −0.291∗∗∗ −0.350∗∗∗ −0.056∗∗∗ 0.015∗∗∗ m 0.005 0.006 0.002 0.001 Observations 184,000 184,000 184,000 48,500 R-squared 0.015 0.018 0.003 0.006 Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingimportercharacteristicsinthe yearoftheimporter’sfirsttransactiononsellerspershipment(SPS )averagedacrossallquadruplesinvolving mhcz theimporter. Allregressionsexcludequadrupleswithlessthanfiveshipments. (salesm),(paym),(wagem),and ((inv/sales)m)aretotalsales,totalpayroll,averagewage(i.e.,payrolldividedbynumberofemployees),andtotal inventoryatthebeginningoftheyeardividedbytotalsales,respectively. Robuststandarderrorsarereported belowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percentlevels. Buyer Characteristics: In Appendix B, we show that the importer dimension is the most important for explaining variation in SPS . We therefore next investigate mhcz how various firm-level attributes are related to import sourcing strategy, measured by SPS . We aggregate the quadruples across products, countries, and modes to mhcz the importer-level and run the importer-level regression ln(Y ) = β ln(SPS )+(cid:15) ., (8) m 1 m m where Y is one of importer m’s total sales, total payroll, average wage, or the firm’s m inventory-to-sales ratio, and SPS is an average of SPS across all quadruples m mhcz of the importer. We obtain sales, payroll, and wages at the firm-level from the Longitudinal Business Database (LBD), where the average wage is constructed as the firm’s total payroll divided by the number of employees. We obtain beginning-of-year inventories for manufacturing firms from the Annual Survey of Manufactures (ASM) and the Census of Manufactures (CMF). We use for each firm attribute the earliest non-missing observation available for the firm.28 Table 5 shows the regression results. We find that firms that on average rely on more A procurement practices tend to be smaller, pay lower wages, and hold higher inventories. An increase in average sellers per shipment by one standard deviation from its mean is associated with a 16 log point decline in sales, 19 log point decline in payroll, and a 3 log point decline in the average wage.29 A one standard deviation increase in SPS from its mean mhcz 28Results are robust to using an average across all active years (see Appendix D). 29As we will show in Section 6 below, these findings are qualitatively consistent with our model, 20

raises the inventory-to-sales ratio by 0.8 log points, consistent with A procurement leading to larger inventories.30 Finally, consistent with a firm-wide sourcing strategy, we find that importers’ procurement system is correlated across products. Using all importers with at least two products in a given country-mode bin, we randomly draw two of these products foreachimporter. WethenusetheJ indicatorJhcz , computedusingthedistribution mhcz of SPS within hcz bins for the entire sample period, and regress Jhcz of the mhcz mhcz,1 first product on Jhcz of the second product. We re-run this regression 1000 times, mhcz,2 where we re-draw the two products on every run. Our estimated average coefficient on Jhcz is 0.234 (bootstrap s.e. = 0.001) with a constant of 0.214 (s.e. = 0.001), mhcz,2 indicating that the probability of the second product being J approximately doubles when the first one is. 4 PNTR and the Choice of Procurement System A key insight from the model presented in Section 2 is that trade policy can alter buyers’ choice of procurement system by affecting the probability of trade wars. In this section, we examine the prediction that a decrease in the probability of a trade war can induce buyers to shift from A to J procurement using a plausibly exogenous change in US trade policy, the US granting of Permanent Normal Trade Relations (PNTR) to China in 2001. We assess these shifts across both continuing and new mxhcz quintuples, and in terms of importers’ sellers per shipment (SPS). As described in Pierce and Schott (2016), prior to PNTR, US imports from China were subject to the risk of punitive tariff increases absent annual action from the President and Congress. Pierce and Schott (2016) and Alessandria et al. (2024) document the trade-dampening effects of this uncertainty on US importers prior to PNTR,andHandleyandLima˜o(2017)provideatheoreticalbasisfortheseeffectsthat operates via suppressed entry by Chinese exporters. We measure exposure to PNTR via the “NTR Gap” from Pierce and Schott (2016), which measures the amount that tariffs could have increased prior to PNTR and varies by product.31 where we find that larger importers are more likely to use the J system. 30Note that we only observe the overall inventories of the firm, across all products and including domestic purchases. Our results suggest that variation in international procurement is associated with tangible differences in firms’ overall inventories. 31See Supplemental Appendix M, on the authors’ websites, for additional details on the NTR gap 21

PNTR and continuing mxhcz quintuple attributes: Our first approach to testing whether PNTR influences procurement is to examine its impact on the procurement attributes examined in Section 3: quantity per shipment, weeks between shipments and unit value. These attributes are observed at the buyer-seller mxhcz quintuple level. We therefore analyze procurement attributes among continuing quintuples, which trade in both the pre- and the post-PNTR period, in this subsection, and for new quintuples in the next subsection. Our OLS triple difference-in-differences (DID) identification strategy examines the relationship between PNTR and the procurement attributes before versus after the change in policy (first difference), for imports from China versus other source countries (second difference), for products with higher versus lower NTR gaps (third difference), ln(Y ) = β 1{t = Post}∗1{c = China}∗NTRGap (9) mxhczt 1 h +β ln(QPW )+β χ +λ +λ +(cid:15) . 2 mxhczt 3 mxhczt mxhcz t mxhczt The last difference captures the fact that products with larger NTR gaps experience a greater decline in the relationship termination probability, which is a function of the change in China’s NTR status (identical for all products) and the increase in tariff rates that could have occurred before PNTR, which varies by product. We expect the largest shift toward J procurement after PNTR to occur in US imports of high-NTR-gap products from China. The variable Y on the left-hand side of specification (9) represents one of the mxhczt three procurement attributes: quantity per shipment (QPS ), weeks between mxhczt shipments (WBS ), and unit value (UV ).32 The first term on the rightmxhczt mxhczt hand side is the triple difference-in-differences (DID) term of interest, an interaction of an indicator for the post period, 1{t = Post}, a dummy for imports from China, 1{c = China}, and the NTR Gap . The variable χ represents the full set of h mxhczt interactions of those variables required to identify β . The remaining terms on the 1 right-hand side control for the average quantity traded per week in each of the two periods (QPW ) as well as buyer-seller quintuple (λ ) and period (λ ) fixed mxhczt mxhcz t variable. As we show, the NTR gap varies widely across products. While the probability that tariff increases would occur was identical across products, the probability of such an increase severing importer-supplier relationships varies with the NTR Gap. 32Appendix C provides more details on how the variables in this section are constructed. 22

Table 6: Baseline Within mxhcz Quintuple PNTR DID Regression (1) (2) (3) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) mxhczt mxhczt mxhczt Post ∗China ∗NTRGap -0.197*** -0.168*** 0.092*** t c h 0.009 0.009 0.023 ln(QPW ) 0.368*** -0.632*** -0.124*** mxhczt 0.009 0.008 0.013 Observations 439,000 439,000 439,000 R-squared 0.982 0.894 0.985 Fixed effects mxhcz,t mxhcz,t mxhcz,t Controls Yes Yes Yes Source: LFTTDandauthors’calculations. TablereportstheresultsofregressingnotedattributeofUSimporterby exporterbyproductbycountrybymodeoftransport(mxhcz)binsonthedifference-in-differencestermofinterest andquantityshippedperweek. Pre-andpostperiodsare1995to2000and2002to2007. QPS ,WBS , mxhczt mxhczt andUV areaveragequantitypershipment,averageweeksbetweenshipment,andaverageunitvalue(i.e. mxhczt valuedividedbyquantity)inperiodt. Allregressionsincludemxhcz andperiodtfixedeffects,controlforthe beginningandendweekofthequadrupleaswellasallvariablesneededtoidentifytheDID termofinterest. Standarderrors,adjustedforclusteringbycountry(c)andproduct(h),arereportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percentlevels. effects. Our two five-year periods (t), 1995 to 2000 and 2002 to 2007, are chosen to straddle the change in policy in 2001 and end before the Great Recession.33 Standard errors are two-way clustered at the country and product level. Conducted at the mxhcz level, equation (9) is restricted to continuing buyerseller relationships via the mxhcz quintuple fixed effect. We restrict the sample to quintuples that transact at least twice both before PNTR and after the policy change so that weeks between shipments (WBS ) can be computed. mxhczt Results, reported in Table 6, indicate that higher exposure to PNTR is associated with changes in shipping attributes that are consistent with a move toward Japanesestyle procurement within existing buyer-seller quintuples. Coefficient estimates in the first two columns show that a one standard deviation increase in the NTR Gap (0.23) induces a relative decline in quantity per shipment and weeks between shipments of 4.5 log points and 3.9 log points respectively. Moreover, results in column 3 reveal that a one standard deviation increase in exposure to PNTR is associated with a relative increase in unit value of 2.1 log points. In each case, the findings in Table 6 are consistent with the predictions of Propositions 2.1 and 2.3, indicating a switch 33In Appendix Section E, we demonstrate that all results in this section are robust to using a different post-PNTR period, 2004 to 2009. 23

from A to J procurement, as opposed to an adjustment within the J system.34 PNTR and new mxhcz quintuple attributes: We next compare the procurement attributes of new buyer-seller mxhcz quintuples formed in the post-PNTR period to relationships that were new in the pre-PNTR period. For both periods, we define new quintuples as those involving buyer-seller mx pairs that had not yet appeared before the beginning of the period, i.e., from 1992 to 1994 for the first period and from 1992 to 2001 for the second period. As in the previous section, the regression is performed at the mxhcz level and standard errors are two-way clustered at the country and product level. Instead of mxhcz quintuple fixed effects, however, we include separate buyer quadruple (mhcz), exporter (x), and period (t) fixed effects, thereby focusing on buyers and sellers that exist in both time periods (with at least one trading partner), but who form new relationships across the time periods.35 Results, reported in Table 7, are consistent with relatively greater entry of J relationshipsafterPNTR:buyer-sellerquintuplestradinggoodswithgreaterexposure to the change in policy formed after it was implemented exhibit relatively smaller and more frequent shipments, at relatively higher prices, than quintuples formed before PNTR. Point estimates indicate that a one standard deviation increase in exposure is associated with a 2.7 log point and 2.2 log point decline in shipment size and weeks between shipments, respectively, and a 2.1 log point rise in price. PNTR and Sellers per Shipment (SPS): The previous two exercises demonstrate that higher exposure to PNTR is associated with relatively more J procurement attributes after the policy change. We next focus on the impact of PNTR on buyers’ sellers per shipment, the metric for identifying J relationships introduced in Section 3. We consider both the continuous measure SPS as well as the indicator for mhcz whether this ratio falls into the first quartile of the pre-PNTR period distribution within product by country by mode bins, Jhcz = 1. mhcz 34ConsistentwithProposition5.1,thecoefficientestimatesforln(QPW )indicatethataninmxhczt creaseintheprocurementquantityincreasesthesizeofshipments,raisesshippingfrequency,andreducesunitvalues. WeshowinAppendixEthatourconclusionsarequalitativelyunchanged,though the coefficient on WBS is not statistically significant, when we do not include QPW as mxhcz mxhczt acovariate. InSupplementalAppendixN,weanalyzetheeffectofPNTRonthethreeprocurement attributes at the mhcz quadruple level and find similar results. 35AsnotedinSupplementalAppendixN,resultsarerobusttoincludingbothcontinuingandnew mxhcz buyer-seller quintuples simultaneously in one regression. 24

Table 7: New mxhcz Quintuple PNTR DID Regression (1) (2) (3) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) mxhczt mxhczt mxhczt Post ∗China ∗NTRGap -0.116*** -0.097*** 0.090** t c h 0.023 0.023 0.038 ln(QPW ) 0.409*** -0.594*** -0.129*** mxhczt 0.013 0.012 0.018 Observations 3,184,000 3,184,000 3,184,000 R-squared 0.966 0.842 0.972 Fixed effects mhcz,x,t mhcz,x,t mhcz,x,t Controls Yes Yes Yes Source: LFTTDandauthors’calculations. Tablereportstheresultsofcomparingnewbuyer-sellerrelationshipsin thepre-versuspost-PNTRperiod. Pre-andpostperiodsare1995to2000and2002to2007. Newrelationshipsare definedasmxpairsappearforthefirsttimeineachperiod. (QPS ),(WBS ),and(UV )are mxhczt mxhczt mxhczt averagequantitypershipment,averageweeksbetweenshipment,andaverageunitvalue(i.e. valuedividedby quantity)inperiodt. Allregressionsincludemhcz,xandperiodtfixedeffects,controlforthebeginningandend weekofthequadrupleaswellasallvariablesneededtoidentifytheDIDtermofinterest. Standarderrors,adjusted forclusteringbycountry(c)andproduct(h),arereportedbelowcoefficientestimates. ***,**,and*represent statisticalsignificanceatthe1,5and10percentlevels. Our triple DID specification is similar to equation (9), but takes place at the buyer mhcz quadruple level, ln(Y ) =β 1{t = Post}∗1{c = China}∗NTRGap +β ln(QPW )+ (10) mhczt 1 h 2 mhczt β χ +λ +λ +(cid:15) . 3 mhczt mhcz t mhczt The triple DID term of interest is the same as above, an interaction of post-period and China-import dummies with the NTR gap, and the variable χ represents mhczt the full set of interactions of those variables required to identify β . The remaining 1 terms on the right-hand side control for the average quantity traded per week in each of the two periods (QPW ) as well as buyer quadruple (λ ) and period (λ ) mhczt mhcz t fixed effects. Once again, standard errors are two-way clustered at the country and product level. Conducted at the mhcz level, equation (10) is restricted to continuing importers—i.e. those active before and after granting of PNTR—via the mhcz buyer quadruple fixed effect. While our model requires repeated interactions between buyers and sellers, it does not mandate relationships be long-established. Moreover, existing research finds substantial relative growth in US-importer-Chinese-exporter relationships after PNTR (Pierce and Schott, 2016). As a result, we also estimate equation (10) at the more 25

Table 8: Within-Importer PNTR Regression, Buyer Characteristics (1) (2) (3) (4) Dep. var. ln(SPS ) 1{Jhcz =1} ln(SPS ) Jhcz mhczt mhczt hczt hczt Post ∗China ∗NTRGap -0.006 0.041* -0.021** 0.034* t c h 0.031 0.022 0.009 0.019 ln(QPW ) -0.171*** 0.124*** -0.062*** 0.032*** mhczt 0.006 0.005 0.002 0.003 Observations 738,000 291,000 368,000 28,500 R-squared 0.772 0.675 0.695 0.547 Fixed effects mhcz,t mhcz,t hcz,t hcz,t Controls Yes Yes Yes Yes Source: LFTTDandauthors’calculations. FirsttwocolumnsreporttheresultsofregressingnotedattributeofUS importerbyproductbycountrybymodeoftransport(mhcz)binsonthedifference-in-differencestermofinterest andquantityshippedperweek. Secondtwocolumnsareanalogousbutatthehcz levelofaggregation. Pre-and post-PNTRperiodsare1995to2000and2002to2007. Allregressionsincludemhcz andperiodtfixedeffects, controlforthebeginningandendweekofthequadrupleaswellasallvariablesneededtoidentifytheDID termof interest. Columns2and4excludequadrupleswithlessthanfiveshipmentsinbothperiods. Standarderrors, adjustedforclusteringbycountry(c)andproduct(h),arereportedbelowcoefficientestimates. ***,**,and* representstatisticalsignificanceatthe1,5and10percentlevels. aggregated hcz level, which broadens the analysis to include entering importers. For this regression, SPS is defined as the average SPS within hczt cells. The hczt mhczt variable Jhcz is defined analogously as average Jhcz . hczt mhczt Results in Table 8 indicate that PNTR induced a shift towards more J importing, with this effect driven by the entry of new importers. As shown in the first two columns, we find only a modest relationship between the policy change and SPS , mhczt though continuing buyer quadruples more exposed to the change in policy exhibit relative increases in the probability of being in the first SPS quartile (Jhcz = 1) mhczt after PNTR. When we re-estimate equation (10) at the hcz level—which accounts for the role of new importers that enter in the post-PNTR period—we find that higher exposure to PNTR is associated not only with a higher probability of Jhcz = 1, but mhczt also with a precisely estimated reduction in SPS . The estimates in columns 3 and hczt 4 indicate that a one standard deviation increase in exposure to PNTR is associated with a 0.5 percent relative decline in SPS and a 0.8 percent increase in falling within the first quartile of the SPS distribution.36 36To analyze the influence of initial buyer experimentation during the years immediately after PNTR on our results, we also consider, in Appendix E, similarly constructed outcomes but for a slightly later — 2004 to 2009 — post-PNTR time period. Coefficient estimates for this alternate postperiodhavethesamesignpatterns,butarelargerinabsolutemagnitudeandaremoreprecisely 26

Overall, the results in this section provide support for the model’s prediction that a lower likelihood of a trade war can bring buyers to switch from A to J procurement in terms of the procurement attributes with importers’ partners, the formation of new J relationships, and the number of seller partners. 5 Multi-Country Setup with Endogenous Demand Inthissection, weembedthepartialequilibriummodelintroducedinSection2within the multi-country, multi-product general equilibrium model of Eaton and Kortum (2002). We use the model to assess the potential welfare implications of shutting down J procurement in Section 7. Such analysis is of particular relevance given recent efforts to reverse globalization, such as “Brexit” and the Trump trade wars, that have increased trade policy uncertainty worldwide. Our main point of departure from Eaton and Kortum (2002) is the introduction of homogeneous buyer firms in each country, which purchase manufacturing goods from sellers and distribute these goods to consumers. Buyer and seller firms are subject to the procurement problem described in Section 2. 5.1 Environment Households: Our modeling is standard. There are N countries, indexed by n and i. Each country is populated by L consumers, who purchase a continuous flow of n a manufactured composite good and a homogeneous “outside” good to maximize a Cobb-Douglas utility of the form QαZ1−α, where Q is the quantity of a composite n n n manufactured good and Z is the quantity of a homogeneous good. The composite n good is a CES aggregate of a continuum of differentiated products indexed by ω ∈ [0,1], (cid:18)(cid:90) 1 (cid:19)σ/(σ−1) Q = q (ω)(σ−1)/σdω , (11) n n 0 where σ > 0 is the elasticity of substitution and q (ω) is quantity. This aggregator n implies the standard price index P = (cid:0)(cid:82) p (ω)1−σdω (cid:1)1/(1−σ) . We assume that each n n consumer supplies one unit of labor. estimated, suggesting adjustment to PNTR may have occurred gradually. 27

Homogeneous good: The homogeneous good in country n is produced by a representative firm according to Z = a LO, where a is productivity and LO is the aggregate n n n n n labor used in the production of the good. Labor is paid the wage rate w . The n homogeneous good is directly sold to households and can be costlessly traded across countries. Wesetitspriceasthenumeraireandnormalizeittoone. Laborisperfectly mobile between manufacturing and the homogeneous good sector. Manufacturing sellers: Manufactured good ω can be produced by homogeneous seller firms in country n with the linear production function q = Υl introduced in Section θ 2. Sellers are perfect competitors, taking prices as given. Their productivity Υ (ω) is n specific to each origin country-product combination. Sellers in country n incur fixed logistic and transport costs f in units of seller country labor for each destination n supplied. We assume that a country’s firms are owned by their households. Manufacturing buyers: We add a continuum of homogeneous buyer firms in each country into the standard framework. Buyer firms purchase manufactured goods from sellers domestically or abroad, and offer them to the households in their country atpricesp (ω). Thetransactionsbetweenbuyersandsellerstakeplaceasdescribedin n Section 2: given household demand q (ω), buyers in country n choose the lowest-cost n sourcing country i for product ω, the procurement system, and the optimal order size. Buyers using the A system need to use an additional m (ω) labor units to inspect n the quality of the good. Buyers choosing the J system pay an incentive premium to ensure quality.37 As discussed in Section 2, due to the fixed procurement cost each buyer optimally places each order with a single seller. 5.2 Partial Equilibrium with Endogenous q In this section, we describe how q (ω) is determined in equilibrium. We assume that n the buyer has already chosen the source country and procurement system and discuss how these are chosen in the next section. As we are focusing on a single market in this section, we omit country and product subscripts. Ourfirststeptodeterminetheequilibrium, Proposition5.1, establishesthatbatch size and shipping frequency increase with quantity ordered, q: 37The incentive payments imply that sellers obtain positive profits under the J system. These profits are not competed away since sellers offering a lower price would violate the incentive constraint. 28

Proposition 5.1. An increase in the procurement target q raises batch sizes x∗ and s the shipping frequency q/x∗ in both systems, and, as a corollary, lowers unit values s in both systems. Proof. See Appendix A.5. Intuitively, foragivenfixedshippingfrequency, buyersmustincreasethebatchsizex s in both systems to meet an increase in q. But by the first-order condition (5), buyers trade-off variable procurement costs against fixed per-shipment costs. Therefore, as variableprocurementcostsincrease, buyersrespondbyspreadingthelargerquantities overmoreshipments. Asaresult,largerquantitiesleadtobothgreatershipmentsizes, x , but also greater order frequencies. Unit values decrease since fixed per-shipment s costs are spread over greater per-shipment quantities. Additionally, in the J system, an increase in the shipping frequency implies a lower premium to motivate desired quality, which lowers the unit value further. Thecomparativestaticswithrespecttoq aresupportedbytheempiricalestimates in Sections 3 and 4. As indicated in Tables 3, 6, and 7, we find that shipment size is positively related to the quantity shipped per week (QPW), and that both weeks between shipments and unit values are negatively related to QPW. We next show that buyers’ average cost curves are downward sloping: Lemma5.2. Attheoptimalordersizex∗, bothprocurementsystemsprovideeconomies s of scale, i.e., ∂AC(x∗ s ,q) < 0. Moreover, the second derivative of the average cost with ∂q respect to q is positive, ∂2AC(x∗ s (q),q) > 0, and the average cost in both systems reaches ∂q2 a positive and finite limit as q → ∞. Proof. Appendix A.6 shows that average cost curves are downward sloping. Supplemental Appendix J.2 shows that they are convex and converge to a finite limit. In our model, sellers face the standard constant marginal costs and perfect competition, but the fixed logistic and transport costs generate a natural monopoly for buyers in the downstream market. Downward-sloping average cost curves are a key departure of our model from trade models based on Eaton and Kortum (2002), which generally assume constant marginal cost. We therefore need to choose an appropriate market structure. Our assumption is that buyers compete in a “contestable” market for consumers, a natural extension of Bertrand competition when firms’ costs exhibit economies of scale (Baumol et al., 1982; Tirole, 1988). In a contestable market, there 29

exist several homogeneous competitors whose entry is costless. Due to downwardsloping average costs, in equilibrium a single buyer serves the entire consumer market for each product. Lemma 5.2 indicates that average cost curves are convex, and therefore a demand curve that uniquely intersects the single buyer’s optimized average cost curve from above determines a unique, sustainable, and feasible equilibrium in the product market, q∗. The buyer prices and supplies the final consumers along its average cost curve. If the buyer were to price above average costs, entrants would contest the positive profits and take over the market. If the buyer were to price below average costs, she would realize negative profits. Since for any q < q∗ consumers are willing to pay prices greater than average costs, potential entry forces an incumbent offering q to lower its prices and to increase quantity to the level q∗ where supply equals demand. Under appropriate assumptions on the demand system, the market equilibrium is a corollary of Lemma 5.2.38 Corollary 5.2.1. If markets are contestable and demand intersects average costs from above at q∗and remains below average costs as q∗ < q → ∞, then a single buyer procures the product from the seller and distributes it on the consumer market using the buyer’s cost minimizing procurement system at optimal shipping frequencies. 5.3 General Equilibrium with Endogenous q We now embed the product market equilibrium into the equilibrium of the overall economy. Equilibrium requires that (i) buyer firms minimize costs such that the contestable market equilibrium is feasible and sustainable in each product-destination country market, (ii) the household maximizes the CES objective, and (iii) the goods and labor markets clear. Cost minimization: Buyer firms in country n minimize average costs AC (q (ω)) of n n 38In principle our CES demand system may intersect the downward sloping average cost curve multiple times. For equilibrium to exist in that case, the demand curve must cut the average cost curve from above at the intersection that determines the greatest equilibrium quantity, q∗ . high Intuitively, if the demand curve were to cut from below, it would be above the average cost curve for all q∗ < q → ∞, implying that consumers are willing to buy an infinite quantity of the good high when the buyer sets price equal to average costs. 30

purchasing q (ω) by choosing the lowest-cost system and country: n (cid:8) (cid:8) (cid:9) (cid:9) AC (q (ω))∗ = min min AC (x∗ (ω),q (ω)),AC (x∗ (ω),q (ω)) ; i = 1,...,N , n n ni,A ni,A n ni,J ni,J n (12) where AC (x∗ (ω),q (ω)) are average costs of purchasing q (ω) under system s ni,s ni,s n n from country i, and x∗ (ω) is the optimal batch size determined by the first-order ni,s condition (5). Since average costs are downward sloping in q and the market is contestable, in equilibrium there is only one buyer firm serving each market. The contestable market price is p (ω) = AC (q (ω))∗. n n n Utility maximization: Consumptionofeachmanufacturedgoodischosentomaximize (11) subject to the budget constraint (cid:32) (cid:33) (cid:90) 1 (cid:90) (cid:88)(cid:88) p (ω)q (ω)dω ≤ α w L + πs (ω)I (ω)dω . (13) n n n n in,s in,s 0 i s The right-hand side of the equation is the share of country n’s total income W n spent on manufacturing goods. Since labor is perfectly mobile between sectors, the wage rate is pinned down by the productivity of the homogeneous good sector as w = a . The second term on the right-hand side, which is new relative to the n n standard framework, represents the incentive premia collected from shipments to countries i under s = J. Here, πs (ω) is the continuous flow of profits to sellers in in,s country n from sales to country i of product ω under system s, and I (ω) is an in,s indicator that is equal to one if seller n uses system s to country i. Profits are zero if shipments are under the A system. Consumption of the homogeneous good satisfies Z = (1−α)W . n n Market clearing: Equilibrium requires market clearing for each manufactured good ω and for the homogeneous good, and labor market clearing in each country. We provide these market clearing conditions in Appendix F.39 39In the quantitative simulations, we verify that a positive amount of labor is allocated to both manufacturing and the production of the homogeneous good in each country in equilibrium. 31

6 Quantitative Analysis In this section, we estimate the model quantitatively before using it in Section 7 to analyze the effects of changes in trade policy on trade flows and welfare. This analysis highlights the impact of firms’ choice of procurement system on the trade and welfare effects of a higher probability of trade war, as well as the relevance of the model for the current international trading environment. We parametrize the model using a combination of external calibration and within-model moment matching. Due to the non-linearity of the buyer’s problem, our model does not admit an analytical solution. We therefore use an iterative algorithm. First, given parameter values, we compute the average cost curves for each market and system. Next, we guess each country’s price index and income to compute the demand curve in each market and find the last intersection where demand intersects the lowest average cost curve from above. Given this equilibrium in each market, we compute a new price index and income in each country, construct a new demand curve, and iterate to convergence. Appendix G provides further details. 6.1 Parametrization and Calibrated Parameters We set each time period to one quarter. We set N = 3 countries and interpret these countries to be the United States, China, and the Rest of the World (RoW).40 As in Eaton and Kortum (2002), productivity Υ (ω) is drawn from a Fr´echet distribution n F (Υ) = e−ΛnΥ−ζ, where the country-specific parameter Λ scales the mean of the n n distributionandζ scalesthevariation. Theproductivitydrawsareindependentacross products within each country. We assume inspection costs for domestic procurement to be zero, implying that all domestic sourcing takes place under the A system.41 For imports, we assume that the distribution of inspection costs is Pareto and given by G (m) = 1−(m/m)γn, where n m is the lower bound of inspection costs, and γ is a parameter to be estimated.42 We n 40While our model generalizes to an arbitrary number of countries, for our purposes three are sufficient. 41This is a normalization. Since we do not have domestic transactions data, we cannot estimate the share of J and A trade for within-country transactions. Equivalently, since domestic inspection costs are zero, we could also refer to “domestic” sourcing as a third type of procurement system that does not face an incentive problem and hence corresponds to the first-best outcome. 42We perform an alternative estimation below where we assume that inspection costs are distributedaccordingtoaFr´echetdistributioninsteadofPareto. Wefoundthatthemodelfitisbetter 32

set m = 0.001 to reflect the fact that inspection is essentially costless for some goods, e.g., commodities. Heterogeneous inspection costs generate dispersion in the relative costs of A and J procurement, and hence in the system used, across goods coming from the same country. The shape of the inspection cost distribution is directly tied to the welfare effects of policy: if some products have more extreme inspection costs, then a high probability of trade war that forces firms to use the A system for these products can lead to large welfare losses. We calibrate a number of parameters outside of the model, and summarize their values in Table 9. We provide more information on the calibration in Appendix H, and discuss here only the rate of exogenous relationship break-ups, ρ . In the ni model, this variable reflects any exogenous shock that ends relationships. We assume that this break-up rate is symmetric between country pairs, ρ = ρ , and set it ni in for the US by fitting the exponential decay parameter that best matches the empirically observed fraction of plausibly J buyer-seller (mxhcz) quintuples that survive for 2,...,100 quarters in the US trade data. Since trade wars between the United States and the RoW are unlikely in steady state, we interpret the estimated decay parameter for relationships between US and RoW firms, equal to 0.087, as normal churn due to firm exits, product obsolescence, and so on.43 We therefore set ρ = 0. For US,RoW relationships between US and Chinese suppliers, we estimate a decay parameter of 0.114. We interpret this higher likelihood of break-ups as arising due to the additional uncertainty of trading with China, and thus set the relationship break-up rate between the US and China equal to the difference in the decay parameters, leading to ρ = 0.0264. For trade between China and RoW, we set ρ = 0 as well.44 US,CN CN,RoW Appendix H provides more details. 6.2 Targeted Moments and Estimation We estimate the remaining productivity scales T , the country-specific fixed costs f , n n and the inspection cost distribution parameters γ via simulated method of moments n under Pareto, and therefore choose it as our baseline. We also assume that a given destination country hasthe same distributionof inspection costs forall originsto reduce thedegrees of freedom in the estimation. We show below that the model fits the data quite well despite this restriction. 43While narrow trade disputes between the United States and RoW—such as safeguards and antidumping duties—occur often, the WTO’s formal dispute settlement system was an effective deterrent to full-fledged trade war between the US and RoW during our sample period. 44While trade tensions were also present between RoW and China, a variety of bilateral disagreements between the US and China meant that the risk of RoW-China trade war was substantially lower. 33

Table 9: Calibrated Parameters Parameter Value Source Interest rate (r) 0.01 Caliendo et al. (2019) Elasticity of substitution (σ) 3.85 Antr`as et al. (2017) Cost of low quality (θ) 0 Normalization Cost of high quality (θ¯) 1 Normalization Consumption share of manufactured goods (α) 0.5 Duarte (2020) Dispersion of productivities (ζ) 3.6 Eaton and Kortum (2002) Homogeneous good sector productivity (a ) n - US 1 Normalization - China 0.12 Average wage relative to US - RoW 0.47 Average wage of top-ten US partners Labor Force (L ) n - US 1 Normalization - China 5 Labor force relative to US - RoW 2.5 Labor force of top-ten US partners Rate of exogenous break-ups, US-China (ρ ) 0.0264 Census Bureau (LFTTD) US,CN Rate of exogenous break-ups, US-RoW (ρ ) 0 Assumption US,RoW Notes: Table presents the exogenously fixed parameters. Column (1) displays the parameter value, and column (2) showsitssource. using the LFTTD and aggregate data. The column labeled “Moment in Data” in Table 10 summarizes the values of the targeted moments in the data. We next describe the empirical moments targeted and the underlying identification assumptions. Appendix H provides more details. We normalize T = 1, and estimate the other two productivity parameters using US the share of imports from China and from the rest of the world in US domestic manufacturing sales in 2016 (rows 1 and 2 of Table 10). A lower value of T increases n country n’s productivity, which raises that country’s share in US domestic sales. We estimate the remaining four parameters using the observed shipping patterns inthetradedata. AcorollaryofProposition2.2isthat, givenatotalquantityordered q, higher fixed costs lead to shipments that are less frequent under both systems. We can therefore estimate the fixed shipment costs f and f by running a modified CN RoW classification regression (7) with average weeks between shipments (WBS ) as mhcz dependent variable, separately for China and for the rest of the world, ln(WBS ) = β +β 1{WBS = Q4}+β ln(QPW ) (14) mhcz 0 1 mhcz 2 mhcz +β beg +β end +λ +(cid:15) . 3 mhcz 4 mhcz hcz mhcz 34

Table 10: Estimated Parameters and Targeted Moments (1) (2) (3) (4) (5) Estimated MomentthatPrimarily Moment Moment Parameter Value IdentifiestheParameter inData inModel (1) ProductivityChina(TCN) 15.482 ShareofChineseimportsindomesticsales 0.074 0.066 (2) ProductivityRoW(TRoW) 2.745 ShareofRoWimportsindomesticsales 0.270 0.276 (3) Fixedcosts,China(fCN) 0.310 exp(βˆ 0+βˆ 1+βˆ 3beg+βˆ 4end)from(14)forCN 91.00 91.10 (4) Fixedcosts,RoW(fRoW) 0.061 exp(βˆ 0+βˆ 1+βˆ 3beg+βˆ 4end)from(14)forRoW 60.90 62.66 (5) Dispersionofinspection 0.290 βˆ 1 from(14)forChina 0.871 0.814 (6) costs,China(γCN) Sdof(cid:15)ˆfrom(14)forChina 0.227 0.180 (7) Dispersionofinspection 0.101 βˆ 1 from(14)forRoW 0.822 0.818 (8) costs,RoW(γRoW) Sdof(cid:15)ˆfrom(14)forRoW 0.219 0.207 (9) TotalobjectiveT(·) 0.062 Source: LFTTDandauthors’calculations. Column(1)liststheparametersestimatedforthemodel. Column(2) containstheestimatedparametervalues. Column(3)reportsthemomenttargetedtoidentifytheparameter. Column(4)presentsthevalueofthemomentinthedata,andColumn(5)presentsthevalueofthemoment computedinoursimulatedmodel. ThelastrowpresentsthevalueofthefunctionT(·)from(15). We control for the total quantity per week, QPW, to be consistent with the theory, and for time variation and fixed effects by product by country by mode to remove potentially confounding variation that is unrelated to fixed costs. To isolate sourcing that is most likely under the A and the J system, our regression sample includes only quadruples that fall into the first or the fourth quartile of the SPS dismhcz tribution (hence, are most likely J and A, respectively), and includes a dummy, 1{WBS = Q4}, indicating whether WBS falls into the fourth quartile. We mhcz mhcz set f by targeting the predicted average shipping frequency in the fourth quartile, n ˆ ˆ ˆ ˆ exp(β +β +β beg+β end), where beg and end are the simple averages of beg and 0 1 3 4 mhcz end in the data (rows 3 and 4).45 Since we do not have information on the promhcz curement choice of foreign importers sourcing from the US, we assume f = f . US RoW Regression (14) is also informative about the dispersion of the inspection cost parameters γ and γ , which are crucial for the share of J sourcing estimated CN RoW by the model. Starting from γ → ∞, at which point all inspection costs are zero n and all sourcing is under the A system, lowering γ increases the number of high n inspection cost draws and therefore raises the share of J sourcing. We target two sets of moments that we obtain from regression (14). First, we target the difference 45Sincequantityunitsareheterogeneousacrossgoodsinthedata,wetargettheshippingfrequency at ln(QPW ) = 0. We target the average shipping frequency within the fourth quartile, hence mhcz likely A procurement, to remove variation in shipping patterns that is due to different mixes of A versus J sourcing. 35

in shipping frequencies between the first and the fourth quartile of the WBS mhcz ˆ distribution, given by β in specification (14) (rows 5 and 7). A greater dispersion 1 of inspection costs (a smaller γ ) increases the difference in average shipping times n between those quadruples that are more likely A and those that are more likely J. Second, we target the dispersion in shipping times across more A mhcz quadruples. When γ is low, the inspection cost draws are more dispersed, leading to a higher n variance of the shipping frequencies within the A system. We construct this moment by taking the residuals from (14) for all observations that fall into the fourth quartile of the WBS distribution, and compute the standard deviation of these residuals. We generatethemomentsinexactlythesamewayinthemodel.46 Wepreferthisapproach to the alternative of simply setting the shares of A and J sourcing exogenously. Rows 6 and 8 show the estimated moments. Similar to the fixed costs, we assume that γ = γ . US RoW Our estimation algorithm is standard: we solve for a vector of parameters satisfying (cid:88) φ∗ = argmin T(M (φ),M ˆ ) (15) x x φ∈F x ˆ where T(·) is the percentage difference between the model, M (φ), and data, M , x x moments. Appendix I.1 provides more details on the estimation algorithm and outcomes. We present the estimated values of the parameters in the column labeled “Estimated Value” in Table 10, and the “Moment in Model” column shows the values of the simulated moments with these parameters. Themodelprovidesagoodfitalongseveraldimensions. First,themodel-generated shares of Chinese and RoW imports in US manufacturing consumption are 6.6% and 27.6%, respectively, compared to 7.4% and 27.0% in the data. Second, the model generates shipping frequencies consistent with the data: the time between shipments is about 91 weeks for China and 63 weeks for the rest of the world, conditional on ln(QPW ) = 0.47 Finally, the model generates substantial variation in shipping mhcz frequencies across goods, similar to the data. Our results slightly underestimate the dispersion of inspection costs for China (rows 5-6). Increasing the dispersion of in- 46Since in the model there are no changes over time and the random parameter values are drawn from the same stationary distribution for all products, we do not include beg , end , and the mhcz mhcz fixed effects λ in regression (14) run in the model. hcz 47The empirically observed number of weeks between shipments is much lower since shipping frequencyincreaseswithquantityshipped. InthefirstquartileoftheWBS distributionfromChina the average number of weeks between shipments is 9 weeks, in the fourth quartile it is 39 weeks. 36

Table 11: Comparison of Base-Model and Counterfactual Equilibria (1) (2) (3) (4) Equilibrium Baseline Without Japanese Removal of Equilibrium Sourcing Autarky PNTR (1) ShareofconsumptionfromChina(%) 6.6% 7.1% . 6.6% (2) -ofwhich,J 9.5% . . 7.1% (3) ShareofconsumptionfromROW(%) 27.6% 19.6% . 27.6% (4) -ofwhich,J 52.1% . . 52.1% (5) ShareofconsumptionfromUS(%) 65.8% 73.3% 100.0% 65.8% (6) Avg. inspectioncosts 0.4% 1.3% . 0.4% (7) Avg. fixedcosts(imports) 4.5% 3.3% . 4.5% (8) Manufacturingpriceindex 1.000 1.029 1.122 1.000 (9) Utility 1.000 0.982 0.940 0.9998 TableshowsvariousstatisticsoftheequilibriumundertheassumptionofaParetodistributionforinspectioncosts. Thefirstcolumnpresentsthestatisticsforthebaselineequilibrium,usingtheparametersthatminimizethe objectivefunction. Thesecondcolumnshowsthesamestatisticsforacounterfactualeconomyinwhichthe formationofJ relationshipsisnotpossibleduetoρ→∞. Thethirdcolumnshowsanautarkyeconomyinwhich tradeisnotpossible. Thefourthcolumnshowsacounterfactualeconomyinwhichwereducethearrivalrateof tradewarsfromChinatozero. Rows1-5showtheshareofUSmanufacturingsales,PUSQUS,thatisfromChina, fromtherestoftheworld,andfromtheUS,respectively,andtheshareofthesemanufacturingsalesthatissourced undertheJ system. Row6presentstheaverageinspectioncostsasashareoftheimportvalue,computedoverall imports,includingundertheJ system. Row7showstheaveragefixedcostsasashareoftheimportvalue. Row8 showsthemanufacturingpriceindex,PUS,normalizedtooneinthebaseline. Row9showstotalutility, WUS =Qα US Z U 1− S α,normalizedtooneinthebaseline. spection costs further would raise the average time between shipments beyond its empirical target (row 3), but would tend to increase the share of J sourcing. The fixed costs of production in terms of labor are about five times larger for China than for the rest of the world (rows 3 and 4). Since wages in China are four times lower than in RoW, the fixed costs in terms of the numeraire good are only slightly higher (about 20 percent). These higher fixed costs are an implication of the lower shipping frequency from China compared to the rest of the world. Since the estimation target includes the intercept β , which is estimated using the observed 0 trade flows in our sample period, the higher fixed cost reflects any trade barriers between countries in our sample, such as distance (Hummels and Schaur, 2013). 6.3 Model Results The first column of Table 11 summarizes the estimated equilibrium. The first four rows show the share of manufactured goods consumption that is imported from China and the rest of the world, as well as the share of the imports that are obtained under the J system. Our estimates imply that 10 percent of imports from China are under 37

Figure 4: Quantity Imported vs Share of J Importers (a) China (b) Rest of the World Notes: ThefigureshowsforeachpercentileofthedistributionofUSimportstheaveragequantityimportedagainst the average share of importers using the J system. The left panel presents the results for imports from China, the rightpanelisforimportsfromtherestoftheworld. the J system, while 52 percent of imports from the rest of the world take place under J procurement. The higher share for the rest of the world reflects the higher trade war probability with China, which discourages trade under the J system, as well as the higher fixed costs for China, which makes the frequent shipments under the J system more expensive. The structurally estimated J shares are somewhat smaller than the empirical estimates we obtained using shipments in the first quartile of the SPS distribution in Table 2 for China, but they are in the ballpark for the rest mhcz of the world. Rows 6 to 7 of Table 11 show that the average product imported by the US is subject to an inspection cost of 0.4 percent and a fixed cost of 4.5 percent of the import value, respectively. These figures provide a validity check of the model, since they are in line with estimates by Kropf and Saur´e (2014), who estimate that Swiss exporters face total fixed shipment costs of 0.8 percent to 5.4 percent of the value imported. The final two rows present the price index in manufacturing in the United States, P , and the utility Qα Z1−α, normalized to 1 for ease of interpretation. US US US As a further check of the model, we verify that larger importers are more likely to use the J system, as found in Table 5 above. We plot in Figure 4 the average share of J importers against the average quantity imported for each percentile of the quantity distribution of imports, for China and RoW.48 The figure shows that larger importers 48We drop outliers below the 1st and above the 99th percentile of the distribution. 38

are more likely to use the J system, as in the data. Intuitively, a higher seller productivity raises imports under both systems by reducing variable costs. Under the J system, a higher seller productivity additionally lowers the incentive premium, which makes J sourcing relatively more attractive for high-productivity imports. 7 Counterfactuals In this section, we use the calibrated model to estimate US welfare under two counterfactuals. First, to determine the importance of J sourcing, we compare elimination of J sourcing vis `a vis autarky. This counterfactual then provides context for estimating the welfare gain associated with PNTR. Each of these analyses is highly relevant for considering the effects of recent increases in uncertainty in the global trading system. No Japanese Sourcing: We shut down J importing by setting ρ = ∞ for trade US,n between the US and both of its trading partners. As shown in the second column of Table 11, US imports rise slightly from 6.6 to 7.1 percent for China (row 1), while imports fall significantly from 27.6 to 19.6 percent from RoW (row 3).49 Intuitively, buyers’ procurement choice in our model is shaped by three factors: (i) seller productivity, (ii) country-product inspection costs, and (iii) the country-pair probability of trade peace. Products in which the domestic country has a high productivity are sourced domestically. Products not sourced domestically are imported under the A system if inspection costs are low, and under the J system if they are high and a trade war is unlikely. A greater likelihood of trade war raises the incentive premia under the J system, rendering A and domestic sourcing more attractive. As the arrival rate of trade wars goes to infinity, no goods are imported under the J system. Table 11 shows that average inspection costs jump from 0.4 to 1.3 percent (row 6) because the imports which switch from J to A are precisely those with relatively high inspection costs, for which A sourcing was previously not optimal. Higher import prices drive down the average fixed cost as a share of import value (row 7). The manufacturing price index P rises 2.9 percent (row 8) due to higher sourcing costs. US Overall, welfare falls by 1.8 percent. This drop in welfare is about one third as severe as moving the US to autarky, as illustrated in the third column of Table 11. 49This exercise entails a relatively larger increase in trade costs for RoW than for China since in the baseline the trade war arrival rate with the rest of the world is zero while it is 0.0264 for China. As a result, there is a relative shift of trade towards China in this counterfactual. 39

In Appendix I.2, we check the robustness of these findings by re-estimating the model with a Fr´echet rather than Pareto distribution for inspection costs. This estimation matches our targeted moments slightly less well than the baseline, but generates significantly higher import shares under the J system. We find that welfare costs of removing J relationships are significantly larger, at 3.5 percent, indicating that the losses rise substantially with the share of J relationships.50 Removal of PNTR: Our second counterfactual, summarized in the fourth column of Table 11, analyzes a hypothetical scenario in which PNTR is removed. Handley and Lima˜o (2022) estimate an annual probability that NTR is revoked of around 13 percent, similar to that estimated by Alessandria et al. (2022) for the mid-1990s.51 Accordingly,weincreaseρ fromthebaselinerelationshipbreak-uprateof0.0264, US,CN which implies that relationships break with about 10 percent probability over four quarters, by 13 percentage points so that it implies a break-up rate of 23 percent over four quarters, leading to ρ = 0.0654.52 We then re-simulate the model. US,CN As indicated in the last column of the table, we find that the share of J imports from China decreases by 2.4 percentage points as a result of the higher possibility of relationship break-ups. The overall price and welfare effects are very minor, leading to a welfare loss of 0.02 percent. Our results differ significantly from Handley and Lima˜o (2017), who find larger effectsofPNTRonconsumerincome,forseveralreasons. First,inourmodelchanging the probability of a trade war only affects products imported under the J system, which account for less than one tenth of consumer expenditures on Chinese goods. Importers do not bear the full costs of the trade war but can switch to the A system, which mutes the increase in costs. Our exercise highlights that the welfare costs of a trade war could be significantly higher if a trade war affects countries with a high share of J relationships, such as RoW, or additionally impedes contract enforcement under the A system. Second, in the Handley-Lima˜o model a reduction of uncertainty leads to the entry of foreign exporters, thus expanding the set of available varieties 50In Supplemental Appendix O, we illustrate the effect of changing ρ for intermediate values US,n between zero and infinity on the share of US consumption, welfare, and consumer income. 51Alessandria et al. (2022) estimate a somewhat lower probability of revocation in surrounding years. 52Whileourbaselineρ iscomputedusingtheentiresampleperiod,thepost-PNTRbreak-up US,CN rate is very similar, ρpost =0.022. Hence, when we add 13 percentage points to this number the US,CN results are very similar. 40

and driving down the price index, as in the Melitz (2003) model. In contrast, while in our framework a change in trade policy uncertainty may change the identity of the supplier of a good, the set of available varieties is fixed as in Eaton and Kortum (2002). We view our channel as complementary to the mechanisms described by Handley and Lima˜o (2017).53 Discussion: The counterfactuals considered in this section, though stylized, highlight the potential importance of relational contracting in the welfare gains from trade. They also demonstrate that the firm and country losses associated with greater trade policy uncertainty depend on the choice of procurement system, and therefore the costs associated with switching systems. Firms (and countries) that disproportionately import hard-to-inspect goods that make greater use of the J system when trade wars are unlikely will experience the largest welfare losses when uncertainty rises, as switching to the A system will be most costly. We note that the welfare losses implied by our framework likely capture only a fraction of the true losses associated with greater trade policy uncertainty because our framework considers trade only in final goods, and just 34 percent of US consumption is imported. In reality, many of the 66 percent of domestically produced consumption goods contain imported inputs and would therefore also be susceptible cost increases as trade wars break out. We leave modeling this channel to future research. 8 Conclusion This paper analyzes the impact of changes in trade policy on procurement patterns along a supply chain using theory, data and quantitative methods. We develop a theoretical model in which importers’ solution to a quality control problem depends upon exporters’ beliefs about the possibility of a trade war between the firms’ countries. When the probability of trade war is high, buyers choose “American”-style procurement, characterized by large, infrequent orders and costly inspections. When the probability of trade war is low, buyers can induce sellers to provide high quality by paying a premium over a long-term relationship. We show that changes in trade policy can induce a switch between procurement systems. 53Handley and Lim˜ao (2017) also allow exporters to pay a fixed cost to reduce their marginal cost, and the set of firms that choose to pay this cost rises when uncertainty is lower, which further increases the gains from low uncertainty they find. 41

We examine the model’s key implications using transaction-level US import data, and show that importer-exporter relationships differ along the dimensions – such as shipment size, shipment frequency and unit value – emphasized in the model. Usingatripledifference-in-differencesspecification, wealsoshowthattheUSgranting of Permanent Normal Trade Relations – which substantially reduced the possibility of a US-China trade war – is associated with a movement toward more Japanesestyle procurement among US importers and Chinese exporters along the dimensions highlighted by the model. Quantitative simulations reveal that an increase in the probability of trade war that is sufficient to eliminate “Japanese”-style procurement reduces US welfare about one third as much as placing the US in autarky. Our findings suggest that an important but under-examined aspect of trade agreementsinaworldwithalreadylowtariffsmaybetheireffectonrelationshipformation. That is, trade agreements promoting institutions that allow firms to develop more stable relationships may give rise to an additional source of welfare gains from trade associated with reducing inventory and monitoring costs.54 The extent to which such gains are smaller or larger than those that allow firms better access to contract enforcement or dispute resolution is an interesting area for further research. 54Indeed, improving the efficiency of trade relationships is a goal of the recent WTO agreement on trade facilitation. See https://www.wto.org/english/thewto e/minist e/mc9 e/desci36 e.htm. 42

References Alessandria,George,JosephP.Kaboski,andVirgiliuMidrigan(2010).“Inventories,LumpyTrade,andLargeDevaluations”.American Economic Review 100.5,2304–39. — (2011).“USTradeandInventoryDynamics”.American Economic Review 101.3,303–07. Alessandria,GeorgeA,ShafaatYKhan,andArmenKhederlarian(2024).“TakingStockofTradePolicyUncertainty: EvidencefromChina’sPre-WTOAccession”.Journal of International Economics,forthcoming. Alessandria,GeorgeA,ShafaatYKhan,ArmenKhederlarian,KimJRuhl,andJosephBSteinberg(2022).“TradepolicyDynamics:Evidencefrom60yearsofUS-ChinaTrade”.NBERWorkingPaperNo.29122. Amiti,Mary,MiDai,RobertCFeenstra,andJohnRomalis(2020).“HowDidChina’sWTOEntryAffectUSPrices?” Journal of International Economics 126,103339. Amiti, Mary, Stephen J. Redding, and David E. Weinstein (2019). “The Impact of the 2018 Tariffs on Prices and Welfare”.Journal of Economic Perspectives 33.4,187–210. Antoniades,Alexis(2015).“HeterogeneousFirms,Quality,andTrade”.JournalofInternationalEconomics 95.2,263 –273.issn:0022-1996. Antr`as,Pol(2003).“Firms,Contracts,andTradeStructure”.Quarterly Journal of Economics 118.4,1375–1418. — (2005).“IncompleteContractsandtheProductCycle”.American Economic Review 95.4,1054–1073. Antr`as, Pol and Davin Chor (2018). “On the Measurement of Upstreamness and Downstreamness in Global Value Chains”.WorldTradeEvolution:Growth,ProductivityandEmployment.Routledge. Antras,PolandDavinChor(2022).“GlobalValueChains”.Handbook of International Economics.Vol.5,297–376. Antr`as,Pol,TeresaC.Fort,andFelixTintelnot(2017).“TheMarginsofGlobalSourcing:TheoryandEvidencefrom USFirms”.American Economic Review 107.9,2514–64. Antr`as,PolandElhananHelpman(2008).“ContractualFrictionsandGlobalSourcing”.The Organization of Firms in a Global Economy.Ed.byElhananHelpman,T.Verdier,andD.Marin.HarvardUniversityPress,9–54. Baumol,W.,J.Panzar,andR.Willig(1982).ContestableMarketsandtheTheoryofIndustryStructure.NewYork. B´ek´es,G´abor,LionelFontagn´e,Bal´azsMurako¨zy,andVincentVicard(2017).“Shipmentfrequencyofexportersand demanduncertainty”.Review of World Economics 153.4,1610–2886. Bernard, Andrew B., J. Bradford Jensen, and Peter K. Schott (2009). “Importers, Exporters and Multinationals: A Portrait of Firms in the U.S. that Trade Goods”. Producer Dynamics: New Evidence from Micro Data. Ed. by T.Dunne,J.B.Jensen,andM.J.Roberts.Chicago:ChicagoUniversityPress. Blanchard,EmilyJ,ChadPBown,andRobertCJohnson(2016).GlobalSupplyChainsandTradePolicy.Working Paper21883.NationalBureauofEconomicResearch. Boehm, Christoph E., Aaron Flaaen, and Nitya Pandalai-Nayar (2019). “Input Linkages and the Transmission of Shocks: Firm-Level Evidence from the 2011 To¯hoku Earthquake”. The Review of Economics and Statistics 101.1,60–75. — (2020).“Multinationals,Offshoring,andtheDeclineofU.S.Manufacturing”.JournalofInternationalEconomics 127,103391. Bown,Chad,PaolaConconi,AkselErbahar,andLorenzoTrimarchi(2021).“TradeProtectionAlongSupplyChains”. CEPRDiscussionPaperNo.15648. Cajal-Grossi, Julia, Rocco Macchiavello, and Guillermo Noguera (2023). “Buyers’ sourcing strategies and suppliers’ markupsinbangladeshigarments”.The Quarterly Journal of Economics 138.4,2391–2450. Caliendo, Lorenzo, Maximiliano Dvorkin, and Fernando Parro (2019). “Trade and labor market dynamics: General equilibriumanalysisofthechinatradeshock”.Econometrica 87.3,741–835. Chernozhukov,VictorandHanHong(2003).“AnMCMCApproachtoClassicalEstimation”.JournalofEconometrics 115.2,293–346. Defever,Fabrice,ChristianFischer,andJensSuedekum(2016).“RelationalContractsandSupplierTurnoverinthe GlobalEconomy”.Journal of International Economies 103,147–165. Duarte, Margarida (2020). “Manufacturing consumption, relative prices, and productivity”. Journal of Macroeconomics 65,103232. Eaton,JonathanandSamuelKortum(2002).“Technology,Geography,andTrade”.Econometrica 70.5,1741–1779. Engbom, Niklas and Christian Moser (2022). “Earnings inequality and the minimum wage: Evidence from Brazil”. American Economic Review 112.12,3803–3847. 43

Fajgelbaum,PabloD,PinelopiKGoldberg,PatrickJKennedy,andAmitKKhandelwal(Nov.2019).“TheReturn toProtectionism*”.The Quarterly Journal of Economics 135.1,1–55. Feenstra, Robert C. and Gordon H. Hanson (2005). “Ownership and Control in Outsourcing to China: Estimating theProperty-RightsTheoryoftheFirm”.Quarterly Journal of Economics 120.2,729–761. Feenstra,RobertC.,JohnRomalis,andPeterK.Schott(2002).“U.S.Imports,Exports,andTariffData,1989-2001”. NBERWorkingPaperNo.9387. Flaaen,Aaron,AliHorta¸csu,andFelixTintelnot(2020).“TheProductionRelocationandPriceEffectsofUSTrade Policy:TheCaseofWashingMachines”.American Economic Review 110.7,2103–27. Flaaen,AaronandJustinPierce(2019).“DisentanglingtheEffectsofthe2018-2019TariffsonaGloballyConnected U.S.ManufacturingSector”.Federal Reserve Finance and Economics Discussion Paper 2019-086. Gelman,Andrew,JohnBCarlin,HalSStern,andDonaldBRubin(2013).Bayesian Data Analysis.Chapmanand Hall/CRC. Grossman,GeneM.andElhananHelpman(2004).“ManagerialIncentivesandInternationalOrganizationofProduction”.Journal of International Economics 63.2,237–262. Hallak,JuanCarlosandPeterK.Schott(2011).“EstimatingCross-CountryDifferencesinProductQuality”.Quarterly Journal of Economics 126.1,417–474. Handley, Kyle(2014).“ExportingunderTrade PolicyUncertainty: TheoryandEvidence”. Journal of International Economics 94.1,50–66. Handley,KyleandNunoLim˜ao(2017).“PolicyUncertainty,Trade,andWelfare:TheoryandEvidenceforChinaand theUnitedStates”.American Economic Review 107.9,2731–83. — (2022).“TradePolicyUncertainty”.Annual Review of Economics 14.1,null. Helper,SusanR.andMariSako(1995).“SupplierRelationsinJapanandintheUnitedStates:AreTheyConverging?” Sloan Management Review 36.3,77–84. Hornok,Cec´ıliaandMikl´osKoren(2015a).“AdministrativeBarrierstoTrade”.Journal of International Economics 96,S110–S122. — (2015b). “Per-Shipment Costs and the Lumpiness of International Trade”. Review of Economics and Statistics 97.2,525–530. Hummels, David and Alexandre Skiba (2004). “Shipping the Good Apples Out? An Empirical Confirmation of the Alchian-AllenConjecture”.Journal of Political Economy 112.6,1384–1402. Hummels,DavidLandGeorgSchaur(2013).“TimeasaTradeBarrier”.AmericanEconomicReview 103.7,2935–59. Johnson,RobertC.(2018).“MeasuringGlobalValueChains”.Annual Review of Economics 10.1,207–236. Kamal,FarihaandRyanMonarch(2018).“IdentifyingForeignSuppliersinUSImportData”.ReviewofInternational Economics 26.1,117–139. Kamal,FarihaandHeiwaiTang(2015).“RelationalTrade:EvidencefromtheUnitedStates”.mimeograph. Kandori,Michihiro(2002).“IntroductiontoRepeatedGameswithPrivateMonitoring”.JournalofEconomicTheory 102.1,1–15. Khandelwal,Amit(2010).“TheLongandShort(of)QualityLadders”.ReviewofEconomicStudies 77.4,1450–1476. Khandelwal, Amit, Peter Schott, and Shang-Jin Wei (2013). “Trade Liberalization and Embedded Institutional Reform:EvidencefromChineseExporter”.American Economic Review 103.6,2169–95. Kropf, Andreas and Philip Saur´e (2014). “Fixed Costs Per Shipment”. Journal of International Economics 92.1, 166–184. Kugler,MauriceandEricVerhoogen(2012).“Prices,PlantSize,andProductQuality”.ReviewofEconomicStudies 79.1,307–339. Kukharskyy,Bohdan(2016).“Relationalcontractsandglobalsourcing”.Journal of International Economics 101.C, 123–147. Kukharskyy, Bohdan and Michael Pflu¨ger (2010). “Relational Contracts and the Economic Well-Being of Nations”. IZADiscussionPaperNo.5394. Lise, Jeremy, Costas Meghir, and Jean-Marc Robin (2016). “Matching, sorting and wages”. Review of Economic Dynamics 19,63–87. Macchiavello,RoccoandAmeetMorjaria(Dec.2020).“CompetitionandRelationalContractsintheRwandaCoffee Chain*”.The Quarterly Journal of Economics 136.2,1089–1143. 44

Manova, Kalina and Zhihong Yu (2017). “Multi-product firms and product quality”. Journal of International Economics 109,116–137.issn:0022-1996. Martin,Julian(2012).“Markups,Quality,andTransportCosts”.European Economic Review 56.4,777–791. Melitz,MarcJ.(2003).“TheImpactofTradeonIntra-IndustryReallocationsandAggregateIndustryProductivity”. Econometrica 71,1695–1725. Ossa,Ralph(2014).“TradeWarsandTradeTalkswithData”.American Economic Review 104.12,4104–4146. Pierce, Justin and Peter K. Schott (2016). “The Surprisingly Swift Decline of U.S. Manufacturing Employment”. American Economic Review 106.7,1632–1662. Pierce,JustinR.andPeterK.Schott(2012).“ConcordingU.S.HarmonizedSystemCategoriesOverTime”.Journal of Official Statistics 28.1,53–68. Rauch,JamesE.(1999).“NetworksversusMarketsinInternationalTrade”.JournalofInternationalEconomics48.1, 7–35. Schott, Peter K. (2004). “Across-Product versus Within-Product Specialization in International Trade”. Quarterly Journal of Economics 119.2,647–678. Spencer,BarbaraJ.(2005).“InternationalOutsourcingandIncompleteContracts”.CanadianJournalofEconomics 38.4,1107–1135. Taylor, Curtis R. and Steven N. Wiggins (1997). “Competition or Compensation: Supplier Incentives under the AmericanandJapaneseSubcontractingSystems”.American Economic Review 87.4,598–618. Tirole,Jean(1988).The Theory of Industrial Organization.Cambridge,MA:MITPress. Verhoogen,EricA.(2008).“Trade,QualityUpgrading,andWageInequalityintheMexicanManufacturingSector”. The Quarterly Journal of Economics 123.2,489–530. WorldBank(2020).“TradingforDevelopmentintheAgeofGlobalValueChains”.World Development Report. 45

Online Appendix A Analytical Results A.1 Effect of Quality and Trade Wars on Average Costs (cid:12) (cid:30) ∂p J(cid:12) (cid:12) = (cid:2)(cid:0) e(r+ρ)xJ/q −1 (cid:1) x r (cid:3) (cid:2) Υ(e−rx/q −1)q (cid:3) < 0 J ∂θ (cid:12) θ<θ¯ (cid:12) (cid:30) ∂p J(cid:12) (cid:12) = x re(r+ρ)xJ/q (cid:2) Υ(1−e−rxJ/q)q (cid:3) > 0 ¯ J ∂θ (cid:12) θ<θ¯ (cid:19)(cid:30) ∂p (cid:16) (cid:17) J = (cid:0) e(r+ρ)xJ/qx2(θ ¯ −θ)r (cid:1) q2Υ 1−e−r q x > 0 ∂ρ J Finally, comparing procurement costs in both systems note that: rf +θ ¯1x∗ +(θ ¯ −θ)1x∗ (cid:2) erx∗ J /q −1 (cid:3) r f +θ ¯1x∗ r f +θ ¯1x∗ Υ J Υ J > Υ J > Υ A q 1−e−rx∗/q q1−e−rx∗/q q1−e−rx∗/q J J A The first inequality holds since erx∗/q > 1, and the second inequality holds because J the batch size that minimizes average costs in the J system is strictly less than the batch size that minimizes average costs in the A system when m = 0, i.e., x∗ < J x∗(m = 0). Hence, the average procurement cost under the J system is strictly A greater than under the A system for any ρ ≥ 0 when m = 0. A.2 Proof of Proposition 2.1 ¯ Forθ−θ > 0andρ > 0,whenm = 0averagecostsundertheJ systemmustbehigher A than under the A system by the discussion above Proposition 2.1 and in Appendix A.1. Since average costs under the A system grow without bound as m → ∞, there A must be an m∗ such that average costs under the systems are equalized. A.3 Proof of Proposition 2.2 Japanese System: We apply the implicit function theorem to the FOC (5): xρ (cid:0)¯ (cid:1) (cid:20) (cid:18)(cid:18) (cid:19) (cid:19)(cid:21) ∂FOC J 2xe q θ−θ xρ (cid:16) rx (cid:17) rx rx rx = e q −1 +q +1 e q − −1 ∂ρ q2Υ(e−r q x −1) 2 2q q 1

lim Define y = rx/q. Note that (cid:0)y +1 (cid:1) ey −y−1 = 0 and d (cid:0)y +1 (cid:1) ey −y−1 = y ↓ 0 2 dy 2 −1+ 1(y +3)ey > 0. Therefore ∂FOCJ > 0. Then by the implicit function theorem 2 ∂ρ ∂x ∂FOCJ ∂ρ = − < 0, ∂ρ SOC J where we denote by SOC the second-order condition, which is greater than zero as J shown in Supplemental Appendix J.1. Remember that v (x ,ρ) = f + θ ¯1x∗ + (θ ¯ − θ)1x∗ (cid:2) erx∗/q −1 (cid:3) . Average costs J J Υ J Υ J J in the “Japanese” system are then r vJ(xJ,ρ) . Taking the first-order condition of q1−exp(−rxJ) q these average costs and setting zero we can write. ∂v(x J ,ρ) rv(x J ,ρ)exp(−rx q J) = ∂x q 1−exp(−rxJ) J q Now take the derivative of the unit value, vJ(xJ,ρ),with respect to ρ to obtain xJ (cid:18) (cid:19) ∂v(x ,ρ)∂x ∂v(x ,ρ) ∂x 1 J J J J x+ x −v(x ,ρ) ∂x ∂ρ ρ J J ∂ρ x2 J J Substituting for ∂ v(x ,ρ) from the equilibrium condition (22) into (23) we can ∂x J rewrite (23) to obtain (cid:34)(cid:32) (cid:33) (cid:35) rx exp(−rxJ) ∂x ∂v(x ,ρ) 1 J q J J −1 v(x ,ρ)+ x q 1−exp(−rxJ) ∂ρ J ρ J x2 q J Note that ∂v(xJ,ρ)x = x3 J (θ¯−θ) > 0. Also note that rxJ exp(−rx q J) −1 < 0 ρ J exp(−(r+ρ q )xJ)qΥ q 1−exp(−rx q J) for 0 < rx < 1. Then because ∂xJ < 0 we have shown that ∂ vJ(xJ,ρ) > 0 q ∂ρ ∂ρ xJ American System: We apply the implicit function theorem to show: ∂x∗ ∂FOCA r2e−rx q A A = − ∂m = > 0 ∂m SOC A q2 (cid:16) 1−e−rx q A (cid:17)2 2

Notethatunitvaluesinthe“American”systemaresimply vA(xA) = f + θ¯ .Therefore, xA xA Υ ∂x∗ A > 0 ⇒ ∂vA x ( A xA) < 0. ∂m ∂m A.4 Proof of Proposition 2.3 Part 1: Comparing shipping sizes: x∗ < x∗ First note that if m = 0 and J A ¯ θ − θ = 0, then average costs in the two procurement systems are identical. If ∂x∗ A > 0 and ∂x∗ J > 0, then x∗ < x∗all else equal. We apply the implicit function ∂m ∂θ J A theorem. Let FOC and FOC denote the first-order conditions to minimize average A J procurement costs, and, let SOC > 0 and SOC > 0 be the associated second-order A J conditions that are greater than zero as shown in Supplemental Appendix J.1. American System ∂x∗ ∂FOCA r2e−rx q A A = − ∂m = > 0 ∂m SOC A q2 (cid:16) 1−e−rx q A (cid:17)2 Japanese System (cid:104) (cid:104) (cid:16) (cid:17) (cid:105)(cid:105) ∂x∗ J = − ∂F ∂ O θ CJ = (cid:18) r (cid:19) 1 1−e(r+ρ)x∗ J /q 1+ r+ q ρ x∗ J (cid:2) 1−e−rx∗ J /q (cid:3) ∂θ SOC J q Υ (cid:0) 1−e−rx∗ J /q (cid:1)2 (cid:18) r (cid:19)2 1 x∗e−rx∗ J /q (cid:2) 1−e(r+ρ)x∗ J /q (cid:3) − J . q Υ (cid:0) 1−e−rx∗/q (cid:1)2 J For (r+ρ)x∗/q > 0, this expression is negative if and only if J (cid:104) (cid:104) (cid:16) (cid:17) (cid:105)(cid:105) (cid:16) (cid:17) 1−e(r+ρ)x∗/q 1+ r+ρ x∗ r x∗e−rx∗/q J J q J q J > . (A.1) (cid:2) 1−e(r+ρ)x∗/q (cid:3) (cid:2) 1−e−rx∗/q (cid:3) J J Note that the left-hand side is greater than 1. Hence, we need to show that the right-hand side is less than 1. Define y ≡ rx∗/q, where 0 < y < 1. We find for the J ye−y d ye−y right-hand side lim = lim 1 − y = 1. Next, note that = y→0 1−e−y y→0 dy1−e−y e−y[(1−y)−e−y] < 0. It follows that the right-hand side of (A.1) is never greater [1−e−y]2 3

than 1. Therefore, ∂FOC/∂θ < 0 and∂x∗/∂θ > 0. J Part 2: Comparing unit values: v (x )/x < v (x )/x A A A J J J   f + θ¯ if s = A x∗ Υ v s (x s )/x s =  f A + θ¯ + (cid:16) e (r+ q ρ)x −1 (cid:17) (θ ¯ −θ) 1 if s = J x∗ Υ Υ J (cid:16) (cid:17) 1 Comparing the expressions, x∗ > x∗(see Part 1) and e (r+ q ρ)x −1 (θ ¯ − θ) ⇒ A J Υ v (x )/x < v (x )/x . A A A J J J A.5 Proof of Proposition 5.1 Part 1: Order size and shipping frequency increase in q. American System We apply the implicit function theorem to the first-order condition in the “American” system. From the first-order condition and setting to zero we obtain v(cid:48)(x) = r(v(x)+m)e−rx/q . Substituting this optimality condition into ∂FOCAwe q(1−e−rx/q) ∂q obtain (cid:20) rxe−r q x (cid:21) 1− q − rx ∂x A ∂FO q CA 1−e−r q x q r2(v(x)+m)e−r q x = − = ∂q SOC A SOC A q3 (cid:16) 1−e−r q x (cid:17)2 Then, 0 < rx < 1 ⇒ [·] < 0 ⇒ ∂xA > 0 over the relevant parameter range where costs q ∂q are positive. Forthe shipmentfrequency, d(x∗/q)/dq < 0, defineψ = x∗/q. Then, simplifying A A A the first-order condition under the “American” system we have (cid:18) (cid:19) (cid:20) (cid:21) 1 r 1 FOC(ψ ) = θ ¯ (cid:2) 1−e−rψA (cid:3) − e−rψA f +m+θ ¯ qψ = 0. A A Υ q Υ Applying the implicit function theorem to this expression yields ∂ψ ∂FOC(ψA) [f +m] A ∂q = − = − < 0, ∂q ∂FOC(ψA) rq (cid:2) f +m+θ ¯1qψ (cid:3) ∂ψJ Υ A and hence the time between shipments decreases, i.e., shipping frequency increases. 4

Japanese System We follow the same strategy as in the proof for the American system. From the first-order condition, FOC , we obtain ∂vJ(xJ,q) = rvJ(xJ,q)e−r q x J ∂xJ q (cid:16) 1−e−r q x(cid:17) which we substitute into ∂FOCJ to obtain: ∂q     ∂FO q C J = 1− q (cid:16) 1 rx − e− e r − q x r q x (cid:17) − r q x    q r 3 2 (cid:16) v 1 (x − ,q e ) − e− r q x r (cid:17) q x 2   2(r+ρ)(θ ¯ −θ)xre x q ρ (cid:18) xρ (cid:16) rx (cid:17) (cid:20)(cid:18) rx (cid:19) rx rx (cid:21) (cid:19) − e q −1 + +1 e q − −1 q q4Υ(e−r q x −1)2 2 2q q (cid:20) (cid:21) Note that 0 < r q x < 1 ⇒ 1− q (cid:16) r 1 x − e e − − r q r x q x(cid:17) − r q x < 0& (cid:104)(cid:16) r 2 x q +1 (cid:17) e r q x − r q x −1 (cid:105) > 0 ⇒ ∂FOCJ ∂x∗ − q > 0 ⇒ J > 0, because all other terms are positive by inspection. SOCJ ∂q To see that d(x∗/q)/dq < 0, define ψ = x∗/q. The first-order condition under J J J the “Japanese” system can then be simplified to FOC(ψ ) = (cid:2) θ1 + (cid:0) θ ¯ −θ (cid:1) 1e(r+ρ)ψJ [1+(r+ρ)ψ ] (cid:3)(cid:0) 1−e−rψJ (cid:1) (A.2) J Υ Υ J (cid:18) (cid:19) r − e−rψJ (cid:2) f +θ1ψ q +(θ ¯ −θ)1e(r+ρ)ψJψ q (cid:3) = 0. q Υ J Υ J Applying the implicit function theorem to this expression yields ∂ψ ∂FOC(ψJ) J ∂q = − . ∂q ∂FOC(ψJ) ∂ψJ For the numerator, we have ∂FOC(ψ ) r J = e−rψJf > 0. ∂q q2 For the denominator we find ∂FOC(ψ ) J = (r+ρ)(θ ¯ −θ)1e(r+ρ)ψJ [2+(r+ρ)ψ ] (cid:2) 1−e−rψJ (cid:3) ∂ψ Υ J J r2 + e−rψJ (cid:2) f +θ1ψ +(θ ¯ −θ)1e(r+ρ)ψJψ (cid:3) > 0. q Υ J Υ J 5

Therefore, ∂FOC(ψ )/∂q > 0, and thus d(x∗/q)/dq < 0. J J A.6 Proof of Lemma 5.2: Average cost curves are downward sloping Part 1: Average cost curves are downward sloping American System The average cost function under the “American” system is θx + f + m q q q AC(q) = . 1−exp(−rx) q Taking the first derivative of the expression with respect to q, and fully writing out also the terms that involve x, we get (cid:104) (cid:105) (cid:16) (cid:17) (cid:104) (cid:105) −f+m +θx(cid:48)(q) −θ x rexp(−rx) θx + f + m x(cid:48)(q) rx exp(−rx) θx + f + m AC(cid:48)(q) = q2 q q2 − q q q q q + q2 q q q q . 1−exp(−rx) (cid:104) (cid:105)2 (cid:104) (cid:105)2 q 1−exp(−rx) 1−exp(−rx) q q Re-arranging this expression, we obtain   −f+m 1   θ rexp(−rx)[θx+f +m]  AC(cid:48)(q) = q2 + x(cid:48)(q) − q q 1−exp(−rx) q 1−exp(−rx) (cid:104) (cid:105)2 q   q 1−exp(−rx)   q   x   θ rexp(−rx)[θx+f +m]  q q − − . q2 1−exp(−rx) (cid:104) (cid:105)2   q 1−exp(−rx)   q Note that the two terms in brackets are the first-order condition of the cost function with respect to x, which is equal to zero (this is the “Envelope condition”)! This is key: because in the average cost function x and q almost always appear as x/q, we can re-arrange terms to not only cancel the expression containing x(cid:48)(q), but also the term involving x/q2. Thus, we get −f+m AC(cid:48)(q) = q2 . (A.3) 1−exp(−rx) q This clearly shows that average cost curves are decreasing. 6

Japanese System The proof proceeds in the same way as before. Average costs under the “Japanese” system are θxexp((r+ρ)x)+ f q q q AC(q) = . 1−exp(−rx) q The first derivative with respect to q is (ignoring the derivative with respect to x here, which we know must be zero) (cid:16) (cid:17) (cid:104) (cid:105) −f −θ xexp((r+ρ)x)−θ(r+ρ)x2exp((r+ρ)x) rx exp(−rx) θxexp((r+ρ)x)+ f AC(cid:48)(q) = q2 q2 q q3 q + q2 q q q q . 1−exp(−rx) (cid:104) (cid:105)2 q 1−exp(−rx) q Re-arranging yields  (cid:104) (cid:105) (cid:104) (cid:105) AC(cid:48)(q) = − q f 2 − x   θexp((r+ q ρ)x) 1+(r+ρ)x q − q rexp(−r q x) θxexp((r+ q ρ)x)+f   . 1−exp(−rx) q2 1−exp(−rx) (cid:104) (cid:105)2 q   q 1−exp(−rx)   q Similar to before, the term in curly brackets is the first-order condition with respect to x and is equal to zero. Therefore, we have −f AC(cid:48)(q) = q2 . (A.4) 1−exp(−rx) q This function must be convex because the function under the American system was convex for all m, and thus also for m = 0. Part 2: Average cost curves are convex and converge to a finite limit. See Supplemental Appendix J.2, available on the authors’ websites. B Data Refinement and Summary Statistics Weuseversionc201601oftheLFTTDdata, whichwerefineasfollows. First, wedrop all transactions that are warehouse entries. Second, we remove all transactions that do not include a valid importer identifier, an HS code, a value, a quantity, or a valid transaction date. We also drop observations with invalid exporter identifiers, e.g., those that do not begin with a letter (identifiers should start with the country name). 7

Third, we exclude from our analysis all related-party transactions.55 We choose a conservative approach and exclude all relationships in which the two parties ever report being related, as well as all observations for which the related-party identifier is missing. Fourth, we use the concordance developed by Pierce and Schott (2012) to create time-consistent HS10 codes so that purchases of goods can be tracked over time. Fifth, we deflate transaction values using the quarterly GDP deflator of the Bureau of Economic Analysis, so that all values are in 2009 real dollars.56 Sixth, since shipments of the same product between the same buyer and seller spread over multiple containers are recorded as separate transactions, we aggregate the dataset to the weekly level. We perform this aggregation to ensure that each observation in our data reflects a genuinely new transaction rather than being part of a larger shipment. Finally, to remove unit value outliers, we follow Hallak and Schott (2011) in dropping observations where the unit value is below the 1st or above the 99th percentile within HS10 by country by mode of transportation by quarter cells. Our baseline sample restricts our cleaned data to importer (m) by HS10 product (h) by country (c) by mode of transportation (z) mhcz quadruples with at least five transactions. Table A.1 provides some details for our sample period 1992-2016. We compare this sample to an alternative arm’s-length sample that does not restrict to buyer quadruples with at least five transactions in Supplemental Appendix K. Table A.2 provides information on the average number of sellers per shipment (SPS ) by ten-digit HS code, analogous to Table 2 in the main text. For columns mhcz (3) and (4), we define J dummies Jk that take a value of one if SPS falls in mhcz mhcz the first quartile of its distribution within country-mode bins in the first time period (k = cz)toretainvariationacrossproducts. WefindthatJ sourcingismostprevalent for transportation equipment, machinery, plastics, and optical products. We show a similar table by the main 6-digit NAICS industry of the importer in Supplemental Appendix K, and show that manufacturers are the most likely to use J sourcing. Most of the variation in SPS is driven by importers. We run a series of remhcz gressions of SPS separately on importer, product, country, importer industry, mhcz and mode of transportation fixed effects, and examine the R-squared from these regressions to study how much of the variation is explained.57 We find that importer, 55TheCensusBureaudefinespartiesasrelatedifeitherpartyowns,controlsorholdsvotingpower equivalent to 6 percent of the outstanding voting stock or shares of the other organization. 56https://fred.stlouisfed.org/series/GDPDEF 57For industry, we use 6-digit NAICS fixed effects. We define the importer’s main industry in 8

product, industry, country, and mode fixed effects individually explain 35%, 12%, 10%, 8%, and 7% of the variation in SPS , respectively. The large heterogenemhcz ity in SPS across importers is consistent with different firms choosing different mhcz procurement strategies. Table A.1: U.S. Import Transaction Summary Statistics TotalImports($Bill) 5,680 VesselImports($Bill) 4,030 AirImports($Bill) 988 UniqueImporters(m) 360,000 UniqueExporters(x) 5,037,000 UniqueImporter-Product-Country-ModeQuadruples(mhcz) 2,966,000 UniqueExporter-Importer-Product-Country-ModeRelationshipQuintuples(mxchz) 21,700,000 Source: LFTTDandauthors’calculations. TablesummarizesU.S.arm’s-lengthimportsfrom1992to2016. Observationsarerestrictedtoquadrupleswithatleastfivetransactions. Importvaluesareinbillionsofreal2009dollars. Vessel imports refer to imports arriving over water. The final four rows of the table provide counts of unique importers,exporters,buyerquadruples,i.e.,U.S.importerbyHSproductbyorigincountrybymodeoftransportcells, and buyer-seller relationships, i.e., U.S. importer by foreign exporter by HS product by origin country by mode of transportcells. ObservationcountsareroundedtothenearestthousandperU.S.CensusBureaudisclosureguidelines. Table A.2: “Japanese” Relationships by HS Category Jcz =1 MeanSPS mhcz ShareofImportValue (1) (2) (3) (4) Productcode(HSchapter) 1995-2000 2002-2007 1995-2000 2002-2007 Transportation(86-89) 0.107 0.081 0.783 0.880 Machinery(84-85) 0.130 0.133 0.754 0.763 Plastics(39-40) 0.130 0.096 0.727 0.820 Opticalproducts(90-92) 0.137 0.127 0.726 0.768 Footwear(64-67) 0.142 0.117 0.750 0.827 Other products (93-99) 0.151 0.124 0.697 0.808 Metals(72-83) 0.154 0.128 0.600 0.737 Food(16-24) 0.155 0.120 0.601 0.747 Chemicals(28-38) 0.156 0.121 0.600 0.736 Stones&Jewelry(68-71) 0.159 0.141 0.658 0.674 Animalproducts&vegetables(01-15) 0.166 0.132 0.511 0.608 Minerals(25-27) 0.182 0.203 0.570 0.500 Leatherandwoodproducts(41-49) 0.188 0.153 0.556 0.688 Textiles(50-63) 0.224 0.177 0.463 0.604 Source: LFTTDandauthors’calculations. Thefirsttwocolumnsreporttheweightedaveragesellerspershipment (SPS )acrossbuyerquadrupleswithatleastfivetransactionsbyHScategoryandperiod,whereimportvalues mhcz areusedasweights. NumbersinparenthesesrefertotheHarmonizedSystemchapteroftheproduct. Thesecondtwo columnsreporttheshareofthevalueofUSimportsaccountedforbyquadrupleswithSPS inthefirstquartile mhcz ofthedistributionofSPS withincountry-modeinthefirstperiod. Rowsofthetablearesortedbycolumn(1). mhcz each year as the one with the largest share of employment, and then take the modal main industry across the years in which the quadruple is active. 9

C Construction of the Variables As discussed in the main text, we collapse all transactions of the same importer (m) - product (h) - country (c) - mode of transportation (z) quadruple in the same week into one. Therefore, a “transaction” (i) refers to a week in which the quadruple imports. Table A.3 provides a summary of how we construct the variables in Section 3. Table A.4 describes the variables used in Section 4. Table A.3: Classification Regressions Formula Description QuantityperShipment (cid:80) iQuantitymhczi Quantity isthequantityimportedbyquadruple Ntransmhcz mhczi (QPS ) mhcz attransactioniandNtrans isthetotal mhcz mhcz numberoftransactionsbythequadruplein1992-2016. ValueperShipment (cid:80) iValuemhczi Value isthevalueimportedbyquadruple Ntransmhcz mhczi (VPS ) mhcz attransactioniandNtrans isthetotal mhcz mhcz numberoftransactionsbythequadruplein1992-2016. WeeksbetweenShipments endmhcz−begmhcz end isthenumberoftheweekofthelasttransaction Ntransmhcz−1 mhcz (WBS ) ofthequadrupleandbeg isthenumberoftheweekof mhcz mhcz thefirsttransactionofthequadruple(seedefinition below). Thedenominatorrepresentsthenumberoftime periodsbetweensubsequenttransactionsofthequadruple, whichisonelessthanthenumberoftransactions. Since werequireatleastfivetransactionsinourbaseline,the expressionisfinite. UnitValue(UV ) 1 (cid:80) Valuemhczi Value isthevalueimportedbyquadruplemhcz at mhcz Ntransmhcz i Quantitymhczi mhczi transactioni,Quantity isthecorrespondingquantity. mhczi QuantityperWeek (cid:80) iQuantitymhczi IncontrasttoQPS ,thisvariabledoesnotdivideby endmhcz−begmhcz mhcz (QPW ) thenumberoftransactionsbutbythe“flow”ofimportsinan mhcz averageweek. Wenotethatsincewerequireatleastfive transactionsinourbaseline,thebeginningandendweekare neverthesameandthereforetheexpressionisfinite. Firstweek(beg ) min{Week } Week istheweeknumberofthetransaction,relative mhcz mhczi mhczi Lastweek(end ) max{Week } tothefirstweekof1960. Thus,forexamplethefirstweekof mhcz mhczi 2016hasweeknumber2912. Avg. relationshiplength (cid:80) Se x ll l e e r n s g m th h m cz x lengthmx=max{Weekmxi}−min{Weekmxi}. Weekmxi (length ) istheweeknumberofatransactioniofthebuyer-seller mhcz pairmxinanygoodormodeoftransportation,relative tothefirstweekof1960. Sellers isthenumberof mhcz exporters(x)withwhichthequadruple (mhcz)hasanmxhcz quintuplerelationship. 10

Table A.4: PNTR Regressions Formula Description QuantityperShipment (cid:80) iQuantitymxhczti Quantity isthequantityimportedbyquintuple Ntransmxhczt mxhczti (QPS ) mxhcz inperiodt(either1995-2000or2002-2007)at mxhczt transactioniandNtrans isthetotalnumber mxhczt oftransactionsbythequintupleinperiodt. WeeksbetweenShipments endmxhczt−begmxhczt end isthenumberoftheweekofthelast Ntransmxhczt−1 mxhczt (WBS ) transactionofthequintupleinperiodt(either1995-2000 mxhczt or2002-2007)andbeg isthenumberoftheweek mxhczt ofthefirsttransactionofthequintuple. Theweek numberisrelativetothefirstweekof1960. Thus, forexamplethefirstweekof2016hasweeknumber 2912. Thedenominatorrepresentsthenumberoftime periodsbetweensubsequenttransactionsofthequintuple, whichisonelessthanthenumberoftransactions. If Ntrans =1,theaveragetimegapcannotbe mxhczt computed. ThePNTRregressionsthereforerequirefor eachquintupleatleasttwotransactionsineachperiodt. UnitValue 1 (cid:80) Valuemxhczti Value isthevalueimportedbyquintuplemxhczt Ntransmxhczt i Quantitymxhczti mxhczti (UV ) attransactioniinperiodt,andQuantity mxhczt mxhczti isthecorrespondingquantity. QuantityperWeek (cid:80) iQuantitymxhczti IncontrasttoQPS ,thisvariabledoesnotdivide endmxhczt−begmxhczt mxhczt (QPW ) bythenumberoftransactionsbutbythe“flow”of mxhczt importsinanaverageweek. Asdescribedabovefor WBS ,werequireforeachquintupleat mxhczt leasttwotransactionsineachperiodtsothatthis variablecanbecomputed. D Additional A vs J Classification Regressions Thicker Relationships: Our baseline regressions in Section 3.2 are restricted to mhcz quadruples with at least five transactions over our sample period. One concern might be that for quadruples that trade only relatively few times, our variable suppliers per shipment (SPS ) is mismeasured because we did not observe a sufficient number mhcz of transactions. In Table A.5, we show that our results are robust to restricting the regression to quadruples with at least 10 transactions. More Aggregated Suppliers per Shipment: Another concern with our measure of SPS might be that buyers obtain shipments across multiple modes of transportation, and therefore procurement systems – and hence SPS – should be better defined at the mhc or even mh level. In Tables A.6 and A.7 we show that our results are robust to defining SPS at these higher levels of aggregation (i.e., SPS or SPS ), where mhc mh we keep all other variables at the mhcz level of the baseline. Different Modes of Transportation: We next investigate whether the results hold separately for vessel vs. air shipments. Results in Table A.8 indicate similar results 11

for both forms of transport. Average Firm Attributes: In regression (8), we use the firm-level attribute in the year of the firm’s first import transaction. In Table A.9 we instead compute for each buyer quadruple an average of the firm attribute across all years in which the quadruple is active, and then average across quadruples. The two specifications could generate different results if the firm’s attributes change significantly over time. The results are similar to the baseline. Table A.5: A vs J Classification Regression With At Least 10 Transactions (1) (2) (3) (4) Dep. var. log(QPS ) log(WBS ) log(UV ) log(length ) mhcz mhcz mhcz mhcz log(SPS ) 0.359∗∗∗ 0.370∗∗∗ −0.064∗∗∗ −0.504∗∗∗ mhcz 0.015 0.016 0.020 0.013 log(QPW ) 0.700∗∗∗ −0.306∗∗∗ −0.273∗∗∗ −0.134∗∗∗ mhcz 0.014 0.014 0.019 0.005 Observations 1,645,000 1,645,000 1,645,000 1,645,000 R-squared 0.950 0.659 0.855 0.488 Fixedeffects hcz hcz hcz hcz Controls beg,end beg,end beg,end beg,end Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingnotedattributeofimporterby productbycountrybymodeoftransport(mhcz)binsonsellerspershipment(SPS )andtotalquantity mhcz shippedperweek(QPW ). QPS ,WBS ,P ,andlength areaveragequantitypershipment, mhcz mhcz mhcz mhcz mhcz averageweeksbetweenshipment,averageunitvalue,andaveragerelationshiplength. Allregressionsinclude productbycountrybymodeoftransport(hcz)fixedeffects,controlforthebeginningandendweekofthe quadruple,andexcludequadrupleswithlessthan10shipments. Standarderrors,adjustedforclusteringbycountry (c)andproduct(h)arereportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1, 5and10percentlevels. Table A.6: A vs J Classification Regression With SPS at mhc Level (1) (2) (3) (4) Dep. var. log(QPS ) log(WBS ) log(UV ) log(length ) mhcz mhcz mhcz mhcz log(SPS ) 0.346∗∗∗ 0.376∗∗∗ −0.083∗∗∗ −0.578∗∗∗ mhc 0.014 0.015 0.018 0.013 log(QPW ) 0.687∗∗∗ −0.322∗∗∗ −0.279∗∗∗ −0.147∗∗∗ mhcz 0.015 0.015 0.020 0.005 Observations 2,966,000 2,966,000 2,966,000 2,966,000 R-squared 0.944 0.654 0.844 0.442 Fixedeffects hcz hcz hcz hcz Controls beg,end beg,end beg,end beg,end Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingnotedattributeofimporterby productbycountrybymodeoftransport(mhcz)binsonsellerspershipmentdefinedforbroadermhcbins (SPS )andtotalquantityshippedperweek(QPW ). QPS ,WBS ,P ,andlength are mhc mhcz mhcz mhcz mhcz mhcz averagequantitypershipment,averageweeksbetweenshipment,averageunitvalue,andaveragerelationship length. Allregressionsincludeproductbycountrybymodeoftransport(hcz)fixedeffects,controlforthebeginning andendweekofthequadruple,andexcludequadrupleswithlessthanfiveshipments. Standarderrors,adjustedfor clusteringbycountry(c)andproduct(h)arereportedbelowcoefficientestimates. ***,**,and*represent statisticalsignificanceatthe1,5and10percentlevels. 12

Table A.7: A vs J Classification Regression With SPS at mh Level (1) (2) (3) (4) Dep. var. log(QPS ) log(WBS ) log(UV ) log(Length ) mhcz mhcz mhcz mhcz log(SPS ) 0.285∗∗∗ 0.311∗∗∗ −0.063∗∗∗ −0.483∗∗∗ mh 0.019 0.020 0.021 0.009 log(QPW ) 0.668∗∗∗ −0.343∗∗∗ −0.274∗∗∗ −0.115∗∗∗ mhcz 0.014 0.014 0.020 0.006 Observations 2,966,000 2,966,000 2,966,000 2,966,000 R-squared 0.940 0.631 0.844 0.379 Fixedeffects hcz hcz hcz hcz Controls beg,end beg,end beg,end beg,end Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingnotedattributeofimporterby productbycountrybymodeoftransport(mhcz)binsonsellerspershipmentdefinedforbroadermhbins(SPS ) mh andtotalquantityshippedperweek(QPW ). QPS ,WBS ,P ,andlength areaverage mhcz mhcz mhcz mhcz mhcz quantitypershipment,averageweeksbetweenshipment,averageunitvalue,andaveragerelationshiplength. All regressionsincludeproductbycountrybymodeoftransport(hcz)fixedeffects,controlforthebeginningandend weekofthequadruple,andexcludequadrupleswithlessthanfiveshipments. Standarderrors,adjustedfor clusteringbycountry(c)andproduct(h)arereportedbelowcoefficientestimates. ***,**,and*represent statisticalsignificanceatthe1,5and10percentlevels. Table A.8: A vs J Classification Regression Across Mode of Transport (1) (2) (3) (4) Dep. var. log(QPS ) log(WBS ) log(UV ) log(length ) mhcz mhcz mhcz mhcz Vessel log(SPS ) 0.419*** 0.451*** -0.172*** -0.570*** mhcz 0.015 0.015 0.013 0.018 log(QPW ) 0.661*** -0.347*** -0.263*** -0.177*** mhcz 0.011 0.011 0.018 0.008 Observations 1,506,000 1,506,000 1,506,000 1,506,000 R-squared 0.924 0.686 0.829 0.434 Air log(SPS ) 0.410*** 0.443*** -0.058** -0.609*** mhcz 0.022 0.022 0.025 0.018 log(QPW ) 0.737*** -0.272*** -0.300*** -0.106*** mhcz 0.015 0.015 0.023 0.005 Observations 1,029,000 1,029,000 1,029,000 1,029,000 R-squared 0.933 0.635 0.764 0.416 Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingnotedattributeofimporterby productbycountrybymodeoftransport(mhcz)binsonbins’sellerspershipment(SPS )andtotalquantity mhcz shippedperweek(QPW ). QPS ,WBS ,P ,andlength areaveragequantitypershipment, mhcz mhcz mhcz mhcz mhcz averageweeksbetweenshipment,averageunitvalue(i.e. valuedividedbyquantity),andaveragerelationship length. Allregressionsincludeproductbycountrybymodeoftransport(hcz)fixedeffects,controlforthebeginning andendweekofthequadruple,andexcludequadrupleswithlessthanfiveshipments. Standarderrors,adjustedfor clusteringbycountry(c)andproduct(h),arereportedbelowcoefficientestimates. ***,**,and*represent statisticalsignificanceatthe1,5and10percentlevels. 13

Table A.9: SPS and Firm Characteristics m (1) (2) (3) (4) Dep. var. log(salesm) log(paym) log(wagem) (inv/sales)m log(SPSm) −0.255∗∗∗ −0.313∗∗∗ −0.066∗∗∗ 0.016∗∗∗ 0.005 0.006 0.002 0.001 Observations 184,000 184,000 184,000 48,500 R-squared 0.012 0.014 0.004 0.007 Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingimportercharacteristicsaveraged acrossallyearsinwhichtheimporterisactiveonsellerspershipment(SPS )averagedacrossallquadruples mhcz involvingtheimporter. Allregressionsexcludequadrupleswithlessthanfiveshipments. (salesm),(paym), (wagem),and((inv/sales)m)aretotalsales,totalpayroll,averagewage(i.e.,payrolldividedbynumberof employees),andtotalinventoryatthebeginningoftheyeardividedbytotalsales,respectively. Robuststandard errorsarereportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and10 percentlevels. E Additional DID Regressions Alternate Time Periods: We show that our baseline DID results also hold if we use a different post-PNTR period from 2004 to 2009. Table A.10 presents the results from the continuing relationship PNTR regression (9), and Table A.11 shows the results for the regression with only new relationships. All results retain their expected sign and remain significant. Table A.12 presents the results from the within-importer regression, equation (10), both at the mhcz level and at the hcz level. On average, we find that the results from the main text become stronger for this later post-period, possibly because the shift of systems takes time. No Quantity Control: Oneconcernwithouranalysiscouldbethatbyconditioning on quantity we do not take into account that PNTR also affects the quantity traded, which could in turn affect the procurement system. We therefore run the baseline PNTR regression (9) without quantity control, QPW . Results in Table A.13 mxhczt show that we still find a decline in the quantity per shipment and an increase in the unit value. The effect on weeks between shipments is qualitatively consistent with the theory, though not significant at conventional levels. 14

Table A.10: Within mxhcz Quintuple PNTR DID Regression: 2004-2009 vs 1995- 2000 (1) (2) (3) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) mxhczt mxhczt mxhczt Postt∗Chinac∗NTRGap h -0.199*** -0.163*** 0.149*** 0.017 0.021 0.031 ln(QPW ) 0.403*** -0.606*** -0.133*** mxhczt 0.009 0.008 0.014 Observations 221,000 221,000 221,000 R-squared 0.980 0.883 0.982 Fixedeffects mxhcz,t mxhcz,t mxhcz,t Controls Yes Yes Yes Source: LFTTDandauthors’calculations. TablereportstheresultsofregressingnotedattributeofUSimporterby exporterbyproductbycountrybymodeoftransport(mxhcz)binsonthedifference-in-differencestermofinterest andquantityshippedperweek. Pre-andpostperiodsare1995to2000and2004to2009. (QPS ), mxhczt (WBS ),and(UV )areaveragequantitypershipment,averageweeksbetweenshipments,andaverage mxhczt mxhczt unitvalue(i.e. valuedividedbyquantity)inperiodt. Allregressionsincludemxhcz andperiodtfixedeffects, controlforthebeginningandendweekofthequintupleaswellasallvariablesneededtoidentifytheDID termof interest. Standarderrors,adjustedforclusteringbycountry(c)andproduct(h),arereportedbelowcoefficient estimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percentlevels. Table A.11: New mxhcz Quintuple PNTR DID Regression: 2004-2009 vs 1995-2000 (1) (2) (3) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) mxhczt mxhczt mxhczt Postt∗Chinac∗NTRGap h -0.087** -0.067* 0.075* 0.036 0.035 0.045 ln(QPW ) 0.414*** -0.590*** -0.127*** mxhczt 0.012 0.011 0.017 Observations 3,158,000 3,158,000 3,158,000 R-squared 0.968 0.845 0.973 Fixedeffects mhcz,x,t mhcz,x,t mhcz,x,t Controls Yes Yes Yes Source: LFTTDandauthors’calculations. TablereportstheresultsofregressingnotedattributeofUSimporterby exporterbyproductbycountrybymodeoftransport(mxhcz)binsonthedifference-in-differencestermofinterest andquantityshippedperweek. Pre-andpostperiodsare1995to2000and2004to2009. (QPS ), mxhczt (WBS ),and(UV )areaveragequantitypershipment,averageweeksbetweenshipments,andaverage mxhczt mxhczt unitvalue(i.e. valuedividedbyquantity)inperiodt. Allregressionsincludemxhcz andperiodtfixedeffects, controlforthebeginningandendweekofthequintupleaswellasallvariablesneededtoidentifytheDID termof interest. Standarderrors,adjustedforclusteringbycountry(c)andproduct(h),arereportedbelowcoefficient estimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percentlevels. 15

Table A.12: Within-Importer PNTR Regression: 2004-2009 vs 1995-2000 (1) (2) (3) (4) Dep. var. ln(SPS ) 1{Jhcz =1} ln(SPS ) Jhcz mhczt mhczt hczt hczt Postt∗Chinac∗NTRGap h -0.076** 0.076** -0.027** 0.042 0.037 0.029 0.011 0.027 ln(QPW ) -0.186*** 0.125*** -0.059*** 0.031*** mhczt 0.005 0.005 0.002 0.004 Observations 556,000 225,000 355,000 28,000 R-squared 0.757 0.660 0.687 0.550 Fixedeffects mhcz,t mhcz,t hcz,t hcz,t Controls Yes Yes Yes Yes Source: LFTTDandauthors’calculations. FirsttwocolumnsreporttheresultsofregressingnotedattributeofUS importerbyproductbycountrybymodeoftransport(mhcz)binsonthedifference-in-differencestermofinterest andquantityshippedperweek. Secondtwocolumnsareanalogousbutatthehcz levelofaggregation. Pre-and post-PNTRperiodsare1995to2000and2004to2009. Allregressionsincludeperiodtfixedeffects,andcontrolfor thebeginningandendweekofthequadrupleaswellasallvariablesneededtoidentifytheDID termofinterest. Regressionsincolumnstwoandfourarerestrictedtoquadrupleswithatleastfivetransactionsinbothperiods. Standarderrors,adjustedforclusteringbycountry(c)andproduct(h),arereportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percentlevels. Table A.13: Baseline Within mxhcz Quintuple PNTR DID Regression Without Quantity: 2002-2007 vs 1995-2000 (1) (2) (3) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) mxhczt mxhczt mxhczt Postt∗Chinac∗NTRGap h -0.2753*** -0.0339 0.1186*** 0.0076 0.0318 0.0191 Observations 439,000 439,000 439,000 R-squared 0.97 0.69 0.98 Fixedeffects mxhcz,t mxhcz,t mxhcz,t Controls Yes Yes Yes Source: LFTTDandauthors’calculations. TablereportstheresultsofregressingnotedattributeofUSimporterby exporterbyproductbycountrybymodeoftransport(mxhcz)binsonthedifference-in-differencestermofinterest andquantityshippedperweek. Pre-andpostperiodsare1995to2000and2002to2007. (QPS ), mxhczt (WBS ),and(UV )areaveragequantitypershipment,averageweeksbetweenshipment,andaverage mxhczt mxhczt unitvalue(i.e. valuedividedbyquantity)inperiodt. Allregressionsincludemxhcz andperiodtfixedeffects, controlforthebeginningandendweekofthequadrupleaswellasallvariablesneededtoidentifytheDID termof interest. Standarderrors,adjustedforclusteringbycountry(c)andproduct(h),arereportedbelowcoefficient estimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percentlevels. 16

F Market Clearing Conditions Goods market clearing implies that production equals consumption for each ω: (cid:88)(cid:88)(cid:88) (cid:88)(cid:88)(cid:88) (cid:90) x∗ ni,s (ω)/qn(ω) I (ω)x∗ (ω) = I (ω) q (ω)dt ∀ω, (A.5) ni,s ni,s ni,s n n i s n i s 0 where I (ω) is an indicator function that is equal to one if the buyer in country n ni,s procures product ω from country i under system s, and zero otherwise. The market for the homogeneous good clears as well, (cid:88) (cid:88) Z = a LO. (A.6) n n n n n Finally, labor market clearing in each country requires that (cid:88)(cid:88) (cid:90) 1 θ ¯ (cid:88)(cid:88) (cid:90) 1 q (ω) i L = I (ω) q (ω)dω +f I (ω) dω n in,s Υ (ω) i n in,s x∗ (ω) i s 0 n i s 0 in,s (cid:88) (cid:90) 1 q (ω) + I (ω)m(ω) n dω +LO ∀n ∈ N, (A.7) ni,A x∗ (ω) n i 0 ni,s where the left-hand side is total labor supply in country n, and on the right-hand side we have labor used in manufacturing production, labor used for fixed costs, labor used for inspections, and the homogeneous “outside” good labor, respectively. Since the fixed costs and the inspection costs are paid for each shipment, we scale these costs by the number of shipments per period. G Equilibrium Solution Algorithm We discretize the product space to Ω = 5,000 products, and follow the steps in Table A.14. Our algorithm first computes the average cost curves and shipment sizes on a grid of inspection costs, productivities, trade war arrival rates, and quantities. We then guess a price index and total income for each country, trace out the demand curves, find the intersection of supply and demand, and iterate to convergence. We compute the average cost curves outside of the iteration algorithm since the numerical solution of the buyer’s problem is quite time consuming. While in principle it would 17

be possible to solve the buyer’s problem within each iteration for each niω tuple, using linear interpolation on a grid during the iteration process is much faster. Table A.14: Equilibrium Solution Algorithm Step Description 1 Initiatethemodelbydrawinganinspectioncostm(ω)foreachproductω andcountrynfromGn(m) andbydrawingaproductivityΥn(ω)fromFn(Υ). Alsosetthetradewararrivalratesρni for eachcountrypair. 2 Defineafour-dimensionalgridwith(K1×K2×K3×Q)gridpoints,whereK1=70,K2=60,K3=60, andQ=70. Letk≡(k1,k2,k3,q k )denoteagivengridpoint. SolvenumericallyfortheaveragecostsAC(k) ateachgridpointundereachsystem,usingequation(4),i.e. ACA(k)=minx (cid:18) q r k (cid:19) (cid:2) 1 k − 1 e + −r k x 2 / x qk (cid:3) andACJ(k)=minx (cid:18) q r k (cid:19)k1+ (cid:2) 1 e − (r+ e− k3 r ) x x / / q q k k (cid:3) k2x .WedenotebyxA(k)andxJ(k) thecost-minimizingshipmentsizesundereachsystematgridpointk. 3 Mapthedraw(m(ω),Υi(ω),ρni)ofeachorigincountry(i)-destinationcountry(n)-product(ω)triplettoan estimatedaveragecostforeachq usinglinearinterpolationonthegridofaveragecostscomputedinStep2, k w w e he u r s e e u k n 1 d = er f t i h w e i A ,k s 2 y = ste Υ m i θ¯ ( w ω) e w u i s , e a k n 1 d = k3 fi = wi ρn + i. m S ( i ω m ) i w la n r , ly k , 2 o = bta Υ in i θ¯ (ω th ) e w s i h a i n p d me u n n t d s e i r ze t s h , e x J ∗ ni s ,s y , stem fromlinearinterpolationonthegridofshipmentsizescomputedinStep2. 4 Determinethecostminimizingsystemandorigincountryateachquantityq foreachdestination-product k marketnω,usingequation(12). ThistracesouttheaveragecostcurveACnω(q k )ofeachmarket. 5 Beginiterationt=0. Guessaninitialmanufacturingpriceindexineachdestinationcountry,Pn(t),and aninitialtotalincome,Wn(t). 5.a Computeeachdestination-productmarketnω’sdemandcurve,usingutilitymaximization,bycomputingfor eachq k thepricepn(ω;q k ,t)= (cid:18)αW q n(t)(cid:19) σ 1 Pn(t) σ− σ 1 . k 5.b Findtheintersectionbetweensupplyanddemandcurveineachmarket,usinglinearinterpolationbetween gridpoints,toobtaintheequilibrium(p∗(ω),q∗(ω)). Ifthereareseveralintersections,findthelast n n intersectionatwhichthedemandcurveintersectsthesupplycurvefromabove. Usingtheequilibrium pricesineachmarket,computeanewpriceindex,Pn(t+1). 5.c Determinethelaborusedforproduction,fixedcosts,andinspectioncosts. Usethelabormarketclearing condition(A.7)todeterminelaborusedforthehomogeneousgoodsectorLO . n Verifythatthislaborisnon-negative. 5.d Computethetotalincomeineachcountry,Wn(t+1),whichisequaltolaborincomewnLn plusprofits underthe“Japanese”system,seeequation(13). ReturntoStep5.awith{Pn(t+1),Wn(t+1)} anditeratetoconvergence. H Parameters and Empirical Moments Table A.15 provides more detail on how we set the calibrated parameters in Table 9. Table A.16 contains more detail on how we construct the moments for the estimation. 18

Table A.15: Calibrated Parameters Parameter Description Interestrate(r) AsinCaliendoetal.(2019) Elasticityofsubstitution(σ) WefollowAntra`setal.(2017). Theyfindamedianmarkupof35percentacross establishments. Thisestimateimpliesanelasticityofsubstitutionofσ =3.85. Consumptionshareof WeconstructthisparameterbasedonestimatesbyDuarte(2020),whouses manufacturedgoods(α) detaileddataonhouseholdconsumptionexpenditurefromtheInternational ComparisonsPrograms(ICP)tocomputeconsumptionexpendituresandrelative pricesofmanufacturedgoodsandservicesinmanycountries. Shecomputesa realshareofmanufacturedgoodsconsumptioninallconsumptionexpendituresof 45%−50%forhigh-incomecountriessuchastheU.S.(Table4). Dispersionofproductivities(ζ) WesetthisparameterbasedonEatonandKortum(2002),whoestimateitfrom agravityequationthatrelatesbilateraltradeflowstothecharacteristicsof thetradingpartnersandthedistancebetweenthem. Productivity(an) Weexploitthatan=wn andsetproductivitybasedonaveragewages. Weestimate wagesastwothirdstimesGDPdividedbythesizeofthelaborforce(i.e.,GDP perworker)fromtheWorldBankWorldDevelopmentIndicators(WDI)in2016. ForeachcountryweobtainGDPincurrentUSD(seriesNY.GDP.MKTP.CD) andthetotalsizeofthelaborforce(seriesSL.TLF.TOTL.IN).ForRoW, wetakeanaverageacrosstheUS’top-tentradingpartners(listedinTable2) usingUSimportsfromeachcountryin2016asweight. USisnormalizedto1. Laborforce(Ln) WeobtainthesizeofthelaborforcefromtheWorldDevelopmentIndicators (WDI)in2016(seriesSL.TLF.TOTL.IN).ForRoW,wesumthelaborforceof thetoptenUStradingpartnersintheperiod1992-2016. USis normalizedto1. Rateoftradewars WetakeallJ buyer-seller(mxhcz)quintuplesinourdata,identifiedasthosewhere U.S.-China(ρUS,CN) theassociatedmhcz quadrupleisinthefirstquartileofthewithin-country-productmode(hcz)SPS distributionintheentiredataset. Wecomputeforthesetheprobabilitythatarelationshipseparatesafterτ quarters,separatelyforChinaandRoW (cid:80) IT(τ =τ) Scτ = (cid:80) mxhzt I(τ mxhczt =τ) mxhzt mxhczt whereI(τ =τ)isequaltooneifquintuplemxhcz isatageτ =τ mxhczt mxhczt quartersinquartert,andIT(τ =τ)isequaltooneforallsuchquintuples mxhczt thatadditionallytradeforthelasttimeinquartert. Wethenfittheexponential decayfunctione−ψUS,it totheestimatedseparationprobabilitiestominimizethe squareddeviationfori=Chinaandi=RoW.Sincemanyquintuplestradeonlyonce, wefitthisfunctionfromquartertwoonwards,τ =2,...,100. Weobtain ψUS,RoW =0.0873andψUS,CN =0.1137yieldingadifferenceofρUS,CN =0.0264. I Additional Estimation Details and Robustness I.1 Baseline Estimation The objective is to find a parameter vector φ∗ that solves (cid:88) ˆ argmin T(M (φ),M ) (A.8) x x φ∈F x ˆ where T(·) is the percentage difference between the model, (M (φ)), and data, (M ), x x moments, and F is the set of admissible parameter vectors, which is bounded to be 19

Table A.16: Construction of Empirical Moments Moment Description ShareofChineseimportsindomestic WetargettheUSimportpenetrationfromChinain2016, manufacturingsales computedas Imports IPCN = CN , Domesticoutput+Totalimports−Totalexports whereImports areUSimportsfromChinafrom CN https://www.census.gov/foreign-trade/balance/c5700.html, Domesticoutputdenotesgrossoutputinthemanufacturing sectorfromhttps://www.bea.gov/itable/gdp-by-industry, andTotalimportsandTotalexportsareU.S.imports andexportsofgoodsfrom https://www.census.gov/foreign-trade/balance/country.xlsx Shareofrestofworldimportsindomestic WetargettheUSimportpenetrationfromtherestofthe manufacturingsales worldin2016,computedas: Imports IPRoW = RoW Domesticoutput+Totalimports−Totalexports whereImports areUSimportsfromallcountriesexcept RoW Chinafrom https://www.census.gov/foreign-trade/balance/country.xlsx. Standarddeviationof(cid:15)ˆ Wetaketheresidualsfrom(14)andretainonlythosethat haveWBS inthefourthquartileoftheWBS distribution, mhcz i.e.,thosemostlikelyassociatedwithAsourcing,separatelyfor importsfromChinaandfromtherestoftheworld. Wecollapse theresidualstotheHS10leveltoremovevariationinshipping frequencywithinthesameproductthatisunrelatedto inspectioncostsandthentakethestandarddeviationof theresultingproduct-levelaverageresiduals. ˆ strictly positive and finite. In the choice of the function T((M (φ),(M )) we follow x x Lise et al. (2016) and minimize the sum of the percentage deviations between modelgenerated and empirical moments. The minimization algorithm that we use to solve the problem combines the approaches of Lise et al. (2016) and Engbom and Moser (2022), adapted to our needs. We simulate, using Markov Chain Monte Carlo for classical estimators as introduced in Chernozhukov and Hong (2003), 100 strings of length 1,000 (+ 200 initial scratch periods used only to calculate posterior variances) starting from 100 different guesses for the vector of parameters φ . In the first run, we choose the initial guesses to span 0 a large space of possible parameter vectors. In updating the parameter vector along the MCMC simulation, we pick the variance of the shocks to target an average rejection rate of 0.7, as suggested by Gelman et al. (2013). The average parameter values across the 20 strings with the lowest values of the objective function provide a first estimate of the vector of parameters. We then repeat the same MCMC procedure, but we start each of our 100 strings from these parameter estimates. Figure A.1 illustrates our approach. The black dotted line shows the density 20

Figure A.1: Estimation Outcomes Source: Author’scalculations,basedontheestimationproceduredescribed. Eachpanelshowstheestimatedparametervaluesfortheparameterindicatedinthetitle,undertheassumptionofaParetodistributionforinspectioncosts. Theblackdottedlineshowsthedensityfunctionoftheparametervaluesassociatedwiththelast200iterationsofour 100strings. Thereddashedlineshowstheaverageparametervaluesacrossthe100bestoutcomesfromallthedraws. Thebluedensityfunctionsshowsthedensityofthe10bestoutcomesofeachstring,computedacrossallstrings. function of the parameter values associated with the last 200 iterations of our 100 strings. We pick the optimal parameters (red dashed lines) following Engbom and Moser (2022) as the average across the 100 best outcomes across all the draws. These correspond to the estimates reported in Table 10. For comparison, the blue density function shows the density of the 10 best outcomes of each string, computed across all strings. This density provides an alternative way to select the best parameter values. All the densities are single-peaked, which suggests that the model is, at least locally, identified. Moreover, our chosen parameter values are generally very close to the peak of the densities. Figure A.2 provides more detail on how each parameter is identified. We start from the optimal parameter values (red dashed lines in the previous figure) and vary each of the six parameters one-by-one on a grid of 100 values. For each parameter combination we solve the model 100 times, re-drawing the random productivity and inspectioncosts,andcomputetheaveragevalueofeachmoment. ThepanelsinFigure A.2 plot the different values of each parameter (rows) against the values of the eight moments (columns). The main moments identifying the parameters are along the 21

Figure A.2: Identification of Parameters Source: Author’scalculations,basedontheestimationproceduredescribed. Eachpanelplotsdifferentvaluesofthe parameter indicated on the row against the moment indicated on the column, keeping all other parameters fixed at theiroptimalvalue. Thebluedotsshowtheaveragedmomentvalueacross100runswiththegivenparameterchoice, wheretheaveragingisneededsincetheinspectioncostandproductivitydrawsdifferacrossruns. Theredhorizontal linesrepresentthevalueofthemomentinthedata. Weaddtheseonlyforthemainpanelsusedtoidentifyagiven parameterinthedata. diagonal. The red horizontal line represents the value of the moment in the data, and henceidentifiestheparametervaluethatwouldleadthemodeltoperfectlymatchthis moment. While the relationships between the first four parameters and their main identifying moments are monotonic, for the last two parameters (the dispersion of inspection costs, γ ) the relationships with some of the targeted moments are humpn shaped. Thus, there could be multiple values for each of these parameters that match a given moment equally well. We therefore target two sets of moments for these parameters (in the last four columns). This strategy yields a unique value for these parameters that minimizes the objective function. In Supplementary Appendix O.1, we perform an alternative exercise and plot the relationships between parameters and moments when we vary all parameters jointly. We show that the results are similar in this exercise. Overall, theseexerciseshighlightthatourparametersofinterestarewell-identified from the moments we target. 22

I.2 Fr´echet Distribution of Inspection Costs We re-estimate the model using a Fr´echet distribution instead of a Pareto distribution for the inspection costs: G (m) = e−m−γn, (A.9) n where γ is to be estimated. The other model parameters are set as before. n Figure A.3 presents our estimated parameter values analogously to Figure A.1. We find that all the densities are less tightly estimated than in the Pareto case. Our chosen parameter values are close to the peak of the densities. Table A.17 presents the estimated parameter values and the values of the targeted moments in the simulations and in the data. The moments are reasonably wellmatched, though less well than with the Pareto distribution. The model generates shares of Chinese and RoW imports in US manufacturing consumption that are close to the data, and generates shipping frequencies somewhat in line with their empirical analogues. The model does not match well the difference in shipping frequencies between the first and the fourth quartile for shipments from China in row (5). In the data, the difference in shipping times between the first and the fourth quartile of the WBS distribution is relatively small, while the dispersion of shipping times mhcz within the first quartile is relatively large. To match the latter the model estimates a high volatility of inspection costs (low γ ), which causes the model to overshoot the CN former moment for China. For the rest of the world, the two moments are relatively well matched. Due to this deviation from the targeted moments, we prefer the Pareto distribution as our baseline, which matches all moments better due to its different shape. Table A.18 shows selected moments from our baseline equilibrium and the counterfactual without J relationships. Compared to the equilibrium with a Pareto distribution, the estimated share of J relationships is significantly higher for both China andfortherestoftheworld, withmorethanhalfofimportsestimatedtobeunderthe J system. This higher share of J relationships results from the higher dispersion of inspection costs in this estimation, which generates more high inspection cost draws, leading J sourcing to be cheaper than A sourcing for more products. The structurally estimated J shares are in the ballpark of the empirical estimates we obtained using shipments in the first quartile of the SPS distribution in Table 2. As a result of mhcz thehighershareofJ relationships, thewelfarelossesfromremovingsuchrelationships 23

rise by almost two percentage points compared to the baseline to 3.5 percent. The cost from eliminating J sourcing in the Fr´echet case is therefore about two thirds as high as placing the US in autarky. This exercise suggests that the welfare losses from policy uncertainty can be much higher when the share of J relationships is greater. Figure A.3: Estimation Outcomes with Fr´echet Distribution Source: Authors’calculations,basedontheestimationproceduredescribed,usingaFr´echetdistributionforinspection costs. Each panel shows the estimated parameter values for the parameter indicated in the title. The black dotted lineshowsthedensityfunctionoftheparametervaluesassociatedwiththelast200iterationsofour100strings. The reddashedlineshowstheaverageparametervaluesacrossthe100bestoutcomesfromallthedraws. Thebluedensity functionsshowsthedensityofthe10bestoutcomesofeachstring,computedacrossallstrings. 24

Table A.17: Estimated Parameters and Targeted Moments (1) (2) (3) (4) (5) Estimated MomentthatPrimarily Moment Moment Parameter Value IdentifiestheParameter inData inModel (1) ProductivityChina(TCN) 15.973 ShareofChineseimportsindomesticsales 0.074 0.049 (2) ProductivityRoW(TRoW) 2.769 ShareofRoWimportsindomesticsales 0.270 0.273 (3) Fixedcosts,China(fCN) 0.613 exp(βˆ 0+βˆ 1+βˆ 3beg+βˆ 4end)from(14)forCN 91.00 105.49 (4) Fixedcosts,RoW(fRoW) 0.092 exp(βˆ 0+βˆ 1+βˆ 3beg+βˆ 4end)from(14)forRoW 60.90 66.35 (5) Dispersionofinspection 0.068 βˆ 1 from(14)forChina 0.871 1.411 (6) costs,China(γCN) Sdof(cid:15)ˆfrom(14)forChina 0.227 0.187 (7) Dispersionofinspection 0.056 βˆ 1 from(14)forRoW 0.822 0.726 (8) costs,RoW(γRoW) Sdof(cid:15)ˆfrom(14)forRoW 0.219 0.238 (9) TotalobjectiveT(·) 0.580 Source: LFTTDandauthors’calculations. Column(1)liststheparametersestimatedforthemodel. Column(2) containstheestimatedparametervalues. Column(3)reportsthemomenttargetedtoidentifytheparameter. Column(4)presentsthevalueofthemomentinthedata,andColumn(5)presentsthevalueofthemoment computedinoursimulatedmodel. Table A.18: Comparison of Equilibria with Fr´echet Distribution (1) (2) (3) (4) Equilibrium Baseline Without Japanese Removal of Equilibrium Sourcing Autarky PNTR (1) ValueimportedfromChina(%) 4.9% 2.9% . 4.5% (2) -ofwhich,“Japanese” 56.7% . . 50.3% (3) ValueimportedfromROW(%) 27.3% 13.7% . 27.4% (4) -ofwhich,“Japanese” 67.6% . . 67.6% (5) ValueimportedfromUS(%) 67.8% 83.4% 100.0% 68.1% (6) Avg. inspectioncosts 0.2% 1.1% . 0.2% (7) Avg. fixedcosts(imports) 6.8% 4.4% . 6.7% (8) Manufacturingpriceindex 1.000 1.060 1.115 1.002 (9) Utility 1.000 0.965 0.941 0.9994 Table shows various statistics of the equilibrium under the assumption of a Fr´echet distribution for inspection costs. The first column presents the statistics for the baseline equilibrium, using the parameters that minimize the objective function. The second column shows the same statistics for a counterfactual economy in which the formation of “Japanese” relationships is not possible due to ρ → ∞. The third column shows an autarky economy in which trade is not possible. The fourth column shows a counterfactual economy in which we reduce the arrival rate of trade wars from China to zero. Rows 1-5 show the share of US manufacturing sales, PUSQUS, that is from China, from the rest of the world, and from the US, respectively, and the share of these manufacturing sales that is sourced under the “Japanese” system. Row 6 presents the average inspection costs as a share of the import value, computed over all imports, including under the “Japanese” system. Row 7 shows the average fixed costs as a share of the import value. Row 8 shows the manufacturing price index, PUS, normalized to one in the baseline. Row 9 shows total utility, WUS = Qα US Z U 1− S α, normalized to one in the baseline. 25

Supplemental Appendix J Additional Proofs J.1 Second Order Conditions Hold American System The second derivative of the average cost yields (cid:16) (cid:17) (cid:104) (cid:16) (cid:17) (cid:104) (cid:105)(cid:105) r e−rx/q θ¯ −2 (cid:0) 1−e−rx/q (cid:1) + r (cid:2) 1+e−rx/q (cid:3) x+ f+m r q Υ q θ¯/Υ AC(cid:48)(cid:48)(x,q) = . A q [1−e−rx/q] 3 Thus the first-order condition is strictly upward sloping, AC(cid:48)(cid:48)(x,q) > 0, if and A only if (cid:20) (cid:18) (cid:19)(cid:18) (cid:19)(cid:21) x r f +m (cid:2) (cid:3) (cid:2) (cid:3) 1+e−rx/q r + −2 1−e−rx/q > 0. (S.1) q q θ ¯ /Υ Consider the case when f +m = 0. If the condition holds for this case, it must also hold for f + m > 0,because (S.1) is increasing in f + m. Define y ≡ rx/q. Note that for y = 0 and f + m = 0 the left-hand side of equation (S.1) is equal to zero. Taking the derivative of the left-hand side of equation (S.1) with respect to y we obtain 1−e−y(1−y) > 0. Thus, the left-hand side of (S.1) is strictly increasing in y for 0 < y < 1. Therefore, if 0 < y < 1, then AC(cid:48)(cid:48)(x,q) > 0. A Japanese System (cid:34) (cid:16) r (cid:17)2 e−rx/q (cid:2) f +θ1x+e(r+ρ)x/q(θ ¯ −θ)1x (cid:3)(cid:2) 1+e−rx/q (cid:3) q Υ Υ AC(cid:48)(cid:48)(x) = J [1−e−rx/q] 3 (cid:16) (cid:17) (cid:104) (cid:16) (cid:16) (cid:17) (cid:17)(cid:105) 2 r e−rx/q θ1 +e(r+ρ)x/q(θ ¯ −θ)1 1+ r+ρ x (cid:2) 1−e−rx/q (cid:3) q Υ Υ q − [1−e−rx/q] 3 (cid:16) (cid:17) (cid:104) (cid:16) (cid:17) (cid:105) r+ρ e(r+ρ)x/q(θ ¯ −θ)1 2+ r+ρ x (cid:2) 1−e−rx/q (cid:3)2(cid:35) q Υ q r + . [1−e−rx/q] 3 q Then AC(cid:48)(cid:48)(x) > 0 if and only if the numerator is greater than zero. Note that the J numerator increases in f. Therefore, if the numerator is positive for f = 0, it is 1

positive for f > 0. Assume f = 0, and factor the numerator of AC(cid:48)(cid:48)(x) to obtain J (cid:18) (cid:19) (cid:20)(cid:18) (cid:19) (cid:21) r r e−rx/q (cid:2) θ1 +e(r+ρ)x/q(θ ¯ −θ)1 (cid:3) x (cid:0) 1+e−rx/q (cid:1) −2 (cid:0) 1−e−rx/q (cid:1) q Υ Υ q (cid:18) (cid:19) (cid:26) (cid:18) (cid:19) (cid:27) r+ρ (cid:104) (cid:16) (cid:17) (cid:105) r + e(r+ρ)x/q(θ ¯ −θ)1 (cid:2) 1−e−rx/q (cid:3) (cid:2) 1−e−rx/q (cid:3) 2+ r+ρ x −2 xe−rx/q q Υ q q Define y ≡ rx/q. For the first term note that (1+e−y)y−2(1−e−y) > 0 for 0 < y < (cid:16) (cid:104) (cid:16) (cid:17) (cid:105) (cid:17) 1. Forthesecondtermtobepositive,werequirethat [1−e−y] 2+y + ρ x −2ye−y > q 0. If ρ = 0, then (·) > 0 for 0 < y < 1. Because (·)increases in ρ, it must be true that (·) > 0 for ρ > 0 and 0 < y < 1. Therefore, if ρ > 0 and 0 < y < 1, then AC(cid:48)(cid:48)(x) > 0. J J.2 Continued Proof of Lemma 5.2: Average cost curves are convex and reach a limit Part 1: Average cost curves are convex American System Using (A.3) in Appendix A, the second derivative of average costs is (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) 2f+m rx exp(−rx) f+m rx(cid:48)(q) exp(−rx) f+m AC(cid:48)(cid:48)(q) = q3 − q2 q q2 + q q q2 . 1−exp(−rx) (cid:104) (cid:105)2 (cid:104) (cid:105)2 q 1−exp(−rx) 1−exp(−rx) q q The last term is positive since x(cid:48)(q) > 0. Therefore, to prove that the average cost functionisconvex, weonlyneedto show that thefirsttwotermstogetherarepositive. These terms can be re-written as (cid:104) (cid:105)(cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) 2 1−exp(−rx) f+m − rx exp(−rx) f+m q q3 q q q3 , (cid:104) (cid:105)2 1−exp(−rx) q which is positive if (cid:20) (cid:21) rx (cid:16) (cid:17) 2 1−exp(− ) > rx exp(−rx). q q q This expression holds if (cid:20) (cid:21) rx (cid:16) (cid:17) 2 exp( )−1 > rx , q q 2

which is true. Therefore, average costs are convex, for any m and f. Japanese System Equation (A.4) in Appendix A gives the slope of the average cost curve in the “Japanese” system. By the same arguments as in the “American” system AC(cid:48)(cid:48)(q) > 0. Part 2: Average cost curves reach a limit Asymptote for both systems We first show (x(q)/q) → 0 as q → ∞. From the Monotone Convergence Theorem, since (x(q)/q) is strictly decreasing and bounded from below by zero, it must converge to a limit. Call this limit ψ∗ ≥ 0. To show that ψ∗ = 0, assume for contradiction that ψ∗ = K > 0. Then, it must be the case that there exists no combination of ψ = x(q)/q < K and q that solves the first-order condition of the cost minimization problem. Thus, if we can find a q solving the first-order condition for a ψ < K, then K cannot have been the limit since ψ is strictly decreasing. For the “American” system, pick any 0 ≤ ψ < K. The first-order condition of A the cost minimization problem under the American system is (cid:18) (cid:19) w r (cid:104) w (cid:105) θ ¯ z (cid:2) 1−e−rψA (cid:3) = e−rψA f +mw +θ ¯ z qψ . b A Υ q Υ Re-arranging this expression, we can solve for q as a function of ψ and find that A [f +mw ]re−rψA b q = . (S.2) θ ¯w Υ z [1−e−rψA[1+rψ A ]] This expression gives the q that solves the first-order condition for a given pick of ψ = x /q. If we can show that for any pick ψ ≥ 0 there exists a q ≥ 0 solving the A A A equation, then it cannot be the case that K > 0 is the limit. For this result to hold, we need to show that the denominator is non-negative. To see that it is non-negative, note that 1−e−rψA[1+rψ ] ≥ 0 A ⇔ erψA ≥ 1+rψ , A 3

which holds. Thus, for any ψ ≥ 0 there exists a q ≥ 0 solving the equation. In A particular, such a q exists for any ψ < K. Therefore, (x(q)/q) must converge to A zero. Indeed, from the equation we can see that for ψ = 0, q must be infinite. A We can construct a similar proof for the “Japanese” system. The first-order condition under the “Japanese” system is (cid:16) (cid:17) e(r+ρ)ψJθ ¯ Υ w [1+(r+ρ)ψ J ] = q r e−rψJ (cid:2) f +e(r+ρ)ψJθ ¯ Υ wqψ J (cid:3) . 1−e−rψJ [1−e−rψJ]2 We can re-arrange this expression to solve for q and find that fre−rψJ q = . (S.3) θ ¯w Υ ze(r+ρ)ψJ [(r+ρ)ψ J [1−e−rψJ]+1−e−rψJ [1+rψ J ]] By the same argument as before, the term in the denominator is non-negative and therefore for any ψ ≥ 0 there exists a q ≥ 0 solving the equation. Therefore, (x(q)/q) J must converge to zero. Indeed, from the equation we can see that for ψ = 0, q must J be infinite. Convergence in the “American” System Consider average costs C(x,q)/q. Under the “American” system, we have that C(x,q) θx f + m q q q = + . q 1−exp(−rx) 1−exp(−rx) q q We want to show the limit of this expression goes to a positive number as q → ∞. For the second term we have that (f +m)x∗(q) 1 (f +m)x∗(q) 1 (f +m)ψ f +m q x∗(q) q A lim = lim ·lim = lim ·0 = ·0, q→∞ 1−exp(−rx∗(q)) q→∞ 1−exp(−rx∗(q)) q→∞ x∗(q) ψA→0 1−exp(−rψ A ) r q q by the multiplication rule of limits, where the first term converges to (f +m)/r by L’Hopital’s rule since ψ → 0 as q → ∞, and the second term converges to zero A because x∗(q) → ∞ as q → ∞. Therefore, the overall term converges to 0. 4

For the first term we have that θx θψ θ q A lim = lim = , q→∞ 1−exp(−r q x) ψA→0 1−exp(−rψ A ) r where we again applied L’Hopital’s rule. Therefore, overall, the average cost function under the “American” system converges to (θ/r), which is positive. Convergence in the “Japanese” System Next consider the “Japanese” system. We have that average costs are C(x,q) θe(r+ρ)(x/q)x f q q = + . q 1−exp(−rx) 1−exp(−rx) q q The second term converges to zero by the same argument as before. For the first term we find θe(r+ρ)ψJψ θψ θ lim J = lim e(r+ρ)ψJ · lim J = 1· , ψJ→0 1−exp(−rψ J ) ψJ→0 ψJ→0 1−exp(−rψ J ) r and hence average costs under the “Japanese” system asymptote to exactly the same positive limit as under the “American” system. K Additional Summary Statistics We compare our baseline sample to an alternative arm’s-length sample that does not restrict to buyer quadruples with at least five transactions. Since we cannot compute somevariablessuchasweeksbetweenshipments(WBS )forquadruplesthattrade mhcz only a single time, we focus for consistency on the arm’s length sample consisting of quadruples with two or more transactions. Table S.1 presents an overview of the samples. The first column repeats some statistics of our baseline sample from Table A.1 in Appendix B. The second column presents the same statistics for the larger sample of quadruples with at least two transactions. The first row shows that the baseline sample accounts for slightly more than 80 percent of the broader sample of arm’s-length trade by quadruples with at least two transactions. The next row shows that the broader sample contains almost twice as many importers, suggesting that most of the additional importers in the 5

Table S.1: U.S. Import Transaction Summary Statistics Baselinet≥5 Samplet≥2 TotalImports($Bill) 5,680 6,990 UniqueImporters(m) 360,000 637,000 UniqueExporters(x) 5,037,000 6,531,000 UniqueImporter-Product-Country-ModeQuadruples(mhcz) 2,966,000 7,615,000 UnigueExporter-Importer-Product-Country-ModeQuintuples(mxchz) 21,700,000 30,600,000 Source: LFTTD and authors’ calculations. Table summarizes U.S. arm’s-length imports from 1992 to 2016. Observations are based on the cleaned data described in Appendix B. The first column restricts to our baseline sample of quadruples with at least five transactions (t ≥ 5), analogous to Table A.1. The final column restricts to the broader sample of quadruples with two or more transactions (t ≥ 2). Import values are in billions of real 2009 dollars. The final four rows of the table provide counts of unique importers, exporters, buyer quadruples, i.e., U.S. importer by HS product by origin country by mode of transport cells, and buyerseller relationships, i.e., U.S. importer by foreign exporter by HS product by origin country by mode of transport cells. Observation counts are rounded to the nearest thousand per U.S. Census Bureau disclosure guidelines. broader sample do not have substantial imports. The third row presents the number of unique exporters and the fourth row shows the number of unique importer (m) by HS10 product (h) by country (c) by mode of transportation (z) mhcz quadruples. The latter rises more than twofold in the broader sample. The last row presents the number of unique quintuplets. These do not increase nearly as much in percentage terms as the number of quadruples, as most of the quadruples unique to the broader sample have only few suppliers. Table S.2 compares the mhcz quadruples in the two samples. The first row shows that the average value traded by a quadruple in the broader sample is only about half of the trade value in the baseline sample. Rows two to four show that quadruples in the broader sample are shorter-lived, contain fewer shipments, and source from fewer suppliers on average. However, the average value per shipment is relatively similar to the baseline sample (row 5). Shipments in the broader sample are significantly more spaced out over time (row 6). The last two rows show that the average importerexporter relationship length associated with a quadruple in the broader sample is shorter than in the baseline sample and that quadruples in the broader sample have a higher ratio of suppliers to shipments. The latter fact suggests that many of the additional quadruples not in the baseline sample conduct their few transactions with different suppliers. TableS.3showsstatisticsontheaveragenumberofsellerspershipment(SPS ) mhcz by main 6-digit NAICS industry of the importer, analogous to Table A.2 in Appendix B. For columns (3) and (4), we define J dummies Jk that take a value of one if mhcz SPS falls in the first quartile of its distribution within country-mode bins in mhcz 6

the first time period (k = cz) to retain variation across products. Manufacturers are the most likely to use “Japanese” sourcing, consistent with these firms obtaining relatively customized inputs for their production processes. Table S.2: Attributes of mhcz Quadruples BaselineSamplet≥5 BroaderSamplet≥2 Standard Standard Mean Deviation Mean Deviation TotalValueTraded($) 1,914,000 36,300,000 918,400 24,100,000 LengthBetweenBuyer’sFirstandLastShipment(Weeks) 304.3 266 187.9 229.8 TotalShipments 38.6 157.9 17.8 100.4 NumberofSellers(x) 7.3 25.5 4.0 16.2 ValueperShipment(VPS),($) 35,910 386,100 38,090 470,500 WeeksBetweenShipments(WBS) 23.5 28.5 44.5 79.8 AverageRelationshipLengthinWeeks(length) 180.8 154.7 147.2 156.7 RatioofSellerstoShipments(SPS) 0.334 0.241 0.512 0.306 Source: LFTTDandauthors’calculations. Tablereportsthemeanandstandarddeviationacrossimporter(m)by country(c)byten-digitHarmonizedSystemcategory(h)bymodeoftransport(z)quadruplesduringour1992to 2016sampleperiod. ObservationsarebasedonthecleaneddatadescribedinAppendixB.Importvaluesareinreal 2009dollars. Thefirsttwocolumnsrestricttoourbaselinesampleofquadrupleswithatleastfivetransactions, analogoustoTable1. Thefinaltwocolumnsrestricttothebroadersampleofquadrupleswithtwoormore transactions. ObservationcountsareroundedtothenearestthousandperU.S.CensusBureaudisclosureguidelines. Table S.3: “Japanese” Relationships by Main Industry of the Importer Jcz =1 MeanSPS mhcz ShareofImportValue (1) (2) (3) (4) Industrycode(NAICS) 1995-2000 2002-2007 1995-2000 2002-2007 Manufacturing(31-33) 0.119 0.113 0.739 0.778 Agriculture(11) 0.123 0.106 0.584 0.630 Wholesale(42-43) 0.158 0.128 0.623 0.729 Other services 0.160 0.130 0.655 0.713 Professionalservices(54-55) 0.177 0.220 0.586 0.415 Mining,utilitiesandconstruction(21-23) 0.182 0.131 0.561 0.684 Financeandinsurance(52-53) 0.187 0.213 0.516 0.514 Retail(44-45) 0.208 0.157 0.532 0.688 Information(51) 0.211 0.182 0.553 0.566 Adminsupport&wastemgmt(56) 0.213 0.195 0.312 0.423 TransportationandWarehousing(48-49) 0.216 0.210 0.487 0.511 Source: LFTTDandauthors’calculations. Thefirsttwocolumnsreporttheweightedaveragesellerspershipment (SPS )acrossbuyerquadrupleswithatleastfivetransactionsbymain6-digitNAICSindustry-period. To mhcz obtainthemainNAICS,wefindineachyeartheindustrywiththeimporter’slargestshareofemployment,and thentakethemodalmainindustryacrosstheyearsinwhichthequadrupleisactive. WeaggregateSPS across mhcz quadruplesusingimportvaluesasweights. ThesecondtwocolumnsreporttheshareofthevalueofUSimports accountedforbyquadrupleswithSPS inthefirstquartileofthedistributionofSPS within mhcz mhcz country-modeinthefirstperiod. Rowsofthetablearesortedbythecolumn(1). 7

L Supplemental A vs J Classification Regressions Differentiated Products Versus Commodities: We examine whether buyers are more likely to use J procurement for differentiated goods. If differentiated products have higher inspection costs, then by Proposition 2.1 buyers are more likely to use J procurement for them, which implies smaller shipment size, greater frequency, and higher unit import values than products sourced under the A system (Proposition 2.3). Moreover, as discussed in Section 3.3, this J sourcing of differentiated products should be associated with fewer suppliers and longer relationships. We examine these features of the model using the commonly cited measure of product-differentiation from Rauch (1999) in the following mhcz-level OLS specification, Y = β +β Diff +β ln(VPW )+β beg +β end +λ +(cid:15) . mhcz 0 1 h 2 mhcz 3 mhcz 4 mhcz cz mhcz (S.4) We consider four dependent variables. The first is the average number of weeks between shipments WBS as in the main text. We do not consider quantity per mhcz shipment or unit value here since the regression compares shipping systems across products, which are recorded in different units.58 Instead, we use as our second dependent variable the average transaction value per shipment, VPS , as a meamhcz sure of average transaction size. Third, we consider the average relationship length (length ) as in Section 3.3. Finally, the fourth variable is a measure of the buyer’s mhcz procurement type, sellers per shipment (SPS ) introduced in the main text. On mhcz the right-hand side, Diff is a dummy variable indicating that product h is either h differentiated or has a reference price, as opposed to being a commodity, according to the product categorization scheme proposed by Rauch (1999).59 Because the right-hand-side variable of interest varies only at the product level, we are unable to include product fixed effects, so comparisons are made within country-mode bins by including fixed effects at that level (λ ). Since we cannot standardize quantities to cz be consistent across products, we control for potential scale effects using value per week (VPW ), rather than quantity per week, which was used in the main text. mhcz 58For example, we cannot really compare the price of one barrel of oil to the price of one shoe. 59Rauch (1999) provides both a liberal and a conservative definition of differentiated goods. We use the liberal definition for the results reported in the main text, but note that these results are similar when we use the conservative definition. 8

The sample period is 1992 to 2016, we include only buyer quadruples with at least five transactions, and standard errors are clustered at the country-product level. Results, reported in Table S.4, are consistent with the model’s predictions regardinginspectioncosts, whileprovidingfurthersupportfortheuseofsellerspershipment to identify buyer types. As indicated in the first three columns of the table, we find that differentiated products are more J: they are shipped with fewer weeks between shipments, the average transaction size is smaller, and the average relationship length is longer. Results in the final column provide further support for this view, as buyer quadruplesencompassingdifferentiatedgoodstendtohavelowersellerspershipment. Regressions by Sector: One concern with our findings could be that the results might only hold in some sectors, such as manufacturing, but not in others. We show in Tables S.5 to S.8 that our results regarding the relationship between SPS and mhcz shipmentattributesholdwithindifferentsectors: miningandutilities, manufacturing, wholesale, and retail. A vs J Within Sellers: We next examine whether mhcz buyer quadruples’ sellers per shipment, SPS , predicts theory-consistent procurement patterns within each mhcz of their exporter relationships. In principle, a buyer quadruple could appear J in aggregate even if it were not with respect to each of its sellers. For example, a buyer quadruple might obtain frequent shipments from a few sellers, thus appearing to be J , but shipments within each seller might be dispersed if the buyer alternates among them. We use the following mxhcz-level OLS regression, Y = β +β SPS +β ln(QPW )+β beg +β end mxhcz 0 1 mhcz 2 mxhcz 3 mxhcz 4 mxhcz +λ +(cid:15) . (S.5) xhcz mxhcz In this specification, Y represents procurement attributes at the buyer-seller mxhcz relationship quintuple (mxhcz) level, and the right-hand-side variables are defined at this level as well, with the exception of SPS which continues to be at the mhcz mhcz level. We also include exporter by product by country by mode fixed effects (λ ) xhcz to compare buyer procurement patterns within sellers who may be heterogeneous in a number of attributes, including production costs. Standard errors are two-way clustered at the country (c) and product (h) level. Results, reported in Table S.9, are similar to those in Section 3.2, providing fur- 9

ther support for Proposition 2.3, as well as the use of SPS . Across US buyer mhcz quadruples within foreign exporters, we find that increasing sellers per shipment by one standard deviation from its mean (from 0.33 to 0.58) is associated with a 5 log point rise in quantity per shipment, a 38 log point increase in weeks between shipments, a 3 log point decline in price, and a 16 log point drop in average relationship length. Alternative Definition of Relationship Length: We next analyze the robustness of our measure of relationship length. If firms treat relationships with the same supplier across different products or modes of transportation as different relationships, then relationship length should not be defined using the time passed since the first ever transaction with the supplier overall but instead using the duration of the quintuple. We therefore construct an alternative relationship duration variable. First, for each mxhcz quintuple, we compute the total number of weeks passed between the first and thelasttransaction. Second, foreachmhcz buyerquadruple, wetaketheaverageover the length of the mxhcz quintuples within it. We refer to this variable as Qlength mhcz to indicate that it is based on the duration of the quintuple, rather than the overall length of the relationship between the importer and the exporter. We run the same specification outlined in equation (7) using Qlength as the mhcz dependent variable. The results, reported in Table S.10, are similar to those in Table 4 in the main text, with coefficients that are about twice as large. The first column of the table shows that increasing sellers per shipment by one standard deviation from its mean is associated with a 61 log point decline in average relationship length. The second column shows that the average relationship length for quadruples in the fourth quartile is about 235 log points lower than the average relationship length for quadruples in the first quartile. 10

Table S.4: A vs J Classification Regression for Differentiated Goods (1) (2) (3) (4) Dep. var. log(WBS ) log(VPS ) log(length ) log(SPS ) mhcz mhcz mhcz mhcz Diff -0.234*** -0.225*** 0.073** -0.082*** h 0.026 0.025 0.028 0.025 log(VPW ) -0.464*** 0.557*** -0.045*** -0.203*** mhcz 0.002 0.002 0.001 0.001 Observations 2,589,000 2,589,000 2,589,000 2,589,000 R-squared 0.611 0.730 0.193 0.278 Fixedeffects cz cz cz cz Controls beg,end beg,end beg,end beg,end Source: LFTTDandauthors’calculations. TablereportstheresultsofregressingnotedattributeofUSimporterby productbycountrybymodeoftransport(mhcz)binsonadummyforwhetherthebin’sproductcodeis differentiatedorreferencepricedaccordingtotheliberalclassificationbyRauch,1999andonvalueshippedper week(VPW ). WBS ,VPS ,length ,andSPS areaverageweeksbetweenshipment,average mhcz mhcz mhcz mhcz mhcz valuepershipment,averagerelationshiplength,andsellerspershipment. Allregressionsincludecountrybymode oftransport(cz)fixedeffects,controlforthebeginningandendweekofthequadruple,andexcludequadrupleswith lessthanfiveshipments. Standarderrors,adjustedforclusteringbycountryandproduct,arereportedbelow coefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percentlevels. Table S.5: SPS and Procurement Attributes - Mining and Utilities mhcz (1) (2) (3) (4) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) ln(length ) mhcz mhcz mhcz mhcz ln(SPS ) 0.413∗∗∗ 0.455∗∗∗ −0.106∗∗ −0.692∗∗∗ mhcz 0.021 0.022 0.041 0.017 log(QPW ) 0.704∗∗∗ −0.305∗∗∗ −0.283∗∗∗ −0.190∗∗∗ mhcz 0.031 0.032 0.019 0.014 Observations 25,500 25,500 25,500 25,500 Fixedeffects hcz hcz hcz hcz R-squared 0.972 0.756 0.925 0.562 Controls beg,end beg,end beg,end beg,end Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingnotedattributeofimporterby productbycountrybymodeoftransport(mhcz)binsonbins’sellerspershipment(SPS )andtotalquantity mhcz shippedperweek(QPW ). Industriesareassignedusingthemain6-digitNAICSindustryoftheimporterbased mhcz ontotalemployment. QPS ,WBS ,UV ,andlength areaveragequantitypershipment,average mhcz mhcz mhcz mhcz weeksbetweenshipment,averageunitvalue,andaveragerelationshiplength. Allregressionsincludeproductby countrybymodeoftransport(hcz)fixedeffects,controlforthebeginningandendweekofthequadruple,and excludequadrupleswithlessthanfiveshipments. Standarderrors,adjustedforclusteringbycountry(c)and product(h)arereportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and 10percentlevels. 11

Table S.6: SPS and Procurement Attributes - Manufacturing mhcz (1) (2) (3) (4) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) ln(length ) mhcz mhcz mhcz mhcz ln(SPS ) 0.500∗∗∗ 0.538∗∗∗ −0.181∗∗∗ −0.540∗∗∗ mhcz 0.014 0.014 0.022 0.012 log(QPW ) 0.769∗∗∗ −0.238∗∗∗ −0.367∗∗∗ −0.131∗∗∗ mhcz 0.018 0.018 0.022 0.008 Observations 560,000 560,000 560,000 560,000 Fixedeffects hcz hcz hcz hcz R-squared 0.950 0.712 0.816 0.434 Controls beg,end beg,end beg,end beg,end Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingnotedattributeofimporterby productbycountrybymodeoftransport(mhcz)binsonbins’sellerspershipment(SPS )andtotalquantity mhcz shippedperweek(QPW ). Industriesareassignedusingthemain6-digitNAICSindustryoftheimporterbased mhcz ontotalemployment. QPS ,WBS ,UV ,andlength areaveragequantitypershipment,average mhcz mhcz mhcz mhcz weeksbetweenshipment,averageunitvalue,andaveragerelationshiplength. Allregressionsincludeproductby countrybymodeoftransport(hcz)fixedeffects,controlforthebeginningandendweekofthequadruple,and excludequadrupleswithlessthanfiveshipments. Standarderrors,adjustedforclusteringbycountry(c)and product(h)arereportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and 10percentlevels. Table S.7: SPS and Procurement Attributes - Wholesale mhcz (1) (2) (3) (4) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) ln(length ) mhcz mhcz mhcz mhcz ln(SPS ) 0.443∗∗∗ 0.475∗∗∗ −0.181∗∗∗ −0.571∗∗∗ mhcz 0.015 0.015 0.013 0.020 log(QPW ) 0.682∗∗∗ −0.328∗∗∗ −0.281∗∗∗ −0.167∗∗∗ mhcz 0.012 0.012 0.017 0.007 Observations 1,215,000 1,215,000 1,215,000 1,215,000 Fixedeffects hcz hcz hcz hcz R-squared 0.945 0.708 0.856 0.469 Controls beg,end beg,end beg,end beg,end Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingnotedattributeofimporterby productbycountrybymodeoftransport(mhcz)binsonbins’sellerspershipment(SPS )andtotalquantity mhcz shippedperweek(QPW ). Industriesareassignedusingthemain6-digitNAICSindustryoftheimporterbased mhcz ontotalemployment. QPS ,WBS ,UV ,andlength areaveragequantitypershipment,average mhcz mhcz mhcz mhcz weeksbetweenshipment,averageunitvalue,andaveragerelationshiplength. Allregressionsincludeproductby countrybymodeoftransport(hcz)fixedeffects,controlforthebeginningandendweekofthequadruple,and excludequadrupleswithlessthanfiveshipments. Standarderrors,adjustedforclusteringbycountry(c)and product(h)arereportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and 10percentlevels. 12

Table S.8: SPS and Procurement Attributes - Retail mhcz (1) (2) (3) (4) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) ln(length ) mhcz mhcz mhcz mhcz ln(SPS ) 0.424∗∗∗ 0.458∗∗∗ −0.120∗∗∗ −0.556∗∗∗ mhcz 0.030 0.031 0.023 0.022 log(QPW ) 0.643∗∗∗ −0.366∗∗∗ −0.195∗∗∗ −0.115∗∗∗ mhcz 0.007 0.007 0.012 0.008 Observations 525,000 525,000 525,000 525,000 Fixedeffects hcz hcz hcz hcz R-squared 0.945 0.708 0.856 0.955 Controls beg,end beg,end beg,end beg,end Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingnotedattributeofimporterby productbycountrybymodeoftransport(mhcz)binsonbins’sellerspershipment(SPS )andtotalquantity mhcz shippedperweek(QPW ). Industriesareassignedusingthemain6-digitNAICSindustryoftheimporterbased mhcz ontotalemployment. QPS ,WBS ,UV ,andlength areaveragequantitypershipment,average mhcz mhcz mhcz mhcz weeksbetweenshipment,averageunitvalue,andaveragerelationshiplength. Allregressionsincludeproductby countrybymodeoftransport(hcz)fixedeffects,controlforthebeginningandendweekofthequadruple,and excludequadrupleswithlessthanfiveshipments. Standarderrors,adjustedforclusteringbycountry(c)and product(h)arereportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and 10percentlevels. Table S.9: A vs J Classification Regression Across mxhcz Quintuples (1) (2) (3) (4) Dep. var. log(QPS ) ln(WBS ) ln(UV ) ln(length ) mxhcz mxhcz mxhcz mxhcz ln(SPS ) 0.100∗∗∗ 0.696∗∗∗ −0.062∗∗∗ −0.302∗∗∗ mhcz 0.015 0.041 0.006 0.011 ln(QPW ) 0.511∗∗∗ −0.171∗∗∗ −0.130∗∗∗ −0.241∗∗∗ mxhcz 0.010 0.009 0.011 0.008 Observations 4,783,000 4,783,000 4,783,000 4,783,000 R-squared 0.966 0.621 0.953 0.786 Fixedeffects xhcz xhcz xhcz xhcz Controls beg,end beg,end beg,end beg,end Source: LFTTDandauthors’calculations. TablereportstheresultsofregressingnotedattributeofUSimporterby foreignexporterbyproductbycountrybymodeoftransport(mxhcz)binsonbins’sellerspershipment(SPS ) mhcz andtotalquantityshippedperweek(QPW ). QPS ,WBS ,P ,andlength areaverage mxhcz mxhcz mxhcz mxhcz mxhcz quantitypershipment,averageweeksbetweenshipment,averageunitvalue(i.e. valuedividedbyquantity),and averagerelationshiplength. Allregressionsincludeexporterbyproductbycountrybymodeoftransport(xhcz) fixedeffects,controlforthebeginningandendweekofthequintuple,andexcludebuyerquadrupleswithlessthan fiveshipments. Standarderrors,adjustedforclusteringbycountry(c)andproduct(h)binsarereportedbelow coefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percentlevels. 13

Table S.10: SPS and Alternative Relationship Length mhcz (1) (2) Dep. var. log(Qlength ) log(Qlength ) mhcz mhcz log(SPS ) −1.126∗∗∗ mhcz 0.039 (SPS =Q2) −0.653∗∗∗ mhcz 0.013 (SPS =Q3) −1.230∗∗∗ mhcz 0.024 (SPS =Q4) −2.348∗∗∗ mhcz 0.046 log(QPW ) −0.164∗∗∗ −0.137∗∗∗ mhcz 0.008 0.006 Observations 2,966,000 2,966,000 R-squared 0.619 0.613 Fixedeffects hcz hcz Controls beg,end beg,end Source: LFTTDandauthors’calculations. Tablereportstheresultsofregressingtheaveragequintuplerelationship lengthwithineachquadruple(Qlength )quadruples’sellerspershipment(SPS ),sellerspershipment mhcz mhcz quartiledummiesandtotalquantityshippedperweek(QPW ). Theregressionsincludeproductbycountryby mhcz modeoftransport(hcz)fixedeffects. Allregressionscontrolforthebeginningandendweekofthequadruple,and excludequadrupleswithlessthanfiveshipments. Standarderrors,adjustedforclusteringbycountry(c)and product(h)binsarereportedbelowcoefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5 and10percentlevels. 14

M Description of PNTR This section provides more detail on the US granting permanent normal trade relations (PNTR) to China. US imports from non-market economies such as China are generally subject to relatively high “column two” tariff rates originally set under the Smoot-Hawley Tariff Act of 1930, as opposed to the generally low Normal Trade Relations (NTR) tariff rates the US offers to trading partners that are members of the World Trade Organization (WTO). A provision of US trade law, however, allows imports from non-market economies to enter the United States under NTR tariffs subject to annual approval by both the President and Congress. Chinese imports first began entering the United States under this provision in 1980 after the warming of bilateral relations. Annual approval became controversial and less certain after the Tiananmen Square incident in 1989, and this uncertainty continued throughout the 1990s. During this time, firms engaged in or considering US-China trade faced the possibility, each year, of substantial tariff increases if China’s NTR status was not re-approved. The magnitude of these potential tariff increases—32 percentage points for the average product—make clear that some buyer-seller relationships that were profitable under NTR tariff rates would not be profitable under a shift to “column two” tariffs. Indeed, Pierce and Schott (2016) document extensive discussion by US firms of the trade-dampening effects of this uncertainty in the 1990s, and Handley and Lima˜o (2017) provide a theoretical basis for these effects that operates via suppressed entry by Chinese exporters.60 Alessandria et al. (2024) show that uncertainty regarding the annual renewal of China’s NTR status each summer reduced US imports from China, while also driving intra-year seasonal patterns in imports. When the United States granted PNTR to China in 2001, it locked in NTR rates, eliminating the need for annual renewals and the potential for relationship-severing tariff increases. This plausibly exogenous policy change provides a useful opportunity for testing Proposition 2.1, i.e., whether a decrease in the probability of a trade war leads to the adoption of more “Japanese” sourcing.61 Our strategy follows Pierce and Schott (2016) in defining a product’s exposure to PNTR as the difference between 60Handley and Lim˜ao (2017) also estimate that the reduction in uncertainty associated with PNTR’s ultimate approval was equivalent to a 13 percentage point permanent reduction in tariff rates. 61SeealsoBlanchardetal.(2016),whoexaminehowthepresenceofglobalvaluechainscanaffect the longer-term endogenous determination of tariff rates as part of multilateral trade negotiations. 15

Figure S.1: Distribution of the NTR Gap Source: Feenstraetal.,2002andauthors’calculations. FiguredisplaysthedistributionoftheNTRGap ,the h differencebetweentherelativelylowNTRtariffratethatwaslockedinbyPNTRandthehigherratetowhichUS tariffsonChinesegoodsmighthaverisenabsentthechangeinpolicy. the non-NTR rate to which its tariff could have risen before PNTR and the lower NTR rate that was locked in by the policy change, NTRGap = NonNTRRate −NTRRate . (S.6) h h h We compute these gaps as of 1999, the year before the change in policy, using ad valorem equivalent tariff rates provided by Feenstra et al. (2002). As indicated in Figure S.1, these gaps vary widely across products, and have a mean and standard deviation of 0.32 and 0.23, respectively. 16

N Supplemental DID Regressions mhcz Quadruple Level: In the main text we show that PNTR changed the shipping patterns (quantity per shipment, weeks between shipments, and unit value) at the mxhcz level. We now examine whether the shift from A to J procurement in response to PNTR also altered the shipping patterns at the mhcz quadruple level. Compared to the regressions of continuing relationships at the mxhcz level, this regression aggregates across the supplier dimension, and computes shipping attributes of the quadruple using transactions with all suppliers. It also allows for an additional margin of extensive margin adjustment, namely the formation of relationships with new suppliers that did not sell to the United States prior to PNTR. We use the following mhczt-level DID regression, ln(Y ) =β 1{t = Post}∗1{c = China}∗NTRGap +β ln(QPW) + mhczt 1 h 2 mhczt β χ +λ +λ +(cid:15) . (S.7) 3 mhczt mhcz t mhczt Asbefore, Y representsoneofthethreeprocurementattributes: averagequantity mhczt pershipment(QPS ),averageweeksbetweenshipments(WBS ),andaverage mhczt mhczt unit value (i.e. value divided by quantity) (UV ). mhczt Results, displayed in Table S.11, show a significant decline in the average shipping size and weeks between shipments, consistent with a shift towards J procurement. The increase in unit values, while positive, is statistically insignificant at conventional levels. One potential explanation for this outcome is the entry of new Chinese exporters during this period (Pierce and Schott, 2016; Amiti et al., 2020), including privately owned firms that tend to have lower prices than state-owned incumbents (Khandelwal et al., 2013). New suppliers might also charge low, introductory prices to gain market share, further dampening unit values. All Relationships: We re-run our relationship-level PNTR regression (9) using both continuing and new relationships simultaneously for all buyer quadruples and sellers that appear in both. Specifically, we run a modified version of the regression, ln(Y ) =β 1{t = Post}∗1{c = China}∗NTRGap +β ln(QPW )+ mxhczt 1 h 2 mxhczt β χ +λ +λ +λ +(cid:15) , (S.8) 3 mxhczt mhcz x t mxhczt 17

where we use importer-product-country-mode of transportation (mhcz) fixed effects, exporter (x) fixed effects, and period (t) fixed effects. Our results in Table S.12 indicatethatPNTRleadstoadeclineinthequantitypershipmentandthenumberof weeksbetweenshipments,andanincreaseintheunitvalueforthissetofrelationships, consistent with a shift to J procurement. Table S.11: Within mhcz Quadruple PNTR DID Regression (1) (2) (3) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) mhczt mhczt mhczt Postt∗Chinac∗NTRGap h -0.043*** -0.058*** 0.018 0.014 0.013 0.024 ln(QPW ) 0.436*** -0.584*** -0.207*** mhczt 0.018 0.018 0.026 Observations 738,000 738,000 738,000 R-squared 0.978 0.887 0.974 Fixedeffects mhcz,t mhcz,t mhcz,t Controls Yes Yes Yes Source: LFTTDandauthors’calculations. TablereportstheresultsofregressingnotedattributeofUSimporterby productbycountrybymodeoftransport(mhcz)binsonthedifference-in-differencestermofinterestandquantity shippedperweek. Pre-andpostperiodsare1995to2000and2002to2007. (QPS ),(WBS ),and mhczt mhczt (UV )areaveragequantitypershipment,averageweeksbetweenshipments,andaverageunitvalue(i.e. value mhczt dividedbyquantity)inperiodt. Allregressionsincludemhcz andperiodtfixedeffects,controlforthebeginning andendweekofthequadrupleaswellasallvariablesneededtoidentifytheDID termofinterest. Standarderrors, adjustedforclusteringbycountry(c)andproduct(h),arereportedbelowcoefficientestimates. ***,**,and* representstatisticalsignificanceatthe1,5and10percentlevels. TableS.12: Withinmxhcz QuintuplePNTRDIDRegressionUsingAllRelationships: 2002-2007 vs 1995-2000 (1) (2) (3) Dep. var. ln(QPS ) ln(WBS ) ln(UV ) mxhczt mxhczt mxhczt Postt∗Chinac∗NTRGap h -0.131*** -0.115** 0.078*** 0.012 0.012 0.027 ln(QPW ) 0.407*** -0.597*** -0.130*** mxhczt 0.013 0.012 0.018 Observations 4,023,000 4,023,000 4,023,000 R-squared 0.966 0.838 0.971 Fixedeffects mhcz,x,t mhcz,x,t mhcz,x,t Controls Yes Yes Yes Source: LFTTDandauthors’calculations. TablereportstheresultsofregressingnotedattributeofUSimporterby exporterbyproductbycountrybymodeoftransport(mxhcz)binsonthedifference-in-differencestermofinterest andquantityshippedperweek. Pre-andpostperiodsare1995to2000and2002to2007. (QPS ), mxhczt (WBS ),and(UV )areaveragequantitypershipment,averageweeksbetweenshipment,andaverage mxhczt mxhczt unitvalue(i.e. valuedividedbyquantity)inperiodt. Allregressionsincludemhcz,exporterx,andperiodtfixed effects,andcontrolforthebeginningandendweekofthequadrupleaswellasallvariablesneededtoidentifythe DID termofinterest. Standarderrors,adjustedforclusteringbycountry(c)andproduct(h),arereportedbelow coefficientestimates. ***,**,and*representstatisticalsignificanceatthe1,5and10percentlevels. 18

O Additional Quantitative Results O.1 Identification We perform an additional identification exercise. We vary all six parameters from the estimation jointly by drawing 100,000 different combinations of parameter values. We then simulate the model for each combination, obtain the simulated moments, and plot the resulting relationships between parameters and moments as a binscatter in Figure S.2. This exercise differs from Figure A.2, where we only varied one parameter at a time. The values of the six parameters are obtained as quasi random numbers drawn from a Sobol sequence. The figure shows similar relationships as Figure A.2, although the associations are noisier since all parameters vary jointly. In particular, there are strong and monotone relationships between the first four parameters and their targeted moments, and more hump-shaped relationships for the final two parameters. Figure S.2: Joint Identification of Parameters Source: Authors’ calculations, based on the estimation procedure described. Each panel plots different values of the parameter indicated on the row against the moment indicated on the column, where all parameters vary jointly basedon100,000randomparameterdrawsfromaSobolsequence. Lightercolorsindicatemorefrequentlyobserved combinationsofparametervaluesandmomentvalues. Theredhorizontallinesrepresentthevalueofthemomentin thedata. Weaddtheseonlyforthemainpanelsusedtoidentifyagivenparameterinthedata. 19

O.2 Additional Results Figure S.3 provides further intuition for the welfare implications of eliminating J sourcing. The left and right panels display the share of expenditures of US imported versus domestically manufactured goods and welfare, respectively, as ρ increases US,n from zero to infinity.62 As the trade war arrival rate rises, J sourcing declines as buyers switch to A sourcing for goods where the foreign productivity advantage is relatively large, and to domestic sourcing for goods where it is relatively low. These trade responses are most dramatic at initial increases in the arrival rate of trade war. A source of welfare gains arising from changes in the arrival rate of trade wars is that J exports generate additional income due to the incentive premium (the second term on the right-hand side in equation (13)). For exports sold under the J system, the exporting country appropriates the incentive premium instead of having the foreign buyer country inspect the goods. As the arrival rate of trade wars rises, the number of products sourced under the J system falls. At the same time, a higher arrival rate of trade wars increases the incentive premium for each good that is still shipped under the J system.63 The overall effect of these two opposing forces on US income, W , is highlighted by Figure S.4. There is an interior point which maximizes n total US income, highlighting a potentially interesting avenue for trade policy. It is beneficial for a country to be associated with a lower arrival rate of trade wars, as this will allow its exporters to ship more under the J system and to collect the incentive premium. However, as the arrival rate of trade wars becomes too low, in our estimated equilibrium the reduction of the incentive premium dominates the extensive margin effect of additional products shipped under the J system. Thus, some trade policy uncertainty can be good to allow exporters to collect incentive premia. In our model the trade war arrival rate is symmetric for any country pair, and since importers always benefit from a lower arrival rate of trade wars overall welfare strictly falls with ρ , as shown in Figure S.3b. However, in a more general model US,n in which ρ (cid:54)= ρ , a country would want to be perceived as slightly uncertain to n,i i,n maximize exporters’ incentive income from J exports, while it would simultaneously want to commit its trade partners to never start a trade war to reduce import costs. 62We set the trade war arrival rate from China and from ROW to be equal in this exercise, ρ =ρ , to facilitate the interpretation of the figure. US,CN US,ROW 63Note from equation (2) that the incentive premium is positive even for ρ=0. 20

Figure S.3: Effect of Trade War Arrival Rate on Sourcing and Consumption (a) Manufacturing Expenditures (b) Utility Notes: TheleftpaneldisplaystheshareofexpendituresonmanufacturedgoodsbytheUnitedStatesasafunctionof thearrivalrateoftradewarsfromtherestoftheworld,wherewedistinguishimportsunderthe“American”system (red),importsunderthe“Japanese”system(black),anddomesticsourcing(blue). TherightpanelshowsUSutility, calculatedasQα Z1−α,asafunctionofthetradewararrivalratefromtherestoftheworld. Welfareatanarrival US US rateofzeroisnormalizedtoone. Figure S.4: Effect of Trade War Arrival Rate on Income Notes: ThefigureshowsUStotalincome,i.e.,wageincomeplusincentivepremia,normalizedtooneforthebaseline case,asafunctionofthetradewararrivalrateρUS,n. 21