Input Linkages and the Transmission of Shocks: Firm-Level Evidence from the 2011 Tohoku Earthquake

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Input Linkages and the Transmission of Shocks: Firm-Level Evidence from the 2011 Toh¯oku Earthquake Christoph E. Boehm, Aaron B. Flaaen, and Nitya Pandalai-Nayar 2015-094 Please cite this paper as: Boehm, Christoph E., Aaron B. Flaaen, and Nitya Pandalai-Nayar (2015). “Input Linkages and the Transmission of Shocks: Firm-Level Evidence from the 2011 Toh¯oku Earthquake,” FinanceandEconomicsDiscussionSeries2015-094. Washington: BoardofGovernorsofthe Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2015.094. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) 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 Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Input Linkages and the Transmission of Shocks: Firm-Level Evidence from the 2011 To¯hoku Earthquake∗ Christoph E. Boehm1 Aaron Flaaen2 Nitya Pandalai-Nayar1 1University of Michigan 2Federal Reserve Board of Governors October 22, 2015 Abstract Using novel firm-level microdata and leveraging a natural experiment, this paper provides causalevidencefortheroleoftradeandmultinationalfirmsinthecross-countrytransmission of shocks. Foreign multinational affiliates in the U.S. exhibit substantial intermediate input linkages with their source country. The scope for these linkages to generate cross-country spilloversinthedomesticmarketdependsontheelasticityofsubstitutionwithrespecttoother inputs. Usingthe2011To¯hokuearthquakeasanexogenousshock,weestimatethiselasticity forthosefirmsmostreliantonJapaneseimportedinputs: theU.S.affiliatesofJapanesemultinationals. These firms suffered large drops in U.S. output in the months following the shock, roughly one-for-one with the drop in imports and consistent with a Leontief relationship between imported and domestic inputs. Structural estimates of the production function for all firmswithinputlinkagestoJapanyielddisaggregatedproductionelasticitiesthataresimilarly low. Our results suggest that global supply chains are sufficiently rigid to play an important roleinthecross-countrytransmissionofshocks. JELCodes: F44,F23,E32,F14 Keywords: Multinational Firms, International Business Cycles, Business Fluctuations, ElasticityofSubstitution ∗Boehm and Pandalai-Nayar: University of Michigan Department of Economics Flaaen: Federal Reserve Board ofGovernors,20thSt. andConstitutionAve,NW,WashingtonDC20551,aaron.b.flaaen@frb.gov. Wewouldliketo thankAndreiLevchenko,KyleHandley,MatthewShapiro,andLindaTesarforvaluablecomments,suggestions,and support. We also thank our discussants Rob Johnson, Eduardo Morales, Joan Monras, and Sebnem Kalemli-Ozcan, aswellasseminarparticipantsattheIMF,Michigan,Stanford,FRB,Colorado,Washington,BU,DallasFed,FREIT- EITI, Barcelona GSE-SI, NBER SI-ITM, SED, FREIT -RMET and Johns Hopkins-SAIS for helpful comments and suggestions. This research has received research grants from the Michigan Institute for Teaching and Research in Economics(MITRE),forwhichweareverythankful. SupportforthisresearchattheMichiganRDCfromNSF(ITR- 0427889) is also gratefully acknowledged. Any opinions and conclusions expressed herein are those of the authors anddonotnecessarilyrepresenttheviewsoftheU.S.CensusBureau, theBoardofGovernors, oritsresearchstaff. Allresultshavebeenreviewedtoensurenoconfidentialinformationisdisclosed.

Thespillovereffectsoftradeandfinanciallinkageshasbeenapreeminenttopicininternational economicsinrecentdecades. Thelargeexpansionsintradeandforeigndirectinvestment(FDI)in the past twenty years have generated much discussion on whether they increase volatility (di Giovanni and Levchenko, 2012), increase comovement (Frankel and Rose, 1998; Burstein, Kurz, and Tesar, 2008) or lead to less diversified production and specialization (Imbs, 2004). Identifying the micro-foundations underlying the role of these linkages in the increased interdependence of nationaleconomiesischallenging. Advancedeconomiesarehighlyconnected,andmostvariables influencedbyanycandidatemechanismareoftencorrelatedwithotherdevelopmentsinthesource and destination countries. There is often little in the way of exogenous variation to isolate any particularmechanismfromahostofconfoundingfactors. Moreover,therequisitedatatoexamine theseissuesatthenecessarydetailanddisaggregationhavebeen,untilrecently,unavailable. This paper provides empirical evidence for the cross-country transmission of shocks via the rigid production linkages of multinational firms. The principal mechanism at work is not new; the idea of input-output linkages as a key channel through which shocks propagate through the economydatesbacktoatleastLeontief(1936)orHirschmann(1958). Twoadvancesinthispaper permit a new quantitative evaluation of the nature and magnitude of these linkages. First, we utilize a novel dataset that, for the first time, links restricted U.S. Census Bureau microdata to firms’ international ownership structure. This information permits a forensic focus on particular firms and their underlying behavior. Second, we utilize the March 2011 To¯hoku earthquake and tsunamiasanaturalexperimentofalargeandexogenousshockdisruptingtheproductionlinkages originatingfromJapan. We study the role of imported intermediate inputs in the transmission of this shock to the United States economy. Because disruptions to imports of final goods would be unlikely to affect U.S. production, we develop a new methodology for isolating firm-level imports of intermediate inputs. We show that the U.S. affiliates of Japanese multinationals are the most natural source of this transmission, due to their high exposure to imported intermediates from Japan. The scope for shocks to these imported inputs to pass through and affect the firm’s U.S. production depends on how substitutable they are with inputs from alternative sources. In other words, the role of 1

imported inputs in the transmission of shocks is governed by the elasticity of substitution with respecttodomesticfactorsofproduction. We estimate this elasticity using the relative magnitudes of high frequency input and output shipments in the months following the To¯hoku earthquake/tsunami. This proceeds in two steps. First, reduced form estimates corresponding to Japanese multinational affiliates on average show that output falls, without a lag, by a comparable magnitude to the drop in imports. These results suggest a near-zero elasticity of imported inputs. Second, we structurally estimate a firm-level production function that allows for substitution across different types of inputs. The structural estimation procedure we use is uniquely tailored to the experiment. In an initial period prior to the To¯hoku disruption, we infer information on the firm’s productivity and optimal input mix. Then, applying this production function to the period of the disruption, we estimate the elasticity parametersbasedonhowchangesinthefirm’sinputmixtranslateintochangesinoutput. Thisestimationstrategyhasanumberofattractivefeatures. Mostimportantly,itreliesonvery few assumptions. Direct estimation of the production function circumvents the many difficulties associated with specifying a firm’s optimization problem in the period after the shock. Second, it yields transparent parameter identification. This is an advantage over traditional estimation strategies as it does not suffer from omitted variables and endogeneity concerns arising from correlated shocks. Third,itallowsfortheestimationacrossdifferentsubgroupsoffirms. The structural estimates are broadly in agreement with the results from our reduced form exercise. For Japanese multinationals, the elasticity of substitution across material inputs is 0.2 and theelasticitybetweenmaterialinputsandacapital/laboraggregateis0.03. Fornon-Japanesefirms using inputs from Japan, the estimates of the elasticity of substitution across material inputs are somewhat higher, ranging from 0.42 to 0.62. While the high cost share and particularly low elasticity for Japanese affiliates explains their predominant contribution to the direct transmission of this shock to the U.S., the elasticity estimates for non-Japanese firms are still substantially lower than typical estimates used in the literature. We argue that the substantial share of intra-firm intermediatetradeimpliesgreatercomplementaritiesinaggregatetradethaniscurrentlyrecognized. There are a number of important implications for such low values of the elasticity of substitu- 2

tion. This parameter appears in various forms in a wide span of models involving the exchange of goods across countries. As discussed by Backus, Kehoe, and Kydland (1994) and Heathcote and Perri (2002) among others, this parameter is critically important for the behavior of these models and their ability to match key patterns of the data. Prior estimates of this parameter were based on highly aggregated data that suffered from concerns about endogeneity and issues of product composition.1 Reflecting the uncertainty of available estimates for this elasticity, it is a common practicetoevaluatethebehaviorofthesemodelsalongawiderangeofparametervalues. It is well known that a low value for this parameter (interpreted as either substitution between importedanddomesticgoodsinfinalconsumptionorasintermediatesinproduction)improvesthe fit of standard IRBC models along several important dimensions. In particular, the elasticity of substitutionplaysaroleintwohighlyrobustfailingsofthesemodels: i)atermsoftradethatisnot nearly as variable as the data, and ii) a consumption comovement that is significantly higher than thatofoutput,whereasthedatashowtheoppositerelativeranking.2 To understand the relationship between the elasticity and comovement, it is helpful to recall that these models generate output comovement by inducing synchronization in factor supplies, a mechanism that by itself generally fails to produce the degree of comovement seen in the data. Complementarities among inputs together with heterogeneous input shocks will generate direct comovement in production, augmenting the output synchronization based on factor movements. Burstein, Kurz, and Tesar (2008) show that a low production elasticity of substitution between importedanddomesticinputsreducessubstitutionfollowingrelativepricemovements,andthereby increases comovement. Johnson (2014) is a more recent and detailed treatment of this topic. It is also straightforward to see how a lower elasticity increases volatility in the terms of trade. When twoinputsarehighlycomplementary,deviationsfromthesteadystatemixareassociatedwithlarge changes in their relative prices. In the words of Heathcote and Perri (2002, page 621): “greater complementarityisassociatedwithalargerreturntorelativescarcity.” The estimates in this paper have implications for the role of trade in firm-level and aggregate 1Foraveryusefulcompendiumofthisresearchfromthisera,seeStern,Francis,andSchumacher(1976). 2Duetotherobustnatureoftheseshortcomings,Backus,Kehoe,andKydland(1995)refertothemasthe“price anomaly”and“quantityanomaly”respectively. 3

volatility. Other research has argued that firms can diversify risk arising from country specific shocksbyimporting(Casellietal.(2014))orthatfirmswithcomplexproductionprocessesofseveral inputs are less volatile as each input matters less for production (Koren and Tenreyro (2013)). Ontheotherhand,thereisawell-establishedfactthatcomplementaritiesandmulti-stageprocessing can lead to the amplification of shocks as in Jones (2011) and Kremer (1993). We discuss the potentialformeasuredamplificationinourcontextinSection4. Thispaperalsocontributestotheempiricalevidenceontheroleofindividualfirmsinaggregate fluctuations, emanating from the work of Gabaix (2011). Other related evidence comes from diGiovanni,Levchenko,andMe´jean(2014),whouseFrenchmicro-datatodemonstratethatfirmlevel shocks contribute as much to aggregate volatility as sectoral and macroeconomic shocks combined. Theso-calledgranularityoftheeconomyisevidentinourexercise;thoughthenumber of Japanese multinationals is small, they comprise a large share of total imports from Japan, and arearguablyresponsibleforameasurabledropinU.S.industrialproductionfollowingtheTo¯hoku earthquake(seeFigure3). The strong complementarity across material inputs implies that non-Japanese input use falls nearlyproportionately,therebypropagatingtheshocktootherupstream(anddownstream)firmsin the U.S. economy and abroad. Many suppliers were thus indirectly exposed to the shock via linkageswithJapaneseaffiliatesthathadi)highexposuretoJapaneseinputsandii)arigidproduction function with respect to other inputs. Network effects such as these can dramatically magnify the overall transmission of the shock (both across countries and within). And while such effects are commonlyunderstoodtoexist,weprovideuniqueempiricalevidenceofthemechanismsatwork. Asisthecasewithmostresearchbasedonanevent-study,careshouldbetakeningeneralizing the results to other settings. As argued by Ruhl (2008), the elasticity of substitution is necessarily tied to the time horizon and nature of shocks to which it is applied. More generally, one might worrythatthecompositionofJapanesetradeorfirmsengagedinsuchtradeisnotrepresentativeof tradelinkagesmorebroadly. Webelieveourresultsareinformativebeyondthecontextofthisparticular episode for two reasons. First, the features of Japanese multinationals that are underlying the transmission of this shock are common to all foreign multinational affiliates in the U.S.3 Sec- 3Intra-firm trade accounts for a large majority of the trade of Japanese affiliates. More generally, the intra-firm 4

ond,estimatescorrespondingtoallfirmsinoursamplealsoexhibitsubstantialcomplementarities, andasawholethesefirmsaccountforover70percentofU.S.manufacturingimports. The next section describes the empirical strategy and data sources used in this paper. Section 2 presents reduced form evidence in support of a low production elasticity of imported inputs for Japanesemultinationalaffiliates. InSection3,weexpandthescopeofparametersweidentifywith astructuralmodelofcross-countryproductionlinkages,andestimatetheparametersofthismodel across several firm subgroups. Section 4 discusses the implications of these estimates, and details issuesofaggregationandexternalvalidity. Thefinalsectionconcludes. 1 Empirical Strategy and Specification This section outlines the empirical approach of using an event-study framework surrounding the 2011To¯hokueventtoestimatetheproductionelasticityofimportedinputs. Wediscusstherelevant details of this shock, document the aggregate effects, and then outline the empirical specification forthefirm-levelanalysis. 1.1 Background TheTo¯hokuearthquakeandtsunamitookplaceoffthecoastofNortheastJapanonMarch11,2011. It had a devastating impact on Japan, with estimates of almost twenty thousand dead or missing (Schnell and Weinstein (2012)) and substantial destruction of physical capital. The magnitude of the earthquake was recorded at 9.0 on the moment magnitude scale (M ), making it the fourth w largest earthquake event recorded in the modern era.4 Most of the damage and casualties were a result of the subsequent tsunami that inundated entire towns and coastal fishing villages. The effectsofthetsunamiwereespeciallydevastatingintheIwate,Miyagi,andFukushimaprefectures. The Japanese Meteorological Agency published estimates of wave heights as high as 7-9m (23- 29ft),whilethePortandAirportResearchInstitute(PARI)citeestimatesofthemaximumlandfall shareofimportedintermediatesforallforeignaffiliatesintheU.S.is71percent. 4Since1900,thethreeearthquakesofgreaterrecordedmagnitudeare:the1960GreatChileanearthquake(magnitude9.5),the1964GoodFridayearthquakeinPrinceWilliamSound,Alaska(magnitude9.2);andthe2004Sumatra- Andamanearthquake(magnitude9.2). 5

heightofbetween7.9mand13.3m(26-44ft). Figure 1 shows the impact of the To¯hoku event on the Japanese economy. Japanese manufacturing production fell by roughly 15 percentage points between February and March 2011, and did not return to trend levels until July. Much of the decline in economic activity resulted from power outages that persisted for months following damage to several power plants – most notably the Fukushima nuclear reactor.5 Further, at least six Japanese ports (among them the Hachinohe, Sendai, Ishinomaki and Onahama) sustained damage and were out of operation for more than a month, delaying shipments to both foreign and domestic locations. It should be noted, however, that the largest Japanese ports (Yokohama, Tokyo, Kobe) which account for the majority of Japanesetrade,re-openedonlydaysaftertheevent. As expected, the economic impact of the event was reflected in international trade statistics, including exports to the United States. Figure 2 plots U.S. imports from Japan around the period of the To¯hoku event, with imports from the rest of the world for comparison. The large fall in imports occurs during the month of April 2011, reflecting the several weeks of transit time for container vessels to cross the Pacific Ocean. The magnitude of this drop in imports is roughly similar to that of Japanese manufacturing production: a 20 percentage point drop from March to April,witharecoverybyJuly2011. More striking is the response of U.S. industrial production in the months following the event. Figure 3 demonstrates that there is indeed a drop in U.S. manufacturing production in the months following the Japanese earthquake. Although the magnitudes are much smaller — roughly a one percentage point drop in total manufacturing and almost two percentage points in durable goods —theexistenceofameasurableeffectisclear.6 Though tragic, the To¯hoku event provides a rare glimpse into the cross-country spillovers following an exogenous supply shock. This natural experiment features many characteristics that are advantageous for this type of study. It was large and hence measurable, unexpected, and directly 5Forprecautionaryreasons,allnuclearpowerplantswereimmediatelyshutdownfollowingtheearthquake,and remainedlargelyofflineuntil2015orlater. Becausetheelectricityinfrastructureexistsontwoseparategrids(a60Hz tothesouthandwest,and50Hztothenorthandeast),thereductioninpowersupplyinNortheastJapanwasnoteasily remedied,andpoweroutagespersistedformonths. 6AttheleveloftotalU.S.GDP,bothDeutscheBankandGoldmanSachsrevised2ndquarterU.S.estimatesdown by50basispointsexplicitlyduetotheeventsinJapan. 6

affected only one country. On the other hand, the short duration of the shock presents a challenge formeasurementasitlimitstheavailabledatasetswithinformationattherequiredfrequency. 1.2 Data Severalrestricted-useCensusBureaudatasetsformthecoreofourfirm-levelanalysis. TheLongitudinal Business Database (LBD) collects the employment, payroll, and industry of all establishments operating in the United States, and is maintained and updated as described by Jarmin and Miranda(2002). Longitudinallinkagesallowtheresearchertofollowtheestablishmentovertime, and the annual Company Organization Survey (COS) provides a mapping from establishments to firms. Alloftheanalysisinthispaperwillbeatthefirm-level. The Longitudinal Foreign Trade Transactions Database (LFTTD) links individual trade transactions to firms operating in the United States. Assembled by a collaboration between the U.S. Census Bureau and the U.S. Customs Bureau, the LFTTD contains information on the destination (or source) country, quantity and value shipped, the transport mode, and other details from pointof-trade administrative documents. Importantly for this study, the LFTTD includes import and export trade transactions at a daily frequency, which is easily aggregated to monthly-level trade flows. Anumberofimportantpapershaveutilizedthisresource,suchasBernardetal.(2007)and Bernard,Jensen,andSchott(2006). We utilize two novel extensions to this set of Census data products. First, a new link between two international corporate directories and the Business Register (BR) of the Census Bureau provides information on the international affiliates of firms operating in the United States. These directories allow us, for the first time, to identify those U.S. affiliates part of a foreign parent company, as well as those U.S. firms with affiliate operations abroad. This information is an importantresourceforidentifyingthecharacteristicsofU.S.firmsaffectedbytheTo¯hokuevent. For informationonthesedirectoriesandthelinkingprocedure,seeFlaaen(2014)andAppendixB.1. The second novel data resource is a system to classify firm-level import transactions as intermediateorfinalgoods. Althoughintermediateinputtraderepresentsasmuchastwo-thirdsoftotal trade (see Johnson and Noguera (2012)), the LFTTD does not classify a trade transaction based 7

on its intended use. To overcome this limitation, we use information on the products produced by U.S. establishments in a given industry to define a set of products intended for final sale for that industry.7 Theremainingproductsarepresumablyusedbyestablishmentsinthatindustryeitheras intermediate inputs or as capital investment. Details on this classification procedure are available in Appendix B.2. In the aggregate, this firm-level classification procedure yields estimates of the intermediate share of trade that are consistent with prior estimates: 64 percent of manufacturing importsareclassifiedas“intermediates”in2007. In Appendix B.3.2 we outline methods to integrate geographic information on the severity of the earthquake to the Japanese locations of U.S.-based firms. Due to limitations in within- Japansupply-chainlinkages,however,weconditionoursampleonthisinformationforrobustness purposesonly. TheidealdatasettoevaluatethetransmissionoftheTo¯hokueventonU.S.firmswouldconsist of high frequency information on production, material inputs, and trade, separated out by geographic and ownership criteria. Information from the LFTTD on import shipments is ideal for these purposes. Census data on production and domestic material usage, however, is limited. The Annual Survey of Manufacturers (ASM) contains such information, but at an annual frequency andonlyforasubsetofmanufacturingfirms. Recognizingthechallengesofhigh-frequencyinformation on firms’ U.S. production, we utilize a proxy based on the LFTTD — namely the firm’s exportsofgoodstoNorthAmerica(CanadaandMexico). Theunderlyingassumptionofthisproxy isthatallfirmsexportafixedfractionoftheirU.S.outputtoneighboringcountriesineachperiod. Theadvantageofthisapproachistheabilitytocapturetheflowofgoodsataspecificpointintime. There are few barriers to North American trade, and transport time is relatively short. Moreover, as documented in Flaaen (2014), exporting is a common feature of these firms, of which exports to North America is by far the largest component. The disadvantage of this approach is that it conditions on a positive trading relationship between firms in the U.S. and Canada/Mexico. We willassessthequalityofthismeasureasaproxyforoutputinsection4.3.1.8 7Notethatproductsintendedforfinalsaleforagivenindustrymaystillbeusedasintermediatesforotherfirmsin adifferentindustry. Alternatively,such“finalgoods”canbesolddirectlytoconsumersforultimateconsumption. 8Anotherconsiderationwiththeuseofthisproxyiswhetheritmoreaccuratelyreflectsproductionorsales,asthe two are distinct in the presence of output inventories. In our case, this depends on whether the inventories are held 8

1.3 Basic Theory Before moving to our firm-level analysis, it is useful to describe the basic theory underlying the features of firm-level production that we estimate. The transmission of shocks within a firm’s productionchainisgovernedbytheflexibilityofproductionwithrespecttoinputsourcing. Rather than model these complex networks directly, the literature typically summarizes this feature with thewell-knownelasticityofsubstitutionwithinaC.E.S.productionfunction. Ouridentificationof this elasticity will rely on the relative impacts on output and imported inputs following the shock. ConsidertheC.E.S.productionfunction (cid:104) (cid:105) ψ x = (1−µ)ψ 1 [F D ] ψ ψ −1 +µψ 1 [IM] ψ ψ −1 ψ−1 (1) where output consists of combining a domestic bundle of factors F (e.g. capital and labor) with D a foreign imported input IM. The parameter µ reflects the relative weight on the input IM in production, conditional on prices and a given elasticity value. Suppose the firm purchases its inputs in competitive markets with prices p and p , respectively, and sells its good at price p . D M x Ourapproachinsection2willbetoestimatetheparameterψ governingthedegreeofsubstitution between these inputs, using information on the output elasticity with respect to imported inputs, ∂lnpxx ,inthemonthsfollowingtheshock. ∂lnpMM Thefirstorderconditionsimplythat F∗ 1−µ (cid:18) p (cid:19)ψ D = M , (2) IM∗ µ p D where F∗ and IM∗ denote the optimal quantities of inputs. We will show the theoretical foun- D dations underlying the intuitive result that a one-for-one drop in output with the fall in imported inputs implies an elasticity of zero. To do this, we make the following assumptions, all of which wewillrelaxtosomedegreeintheestimationframeworkinSection3: 1. Imported inputs shipments are disrupted, such that the firm receives a suboptimally low quantityofIM: IM < IM∗; in the U.S. or Canada/Mexico. Without further evidence, we interpret the proxy to be capturing some mix between productionandsales. Thestructuralestimationinsection3willallowforsuchamix. 9

2. The firm is unable to adjust domestic inputs F∗ or its price p after learning that it receives D x IM; 3. Thefirmdoesnotshutdown. Giventheseassumptions,thefollowingresultholds: Result1. Underassumptions1)to3): ∂lnp x 1 x = ∈ (0,1) (3) ∂lnp M IM 1+ (cid:0) IM∗(cid:1)ψ ψ −1 (cid:16) 1−µ (cid:17)(cid:16) pM (cid:17)ψ−1 IM µ pD foranyψ ∈ (0,∞). Proof. SeeAppendixA.1fordetails. An immediate implication of this result is that the output elasticity is unity only when ψ approacheszero.9 Inthiscase (cid:0) IM∗(cid:1)ψ ψ −1 → 0(recallthatIM < IM∗)andhencelim ∂lnpxx = IM ψ→0 ∂lnpMIM 1. Hence, observing a one-for-one drop in the value of output with the value of imported inputs, we infer that ψ is close to zero. It is also easy to show that conditional on a value for ψ ∈ (0,∞), the output elasticity in (3) is increasing in the parameter µ. That is, conditional on a given drop in theimportedinput,alargerweightonthisinputleadstoalargerpercentresponseinoutput. Ouruseofthenaturalexperimentiscriticalforobservingtheeffectsofsuboptimalinputcombinations (F∗,IM). To see this, suppose the firm could freely adjust F after learning it will D D receive IM < IM∗. Then, it would choose F such that FD = F D ∗ and the firm would con- D IM IM∗ tract one-for-one with the drop in imports. It is a well-known fact that constant returns to scale production functions in competitive environments lead to indeterminate firm size. This has the implicationthat: ∂ln(p x) ∂ln(p x) ∂ln(p F ) x x D D = = = 1. (4) ∂ln(p IM) ∂ln(p F ) ∂ln(p IM) M D D M In this case it is not possible to learn anything about ψ from the joint behavior of output and the value of intermediate inputs. We provide evidence below that firms did not significantly adjust 9Thereisasecondcasewhichwedonotexamine,whereψ →∞andp <p andthusthefirmonlyusesIM. M D Wediscardthisscenariobecausesuchafirmwouldnotshowupinourdata(i.e. thisimplieszeroU.S.employment). 10

their domestic labor force following the disruption, so that a constant F is indeed a reasonable D assumption in this simple framework. To be sure, there are a number of alternative frameworks where such behavior would not hold. We discuss some of these in Appendix A.1, and show that themappinglim ∂lnpxx = 1ismoregeneral. ψ→0 ∂lnpMIM 2 Reduced Form Evidence 2.1 Framework Our analysis of the production function (1) above demonstrates that a natural measure to evaluate the potential conduits of the To¯hoku shock to the United States would be the degree of reliance on Japanese imported inputs. This is best expressed as the firm’s cost share of inputs from Japan, and can be constructed in a Census year by taking Japanese imported inputs and dividing by all other inputs (which includes production worker wages and salaries, the cost of materials, and the cost of new machinery expenditures). Exposure to Japanese imported inputs is heavily concentrated among Japanese affiliates. In the year 2007, which is the closest available Census year, this cost share was nearly 22% on average for Japanese affiliates (see Panel A of Table 1), compared to just 1% for other firms. For more detail on the heterogeneity across and within these firm groups, we construct a density estimate of such an exposure measure for the Japanese affiliates and non-Japanese multinationals. The results, shown in Figure 4, show little overlap between thesedistributions: therearefewJapaneseaffiliateswithlowexposuretoJapaneseinputs,andfew non-Japanesefirmswithsubstantialexposure.10 We now estimate the relative impacts on imported inputs and output for the Japanese affiliates as a group. To do this, we implement a dynamic treatment effects specification in which a firm is defined as being treated if it is owned by a Japanese parent company.11 The effect on these firms can be inferred from the differential impact of the variable of interest relative to a control 10TheexposuremeasureusedinFigure4isfrom2010anddoesnotincludethecostofdomesticmaterialusage. 11WecouldhavealsousedathresholdofJapaneseinputusagefortheclassificationoftreatmentstatus. Doingso yieldsestimatesthatareverysimilar,whichisduetothepatternsevidentinFigure4. Wehavealsotriedconditioning onourgeographicinformation(i.e. thefirm-levelJapaneseMMIindex)indefiningtreatmentstatus. Theresultsare largelyunchangedfromthosewereporthere,andforthesakeofclaritywereportresultspertainingtothefullsample. 11

group, which soaks up common seasonal patterns and other demand-driven factors in the U.S. market. While there are a number of competing methodologies for this type of estimation, we use normalized propensity score re-weighting due to the relatively favorable finite-sample properties as discussed in Busso, DiNardo, and McCrary (2014), as well as for its transparent intuition. Consistent estimation of the average treatment effect on the treated requires the assumption of conditional independence: the treatment/control allocation is independent of potential outcomes conditional on a set of variables. As the average Japanese firm differs considerably from other firms in the data, we use other multinational firms – both US and non-Japanese foreign- as our baselinecontrolgrouppriortoreweighting. Tocomputethepropensityscoresforreweighting,we control for size and industry, which ensures the control group has a similar industrial composition and size distribution as our treated sample.12 Table 1 reports summary values for the sample, includingstatisticsonthebalancingprocedureusingthenormalizedpropensityscore. ThemagnitudeoftheshockforarepresentativeJapanesemultinationaliscapturedbytheeffect on total imported intermediate inputs at a monthly frequency.13 Including non-Japanese imported intermediates is important for applying the control group as a counterfactual, and the shares by source-country gives the necessary variation for identification: as shown in Table 1 the share of importedinputsfromJapanis70%ofthetotalforJapanesefirmsandonly3.5%fornon-Japanese multinationals. LetVM bethevalueofintermediateimportsoffirmiinmontht,afterremovinga i,t firm-specificlineartrendthroughMarch2011. Wefitthefollowingregression: 9 9 (cid:88) (cid:88) VM = α + γ E + β E JPN +u (5) i,t i p p p p i,p i,t p=−4 p=−4 where α are firm fixed-effects, γ are monthly fixed effects (with the indicator variables E i p p correspondingtothecalendar-monthssurroundingtheevent),andu isanerrorterm. Thebaseline i,t samplewillconsistofJanuary2009toDecember2011. WedenoteMarch2011ast=0. The β coefficients are of primary interest. The JPN is an indicator variable equal to one p i,t 12Using the predicted values (p) from the first stage regression, the inverse probability weights are 1 for the 1−p controlgroupand 1 forthetreatedgroup. Tonormalizetheweightssuchthatthetreatedfirmshaveweightsequalto p one,wethenmultiplyeachsetofweightsbyp. 13WeconsiderJapaneseandnon-Japaneseintermediateimportsseparatelyinsection3. 12

if the firm is owned by a Japanese parent company. Interacting these indicator variables with eachmonthofthepanelallowsforatime-varyingeffectofJapaneseownershiponafirm’soverall intermediateinputimports,particularlyduringandaftertheTo¯hokuevent. Theβ coefficientswill p estimatethedifferentialeffectoftheTo¯hokueventonJapanesemultinationalaffiliatesintheU.S., compared to the control group of non-Japanese firms. A useful interpretation of the {E JPN } p i,p variables is as a set of instruments that captures the exogeneity of imports during these months, reflecting the source-country share of imports from Japan as evident in Table 1. To evaluate the differential impact on production for Japanese firms, we simply replace the dependent variable in equation(5)withthefirm’sNorthAmericanexports,denotedVNA. i,t It is important to highlight that equation (5) is in levels. There are several reasons for doing so, as opposed to using log differences or growth rates. First, allowing for the presence of zeros is importantwhenthedataareatamonthlyfrequency,particularlygiventhemagnitudeoftheshock to imports for Japanese firms. The second reason is more conceptual. Because we are interested in calculating the average effect of these firms that represents (and can scale up to) the aggregate impact on the U.S. economy, it is appropriate to weight the firms based on their relative size. The levels specification does exactly this: the absolute deviations from trend will be greater for the biggerfirmsandhencewillcontributedisproportionatelytothecoefficientestimates.14 Wediscuss aggregationandweightedvsunweightedelasticityestimatesinsection4.1. InadditiontotheConditionalIndependenceAssumptionhighlightedearlier,theβ coefficients p arevalidestimatesofthemeaneffectforJapaneseaffiliatesonlyinsofarasthecontrolgroupisnot itselfimpactedbytheshock. ThisStableUnitTreatmentValueAssumption(SUTVA)impliesthat generalequilibriumeffectsorpeereffects(e.g. strategicinteraction)donotmeaningfullyeffectthe estimates. TheshareofimportedinputsfromJapanislowforthecontrolgroup,andthustheshock isunlikelytohaveameasurableeffectonimportedinputsasawhole. Wediscussthepotentialfor strategicinteractioninAppendixC.3. 14SeeAppendixC.6formorediscussion, aswellasresultsobtainedusingotherspecifications. Importantly, ina reducedsampleabstractingfromzeros,aweightedregressionusingpercentagechangesdirectlyyieldsestimatesthat areveryclosetothosepresentedhere. 13

2.2 Results: Total Manufacturing Sector The top panel of Figure 5 plots the β coefficients from equation (5) for the months surrounding p the To¯hoku event. Relative to the control group, there is a large drop in total intermediate input importsbyJapanesefirmsinthemonthsfollowingtheearthquake. Thedropinintermediateinputs bottoms out at 4 million USD in t = 3 (June 2011) and the point estimates do not return back to thepre-shocktrenduntilmontht = 7(October2011). More interesting are the results from panel B of Figure 5, which looks for evidence of the production/sales impact of this shock on Japanese firms via their North American exports. The differential time-path of N.A. exports also exhibits a substantial drop following the To¯hoku event, hitting a trough of 2 million USD below baseline in t = 2 (May 2011). The standard errors, which are clustered at the firm level, are themselves interesting. As made clear via the 95-percent confidencebandsonthepointestimatesofFigure5,thestandarderrorsincreasedramaticallyinthe months following the shock, a feature we interpret to reflect heterogeneous incidence and timing oftheshocks(aswellastherecoveries)fortheJapanesemultinationals. To gain a sense of the average percentage drops of these two data series for Japanese multinationalsasagroup,wetakethetwoplotsofthedifferentialdollaramountsfromFigure5anddivide bytheaveragepre-shocklevelforthesefirms(seeTable1). Theresults,plottedjointlyinFigure6, show the fraction below pre-shock trend levels for these firms, on average. There is a remarkable correlationbetweenthesetwoseries–wherebythereisessentiallyaone-for-onedropinoutputfor agivendropinintermediateimports. UsingthemappingfromResult1,thesereducedformresults suggestaproductionfunctionthatisessentiallyLeontiefintheimportedinput. Onepotentialconcernwiththeinterpretationoftheseresultsisseparatingouttheintermediate input channel with other channels, such as a direct “productivity shock” affecting the U.S. operations of Japanese affiliates. Separating an ownership channel from an imported input channel is difficult due to lack of substantial overlap evident in Figure 4: few Japanese firms have low input exposureandfewnon-Japanesefirmshavehighinputexposure. InappendixC.7wepresentresults using a binary response model, as one attempt to disentangle the defining features of the import andoutputdisruptionsduringthistime. 14

3 Structural Estimation of Cross Country Input Linkages TherelativemovementsofimportedinputsandoutputofJapanesemultinationalfirmspointtolittle substitutabilityofintermediateinputs. Thissectionexpandsouranalysisbystructurallyestimating the production function of firms affected by the To¯hoku shock. Unlike in the previous section, which used a set of instruments based on the differential import shares of Japanese intermediates,thisestimationreliesonleveragingthehighdegreeofexogenousvariationinJapaneseinputs comingfromtheTo¯hokuevent,whilealsoexpandingtheproductionfunctionunderstudy. Thisestimation serves multiple purposes. First, it is reassuring to find elasticities that are consistent with theheuristicevidenceimpliedbyourreduced-formresults,whenimposingaconventionalproduction function framework. Second, by adding further structure, we can distinguish two elasticities: onebetweenJapanesematerialinputsandothermaterialinputs,andanotherbetweenanaggregate bundleofmaterialinputsanddomesticcapital/labor. Finally,byusinganestimationprocedurenot relyingonacontrolgroupweobtainseparateestimatesforJapaneseandnon-Japanesefirms. 3.1 Framework Theestimationprocedurewillutilizeinformationfromtwodistinctperiods: thesixmonthspreceding and the six months following the March 11 event. The pre-period, which we denote by τ −1, yields information on the production function of the firm under profit-maximizing conditions. In the post-period, denoted τ, we do not impose that the firm is optimizing over its input use, due to the fact that shipments from Japan are to some extent beyond the control of the firm. We assume thatthefirm’stechnologyinanyperiodtisgivenbythenestedCESaggregate (cid:20) (cid:21) ζ x i,t = φ i µ i ζ 1 (cid:0) K i α ,t L1 i, − t α (cid:1)ζ− ζ 1 +(1−µ i )ζ 1 M i ζ ,t − ζ 1 ζ−1 , (6) where M i,t = (cid:16) ν i ω 1 (cid:0) m− i,t J (cid:1)ω ω −1 +(1−ν i )ω 1 (cid:0) mJ i,t (cid:1)ω ω −1(cid:17) ω ω −1 . (7) 15

In this production function x , K , and L denote the output, capital, and labor of firm i. The i,t i,t i,t variable M denotes an aggregate of intermediate inputs of materials sourced from Japan (mJ ) i,t i,t and materials sourced from all places other than Japan (m−J), including domestic materials. We i,t areinterestedinestimatingω andζ,whichparameterizethesubstitutabilitybetweenJapaneseand non-Japanesematerialsandthatbetweenthecapital-laboraggregateandtheaggregateofintermediate inputs. The parameters µ and ν are firm-specific weights and φ parameterizes the firm’s i i i productivity, all of which we assume are constant over such a short time horizon. Further, we assumethatthefirmismonopolisticallycompetitiveandfacesaCESdemandfunction (cid:18) (cid:19)1 Y ε px = i,t . (8) i,t x i,t As usual, Y is the bundle used or consumed downstream and serves as a demand shifter beyond i,t thecontrolofthefirm. 3.1.1 Pre-Tsunamiperiod Period τ corresponds to the period April-September 2011, and τ − 1 the period September 2010 - February 2011. We exclude the month of March 2011. In period τ − 1 the firm operates in a standardenvironment,choosingcapital,labor,andmaterialstomaximize px x −w L −R K −p−J m−J −pJ mJ i,τ−1 i,τ−1 τ−1 i,τ−1 τ−1 i,τ−1 i,τ−1 i,τ−1 i,τ−1 i,τ−1 subject to (6), (7), and (8). The firm takes all factor prices as given. Material prices pJ and i,τ−1 p−J are firm-specific to indicate that different firms use different materials. It is straightforward i,τ−1 toshowthatthisoptimizationproblemimplies α w L τ−1 i,τ−1 K = , (9) i,τ−1 1−α R τ−1 (cid:0) p−J (cid:1)ω m−J i,τ−1 i,τ−1 ν = , (10) i (cid:0) pJ (cid:1)ω mJ + (cid:0) p−J (cid:1)ω m−J i,τ−1 i,τ−1 i,τ−1 i,τ−1 16

(cid:16)(cid:16) Rτ−1 (cid:17)α(cid:0)wτ−1 (cid:1)1−α (cid:17)ζ Kα L1−α α 1−α i,τ−1 i,τ−1 µ = , (11) i (cid:0) PM (cid:1)ζ M + (cid:16)(cid:16) Rτ−1 (cid:17)α(cid:0)wτ−1 (cid:1)1−α (cid:17)ζ Kα L1−α i,τ−1 i,τ−1 α 1−α i,τ−1 i,τ−1 where (cid:104) (cid:105) 1 PM = ν (cid:0) p−J (cid:1)1−ω +(1−ν ) (cid:0) pJ (cid:1)1−ω 1−ω . i,τ−1 i i,τ−1 i i,τ−1 Wewillusetheserelationshipsinthestructuralestimationthatfollowsbelow. 3.1.2 Post-Tsunamiperiod At the beginning of period τ many firms’ production processes in Japan are disrupted. Obtaining the desired amount of shipments of materials from Japan may either be prohibitively expensive or simplyimpossible. Modelingfirmbehaviorinthisenvironmentthereforerequiresmodificationsto theprevioussetup. Onepossibilityistoassumethatthequantityofmaterialsthatfirmsobtainfrom Japan is exogenous and that firms freely choose non-Japanese materials, capital and labor. This optionisunattractivefortworeasons. First,duetoexistingcontractsitisunlikelythatafirmisable to adjust the quantities of non-Japanese materials, capital, and labor without costs in such a short timeframe. Oneremedywouldbetoaddadjustmentcoststothemodel. Althoughstraightforward, this approach would require us to estimate additional parameters. Second, and more importantly, the materials sourced from Japan (mJ ) may not be exogenous for every firm. Some suppliers i,t in Japan may have been unaffected by the earthquake and tsunami such that materials could be shipped as desired. Hence, using this approach would require us to distinguish between firms whose supply chains are disrupted and those whose are not. That is, we would have to classify firmsbasedonanendogenousoutcome. Forthesereasonswepreferanalternativeapproach,namelytoestimatetheproductionfunction without specifying the full optimization problem. We only assume that in period τ, firms operate the same technologies given by (6) and (7), and that no firm adjusts its capital stock such that K = K .15 Conditional on knowing the time-invariant features of the production function i,τ i,τ−1 15WehaveexploredrelaxingthisassumptiontoallowourmeasureofK tovaryacross{τ,τ −1}. Theresultsare quantitativelysimilar. 17

(φ ,µ ,ν ),wenextdescribeanestimationprocedurethatallowsustofindtheelasticityparameters i i i mostconsistentwiththeobservedinputchoicesandoutputevidentinthedata. 3.2 Estimation Recall that we use North American exports as a proxy for a firm’s output px x , with the underi,t i,t lying assumption that the former is proportional to the latter. We continue here in the same spirit, though we now make this assumption explicit. Let VNA be the value of North American exports i,t attimetanddefine VNA i,τ−1 κ = . (12) i px x i,τ−1 i,τ−1 Inwords,κ isthefractionoffirmi’sshipmentsexportedtoCanadaandMexicointhesixmonths i preceding the tsunami. We next make two assumptions that allow us to construct an estimation equation. First, we assume that a relationship analogous to (12) continues to hold in period τ, exceptforalog-additiveerroru . Thatis, i,τ lnVNA = lnκ px x +u . (13) i,τ i i,τ i,τ i,τ The second assumption is that E[u |X ] = 0 where X is a vector of all right-hand-side varii,τ i i ables. Setting the conditional mean of u to zero is a standard exogeneity assumption requiring i,τ that, loosely speaking, the error is uncorrelated with all right-hand-side variables. It rules out, for example, that in response to a fall in Japanese intermediate imports firms export a fraction of theirshipmentstoCanadaandMexicothatsystematicallydiffersfromκ . Weprovideevidencein i section4.3.1thatdemonstratesthatthisisareasonableassumption. Usingequation(6)wecanrewrite(13)as   ln (cid:0) V i N ,τ A(cid:1) = ln(κ i φ i )+lnpx i,τ (cid:20) µ i ζ 1 (cid:16) K i α ,τ L i 1 , − τ α (cid:17)ζ− ζ 1 +(1−µ i )ζ 1 (M i,τ ) ζ− ζ 1 (cid:21) ζ− ζ 1 +u i,τ . (14) Values for ν and µ are obtained from equations (10) and (11).16 Using (12), the intercept can be i i 16Afterconstructingµ accordingtoequation(11)weaveragebyindustrytoreducethelevelofnoise. i 18

constructedfromthepreviousperiod VNA i,τ−1 κ φ = . i i (cid:20) (cid:21) ζ px i,τ−1 µ i ζ 1 (cid:0) K i α ,τ−1 L1 i, − τ− α 1 (cid:1)ζ− ζ 1 +(1−µ i )ζ 1 (M i,τ−1 ) ζ− ζ 1 ζ−1 Noticethatκ andφ arenotseparatelyidentified. Understandardassumptions,wecanconsistently i i estimateequation(14)using,e.g.,nonlinearleastsquares. Theonlyparameterstocalibratearethe rentalrateofcapitalR andthecapitalshareinthecapital/laboraggregateα. Weestimatethetwo τ elasticities,ζ andω. Noticethatω appearsintheintermediateaggregateM asshowninequation i,τ N (cid:88) (7). Theestimates(ζ ˆ ,ωˆ)solve min (u )2. i,τ {ζ,ω} i=1 Why do we restrict the sample to the year surrounding the To¯hoku event? To understand this, recall that a principal difficulty of estimating production functions lies in unobserved inputs and productivity. Since both are unobserved by the econometrician, they are absorbed into the error term. However, because they are known to the firm, other input choices depend on them. Hence, right-hand-side variables and the error term will generally be correlated, rendering estimates inconsistent.17 Byrestrictingthesampleperiodtoasingle12-monthinterval,theassumptionofconstantfirm productivity seems appropriate. If productivity is constant, it cannot be correlated with the error term, thereby ruling out one of the concerns.18 The fact that the To¯hoku event was an unexpected shocknegatesmuchoftheconcernaboutendogeneityarisingfromunobservedinputs. Toseewhy, considerthecasewhenthefirmanticipatesaninputdisruptioninafutureperiod. Firmadjustment of unobserved inputs in expectation of this shock will impact input choices – leading to an endogeneity problem where inputs are correlated with the shock. Put simply, the unexpected nature of the To¯hoku event works towards equalizing the information sets between the econometrician and thefirmbecausefactorchoicesarenotaffectedpriortotheshockbeingrealized.19 17Thisproblemisdiscussedingreaterdetailin,forexample,Ackerberg,Caves,andFrazer(2006). 18Of course, the size and exogeneity of the shock also helps with this concern: any idiosyncratic productivity movementsduringthistimearesurelysubsumedbytheearthquake/tsunami. 19An unobserved input that could remain operative in our case is that of factor utilization. Since the scope for substantial adjustment along this dimension seems quite limited, we remain confident that our estimates would be robusttotheinclusionofthismissingingredient. 19

Before turning to the data we briefly discuss the intuition of parameter identification. Unlike other approaches to estimating elasticities of substitution (e.g. Feenstra et al. (2014)), our method does not rely on the response of relative values to a change in relative prices.20 In fact, in an econometricsense,ourapproachtreatsallinputsasindependent variables. A simple example illustrates how the parameters are identified. Consider the production function (6) and suppose that, for a particular firm, the initial period yields a value of (1 − µ) = 0.4. Theelasticityζ determineshowdeviationsfromthismeasureoftheoptimalinputmixbetweenthe intermediate aggregate M and the capital labor aggregate translate into measured output. Thus, i,τ if we observe comparatively fewer intermediates M , reflecting a different mix of inputs than i,τ that given by 0.4, we obtain an elasticity estimate for ζ that best matches the response in output. Becausetheestimatesforµ,ν,andκ φ arethemselvesfunctionsoftheelasticities,thisprocedure i i must iterate across the parameter space to find the estimate most consistent with the data. Similar reasoningappliesfortheidentificationoftheω elasticitybasedonrelativemovementsinJapanese materials, non-Japanese materials, and output. The estimates we obtain are the best fit across the firmsineachsample. 3.3 Connecting Model and Data Estimationofthemodelrequiresdataonemployment,Japaneseandnon-Japanesematerialinputs, exports to North America, and output prices for periods τ −1 and τ. Since data on firm-specific capital stocks are hard to obtain and likely noisy, we use equation (9) to construct it from firm payrollandasemi-annualrentalrateof7percentforperiodτ −1.21 Recallthatthecapitalstockis notadjustedoverthistimehorizonsothatK = K . Theparameterα iscalibratedto1/3.22 i,τ i,τ−1 Quarterly employment information comes from the Business Register, which we adjust to reflect the average value over the 6 month periods we study, as they do not align with the quarters 20Weobservelittlesystematicvariationinprices(seeappendixC.4),andsothisapproachseemsmoreappropriate inthissetting. 21Thiscomesfromassumingarealinterestrateof4percent, anannualdepreciationrateof10percent, andthen adjustingforasemi-annualfrequency. Theestimatesareinsensitivetoalternativevaluesoftherentalrate. 22In principle it is possible to construct a firm-specific value for α, using value-added information available in a censusyear. Wearecurrentlyexploringthefeasibilityofthisoption. 20

defined within a calendar year.23 As discussed in earlier sections, the LFTTD contains firm-level dataofJapaneseimportsandNorthAmericanexports. Fornon-Japanesematerialinputs,wewould ideallycombinethenon-Japaneseimportedmaterialswithinformationondomesticmaterialusage for these firms. As information on domestic material inputs is not available in Census data at this frequency, we utilize information on the total material expenditures from the Census of Manufacturers(CM)toconstructafirm-levelscalingfactortogrossupnon-Japaneseintermediateimports. Put differently, we impute non-Japanese material inputs from non-Japanese input imports. For eachfirm,weconstructthescalingfactoras PMM −pJmJ i i i i (15) p−Jm−J i i from the latest CM year. Because the closest available CM year is 2007 in our data, there is some concern about missing or outdated information for this factor. We mitigate this by using industryspecificmeansformissingvalues,andwinsorizinglargeoutliersatthe90th/10thpercentiles. Regarding information on prices, the LFTTD records the value and quantity of each trade transaction (at the HS10 level), and thus it is possible to construct the associated price, or “unitvalue”ofeachshipmentdirectly.24 Aggregatinguptheseshipmentsintoafirm-monthobservation iscomplicated,ofcourse,bythedifferingquantityunits. Lackinganybetteralternative,wesimply averagethetransactionpricesusingthedollarvalueofeachtransactionasweights. Finally, we restrict the sample of firms to those that have regular imports from Japan and non-Japan over the periods we study, as well as regular North American exports.25 While this substantially limits the number of firms in each sample, the shares of trade represented by these firmsineachcategoryremainsveryhigh(seeTable2). We obtain standard errors using bootstrap methods, which also allow us to account for the uncertainty implied by the imputation of non-Japanese material inputs. We draw randomly with replacement from our set of firms to construct 5000 distinct bootstrap samples. For each of these 23Specifically: L = 1Emp + 1Emp + 1Emp andL = 1Emp + 1Emp . τ−1 6 2010Q3 2 2010Q4 3 2011Q1 τ 2 2011Q2 2 2011Q3 24Those transactions with missing or imputed quantity information are dropped. Future efforts will evaluate whetheritispossibletorecoverthequantityvaluesfrompriortransactiondetails. 25Specifically,wedropanyfirmthathasmorethan3monthsofzerosforanyofthesevalues,inperiodτ −1orτ. 21

samples,thenon-Japanesematerialsshareisimputedasdescribedabovepriortoestimation. 3.4 Summary of Results The results of the estimation are shown in Table 2. The elasticity between material inputs for Japaneseaffiliatesis0.2,whiletheelasticitybetweentheaggregatematerialinputandcapital/labor is0.03. Together,theseestimatesareindeedconsistentwiththereduced-formevidenceforthe(ψ) elasticity from section 2.2. The relative magnitudes are also intuitive: while Japanese imported inputs are strong complements with other material inputs — consistent with the high share of intra-firm transactions comprising this trade — there is even less scope for substitution between materialinputsanddomesticcapital/labor. The estimation procedure also allows us to estimate these elasticities for two samples of non- Japanese firms: non-Japanese multinationals and non-multinational firms. While the estimates for theζ elasticityareindeedveryclosefortheseothersamples,theelasticityestimatescorresponding to material inputs are higher, at 0.6 and 0.4 respectively. The lower share of intra-firm imports from Japan for the non-Japanese multinationals aligns with the argument that this type of trade is the key source of non-substitutability in the short-run. On the other hand, the low estimates for non-multinational firms, which have essentially zero intra-firm imports, may point to other mechanisms at work beyond the role of intra-firm trade. More generally, however, the estimates fortheseparametersareallsignificantlylowerthanwhatiscommonlyassumed(typicallyunityor higher)intheliterature. Although the number of firms included in this estimation is small (550 firms in total across the three subgroups), they account for a large share of economic activity in the United States. Looking at their combined share of total trade, these firms account for over 80% of Japanese intermediate imports, 68% of non-Japanese intermediate imports, and well over 50% of North American exports. Such high concentration of trade among relatively few firms is consistent with otherstudiesusingthisdata(seeBernardetal.(2007)). 22

4 Discussion The structural estimates of the model are broadly in agreement with the evidence in section 2.2: imported inputs are strong complements with other inputs in production. The rigidity of the productionfunctionformultinationalfirmsinparticularislikelyduetoi)thehighdegreeofintra-firm trade in what is presumably highly specialized inputs, and ii) a high-degree of supplier concentration. Ourresultshaveanumberofimportantimplicationsforhowweshouldthinkaboutmultinationalfirms,aswellasaggregatetopicssuchasvolatilityandbusinesscycleco-movement. 4.1 Aggregation Before relating our estimates to macroeconomic topics, it is necessary to discuss aggregation. Indeed, in any study utilizing micro-level estimates to inform macro-level objects of interest, the details of aggregation and heterogeneity are of critical importance. Work by Imbs and Me´jean (2015)arguesthatimposinghomogeneityacrosssectorswhenestimatingconsumptionelasticities can be overly restrictive, creating a heterogeneity bias which can be quantitatively large. In our case one could discuss aggregation along various dimensions: across products, industries, firms, andsoon. Weexaminetheeffectsofproduct-levelaggregationinAppendixC.2. Aprimaryconcernishowtotranslatetheresultsfromthefirm-levelsubsamplesintoestimates thatwouldpertaintomacro-orientedmodels. Asafirststep,thefinalcolumninTable2showsthe elasticityestimateswhenaggregatingacrossallfirmsinthesample. Theresultsareconsistentwith the estimates by subgroup, suggesting substantial complementarities across inputs. All estimates in Table 2, however, correspond to the average across firms in each group, and do not take into account heterogeneity in firm size within the groups. It is relatively straightforward to modify our estimation procedure to weight firms according to their relative size.26 We report the results from this modified estimation in Panel B of Table 3. When comparing the results to those in Table 2, it isevidentthattheweightedestimatesarenotsubstantiallydifferentthantheunweightedestimates. Althoughthesamplesoffirmscomprisingtheseestimatesdonotamounttothetotalmanufacturing 26Since the appropriate measure of size in our context is output, we follow our convention and use the relative amountsofNorthAmericanexportsintheperiodbeforetheshockastheweights. 23

sectoroftheUnitedStates,theydoaccountfortheconsiderablemajorityofU.S.trade. 4.2 Implications The rigid production networks of foreign-owned multinationals will have direct consequences on destination and host economies. Previous literature has hypothesized that input linkages could generate business-cycle comovement, but supportive empirical evidence has been difficult to find. Thispapercanbeseenasafirststepinestablishingempiricalevidenceforacausalrelationshipbetween trade, multinational firms, and business cycle comovement. In a companion paper (Boehm, Flaaen, and Pandalai-Nayar (2014)), we evaluate the quantitative importance of such complementaritiesofimportedinputsbymultinationalaffiliates. Whenseparatelyaccountingforintermediate input trade by multinationals and traditional trade in final goods, the model distinguishes between theproductionelasticityofimportedinputsandthetraditional“Armington”elasticityusedtobundle together international goods for consumption. The complementarities in import linkages by multinationalsincreasesvalue-addedcomovementinthemodelby11percentagepointsrelativeto abenchmarkwithoutsuchfirms. This model shares similarities with several other existing models, particularly Burstein, Kurz, and Tesar (2008). A key advantage of Boehm, Flaaen, and Pandalai-Nayar (2014), however, is a tight link to Census data for matching other features of multinationals and trade. Johnson (2014) alsolooksattheroleofverticallinkagesoncomovement,butappliesgreaterinput-outputstructure on the model. Such features will generate increases in value-added comovement in his model, the magnitude of which becomes significant only when the elasticity of substitution among inputs is sufficiently low. Other work also identifies multinationals as a key source of the transmission of shocks: Cravino and Levchenko (2015) demonstrates that foreign multinational affiliates can accountforabout10percentofaggregateproductivityshocks.27 The low value for ω indicates the presence of spillovers beyond the immediate effect from Japan. That is, imports from non-Japanese locations are lower as a result of the shock in Japan28, 27Of course, shocks can be passed through to affiliates through other means as well. See Peek and Rosengren (1997)andPeekandRosengren(2000)forthecaseofU.S.affiliatesfromJapan. 28SeeAppendixFigureA2,whichreplicatesFigures5(PanelA)and6,butonlyfornon-Japaneseimports. 24

and we would presume this applies to suppliers within the United States as well. Specifically, upstream suppliers (in countries other than Japan as well as within the U.S.) were affected indirectly via their exposure to those firms with direct exposure to Japanese inputs, combined with the rigidity of their production with respect to those inputs. Downstream suppliers that rely on the inputs from the disrupted firms would likewise be adversely affected. The presence of such spilloverscombinedwiththelargenetworkofinputlinkagescanindeedmagnifythetotaleffectof the transmission of the shock to the U.S. market. Such effects are also evident in a related paper, Carvalho, Nirei, and Sato (2014), which finds large spillovers in both upstream and downstream firmsinJapanfollowingthe2011earthquake. Anotherbranchofliteratureonthediversificationofriskhasstudiedwhetherfirmsusingcomplex production structures with several intermediates could be less volatile (Koren and Tenreyro (2013)). Kurz and Senses (2013) establish that firms with substantial imports and exports have lower employment volatility than domestic firms in the medium to long term, which they attribute partly to the diversification of risk.29 The key result in this paper points to a possibly overlooked fact: theextentofthebenefitsfromdiversificationdependsheavilyonthesubstitutabilityofinputs. Conditional on a given number of inputs used in production, a firm will likely experience greater volatility if each input is key to the production process and inputs are subject to heterogeneous shocks.30 Conceptually,anincreaseintheuseofimportedinputsshouldnotbeviewednecessarily as diversification. A fragmentation of production can lead to an increased supply chain risk that is an important counterweight to whatever efficiencies such complex input sourcing might afford, particularlywhentheproductionelasticitiesarelow. Therigidproductionnetworksofmultinationalfirmsalsoinfluencesourunderstandingofwhy firms segment production across countries. In a related paper, Flaaen (2014) shows that despite the presence of substantial and complex import linkages with the source country (consistent with a vertical framework of FDI), the motive for multinational production appears to be to serve the 29AninterestingresultfromKurzandSenses(2013)isthatfirmsthatonlyimportareactuallymorevolatilethan thedomestic-onlybenchmark. 30KrishnaandLevchenko(2014)outlinetheoreticalresultsshowingthatforagivenelasticityvalue(intheircase, Leontief),volatilityinoutputperworker shouldbeactuallydecreasinginthenumberofinputsused. Aninteresting extensionwouldbetolookatresultsfortotaloutput. 25

domestic market (consistent with the horizontal framework of FDI). The result could be called “horizontal FDI with production sharing.”31 Evidence of strong complementarities in this production sharing, however, presents a puzzle. Why does the firm replicate only select portions of the supply chain, considering the penalties for disruptions and mismatched inputs are so great? It is perhaps the case that the segments of the production chain that remain in the source country have a location-specific component that is not easily transferable when the firm moves production abroad.32 Agreaterunderstandingofthesesourcingdecisionsisanareaforfutureresearch. 4.3 Robustness 4.3.1 Mis-measurementofFirmProduction AnaturalconcernwithouranalysisistheuseofN.A.exportsasaproxyforfirm-levelproduction. Perhaps it is the case that export shipments fall disproportionately more than domestic shipments following a shock to production. If this were true, the N.A. exports would indeed be a poor proxy forproduction,anditsusefulnessinevaluatingaproductionelasticitysubstantiallycompromised. To evaluate this concern, we narrow our study to the automotive sector, which has data on production,sales,andinventoryatamonthlyfrequency. UsingtheWard’selectronicdatabank,we obtainplant-levelinformationonproduction,andmodel-lineinformationoninventoryandsales.33 Thespecificationisidenticaltoequation(5),wherethedependentvariableisnowQ : production jit ofplantj offirmiinmontht. TheJapanesemultinationalfirmsare,inthiscase,thoseautomakers withplantslocatedinNorthAmericabutwhoseparentcompanyisheadquarteredinJapan.34 Figure 7 shows the results, where we once again divide by pre-shock levels to gain a sense of the percentage effects of these changes. Relative to their U.S. counterparts, Japanese automakers intheUnitedStatesexperiencedlargedropsinproductionfollowingtheTo¯hokuevent. Production bottomedoutinMayof2011—twomonthsaftertheevent—atalmost60percentbelowtrend.35 31Ramondo,Rappoport,andRuhl(2015)isanotherexamplearguingforamorenuancedframeworkforMP. 32The model of knowledge sharing in Keller and Yeaple (2013) is one attempt to analyze the dynamics between suchtransfersbeingaccomplishedinembodied(intra-firmtrade)ordisembodied(directcommunication)form. Alternatively,domesticcontentrequirementsmayprovideincentivestoproduceinputsinonelocationoveranother. 33AppendixC.10detailsfurtherfeaturesofthisdataandexplainshowthesamplewasconstructed. 34ThesefirmsareHonda,Mitsubishi,Nissan,Toyota,andSubaru. 35The average monthly plant-level production at these firms during December 2010 through February 2011 was 26

The point estimates return to a level near zero in September of 2011, implying that the shock affected production for nearly 6 months.36 We interpret these results to be largely supportive of theresultsobtainedusingtheexports-basedproxyforproduction. Thepercentagedropsinthetwo series are remarkably similar: a trough of 59% at t = 2 in the automotive data vs 53% at t = 2 using the proxy. We conclude that, at least for this exercise, the proxy appears to be providing valuableinformationonafirm’sU.S.productionbehavior.37 4.3.2 OtherRobustnessWork We discuss a number of other results and extensions to this work in the online appendix. We exploreevidenceforinputinventoriespriortotheshock,evidenceforproduct-levelheterogeneity, movementsinotherdomesticinputs,importpricesmovements,andexportsbehaviorbacktoJapan. 4.4 External Validity Finally, we discuss the external validity of this result. The exogenous variation we use to identify this elasticity is tied to a particular event in time, making generalization subject to some caveats. On the other hand, there are few, if any, estimates of this parameter in the existing literature. The critical question is whether the mechanisms underlying the elasticity estimates are operative beyondthecircumstancessurroundingthiseventstudy. The pattern of strong intermediate input linkages with the source country is not restricted to Japanese affiliates only. As shown in Flaaen (2014), over 45 percent of the imports for all foreign multinationalaffiliatesaresourcedfromthecountryoftheparentfirm. Thecostshareofimported intermediatesfromthesourcecountryis0.12forallforeignaffiliates,whichislowerthanthe0.22 for Japanese affiliates but still much larger than the representative importing firm in the United about12,200unitsamonth. ThemagnitudeofthedropinMaywas-7200units. 36Wedescribeadditionalresultsonthebehaviorofinventories,sales,andproductioninJapaninAppendixC.3. 37In addition, one might be concerned that the N.A. exports series may be contaminated with Japanese imports whose country of ultimate destination is Canada/Mexico (a.k.a “in-transit shipments” – imports to Canada/Mexico via U.S.). These shipments should not be picked up in the reporting systems underlying the LFTTD. According to section30.2(d)(1)oftheU.S.CodeofFederalRegulations,“In-transitshipmentsofgoodsfromoneforeigncountry toanotherwheresuchgoodsdonotentertheconsumptionchannelsoftheUnitedStatesareexcludedfromfilingthe ElectronicExportInformation(EEI).”Additionally, theArmyCorpsofEngineershassuspendedtherequirementto filetheForm7513,ShippersExportDeclaration(SED)forIn-transitGoodsleavingtheUnitedStatesviavessel. 27

States. The cost share of all imported inputs is actually quite close: 35 percent for Japanese affiliatesvs32percentforallforeignaffiliates. A related concern is whether the estimates for Japanese affiliates are driven solely by the automotive sector. The ideal check would be to run industry-by-industry subgroup estimates for the elasticities, thereby generating heterogeneity that could be assessed relative to expectations. Unfortunately, the small number of firms applicable for this analysis, combined with disclosure requirementsassociatedwithCensusBureaudatausage,preventsthisdegreeofdetail. Instead,we addressthisconcernbysplittingthesampleintoamotorvehicleandnon-motorvehiclesubsample. We do this for the Japanese multinationals as well as the total sample. The results for these four subsamples are reported in Panel C of Table 3. We find that the low elasticity estimates are not drivenexclusivelybyfirmsinthemotor-vehiclesector. Whenviewedinlightofthesubstantialfractionofintra-firmimportscomprisingmultinational affiliatetrade,thelowelasticityofsubstitutionshouldnotcomeasasurprise. Onewouldnotexpect close substitutes for the sort of specialized products reflecting firm-specific knowledge that likely comprises this trade. Moreover, such a low estimate for an elasticity of this nature is not without precedent.38 Using different methodologies, recent work by Atalay (2014) highlights strong complementaritiesbetweenintermediateinputs,usingindustry-leveldatafortheUnitedStates.39 Anyelasticityestimateistiedtothetime-horizontowhichitcorresponds. Ruhl(2008)emphasizes the difference between elasticities implied by responses to temporary vs permanent shocks. Larger values are calculated for an elasticity following a permanent shock, owing in part to firm responses along the extensive margin. In our context, we estimate the elasticity subject to a shortlived shock where the structure of the supply chain is plausibly fixed and extensive margin movements of supplier relationships would not apply. For this reason the elasticity parameters (ω,ζ) should likely generalize to other contexts of this horizon and for shocks of this general duration. Evenforalong-livedshock,theestimatedelasticitieswouldremainrelevantwhilethefirmmakes changes to its network of suppliers. Evaluating whether there is evidence for long-term supply- 38Recentworkfindsthatmaterialinputsfromforeigncountriesareimperfectlysubstitutablewithdomesticinputs forHungary(Halpern,Koren,andSzeidl(2015))andIndia(Goldbergetal.(2010)) 39ThepointestimatefortheelasticityofsubstitutionamongintermediateinputsfromAtalay(2014)is0.03. 28

chainreorganizationfollowingtheTo¯hokueventisanareaofongoingwork. 5 Conclusions Using a novel firm-level dataset to analyze firm behavior surrounding a large exogenous shock, thispaperrevealsthemechanismsunderlyingcross-countryspillovers. Wefindcomplementarities intheglobalproductionnetworksofJapaneseaffiliates,suchthattheU.S.outputofthesefirmsdeclineddramaticallyfollowingtheTo¯hokuearthquake,roughlyinlinewiththedeclineinimported inputs. Theelasticityofsubstitutionbetweenimportedanddomesticinputsthatwouldbestmatch this behavior is very low – nearly that implied by a Leontief production function. The reliance on intra-firm imports by multinational affiliates from their source country is the most plausible explanation for such strong complementarities in production. Structural estimates of disaggregated elasticities are similarly low, and imply spillovers to upstream and downstream firms in the U.S. and abroad. The large impacts to Japanese affiliates together with the propagation to other U.S. firmsexplainsthelargetransmissionoftheshocktotheU.S.economyintheaggregate. These elasticities play a critical role in the way international trade impacts both source and destination economies. Such complementarities between domestic and foreign goods have been showntoimprovetheabilityofleadingtheoreticalmodelstofitkeymomentsofthedata. Weemphasize here the distinction between substitutability between domestic and foreign final goods (a “consumption”elasticityofsubstitution,ortheso-calledArmingtonelasticity)andsubstitutability between domestic and foreign intermediate goods (a “production” elasticity of substitution). In a companion paper (Boehm, Flaaen, and Pandalai-Nayar (2014)), we document the behavior of a model with such complementarities in imported intermediates, and discuss how these elasticity parameters interact. Calibrating this model to the share of multinational affiliate trade in intermediatesyieldsanincreaseinvalue-addedcomovementof11p.p. Suchrigidproductionnetworkswillalsoplayaroleinaggregatevolatility,productivitygrowth and dispersion, and the international ownership structure of production. The novel datasets describedinthispapermayhelptoshedlightontheseandotherareasofresearchinthefuture. 29

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Table1: SummaryStatistics PanelA:CostShareOfImportedInputs Japanese Non Firms Multinationals fromJapan 21.8 1.0 fromallcountries 35.0 17.5 PanelB:TreatmentEffectsSampleDetails Japanese Other BalancingTests %Reduct Firms Multinationals t p > |t| |bias| N.A.Exports 3,504,894 3,413,058 0.38 0.706 79.1 shareintra-firm 72.0 52.2 Intermediate 8,075,893 7,596,761 0.87 0.384 88 InputImports sharefromJapan 70.0 3.5 shareintra-firm 86.0 21.7 Industry(Avg) – – 0.009 0.965 97.8 Source: LFTTD,DCA,andUBPasexplainedinthetext. PanelAdataareforyear2007. PanelBreportsthebaselineaveragevaluesofN.A.exportsandintermediate inputimports,aswellasthecharacteristicsofthattrade,forthetwogroupsoffirms: Japaneseaffiliatesand other multinational firms. The statistics are calculated in the three months prior to the To¯hoku earthquake: Dec. 2010, Jan. 2011, andFeb2011. Thecontrolgroupofothermultinationalfirmshasbeenre-weighted usingthenormalizedpropensityscore,fromaspecificationincludingthelevelofN.A.exports,intimports, andindustrydummies. Thefinalthreecolumnsreportbalancingtestsoftheequalityofthemeansbetween thetreatedandcontrolgroup. 33

Table2: Firm-LevelEstimation: ResultsandSampleDetails PanelA:Calibration Parameter Value R 0.07 t α 1/3 PanelB:EstimationResults Japanese Non-Japanese Non- All Multinationals Multinationals Multinationals Firms ω 0.201 0.624 0.423 0.552 [0.02 0.43] [0.16 0.69] [0.26 0.58] [0.21 0.62] ζ 0.032 0.038 0.032 0.037 [0.030 0.673] [0.035 0.508] [0.029 1.68] [0.034 0.038] SampleDetails WeightonK/L 0.223 0.514 0.278 0.409 Aggregate(µ¯) WeightonJPN 0.173 0.044 0.147 0.096 Materials(1−ν¯) NumberofFirms 105 304 141 550 ShareofTotalTrade JPNintimports 0.60 0.23 0.03 0.86 Non-JPNintimports 0.02 0.66 0.01 0.69 N.A.exports 0.08 0.47 0.01 0.56 Source: CM,LFTTD,DCA,andUBPasexplainedinthetext. Thistablereportstheresultsfromthefirm-levelestimationdetailedinsection3.PanelAoutlinestheparametersthat arecalibratedpriortoestimation. ThetoptworowsofPanelBreportsthepointestimatesoftheelasticities,andthe corresponding95percentconfidenceintervalsusingabootstrappingprocedure. (SeeAppendixC.8formoredetails onthemeasurementofdispersionfortheseestimates.) Rows3and4reportotherestimatesrelatedtothecalculated productionfunctions. ThefinalrowsofPanelBdescribefeaturesoftheestimationsamples. 34

Table3: Firm-LevelEstimation: OtherResults PanelA:Calibration Parameter Value R 0.07 t α 1/3 PanelB:EstimationResults(Weighted) Japanese Non-Japanese Non- All Multinationals Multinationals Multinationals Firms ω 0.157 0.611 0.543 0.606 [0.02 0.40] [0.30 1.23] [0.305 0.57] [0.28 0.70] ζ 0.241 0.038 0.032 0.037 [0.03 0.884] [0.034 0.51] [0.029 0.55] [0.034 0.038] NumberofFirms 105 304 141 550 PanelC:EstimationResults: MVSector JapaneseMult. AllFirms Motor Non-Motor Motor Non-Motor Vehicles Vehicles Vehicles Vehicles ω 0.311 0.094 0.414 0.574 [0.019 0.398] [0.016 0.59] [0.27 0.60] [0.16 0.66] ζ 0.032 0.071 0.037 0.037 [0.030 0.48] [0.028 1.27] [0.031 0.64] [0.033 0.037] NumberofFirms 35 70 100 450 Source: CM,LFTTD,DCA,andUBPasexplainedinthetext. This table reports additional estimation results. Panel B recalculates the results from Table 2 using a vector of weights to assign larger firms a greater share in the estimation. Panel C divides the samples based on the motor vehicleindustry. 35

Figure1: IndexofJapaneseIndustrialProduction: ManufacturingJul.2010-Jan.2012 Source: Japanese Ministry of Economy, Trade, and Industry (METI). Theseriesarelogged,HP-Filtered,afterseasonallyadjusting. 36

Figure2: U.S.ImportsfromJapanandRestofWorld,Jul.2010-Jan.2012 Source: U.S.CensusBureau(FT900: U.S.InternationalTradeinGoods and Services). The series are logged, HP-Filtered, after seasonally adjusting. Figure3: U.S.IndustrialProduction: ManufacturingandDurableGoods Source: FederalReserveBoard,IndustrialProductionandCapacityUtilization-G.17Series. SeriesisSeasonallyAdjusted. 37

Figure4: DensityofFirm-LevelExposuretoJapaneseImportedInputs: ByFirmType Source: LFTTD-DCA-UBP as explained in text. The estimates correspond to year 2010. This figure displays density estimates of the log exposure measure to Japanese imported inputs, separately for Japanese affiliates andnon-Japanesemultinationalfirms. ThemeasureisdefinedastheratioofJapaneseimportedinputstototal importedinputsplusU.S.salariesandwages. Estimatesateithertailaresuppressedforconfidentialitypurposes. 38

Figure5: DynamicTreatmentEffects: JapaneseFirms A.RelativeIntermediateInputImportsofJapaneseFirms B.RelativeNorthAmericanExportsofJapaneseFirms Source: LFTTD-DCA-UBPasexplainedintext. ThesefiguresreporttheintermediateimportsandNorthAmericanexportsoftheU.S.affiliatesofJapanese firmsrelativetoacontrolgroupofothermultinationalfirms. Thevaluesarecoefficientestimatestakenfrom an interaction of a Japanese-firm dummy with a monthly dummy – additional baseline monthly dummies removeseasonaleffects. Seeequation5inthetext. Standarderrorsareclusteredatthefirmlevel. 39

Figure 6: Relative Imported Inputs and Output (Proxy) of Japanese Firms: Fraction of Pre-Shock Level Source: LFTTD-DCA-UBPasexplainedintext. Thisfigurereportstheintermediateimportsandoutputproxy(NorthAmericanexports)oftheU.S.affiliates of Japanese firms relative to a control group of other multinational firms. The values are percent changes fromthepre-shocklevelofeachseries,definedastheaverageofthemonthsDecember2010,January2011, andFebruary2011. 40

Figure7: AssessingtheOutputProxyUsingMonthlyAutomotiveProduction Source: Ward’sAutomotiveDatabase ThisfigurereportstheproductionlevelsofJapaneseautoplantsrelativetoacontrolgroupofnon-Japanese auto plants. The values are percent changes from a pre-shock level, defined as the average of the months December2010,January2011,andFebruary2011.SeeequationA16inthetext.Forpurposesofcomparison, wealsoincludetheequivalentmeasurecorrespondingtototalmanufacturingofJapaneseaffiliatesusingthe output proxy from Census data (from Figure 6). The Japanese automakers are Honda, Mazda, Mitsubishi, Nissan, Toyota, and Subaru. For the sake of clarity, we suppress the standard errors for the automotive series,thoughthereare4monthswithbelowzeroproductionbasedona95percentconfidenceinterval. See AppendixC.10formoredetails. 41

Input Linkages and the Transmission of Shocks: Firm-Level Evidence from the 2011 To¯hoku Earthquake ChristophE.Boehm AaronFlaaen NityaPandalai-Nayar October 22, 2015 For Online Publication A Basic Theory Appendix A.1 Proof of Result 1 Supposethatthefirmsolves maxp x−p F −p IM x D D M subjectto (cid:104) (cid:105) ψ x = (1−µ)ψ 1 [F D ] ψ ψ −1 +µψ 1 [IM] ψ ψ −1 ψ−1 and (cid:18) (cid:19)1 Y ε p = x x Thefirstorderconditionsare (cid:18) (cid:19) 1 1− (Y) 1 ε (x)ψ 1−1 ε (1−µ)ψ 1 [F D ]− ψ 1 = p D ε (cid:18) (cid:19) 1 1− (Y) 1 ε (x)ψ 1−1 ε µψ 1 [IM]− ψ 1 = p M ε Dividingonebytheothergives F∗ 1−µ (cid:18) p (cid:19)ψ D = M . IM∗ µ p D Thesameequationcanbeobtainedunderperfectcompetition. Nowtaketheproductionfunctionandmultiplyitbyp x (cid:104) (cid:105) ψ p x x = p x (1−µ)ψ 1 [F D ] ψ ψ −1 +(p M )−ψ ψ −1 µψ 1 [p M IM] ψ ψ −1 ψ−1 Takinglogsgives 42

ψ (cid:16) (cid:104) (cid:105)(cid:17) ln(p x x) = ln p x (1−µ)ψ 1 [F D ] ψ ψ −1 +(p M )−ψ ψ −1 µψ 1 [p M IM] ψ ψ −1 (A1) ψ −1 (cid:18) (cid:20) (cid:18) (cid:19) (cid:18) (cid:19)(cid:21)(cid:19) ψ ψ −1 ψ −1 = ln p x (1−µ)ψ 1 exp ln[F D ] +(p M )−ψ ψ −1 µψ 1 exp ln[p M IM] ψ −1 ψ ψ (A2) Before differentiating, recall the assumption that the firm takes prices p as given and that it M cannotchangep afterlearningabouttheshock. Then x (cid:16) (cid:17) ∂lnp x x ψ p x (P M )−ψ ψ −1 µψ 1 exp ψ ψ −1 ln[p M IM] ψ ψ −1 = (cid:104) (cid:16) (cid:17) (cid:16) (cid:17)(cid:105) ∂lnp M M ψ −1 p x (1−µ)ψ 1 exp ψ ψ −1 ln[F D ] +(p M )−ψ ψ −1 µψ 1 exp ψ ψ −1 ln[p M IM] (A3) 1 = (A4) 1+ (cid:16) 1−µ (cid:17) ψ 1 (cid:2)FD (cid:3)ψ ψ −1 µ IM Weevaluatethiselasticityat F∗ IM∗1−µ (cid:18) p (cid:19)ψ D = M IM IM µ p D sothat ∂lnp x 1 x = ∂lnp M IM 1+ (cid:0) IM∗(cid:1)ψ ψ −1 1−µ (cid:16) pM (cid:17)ψ−1 IM µ pD A.2 On Flexibility in Domestic Inputs Undertheassumptionofperfectcompetition,thefirstorderconditionsare: x(1−µ) = (p )ψF D D xµ = (p )ψIM M Ifthefirmtakespricesp ,p ,andp asgiven,thefollowingelasticitiesareimmediate: x M D ∂ln(p x) ∂ln(p x) ∂ln(p F ) x x D D = = = 1. ∂ln(p F ) ∂ln(p M) ∂ln(p M) D D M M The above equations demonstrate that a constant returns to scale production function combined with these assumptions on market structure imply that the output elasticity will equal one for all values of the elasticity of substitution. For this reason, we require some assumptions limiting the flexibilityofdomesticinputsfollowingtheimportdisruption. 43

Below we show an alternative way of understanding the interaction of competitive factor markets,changesindomesticinputs,andthemappingoftheoutputelasticityintoparametervaluesfor theelasticityofsubstitution. Considerthetotalderivativeofln(x): ∂lnx ∂lnx dlnx = dlnIM + dlnF (A5) ∂IM ∂F 1 ψ−1 1 ψ−1 µψ(IM) ψ dlnIM (1−µ)ψ(F D ) ψ dlnF D dlnx = + (A6) 1 ψ−1 1 ψ−1 1 ψ−1 1 ψ−1 (1−µ)ψ [F D ] ψ +µψ [IM] ψ (1−µ)ψ [F D ] ψ +µψ [IM] ψ DividingbydlnIM yields: 1 ψ−1 1 ψ−1 dlnx µψ(IM) ψ (1−µ)ψ(F D ) ψ dlnF D = + dlnIM 1 ψ−1 1 ψ−1 1 ψ−1 1 ψ−1 dlnIM (1−µ)ψ [F D ] ψ +µψ [IM] ψ (1−µ)ψ [F D ] ψ +µψ [IM] ψ Now,asbefore,combiningthefirstorderconditionsfromtheprofitmaximizationproblem,we have: F (·) 1−µ (cid:18) p (cid:19)−ψ D D = (A7) IM µ p M Log-differentiatingthisexpression: (cid:18) (cid:19) (cid:18) (cid:19) F p D D dln = −ψdln IM p M (cid:18) (cid:19) p D dlnF −dlnIM = −ψdln D p M (cid:16) (cid:17) dln pD dlnF D = 1−ψ pM (A8) dlnIM dlnIM Finally,wehave: 1 ψ−1 (cid:20) dln (cid:16)pD (cid:17)(cid:21) dlnx µψ 1 (IM) ψ ψ −1 (1−µ)ψ(F D ) ψ 1−ψ dln p I M M = + (A9) dlnIM 1 ψ−1 1 ψ−1 1 ψ−1 1 ψ−1 (1−µ)ψ [F D ] ψ +µψ [IM] ψ (1−µ)ψ [F D ] ψ +µψ [IM] ψ Thus, if there is no change in the relative input price following the disruption in IM of the firm: dln (cid:16)pM (cid:17) pD = 0, then the output elasticity will be equal to one regardless of the value of ψ. On the dlnIM otherhand,anyassumptionsthatyieldanon-zerochangeintherelativeinputpriceswillthenyield theresultthat dlnx = 1providedψ → 0. dlnIM 44

B Data Appendix B.1 Matching Corporate Directories to the Business Register The discussion below is an abbreviated form of the full technical note (see Flaaen (2013)) documentingthebridgebetweentheDCAandtheBusinessRegister. B.1.1 DirectoriesofInternationalCorporateStructure The LexisNexis Directory of Corporate Affiliations (DCA) is the primary source of information ontheownershipandlocationsofU.S.andforeignaffiliates. TheDCAdescribestheorganization and hierarchy of public and private firms, and consists of three separate databases: U.S. Public Companies,U.S.PrivateCompanies,andInternational–thoseparentcompanieswithheadquarters located outside the United States. The U.S. Public database contains all firms traded on the major U.S.exchanges,aswellasmajorfirmstradedonsmallerU.S.exchanges. TobeincludedintheU.S. Privatedatabase,afirmmustdemonstraterevenuesinexcessof$1million,300ormoreemployees, orsubstantialassets. ThosefirmsincludedintheInternationaldatabase,whichincludebothpublic and private companies, generally have revenues greater than $10 million. Each database contains information on all parent company subsidiaries, regardless of the location of the subsidiary in relationtotheparent. The second source used to identify multinational firms comes from Uniworld Business Publications (UBP). This company has produced periodic volumes documenting the locations and international scope of i) American firms operating in foreign countries; and ii) foreign firms with operationsintheUnitedStates. Althoughonlypublishedbiennially,thesedirectoriesbenefitfrom afocusonmultinationalfirms,andfromnosalesthresholdforinclusion. Because there exist no common identifiers between these directories and Census Bureau data infrastructure, we rely on probabilistic name and address matching — so-called “fuzzy merging” —tolinkthedirectoriestotheCensusdatainfrastructure. B.1.2 BackgroundonNameandAddressMatching Matchingtwodatarecordsbasedonnameandaddressinformationisnecessarilyanimperfectexercise. Issues such as abbreviations, misspellings, alternate spellings, and alternate name conventionsruleoutanexactmergingprocedure,leavingtheresearcherwithprobabilisticstringmatching algorithms that evaluate the “closeness” of match — given by a score or rank — between the two character strings in question. Due to the large computing requirements of these algorithms, it is common to use so-called “blocker” variables to restrict the search samples within each dataset. A “blocker” variable must match exactly, and as a result this implies the need for a high degree of conformity between these variables in the two datasets. In the context of name and address matching,themostcommon“blocker”variablesarethestateandcityoftheestablishment. The matching procedure uses a set of record linking utilities described in Wasi and Flaaen (2014). Thisprogramusesabigramstringcomparatoralgorithmonmultiplevariableswithdiffer- 45

ing user-specified weights.40 This way the researcher can apply, for example, a larger weight on a nearnamematchthanonaperfectzipcodematch. Hence,the“matchscore”forthisprogramcan beinterpretedasaweightedaverageofeachvariable’spercentageofbigramcharactermatches. B.1.3 TheUnitofMatching The primary unit of observation in the DCA, UBP, and BR datasets is the business establishment. Hence, the primary unit of matching is the establishment, and not the firm. However, there are a number of important challenges with an establishment-to-establishment link. First, the DCA (UBP) and BR may occasionally have differing definitions of the establishment. One dataset may separate out several operating groups within the same firm address (i.e. JP Morgan – Derivatives, and JP Morgan - Emerging Markets), while another may group these activities together by their common address. Second, the name associated with a particular establishment can at times reflect thesubsidiaryname,location,oractivity(i.e. Alabamaplant,processingdivision,etc),andattimes reflect the parent company name. Recognizing these challenges, the primary goal of the matching will be to assign each DCA (UBP) establishment to the most appropriate business location of the parentfirmidentifiedintheBR.Assuch,theprimarymatchingvariableswillbetheestablishment name,alongwithgeographicindicatorsofstreet,city,zipcode,andstate. B.1.4 TheMatchingProcess: AnOverview The danger associated with probabilistic name and address procedures is the potential for falsepositive matches. Thus, there is an inherent tension for the researcher between a broad search criteria that seeks to maximize the number of true matches and a narrow and exacting criteria that eliminates false-positive matches. The matching approach used here is conservative in the sense that the methodology will favor criteria that limit the potential for false positives at the potential expense of slightly higher match rates. As such, the procedure generally requires a match score exceeding95percent,exceptinthosecaseswhereancillaryevidenceprovidesincreasedconfidence inthematch.41 This matching proceeds in an iterative fashion, in which a series of matching procedures are applied with decreasingly restrictive sets of matching requirements. In other words, the initial matchingattemptusesthemoststringentstandardspossible,afterwhichthenon-matchingrecords proceed to a further matching iteration, often with less stringent standards. In each iteration, the matchingrecordsareassignedaflagthatindicatesthestandardassociatedwiththematch. See Table A1 for a summary of the establishment-level match rate statistics by year and type offirm. TableA2liststhecorrespondinginformationfortheUniworlddata. 40The term bigram refers to two consecutive characters within a string (the word bigram contains 5 possible bigrams:“bi”,“ig”,“gr”,“ra”,and“am”).Theprogramisamodifiedversionofanexistingstringcomparatoralgorithm byMichaelBlasnik,andassignsascoreforeachvariablebetweenthetwodatasetsbasedonthepercentageofmatching bigrams. SeeFlaaen(2013)orWasiandFlaaen(2014)formoreinformation. 41Theprimarysourcesofsuchancillaryevidenceareclericalreviewofthematches,andadditionalparentidentifier matchingevidence. 46

B.1.5 ConstructionofMultinationalIndicators The DCA data allows for the construction of variables indicating the multinational status of the U.S.-basedestablishment. IftheparentfirmcontainsaddressesoutsideoftheUnitedStates,butis headquarteredwithintheU.S.,wedesignatethisestablishmentaspartofaU.S.multinationalfirm. IftheparentfirmisheadquarteredoutsideoftheUnitedStates,wedesignatethisestablishmentas partofaForeignmultinationalfirm. Wealsoretainthenationalityofparentfirm.42 TherecanbeanumberofissueswhentranslatingtheDCA-basedindicatorsthroughtheDCA- BR bridge for use within the Census Bureau data architecture. First, there may be disagreements between the DCA and Census on what constitutes a firm, such that an establishment matches mayreportdifferingmultinationalindicatorsforthesameCensus-identifiedfirm. Second,suchan issuemightalsoariseduetojoint-ventures. Finally,incorrectmatchesmayalsoaffectthedegreeto which establishment matches agree when aggregated to a firm definition. To address these issues, we apply the following rules when using the DCA-based multinational indicators and aggregating tothe(Census-based)firmlevel. Therearethreepotentialcases:43 Potential 1: A Census-identified firm in which two or more establishments match to different foreign-countryparentfirms 1. CollapsetheCensus-identifiedfirmemploymentbasedontheestablishment-parentfirmlink bycountryofforeignownership 2. Calculatethefirmemploymentshareofeachestablishmentmatch 3. If one particular link of country of foreign ownership yields an employment share above 0.75,applythatlinktoallestablishmentswithinthefirm. 4. Ifoneparticularlinkofcountryofforeignownershipyieldsanemploymentshareabove0.5 and totalfirm employment is below10,000, then apply thatlink to all establishmentswithin thefirm. 5. Allothercasesrequiremanualreview. Potential 2: A Census-identified firm in which one establishment is matched to a foreign-country parentfirm,andanotherestablishmentismatchedtoaU.S.multinationalfirm. 1. CollapsetheCensus-identifiedfirmemploymentbasedontheestablishment-parentfirmlink bytypeofDCAlink(ForeignvsU.S.Multinational) 2. Calculatethefirmemploymentshareofeachestablishmentmatch 3. If one particular type of link yields an employment share above 0.75, apply that link to all establishmentswithinthefirm. 42ThemultinationalstatusoffirmsfromtheUBPdirectoriesaremorestraightforward. 43SomeofthesecasesalsoapplytotheUBP-BRbridge. 47

4. If one particular type of link yields an employment share above 0.5 and total firm employmentisbelow10,000,thenapplythatlinktoallestablishmentswithinthefirm. 5. Allothercasesrequiremanualreview. Potential3: ACensus-identifiedfirminwhichoneestablishmentismatchedtoanon-multinational firm, and another establishment is matched to a foreign-country parent firm (or U.S. multinational firm). ApplysamestepsasinPotential2. B.2 Classifying Firm-Level Trade The firm-level data on imports available in the LFTTD does not contain information on the intended use of the goods.44 Disentangling whether an imported product is used as an intermediate input for further processing — rather than for final sale in the U.S. — has important implications for the nature of FDI, and the role of imported goods in the transmission of shocks. Fortunately, the Census Bureau data contains other information that can be used to distinguish intermediate input imports from final goods imports. Creating lists of the principal products produced by firms in a given detailed industry in the United States should indicate the types of products that, when imported, should be classified as a “final” good – that is, intended for final sale without further processing. The products imported outside of this set, then, would be classified as intermediate goods.45 Suchproduct-levelproductiondataexistsaspartofthe“Products”trailerfileoftheCensus of Manufacturers. As detailed in Pierce and Schott (2012) (see page 11), combining import, export,andproductioninformationataproduct-levelisusefulforjustsuchapurpose. B.2.1 CreatingaNAICS-BasedsetofFinal/IntermediateProducts As part of the quinquennial Census of Manufacturers (CM), the Census Bureau surveys establishmentsontheirtotalshipmentsbrokendownintoasetofNAICS-based(6digit)productcategories. Each establishment is given a form particular to its industry with a list of pre-specified products, with additional space to record other product shipments not included in the form. The resulting product trailer file to the CM allows the researcher to understand the principal products produced ateachmanufacturingestablishmentduringacensusyear. ThereareseveraldataissuesthatmustbeaddressedbeforeusingtheCM-Productsfiletoinfer information about the relative value of product-level shipments by a particular firm. First, the trailer file contains product-codes that are used to “balance” the aggregated product-level value of shipments with the total value of shipments reported on the base CM survey form. We drop these productcodesfromthedataset. Second,thereareoftencodesthatdonotcorrespondtoanyofficial 7-digit product code identified by Census. (These are typically products that are self-identified by thefirmbutdonotmatchanyofthepre-specifiedproductsidentifiedforthatindustrybyCensus.) 44ThisisoneadvantageofthesurveydataonmultinationalfirmsavailablefromtheBureauofEconomicAnalysis. Thereare,however,anumberofcriticaldisadvantagesofthisdatasource,asoutlinedinFlaaen(2014). 45Tobemoreprecise,thissetwillincludeacombinationofintermediateandcapitalgoods. 48

Rather than ignoring the value of shipments corresponding to these codes, we attempt to match at a more aggregated level. Specifically, we iteratively try to find a product code match at the 6, 5, and4digitproductcodelevel,andusetheexistingsetof7-digitmatchesasweightstoallocatethe productvalueamongthe7-digitproductcodesencompassingthemoreaggregatedlevel. We now discuss how this file can be used to assemble a set of NAICS product codes that are thepredominantoutput(finalgoods)foragivenNAICSindustry. Letx denotetheshipmentsof pij product p by establishment i in industry j during a census year. Then the total output of product p inindustryj canbewrittenas: Ij (cid:88) X = x , pj pij i=1 whereI isthenumberoffirmsinindustryj. Totaloutputofindustryj isthen: j Pj (cid:88) X = X . j pj p=1 Theshareofindustryoutputaccountedforbyagivenproductpistherefore: X pj S = . pj X j Onemightarguethatthesetoffinalgoodsproductsforagivenindustryshouldbedefinedasthe set of products where S > 0. That is, a product is designated as a “final good” for that industry pj if any establishment recorded positive shipments of the product. The obvious disadvantage of employing such a zero threshold is that small degrees of within-industry heterogeneity will have oversizedeffectsontheclassification. Acknowledgingthisconcern,wesetanexogenousthresholdlevelW suchthatanypinagiven j with S > W is classified as a final good product for that industry. The upper portion of Table pj A3 documents the number of final goods products and the share of intermediate input imports based on several candidate threshold levels. The issues of a zero threshold are quite clear in the table; a small but positive threshold value (0.1) will have a large effect on the number of products designatedasfinalgoods. Thisshowsindirectlythattherearealargenumberofproductsproduced by establishments in a given industry, but a much smaller number that comprise the bulk of total value. There are several advantages to using the CM-Products file rather than using an input-output table.46 First, within a given CM year, the classification can be done at the firm or establishment level rather than aggregating to a particular industry. This reflects the fact that the same imported product may be used as an input by one firm and sold to consumers as a final product by another. Second, the CM-Products file is one of the principal data inputs into making the input-output tables,andthusrepresentsmorefinelydetailedinformation. Relatedtothispoint,theinput-output 46Another option is to use the CM-Materials file, the flip side of the CM-Products file. Unfortunately, the CM- MaterialsfilecontainssignificantlymoreproblematicproductcodesthantheProductsfile, andsoconcordingtothe tradedataisconsiderablymoredifficult. 49

tables are produced with a significant delay – the most recent available for the U.S. is for year 2002. Third, the input-output tables for the U.S. are based on BEA industry classifications, which imply an additional concordance (see below) to map into the NAICS-based industries present in theCensusdata. We now turn to the procedure to map firm-level trade into intermediate and final goods using theindustry-levelproductclassificationscalculatedabove. B.2.2 MappingHSTradeTransactionstotheProductClassification The LFTTD classifies products according to the U.S. Harmonized Codes (HS), which must be concorded to the NAICS-based product system in order to utilize the classification scheme from the CM-Products file. Thankfully, a recent concordance created by Pierce and Schott (2012) can be used to map the firm-HS codes present in the LFTTD data with the firm-NAICS product codes presentintheCM-Productsdata. A challenge of this strategy is that the LFTTD exists at a firm-level, while the most natural construction of the industry-level classification scheme is by establishment. More concretely, for multi-unit, multi-industry firms, the LFTTD is unable to decompose an import shipment into the preciseestablishment-industryofitsU.S.destination. 47 Whilerecognizingthecautionthatshould be used in this regard, we adopt the approach that is commonly used in such circumstances: the industryofthefirmisdefinedasthatindustryencompassingthelargestemploymentshare. Once the firm-level trade data is in the same product classification as the industry-level filter created from the CM-Products file, all that is left is to match the trade data with the filter by NAICS industry. Thus, letting M denote total imports from a firm i (firm i is classified as being ij inindustryj),wecanthencategorizethefirm’stradeaccordingto: Mint = (cid:80) M  ij ipj   p∈/Pj   where P = {p|S ≥ W}. (A10) j pj Mfin = (cid:80) M   ij ipj   p∈Pj The bottom section of Table A3 shows some summary statistics of the intermediate share of trade according to this classification system, by several values of the product-threshold W. There are at least two important takeaways from these numbers. First, the share of intermediates in total imports is roughly what is reported in the literature using IO Tables. Second, the share of total trade occupied by intermediate products is not particularly sensitive to the exogenous threshold level. While there is a small increase in the share when raising the threshold from 0 to 0.1 (about 3percentagepoints),thenumberisessentiallyunchangedwhenraisingitfurtherto0.2. 47Itisworthpointingoutthatthemostobviouswaythatthiswouldmaterializeisbyverticalintegrationofthefirm initsU.S.operations. Providedthattheindustrydesignationofthefirmpertainstoitsmostdownstreamoperations, thenthisiswouldnotservetobiasthefirms’classificationofimportedgoods,astheupstreamproductsarenotactually “final”goodsforthatfirm. 50

B.3 Sample Selection B.3.1 ConstructingtheBaselineDataset Thissectionwilldiscussthestepstakentoconstructthesampleusedinsection2.1. Beginning with the raw files of the LFTTD export/import data, we drop any transactions with missing firm identifiers, and those pertaining to trade with U.S. territories. Next, we merge the LFTTD files with the HS-NAICS6 product concordance from Pierce and Schott (2012); if there is nocorrespondingNAICS6codeforaparticularHScode,thenwesetNAICS6equaltoXXXXXX. We then aggregate up to the level of Firm-Country-Month-NAICS6, and then create extracts according to three sets of destinations/sources: Japan, Non-Japan, and North America (Canada and Mexico). Then, assigning each firm to an LBD-based industry (see below), we run the NAICSbasedtradecodesthroughtheintermediate/finalgoodsfilterdiscussedinAppendixB.2. Thefirms’ monthly trade can then be split into intermediate and final goods components. We repeat this step foryears2009,2010,and2011. UsingtheLongitudinalBusinessDatabase,wedropinactive,ghost/deletedestablishments,and establishments that are not in-scope for the Economic Census. To create the sample of manufacturing firms in the U.S., we first create a firm industry code defined as the industry encompassing the largest share of firm employment. We then drop non-manufacturing firms. Next, we merge theLBDforeachyearwiththeDCA-Bridge(seesectionB.1)containingmultinationalindicators. We then apply the rules specified above for clarifying disagreements with the DCA-based multinational indicators. After creating monthly copies of each firm, we merge by firm-month to the trade data. Missing information of trade data is altered to represent zeros. We repeat these steps for years 2009-2011, and then append the files together. Firms that do not exist in all three years aredroppedfromthesample. B.3.2 GISMappingofEarthquakeIntensityMeasurestoAffiliateLocations As part of the Earthquake Hazards Program, the U.S. Geological Survey produces data and map products of the ground motion and shaking intensity following major earthquakes. The preferred measure to reflect the perceived shaking and damage distribution is the estimated “Modified Mercalli Intensity (MMI)” which is based on a relation of survey response and measured peak acceleration and velocity amplitudes. The USGS extends the raw data from geologic measurement stations and predicts values on a much finer grid using standard seismological inferences and interpolation methods. The result is a dense grid of MMI values covering the broad region affected bytheseismicevent. Formoreinformationonthismethodology,seeWaldetal.(2006). To utilize this information, we take all Japanese addresses from the DCA/Uniworld directories that correspond to any U.S. operation via an ownership link. We geocode these addresses into latitude/longitude coordinates using the Google Geocoding API, and then compute the inverse distance-weighted mean of the relevant seismic intensity measure based on a 10km radius surrounding a given establishment. The firm identifiers within the corporate directories allow us to create firm-specific measures (average and maximum values, by manufacturing/nonmanufacturing), which can then be brought into the baseline Census dataset via the bridges discussedinappendixB.1. 51

TableA1: DCAMatchStatistics: 2007-2011 #ofDCA Matched Percent Establishments toB.R. Matched Total 2007 112,346 81,656 0.73 2008 111,935 81,535 0.73 2009 111,953 81,112 0.72 2010 111,998 79,661 0.71 2011 113,334 79,516 0.70 U.S.Multinationals 2007 22,500 16,396 0.73 2008 23,090 16,910 0.73 2009 22,076 16,085 0.73 2010 21,667 15,785 0.73 2011 21,721 15,557 0.72 ForeignMultinationals 2007 10,331 7,555 0.73 2008 9,351 6,880 0.74 2009 11,142 8,193 0.74 2010 11,308 8,181 0.72 2011 11,619 8,357 0.72 52

TableA2: UniworldMatchStatistics: 2006-2011 #ofUniworld Matched Percent Establishments toB.R. Matched ForeignMultinationals 2006 3,495 2,590 0.74 2008 3,683 2,818 0.76 2011 6,188 4,017 0.65 U.S.Multinationals1 2007 4,043 3,236 0.80 2009 4,293 3,422 0.80 1U.S.multinationalsincludeonlytheestablishmentidentifiedastheU.S. headquarters. TableA3: AppendixTableComparingtheResultsfromThresholdValuesW ThresholdValues W = 0 W = 0.1 W = 0.2 NumberofFinalGoodProductsperIndustry Median 19 1 1 Mean 25 1.52 1.14 Min 1 1 0 Max 154 6 3 ImpliedShareofIntermediateInputs Imports 60.9 63.90 63.97 Exports 52.0 54.96 55.04 53

FigureA1: GeographicDistributionofEarthquakeIntensityandAffiliateLocations Source: USGSandDCA/UniworldDirectories This figure plots the geographic distribution of the To¯hoku earthquake, based on recorded measurements taken directly after the event. The “Modified Mercalli Intensity” (MMI) scale is constructed based on a relationofsurveyresponseandmeasuredpeakaccelerationandvelocityamplitudesfrompriormajorseismic events. Each dot corresponds to a geocoded Japanese affiliate location corresponding to a firm with U.S. operations. Formoredetails,seeAppendixB.3.2. 54

C Appendix: Other Results C.1 Intermediate Input Inventories Inventories are another obvious feature that should influence the relationship between input shipments, production, and the elasticity of substitution. In particular, inventories of intermediate inputs allow the firm to absorb unforeseen shocks to input deliveries without an impact on the production process.48 As it relates to the production elasticity, however, the presence of these inventoriesshouldservetodiminishordelaytheproductionimpact,therebyincreasingtheelasticity relativetowhatitwouldbewithoutsuchinventories. In fact, it is striking the extent to which we do not see any evidence for the role of intermediate input inventories in the production impacts of Figure 5 (Panel B) or Figure 7. The effect on production appears to be almost immediate, indicating that the stock of inventories of imported intermediatesislow(lessthanonemonth’ssupply)forthesefirms. WeobtainaroughsenseofthedegreeofinventoryholdingsfromtheCensusofManufacturers micro-data. Combining information on the beginning period stock of materials inventories with the annual usage of materials, we calculate the average monthly supply of inventories for each firm.49 Table A4 calculates the production-weighted averages over a select set of firm groups.50 We see that on average, Japanese multinationals hold a little over 3-weeks supply of intermediate inputsasinventory. Thisisslightlylessthannon-multinationalfirms,afactthatalignswiththeoftcited “lean” production processes made famous by Japanese firms in previous decades. Though these data are for the year 2007, there is little reason to believe these relative magnitudes have changed substantially over a period of a few years. For completeness, Table A4 also reports the correspondingestimatesforoutputinventories.51 Lowinventoryholdingscombinedwithaninelasticproductionfunctionsuggeststhatfirmsare willingtotoleratesomedegreeofexpectedvolatilityintheirproduction. Eitherthecostsofholding inventories or diversifying sources of supply are sufficiently high, or firms believe the probability ofdisruptionislow. Ineithercase,theseleanproductionstrategiescarryagreaterpotentialforthe propagation of shocks across countries, perhaps affecting firms with limited knowledge of their indirectexposurethroughcomplicatedproductionchains. 48Theexistenceoffinalgoodinventories,ontheotherhand,makesadistinctionbetweentheproductionandsales of a particular product. Here, the presence of final good inventories implies that the firm can continue to sell from existinginventorystocksevenwhileproductionistemporarilyaffected. 49Unfortunately,theCMdatadoesnotreportimportedmaterialsinventoryseparately. 50These numbers are broadly similar, though somewhat lower than other estimates in the literature. See Ramey (1989)foroneexample. 51At first glance, the average monthly supply of these output inventories looks surprisingly low. On the other hand,itisprobablythecasethatinventoriesareheldjointlybythemanufacturerandwholesale/retailestablishments Thus,consideringtheinventoriesofmanufacturersalonecouldpotentiallyunder-representthe“true”levelofoutput inventoriesavailableforsmoothingoutproductiondisturbances. 55

C.2 Multi-Products and Sub-Optimal Mix In the frameworks used in sections 2.1 and 3, we consider the aggregate bundles of imported intermediates, abstracting away from product-level detail. In reality, the firms in our dataset often import many distinct intermediate inputs from Japan. The structure of a CES production function implies that if each of these within-country inputs was non-substitutable with one another (a further, nested Leontief structure), the production impact of a disruption in the supply of just one inputcouldbeamplifiedrelativetothevalueofthatinput.52 Weevaluatethispossibilitybelow. This is particularly true given the heterogeneous impact of the To¯hoku event across Japan (see Figure A1). This could translate into considerable dispersion in the impact on the products importedbyaparticularU.S.firmorJapaneseaffiliate. Withproduct-levelshocks,consideringthe effectontheaggregateimportbundleamountstoassumingeither1)perfectsubstitutabilityamong products,or2)thatthefirmmaintainsanoptimalwithin-countryproductmixatalltimes. To be concrete, it may be more accurate to view the M in equation (1) as a further C.E.S. t functionofmultipleproducts. Thus,wecandefinethepropermeasurementofthisvariableas (cid:32) (cid:33) χ N χ−1 V i M ,t = P i M ,t (cid:88) η n χ 1 (mJ n,i,t ) χ− χ 1 , (A11) n=1 where now VM is the value based on a combination of N distinct products, with weights η and i,t n elasticityχ. Product-levelheterogeneityintheproductionimpactoftheshockcombinedwithimperfectcoordinationamonginputsuppliersimpliesthattheaggregate(measured)importbundleforaparticularfirmmayturnouttobesuboptimal. Inthiscase,wearemeasuringV(cid:100)M = (cid:80)N (pm m ) ≥ i,t n=1 n,t n,t VM. And the lower the elasticity of substitution among products, the more severe the disconnect i,t betweenthemeasuredimportsandthe“effective”imports—thatwhichisactuallyusefulindownstreamproduction. Asuboptimalproductmixindicatesthatmeasuredimports(V(cid:100)M )aregreaterthantheeffective i,t imports (VM). As a result the measured output response to the import shock will be larger than i,t otherwise,resultinginadownward“bias”intheelasticityestimatesfromsection2.1and3.53 Such an effect is decreasing in the product-level elasticity parameter χ, as complementarity itself is the drivingforcebetweendifferencesinV(cid:100)M andVM. Inaddition,theeffectisalsoincreasinginthe i,t i,t degreeofdeviationfromtheoptimalproductmix. Doesthisexertaquantitativelylargeeffectonourpointestimates? Giventheemphasisonlow inventoriesandleanproductionprocessesindownstreamoperations,onemightexpectthatacrossproductadjustmentwouldtakeplacebeforesendingtheinputsabroad. Toanalyzethisempirically, weanalyzewhethertherearesignificantdeviationsintheproductcompositionofJapaneseimports during the months following the To¯hoku event. To do this, we construct a measure of the distance ofafirm’simportbundlefromabenchmark,whichwewillinterprettobetheoptimalbundle. Let 52Thispointhasbeenmadeinsomewhatdifferingcontexts,byKremer(1993)andJones(2011). 53Because the source of this downward pressure on the estimate for ψ (or ω) is itself a very low product-level elasticity,itisunclearwhetherthisshouldbeconsideredabiasinthetraditionalsense. 56

t = s∗ be such a benchmark date. Then, using the product-level information in the LFTTD data we construct for each firm i, the share of total imports from Japan for a given product code n. Definingthissharetobes ,wethenconstructtheaverageproduct-leveldistancefromoptimum n,i,t DO as: i,t Ni 1 (cid:88) DO = (|s −s |) (A12) i,t Ni n,i,t n,i,s∗ n=1 where Ni is the total number of products imported by firm i. We define the period s∗ to be the months of April-June of 2010, and then evaluate DO at a monthly frequency, with particular i interest in the months following the To¯hoku event. While there may be natural movements in the bundle of products imported from Japan, evidence for substantial coordination failure in product composition or heterogeneity in product-level shocks would come from any abnormal jumps in this index in the months of the disruption. One can calculate this at various levels of product aggregation(i.e. HS4,HS6,HS8,HS10),thoughwereportresultsusingtheHS6level.54 The results of this exercise are shown in Figure A3. We plot the average DO across Japanese i firms for each month (the figure shows a 3-month moving average) during the period 2009-2011. Mechanically,thismeasureshouldberelativelyclosetozerointhemonthsconsistingofthebenchmark (April-June 2010). While there is a secular rise in this measure on either side of this benchmarkperiod,theredonotappeartobeanylargejumpsinthemonthsdirectlyfollowingtheTo¯hoku event. More interesting, perhaps, are the considerably larger values for this measure during early 2009,whichmightreflecttheeffectsofthetradecollapseassociatedwiththeGreatRecession. We interpret Figure A3 as evidence that the potential for suboptimal mix across products from Japan doesnotposeaseriousproblemtoourmeasurementinprevioussections. C.3 Strategic Behavior AnotherpossibilitythatcouldaffecttheinterpretationoftheresultsfromFigure6mightbestrategic behavior, particularly on the part of the competitors of Japanese firms in the United States. These firms could raise production or prices following the negative supply shock affecting their competitors,whichwouldservetobiasdownwardtheβ coefficientsfromtheequationwithXNA p i,t asthedependentvariable.55 Toevaluatethispossibility,weturntotheWard’sautomotivedataand consider the production of non-Japanese automakers in the months directly following the To¯hoku event. Figure A4 plots the relative production of these firms, using time-series variation only. There appears to be no quantitatively meaningful responses in the months following March 2011. This should not come as a surprise given capacity constraints and utilization adjustment costs, particularlygiventheshorttimehorizonofthisshock. 54Thelevelofaggregationweuseattemptstobalanceconcernsalongtwodimensions. Withlessproductaggregation(i.e.HS10level),onemightbeconcernedwiththeinherentlumpinessofproduct-levelfirmimports.Moreproduct aggregation,ontheotherhand,couldmaskimportantproductdifferenceswithinaparticularproductgrouping. 55Specifically,inequation(5)theγ ’swouldbehigherthanwouldbeexpectedwithouttheshock,andhencethe p β ’sartificiallylow. p 57

C.4 Effects on Unit Values (Prices) of Trade Traditionally, estimating the elasticity of substitution is accomplished via price and quantity data for products over extended periods of time. For the short horizon we consider in this paper, there are several reasons why prices may not have the scope to adjust. Many supplier relationships negotiate prices for longer periods of time than one or two months. Second, and perhaps more importantly,Table1demonstratesthatthelargemajorityofimportedintermediateinputsareintrafirm. The observed prices of these transactions are transfer-prices (within firm) and not likely to changereflectinganyshort-termdisturbance. The LFTTD contains information on quantities as well as values for each trade transaction, recordedatahighlydisaggregatedproductdefinition(HS10digit). Thisallowsfortheconstruction of unit values (prices) for each firm-product-month observation, which allows for an analysis of pricemovementssurroundingtheTo¯hokuevent. The majority of the data construction is identical to that in section B.3, however there are a number of modifications. First, we drop all transactions with missing or imputed quantities in the LFTTD, and then aggregate to the Firm-HS10-month frequency, separately for each type of trade transaction: 1) Related-Party imports from Japan; 2) Non Related-Party imports from Japan; 3) Related-Party exports to Canada/Mexico; and 4) Non Related-Party exports to Canada/Mexico. Next, we select only those firms identified as manufacturing in the LBD. We keep the relatedparty and arms-length transactions separate as one may expect these prices to behave differently following a shock. As above, we keep only manufacturing firms, append the annual files together, andthenselectonlythosefirmsidentifiedasamultinationalineither2009,2010,or2011. At the product level, there is little reason to suspect trends or seasonal variation over this short ofatimeperiod. Moreover,thereisnoconcernhereaboutaccountingforzerosinthedata. Assuch wetakeafirmj’simports(exports)ofproductpinmontht,andrunthefollowingspecificationin logs(m = log(M ): p,j,t p,j,t 9 9 (cid:88) (cid:88) m = α + γ E + β E D +u (A13) p,j,t pj i i i i j,i j,t i=−19 i=−19 where α are firmXproduct fixed-effects, γ are monthly fixed effects (with the dummy varipj i able E(cid:48)s corresponding to each calendar month), and u are random effects. The variables D i j,t j,t aredummyvariablesequaltooneifthefirmisownedbyaJapaneseparentcompany. AqualitativeversionoftheresultsisshowninTableA7. Theresultsconfirmthattherearefew significant price movements on import or export transactions for either Japanese or non-Japanese multinationalssurroundingtheTo¯hokuevent. C.5 Domestic Inputs It is also possible to evaluate the response of domestic inputs directly, using the limited information we have on quarterly firm-level employment and payroll information, taken from the Census 58

Bureau’sBusinessRegister(BR).56 TheStandardStatisticalEstablishmentList(SSEL)containsquarterlyemploymentandpayroll information for all employers (with some small exceptions) in the U.S. economy. This list is held separatelyasasingle-unit(SSEL-SU)andmulti-unit(SSEL-MU)file. TheReportofOrganization Survey (ROS) asks firms to list the establishments which report under a particular EIN, and this information is then recorded to the firm identifier on the Multi-Unit File. To build a quarterly employmentseriesatthefirm-level,welinktheEINvariablesontheSUfilewiththefirm-identifier linked with each EIN on the MU file. In principle, the four quarters of payroll listed on the SSEL iscombinedbyCensustocreateanannualpayrollfigureforeachestablishment,whichisthevalue recorded in the LBD. Similarly, the employment variable corresponding to the 1st quarter (week ofMarch12)fromtheSSEListhatusedbytheLBD. Once we merge the SSEL-based data with quarterly employment and payroll to the LBD for a particular year, we conduct a series of reviews to ensure that the annual payroll (and 1st quarter employment) roughly align. Any establishments with disagreements between the SSEL-based payrollandLBD-basedpayrollsuchthattheratiowasgreaterthan2orlessthan0.6weredropped. Afterthesemodificationsweremade,theremainderofthedataconstructionwassimilartothat in section B.3. We merge multinational indicators from the DCA, drop non-manufacturing firms, append the 2009, 2010, and 2011 files together, and keep only those firms that exist in each year. Using the same set of firms as a control group as specified in section 2.1, we run the following regression: 3 3 (cid:88) (cid:88) ∆emp = γ E + β E D +u (A14) j,t i i i i j,i j,t i=−3 i=−3 where∆emp ≡ ln(emp /emp ),whereemp indicatesemploymentatfirmj inquarter j,t j,t j,t−4 j,t t. We also re-run the equation specified in equation A14 using payroll pay as the dependent j,t variable (where ∆pay ≡ ln(pay /pay ). The qualitative results are shown in Table A6. j,t j,t j,t−4 We find no significant effects on either employment or payroll for Japanese firms in the quarter(s) following the shock. Of course, there are a number of reasons — principally labor adjustment costs — why one would expect little, if any, impacts on employment following this short-lived shock. Press releases dispatched by the Japanese automakers during this time indicated that no layoffs would occur. Rather, the firms indicated that they would use the production stoppages for employeeskillandsafetytraining. C.6 Alternate Specifications for Treatment Effects Regressions Our results from section 2.2 are based on a sample including all Japanese multinationals in manufacturing, and therefore uses a levels specification to allow for zeros in the firm-month observations. Becauselarger firms exhibitgreater absolutedeviations from trend,this roughly amountsto 56TheBRitselfreceivesquarterlypayrollandemploymentinformationforbusinessandorganizationalemployers fromtheIRS:Form941,theEmployer’sQuarterlyFederalTaxReturn. FormoreinformationontheBR(formerlythe SSEL),seeWalker(1997). 59

weighting firms based on size, such that the results correspond to a representative firm based on theaggregateeffectofthegroup. To see this, and to explore how the levels specification influences our interpretation, we repeat theanalysisonasubsetofthefirmsforwhichwecanviewthepercentagechangesdirectly. Specifically, we drop any firms with zeros in any month for intermediate imports or N.A. exports during thesample,andthentakelogsandHP-filtereachseriestoobtainpercentagedeviationsfromtrend for each firm.57 The results of this exercise are shown in Panel A of Figure A5. We suppress standarderrorsforthesakeofclarity;thedropsaresignificantatthe95%levelforbetween2-4months followingtheshock. Ifwereruntheseregressionswhilealsoweightingaccordingtothepre-shock sizeoffirms,weobtainapicturethatlooksmuchclosertoFigure6,seePanelBofFigureA5. Theseresultsindicatethatthelargerfirmsappeartobeaffectedthemostfromthisshock. This could be partly a result of our proxy being less effective for smaller firms that may not engage in consistentexportstoNorthAmerica. C.7 Probit Model of Import/Output Disruptions Wespecifyasimpleprobitmodeltounderstandtherelativeimportanceofvariousfirm-levelcharacteristicsintheimportandoutputdeclinesfollowingthetsunami. Themodelis Pr(XD = 1) = Φ[β JPN +β Exposed +β MMI +β Port +γ ] (A15) ik 1 ik 2 ik 3 ik 4 ik k where the dependent variable (XD) is an indicator equal to one if the N.A. exports of firm i in ik industry k are on average 20% below trend during the five months following the To¯hoku event. The independent variables are also indicators: JPN , for affiliates of Japanese multinationals; ik Exposed ,forfirmswithanexposuretoJapaneseinputsabove0.05oftotalmaterial;MMI for ik ik firms with an elevated MMI value pertaining to their average Japanese manufacturing locations; andPort forfirmsthattypicallyrelyonimportsviaportsdamagedbythetsunami.58 Theγ term ik k allows for industry-specific intercepts. To evaluate the determinants of an input disruption from Japan, we replace the dependent variable with JD, an indicator for a drop in Japanese imported ik inputsof20%relativetotrend. Panel A of Table A5 evaluates firm characteristics predicting a drop in U.S. output (XD), ik as measured by our proxy. The columns (1)-(4) show the results from different specifications with various combinations of the covariates in equation (A15). Both Japanese ownership and high exposure to Japanese inputs significantly increase the probability of an output disruption, as expected. In columns (3) and (4), we demonstrate that Japanese ownership is substantially more indicative of an output decline than high input exposure alone. In Panel B, we replace the dependent variable with the binary measure of a drop in Japanese intermediate inputs (JD). The i 57Were-weightthecontrolgroupasdescribedinsection2.1. 58Specifically, the MMI = 1 if the average Japanese manufacturing establishment corresponding to a U.S. ik firmisabovethemedian(roughlyanMMIof5.2)ofallfirmswithJapanesemanufacturinglocations. Theaffected ports are: Onahama, Hitachi, Kashima, Haramachi, Shiogama, Sendai, Shimizu, Ishinomaki, Hashinohe, Miya Ko, Kamaishi,Ofunato,andKessennuma. 60

results from these regressions indicate, unsurprisingly, that high exposure to Japanese imports are highly predictive of a subsequent disruption following the To¯hoku event. Apart from their exposure to imports from Japan, the Japanese affiliates are no more likely to suffer a disruption to these imports (see column 8).59 While the results from Table A5 are somewhat inconclusive, they nevertheless point to unique features of the production function of Japanese affiliates that yields directpass-throughofJapaneseshockstotheU.S.economy. Ourestimationprocedurethatfollows shouldhelptoclarifythispointfurther. C.8 Bootstrapping Standard Errors We use bootstrapping methods to compute measures of the dispersion of our point estimates. Using random sampling with replacement within each group of firms, we create 5000 new artificial samples and re-run the estimation procedure. The standard deviation of the point estimates across these bootstrap samples is shown in Table 2. To gain a more complete picture of the dispersion, wecreatedensityestimatesforeachsampleoffirmsacrosstheparameterspacefortheelasticities. ThesedensitiesareshowninFigureA7. C.9 Effects on U.S. Exports to Japan Another dimension of the transmission of the To¯hoku shock to the United States is U.S. exports backtoJapan. TotheextentthatfirmsintheU.S.receiveinputsfromJapanforprocessingandreshipmentbacktoJapan,onemightexpecttheU.S.exportstoJapanmayfallfollowingtheTo¯hoku event. On the other hand, U.S. firms may have increased shipments to Japan following the shock inordertooffsettwhatwerelargeproductionandsupplyshortageswithinJapan. Toevaluatethis, we re-run the specification in equation (5) but replace VM, the value of intermediate imports of i,t firm i in month t, with VJEXP, the value of Japanese exports of firm i in month t. The results are i,t shown in Figure A6. As is clear from the figure, we do not see strong evidence to support either hypothesis regarding this particular trade flow, at least as it pertains to Japanese multinationals in particular. C.10 Ward’s Automotive Data Ward’s electronic databank offers a variety of data products for the global automotive industry at a monthly frequency. We obtain Japanese production (by model), North American production (by plant and model), U.S. inventory (by model), and North American sales (by model) all for the period January 2000 to December 2012. The inventory and sales data also contain the country of origin, so one can separate out these variables based on whether a particular model was imported vs domestically-produced. The series cover the universe of the assembly operations of finished carsandlighttrucks. Unfortunately,thereisnoinformationoninputshipments. Fortheplant-levelanalysisofproduction,thebasesampleconsistsof167plantsactiveatsome point during 2000-2012. We remove plants that were not continuously in operation during the 59ThecombinedeffectofthecoefficientsonJapanandJPN*Expis-0.16,andnotsignificant. 61

period 2009-2012, and combine several plants that are recorded separately in the data, but are in effect the same plant. After these modifications, the sample reduces to 62 plants, 22 of which are owned by a Japanese parent. The average monthly production in the three months preceding the shock is 12,904 for Japanese plants, and 14,903 for Non-Japanese plants. The specification is identicaltothatinsection2.1: 9 9 (cid:88) (cid:88) Q = α +α + γ E + β E JPN +u (A16) i,t 0 i p p p p i,p i,t p=−14 p=−14 where here the variable Q is auto production by plant i in month t, after removing a planti,t specifictrendthoughMarch2011. Becausetheseplantscanbetrackedwithsomeconfidenceback in time, it is reasonable here to remove seasonality directly, rather than assume a shared seasonal component between the treated and control groups as in section 2.2. We use the X12-ARIMA model,providedbytheNationalBankofBelgium,andapplyittoeachseriesbeforecorrectingfor trend. TheresultsfortheJapaneseplantsaremostlysimilar,asshownintableA8. 62

TableA4: SummaryStatistics: InventoriesbyFirmType Japanese Non Multinationals Multinationals Inputs 0.83 1.08 Output 0.31 0.45 Source: CM,LFTTD, DCA, and UBP asexplained in the text. The data are for year 2007. This table reports the average monthly supply of inventories [(usage/12)/beginningperiodinventorystock]formaterialsandoutput. Figure A2: Evidence of Potential Spillovers: Relative Non-Japanese Imported Inputs of Japanese Firms: FractionofPre-ShockLevel Source: LFTTD-DCA-UBPasexplainedintext. Thisfigurereportsthenon-JapaneseintermediateimportsoftheU.S.affiliatesofJapanesefirmsrelativetoa controlgroupofothermultinationalfirms. Thevaluesarepercentchangesfromthepre-shocklevelofeach series, defined as the average of the months December 2010, January 2011, and February 2011. Standard errorsaresuppressedtoreporttheseriesinpercentageterms. Thedropsaresignificantatthe95percentlevel formonths0,1,2,3,and5followingtheearthquake. 63

FigureA3: JapaneseProducts: AverageDistancefromBenchmarkCostShares: JPNMultinationals Source: LFTTD-DCA-UBPasexplaininthetext Underlyingthisfigureisthecalculationoftheaveragetotal(absolute)deviationsfromabenchmarkmeasure ofafirm’scostsharesacrossinputproductsfromJapan. SeeequationA12inthetext. Thefigurereportsthe meanacrosstheJapanesemultinationalsusedinthesection3. 64

FigureA4: AutomotiveProduction,Inventory,SalesbyFirmType,DistributedLagModel Source: Ward’sAutomotiveDatabase This figure reports North American production, and U.S. sales and inventory data according to firm type: Japanese and non-Japanese firms. The values are coefficient estimates taken from a distributed lag model, exploitingtime-seriesvariationonly. Theunderlyingserieshavebeenseasonallyadjusted,logged,andHP- FilteredStandarderrorsaresuppressedintheinterestsofclarity.TheJapaneseautomakersareHonda,Mazda, Mitsubishi,Nissan,Toyota,andSubaru. 65

Figure A5: Relative Inputs and Output (Proxy) of Japanese Firms (Reduced Sample) Logged, HP-Filtered A.NoSize-Weighting B.Size-Weighted Source: LFTTD-DCA-UBPasexplainedintext. These figures report the relative percentage deviations from trend of Japanese affiliates relative to a control group of other multinational firms. The values are coefficient estimates taken from an interaction of a Japanese-firmdummywithamonthlydummy–additionalbaselinemonthlydummiesremoveseasonaleffects. These results reflect a reduced sample with no firm-month zeros in imported inputs or N.A. exports. Thedataislogged,andHP-filteredusingamonthlys6m6oothingparameter.

FigureA6: DynamicTreatmentEffects: RelativeJapaneseExportsofJapaneseFirms Source: LFTTD-DCA-UBPasexplainedintext. ThesefiguresreporttheJapaneseexportsoftheU.S.affiliatesofJapanesefirmsrelativetoacontrolgroupof othermultinationalfirms. ThevaluesarecoefficientestimatestakenfromaninteractionofaJapanese-firm dummy with a monthly dummy – additional baseline monthly dummies remove seasonal effects. Standard errorsareclusteredatthefirmlevel. 67

scitsiretcarahCmriFybnoitpursiDtuptuO.S.UdnatropmIesenapaJgnitciderP :5AelbaT stropmIesenapaJotnoitpursiD:BlenaP )yxorp(tuptuO.S.UotnoitpursiD:AlenaP 1 = DJ 1 = DX i i )8( )7( )6( )5( )4( )3( )2( )1( ***686.0 ***013.0 ***707.0 **743.0 ***253.0 ***344.0 napaJ )051.0( )511.0( )7190.0( )251.0( )711.0( )1290.0( ***199.0 ***636.0 ***418.0 041.0 541.0 ***153.0 desopxE )441.0( )011.0( )0880.0( )941.0( )211.0( )6880.0( ***848.0- 17700.0pxE*NPJ )222.0( )822.0( ***603.0 ***143.0 ***983.0 ***643.0 ***871.0- ***871.0- *121.0- ***671.0- IMM )4070.0( )4960.0( )7660.0( )1960.0( )3860.0( )6760.0( )6460.0( )6760.0( 471.0 861.0 712.0 842.0 791.0- 441.0- 471.0stroP )312.0( )312.0( )212.0( )112.0( )622.0( )522.0( )422.0( 866.4- 276.4- 276.4- 276.4- 476.0- 476.0- 476.0- 476.0tnatsnoC )00.58( )87.58( )87.58( )87.58( )186.0( )186.0( )186.0( )186.0( seY seY seY seY seY seY seY seY yrtsudnI seimmuD 1542 1542 1542 1542 1542 1542 1542 1542 snoitavresbO 1.0<p*,50.0<p**,10.0<p*** dnatropmiNPJfonoitciderpledomtiborpafostluserehtstroperelbatsihT .txetehtnidenialpxesaSGSUdna,PBU,ACD,DTTFL :ecruoS .selbairavehtfonoitinfiedarof1.2noitceseeS .scitsiretcarahcmrfinodesabnoitpursid)tuptuo(stropxe.A.N 68

FigureA7: DensityEstimatesofElasticitiesAcrossBootstrapSamples A.Japanesevsnon-JapaneseMultinationals: MaterialsElasticity(ω) B.Japanesevsnon-JapaneseMultinationals: Materials-Capital/LaborElasticity(ζ) 69

FigureA7: DensityEstimatesofElasticitiesAcrossBootstrapSamples C.Non-multinationalsandAllFirms: MaterialsElasticity(ω) D.Non-multinationalsandAllFirms: Materials-Capital/LaborElasticity(ζ) Source: LFTTD-DCA-UBPasexplainedintext. 70

TableA6: DynamicTreatmentEffects: QuarterlyEmployment/PayrollSurroundingTo¯hokuEvent Log4-QuarterDifference Employment Payroll IndependentVariables (1) (2) Q2 2010(t=-3) pos*** pos*** Q3 2010(t=-2) pos*** pos*** Q4 2010(t=-1) pos*** pos*** Q1 2011(t=0) pos*** pos*** Q2 2011(t=1) pos*** pos*** Q3 2011(t=2) pos*** pos*** Q4 2011(t=3) pos*** pos*** JPNxQ2 2010(t=-3) neg neg JPNxQ3 2010(t=-2) neg neg JPNxQ4 2010(t=-1) neg neg JPNxQ1 2011(t=0) neg neg JPNxQ2 2011(t=1) neg neg JPNxQ3 2011(t=2) neg neg JPNxQ4 2011(t=3) neg pos constant neg*** neg*** FirmFixedEffects Yes Yes Observations R-squared Source: SSELandDCAasexplainedinthetext. Robuststandarderrors(clusteredatthefirmXProductlevel)pertainingto eachsigncoefficientareindicatedby: ***p<0.01,**p<0.05,*p<0.1. ThistablereportsqualitativefeaturesoffirmemploymentandfirmpayrollinthequarterssurroundingtheTo¯hokuearthquakeandtsunami. The firstsetofcoefficientscorrespondtoquarterdummies,whereasthesecondset(JPNx)correspondtotheinteractionofaJapanesefirmdummy with quarter dummies. See equation A14 in the text. The dependent variableisthefour-quarterlogdifferenceofemployment(payroll). 71

TableA7: DynamicTreatmentEffects: UnitValuesofTradeSurroundingTo¯hokuEvent LogUnit-Valueof: JPNImports: JPNImports: N.A.Exports N.A.Exports RelatedParty Non-RelatedParty RelatedParty Non-RelatedParty IndependentVariables (1) (2) (3) (4) Sep2010(t=-6) neg** pos pos* pos Oct2010(t=-5) pos neg pos** pos Nov2010(t=-4) pos pos pos** pos Dec2010(t=-3) pos neg pos pos Jan2011(t=-2) neg pos neg pos Feb2011(t=-1) pos neg pos** pos Mar2011(t=0) neg pos pos pos Apr2011(t=1) pos pos pos pos May2011(t=2) neg pos neg pos** Jun2011(t=3) pos** neg pos** neg Jul2011(t=4) neg neg pos neg Aug2011(t=5) pos pos neg pos Sep2011(t=6) pos pos pos pos** Oct2011(t=7) neg neg pos pos Nov2011(t=8) pos neg pos neg Dec2011(t=9) neg pos pos** pos JPNxSep2010(t=-6) pos** neg* neg** neg JPNxOct2010(t=-5) neg* pos pos pos JPNxNov2010(t=-4) neg pos neg neg JPNxDec2010(t=-3) neg neg* pos pos JPNxJan2011(t=-2) pos neg neg neg JPNxFeb2011(t=-1) neg pos pos pos** JPNxMar2011(t=0) pos pos neg neg JPNxApr2011(t=1) neg pos neg neg JPNxMay2011(t=2) pos neg pos neg JPNxJun2011(t=3) neg pos* neg neg JPNxJul2011(t=4) pos neg pos neg JPNxAug2011(t=5) neg* neg* neg pos JPNxSep2011(t=6) neg neg neg neg JPNxOct2011(t=7) pos neg neg neg JPNxNov2011(t=8) neg neg neg pos JPNxDec2011(t=9) neg neg pos neg constant pos neg neg neg FirmXProductFixedEffect Yes Yes Yes Yes Observations R-Squared Source: LFTTD,DCA,andUBPasexplainedinthetext. 72 Robuststandarderrors(clusteredatthefirmXProductlevel)pertainingtoeachsigncoefficientareindicatedby: *** p<0.01,**p<0.05,*p<0.1. Thistablereportsqualitativefeaturesoftheunitvaluesoftradesurroundingthe2011To¯hokuearthquakeandtsunami. Thefirstsetofcoefficientscorrespondtomonthlydummies,whereasthesecondset(JPNx)correspondtotheinteractionofaJapanesefirmdummywithmonthlydummies. SeeequationA13inthetext.

TableA8: DynamicTreatmentEffects: N.A.AutomotiveProduction (1) (2) (1) (2) VARIABLES Prod Prod VARIABLES(cont’d) Prod(cont’d) Prod(cont’d) Nov2010(t=-4) 91.06 17.78 JPNxNov2010(t=-4) -195.8 -341.7 (649.9) (608.8) (841.9) (799.2) Dec2010(t=-3) -1,973*** 310.3 JPNxDec2010(t=-3) -385.0 -408.3 (467.5) (497.5) (736.5) (706.4) Jan2011(t=-2) -611.5 1,083* JPNxJan2011(t=-2) 781.0 -1,092 (637.3) (618.7) (792.1) (804.6) Feb2011(t=-1) 694.9* 756.3* JPNxFeb2011(t=-1) -1,142 -1,210* (401.9) (394.7) (696.2) (666.8) Mar2011(t=0) 4,356*** 1,483*** JPNxMar2011(t=0) -3,515*** -2,592*** (524.9) (389.1) (812.0) (842.7) Apr2011(t=1) -216.2 305.5 JPNxApr2011(t=1) -6,239*** -6,099*** (707.7) (620.4) (1,303) (1,282) May2011(t=2) 1,584*** 799.1 JPNxMay2011(t=2) -7,244*** -6,625*** (525.4) (511.3) (1,651) (1,740) Jun2011(t=3) 1,366** -499.3 JPNxJun2011(t=3) -4,564*** -3,423** (623.6) (594.9) (1,248) (1,320) Jul2011(t=4) -4,512*** 123.3 JPNxJul2011(t=4) -2,143 -3,723*** (878.4) (606.2) (1,430) (1,045) Aug2011(t=5) 685.6 -1,323** JPNxAug2011(t=5) -1,275 -1,108 (744.0) (648.1) (970.8) (1,012) Sep2011(t=6) -836.5 -1,895*** JPNxSep2011(t=6) -359.4 40.37 (663.7) (641.5) (930.7) (959.8) Oct2011(t=7) -338.0 -1,434** JPNxOct2011(t=7) 93.27 -265.4 (662.3) (632.4) (885.6) (785.8) Nov2011(t=8) -1,393** -1,443** JPNxNov2011(t=8) -1,318 -2,059* (582.8) (601.2) (1,159) (1,183) Dec2011(t=9) -4,511*** -1,619** JPNxDec2011(t=9) 759.1 24.95 (774.4) (655.5) (1,105) (803.9) Constant -1,535*** -1,683*** (89.30) (91.95) PlantFixedEffects Yes Yes RemovePlant-SpecificPre-ShockTrend Yes Yes RemoveSeasonalComponent No Yes Observations 2,976 2,976 R-squared 0.260 0.272 Source: Ward’sAutomotiveYearbook Robuststandarderrors(clusteredattheplantlevel)inparentheses. ***p<0.01,**p<0.05,*p<0.1. 73