The Effect of Foreign Productivity on FDI Decisions Jennifer L. Steele May 12, 2006 Abstract A firm’s decision of whether or not to undertake foreign direct investment (FDI) depends on their expected payoff. The more productive they expect to be, relative to their home productivity, the more likely they are to produce in the foreign country. When firms have varying levels of productivity in the home country, the decision of whether or not to invest in a foreign country will be based on the firm’s expectation of their productivity in that foreign country, and will differ from firm to firm. If their foreign productivity is proportional to their home productivity, only the relatively more productive firms choose to produce in the foreign country. Dependent on the distribution of foreign productivities, incomplete information may yield an equilibrium where only the firms that are less productive in the home country choose to enter the foreign country. A firms’ choice of whether or not to serve a foreign market, and then whether to serve it through export or FDI, is dependent on both their home and foreign productivities. If firms know both their home and their foreign productivities then as their foreign productivity increases their expected cost of producing in the foreign country decreases. Factor price equalization suggests that the large differences in wages across countries are reflective of the differences in productivities between workers. However, due to limited capital mobility, wage differentials may not accurately 1 reflect the differences in productivities, but instead reflect other factors, such as level of industry operating in the country, barriers to entry, opportunity costs for the workers and trade barriers. Most trade literature treats FDI as a method of avoiding transport costs when serving a new market. However, in developing economies a large portion of FDI is an effort to cut the costs of production, rather than to serve a new market. At times the firm may not even serve the market in the country where they produce, choosing to export all production. This paper explores the motivations behind FDI when the foreign demand may not be sufficient to warrant producing in the foreign country just to serve the foreign market, and when there are potential cost savings from producing in the foreign country over producing at home. Differences between a firm’s productivity in the home country and the foreign country can be divided into two main sources. First, the industry-specific difference in productivity. This could be influenced by the educational system, cultural practices, or institutions. Some countries may be more productive in textile industries because of cultural emphasis on handicrafts, or becuase of the group culture leading to more productive assembly lines, while other countries may be more adept at work involving machines because of the emphasis on machinery in the educational system. These are not to be thought of as innate abilities, or characteristics of certain countries. Rather they should be thought of as learned skills from social interaction in different cultural environments or the educational system, which can vary dramatically from country to country in terms of both degree of education and educational focus. The second difference is derived from the individual firms’ technology, the ability to adapt that technology to a foreign workplace. Firms are heterogeneous with respect to labor productivity in the home market, and this is based on their firm specific technology. Some technologies may be more productive than others in a foreign workplace, and may not differ in the same way as in the home country (i.e. more productive technologies in the home market are not necessarily more productive in the foreign market). 2 Current theory suggests that FDI should be undertaken at much higher levels than is seen in the data. In their 2002 paper Rodrik and Hausmann [3] suggest that industrial investment is lower than expected due to incomplete information. Entrepreneurs do not know what they are good at producing. In section 4 the concept is expanded to evaluate firm’s FDI decisions when they do not know their foreign productivity. Increases in uncertainty lead to the underprovision of FDI under certain conditions. Generally the spillovers from FDI make it a very appealing method to developing countries to promote economic growth. However, the means of encouraging FDI continue to elude policy makers. Traditionally countries have been urged to follow free market policies in order to increase growth. Countries which have resisted this open economy push in the short run, like South Korea and Taiwan, saw strong growth, while countries making the requisite open economy changes, like Brazil or Argentina, have not. Assymetric information also suggests a reason why, when FDI does occur, it often clusters in a few select industries, often quite different between countries. For example, Bangladesh has a large concentration of hat and pant producers, Columbia cut flowers, and India software design. If firms learn about the productivity of their industry from other firms’ investment decisions, then the effects of assymetric information are decreased for that industry. In section 1 I’ll look at what has been done in the FDI literature, and where my paper differs. Then in section 2 the basic model is introduced and the autarkic equilibrium is outlined. The model is extended to two countries, and the complete information case is identified in section 3. In section 4 some effects of incomplete information are outlined. Finally in section ?? the policy implications of differing productivities and incomplete information are explored. 1 Background There have been many models that determine how a firm decides on type and level of FDI. However, few have explained the underinvestment in developing 3 countries, where differences in factor prices would suggest much higher levels of investment. Models that have attempted to explain this gap used a variety of econometric and analytic methods to create the asymmetries. Nocke and Yeaple [7] set up an econometric test of a firm’s decision between FDI through greenfield investment and FDI through cross-border acquisition, allowing countries to have different levels of development, evidenced by their factor prices. They find that both the efficiency of the firm and the level of development of the recipient country affect the choice of FDI. Markusen and Wigle [5] look at ’explaining the volume of North-South trade’. They use the hypotheses of high protectionism in the south and economic size to explain the levels of trade, and conclude that without these barriers the level of North-South trade would be higher than North-North trade. Using a different angle, Grossman and Helpman [2] look at the decision between outsourcing and FDI where the level of monitoring in outsourcing contracts is country specific, and there is a wage differential between the home and foreign countries. They find that countries with lower levels of monitoring receive fewer outsourcing contracts. The hypothesis in this paper is that although trade costs and country size do play important roles in a firm’s FDI decision, the presence of incomplete information explains more of the gap between expected and actual FDI, and also helps explain the existence of industry-clusters within a country. In terms of information asymmetries, there have been a variety of different approaches to FDI and uncertainty. Rob and Vettas [8] look at the decision to invest in FDI when there is demand uncertainty in the recipient country. As with most FDI papers, they look at FDI as a choice between exporting to a foreign market, and setting up a subsidiary to serve that foreign market. Horstmann and Markusen [4] incorporate uncertainty as to the consumer’s perception of the firm’s quality. By incorporating firm-specific reputation assets, they study the firm’s decision between outsourcing, exporting and FDI. The uncertainty leads to a higher than expected probability of choosing FDI to serve the foreign market. Helpman, Melitz and Yeaple [1] explore the choice between export and FDI 4 with heterogeneous firms. Every firm faces the decision of whether or not to serve a foreign market, and whether to serve it through FDI or exporting. Their framework suggests that heterogeneity in productivity determines the firms’ FDI decisions, the least productive produce domestically and serve the domestic market only, more productive firms export to the foreign market and the most productive firms set up subsidiaries in the foreign market. However they do not allow for differences in productivity between the two countries. The strength of their paper lies in its empirics, where they use firm level data to show the predicted link between firm-level heterogeneity and the ratio of exports to FDI sales. Although not an FDI paper, Rodrik and Hausmann [3] explain why Latin America has not experienced the growth that Asia has, although Latin America has made more attempts to follow the growth-creating policies suggested by development economists. They use a two sector model with a traditional and a modern sector, and allow uncertainty to enter in the production functions of the goods in the modern sector. They conclude that uncertainty can lead to too little investment and entrepreneurship, but once firms have invested there is too much product variety in the market, as unproductive firms stay in once the sunk costs are committed. Empirically they look at three ’building blocks’ for their argument, i) large element of uncertainty as to what a country will be good at producing, ii) significant difficulties entailed in importing technology off-the-shelf, with many changes required for local adaptation, iii) imitation follows quickly once the first two blocks are overcome. 2 Model Overview Using a two country, general equilibrium model, the effects of differences in factor prices, incomplete information, and heterogeneity in productivity levels on the decisions of the firm is outlined. For this paper I concentrate on trade between a developed country (the home country), and a less developed country 5 (the foreign country). The foreign country spends a smaller amount of money on the heterogeneous good industries, and may have lower wages. There are M industries in the world. In each mM industry a modern good is produced, of which an infinite number of varieties are available for production. For ease of analysis we assume each firm employs labour as the sole factor of production. In each industry the set of varieties being sold in country c’s market is denoted as V c . Each firm in the industry thus produces a variety vV c . Each firm produces output by the following production function: Yic = Lci ãci (1) where Yic is the output of firm i in country c, Lci is the labour hired by firm i in country c, ãci is the productivity of firm i in country c and 1/ãci is the number of workers required by firm i in country c to produce one unit of output. ãci is then referred to as the firm’s productivity in terms of output units produced per unit of labour. Letting wc indicate the wage in country c. aci = ãci wc (2) Now aci represents the output units produced per dollar and is henceforth referred to as the firm’s productivity in country c. Consumer Preferences Consumers in both countries have CES preferences, represented by the log utility function: u = (1 − M X βm ) log(z) + m=1 Z M c X βm log( xm (v)αm dv) α c m vVm m=1 (3) Where xm (i) is the consumption of variety i (from firm i) in sector m, and Vmc is the set of all firms in sector m selling their good in the country c. The elasticity of substitution is ε = 1 1−α . It is assumed that ε is greater than one, and in section 4 it is assumed that ε lies between one and two. The proportion 6 of income spent on goods in sector m is fixed at βm and Σm βm = 1. From these preferences we find that the demand for good i in sector m is xcm (i) = R V c 0 βm E c pc (v)1−ε dv pc (i)−ε (4) and the monopolistic firm producing in country c will offer their good in country c at price pcc (i) = (aci α)−1 . A firm producing in country c exporting their good for sale in country ¬c will offer their good at price pc¬c (i) = τ c¬c (aci α)−1 . E c is the income of country c and τ c¬c represents the iceberg transport costs of shipping a good from country c to country ¬c, and τ c¬c = τ ¬cc = τ > 1. This gives us the following profit for a firm producing in country c and serving country c: π cc = (1 − α)(ac α)ε−1 Ac (5) And for a firm producing in country c and serving country ¬c π c¬c = (1 − α)(ac α)ε−1 A¬c τ 1−ε (6) Each firm faces fixed costs from three different sources. First, they must pay fe to enter the industry, after which they draw their productivity ac from the distribution G(a). Then, if they choose to produce, they bear fixed costs fp for each plant location. Finally, they must pay distribution costs fx for each market they wish to sell their good in. Autarkic Equilibrium We begin by looking at the equilibrium in the home country, assuming the home country is currently in an autarkic equilibrium, with no firms exporting to or operating in the foreign country. Following Melitz (2003) [6] the firms are heterogeneous with respect to their productivity in the home country. Firms that are currently producing goods know their productivity in the home country, and firms that are not currently producing know the distribution of productivities they could draw from, were they to enter the market. Each industry consists 7 of an equilibrium determined number of heterogeneous firms, differentiated by their productivity levels. Firm i producing at home has productivity ahi Because the firm’s only option is to produce for the domestic market or not produce, we only have one cutoff point ah∗ i 1 above which it will be profitable to produce, and below which the firm will choose not to produce. Given the cutoff we can determine whether or not the firm will choose to pay fe and draw a productivity. Because we are summing over the prices of all firms in the sector, an increase in the number of firms decreases the expected profits of a potential entrant, so firms will continue to enter until the expected profits reach zero, noting that the cutoff point, ah∗ is increasing in the number of firms in the market. From there, given the fixed entry costs fe we can determine how many firms will serve the home market under autarky (na ). Export Equilibrium If we open up the foreign country, and allow the firms producing in the autarkic equilibrium in the home country to start exporting to the foreign country, firms now have three options: a1 do not produce, a2 produce in the home country and serve the home market only, a3 produce in the home country and serve both the home and foreign market. It is assumed that the foreign country is sufficiently small 2 so it will never be optimal to produce in the home country and serve only the foreign market. There are a number of reasons why at some point in time a foreign country may ’open up’. It may be that previously it was simply too expensive to export to that market (τ was too large). This encompasses both trade restrictions (tariffs) or transport costs. A decrease in transport costs or tariffs could lead to the foreign country suddenly being attractive to home firms. Another reason could be the size of the foreign market. If the foreign economy is growing, 1 (ah∗ )ε−1 = fx +fp (1−α)Ah αε−1 where Ah = R V h βE h ph (v)1−ε dv 2 β f E f is sufficiently small, so it could mean that they have a lower GDP or that they spend a smaller amount of their income in that specific industry 8 at some point home firms will choose to export to the foreign market to take advantage of the growth in income. Using the firm’s payoffs from each possible action we get the following productivity cutoff points: ah1 = ah2 = fp + fx (1 − α)Ah αε−1 fx (1 − α)Af τ 1−ε αε−1 Once a firm has drawn a productivity level, they will not produce if ah < ah1 , will produce and only serve the home market if ah1 < ah < ah2 and will produce and serve both the home and foreign markets if ah > ah2 . Compared to the autarkic equilibrium, the expected profit from entering the market is higher because the firms retain the payoff from serving the home market, plus get profits from serving the foreign market. As a result, more firms will now enter the market. Thus if firms are allowed to export their products to a foreign market, the number of firms, ne , producing in the home market in equilibrium will be higher. 3 Benchmark Model In the benchmark model we look at two countries. The home country is currently operating in an export equilibrium in industry m, and there are (ne ) firms producing and selling their good in the home market. There are no firms in industry m producing in the foreign country although they may be exporting their goods to the foreign market. Now firms have six possible actions (given their home and foreign productivities) 3 . 3 assuming that the foreign market is sufficiently small, producing at home only for the foreign market, and producing only in the foreign country for only the foreign market will f +f never be optimal. Algebraically this requires Af < τ ε−1 Ah xf p x 9 • a1 = do not produce • a2 = produce in the home country and serve the home market only • a3 = produce in the home country and serve both the home and foreign markets • a5 = produce in the foreign country and serve the home market • a6 = produce in the foreign country and serve both the home and foreign markets • a8 = produce in the home country and the foreign country to serve their respective markets Given these actions and the firm’s profit function (equations (5) and (6)), we can determine the optimal actions for any set of productivities {ah , af }. If the foreign market is sufficiently small4 , it may be profitable to produce in the foreign market and not serve the foreign market. For example, Banana Republic makes many of its items in the Philippines, but does not sell its goods 4 Af fx x +fp < Ah τ 1−ε f 10 in the Philippines. This is even more apparent in input goods, where a firm that produces inputs for another industry may choose to produce some of their components in a foreign country, even though there are no firms that demand their good in the foreign market. Looking at figure 1, the optimal actions for each possible set of productivities are outlined. If the firm is relatively unproductive ({ah , af } are sufficiently close to zero) then the firm will choose not to produce in either country. As ah increases the firm chooses to produce in the home country, serving the home market, and as ah continues to increase, they will produce in the home market and export to the foreign market. If af is increasing, and the foreign market is sufficiently small, the firm may go from not producing to producing in the foreign market and only serving the home market, to producing in the foreign market and serving both market. If both home productivity and foreign productivity are sufficiently large the firm may choose to produce in both the home and foreign markets, serving their respective markets. If we allow the firm’s foreign productivity to be a linear transformation of their home productivity (for all home productivity levels), we can see the effects of differences in wage, or in human capital levels. If the number of workers required to make one unit of output is the same in both the home and foreign countries, then the only differentiating factor would be the wage. Allowing (af )ε−1 = c(ah )ε−1 , if the productivity levels were the same in both countries, but the wages were different, c would simply equal wh . wf If we had factor price equalization, where wages counteracted any difference in productivity, c would equal one. The concept of comparative advantage suggests that relative productivities across industries may differ from country to country. We could then denote the industry specific productivity difference as cm . If the home country had a comparative advantage in industry i and the foreign country had a comparative advantage in industry j then cj > ci . Looking at a firm in industry i (but dropping the subscript) with both the large foreign market and the small foreign market, as c grows the firm becomes 11 increasingly likely to engage in FDI. However, because we assume that fixed costs are the same in both countries the firm’s actions depend largely on shipping costs. If c < τ 1−ε no firms will produce in the foreign country. This is because the increased costs of production are greater than the savings from no longer shipping to the foreign market, even for the most productive firms. For any values of c between τ 1−ε and τ ε−1 the firm will decide between producing at home, and producing in the foreign country based on their productivity level at home. As their home productivity level increases they are more likely to produce in the foreign country. Finally, if c > τ ε−1 all firms will produce in the foreign country. In this case the lower cost of production in the foreign country outweighs the cost of shipping the products from the foreign country to the home market even for the least productive firms. In the benchmark model there will be more weakly more firms producing in equilibrium than in the export equilibrium. Assuming that all firms know the transformation from ah to af then they just have to pay fe once, to determine their productivity levels in both countries. Allowing c to vary across productivities (firms then know c(ah ) for all possible ah ), if c(ah ) < τ 1−ε for all ah then the equilibrium will be the same as the export equilibrium. If c(ah ) > τ ε−1 for all values of ah once the foreign country is open to FDI all firms will choose to produce in the foreign country, profits then must be higher than under the export equilibrium (given the distribution of ah ), so the expected profits would be higher with only ne firms in the market, so there must be more than nE firms in the market. More generally, if c(ah ) > τ 1−ε for some value of ah then the expected profits are weakly greater than in the export equilibrium for all firms, and there will be weakly more firms producing. In terms of comparative advantage and gains from trade, if the productivity gain is great enough, all firms in an industry will produce in the foreign country. Likewise, if there is no productivity gain all firms will produce in the home country, and only the most productive firms will produce in the foreign country for the foreign market (in order to save the shipping costs). Opening up the foreign economy to imports from the home country will always result in more 12 firms producing in the home country. Further opening up the foreign economy to FDI may result in additional firms producing, but where the firms choose to produce depends on the relative productivity of the foreign country to the home country. The size of the comparative advantage will determine the equilibrium structure. 4 Incomplete Information In many cases a firm may not be able to infer their foreign productivity from their home productivity. Instead they may have some beliefs about the distribution of the productivity, where the cdf of their beliefs is G(af |ah ) and G0 (af |ah ) = g(af |ah ). We assume that this cdf is common knowledge. Assumption If ahi > ahj then G(af |ahi ) < G(af |ahj ). If firm i’s productivity at home is higher than firm j’s productivity at home, then firm i’s expected productivity in the foreign country must first order stochastically dominate firm j’s. So if a firm is less productive in the home country, ex-ante they expect to be less productive in the foreign country as well. Now firms must choose whether or not to invest in the foreign country based on the expectation of their productivity in the foreign country and their beliefs about the distribution of that productivity. They must also choose whether or not to serve the foreign market when producing in the foreign country, and whether or not to close their home country production facilities when producing abroad. If a firm is already operating in the home country, their expected profits for each action are now a function of the expected distribution of productivity levels in the foreign country, and can be written as follows: (a1 ) Do not produce at home or in the foreign market: π=0 13 (7) (a2 ) Produce at home and serve the home market: π hh − fx − fp = Ah (1 − α)(ah )ε−1 αε−1 − fx − fp (8) (a3 ) Produce at home and serve both the home and foreign markets: π hh + π hf − 2fx − fp = Ah (1 − α)(ah )ε−1 (Ah + Af τ 1− )αε−1 − 2fx − fp (9) (a5 ) Produce in the foreign country and serve the home market (Only optimal if home productivity is sufficiently low, and the foreign market is sufficiently small): R af2 π fh h 1− − fx − fp = (1 − α)(A τ )α f ε−1 a1 aε−1 g(a|ah )da G(af2 ) − G(af1 ) − fx − fp (10) (a6 ) Produce in the foreign country and serve both the home and foreign markets: R∞ π fh +π ff − 2fx − fp = (1 − α)α ε−1 h 1− (A τ f +A ) af2 aε−1 g(a|ah )da 1 − G(af2 ) − 2fx − fp (11) (a8 ) Produce at home and serve the home market and produce in the foreign country to serve the foreign market (Only optimal if home productivity is sufficiently high): hh ff ε−1 π +π −2(fx +fp ) = (1−α)α Ah (ah )ε−1 +Af R af2 aε−1 g(a|ah )da −2(fx +fp ) G(af2 ) − G(af0 ) (12) af0 Choosing between a1 , a2 and a3 depend solely on the firm’s home productivity (ah ) and exogenous variables, specifically the size of the home and foreign markets, and the fixed costs. The payoffs from actions a4 , a6 and a8 depend on the distribution of foreign productivities, G(af |ah ). 14 Looking back at figure 1, we can identify three ranges of home productivity which involve firms putting positive weights on one or two of the foreign production actions {a5 , a6 or a8 }. The first range is if the foreign market is sufficiently small, and home productivity is sufficiently low ((ah )ε−1 < fx τ 1−ε ) Af (1−α)αε−1 x Af < Ah τ 1−ε fxf+f p In this case the firm will not produce in the foreign country if af < af1 , where af1 is a function of the firm’s home productivity. They will produce in the foreign country, only serving the home market if af1 < af < af2 and will produce in the foreign country serving both markets if af > af2 . The second range involves moderate levels of home productivity. Here the firm will not produce in the foreign country if af < af2 and will produce in the foreign country, serving both markets (action a6 ), otherwise. In this case af2 is a function of the firm’s home productivity. The final range is sufficiently high levels of (ah )5 . In this case the firm will choose action a8 , produce in both countries, serving both markets, if af0 < af < af2 , and will choose action a6 , produce only in the foreign country, serving both markets, if af > af2 . Here both af0 and af2 are functions of the firm’s home productivity. If the foreign country is sufficiently large, then only the second and final ranges will be applicable (whenever the firm is producing in the foreign market they will also want to serve the foreign market). Assumption ε[1, 2] The elasticity of substitution, ε, is assumed to be between one and two. This is a common macroeconomic assumption, and in this case it implies that profits are concave with respect to productivity. 5 (ah )ε−1 > fp Ah τ 1−ε +Af (1−α)αε−1 Ah Af (τ ε−1 −τ 1−ε ) 15 Assuming that the fixed cost of drawing your productivity in the foreign country is the same as in the home country (fe ), a firm currently producing in the home market has two options: draw (and pay fe ) or don’t draw and limit their action set to {a1 , a2 , a3 }. If the firm draws they can then choose from actions {a1 , a2 , a3 , a5 , a6 , a8 }. When deciding whether or not to draw the firm looks at the expected payoff from drawing (the probability of a5 , a6 or a8 being optimal multiplied by the payoff less the optimal action had the firm chosen not to draw the foreign productivity)), and if it’s higher than fe the firm will draw. As the number of firms who draw their foreign productivity grows, the number of firms producing in the foreign country will also grow, and expected profits will decrease until the market is in equilibrium. However, it’s not necessarily true that firms with higher home productivity are more likely to draw their foreign productivity. If they are more productive at home the gains from drawing the foreign productivity may be lower, dependent upon the distribution G(af |ah ) If the first moment of the distribution increases less than proportionally with home productivity (E(af |ah ) is a concave function of ah ) then the more productive a firm is, the lower their expected profit from drawing a foreign productivity (because their opportunity cost is higher). As a result, the equilibrium could consist of only the firms that are less productive at home producing in the foreign country. Using backwards induction, if a firm is not currently producing in the home country, the expected profit from drawing a home productivity level (given the set of all actions) must be weakly greater than that in the export equilibrium. As a result, with incomplete information we would expect to see more firms active in equilibrium than in the export equilibrium. Given certain distributions, G, we could see fewer firms than in the complete information model, as the uncertainty may decrease the expected profits, leading fewer firms to draw their foreign productivity. Some distributions G yield an equilibrium where only the more unproductive home firms will draw their foreign productivity, yielding a weakly less productive foreign market than a complete information equilibrium. 16 Looking at this model from a development perspective, it is unclear whether incomplete information decreases FDI. However, it is clear that certain distributions yield unsavory results, and there are equilibriums where only the less productive firms produce in the foreign market. 17 References [1] M. J. M. Elhanan Helpman and S. R. Yeaple. Export versus fdi with heterogeneous firms. American Economic Review, 94(1):300, 2004. [2] G. M. Grossman and E. Helpman. Outsourcing versus fdi in industry equilibrium. Journal of the European Economic Associaton, 1(2), 2003. [3] R. Hausmann and D. Rodrik. Economic development as self-discovery. NBER Working Paper, 8952, May 2002. [4] I. J. Horstmann and J. R. Markusen. Licensing versus direct investment: A model of internalization by the multinational enterprise. Canadian Journal of Economics, 20(3):464, 1987. [5] J. R. Markusen and R. M. Wigle. Explaining the volume of north-south trade. Economic Journal, 100(403):1206, 1990. [6] M. J. Melitz. The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica, 71(6):1695, 2003. [7] V. Nocke and S. Yeaple. An assignment theory of foreign direct investment. NBER Working Paper, 11003, 2004. [8] R. Rob and N. Vettas. Foreign direct investment and exports with growing demand. Review of Economic Studies, 70(3):629, 2003. 18