Multiproduct multinationals and reciprocal FDI dumping

Journal of International Economics 54 (2001) 429–448 www.elsevier.nl / locate / econbase

Multiproduct multinationals and reciprocal FDI dumping Richard E. Baldwin a , *, Gianmarco I.P. Ottaviano b a

Graduate Institute of International Studies, 11 a Ave de la Paix, CH-1202 Geneva, Switzerland b Bocconi University, Milan, Italy

Received 23 March 1998; received in revised form 30 December 1999; accepted 31 May 2000

Abstract Global patterns of FDI and trade are remarkably similar, yet mainstay theory has them as substitutes. We posit a model where multiproduct, final-goods firms simultaneously engage in intraindustry FDI and intraindustry trade. The logic behind this two-way FDI is analogous to that of two-way trade in the Brander–Krugman reciprocal-dumping model. Namely, multiproduct firms use trade costs to reduce inter-variety competition by placing production of some varieties abroad. Since the varieties are differentiated, all varieties are sold in all markets. Thus while FDI displaces some exports, it also creates trade via reverse imports. This naturally leads to parallelism in the trade and FDI patterns.  2001 Elsevier Science B.V. All rights reserved. Keywords: Multinational corporations; International trade; International investment; Foreign direct investment JEL classification: F23; F12

1. Introduction The world pattern of foreign direct investment (FDI) is remarkably similar to the world trade pattern, yet the mainstay theory of FDI (see the Markusen, 1995 survey) has trade and FDI as substitutes. This paper posits a model where multiproduct firms simultaneously engage in intraindustry FDI and intraindustry *Corresponding author. Tel.: 141-22-734-3643; fax: 141-22-733-3049. E-mail address: [email protected] (R.E. Baldwin). 0022-1996 / 01 / $ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S0022-1996( 00 )00099-4

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trade in a manner that naturally leads to parallelism in the trade and FDI patterns. The model cannot explain all aspects of the trade and FDI correlation, and it is clearly irrelevant to some industries. It is, however, based on a novel motive for FDI. Before delineating the logic of our model, we review some facts on the similarity of the FDI and trade patterns. The similarity begins with aggregate figures. When it comes to goods trade, the advanced industrialised nations are both the biggest exporters and their own best customers. The same is true of foreign direct investment, according to Hummels and Stern (1994). The European Union, for example, is both the largest ‘home’ and the largest ‘host’ region, accounting for about 40% of global flows; the United States, with about a quarter of world FDI flows, is the largest single host nation and the largest single home nation for FDI (UNCTAD, 1997). The similarity extends to the composition of the flows. For instance, intraindustry trade among rich nations accounts for the bulk of world trade. Similarly, there is a great deal of two-way foreign direct investment among rich nations, even within industries. The Markusen (1995) survey of multinationals, for instance, includes the importance of intraindustry FDI (IIFDI) as one of six stylised facts. Recent work by Greenaway et al. (1998) strengthens this. These authors use the Grubel–Lloyd index to construct measures of intraindustry FDI for US trade partners.1 Using trade data aggregated into matching categories, they also calculate classic intraindustry trade (IIT) indices. As Table 1 shows, there is remarkable similarity between the IIT and IIFDI indices, at least at this level of aggregation (corresponding to between the two and three digit SIC level) and for these nations. Additionally, the industries in which we see a lot of intraindustry trade among similar nations are also typically the industries in which there is a great deal of intraindustry FDI, according to Rugman (1985). Anecdotal evidence can be found in sectors such as transport equipment, chemicals, pharmaceuticals, and processed foods. Recent empirical work provides a more detailed picture of this similarity, at least for some nations and some sectors. Greenaway et al. (1998), for instance, use Table 1 US bilateral intraindustry indices for trade and foreign affiliate sales, 1992–1994 averages a US with

Trade

Foreign production

Germany UK France Netherlands Canada

0.67 0.66 0.50 0.44 0.37

0.64 0.58 0.44 0.48 0.45

a The Grubel–Lloyd index is used and foreign production is sales of foreign affiliates. Source: Greenaway et al. (1998).

1

Greenaway et al. (1998) use US data on foreign affiliate sales as a measure of FDI.

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data on US–UK bilateral trade and foreign affiliate sales to calculate ‘extended intraindustry trade’ indices on a sectoral level. The extended index accounts for two-way ‘sales’ stemming from both exports and foreign affiliate sales. This total is decomposed into a measure of IIT, a measure of IIFDI, and an interaction term that arises from the algebraic decomposition. The sectoral correlation of the IIT and IIFDI measures is not strikingly positive, and some sectors are clearly dominated by either trade or investment. The two-way commerce in construction, for example, is almost all FDI, while in ‘other transport equipment’ it is mainly trade. Importantly though, they do find many sectors displaying substantial amounts of both intraindustry trade and intraindustry FDI (e.g., electrical machinery, audio, video and communications, electronic components, textiles and apparel, and miscellaneous plastic products). Finally, a related branch of the literature establishes that trade and FDI, at some level of aggregation, are complements rather than substitutes. The classic papers — Swedenborg (1979) and Lipsey and Weiss (1981) — find foreign affiliate sales ¨ et al. (1988) show that trade increase exports from the home country. Blomstrom is not a substitute for investment, even at the firm level. Subsequent studies such as Head and Ries (1999) have largely confirmed this. Blonigen (1999) finds a more subtle result for Japanese FDI in the US using detailed, product-level trade data (e.g. laminated safety glass for autos) together with Japan-to-US FDI data disaggregated into car production and car parts production. He finds that FDI in car parts substitutes for Japanese exports of car parts, but FDI in car production is complementary to Japanese exports of cars. He also finds that for some final consumer products (e.g. golf balls and grand pianos), FDI and trade are substitutes.

1.1. Relation to the theoretical literature These findings pose several conundrums for the theory of multinational corporations (MNC). The early ‘new trade’ theory of MNCs, e.g. Markusen (1984), Helpman (1984) and Horstmann and Markusen (1987) were inspired by the classic Hymer (1976) ‘advantages’ approach to multinationals.2 This approach asserts that multinationals must have some sort of advantage over local firms. Intraindustry FDI, however, is a puzzle for the ‘advantages’ approach. After all, if French pharmaceutical firms have an advantage over German drug companies in Germany, how can German pharmaceutical firms have an advantage in France? More recent theoretical work addressed this conundrum using imperfect competition to generate IIFDI between identical nations. Horstmann and Markusen (1992) sets out the basic paradigm that has been pursued by Brainard (1993), Markusen and Venables (1995), and others. In essence, single-product firms must choose to either save on trade costs (by producing in proximity to their customers), 2

Dunning (1981) subsequently focused on three advantages (ownership, location and integration) in his rather indistinct but popular ‘eclectic’ OLI theory of MNCs.

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or to exploit scale economies (by consolidating production at home). And with imperfect competition, it is natural to have home firms involved in the foreign market and foreign firms simultaneously involved in the home market. IIFDI between identical nations therefore emerges when proximity is more important than scale. This proximity-versus-scale approach, however, poses puzzles of its own.3 In the original versions of these models, firms either engage in trade, or in FDI, but not both. Indeed with symmetric nations, such models predict that international commerce in each sector should be dominated either by IIT or by IIFDI.4 While this extreme result can be softened (see Markusen and Venables, 1995, for example), such models must struggle to explain the connection between the patterns of trade and investment. The point is simple. At a very deep level, these models assert that certain factors favour exports in some industries and with some partners, while other factors favour FDI. Why then do we observe two-way FDI and two-way trade between similar nations in the same industry? The latest evolution of the mainstay model addresses the parallelism of trade and FDI by introducing intermediate goods. Blonigen (1999), and Head and Ries (1999), for instance, allow a vertically integrated firm to slice-up its value-added chain, placing one stage of its production process abroad. FDI does not therefore fully displace exports since the overseas factory buys intermediate goods from the home-based factory. Blonigen (1999), and Head and Ries (1999) also compile evidence suggesting that intermediate goods are indeed responsible for the complementarity of trade and FDI in one very specific situation, namely the case of US–Japanese trade and investment in cars and car parts. While the intermediate-goods story seems important in certain industries and between certain partners, the intermediates-augmented proximity-versus-scale model still has trade and FDI as substitutes. Indeed, the complementarity between trade and FDI in these models stems mainly from aggregation of goods that are very dissimilar in terms of scale economies or factor intensities. Suppose, for the sake of illustration, a car is made up of a motor and a chassis. Let the car company face two production strategies. It can produce both parts at home, supplying cars to the home market via local sales and cars to the foreign market via exports. Or it can produce motors and chassises at home to supply the home market, supplying the foreign market by combining chassises made abroad with motors made at home (motor production is consolidated due to overriding scale economies in this example). When the second production strategy is adopted, one would expect a correlation between the trade and investment patterns — at least when one 3 Brainard uses the phrase ‘proximity versus concentration’, but ‘concentration’ is reserved for a specific concept in the theory of imperfect competition. 4 These single-good / multiplant MNCs do conduct intrafirm trade in intangible ‘headquarter services’ and / or intellectual property rights. Thus scale-versus-proximity FDI does encourage trade in invisibles, but this does not explain FDI’s correlation with visible trade.

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aggregates all the firm’s activities together. However, at the level of chassises, which is after all what the FDI is concerned with, the firm is still deciding whether to supply chassises to the foreign market via FDI or via exports. The only subtleties here are that the exported chassises are pre-attached to motors under the export option, and FDI may slightly raise the total number of chassises sold in the foreign market. The Blonigen (1999) findings discussed above tend to confirm this notion. However, the US–Japanese FDI and trade relationship is quite atypical. For instance, there is very little intraindustry FDI or intraindustry trade between the US and Japan in this sector. Blonigen (1999) cannot, therefore, be viewed as having solved the paradoxical parallelism between IIT and IIFDI that is often observed, say within Europe.

1.2. A new model of FDI and trade This paper posits an MNC model that differs sharply from existing ones. In our model, obstacles to trade generate a natural incentive for multiproduct firms to engage simultaneously in IIFDI and IIT. The economic forces driving this are analogous to the motive for trade in the reciprocal-dumping model of Brander and Krugman (1983). Before expanding on this point, we discuss the type of trade and investment to be modelled. Western Europe accounts for about half of world trade and two-fifths of world FDI with much of this taking place within the region. In certain sectors, the European trade and investment pattern line up closely for a simple reason. Multinationals like Nestle, or Procter & Gamble, produce a vast range of consumer goods. While not all varieties are sold in every European nation, the range available in each nation far exceeds the range of varieties produced locally. The point is that each product is typically supplied to many European nations from one or two European factories. The locations of these factories are not always — or even mainly — in the multinational’s home country. The Swiss company Nestle, for example, produces its Buitoni-brand frozen pizzas in France, its Buitoni-brand fresh pasta in Italy, and it sells both products in both markets. Moreover, it imports both products into Switzerland. In such industries, trade and investment patterns are intrinsically similar in terms of aggregate bilateral flows as well as in terms of their intraindustry nature and their sectoral composition. Similar phenomena are observed in other industries such as automobiles. FIAT supplies the European markets from assembly plants in Brazil, France, Italy, and Poland; Ford from Belgium, Germany, Portugal, Spain, the UK, and the US; Honda from Japan, the UK, and the US; GM from Argentina, Belgium, Germany, Spain, and the US; Volkswagen from Belgium, Germany, Mexico, Portugal, Spain, and the Czech Republic. In some cases the proximity-versus-scale model explains the pattern since different plants supply identical cars to the local market only (e.g. the GM Opel Astra is made in Belgium, Germany, and the UK). In other cases,

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however, factories in different countries produce different models and these are sold in all countries. This is the type of IIFDI and IIT we model — cross hauling of foreign investment that generates two-way trade in differentiated final products. Imperfect competition is at the heart of our explanation of this sort of cross-hauling FDI, just as imperfect competition is at the heart of Brander (1981) and Brander and Krugman (1983) reciprocal-dumping trade. To fix ideas, recall the driving force behind Brander–Krugman reciprocal dumping. Profit maximising firms operate at the point where perceived marginal revenue equals marginal cost. Perceived marginal revenue has two components — the price effect (the direct gain from an extra sale) and the ‘revenue depressing’ effect (the level of sales times the price-lowering impact of an extra sale). A firm finds it optimal to accept a lower price-marginal-cost gap in markets where it sells little since sales in such markets are associated with a reduced revenue-depressing effect. Applying this to a trading world with segmented markets and trade costs, Brander (1981) showed that firms based in identical nations would accept lower producer prices on their exports to each other’s markets. But how can this explain FDI? Multinationals in our model are multiproduct firms that supply a range of imperfectly substitutable products (varieties). The decision of how many varieties to produce faces a similar trade-off between a direct effect (operating profit of the new variety) and a revenue-depressing effect. In the jargon of multiproduct firms, this revenue-depressing effect is often called the ‘cannibalisation’ effect because of the way that each new variety eats into the sales of the firm’s existing varieties (Brander and Eaton, 1984). By analogy with the Brander–Krugman insight, multiproduct firms are willing to accept a lower rate of return on new varieties produced abroad as producing the variety abroad is associated with a reduced cannibalisation effect. That is, firms find it optimal to produce some of their varieties abroad since trade barriers partially shield home-produced varieties from the cannibalisation effect of foreign-produced varieties, and vice versa. Yet since products are differentiated, placing a factory abroad has a trade enhancing effect (in the form of reverse imports) in addition to the usual trade displacing effect (displacement of exports with local sales of foreign affiliates). As such, the kind of parallelism between the pattern of trade and investment we discussed above is indeed at the heart of our model. The paper has four sections after the introduction. Section 2 details the logic of reciprocal FDI dumping in the context of a ‘model of our model’. Section 3 presents our explicit model and Section 4 analytically interprets the equilibrium. The final section contains a summary and our concluding remarks.

2. Cannibalisation and two-way FDI Consider a world with two symmetric countries and an arbitrary number of multiproduct firms, each of which produces a fixed number of differentiated

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varieties. Each variety is produced in a single factory, but firms may locate the factory for each of its varieties at home or abroad. Firms play a two-stage game in which first they decide where to locate production and then how much to sell in each market.5 Trade is costly for firms and prohibitively costly for third parties (consumers or other firms), so markets are segmented. We are interested in subgame perfect Nash equilibria of the two-stage game. We limit ourselves to the universe of tastes, technology, and market structures for which two properties hold: (i) trade costs are not entirely absorbed by firms so that imported varieties are more expensive to consumers; (ii) the equilibrium operating profit from sales in a given market is increasing and convex in equilibrium sales, as shown in Fig. 1.6 Note that the convexity property requires the price-marginal-cost mark-up to rise with sales. Two facts follow immediately.

Fig. 1. Operating profit convexity and gains from FDI.

5

In principle price competition in the second stage should also be considered as an interesting option. We restrain, however, from presenting the results of the price game. First, it turns out that they do not alter the basic insight gained through the quantity game. Second, the choice of quantity aligns our exposition to classical work on multiproduct firms (see, e.g., Brander and Eaton, 1984). 6 Notice that these are features not only of Cournot competition with linear or constant-elasticity demand curves but also of Bertrand competition with imperfectly substitutable varieties.

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Due to trade costs and symmetry, local-market sales exceed export sales and the mark-up is higher for local sales than for exports. In this fairly abstract set-up, we can illustrate the fundamental force driving two-way FDI by multiproduct firms. Start with the no-FDI equilibrium where firms produce domestically and sell in both markets. To check whether this is an equilibrium, consider the profit effect of a single home firm shifting production of a single variety abroad, taking as given the locations of all other firms. Sales of a typical home variety to the home market in the initial no-FDI situation are shown in Fig. 1 as x c . In the foreign market, sales are x b . When the firm deviates from the no-FDI outcome by shifting production of one variety abroad, two changes occur for the firm’s un-shifted varieties. First, the shift leads to price and quantity changes that harm, i.e. ‘cannibalise’, export sales of the firm’s un-shifted varieties. The reason is that, since the shifted variety is sold for less in the foreign market than previously, now the un-shifted varieties face more competition in the foreign market than previously. Thus x b falls to x a . In contrast, the shift raises local sales of the firm’s un-shifted varieties from x c to x d (because the shifted variety costs more in the home market than it did before). By convexity, this greater disparity of home and foreign sales tends to boost average profit per un-shifted variety. The shift also increases the disparity of the shifted variety’s sales in the two markets. After the shift, the local sales of the shifted variety, which are now in the foreign nation, exceed the local sales it achieved in the no-FDI equilibrium because trade costs dampen the competition from the un-shifted varieties. Likewise, the export sales of the shifted variety, which are now in the home market, are lower than its export sales were in the no-FDI equilibrium. The reason is that it faces more competition in the home market after the shift than it did in the foreign market before the shift. Again, convexity ensures that this heightened disparity of sales tends to raise profitability of the shifted variety. Plainly, if the extra cost of locating a factory abroad is sufficiently small, at least one firm will want to produce at least one variety abroad. When this is true, the no-FDI outcome is not an equilibrium. The non-existence of the no-FDI equilibrium does not, of course, mean that an equilibrium with two-way FDI exists. To examine this, we need to put much more structure on the problem. This brings us to the details of our model.

3. The model Consider a world with two sectors (X and Z) and two identical countries endowed with L units of labour each. The X-sector consists of differentiated varieties produced under imperfect competition and increasing returns. For all varieties, the cost function is w(F 1 a x x), where w is the wage, F is the fixed cost, ‘a x ’ is the variable cost and x is output. To reflect the cost of multinationality, production of a variety abroad entails greater fixed cost, viz. G 1 F . F. In

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principle, firms could choose to produce a single variety in two factories (one at home and one abroad). To distinguish our model sharply from the standard Markusen–Horstmann model, however, we rule out this option by fiat; firms must produce each variety in a single factory. Firms have two strategic choices, production location and sales. Firms decide on plant location in stage one and then on sales in the segmented markets in stage two. The equilibrium concept is subgame perfect Nash (discounting is ignored). The Pareto refinement is used when there are multiple equilibria. Trade costs in X are specific; it costs t . 0 units of numeraire to export a unit of X. This includes transport and trade barrier costs as well as sales and distribution costs. Due especially to the latter, trade costs for consumers or third parties are higher, namely T per unit.7 If T is sufficiently large (we assume T 5 `) no arbitrage will occur and the markets are segmented (i.e., third-degree price discrimination is possible). For simplicity, there is one firm per nation and two varieties per firm. By convention, the home firm produces varieties 1 and 2; the foreign firm produces varieties 3 and 4. An earlier version of this paper, Baldwin and Ottaviano (1998), showed that reciprocal FDI dumping arises in a model with two firms, each with a continuum of varieties. The Z-sector is Walrasian with the cost function wa Z Z, where a Z is the unit input coefficient. Units are chosen such that a Z 5 1. Taking L as numeraire, the price of Z is unity. We assume costless trade in Z and this equalises wages internationally. Preferences are quasi-linear and quadratic in X varieties, namely:

O sax 2 x / 2d 2 bx x 2 bx x 2 x (cx 1 dx ) 2 x (cx 1 dx ) 4

U 5Z 1

i

2 i

1 2

3 4

1

3

4

2

4

3

i 51

(1) where x 1 and x 2 are consumption of home-firm varieties and x 3 and x 4 consumption of foreign-firm varieties; Z is consumption of the Walrasian good. All goods are substitutes, so b, c and d are positive and the parameter restrictions c 2 d , 1 2 b, 2 c 1 d , 1 2 b, c 1 d , 1 1 b, b , 1 and a . 0 are necessary and sufficient for U ’s concavity.8 The demand functions from (1) are: p1h 5 a 2 x 1h 2 bx 2h 2 cx 3h 2 dx 4h , p2h 5 a 2 x 2h 2 bx 1h 2 cx 4h 2 dx 3h , p3h 5 a 2 x 3h 2 bx 4h 2 cx 1h 2 dx 2h , p4h 5 a 2 x 4h 2 bx 3h 2 cx 2h 2 dx 1h , (2) 7

The idea is that firms sell to retailers and T is the cost that retailers would face in attempting to re-export the product. To avoid unenlightening complications, retailers are not explicitly modelled. 8 The eigenvalues of the U ’s Hessian are: 2 1 1 b 1 c 2 d, 2 1 1 b 2 c 1 d, 2 1 2 b 1 c 1 d and –1 2 b 2 c 2 d. These must be negative for U to be concave.

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Fig. 2. Forms of parameter symmetry.

where pij indicates the price of variety i in market j. Demand functions for the four goods in the foreign market are isomorphic. To avoid redundancy, we rank varieties so that c $ d. This implies that variety 3 is a better (worse) substitute for variety 1 (2) than variety 4. Varieties 1 and 3 (2 and 4) are thus ‘matching’ varieties. Even with this symmetry five parameters matter, b, c, d, G and t. To sharpen intuition and reduce un-instructive complexity in the formulas, three special cases are considered (Fig. 2 illustrates these for variety 1). The first, ‘full symmetry’, has all varieties as equally good substitutes, i.e. c 5 d 5 b and, with the concavity conditions, a . 0 and 0 , b , 1. The second, ‘firm-wise symmetry’, is where a firm’s own varieties are better substitutes for each other than they are for those of the other firm (b . c and b . d) and each foreign variety is an equally good substitute for either home variety (c 5 d). Here the concavity conditions require a.0 and 0 , c , b , 1.The third is ‘matching product lines’ where a firm’s own varieties are less good substitutes for each other than they are for the other firm’s varieties. For example if the product is washing machines, each firm may make a large high-volume model and a small economy model, so c . b 5 d and, with the concavity conditions, a.0 and 0 , b , c , 1. Note that the first case is standard in the Dixit–Stiglitz monopolistic competition literature. The other two are standard in the multiproduct oligopolistic competition literature (Brander and Eaton, 1984), where they are called the ‘segmentation’ and ‘interlacing’ cases, respectively. With linear demand, we assume a x 5 0 without loss of generality.

4. Reciprocal FDI dumping In stage one, each firm decides either to produce both varieties domestically (‘N-type’ firm) or to be multinational and produce one variety domestically and

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one abroad (‘M-type’ firm).9 In stage two, firms choose sales in each segmented market without considering cross-market effects; they do, however, consider cross-variety effects within markets. Three types of location outcomes are possible. All firms are N-types, all are M-types, or one firm is an N-type and the other is an M-type (the asymmetric, or A-type outcome). In the N-only outcome, firms produce both varieties domestically, exporting them to the other nation (throughout, trade costs are assumed low enough to permit trade). The result is standard two-way trade in differentiated products among identical nations, but no FDI. In the M-only outcome, firms split production of their varieties geographically and sell both varieties in both markets. Again two-way trade in differentiated products occurs with some of this consisting of ‘reverse imports’ (home imports of home goods made abroad). Furthermore, two-way FDI in the same industry between identical nations takes place. Thus the M-only outcome naturally gives rise to parallelism in the trade and investment patterns. The A-type outcome has intraindustry trade in differentiated goods and FDI by only one firm (so no IIFDI).

4.1. The stage-two equilibria We evaluate stage-two profits under the three types of stage-one outcomes before turning to stage one. When all firms are N-types, the home firm, which makes varieties 1 and 2, maximises o i 51,2 [ pih x ih 1 ( pif 2 t) x if ] 2 2F, where x ih and x if indicate sales of variety i in home and foreign, respectively while pih and pif are the corresponding consumer prices. By symmetry, there will be only two distinct equilibrium levels of sales — local sales x N and export sales x N * . Solving the first order conditions for a typical variety and using symmetry: a[2(1 1 b) 2 (c 1 d)] 1 t(c 1 d) x N 5 ]]]]]]]]]]], [2(1 1 b) 1 (c 1 d)][2(1 1 b) 2 (c 1 d)] t x N * 5 x N 2 ]]]]] 2(1 1 b) 2 (c 1 d)

(3)

An interior solution (i.e. positive trade flows) requires t , a(2(1 1 b) 2 (c 1 d)) / 2(1 1 b). The equilibrium level of operating profit, P N , is 2(1 1 b)[(x N )2 1 (x N * )2 ]; this satisfies the Fig. 1 convexity criteria. Given the quasi-linearity of utility (1), the production and consumption of Z is determined as a residual. In particular, since a X 5 0, the equilibrium Z output and consumption per nation is L 2 2tx N * 2 2F. In the M-only stage-one outcome, the home firm makes variety 1 at home and 2

9

The outcome where each firm produces both its varieties abroad is dominated by the N-type outcome when G is positive.

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abroad, with the foreign firm matching this pattern.10 Home’s stage-two objective function is: p1h x 1h 1 ( p1f 2 t)x 1f 1 p2f x 2f 1 ( p2h 2 t)x 2h 2 2F 2 G. As before, M M there are only two distinct sales levels, local sales x and export sales x * . Solving the first order conditions: a(2(1 2 b) 2 c 1 d) 1 (2b 1 c) x M 5 ]]]]]]]]]]]t (2(1 1 b) 1 c 1 d)(2(1 2 b) 2 c 1 d) t x M * 5 x M 2 ]]]]] 2(1 2 b) 2 c 1 d

(4)

For variety 1, local sales are in the home market, but for variety 2 they are in the foreign market. Foreign firm sales are the mirror image. For the M-only outcome, operating profit, (x M )2 1 (x M * )2 1 2x M x M * , again meets the Fig. 1 convexity criteria. National production and consumption of Z is L 2 2tx M * 2 2F 2 G. In the A-outcome, the home firm is an M-type and the foreign firm is an N-type, so the stage-two home objective function is p1h x 1h 1 p2f x 2f 1 ( p2h 2 t)x 2h 1 ( p1f 2 t)x 1f 2 2F 2 G and the correspondent for foreign is p4f x 4f 1 p3f x 3f 1 ( p4h 2 t)x 4h 1 ( p3h 2 t)x 3h 2 2F. Nash maximisation yields eight first order conditions, solvable for the eight sales levels. The resulting expressions for the eight sales levels, and the two operating profits, P AN (for the N-type) and P AM (for the M-type) are not reported since they are too unwieldy to be revealing and, as shown below, the A-outcome is never sub-game perfect.11

4.2. Stage-one equilibrium Profits earned in the four possible stage-one outcomes (N-only, M-only and two mirror image A-types) can be displayed in a 232 normal form diagram (not shown). Consider first the N-only outcome. This is an equilibrium only if no firm wishes to deviate in stage one, i.e. if P AM 2 2F 2 G , P N 2 2F, where P AM is the stage-two operating profit of the M firm in the A-type outcome. Likewise, the M-only outcome is an equilibrium, if P AN 2 2F , P M 2 2F 2 G. If both M-only and N-only outcomes are subgame perfect, the Pareto dominance refinement is used. Finally, only if (P N 2 P AM 1 G ) , 0 and (P M 2 P AN 2 G ) , 0 hold is the A-type outcome subgame perfect. Thus the condition [(P N 1 P M ) 2 (P AN 1

10 For expositional purposes, we do not present the details of the alternative configuration, in which twin varieties are made in the same country. The reason why is that such an alternative increases competition so that it is always Pareto-dominated by the one we present. In particular, the profit gain from the geographical separation of the production of twin varieties is t(1 2 b)2 (c 2 d) / [4(1 2 b)2 2 (c 2 d)2 ] 2 which is always positive given the assumption c $ d. 11 Detailed calculations and complete expressions for all results can be found in the Maple worksheet Cournt2s.mws from http: / / heiwww.unige.ch / |baldwin /.

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P AM )] . 0 can rule out the A-outcome because it implies (P N 2 P AM 1 G ) . 0 and / or (P M 2 P AN 2 G ) . 0. To summarise, the sub-game perfect equilibrium is characterised by three main conditions: M is SGP: P M . P AN 1 G, N is SGP: P N . P AM 2 G, M dom N: P M 2 G . P N

(5)

The parameter space in which two-way FDI arises is defined implicitly by (5). Specifically, two-way FDI arises if the first expression in (5) holds and the second expression fails, or if all three expressions hold. Analytic solutions for (5) exist, but are too cumbersome to be revealing (see footnote 11). We turn therefore to our three special cases. Full symmetry. With full symmetry 1 , b 5 c 5 d , 0 and [(P N 1 P M ) 2 (P AN 1 P AM )] equals t 2 b(1 1 b) / [2(1 1 2b)] . 0, so the A-outcome is not an equilibrium. Also, (5) becomes: b(1 1 b)2 1 3b 1 2 2 1 4b 1 3b 2 2 2 ]]]]]] ]]]]] M is SGP: t b . G, N is SGP: t b , G, 4(1 2 b)(1 1 2b)2 4(1 2 b)(1 1 2b)2 2

t 2b 2 ]]] M dom N: .G 4(1 2 b)

(6)

Fig. 3 facilitates interpretation of (6) by plotting the inequalities in (b, G /t 2 ) space. The curves define four regions of parameter space. Increasing ‘b’ exacerbates the cannibalisation effect and thus encourages FDI, and the cannibalisation-reducing effect of FDI is magnified by trade costs, t. By raising the cost of separating production, a high G has the opposite effect. More precisely, the M-only outcome is a Nash equilibrium below the line marked ‘M is SGP’, i.e. in regions 2, 3 and 4. Similarly, the N-only outcome is a Nash equilibrium above the ‘N is SGP’ line, i.e. in regions 1 and 2. Above the ‘M dom N’ curve the N-type Pareto is dominated by the M-type. Since M dom N is below N-is-SGP, reciprocal FDI arises only when N-is-SGP fails, i.e. in regions 3 and 4. (See footnote 11 for calculations establishing the order of curves). This special case clearly illustrates how FDI arises in this model as a means of minimising the cannibalisation effect faced by multiproduct firms. Inspection of the key N-is-SGP condition shows that if the sale of one variety has no impact on sales of another (i.e. b50), or FDI has no ability to reduce inter-variety competition (t50), then the FDI incentive is zero. Moreover the incentive rises not only with substitutability, it also rises with trade costs, t, since this increases the ability of FDI to reduce the cannibalisation effect on profits. We summarise this as: Result 1. In the symmetric-varieties case, IIFDI arises when varieties are sufficiently good substitutes (so the cannibalisation effect is powerful), trade costs

442 R.E. Baldwin, G.I.P. Ottaviano / Journal of International Economics 54 (2001) 429 – 448

Fig. 3. The full symmetry case.

are sufficiently high (so geographical separation reduces cannibalisation a lot), and the cost of multinationality is not too great. Formally, t 2 b 2 [2 1 4b 1 3b 2 ] / [4(1 2 b)(1 1 2b)2 ] . G is the condition. Firm-wise symmetry. In the more general case of firm-wise symmetry, viz. b . c 5 d, [(P N 1 P M ) 2 (P AN 1 P AM )] equals t 2 c(1 1 b) / [2(b 2 2 c 2 1 1 1 2b)(1 1 b 2 c)] . 0, so again the A-outcome is not an equilibrium. Moreover, (5) becomes: 2(1 1 b)2 (b 2 2 c 2 1 b) 1 c 4 2 M is SGP: ]]]]]]]] t . G, 4(1 2 b)[(1 1 b)2 2 c 2 ] 2 (b 2 c)2 1 2(b 2 c) 1 b 2 2 M dom N: ]]]]]]] t .G 4(1 2 b)(1 1 b 2 c)2 2(1 1 b)[(b 2 c)[1 1 (b 1 c)(1 1 b)] 1 b 2 (1 1 c)] 1 c 4 2 N is SGP: ]]]]]]]]]]]]]]] t ,G 4(1 2 b)[(1 1 b)2 2 c 2 ] 2

(7)

Notice that the left-hand sides of all three inequalities are positive. Thus, when G is sufficiently close to zero the first inequality holds and the third fails, so reciprocal FDI will arise. However, for larger values of G /t 2 both N and M type outcomes can be subgame perfect, so IIFDI arises only when the M dom N condition holds.

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Intuition for the impact of substitutability on the ‘incentive to go multinational’ is gained by considering the critical M dom N condition in (7). The left hand side is increasing in b and decreasing in c. Consequently, the net gain from multinationality involves a trade-off between the benefit from reducing own variety competition (measured by b) and the cost from facing fiercer ‘alien’ variety competition (measured by c). For example when c 5 0, firms face competition only from their own varieties and are thus monopolists in the partial equilibrium sense; the M dom N condition becomes bt 2 / [2(1 2 b 2 )] . G and we see that the gain from geographically separating production depends uniquely on the reduction in competition among each firm’s own varieties. More precisely, P M 2 P N 5 t 2 (d 2 1 2d 1 b 2 ) / [4(1 2 b)(1 1 d )] 2 , where d ; b 2 c. Differentiating this with respect to d yields: t 2 (1 1 b) / [2(1 1 d )3 ]. With d . 0 this is positive and increasing in t and d. Thus the more similar own varieties are compared to alien varieties, the bigger is the operating profit gain from going multinational. The firm-wise symmetry case assumes b . c, but considering the artificial situation where own varieties are worse substitutes than alien varieties, i.e. c . b, provides further intuition. In this case, multinational production reduces direct competition among own varieties, but may increase overall local competition by putting production of good substitutes near each other. Indeed, solving P M 2 P N , 0 for d we see that going multinational lowers operating profit if c is sufficiently greater than b; c 2 b . 1 2 (1 2 b 2 )1 / 2 is the precise condition. Interestingly, the firm-wise symmetry case itself includes a version of the standard scale-versus-proximity model. When b approaches unity, the firm’s two varieties become very good substitutes and in the limit, they are perfect substitutes. If c is fixed below unity as b approaches unity, the model collapses to a duopoly between single-product firms that must (rather artificially) have two factories. This corresponds roughly to the classic Markusen–Horstmann set up except that there is no possibility of achieving scale efficiency by consolidating production in a single factory. Here the incentive for FDI is huge since the left-side of the second inequality in (7) gets arbitrarily large as b → 0. To summarise all the above reasoning, we write: Result 2. In the firm-wise symmetry case, the incentive to go multinational increases as a firm’s own varieties become better substitutes for each other relative to their substitutability with the other firm’s varieties. This incentive also rises with trade costs, but falls with the cost of multinationality. Matching product lines. In the matching products case a firm’s varieties are pair-wise good substitutes with their competitor’s goods. Here a particularly strong incentive to go multinational exists. Using the large and small machine example, the N-only outcome and the M-only outcome both involve a large and small machine made in each nation. However, in the M-only outcome, different firms

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make the large and small machines in each nation. The cannibalisation effect is thus always lower in the M-only outcome, and consequently, the M-only outcome always dominates the N-only outcome, when the costs of multinationality are sufficiently small. More formally when G 5 0, the M-only outcome is always a Nash equilibrium and the N-only outcome is a Nash equilibrium when c is sufficiently larger than b (see footnote 11 for details). However M dominates N when: 2t 2 b[2c(1 2 b) 2 (b 2 c)2 ] ]]]]]]]] .G (2 1 b 2 c)2 (2 2 b 2 c)2

(8)

This holds when G is small enough since the left-hand term is always positive with b , c , 1. We see therefore that as in the other cases, IIFDI tends to arise when G /t 2 is small.

4.3. Reciprocal FDI dumping The two-way FDI in this model can be viewed as reciprocal FDI dumping in the sense that firms accept a lower ‘apparent’ rate of return on their FDI investment than on their domestic investment. Two facts establish this directly. By symmetry, all varieties earn the same operating profit and, second, the fixed cost associated with the variety produced domestically (F ) is smaller than the fixed cost associated with the variety produced abroad (F 1 G ). Accordingly, the operating profit per dollar invested is greater for the domestic factory. This is true for both home and foreign firms so that all FDI is reciprocal investment dumping. Thus: Result 3. When two-way FDI arises, the ratio of operating profit to fixed cost is higher for the local factory than it is for the factory abroad. In this sense, the FDI may be thought of as reciprocal FDI dumping.

4.4. FDI and trade: the trade displacement metric We turn now to characterising the IIFDI and IIT equilibrium. To reduce uninformative complexity, we henceforth concentrate on the full symmetry case. The standard proximity-versus-scale approach has trade and FDI as substitutes. In our approach IIFDI and IIT arise in parallel since even though FDI replaces some exports, it also creates re-imports. To measure the total effect, we posit a ‘trade displacement metric’ (TDM), which measures the reduction in sectoral bilateral trade between our two symmetric nations when firms switch from N-types to M-types. From (3) and (4) the TDM is: tb TDM 5 ]] 12b

(9)

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Note that in the proximity-versus-scale model (i.e. b → 1) TDM is infinite — foreign production entirely replaces exports. In contrast, in our model (i.e. b , 1) the degree of trade displacement is finite and possibly modest, when FDI occurs — a fortiori when exports are measured in value terms (as in much empirical work) since, as we shall see below, the N-to-M switch raises the price of imports. In short: Result 4. FDI displaces some, but not all, trade in this model. Importantly, this trade displacement may be very difficult to identify in data. Due to policy and / or technology changes, greater integration of goods markets (reducing t) is often accompanied by easier investment (reduction of G ). And this is true for single sectors over time and across sectors at any point in time. Thus if one runs exports on a standard regression that includes some measure of FDI activity — without controlling for both trade costs and FDI costs — one may find a spurious positive correlation between FDI and trade.

4.5. Price and welfare effects The price and welfare effects of two-way FDI can be calculated by comparing the M-type and the N-type equilibria. In both cases, due to full symmetry, there are only two prices per equilibrium, the price of locally produced and imported goods. From (1), (3) and (5): tb N M N pM x1 2 p x1 5 2 ( p x 4 2 p x 4 ) 5 2 ] 4

(10)

Thus IIFDI lowers the price of the typical locally produced and sold variety (variety 1), but raises the price of the typical imported variety (variety 4) by the same amount. This pair of price changes may seem counterintuitive. Price equals the price-cost mark-up (marginal costs are zero) and typically, mark-ups rise with sales. Here, however, the mark-up on imports rises as the level of imports falls. The positive link between sales and mark-ups, however, come from intuition based on singleproduct firms. For a multiproduct firm, what matters — roughly speaking — is the sum of sales of all varieties. Given this, and the fact that total home-firm sales in the foreign market rise, it is natural that the price of exports should rise. Likewise, total two-variety home sales in the home market fall as we shift to the M-only equilibrium, so again that price drop is natural. Consider next the welfare effects. Consumers see the price of the two locally produced goods fall, but the price of the two imported varieties rise by the same amount. Since consumers always consume more of the locally produced goods, this pair of price changes tends to improve consumer welfare. Counterbalancing this is the fact that FDI requires higher fixed cost and this reduces welfare by

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reducing the production and consumption of the residual good Z. Using the equilibrium quantities in the utility function, the change in welfare is: (2 1 b)b U M 2 U N . 0 ⇔ ]]] . G /t 2 8(1 2 b)

(11)

It is straightforward (see footnote 11) to show that the U M 2 U N line would lie above the ‘N-is-SGP’ line in Fig. 3. Accordingly, consumers gain whenever IIFDI arises. The impact on firms is subtler. The M dom N condition in (6) tells us when IIFDI raises profits. Fig. 3 shows that the range of parameters for which IIFDI arises (regions 3 and 4) is wider than the range of parameters for which M Pareto dominates N (region 4). Consequently, we have the somewhat paradoxical result that for some parameter values (region 3) firms may lose from IIFDI while consumers gain. To summarise: Result 5. Consumers gain from reciprocal FDI dumping. Firms gain only when the cost of multinationality is low compared to trade costs and the substitutability of varieties; the formal condition is given by the third inequality in (6). The result that equilibrium FDI may arise even though it lowers profit is easy to understand. Suppose that we start with the parameter configuration described by point A in Fig. 3. If we continuously raise the degree of substitutability ‘b’, we would cross from region 1 into 2. Although FDI is a possibility in region 2, it is unlikely (the N-only outcome Pareto dominates). However, as b rises still further, the N-only outcome becomes Nash-unstable. The asymmetric outcome is never an equilibrium, so in region 3 we see reciprocal FDI dumping, even though both firms would prefer the N-only outcome. If firms could collude on type, they would choose to be N-types. If b rises even further, we reach region 4 where firms both prefer to be M-types. The fact that FDI might raise both welfare and profits, as it does in region 4, is also easily understood. When the FDI occurs, some trade displacement occurs. Since trade involves real costs, the reduced trade volume yields some pure efficiency gain that can be split between consumers and producers. To put this differently, both the N and M type equilibria are marked by socially inefficient ‘cross-hauling’ since firms, who base exports on marginal revenue rather than price, ‘overvalue’ trade relative to the planner. In the M-only equilibrium less of this goes on allowing a Pareto improvement. 5. Concluding remarks Global MNC activity is an amalgamation of several very distinct types that must be explained by several very distinct models. This paper focuses on the cross hauling of foreign investment that generates reciprocal trade in differentiated final

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products. It posits a model that differs sharply from the standard proximity-versusscale model. In our model, firms simultaneously engage in intraindustry FDI and intraindustry trade in a manner that naturally leads to similarity in the trade and FDI patterns. The two-way FDI is driven by forces analogous to those driving trade in the reciprocal-dumping model of Brander and Krugman (1983). Specifically, firms producing multiple differentiated varieties have an incentive to use trade costs to reduce inter-variety competition. They do this by placing production of some varieties abroad. Since the varieties are differentiated, all varieties are sold in all markets, regardless of where they are produced. While FDI does displace some exports, it also creates some reverse imports. Consequently, the pattern of trade and investment are intrinsically similar. Our model is not intended to explain all types of FDI or all aspects of the trade and FDI correlation. Nor is the model appropriate for industries in which intermediate goods and vertical integration are dominant features. It is, however, based on a novel motive for FDI and it addresses two-way trade and investment in final-goods sectors.

Acknowledgements Thanks to Jim Brander, Keith Head, Jim Markusen, Philippe Martin, Massimo Motta, Diego Puga, Nadia Soboleva, Jacques Thisse, Dan Trefler, Tony Venables, seminar participants at Bocconi University, University of British Columbia, University of Tokyo, University of Toronto, and the NBER Summer Institute 1999 for helpful comments. Ideas from the anonymous referees and Rob Feenstra simplified our exposition and improved the paper. Financial support came from Swiss FNS grant 1214-043580.95. The first revision was carried out while Ottaviano visited EUI in Florence thanks to a Jean Monnet fellowship.

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