Export Versus FDI with Heterogeneous Firms

Export Versus FDI with Heterogeneous Firms By ELHANAN HELPMAN, MARC J. MELITZ, AND STEPHEN R. YEAPLE* Multinational sales have grown at high rates over the last two decades, outpacing the remark- able expansion of trade in manufactures. Con- sequently, the trade literature has sought to incorporate the mode of foreign market access into the “new” trade theory. This literature rec- ognizes that firms can serve foreign buyers through a variety of channels: they can export their products to foreign customers, serve them through foreign subsidiaries, or license foreign firms to produce their products. Our work focuses on the firm’s choice be- tween exports and “horizontal” foreign direct investment (FDI). Horizontal FDI refers to an investment in a foreign production facility that is designed to serve customers in the foreign market.1,2 Firms invest abroad when the gains from avoiding trade costs outweigh the costs of maintaining capacity in multiple markets. This is known as the proximity-concentration trade- off.3 We introduce heterogeneous firms into a simple multicountry, multisector model, in which firms face a proximity-concentration trade-off. Every firm decides whether to serve a foreign market, and whether to do so through exports or local subsidiary sales. These modes of market access have different relative costs: exporting involves lower fixed costs while FDI involves lower variable costs. Our model highlights the important role of within-sector firm productivity differences in explaining the structure of international trade and investment. First, only the most productive firms engage in foreign activities. This result mirrors other findings on firm heterogeneity and trade; in particular, the results reported in Melitz (2003).4 Second, of those firms that serve foreign markets, only the most productive engage in FDI.5 Third, FDI sales relative to exports are larger in sectors with more firm heterogeneity. Using U.S. exports and affiliate sales data that cover 52 manufacturing sectors and 38 countries, we show that cross-sectoral differ- ences in firm heterogeneity predict the compo- sition of trade and investment in the manner suggested by our model. We construct several measures of firm heterogeneity, using different data sources, and show that our results are ro- bust across all these measures. In addition, we confirm the predictions of the proximity- concentration trade-off. That is, firms tend to substitute FDI sales for exports when transport * Helpman: Department of Economics, Harvard Univer- sity, Cambridge, MA 02138, Tel Aviv University, and CIAR (e-mail: ehelpman@harvard.edu); Melitz: Depart- ment of Economics, Harvard University, Cambridge, MA 02138, National Bureau of Economic Research, and Centre for Economic Policy Research (e-mail: mmelitz@ harvard.edu); Yeaple: Department of Economics, Univer- sity of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104, and National Bureau of Economic Research (e-mail: snyeapl2@ssc.upenn.edu). The statistical analysis of firm- level data on U.S. Multinational Corporations reported in this study was conducted at the International Investment Division, U.S. Bureau of Economic Analysis, under an arrangement that maintained legal confidentiality require- ments. Views expressed are those of the authors and do not necessarily reflect those of the Bureau of Economic Anal- ysis. Elhanan Helpman thanks the NSF for financial sup- port. We also thank Daron Acemoglu, Roberto Rigobon, Yona Rubinstein, and Dani Tsiddon for comments on an earlier draft, and Man-Keung Tang for excellent research assistance. 1 See Wilfred J. Ethier (1986), Ignatius Horstmann and James R. Markusen (1987), and Ethier and Markusen (1996) for models that incorporate the licensing alternative. 2 We therefore exclude “vertical” motives for FDI that involve fragmentation of production across countries. See Helpman (1984, 1985), Markusen (2002, Ch. 9), and Gor- don H. Hanson et al. (2002) for treatments of this form of FDI. 3 See, for example, Horstmann and Markusen (1992), S. Lael Brainard (1993), and Markusen and Anthony J. Ven- ables (2000). 4 See also Andrew B. Bernard et al. (2003) for an alter- native theoretical model and Yeaple (2003a) for a model based on worker-skill heterogeneity. James R. Tybout (2003) surveys the recent micro-level evidence on trade that has motivated these theoretical models. 5 This result is loosely connected to the documented empirical pattern that foreign-owned affiliates are more productive than domestically owned producers. See Mark E. Doms and J. Bradford Jensen (1998) for the United States and Sourafel Girma et al. (2002) for the United Kingdom. 300 costs are large and plant-level returns to scale are small. Moreover, the magnitude of the im- pact of our heterogeneity variables are compa- rable to the magnitude of the impact of the proximity-concentration trade-off variables. We conclude that intra-industry firm heterogeneity plays an important role in explaining interna- tional trade and investment. As mentioned above, our model predicts that the least productive firms serve only the domes- tic market, that relatively more productive firms export, and that the most productive firms en- gage in FDI. We provide some evidence sup- porting this sorting pattern. We compute labor productivity (log of output per worker) for all firms in the COMPUSTAT database in 1996. We then regress this productivity measure on dummies for multinational firms (MNEs) and non-MNE exporters, controlling for capital in- tensity and 4-digit industry effects. Table 1 re- ports the resulting estimates for the productivity advantage of MNEs and non-MNE exporters over the remaining firms.6 These results confirm previous findings of a significant productivity advantage of firms engaged in international commerce. In addition, they highlight a new prediction of our model: MNEs are substan- tially more productive than non-MNE export- ers; the estimated 15-percent productivity advantage of multinationals over exporters is significant beyond the 99-percent level. The remainder of this paper is composed of four sections. In Section I, we elaborate the model and we map the theoretical results into an empirical strategy. In Section II, we describe the data. We report and interpret the empirical find- ings in Section III, and we provide concluding comments in the closing section. I. Theoretical Framework There are N countries that use labor to pro- duce goods in H � 1 sectors. One sector pro- duces a homogeneous product with one unit of labor per unit output, while H sectors produce differentiated products. An exogenous fraction �h of income is spent on differentiated products of sector h, and the remaining fraction 1 � ¥h�h on the homogeneous good, which is our nu- meraire. Country i is endowed with Li units of labor and its wage rate is wi. Now consider a particular sector h that pro- duces differentiated products. For the time be- ing we drop the index h, with the implicit understanding that all sectoral variables refer to sector h. To enter the industry in country i, a firm bears the fixed costs of entry fE, measured in labor units. An entrant then draws a labor- per-unit-output coefficient a from a distribution G(a). Upon observing this draw, a firm may decide to exit and not produce. If it chooses to produce, however, it bears additional fixed overhead labor costs fD. There are no other fixed costs when the firm sells only in the home country. If the firm chooses to export, however, it bears additional fixed costs fX per foreign market. On the other hand, if it chooses to serve a foreign market via foreign direct investment (FDI), it bears additional fixed costs fI in every foreign market. We think about fX as the costs of forming a distribution and servicing network in a foreign country (similar costs for the home market are included in fD). The fixed costs fI include these distribution and servicing network costs, as well as the costs of forming a subsid- iary in a foreign country and the duplicate over- head production costs embodied in fD. The difference between fI and fX thus indexes plant- level returns to scale for the sector.7 Goods that 6 Our controls include the log of capital (book value net of depreciation) per worker, this variable squared, and 4-digit industry fixed effects. Controlling for material usage intensity does not change the results. 7 Part of the cost difference fI � fX may also reflect some of the entry costs represented by fE, such as the initial cost of building another production facility. TABLE 1—PRODUCTIVITY ADVANTAGE OF MULTINATIONALS AND EXPORTERS Multinational 0.537 (14.432) Nonmultinational exporter 0.388 (9.535) Coefficient difference 0.150 (3.694) Number of firms 3,202 Notes: T-statistics are in parentheses (calculated on the basis of White standard errors). Coefficients for capital intensity controls and industry effects are suppressed. 301VOL. 94 NO. 1 HELPMAN ET AL.: EXPORT VERSUS FDI are exported from country i to country j are subjected to melting-iceberg transport costs �ij � 1. Namely, �ij units have to be shipped from country i to country j for one unit to arrive. After entry, producers engage in monopolistic competition. Preferences across varieties of product h have the standard CES form, with an elasticity of substitution � � 1/(1 � �) � 1. These prefer- ences generate a demand function Aip�� in country i for every brand of the product, where the demand level Ai is exogenous from the point of view of the individual supplier.8 In this case, the brand of a monopolistic producer with labor coefficient a is offered for sale at the price p � wia/�, where 1/� represents the markup factor. As a result, the effective consumer price is wia/� for domestically produced goods—sup- plied either by a domestic producer or foreign affiliate with labor coefficient a—and is �jiwja/� for imported products from an exporter from country j with labor coefficient a. A firm from country i that remains in the industry will always serve its domestic market through domestic production. It may also serve a foreign market j. If so, it will choose to access this foreign market via exports or affiliate pro- duction (FDI). This choice is driven by the proximity-concentration trade-off: relative to exports, FDI saves transport costs, but dupli- cates production facilities and therefore requires higher fixed costs.9 In equilibrium, no firm en- gages in both activities for the same foreign market.10 We assume (1) �wj wi � �� 1 fI � ��ij��� 1 fX � fD . These conditions will be clarified in the follow- ing analysis. For expositional simplicity, assume for the time being unit wages in every country (wi � 1).11 Then, operating profits from serving the domestic market are �Di � a1��Bi � fD for a firm with a labor-output coefficient a, where Bi � (1 � �) Ai/�1��.12 On the other hand, the additional operating profits from exporting to country j are �Xij � (�ija)1�� Bj � fX, and the additional operating profits from FDI in country j are �Ij � a1�� Bj � fI. These profit functions are depicted in Figure 1 for the case of equal demand levels Bi � Bj.13 In this figure, a1�� is represented on the horizontal axis. Since � � 1, this variable increases monotonically with labor productivity 1/a, and can be used as a produc- tivity index. All three profit functions are in- creasing (and linear): more productive firms are more profitable in all three activities. The profit functions �Di and � Ij are parallel, because we assumed Bi � Bj. However, profits from FDI are lower, as the fixed costs of FDI, fI, are higher than the fixed costs of domestic produc- tion, fD. The profit function �Xij is steeper than both �Di and � Ij due to the trade costs �ij. To- gether with the first inequality in (1), these relationships imply that exports are more prof- 8 As is well known, our utility function implies that Ai � �Ei/[�0n i pi (v)1�� dv], where Ei is the aggregate level of spending in country i, ni is the number (measure) of vari- eties available in country i and pi (v) is the consumer price of variety v. 9 We exclude the possibility of exports by foreign affil- iates. See, however, the Appendix of our working paper, Helpman et al. (2003), for a discussion of this possibility. 10 In a dynamic model with uncertainty, an individual firm may choose to serve a foreign market through both exports and FDI. Rafael Rob and Nikolaos Vettas (2003) provide a rigorous treatment of this case. 11 This will be the case so long as the numeraire good is produced in every country and freely traded. 12 Note that the demand function Aip�� implies output Ai (a/�)�� when the price is a/�. Under these circumstances, costs are �Ai (a/�)1��, while revenue is Ai (a/�)1��. There- fore, operating profits are �Di � (1 � �) Ai (a/�)1�� � fD. 13 We thank Dani Tsiddon for proposing this figure. In the figure fX � fD, which is a sufficient condition for the second inequality in (1). Evidently, this inequality can also be satisfied when fX � fD, and we need only the inequality in (1) in order to ensure that some firms serve only the domestic market. FIGURE 1. PROFITS FROM DOMESTIC SALES, FROM EXPORTS, AND FROM FDI 302 THE AMERICAN ECONOMIC REVIEW MARCH 2004 itable than FDI for low-productivity firms and less profitable for high-productivity firms. Moreover, there exist productivity levels at which exporters have positive operating profits that exceed the operating profits from FDI [since (aIij)1�� � (aXij)1��], which ensures that some firms export to country j. In addition, the second inequality in (1) implies (aXij)1�� � (aDi )1��, which ensures that some firms serve only the domestic market. The least productive firms expect negative operating profits and therefore exit the industry. This fate befalls all firms with productivity lev- els below (aDi )1��, which is the cutoff at which operating profits from domestic sales equal zero. Firms with productivity levels between (aDi )1�� and (aXij)1�� have positive operating profits from sales in the domestic market, but expect to lose money from exports and FDI. They choose to serve the domestic market but not to serve country j. The cutoff (aXij)1�� is the productivity level at which exporters just break even. Higher-productivity firms can export profitably. But those with productivity above (aIij)1�� gain more from FDI. For this reason, firms with productivity levels between (aXij)1�� and (aIij)1�� export while those with higher pro- ductivity levels build subsidiaries in country j, which they use as platforms for servicing coun- try j’s market. It is evident from the figure that the cutoff coefficients (aDi )1��, (aXij)1��, and (aIij)1�� are determined by (2) �aDi �1� �Bi � fD , @i, (3) ��ijaXij�1� � Bj � fX , @j� i, (4) 1 ��ij�1� � �aIij�1� � Bj � fI fX , @j� i. Free entry ensures equality between the ex- pected operating profits of a potential entrant and the entry costs fE. The form of this condi- tion is reported in our working paper (Helpman et al., 2003). The free entry condition together with (2)–(4) provide implicit solutions for the cutoff coefficients aDi , aXij, aIij, and the demand levels Bi in every country. These solutions do not depend on the country-size variables Li as long as productivity-adjusted wages wi remain equalized (the numeraire outside good is pro- duced everywhere and freely traded). More- over, we can also allow cross-country variations in the fixed-cost coefficients, as long as these variations do not lead some countries to stop producing the outside good. These generaliza- tions are useful for empirical applications. We report in our working paper general- equilibrium results for a special case in which countries only differ in size and trade costs per product are symmetric (implying �ij � � for j � i). These restrictions apply within each sector, so there can be arbitrary variations across sec- tors. Under these circumstances, (2)–(4) and free entry imply that, as long as countries do not differ too much in size, wages are the same everywhere, all countries share the same cutoffs aD i � aD, aX ij � aX, aI ij � aI, and the same demand levels Bi � B. Larger countries attract a disproportionately larger number of entrants (relative to country size) and a larger number of sellers (hence, more product variety). We also show that larger markets are disproportionately served by domestically owned firms, i.e., the market share of domestically owned firms is larger in the home market of a larger country. A. Exports Versus FDI Sales We now consider the relative magnitude of exports and local FDI sales for a pair of coun- tries i and j. Let sXij be the market share in country j of country i’s exporters and let sIij be the market share in country j of affiliates of country i’s multinationals. The relative size of these market shares is then (5) sX ij sI ij � � 1� � �V �aX �V �aI � 1� in the symmetric case, where (6) V �a� � � 0 a y1� �dG �y�. Given our symmetry assumptions, this ratio is independent of i and j. That is, every country has the same relative sales of exporters and affiliates in every other country. This ratio rises 303VOL. 94 NO. 1 HELPMAN ET AL.: EXPORT VERSUS FDI with the exporting cutoff coefficient aX and declines with the FDI cutoff coefficient aI. The cutoffs, in turn, are determined by the system of equilibrium conditions. A rise in the export costs fX or �, or a decrease in the FDI costs fI, all have similar impacts on the aX and aI cutoffs: they induce an increase in aI and a decrease in aX. The relative sales of exporters thus decline in all these cases. Recall that fI encompasses both the country-level fixed costs embodied in fX and the duplicate plant overhead costs represented by fD. It is therefore natural to consider the effects of equivalent increases in fI and fX (representing higher country- level costs), and the effects of equivalent decreases in fI and fD (representing lower over- head plant costs, and hence smaller returns to scale). Again, we show that the aI and aX cutoffs move in the same directions as before, entailing a decrease in relative export sales. These are sensible comparative statics pre- dicting the cross-sectoral variation in relative exports sales. We expect the relative sales of exporters to be lower in sectors with higher transport costs or higher fixed country-level costs (even when the latter costs are also borne by multinational affiliates). We also expect them to be lower in sectors where plant-level returns to scale are relatively weak. These re- sults show how the firm-level proximity- concentration trade-off results can be extended to sectors with heterogeneous firms that select different modes of foreign market access. We now shift the focus to the role of firm- level heterogeneity in explaining the cross- sectoral variation in relative export sales. Note from (5) that the function V� directly impacts the relative sales (holding the cutoff levels fixed). Recall also that firm sales and variable profits are proportional to a1�� in every market. V(a) therefore captures (up to a multiplicative constant) the distribution of sales and variable profits among firms that make the same export or FDI decisions. It also captures the distribu- tion of domestic sales and variable profits among all surviving firms. We think of V(a) as summarizing firm-level heterogeneity in a sec- tor. It is exogenously determined by the distri- bution of unit costs G(a) and the elasticity of substitution �. In order to index differences in firm-level heterogeneity across sectors, we parametrize G(a). We use the Pareto distribution as a benchmark. When labor productivity 1/a is drawn from a Pareto distribution with the shape parameter k, the distribution of firm domestic sales, indexed by V(a), is also Pa- reto, with the shape parameter k � (� � 1).14 The