The Dynamics of Global Sourcing

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1337 February 2022 The Dynamics of Global Sourcing Trang Hoang Please cite this paper as: Hoang, Trang (2022). “The Dynamics of Global Sourcing ,” International Finance Discussion Papers 1337. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2022.1337. 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.

The Dynamics of Global Sourcing Trang Hoang † December, 2021 This paper studies an import model that incorporates both static crosscountry interdependence and dynamic dependence in firm-level decisions. I find that the benefit of sourcing from one country increases as a firm imports from more countries. Furthermore, using a partial identification approach under the revealed preferences assumption, I provide evidence for the sunk costs of importing, which make establishing relationships with new sellers costlier than maintaining existing ones. The coexistence of cross-country interdependence and sunk costs implies that temporary trade policy changes can have long-lasting effects on both the targeted and non-targeted markets through firm-level decisions. JEL: F1, L2 Keywords: Intermediate goods, Imports, Sunk costs, Exit and entry, Interdependence, Partial identification † Federal Reserve Board of Governors. Email: trang.t.hoang@frb.gov. I am indebted to Joel Rodrigue, EricBond,PedroSant’Anna,andJeffreyWooldridgefortheirinvaluableguidanceandadvicethroughoutthis project. IwouldalsoliketothankTrebAllen, AndrewBernard, DavinChor, TeresaFort, NinaPavcnik, Bob Staiger, and other faculty members during my fellowship at Dartmouth College. I am grateful to Eduardo Moralesforhisdiscussionatthe2020EmpiricalInvestigationsinInternationalTradeConference. Iwouldlike to thank Sina Ates, Colin Hottman, Logan Lewis, Andrew McCallum, Ryan Monarch, Justin R. Pierce, Rob Vigfusson,andseminarparticipantsanddiscussantsattheUniversityofToronto,UBCSauder,FederalReserve Board,FederalReserveBankofDallas,AarhusUniversity,SingaporeManagementUniversity,AcademiaSinica, BielefeldUniversity,UniversityofTokyo,KobeUniversity,SocietyofEconomicDynamics,MidwestTradeand Theory Conference, Virtual International Trade and Macro Seminars, Econometric Society Winter Meetings, EuropeanEconomicAssociationCongress,GEP/CEPRAnnualPostgraduateConference,DelhiWinterSchool, SouthernEconomicAssociation,YoungEconomistsSymposium,andMissouriValleyEconomicAssociationfor usefuldiscussionsandfeedback. ThisworkissupportedbytheWalterB.NoelDissertationFellowshipandKirk DornbushResearchGrant. Theviewsexpressedinthispaperaremyown,anddonotrepresenttheviewsofthe BoardofGovernorsoftheFederalReserve,noranyotherpersonassociatedwiththeFederalReserveSystem. 1

2 Input trade accounts for as much as two-thirds of international trade and one-half of globalvaluechains(JohnsonandNoguera,2012;Antr`as,2020;Antr`asandChor,2021). Foreign inputs can also affect firm-level productivity, varieties of final goods, product quality(AmitiandKonings,2007;KasaharaandRodrigue,2008;Goldbergetal.,2010; Gopinath and Neiman, 2014), and aggregate welfare gains from trade (Caliendo and Parro, 2015; Blaum, Lelarge and Peters, 2018; Ramanarayanan, 2020). Nonetheless, the trade literature has almost exclusively focused on the dynamics of exporters and not those of importers. The paper addresses this gap by studying the dynamics of firm-level input imports, with a focus on the dependence of firms’ import path over time and across countries. This paper is the first to incorporate simultaneously two features in the decision problemforimporters. First,firm-levelinputimportsdirectlyaffectthefirm’smarginal costs, rendering foreign sourcing decisions interdependent across markets (Antr`as, Fort and Tintelnot, 2017). In this environment, sunk costs of input trade–if they do exist– gain a crucial role, as they would also introduce a history-dependence dimension to sourcingdecisions. Suchcostsariseasfirmsmustincurcoststosearchfornewsuppliers, negotiate contracts with foreign partners, or adapt the production process to utilize foreign inputs.1 With the sunk entry costs of importing, the firm’s decision to import from one country depends not only on its sourcing decisions from other markets but also on its past import locations. As such, an important contribution of this paper is to provide a coherent framework to understand the firm’s sourcing decisions. Combining two separate firm-level Chinese data sets from 2000 to 2006, I study Chinesechemicalfirmsandestablishtwomainempiricalfindings. First,afirm’simport decision in one market is not independent of its decision in other markets. Moreover, there is persistence over time regarding where firms import intermediate inputs. Firms 1Indeed,relatedpapersfromtheliteratureonexportdynamicshavefoundstrongsupportforthepresenceof sunkentrycosts,whichincombinationwithfutureprofituncertaintyintroducesanoptionvalueinthedecision to enter or exit the export market. The early theoretical work by Baldwin (1988), Baldwin and Krugman (1989),Dixit(1989a),andDixit(1989b)emphasizestheimportanceofsunkcoststoexplainfirm-leveldecisions toparticipateinexportmarkets. EmpiricalevidenceofexportingsunkcostswasinitiallyprovidedbyRoberts and Tybout (1997) in the context of Colombia and Bernard and Jensen (2004) for US manufacturing plants. More recently, Das, Roberts and Tybout (2007) structurally estimate the sunk export costs and find them to besubstantial. Exportersandimporters,however,donotfaceequivalentproblems. Whilethecanonicalexport model ensures that a firm’s decision to enter each market can be analyzed separately by assuming constant marginalcosts,importdecisionsareinterdependentacrossmarkets.

THE DYNAMICS OF GLOBAL SOURCING 3 are more likely to import from a country if it has imported from the same country in the past, even after accounting for different combinations of firm-country, country, and year fixed effects. Buildingontheseempiricalfacts, Iproposeadynamicpartialequilibriumframework ofimportswithheterogeneousfirmsinamulti-countrysetting. Themodelincorporates twocrucialfeaturesoffirm-levelimportdecisions: (1)Inputsourcesareinterdependent in the marginal cost, and (2) firms pay a sunk entry cost when importing from a new location. The mechanism for interdependence across input sources is similar to that in Antr`as, Fort and Tintelnot (2017) (hereafter AFT), which considers the firm’s sourcing decisioninastaticsetting. Thedecisiontoincurthefixedcostsofsourcinginputsfrom onecountrygivesthefirmaccesstolowercostsuppliers, reducingfirmproductioncosts and prices. These lower prices, in turn, imply a larger scale of operation, which makes it more likely that the firm will find it profitable to incur the fixed costs of sourcing inputs from other countries. Conversely, sourcing from an additional country leads to market shares shifting away from the current sources, thus diminishing the value of each current source. In a static environment, the firm decision is essentially to balance the gain in static variable profits and the increase in the fixed costs of importing. In addition to the static interdependence, my model includes sunk entry costs of importing, which introduces an inter-temporal linkage between current and future decisions.2 The dynamic solution thus depends not only on static profit gains and fixed costs, but also on expected future profit gains and sunk costs. Alternatively, one can interpret firm-specific sunk costs as heterogeneity in firms’ information sets. Given the differences in their import histories, firms acquire different information about potential import sources, giving rise to distinct sequential import decisions even if they have the same level of core productivity. In other words, firms are heterogeneous not only in terms of productivity but also in regard to the information set they acquire given their previous import experience. Estimating the model constitutes a challenging task because of (1) the large dimen- 2In Section V.A, I provide an extension of the model which allows for dynamic productivity gains from importing. Thisaddedfeaturegeneratesanotherinter-temporallinkagethroughwhichcurrentdecisionsaffect futureprofits.

4 sionality of the firm choice set (with J countries, the firm faces with 2J choices), which is complicated by (2) the evaluation of dynamic implications of each choice and (3) the interdependence across markets in the marginal cost. To address (1) and (2), I employ a moment inequality approach based on the revealed preference assumption similar to Morales, Sheu and Zahler (2019) (hereafter MSZ). For each firm in a particular year, I change its import status in each market, one at a time, and compute the difference in observed profits and counterfactual profits to estimate the bounds for the fixed and sunk costs. Consequently, for a firm-year pair, the number of deviations I have to analyze is only J, which sharply contrasts with the standard method. The moment inequality method also avoids estimating the value function for each choice, despite the model’s dynamic structure. To address (3), I build on results from AFT’s static model toderivethecounterfactualstaticprofits. Thismethodallowsmetoidentifythesourcing potential of each import market and thus, the ratio between the firm’s marginal cost at the observed import path and its marginal cost at the counterfactual import path. Because of this feature, even in the presence of interdependence across markets, I can estimate the fixed and sunk costs of importing as if markets are independent. I find that countries are complementary: The marginal revenue gain of a source country increases with the number of sources from which a firm imports. This result is consistentwithpreviousstudies. Moreover,themarginalrevenuegainofasourcecountry is correlated with a firm’s status in that country. The revenue gain is particularly high for new and continuing importers, at 7.9 million and 6.6 million of 1998 RMB, respectively. For exiting importers and firms that never import, adding a new source increases revenues by about 2.5 million and 3.6 million RMB, respectively. I also find that the fixed cost of importing is between 0.5 and 1.8 million RMB for each market, meaning that firms pay between 10% and 40% of the average marginal revenue gain– i.e., the increase in revenues by importing from a source. Finally, a new importer pays between 1 and 3.2 million RMB for both fixed and sunk entry costs when importing from a new market, which accounts for 20% to 70% of the average marginal revenue. The existence of interdependence across markets and sunk entry costs has significant implications for trade policies. Changing trade barriers in one market not only influ-

THE DYNAMICS OF GLOBAL SOURCING 5 ences entry in its own country, but also affects trade flows in other markets. While thisthird-marketeffectoftargetedtradepoliciesisinherentinstandardgravitymodels (AndersonandVanWincoop,2003), thechannelsaredifferent. Inthosemodels, theeffectonthirdmarketsmanifestsindirectlythroughgeneralequilibriumforces–i.e.,prices and terms of trade. However, even when we ignore the general equilibrium channel, externalities remain in a partial equilibrium framework because of the interdependence acrossmarketsatthefirmlevel(AFT;MSZ;Alfaroetal.,2021; Albornozetal.,2021).3 Furthermore, the persistence in the firm-level decisions implies that even temporary trade policy changes can have permanent consequences. While this mechanism is present in standard models of exporting with sunk entry costs, it is often contained to a single market. By contrast, the path dependence coupled with the interdependence across markets generates widespread and long-lasting effects on both the targeted and non-targeted markets. My paper makes three main contributions. First, I provide a new theoretical framework that unifies the theory from the import literature and the export dynamics literature. Specifically,thebaselinemodelcombinesthestaticmodelinAFTwithsunkentry costs common in dynamic models of trade. Most theoretical frameworks of importing have been static in nature, and therefore unable to address the path dependence of import decisions.4 A few exceptions include Lu, Mariscal and Mejia (2016), Ramanarayanan (2017), and Imura (2019), who develop dynamic models of importing with sunk entry costs and find that these costs can be substantial and critical to explaining the slow adjustments of trade flows. Nonetheless, the existing papers on importer dynamicsoverlooktheinterdependenceacrossinputsources. Tomyknowledge,thispaper is the first to combine both the cross-country interdependence and history dependence in a model of importing. 3There is, however, a subtle difference between my model and supply chain frameworks in which tariffs imposedongoodsinonestagemightinfluencetradeatotherstagesofthevaluechains(Blanchard,Bownand Johnson, 2016; Erbahar and Zi, 2017; Bown et al., 2020). In my baseline model, the effect takes place across producersatthesamestageofproduction. Nevertheless,SectionVprovidesanextensionofthebaselinemodel thataccountsforlinkagesacrosscountriesandalongthesupplychainsbyallowingfirmstoimportintermediate goodsandexportfinalgoods. 4This literature emphasizes the interdependence across inputs and markets. For example, Halpern, Koren and Szeidl (2015) and Goldberg et al. (2010) build on an Armington-style model, in which inputs are complementary in production. AFT provide micro-foundations for the interdependence by allowing for countries’ technologylevelstoaffecttheinputprices,andthusfirms’choiceofimportsourcesandmarginalcosts.

6 Second, I estimate country-specific sunk costs in the presence of interdependence using a partial identification approach. Thus, the paper contributes to a small but growing number of papers that employ moment inequalities in international trade, including Dickstein and Morales (2018), MSZ, Bombardini, Li and Trebbi (2020), and Ciliberto and J¨akel (2021). The closest to this work is MSZ, in which the authors estimate the effects of extended gravity–i.e., the size of the sunk cost reductions when firms export to destinations with characteristics similar to their previous destinations. Building on MSZ, this paper utilizes Euler perturbations from the observed sourcing decisions to estimate the bounds of the costs of importing. The difference between the two papers is that in MSZ, the cross-country interdependence is placed on the sunk costs, whereas the interdependence in my setting is inherent in the marginal costs, which affect both the intensive and extensive margins. As a result, deviations from a firm’s observed path would change both its static and dynamic profits. Indeed, this framework has the ability to accommodate both static interdependence and dynamic dependence in the marginal costs. In Section V.A, I provide an example that allows for dynamic productivity gains of importing, which creates a new dynamic linkage in addition to the sunk costs. Finally, to my knowledge this paper is the first to allow for complementarity between multiple trade margins in a multi-country dynamic trade model. While canonical trade models often focus on one particular trade margin, strong evidence shows that firms have been increasingly engaged in the global markets through many channels (Bernard et al., 2018). The interaction of these decisions implies that researchers need to be able to study the breadth and richness of the global firm’s decisions. Allowing for a multi-country setting withmultiple trade margins, nevertheless, gives rise toa complex combinatorial problem, which cannot be addressed with most conventional estimation methods. The partial identification approach in this paper allows for both model complexity and flexible assumptions on the firm’s optimization behavior. In Section V.B, I show how this method can be extended to account for multiple trade margins whilepreservingtherangeoffeasiblespatialchoices. Therestofthepaperisorganized asfollows. SectionIprovidesadescriptionofthedatasourcesandseveraldatapatterns.

THE DYNAMICS OF GLOBAL SOURCING 7 Section II presents a model that is consistent with the data patterns. Section III discusses the identifying assumptions. Section IV details the estimation procedures and results. Section V presents two extensions of the baseline model. Section VI concludes. I. Data and Stylized Facts A. Description of the Data Sources To explore the firm’s import decisions across global markets and over time, I construct a rich data set that contains detailed firm-level characteristics and trade flows. My sample combines several sources. The information on firm-level trade flows was collected by the General Administration of Customs. The data report the activities of the universe of Chinese firms participating in international trade between 2000 and 2006. They consist of transaction-level information, including trade volumes, partner countries, and free on board values in U.S. dollars. The second crucial data source for my project is National Bureau of Statistics of China (NBS), which conducts annual surveys that cover the population of registered firms with sales greater than 5 million RMB. The data report detailed firm-level information on total sales, export values, intermediate costs, and wages. Other sources include the Centre d’Etudes Prospectives et d’Informations (CEPII) for distance and country characteristics to construct standard gravity variables, Penn World Tables for international exchange rates and capital stocks, World Development Indicators for educational attainment and R&D spending at the national level, the International Labor Organization (ILO) for manufacturing wages, and Barro and Lee (2013) for educational attainment.5 A key step in the data construction is to match the customs data with the NBS annual surveys. Because the two data sets do not have a common firm identifier, I follow the procedure in Feng, Li and Swenson (2016) to match the customs data with the firm surveys using firm names, zip codes, and telephone numbers. About 60% of firms in the customs data can be matched with the NBS firm surveys. Data are then aggregatedatthefirm-country-yearlevel. MonetaryvaluesareconvertedtoRMB1998 5SeeAppendixforadetaileddescriptionofvariableconstruction.

8 using input and output deflators from Brandt, Van Biesebroeck and Zhang (2012). Importersaredefinedasfirmsthatimportedatleastoncefrom2000to2006andnonimporters are defined as those that did not import during any of those years. Because there is not a perfect match between the customs data and the manufacturing survey, a fraction of importers would be mis-classified as non-importers because they cannot be identified in the customs data.6 As a result, I restrict my estimation to importers only to prevent biased estimates that come from misclassification of firms, but acknowledge that importers and non-importers may be inherently different and excluding the latter will potentially lead to selection bias.7 Nevertheless, because the paper focuses on the firm’s sourcing decisions and the evolution of these decisions over time, including firms that never import may not add much further information. Furthermore, a proportion of the firms did not start importing until the latter sample years, and exploiting the yearswhentheydidnotimportgivesussomeinformationonnon-importers’behavior.8 Intermediary firms are excluded from the sample, as these firms do not face the same production decisions as the typical manufacturing firms. Following Ahn, Khandelwal and Wei (2011), I identify intermediary firms by searching for Chinese characters in each firm’s name that mean “trading”, “exporter”, or “importer”. I also exclude firms that do not report domestic sales or total input costs and focus on ordinary trade.9 Because different industries have different production technologies and utilize different input mixes, which might affect firm-level sourcing decisions, the empirical analysis in this paper is restricted to one industry–i.e., the chemicals industry.10 Chemicals is an important industry to study for a few reasons. In 2007, China became the world’s second largest chemicals manufacturer, just behind the United States and ahead of Japan and Germany (Griesar, 2009). In 2017, China’s chemical industry accounted for $1.5 trillion of sales, equivalent to 40% of the global chemical-industry revenue. 6Another reason for why not all importers can be identified in the NBS data is the latter only surveys above-scalefirms,andasaresultexcludesmanysmallimporters. 7TheNBSdatadoesnotcontaininformationaboutfirms’importstatusandthusitisimpossibletoidentify unmatchedimportersandnon-importersinthefirm-levelsurveys. 8See Appendix for the number of importers and share of total importers for each year between 2000 and 2006. 9Foradetaileddiscussiononsampleselection,seeSectionC.C3. 10Chemicals producers are defined based on both the customs data and the firm surveys. I include firms whose chemicals exports account for at least 50% of their total exports and firms that reported to be in the chemicalfeedstockandchemicalmanufacturingindustry(ChinaIndustryClassificationcode26).

THE DYNAMICS OF GLOBAL SOURCING 9 Furthermore, the industry also provides critical inputs to pharmaceutical and plastic industries, especially in the United States. The chemicals industry accounts for $10.8 billion of US exports and $15.4 billion of Chinese exports that are subject to increased tariffs during the current U.S.-China trade war. Thefinaldatasetcomprises1,537uniqueimportersfrom2000to2006thatimported from the 40 most popular import sources in terms of number of importers. Restricting attention to the top 40 countries ensures sufficient observations per market. Nevertheless, the main results remain the same when I include all 96 import markets that appear in the customs data. From 2000 to 2006, China’s economy experienced significant growth. The total domestic sales for the chemicals sample grew by 400% from 840 to 4,239 billion RMB, total import values grew from 10 billion to 60 billion, and the number of importers more than doubled between the first and last years of the sample period. This implies that static models under the assumption of a stable aggregate environment might not be suitable to apply to the context of China during this period. Furthermore, the fast growth rate guarantees high turn-over rates and large variation in terms of exit and entry rates to study the dynamics of firms’ importing behaviors.11 In the next section, I document a number of facts about the importing behavior of Chinese chemical producers during the sample period. B. Stylized Facts Stylized fact 1: There is persistence in firm-level import decisions. Firms are more likely to import from a country if they have imported from the same country in the past, even after accounting for different combinations of firm-country, country, and year fixed effects. I present the evidence for the persistence in import status at country level in Table 1. Columns1and2reporttransitionprobabilitiesinyeartforsourcecountryj giventhat firmdoesnotimportfromcountryj inyeart−1. Columns3and4reportthetransition probabilities when firms import from country j in the previous year. The probabilities 11DescriptivestatisticsareprovidedinAppendixB.B2.

10 in column 1 are overwhelmingly higher than those in column 2. This pattern implies onceafirmchoosesnottoimportfromacertainmarket, itishighlyunlikelytoenterin the following year. By contrast, once a firm enters an import market, it is more likely to keep importing from that market in the following year. The pattern is consistent across all sample years. The persistence in firm-country level import status implies that there may be country-specific sunk costs of importing.12 Table 1—: Country-Specific Transition Rates Status in year t−1 No Exports Exports Status in year t No exports Exports No exports Exports 2000–2001 99.62 0.38 34.99 65.01 2001–2002 99.53 0.47 37.27 62.73 2002–2003 99.43 0.57 36.64 63.36 2003–2004 99.38 0.62 38.85 61.15 2004–2005 99.43 0.57 39.79 60.21 2005–2006 99.41 0.59 36.86 63.14 All 99.47 0.53 37.66 62.34 Note: This table summarizes the transition rates into and out of the average import source. Each column describesthetransitionfromtheimportingstatusinthefirstrowtothestatusinthesecondrow. Source: GeneralAdministrationofCustoms. The persistence we observe in the data, nevertheless, may be caused by persistence in country, or firm-country-specific components.13 If these characteristics induce a firm to self-select into certain markets but chooses not to enter others, then as long as these characteristics stay constant over time this firm will continue to import from the same set of countries. If this is the case, we might misattribute the path dependence exhibited in the data to sunk costs of importing. To investigate these possibilities, in Table 2 I run a dynamic linear probability model of a firm’s current entry decision in each import market on past entry, while accounting for firm-country fixed effects and country dummies. The inclusion of these fixed effects ensures that the effect of past entry on current entry does not come from time-invariant factors that also affect the firm’s import decision. In column 3, I include a set of year dummies to 12SeeFigureB1forthetransitionratesforeachimportsource. 13Country-specific characteristics such as technology level and labor wages can influence a firm’s import decision. Lincoln and McCallum (2018) document that in addition to the entry costs, the development of the internet, trade agreements, and foreign income growth affect the extensive margin of US firms. Furthermore, given the same country characteristics, some firms may be a better match than others due to firm-countryspecific factors such as origins of immigrant labor. The persistence in these characteristics can generate the persistenceinthefirm’simportbehaviors.

THE DYNAMICS OF GLOBAL SOURCING 11 control for macroeconometric trends that might influence the likelihood of importing in a particular year. Yet, this variable may pick up the effect that comes from timevarying characteristics that are correlated with a firm’s import history (e.g.: firm’s past productivity affects both its past import decision and its current productivity), which leads to omitted variable bias. In column 4, I include domestic sales to proxy for productivity growth that is due to the firm’s past import decisions.14 Regardless of the specification, the coefficient on past import status remains positive andsignificant, implyingthatthepersistenceinimportingcannotbeentirelyexplained by the time-invariant factors or larger economic trends. The estimates range between 0.21 and 0.52, meaning that if a firm imported from country j in the previous period, it is at least 21 percentage points more likely to continue importing from country j. There is a big decrease in the effect of past import status when including firm-countryspecific fixed effects. This decline implies that firm-country-specific components might be important in explaining the persistence in firms’ importing decisions. In the theoretical framework developed in Section II, I allow for firm-country-specific components that can account for the pattern observed here. Finally, firms may only pay a one-time global sunk cost regardless of the number of countries from which they import and the country-specific past entry variable may simply pick up the effect of previously entering the import market. For this reason, in the last column of Table 2, I include an additional dummy that takes the value of unity if the firm imported from any country in the previous year. I find that the estimated coefficient on this variable is negligible, albeit statistically significant, whereas the effect of importing from country j in year t−1 on importing from j in year t is largely unchanged. This suggests that its magnitude might be small compared with countryspecific sunk costs.15 Hence, I focus on the country-specific sunk costs in the main analysis of the paper. Stylized fact 2: The average importer sources from multiple countries. The set of countries from which a firm sources cannot be explained by random entry. 14SectionV.Aprovidesanextensionofthemodelthataccountsforproductivitygainofimporting. 15Moxnes (2010) and McCallum (2015) find that country-specific sunk costs of exporting are much larger thanglobalsunkcost. Mix(2020)showsthatcountry-specificfixedcostsareimportantinexplainingvariation inexportchurningacrossdestinations.

12 Table 2—: Persistence in Import Status (1) (2) (3) (4) (5) Import to country j 0.52 0.34 0.34 0.21 0.21 in year t−1 (0.005) (0.01) (0.01) (0.02) (0.02) Import in year t−1 0.01 (0.005) Observations 1934730 1612275 1612275 426018 426018 Country Dummies Yes Yes Yes Yes Yes Firm-Country FE Yes Yes Yes Yes Year Dummies Yes Yes Yes Domestic sales Yes Yes Note: Thistablereportsresultsonregressingcurrentimportstatusonpastimportstatusatthefirm-country level. Columns2to5accountforfirm-countryunobservedheterogeneityusingtheArellano-Bond(1991)GMM estimator. In the last column, both country-specific and global import status terms are treated as endogenous variables. Results using OLS estimation and under a modified random effects probit model proposed by Wooldridge(2005)arequalitativelysimilar. Columns4and5includedomesticsales,thusrestrictingthesample tofirmsthatappearinboththecustomsandtheNBSdata. Source: GeneralAdministrationofCustomsandNationalBureauofStatisticsofChina On average, a firm imports from one to two countries per year and firms that import in at least two consecutive years import from more than three countries. Table 3 reports the ranking of the top 10 countries by number of importers in 2000 and 2006. Surprisingly, the ranking is stable across years, with the most five common import sources being Japan, United States, Germany, South Korea, and Taiwan in both 2000 and 2006. This pattern is not particular to chemicals producers. Indeed, the ranking constructed from the universe of Chinese importers also shows similar stability over time, despite China’s WTO accession at the end of 2001.16 In Table 4, I follow Eaton, Kortum and Kramarz (2011) to examine firms importing fromdifferentsetsofsources. Icomputetheprobabilityofentrythatfollowsahierarchy inthesensethatfirmsthatimportfromthek+1stmostpopularsourcealsoimportfrom thekstpopularsource. Columns1and3reporttheshareoffirmsthatimportfromeach set of countries as observed in the data, whereas columns 2 and 4 predict these entry probabilities if firms enter import markets randomly based on the patterns in Table 3. As in Eaton, Kortum and Kramarz (2011) and AFT, under the assumption that a firm’sdecisionstoimportfromdifferentcountriesareindependent(i.e., randomentry), the fraction of firms that follow a pecking order is much lower than what is presented in the data. This pattern implies certain countries or combinations of countries have 16CountryrankingsusingallindustriesarereportedinTableB1.

THE DYNAMICS OF GLOBAL SOURCING 13 Table 3—: Top 10 Source Countries by Number of Importers 2000 2006 Country Rank No. of firms Country Rank No. of firms Japan 1 128 Japan 1 302 United States 2 113 United States 2 234 Germany 3 89 Germany 3 209 South Korea 4 72 South Korea 4 187 Taiwan 5 67 Taiwan 5 160 Singapore 6 37 Singapore 6 88 France 7 36 India 7 73 United Kingdom 8 32 United Kingdom 8 72 Italy 9 26 Netherlands 9 64 Belgium 10 26 Italy 10 62 Note: This table presents the top 10 source countries based on the number of unique importers in 2000 and 2006. CountryrankforallindustriesarereportedinTableB1. Source: GeneralAdministrationofCustoms. characteristics that make them more attractive to Chinese firms compared with others. II. Model To explain the empirical patterns documented in Section I, I propose a model in which sourcing locations affect firm-level marginal costs. This feature generates interdependence across countries in the spirit of AFT. I further impose that firms have to pay sunk entry costs for each country that they start sourcing from to explain the persistence in firm-country level import status. A. Setup There are J countries (including home) with standard symmetric constant elasticity of substitution (CES) preferences and two markets: intermediate and final goods. The intermediategoodsmarketisperfectlycompetitiveandfirmsmakezeroprofitbyselling intermediate goods. The final goods market, however, is characterized by monopolistic competition. All final goods producers active in time t are indexed by i = 1,...,N . t Time is discrete and indexed by t. I focus on the final goods producers located in the home market (i.e., China). The exit and entry of firms in the domestic market is treated as endogenous. The labor wage in the manufacturing sector is pinned down by the non-manufacturing sector and is normalized to one. A firm’s optimization problem in each period involves (1) where to source intermedi-

14 Table 4—: Share of Chinese chemicals firms importing from strings of top 10 countries 2000 2006 Data Random entry Data Random entry 1 13.83 4.92 13.85 4.76 1-2 2.37 3.97 2.84 3.38 1-2-3 1.19 2.15 1.42 2 1-2-3-4 0.40 .86 1.07 .99 1-2-3-4-5 1.98 .31 1.78 .39 1-2-3-4-5-6 0.40 .05 1.07 .07 1-2-3-4-5-6-7 0.40 .01 0.18 .01 1-2-3-4-5-6-7-8 0 0 0.18 0 1-2-3-4-5-6-7-8-9 0 0 0 0 1-2-3-4-5-6-7-8-9-10 0 0 0.71 0 % following pecking order 20.55 12.26 23.09 11.62 Note: Thistablepresentsthesharesoffirmsthatfollowapeckingorderobservedinthedataversuspredicted by a random entry model. Countries are indexed by their ranks reported in Table 3. The first row shows the shareoffirmsthatimportfromthetopsourcecountry(i.e., Japan). Thesecondrowshowstheshareoffirms that import only from the top two countries (i.e., Japan and the United States) in a given year. The random entry predictions are based on the assumption that the unconditional probability of importing from country j is the same as the probability of importing from country j conditional on a firm’s import decisions in other countries. Source: GeneralAdministrationofCustoms. ate goods, or its sourcing strategy, (2) how much to source from each market, and (3) how much to charge for each unit of final goods. Throughout the paper, I denote b as the generic set of import sources, J as the optimal set, and o as the observed set. Demand Individuals in country j value the consumption of differentiated varieties of manufactured goods according to a standard symmetric CES aggregator (cid:18)(cid:90) (cid:19)σ/(σ−1) (1) U = q (ψ)σ/(σ−1)dψ ,σ > 1, jt jt ψ∈Ψjt where Ψ is the set of varieties available to consumers in country j in year t, and σ jt is the elasticity of substitution between varieties. These preferences give rise to the following demand for variety ψ (2) q (ψ) = p (ψ)−σPσ−1Y jt jt jt jt

THE DYNAMICS OF GLOBAL SOURCING 15 where p (ψ) is the price of variety ψ, P is the standard price index, and Y is the jt jt jt aggregate expenditure in country j. Technology and Market Structure There exists a measure N of final goods producers in year t, and each produces a t single differentiated variety. The final goods market is monopolistically competitive, and I assume that the final goods varieties are non-traded.17 Production of final goods requires the assembly of a bundle of intermediates, which containsacontinuumofmeasureoneoffirm-specificinputs. Theseinputsareimperfect substitutesforeachother,withaconstantandsymmetricelasticityofsubstitutionofρ. All intermediates are produced with labor under constant return-to-scale technologies. Let a (v) denote the unit labor required to produce firm i’s intermediate v in country ikt k in year t. Also let τm be the iceberg trade cost firm i pays to offshore in k, while ikt w is the labor wage in country k in year t. Because the intermediate goods market is kt perfectly competitive, a firm will buy from the lowest-price producer for each input v. The price of input v paid by firm i in year t is z (v;Jm) = min {τma (v)w } it it k∈J i m t ikt ikt kt where Jm denotes the set of source countries from which firm i imports in year t. it Let ϕ denote firm i’s productivity in year t. The marginal cost of firm i to produce it a final goods variety is 1 (cid:18)(cid:90) 1 (cid:19)1/(1−ρ) (3) c = z (v;Jm)1−ρdv it ϕ it it it 0 As in Eaton and Kortum (2002), the value of 1/a (v) is drawn from a Frechet disikt tribution: Prob(a ikt (v) ≥ a) = e−T k aθ with T k > 0. These draws are independent across locations and inputs. T governs the state of technology in country k, while k θ determines the variability of productivity draws across inputs. Lower θ generating greater comparative advantage within the range of intermediates across countries. As discussed in Section I, persistence in firm-country-specific characteristics can be 17InSectionV,Iprovideanextensionofthebaselinemodelinwhichfinalgoodsarealsotraded. finalgoods producersdeterminethesetofcountriestopurchaseinputsandatthesametimechoosethesetofdestinations to export outputs. The inclusion of export platforms provides an additional channel for the interdependence acrossmarkets.

16 important for explaining path dependence in firm-level importing behavior. Here I allow for two sources of heterogeneity at the firm-country level in input prices: variable tradecostsτm andunitlaborrequiredtoproduceaninputvarietya . Itispossibleto ijt ijt imposethateitherorbothcomponentsaretimeinvariant. Forexample, wecanassume variabletradecostsareconstantovertime,orthatfirmsgetonepermanentproductivity draw for each input variety in each market. I remain agnostic about the source of heterogeneity. However, each assumption has different implications in equilibrium. Whereas variable trade costs are common across input varieties within each marketyear pair, input production efficiency determines the price of each input variety and thus from which market the firm would purchase an input variety. Nonetheless, only the distribution of a matters for aggregate imports, as shown in the next section. ijt B. Firm Behavior Conditional on Sourcing Strategy In this section, I describe the firm’s decision once it has chosen the sourcing strategy, Jm. Under the Frechet distribution, the share of intermediate input purchases sourced it from any country j (including the home country) is S ijt (4) X = ijt Θ it where S ≡ T (τmw )−θ captures the country j’s sourcing potential in year t. The ijt j ijt jt term Θ (Jm) ≡ (cid:80) S captures the sourcing capacity of firm i in year t. The it it k∈Jm ikt it marginal cost given the firm’s sourcing strategy can be rewritten as 1 (cid:18) (cid:19)−1/θ (5) c (Jm) = γΘ (Jm) it it ϕ it it it where γ = [Γ(θ+1−ρ)]θ/(1−ρ) and Γ is the gamma function. θ The final goods market is monopolistically competitive, and thus, from the demand equation 2 the firm’s optimal pricing rule is p = σ/(σ−1)c , and the revenue of firm it it

THE DYNAMICS OF GLOBAL SOURCING 17 i in its home market in year t is given by (cid:20) σ c (cid:21)1−σ it (6) r ≡ p q = Y iht it it ht σ−1P ht Pluggingequation5into6,wecanrewritethefirm’srevenuegivenitssourcingstrategy: (7) r iht (J i m t ) = (cid:20) σ− σ 1ϕ 1 P (cid:21)1−σ Y ht [γΘ it (J i m t )] σ− θ 1 it ht As can be seen from equation 5 and the definition of Θ , adding one location increases it thefirm’ssourcingcapacityandreducesitsmarginalcost, whichwillincreasethefirm’s revenues. Furthermore, the marginal revenue of a location depends on the sourcing potential of the incumbent import locations. The direction of this relationship relies on the term (σ−1)/θ. Toseethispoint,letrm(Jm)denotethemarginalrevenueofcountryj tofirmiatthe ijt it setJm–i.e.,thechangeintotalrevenuewhenswitchingfirmi’simportstatusincountry it j given its sourcing strategy Jm. Specifically, rm(Jm) = r (Jm ∪j)−r (Jm) if it ijt it iht it iht it j ∈/ Jm and rm(Jm) = r (Jm)−r (Jm\j) if i ∈ Jm. With a few derivations, we it ijt it iht it iht it it can express the marginal revenue at the optimal set Jm as18 it  (cid:20)(cid:18) (cid:19)σ−1 (cid:21)     (Θ it (J i m t )+S ijt )/Θ it (J i m t ) θ −1 r iht (J i m t ) if j ∈/ J i m t (8) rm(Jm) = ijt it (cid:20) (cid:18) (cid:19)σ−1(cid:21)  θ   1− (Θ (Jm)−S )/Θ (Jm) r (Jm) if j ∈ Jm  it it ijt it it iht it it Themarginalrevenuerm(Jm)containstwoterms. Thefirstterminthesquarebracket ijt it captures the rate of change in marginal cost when we deviate from the set Jm. The it second term is simply the total revenue of the firm at the set Jm, or r (Jm). While it iht it the rate of change in marginal cost is decreasing in the sourcing capacity Θ (Jm), it it the total revenue is increasing in Θ (Jm). The relative magnitudes of these two forces it it dependonthesizeof(σ−1)/θ. Specifically, rm(Jm)isincreasinginthetermΘ (Jm) ijt it it it if(σ−1)/θ > 1anddecreasinginΘ (Jm)when(σ−1)/θ < 1. When(σ−1)/θ > 1,the it it 18SeedetailsinAppendixF.

18 demandisrelativelyresponsivetopricereductionsandtechnologyisrelativelydispersed across markets, making sourcing from an additional market more beneficial–markets are complementary. When (σ −1)/θ < 1–i.e., demand is inelastic and technology is similar among input sources–the marginal value of a market decreases with the number of countries or the sourcing potential of other countries from which a firm imports. In the knife-edge case when (σ−1)/θ = 1, the marginal revenue of a country is unaffected by the sourcing potential of other countries and Jm–i.e., markets are independent. it Interestingly, in the case when (σ−1)/θ > 1, the marginal revenue of adding a new source country is larger than the marginal revenue of keeping a country from which firm already imports. In other words, all else being equal, if j ∈ om, j(cid:48) ∈/ om, and it it S = S , then |rm(o )| < |rm (o )|. By contrast, when countries are substitutes, ijt ij(cid:48)t ijt it ij(cid:48)t it |rm(o )| > |rm (o )|. Keeping an existing source has bigger revenue gain than adding ijt it ij(cid:48)t it a country with the same sourcing potential. Finally, for every period for which the firm imports from country j it has to pay a fixed cost, denoted by f . If the firm has not imported from market j in year t−1, ijt it has to pay an additional sunk cost s .19 Furthermore, I assume that the fixed and ijt sunk costs have the following structure: f = fo +(cid:15)f where E((cid:15)f |Ω ,d ) = 0 and ijt ijt ijt ijt it ijt s = so +(cid:15)s where E((cid:15)s |Ω ,d ) = 0. fo and so are the observable part of the ijt ijt ijt ijt it ijt ijt ijt fixed and sunk costs.20 Conditional on the firm’s import history, b , the static firm-level profit after imit−1 porting from a set b sources in year t is it (9) π (b ,b ) = σ−1r (b )−f (b )−s (b ,b ) it it it−1 iht it it it it it it−1 where σ−1r (b ) is the firm’s operating profits. The term f (b ) = (cid:80) f is the iht it it it j∈bit ijt (cid:80) sum of fixed cost firm i pays in year t and s = s is the sum of sunk cost it j∈bit ijt j∈/bit−1 firm i pays to enter new import markets in year t.21 19I assume the sunk cost advantage fully depreciates after one year. This assumption is standard in the literature of firm dynamics. However, the framework presented here can be extended to account for longer historydependence. 20There is no restriction on the costs of domestic versus foreign sourcing in the model. However, in the empirical work, as I only use firms that are active and source inputs, I will impose that there are no fixed or sunkcostsofdomesticsourcing–i.e. f =0ands =0. iht jht 21Animplicitargumentinthefirm’sstaticprofitisitsproductivity,ϕit,whichinfluencesthefirm’srevenue. I

THE DYNAMICS OF GLOBAL SOURCING 19 Sourcing from an additional country will increase the firm’s sourcing capacity, lower the marginal cost, and hence increase the firm’s operating profits. However, the firm has to pay an extra fixed cost for the additional source country. The trade-off between marginal cost saving and fixed cost reductions is the main tension in AFT. My model departs from their framework by adding sunk costs, which depends on the firm’s past import decisions. This simple addition of the sunk costs will indeed complicate the firm’s decision, as now the firm avoids paying sunk costs if it continues importing from last year’s source countries. The sunk costs also create the differentiation between old sources and new sources. In other words, even in the absence of heterogeneity in fixed costs, firms face different costs of importing from different countries due to the heterogeneity in their import history. As discussed in Section I, the presence of sunk costs allows us to explain the persistence in import behavior and exploits the differences in the firm’s history to account for the heterogeneity in the firm’s import strategies. In the next section, I describe the firm’s dynamic problem. C. Optimal Sourcing Strategy For each t, firm i chooses a set of import sources, b ∈ B , that maximizes its it it discounted expected profit stream over a planning horizon L it t (cid:88) +Lit (10) E[ δτ−tπ (b ,b )|b ,Ω ] iτ iτ iτ−1 it it τ=t where B is the set of all import sources that firm i considers in year t, and Ω denotes it it the firm’s information set, which includes the firm’s past import set b . Finally, δ is it−1 the discount factor. Under Bellman’s optimality principle, the optimal set of import sources satisfies: (11) V (Ω ) = maxπ (b,b )+δE[V (Ω )|b,Ω ] it it it it−1 it+1 it+1 it b donotincludeitbecausethemodelfocusesonthefirm’importhistory. However,asinthestandardMelitz-styled models,inequilibriumtherewouldbeaproductivitycutoffforfirmstoentereachmarket.

20 where π (.) is the expected value of equation 9. The choice-specific value function for it set b is V (b,Ω ) = π(b,b )+δE[V (Ω )|b,Ω ]. Given this expression, firm i it it it−1 it+1 it+1 it will choose set b over set b(cid:48) (b(cid:48) (cid:54)= b, b(cid:48) ∈ B ) during period t if V (b,Ω ) ≥ V (b(cid:48),Ω ). it it it it it Plugging in the expression for the firm’s static profits in equation 9, we can rewrite the above condition in terms of differences in current profits, fixed costs, sunk costs, and future profits as follows σ−1E[r b−r (b(cid:48))|Ω ]+{δE[V (Ω )|b,Ω ]−δE[V (Ω )|b(cid:48),Ω ]} iht iht it it+1 it+1 it it+1 it+1 it (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (1) (2) (cid:88) (cid:88) (cid:88) (cid:88) ≥ E[ f − f |Ω ]+E[ s − s |Ω ] ijt ijt it ijt ijt it j∈b j∈b(cid:48) j∈b j∈b(cid:48) (cid:124) (cid:123)(cid:122) (cid:125) j∈/bit−1 j∈/bit−1 (3) (cid:124) (cid:123)(cid:122) (cid:125) (4) Four factors determine the solution to the firm’s dynamic problem. The firm balances current and expected future profit gains, captured by the first and second terms, with fixedandsunkcostsaving,capturedbythelasttwoterms. Theadditionofthecountryspecific sunk costs adds an inter-temporal link between last year’s sourcing strategy and this year’s sourcing strategy. Whetherthedynamicproblemimpliesanincreaseordecreaseinthevalueofsourcing compared with the static problem is unclear. In a static environment, when sourcing from a new market, the firm benefits from marginal cost reductions and thus increased current variable profits, but pays an additional fixed cost. In a dynamic setting, it incurs the additional startup cost of importing from the new market, but at the same time reduces expected future costs. The dynamic solution may differ from a static one, depending on the size of sunk costs, discount factor, and the expected profit gains from adding a new source. III. Estimation Approach Estimating the firm’s optimization problem described in equation 10 is challenging for two main reasons. First, the interdependence across input sources gives rise to a combinatorialproblemasresearchersneedtoevaluatecombinationsofcountriesinstead

THE DYNAMICS OF GLOBAL SOURCING 21 ofeachcountryseparately. Forexample, keepingthenumberofcountriesat40requires evaluation of 1.1×1012 choices. Because of the enormous choice set, evaluating every potential choice is computationally infeasible. Second, the dynamic features of the model require computing the expected future value of each choice, which adds to the computational burden of the estimation. Existing studies deal with these challenges in several ways: (1) reduce the choice set of the firm by restricting the set of feasible source countries, (2) impose strict assumptions on the firm’s behavior, or (3) archive partial identification. While the first approach is common in the literature, it may not be ideal in the presence of interdependence across countries.22 The second approach requires strong assumptions on the firm’s optimization behavior, which unavoidably reduces the credibility of inference (Manski, 2003). With the exception of MSZ, most entry models in international trade settings have point-identified structural parameters by specifying a planning horizon L , imposing the exact content of the information set Ω , ex-ante determining the set it it of countries that a firm considers every period B , and imposing strong parametric it assumptions on the unobserved components in the profit function.23 For these reasons, I pursue a partial identification approach that both maintains a wide range of feasible choices and requires mild assumptions on the firm’s behavior.24 In the next section, I provide an intuition for the identification strategy and key assumptions to identify the fixed and sunk costs of importing and provide formal statements of these assumptions in Appendix A. A. Revealed Preferences Approach: Intuition Thekeyidentificationassumptionisbasedonrevealedpreferences: Afirm’sobserved import decision in a given year maximizes its expected profit stream, given its informa- 22When we restrict the set of source countries to a small number–e.g., fewer than 10–most firms would be likelytoimportfromoutsidethatset. Asaresult,restrictingdatainsuchmannerwouldleadtoahugelossof information. 23Indeed, MSZshowthatmisspecificationsofmodelelementssuchasplanninghorizons, considerationsets, andinformationsetleadtobiasintheirestimates. 24One main disadvantage of this method is its inability to perform counterfactual experiments due to the multiplicity of admissable parameter values and unidentified distribution of the unobservables. However, Li (2019) develops amethod toconduct counterfactual analysis under certainassumptions on the unobservables. Inadifferentpaper,ChristensenandConnault(2019)providesensitivitytestsforcounterfactualresultsaround aneighborhoodoftheunobservables’distribution.

22 tion set in the same year. Following MSZ, I create a series of minor deviations from the firm’s observed history by applying a discrete analog of Euler’s perturbation method. More specifically, I switch the import status for each firm-country-year pair one-by-one while keeping the firm’s import decisions in other years and in other markets intact.25 Importantly, by revealed preferences any deviation from the observed import decisions would lower the firm’s expected profits. Formally, let J b denote the optimal it+l set in year t+l given that it chooses set b in year t. It can be shown that E(π (o ,o )+δπ (J (o ),o )|Ω ) it it it−1 it+1 it+1 it it it (12) ≥ E(π (b,o )+δπ (J (o )),b)|Ω ) it it−1 it+1 it+1 it it See detailed proof in Appendix A. Intuitively, equation 12 states that given the firm’s information set in year t, the firm’s expected sum of profits in years t and t+1 at the observed decision is larger than that in these two years if it would choose b in year t but in the subsequent year act as if it had chosen o instead. As shown later, equation it 12 provides the inequalities that identify the bounds of the fixed and sunk costs. Thismethodhasthreemainadvantages. First, becauseequation12onlyinvolvesthe comparison of static profits in two periods, I can avoid dealing with the firm’s dynamic problem, which substantially decreases the computation burden when estimating the fixed and sunk costs. Second, equation 12 holds under flexible assumptions on the firm’splanninghorizonL orthefirm’sconsiderationsetB .26 Finally,Icanreducethe it it numberofchoicestoanalyzeineachperiod. Whilethetotalnumberofpossiblechoices in each period is 2J with J markets, it is sufficient to consider only J deviations.27 Finally, note that inequality 12 is conditional on the firm’s information set, Ω . To it bringthistothedata, researchersoftenneedtofullyspecifytheinformationsetandassume full distributions for the unobserved error terms. Furthermore, using conditional 25For example, if a firm imports from the United States and Mexico in 2001, I create multiple alternative pathsbydroppingeithertheUnitedStatesorMexicofromthefirm’simportsetin2001,orbyaddinganother countrytoitsimportsetin2001. SeeSectionIII.Bformoreexplanation. 26TherequiredassumptionsarethatLit ≥1andtheconsiderationsetBit includesfirmi’sobservedchoice andtheone-perioddeviationsthatareusedtoidentifytheboundsforfixedandsunkcosts. 27Obviously,thereare2J−1possibledeviations,butresearcherscandeterminehowmanyandwhichsetof deviationstoanalyze. Thiscreatesatrade-offbetweenefficiencyandcomputationalfeasibility. Alargernumber ofdeviationsgivesustighterbounds,butrequiresmorecomputingpower.

THE DYNAMICS OF GLOBAL SOURCING 23 moments implies that the number of potential inequalities is generally large. Instead, I use a set of instrumental variables, Z , to construct unconditional moment inequalities it from equation 12. The transformation from conditional to unconditional moments may lead to a loss of information. However, researchers have to make this trade-off between efficiency and computational feasibility. I further assume that the firm has knowledge about the set of instruments–i.e., Z ∈ it Ω . To simplify notation, let it π = [π (o ,o )−π (b,o )]+δ[π (J (o ),J (o ))−π (J (o )),b)] idt it it it−1 it it−1 it+l it+l it it+l−1 it it+l it+1 it be the difference between the observed profits and the profits under the alternative choice b. Let g (.) be a non-negative function. From equation 12, it can be shown that k (13) E[g (Z )π ] ≥ 0. k it idt The term g (Z ) serves as the bridge between the conditional and unconditional mok it ments. Except that g (.) is required to be non-negative to preserve the sign of the k conditional moment inequalities, there are few restrictions on its functional form. Different functions g will generate different moments. Because equation 13 relies only on k observables and parameters in the profit function, it can be taken directly to the data. The next section provides examples of instrument variablesZ , the moment function it g , and deviations that will generate the profit difference π . k idt B. Deriving Moment Inequalities Consider a simple example illustrated by Table 5 with four countries: A, B, C, and D. The top panel presents a firm’s observed import decisions in each country for three consecutive years. In year t−1, the firm imports from A and C but not from B and D– i.e., om = (A,C). In year t, this firm imports from countries A and B, but not from it−1 countries C and D.–i.e. om = (A,B). Thus, the firm’s import status in each country in it yeartisA–continuingimporter, B–newimporter, C–exitingimporter, D–neverimport. Thebottompanelshowshowwecancreatefouralternatepathsinyeartbyswitching

24 the firm’s import status in each country one-by-one. Its import decisions in years t−1 and t+1 are unchanged, however. This procedure is repeated for every year that I observe both the firm’s past and future import decisions. As shown in the previous Table 5—: Examples of One-Period Deviations Year A B C D t−1 1 0 1 0 t 1 1 0 0 t+1 0 0 0 0 (a) Observed import path A B C D Parameters identified Deviation 1 0 1 0 0 Upper bound of γf Deviation 2 1 0 0 0 Upper bound of γf +γs Deviation 3 1 1 1 0 Lower bound of γf Deviation 4 1 1 0 1 Lower bound of γf +γs (b) Deviations in year t Note: Thistableillustratestheobservedimportdecisionsinthreeconsecutiveyearsanddeviationsinagiven yearfromtheobservedpathforahypotheticalfirminfourcountries: A,B,C,andD.Thenumber1indicates import and 0 indicates no import. In each deviation, I switch the firm’s import status in one country while maintainingitsimportstatusinothercountries. Panelbalsopresentstheparametersbeingidentifiedwitheach deviation. section, the difference in the discounted sum of profits generated by the observed and alternative paths depends only on the difference in static profits in years t and t+1. In this example, since this firm does not import in year t+1, there is no change in the static profit year t+1. Assume f = γf + (cid:15)f and s = γs + (cid:15)s . Recall that the marginal revenue ijt ijt ijt ijt rm(om), or the change in firm i’s revenue when we deviate from om, is defined as ijt it it rm(om) = r (om ∪j)−r (om) if j ∈/ om and rm(om) = r (om)−r (om \j) if ijt it iht it iht it it ijt it iht it iht it i ∈ om. Thus, the profit difference, π under each alternative path is it idt Deviation 1 : π = σ−1rm(om)−γf −(cid:15)f idt ijt it ijt Deviation 2 : π = σ−1rm(om)−γf −(cid:15)f −γs−(cid:15)s idt ijt it ijt ijt Deviation 3 : π = −σ−1rm(om)+γf +(cid:15)f idt ijt it ijt Deviation 4 : π = −σ−1rm(om)+γf +(cid:15)f +γs+(cid:15)s idt ijt it ijt ijt

THE DYNAMICS OF GLOBAL SOURCING 25 Next, to create the moment inequalities in the form of equation 13, I use the following four moment functions g to g : 1 4 g (Z ) = 1(d = 1,d = 1) g (Z ) = 1(d = 1,d = 0) 1 it ijt ijt−1 2 it ijt ijt−1 g (Z ) = 1(d = 0,d = 1) g (Z ) = 1(d = 0,d = 0) 3 it ijt ijt−1 4 it ijt ijt−1 Thus, g (Z ),g (Z ),g (Z ), and g (Z ) are indicator functions that take the value 1 it 2 it 3 it 4 it of one if in year t firm i is a continuing importer, new importer, exiting importer, or never imports from country j. When g (Z ) = g (Z ), equation 13 becomes k it 1 it E[g (Z )π ] = E[g (Z )(σ−1rm −γf −(cid:15)f )] 1 it idt 1 it ijt ijt = E[g (Z )(σ−1rm −γf)] ≥ 0 1 it ijt The second equality holds under the assumption that E((cid:15)f |Ω ,d ) = 0. Rearranging ijt it ijt the terms, we can identify the upper bound for γf: E[g (Z )(σ−1rm)] (14) γf ≤ 1 it ijt E[g (Z )] 1 it By similar logic, when g (Z ) = g (Z ) = 1(d = 1,d = 0), we have k it 2 it ijt ijt−1 E[g (Z )π ] = E[g (Z )(σ−1rm −γf −(cid:15)f −γs−(cid:15)s )] 2 it idt 2 it ijt ijt ijt = E[g (Z )(σ−1rm −γf −γs)] ≥ 0 2 it ijt As before, the second equality is due to E((cid:15)f |Ω ,d ) = 0 and E((cid:15)s |Ω ,d ) = 0. ijt it it ijt it ijt Arranging the terms, we can write E[g (Z )(σ−1rm)] (15) γf +γs ≤ 2 it ijt E[g (Z )] 2 it This time γs appears as firm i does not import to j in year t−1 and thus has to pay the sunk entry cost. The previous two examples provide upper bounds for γf and γs. When d = 0, we can create moment inequalities that identify the lower bounds for ijt

26 these parameters. To be more specific, E[g (Z )(−σ−1rm)] (16) γf ≥ 3 it ijt E[g (Z )] 3 it when g (Z ) = g (Z ) = 1(d = 0,d = 1) and k it 3 it ijt ijt−1 E[g (Z )(−σ−1rm)] (17) γf +γs ≥ 4 it ijt E[g (Z )] 4 it when g (Z ) = g (Z ) = 1(d = 0,d = 0). k it 4 it ijt ijt−1 In a nutshell, the bounds for the fixed costs are identified using continuing importers and exiting importers (inequalities 14 and 16) as these firms pay only fixed costs to import. The bounds for both fixed and sunk costs are identified using new importers and non-importers (inequalities 15 and 17) as these firms would have to pay both types of costs in order to import. When adding a country from which the firm does not import (inequalities 16 and 17), we identify the lower bounds of the costs, and when dropping a country from which the firm indeed imports (inequalities 14 and 15), we identify the upper bounds. Notice that a key component in inequalities 14 to 17 is the marginal revenues of importing rm. In Section IV, I describe how to compute this ijt variable and other unknown quantities used to construct the bounds for fixed and sunk costs of importing. IV. Estimation Procedure and Results The estimation procedure consists of two steps. In the first step, I compute rm(om), ijt it orthepredictedchangesinrevenueswhenaddingordroppingasourcinglocationbased on equation 8. In the second step, I estimate the bounds and conduct inference for the fixed and sunk cost parameters.

THE DYNAMICS OF GLOBAL SOURCING 27 A. Step 1: Marginal Revenues of Importing To estimate rm(om), recall that we can express this quantity as ijt it  (cid:20)(cid:18) (cid:19)σ−1 (cid:21)     ( (cid:88) S ikt +S ijt )/( (cid:88) S ikt ) θ −1 r iht (om it ) if j ∈/ om it  rm(om) =  k∈om it k∈om it ijt it (cid:20) (cid:18) (cid:19)σ−1(cid:21)  (cid:88) (cid:88) θ   1− ( S −S )/( S ) r (om) if j ∈ om   ikt ijt ikt iht it it  k∈om k∈om it it This quantity depends on (1) total revenues at the observed set, r (om); (2) elasticity iht it of substitution σ; (3) dispersion of technology θ; and (4) firm-country-year-specific sourcing potential S . In the remainder of the section, I briefly describe how to ijt recover the unobserved components required to compute rm(om). ijt it Elasticity of substitution (σ): With the CES preferences and monopolistic competition, the ratio of sales to variable input purchases (or markup) is σ/(σ − 1). The average mark-up is 33%, which implies that the elasticity of substitution σ is about 4.02. This value is within the range documented in previous studies.28 Dispersion of technology (θ) and firm-country-year specific sourcing potential (S ): ijt I follow a modified version of the estimation procedure in AFT and rely on variation in the share of imported inputs across firm-country-year pairs. Intuitively, the parameter θ plays the role of trade elasticity and can be captured as the elasticity of firm-country level input shares to labor wages. Next, based on the definition of the firm-countryyear-specific sourcing potential–i.e. S = T (τmw )−θ–I use observed information on ijt j ijt jt country-level technology, trade costs, and wages to proxy for the sourcing potential.29 ResultsaresummarizedinTable6. Theestimateforθ is1.99(standarderror=0.49) and the average value of S is 2.68 (standard error = 7.19). With respect to the types ijt of countries from which firms choose to import, it seems that new import markets tend to have higher sourcing potential (3.10) compared with markets firms already have experience with (2.65), whereas firms exit markets with the lowest sourcing potential 28See,forexample,SimonovskaandWaugh(2014)andDonaldson(2018). 29DetailsoftheestimationareprovidedinAppendixC.C1.

28 (1.43).30 This result is consistent with the sunk cost hypothesis: New importers justify incurring sunk entry costs by importing from high-technology low-cost suppliers, whereas firms exit high-cost markets despite already incurring the entry costs. Table 6—: Step 1: Predicted Marginal Revenues of Importing Elasticity of Technology substitution (σ) dispersion (θ) 4.02 1.99 (31.53) (0.49) (a) Parameter Values (1) (2) (3) (4) (5) All Never Exiting New Continuing Sourcing potential (S ) 2.68 2.63 1.44 3.11 2.65 ijt (7.19) (6.67) (3.57) (10.05) (7.27) Marginal revenue (rm) 4.44 3.66 2.47 7.99 6.65 ijt (20.25) (16.93) (6.4) (36.54) (20.87) Total revenue (r ) 239.2 179.6 344.9 387.6 504.9 iht (386.4) (298.4) (478.3) (520.1) (594.5) Rate of MC saving (rm/r ) 0.024 0.026 0.011 0.023 0.015 ijt iht (0.07) (0.07) (0.02) (0.06) (0.03) Observations 42994 31128 615 4612 4312 (b) Variable values Note: Panelareportsestimatesforthekeyparameterstocomputethemarginalrevenues(rm). Panelbreports ijt thevaluesofmarginalrevenuesandothervariablesforallfirms(column1)andfordifferenttypesofimporters (columns 2 to 5) based on the firm’s import status in each country for a given period. The last two rows of Panelbbreakdownthemarginalrevenuesintotwocomponents: theobservedtotalrevenuesandtheestimated rates of change in marginal costs. Monetary values are in millions of 1998 RMB. Sample includes the top 40 popularsourcecountries. Standarderrorsinparentheses. Source: GeneralAdministrationofCustomsandNationalBureauofStatisticsofChina At this point, I have computed all components to predict the marginal revenues rm(om), which captures the change in total revenues for each deviation from the obijt it served import path. On average, when a firm drops or adds a country to its import set, its total revenue changes by 4.44 million RMB. This quantity varies across a firm’s import histories in a source country. For example, dropping a new source country reduces the firm’s revenues by 7.9 million RMB and dropping a source country that the firm has previous experience with reduces its revenues by 6.6 million RMB. For 30Recallthatsourcingpotentialisacombinationoftechnology,tradecosts,andwages,andlooselycaptures themarginalcostsavingcontribution. Highersourcingpotentialreflectslowercost.

THE DYNAMICS OF GLOBAL SOURCING 29 exiting importers and firms that never import, adding a new source increases revenues by about 2.5 and 3.6 million RMB. Next, I break down the marginal revenues into two components: the observed total revenues and the rates of marginal cost saving. The rate of marginal cost saving is similar for new importers and those that never import: Each market saves about 2.3% to 2.6% of total revenues. For exiting and continuing importers, the rate of marginal cost saving is about 1.1% to 1.5%. Regardless, the absolute revenue gain is highest for a new importer: Adding a new source increases revenue by 8 mil RMB, followed by a continued source with6.6 milRMB. Forexiting importers and firmsthat never import, addinganewsourceincreasesrevenuebyabout2.5and3.6milRMB,respectively. Here we see the interaction between the scale and substitution effects: continuing importers already have high sourcing capacity (i.e., they already import from low-cost suppliers) and thus have a lower rate of marginal cost saving (substitution effect). However, their large scale of operation leads to a large absolute gain from each individual import source (scale effect). By contrast, new importers tend to be smaller in size but the marginal cost saving is large, resulting in large absolute revenue gains. B. Step 2: Fixed and Sunk Costs To estimate the bounds for the fixed and sunk costs, I first assume that these terms have following functional forms: f = γf +γf ·X +(cid:15)f and s = γs+γs·X +(cid:15)s , ijt o j ijt ijt o j ijt where X is a vector of country characteristics. Let γ = (γf,γf,γs,γs) collect the fixed j o o and sunk cost parameters. As the bounds for each element in γ become larger with the dimension of γ, I choose a parsimonious specification for the fixed and sunk costs. Specifically, to capture distance between China and country j, I use a dummy variable, Border , that equals 1 if the two countries do not share a border. I also include the j binary variable Language where Language = 1 if China and country j do not share j j the same language. By construction, a continuing importer incurs only the fixed cost f and a new ijt importerpaysboththefixedandsunkcosts, f +s . Fortheestimation, Iwillreport ijt ijt the cost to a continuing importer and the cost to a new importer. Define γ˜s = γf +γs.

30 The vector of parameters is γ = (γf,γf,γ˜s,γ˜s) o o I compute the 95% confidence set for γ using the general moment selection method developed by Andrews and Soares (2010). Specifically, I employ the modified method of moment test statistics: Q (γ) = (cid:80)K [m¯ (γ)/σˆ (γ)]2 where [x] = min{0,x} and n k=1 k k − − m¯ (γ) ≡ 1 (cid:80) (cid:80) (cid:80) g (Z )π is the sample analog of the moment inequalk N i∈Ni j∈J t∈T k it idt ities defined in Section III, and σˆ (γ) is the standard deviation of the observations k entering moment k. Table 7 reports the 95% confidence sets for linear combinations of the fixed and sunk cost parameters under three specifications. In the first one, I include a constant term for both the fixed and sunk costs. Note that this specification does not imply that fixed and sunk costs are homogeneous across firm-country-year triplets, as I allow for the unobserved components of fixed and sunk costs, (cid:15)f and (cid:15)s , to be different from ijt ijt zero and heterogenous across firm-year-country triplets. In the next two specifications, I include the country characteristics to proxy for distance and common language. Table 7 shows that if a firm has import experience in country j, it pays a fixed cost of 0.48 million to 1.80 million RMB to continue importing from the same location, equivalent of 10.8% to 40.5% of average marginal revenue. For a new importer, the total fixed and sunk costs ranges from 0.96 to 3.12 mil RMB, or 21.6% to 71.6% of average marginal revenue. This amount is consistent across specifications, between 1 million to 2.98 million in the second specification and 1.12 and 3.67 million in the last specification. Even though zero is often the lower bound of individual parameters, jointly they are always significantly different from zero. Figure 2 shows the 95 % confidence set projections of the total costs to continuing versus new importers when they import from a market that does not share either language or border with China. The costs to a new importer are always positive, even when fixed cost is zero. These results are robust to different sample selection criteria, including country group, firm size, and ownership types (see Appendix C.C3).

THE DYNAMICS OF GLOBAL SOURCING 31 Table 7—: Step 2: Fixed and Sunk Costs of Importing Costs to Continuing Importers Costs to new importers (1) (2) (3) (1) (2) (3) Const. [0.48,1.80] [0,1.81] [0,1.85] [0.96,3.12] [0.60,2.94] [0.39,2.96] Const. +language - [0,1.81] [0,1.92] - [1.00,2.98] [0.76,3.66] Const. +border - - [0,1.86] - - [0.39,3.65] Const. +language+border - - [0,1.93] - - [1.12,3.67] Note: Thistablereportstheprojectedconfidenceintervalforeachparameterusingthegeneralmomentselection methodinAndrewsandSoares(2010). Thefirstcolumnreportsthelowerboundsandthesecondcolumnreports theupperbound. Foreachspecification,thetotalrowpresentsthesumofthefixedandsunkcosts. Thediscount factorδ issetto0.9. Monetaryvaluesareinmillionof1998RMB. Figure 1. : 95% Joint Confidence Sets (a) Specification 1 (b) Specification 2 (c) Specification 3 Note: This figure illustrates the 95% confidence sets of the total costs to continuing versus new importers for threespecifications. Thetotalcostsaredefinedasthecostsfirmspayiftheforeignmarketdoesnotsharethe samelanguageorborderwiththehomemarket. Monetaryvaluesareinmillionsof1998RMB. C. Comparison with Alternative Models and Parameter Values In this section I compare the baseline results of fixed and sunk costs with those under different assumptions and parameter values: (1) Firms are not forward looking by setting the discount factor to zero, and (2) Countries are either independent or substitute. Static Model with Zero Discount Factor First, I estimate a model in which firms are not forward looking by setting the discount factor to zero. Figure 2a illustrates the comparison for the first specification. The results indicate that under the assumption that firms do not consider effects on future revenues, the sunk cost decreases substantially. In other words, when firms take into account the future profit gains of importing, they are willing to incur bigger costs

32 to import. Not accounting for dynamic gains is thus likely to create downward bias in the sunk cost estimates. Figure 2. : Comparisons with Baseline Results (a) Static model (δ = 0) (b) Interdependence levels Note: Panelacomparesthe95%confidencesetsinthebaselinemodel(discountfactorδ=0.9)versusamodel in which firms are not forward looking (discount factor δ = 0). Panel b compares the 95% confidence sets in the baseline model (countries are complementary–i.e., (σ−1)/θ =1.52) versus models in which countries are independent(σ−1)/θ=1,orsubstitute(σ−1)/θ=0.5. Monetaryvaluesareinmillionsof1998RMB. Static Interdependence Next, I estimate a model when countries are either independent or substitute for each other. Recall that the direction of interdependence depends on the values of the elasticity of demand σ and technology dispersion θ. Because σ affects the estimate through both the interdependence and markup, I keep σ at the baseline estimate but alter the value of θ. Specifically, to simulate an independent scenario, I set θ = 3.02 so that(σ−1)/θ = 1. Tocreatethesubstitutescenario, Ifixθ = 6.04and(σ−1)/θ = 0.5. Figure 2b shows that as θ increases, the estimates for both fixed and sunk costs decrease. The reason is that when there is less dispersion of technology across inputs (i.e., higher θ), the benefit of an additional draw diminishes because the probability firms will find a lower-cost supplier is reduced. This leads to lower marginal revenue from a given import source, thus generating smaller fixed and sunk cost estimates. We canintuitivelyanticipatethatascountriesbecomeclosetoperfectsubstitutes–i.e. (σ− 1)/θ converges to 0, the confidence set for fixed and sunk costs collapses. The intuition

THE DYNAMICS OF GLOBAL SOURCING 33 is that when countries are perfect substitutes, firms obtain no additional revenue gain from sourcing from more than one market (including the domestic market). Thus, if they choose to import, it must mean that firms are indifferent between importing and not importing, and that the fixed and sunk costs should be close to zero.31 However, because the change in θ affects each of the four importer types in the same manner, the ratio of fixed and sunk costs to average marginal revenue is similar across different models, as reflected by the similar shapes of the three confidence regions. In other words, the level of interdependence matters for the static revenue gains and thus the static decision, but does not alter the fundamental relationship between sunk and fixedcosts. Thisexercisealsoshowsthattheestimationoffixedandsunkcostsherecan accommodate different levels of interdependence across import sources in production. V. Extensions Inthefollowingsections,Idiscusstwoextensionsofthebaselinemodel. First,Section V.A provides an estimation approach that can allow for productivity to be affected by the set of countries from which a firm purchases its intermediate goods. In Section V.B, I introduce exporting decisions into the model. In this setting, a firm can choose where to import intermediate goods and export final goods. A. Productivity Gains from Importing The baseline model assumes that marginal cost is affected only by changes by input prices when firms change their import sources. However, existing evidence indicates that imported inputs affects firm-level productivity (Kasahara and Rodrigue, 2008; AmitiandKonings,2007;Halpern, KorenandSzeidl,2015). Afirm’scoreproductivity (ϕ ) may also be influenced by its choice of import set. For instance, if a firm imports it from high-income countries, it may have exposure to more managerial know-how or 31When(σ−1)/θ convergestozero, eitherσ convergestooneorθ becomesextremelylarge. Intheformer case,demandisinelastictopriceandthusfirmshavelittleincentivetoreducecosts;theycansimplypasshigher coststoconsumersthroughhigherprices. Firmswouldthenbecomeindifferentbetweenanytwosetsofimport sources. Inthelattercase,thereisnovarianceinefficiencyacrossinputs,meaninginputpricesaredetermined by a country’s technology level Tj and should be the same across inputs within each country. Firms would purchasealloftheirinputsfromonesinglesourcethatprovidesthatlowestprice. Othercountriesbeyondthat simplyprovidenoadditionalbenefits.

34 technological advances embedded in the foreign inputs. While these channels may not change input prices, they may increase the firm’s productivity and thus lower marginal costs. Ignoring the productivity channel may lead to biased estimates of the countries’ marginal revenue gains in the first stage of estimation because we attribute all of the effect on marginal costs to input price reductions. Furthermore, even if we hold all future import decisions constant, future revenues might be affected through the productivity channel and thus not accounting for productivity gains will bias the estimate of import sunk costs.32 Consider the case when productivity is affected by import decisions with a lag. Allowing for the productivity effect substantially complicates the firms’ dynamic problem. Apart from sunk costs, productivity gains provide another channel for the intertemporal linkages between current and future decisions.33 While the change in future sunk costs alters future profits but has no bearing on future revenues, the change in future productivity will affect future revenues. Thus, when deviating from the firm’s observed import path, we need to consider the effects on future productivity to predict the revenue changes. To fix ideas, let ϕ = g(ϕ ,X ,ξ ), where g is some unknown function, X it+1 it it it it captures import decisions in the current year, and ξ captures productivity shock. it I use different measures of X , including a binary variable for importing from high it income countries, import intensity, and number of import markets. Recall that the σ−1 revenue function in equation 7 can be expressed as r = A × ϕσ−1 × Θ θ where iht t it it A captures market demand factors that are common across firms. Under the above t assumption on productivity, future revenue is then a function of last period’s import decision–i.e. r = k(A ,Θ ,ϕ ,X ,ξ ) for some unknown function k. it+1 t+1 it+1 it it it Toapproximatefortheeffectofcurrentimportdecisionsonfuturerevenue,Iestimate the following regression (18) logr = λ +ηX +lnΘˆ +ν it+1 t+1 it it+1 it+1 32On the export side, Timoshenko (2015) shows that the persistence in export status can be explained by bothlearningandsunkcosts,andthatoncelearningiscontrolledfor,thesunkcostestimatebecomessmaller. 33Nevertheless, because current import decision does not affect current productivity, the static problem remainsthesame.

THE DYNAMICS OF GLOBAL SOURCING 35 whereΘˆ isthefirm’ssourcingcapacityestimatedusingtheprocedureinSectionIV. it+1 Note that given the construction of the deviations in Section III, the import decision in year t+1 is unchanged and thus the firm’s sourcing capacity Θ is not affected. it+1 The coefficient of interest is η, which captures how the current import set affect future revenues. X is endogenous as it is correlated with the unobserved productivity. it To address the endogeneity, I use tariffs on imported inputs in China between 2000 and 2006 as an instrumental variable for X . The exclusion assumption is that input it tariffs affect only firm-level revenues through their choice of input sources. Once we obtain a reliable estimate of η, I compute the counterfactual variable X(cid:48) it for each deviation from the observed import set and get the predicted values for r it+1 given X(cid:48) . The change in future revenue from the productivity channel is then the it difference between r (X ) and r (X(cid:48) ). it+1 it it+1 it Results Table8reportstheresultforequation18withthreedifferentmeasurestocharacterize the import set: (1) the total number of import sources, (2) the number of advanced technologycountries, and(3)thenumberofhighincomecountries.34 Theinstrumental variable is firm-level input tariffs.35 As we can see from columns 1, 4, and 7, the coefficients on different measures of X are consistently positive. The estimated it−1 coefficient ranges between 0.088 and 0.108, meaning a 10% increase in the number of productivity-enhancing sources leads to an increase in revenues by 8.8% to 10.8%. The remaining columns look at the effects on firms with different levels of initial revenues. The results suggest potential heterogeneous effects of import decisions on revenue by firmsize. Smallerfirmstendtoenjoybiggerproductivitygainsbyimportingfrommore (high income or advanced technology) countries. Table9showsthechangesinrevenuesbyimportstatusatthefirm-countrylevelwhen X is chosen as the number of high-income countries. Similar to the baseline findings, it new and continuing importers enjoy bigger total revenue gains than exiting importers 34Eventhoughthebaselinemodeldoesnotincorporateexportdecisions,Ialsoincludethenumberofexport destinationstoproxyforexportrevenues. 35SeeAppendixB.B1foradetaileddescriptionofthefirm-levelinputtariffs.

36 and firms that never import. However, when breaking down the total revenue gains into the static changes due to input prices and dynamic changes due to productivity, I find that both components play equally important roles. This evidence suggests that ignoring the dynamic effect of import decisions on productivity can lead to bias in the fixed and sunk cost estimates. PanelainFigure3showsthenew95%confidencesetforthecostsofimportingwhen taking into account the productivity effect. As expected, as the gain from importing increases, the estimated costs to both new and continuing importers also increase. To compare costs relative to the revenue gains, in Panel b I scale each point in the confidence sets by the corresponding average marginal revenue.36 Even after adjusting for revenue gains, I find that new estimates are more likely to produce high estimates for fixed costs, between 19% and 30% of revenue gains, whereas the baseline estimates lie between 13% and 30%. However, the costs to new importers now fall into a lower range (as a percentage of revenue changes). Without the productivity effect, the costs for a new importer can be as much as 40% of marginal revenue, whereas the new upper bound lies around 32% of total revenue gains. 36Specifically, the x-dimension values are scaled by the average revenue change for continuing importers, whereasthey-dimensionvaluesarescaledbytheaveragerevenuechangefornewimporters.

THE DYNAMICS OF GLOBAL SOURCING 37 Table 8—: Revenues and Productivity Gains #countries #advanced-techcountries #high-incomecountries (1) (2) (3) (4) (5) (6) (7) (8) (9) L.import 0.0884 0.101 0.188 0.0903 0.103 0.190 0.108 0.122 0.225 (0.0231) (0.0272) (0.0684) (0.0235) (0.0278) (0.0694) (0.0276) (0.0329) (0.0829) L.import×1(≥medsize) -0.0228 -0.0239 -0.0269 (0.0177) (0.0182) (0.0221) L.import×initialsize -0.0264 -0.0266 -0.0311 (0.0139) (0.0142) (0.0168) Logsourcingcapacity -0.576 -0.527 -0.441 -0.577 -0.526 -0.439 -0.489 -0.449 -0.383 (0.170) (0.158) (0.134) (0.169) (0.158) (0.134) (0.145) (0.136) (0.117) #exportmarkets 0.00369 0.00373 0.00371 0.00374 0.00377 0.00376 0.00400 0.00401 0.00397 (0.000536) (0.000533) (0.000526) (0.000536) (0.000533) (0.000526) (0.000544) (0.000541) (0.000533) Foreignaffiliated -0.0415 -0.0444 -0.0467 -0.0419 -0.0449 -0.0470 -0.0501 -0.0528 -0.0551 (0.0155) (0.0159) (0.0164) (0.0155) (0.0159) (0.0164) (0.0169) (0.0174) (0.0179) Stateowned -0.000756 -0.00128 -0.00329 -0.00106 -0.00152 -0.00337 -0.00169 -0.00206 -0.00410 (0.0155) (0.0153) (0.0153) (0.0155) (0.0153) (0.0153) (0.0155) (0.0154) (0.0154) Initialsize 0.963 0.969 0.981 0.963 0.969 0.981 0.962 0.968 0.980 (0.00779) (0.00842) (0.00880) (0.00787) (0.00846) (0.00879) (0.00799) (0.00864) (0.00879) Constant 3.557 3.291 2.816 3.563 3.287 2.809 3.124 2.902 2.535 (0.862) (0.803) (0.676) (0.861) (0.800) (0.675) (0.738) (0.691) (0.590) Observations 4943 4943 4943 4943 4943 4943 4943 4943 4943 AdjustedR2 0.901 0.902 0.903 0.901 0.902 0.903 0.899 0.900 0.901 Note: Thistablereportstheeffectsofpastimportdecisionsoncurrentrevenues. Columns1-3usethetotalnumberofimportcountriesasthekeyindependent variable, columns 4 to 6 use the number of advanced technology countries, and columns 7 to 9 use the number of high-income countries. Except for columns 1, 4, and 7, I allow for heterogeneous effects of import decisions on revenue by a firm’s initial revenue. 1((≥ med size) takes the value of one if the initial size is equal to or greater than the median value. A set of year dummies is included in all equations. Input tariffs (and interactions with initial size) are used as instrumentvariablesforpastimportdecisions. ThefirststageresultsarereportedinTableD1. MonetaryvaluesareinunitsofmillionofRMB1998. Standarderrorsinparentheses. Source: GeneralAdministrationofCustomsandNationalBureauofStatistics

38 Table 9—: Revenue Changes - Number of High Income Countries All Never Exiting New Continuing Current revenue changes 6.33 6.13 3.29 7.52 6.65 (22.50) (22.34) (8.08) (27.54) (20.28) Future revenue changes 4.15 2.32 6.01 9.09 8.16 (11.09) (5.53) (6.90) (19.99) (16.97) Total revenue changes 10.07 8.23 8.69 15.70 13.99 (23.89) (22.40) (9.09) (31.47) (24.24) Observations 25793 17325 364 3351 3181 Note: Thistablereportstheaveragerevenuechangesforeachdeviationfromtheobservedpathwhenaccounting for productivity effect. Monetary values are in units of million of RMB 1998. The future revenue changes are discountedbyafactorof0.9. Standarderrorsinparentheses. Source: GeneralAdministrationofCustomsandNationalBureauofStatistics Figure 3. : 95% Joint Confidence Sets - Productivity Gains vs Baseline (b) Scaled by average revenue (a) Absolute values changes Note: Thisfigureillustratesthe95%confidencesetsofthetotalcoststocontinuingversusnewimporters. The redregiondepictstheCIunderthebaselinemodel,whereastheblueregiondepictstheCIwhenaccountingfor productivitychannel. Monetaryvaluesareinmillionof1998RMB. B. Export Decisions A firm’s past experience with exporting in a market can affect import entry costs in the same market, and vice versa. When entering a new export destinations, firms may learn about potential suppliers and distribution networks, which facilitates their initial imports from the same location. Thus, ignoring other channels through which

THE DYNAMICS OF GLOBAL SOURCING 39 firms participate in foreign markets may bias the estimate of sunk costs of importing.37 For this reason, I modify the baseline model by allowing firms to choose not only from which countries to source intermediate inputs, but also to which markets to export their outputs. The demand and market structures of the final goods are the same as in the baseline model. However, firm i has to pay a variable trade cost τx for each ijt unit of goods it sells in market j at time t. Conditional on the firm’s sourcing strategy, Jm, the export revenue in each market is it (19) r i x jt (J i m t ) = (cid:20) σ− σ 1ϕ τ i x P jt (cid:21)1−σ Y jt (γΘ it (J i m t )) σ− θ 1 it jt Equation 19 depicts the interdependence in the marginal cost between export and import decisions. The choice of input sources affects the marginal cost, which in turns affects the firm’s export revenues. However, exporting to more profitable destinations increasesthetotalrevenueandthusthemarginalrevenuegainofanimportsource. Let Jx denote the optimal set of export destinations. Conditional on the optimal export it and import decisions, the total revenue of the firm is simply the sum of its domestic revenue and export revenues: r (Jx,Jm) = r (Jm)+ (cid:80) rx (Jm). iht it it iht it j∈Jx ijt it it Similar to the import problem, firms will have to pay a fixed cost of each country to which they export, and a sunk cost if they enter the market for the first time. Denote fm and sm as firm i’s fixed and sunk cost of importing from j in year t and fx and ijt ijt ijt sx as firm i’s fixed and sunk costs of exporting to j in year t. Furthermore, I allow for ijt potential complementarity between export and import in the sunk costs. Simply put, the sunk entry cost of importing that firm i has to pay to enter country j is reduced if it already exported to j in the previous year–i.e., sm −dx em, where em captures ijt ijt−1 ijt ijt the reduction in importing sunk cost due to past export experience. And vice versa, past import experience with j also reduces the sunk entry cost of exporting to j–i.e. sx −dm ex , where ex is the reduction in exporting sunk cost.38 ijt ijt−1 ijt ijt 37The same argument can be made about other international activities, including multinational production oroffshoreR&D.Ifocusonexportingasthischannelisstillthemostcommonthroughwhichfirmsengagein internationalmarkets. However,theestimationframeworkcanbeadaptedtoaccountformoretrademargins. 38Allowingforcomplementarityinthefixedcostsofexportingandimportingisalsofeasible. Asthefocusis onthesunkentrycosts,Ichoosethemoresimplefixedcoststructure.

40 Conditional on the firm’s import history, denoted by bm , and export history, deit−1 noted by bx , the static firm-level profit after importing from set bm sources and it−1 it exporting to set bx destinations in year t is it−1 π (bm,bm ,bx,bx ) = σ−1r (bm,bx)−fm(b )−sm(bm,bm ,bx ) it it it−1 it it−1 iht it it it it it it it−1 it−1 (20) −fx(b )−sx(bx,bx ,bm ) it it it it it−1 it−1 where σ−1r (bm,bx) is the firm’s operating profits. The term fm(bm) = (cid:80) fm iht it it it it j∈bm ijt it is the sum of fixed costs of importing the firm i pays in year t. Analogously, fx(bx) = it it (cid:80) fx isthesumoffixedcostsofexportingthatfirmipaysinyeart. Furthermore, j∈bx ijt it sm it (bm it ,bm it−1 ,bx it−1 ) = (cid:80) j∈bm it (sm ijt −dx ijt−1 em ijt ) is the sum of sunk costs firm i pays to j∈/bm enter new import markets i i n t−1 year t and sx it (bx it ,bx it−1 ,bm it−1 ) = (cid:80) j∈bm it (sx ijt −dm ijt−1 ex ijt ) j∈/bm it−1 denotes the sum of sunk costs firm i pays to enter new export markets in year t. We now turn to the dynamic problem with both export and import decisions. In each period t, firm i chooses a sequence of import sources and export destinations, {(bm,bx ) : bm,bx ∈ B }t+Lit, that maximizes its discounted expected profit stream iτ iτ iτ iτ it τ=t over a planning horizon L it t (cid:88) +Lit (21) E[ δτ−tπ (bm,bm ,bx,bx )|Ω ] iτ it it−1 it it−1 it τ=t where B is the set of all import sources and export destinations that firm i considers it in year t, and Ω denotes the firm’s information set, which includes the firm’s past it import and export sets (bm and bx ).39 it−1 it−1 Despitetheinterdependencebetweenexportandimportdecisionsinboththemarginal costsandsunkcosts,undertherevealedpreferencesassumptionwecanindeedestimate the export and import parameters separately. Intuitively, I assume that the observed export and import path is the optimal, and thus any deviation from the observed path will lower the firm’s expected profits. The implication is that we can keep the export decision intact and deviate from the observed import path to estimate import parame- 39HereIallowtheconsiderationsetstobedifferentforexportdestinationsandimportsources. Wecanthink ofBit astheunionofthetwoconsiderationsets–i.e.,Bit=B i m t ∪B i x t .

THE DYNAMICS OF GLOBAL SOURCING 41 ters, and keep the import path fixed while changing the export path to get the bounds for the export parameters. Under the same deviation construction, the number of choices to analyze for each firm-year-country pair is 2J. As the one-period dependency in the static profits is preserved, this method again reduces the dynamic problem to a static problem as explained in Section III. The same logic can be applied to a large class of multi-country models that incorporate multiple trade margins, such as multinational production as in Tintelnot (2017) or offshore R&D as in Fan (2019). The key lies in the ability to compute the marginal value of a location with respect to one trade activity, while keeping other markets intact. The method is flexible enough to allow for interdependence across locations and/or among trade margins. To estimate the model, I assume the following structures on the fixed and sunk costs: fx = γf,x + (cid:15)f,x, fm = γf,m + (cid:15)f,m, sx = γs,x + (cid:15)s,x, sm = γs,m + (cid:15)s,m ijt ijt ijt ijt ijt ijt ijt ijt where E((cid:15)g,x|Ω ,dx ,dm) = 0 and E((cid:15)g,m|Ω ,dx ,dm) = 0, with g = f,s. Finally, ijt it ijt ijt ijt it ijt ijt ex = γe,x and em = γe.m. Let γ collect all the parameters in the fixed and sunk costs: ijt ijt γ = (γf,m,γs,m,γf,x,γs,x,γe,m,γe,x). Following MSZ, I compute predicted export revenues as a function of domestic revenues. Theaveragepredictedrevenuesforexiting,continuing,never,andnewexporters are 0.45, 2.29, 1.39, and 1.94 mil RMB, respectively.40 Next, I apply the same deviation procedure in Section III to create the moment inequalities from both export and import decisions. Figure 4 illustrates the confidence regions of the cost that an average importer/exporter pays in the first year of importing/exporting. If a firm has neither export nor import experience in a market, it pays between 0.98 and 4.89 mil RMB to start importing (computed as the bounds on γf,m + γs,m), and between 0.39 and 0.95 mil RMB to export in the initial year (γf,x +γs,x). However, if the firm exported to the same country in the previous year, then it may enjoy a substantial reduction in the sunk cost of importing, up to 3.7 mil RMB. Likewise, a new exporter experiences a reduction on its sunk cost of exporting if it imported from the same market previously. The results document high degree of 40SeeTableD3fortheexportrevenuepredictionregressionresults.

42 complementarity between exporting and importing. One interesting pattern is that the upper bounds of the confidence intervals for the γm parameters are much bigger than those for γx, indicating that importing is more costly for some firms. Note that what is captured here is the cost firms pay per market. Indeed, I find that the number of export destinations tends to be higher than the number of import sources. Conditional on importing, the median firm imports from two countries, whereas conditional on exporting, the median exporter sells to six markets.41 As a result, when accounting for the number of countries that a firm imports from or exports to, I find that the total costs of importing for the median firm is indeed similar to the total costs of exporting.42 Figure 4. : 95% Joint Confidence Sets (a) Import costs (b) Export costs Note: This figure illustrates the 95% confidence sets of the total costs to new importers (top panel) and new exporters (bottom panel). The horizontal axis presents the costs when the new importer (exporter) does not have prior export (import) experience, whereas the vertical axis presents the costs when the firm has prior experienceintheothertrademargin. Monetaryvaluesareinmillionof1998RMB. VI. Conclusion This paper introduces and estimates a dynamic multi-country model of imports with heterogeneous firms. The main findings show that it is more costly for firms to establish new import relationships than to maintain their existing import sources, implying 41Thesamepatternisobservedfornewexportersandimporters. Themedianimporterpurchasesfromone newcountry,whereasthemedianexportersellstothreenewdestinations. 42ThisevidenceexplainsthedifferencebetweenmyestimatesandtheresultsinKasaharaandLapham(2013), inwhichtheauthorsfindthethecostsofexportingarecomparabletothecostsofimporting.

THE DYNAMICS OF GLOBAL SOURCING 43 there are sunk costs of importing from a new location. Furthermore, import decisions are interdependent across countries–i.e., the benefits of importing from one location increasesasfirmsimportfrommorelocations. Thesetwofeaturesoftheimportdecisions together imply that there might be complicated responses to targeted trade policies. Reducing trade barriers in one market not only affects entry in its own country, but also affects trade flows in other markets. Moreover, temporary trade policy changes might have long-run effects due to path dependence in the firm-level decisions. Other mechanisms can generate similar predictions to those from the baseline model. In terms of persistence in firm-level import decisions, firms may obtain productivity gains from importing which increase the likelihood of importing from the same set of input sources in subsequent periods. Section V.A proposes a modified estimation procedurethataccountsforsuchproductivitygains. Inadditiontotheinterdependence in marginal costs, the interdependence across countries might also be inherent in the sunk costs through extended gravity. As in MSZ, firms learn about new markets from theirpreviousexperiencewithsimilarmarkets. Thecurrentframeworkcanbeadjusted to account for these extended gravity factors. Finally, although the baseline model focuses on the import side, Section V.B demonstrates an extension that incorporates the firm’s export decision. The extended model preserves the interdependence across locations while introducing complementarity betweenimportingandexportinginboththemarginalcostsandthefixedandsunkcosts. Though adding export platforms complicates the firm’s optimization problem, it does not require substantial modification to the estimation approach due to its flexibility andmildrestrictionsonthefirm’sbehavior. Thisisanimportantfeaturebecausefirms are likely to engage in the global economy through multiple channels. The next step is to expand the current framework to allow for other trade margins and provide a comprehensive picture of firm-level global supply chains. REFERENCES Ahn, JaeBin, Amit K Khandelwal, and Shang-Jin Wei. 2011. “The Role of IntermediariesinFacilitatingTrade.”Journal of International Economics,84(1):73–

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50 For Online Publication , Identification Appendix A1. Identification Assumptions ASSUMPTION 1: (Revealed preferences) Let om be firm i’s observed import set in it year t. Then om is the solution to it (cid:88) Lit (A1) maxE[π (b,b )+ δlπ (J b,J b)|Ω ] it it−1 it+l it+l it+l−1 it b∈Bit l=1 where J b denotes the optimal set in year t+l given that it chooses set b in year t. it+l ASSUMPTION 2: (Planning horizon) L ≥ 1. it ASSUMPTION 3: (Consideration set) A ⊆ B , where A = o ∪ {o ∪ j,∀j ∈/ it it it it it o }∪{o \j,∀j ∈ o }. it it it ASSUMPTION 4: (Information set) Z ⊆ Ω , where Z is a vector of observed coit it it variates. Essentially, Assumption 1 states a firm’s observed import decision in year t is optimal given its current information set. Assumption 2 imposes that firms are forward looking and plan at least one period in advance. Assumption 3 states that the deviations considered by researchers are also in the firm’s consideration set. Assumption 4 implies that the instrument variables used to create unconditional moment inequalities are known to the firms. A2. Proof and Discussion of Equation 12 LetΠ ≡ π (b,o )+ (cid:80)Lit δlπ (J b,J b)bethediscountedsumofprofits ibt it it−1 l=1 it+l it+l it+l−1 ifthefirmchoosesbinyeart. LetΠ ≡ π (o ,o )+ (cid:80)Lit δlπ (J (o ),J (o )). ioitt it it it−1 l=1 it+l it+l it it+l−1 it Then, ∀b ∈ B , we should have E(Π |Ω ) ≥ E(Π |Ω ).43 Recall that J b is it ioitt it ibt it it+l 43Notethatwekeepthesameimporthistoryonbothsidesoftheinequality. Ifwealsoallowforthedecision inyeart−1tobedifferentfromtheobservedpath,theinequalityisnolongervalid.

THE DYNAMICS OF GLOBAL SOURCING 51 the firm’s optimal choice in year t + l should it choose b in year t. It follows that E(Π |Ω ) ≥ E(π (b,b ) + (cid:80)Lit δlπ (J (o ),J (o ))|Ω ) as the second ibt it it it−1 l=1 it+l it+l it it+l−1 it it expectation is over the profits of the firm if it would choose b in year t but in the subsequent periods act as if it had chosen o instead. By transitivity of preferences, it E(Π |Ω ) ioitt it (cid:88) Lit = E(π (o ,o )+ δlπ (J (o ),J (o ))|Ω ) it it it−1 it+l it+l it it+l−1 it it (A2) l=1 (cid:88) Lit ≥ E(π (b,o )+ δlπ (J (o ),J (o ))|Ω ) it it−1 it+l it+l it it+l−1 it it l=1 Because of the one-period dependency of π , static profits for years t+l where l ≥ 2 it will be the same on both sides of the inequalities. Thus, ∀b ∈ B , equation A2 is it reduced to E(π (o ,o )+δπ (J (o ),o )|Ω ) it it it−1 it+1 it+1 it it it ≥ E(π (b,o )+δπ (J (o )),b)|Ω ) it it−1 it+l it+1 it it Thesamelogicappliesifthesunkcostinvestmentfullydepreciatesafterafinitenumber of periods. I impose the one-period dependency assumption for two reasons. First, allowing for a longer horizon would generate more loss of information, which is not ideal given the short panel data. Second, strong empirical evidence supports that the sunk cost investment depreciates quickly after the first period (Roberts and Tybout, 1997; Das, Roberts and Tybout, 2007). Thus, any bias created by the one-period dependency assumption would be minimal. Data Appendix B1. Variable Construction Wages Data on wages for the countries in my sample are downloaded from the ILO. I use reporteddataonmonthlywagesforthemanufacturingsector,dividedbythetotalnum-

52 ber of hours worked in a month. In a few occasions, a single country multiple reported values in the same year, which come from different survey data sources. To address this problem, I relied on the surveys’ description of reference group and methodology to ensure consistency across countries. The ILO does provide a harmonized series; however, many missing data would compromise the range of countries I can include. The ILO differentiates between employees and employed persons. In the main analysis, I use data for employees (wages data only for employees) but also conduct a robustness check using total work hours for each person employed. Moreover, I converted the wages in local currency to U.S. dollars using exchange rates from the Penn World Tables. I use official instead of purchasing power exchange rates, as the goal is to capture the differences in cost of production across countries. Finally, as in Eaton and Kortum (2002), I adjust hourly wages for human capital by multiplying wages in country j by exp−gHj where g = 0.06 is the return to education and H is the years of schooling in country j in the initial year (2000). I set g = 0.06, j which Bils and Klenow (2000) suggest is a conservative estimate. Data on schooling come from Barro and Lee (2013). Country Characteristics Data on language and contiguity come from the CEPII. Countries’ income bracket is based on World Bank classification and the World Development Indicators. I construct binary variables that take the value of unity if the import source does not share the correspondingcharacteristicswithChina. Inotherwords,whenlanguage = 1,Chinese j is not the official language in country j. Similarly, border = 1 implies country j and j China do not share the same border. The U.S. Census Bureau defines 10 categories of Advanced Technology Products (ATP) including (1) biotechnology (2) life science (3) opto-electronics (4) information and communication (5) electronics (6) flexible manufacturing (7) advanced materials (8) aerospace (9) weapons and (10) nuclear technology. I merge this list of products with HS codes at the six-digit level and group countries into those with a high share of ATP imports and those with a low share of ATP imports to proxy for the level of

THE DYNAMICS OF GLOBAL SOURCING 53 technology embedded in goods from each country. I use both U.S. and Chinese import data to construct the variable. Data on ATP imports in the United States are from the U.S. Census Bureau.44 The share of ATP imports is calculated with respect to total ATP imports and total imports. Let AT denote the measure of advanced technology level of country j in jt year t. I employ different approaches to construct this variable ImportAT (1) jt AT = jt ImportAT t ImportAT (2) jt AT = jt Import jt ImportAT , ImportAT , and Import denote the import values of ATP, total ATP jt t jt import, and total imports from country j in year t. The first measures compares the shares of ATP imports across countries, whereas the second measure compares the relative share of ATP imports versus other imports from the same country. The larger (2) AT is, the higher the likelihood that firms import ATPs if they import from country jt j. Input Tariffs I construct measures of firm-level input tariffs by computing average tariffs weighted by firm-level input imports. Let Z denote firm i’s total import value in year t, Z it ipt denote firm i’s import value of input p, and τ is the tariffs on input p in China.45 The pt firm-level input tariffs are defined as τ (1) = N−1 (cid:88) 1(Z > 0)τ it p it pt p (2) (cid:88) Z ipt τ = τ it Z pt it p 44ThelistofATPschangedovertime,thoughthebulkoftheproductsremainedinthelist. Iusethelistof importedATPsin2004. 45Input tariffs are downloaded from the World Integrated Trade Solution and are average tariffs across markets.

54 (3) (cid:88) Z ipt−1 τ = τ it Z pt it−1 p (4) (cid:88) Z ip0 τ = τ it Z pt i0 p (1)−(4) where N is the number of products and τ are average tariffs with different p it weights. The first one is unweighted, the second and third are weighted by current and lagged import values, and the fourth one is weighted by initial import values. One issue with this approach to measuring firm-level input tariffs is that we observe import values for only the years that firms imported, implying using observed import (4) values will lead to selection bias. The last measure of input tariffs, τ , relies on the it initialinputimportstructureandthusavoidstheendogeneityissue. Nevertheless,using only the initial year leads to a loss of observations because not every firm imported in thefirstsampleyear. Forthesereasons, IreplaceZ /Z –i.e., theshareofinputpover ipt it total input costs for firm i in year t–with firm i’s average share over the entire sample period. More specifically, for each input p, the average share for firm i is computed as Z ip = N−1 (cid:88) Z ipt . Z T Z i it t The final measure of firm-level input tariffs is (cid:88) Z ip τ = τ it pt. Z i p In a sense, the weight for the input tariffs is unchanging over time for each firm and hence the time-series variation comes solely from changes in input tariffs in China. B2. Descriptive Statistics TableB1reportsthecountryrankingbynumberofimportersin2000and2006forall industries. Thetop10countriesremainintheexactpositioninbothyears. Correlation between the 2000 and 2006 ranking for all countries is 0.94. Table B2 reports the growth rates between 2000 and 2006 for the sample of Chi-

THE DYNAMICS OF GLOBAL SOURCING 55 Figure B1. : Persistence in Import Status Note: Thisfigurepresentsthescatterplotoftheunconditionalprobabilityofimportingfromacertaincountry (x-axis)andtheprobabilityofimportingconditionalonhavingpreviousimportexperienceinthesamecountry (y-axis). Source: GeneralAdministrationofCustoms. Table B1—: Country Ranking and Number of Importers in 2000 and 2006 - All Industries Country Rank 2000 2006 Japan 1 12824 30204 United States 2 10999 27367 Taiwan 3 9212 21044 Germany 4 8239 20633 South Korea 5 7993 18841 Hong Kong 6 6307 13851 Italy 7 4660 11632 United Kingdom 8 4436 9946 France 9 4104 8680 Singapore 10 3682 7749 nese chemical producers in terms of domestic revenues, import values, and number of importers. As can be seen from the table, there was tremendous growth during this period. Domestic sales grew by 400%, imports by 500%, and the number of importers in 2006 was more than double that in 2000.

56 Table B2—: Growth Rates between 2000 and 2006 for The Chemicals Sample Domestic revenues Import values # Importers 2000 840 10 268 2006 4,239 60 618 Rate of change (%) 404.5 502.7 130.6 Note: This table provides nominal domestic revenues, import values, and number of importers for 2000 and 2006. The last row reports the percentage change between the two years. Monetary values are in billions of RMB. Table B3 provides descriptive statistics for the sample of chemical producers in the main analysis. Table B3—: Firm-Level Summary Statistics Mean Std. dev. Min. Max. Log domestic revenues 10.534 1.734 -0.169 16.341 Log import values 7.627 3.284 -4.794 15.201 Log export values 8.223 2.199 -4.110 13.722 Import status 0.173 0.378 0 1 Export status 0.312 0.463 0 1 Number of import markets 0.582 1.873 0 23 Number of export markets 2.764 6.523 0 71 State-owned 0.164 0.370 0 1 Private 0.327 0.469 0 1 Foreign 0.115 0.319 0 1 Joint venture 0.205 0.404 0 1 Note: Thistableprovidesthefirm-year-leveldescriptivestatisticsforthemainsample. Importvaluescapture the average total values that a firm imports in a year. A firm’s import status takes the value of one if a firms importsinthatyearfromanycountry. Theexportvariablesaredefinedinthesameway. Estimation Appendix C1. Estimating θ and S ijt To estimate the dispersion of technology, θ, and firm-country-year specific sourcing potential, S , I follow a modified version of the estimation procedure in AFT. Specifijt ically, from the share of imported intermediate inputs equation 4, we get X /X = ijt iht S /S . I assume that S = S –i.e., the domestic sourcing potential is constant ijt iht iht ht across firms in a year but varies over time. Taking log on both sides of the above

THE DYNAMICS OF GLOBAL SOURCING 57 Table B4—: Country List South Africa Australia Germany Malaysia South Korea Austria Hong Kong Mexico Spain Belgium Hungary Netherlands Sweden Brazil India New Zealand Switzerland Canada Indonesia Norway Taiwan Chile Iran Philippines Thailand Czech Republic Ireland Poland Turkey Denmark Israel Russia Ukraine Finland Italy Saudi Arabia United Kingdom France Japan Singapore United States Note: This table lists the source countries used in my analysis. Countries are ranked by the total number of importersfrom2000to2006andthetop40areincluded. (Forty-onecountriesareincludedinthelistduetoa tie.) equation (C1) logX −logX = logS −logS +(cid:15)x ijt iht ijt ht ijt where (cid:15)x is some unobserved firm-country-year-specific shock, assumed to be mean ijt independent of the countries’ sourcing potential. This term can also be considered as measurement error in the observed values of imported input shares. The firmcountry-year sourcing potential and shocks together are the residuals after regressing the dependent variable on a set of year fixed effects, which capture the time-varying domestic sourcing potential S .46 To get predicted values of S , I face two issues. ht ijt First, it is impossible to separately identify logS from (cid:15)x .47 Second, the sparsity ijt ijt of the import data at the firm-country-year level means I cannot recover S for all ijt possible pairs from equation C1. To address these problems, I employ the definition of the firm-country-year-specific sourcing potential–i.e. S = T (τmw )−θ–in combination with the information from ijt j ijt jt equationC1torecoverthepredictedvaluesofthesourcingpotential. Letλˆ denotethe t estimateddomesticsourcingpotentialforeachyeart,andξˆ = (logX −logX )−λˆ ijt ijt iht t 46AnimplicitassumptiontogetunbiasedestimatesoflogS ht isthatSijt isuncorrelatedwithS ht . 47OnecanmakeasimplifyingassumptionthatSijt=Sjt,meaningthesourcingpotentialisconstantacross firms. Nonetheless,underthisapproachwewillbeunabletoseparatelyidentifythosetermsfromthedomestic sourcing potential S , unless we further assume that S is constant across time and normalize this term to ht ht unity. In addition, the ability of sourcing potential to vary at the firm-country-specific level is consistent with thedatapatternsinTable2.

58 is the composite residual term from equation C1. I then regress that residual terms ξˆ on proxies for technology T , wage rates w , and variable trade costs τm. ijt j jt ijt (C2) ξˆ = β +g(XTβT)−θh(Xτ βτ)−θlnw +λ +ν ijt 0 jt ijt jt t ijt where XT is a set of technology proxies, including R&D expenditure and capital stock. jt Xτ is a set of controls to proxy for variable trade costs, which includes the firm’s ijt ownership type and size, distance, GDP, common language, contiguity, whether the country is landlocked, and GATT/WTO membership. g and h are two non-parametric functions to allow for flexible estimation of technology and trade costs. lnw is the log jt ofhumancapital-adjustedhourlywages.48 Inthefinalspecification, Ialsoincludeaset of years fixed effects, λ , to account for anytime time-varying factors that are common t across firms that can influence the trade elasticity (θ). By definition, the term ξ contains both the sourcing potential and the unobserved ijt component–i.e., ξ = logS +(cid:15)x . However, under the assumption that (cid:15)x is unijt ijt ijt ijt correlated with logS , it will not bias the estimates of βT, βτ and θ, though it will ijt increase standard errors.49 As a result, I can recover the values of sourcing potential for each firm-country-year pair as the predicted values in equation C2. The last component in the revenue change is θ, which is the coefficient on log wages in C2. Column 1 in table C1 reports the ordinary least squares results. In column 2, I follow AFT and instrument log wages with population to account for unobserved factors that are correlated with countries’ productivity. The IV specification implies that θ is about 1.99. The estimated values of θ and σ confirm that input sources are complementary in production as in AFT.50 C2. Alternative Procedure to Predict Sourcing Potential S ijt InsteadofpredictingS throughtwostepsasdescribedinSectionIV,Iproposeadifijt ferent procedure to back out S directly through the imported input share X /X . ijt ijt iht 48SeeAppendixB.B1foradetaileddescriptionoftheconstructionofhuman-capital-adjustedwagerates. 49These terms can be interpreted as either measurement error or expectational errors. As long as firms do notobservetheshocksbeforechoosingasourcingstrategy,thesetermswillnotbiasourestimatesinequation C2. 50(σ−1)/θ=1.52>1.

THE DYNAMICS OF GLOBAL SOURCING 59 Table C1—: Predicting Sourcing Potential OLS IV (1) (2) log hourly wage -0.28 -1.99 (0.06) (0.49) log R&D -0.04 0.65 (0.05) (0.20) logk -0.002 0.005 (0.0004) (0.002) Landlocked -0.57 0.24 (0.16) (0.28) GDP 0.07 0.26 (0.01) (0.06) log distance -0.69 -0.24 (0.04) (0.13) Observations 9341 9341 Adjusted R2 0.11 0.05 Note: ThistablereportsregressionresultsforequationC2inSectionIV. Column1showsOLScoefficientswhile column 2 shows results when the variable log hourly wage is instrumented by log population. Other variables arelistedinthemaintext. Sampleincludesthetop40popularsourcecountries. Standarderrorsinparentheses. Source: GeneralAdministrationofCustomsandNationalBureauofStatistics I maintain the assumption that S = S –i.e., the domestic sourcing potential is iht ht constant across firms but can vary across years. Additionally, S is mean independent ht of S –i.e., E(S |S ) = E(S ). As before, I assume there may be a multiplicative ijt ht ijt ht measurement error in the share of imported input over total inputs X , denoted by ijt (cid:15)x . We can also assume there is a multiplicative measurement error in the share of ijt domestic inputs X . In that case (cid:15)x is treated as the ratio of the two measurement iht ijt errors. X S ijt = ijt (cid:15)x X S ijt iht ht Next, suppose we run a linear regression of logX −logX on the set of independent ijt iht variables in equation C2: (C3) logX −logX = β +g(XTβT)−θh(Xτ βτ)−θlnw +λ ijt iht 0 jt ijt jt t Under the new specification, the estimated values of the year dummies λ will be t reduced by E(logS ), assuming E(log(cid:15)x ) = 0. If we restrict S to be constant ht ijt ht across time, then the constant coefficient β is affected. In either case, other coefficient 0 estimatesshouldstillbeconsistent,thoughthepredictedvaluesoflogS willbebiased ijt

60 by E(logS ). ht Because what we want to obtain is the predicted values for S , the log-linearized ijt model may not be ideal as lnE(S ) (cid:54)= E(lnS ). For that reason, I run a Poisson ijt ijt regression (cid:18) (cid:19) X (C4) ijt = exp β +g(XTβT)−θh(Xτ βτ)−θlnw +λ X 0 jt ijt jt t iht In principle, the Poisson regression allows us to include zeros on the left hand side. That said, recall the definition of sourcing potential: S = T (τmw )−θ. This means ijt j ijt jt S = 0 if either country-level technology, variable trade costs, or wages is 0. In ijt practice, this scenario seems implausible that any of these terms is actually zero. For this reason, I exclude observations with zero imported inputs. Note that the Poisson regression is still subject to the previous issue with a predicted value of S being ijt biased, now by a scale of E(S ). ht Table C2 reports results for different methods of estimating country-level sourcing potential. The first two columns are the baseline results reported in Section IV. The next two columns report results for equation C3 under a log-linearized model. As expected, except for the year dummies and constant term, the two sets of estimates are identical. C3. Sample Selection and Potential Data Issues Country list: Table B4 presents the list of all 40 countries included in the data. Though the firms in my sample imported from 96 countries, more than half of the countries had fewer than 20 importers during the sample period. To avoid sources with few observations, I included only the top 40 countries ranked by the number of importers. The main results are not affected by choosing a different cutoff point (see Figure C1). Processing firms: In China, there is a dual trade regime: ordinary trade and processing trade.51 Existing studies have documented that Chinese firms selecting into 51FormoreinstitutionalbackgroundabouttradingregimesinChina,seeManovaandYu(2012),Jarreauand Poncet(2012),BrandtandMorrow(2017),andManovaandYu(2016).

THE DYNAMICS OF GLOBAL SOURCING 61 Table C2—: Robustness Check - Predicting S ijt Residuals log X /X X /X j h j h OLS IV OLS IV Poisson IV Poisson (1) (2) (3) (4) (5) (6) log wages -0.299 -1.985 -0.299 -1.985 0.0137 -0.596 (0.0639) (0.478) (0.0639) (0.478) (0.0586) (1.252) R&D expenditure -0.0332 0.643 -0.0332 0.643 -0.0505 0.262 (0.0469) (0.196) (0.0469) (0.196) (0.0515) (0.693) logk -0.00168 0.00515 -0.00168 0.00515 0.000996 0.00335 (0.000380) (0.00196) (0.000380) (0.00196) (0.000371) (0.00529) landlocked -0.576 0.242 -0.576 0.242 -1.070 -0.793 (0.161) (0.284) (0.161) (0.284) (0.274) (0.580) GDP 0.0692 0.255 0.0692 0.255 0.0257 0.0967 (0.0145) (0.0542) (0.0145) (0.0542) (0.0156) (0.159) log distance -0.683 -0.246 -0.683 -0.246 -0.459 -0.304 (0.0448) (0.131) (0.0448) (0.131) (0.0421) (0.346) 2001 0.0610 -0.117 0.152 -0.0263 -0.154 -0.250 (0.142) (0.155) (0.142) (0.155) (0.143) (0.394) 2002 0.0814 -0.200 0.0846 -0.196 0.241 0.0733 (0.137) (0.162) (0.137) (0.162) (0.134) (0.411) 2003 0.259 0.235 0.216 0.193 -0.0937 -0.169 (0.133) (0.137) (0.133) (0.137) (0.137) (0.427) 2004 0.177 0.0287 0.435 0.286 0.545 0.420 (0.127) (0.138) (0.127) (0.138) (0.123) (0.489) 2005 0.112 0.233 0.0916 0.213 -0.604 -0.650 (0.130) (0.138) (0.130) (0.138) (0.141) (0.382) 2006 0.254 0.449 0.361 0.556 0.102 0.0605 (0.132) (0.148) (0.132) (0.148) (0.132) (0.411) Constant 5.413 4.956 0.287 -0.170 2.169 1.897 Observations 9341 9341 9341 9341 9341 9341 Adjusted R2 0.114 0.047 0.115 0.049 Pseudo R2 0.117 Note: This table provides estimation results for the country-level sourcing potential equation under different specifications. Columns1and2reportthebaselineresults. Columns3and4reportresultsforthelog-linearized model with log(Xijt/X iht ) on the left hand side. Finally, columns 5 and 6 report the estimation results for a Poisson regression with Xijt/X iht as the dependent variable. The independent variables are the same in all regressions. Incolumns2,4,and6,log populationisusedasIVforlog wages. Thelastequationisestimated viageneralizedmethodofmoments. Standarderrorsinparentheses.

62 processing trade make different sourcing choices from those engaged in ordinary trade (Koopman, Wang and Wei, 2012; Manova and Yu, 2012; Jarreau and Poncet, 2012; Wang and Yu, 2012). Several reasons can explain the difference in sourcing behaviors. First, the latter regime exempts from import duties on foreign inputs used for further processing and assembling and re-exporting. Processing firms are not allowed to sell in the domestic market. Apart from the import duty exemptions, other policies favor pure exporters, such as the attraction of foreign-invested enterprises, the promotion of processing trade enterprises and the establishments of free-trade zones (Defever and Rian˜o, 2012). There are potentially differences in foreign contracts, capacity and credit constraints, and lack of input flexibility in the assembling process between processing and other firms. Furthermore, the lack of import duties incurred by these firms is problematic because variation in input tariffs is used as an IV for the analysis in Section V.A For these reasons, I exclude firms that engage in processing trade from the sample. Trade intermediaries: BecauseIammatchingfirmsintheNBSdatawiththecustoms data, I exclude transactions conducted by intermediaries.52 However, some firms that are classified as non-importers in the data might import indirectly through trade intermediaries. Because the NBS data set does not report domestic firm-level transactions and import values, I cannot differentiate between non-importers and indirect importers.53 This misclassification can affect the sunk cost estimates in several ways. First, firms thatuseintermediariesmayhavemoreinformationabouttheforeignsourcingcountries and thus pay a lower sunk cost to directly import in subsequent periods.At the same time, firms that have access to foreign inputs may enjoy higher future productivity. Both channels increase the likelihood of importing in subsequent periods conditional on using intermediaries.54 Nonetheless, while the first one introduces an attenuation 52About 19.7% of firms in the customs data that exported chemical products between 2000 and 2006 are intermediaries. Thosefirmsaccountedfor24.7%oftotalimportvalues. 53Bai, Krishna and Ma (2017) are able to identify direct and indirect exporters based on the total export valuesreportedintheNBSdata–i.e., ifafirmreportsexportvaluesbutdoesnotappearinthecustomsdata, it is classified as an indirect exporter. Since import values are not reported, I cannot use the same method to identifyindirectimporters. 54Ahn,KhandelwalandWei(2011)findsuggestiveevidencethatoncesmallfirmsexportindirectlybyusing intermediaryservices,theycouldswitchtoexportingdirectly.

THE DYNAMICS OF GLOBAL SOURCING 63 bias, the second channel creates an upward bias in the sunk cost estimate. It is, therefore, unclear which direction of the bias would be. However, there are several reasons why this might not be a concern for my study. First, because I focus on country-specific sunk costs, the bias might not be severe if the countries from which firms indirectly import are not the same as those with which they directlytrade. Second, Ilimitthesampletothosethatimportedatleastonce, meaning thatthesampledoesnotcontainfirmsthatonlyindirectlyimportedfrom2000to2006. Yet some firms might indirectly import in the earlier years and then switch to direct importing later. To address this problem, I exploit the fact that intermediation is used mostly by small firms. For example, Ahn, Khandelwal and Wei (2011), Akerman (2018) and Blum, Claro and Horstmann (2010) show that smaller firms matched with intermediariestoavoidthecostofdirectexporting. Thus, Iconductarobustnesscheck that excludes firms with average sales in the bottom 25 percentiles. The new sunk cost estimate is slightly bigger, indicating that firms that use intermediaries may incur small costs of directly importing later. However, the difference in the two estimates is negligible. Intra-firm trade: Foreign firms in China might import from their parent countries andthusdonotpaythefullsunkcostofimporting. ThoughIdonotobservetheforeign suppliers and cannot identify whether a firm is purchasing from its parent company, I conduct a robustness check that excludes foreign firms from the main analysis. As expected, the sunk cost estimate is bigger, but not by a large extent. Additional Tables and Figures

64 Figure C1. : Robustness Checks - Sample Selection (a) Top20countries (b) Excludesmallfirms (c) Excludeforeignfirms Note: This figure illustrates the 95% confidence sets of the total costs to continuing versus new importers for different samples. The baseline result is presented by the red region. Panel a reports estimates for the top 20 countries, panel b reports estimates when small firms are excluded from the sample, and panel (c) reports resultswhenforeignfirmsareexcluded. Monetaryvaluesareinmillionof1998RMB.

THE DYNAMICS OF GLOBAL SOURCING 65 Table D1—: Productivity Gain - First Stage # countries # advanced-tech countries # high-income countries (1) (2) (3) (4) (5) (6) (7) (8) (9) L.Input tariffs 0.0706 -0.0290 -0.729 0.0691 -0.0285 -0.709 0.0580 -0.0222 -0.591 (0.00918) (0.00585) (0.121) (0.00883) (0.00565) (0.111) (0.00695) (0.00444) (0.0954) L.Input tariffs ×1(≥ med size) 0.145 0.142 0.116 (0.0110) (0.0107) (0.00839) L.Input tariffs × initial size 0.283 0.276 0.231 (0.0428) (0.0392) (0.0332) Log sourcing capacity 6.837 5.672 30.52 6.710 5.593 30.02 4.806 3.966 21.34 (0.338) (0.357) (1.612) (0.338) (0.357) (1.611) (0.271) (0.271) (1.259) # export markets -0.00313 -0.00134 -0.0103 -0.00353 -0.00157 -0.0116 -0.00539 -0.00331 -0.0208 (0.00249) (0.00243) (0.0114) (0.00241) (0.00236) (0.0111) (0.00209) (0.00200) (0.00959) Foreign affiliated 0.383 0.138 1.335 0.380 0.136 1.322 0.395 0.163 1.412 (0.0455) (0.0410) (0.196) (0.0444) (0.0400) (0.191) (0.0381) (0.0334) (0.163) State owned 0.0956 0.0393 0.320 0.0970 0.0435 0.332 0.0872 0.0420 0.299 (0.0496) (0.0477) (0.222) (0.0482) (0.0463) (0.215) (0.0413) (0.0397) (0.186) Initial size 0.229 0.0826 0.00354 0.229 0.0827 0.0270 0.199 0.0829 0.0593 (0.0241) (0.0276) (0.206) (0.0236) (0.0275) (0.192) (0.0209) (0.0221) (0.161) year=2002 -0.562 -0.538 -2.623 -0.549 -0.526 -2.563 -0.405 -0.384 -1.885 (0.103) (0.0976) (0.454) (0.101) (0.0958) (0.444) (0.0860) (0.0790) (0.377) year=2003 -0.556 -0.598 -2.627 -0.552 -0.587 -2.605 -0.377 -0.417 -1.788 (0.110) (0.101) (0.477) (0.108) (0.100) (0.471) (0.0922) (0.0827) (0.400) year=2004 1.253 0.994 5.599 1.228 0.982 5.505 0.888 0.694 3.935 (0.103) (0.100) (0.469) (0.101) (0.0981) (0.459) (0.0852) (0.0808) (0.385) year=2005 -0.258 -0.284 -1.174 -0.261 -0.285 -1.190 -0.163 -0.189 -0.758 (0.102) (0.0954) (0.445) (0.100) (0.0939) (0.438) (0.0841) (0.0768) (0.366) year=2006 0.609 0.393 2.634 0.589 0.382 2.555 0.441 0.275 1.893 (0.0972) (0.0896) (0.428) (0.0948) (0.0871) (0.417) (0.0801) (0.0726) (0.353) Constant -35.67 -29.10 -155.6 -35.01 -28.69 -153.1 -25.21 -20.42 -109.0 (1.689) (1.796) (8.239) (1.686) (1.795) (8.202) (1.353) (1.364) (6.419) Observations 4943 4943 4943 4943 4943 4943 4943 4943 4943 R-squared 0.461 0.452 0.484 0.462 0.454 0.485 0.390 0.397 0.419 F-statistic 102.8 76.81 83.15 101.5 75.98 81.95 87.33 66.28 71.95 Note: Thistableprovidesresultsonthefirst-stageestimationinTable8. Standarderrorsinparentheses.

66 Table D2—: Productivity Gain - OLS # countries # advanced-tech countries # high-income countries (1) (2) (3) (4) (5) (6) (7) (8) (9) L.import 0.0179 0.0252 0.0442 0.0180 0.0256 0.0446 0.0184 0.0259 0.0428 (0.00369) (0.00689) (0.0149) (0.00375) (0.00718) (0.0154) (0.00397) (0.00749) (0.0163) L.import × ×1(≥ med size) -0.00980 -0.0102 -0.0104 (0.00661) (0.00686) (0.00743) L.import × initial size -0.00612 -0.00620 -0.00575 (0.00305) (0.00315) (0.00339) Log sourcing capacity -0.0829 -0.0766 -0.0746 -0.0811 -0.0745 -0.0724 -0.0488 -0.0429 -0.0421 (0.0467) (0.0460) (0.0459) (0.0466) (0.0459) (0.0459) (0.0423) (0.0419) (0.0417) # export markets 0.00376 0.00377 0.00376 0.00377 0.00378 0.00377 0.00381 0.00382 0.00381 (0.000513) (0.000513) (0.000513) (0.000514) (0.000513) (0.000513) (0.000514) (0.000514) (0.000514) Foreign affiliated -0.00952 -0.0117 -0.0122 -0.00947 -0.0118 -0.0122 -0.00976 -0.0117 -0.0119 (0.0103) (0.0105) (0.0105) (0.0103) (0.0105) (0.0105) (0.0104) (0.0105) (0.0105) State owned 0.00925 0.00873 0.00820 0.00924 0.00872 0.00821 0.00949 0.00910 0.00871 (0.0146) (0.0146) (0.0147) (0.0146) (0.0146) (0.0147) (0.0146) (0.0146) (0.0147) Initial size 0.980 0.982 0.983 0.980 0.982 0.983 0.980 0.982 0.983 (0.00538) (0.00562) (0.00575) (0.00539) (0.00562) (0.00575) (0.00537) (0.00562) (0.00574) year=2002 0.0710 0.0699 0.0697 0.0707 0.0697 0.0695 0.0681 0.0672 0.0671 (0.0212) (0.0212) (0.0212) (0.0212) (0.0212) (0.0212) (0.0212) (0.0212) (0.0212) year=2003 0.183 0.181 0.181 0.183 0.181 0.181 0.180 0.178 0.178 (0.0203) (0.0202) (0.0202) (0.0203) (0.0202) (0.0202) (0.0202) (0.0201) (0.0201) year=2004 0.217 0.218 0.218 0.217 0.218 0.219 0.222 0.223 0.223 (0.0207) (0.0207) (0.0207) (0.0207) (0.0207) (0.0207) (0.0204) (0.0204) (0.0204) year=2005 0.425 0.424 0.424 0.425 0.424 0.424 0.423 0.422 0.422 (0.0192) (0.0192) (0.0192) (0.0192) (0.0192) (0.0192) (0.0192) (0.0192) (0.0192) year=2006 0.578 0.577 0.577 0.578 0.577 0.578 0.580 0.580 0.580 (0.0208) (0.0208) (0.0208) (0.0208) (0.0208) (0.0208) (0.0208) (0.0207) (0.0208) Constant 0.470 0.430 0.416 0.461 0.419 0.405 0.296 0.259 0.252 (0.238) (0.235) (0.234) (0.238) (0.234) (0.234) (0.215) (0.214) (0.213) Observations 4943 4943 4943 4943 4943 4943 4943 4943 4943 Adjusted R2 0.910 0.910 0.910 0.910 0.910 0.910 0.910 0.910 0.910 Note: ThistableprovidesOLSestimatesontheeffectofpastimportdecisionsoncurrentrevenues. SeeTable8forIVestimates. Standarderrorsinparentheses.

THE DYNAMICS OF GLOBAL SOURCING 67 Table D3—: Predicting Export Revenues Dep. variable Export revenues log domestic revenues 0.18 (0.00007) Export to other markets -28.89 (608.5) Landlocked -0.29 (0.001) GDP 0.11 (0.00003) GATT/WTO member=1 0.29 (0.001) log distance -0.23 (0.0001) Constant 6.41 (0.002) Observations 43598 Pseudo R2 0.15 Note: This table reports the PPML regression results of export revenues. The independent variables include log of domestic revenues, ownership types, whether firms export to other markets, destination characteristics suchasdistance,GDP,landlocked,andGATT/WTOmembership,andasetofyeardummies. Standarderrors inparentheses. Source: GeneralAdministrationofCustoms.andNationalBureauofStatistics Back-of-The-Envelope Calculations: Effect of A Temporary Trade War Atthispoint, Ihaveprovidedevidencefortheinterdependenceacrossimportsources and sunk entry costs of importing. To demonstrate how–in the presence of these two features–temporary trade policy changes might create long-lasting effects on firm-level sourcing decisions, I conduct the following thought experiment. Suppose there are two periods, t = 0,1. At the beginning of period t = 0, there is a trade war between China and the United States. I assume that because the trade war, Chinese firms exclude the United States from their import sets in year t = 0 but keep their decisions in other markets unchanged. While there would likely be immediate effects of the trade war, this assumption allows us to focus on its effects after the trade war. I investigate (1) the trade war’s direct effect on firms’ decisions in the United States in the second period and (2) its indirect effect on firms’ decisions in other countries in the second period. Intuitively, the direct effect will depend on the magnitude of the sunk cost of importing from the United States whereas sourcing relationships across

68 international markets will determine the indirect effect. Because the framework provides us with an incompletely specified structural model, we need to impose additional assumptions to estimate the effects of the trade war on firms’ decisions. In addition to the ”no immediate response” assumption stated above, I further assume that firms plan for only one period. Finally, there is a random fixed cost shock common across firms that import from the United States and the shock is big enough to rationalize the import decision of the least profitable firms.55 Under these assumptions, the firm’s decision to import from the United States after the trade war will solely depend on the relative size of the marginal revenue of the United States and its fixed and sunk costs. If the sunk cost of importing from the United States is big, the firm is likely to drop the United States from its import set in the second period. The firm’s decisions in other markets are more complicated, but we can draw a few conclusions. First, if a firm does not change its decision in the United States, it would not change its decision in other markets. The reason is that in period t = 1 after the trade war is over, importing from the United States becomes more costly but the relative ranking among all countries other than the United States remains the same. Second, whencountriesaresubstitutes, firmsmayreplacetheUnitedStateswithanew market. When countries are complementary, however, no firms will add a new market, even if they decide to drop the United States. I focus on firms that would import from the United States in t = 0 in the absence of a trade war.56 Furthermore, I fix the values of the fixed and sunk costs: γf = 1 and γs at three different values—0.1, 1.1, and 2.2—which roughly correspond to the lower bound, mid-point, and upper bound of the estimate on sunk cost. Table E1 reports the shares of incumbent importers that would switch their import status in the United States after the trade war at these different values of the sunk 55A more serious treatment of the error term is left for future research on counterfactual experiments in incompletely specified models. The exercise here simply provides a demonstration of the long-term effect of a hypothetical temporary trade policy change in the presence of spatial interdependence and sunk entry costs. Nonetheless,imposingpositiveshockimpliesthattheestimatedshareoffirmsthatwouldstopimportingfrom theUnitedStateswouldfallintoaconservativerangeoftheactualeffects. 56About 15% of the firms in my sample imported from the United States at some point during 2000-2006. Sincethemodelabstractsfromgeneralequilibriumeffects,firmsthatwouldnotimportfromtheUnitedStates int=0regardlessofthetradewarareunaffectedinthisthoughtexperiment.

THE DYNAMICS OF GLOBAL SOURCING 69 entry cost. In general, the effect is stronger in the earlier years, which results from the fact that firms grew bigger over time during this sample period and thus would be less affected by the trade war. As expected, the bigger the sunk cost, more firms drop the United States from their import set after the trade war has ended. At the lower bound (γs = 0.1), only 11.9% of firms that would have imported from the United States change their status in this country. However, this share quickly rises to 53.8% when I increase the sunk cost to 1.1 million RMB and 62% when sunk cost is at 2.2 million RMB. The large share of firms affected even after the trade war demonstrates the long-lasting effect of temporary trade policy changes. This outcome also confirms the model prediction that in a static model with no sunk cost, there would be minimal long-termeffectofatemporarytradewar, whereasinadynamicmodelwithsunkentry costs, the effect of a trade war could remain substantial even when the two countries normalize their trade relations. Table E1—: Direct Effect of Trade War (1) (2) (3) γs = 0.1 γs = 1 γs = 2.2 2001 14.3 62.3 68.8 2002 17.1 60.4 66.7 2003 19.2 66.4 72.8 2004 7.5 48.3 59.2 2005 10.0 49.8 56.9 2006 7.8 45.8 56.6 Average 11.9 53.8 62.0 Note: ThistablereportsthesharesoffirmsthatwoulddroptheUnitedStatesfromtheirimportsetinthesecond year if there was a trade war in the first period. The year corresponds to the first year after the hypothetical tradewar(t=1). ThesampleisrestrictedtofirmsthatwouldimportfromtheUnitedStatesint=0ifthere isnotatradewar. Source: GeneralAdministrationofCustomsandNationalBureauofStatistics I also explore how the firm’s second-period decisions in other markets are affected by the trade war in the first period. As mentioned previously, the third-market effects depend on the level of interdependence across countries. When countries are independent, the effect of the trade war will be contained to Chinese firm-level decisions in the United States market while the their decisions in other markets remain intact. However, when countries are either substitutes or complementary, the firm’s decision in other markets might also be altered as a result of the trade war.

70 Whencountriesarecomplementary,firmswouldnotadmitmorecountriesevenifthey stop importing from the United States. It is also possible that firms drop additional import sources if they decided to drop the United States. This happens when the synergy between the United States and other countries is large enough to cover the cost of importing from multiple countries, but without the United States, importing from the remaining markets might not be worth it. In other words, when firms cannot find substitutes for the United States, they are subject to higher marginal costs and lower scales, and thus cannot afford importing from other countries.57 In Table E2, I report the share of firms that would drop at least one market other than the United States from their import set after the trade war in the complementary case. Asexpected, afractionoffirmswouldstopimportingfromothermarketsbecause of the U.S.-China trade war. As sunk cost increases, the externality of the trade war on other markets also becomes bigger. At the lower bound of the sunk cost, only 6.9% of firms would change their decisions in third markets, whereas 47.4% of firms would alter their decisions at the upper bound of the sunk cost.58 The long-term effect on third markets of the temporary trade war results from both thesunkentrycostsandinterdependenceacrossimportmarketsandcannotbeobtained in previous models that do not incorporate both features in one coherent framework. A model with sunk costs alone would not generate third market effects without general equilibrium, whereas a static model that allows forinterdependence would overlook the dynamic costs of temporary trade policy changes. 57When countries are substitutes, firms may be able to replace the United States with a new country that they have not already imported from. In this case, it is unclear whether they will keep the remaining set of importsources. 58Ifweallowforfirmstomakeimmediateadjustmentsint=0,thereislikelytobeanincreaseinboththe share of firms that drop the United States and other markets in t=1, as the indirect effects happen in both thefirstandsecondperiods. Inthefirstperiod,asfirmscannotimportfromtheUnitedStates,theyalsodrop othermarkets(duetocomplementarity),whichincreasesthefuturecostsofimportingfromtheUnitedStates andothermarkets. Inshort,allowingforalongerplanninghorizonwouldpotentiallydampentheeffectsofthe tradewarwhereasallowingforintermediateresponseswouldamplifytheseeffectsthetemporarytradewar.

THE DYNAMICS OF GLOBAL SOURCING 71 Table E2—: Indirect Effect of the US-China Trade War on Third Markets (complementary Case) (1) (2) (3) γs = 0.1 γs = 1 γs = 2.2 2001 8.2 39.3 47.5 2002 9.1 47.5 53.5 2003 13.6 52.7 60.9 2004 4.0 35.5 46.8 2005 5.2 34.1 39.3 2006 4.2 32.4 43.0 Average 6.9 39.2 47.4 Note: ThistablereportsthesharesoffirmsthatwoulddropatleastanothermarketinadditiontotheUnited Statesfromtheirimportsetatthreedifferentvaluesofsunkentrycost. Theyearcorrespondstothefirstyear afterthehypotheticaltradewar(t=1). ThesampleisrestrictedtofirmsthatwouldimportfromtheUnited Statesint=0ifthereisnotatradewar. Source: GeneralAdministrationofCustomsandNationalBureauofStatistics Table E3—: Descriptive Statistics All Never Exiting New Continuing # advanced tech countries 2.181 1.017 2.691 5.547 6.787 (3.460) (1.974) (3.105) (4.254) (4.597) # high income countries 1.717 0.816 2.148 4.269 5.291 (2.771) (1.653) (2.532) (3.343) (3.780) # import countries 2.243 1.049 2.774 5.696 6.979 (3.577) (2.046) (3.218) (4.383) (4.843) Observations 42998 31128 615 4612 4312 Note: Thistablereportsthenumberofadvancedtechnologycountries,highincomecountries,andtotalnumber ofcountriesfromwhichanaveragefirmimports. Definitionsforadvanced-technologycountriesareprovidedin AppendixB.B1. Standarderrorsinparentheses. Source: GeneralAdministrationofCustomsandNationalBureauofStatistics Derivation of Equation 8 From equation 7 and the definition of Θ (Jm), the firm’s revenue when we add it it country j (j ∈/ Jm) is it (cid:20) σ 1 (cid:21)1−σ (cid:20) (cid:18) (cid:88) (cid:19)(cid:21)σ− θ 1 r (Jm∪j) = Y γ S +S iht it σ−1ϕ P ht ikt ijt it ht k∈Jm it

72 The marginal revenue of country j to firm i at the set Jm, for j ∈/ Jm, is then it it rm(Jm) ≡ r (Jm∪j)−r (Jm) ijt it iht it iht it (cid:18) (cid:19) = r (Jm) r (Jm∪j)/r (Jm) −r (Jm) iht it iht it iht it iht it (cid:18) (cid:19)σ−1 (cid:88) (cid:88) θ = r (Jm) ( S +S )/( S ) −r (Jm) iht it ikt ijt ikt iht it k∈Jm k∈Jm it it (cid:20)(cid:18) (cid:19)σ−1 (cid:21) (cid:88) (cid:88) θ = ( S +S )/( S ) −1 r (Jm) ikt ijt ikt iht it k∈Jm k∈Jm it it The derivations for rm(Jm) when j ∈ Jm are similar. ijt it it