A Coasian Model of International Production Chains Thibault Fally and Russell Hillberry UC-Berkeley ARE and World Bank∗ [PRELIMINARY AND INCOMPLETE] Abstract The fragmentation of production over the last two decades represents a revolution- ary change in global economic relations. Complex supply chains require coordination of numerousactivitiesacrossmultiplefirmsandcountries. Cross-bordertradecosts,transac- tion costs within countries and coordination costs are inherently incurred multiple times along production chains and determine the extent of fragmentation across and within countries. In this paper, we develop a model that incorporates these costs to examine the optimal allocation of tasks across firms, within and across countries, as well as the opti- mal length and location of production chains. While transaction costs matter for welfare and comparative advantage across chains, we find the relative position in downstream vs. upstream industries to reflect the ability to manage a larger range of tasks within a firm, with downstream industries featuring larger firm scope. In a general-equilibrium setting, we examine how the elasticity of trade to trade costs and the gains from trade are mag- nified when firms along the chain are optimally located in different countries. The model also formalizes recently developed summary indicators of supply chain length and relative position(Fally2012, Antrasetal, 2012, AntrasandChor, 2013). Usinginput-outputdata on East Asia, we calibrate the model to match key features of the data such as the value- added-to-gross-outputratiosandexportsharesinintermediategoodsandfinalgoods. We use the calibrated model to explore implications of trade costs, technology parameters for the length of production chains, their location in space, and their implications for trade and welfare. Keywords: Fragmentationofproduction,Transactioncosts,Tradeinintermediategoods JEL Classification: ∗We would like to thank Andres Rodriguez-Clare and Tomoo Kikuchi for helpful comments and discussions. Contact: [email protected], Department of Agricultural and Resource Economics, University of California, Berkeley, CA 94720-3310, USA. 1 1 Introduction The nature of international trade changed dramatically in recent decades, as vertically inte- grated production processes spread across international borders, increasing trade in parts and components as they went. A thorough understanding of these phenomena should require a model that embeds the spatial organization of sequential processes in a larger framework with trade costs and equilibrium in markets for final and intermediate goods and in factor markets. This paper proposes a tractable framework that accomplishes these tasks in a multi-country setting. Among other novel features, the model formalizes recently developed summary indica- tors of supply chain length (Fally 2012, Antras et al. 2012, Antras and Chor 2013). The model distinguishes firms from tasks, with sequentially organized firms determining the measure of tasks to bring in house. Trade in the model is motivated by two types of comparative advantage: specialization across goods, as in Eaton and Kortum (2002), and specialization across tasks within produc- tion chains. Our model allows for tasks to be performed in different firms within and across countries, with the length of production chains being an endogenous outcome. As in Kikuchi et al (2013), the optimal extent of fragmentation is the result of two competing forces: within-firm coordinationcostscreategainsfromfragmentationwhereastransactioncosts, withinandacross borders, tend to limit the extent of fragmentation. Moreover, our model features cross-country heterogeneityinaparameterthatgovernsthese‘coordinationcosts’, whichcouldbeunderstood as diseconomies of scope in a Coasian framework. Differences in productivity, transaction costs and diseconomies of scope create opportunities to trade, not just in final goods but also in intermediate goods along the chain. Vertical specialization in our model is tightly related to firm scope. Firms in the model make marginal choices about the scope of their activities, and these choices are central to the organization of supply chains across countries. In equilibrium, firm scope decreases as we move upstream along the chain. In turn, this pattern affects the sorting of countries along the chain: countries with lower abilities to manage large firms tend to specialize upstream. Our model exploits a continuous representation of firms to model the Coasian tradeoff and to facilitate a tractable closed-form solution. The tractability of the framework is useful in that it allows us to directly relate the model to observable data outcomes and to other parts of the literature. As noted above, the model provides a structural interpretation of quantitative measures of the length of production chains and industries’ relative position. We also link the gross output to value added (GOVA) ratio to the underlying Coasian structural parameters: transaction costs and diseconomies of scope. As in Kikuchi et al (2013), the model predicts that upstream firms are smaller than downstream firms, although our model adds an international 2 dimension to the explanations in Kikuchi et al (2013): countries in which the coordination of activities is more difficult tend to host firms that are smaller, and more upstream. Finally, differences in transaction costs play an important role that can be quantified. Transaction costs have a negative effect on aggregate productivity, especially when within-firm coordination costs are high. As an indirect consequence, countries with high transaction costs tend to specialize downstream where firms are more integrated. The paper examines in particular on the effect of trade costs on trade and fragmentation. As expected, we find that opening to trade tends to increase the extent of fragmentation along several dimensions and facilitates production sharing across countries. The channels, however, are not trivial. Trade affects fragmentation at all stages and decreases firm scope for firms that do not directly offshore production but are related to firms that do. The reduction in firm scope along the chain is associated with a decrease in average costs, especially downtream, and contributes to the reduction in final goods prices. As trade costs decrease, countries tend to move downstream along chains and enter new chains. We illustrate our finding in a partial- equilibrium setting, holding the set of participating countries and their labor cost constant, and in a two-country general equilibrium setting. In the latter, we also use our framework to examine the response of trade flows to trade costs, both in gross flows and value added content, and the welfare gains from trade. In order to explore the quantitative implications of our framework, we calibrate our model to match key features of input-output relationships in East Asia. This exercise relies on inter- national input-output tables produced by IDE-JETRO. The data cover the US and 9 Asian countries: Japan, China, Taiwan, Korea, Thailand, Malaysia, Singapore, Indonesia and the Philippines. This region is interesting because production fragmentation there has grown quickly and is highly prevalent. The importance of international production in the region is a primary reason for the existence of the detailed cross-country input-output data that we employ, the IDE-JETRO tables. These data are unique in that they track flows in four dimen- sions: from the making industry in the origin country to the using industry in the destination country.1 To illustrate our findings, we adapt recently developed quantitative measures of firm position (i.e. upstreamness) so that they track the average number of international borders crossed, rather than plant boundaries as in the original. Our calculations indicate increasing international fragmentation over time, especially in key industries like electronics. While the model has rich implications for trade and the fragmentation of production, it remains parsimonuous with only a few parameters to calibrate. We calibrate our model by targetting key moments such as GDP per capita, value added, export shares in intermediate 1Other data that report such figures, like the World Input-output Database (WIOD), impute these values assuming proportional treatments. 3 goods and the gross-output-to-value-added ratios. All these moments imply large differences in productivity, transaction costs, diseconomies of scope among others. We then use the cali- brated model to conduct counterfactual exercises regarding changes in key structural parame- ters. We first examine what happens when cross-border trade costs decrease by 10%. In this counter-factual simulation, we tend to find larger gains from trade than predicted by Arkolakis, Costinot and Rodrigues-Clare (2012)’s formula (based on imported final goods), especially for downstreamcountries. Mostcountriestendtomovedownstream. Wealsoexaminetheresponse in terms of the VAX ratio (value-added content of exports) as defined by Johnson and Noguera (2012). We find that a decrease in trade costs leads to a decrease in the VAX ratio for most countries, which can be interpreted as an increase in cross-border fragmentation. Interestingly, we also find a decrease in the share of intermediate goods in trade.2 In other counterfactual exercises, we simulate a 10% increase in productivity in China and a 10% decrease in coordina- tion costs (parameter governing diseconomies in firm scope). We find large effects on China but also other countries. While these change induce China to move downstream, other countries adjust by moving upstream. These two counterfactual simulations lead to an decrease in the share of intermediate goods in Chinese exports as well as a decrease in the value-added content of Chinese exports, with opposite effects in other countries. Finally, we leave a fourth coun- terfactual exercise for a future version: simulating a 10% decrease in transaction costs across firms within borders. Contributions to the literature: The paper contributes to the literature in two broad ways: 1) we develop a model that formalizes a role for firms (distinct from stages) in a sequential, multi-country general equilibrium, 2) we consider quantitative implications of the model in the context of East-Asian production. We discuss the literature surrounding each of these contributions in turn. Models of production chains. An important question in the literature surrounding inter- national production chains is the spatial organization of production across countries. Costinot et al (2012) derive an explicitly sequential multi-country model in which mistakes can occur with given probability and these mistakes destroy all accumulated value. They show that countries with relatively high probabilities of mistakes are situated upstream. The intuition for this result broadly follows Kremer (1993), that higher rates of mistakes do less damage if they occur upstream. The Costinot et al (2012) framework has no implications for the extent of fragmentation across firms and the allocation of tasks across firms. 2This finding is consistent with the decrease in average “upstreamness” over the past decades, documented in Fally (2012), which implies that trade flows have grown faster in downstream industries than upstream industries. 4 Instead, we formalize the firm’s internalization decision and endogenize the range of firms involved in the chain. The motivation for this follows Coase (1937), and our mathematical framework is inspired by Kikuchi et al (2012), who show how Coase’s insights can be applied to production chains. Kikuchi et al (2012) solve their model in a sequential partial equilibrium setting, and employ discrete firms. We adapt their framework to a continuum of firms in a multi-country general equilibrium setting where countries differ in key parameters governing transaction costs and diseconomies of scope. As in Costinot et al (2012), we examine how countries specialize along the chain but the patterns of specialization are now driven by inter- actions between firm scope, transaction costs and ad-valorem trade costs affecting cross-border transactions. It is also easier to calibrate our model. We show how input-output tables can be used to recover key parameters that govern the vertical specialization of countries and the extent of fragmentation. In contrast to the endogenous allocation of stages across tasks, another set of models fixes the number of production stages (Krugman and Venables 1996, Hillberry and Hummels 2002, Yi2010, JohnsonandMoxnes, 2013). Thefocusofthisliteratureisoftenisoftenthegeographic location of each production stage, relative to the other(s), and so a finite and countable number of stages is useful for analytical purposes. Relative to our work, and others, these models avoid the question of the allocation of activities or tasks across stages, and focus on the extensive margin of completing a specific stage in a certain location. In Yi (2010) Johnson and Moxnes (2013), for example, the specialization of countries along the chain in such models is driven by exogenous productivity shocks and trade costs. Our model also contains these forces, but we introduce intra-firm coordination costs and inter-firm transaction costs as additional sources of cross-country heterogeneity. The length of production chains in our framework is also endoge- nous - e.g. reductions in inter-firm trade costs can expand the number of firms involved in the chain. The literature makes important insights about non-linear responses of trade to trade costs and differences between gross and VA trade. One goal of our paper is to understand the robustness of these insights to the richer theoretical structure we offer. We adapt their framework to a continuum of firms in a multi-country general equilibrium settingwhere countries differin key parametersgoverningtransactioncosts anddiseconomies of scope. As in Costinot et al (2012), we examine how countries specialize along the chain but the patterns of specialization are now driven by interactions between firm scope, transaction costs and ad-valorem trade costs affecting cross-border transactions. It is also easier to calibrate our model. We show how input-output tables can be used to recover key parameters that governs the vertical specialization of countries and the extent of fragmentation. Quantitative implications. A number of recent papers exploit information in input-output 5 tables to calculate industries’ relative position in production chains, and the length of pro- duction chains. Under the assumption that the IO tables effectively summarize plant-to-plant movements for a representative firm in each industry, matrix algebra can be used to calculate, for each industry in the table, two numerical values (1) a measure of the industries ”distance” from final demand (where distance is a count of the number of plant boundaries that will be crossed prior to final consumption) and 2) the average number of stages embodied in an indus- tries production. The first of these, described as “distance to final demand” in Fally (2012) and ”upstreamness” Antras et al (2012). The second was developed in Fally (2012) and computed usingtheBEAinput-outputtablesfortheUS.UsingthehighlydisaggregatedUStable, thetwo indicators are not correlated, and that the indicators do not appear to be especially sensitive to aggregation concerns. As yet the indicator remains relatively unconnected from the theory. One of the contributions of this paper is to derive theory that will map structural parameters onto these indicators in equilibrium.3 These mappings are useful when we calibrate the model to data on interregional input- output relationships in East Asia. A key purpose of this exercise is to offer a model comparison vis a vis other papers in the literature. A prominent literature has emphasized that interme- diate goods trade magnifies the effect of trade costs on trade. Yi (2010) and Johnson and Moxnes (2013) focus on the response of trade to trade cost shocks, whereas Krugman and Ven- ables (1996), Hillberry and Hummels (2002), Yi (2010) and Johnson and Noguera (2014) link the spatial clustering of activities to trade costs in the presence of intermediate goods trade. Clustering occurs in our model, with sequential activities locating so as to avoid trade costs. Our calibrated model can be used, like Johnson and Moxnes (2013) or Yi (2010) to investigate the response of trade to trade cost shocks. Our paper contributes to the quantitative literature by exploiting input-output matrices in a new way. Input-output matrices and direct requirement coefficients are traditionally taken as an exogenous recipe essentially determined by technology. Instead, we argue that input- output matrices reflect transactions in intermediate goods between firms (not just across but also within countries) that are endogenous economic outcomes and can be informative about how firms are integrated, depending on their position on value chains. Unlike any of the papers mentioned above, our theory also determines the allocation of tasks across firms and the length of production chains endogenously, and can thus shed some light on equilibrium input-output relationships when fragmentation is endogenous. We also contribute to the recent literature on the welfare implications of trade cost change. Arkolakis, Costinot and Rodriguez-Clare (2012) show that a broad class of models imply the 3Another contribution is to extend the indicators to locate countries’ relative positions in production chains 6 same response of welfare to trade costs, provided that the models are calibrated to generate the same trade response to trade cost change. Costinot and Rodriguez-Clare (2014) show that welfare effects are magnified when intermediate goods trade is involved. Like other papers in the literature, the Armington framework presumes an explicit input-output relationship that governssupplychainlength, incontrasttotheendogenouslengthinourmodel. TheArmington framework also precludes movement along the extensive margin (in terms of countries involved in supply chains), while our theory allows this. Our calibrated model implies larger gains than in standard trade as desribed by Arkolakis et al (2012), but smaller gains than Costinot and Rodriguez-Clare (2014). 2 Model setup We develop a model where the production of each variety of final good requires a continuum of tasks and firms organized across countries. We describe, in turn, consumers’ preferences in final goods, tasks and firms involved in the production of each good, the forces shaping firm scope and firm entry along the chain, the differences between varieties and the labor market. Preferences: Consumers have identical Cobb-Douglas preferences over varieties of final goods indexed by ω: (cid:90) U = logqF(ω)dω (1) ω where qF(ω) denotes quantites of final goods. All countries have access to the same set of product varieties ω but at different prices. Tasks and firms along the chain: In order to obtain the final good variety ω, a range [0,1] of tasks has to be performed sequentially. These tasks may be performed across different firms and different countries. Firms are involved sequentially along the chain to produce each good ω. A chain is specific to each variety ω of the final good and the location of final consumers. On each chain, we assume that there is a continuum of firms indexed by f. Firms may be located in different countries. For each chain, we rank countries along the chain and index by i the i’th country, i = 1 being the most downstream country and i = N(ω) being the most upstream country along the chain. We denote by F (ω) the range of firms involved in the chain in country i. An elementary i firm df performs a range s (ω) of tasks. Both the range of firms F (ω) and firm scope s (ω) if i if are endogenous, but the range of tasks performed across all firms must sum up to one to obtain 7 a final good: (cid:88)(cid:90) Fi(ω) s (ω)df = 1 (2) if f=0 i Denoting S (ω) = (cid:82)Fi(ω)s (ω)df the total range of tasks to be performed in country i, the last i f=0 if constraint can be rewritten: (cid:88) S (ω) = 1 i i for all chains ω. Coordination costs: There are costs and benefits to fragment production across firms and countries. Fragmentation across firms reduces total costs because of diseconomies of scope. As firms need to manage employees across different tasks and perform tasks that are away from their core competencies, unit costs increase with the scope of the firm. We will refer to these costs as “coordination costs” that occus within the firm and increase with firm scope. Formally, we assume that an elementary firm df at stage f in country i requires one unit of intermediate goods and c (s ,ω)df units of labor at each stage. The cost of labor is w in i if i country i and is the only production input besides intermediate goods. We assume that c is i convex in firm scope s , thus generating gains from fragmentation across firms. if In particular, we specifying the following labor requirements: (cid:90) s c (s ,ω) = a (ω) if tθi(ω)dt i if i t=0 whereby the marginal cost of performing additional tasks within the firm increases with the distance t from the first task. This follows, for instance, recent work on the division of labor (Chaney and Ossa, 2014) and may also be interpreted as the productivity loss from going away from the firm’s core competencies. After integrating and multiplying by the cost of a unit of labor in country i, the cost function writes: sθi(ω)+1 w c (s ,ω) = w a (ω) if (3) i i if i i θ (ω)+1 i where a (ω) and θ (ω) are specific parameters for each country i for variety ω. Note however i i that a (ω) and θ (ω) are constant along the chain (for a given country). In particular, θ (ω) i i i parameterizes “coordination costs” and the convexity of the cost function. The higher is θ (ω), i the higher is the increase in costs as firms need to manage a larger range of tasks.4 4Note that we assume diseconomies of scope but constant returns to scale in production. This differs from ChaneyandOssa(2014)andmorecloselyfollowsKikuchietal(2013). InkeepingwithKikuchietal(2013),this framework allows us to examine patterns of fragmentation across firms while keeping a perfectly-competitive 8 Transaction costs: Fragmenting production across firms incur transaction costs. We model transaction costs like iceberg transport costs in standard trade models. More specifically, a transaction in country i with an elementary firm df involves loosing a fraction γ df of the good. i q (ω) = q (ω)(1+ γ df) (4) i,f+df i,f i Within each country, quantities thus follow a simple evolution depending on transaction costs γ and the position on the chain f. As we go upstream, quantities increase exponentially i with the number of firms f to cross along the chain: q (ω) = eγifq (ω) (5) i,f i,0 Since part of the production is lost when transactions occur, larger quantities are required for upstream firms. In particular, the increase in quantities is starker when transaction costs are high and when the chain is more fragmented. In a similar fashion, a cross-border transaction between two consecutive countries i and j along the chain involves an iceberg trade cost τ > 1 such that: ij q (ω) = τ q (ω) (6) j,0 ij i,Fi where q (ω) denotes the quantities produced by the most downstream plant in the upstream j,0 country and q (ω) denotes quantities produced by the next plant, i.e. the most upstream i,Fi plant in the next country along the chain. For simplicity, we assume away other geographical elementsthanbordersandimposeacommonbordercost: τ = τ. Here, quantitiesalsoincrease ij exponentially as we cross borders along the chain. Market structure: In addition to assuming constant returns to scale in production, we assume perfect competition. In this setup, the market equilibrium and the optimal allocation correspond to the social optimum.5 Prices along the chain: The price of intermediate goods is thus equal to their unit cost of production. Here, this cost accounts for all transaction costs incurred along the chain (going upstream) and the labor costs incurred by each firm. Within country borders, the price of intermediate goods satisfies the following differential equation which describes its evolution framework where the competitive allocation of tasks across firms is optimal. 5While there are decreasing return to scale in terms of firm scope, there are constant returns to scale in production in terms of quantities. The equilibrium under perfect competition corresponds to the social optimum. This insight follows Kikuchi et al (2012) generalized to a multi-country setting with heterogenous costs and a continuum of firms. 9 along the chain: p (ω) = w c (s ,ω)df +(1+ γ df)p (ω) (7) fi i i if i f+df,i This equation is close to Costinot, Vogel and Wang (2012) and also feature increasing interme- diate goods prices as we go downstream. A key difference, however, is that the labor share is endogenous since s is endogenous and thus not simply driven by differences in input prices if along the chain. In particular, the cost of inputs by unit of labor is no longer necessarily larger for downstream firms. Many of the results in Costinot et al (2012) are driven by this feature and thus no longer hold in our framework. Across borders, the price is simply multiplied by the international trade cost τ: p (ω) = τ p (ω) (8) i,Fi j,0 for cross-border transactions from the most downstream plant in j to the most upstream plant in i, with w c (s,ω) = w a (ω)sθi(ω)+1 as specified above. i i i i θi(ω)+1 Industry heterogeneity: While the previous assumptions are sufficient to generate interest- ing patterns of specialization along a particular chain, we still need to specify how chains vary across varieties. Following Eaton and Kortum (2002), we assume that labor efficiency is a ran- dom variable drawn independently across varieties and countries. Specifically, we assume that the labor cost parameter a (ω) is drawn from a Frechet distribution as in Eaton and Kortum i (2002). For each country i, the cumulative distribution function for a is: i Proba(a < a) = 1−e−Tiaξ (9) i where T parameterizes the country average productivity and where ξ is inversely related to i productivity dispersion.6 Note that a (ω) is thus constant along the chain for a specific country and variety ω. Unlike i Yi (2003, 2010), Rodriguez-Clare (2010) and Johnson and Moxnes (2013), our framework does not require a (ω) to differ across tasks along the chain to generate trade in intermediate goods. i Another component of the cost function is θ (ω). We will explore different settings. In i section 4.1 we simply consider two countries U and D: one where θ (ω) = θ across all U U varieties, and another country with θ (ω) = θ < θ across all varieties. In sections 4.2 and D D U 5 (calibration exercise), we allow θ (ω) to vary across countries and varieties. Specifically, we i ¯ assume that θ (ω) is log-normally distributed with a country-level shifter θ and a common i i standard deviation. 6Parameter ξ corresponds to the notation θ in Eaton and Kortum (2002). 10