A theory on the role of wholesalers in international trade based on economies of scope

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1 156 A theory on the role of wholesalers in international trade based on economies of scope Anders Akerman Department of Economics, Stockholm University Abstract. This paper offers a theoretical foundation for the existence of wholesalers and other intermediaries in international trade and analyzes their role in an economy with heterogeneous manufacturing firms and fixed costs of exporting. Wholesalers are assumed to possess a technology such that they can buy manufacturing goods domestically and sell in foreign markets and they can, unlike manufacturers, export more than one good. A wholesaler therefore faces an additional fixed cost, which increases in the number of goods it handles. The presence of wholesale firms leads to productivity sorting. The most productive firms export on their own by paying a fixed cost, but a range of firms with intermediate productivity levels export through international wholesalers. A higher fixed cost of exporting to a destination means that wholesalers handle: (i) a higher share of total export volumes to this destination and (ii) a higher share of the exported product scope (i.e., the number of exported products) to this destination. A higher fixed cost of exporting gives wholesalers a larger role, since these can spread the fixed cost across more than one good. The wholesale technology therefore exhibits economies of scope. An empirical analysis using Swedish firm-level data supports the main assumption and predictions of the model. Résumé. Une théorie du rôle des grossistes dans le commerce international fondée sur les économies de portée. Ce texte offre un fondement théorique pour l existence des grossistes et d autres intermédiaires dans le commerce international, et analyse leur rôle dans une économie riche de firmes manufacturières hétérogènes face à des coûts d exportation fixes. Les grossistes sont censés posséder une technologie Corresponding author: Anders Akerman, anders.akerman@ne.su.se I am grateful for helpful comments and suggestions from two anonymous referees, Andrew Bernard, Gregory Corcos, Matthieu Crozet, Jonathan Eaton, Gabriel Felbermayr, Harry Flam, Rikard Forslid, Benjamin Jung, Sebastian Krautheim, James Markusen, Lindsay Oldenski, Horst Raff, Peter Schott, Anson Soderbery, Heiwai Tang and Stephen Yeaple as well as seminar participants at the Midwest International Trade Meetings in Chicago, NOITS in Helsinki, RIEF in Kiel, Uppsala International Trade Workshop, the EEA Meetings in Glasgow, the ETSG in Lausanne and the EITI in Tokyo. Financial support from the Jan Wallander and Tom Hedelius Research Foundation and the Torsten Söderberg Foundation is gratefully acknowledged. Canadian Journal of Economics / Revue canadienne d économique (1) February Printed in Canada / Février Imprimé au Canada ISSN: / 18 / pp / Canadian Economics Association

2 Wholesalers in international trade 157 telle qu ils peuvent acheter des biens manufacturiers dans une économie nationale et les vendre à l étranger, et peuvent, ce qui n est pas nécessairement le cas pour les manufacturiers, exporter plus qu un bien. Un grossiste fait donc face à un coût fixe additionnel à proportion que le nombre de biens dont on s occupe s accroît. La présence des firmes grossistes mène à un départage des producteurs selon leur productivité. Les producteurs les plus productifs s occupent eux-mêmes de leurs exportations en déboursant un coût fixe, mais un éventail de producteurs à productivité intermédiaire va exporter par le truchement de grossistes internationaux. Un coût fixe plus élevé de l exportation vers une destination donnée veut dire que les grossistes s occupent (i) d une portion plus grande du volume total des exportations vers cette destination, et (ii) d une portion plus grande de la portée de produits exportés (i.e., du nombre de produits exportés) vers cette destination. Un coût fixe plus élevé de l exportation donne aux grossistes un rôle plus important puisqu ils peuvent étaler ce coût fixe sur plus qu un produit. La technologie du commerce en gros bénéficie donc d économies de portée. Une analyse empirique utilisant des données suédoises au niveau de la firme confirme le postulat de base de ce modèle et ses prédictions. JEL classification: D21, F12, F15 1. Introduction I I tisbynowa well-known empirical regularity that wholesalers other intermediaries account for a substantial share of exports from most countries and that they assist less productive firms in overcoming barriers to foreign markets. Recent research has shown that intermediary firms handle about 22% of aggregate Chinese export sales (Ahn et al., 2011), 10% of US and Italian exports (Bernard et al. 2010a, 2015), 20% of French exports (Crozet et al., 2013) and about 35% of imports into Chile (Blum et al., 2010). Feenstra and Hanson (2004) examine the role of Hong Kong in re-exporting goods from China during and find that 53% of Chinese exports were shipped through Hong Kong as re-exports. The authors argue that intermediation was one of the more important reasons. These ratios are even larger for some goods typically associated with China s rapid export growth in the 1990s, such as 77% for footwear and 83% for toys. Basker and Van (2011) document the role of Wal-Mart as a catalyst for US imports from China and note that this large US retailer accounts for 15% of US imports from China. It has also become clear that firms in most countries and sectors are highly heterogeneous in several dimensions and that this is strongly correlated with export performance (see, for example, Mayer and Ottaviano 2008). It is thus highly likely that the effect of intermediaries on producing firms is asymmetric. Bernard et al. (2010a) find that exporting firms in the US exhibit substantial heterogeneity as regards export mode, i.e., whether firms manage their own exporting activities or export through intermediaries. McCann (2013) and Abel-Koch (2013) use East European and Turkish datasets, respectively, to find that indirect exporting (exporting through intermediaries) is correlated with important firm characteristics. Most importantly, the largest and most

3 158 A. Akerman productive firms export directly while firms in the middle of the productivity distribution instead choose to export indirectly through an intermediary. 1 Based on an assumption of why wholesalers exist and how they operate, this paper develops a model of international trade with wholesalers in a setting of heterogenous manufacturing firms. 2 Unlike much of the related literature, the model is characterized by free entry in all sectors and it therefore allows for a welfare analysis of the presence and structure of a wholesale industry in a general equilibrium framework. As in Melitz (2003), exporting is subject to a fixed cost. The role of wholesalers in international trade is that they are able to pool the fixed cost of exporting across more than one good. They do not produce goods themselves but instead buy goods in their local market and export these to foreign markets. The fixed cost of exporting for wholesalers is assumed to be convex and increasing in product scope (the number of goods that a wholesaler exports) since a more complex product portfolio is more costly to handle, but they have to incur the fixed cost only once (regardless of how many goods they export). For a producer, exporting through a wholesaler is therefore an alternative to setting up its own distribution channel. Wholesalers are assumed to be homogeneous since the main focus of this study is on how aggregate trade flows and heterogeneous producers of goods respond to the possibility of exporting through wholesalers as an alternative to managing their own distribution networks. The core mechanism that operates in the model is thus the following. Wholesalers spread the fixed cost of exporting across more than one good. But to cover the fixed cost, they need to charge a markup between the procurement price of the good and what it charges the final consumer in the foreign country. This markup causes productivity sorting in the choice of export mode: the most productive firms choose to incur their own fixed cost of exporting since their operating profit of exporting is large enough. However, some goods, which cannot be profitably exported by the producer itself, can be exported at a lower fixed cost (per good) by wholesalers, who export several goods but have to make only one investment in the fixed cost. 3 This means that the wholesale technology exhibits economies of scope. When fixed costs increase, wholesalers become more important, since fewer firms find it profitable to export on their own. Moreover, wholesalers have to expand and handle more goods to be able to cover the higher fixed cost. Wholesalers therefore help producers in overcoming 1 See also Bai et al. (2015) and Davies and Jeppesen (2012) for additional evidence. 2 The term wholesalers will be used in the paper since the empirical analysis uses data for wholesale firms, but the theoretical model could be applied to intermediaries in general. 3 The mechanisms that cause sorting are analogous to those in Helpman et al. (2004). They model horizontal FDI as a mode of foreign market entry, which, compared to exporting, is associated with a higher fixed cost but a lower variable cost. Here, exporting through a wholesaler is instead associated with a lower fixed cost but a higher variable cost.

4 Wholesalers in international trade 159 destination-specific barriers to entry. In an appendix section, I develop a multicountry gravity model where the multilateral resistance variable of a country is found to include the number of wholesalers of trading partners. The presence of wholesalers lowers a country s price index as well as mitigates the positive effect of fixed trade costs on the price level. Since the price level is indirectly a measure of welfare, I therefore also show that wholesalers increase welfare. This generates a number of predictions about how exporting is conducted in the presence of intermediation. First, producers sort according to productivity in determining their mode of exporting. The most productive firms continue to manage their own exporting activities and incur the fixed cost associated with this as in the standard model. However, some firms that were almost productive enough to export on their own in the standard model now choose to do so, but instead through wholesalers. The least productive firms do not export through any of the two modes. Second, a higher fixed cost of exporting is associated with a larger importance of wholesalers both in terms of export volumes and export scope. Finally, a higher fixed cost of exporting is also associated with each wholesaler handling more goods (having a larger scope). Swedish data from 2005 are used to test the main predictions of the model. I match data from Swedish Customs with production data for the universe of Swedish firms. The dataset contains a sector classification of firms according to main business activity as well as each firm s export transactions for each eightdigit Combined Nomenclature (CN8) product code and destination. Therefore, it can be observed what goods that are exported by wholesalers versus manufacturers where the latter are treated as the producers of goods. The empirical analysis supports the main predictions of the model. Crucially for the basic assumption about economies of scope, Swedish wholesalers export a larger scope of products than producers. A wholesaler exports about 54% more products per firm when destination-specific effects and firm size are accounted for, an empirical fact that supports the notion that there is a technological difference between wholesalers and producers related to the product scope in exporting. Moreover, as predicted by the model, wholesalers do, on average, export substantially lower volumes (between 33 and 54% less) per firm within a product category than producers. Finally, wholesalers play a more important role in aggregate exports (both in terms of total volumes and product scope) from Sweden to countries characterized by higher fixed costs. The result for aggregate export volumes is in line with previous studies by Ahn et al. (2011) for China, Bernard et al. (2015) for Italy and Crozet et al. (2013) for France. This paper is most directly related to a growing literature that studies the effects of intermediary firms on international trade in a setting with heterogeneous producing firms. Ahn et al. (2011) introduce the choice of indirect exporting through an intermediary into a partial equilibrium model of firm heterogeneity along the lines of Melitz (2003). This new export mode is assumed to be associated with lower fixed costs but higher variable costs and therefore, it causes productivity sorting among producers regarding export mode. These assumptions also mean that intermediaries become more important for destina-

5 160 A. Akerman tions characterized by higher fixed costs of entry. Felbermayr and Jung (2011) develop a similar model but where the difference in the ratio between fixed costs versus de facto variable costs instead comes from contracting frictions between producers and intermediaries. The predictions of these papers are in line with the predictions that I generate but this paper goes further. First, my model allows free entry and exit in all sectors and therefore provides a general equilibrium framework unlike the previous literature. This also enables a welfare analysis, and I show formally how intermediation in international trade increases welfare and through what mechanisms. Moreover, I specifically derive the additional marginal cost of indirect exporting as a result of the double marginalization based on the elasticity of substitution. This generates several predictions of, for example, product scope and intermediation, as well as the role of elasticity of substitution and competitive pressure in explaining crosssector variation in the importance of intermediated trade. Blum et al. (2011) also analyze the role of intermediaries in a setting with heterogeneous firms but do instead focus on how intermediaries reduce the costs of matching between producers and foreign consumers and find that intermediaries are especially important in matching small producers with small foreign consumers. Finally, Tang and Zhang (2011) and Crozet et al. (2013) analyze how quality differentiation among producers interacts with the possibility of choosing intermediation as an alternative export mode. Other theoretical work has also explored the issue of intermediation in international trade but has instead focused either on the role of intermediaries in reducing contracting or matching frictions between buyers and sellers, as in Antràs and Costinot (2010, 2011), Biglaiser (1993), Olsen (2013) or Rubinstein and Wolinsky (1987) or on their positions in networks in international trade, as in Petropoulou (2008), Rauch (1999, 2001) or Rauch and Watson (2004). An emerging literature also analyzes the fact that many producing firms appear to also export products that they do not produce themselves. Such carry-along trade, in the words of Bernard et al. (2012), is something that I do not analyze since I want to make the distinction between firms with versus without an intermediation technology as clear as possible. The paper is structured as follows. Section 2 develops the model by introducing a wholesale industry into the model in Melitz (2003) and derives the main results. Section 3 describes the Swedish data and provides the empirical analysis. Section 4 concludes the paper. 2. The model 2.1. Basic setup without wholesalers The model builds on the structure in Melitz (2003) but with an additional agricultural sector characterized by constant returns to scale. It depicts two economies (Home and Foreign, the latter denoted by superscript F) with a primary production factor labour, L, which is used in all sectors. As in Krugman

6 Wholesalers in international trade 161 (1980), consumers in each country have two-tier utility functions with the upper tier (Cobb Douglas) determining the consumer s division of expenditure among sectors and the second tier (CES) dictating the consumer s preferences over the various differentiated varieties within the manufacturing sector. All individuals in Home have the utility function U = C ¹ M C1 ¹ A where ¹ (0, 1), and C A is the consumption of the homogeneous good. Manufactures enter the utility function through the index C M, defined by C M = ( N 0 c ¾ 1 ¾ i di) ¾ 1 ¾ where N is the mass of varieties consumed, c i the amount of variety i consumed and ¾ > 1 the elasticity of substitution between varieties. Each consumer spends a share ¹ of his income on manufactures and demand for a variety i is therefore x i = Ap ¾ i, where A ¹L is the demand per firm, p P 1 ¾ i is the consumer price of variety i, L is the population size and P ( i Ä p1 ¾ i di) 1 ¾ 1 the price index of manufacturing goods available in the Home country. The set of available varieties is denoted by Ä. Ignoring the wholesale sector for now, the economy consists of an agricultural and a manufacturing sector. The agricultural sector is a Walrasian, homogeneous-good sector with costless trade. The manufacturing sector is characterized by increasing returns, Dixit Stiglitz monopolistic competition and iceberg trade costs. Manufacturers face constant marginal production costs and three types of fixed costs. The fixed cost, F E, is the standard Dixit Stiglitz cost of developing a new variety. Manufacturing firms are assumed to be singleproduct firms. 4 The other two fixed costs involved reflect the one-time expense of introducing a new variety into a market: F D (μ, wl) for the domestic market and F X (μ F, w F L F ) for the foreign market, where μ denotes a vector of country-specific characteristics that determine the difficulty of entry (such as, for example, the quality of institutions) and w denotes the wage level in a country. Consequently, wl denotes the gross domestic product of a country. When analyzing comparative statics of the model, I will use these relationships to see how country characteristics affect outcomes through the fixed cost of entry but, for ease of exposition, I denote F j F j (μ j, w j L j ) until then. 5 4 Modelling manufacturing firms as single-product firms is convenient for tractability and facilitates the focus of the paper on the unique feature of the wholesaler firms technology, namely the economies of scope in exporting. I should also add that assuming that multi-product manufacturing firms pay separate fixed costs of exporting and make independent choices on exporting for each product makes it theoretically possible to treat such firms as several independent single-product firms as long as their decisions do not change the underlying productivity distribution of products. For an extensive analysis of multi-product manufacturing firms in international trade, see, for example, Bernard et al. (2011) or Mayer et al. (2014). 5 I will not make any assumption on exactly how the fixed cost is affected by country size since this is difficult to know. For example, Arkolakis (2010) points out that due to returns to scale in the technology of entry (i.e., advertising technology), firms tend to pay a smaller fixed cost per customer in large economies but a higher total fixed cost. Moreover, larger destinations tend to attract more exporters; see, for example, Mayer and Ottaviano (2008). This may make it easier for a potential new exporter to enter since it can observe the methods of entry of other exporters.

7 162 A. Akerman There is heterogeneity in firms productivity levels, '. Each Dixit Stiglitz firm/variety is therefore associated with a particular labour output coefficient denoted by ' i for firm i. After spending F E units of labour in the product innovation process, the firm is randomly assigned ' i from the cumulative distribution function G('). The analysis focuses on steady-state equilibria and intertemporal considerations are ignored; the present value of firms is kept finite by assuming that firms face a constant Poisson hazard rate ± of forced exit. The unit factor requirement of the homogeneous good is one unit of labour. This good is freely traded and, since it is chosen as the numeraire, its price p A = w = 1, where w is the nominal wage of workers. Shipping the manufactured good involves a frictional trade cost of the iceberg form: for one unit of a good from Home to arrive in the Foreign country, > 1 units must be shipped. It is assumed that trade costs are equal in both directions. Profit maximization by a manufacturing firm i located in Home exporting to the Foreign country leads to the following ¾ ¾ 1 '. consumer price in Foreign of firm i s good: p F i = Entrepreneurs entering the manufacturing sector draw their marginal productivity, ' i, from the probability distribution G(') after having sunk F E units of labour to develop a new variety. Having learned their productivity, firms decide on entry in the domestic and foreign market, respectively. Doing so is associated with fixed market entry costs; firms pay F D to enter the domestic market and F X to enter the foreign market. Firms will therefore enter a market as long as the operating profit in this market is sufficiently large to cover the market entry cost associated with the market. The critical cut-off levels of productivity needed in order to enter the domestic and foreign markets (for the operating profit to be as large as the discounted fixed cost of entry) are given by ' ¾ 1 D A = F D and (1) ' X ¾ 1 1 ¾ A F = F X, (2) where F D ±(¾ 1) 1 ¾ ¾ ¾ F D and F X ±(¾ 1) 1 ¾ ¾ ¾ F X. Accounting also for free entry, which means that the expected operating profit, ¼, equals the fixed cost of entry, E(¼) = F E, yields that A = A F (see, for example, Helpman et al., 2004). Equations (1) and (2) yield the well-known result from Melitz (2003), 1 F which can be summarized as follows (provided that X 1 ¾ FD > 1). In a world without wholesalers, only firms with a marginal productivity above ' X choose to export, firms with a productivity between ' D and ' X serve the domestic market only and firms with a marginal productivity below ' D exit immediately Wholesalers The third sector, and the novel feature of this model, is the wholesale sector (variables relating to this sector are denoted by superscript W). Wholesale firms are indexed by j and are homogeneous. The wholesale technology gives a wholesaler firm j the ability to source a range of goods and ship these to the Foreign country. The mass of goods that wholesaler j ships (equal to the mass

8 Wholesalers in international trade 163 of manufacturing firms from which the wholesaler is buying goods) is denoted by mj W. The sector is characterized by free entry. A wholesaler faces the same cost as manufacturing firms to establish a retail channel in the foreign country, F X, but has the technology to export several goods. Operations are assumed to become more costly the more goods a firm handles, so it also faces a per-period fixed cost that is monotonically and convexly increasing in the range of goods it handles. Its total fixed cost of foreign market entry is therefore F W Xj = F X + (mw j ), (3) where > 1 and mj W is the mass of domestic manufacturing goods that the wholesale firm j is handling. Since manufacturing firms are atomistic and have a mass equal to zero, if a wholesale firm were to export only one single good, its scope measure mj W would be zero and lim m W j 0 FW Xj = F X. A wholesale firm that exports only one good therefore has the same fixed cost of exporting as a manufacturer. Moreover, the functional form in (3) is chosen both for technical and intuitive reasons. The technical reason is that some convexity needs to be included in this function to put an upper bound on the scope of wholesalers. If not (i.e., if =0), the economies of scope would be infinite and only one wholesaler would exist and this firm would export all goods. The intuitive reason is that it is more costly to maintain an international distribution system the more different goods are in nature. If mj W is low, the wholesaler is more specialized in a more narrow range of products, for example sport cars of different kinds. However, as mj W increases, the products necessarily become more different; in the specific example, the wholesaler firm also starts to export other types of cars or motor vehicles etc., which means that the level of specialization decreases and the cost per product increases. The wider the scope, the more costly each product is to export. I assume that a wholesaler gets the exclusive right to sell the manufacturing good in the foreign market. Since the wholesaler faces CES demand abroad, its demand function towards manufacturing firms when procuring their products is also characterized by a CES structure. This causes manufacturing firms to charge the same price to wholesalers as they do to consumers. And since the manufacturer imposes a CES markup over its marginal cost and the wholesaler does the same, the final consumer price in the foreign economy for a good sold by a wholesaler is characterized by a double marginalization ; the CES markup of ¾=(¾ 1) is imposed twice: ( ) ¾ 2 p W ij =, (4) ¾ 1 ' i where p W ij is the price charged by wholesaler j selling manufacturing firm i s good in the foreign market. 6 One can also immediately see that the term ( ¾ 1 ¾ )2 6 See proof 1 in online appendix A.3.

9 164 A. Akerman FIGURE 1 Relative profits for different export modes NOTE: ¼ X indicates the operating profit of a producer that exports on its own and ¼ W indicates the operating profit of a producer exporting through a wholesaler. decreases in the elasticity of substitution, which means that the degree of double marginalization is smaller in sectors where varieties are more substitutable. One might argue that double marginalization is a strong assumption. However, it is an endogenous outcome of a CES demand structure: wholesalers choose a CES markup since this is profit maximizing. The demand of their consumers is characterized by CES preferences, which cause their input demand (as derived by Shephard s lemma from the cost function of wholesalers) to be characterized by CES preferences as well, which motivates the markup choice by manufacturing firms. Moreover, even if wholesalers and manufacturers are able to negotiate, there are many reasons to believe that such contracts would not be completely non-distortionary in reality and that there would indeed be some additional margin component that is paid to the wholesaler. In any case, for wholesalers to generate non-negative profits, they must charge the manufacturer (whose product it is buying) some strictly positive price for their services in order to cover their fixed costs. Such an additional price will make it more profitable for the manufacturer to export on its own if it can. 7 Finally, the empirical facts that wholesalers and manufacturers co-exist in most export markets and that the most productive manufacturers choose to export on their own, as in McCann (2013) and Abel-Koch (2013), suggest that there is some reason for manufacturers to avoid using intermediation services if they can. Since manufacturers can choose their export mode (i.e., by establishing their own distribution system or exporting through a wholesaler), their choices are 7 In the Swedish data, wholesalers charge higher unit prices than manufacturing firms when exporting. And this difference decreases in the elasticity of substitution, which is in line with corollary 2. The estimates of this relationship are, however, very imprecise and therefore not reported here. They are instead available from the author upon request.

10 Wholesalers in international trade 165 determined by what mode yields the highest profits from exporting. The expected profits (discounted by the forced exit rate ±) of a manufacturing firm i that exports through wholesaler j are 1 ± ( p ij,px ij (p W ij ) ' i x ij (p W ij )) where x ij(p W ij ) indicates foreign sales of good i at price p W ij, i.e., the price set by the wholesaler. The expected discounted profits of a manufacturing firm exporting on its own are instead 1 ± ( p ix i ( p i ) ' i x i ( p i )) F X. Comparing the profits between the two export modes yields the following condition for a manufacturer to choose to export on its own: ' ¾ 1 i > F X 1 1 ¾ A F ( ( 1 ¾ 1 ¾ ) ¾ ). (5) This means that more productive firms will want to export on their own rather than through a wholesaler. This is due to the fact that they are productive enough to take the fixed cost of exporting themselves and avoid the markup incurred by the wholesaler. Note also that (5) defines the new export cut-off ' X ¾ 1 = F X 1 1 ¾ A F ( 1 ( ¾ 1 ¾ ) ¾ ) > F X 1 ¾ A F = ' ¾ 1 X. The inequality sign demonstrates that, with wholesalers present, some producers that previously exported on their own now decide to use wholesalers instead. Therefore, the export cut-off is higher with wholesalers in the model than without. This phenomenon is illustrated in figure 1. The lines ¼ X and ¼ W show the operating profits of a manufacturing firm exporting on its own and exporting through a wholesaler, respectively, as functions of the manufacturing firm s productivity. The line ¼ W starts from zero since a manufacturing firm does not have to pay any fixed costs when exporting through a wholesaler. However, exporting directly requires paying a fixed cost F X. The slope of ¼ W is lower than that of ¼ X due to the additional markup charged by the wholesaler. A manufacturer with a productivity higher than ' X will always have higher profits from exporting on its own (¼ X > ¼ W if and only if ' > ' X ). Supposing that wholesalers find it profitable to buy only goods with a productivity higher than ' W means that firms with productivity levels between ' W and ' X will prefer to export through a wholesaler rather than on their own. Moreover, the export cut-off in an economy without wholesalers, ' X, will always lie to the left of ' X, which can be seen in the graph. The model generates productivity sorting as regards choice of export mode. The most productive firms, ' > ' X, export their products on their own, firms with intermediate productivity levels, ' [' W, ' X ), export through wholesalers and the least productive firms, ' [' D, ' W ), do not export (it must, however, be assumed that ' D < ' W ). Note also that since wholesaler prices are higher, they also export smaller volumes per good. Their prices are higher due to: (i) their additional

11 166 A. Akerman FIGURE 2 Productivity sorting and export mode markup and (ii) the fact that they export goods produced by less productive firms. Finally, equation (5) shows that the degree of competition (the elasticity of substitution across varieties) in a sector affects the productivity cutoff for direct exporting since it determines the impact of the double marginalization imposed by wholesalers. Less competition (i.e., a smaller ¾) means that the cutoff for direct exporting is lower since the wholesaler s additional margin is higher, making it relatively more expensive to use. 8 Wholesale firms are homogeneous and I make the simplifying assumption that the atomistic manufacturing firms that use wholesalers for the distribution of their goods are randomly matched with wholesaler firms (see figure 2). This ensures that wholesaler firms will, in equilibrium, on average have identical baskets of goods that they export. 9 8 See proof 2 in online appendix A.3. 9 The assumption of random matching between manufacturing firms and wholesalers may appear to be strong, especially given the convexity in the fixed cost function of wholesalers, which indicates that wholesalers prefer to export products that are closer to each other in nature. However, the results would hold also if manufacturing firms were matched within only, for example, broader sector categories as long as wholesalers are homogenous in terms of costs. Moreover, the key mechanism in the model, that wholesalers face a lower fixed cost per product, would hold even if manufacturers were matched less randomly. One example would be that some wholesalers are matched with more productive manufacturers than others. These wholesalers with a portfolio of more productively produced products would, however, still demand a markup from the producers, ¾=(¾ 1) under CES preferences, and therefore deter the most productive exporters but attract manufacturers from the intermediate productivity range. Finally, even if

12 Wholesalers in international trade 167 Therefore, they will have the same number of products and also the same productivity distribution among the goods in their baskets. 10 The scope of goods that wholesaler firms handle will be equal to the mass of manufacturing firms that use wholesalers for exporting (i.e., those with a level of productivity between ' W and ' X ). The mass of manufacturers in this range is M M G(' X ) G(' W ) 1 G(' D ), where M M is the mass of manufacturing firms in total. The scope per wholesaler, mj W, is then equal to this expression divided by the number of wholesale firms, n W : mj W = MM G(' X ) G(' W ) n W 1 G(' D ). A wholesaler takes as given the number of other wholesale firms and the mass of domestic manufacturing firms and its pricing mechanism is, as described in equation (4), a constant markup over the marginal cost. Therefore, the number of wholesale firms and the range of goods they consume can be determined by two conditions. First, the free entry condition for wholesalers states that the profits of wholesale firms should be zero. Second, an optimal scope condition by wholesalers, i.e., that the marginal increase in operating profits for a wholesaler firm to expand its set of goods distributed (its scope) must equal the resulting marginal increase in fixed costs, specifies the scope of each wholesale firm: F X + (mw j ) = mj W ¼ W j (Zero W j ( F X + (mw j ) W ( m W j ¼ W j ) (Optimal scope) wholesalers were assumed to be heterogeneous in terms of their cost function, and even if this were to be correlated with the markup they choose, the key difference between the two export modes would prevail since all wholesalers, regardless of costs, must charge some markup for each good for them to finance the extra cost of adding an additional product to their existing scope. 10 Wholesalers control more than one good and are therefore no longer atomistic like the manufacturing firms. This could potentially have implications for how they affect prices, but it is assumed here that the parameters are such that these baskets of atomistic products are still small enough not to have an effect on the aggregate price level. In a sense, a wholesaler could be labelled moleculistic, i.e., larger than an atomistic firm but still small enough not to have an effect on the aggregate price level. In this context, it can also be noted that in the seminal contributions by, for example, Dixit and Stiglitz (1977) and Krugman (1979, 1980), the distribution of differentiated varieties is discrete and not continuous such as in the more recent trade literature. With a discrete and finite set of varieties, all manufacturing firms are theoretically able to affect the aggregate price index so it has to be assumed that they do not.

13 168 A. Akerman These two conditions jointly determine the mass of manufacturing firms exporting through each wholesaler, m W j, and the weighted average of profits per good handled, ¼ W j : m W j ( ) 1 1 = FX (6) 1 ¼ W 1 ( ) 1 j = FX (7) 1 The fixed cost of exporting, F X, is the key variable in understanding how the size of wholesaler firms is determined. A higher fixed cost of exporting forces wholesale firms to expand their scope so that the fixed cost is spread across more goods. It also makes the operating profit per good handled larger in equilibrium. The parameter determining how difficult it is for wholesalers to handle more goods,, also plays an important role. The elasticity of the optimal scope with respect to the fixed cost in equation (6) is 1 which decreases in ; the more difficult it is to handle many goods, the less responsive is the scope of wholesalers to fixed costs. One can also note that the elasticity of the optimal scope of wholesalers with respect to the fixed cost of exporting is lower when it is more difficult for wholesalers to expand their scope (when is high). To close the equilibrium, I note that the operating profit of wholesaler j selling good i is ¼ij W = p W ij x ij p ij,p x ij = A F 1 ¾ ' i ¾ 1 ( ¾ 1 ¾ )1 2¾ ¾ 1 1. Therefore, the total operating profit of wholesale firm j is m W j ¼ W j (' W, ' X ) = mw j 1 ¾ A F G(' X ) G(' W ) ( ¾ ¾ 1 ) 1 2¾ 1 ¾ 1 'X ' W ' ¾ 1 dg('), where ¼ W j (' W, ' X ) is the average operating profit per good handled given the range of productivity in the basket. Combining this with (7) gives 1 ¾ A F ( ¾ ) 1 2¾ 1 G(' X ) G(' W ) ¾ 1 ¾ 1 'X ' W ' ¾ 1 1 ( ) 1 dg(') = FX, (8) 1 where ' W is the equilibrium level of the lowest productivity needed for a manufacturing firm to use a wholesaler firm to export. 11 The export cut-off, ' X,is determined according to equation (2) by, F X and A F. The variable and fixed trade costs are exogenous but A F is endogenous. Since the left-hand side of equation (8) is monotonically increasing in ' W, equation (8) yields an implicit solution for ' W as a function of A F. 11 There is nothing in the model that ensures that ' W > ' D (that manufacturers exporting through wholesalers need to be more productive than manufacturers producing for the domestic market). This has to be assumed but this restriction is similar to the assumption in the literature that ' X > ' D (that exporters are more productive than non-exporters). However, this does not matter for the final results.

14 Wholesalers in international trade 169 Using the equilibrium value for ' W, it is also possible to find a solution for the number of wholesale firms by combining mj W = MM G(' X ) G(' W ) n W 1 G(' D ) and (6): M M ( ) ( ) 1 G('X 1 ) G(' W ) n W = FX (9) 1 G(' D ) 1 Finally, the free entry condition for manufacturing firms says that, in expectation, the expected total profit of the entrepreneur must equal the fixed entry cost: 'X ( ) ¾ 1 ¾ (' ¾ 1 A F D )dg(')+ ' ¾ 1 1 ¾ A F dg(') ' D ' W ¾ (10) + (' ¾ 1 1 ¾ A F F X )dg(') = F E, ' X where F E ±(¾ 1) 1 ¾ ¾ ¾ F E. The set of equations (1), (5), (8), (9) and (10) yields implicit solutions for the productivity cutoffs ' D, ' W, ' X and the mass of wholesale and manufacturing firms, n W, M M. The per-firm demand A in Home and A F in Foreign is determined by the mass of firms, the number of wholesalers together with the productivity cutoff levels through the expression for the price levels. This set of equations therefore defines a general equilibrium in the sense that there is free entry in all sectors and that price levels and market demand are endogenous Imposing the Pareto distribution To find exact expressions for the importance of wholesalers in the economy, the exact distribution of productivity, G(') has to be specified. Therefore, I impose the scale-free Pareto distribution which has been found to correspond reasonably well with observed distributions of firm productivity. 12 Therefore, G(') = 1 ' k where ' [1, ). As is well known in the literature, it is also required that ¾ 1 k > 1 for a solution to exist in equilibrium. To calculate the relative export volumes that occur by firms exporting on their own versus through wholesalers, it can be noted that the export volume of a good through the two export modes is ( ¾ V i,x (' i ) = p i x i = V j,w (' i ) = p W ij xw ij = ¾ 1 ( ¾ ¾ 1 ) 1 ¾ 1 ¾ ' i ¾ 1 A F (direct exporting) ) 2(1 ¾) 1 ¾ ' i ¾ 1 A F (wholesale). 12 See Axtell (2001) or Luttmer (2007).

15 170 A. Akerman The ratio of total export volumes will therefore be V W V X = 'X V W (')dg(') ' W = V X (')dg(') ' X ( ) ( ¾ 1 ¾ 1 ( ) k (¾ 1) 'X 1), (11) ¾ which is an explicit function of the relative productivity cut-off levels ' X and ' W. The relative mass of firms exporting on their own versus through wholesalers can be written 'X dg ( ' ) ( ) k ' W 'X dg ( ' ) = 1, (12) ' W ' X which is also an explicit function of the relative productivity cutoffs. To see what affects the relative importance of wholesalers in total export volumes, equation (11), and scope, equation (12), it is thus necessary to understand what affects the relative productivity cut-off, ' X ' W. An explicit solution for ' W cannot be found but using equation (5) in equation (8) yields the following nonlinear relationship: ( ) k 'X 1 ' W ( 'X ' W ) k (¾ 1) 1 = 1F X (μ, w F L F ) 1, (13) ' W where 1 is a constant of parameters. 13 The expression shows that the relative productivity cut-off increases in the fixed cost of exporting where I now, again, include country-specific characteristics as mentioned at the beginning of this section. First, a higher fixed cost causes the relative productivity cut-off to increase. This causes: (i) more firms to export through wholesalers (which is equivalent to more varieties or products being exported through wholesalers) and (ii) the relative export volume that is managed by wholesalers to increase. 14 This result originates in the central mechanism provided by the model: the wholesale industry pools the fixed costs of exporting across goods and therefore reduces the fixed cost per good, a feature that is more important when fixed costs are large. We saw previously that a higher fixed cost causes wholesale firms to expand the set of goods that they handle. By doing so, the fixed cost per good decreases. Second, neither the variable trade cost,, nor per firm demand, A F, play any direct role for the choice of export mode. This is due to the fact that 13 1 k k (¾ 1) ( 1 ) ( ¾ 1 ¾ )¾ 1 ¾ ( ¾ 1 ¾ )2(¾ 1). 14 See proof 3 in online appendix A.3.

16 Wholesalers in international trade 171 for the operating profit, these variables affect wholesalers and direct exporters in identical ways (the only way in which they can affect the relative productivity cut-off is through their effect on the fixed cost). 15 The wholesale technology therefore exhibits an increasing returns to scale property with regard to product scope. An increase in the number of products that a wholesaler exports lowers the fixed cost per good, thus making wholesalers more important as fixed costs increase. The net effect of the elasticity of substitution, however, is unclear. More competition (higher ¾) makes firms at the margin between choosing direct or wholesale exporting opt for exporting through wholesalers. This should make ¾ increase the role played by wholesalers. However, a higher ¾ also makes price differences more important for revenues and profitability. When the elasticity of substitution is high, the additional markup imposed by wholesalers becomes more important for how much is actually sold and this has a negative effect on the aggregate role played by wholesalers in exporting. Finally, a welfare analysis of a multi-country setting of the model is conducted in online appendix A.1. This adds two main insights to what has been described so far. First, the ratio of the productivity cutoffs, 'J X, to each export ' J W destination J depends on country J s fixed cost of entry. Since such costs differ across countries, many manufacturing firms would export directly to some countries but through a wholesaler to other countries. A firm s export mode also depends on each country s multilateral resistance (as proposed by Anderson and van Wincoop, 2003), which takes into account the industry structure in the destination but also the level of exports from other countries to that specific market. In this case, the equilibrium would contain firms that use both export modes at the same time but not both export modes to the same country. 15 Distance and size appear to significantly affect the importance of intermediaries in activities relating to foreign trade in many empirical studies. Indeed, the empirical analysis in this paper shows that wholesalers are more important in distant and small markets, while contrary to the results of this paper, a range of possible mechanisms could create this pattern. An obvious candidate is that the fixed cost of entering a foreign market increases with distance, since cultural barriers, supervision costs etc. are larger in markets far away than in those close to the home country of a firm. This would be in line with the theoretical predictions presented here. As argued at the beginning of this section, there are also several potential mechanisms through which the fixed cost varies with size. Arkolakis (2010) shows how returns to scale in marketing technologies potentially make it easier for firms to enter large countries. Alternatively, the fact that more firms export to larger destinations could also create potential spillover effects across firms, thus making it easier to access larger markets. The main technical reason why my model does not give an explicit role to distance and size is the combination of using CES preferences and the Pareto distribution of firm productivity. The purpose of this paper, however, is to show what the specific assumption of wholesalers possessing economies of scope in international trade can explain; therefore, I do not extend the model further to incorporate these empirical facts.

17 172 A. Akerman Second, I find that the presence of wholesalers contributes positively to welfare by assisting firms at intermediate levels of productivity to overcome fixed costs of exporting. Therefore, wholesalers increase the range of products available for consumption in each country and reduce price indices and increase real wages. In other words, wholesalers mitigate the effects of fixed costs in international trade on welfare. This analysis also shows that the expression for a country s welfare can be reduced to a simple expression that makes it directly comparable to Chaney (2008) (one of the standard references for analyzing the welfare consequences of firm heterogeneity in a Melitz-style economy) and how the existence of wholesalers strictly raises welfare as compared to a world without wholesalers as in Chaney (2008). 3. Empirical evidence 3.1. Data I use a dataset from Statistics Sweden that contains information on the economic activities of the universe of Swedish firms in 2005 (a firm is defined as the legal unit). The data are collected by the Swedish Tax Agency (Skatteverket) and contain information on, for example, total annual revenues, number of employees (reported once every year at a certain point in time) and total fixed assets. A firm in this dataset is classified according to its main business activity, and the following analysis will use firms that are listed as wholesalers and firms active in any of the manufacturing sectors. The only restriction I make is to exclude firms with no employees. Since misreporting is prosecuted and these data are subjected to quality controls by statisticians at Statistics Sweden, measurement errors are most likely rare. Through a common firm identifier, I match these data with a trade dataset collected by Swedish Customs (Tullverket) that records all trade flows per firm, product code (according to the Combined Nomenclature, CN, up to 8 digits) and destination country. 16 I use only exporting firms (about 35% of both manufacturers and wholesalers export) and in 2005, there were 7,248 wholesaler firms exporting and 8,768 manufacturing firms. In total, 468,710 transactions are reported over 8,272 CN8 categories and 194 destination countries. I conduct only a cross-sectional analysis in this study since a panel study with several years would use only variation in the definition of a firm s main business activity, which would not be very informative, or in the destination country characteristics and this variation is very small. Due to the extreme detail of the CN8 classification, I use the number of CN8 categories exported by a firm as a proxy for the number of products exported by a firm. 17 The average number of CN8 product categories that a 16 The CN is a classification system used by the European Commission in its external statistics and it is based on the Harmonized System of product classification. 17 As stated, I observe more than 8,000 product categories in the data. An example of its level of detail is the subcategory CN code 6601, containing umbrellas. It is

18 Wholesalers in international trade 173 firm exported was 11 for wholesalers and nine for manufacturers. In terms of volumes, however, manufacturers were much larger and accounted for 86% of aggregate export volumes. As for market size (GDP) and the institutional variables used, all data come from the World Bank s World Development Indicators (WDI) and Doing Business databases. Distance measures are from Centre d études prospectives et d informations internationales (CEPII). A full list and description of each variable can be found in online appendix table A1. Table 1 reports descriptive statistics for exporting wholesalers and manufacturers. The main conclusion from this table is that manufacturing firms are, on average, much larger than wholesale firms in terms of turnover, number of workers as well as capital employed. Moreover, despite the smaller size of wholesalers, they export a larger number of products than manufacturers. This difference between manufacturing firms and wholesale firms in the sense that manufacturing firms tend to be larger in terms of export volumes while wholesalers, instead, export a larger scope, can also be seen in figure 3 which shows how wholesalers share of export volumes and export scope, respectively, are distributed across destinations. It can be seen that the distribution of the share of the scope controlled by wholesalers clearly lies to the right of the distribution of the share of export volumes controlled by wholesalers Main assumption and predictions This section will empirically assess the main predictions of the model: 1. Wholesalers export more products than manufacturers. 2. Export sales per good are lower for wholesalers than for producers exporting on their own. 3. A larger share of aggregate export volumes is handled by wholesalers to countries with high fixed costs of entry. 4. A larger share of the number of exported products is handled by wholesalers to countries with high fixed costs of entry. The underlying assumption of the model is that the wholesale technology is characterized by economies of scope, while that of manufacturers is not. This is a simplification of the case in which wholesalers have more economies of scope as compared to manufacturers (i.e., that wholesalers have a comparative advantage in generating economies of scope in exporting). We already know from a vast literature that manufactures often sell more than one product and that firms doing so are often important in terms of size and export volumes. 18 However, one way of seeing whether this assumption is reasonable is to look at divided into Garden or similar umbrellas and Other umbrellas. The latter category is divided into umbrellas with a telescopic shaft and those without. These are then divided into umbrellas with a cover of woven textiles and those without. Therefore, it seems reasonable to view a CN8 category as a manufacturing variety (or a product the two are equivalent in the model) in the analysis. 18 See, for example, Bernard et al. (2010b) and Mayer and Ottaviano (2008).