Managerial versus Production Wages: Offshoring, Country Size, and Endowments
This is a revised version of CESifo Working Paper No. 3292 and University of Tuebingen Working Papers in Economics and Finance No. 13. We thank Gene Grossman, Benedikt Heid, Udo Kreickemeier, Mario Larch, Erdal Yalcin, and two anonymous referees for valuable suggestions and critical comments. We are also grateful to participants of the CESifo Area Conference on the Global Economy 2011, ETSG 2010, Verein für Socialpolitik Jahrestagung 2010, Göttinger Workshop Internationale Wirtschaftsbeziehungen 2010, and THE Graduate Christmas Workshop 2009 for helpful discussion. Wilhelm Kohler is also affiliated to CESifo and GEP. Sebastian Benz is also affiliated to the University of Tübingen and gratefully acknowledges funding from the Leibniz-Gemeinschaft (WGL) under project “Pakt 2009 Globalisierungsnetzwerk.” E-mail: firstname.lastname@example.org
We explore the role of trade in differentiated final goods as well as offshoring of tasks for inequality both within and between countries, emphasizing the distinction between managerial and production labour. We extend Grossman and Rossi-Hansberg (2012), where task trade is driven by external economies of scale, by considering asymmetric endowments. Identifying possible equilibrium patterns of task trade, we find little scope for two-way trade if endowments are asymmetric. Our numerical simulations identify non-monotonicities between the level of offshoring and measures of within-country as well as between-country inequality.
Rémunérations des gestionnaires et des travailleurs : délocalisation, taille du pays, et dotation de facteurs. On explore le rôle du commerce de biens différenciées finaux ainsi que celui de la délocalisation des tâches dans l'explication de l'inégalité, à la fois intra et entre pays, en mettant l'accent sur la distinction entre travail de gestion et travail de production. On développe le modèle de Grossman et Rossi-Hansberg (2012) où le déplacement des tâches est enclenché par les économies d'échelle externes, en considérant les dotations asymétriques de facteurs. En identifiant les patterns d'équilibres possibles du déplacement des tâches, on trouve peu de possibilité pour un commerce bilatéral si les dotations sont asymétriques. Des simulations numériques identifient des relations non-monotones entre le niveau de délocalisation et des mesures d'inégalités intra-pays ou entre pays.
In this paper, we explain the pattern of international trade in narrowly defined production tasks through the interplay of three forces: (i) the cost of offshore performance of tasks, (ii) the advantage from local concentration of task performance by many firms, and (iii) the abundance in different countries of production labour, relative to managerial labour. Local concentration of tasks is advantageous because of external economies of scale. Thus, firms located in different countries may jointly gain if they all locate a certain task in a single country, provided that offshoring the task is not too costly. Intuitively, if countries are symmetric in their relative labour endowments this gain should be particularly large for firms located in a relatively small country. Country size thus becomes an important determinant of task trade. However, if countries differ in their relative endowments with production and managerial labour, the local availability of production labour becomes a crucial constraint for the concentration of tasks, and relative labour abundance, in addition to country size, becomes an important determinant of trade in tasks.
We build upon Grossman and Rossi-Hansberg (2012), who are the first to provide an analysis of relative country size as a determinant of task trade driven by external economies of scale. They identify possible equilibrium patterns of task trade between two countries that share the same relative labour endowment, but differ in size. They also show that such trade is a potential source of wage differences across countries that would otherwise have the same wage rates. The authors argue convincingly that scale economies are an important characteristic of modern industrial production that may explain two-way task trade between similar countries. Such “North-North” offshoring is empirically important, but it cannot be explained by models of offshoring that rely on comparative advantage, such as Grossman and Rossi-Hansberg (2008).
We depart from the analysis by Grossman and Rossi-Hansberg (2012) in two ways. First, we look at task trade between countries that differ in relative endowment with managerial and production labour. Secondly, we ask new questions inspired by policy concerns about inequality. Grossman and Rossi-Hansberg (2012) focus on inter-country comparisons of production wages. We look at within-country income distribution, that is, managerial wage income relative to production wages, as well as cross-country inequality in terms of income per capita. We ask how these two types of income distribution are affected by varying country size and asymmetric endowment changes if trade is restricted to final goods. We then seek answers to these same questions for a world with trade in tasks. We identify possible equilibrium patterns of task trade between asymmetric countries and offer numerical simulations that highlight orders of magnitude in the relationship between offshoring and within-country as well as between-country inequality.
These extensions of Grossman and Rossi-Hansberg (2012) are motivated in part by an empirical observation, which is summarized in Table 1. As is well known, the premium of US non-production over US production wages has been on an upward trend over the two decades from 1984 to 2005. However, there were ups and downs. Looking at annual changes, for 16 years we observe increases, and for 6 years we observe reductions. Table 1 presents average annual increases and reductions of the managerial wage premium for these two types of years, alongside average annual changes in the volumes of offshoring to developing and developed countries, respectively.1 Years with a rising wage inequality were characterized by substantially higher growth rates of offshoring and this pattern is more pronounced for offshoring with developing countries. Of course, all of this does not establish any causality, but if there is a causal relationship between the managerial wage premium and offshoring, then these numbers suggest that offshoring to developing countries may be different from and more important than offshoring to other industrial countries.
Table 1. US Managerial Wage Premium and Levels of Offshoring
But what is the exact meaning of the distinction between production labour and non-production (or managerial) labour? We argue that identifying production workers with low-skilled labour and non-production (or managerial) workers with high-skilled labour, as often done in the literature, is highly questionable. Putting this question aside, Grossman and Rossi-Hansberg (2012) stress a different distinction. They assume that managers constitute the fixed input, while production labour is a variable input. This is in line with a strand of literature that explains income distributions through indivisibilities that are typically inherent in managerial activities.2 To the extent that skill levels play a role for self-selection into activities, this literature is able to explain why the resulting managerial wage premia are sometimes far larger than the underlying educational premia.3 Nonetheless, in focusing on task trade driven by external scale economies for production labour, coupled with managerial labour as a fixed input, this model seems particularly well suited to address income distribution effects of globalization and endowment asymmetry.
In terms of methodology, Grossman and Rossi-Hansberg (2012) achieve a major breakthrough in identifying a trading equilibrium that is mostly unique. This is in sharp contrast to earlier literature on trade with external scale economies, which has emphasized the potential for multiple equilibria, driven by history as well as well as arbitrary, but self-fulfilling expectations.4 The tendency to generate multiple equilibria has always been viewed as a liability, which perhaps explains why this literature has taken somewhat of a back seat in modern trade theory. However, Grossman and Rossi-Hansberg (2010) have shown that this tendency to a large extent disappears if one assumes, plausibly, that firms engage in Bertrand-type price competition aimed at capturing entire world markets.5 This serves as a mechanism that effectively solves the coordination failure caused by scale economies being an externality. In Grossman and Rossi-Hansberg (2012), what delivers this mechanism is a firm's ability to perform a task not just for its own, but also for others through an outsourcing relationship.
In terms of results, Grossman and Rossi-Hansberg (2012) establish that the equilibrium of task concentration is unique, provided that offshoring is sufficiently costly and countries are not too similar in size. Ranking tasks according to the costliness of offshore performance, a robust pattern of two-way task trade emerges. A range of tasks that are least costly to offshore is concentrated in the smaller country. A range of tasks that feature a higher cost of offshoring is concentrated in the larger country. Potentially, the range of tasks for which offshoring is particularly costly is not traded at all. This generates a characteristic pattern of production wages. The country that hosts concentrated performance of the intermediate range of tasks for which offshoring is more costly enjoys the advantage of not having to bear this cost, importing tasks that are less costly to offshore. Accordingly, it can pay higher wages to its production workers.6
Our paper adds a number of new and interesting results. First, we provide comparative static results on inequality and asymmetric endowment changes for a world of prohibitive costs of offshoring. The domestic inequality effects are straightforward, but the effects on international inequality, measured by the ratio of incomes per capita, are more involved. While becoming larger through equi-proportional endowment changes is always gainful, the same is not true if a country becomes larger with a changing composition of the labour force. We establish a condition under which a positive productivity effect from scale economies dominates a negative terms-of-trade effect. In a similar fashion, we investigate how a changing composition of the labour force affects real wages for production and managerial labour within a country. While cross effects are dominated by the usual complementarity, own effects are ambiguous. Again, we establish conditions under which scale effects are dominating. Introducing task trade, we show that hosting a substantial amount of concentrated task performance generally lowers a country's aggregate managerial wage income, relative to aggregate income of its production workers.
Our main analytical result relates to the pattern of task trade between countries that are equal in size, but asymmetric in relative endowments. There are two types of equilibria. On the one hand, if the cost of offshoring across all tasks surpasses a certain threshold value, the country with a higher ratio of production to managerial labour endowment has a lower production wage, and task trade will be one way, and this country will export tasks against imports of final goods. On the other hand, for a sufficiently low cost of task trade three scenarios are possible. If endowment asymmetry is above a certain threshold, the same pattern of one-way task trade and wages arises. If relative endowments are exactly equal to the threshold value, one-way task trade still prevails, but wages of production workers in the two countries are equal. For sufficiently similar endowments, there exists a unique equilibrium with equal production wages, but with two-way task trade and a pattern of task concentration that is indeterminate. The potential of two-way trade is thus reduced as soon as we depart from symmetry. This is due to the above-mentioned disciplinary force of Bertrand-type pricing strategies aimed at capturing entire world markets.
Our numerical results highlight non-monotonicities in the relationship between the level of offshoring and income inequality. Comparing incomes per capita across countries, we find that a lower cost of offshoring works in favour of the larger country as well as in favour of the production labour abundant country, provided that the initial level of offshoring is zero or small, induced by the concentration of tasks in these countries. However, if the initial level of task trade is already large this effect is dominated by the (second-order) cost-savings effect on infra-marginal tasks. This effect weighs more heavily for the smaller country as well as the country with a relatively low production labour endowment, both of which import a larger range of tasks. Comparing incomes of managers and production workers within symmetric countries, we find that a lower cost of offshoring initially works in favour of manager incomes. But once the level of offshoring rises beyond a certain threshold, such that the marginal task is governed by a global (instead of a local) deviation condition, a lower cost of offshoring works in favour of production wages.
The remainder of our paper is structured as follows. The next section looks at the case where trade is restricted to final goods alone, meaning prohibitive trade costs for individual tasks. It derives analytical results for the comparative statics of inequality with respect to symmetric and asymmetric endowment changes. Section 'Trade in Production Tasks' then introduces trade in tasks. We abstain from reiterating any of the results obtained in Grossman and Rossi-Hansberg (2012) and look at the asymmetric case, deriving propositions on aggregate within-country inequality as well as the possible task trade equilibria. Section 'Simulation Results' finally turns to numerical simulations, tracing out measures of internal and between-country inequality for alternative combinations of offshoring levels and measures of size and asymmetry in the two countries' endowments with managerial and production labour. Section 'Conclusion' concludes with a brief summary.
2. Trade in Final Goods
In order to highlight the role of offshoring as an explanatory factor for inequality, both within and across countries, we first explore a world with trade only in final goods where inequality is determined by country size and relative endowments. In this section, we present this baseline model as a reference point for a world with trade in tasks, which is presented subsequently.
2.1. Model Setup
Following Grossman and Rossi-Hansberg (2012), we assume two countries, home and foreign (denoted by *), sharing identical preferences and technology but differing in their exogenous endowments of managerial labour M ( ) and production workers L (). Both types of labour are immobile across countries. Preferences feature “love of variety,” modelled through a Dixit-Stiglitz-type utility function for symmetric varieties of a single final good. Producing any variety requires hiring f managers as a fixed input. In addition, production requires a continuum of different tasks, indexed by , to be performed by production workers. Firms are headquartered in the country where they hire their managers.7
Given Dixit-Stiglitz preferences, final goods producers have price-setting power and charge a markup over marginal cost equal to , where is the elasticity of substitution between any two varieties.8 Assuming free entry, the number of firms is given by
and competitive managerial wages are determined from the condition that all profits end up in managerial income:
where c and are marginal cost from production workers employed by a firm headquartered in the home and the foreign economy, respectively, and with x and denoting quantities produced and sold of final goods.9 There are no trade costs for final goods; hence, goods market equilibrium requires
We use to denote the amount of labour needed per unit of task i, if performed in the home economy, and analogously for the foreign economy. Owing to external economies of scale that are national in scope, depends on the entire amount of task i performed domestically.10
We now define as the unit cost function for a final good that arises for a firm headquartered in the home country, if trade is possible only for final goods, and analogously for . All tasks are needed in equal amounts and the entire amount of all tasks required per unit of the final good is assumed to be of measure 1. Following Grossman and Rossi-Hansberg (2012), we model scale economies in constant elasticity form such that , where . By analogy, , and unit costs emerge as
Given these assumptions, and may also be interpreted as the cost of performing a unit of any task, respectively, in the home and the foreign economy.11 The labour market equilibrium for production workers requires
2.2. Comparative Statics of Inequality
Substituting equation (4) into (2) and using equations (1) and (5), we obtain the managerial wage premium in the home and the foreign economy as
The managerial premium is not affected by changes in country size that do not alter the relative endowment. However, changing the composition of the workforce affects the managerial premium with the expected sign.
In the next step, we look at cross-country inequality in terms of income per head in the home, relative to the foreign economy. We define
where is the share of managers in the home economy, and equivalently for all other shares. The home wage is governed by commodity market clearing (3), which leads to . Taking into account full employment of production workers, , and using , we arrive at
This allows us to solve for our measure of cross-country inequality:
Equation (9) tells us that a change in the composition of endowment has an asymmetric influence on international inequality. Holding L constant, we obtain
which is positive if the degree of substitution σ is low or the share of managers in home endowment is small. Intuitively, a higher number of managers implies a lower output per firm, which leads to a terms of trade improvement, which is larger, the smaller σ is. However, each manager now employs fewer production workers. This reduces the volume of sales for residual profit claims. The lower the initial share of managers in the workforce, the smaller is the resulting negative effect on aggregate income.
Holding M constant, we obtain
For obvious reasons, the terms-of-trade effect and residual profit effect now run in the opposite direction, again determined by σ and . In addition, there is a positive productivity effect, which increases with the magnitude of scale economies θ.
For equi-proportional changes of L and M we obtain
which is simply the sum of equation (10) and equation (11), so that a positive productivity effect dominates a negative terms-of-trade effect. We summarize these results in the following proposition.
Proposition 1. (International inequality). A change in the composition of factor endowment in one country has an ambiguous effect on international inequality. In contrast, a country unambiguously gains from becoming larger with a constant composition of the labour force.
Proof. See the comparative statics in equations (10) to (12). Q.E.D.
All of these relative wage effects may be interpreted as relative welfare effects for the respective group of workers, provided that trade in final goods is free and costless, as assumed. Consumers in both countries then pay identical prices for final goods, and they also face the same degree of variety. However, one needs to be cautious when considering absolute levels of real wages. Two additional channels need to be taken into account for real wages. The first is a change in variety that follows from any change in a country's endowment of managers; see the managerial labour market equilibrium condition (1) above. With “love for variety,” such changes are of direct relevance for real wages. The second channel runs through final goods prices, which are related to marginal cost by a constant markup. From (4) and (5), marginal costs in the home and the foreign economy are related to endowment changes according to
It is relatively straightforward to extend the above analysis to real wages. Denoting the exact price index dual to Dixit-Stiglitz preferences as , and using to define the real production wage, we obtain
By complete analogy, endowment changes entail a change in real manager income according to
In these equations, the term is equal to the income share that is spent on domestic varieties. We summarize the above equations in the following proposition.
Proposition 2. (Real factor rewards). Real income of any factor unambiguously rises if the endowment of the other factor increases. In contrast, endowment changes generally have an ambiguous effect on own real income.
Proof. See the comparative statics in equations (14) and (15). Q.E.D.
3. Trade in Production Tasks
We now proceed to describe a world where trade is extended to production tasks. Grossman and Rossi-Hansberg (2012) focus on country size effects, assuming symmetry in relative endowments. An important purpose of this paper is to explore asymmetry in relative endowments with production and managerial labour.
3.1. Model Setup
In line with the literature, we assume a continuum of tasks indexed by and that performing a certain task i outside the country of a firm's headquarter requires an additional amount of labour by a factor from the country where the task is located. We order tasks according to the ease with which they can be dislocated, where and without loss of generality we normalize and assume that the offshoring cost schedule is sufficiently steep that . The range of tasks performed offshore is determined by the trade-off between these offshoring costs and the benefits from concentrated task performance through larger scale as well as the disparity of production workers' wages between the two countries.
Let denote the Lebesgue-measure of tasks concentrated in the home economy and analogously for tasks concentrated in the foreign country . Tasks performed domestically by firms in both countries are denoted by . This allows us to rewrite the marginal cost for a final good in the home and foreign economy, respectively, as
In these expressions denotes the Lebesgue-measure of tasks augmented by the cost of trade, such that di. In what follows we shall occasionally use and analogously for the set of home-concentrated tasks . The full employment conditions for production labour can now be written as
Note that our scaling assumptions imply , which allows us to rewrite the marginal cost equations as
In these expressions, we define labour requirement coefficients , , and . The productivity of performing non-concentrated tasks relative to concentrated tasks is and .
Obviously, without task trade we have and . Each of the bracketed terms in equations (20) and (21) is smaller than 1 and represents the cost advantage from task trade. This corresponds to the productivity effect in Grossman and Rossi-Hansberg (2008).12
In a similar fashion, we may write the full employment conditions as
The bracketed terms in these equations may be compared to the labour supply effect of offshoring identified by Grossman and Rossi-Hansberg (2008). In their case, since offshoring is one-way with concentration in the foreign economy, the labour supply effect is unambiguously positive for the home economy. In the present case, offshoring is potentially two-way. Hence, the labour supply effect is ambiguous, meaning that the bracketed terms can be smaller or larger than one. The condition for a positive labour supply effect for the home economy can be written as
and equivalently for the foreign economy.13
3.2. Factor Income and the Pattern of Offshoring
Employing equation (2) we can derive total income earned by home managers as
Note that production and offshoring volumes are all determined endogenously. However, this expression still yields interesting insights into the distributional mechanisms, which are summarized in the following proposition.
Proposition 3. (Offshoring and income distribution). If , then is lower than in an equilibrium with trade only in final goods. An equivalent condition holds for the foreign country.
Proof. See equation (25) and a corresponding equation for . Q.E.D.
This proposition means that, if a country hosts a substantial amount of concentrated tasks while relatively few tasks are concentrated in the other economy, then aggregate managerial income relative to worker income in this economy is lower than in an equilibrium with trade only in final goods. We can combine equation (25) with a corresponding equation for to obtain
which states that in the presence of offshoring the distribution between managers and workers in the aggregate of the two countries is the same as the one that is obtained for each country individually in an equilibrium where offshoring is ruled out.
To sharpen our focus on an equilibrium with relative endowment differences we now impose the condition , which neutralizes all size effects on productivity that would otherwise result from variations in relative endowments. Note that both the number of firms n and firm size x are endogenous variables. Hence, to be consistent with the equilibrium conditions introduced above, adding this size-neutrality condition implies endogenous adjustment of a variable that we have so far treated as exogenous. Suppose, for instance, that the relative endowment of the home economy, , is fixed and is fixed as well. Suppose, moreover, that initially the two countries have the same relative endowment and that we now want to make the foreign economy a more production labour abundant economy in order to explore the effect of asymmetric endowment changes. Given , this implies an exogenous increase in . To ensure that the size-neutrality condition is satisfied, factor endowments in the home economy must increase as well without changing their relative proportion. We can illustrate this adjustment by a scale variable for endowment in the domestic economy, z, and write the relative endowment of the home economy as , whereby in the initial equilibrium we have . Given the size-neutrality condition, any exogenous variation in implies an endogenous adjustment in z. The resulting pattern of task trade and wages can be summarized by the following proposition.
Proof. The proof is in the appendix. Q.E.D.
The intuition for case (1) is that full employment of asymmetric endowments in both countries can be reached only if the production labour abundant economy uses part of its workers to perform tasks for the other economy. An equilibrium without trade in tasks is not feasible, given asymmetric endowments and our anchoring assumption , as can be seen from equations (22) and (23). For any the scale advantage from concentrated task performance can only make firms indifferent between offshoring and domestic performance of the task with lowest offshoring costs. This means that a wage advantage is necessary for profitable concentration of at least some tasks at the lower end of the continuum .
Now imagine a . This implies that offshoring of at least some tasks is profitable for equal wages, based on the scale effect alone. Hence, there must exist a value of such that offshoring of the well-defined range of tasks below the cutoff determined by absorbs the excess production labour of the foreign economy, implying equal wages . Moving to more asymmetric endowments requires a higher level of offshoring, which is conceivable only with unequal wages . This is case (a) of the proposition. Conversely, moving to a less asymmetric endowment requires a smaller range of tasks concentrated in the foreign economy. This necessarily gives rise to two-way task trade with equal wages, described in case (c). No other equilibrium is possible, given the deviation possibilities of firms in the two countries.
4. Simulation Results
There are two reasons for using simulation methods. First, the model is analytically intractable, since the equilibrium depends on integrals over the different sets of tasks, which themselves are functions of the model parameters, with a potential of multiple equilibria due to external economies of scale. Perhaps more important, numerical simulation allows us to identify likely orders of magnitude and to highlight non-monotonic outcomes. The outcomes we are interested in are inequality within and across countries, as determined by country size and relative endowments in combination with different volumes of offshoring. By offshoring volume we mean the share of tasks concentrated in either of the two countries. Looking at alternative offshoring volumes seems natural, given the focus of the policy debate. Moreover, it allows us to conveniently relate the figures in this section to our analytical results of Section 'Comparative Statics of Inequality'. Note that different volumes of offshoring implicitly reflect different values of β, which measures the costliness of trade in tasks. We design all figures below such that the “far south” consistently corresponds to zero levels of offshoring. In addition to allowing for asymmetric relative endowments, our focus on inequality adds a new perspective to the symmetric case with equal relative endowments but differences in total endowments as described by Grossman and Rossi-Hansberg (2012).
We choose parameter values so as to ensure comparability with Grossman and Rossi-Hansberg (2012): , , , and .14 First, we look at their symmetric case, where relative endowments are equal to 1 in both countries and world the endowment is fixed at and . Subsequently, we analyze an asymmetric case, where the home economy is abundantly endowed with managers, meaning . As discussed at length in the preceding section, we sharpen our focus on relative endowment asymmetry by shutting down the country size channel through the assumption .
We start by analyzing inequality between the two countries. Figure 1 looks at the symmetric case with equal relative endowments but differences in aggregate endowments of the two countries, depicting international inequality as defined in equation (9) for varying degrees of size advantage as well as varying amounts of offshoring. The figure indicates that external economies of scale for tasks work to the benefit of the large country for all offshoring levels, as expected from equation (12). Moreover, the larger (richer) country gains more from incipient offshoring, but less from increments of offshoring at higher levels of integration. The intuition is as follows. Since the larger country hosts tasks with high task-specific offshoring cost, it gains more from incipient task trade than the small country, which hosts tasks with lower trade costs. Moreover, the set of tasks concentrated in the large country is larger, implying less spending on transport costs and more efficient production due to the scale effect. However, if the offshoring level is high already, small country producers benefit more than large country producers from a further reduction in trade costs, since their infra-marginal range of imported tasks is larger.
Figure 1 depicts only the equilibrium in which the larger country produces a higher aggregate output with higher wages and hosts concentrated performance of tasks with intermediate offshoring costs. However, for parameter values to the southeast of the white line, where countries are of similar size and offshoring costs are low, two further equilibria can arise. The larger country may end up having a lower aggregate output level and lower wages, and producing tasks with relatively low offshoring costs or production wages in the two countries might be equal.15
Figure 2 highlights the role of relative endowments that are asymmetric enough to yield a unique one-way offshoring pattern, excluding the equilibrium described in part (2c) of proposition 4 above, which arises in the southeast of the diagram. Again, the southwestern edge of the figure corresponds to an equilibrium without offshoring, which generally implies an ambiguous reaction of international inequality with respects to asymmetric endowment changes, depending only on the relationship of and the share of managers in the foreign economy . With our choice of parameters, and ; hence, inequality is increasing with the endowment change considered. When the first tasks are concentrated in the production worker-abundant economy, it gains from an increase in productivity and wages. This means that cross-country inequality is reduced. However, this pattern is eventually reversed by a further reduction in β, because the manager-abundant country gains from lower offshoring cost on infra-marginal tasks.
Next, we turn to within-country inequality, looking at the managerial wage premium. We report results for the home economy, assumed to be relatively large in the symmetric case and manager abundant in the asymmetric case. In the symmetric case depicted in Figure 3, initial offshoring drives up the managerial wage premium.16 This is because managers' salaries move proportionally with output per unit of the fixed manager input, which is an increasing function of the total volume of offshoring, whereas production workers benefit from the increased productivity only in tasks concentrated domestically. If the home country is larger, a larger share of tasks is concentrated there, so that workers benefit almost as much as managers, and the increase in the managerial wage premium is less pronounced; see the southwest in the diagram. With zero total offshoring, changes in country size cannot change the location of any task, so that all effects on the wage premium vanish, as shown analytically in equation (6). Interestingly, for very high offshoring levels, further reductions in the costs of task trade lead to a fall in the managerial wage premium. This is due to the different deviation conditions governing the location of tasks. The highest managerial wage premium is characterized by equality of the local and global deviation conditions for domestic firms. For higher offshoring volumes, the task that separates the sets of tasks concentrated in the home and foreign economy is determined by the global deviation condition, increasing the set of tasks concentrated in the home economy and yielding a higher demand for home production workers, which drives up their wages.17
In the asymmetric case (not shown for lack of space) we can identify a very simple pattern of the income distribution in the manager-abundant country. A rising level of offshoring drives up the managerial wage premium, since home managers benefit from the increased productivity of their firms, owing to the offshoring possibility, whereas production workers do not experience a higher productivity. Comparing the symmetric with the asymmetric case, we see that the move from no offshoring to a high level of offshoring can increase the managerial premium by a factor of around 3.5 in the latter, whereas it rises by a factor of only 1.05 in the former. When we consider developing countries to be relatively production labour abundant, this result is very much in line with the stylized empirical facts mentioned in the introduction, and it confirms our view that this model is able to to contribute to our understanding of these trends in income distribution.
In this paper, we have argued that wage and inequality effects of trade should be addressed by focusing on the distinction between managerial and production workers, where managerial labour is a fixed input in production, while production work serves as a variable input. A key tenet of our analysis is that this asymmetry importantly shapes the determination of managerial salaries and production wages. A second fundamental assumption underlying our analysis is that production labour often benefits from local spillover effects related to narrowly defined tasks along complex value added chains, and that modern technology of communication and transport increasingly makes such tasks tradable.
We used a two-country model of task trade recently developed by Grossman and Rossi-Hansberg (2012), which we have extended to the case of asymmetric labour endowment. We presented a number of analytical results. For instance, in a world without trade in tasks, we can neatly identify three different channels through which country endowments affect international inequality. There is a terms of trade effect, but also a productivity effect of countries becoming larger. In addition, there is a composition effect if endowments change in an asymmetric fashion.
Introducing the possibility of trade in tasks between asymmetric countries, we have shown that it is often one-way in nature, provided that the two countries' relative endowments are sufficiently asymmetric. In such an equilibrium the production worker-abundant economy exports task performance against imports of differentiated final goods, and it has a lower production wage than the manager-abundant economy.
We have complemented these analytical results by numerical simulations. An interesting non-monotonicity arises for international inequality between differently sized countries that are symmetrically endowed with managers and workers. Starting out from low levels of offshoring, a reduction in the cost of task trade generates gains mainly for the large country, while the opposite is true once these costs fall below a certain threshold value. A similar non-monotonicity arises in the asymmetric case, where for low levels of offshoring it is the country with more production workers that reaps the bulk of globalization gains, while manager-abundant economies benefit once globalization has gone sufficiently far. Our simulation results are in line with the known facts relating to the wage premium for non-production over production workers in the US.
A.1. Proof of Proposition 4
We prove part (1) of this proposition by assuming an equilibrium with high β and analyzing its stability. After that we show that no other equilibria are possible, given that the one-way task trade equilibrium is stable. Defining , such an equilibrium with task concentration in the labour abundant foreign economy is described by
(A1) (A2) (A3) (A4) (A5)
plus the conditions for final goods market clearing and full employment of managers in either country, and determination of salaries from equations (1), (2), and (3). and imply
Since for and the right-hand side strictly increasing in , requires . With , equation (A5) mandates . This type of equilibrium is always stable because home firms prefer offshoring over domestic production for all tasks if foreign firms do not change the location of production (see equation (A5)). Moreover, a strategy to set up a production site in the home country and deliver to all, home, and foreign firms is not profitable. This is shown by the observation that aggregate production costs in the home economy, inclusive of offshoring costs, are greater or equal than aggregate production costs in the foreign economy, or
as long as . Such a strategy is called global deviation by Grossman and Rossi-Hansberg (2012). No other offshoring pattern can satisfy the full employment condition in equation (A6). This proves that the equilibrium described above is unique.
Now we turn to case (2), where . Exploiting , we define a cutoff endowment proportion denominated by Λ, which is characterized by equalized wages and one-way task trade with concentration in the foreign economy, or
where is the solution to equation (A5), expressed as a function of the relative production wage and the cost of offshoring. Obviously, this function is well defined only for values .18 It can be seen from equation (A5) that as well as the entire right-hand side of equation (A8) are increasing in , so that implies, ceteris paribus, . The arguments for stability and uniqueness from above apply here as well. This means that a sufficiently disproportionate labour endowment yields a unique equilibrium with one-way offshoring, even if technological offshoring costs β are low. With , wages in the two countries are equalized , but any change in the pattern of task trade is still refuted by the fact that local and global deviation conditions still hold and no other equilibrium would fulfil the full employment condition under equalized wages. Hence, we still see one-way offshoring with concentration of all tasks in the foreign economy.
Finally, in a case where an equilibrium with one-way task trade is not stable, given the full employment conditions under one-way task trade. On the one hand, complete foreign concentration would require because the function would have to take a smaller value than . However, then it would be subject to global deviation as defined in equation (A7). At given factor prices, shifting the entire production to the home economy leads to lower aggregate production costs. On the other hand, complete home concentration is not possible either, because it would require . Hence, only an equilibrium with equal wages can be stable, featuring positive levels of offshoring, since . Given the endowment proportion in this equilibrium, it can be seen from equation (A8) that less than all tasks need to be concentrated in the foreign country. Hence, the equilibrium must feature two-way task trade so that full employment is satisfied, and there exist an infinite number of ways in which the interval may be split into subintervals hosted by the foreign and the home economy so that the full employment conditions for both countries hold. In this sense, the pattern of task concentration is indeterminate.19
We define as developed economies the European countries, Canada, Japan, Australia, and New Zealand. Adding the Republic of Korea, Singapore, Taiwan, or South Africa does not change the picture significantly. Wage data are from the NBER productivity database; offshoring is measured by US manufacturing imports of goods from US majority-owned foreign affiliates from the Bureau of Economic Analysis. The managerial premium decreased in 1985, 1986, 1997, 2001, 2002, and 2004 and increased in all other years between 1984 and 2005.
It is worth quoting from a classic paper: “Management involves discrete and indivisible choices and commands, such as which goods to produce, in what varieties and volume, and how to produce them. Supervision insures that management directives are carried through at the production level. Indivisibilities inherent in management decisions are represented analytically as a form of total factor productivity improvement and, as such, imply a strong scale economy, not unlike a public good but limited to the confines of the firm. For example, the decision of which good to produce is largely independent of scale, applying equally well to a very large enterprise as to a very small one” (Rosen 1982, 312).
There are very few models of trade that incorporate similar distinctions between fixed and variable inputs. The only examples we are aware of are Manasse and Turrini (2001) and Egger and Kreickemeier (2012). The vast majority of the literature assumes homothetic technologies where all inputs are used in the same proportions for both fixed and variable costs; see Horn (1983). For an example that focuses on the traditional skill premium, see Epifani and Gancia (2008).
Important contributions to this literature are Markusen and Melvin (1981), Ethier (1982a), Matsuyama (1991), and Krugman (1991).
With this change in firm behaviour comparative advantage regains its force in determining trade patterns, provided that each industry is negligibly small, so that capturing the entire world market never overstretches a country's resource constraint. The analytical trick to achieve “smallness ”is to assume a continuum of industries.
This effect is very similar to the so-called home market effect, first noted by Krugman (1980). That literature, however, assumes internal economies of scale. In models that feature differentiated intermediate inputs, as pioneered by Ethier (1982b), internal economies in input production translates into external economies of scale for final goods production. However, since these are international in scope country, size plays a much different role for trade compared with a case where economies of scale are national in scope, as assumed here; see Ethier (1979).
We make no distinction between firms hiring managers and managers setting up their own firm. In equilibrium, a manager must earn the same income, whether in terms of entrepreneurial profit, if self-employed, or through a perfect contract with a firm.
This assumes a negligible influence of a single firm's pricing policy on the overall price index of varieties, which implies a sufficiently large number of firms and thus sufficiently large endow-ments .
Equation (2) follows from setting . This replaces the zero-profit condition found in conventional models of monopolistic competition.
The external nature of scale economies in tasks is consistent with the assumption of perfect competition.
These scale economies do not translate into scale economies on the final goods level. Final goods producers take marginal costs c and as given parametrically.
In equation (20), the second term in the brackets is negative, since , which simply means that concentrated task performance gives a productivity advantage over dispersed performance. The third plus the fourth term may be written . The explanation for this inequality runs as follows. The term measures the ratio of foreign to domestic cost per unit of task performance, while measures the average labour requirement of domestic task performance, relative to foreign task performance, which is larger than the same ratio at the margin of , due to . By the local deviation condition for foreign concentration derived in Grossman and Rossi-Hansberg (2012), the cost ratio is equal to or smaller than the domestic-to-foreign labour requirement ratio at the margin of . Similar reasoning applies to equation (21).
A sufficient condition for a positive labour supply effect in the home economy is given by if and if . This is proven by and for whereas for and analogously for the foreign economy.
Grossman and Rossi-Hansberg (2012) demonstrate that the choice of implies that the symmetric case involves offshoring in both directions whenever there is offshoring at all. Moreover, as we show in equation (6), it yields equal remuneration for managers and workers in the symmetric case whenever there is no offshoring.
For a description of such multiple equilibria see the discussion in Grossman and Rossi-Hansberg (2012).
As above, in Figure 3 the parameter combinations for which a second equilibrium with higher wages in the small country might occur is separated, to the north-east, by a white line.
Also see the discussion in Grossman and Rossi-Hansberg (2012) about global and local deviation.
It is impossible to derive a closed-form solution for the equilibrium cut-off value , nor is it necessary to do so for a proof of the proposition.
This indeterminacy resembles the well-known “Melvin indeterminacy,” which arises in factor price equalization equilibria for Heckscher-Ohlin models where the number of goods exceeds the number of factors.