Retailers, International Trade and Competition 1

Transcription

1 Retailers, International Trade and Competition 1 Horst Ra Department of Economics and Kiel Institute for the World Economy Christian-Albrechts-Universität zu Kiel 4098 Kiel, Germany Nicolas Schmitt Department of Economics 8888 University Drive Simon Fraser University Burnaby BC, V5A 1S6, Canada schmitt@sfu.ca Preliminary and incomplete: February The authors acknowledge nancial support from the Social Sciences and Humanities Research Council of Canada. We would like to thank Rolf Langhammer for information about global sourcing of German retailers, and Agnès Benassy- Quéré for information about French retail market regulations.

2 Abstract We construct a model of trade with heterogeneous retailers to examine the e ects of trade liberalization on the mass and size distribution of retailers. We nd that retailers sourcing their goods through imports become larger and more pro table while those sourcing domestically become smaller and less pro table. The least e cient retailers are forced to exit the market. We use the model to study the degree of pass-through of import into retail prices and the e ect of retail market regulation. We show that the degree of pass-through may be large even in the short run when market structure e ects are taken into account. We also nd that restrictions on the ability of the retailing industry to adjust to trade liberalization, such as through size constraints, have signi cicant curtailing e ects on retail competition and on the degree of pass-through.

3 1 Introduction The purpose of this paper is to examine how the retailing sector responds to globalization and, in particular, to the increased scope to import consumer products. We are particularly interested in (i) the e ects of trade liberalization on the structure and performance of the domestic retailing sector; (ii) how the structure of retail markets a ects the transmission of external shocks, such as changes in import prices or exchange rates, into domestic consumer prices; and (iii) how retail market regulation a ects consumer prices, imports and social welfare. To study these issues we build a simple model of international trade with heterogeneous retailers. The structure of retail markets has changed dramatically in recent decades. Market concentration has increased markedly, driven by the emergence of large national chains operating large establishments. 1 This concentration process has had a signi cant e ect on international trade, as large retailers increasingly import consumer goods from low-wage countries like China. Wal-Mart provides an extreme example: it alone accounts for 15% of total US imports from China (Basker and Van, 008a). In many retail segments, such as electronics, computers, cameras, housewares, toys, games, clothing, and footwear, retailers in developed countries rely heavily on imports. For instance, in 003, the share of imports in Canada was 55% for clothing, 8% for clothing accessories, 86% for footwear, 100% for audio, video, small electrical appliances, as well as for toys and games (Jacobson, 006, Table 33). It is precisely in these sectors that the market share of large Canadian retailers is the highest: the market shares of the 80 largest retailers in 004 represented 61% for clothing and accessories, 68% for home electronics, computers and cameras, 57% for housewares, 55% for toys and games and 49% for food. On average, this share was 7% for all the commodities sold by Canadian retailers (Jacobson, 006, Table 6). Similarly Basker and Van (008b) nd that over the period 1997 to 00 US imports from China and other less- 1 Whereas large retail rms (with at least 100 establishments) represented 18.6% of US retail sales in 1967, their share has increased to 36.9% in 1997, and the average size of these establishments is twice as large as it was 40 years ago. Overall, the retail and manufacturing sectors have similar ratios of single to multi-unit rms but, not surprisingly, multi-unit retailers operate more establishments on average than multi-unit manufacturers. More signi cantly, the number of establishments operated by multi-unit retailers has increased dramatically between 1977 and 1997 whereas it has decreased in manufacturing during the same period (Jarmin et al., 005). 1

4 developed countries rose especially quickly in retail sectors with the largest consolidation into chains. The current paper argues that these changes in retail market structure have in part been brought about by the increased scope to import consumer goods from low-wage countries. The mechanism we see at work here relies on economies of scale in importing. Due to these economies, any reduction in import prices, whether through a reduction in trade barriers or declining transportation and communication costs, bene ts large retailers disproportionately. By making large retailers more competitive, lower import prices tend to squeeze out smaller retailers. A recent survey of Austrian, German and Swiss retailers (Zentes, Hilt and Domma, 007) illustrates this mechanism. 3 Retailers source their goods in two basic ways, namely through domestic sourcing and direct imports. Domestic sourcing refers to the purchase of domestically produced goods and of goods imported by domestic agents, including wholesalers, importers, buying cooperatives, and domestic wholesale subsidiaries of foreign exporters. Direct imports refer to the purchase of goods from foreign manufacturers, often coordinated by the retailers own overseas buying o ces. 4 Only big retailers engage in direct importing and among these, only the biggest retailers operate their own overseas buying o ces. Small and medium-sized retailers tend to rely on domestic sourcing. Direct importing, according to Zentes, Hilt and Domma (007), is associated with signi cantly lower variable costs. It allows retailers to bypass additional layers of intermediaries, and buying o ces can directly identify the lowest-cost supplier for speci c Basker and Van (008b) nd that between 1997 and 00 the biggest US retailers had a more than three times higher marginal propensity to import from China than smaller retailers. They argue that the expansion of big retailers accounts for 19% of the growth in US imports of consumer goods from China. 3 This survey is based on interviews with purchasing managers of 86 retailers in Germany, Austria and Switzerland accounting for about 50% of total retail sales in the region. 4 A recent survey of Austrian, German and Swiss retailers indicates that direct imports by retailers accounted for 6-9% of total sourcing in 006. Roughly 54% of these direct imports came in the form of direct purchases from manufacturers, including producers of own-label (or store-brand) goods. Another 15% were handled by the retailers own overseas buying o ces. Retailers with own overseas buying o ces sourced around 40% of direct imports through these o ces. Domestic sourcing accounted for the remaining 71 to 74% of retail sales. These indirect imports account for 35-37% of total sourcing and hence roughly half of total domestic sourcing. Overall, imported products (imported both directly and indirectly) accounted for between 61 and 66% of sales of the retailers surveyed (Zentes, Hilt and Domma, 007).

5 items. 5 The reason why only big retailers choose the direct import channel is that it is associated with large xed costs. These include costs of operating buying o ces, searching for suppliers, developing products, specifying product standards, training suppliers, and monitoring quality. 6 The strong interaction between retail market structure and international trade in consumer goods should not come as a surprise. Distribution margins, consisting of retail costs and retailer mark-ups, typically account for 30 to 50 percent of the retail prices of consumer goods (Campa and Goldberg, 006a). Any change in the cost structure and competition in the retail sector will thus have a big impact on consumer prices and hence on the demand for domestic and imported goods, as well as on consumer surplus and social welfare. In fact, the interaction between international trade and retail market structure is at the core of several important policy issues. First, the bene- ts consumers may reap from trade liberalization but also the e ectiveness of monetary and exchange-rate policy depend crucially on how changes in import prices are passed through into consumer prices. Empirical evidence suggests that consumer prices tend to react very little to movements in import prices. In fact, this observation constitutes a major puzzle in international macroeconomics (Bacchetta and van Wincoop, 003). Recent research on this issue (Campa and Goldberg, 006a, 006b; Hellerstein, 008) implies that the retail sector plays a central role in explaining pass-through, since distribution margins make up such a large share of consumer prices. By relating the pass-through of import prices into consumer prices to retail market structure, we able to shed new light on this so-called exchange-rate disconnect puzzle. Speci cally, we demonstrate that the pass-through may be large even in the short run when trade costs are su ciently low. Second, many countries, including France, Belgium, Italy and Japan, have a tradition of regulating retail markets, for instance, by limiting the size of new retail establishments. Our model permits us to examine how 5 Increasingly these suppliers are in low-wage Asian countries: more than half of direct imports by retailers come from Asia, with China being the dominant supplier. 6 Buying o ces can indeed be quite large. For instance, KarstaQuelle AG, Germany s biggest apparel and sixth-largest food retailer, operated 3 buying o ces with a total of 1,100 employees before re-organized its direct importing business in 006 (Zentes, Hilt and Domma, 007). Another survey (Foreign Trade Association, 00, p. 9) of 3 European apparel and textile retailers with combined turnover of around e138 billion cites the sheer number of people involved, from Buying Departments to Sourcing O ces to suppliers...who need to exchange real time information... 3

6 such regulations a ect retail market structure, imports and consumer prices. This is especially interesting as there is evidence that, in the United States, relatively poor consumers bene t from the existence of large retailers such as Wal-Mart and from the high volume of non-durable products that these retailers import from China (Broda and Romalis, 008). In France, however, there is evidence that lower import prices are not passed on to consumers, and consumers bitterly complain about the lack of price competition at the retail level (Economist, 008). We show that retail regulations may indeed have strong negative e ects on pass-through. The model we develop to investigate these issues builds on Melitz and Ottaviano (008) who consider the selection of rms into export markets. By contrast, in our model it is retailers and thus importers that are heterogeneous. This modeling approach seems especially relevant, since the entry and exit of rms have been an important driving force behind the changes in retail market structure; in fact, both rates have been much higher in retailing than in manufacturing (see Jarmin et al., 004). 7 Our paper is related to at least three other strands of literature, namely studies linking retailer market structure to domestic and external shocks, to studies examining the pass-through of import into consumer prices, and to papers examining the e ect of retail market regulation. The size distribution of retail establishments depends partly on market size. Campbell and Hopenhayn (005) show that establishments tend to be larger in larger markets. The e ect of market size on the dispersion of establishment size, however, is ambiguous. The size and size distribution of retail establishments is also likely to depend on technology. That is, lower costs lead to larger establishments. The case of Wal-Mart, which by some measures is today the biggest company in the world (Fishman, 006), seems to be an extreme example where technological advantages have led to strong company growth both in absolute terms and relative to competitors. But these e ects go beyond the case of a particular retailer. However, market growth and technological progress are not the only drivers of retail market structure and the size distribution of retailers. Trade liberalization, too, has played a role. In highlighting the role of international trade, our paper is most closely related to Basker and Van (008a) who study 7 Moreover, it appears that productivity gains in retailing have been due almost exclusively to the entry and exit process (Foster et al., 006). Caves (1998) reports that, although entrants exhibit size heterogeneity at the time of entry, entry and exit are concentrated in the smallest size classes. 4

7 the e ects of trade liberalization on competition between a chain retailer and small single-market retailers. They nd that trade liberalization raises the size of the chain retailer, and that the growth of the chain gives an additional boost to imports. However, their paper is silent about changes in the mass and size distribution of retailers and about welfare e ects. Other papers examining the interaction between trade liberalization and retail market structure include Ra and Schmitt (008) who study the e ects of trade liberalization in an oligopoly model with buyer power; Eckel (008) who examines the e ects of trade on retail market structure, especially as concerns product diversity and accessibility of retailers; Francois and Wooton (008) who show that market structure in distribution becomes increasingly important for trade as tari s fall; and Richardson (004) who studies market access to retail distribution. Another related paper is by Javorcik, Keller and Tybout (006). They examine the e ect of NAFTA on the Mexican soaps, detergents and surfactant industry. They argue that these e ects were less due to the reduction in trade costs or to the entry of foreign manufacturers than to the fundamental change in relationship between manufacturers and retailers once Walmex (Wal-Mart of Mexico) entered the market. In the pass-through literature the paper most closely related to ours are by Hellerstein (008) and Francois, Manchin and Norberg (008). Hellerstein bases her empirical study of pass-through on a model with Bertrand oligopolies at both the manufacturing and retailing level. This set-up generates endogenous mark-ups, like in our paper. However, unlike in our model, market structure remains xed. Endogenizing market structure and examining how changes in this structure a ect pass-through is precisely our contribution to this literature. Francois, Manchin and Norberg also work in an oligopoly framework and examine pass-through of tari and exchange-rate changes into producer and consumer prices empirically using EU data. Bertrand and Kramarz (00) discuss the e ects of retail market regulation in France. Schivardi and Viviano (008) and Miyagiwa (1993) examine the impact of retail market regulations in Italy and Japan, respectively. Except for the latter paper, this literature is not concerned with the e ects of regulations on international trade. Miyagiwa (1993) does not consider market structure e ects of retail regulations. The paper continues as follows. In Section, we present a simple model of international trade with heterogeneous retailers. The equilibria of the model and comparative static results for marginal changes in trade costs are derived in Section 3. In Section 4 we use the model to study the pass-through 5

8 of import prices into retail prices and the e ect of retail market regulation. In Section 5 we use simulations to assess the impact of trade liberalization on retailer concentration and social welfare both for the case with and without retail market regulation. Section 6 concludes, and the Appendix contains proofs. The Model In this section, we develop a simple model of a retailing sector that sources the goods it distributes both domestically and abroad. There is a continuum of retailers selling only in their domestic market (their services are nontraded). From the consumer s point of view, the products sold by di erent retailers are di erentiated varieties. This could be because each retailer sells a di erent bundle of goods, or because the retailers themselves are di erentiated. Retailer di erentiation occurs when consumers value di erent retailer characteristics, such as location or customer services. It is more natural to interpret our model as one of retailer di erentiation. We index retailers by i, and assume that all consumers share the same utility function: Z U = qi c di i Z 1 (qi c ) di i Z 1 qi di c + y; (1) i where qi c denotes the quantity per capita bought from retailer i, and y the consumption of the numeraire good. Parameter describes the degree of substitutability between retailers. If = 0, retailers are perfectly substitutable, and consumers care only about their total consumption level, Q c = R i qc i di. The degree of di erentiation between retailers increases with. Assuming that the demand for the numeraire product is positive, the inverse per-capita demand faced by each retailer i is p i = q c i Q c : () Denoting by L the number of consumers and by N the mass of active retailers, the market demand faced by retailer i can be expressed as a function of the average retail price p: q i (p i ) Lq c i = L N + L p i + N N + L p; (3) 6

9 where p = 1 Z p i di N i and where is the set of active retailers. Labor, the only factor of production, is inelastically supplied and perfectly mobile between the production and the retailing sectors. Since the numeraire good is produced by a competitive industry under constant returns technology and a unit labor requirement of one, the price of labor in the economy is equal to one. All costs are therefore expressed in terms of labor requirements. We assume that retailers rst decide wether to enter the market and thus whether to incur the sunk cost F E. Upon entering, each retailer learns about its speci c level of marginal retailing cost c or, equivalently, its productivity 1=c. We assume that the distribution of c is given by G(c) with support on [0; c M ]. Since the entry cost is sunk, only entrants able to cover their marginal cost are active in the market. All remaining entrants are inactive, i.e., do not buy or sell any goods. We assume that retail productivity follows a Pareto distribution with cumulative distribution function k c G(c) = where k 1. When k = 1, the distribution is uniform on [0; c M ]. As k increases, the distribution shifts toward high marginal costs. Campbell and Hopenhayn (005) nd that there are signi cant productivity di erences among retailers, with few big, technologically advanced rms competing with many relatively ine cient rms. This suggest that in practice k is rather large. Once a retailer has entered the market, he has to decide whether to source goods domestically or to import them. Imports involve a per-unit trade cost t and a xed cost F I. This xed cost includes the cost of maintaining buying o ces, cooperating with foreign partners to source goods, acquiring information, etc. Production (domestic or foreign) involves no xed or sunk cost but foreign production is assumed to be cheaper than domestic production. For simplicity, we normalize the marginal cost of foreign producers to zero, and denote the marginal cost of domestic production by w > 0. Hence, active retailers that buy domestically maximize c M (p i c w)q i (p i ); (4) 7

10 whereas active retailers relying on imports maximize (p i c t)q i (p i ) F I : (5) Taking the mass of active retailers N and average retail price p as given when setting their price, it is easy to check that the pro t-maximizing markups must satisfy (p D i c w) = L q i(p D i ) and (p I i c t) = L q i(p I i ); where the superscript D indicates domestic sourcing, and I indicates imports. Retailer i s pro t-maximizing prices when buying from domestic (foreign) sources are respectively, p D i = 1 c + w + + N p N + and p I i = 1 c + t + + N p : N + +N p De ning c D N+ with marginal cost c are w, the equilibrium prices and outputs of a retailer p D (c) = w + 1 [c D + c] ; (6) p I (c) = 1 [c D + w + c + t] ; (7) q D (c) = L (c D c) ; (8) q I (c) = L (c D + w c t) ; (9) and pro ts are D (c) = L 4 (c D c) F E ; (10) I (c) = L 4 (c D + w c t) F E F I : (11) Only retailers with marginal costs less than or equal to c D will remain active, because only they will be able to cover their marginal cost. Active retailers have to select from which source to buy their goods. A retailer is 8

11 indi erent between domestic sourcing and direct imports if D (c) = I (c) This condition de nes a critical value of the marginal cost c I, c I = c D + (w t) F I L(w t) ; (1) such that rms with c c I prefer imports and rms with c > c I domestic sourcing. We assume that c I < c D so that the least e cient active retailers prefer domestic sourcing. This implies that L 4 (w t) < F I : (13) We also assume that importing is more pro table for the most e cient retailers than domestic sourcing. Thus, at c = 0, we require F I < L 4 (w t) + c D (w t) : (14) These two assumptions together with the quadratic form of the pro t function ensure that the value of c I solving (1) is unique. The two cut-o values of the marginal cost, c D and c I, de ne three categories of retailers. Retailers whose marginal cost is su ciently small (c c I ) import; retailers whose marginal costs are in the middle range (c I < c c D ) source goods domestically; and retailers with high marginal costs (c > c D ) are not active because they are not able to cover their marginal costs. Given these cuto s we can compute the average retail price of active retailers as p = 1 Z ci Z cd p I (c)dg(c) + p D (c)dg(c) : (15) G(c D ) 0 c I Since the marginal active retailer is just indi erent between between buying and not buying, we have q D (c D ) = 0 and p D (c D ) = w + c D. Using this price in (3), the mass of active retailers can be calculated as N = ( w c D) (w + c D p) : (16) The mass of active retailers is related to the mass of entrants into the retail market, N E, by the condition N = N E G(c D ). In equilibrium the mass 9

12 of entrants has to be large enough so that the expected pro t of a retailer is equal to zero: Z ci 0 I (c)dg(c) + Z cd c I D (c)dg(c) + Z cm c D ( F E ) dg(c) = 0: (17) 3 Equilibrium and Comparative Statics In this section we characterize the equilibrium of the model and examine the comparative statics with regard to in nitesimal changes in the trade cost t. The endogenous variables of the model are p, c D, c I and N. The equilibrium values of these variables are given by equations (1), (16), (15) and (17). Consider rst the zero-pro t condition (17). The partial derivative of this condition with respect to c I is zero since, by de nition, I (c I ) = D (c I ). Total di erentiation of this equation hence yields dc D =. We can then derive dc I = from (1), and the marginal change in p from (15). We obtain the following comparative static results: Proposition 1 Trade liberalization (i) forces the least e cient retailers to become inactive (c D decreases); (ii) induces a larger fraction of retailers to source goods from abroad (c I rises); and (iii) reduces the average consumer price p. Proof: see Appendix. The intuition for these e ects is as follows. A reduction in the trade cost, ceteris paribus, raises the pro ts of importers both in absolute terms and relative to those retailers that source their goods domestically. Hence more retailers will turn to imports (c I rises). To keep the zero-pro t condition satis ed ex ante despite the fact that active retailers will ex post earn a larger pro t, c D has to decrease so as to lower the probability of being an active retailer. To explain the e ect on p we apply the Pareto distribution to (15), which yields p = w + kc D k c D (k + 1) (w t) c k I c k D : (18) The four terms of this expression have a natural interpretation: the rst term is, of course, the marginal cost of domestic production; the second term 10

13 is the expected marginal cost of retailing conditional on c < c D ; the third term is the expected markup of retailers sourcing domestically (c D c) = conditional on c < c D ; and the last term is equal to the fraction of cost savings from imports that is passed on to consumers, (w t) =, times the probability of being an importer conditional on c < c D. A reduction in t directly a ects the last term in (18): there are greater savings from imports relative to domestic sourcing, and the probability of importing rises. Indirect e ects arise as trade liberalization eliminates the least e cient retailers. As can be seen from the second and third terms in (18), a decrease in t lowers the expected marginal retail cost, and reduces the mark-up of retailers buying goods domestically. Since the retail sector is imperfectly competitive, retailers that source their goods from abroad pass only part of the reduction in trade costs on to consumers. Their mark-ups, sales and pro ts hence rise. Retailers that buy their goods domestically, on the other hand, are forced to cut their mark-ups, which leads to lower sales and pro ts. These e ects can be summarized as follows: Proposition Trade liberalization (i) lowers the sales, mark-ups and pro ts of retailers that source domestically; (ii) raises the sales, mark-ups and pro ts of retailers that engage in direct imports. Proof: see Appendix. Firms respond to changes in expected pro ts by entering or exiting the retail sector. Propositions 1 and indicate that trade liberalization indeed induces changes in expected pro ts. First, since trade liberalization reduces c D, the likelihood of earning a positive operating pro t, G(c D ), falls. Second, the pro t earned by an importer rises and, since c I goes up, so does the probability of being an importer. Third, the pro t of a retailer buying goods domestically decreases, but so does the probability of falling into this category. We can use (16) to derive how the mass of active rms N changes with marginal changes in t, keeping in mind that N is related to the equilibrium mass of entrants N E via the condition N = N E G(c D ): dn = (w + c D p) ( p) dc D + ( w c D) dp : (19) 11

14 The rst expression in parentheses is negative: a fall in t lowers c D so that the least e cient retailers are forced to leave the market. Holding the average retail price xed, this reduction in the cost of retailing implies a higher number of active retailers. The second expression is positive: a decrease in t reduces the average retail price. Holding c D xed, this drives down the number of active retailers. The sign of dn is therefore generally ambiguous, that is, it depends very much on the characteristics of the retail sector. However, if the xed cost of importing is su ciently small, we can prove: Proposition 3 Trade liberalization reduces the mass of active retailers if the xed cost of importing is su ciently small and the market (as measured by ) is su ciently big. Proof: see Appendix. 4 Pass-Through and Retail Market Regulation Our model of retail market structure is admittedly highly stylized. However, it is precisely its simplicity that allows us to investigate two issues in which the structure of retail markets plays a central role. The rst issue concerns the pass-through of import into consumer prices. We want to show that even in the short run, when there is no entry and exit of retailers, pass-through may be substantial if one takes into account that retailers may become inactive. The second issue concerns the e ects of retail-market regulations, such as limits on the size of retail establishments as traditionally imposed in France, Belgium, Japan, Italy and elsewhere. We will show that such regulations tend to raise average retail prices and reduce pass-through. 4.1 Pass-Through of Import Prices The pass-through of changes in the import price t into the average consumer price p can be studied using (18). As is evident from this equation, changes in t have a direct e ect on p, as well as indirect e ects through changes in the equilibrium values of c D and c I. Before studying these e ects in detail, however, it is important to point out that these indirect e ects do not only work in the long run through 1

15 the entry and exit of retailers, but also in the short run when N E is xed. The reason is that retailers can very quickly become active or inactive in a market, e.g., by adding or dropping product lines, or change their purchasing strategies. In the short run, the equilibrium values of p, c D and c I are given by Equations (15), (1) and (16), where in the latter equation we substitute for N using N = N E G(c D ). We can prove that the e ect of t on the equilibrium values of these variables is qualitatively the same as in the long run when free entry and exit drives expected retail pro ts to zero: Proposition 4 When the mass of entrants N E is xed, trade liberalization (i) forces the least e cient retailers to become inactive (c D decreases); (ii) induces a larger fraction of retailers to source goods from abroad (c I rises); and (iii) reduces the average consumer price p. Proof: see Appendix. Using (18), the pass-through rate for the average retail price in both the short and the long run can be written as dp = 1 + k dc D k dc D (w t) k dc D + (k + 1) c D c k I c k D c k I c k D k dc I : c I (0) The rst term is the standard pass-through e ect: the share of direct cost savings that an importer passes on to consumers (1=) times the probability that a good is being imported. This e ect is clearly less than one and may be very small if the probability that a good is imported (or, equivalently, the share of imports in the consumption basket) is small. This probability depends in a straightforward way on the trade cost. It also depends on the distribution of retailing costs as summarized by parameter k. The last three terms in (0) re ect the fact that trade liberalization (i) changes retailing costs and retail markups as the least e cient retailers become inactive, and (ii) increases the likelihood that a good is being sourced from abroad. Speci cally, the second term re ects the fact that a reduction in t lowers the expected unit cost of retailing. The third term indicates that a lower t reduces the markup of domestically sourced goods. The fourth term shows that trade liberalization, by raising the probability of importing, generates cost savings from importing for a bigger share of the consumption basket. 13

16 Since these three e ects are positive, the pass-through rate may be big even if the rst term is small. How big it is depends in part on the level of trade cost, and on the time horizon, i.e., on whether one considers the short or the long run. For the long run, we are able to show the following surprising result: Proposition 5 The rate of pass-through of import into consumer prices exceeds unity in the long run if the xed cost of importing is su ciently small. Proof: see Appendix. This result demonstrates that an analysis of pass-through that is limited to the standard e ect, i.e., the share of cost savings that retailers sourcing goods from abroad pass on to consumers times the import share in the retail sector, may severely underestimate the actual pass-through. Only if one takes into account key adjustment e ects associated with a change in trade costs, including the changes in retail costs and markups spurred by the elimination of ine cient retailers and the increase in foreign sourcing, does one obtain an unbiased estimate of the true pass-through rate. Although these adjustments may not appear like direct impact e ects, it is important to keep in mind that they are not limited to the long run either. 4. Retail-Market Regulation A regulation limiting the size of retail establishments only a ects the very e cient retailers. In e ect, such a regulation can be thought of as putting an upper bound on their sales. Suppose the maximum level of sales allowed under the regulation is given by ^q. Using ^q in (3) and the de nition of c D, we obtain the price charged by a constrained rm, ^p, as ^p = c D + w ^q: (1) L Assuming that the marginal rm that is just constrained in its sales is an importer, we can write the pro t of a constrained rm as ^(c) = c D + w L ^q c t ^q F E F I : () 14

17 The critical value of the marginal cost ^c at which a rm is just constrained is de ned by ^q q I (^c). Hence ^c = c D + w t L ^q: (3) At this level of marginal cost we have ^(^c) = I (^c). Ceteris paribus, a tightening of the constraint raises ^c, which implies that the sales constraint hits even less e cient rms. Of course a change in ^q also a ects the other critical levels of the marginal cost, i.e., c D and c I, together with the other endogenous variables, p and N E. The equilibrium values of the endogenous variables when the constraint is binding are given by equations (16), (1) and (3), as well as the new expected-zero-pro t condition Z ^c 0 ^(c)dg(c) + Z ci ^c I (c)dg(c) + Z cd c I D (c)dg(c) + Z cm c D ( F E ) dg(c) = 0; and the new equation for the average retail price ^p = 1 Z ^c Z ci Z cd ^pdg(c) + p I (c)dg(c) + p D (c)dg(c) G(c D ) 0 ^c c I (4) (5) To derive the comparative static e ects of a marginal change in the constraint ^q, consider again the zero-pro t condition. Since, by de nition, ^(^c) = I (^c) and I (c I ) = D (c I ), the partial derivatives of (4) with respect to ^c and c I are zero. We therefore directly obtain from (4) the change in c D for marginal changes in ^q. The respective changes in ^c and c I then follow directly from (3) and (1). The following proposition presents these comparative-static e ects: Proposition 6 A tightening of the sales constraint bq: (i) allows less e cient retailers to become active (higher c D ); (ii) reduces the sales of more e cient retailers (higher ^c); and (iii) induces a larger fraction of retailers to source goods from abroad (higher c I ). Proof: see Appendix. Parts (i) and (ii) of the proposition are rather straightforward. A tighter constraint on the sales of the most e cient retailers raises the residual demand for the unconstrained retailers. This allows the least e cient retailers 15

18 to remain in business. The surprising result is in part (iii), namely that a tighter sales constraint raises retailers propensity to import. The reason for this is that the higher residual demand allows retailers that before were too ine cient to import to source their goods from abroad. This increase at the extensive margin of imports is, of course, o set by a decrease at the intensive margin: a tighter constraint reduces the import volume of e cient retailers. To determine the e ect of a tighter constraint on the average retail price, we simplify (5) to obtain ^p = w + kc D k c D (k + 1) (w t) c k I c k D ^c ^c k + : (6) (1 + k) This rst four terms of this equation are the same as in (18). The fth term is an additional term re ecting the direct e ect of the output constraint. It represents the extra expected markup of a constrained rm times the probability that a rm is constrained conditional on its cost being less than c D. The change in the average retail price induced by a tighter constraint comes from changes in the cut-o values ^c, c D and c I. A tighter ^q raises all three cut-o values. This has the following implications. An increase in ^c means that a larger fraction of retailers becomes constrained and thus has higher prices than without the constraint. The increase in c D also raises ^p, since at the margin less e cient retailers remain active in the market. The rise in c I works against the rst two e ects. Retailers are more likely to source goods from abroad, which is associated with lower variable costs than sourcing goods domestically. One would expect that the rst two e ects dominate the last one, so that a tightening of the sales constraint raises the average retail price. Formally, we can show that it is indeed the case if either w t is big and/or F I is small so that the retailers switching to importing have a relatively high unit retailing cost compared with the rest of the industry and thus have only a small market share. We formally state these su cient conditions in the following proposition: Proposition 7 A tightening of the sales constraint bq raises the average retail price ^p if w t is su ciently big and/or F I is su ciently small. Proof: see Appendix. Retail-market regulation also a ects the pass-through of import into consumer prices. As can be seen in (1), the prices of constrained retailers are 16 c k D

19 not a ected at all by the import price, even though we assumed that these retailers do in fact import their goods. The reason for this is that the sales of these rms are below the level at which marginal revenue equals marginal cost, so that changes in marginal cost have no e ect on sales or prices. In the extreme case where the constraint is so restrictive that it a ects all importing rms, the pass-through into the average retail price is therefore zero even if the import share in the total consumption basket of households is large. It follows that for a su ciently tight constraint, i.e., for bq su ciently close to q I (^c), the pass-through rate will be lower than without the regulation. Thus, even if retail-market regulation induces a larger mass of retailers to source from abroad, its impact on the most e cient retailers makes the average retail price less sensitive to variations in import prices. This result can be summarized as follows: Proposition 8 Retail-market regulation reduces the rate of pass-through of import prices into the average retail price if the output constraint is su - ciently tight. 5 Retail Market Concentration and Welfare In this section we use simulations to illustrate how trade liberalization impacts social welfare, as well as retail concentration and pass through. In the context of the present model, the Her ndahl index, H, is an ideal measure of market concentration. This is because this index takes into account the entire size distribution of the retailing sector and thus both the number of retailers as well as the dispersion of retailer size. Indeed, the Her ndahl index, de ned as the sum of the squares of all retailers market shares, can be re-written as (see Waterson, 1984) H = q=q + 1 ; (7) N where q denotes average sales of active retailers and q is the variance of retail sales. Writing it this way reveals the separate e ects on concentration stemming from the mass of retailers and from the impact of retailers heterogeneity. Thus, in a market with heterogeneous rms, market concentration as measured by the Her ndahl index is negatively related to the mass of active retailers, N, and positively related to the coe cient of variation of retail sales, q =q. 17

20 Since 0 H 1, industry concentration is high if a few big retailers account for a large fraction of sales. Another advantage of H is that it can be used for policy purposes, be it for competition policy or market regulation. For example, the purpose of the retail regulations analyzed in the previous section can be interpreted as controlling retail concentration and thus reaching a lower value of H than market forces alone would generate. In addition to measuring concentration, we also want to evaluate social welfare. Social welfare in the current model is captured by the following indirect utility function (see Melitz and Ottaviano, 008): U = I N 1 ( p) + 1 N p; (8) where p denotes the variance of retail prices. Welfare is obviously decreasing in p and increasing in N and p. It is often presumed that if an exogenous shock such as trade liberalization occurs, then H should fall and U increase. This presumption rests on the idea that a decrease in H is associated with an increase in competition and thus with a smaller social deadweight loss. It is easy to see that such a simple one-to-one relationship between H and U does not necessarily exist in the present model. Even if it is the case that an increase in N raises U and decreases H, heterogeneity also plays an important role. Observe in particular that H and U are increasing in q and p, respectively. Thus if d q= and d p= are both positive, trade liberalization reduces q and H, and it also reduces p and U, holding xed the values of the other endogenous variables. In the Appendix, we show that d q= and d p= are indeed both positive, at least when F I is low. Thus, unless trade liberalization changes the mass of retailers in a way that clearly dominates its e ects on the size variation of retailers, it is quite possible that social welfare may increase, even if liberalization increases retail market concentration. Clearly, retailer heterogeneity plays a key role. Table 1 illustrates this case. It depends on the following parameters: L = 5, F E = :0, F I = :1, w = :5, c M = 5, = 1:75, = :9, = :6, k = 1:5. In this example, both welfare (measured by U net of income I) and H monotonically rise with trade liberalization. It is interesting to note that welfare increases despite a decrease in the number of active retailers, N. 8 This occurs because the average price, p, falls a lot as trade costs come down. 8 And despite a small decrease in p for t :15 (not shown in Table 1). 18

21 This is shown by the last column of Table 1 where the degree of pass through is greater than one, except when t is high. This decrease in N naturally contributes to explain why H rises with trade liberalization, but so is the increase in the variance of sales, q, and thus the degree of heterogeneity among retailers. Table 1: t c D c I p N q H U I dp= Simulations are also useful to show the e ects of market regulation. We use as a benchmark a case in which, in the absence of any regulation, trade liberalization monotonically raises U and lowers H. Table illustrates this case for a parameter space identical to the one above except that now k = 1 and F E = :1. Table : t c D c I p N q H U I dp= Suppose now that a regulation is in place that restricts the size of the most e cient retailers. Speci cally, the most e cient retailer (with c = 0) cannot have a volume of sales greater than 75% of its unconstrained free-trade size. In the above example, this corresponds to a maximum size allowed by regulation equal to bq I (c = t = 0) = 1:83. Of course, such a constraint a ects more than just the most e cient retailers but it does so with a smaller relative impact, since less e cient retailers are smaller. Indeed, retailers with a volume of sales less below bq I (c) = 1:83 are not a ected at all. Table 3 shows the percentage changes with respect to the benchmark case without regulation and thus with respect to Table (except for c D and c I, for which we present levels). 19

22 Table 3: t c D c I bp bq N H U I dbp= % -16% +14% -8% -14% -44% % -16% +13% -% -15% -41% % -16% +13% -19% -16% -39% % -15% +1% -17% -17% -43% % -15% +11% -16% -17% -85% The regulation has striking e ects, especially regarding the impact of trade liberalization. It signi cantly increases the number of retailers and decreases H relative to the benchmark case. In this sense, the introduction of the regulation is a very successful policy. However, even if trade liberalization still leads to lower prices and a greater average volume of sales, the impact of freer trade is very much muted since the average price decreases to a much smaller extent and the average quantity sold by retailers increases much less than without the regulation. As already argued, this implies that the degree of pass through is much lower. Indeed it is now much lower than one and, in this example, more than 40% lower than without any regulation. As can be observed in the last column of Table 3, the degree of pass-through decreases even more for relatively high levels of t. This is because pass-through quickly converges to zero for high levels of t. Indeed, the degree of pass-through is necessarily equal to zero whenever all the retailers who choose to source their product from abroad are constrained by the regulation. The overall impact of the regulation is a much smaller increase in social welfare through trade liberalization than in the absence of such a regulation. Based on this example, it may not be very surprising that French consumers complain that they do not bene t from trade liberalization. These simulations should be taken as illustrative but they show forcefully that one should be careful before using concentration indices such as the Her ndahl index in the presence of heterogeneous retailers as there is no simple one-to-one relationship between such an index and social welfare. This point is best illustrated by the case of regulation. While it may have achieved its objective by increasing the number of sellers and lowering H; it does not deliver in terms of social welfare because it mitigates competition and diminishes the impact of trade liberalization, especially the degree of pass through. 0

23 6 Conclusions By focusing on retailers total volume of sales, our model is highly stylized. However, it is precisely its simplicity that allows us to investigate how trade liberalization changes the structure of the retailing industry when retailers are heterogeneous. Because buying foreign products involves a xed cost, only the most e cient retailers source goods from abroad. Trade liberalization is then shown to shift retail sales, mark-ups and pro ts toward retailers that engage in direct imports and away from those that source domestically only. The e ects of trade liberalization on retail competitiveness are very much industry speci c. A decrease in trade costs favors big and e cient retailers at the expense of relatively small and ine cient ones. Average retail sales rise and the variance of retail sales falls at least for low levels of trade costs. Ceteris paribus, this lowers retail market concentration. However, around free trade at least the number of active retailers decreases, which raises market concentration. The ambiguous e ect of trade liberalization on market concentration carries over into social welfare, as the bene cial e ect of the decrease in the average retail price is at least partly o set by a fall in the number of retailers. The model provides clear predictions concerning the sensitivity of retail prices to variations in import prices and thus the degree of pass-through at the retail level. Pass-through is typically studied in connection with exchange rate variations. One can distinguish between two types of exchange-rate passthrough: (i) how changes in producer prices are passed through into import prices; and (ii) how changes in import prices are passed through into retail prices. Our model obviously captures the second type and suggests that retailer heterogeneity plays an important role in explaining the degree of pass-through. The reason is that changes in import prices trigger changes in the structure of retail markets (in terms of the mass of active retailers and sourcing decisions), which in turn a ect retail prices. The model predicts that when these indirect e ects are taken into account, the rate of pass-through at the retail price level may exceed unity. This is in contrast to most of the existing studies on import-price pass-through, which nd that the passthrough rate will be close to zero. This nding, our paper suggests, is no surprise: it simply comes from the fact that these studies treat all rms as being homogeneous and thus ignore the more subtle market structure e ects. The model also shows that the pass-through increases when trade barriers fall. This e ect has two sources: (i) a direct e ect that leads retailers to 1

24 import more when trade costs decrease and which naturally makes the retail prices more sensitive to changes in the trade barrier; and (ii) an indirect e ect that comes from the fact that the average unit retailing cost falls as less e cient retailers become inactive or exit the market. Thus the importance of domestic retailing costs, an element that tends to isolate domestic prices from foreign in uences, falls as well. The sensitivity of the retail prices also depends very much on the characteristics of the retail sector. Thus if some of these characteristics also change with trade liberalization (for instance, due to technological innovation), the rate of pass-through may well increase even more. These predictions are consistent with the empirical evidence presented, for instance, by Campa and Goldberg (006b), and Campa and González Minguez (006). The former nd that the retail price sensitivity to import price variations has generally increased over the last decade, but that the degree of sensitivity is very much product speci c. The latter show that di erences in pass-through rates within the Euro area are driven mainly by di erences in openness to non-euro-area imports. Finally, the model is also very much suited to understand the impact of restrictions on the size of retailers. In countries like France, Belgium or Japan, there is a tradition of protecting small local retailers by placing barriers on the expansion and particularly on the size of large retailers. Not surprisingly, restrictions on the volume of sales a ect rst and foremost the e cient retailers. We show that this allows ine cient retailers to remain active and makes the average retail price higher than it would otherwise be. Interestingly this makes the incentives to source products from abroad stronger for less e cient retailers, not weaker. We also show that it makes the retail price level less sensitive to change in the price of imported products. With higher average retail prices and a lower sensitivity of retail prices to foreign shocks, it should not be surprising if French consumers feel that their pouvoir d achat (purchasing power) has su ered as compared to consumers elsewhere in Europe (Economist, 008). The contrast with the United States is striking. Broda and Romalis (008) show that because poor US households have a di erent composition of their consumption basket than rich households and because the price index of the poor s consumption basket has declined relative to that of the rich, the impact of the rise in income inequality has been signi cantly smaller than rst feared. One thing is certain, this would not have been possible without the instrumental role played by large retailers importing a large volume of products from low-cost Asian countries.