Offshoring, matching, and income inequality☆
Introduction
As transportation costs and communication costs have declined, production processes have become closely intertwined across countries. These developments have made it possible to form cross-country international teams. One example is when US managers residing in the US are paired with Chinese workers residing in China to produce goods or services. The challenge is then to determine the distributional impacts of offshoring (i.e., cross-country team formation). Who would benefit most among four distinct groups (i.e., the group of US managers, the group of US workers, the group of Chinese managers, and the group of Chinese workers)? Who would benefit (or lose) most among the group of US high-skilled workers, the group of US middle-skilled workers, and the group of US low-skilled workers?
This paper answers these questions by developing a matching framework of offshoring in a two-country, two-task model in which workers and managers possess a continuum of skills, and by deriving analytical results regarding the distributional impact of offshoring. Our approach, which is derived from complementary production, extends Eeckhout and Kircher (2018)’s matching framework to allow for cross-country matching between two countries following Kremer and Maskin, 1996, Kremer and Maskin, 2006 and Antràs, Garicano, and Rossi-Hansberg (2006).1 The main innovation in this paper is the application of the monotone comparative statics technique (as in Costinot and Vogel, 2010) to the two-sided cross-country matching framework. The novel (and different) analytical results shed light on the distributional consequences of offshoring.
In our model, a workers’ wage (or a managers’ salary) depends on two functions – a matching function (a function that maps from a worker skill to a manager skill) and a span-of-control function (a function that maps from a worker skill to the number of workers per manager within a team). The higher skill level of a matching counterpart yields a higher wage level (matching effect); and more workers per manager in a team will reduce the wage level from the competition (span-of-control effect). Offshoring, which is defined as cross-country matching between workers and managers, alters this matching mechanism, the span of control, and thereby affects the distribution of earnings (salary and wage) within and between groups (managers and workers) endogenously.
More specifically, to analyze the distributional impacts of offshoring, we first study two closed economies with no cross-country matching between workers and managers. Next, we study an integrated world economy in which frictionless cross-country matching is allowed between workers and managers. Then we compare two equilibria in autarky with the equilibrium in an integrated world economy. In our benchmark cases, we consider four cases of cross-country differences, each of which provides novel insights into the distributional impact of offshoring. These are: (a) cross-country differences in factor endowments, (b) cross-country differences in the first moments of managers’ skill distributions, (c) cross-country differences in the second moments of workers’ skill distributions, and (d) cross-country differences in the first moments of skill distributions allowing for endogenous task choice.
First, we examine the impact of offshoring under cross-country differences in factor endowments, all else equal between two countries. We prove that offshoring increases total production in the world economy; i.e., there are gains from offshoring. On top of that, we demonstrate that total earnings in each country increase as a result of offshoring. This result echoes the idea of gains from trade in both countries, as found by David Ricardo and the Heckscher–Ohlin theory. However, unlike the representative agent international trade model, our model obtains the result of gains from offshoring in both countries even in the context of our two-sided heterogeneous agent model without an international trade mechanism.
At the same time, we show that offshoring does not change the matching functions but alters the span-of-control control functions. Hence it can increase (or decrease) within-country inequality, such that a subset of workers is harmed. Abundant factors gain while scarcer factors lose (i.e., there is between-task inequality), which is similar to Stolper and Samuelson (1941)’s theorem. We derive this classical result even without assuming international trade. Furthermore, the workers’ share and the managers’ share in each country change in response to offshoring, even though we assume a Cobb–Douglas-type parameter in production technology. However, within-worker inequality and within-manager inequality do not change in either country. Unlike the clear-cut result regarding between-task inequality and within-task inequality, overall inequality is less clear and depends on earnings distributions in autarky, which departs clearly from Stolper and Samuelson (1941)’s theorem.
Second, we investigate the impact of offshoring under cross-country differences in factor distributions, all other things being equal between two countries. We conceptualize cross-country differences in factor distributions from two perspectives: (1) centrality–“There are relatively more high-skilled workers/managers in the North than in the South” and (2) dispersion–“Worker/manager skill distribution is more diverse in the North than in the South”. The underlying mechanism, which pieces together all possible cases, is that cross-country differences in factor distributions generate cross-country differences in the matching function and the span-of-control function between two countries.
More specifically, suppose that there are more high-skilled managers in the North than in the South, which captures the factor distributions between the US and a developing country such as China and India (i.e., in North–South offshoring).2 Suppose that there are two managers with the same skill level, one in the North and the other in the South. In autarky, the northern manager is paired with workers who are lower-skilled than the workers the southern manager is paired with. If frictionless cross-country matching is allowed, then the northern manager will desire to match with southern workers, which will entail changes in the matching function and the span-of-control function. Due to the matching effect and the span-of-control effect, salaries of northern managers are bid up while wages of northern workers decrease, which increases the inequality between managers and workers in the North (between-task inequality). Moreover, higher-skilled managers benefit more from the rematching, which generates a skill premium among managers in the North (within-task inequality). In this case, the model explains three salient features of income inequality patterns in the US since the 1960s: the divergence of upper-tail inequality and lower-tail inequality; rising income share of the top 1 percent; and the growing importance of occupations (see Autor et al., 2008, Kopczuk et al., 2010, Piketty and Saez, 2003, Acemoglu and Autor, 2011).
Third, suppose that worker skill distribution is more diverse in the North than in the South, which captures the factor distribution between the US and a developed country such as Denmark or Germany (i.e., in North–North offshoring).3 To the best of our knowledge, the impacts of offshoring under different skill dispersions between two countries have rarely been investigated. We analyze those impacts in this paper. Frictionless cross-country matching (i.e., offshoring) changes the matching mechanism, the span of control, and hence generates different inequality implications. In the North, combining both the matching effect and the span-of-control effect, the wage polarization happens (i.e., leads to a decrease in inequality among low-skilled workers and an increase in inequality among high-skilled workers), and the salary convergence occurs (i.e., leads to an increase in inequality among low-skilled managers and a decrease in inequality among high-skilled managers). In the South, the results are the opposite.
Last, we relax the assumption of exogenous supplies of managers and workers and study the impact of offshoring with endogenous task choice under cross-country differences in agent skill distribution. We consider a case in which there are relatively more high-skilled agents in the North than in the South. Offshoring changes the occupational choice mechanism such that some of the most skilled workers become managers and some of the least skilled managers become workers. The matching patterns from offshoring are more complicated than the ones with exogenous supplies of managers and workers. We categorize the possible results in four cases. Interestingly, in one case, the matching functions in both countries shift upward, implying that all workers match with better managers, resulting in increases in within-worker inequality in both countries. This result breaks from the standard Stolper and Samuelson (1941) mechanism and provides new insight into the distributional consequences of offshoring.
Section snippets
Contribution to the literature
This paper contributes to the theory of offshoring. Feenstra and Hanson (1996) develop an offshoring model in which a single manufactured good is produced from a continuum of intermediate inputs using skilled workers, unskilled workers, and capital. Grossman and Rossi-Hansberg (2008) propose a task-based offshoring model in which a continuum of tasks is performed by skilled workers and a continuum of tasks is performed by unskilled workers. They explicitly distinguish “goods” and “tasks”. Both
The matching model of offshoring
The model builds upon Grossman, Helpman, and Kircher (2017) and Eeckhout and Kircher (2018)’s matching framework. We modify their modeling framework to allow for two countries to study the distributional effects of offshoring, which we define as a cross-country matching between workers and managers. We depart from a setup of two-industry model of Grossman, Helpman, and Kircher (2017). We consider only one sector as in Eeckhout and Kircher (2018) and incorporate a cross-country matching which is
The distributional effects of offshoring
Let us analyze how offshoring, a cross-country matching between managers and workers, changes the matching mechanism, the span of control, and thereby affects the distribution of earnings (salary and wage) within and between groups (managers and workers) in the world economy composed of two countries, North and South. In the world economy, managers can match frictionlessly with workers in their own country or with workers in the other country. In within-country matching, we normalize . In
Endogenizing task
In this section, we relax the assumption of exogenous supplies of managers and workers and study the impacts of offshoring on matching between managers and workers and earnings structure of the economy when agents are allowed to choose tasks endogenously.39 The endogenous occupational choice
Conclusion
This paper generates a rich set of theoretical predictions of the distributional impacts of offshoring where offshoring is defined as cross-country matching between managers and workers. We show how offshoring can be analyzed within the framework developed by Eeckhout and Kircher (2018). We draw on the monotone comparative statics technique developed by Costinot and Vogel (2010) to derive technically challenging comparative static exercises. While we rely on the framework and the technique in
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This article is a revised version of the first chapter of my Ph.D. dissertation at UC Davis. I am deeply indebted to my advisor, Rob Feenstra, who inspired me to initiate this research project in August 2015. He introduced me to his 2000 NBER summary that commented on the paper “Globalization and Inequality”, earlier work done by Michael Kremer and Eric Maskin, which motivated me to pursue this research question. I am also grateful to Alan Taylor for all his insightful comments on this draft. I also thank the editor and one anonymous reviewer for their constructive feedback that immensely improved the quality of the paper. I would also like to thank many participants in numerous seminars and conferences for their invaluable comments.