Trade and Domestic Production Networks

Transcription

1 Trade and Domestic Production Networks Feix Tintenot a,c, Ayumu Ken Kikkawa a, Magne Mogstad a,c, Emmanue Dhyne b a University of Chicago b Nationa Bank of Begium c NBER November 26, 2017 Abstract We use administrative data from Begium with information on domestic firm-to-firm saes and foreign trade transactions to study how internationa trade affects firm efficiency and rea wages. The data aow us to construct the buyer-suppier network of the Begian economy. We document that most firms that do not directy import or export sti have arge indirect exposure to foreign trade, and that a firm s output is affected by idiosyncratic shocks to its buyers and suppiers. These empirica findings motivate and guide the deveopment of a mode with domestic production networks and internationa trade. We obtain new sufficient statistics resuts for the effects of trade in a mode with fixed network structure, and we deveop a tractabe mode of endogenous domestic production networks. Comparing our resuts to those we obtain using existing approaches highights the importance of data on and modeing of domestic production networks in studies of internationa trade. We are gratefu to Costas Arkoakis, Emmanue Farhi, Teresa Fort, Matthew Grant, Basie Grassi, Rob Johnson, Harry Li, Aejandra Lopez Espino, Ferdinando Monte, and Andrei Nagornyi for usefu conversations. The views expressed in this paper are those of the authors and do not necessariy refect the views of the Nationa Bank of Begium or any other institution with which one of the authors is affiiated.

2 1 Introduction Over the past few decades, the focus of research on internationa trade has shifted from countries and industries towards firms. This shift is in no sma part due to the increased avaiabiity of firm-eve transaction data on trade. One important insight from this data is that few firms directy import or export goods (Bernard, Jensen, Redding, and Schott, 2007). However, the concentration of imports and exports does not necessariy impy that few firms benefit from foreign trade. Even if firms themseves do not import or export, they may sti buy from or se to domestic firms that trade internationay. Capturing this channe, however, is chaenging since domestic firm-to-firm transactions are rarey observed. In the absence of such data, quantification of the effects of foreign trade on a firms requires strong assumptions, such as a common intermediate good (Eaton and Kortum, 2002, and Baum, Learge, and Peters, 2016) or the same import shares across importing firms within broad industries (Caiendo and Parro, 2015, and Costinot and Rodríguez-Care, 2014). The goa of this paper is to combine data on domestic firm-to-firm saes with information on foreign trade transactions to study how internationa trade affects rea wages and efficiency of a firms, incuding those that do not directy export or import. Our anaysis empoys a pane dataset with detaied information on Begian firms for the years This dataset is based on severa data sources that we have inked through identifiers. Annua accounts provide data on input factors and output, custom records and intra-eu decarations give information on exports and imports, and a vaue-added tax (VAT) registry provides information on domestic firm-to-firm transactions. Using this data, we empiricay examine severa new dimensions of firms in internationa trade before deveoping and estimating a mode of trade and domestic production networks. In Section 2, we describe the data, construct the domestic production (buyer-suppier) network of the Begian economy, and provide two new empirica findings. The first is that most firms are exposed to foreign trade through their production network. Whie ony 15% of firms import directy, 97% of firms obtain foreign inputs either directy or indirecty through domestic suppiers which use foreign inputs in their production process. Indeed, most firms are heaviy dependent on foreign inputs, but ony a sma number of firms show that dependence through the direct imports observed in firm-eve transaction data on trade. For exampe, in a majority of firms, at east 40% of input costs are spent on goods that are imported directy or indirecty. The second empirica finding is that foreign trade shocks seem to propagate across firms within production networks. Foowing Hummes, Jørgensen, Munch, and Xiang (2014), we measure trade shocks as changes in word export suppy and word import demand of countryproduct combinations in which the firm had a previous trade reationship. They argue that these shocks are pausiby exogenous and that their impact varies markedy across firms, 2

3 because the firms even within the same sector do not have a inputs in common. Using our data, we find that positive export shocks to the firm s buyers and positive import shocks to the firm s suppiers both tend to increase the firm s output, even after controing for direct shocks to the firm itsef and for shocks to the set of potentia buyers and suppiers of the firm. Taken together, these two empirica findings highight that information about domestic firm-to-firm transactions is key to understand the extent to which firms rey on foreign input and to anayze the propagation of trade shocks. Motivated and guided by this evidence, we deveop and estimate a mode of domestic production networks and internationa trade. In our mode, firms combine imports, inputs produced by other domestic firms, and abor to produce differentiated products with a constant easticity of substitution production function. Firms are finite and monopoisticay competitive. In Section 3, we assume a fixed network structure (i.e., the buyer-suppier reationships do not change in response to trade shocks) and quantify how internationa trade affects firms production costs and consumer prices. The cost reduction for an individua firm due to internationa trade depends on two quantities ony: the share of input costs that is spent on goods that are imported directy or indirecty and the easticity of substitution in the production function. We appy this sufficient statistics formua to our data, and find that internationa trade is important in reducing the cost of production for pausibe vaues of the easticity of substitution. For exampe, with an easticity of substitution in the production function of 2, we cacuate that shutting down internationa trade woud increase the cost of the majority of Begian firms by at east 70%. To compute the wefare gains from trade, we combine information on firms saes to domestic househods with an assumption about the easticity of substitution in the utiity function. Our baseine resuts impy that the consumer price index in Begium woud be 77% higher in the absence of internationa trade. Whie assuming a fixed network structure is convenient to take the mode to the data, it does not aow us to capture how buyer-suppier reationships may change in response to trade shocks. In Section 4, we therefore deveop a mode of trade with endogenous network formation. In particuar, we et firms optimay choose their set of suppiers (i.e. the firm s sourcing strategy) subject to a buyer-suppier-specific fixed cost for adding a suppier. Aowing for endogenous network formation is chaenging for two reasons. First, firms face a arge discrete choice probem of which suppiers to incude in their sourcing strategy. Second, firms sourcing strategies are interdependent, creating a arge fixed point probem: firms take into account the expected sourcing strategies of others in order to determine their own optima sourcing strategy, a the whie knowing that other firms are thinking in the same way. Buiding on Jia (2008) and Antras, Fort, and Tintenot (2017), we overcome the first 3

4 chaenge by using attice theory to sove firms arge combinatoria discrete choice probems. To address the second chaenge we consider the formation of an acycic network, postuating an ordering of firms and restricting the eigibe set of suppiers to firms that appear prior to the buyer. 1 Whie restrictive, this assumption aows us aso to sove a mode of firm trade with endogenous formation of domestic buyer-suppier reationships. We use method of simuated moments to estimate the mode, and then perform counterfactuas to draw inference about the impact of shutting down internationa trade with and without endogenous network formation. Our findings suggest that aowing for endogenous formation of buyersuppier reationships tend to attenuate the effects of banning trade on firms cost. Under endogenous network formation, we find a price index increase around 15% ower than under a fixed network. Our paper contributes to a growing iterature on the economy-wide effects of foreign sourcing. 2 Many studies use aggregate data ony, reying on the assumption that firms import intensities are equaized which is at odds with the data. Using firm-eve data on trade transactions, Baum et a. (2016) show that accounting for heterogeneity in import exposure significanty affects the measurement of the gains from internationa trade. Their mode assumes that firms can import directy and purchase a common intermediate good. Taking advantage of data on domestic firm-to-firm transactions, we reax the assumption of a common intermediate good, and derive a parsimonious sufficient statistics formua for a mode with a fixed production network. We aso go beyond the fixed network structure, soving a mode of endogenous network formation with a finite number of firms and fixed costs for adding suppiers. This contribution buids on the goba sourcing mode of Antras et a. (2017). Whie they distinguish between fina good and intermediate good sectors, we consider a more genera input-output structure between firms. In addition, our mode captures not ony the firms decisions with respect to foreign sourcing but aso their choices of domestic sourcing strategies. 3 Our paper aso reates to a iterature on the formation and consequences of domestic production networks. 4 Bernard, Moxnes, and Saito (2016b) adapt the mode of Antras et a. (2017) to search for domestic suppiers in different ocations, where each ocation has a continuum of intermediate-good-producing firms. They find significant improvements in firm 1 See Spieger (2016) for a recent contribution in economics studying beief formation in a directed acycic network. 2 See for exampe Antràs and Hepman (2004), Antràs and Hepman (2008), Rodríguez-Care (2010), Garetto (2013), Hapern, Koren, and Szeid (2015), Gopinath and Neiman (2014), Amiti and Konings (2007), Godberg, Khandewa, Pavcnik, and Topaova (2010), and De Loecker, Godberg, Khandewa, and Pavcnik (2016). 3 Our work is aso reated to the anaysis in Caiendo and Parro (2015) and Ossa (2015). They find the gains from trade to be arger when taking sectora input-output inkages into account. 4 A growing body of work studies how firms meet internationa trading partners. See for exampe Chaney (2014), Chaney (2016), Moraes, Sheu, and Zaher (2015), and Eaton, Kinkins, Tybout, and Xu (2016). 4

5 performance from a reduction in interna search costs in Japan. Furusawa, Inui, Ito, and Tang (2017) deveop a variant of the goba sourcing mode of Antras et a. (2017), and use Japanese buyer-suppier ink data to test the mode s predictions. Oberfied (2017) deveops a theory in which the network structure of production forms endogenousy among firms that each purchase a singe input. Lim (2015) deveops a dynamic mode of network formation in which each firm has a continuum of domestic suppiers. With a continuum of suppiers and buyers, the saes from one firm to another are negigiby sma and a ink between two particuar firms has no effect on aggregate outcomes. In contrast to these papers, we deveop a mode of endogenous network formation with a finite set of suppiers, and incorporate both firm exporting and importing decisions. Whie our theory assumes simpe soutions for the pricing game between firms, Kikkawa, Magerman, and Dhyne (2017) expore the segmentation of markets for different buyers, with suppier firms having heterogeneous bargaining power in the suppier-buyer reationships. Finay, our paper reates to a iterature that anayzes how production networks matter for aggregate effects and transmission of idiosyncratic firm shocks. Gabaix (2011) provides conditions under which granuar shocks can affect aggregate fuctuations. Acemogu, Carvaho, Ozdagar, and Tahbaz-Saehi (2012) study the transmission of shocks aong sectora input-output networks. Magerman, De Bruyne, Dhyne, and Van Hove (2016) test both channes with the Begium domestic firm-to-firm data. Barrot and Sauvagnat (2016), Boehm, Faaen, and Pandaai-Nayar (2015), and Carvaho, Nirei, Saito, and Tahbaz-Saehi (2016) use natura disasters to study the propagation of shocks in production networks. Carvaho and Voigtänder (2015) anayze the adoption of inputs by innovators and the evoution of the domestic production network. Huten (1978) provides conditions under which the underying network structure is irreevant for quantifying the propagation of shocks up to a first-order approximation as ong as firms initia size and the magnitudes of the idiosyncratic shocks are observed. 5 In recent work, Baqaee and Farhi (2017) iustrate that the second-order effects of shock propagation arising from networks can be arge. 6 Our paper extends the anaysis of shock propagation to foreign trade shocks, whie aowing buyer-suppier reationships to change in response to these shocks. 5 As shown by Kikkawa et a. (2017), to appy the Huten theorem to a sma open economy setting one woud need very strong conditions that are immediatey vioated in our data: in particuar, a firms woud need have a constant ratio of export saes to saes to domestic fina consumers. 6 Other recent contributions to determining the effects of networks incude Baqaee (2014), Carvaho and Grassi (2017), as we as in the context of financia frictions, Bigio and La o (2016) and Liu (2016). Ataay, Hortacsu, Roberts, and Syverson (2011) characterize the buyer-suppier network of the US economy. 5

6 2 Trade and production networks: Data and evidence This section describes the data, documents firms direct and indirect exposure to foreign trade, and shows how the output of a firm is affected by trade shocks to its buyers and suppiers. 2.1 Data sources and sampe seection Our anaysis draws on three administrative data sources from Begium, accessibe ony at the Nationa Bank of Begium, for the years These data sources can be inked through unique identifiers, assigned and recorded by the government for the purpose of coecting vaue-added taxes (VAT). Beow we briefy describe our data and sampe seection, whie additiona detais are given in Appendix C. The first data source is the Business-to-Business (B2B) transactions database (see aso Dhyne, Magerman, and Rubinova (2015)). By aw, a Begian firms are required to fie the annua saes to each buyer (provided the annua saes to a given buyer exceeds e250). Thus, the B2B dataset aows us to measure accuratey the identity of the firms suppiers and buyers. The second data source is the annua accounts fied by Begian firms. These data contain detaied information from the firms baance sheets on output (such as revenues) and inputs (such as capita, abor, intermediates) as we as 4-digit (NACE) industry codes and geographica identifiers at the zip code eve. In addition, the annua accounts incude information about ownership shares in other enterprises. The third set of data source is the Begian customs records and the intra-eu trade decarations. These data contain information about internationa trade transactions in each year and for every firm. Both imports and exports are disaggregated by product and origin or destination. One chaenge with using the Begian data is that the information is recorded at the eve of the VAT-identifier. The probem is that a given firm may have severa VAT-identifiers (for accounting or tax reasons). 7 Whie organizationa choices and transactions across units within a firm are of interest, our paper is centered on trade between firms. Thus, if a firm has mutipe VAT-identifiers, we aggregate a data up to the firm eve using information from the baance sheets about ownership structure. Detais of the aggregation are outined in Appendix C.1. In 2012, for exampe, the aggregation converts 896,000 unique VAT-identifiers into 860,000 unique firms. Of these firms, 842,000 had a singe VAT-identifier. However, the 18,000 firms with mutipe VAT-identifiers are important, accounting for around 60% of the tota output in the dataset. 7 Existing papers tend to abstract from this issue, anayzing the data at the eve of the VAT-identifier. See e.g. Amiti, Itskhoki, and Konings (2014), Magerman et a. (2016) and Bernard, Banchard, Van Beveren, and Vandenbussche (2016a)). 6

7 After constructing a firm-eve dataset, we impose a few sampe restrictions. We excude firms in the government or financia sector. In addition, we restrict the sampe to firms with positive abor costs and empoyment, tangibe assets of more than e100, and positive tota assets in at east one year during our sampe period. These criteria are simiar to the ones used by De Loecker, Fuss, and Van Biesebroeck (2014). Appying these criteria reduces the number of firms significanty. In, 2012, for exampe, ony 139,605 firms satisfy the above criteria. The arge reduction in sampe size is mosty driven by the excusion of oca firms without empoyees (sef-empoyment) from the sampe (687,700 firms in 2012). Lasty, we drop foreign firms with no oca production activity in Begium from the sampe. These account for a sizabe fraction of imports and exports, but have no domestic production activity in Begium. Tabe 1 iustrates that our seected estimation sampe of firms provides reativey good coverage of aggregate vaue added, gross output, exports and imports. However, tota saes in our sampe is arger than what are reported in the nationa statistics. The reason is that the output of trade intermediaries in the nationa statistics is measured by their vaue added instead of their tota saes. We refer to Appendix C.2 for the same statistics for a Begian firms. Tabe 1: Coverage of seected sampe Year GDP Output Seected sampe Imports Exports (Exc. Gov. & Fin.) Count V.A. Saes Imports Exports , , , Notes: A numbers except for Count are denominated in biion Euro in current prices. Begian GDP and output are for a sectors excuding pubic and financia sector. See Appendix C.2 for the same statistics for the tota economy. Data for Begian GDP, output, imports and exports are from Eurostat. 2.2 Direct and indirect exposure to foreign trade The Begian data aow us to construct the buyer-suppier reationships of the Begian economy, and therefore document firms direct and indirect exposure to foreign trade. We define firm j s tota foreign input share as the sum of firm j s direct foreign input share, s F j, and the direct foreign input share of firm j s suppiers, suppiers suppiers, and so forth, each weighted by the firm-pair-specific input shares (s ij, s ki,...): 7

8 s T F ota j = s F j + i Z D j s ij s F i + k Z D i s ki (s F k + ), (1) } {{ } s T F ota i where Zj D denotes the set of domestic suppiers of firm j, and the denominator of the input shares is the sum of abor costs, purchases from other firms, and imports. Note that the definition of the tota foreign input share is recursive: a firm s tota foreign input share is sum of its direct foreign input share and the share of its inputs from other firms mutipied by those firms tota foreign input shares. Whie many firm-eve datasets contain information about the direct foreign input share s F j, our data aso offer information about firm-pairspecific input shares, s ij. As a resut, we are abe to cacuate the tota foreign input share for every firm. We note that there is one inherent assumption in our definition of the tota foreign input share: When a firm ses its output to mutipe firms or fina consumers, the foreign input share in the costs of producing these goods is assumed to be the same for a buyers (i.e., independent of the identity of the buyer). This assumption is consistent with the mode we deveop in Sections 3 and 4, where each firm produces a singe product. In Figure 1a, we dispay a histogram of the tota and direct foreign input shares of the Begian firms. Whie ony 15% of firms import directy, 97% of firms obtain foreign inputs either directy or indirecty through domestic suppiers which use foreign inputs in their production process. Indeed, most firms are heaviy dependent on foreign inputs, but ony a sma number of firms show that dependence through the direct foreign input shares observed in firm-eve transaction data on trade. In the median firm, for exampe, the tota foreign input share is 41%. By comparison, the tota foreign input shares are 21% and 60% at at the 20th and 80th percentie. We present direct and tota foreign input shares by sector in Appendix D.1. Even in the service sector, in which firms have a very ow share of direct foreign inputs, the median firm s tota foreign input share is as arge as 28%. Figure 1b performs a simiar exercise, but now ooks at tota export shares and direct export shares. We cacuate the tota export share of firm j, rjf T ota, as the sum of the share of revenue of firm j coming from directy export goods, r jf, and the share of revenue coming from goods sod to other domestic firms, mutipied by those firms tota export shares: r T ota jf = r jf + r ji r T ota if, (2) i W j where W j denotes the set of domestic buyers of firm j, and the denominator of the export shares is the tota revenue of the firm. Direct export is even more concentrated than direct import, both on the intensive and extensive margin. Whie ony 10% of firms export directy, 8

9 Figure 1: Histogram of direct and indirect inkages to foreign trade (a) Direct and tota foreign input share Count Foreign input share Direct Tota (b) Direct and tota export share Count Export share Direct Tota Notes: Tota foreign input share of firm i, s T F ota i is cacuated by soving s T F ota i = s F i + j Z i s ji s T F ota j where s F i is i s direct foreign input share, and s ji is j s share among i s inputs. Tota export share firm i, rif T ota is cacuated by soving rif T ota = r if + j W i r ij rjf T ota where r if is i s share of exports in its revenue, and r ij is share of i s revenue that arises from saes to firm j. The figures are based on the anaysis of 139,605 private sector firms in Begium in The horizonta ines represent scae breaks on the vertica axis. 9

10 Figure 2: Size premium of direct and indirect inkages to foreign trade (a) Foreign inputs Log saes Foreign input share Direct Tota (b) Exports Log saes Export share Direct Tota Notes: The two figures dispay the smoothed vaues with 95% confidence intervas of kerne-weighted oca poynomia regression estimates of the reationship between firms saes and their eves of participation in foreign trade. We use the Epanechnikov kerne function with kerne bandwidth of 0.01, piot bandwidth of 0.02, degree of poynomia smooth at 0, and smooth obtained at 50 points. Log saes are demeaned with 4-digit industry fixed effects. 10

11 82% of firms export either directy or indirecty by seing to domestic buyers which subsequenty trade internationay. In terms of trade voume, however, export remains reativey concentrated even after taking the indirect export into account. The tota export share is ony 2% in the median firm, whereas it is 19% at the 80th percentie. In contrast, Figure 1a showed that most firms are heaviy dependent on foreign inputs. This difference is party driven by the service sector. Whie many firms in this sector (e.g., restaurants) rey on foreign inputs often obtained indirecty through domestic suppiers reativey few export directy or se to domestic firms that are exporting directy or indirecty (see Appendix D.2 for direct and tota foreign input shares by sector). 8 Across a wide range of countries and industries, firms that directy export or import have been shown to be arger than other firms. A natura question is whether the positive association between firm size and internationa trade aso carries over to indirect export or import. Figure 2 investigates this, cacuating the average size of firms by direct and tota foreign input shares as we as by direct and tota export shares. We demean the og of firm saes using the firm s four-digit industry average, so that a firm with og saes of zero is the size of an average firm in its industry. Figure 2 iustrates that average firm size is increasing in both direct and tota foreign input shares. However, firms that import directy tend to be much arger than firms that buy foreign inputs through domestic firms. Indeed, firms with ess than 60% in tota foreign input shares are, on average, of simiar size as the average firm in their industry. A simiar pattern is evident for size and export. Firms with very high tota export shares tend to be arge. However, over most of the tota export share distribution, there is ony a weak reationship between firm size and tota export share. Taken together, the resuts in Figure 2 suggest that firms do not have to be arge to rey heaviy on foreign inputs or to have most of their saes going utimatey to a foreign country. 2.3 Trade shocks and the production network The anaysis in Section 2.2 showed that most firms are exposed to foreign trade through their production network. This finding raises the questions of whether, and to what extent, trade shocks propagate across firms within production networks. To investigate these questions, we buid on the work by Hummes et a. (2014), who construct measures of trade shocks from changes in word export suppy and word import demand of country-product combinations in which the firm had a previous trade reationship. They argue these shocks are pausiby exogenous, and show that their impact varies markedy across firms, because the firms do not have a inputs in common. Hummes et a. (2014) use the trade shocks to estimate wage 8 Another possibe expanation is that it is difficut to measure a forms of export in the service sector. For exampe, when a foreigner eats at a Begian restaurant, it is technicay an export transaction. However, such transactions are not recorded in our data. 11

12 effects of offshoring and exporting in Denmark. We appy the same identification strategy to the Begian setting with the goa of examining whether trade shocks to the firm s actua buyers or suppiers have stronger impact on its output than trade shock to potentia suppiers and customers. To make the identification strategy precise, consider the foowing regression mode in first-differences: og Y it =β C X og X C it + β S M og M S it + βx P C og Xit P C + βm P S og Mit P S + β X og X it + β M og M it + ϕ t + ɛ it. (3) where Y it denotes the tota saes of firm i in year t, and denotes the change in the variabe from year t 1 to t. In addition to caender time fixed effects ϕ t, we incude three sets of expanatory variabes. The first is the measures of import shocks to firm i s suppiers og M S it and export shocks to firm i s buyers og X C it. Our goa is to consistenty estimate the coefficients on these variabes, βx C and βs M. However, there are severa threats to identification. One is that og Mit S and og Xit C are ikey to correate with trade shocks to i s potentia suppiers and buyers. We therefore incude measures of import shocks to firm i s potentia suppiers, og Mit P S, and export shocks to firm i s potentia buyers, og X P C Another concern is that og Mit S and og Xit C coud be correated with trade shocks that affect the firm i directy (through it s direct import demand or suppy). To address this concern, we contro for export shocks, og X it, and import shocks, og M it, to firm i itsef. To take the regression mode to the data, we need to construct the various measures of trade shocks. To this end, we foow the shift-share approach in Hummes et a. (2014). To construct an export shock for firm i, og X it, we use information about the firm s productcountry-eve exports in year t 1 (the share variabe capturing firm-specific exposure), and the aggregate shift in word import demand for each country and product: og X it = og ic,t 1 WID k,c,t og ic,t 1 WID k,c,t 1. k,c k,c }{{}}{{} X it,t 1 X it 1,t 1 r k,x The term r k,x ic,t 1 is the share of exports of firm i at year t 1 that fas on product k sod to country c, and WID k,c,t is the word import demand (excuding imports from Begium) of country c for product k. 9 r k,x it. We measure the export shock for firms buyers in a simiar way. For firm i s buyers, we construct the weighted average of their export demand shocks, 9 We use NACE 4 digit eve to cassify products k. 12

13 og X C it, using i s output share to each buyer in the previous year as the weights: og X C it = og j r ij,t 1 X jt,t 1 og j r ij,t 1 X jt 1,t 1. Finay, we measure the trade shocks to the firms potentia buyers, og Xit P C. The potentia buyers of firm i incude both the buyers of i s goods and other firms in the same (4-digit) sector as the actua buyers. We weight sectors for each firm according to the share of the firm s revenue that is sod to firms from that sector, r iu,t We then construct an export shock for each sector as a weighted aggregate of export shocks to a firms of that sector. 11 We combine these terms to construct an export shock to the potentia buyers of firm i: og X P C it = og u r iu,t 1 X i ut,t 1 og u r iu,t 1 X i ut 1,t 1. To construct the import shock variabes to the firm itsef, its suppiers, and its potentia suppiers, we use a simiar procedure. These variabes use information about changes in aggregate export suppy in foreign countries and the past sourcing of firms from these countries. We describe their construction in Appendix E.1. Tabe 2 shows the estimation resuts from the regression mode with changes in the firm s tota saes as the dependent variabe (see Tabe 14 in Appendix E.2 for resuts with changes in domestic saes and domestic inputs as dependent variabes). The resuts in coumn 1 suggest that firms that experience positive trade shocks tend to increase their saes. The estimates in coumn 2 suggest that trade shocks to potentia buyers and suppiers aso affects the firm s saes. However, as shown in coumn 3, shocks to the firms actua buyers and suppiers matter more for the firm s saes than shocks to the potentia buyers and suppiers. 12 In terms 10 Let sectors, at the NACE 4-digit eve, be denoted with u. r iu,t = Saes ijt j Wit u TotaSaes it, where Wit u denotes the set of customers of i producing sector u goods at time t. We fix a weights at the previous year t For the weights that firm i assigns to each firm within a sector, we use the firms saes to domestic fina demand as corresponding weights. We have experimented with different weights and obtained simiar resuts. These weights vary at the firm i - sector u eve, as we excude firm i s own exports and imports if firm i is producing sector u good. X i ut,t 1 = X i ut 1,t 1 = j U t 1,j i j U t 1,j i V jht 1 k U t 1,k i V kht 1 V jht 1 X jt,t 1 k U V X jt 1,t 1, t 1,k i kht 1 where U t is the set of firms producing sector u good at t, and V iht is firm i s saes to domestic fina demand at t. 12 Note that the actua buyers and suppiers are incuded in the set of potentia buyers and suppiers. Thus, the coefficients βx C and βs M shoud be interpreted as the additiona effect of a trade shocks to the 13

14 Tabe 2: Reduced form resuts n Tota Saes n Tota Saes n Tota Saes n X it (0.008) (0.008) (0.009) n M it (0.010) (0.010) (0.012) n Xit P C (0.002) (0.003) n Mit P S (0.004) (0.005) n Xit C (0.013) n Mit S (0.018) N Notes: Standard errors are custered at the firm eve. A variabes are in terms of yeary og differences for the period A specifications incude year fixed effects. We truncate outiers of each variabes at the top and bottom 1% eve. * p < 0.10, ** p < 0.05, *** p < 0.01 of magnitudes, the estimates suggest that an 10 percent exogenous increase in the foreign demand of goods for firm i s buyers eads to a 1.2 percent increase in the saes of firm i. The pass through of shocks to firm i s suppiers is smaer. A 10 percent exogenous increase in the foreign suppy of goods to firm i s suppiers eads to a.4 percent increase in the saes of firm i. Taken together, the resuts in Tabe 2 suggest that sectora input-output tabes are not sufficient to anayze the propagation of trade shocks. The output of a firm is significanty affected by idiosyncratic shocks to its buyers and suppiers. This finding is consistent with Carvaho et a. (2016), who show that the disruption caused by a Japanese earthquake in 2011 propagated through upstream and downstream suppy chains. Motivated by this evidence, we proceed by deveoping a mode of internationa trade and domestic production networks. firm s actua buyers and suppiers as compared to the effect of trade shocks to the firm s potentia buyers and suppiers 14

15 3 A mode of trade with fixed production networks We now deveop a mode of trade and domestic production networks, and use it to quantify how internationa trade affects firms production costs and consumer prices. Whie this section assumes a fixed network structure which is convenient to take the mode to the data we aow, in Section 4, the buyer-suppier reationships to change in response to trade shocks. 3.1 Mode We describe a sma open economy caed Begium. Before describing the mode, we briefy discuss the notation. Since there exist many biatera directed fows in our mode, we wi often have two subscripts. In such cases, the first subscript denotes the origin of the good and the second subscript denotes the destination of the good Preferences and Demand Each consumer suppies one unit of abor ineasticay. identica, homothetic CES preferences over consumption goods: U = ( k Ω (β kh q kh ) σ 1 σ Consumers are assumed to have ) σ σ 1, (4) where Ω denotes the set of avaiabe products in the sma open economy, k denotes a product, and H denotes domestic fina demand from househods. Since a consumers have the same, homothethic CES preferences for consumption, we can write the aggregate fina consumer demand (in quantities) for product k, given price p kh, as: q kh = β σ 1 kh E, (5) P 1 σ where E denotes the aggregate expenditure in Begium and P denotes the domestic consumer price index: P = ( j Ω p σ kh β σ 1 jh p1 σ jh We assume that fina goods are substitutes and therefore σ > 1. Demand from abroad for product k takes a simiar functiona form: q kf = β σ 1 kf 15 p σ kf P 1 σ F ) 1 1 σ. (6) E F, (7)

16 where β kf is a product-k-specific foreign demand shifter, p kf is the price of product k abroad, and P F and E F denote the foreign price index and expenditure, respectivey Production and market structure Firms produce singe products. We wi use i, j, k to index firms or products. The products are differentiated across firms. Firms se the same product to fina consumers and to other firms as an intermediate input, though not a firms se to other firms, and not each pair of firms has a buyer-suppier reationship. Note that we aow Begian firms to se directy to foreign consumers, whie a foreign products reach Begian consumers indirecty through the importing of inputs by Begian firms. 13 We treat every firm as infinitesima when seing to fina consumers. Hence, when seing to domestic or foreign fina consumers, we assume the market structure is monopoistic competition. When seing to other firms, the assumption of infinitesima size is no onger reasonabe, however, since most firms just have a few seected suppiers. We assume that in the Nash bargaining between buyer and suppier, the buyer has the fu bargaining power. Given the assumptions on technoogy described beow, this wi impy that the suppier ses at margina cost to the buyer firm. We note that in this section with exogenous networks, our main propositions and quantitative resuts are unchanged if firms charge positive and possiby heterogeneous mark-ups to customer firms as ong as these are fixed. Kikkawa et a. (2017) anayze a network economy with variabe firm-to-firm mark-ups. In our paper, the arguaby strong assumption of the bargaining power in firm-to-firm transactions being on the buyer s side wi be critica for modeing the network formation game in a tractabe manner. 14 This section assumes a fixed network structure: we take as given the set of firms, Z j, from which each firm j is eigibe to purchase inputs. For importing firms, Z j contains aso foreign, F, as an eigibe suppier. Sometimes we wi refer to the set of domestic suppiers of firm j, which we denote by Zj D. Firms use a CES input bunde of workers and domestic and foreign inputs with easticity of substitution ρ > 1 in the production function. We assume that σ > ρ, impying that consumers are more price-eastic than firms in their purchase of goods. Given the CES production function, we can write the cost function of firm j as: 13 The assumption that foreign goods reach Begian consumers ony through Begian firms is reasonabe because in the data neary a imports are carried out by firms. We make the assumption that Begian firms can reach foreign consumers directy to avoid modeing foreign firms in detai. 14 Aso in the industria organization iterature, corner soutions in the bargaining game are sometimes assumed to obtain tractabe soutions for network formation probems. For exampe, when studying the determinants of the hospita networks offered by heath pans, Ho (2009) assumes that hospitas make takeit-or-eave-it offers to a heath pans in the market. 16

17 c j (Z j ) = 1 φ j α ρ 1 kj p 1 ρ kj k Zj + α ρ 1 j w 1 ρ 1/(1 ρ). (8) The first term in the cost function, φ j, denotes the exogenous tota factor productivity of firm j. Foowing Antras et a. (2017), we wi ca Θ j (Z j ) = k Z j α ρ 1 kj p 1 ρ kj + α ρ 1 j w 1 ρ the sourcing capabiity of firm j, and Z j the sourcing strategy of firm j. The sourcing strategy may incude both domestic and foreign sourcing. The price of abor is denoted by w. The share of variabe costs by firm j that is spent on intermediate inputs produced by firm k Z j is: s kj = p kjq kj c j q j = αρ 1 kj p 1 ρ kj Θ j (Z j ), (9) where α kj refects how saient the good produced by firm k is as an input for firm j. Anaogousy, the share of variabe costs by firm j that is spent on abor is: s j = w j c j q j whie the direct foreign input share of firm j (assuming F Z j ) is: s F j = p F jq F j c j q j = αρ 1 j w 1 ρ Θ j (Z j ), (10) = αρ 1 F j p1 ρ F j Θ j (Z j ). (11) Before deriving an expression for the tota saes of a firm, we discuss the pricing probem of the firm. Due to CES preferences and monopoistic competition, firms charge a constant mark-up over margina costs, µ = σ, when seing to fina consumers at home or abroad. σ 1 When seing to other firms, firms engage in Nash bargaining with the fu bargaining power on the side of the buying firm. The buyer wi make the suppier just indifferent between seing to the firm or not, and therefore firms se at margina costs to other firms. In order to se abroad, firms incur iceberg transport costs, τ. In this section, we take export participation, I jf, as given (I jf = 1 for a exporting firms and I jf = 0 otherwise) and endogenize it in Section 4. Firms tota saes consist of the sum of domestic saes to fina consumers, foreign saes to fina consumers, and domestic saes to other firms. Let firm j s tota saes be denoted by: 17

18 x j = β σ 1 jh µ1 σ φ σ 1 j Θ j (Z j ) (σ 1)/(ρ 1) E + I }{{ P 1 σ jf β σ 1 jf µ1 σ φ σ 1 j Θ j (Z j ) (σ 1)/(ρ 1) τ 1 σ E F } P 1 σ F }{{} Domestic saes to fina consumers Exports + I(j Z k )µ 1 ρ φ ρ 1 j α ρ 1 jk Θ(j) x k/µ k, (12) Θ k (Z k ) k }{{} Domestic saes to firms where µ k denotes the average mark-up of firm k. Reca that the firm charges a constant mark-up to fina consumers and a zero mark-up to other firms. Hence, µ k depends on the distribution of firm k s saes. Given that firms make their profits ony on saes to fina consumers, we can write the variabe profits of firm j given a sourcing strategy, Z j, and export participation, I jf, as π var j (Z j, I jf ) = 1 σ βσ 1 jh µ1 σ φ σ 1 j Θ j (Z j ) (σ 1)/(ρ 1) E P 1 σ 1 + I jf µ1 σ φ σ 1 j Θ j (Z j ) (σ 1)/(ρ 1) τ 1 σ E F σ βσ 1 jf Firms dependence on foreign inputs P 1 σ F. (13) We now cacuate the exposure of firms to foreign inputs, taking into account that the direct and tota foreign input share can be substantiay different. Let s F j denote the tota foreign input share of firm j: s T ota F j = s F j + s ij s T ota F i. (14) The definition of tota foreign input share is intuitive in a mode with singe product firms in which each firm uses the same fraction of foreign inputs in the production sod to every buyer. Proposition 1 shows the ink between the tota foreign input shares and the cost reduction from internationa trade in our mode. 15. In the proposition, we aso present resuts based on two aternative modeing assumptions that researchers often make when they do not have i Z D j access to domestic firm-to-firm transaction information. Proposition 1 (Cost increases from banning foreign inputs) Assume ρ > 1. Given fixed inkages between firms, and eaving domestic nomina wages, w, unchanged, the tota cost increase from banning foreign inputs is: 15 Note that the assumption made in the proposition that nomina wages are unchanged is not that restrictive, since nomina wages can be normaized to any vaue under autarky 18

19 ĉ j p F tota = ( ) 1 s T F ota 1/(1 ρ) j. (15) Ignoring inkages and indirect effects (i.e., assuming there is no pass-through of cost changes from domestic suppiers) and eaving domestic nomina wages, w, unchanged, the direct cost increase from banning foreign inputs is: ĉ j p F direct = (1 s F j ) 1/(1 ρ). (16) Finay, if one assumes an economy with roundabout production in which firms outputs are aggregated to a composite intermediate input according to equation (4) and the composite intermediate input is the ony firm-to-firm input in equation (8), the cost increase from banning foreign inputs, ĉ j p F roundabout, is impicity defined as: (ĉ j p F roundabout )1 ρ = s j + s Dj ( k ) 1 ρ 1 σ s kd (ĉ k p F roundabout )1 σ, (17) where s Dj is the share of firm j s domestic intermediate good purchases and s kd is the share of firm k in the intermediate good bunde (measured by firm k s share in tota domestic saes). The resut on the firm-eve cost increase from banning imports, ĉ j p F tota, refects that a firm s cost wi not ony rise according to it s own direct foreign input share, but aso according to its suppiers foreign input shares, suppiers suppiers foreign input share, and so forth. This firm-eve exposure is summarized in the tota foreign input share expression. The easticity of substitution in the production function, ρ, indicates how easy it is to switch to aternative inputs, incuding abor. Given the observed tota foreign input share, a ower vaue of ρ eads to arger cost increases from banning foreign trade. In contrast, the expression ĉ j p F direct, yieds ony the direct effect of on firm-eve cost from banning foreign trade (mirroring the resuts in earier work by Arkoakis, Costinot, and Rodríguez-Care (2012) and Baum et a. (2016)). It can be rationaized from our mode under a network in which importers se a their output to fina consumers, and hence the tota foreign input share of domestic suppiers of other firms in equation (14) is zero. Since the observed production networks differ from this extreme case, using the formua from equation (16) eads to cost increases from banning foreign inputs that are too ow compared to the fu effect summarized in equation (15). In the absence of firm-to-firm transaction data, it is possibe to approximate the indirect effect by assuming a roundabout production structure (as for exampe in Baum et a. (2016)). 16 Under the roundabout production assumption, every firm with the same inter- 16 Baum et a. (2016) obtain a tota cost reduction resut from foreign inputs in which each firm buys 19

20 mediate input share wi have the same indirect exposure to foreign goods. However, this assumption is at odds with our data, and coud create bias in the cacuation of the firm-eve cost effects from trade Aggregation and equiibrium We now describe the aggregation of our mode, discuss how firm profits are redistributed to consumers and define the equiibrium. In the mode with a fixed production network we abstract from fixed costs of inkage formation, and hence π j = π var j. We assume that the set of Begian firms is fixed and that firm profits are distributed to workers in Begium. We consider Begium as a sma-open economy and assume that there are no foreign asset hodings and that trade is baanced. Hence aggregate expenditure in Begium is given by E = w L + k π k. (18) Baanced trade impies that aggregate exports are equa to aggregate imports: j I jf β σ 1 jf µ1 σ φ σ 1 j Θ j (Z j ) (σ 1)/(ρ 1) τ 1 σ E F P 1 σ F = j Labor market cearing impies that abor income is equa to firms abor costs: 1 µ j s F j x j. (19) w L = j 1 µ j s j x j. (20) We next define the equiibrium for the sma open economy. Definition 1 (Equiibrium given a fixed network structure) Given foreign expenditure, E F, foreign price index, P F, and a set of prices by foreign suppiers, {p F j } j, an equiibrium for the mode with a fixed network structure and fixed export participation is a wage eve, w, price index for the consumer, P, and aggregate expenditure, E, such that equations (6), (8), (9), (10), (12), (13), (18), (19), and (20) hod. We estabish uniqueness of the equiibrium in the cosed economy in the foowing emma. Lemma 1 (Uniqueness of equiibrium under cosed economy) Define a K K matrix A where where the (i, j) eement is φ ρ 1 j α ρ 1 ij if i Z j and 0 otherwise, and K denotes the same CES bunde of intermediate inputs. The production function in their paper is Cobb-Dougas in intermediate inputs and own abor input. Our roundabout cost reduction resut in equation (17) is simiar to their resut, but derived for a production function which is CES between abor input and intermediates. 20

21 the number of Begium firms. Assume the matrix ( I A ) is invertibe, where I is the identity matrix. Then under a cosed economy, for a given nomina wage, there exists a unique equiibrium defined in Definition 1. Lemma (1) is usefu because it impies that the counterfactua equiibrium without trade is unique. We next proceed to discuss the change in the aggregate price index arising from banning internationa trade. Proposition 2 (Change in aggregate price index from banning internationa trade) Let s ih denote firm i s share in househod demand in in the initia equiibrium prior to raising the barriers to trade. Given a fixed set of firms, network structure and nomina wage, the price index change from banning internationa trade can be summarized as foows: ˆP p F tota = ( i ) 1 1 σ s ih (ĉ i p F tota ) 1 σ. (21) If the price of intermediate goods is assumed to be unchanged, the price index change can be expressed as ˆP p F direct = ( i ) 1 1 σ s ih (ĉ i p F direct ) 1 σ. (22) Finay, if one assumes roundabout production as defined in proposition 1, then the expression becomes ˆP p F roundabout = ( i ) 1 1 σ s ih (ĉ i p F roundabout )1 σ. (23) The change in the price index from banning internationa trade is a weighted aggregate of each firm s cost increase with the weight equa to the firm s share in domestic househod demand, s ih, in the initia economy with internationa trade. Propositions 1 and 2 impy that the change in the aggregate price index depends on the underying network structure. To see this, consider a production network in which a the imports are made by firms that had no saes to other domestic firms or to the domestic fina consumers. In that case, a the cost increases from banning foreign goods woud accrue to firms for which the share in domestic househod demand is zero, and therefore the price index effect woud be zero as we. Suppose instead that importers of foreign goods had no saes to other domestic firms, but sod a their output to domestic fina consumers. Then, the price index increase is given by equations (16) and (22). However, with positive saes to other domestic firms by the importers, the price index effect is given by equations (15) and (21). 21

22 A coroary of the resuts from propositions 1 and 2 is that two economies with the same easticities of substitutions in production and in the utiity functions, and the same eves of aggregate imports and exports, GDP, and gross production, can have different gains from trade. We iustrate this in a simpe numerica exampe in Appendix B. 17 The above resuts iustrates that knowing the underying micro-structure of the economy is reevant for the quantitative anaysis of the gains from trade. In the foowing subsection, we make use of the detaied information about domestic firm-to-firm transactions in our data when we cacuate the wefare gains from trade for the Begian economy. 3.2 Empirica resuts In this section, we provide a quantitative anaysis of how internationa trade affects firms production costs and the consumer price index. As shown above, this anaysis requires information on the observed firm-to-firm transactions, firm-eve output, internationa trade fows, and abor input, in combination with estimates or assumptions for the easticity of substitution in the production function, ρ, and the utiity function, σ. Throughout the paper, the baseine specification assumes σ is equa to 4 and ρ is equa to We perform sensitivity anaysis to examine how the resuts vary with the choice of these parameter vaues. To assess the impications of banning foreign inputs, we compute the firm eve cost increases by making use of proposition 1. We use the firm-to-firm network structure as observed in Proposition 1 tes us that the tota shares of foreign inputs for each firm, s T ota F j, transates to the cost changes that firms face from banning foreign inputs. Figure 3 dispays the cost increase of firms from banning internationa trade (in the red ine). This figure aso reports the cost increase under the assumptions of the direct effect (bue ine) and roundabout economy (green ine). In these two cases, it is not necessary to observe domestic firm-to-firm transactions to cacuate the cost increases. As evident from Figure 3, internationa trade matters much more for firms production costs if we use our mode with fixed domestic production networks than in the direct effect and roundabout economy. For the median firm (in the distribution of cost changes), the cost increase from banning foreign inputs is 70% in our mode with domestic production networks, 41% in the mode with the roundabout economy assumption, and zero when considering ony the direct effect. As expected, the cost increases are the owest under the 17 This exampe is reated to the discussion in Meitz and Redding (2014) that the gains from trade can be arbitrariy arge in a mode with sequentia production, as the number of stages of production increases. However, note that the ratio of gross production to GDP aso rises in their exampe as the number of stages gets arger. Here we hod the eve of gross production and GDP fixed, and iustrate that the gains from trade can sti differ. 18 Using data for the US, Antras et a. (2017) estimate σ = 3.85 and Oberfied and Rava (2014) estimate a eve of σ between 3 and 5 among various manufacturing industries. 22