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American Economic Review 2008, 98:5, 1978–1997 http://www.aeaweb.org/articles.php?d=10.1257/aer.98.5.1978 Trading Tasks: A Simple Theory of Offshoring By Gene M. Grossman and Esteban Rossi-Hansberg* We propose a theory of the global production process that focuses on tradeable tasks, and use it to study how falling costs of offshoring affect factor prices in the source country. We identify a productivity effect of task trade that benefits the factor whose tasks are more easily moved offshore. In the light of this effect, reductions in the cost of trading tasks can generate shared gains for all domes- tic factors, in contrast to the distributional conflict that typically results from reductions in the cost of trading goods. (JEL F11, F16) The nature of international trade is changing. For centuries, trade mostly entailed an exchange of goods. Now it increasingly involves bits of value being added in many different locations, or what might be called trade in tasks. Revolutionary advances in transportation and communica- tions technology have weakened the link between labor specialization and geographic concentra- tion, making it increasingly viable to separate tasks in time and space. When instructions can be delivered instantaneously, components and unfinished goods can be moved quickly and cheaply, and the output of many tasks can be conveyed electronically, firms can take advantage of factor cost disparities in different countries without sacrificing the gains from specialization. The result has been a boom in “offshoring” of both manufacturing tasks and other business functions. 1 In this paper, we develop a simple and tractable model of offshoring based on the trade- able tasks. We conceptualize production in terms of the many tasks that must be performed by each factor of production. A firm can perform each of the continuum of tasks required for the realization of its product either in close proximity to its headquarters or at an offshore location. Offshoring may be attractive, if some factors can be hired more cheaply abroad than at home, but it also is costly, because remote performance of a task limits the opportunities for monitoring 2 and coordinating workers. To capture this aspect of reality, our model features heterogeneous offshoring costs for the various tasks. In each industry, firms choose the geographic organization * Grossman: Department of Economics, Princeton University, Princeton, NJ, 08544 (e-mail: grossman@princeton. edu); Rossi-Hansberg: Department of Economics, Princeton University, Princeton, NJ, 08544 (e-mail: erossi@princ- eton.edu). The authors are grateful to David Autor, Richard Baldwin, Donald Davis, Jonathan Eaton, James Harrigan, Elhanan Helpman, Kala Krishna, Per Krusell, Frank Levy, Marc Melitz, Daniel Müller, Torsten Persson, Michael Pflüger,StephenRedding,RichardRogerson,DanielTrefler,andtwoanonymousrefereesforhelpfulcommentsandsug- gestions. They acknowledge with thanks the support of the National Science Foundation (SES 0211748, SES 0451712, and SES 0453125). Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation or any other organization. 1Theglobaldisintegrationoftheproductionprocesshasbeen documented by José M. Campa and LindaS. Goldberg (1997), David Hummels, Dana Rapoport and Kei-Mu Yi (1998), Alexander J. Yeats (2001), Hummels, Jun Ishii, and Yi (2001), and Gordon H. Hanson, Raymond J. Mataloni, and Matthew J. Slaughter (2001, 2005), among others. 2 Several authors have sought to identify the characteristics of tasks that are good candidates for offshoring. For example, Frank Levy and Richard Murnane (2004) have distinguished “routine” and “nonroutine” tasks, following the lead of David Autor, Levy, and Murnane (2003). Edward E. Leamer and Michael Storper (2001) draw a similar distinc- tion between tasks that require “codifiable” versus “tacit” information. Alan S. Blinder (2006) emphasizes, instead, the need for physical contact when delivering the output of a task. See also Pol Antràs, Luis Garicano, and Rossi-Hansberg (2006), who develop a theory in which the offshoring of certain types of tasks is an equilibrium outcome. 1978 VOL. 98 NO. 5 GROssmAN ANd ROssI-HANsBERG: TRAdING TAsks 1979 of their production to minimize costs. The equilibrium conditions determine the extent of off- 3 shoring in each industry, a continuous variable in our model. Our treatment of offshoring could be applied to a variety of settings with different numbers of goods and factors, production technologies, and market structures. To keep matters simple, we develop the model with at most two active industries, two or more factors of production, constant returns to scale, and perfectly competitive markets. We begin in Section I by allowing remote performance only of the tasks undertaken by low-skilled workers, while permitting such tasks to be conducted offshore in all industries. We introduce a parameter that describes the prospects for offshoring. Reductions in this parameter represent improvements in communication and trans- portation technology that reduce proportionally the cost of offshoring all tasks performed by low-skilled labor. With this parameterization, we can address an important and topical question, namely: how do improvements in the opportunities for offshoring affect the wages and well- being of different types of labor? The rendering of a firm’s geographic organization as a continuous variable permits a useful decomposition of the impact of an economy-wide decrease in offshoring costs on the wages of low-skilled workers. In general, a fall in the cost of separating low-skill tasks induces a produc- tivity effect, a relative-price effect, and a labor-supply effect on low-skill wages. The productiv- ity effect derives from the cost savings that firms enjoy when prospects for offshoring improve. This effect—which is present whenever the difficulty of offshoring varies by task, and task trade is already taking place—works to the benefit of low-skilled labor. A relative-price effect occurs when a fall in offshoring costs alters a country’s terms of trade. The relative price of a good moves opposite to the change in its relative world supply. Such price movements are mirrored by movements in relative cost and have implications for wages that are familiar from traditional trade theories. Finally, the labor-supply effect operates in environments in which factor prices respond to factor supplies at given relative prices. This effect derives from the reabsorption of workers who formerly performed tasks that are now carried out abroad. After developing our decomposition in Section II, we proceed to examine each of the effects in greater detail. Section IIA highlights the productivity effect by focusing on a small economy that produces two goods with two factors. In such an environment the terms of trade are fixed and wages do not respond to factor supplies, which leaves the productivity effect as the only remaining force. We show that improvements in the technology for offshoring low-skill tasks are isomorphic to (low-skilled) labor-augmenting technological progress and that, perhaps sur- prisingly, the real wage for low-skilled labor must rise. We contrast the effect of offshoring and immigration and argue that the latter will not result in a productivity effect. In Section IIB and IIC, we introduce the relative-price effect and the labor-supply effect by analyzing first a large two-sector economy and then an economy in which the high-wage country specializes in the production of a single good. We show that the productivity effect is small when the range of offshored tasks is small, but it can outweigh the other effects when the volume of task trade is large. In Section III, we extend the model to include the possibility of offshoring tasks that require high-skilled labor. Here we identify another productivity effect, this one favor- ing high-skill workers. Much has been written recently about offshoring. Part of this literature focuses on a firm’s choice of organizational form. Although this is an interesting problem, the models used to 3In this respect, our model resembles those in which goods are produced by a continuum of “stages of production,” such as Avinash K. Dixit and Grossman (1982), Robert C. Feenstra and Hanson (1996), Yi (2003), and Wilhelm Kohler (2004b). However, none of these authors associates a production stage with a particular factor of production, and none allows heterogeneous trading costs or stages that can be separated from the partially processed good. 4See, for example, John E. McLaren (2000), Grossman and Helpman (2002, 2004, 2005), Antràs (2003), Dalia Marin and Thierry A. Verdier (2003a, 2003b), Antràs and Helpman (2004), and Antràs, Garicano, and Rossi-Hansberg (2006). 1980 THE AmERIcAN EcONOmIc REVIEW dEcEmBER 2008 address it tend to be complex, incorporating imperfect information and subtle contracting or matching problems, and so the general equilibrium structure has been kept to a bare minimum. Another strand of literature, closer in spirit to this paper, models “fragmentation” of the pro- duction process. This has been conceived as the breakdown of technology for producing some good into discrete parts that can be separated in space. The effects of such fragmentation hinge critically on the industry in which it occurs and the factor intensities of the fragments. A useful taxonomy has emerged, with a myriad of interesting possibilities, but general principles have been obscure. By treating offshoring as a continuous and ubiquitous phenomenon, we are able to synthesize this literature and lay bare its unifying principles. Another related literature examines globalization in models with tradeable intermediate inputs. The distinction between “tasks” and “intermediate inputs” is largely semantic, but our incorporation of heterogeneous trade costs distinguishes our analysis from these earlier papers. The assumption of uniform (or zero) costs of trading intermediate goods has led the authors of these studies to overlook the positive pro- ductivity effect. In sum, our paper makes two distinct contributions. First, it provides a simple and tractable model of offshoring that can be used for many purposes. By modeling the production process as a continuum of tasks, we are able to provide a novel decomposition of the effects of a fall in offshoring costs. Our second contribution is to uncover the productivity effect and to show that this effect is analogous to factor-augmenting technological change. We characterize this effect fully and show that it typically grows with the volume of offshoring. I. The Model We conceptualize the production process in terms of tasks. Each task requires the input of some single factor of production. Some tasks can be performed by workers who have relatively little education or training, while others must be performed by workers who have greater skills. We refer to the former as “L-tasks” and the latter as “H-tasks.” There may be still other tasks that are performed by other factors of production such as capital or additional categories of labor. Firms in the home country can produce two goods, X and Y, with constant returns to scale. The production of a unit of either good involves a continuum of L-tasks, a continuum of H-tasks, and possibly other sets of tasks as well. Without loss of generality, we normalize the measure of tasks in each industry that employ a given factor of production to equal one. Moreover, we define the tasks so that, in any industry, those that can be performed by a given factor require similar amounts of that factor when performed at home. In other words, if L-tasks i and i9 are under- taken at home in the course of producing good j, then firms use the same amount of domestic low-skilled labor to perform task i as they do to perform task i9. The industries may differ in their factor intensities, which means, for example, that a typical L-task in one industry may use a greater input of domestic low-skilled labor than an L-task in the other industry. 5See, for example, Ronald W. Jones and Henryk Kierzkowski (1990, 2001), Alan V. Deardorff (2001a, 2001b), Hartmut Egger and Josef Falkinger (2003), and Kohler (2004a). Kohler (2004b) incorporates a continuum of fragments, but assumes uniform trading costs and allows fragmentation in only one industry. 6See, for example, Feenstra and Hanson (1996) and Yi (2003). 7Jones and Kierzkowski (1990, 2001), Sven W. Arndt (1997), Egger and Falkinger (2003), and Kohler (2004a, b) have recognized the analogy between fragmentation of the production process in some industry and technological progress in that same industry. Egger (2002) allows fragmentation in both sectors of a two-sector economy and points out the possibility of Pareto gains from an expansion of offshoring when the two sectors experience similar cost sav- ings. These authors have not provided a natural framework to treat economy-wide offshoring and so have not drawn the con8ection we do between offshoring and factor-augmenting technological change. If one task needed to produce some good requires twice as much labor as another, we can always consider the former to be two tasks when assigning indexes to the tasks. VOL. 98 NO. 5 GROssmAN ANd ROssI-HANsBERG: TRAdING TAsks 1981 Itiseasiesttodescribetheproductiontechnologyforthecaseinwhichsubstitutionbetweenthe different tasks is impossible. We begin with this case and introduce the opportunities for offshor- ing. Then we return to the issue of task substitution and describe a more flexible technology. If a production technology admits no substitution between factors or tasks, then each task must be performed at a fixed intensity in order to produce a unit of output. That is, each of the unit measures of L-tasks must be performed exactly “once” in order to produce a unit of output of good j, and similarly for each of the H-tasks and each of any other types of tasks that are part of the production process. In industry j, a firm needs a units of domestic factor f to perform a fj typical f-task once. Since the measure of f-tasks has been normalized to one for f 5 5L,H,….6, afjlso is the total amount of domestic factor f that would be needed to produce a unit of good j in the absence of any offshoring. We will take industry X to be relatively skill intensive, which means that a /aHx a Lx . Hy Ly Firms can undertake tasks at home or abroad. Tasks can be performed offshore either within or beyond the boundaries of the firm. Much of the recent literature on offshoring distinguishes between firms that are vertically integrated and those that contract out for certain activities. There are many interesting questions about firms’ choices of organizational form, but we shall neglect them here for the sake of simplicity. Rather, we assume that a firm needs the same amount of a foreign factor whether it performs a given activity in a foreign subsidiary or it out- sources the activity to a foreign supplier. In either case, the factor requirement is dictated by the nature of the task and by the firm’s production technology. As we noted in the introduction, some tasks are more difficult to offshore than others. The cost of offshoring a task may reflect how difficult it is to describe using rules-based logic, how important it is that the task be delivered personally, how difficult it is to transmit or transport the output of the activity, or all of the above (and more). For our purposes, we simply need to recognize these differences, as we take the costs of offshoring the various tasks to be exogenous. For the time being, we focus sharply on the offshoring of tasks performed by low-skilled labor by assuming that it is prohibitively costly to separate all other tasks from the headquarters. We will examine the offshoring of high-skill tasks in Section III. We index the L-tasks in an industry by i [ 30,14 and order them so that the costs of offshoring are nondecreasing. A simple way to model the offshoring costs is in terms of input requirements: a firm producing good j that performs task i abroad requires a bt 1i2 units Lj fjreign labor, where b is a shift parameter that we will use in Section II and beyond to study improvements in the technology for offshoring. We assume that t 1·2 is conjinuously differentiable and that bt ji2 $ 1 for all i and j. Our ordering of the tasks implies that t91i2 j 0. In the main text we will go further in taking this schedule to be strictly increasing, because this simplifies the exposition considerably. The appendix in Grossman and Rossi-Hansberg (2006) takes up the case in which the schedule has flat portions. 10 Which industry finds it easier to move its L-tasks offshore? Note that this question is different from asking whether it is easier to offshore tasks performed by low-skilled workers or high- skilled workers. The two industries may share a set of common L-tasks—such as data entry, call center operations, and simple record-keeping and inventory control—for which the costs of offshoring are similar. Other tasks performed by low-skilled labor may differ across industries, 9 We place quotation marks around “once,” because there is no natural measure of the intensity of task performance. 10The t 1·2 schedule has a flat portion when a finite measure of tasks is equally costly to trade. On the one hand, this would seem possible in light of footnote 8, where we note that the “same” task may receive multiple indexes in order that all tasks use the same amount of a factor. On the other hand, if tasks are perfectly divisible into finer subtasks that are not exactly the same, then it may be plausible to assume that all finite measures of tasks bear slightly different offshoring costs. 1982 THE AmERIcAN EcONOmIc REVIEW dEcEmBER 2008 but we know of no evidence to suggest that such tasks can more readily be moved offshore in labor-intensive sectors than in skill-intensive sectors (or vice versa). Indeed, improvements in transportation and communications technology have spurred the rapid growth of offshoring in a wide range of sectors. For this reason, we take as our benchmark the case in which offshoring costs are similar in the two industries, i.e., t 1x2 5 t 1iy 5 t1i2. But we will briefly address other possibilities in Section IIA. We return now to the issue of factor and task substitution. Our framework can readily accom- modate substitution between L-tasks and H-tasks (or tasks that use other factors) and substitution among the tasks that use a particular factor. But, to keep matters simple, we introduce only the 11 former type of substitution in this paper. The production technology may allow a firm to vary the intensities of L-tasks and H-tasks (and any other tasks) that it performs to produce a unit of output. For example, a firm might conduct the set of assembly (L) tasks repeatedly and oversight (H) tasks rarely, and thereby accept a relatively low average productivity of low-skilled labor, or it might conserve on assembly tasks by monitoring the low-skilled workers more intensively. The intensity of task performance is captured in our framework by the amount of the domestic factor that is used to perform a typical task at home. When substitution between L-tasks and H-tasks (and any others) is possible, a and a become choice variables for the firms, who select these Lj Hj variables to minimize cost subject to a constraint that the chosen combination of task intensities are sufficient to yield a unit of output. A firm that chooses a for the intensity of its L-tasks must Lj 12 employ a btLj2 units of foreign labor to perform task i offshore. We are ready to describe an equilibrium with trade in goods and tasks. Let w and w be, * respectively, the home and foreign wage of low-skilled workers, and suppose that w . bt102w , * so that it is profitable for home firms to conduct some tasks abroad. Home firms offshore L -tasks in order to take advantage of the lower foreign wage, but they bear an administrative cost for doing so that varies with the nature of the job. In each industry, the marginal task performed at home has the same index I, which is determined by condition that the wage savings just balance the offshoring costs, or (1) w 5 bt1I2w . * In a competitive economy, the price of any good is less than or equal to the unit cost of produc- tion, with equality whenever a positive quantity of the good is produced. The unit cost of produc- ing good j is the sum of the wages paid to domestic low-skilled labor, the wages paid to foreign labor for tasks performed offshore, the wages paid to domestic skilled labor for the unit measure of H-tasks, and the payments to any other factors of production. Considering firms’ optimal choices of intensity a ,Lj , Hjc., and the optimal offshoring of L-tasks, we have I (2) p j# wa 1·Lj1 2 I2 1 w a 1·2 btLj2 d3 1 sa 1·2 1 …, Hj for j 5 x,y, 0 where s denotes the high-skill wage, and the arguments in the function for the factor intensity aFjwhich have been suppressed for the time being) are the relative costs of the various sets of tasks when they are located optimally. Notice that the wage bill for domestic low-skilled labor reflects the fraction 1 2 I of L-tasks that are performed at home and that the wage bill for foreign 11Substitution among the tasks that use a particular factor could be introduced by assuming that such tasks generate an aggregate input that might, for example, be modeled as a constant-elasticity-of-substitution function of the intensity with which each task is performed. Qualitative results similar to those derived here will apply whenever the substitution among tasks using a given factor is less than perfect. 12Throughout the paper we assume that the characteristics of a given task do not vary depending on where the task is performed. Hence, foreign and local tasks of a given type are perfect substitutes in production. VOL. 98 NO. 5 GROssmAN ANd ROssI-HANsBERG: TRAdING TAsks 1983 low-skilled workers includes the costs of the “extra” inputs that are needed to do jobs from a distance; i.e., the costs of offshoring. The ellipses at the end of the inequality leave open the possibility that there are additional factors and additional tasks besides those performed by low- skilled and high-skilled labor. By substituting for w using (1), we can rewrite (2) as (3) p j# wa 1LjV1I2 1 sa 1·2 Hj… , for j 5 x,y, where I e0 t1i2 di V t 1I2 ; 1 2 I 1 1I2 The first term on the right-hand side of (3) is the total cost of the unit measure of L-tasks in light of the profit-maximizing geographic allocation of these tasks. Notice that this cost is propor- tional to the chosen (or technologically fixed) intensity of task performance, with proportionality factor wV1I2. Thus, wV1I2 is the average cost of the low-skilled labor used to perform L-tasks, while s is the average cost of the skilled labor used to perform H-tasks. These average factor costs are the arguments in the a 1·2fjunctions, because the tasks using a given factor are per- formed in fixed combination. Notice, too, that t91i2 . 0 for all i [ 30,14 implies that V1I2 , 1 for I . 0; i.e., offshoring reduces the wage bill in proportion to the cost of performing all L-tasks at home, as long as some tasks are performed abroad. Next consider the domestic factor markets. The market for low-skilled labor clears when employment by the two industries in the tasks performed at home exhausts the domestic factor supply, L. Each firm completes a fraction 1 2 I of L-tasks at home, and an L-task in industry j employsa unLjs of labor per unit of output. Letting x and y denote the outputs of the two indus- tries, we have 11 2 I2a 1Lxx 1 11 2 I2a 1·2y LyL, or L (4) a Lx2x 1 a 1·Ly 5 . 1 2 I This way of writing the market-clearing condition highlights the fact that offshoring leverages the domestic factor supply; i.e., that an expansion in I is like an increase in L. For skilled labor, H, we have the usual (5) aHx·2x 1 a 1·Hy 5 H, because we are assuming for the time being that tasks requiring skilled labor cannot be per- formed remotely. Conditions analogous to (5) apply for any additional factors that may take part in the production process. 13 Lastly, we have the markets for consumer goods. We assume as usual that households have identical and homothetic preferences around the globe and take good X as numeraire. If the home country is small in relation to the size of world markets, the relative price p can be treated 13 We assume that factor markets are competitive so firms have no monopsony power. We might alternatively assume that firms can keep some of the benefits that result from a reduction in offshoring costs by using their monopsony power in factor markets. Similarly, we might assume that a reduction in offshoring costs enhances firms’ market power. Then there would be an additional channel through which offshoring could affect wages. To keep our analysis as simple as possible, however, we maintain the assumption of competitive markets throughout the paper. 1984 THE AmERIcAN EcONOmIc REVIEW dEcEmBER 2008 as exogenous by the domestic economy. If the home country is large, the relative price is deter- mined by an equation of world relative demands and world relative supplies. We shall refrain from writing this equation explicitly until we need it in Section IIB below. II. Decomposing the Wage Effects of Offshoring The Internet allows nearly instantaneous transmission of information and documents. Cellular telephones connect remote locations that have limited access to land lines. Teleconferencing provides an ever closer approximation of face-to-face contact. These innovations and more have dramatically reduced the cost of offshoring. We model such technological improvements as a decline in b and use comparative-static methods to examine their effects. In this paper, we are most interested in the effects of offshoring on domestic factor prices. Before proceeding to particular trading environments, we identify the various channels through which changes in the opportunities for offshoring affect the wages of low-skilled and high- skilled labor. Our decomposition results from differentiating the system of zero-profit and factor- market clearing conditions and taking V, p, and I as exogenous variables for the moment. Of course, these variables are endogenous to the full equilibrium, and we shall treat them as such in the subsequent analysis. When both industries are active, the pair of zero-profit conditions in (3) hold as equalities. These two equations, together with the factor-market clearing conditions that apply for all of the inelastically supplied factors, allow us to express the vector of domestic factor prices and the two output levels as functions of p, I, and V. After totally differentiating this system of 2 1 v equa- tions (where v is the number of factors), we can write the expression for the (proportional) change in the wage of low-skilled labor as dI (6) wˆ5 2V 1 m p 2 1 ˆ 2 , 1 2 I where the m ’s collect all the terms that multiply dp/p and dI/11 2 I2, respectively. i We call the first term on the right-hand side of (6) the productivity effect. As the technology for offshoring improves (db , 0), the cost of performing the set of L-tasks declines in both indus- tries (V , 0). A firm’s cost savings are proportional to its payments to low-skilled labor. These savings are much the same as would result from an economy-wide increase in the productivity of low-skilled labor, hence the term we have chosen to describe the effect. The boost in productiv- ity raises firms’ demand for low-skilled labor, which tends to inflate their wages, much as would labor-augmenting technological progress. The second term on the right-hand side of (6) is the relative-price effect. A change in the ease of offshoring often will alter the equilibrium terms of trade. If the relative price of the labor- intensive good Y falls, this typically will exert downward pressure on the low-skill wage via the mechanism that is familiar from Wolfgang F. Stolper and Paul A. Samuelson (1941). Since improvements in the technology for offshoring generate greater cost savings in labor-intensive industries than in skill-intensive industries, ceteris paribus, a fall in b often will induce a fall in 14Strictly speaking, this is true only when I . 0 in the initial equilibrium. Note that dI/db , 0 (as we will argue below) and dV 2 e0 t1i2 di dI [5 t1I2] t91I2, which is zero when I 5 0 and negative when I . 0. VOL. 98 NO. 5 GROssmAN ANd ROssI-HANsBERG: TRAdING TAsks 1985 the relative price of the labor-intensive good (p , 0). Hence, the relative-price effect typically works to the disadvantage of low-skilled labor, as we will see in Section IIB. We refer to the final term in (6) as the labor-supply effect. As technological improvements in communication and transportation cause the offshoring of L-tasks to expand, (dI . 0), this frees up domestic low-skilled labor that otherwise would perform these tasks. These workers must be reabsorbed into the labor market, which may (but need not) contribute to a decline in their wages. We see in equation (4) that the domestic economy operates as if it had a labor supply of L/11 2 I2, which means that an expansion of offshoring of dI/11 2 I2 increases the effective sup- ply of low-skilled labor by a similar amount as would a given percentage growth in the domestic labor supply L. We can also decompose the effects of a decline in the costs of offshoring L-tasks on the income of high-skilled labor. Analogous to (6), we find ˆ ˆ dI (7) s 5 2m p 3 m 4 1 2 I Notice that there is no productivity effect. This is because a fall in b reduces firms’ costs of per- forming their L-tasks, without any direct effect on the cost of performing tasks that require high- skilled labor. Thus, there is no direct boost to productivity of these skilled workers, although there may be indirect effects that result from changes in factor proportions and changes in rela- tive prices. We write the relative-price effect with the opposite sign to that in (6), because, at least in a two-factor model, a movement in relative prices pushes the two factor prices in opposite directions. Similarly, we write the labor-supply effect with a positive sign. Often, an increase in the effective supply of low-skilled labor such as the one that results from increased offshoring will raise the low-skill to high-skill employment ratios in the various industries, thereby increas- ing the marginal product of skilled labor. However, as we know from standard analyses of the Heckscher-Ohlin model, a change in relative factor supplies may be accommodated by a change in the composition of output, without any response of factor proportions in any industry. In such circumstances, we will have m 5 m25 0. 4 We turn now to some specific trading environments, where these effects can be isolated and understood more fully. In so doing, we study a full equilibrium in which all relevant variables are treated as endogenous. A. The Productivity Effect The productivity effect may seem counterintuitive, because it works to the benefit of the factor whose tasks are being moved offshore. But it arises quite generally in all trading environm15ts in which the volume of offshoring is already positive and the cost of offshoring falls. We devote this section to studying it in some detail. The productivity effects are seen most clearly in a small Heckscher-Ohlin economy. Consider * an economy that takes the relative price p and the foreign wage w as given and that produces output with only two factors, L and H. As before, output requires unit measures of L-tasks and H-tasks, and only the former tasks can be moved offshore at reasonable cost. 15Feenstra and Hanson (1996) study an expansion in offshoring that is precipitated by growth in the capital stock of the low-wage country. Since they assume that offshoring is costless, their analysis neglects the productivity effect that we have identified here. 1986 THE AmERIcAN EcONOmIc REVIEW dEcEmBER 2008 16 Assuming that both industries are active in equilibrium, the zero-profit conditions imply (8) 1 5 Vwa 1Vw/s2 1 sa 1Vw/s2 Lx Hx and (9) p 5 Vwa 1VLys2 1 sa 1Vw/s2Hy Here, we have made explicit the dependence of the production techniques on the relative average factor costs, Vw/s, in view of the profit-maximizing choice of offshoring dictated by (1). Since the industries differ in factor intensities, these two equations uniquely determine Vw and s, inde- ˆ pendently of b. Thus, as b falls, wˆ5 2V and s 5 0. We conclude that the productivity effect is the only effect that operates in the present setting. The relative-price effects are absent (m 5 1 m 5 0), because terms of trade are exogenous in a small economy. The labor-supply effects are 3 absent (m 52m 5 04, because factor prices are insensitive to factor supplies (at given commod- ity prices) in an economy with equal numbers of primary factors and produced goods. We can compute the magnitude of the productivity effect by combining wˆ5 2V1I2 and wˆ5 ˆ ˆ * b 1 t1I2, which follows from (1) and the fact that w is fixed for a small country. Solving this pair of equations gives I t1i2 di wˆ5 2V 5 2 e0 b . 11 2 I2t1I2 We see that the productivity effect is zero when I 5 0, but strictly positive for all I . 0. Thus, low-skilled labor benefits from improvements in the technology for offshoring L-tasks whenever some task trade already occurs. Moreover, the wage gain from a given percentage reduction in offshoring costs increases monotonically with I if h1i2 ; t91i211 2 i2/t1i2 , 1 for all i, or if h1i2 is constant 1i.e., t1i2 5 11 2 i22h2. When one of these conditions is satisfied, it guarantees that the ˆ costs of offshoring do not rise “too” fast with i. Then 0V/0I , 0 and 0wˆ/0I . 0. How can low-skilled workers benefit when it becomes easier to move the tasks they perform offshore? To answer this question, consider the cost savings generated by an improvement in the technology for offshoring. Firms’ costs fall for two reasons. First, the firms elect to relocate tasks that previously were carried out at home. Second, firms save on inframarginal tasks that were conducted abroad even before the drop in b. The envelope theorem implies that the first source of savings is negligible for a small change in b. But the second source of savings is of the first order, provided that there exist some inframarginal tasks (i.e., I . 0). The sectoral composition of these cost savings explains the ultimate gain by domestic, low-skilled labor. Firms in both industries benefit at the initial factor prices from the reduction in b. But the increase in profitability is greater in the labor-intensive sector than in the skill-intensive sector, because a firm’s savings are proportional to the share of L-tasks in its total costs. Therefore, the 16To simplify notation, we suppress the arguments of functions whenever this dependence is clear from the context 1e.g., we write V instead of V1I22 . 17The exercise we are undertaking here is somewhat artificial inasmuch as we consider a change in technology that reduces the cost of offshoring in a single, small economy while holding goods prices and foreign wages fixed. This situation can arise only when the costs of offshoring do not also change in other countries that in aggregate are large. Such a scenario would not be an apt description of the recent boom in offshoring triggered by the information technol- ogy revolution. Paul R. Krugman (2000) makes a similar point in his critique of Leamer’s (1998, 2000) small-country analysis of the effects of factor-biased technological change on factor prices. We intend the small-country analysis only as a pedagogic device that lays bare the source of the productivity effect, not as a realistic description of the recent experience with offshoring of any small, industrialized country. VOL. 98 NO. 5 GROssmAN ANd ROssI-HANsBERG: TRAdING TAsks 1987 labor-intensive industry enjoys the greater increase in profitability at the initial factor prices. As it expands relative to the skill-intensive sector, the economy-wide demand for low-skilled labor grows. Only when the domestic wage rises to fully offset the induced increase in productivity can the profit opportunities in both industries simultaneously be eliminated. In the process, the wage of high-skilled labor is left unchanged. Again, we see the strong analogy between improved opportunities for offshoring and labor-augmenting technological progress. It is instructive to compare the incidence of a decline in the cost of offshoring with that of a fall in the cost of immigration. Both generate an expansion in the pool of labor available to performL-tasks and both spell an increase in the fraction of these tasks that are performed by foreign-born labor. Yet, we would argue, the implications for domestic wages are very different. Suppose, for the sake of this comparison, that foreign workers can stay in their (large) native country and earn the wage w , or they can move to the home country at the cost of a fraction of their working time. Let this cost vary across individuals, so that potential immigrant i captures only the fraction 1/bt1i2 of the domestic wage w when he moves to the high-wage country. Assume that foreign workers employed in the home country are equally productive with their domestic counterparts. Then, the marginal immigrant I earns the same net income in both loca- * tions, or w 5 w bt1I2. Note the similarity with equation (1). However, unless the domestic firms know the immigrants’ moving costs and can price discriminate in their wage offers, they will pay the same wage w to all low-skilled immigrant workers, as well as to all such domestic work- ers. As the cost of immigration falls, rents accrue to the immigrants, but not to the domestic firms. Hence, there is no increase in profitability and no pressure for domestic wages to change (as long as the economy remains incompletely specialized). The difference between falling costs of offshoring and falling costs of immigration is that the former create rents for domestic firms— which ultimately accrue to domestic factors in the general equilibrium—whereas the latter create rents for the immigrants. Until now, we have assumed that the distribution of offshoring costs by task is the same in both industries. What if they are different? Suppose first that it is possible to offshore tasks only in the labor-intensive industry and that the technology for offshoring these tasks improves. This is like labor-augmenting technological progress concentrated in industry Y. The wage of low-skilled workers will rise by more than the percentage fall in V , and the wage of high-skilled workers y will fall. In contrast, if the offshoring of L-tasks is possible only in the skill-intensive industry, then an improvement in the technology for offshoring will raise the wage of high-skilled labor and reduce that of low-skilled labor. These scenarios are quite similar to those analyzed by Jones and Kierzkowski (2001), where they considered the effects of fragmentation of the production process in a single industry. They showed that technological improvements that make it possible to import a component that formerly had to be produced at home are like productivity gains in the industry where this occurs. They also noted the analogy of such fragmentation with industry- specific technological progress, which, in a small country, benefits the factor that is used inten- sively in the industry that reaps the productivity gains. The main difference between their result and ours is that they identify a productivity gain for the industry in which fragmentation occurs, 18 Iy We define V y 1 2 I 1y e0 y 1i2 dy/y 1I 2, whyre I is the fraction of tasks performed offshore in industry Y. It is straightforward to calculate that wˆ5 2V aˆy uHx b . 2V ˆ y$ 0 uHx Lyu u Lx Hy and uLx s ˆ5 2 wˆ, 0, uHx where ufjs the cost share of f-tasks in industry j. 1988 THE AmERIcAN EcONOmIc REVIEW dEcEmBER 2008 whereas we associate the productivity gain with the factor performing tasks that become cheaper to trade. When offshoring costs fall for one factor and in one industry, the implications of the alternative approaches converge. 19 More generally, we can write the wage response to a change in the ease of offshoring that affects the two industries differently as u u Hx A2V By2 Hy A2V Bx uLx uLy wˆ5 , uHx u Hy 2 u Lx u Ly where V isxdefined analogously to V . In theynumerator, the productivity gain in the labor- intensive industry Y is weighted by the factor-share ratio, u /u HxwhLxh exceeds the weight u / Hy uLyn the productivity gain in the skill-intensive industry. The denominator is always positive. Therefore, the low-skill wage rate will rise if the productivity gains are similar in the two indus- tries, or if that in the labor-intensive sector is larger. The link between a decline in the cost of task trade and the relative sizes of the productivity gains in the two industries is, however, not obvious when the industries have different trade cost schedules. Take, for example, the case in which t xi2 5 at 1iy and both schedules are multiplied by a common factor b. Then, as b falls, the cost of offshoring the task with index i falls by the same percentage amount in both indus- tries (so V xi2 5 V 1y2 all i), but since the industries do not offshore the same fractions of tasks, the productivity gains are not the same. In fact, the industry in which task trade is less costly offshores a larger fraction of tasks; i.e., Ix. I yf and only if a , 1. But this alone does not guar- antee a larger productivity gain for the industry with the lower cost of offshoring. We define h 1i2 j ; t9ji211 2 i2/t ji2 for i 5 x,y, analogous to our definition of h1i2 above. Then, if h and h xre y constants, or if h xI x , 1 and h 1y 2y, 1,V 1i2jis increasing in i and the industry with the greater ease of offshoring will experience the larger productivity gain when b falls. Turning to the high-skill wage, we find s ˆ 5 u Ly Lx CA2V B 2 A2V BD . u 2 u x y Ly Lx Sinceu .Ly,skilLxdlaborbenefitsfromafallinoffshoringcostsinasmallcountryifandonly if the induced productivity gain in the skill-intensive sector exceeds that in the labor-intensive sector. B. The Relative-Price Effect To examine the relative-price effect, we relax the small-country assumption. Now we need equilibrium conditions for the foreign country and a reason why factor prices differ across coun- tries. To this end, we assume that indigenous firms in the foreign country use inferior tech- nologies. The technology gap generates factor prices that are lower in the foreign country than those in the home country. Since all task trade is costly, only the firms in the technologically 19See also Leamer (1998, 2000), who emphasizes that the factor bias of technological progress has no bearing on the implications for factor prices in a small open economy. Rather, what matters for the wage response is the sector in which the technological progress takes place. But note Krugman’s (2000) critique of the small-economy assumption in the context of global technological change, as discussed in footnote 17. VOL. 98 NO. 5 GROssmAN ANd ROssI-HANsBERG: TRAdING TAsks 1989 advanced country engage in offshoring. We return to our benchmark case in which the offshor- ing of L-tasks has the same distribution of costs in the two industries. * More specifically, we let A . 1 denote the Hicks-neutral technological inferiority of foreign firms in both industries. This means that, were a foreign firm to perform all tasks at the same intensities as a domestic firm, its output would be only 1/A times as great. Assuming incom- plete specialization in the foreign country, the zero-profit conditions for indigenous foreign firms imply * * * * * * * * (10) 1 5 A w a 1w Lx 2 1 A s a 1w /s 2Hx and (11) p 5 A w a 1wLys 2 1 A s a 1w /s Hy * * Comparing (8) and (9) with (10) and (11), we see that incomplete specialization in both countries implies “adjusted factor price equalization”; that is, wV 5 w A and s 5 s A . * * In such an equilibrium, home firms choose their production techniques based on the relative average factor costs wV/s. Foreign firms choose theirs based on the relative factor prices w /s . * * Therefore, with adjusted factor price equalization, the relative cost-minimizing techniques are * * the same in the two countries, i.e., a A 5fj . The fjreign factor-market clearing conditions can be written as I * * * * * A a Lx1 A a y 1 Ly 3 t1i2 di1aLx 1 a y2Ly L 0 and A *aHx 1 A a y 5 Hy,* * where x and y are the industry outputs of indigenous foreign firms in industries X and Y, and * * L and H are the foreign endowments of low-skilled and high-skilled labor. Here, the demand for foreign low-skilled labor comprises three terms: the demand by indigenous foreign firms in industry X, the demand by indigenous foreign firms in industry Y, and the demand by home firms in both industries that are offshoring the set of L-tasks with indexes i # I. The demand for foreign high-skilled labor comprises only the demands of the two foreign industries, because the offshoring of H-tasks still is assumed to be impossible. Now, we combine the factor-market clearing conditions for the foreign country with those for the home country to derive expressions for the world outputs of the two goods. We find 20 20 As an intermediate step, we note that * * L* b I a Lxx 1 a Ly5 * 2 s * 3 t1i2 ditL A 11 2 I2A 0 and H * a Hxx 1 a Hy5* *. A * * Now, we can solve for x and y , and similarly for x and y, and sum the home and foreign outputs of a good to arrive at the expressions in the text. 1990 THE AmERIcAN EcONOmIc REVIEW dEcEmBER 2008 * * H L L a A LyaH 1 *b 2 a Hy A *1 bV (12) x 1 x 5 D a and * * a a L 1 L b 2 a aH 1 H b A Hx * V Lx A * (13) y 1 y 5 , D a where D a a a Hx Ly Lx Hy . 0. Equilibrium in the goods market requires * y 1 y 5 d1p2, x 1 x* where d1p2 is the (homothetic) world relative demand for good Y, which has the standard prop- erty that d91p2 , 0. The expressions for world outputs have some interesting implications. First, note that wV 5 * * * w A and w 5 bt1I2w together imply I A * 5 bt1I 2V1I 2 5 b s11 2 I 2t1I 2 13 t1i2 dit . 0 Therefore, when the cost of offshoring falls (db , 0), home firms broaden the range of tasks that they perform offshore (dI . 0). This reduces the cost of L-tasks for these firms (V , 0), the more so for labor-intensive producers than for skill-intensive producers. Equations (12) and (13) imply that, as V falls, the relative world output of labor-intensive goods must rise. Finally, since 1y 1 y 2/1x1x 2 increases and d91p2 , 0, the relative price of the labor-intensive good falls (p , 0). The relative-price effect rewards high-skilled labor but harms low-skilled labor, for the usual (Stolper-Samuelson) reasons. Given the relative price p, in an incompletely specialized, Heckscher-Ohlin economy, there are no labor-supply effects (m 52m 5 04, because changes in factor supplies induce changes in the composition of output, not changes in factor intensities. It follows that domestic high-skilled labor must gain from an improvement in the technology for offshoring. Domestic low-skilled labor may gain or lose, depending on the relative sizes of the productivity and relative-price effects and on the share of the labor-intensive good in the typical consumption basket. Note that a fall in the cost of task trade can generate a Pareto improvement for the home country if the productivity effect is large enough. This is quite different from the consequences of a fall in the cost of goods trade, which necessarily creates winners and losers. 21 Note that I d c11 2 I2t1I231t1i2 did 5 1 1 2 I2t91I2 . 0. dI 22The real wage of low-skill labor can rise even if w (measured in terms of the numeraire good X) falls, because a fall in b induces a decline in the price of good Y. Note, too, that the effect of globalization on wages need not be mono- tonic, in contrast to a world with only goods trade. Therefore, Krugman’s (2000) argument that the impact of trade on wages is largest when the volume of trade is large need not apply here. VOL. 98 NO. 5 GROssmAN ANd ROssI-HANsBERG: TRAdING TAsks 1991 We highlight one further implication of equations (12) and (13). Notice that the domestic labor supply enters these expressions for the global outputs only in the form L/V. Thus, 1/V acts as a productivity level that multiplies labor units to convert them into “efficiency” units of labor. As should be clear, the analogy between reductions in the cost of offshoring and labor-augmenting technological progress carries over to the large economy. A decline in b that induces an expansion of task trade and thus a fall in V has exactly the same impact on prices, wages, and world outputs as an enhancement in the productivity of domestic low-skilled labor in all of its uses. C. The Labor-supply Effect We have seen that increased offshoring of the tasks performed by low-skilled labor acts, in part, like an expansion of the domestic labor supply. As more tasks are moved offshore, domestic low-skilled workers are freed from their jobs and so must find new tasks to perform elsewhere in the economy. Yet, the labor-supply effect on wages has been absent from the trading environ- ments we have considered so far, because factor prices are insensitive to factor supplies in an economy that produces as many tradable goods as there are primary factors. The labor-supply effect operates in any setting with more factors than produced goods. It would be present, for example, in a small economy that produces two goods with three fac- tors, such as in the familiar specific-factors model. It also operates in a world economy with many goods and two factors in which two large countries produce only one good in common. This is the setting studied by Feenstra and Hanson (1996), and the labor-supply effect features prominently in their analysis. We can elucidate this effect more clearly, however, in an even simpler environment. To this end, we consider a small economy as in Section IIB that takes the foreign wage and relative price as given, but one that is specialized in producing a single good. Suppose the home country produces only the numeraire good X. Then the zero-profit condi- tion for this industry implies that equation (8) must hold, whereas the price p is less than the unit cost of production in industry Y. The factor-market clearing conditions are quite simple in this setting, and they require L (14) aLxwV/s2x 5 , 1 2 I and (15) a Hx 1wV/s2x 5 H. Consider a decline in the cost of trading tasks (db , 0). Differentiating (8) gives uLxwˆ1 V2 1 11 2 u 2s 5Lx,ˆ while differentiating the ratio of (14) to (15) implies s (s 2 wˆ2 V) 5 dI , x 1 2 I where s ix the elasticity of substitution between the set of L-tasks and the set of H-tasks in the production of good X. Combining these two equations, we find that 1992 THE AmERIcAN EcONOmIc REVIEW dEcEmBER 2008 1 2 u Lx dI (16) wˆ5 2V 2ˆ . s x 1 2 I The first term on the right-hand side of (16) is the productivity effect, as before. The second term is the labor-supply effect on low-skilled wages. The former effect is positive, while the latter is negative and reflects the adjustment in wages necessary for all domestic low-skilled workers to be employed when performing the smaller set of tasks undertaken in the home country. Tocomparethemagnitudesoftheseoffsettingeffects,weneedtorelate2V todI/112 I2.This can easily be done using the definition of V1I2 or the derivative dV/dI reported in footnote 14. We find that 2V 5 hgdI/11 2 I2, and so wˆ5 chg 2 1 2 d Lx dI sx 1 2 I where, as before, t91I2(1 2 I2 h 1I2 ; t 1I2 is the elasticity of the trade cost schedule when expressed as a function of 1 2 I, and I e0 t1i2 di g 1I2 ; I t1i2 di 1 11 2 I2t1I2 e0 is a fraction that is zero at I 5 0 and one at I 5 1. The productivity effect is negligible when I 5 0 but can be large when I . 0 and the cost schedule for trading tasks rises steeply. The labor-supply effect is large when the share of skilled labor in total costs is large and when H-tasks substitute poorly for L-tasks in the production process. Clearly, the labor-supply effect dominates when I 5 0, which means that the first bit of offshoring drives down the wages of domestic low-skilled workers. This is because the productivity effect rests on the cost-savings for inframarginal tasks, and there are no such tasks when the complete production process is performed initially at home. However, reductions in the cost of task trade that cause offshoring to grow from an already posi- tive level can produce an increase in low-skill wages despite the existence of an adverse labor- supply effect. We see that, when I . 0, a fall in b causes w to rise if and only if s xh . 1 2 u . Lx Moreover, for some production and offshoring technologies, a sufficiently large fall in the costs of offshoring will leave low-skilled labor with higher real wages than they would have with no offshoring, despite the initial drop in wages that results from a small increase in offshoring when I 5 0.23 The labor-supply effect that may harm low-skilled workers serves to benefit their high-skilled compatriots. The high-skilled domestic workers experience no direct productivity effect, but they enjoy a boost to their marginal product when offshoring becomes less costly, because the expansion in task trade generates an increase in the intensity with which every L-task is per- formed. We find that 23 * For example, if the technology for producing good X is Cobb-Douglas, the foreign wage w is sufficiently low, and limiS1t91i2/t1i2 5 `, then the equilibrium domestic wage of low-skilled workers is higher for b sufficiently low (and, therefore, I . 0) than when I 5 0. VOL. 98 NO. 5 GROssmAN ANd ROssI-HANsBERG: TRAdING TAsks 1993 uLx dI s 5 , s x 2 I which is positive for all I. Thus, with more factors than goods, skilled-labor always gains when the cost of offshoring L-tasks falls. III. Offshoring Skill-Intensive Tasks Much of the recent public debate about offshoring concerns the relocation of white-collar jobs. The media has identified many tasks requiring reasonably high levels of skill that formerly were the sole providence of the advanced economies but now are being performed offshore on behalf of consumers in advanced economies. For example, workers in India are reported to be reading x-rays, developing software, preparing tax forms (Jesse Robertson et al. 2005), and even performing heart surgery on US patients. In this section, we extend our model to include trade in such tasks. We introduce the possibility of offshoring tasks performed by high-skilled workers in the set- ting of a small Heckscher-Ohlin economy. Let b t 1i2 denote the ratio of the input of foreign fac- f f tor f needed to perform the f-task with index i at a given intensity to the domestic input of factor f needed to perform the same task at the same intensity, for f 5 5L,H6. We assume that the two industries share the same schedules of offshoring costs, although it would be straightforward to allow for cross-sectoral variation in these costs, as we have illustrated before. Now, I fs the marginal task using factor f that is performed offshore. For low-skilled labor, we have (17) w 5 w b t L L2L as before. The analogous condition for high-skilled labor is (18) s 5 s b H HI 2H If home firms produce both goods, the zero-profit conditions imply (19) 1 5 V wL 1V LxV sL 1 V Ha 1V w/VHs2 Hx L H and (20) p 5 V waL1V LyV sL 1 V Ha 1V w/V H2,Hy L H where f e0 f1i2 di V f1If2 ; 1 2 I f t fIf2 24Andrew Pollack, “Who’s Reading Your X-Ray?” New York Times, November 16, 2003. 25Scott Thurm, “Tough Shift — Lesson in India: Not Every Job Translates Overseas.” New York Times, March 3, 20026 Unmesh Baker, Simon Montlake, Hilary Hylton, Chris Daniels, and Jenn Holmes. “Outsourcing Your Heart Elective Surgery in India? Medical Tourism is Booming, and US Companies Trying to Contain Health-Care Costs Are Starting to Take Notice.” Time, May 29, 2006. 1994 THE AmERIcAN EcONOmIc REVIEW dEcEmBER 2008 for f 5 5L,H6. Together, (17)–(20) determine w, s, I , Lnd I , Hiven w , s , and p, which the small country takes as given. But, in fact, (19) and (20) determine V w and V s independently of b and b . Therefore, as L H L H long as the country remains incompletely specialized, a fall in the cost of offshoring one or both types of task leaves V w and V s unchanged. It follows that L H
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