metadata: authors: 0: author: Harrison, Ann
1: author: McLaren, John
2: author: McMillan, Margaret
count: World
docna: 0: docna: Recent perspectives on trade and inequality
docty: Policy Research Working Paper
subtopic: Labor Markets,Poverty Reduction Strategies,International Trade and Trade Rules,Poverty and Trade,Employment and Unemployment,Rural Labor Markets
teratopic: Private Sector Development,Macroeconomics and Economic Growth,Social Protections and Labor,International Economics and Trade
abstracts: cdata!: The 1990's dealt a blow to
            traditional Heckscher-Ohlin analysis of the relationship
            between trade and income inequality, as it became clear that
            rising inequality in low-income countries and other features
            of the data were inconsistent with that model. As a result,
            economists moved away from trade as a plausible explanation
            for rising income inequality. In recent years, however, a
            number of new mechanisms have been explored through which
            trade can affect(and usually increase) income inequality.
            These include within-industry effects due to
            heterogeneous?firms; effects of offshoring of tasks; effects
            on incomplete contracting; and effects of labor-market
            frictions. A number these mechanisms have received
            substantial empirical support.
repnme: repnme: Recent perspectives on trade and inequality
display_title: Recent perspectives on trade and inequality
listing_relative_url: /research/2011/08/14753163/recent-perspectives-trade-inequality
topicv3: Trade and Poverty m1326021 1196,Labor Markets m1326488 855,Trade m1326924 698,Income Inequality m1503891 2668,Unemployment m1504051 2747
publishtoextweb_dt: 2011-08-01T00:00:00Z
historic_topic: Private Sector Development,Macroeconomics and Economic Growth,Social Protections and Labor,International Economics and Trade
no_of_pages: 54
model_extractions: WPS5754 Policy Research Working Paper 5754 Recent Perspectives on Trade and Inequality _Ann Harrison John McLaren Margaret McMillan_ The World Bank Development Economics Vice Presidency August 2011
Policy Research Working Paper 5754

# **Abstract**

The 1990’s dealt a blow to traditional Heckscher-Ohlin analysis of the relationship between trade and income inequality, as it became clear that rising inequality in low-income countries and other features of the data were inconsistent with that model. As a result, economists moved away from trade as a plausible explanation for rising income inequality. In recent years, however, a number of new mechanisms have been explored through which trade can affect(and usually increase) income inequality. These include within-industry effects due to heterogeneous firms; effects of offshoring of tasks; effects on incomplete contracting; and effects of labor-market frictions. A number these mechanisms have received substantial empirical support.

This paper is a product of the Development Economics Vice Presidency. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted may be contacted at ann.harrison@berkeley.edu.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Recent Perspectives on Trade and Inequality Ann Harrison<sup>�</sup> John McLaren<sup>y</sup> Margaret McMillan<sup>z</sup> June, 2010 Abstract The 1990’s dealt a blow to traditional Heckscher-Ohlin analysis of the relationship between trade and income inequality, as it became clear that rising inequality in lowincome countries and other features of the data were inconsistent with that model. As a result, economists moved away from trade as a plausible explanation for rising income inequality. In recent years, however, a number of new mechanisms have been explored through which trade can a¤ect (and usually increase) income inequality. These include within-industry e¤ects due to heterogeneous ...rms; e¤ects of o¤shoring of tasks; e¤ects on incomplete contracting; and e¤ects of labor-market frictions. A number of these mechanisms have received substantial empirical support.

> �University of California, Berkeley and World Bank.

> yDepartment of Economics, University of Virginia, P.O. Box 400182, Charlottesville, VA 22904-4182. Email: jmclaren@virginia.edu.

> zTufts University and IFPRI.
# 1 Introduction.

One of the most robust trends in the last three decades of the twentieth century has been a rise in within-country inequality in a wide range of countries. This rise in inequality— whether measured in income, wages, wage premia, or assets— has been observed in both the developed and developing worlds. Within the United States, Latin America, Asia, and Africa the gap between individuals has widened considerably.

One plausible explanation for this increasing inequality is the rise in globalization. Whether measured in trade ‡ows, tari¤s, capital ‡ows, or o¤shoring, globalization has increased markedly in both developed and developing countries. Trade between developed and developing countries has increased substantially, and poles of growth have shifted to the developing world. These parallel developments have naturally led to speculation that the increase in inequality is a result of increased exposure to international trade. Until the 1990’s, the leading framework for understand the possible link between trade and inequality was the Hecksher-Ohlin (HO) model, which, in its simple form, predicts that countries export goods that use intensively the factor with which they are most abundantly supplied. One implication of this framework is that trade increases the real return to the factor that is relatively abundant in each country and lowers the real return to the other factor –known as the Stolper-Samuelson Theorem. This means that in developed countries, with an abundance of skilled labor, wages of skilled workers should increase relative to unskilled workers and inequality should rise with trade. The opposite was expected to happen in developing countries that were well-endowed with unskilled labor: inequality should have declined with trade.

A number of studies published between 1990 and 2010 dealt a serious blow to this theory by documenting an increase in inequality in developing countries that frequently paralleled major trade reforms. Countries exhibiting this trend include Mexico, Colombia, Argentina, Brazil, Chile, India, and China (see Goldberg and Pavcnik (2007a, 2007b), Topalova (2007), Harrison and Hanson (1999) and others). While the evidence providing a direct link between trade 2
reforms and rising inequality is available only for some countries (such as India and Mexico), the preponderance of the evidence of rising inequality in developing countries in a period of rapid globalization is nevertheless at odds with the simple predictions of the HO framework. An additional problem for the HO theory has been widespread evidence of within-industry increases in demand for skilled workers (Lawrence and Slaughter (1993)). For example, both inequality and the demand for skilled workers have increased in the services sector of the US where, prior to the 1990s, there was almost no international trade or o¤shore activity.

These ...ndings led many economists to drop trade as a candidate for explaining rising inequality and look for other factors. One leading explanation for trends in inequality is skillbiased technological change, which means changes in technology (such as the increasing use of computers) that increase the demand for skilled workers. Other factors that have been cited by economists include the weakening of labor market institutions such as unions and the declining real value of minimum wages, di¤erential access to schooling, and immigration. Overall, for a substantial period of time, most labor and trade economists were skeptical of assigning too great an importance to trade-based explanations for the increase in inequality.

That may be changing. The emergence of stylized facts at odds with existing trade theory has led to new theoretical developments focusing on heterogeneous ...rms and bargaining, trade in tasks, labor market frictions, and incomplete contracts. These new theories provide insights into the e¤ects of trade on income and wage inequality. This more recent literature, which has emerged in the last decade, is the focus of our essay. We shall see that there are now a number of ways to explain how trade could contribute to rising within-industry inequality as well as rising inequality in countries at all income levels. However, the empirical literature has not kept pace with the theoretical developments, in part because they are so new. Researchers will need to sort through these di¤erent theories to identify which are most consistent with the data.

For the purpose of this review, trade is broadly de...ned to include trade in goods and 3
services and foreign direct investment. Much has been written about how to de...ne inequality and we do not have the space to go into those details here. For our purposes it is su¢ cient to note two important facts. First, income based measures of inequality are subject to all of the same caveats as income based measures of poverty. See Deaton (2005) for a review of these issues. Second, this review focuses only on inequality within countries as measured by income and wages; it does not focus on inequality across countries. For discussions of trends in inequality across countries –global inequality –the interested reader is referred to Ravallion (2001, 2003), Milanovic (2005), and Sala-i-Martin (2002).

The rest of this review is organized as follows. Section 2 reviews the theoretical literature on trade and inequality beginning with the older literature but emphasizing the new developments that are more consistent with recent empirical evidence. Section 3 reviews the empirical literature on trade and inequality again beginning with the older literature but emphasizing recent work using new datasets and innovative approaches.

# 2 Theory.

## 2.1 Brief synopsis of earlier work.

First, we present a whirlwind synopsis of the theory of trade and income inequality before 2003 (after which date work in the area seems to have accelerated due to the interest in heterogeneous ...rms). Following that, we launch into more recent work. The mainspring of theory behind empirical work on trade and distribution in the 1990’s was the classic comparative-advantage framework. In particular, the distinction between distributive e¤ects in a Heckscher-Ohlin model and in speci...c factors models was a key focus.

In a Heckscher-Ohlin model, each factor of production is able to move costlessly between industries (but not across countries). As a result, each factor earns the same income no matter what industry employs it, and trade a¤ects income inequality by changing the prices of factors.

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In a two-factor version of the model, this means that trade increases the real return to the factor that is relatively abundant in each country and lowers the real return to the other factor –the Stolper-Samuelson theorem. If the two factors are skilled and unskilled labor, that means that trade increases income inequality in rich countries (by raising the real return to abundant skilled labor and lowering the return to scarce unskilled labor) and lowers income inequality in poor countries. In many-factor models, trade on average raises the prices of factors that are more abundant in each country relative to less abundant factors (see Deardor¤ (1982) for a general treatment).

By contrast, in a speci...c-factors model, one or more factors of production cannot change industries at all. As a result, trade tends to lower the real incomes of factors in importcompeting industries and raise those in export industries (Jones (1971) is a classic reference). For example, if human capital is industry speci...c, trade will raise the incomes of workers in exporting industries at the expense of workers in import-competing industries. As a result, trade will increase income inequality if export-sector workers tend to have higher wages, and reduce it otherwise.

Applied economists over the years have noted problems with both of these simple approaches, and particularly the Heckscher-Ohlin framework, as a guide to the income-inequaity e¤ects of trade. For example, Harrison and McMillan (2007) collect a number of the more important ones, including the likelihood that di¤erent countries produce di¤erent goods (which invalidates the Stolper-Samuelson theorem) and the presence of labor market frictions. Accordingly, a number of important quali...cations have been added to this basic framework.

(i) Trade in tasks. Feenstra and Hanson (1996) study a model of o¤shoring, or the practice by which a ...rm producing in one country allocates some tasks to workers in another country.<sup>1</sup> In their model, a single good is produced by a competitive industry, with each ...rm hiring skilled and unskilled workers to perform a continuum of tasks. The tasks can be ranked on

> 1In the popular press, this is often called ‘outsourcing,’but we will follow the usage of the research literature in calling it ‘o¤shoring,’to distinguish it from outsourcing in Industrial Organization.

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the basis of their skill intensity, and a complete set of tasks must be combined with capital to produce output. There are two countries, with di¤erent relative supplies of skilled and unskilled workers. Since skilled workers are relatively inexpensive in the skill-rich country, cost minimization calls for each ...rm to choose a cuto¤ task, allocating tasks more skillintensive than the cuto¤ to workers in the skill-rich country and tasks less skill-intensive than the cuto¤ to workers in the skill-poor country. In other words, if we think of the ...rms as headquartered in the skill-rich country, then they o¤shore less skill-intensive tasks to the skill-poor country (or, equivalently, the skill-rich country imports unskilled-intensive tasks from the skill-poor country). Now, if the environment changes so that it becomes easier to o¤shore from the skill-rich to the skill-poor country (modelled by Feenstra and Hanson as a movement of capital from skill-rich to skill poor country), the initial cuto¤ task is replaced by a new cuto¤ task that is more unskilled intensive. Thus, a range of tasks are moved from the skill-rich country to the skill-poor country. Since the tasks thus reallocated are the least skill-intensive that were being performed in the skill rich country, but are more skill intensive than the tasks initially done in the skill-poor country, the result is that labor demand becomes more skill-intensive in both countries at the same time. Consequently, the equilibrium skill premium rises in both countries. Recall that the simple Heckscher-Ohlin model predicted that trade in goods would raise income inequality in rich countries but lower it in poor ones. By contrast, the Feenstra-Hanson o¤shoring model predicts that trade in tasks will raise income inequality in both countries. This is a striking result, not least because of abundant empirical work suggesting a rise in income inequality accompanying trade liberalization in countries across the income spectrum in the 1980’s.<sup>2</sup>

# (ii) Search frictions and unemployment. Davidson, Martin, and Matusz (1999) incorporate

> 2Zhu and Tre‡er (2005) show that the Feenstra and Hanson insight can apply in a model with only goods trade. If North has a comparative advantage in skill-intensive goods and technological progress allows South to grow relative to the North, then a range of the North’s least skill-intensive goods will shift to the South, where they will become the most skill-intensive goods, raising skill premia in both regions. Matsuyama (2007) shows that similar e¤ects can be obtained in a model in which transport costs are modelled as a separate sector, which uses skilled and unskilled labor and is skilled-labor intensive relative to goods production.

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worker search frictions and unemployment into a standard trade model, showing that such frictions can lead to a substantive revision of the distributional e¤ects of trade. For example, the Stolper-Samuelson theorem does not extend to an environment of that sort when formulated as a statement about the incomes of employed factors, but it does extend to such an environment when formulated as a statement about the expected lifetime income of searching factors. A wide range of e¤ects of search frictions on labor-market outcomes in trade models are gathered in Davidson and Matusz (2009).

(iii) Trade and innovation. A small cluster of theoretical work shows that innovation can be an important channel through which trade a¤ects income distribution, in ways that are very di¤erent from a comparative advantage approach. For example, Dinopoulos and Segerstrom (1999) study a two-country growth model with a continuum of industries, in each of which ...rms compete through research and development (R&D) for technological supremacy. In each industry, the ...rm with the best technology captures the entire market, but its price is limited by the marginal cost of the next-best available technology. At any moment, a large number of ...rms conduct R&D to obtain a breakthrough and become the new leader. Each country exports the products for which the industry leader happens to be, at the moment, one of its domestic ...rms, and each country initially maintains a uniform tari¤ against anything its consumers might import from the other country. The tari¤s cut into the market leader’s pro...t margins, reducing the jackpot that results from being the market leader, and thus reducing the incentive for any ...rm to do R&D to become the market leader. As a result, trade liberalization increases R&D, and growth, in both countries. Now, to the point about income inequality: If R&D is skilled-labor intensive relative to manufacturing, given its reliance on scientists and engineers, then trade liberalization will raise the relative demand for skilled labor in both countries, increasing income inequality all around. A related approach is provided by Neary (2003, section 9), in which identical countries with a large number of Cournot oligopolies open to trade. Each oligopolist now has an incentive to do R&D to lower its marginal cost 7
and obtain an advantage over its foreign competitor, resulting, once again, in a rise in skillintensive R&D spending and a rise in income inequality.<sup>3</sup> A related argument is developed by Thoenig and Verdier (2003) in a model of leapfrogging R&D. Note that these R&D-based theories are fully consistent with North-North trade, and complement approaches such as Heckscher-Ohlin and Feenstra-Hanson that are based on North-South trade.

Now we turn to more recent developments in the theory.

# 2.2 Heterogeneous ...rms and bargaining.

An important element was introduced to trade theory by Melitz (2003), who incorporated heterogeneous-...rms monopolistic competition, following an approach pioneered in Hopenhayn (1992), into a model of international trade. The approach has had considerable in‡uence on a wide scope of trade topics, and income inequality e¤ects are no exception.

To explore the e¤ect of heterogeneous ...rms on trade and inequality, we ...rst should review the features of the basic model. That model can be summarized as follows. Consumers have constant-elasticity-of-substitution preferences over a continuum of potential products. Anyone can choose to become an entrepreneur by incurring a ...xed cost fe, which can be interpreted as the cost of developing a new product. Once this has been done, the entrepreneur can produce the output, with a production function given by: where l is the labor employed per period and q is the output produced per period, f is a ...xed labor requirement per period, and � is the marginal product of labor. The ...xed cost f is a constant of known value across ...rms and time, but the productivity parameter � is a random variable, constant across time for any one ...rm but taking di¤erent values from one ...rm to

> 3Intriguing evidence for this mechanism for Brazil is presented by Nelson (2008).

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another. Importantly, � is something that the entrepreneur can learn only after incurring the ...xed cost fe. As a result, a certain fraction of entrepreneurs exit the market as soon as they have put their toe in the water, because their realization of � is too low for them to be able to break even given the ...xed production cost f .

In autarky, equilibrium is determined by two values: the number of ...rms entering and paying fe, and a cuto¤ productivity �<sup>�</sup> a<sup>forstaying.Thesetwovariablesneedtotakevalues</sup> such that two conditions hold. First, the “zero cuto¤ pro...t”condition requires that variable pro...ts for a ...rm with productivity parameter exactly equal to �<sup>�</sup> a<sup>areequaltof,sothatany</sup> ...rm with a realization �< �<sup>�</sup> a<sup>will exit, and any ...rm with a realization �> ��</sup> a<sup>will stay in the</sup> industry and make positive pro...ts. Second, the “free-entry condition”requires that expected pro...ts net of f for any entrant who has not yet learned her value of � are equal to fe, taking into account the possibility that the ...rm will choose to exit right away. This ensures that entrepreneurs’ex ante pro...ts are equal to zero.

In the open-economy version of the model, there are n + 1 identical countries, and any ...rm can export to any of them by paying an additional ...xed cost fex. In addition, there is an ‘iceberg’transport cost, meaning that a fraction of any shipment is lost in transit. Due to the ...xed cost of exporting, it is not worthwhile to export a small amount of any product, and so only highly productive ...rms export at all. Therefore, equilibrium is characterized not only by a number of entrepreneurs entering and a cuto¤ productivity level for staying, but also by a cuto¤ productivity level for exporting. Denote the latter two by �<sup>�</sup> and �<sup>�</sup> x<sup>,sothata...rm</sup> with �< �<sup>�</sup> will exit without producing anything; a ...rm with �<sup>�</sup> < �< �<sup>�</sup> x<sup>willstayand</sup> produce but not export; and a ...rm with �> �<sup>�</sup> x<sup>will stay and export.A crucial ...nding of the</sup> model is that �<sup>�</sup> a<sup><��,sothat...rmsthatsurviveundertradearemoreproductivethanthe</sup> ...rms that survive under autarky. A way of understanding the mechanism behind this is as follows. Suppose for the moment that the cuto¤ for ...rm exit and the number of ...rms entering do not change when trade is opened up. Now, each entrepreneur contemplating paying fe to 9
create a product knows that in addition to the prospects available under autarky, there is the new possibility that if � turns out to be high enough, the entrepreneur will also be able to earn more pro...t by exporting. Because of this, expected pro...t will now rise, and will now be greater than fe. Therefore, prospective entrepreneurs will see a strictly postive expected pro...t from creating a new product, and the free entry condition will be violated. If the cuto¤ for remaining does not change, this requires an increase in the number of entrepreneurs entering. But then there will be more competition; each ...rm’s share of domestic demand will fall; and the variable pro...t of any ...rm that does not export will fall. Therefore, some marginal ...rms whose variable pro...ts were close to the ...xed production cost f will drop out; in other words, �<sup>�</sup> < �<sup>�</sup> a<sup>.</sup> Therefore, free trade raises productivity. Now, nothing in this argument has anything per se to do with income inequality. The labor market is frictionless and all workers are identical, so all workers receive the same wage. The only possibility for income inequality is in pro...ts, since di¤erent ...rms earn di¤erent levels of pro...ts ex post, but in a model with only risk-neutral individuals and no modelled ...nancial market, the same equilibrium would be obtained if either (i) ...rms are self-...nanced by entrepreneurs out of wage earnings, so that each entrepreneur keeps the pro...t from her own project, some getting rich and others losing their investment completely; or (ii) start-up ...rms are ...nanced by sale of equity, with each citizen buying shares of each start-up and receiving exactly the same share of ex post pro...ts and receiving a zero rate of return on the whole portfolio. The model is not set up with a focus on income distribution, and so does not provide a theory of income distribution. We now turn to two prominent examples of models taking Melitz as a point of departure that do focus on income distribution.

Egger and Kreickemeier (2009) explore a Melitz-type model with a signi...cant form of market friction: Workers care about receiving “fair wages.” The underlying theory is adopted from Akerlof and Yellen (1990), who argued that workers’motivation to provide e¤ort de10
pends on the perceived ‘fairness’of the wages they are paid, apart from any direct incentives regarding performance and shirking. This is one version of an e¢ ciency wage argument, and in common with others of the genre, it features equilibrium unemployment in general, since even in conditions of excess labor supply an employer has an incentive not to lower the wage, for fear of reducing her workers’e¤ort level. In addition, the sense of fairness employed here includes an assumption that workers who work at more productive and pro...table ...rms feel entitled to a higher income as a result, and so this model also implies that wages will di¤er from ...rm to ...rm. Thus, this model generates wage inequality, and this inequality is a¤ected by trade.

The particular formulation of fairness used here makes use of a ‘reference wage,’a hypothetical wage against which a worker compares the wage she actually receives in evaluating how ‘fair’the wage is. For the purposes of the Egger and Kreickemeier model, the reference wage is de...ned, for any given worker, as: ^ where w denotes the reference wage; � is the productivity parameter for the ...rm in which the employer works, modelled exactly as in the Melitz model above; U is the aggregate unemployment rate, w� is the average wage among employed workers; and � is a parameter, common to all workers, indicating how important a workers’own ...rm’s productivity is to workers’evaluation how fair their own wages are. The term [(1 � U ) �w] is the average income of a worker in the economy, taking account the fact that a fraction U are unemployed and therefore have a zero wage. A high value of � indicates that workers in productive ...rms feel themselves entitled to high wages regardless of aggregate conditions, and this tends to lead to a high variance in wages across ...rms. Workers paid their reference wage or more put in full e¤ort, while workers paid less than that reduce their e¤ort in proportion to the shortfall in wages. Consequently, employers never have an incentive to pay a wage di¤erent from their workers’reference wage, 11
and the reference wage acts as if it is a binding minimum wage –except that it varies from ...rm to ...rm, and it responds endogenously to a change in the environment as U and w� change.

This construction is added to the Melitz model together with an assumption that the distribution of the �’s is Pareto, so that the probability that � is greater than �<sup>0</sup> is equal to (�<sup>0</sup> )<sup>�k</sup> , where k > 0 is an exogenous shape parameter. Parallel to the basic Melitz model, an autarky equilibrium consists of two variables, a productivity cuto¤ �<sup>�</sup> a<sup>andanumberof...rms</sup> entering, such that (i) entrepreneurs paying fe to enter receive zero pro...ts in expectation, and (ii) entrepreneurs who have entered stay if and only if their draw of � is at least as high as �<sup>�</sup> a<sup>.The equilibrium features wages that di¤er from ...rm to ...rm according to (2),and also,in</sup> general, positive unemployment. Both of these features emerge more strongly if � is high. As noted, a high value for � implies heterogeneous wages, since workers in more productive ...rms will insist on higher wages than workers in more marginal ...rms. To see why a high value for � also contributes to unemployment; note that if � = 0, wage heterogeneity disappears, the reference wage becomes the average wage, and the reference wage constraint (2) collapses to a vacuous statement that each ...rm o¤er the representative wage. This allows the wage to fall until the labor market clears.

Opening up the model to trade, we again have a cuto¤ for staying, �<sup>�</sup> > �<sup>�</sup> a<sup>,anda</sup> cuto¤ for exporting, �<sup>�</sup> x<sup>> ��.Onceagain,marginal...rmsaresqueezedoutbytheincreasing</sup> competition, and average productivity rises. However, now two new e¤ects occur. First, unemployment increases. This is the net result of two forces working in opposite directions on the demand for labor: A rise in overall output, which increases demand for labor, and a rise in productivity, which decreases it. Second, the average real wage of employed workers rises. Third, wage inequality, as measured by the ratio of the average wage for employed workers to the lowest wage for employed workers, w=� w b(��), rises.

This last result is the key one, and it requires explanation. After all, wage inequality results from heterogeneity in ...rms, and the selection e¤ect of trade (�<sup>�</sup> > �<sup>�</sup> a<sup>)thateliminates</sup> 12
lower-productivity ...rms seems as if it should reduce that heterogeneity. Two points can help understand what drives this result. First, mere truncation of a distribution does not necessarily reduce the inequality in it.<sup>4</sup> In the Pareto case, truncation of the left tail of the distribution merely scales up the distribution, multiplying every moment by a common factor, and leaving every measure of inequality unchanged (this point is discussed at length in Helpman, Istkhoki and Redding (2010)). Consequently, the elimination of less productive ...rms does nothing to reduce inequality in the distribution of �’s. Further, note that the increased pro...tability of high-productivity ...rms does not directly a¤ect wage inequality either, since, by (2), the ratio between the wages paid at two ...rms is a function of the ratio between the �’s at the two ...rms, not their realized pro...ts. On the other hand, when trade is opened, the more productive ...rms hire additional workers to serve foreign markets, while the less productive surviving ...rms shed workers, battered by competition from imports. Consequently, the average wage among the employed, w�, now is more heavily weighted to high-wage, high-productivity ...rms than it was previously. This is what guarantees that the ratio of the average employed workers’wage to the lowest employed worker’s wage rises with trade.

Put di¤erently, the way in which wage inequality is a¤ected in this model can be described as follows: The ratio of the 90th percentile ...rm’s wage to the 10th percentile ...rm’s wage is unchanged by trade, but the ratio of the 90th percentile employed worker’s wage to the 10th percentile worker’s wage goes up, provided that the 90th percentile worker is employed in a ...rm that exports and the 10th percentile worker is not. The employment share of the high-wage ...rms has increased relative to the employment share of the low-wage ...rms.

When we include unemployed workers in the discussion, the ...nding of increased inequality due to trade is strengthened: The fraction of the workforce who earn zero wages goes up, even as the average income per worker rises.

> 4To see a quick example, consider a random variable that takes a value of 1 with probability X, and a value of e and e<sup>3</sup> with probability (1 � X)=2 each. If X is close enough to 1, the log variance of this distribution is very close to zero, but truncating the distribution by eliminating the left-hand tail, in other words, eliminating the value 1, results in a log variance equal to 1.

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A related approach is explored by Davis and Harrigan (2007), who adapt a more conventional e¢ ciency-wage theory to the Melitz model. They use the monitoring approach of Shapiro and Stiglitz (1984), in which employees can shirk on the job and need to be deterred from doing so by a threat of ...ring in the event that they are caught. In the original model, every ...rm was identical, and in particular possessed the same exogenous probability of catching a shirker in any period. In equilibrium, each ...rm charges the minimum wage required to deter shirking given the detection probability, and in the aggregate a positive fraction of workers must be unemployed (or else it would be impossible to deter shirking at all, since a shirking worker will just get a new job with another ...rm right away). In the Davis and Harrigan approach, however, ...rms, indexed by i, di¤er from each other in the marginal product of labor �i, just as in Melitz, but they also di¤er in the probability mi of detecting a shirking worker in any one period. Since the minimum wage required to deter shirking depends on mi, this implies that the wage paid will vary from ...rm to ...rm, with ...rms that are good at catching shirkers (high mi) paying low wages and ...rms that are bad at catching shirkers paying high wages. As a result, “good jobs”are jobs with ...rms that have low detection probabilities. Since a ...rm’s marginal production cost is equal to the wage it must pay divided by �i, ...rms with low mi and �i are the ones that will exit when trade is opened; but since these tend to be high-wage jobs because of the low mi’s, what this means is that free trade tends to eliminate the good jobs along with the high-marginal-cost ...rms. As a result, trade actually reduces wage inequality. Note that unless mi and �i are strongly negatively correlated, the ...rms with the high wages tend to be those with high marginal costs, which are therefore the smaller ones, and the ones that do not export –the exact opposite of what is predicted in Egger and Kreickemeier, and a prediction at odds with the data. However, allowing for a su¢ ciently strong negative correlation reverses these correlations, as the authors show in simulations. In that case, trade once again increases wage inequality, disproportionately killing o¤ the ‘bad’ jobs.

14
A third heterogenous-...rms approach to trade and wage inequality is found in Helpman, Istkhoki and Redding (2010). They add a number of additional elements: Search frictions, bargaining between workers and employers, idiosyncratic match quality, and employer testing to identify which workers will be the most productive. Workers search for employers, and ...nd an employer with a probability that depends on the ratio of vacancies to workers searching (this is a one-period model, so a worker who does not ...nd a job on the ...rst try simply has a zero income). Any worker has an idiosyncratic match quality with any given employer; higher-quality matches result in more productivity on the job, and a low-quality match can actually reduce the ...rm’s overall output, so each ...rm has an interest in hiring only workers who will be good matches. Consequently, when a worker ...nds an employer who is hiring, the employer subjects the worker to a test that reveals whether the match quality is above or below a given threshold chosen by the ...rm. Workers who are revealed to be above the threshold are hired, and then bargain with the employer for the wage. Workers below the threshold remain unemployed, and receive zero income. In equilibrium, more productive ...rms screen more assiduously than less productive ...rms, in the sense that they set their threshold for match quality higher. This is because it is costly to set a higher threshold (this is assumed; the technology of test-taking that would lead to this property is not modelled); and it is worthwhile only for the highest-productivity ...rm, with its high anticipated volume of sales, to incur the high cost of a very stringent test. Consequently, a worker who passes the test at a high-productivity ...rm is revealed to be highly productive at that ...rm, and the combination of the ...rm’s productivity with the worker’s high revealed match quality imply that the bargaining surplus between worker and ...rm is large –and so the worker and ...rm will agree to a high wage. The result is that workers at large, high-productivity ...rms receive higher wages than workers at small, low-productivity ...rms. (However, workers are indi¤erent between applying for work at high- and low-productivity ...rms. A high productivity ...rm pays high wages to the workers it hires, but it does not hire many of the workers who apply. These 15
e¤ects cancel each other out.) In addition, trade intensi...es these e¤ects. It increases the incentive to screen assiduously at high-productivity ...rms due to the extra volume of sales that will come from exports. It decreases the incentive to screen at marginal surviving ...rms, which reduce their output and do not export. As a result, trade unambiguously increases wage inequality (and in a much stronger sense than in the Egger and Kreickemeir model, since it actually produces a new wage distribution that dominates the autarky one by second-order stochastic dominance). In addition, trade increases unemployment by increasing the market share of large ...rms, and then making those large ...rms more picky about hiring. Thus (as in Egger and Kreiemeier) trade further increases income inequality by increasing the fraction of workers receiving zero income.

# 2.3 New approaches to comparative advantage and inequality.

The heterogenous-...rms literature has provided a number of channels in which trade can a¤ect income inequality even between identical countries. Beyond that, a number of recent papers have re-examined and extended the comparative-advantage approach in ways that allow for a more nuanced view of trade and income inequality than was available before.

## 2.3.1 Trade in tasks, revisited.

Grossman and Rossi-Hansberg (2008) explore the implications of trade in tasks, earlier examined by Feenstra and Hanson (1996). Their emphasis is the possibility of productivity bene...ts from o¤shoring, which can in principle make o¤shoring a Pareto-improving phenomenon. In the simplest version of the model, there are two goods, X and Y , both of which can be produced in Home by completing a given set of tasks. Some of the tasks need to be performed by high-skilled labor but others can be performed by unskilled labor. Consider ...rst the production technology if only domestic labor is used. For good j there is a continuum of 16
measure 1 of tasks of each type that must be completed to produce 1 unit of output, and for each high-skill task aHj units of high-skill labor are required, while for each low-skill task aLj units of low-skill labor are required. Thus, a unit of good j requires aHj units of high-skill labor and aLj units of low-skill labor to produce. Assume that aHX=aLX > aHY =aLY , so that good X is skill-intensive. If we let Home be a small economy so that the prices of the two goods are set on world markets, and let X be the numeraire, then this determines income to both kinds of worker as the solution to the two zero-pro...t condtions: where wH is the wage paid to high-skilled labor, wL is the wage paid to low-skilled labor, and P is the price of good Y . Since X is high-skilled-labor intensive, this pair of linear equations has a unique solution for the wages wH and wL. Now, allow for producers in Home to import some low-skill tasks from workers in Foreign. Suppose that to perform task i in Foreign for good j requires aLj�t(i) units of labor, where �t(i) > 1 to re‡ect the logistical and monitoring problems of performing a task abroad. These problems can be weighed against the cost bene...t of employing lower-cost labor, due to the fact that the low-skill wage in Foreign, w<sup>�</sup> , is lower than the low-skill wage in Home, wL. A home ...rm will o¤shore a task i to Foreign if w<sup>�</sup> �t(i) < wL, and will source the task domestically otherwise. Without loss of generality, the function t(�) is increasing, so that tasks with a higher index are harder to o¤shore. In that case, there will be a cuto¤ task, say, I, such that all producers of either good in Home will o¤shore low-skill tasks i 2 [0; : : : ; I] and source all tasks i 2 (I; : : : 1] in Home. As a result, for given factor prices, the low-skill labor costs for a producer in either industry are reduced by a common proportion, say to a fraction �(I) of their original value (it is mechanical to compute �(I) by integrating the cost savings over i, but the details do not concern us here). This changes equations (3) to: 17
It is immediate that setting wH and �(I)wL to the values held by the values wH and wL in the solution to (3) will now solve (4). As a result, o¤shoring has now increased the wages of low-skilled workers in Home, by a factor of 1=�(I), without changing wages for high-skilled workers in Home – a Pareto improvement. This is, of course, the opposite of what many commentators on globalization would expect, particularly since it is only low-skilled workers whose jobs are being shipped overseas. The point is that low-skilled workers in Home are bene...tting from what is in e¤ect an improvement in their productivity. It is as if each bluecollar worker in Home previously had to construct her own chair to sit on to work, but now globalization allows her to hire a low-wage worker overseas to build the chair, allowing the Home blue-collar worker to concentrate on other tasks, get more work done, and earn a higher income as a result.

A few quali...cations to this result are in order. First, the ...nding that o¤shoring can be Pareto improving through productivity e¤ects is not, strictly speaking, new. It shows up as a special case of the Feenstra and Hanson model (1996, p.101), for example, but the mechanism in the Grossman-Rossi-Hansberg model brings it into exceptionally sharp focus. Second, Grossman and Rossi-Hansberg point out that it is mitigated and can be overturned by termsof-trade e¤ects, if the small-country assumption is relaxed. In particular, when o¤shoring becomes possible (or when it becomes more cost e¤ective due to a drop in the parameter �), the equilibrium is changed in a way that is very similar to the e¤ect of increasing the supply of low-skill labor in Home. This increases Home output of the low-skill-intensive good Y relative to the high-skill-intensive good X, which in the event that Home is a large country will tend to push the relative price of Y , namely, P , down. This shifts the zero-pro...t conditions (4) in 18
a way that pushes wH up and wL down, following conventional Stolper-Samuelson logic. If this e¤ect is strong enough, low-skill workers in Home are hurt by o¤shoring. Finally, if the model is modi...ed to allow for the possibility of more factors than goods –if, for example, in equilibrium Home produces only good X, then this same feature of o¤shoring, that it acts like an increase in the supply of unskilled labor, will push wL down even if Home is a small open economy so that there is no terms-of-trade e¤ect. Whether the productivity e¤ect or these labor supply e¤ects dominates is an empirical question.

# 2.3.2 Continuum of skills.

Some recent work has aimed at a richer and more realistic account of income inequality by looking at trade models with a continuum of skill levels and hence a continuum of income levels. Blanchard and Willman (2008) formulate a model with a continuum of goods indexed by j 2 [0; 1] and a labor force with a continuum of ability levels, a 2 [0; 1], exogenously given as realizations of a random variable. In order to produce product j, a worker needs to complete the appropriate education, which costs the worker c(j; a). This is increasing in j, so that industries are ordered in increasing order of skill requirement; and decreasing in a, so that the cost of acquiring any sort of education is smaller for a person endowed with high ability. Further,<sup>@2c(j;a)</sup> < 0, so that the marginal cost of choosing a more di¢ cult industry is @j@a lower for a person of higher ability. Once a worker has acquired the skill required to produce j, she can produce 1 unit of it. In equilibrium goods prices j 2 [0; 1] induce each worker of ability a to choose an industry j such that the quantity of each good produced is equal to the quantity demanded. The price function must be increasing in j, to provide an incentive for workers to acquire the skills required to produce some of each good. The exact shape of the price function is determined as the solution to a di¤erential equation.

This structure allows the authors to look at questions of income distribution that would be unthinkable in a model limited to high-skill and low-skill workers only. For example, the 19
authors are interested in the e¤ects of trade on the middle class. They examine one numerical example in which Home has an educational cost function given by and Foreign has an educational cost function given by: The consequence is that the cost functions are quite similar except as j gets close to 1, in which region Foreign’s cost function becomes sharply higher than Home’s. Thus, Foreign’s educational system has trouble generating the skills required for the most advanced industries. Other than that, the two countries are identical, with a uniform distribution of a’s and Leontie¤ preferences. Solving the equilibrium, we observe ‘sorting down’in Home for low-skill workers, meaning that a worker of a given ability chooses a lower-skill industry than the worker would have chosen under autarky. At the same time, we observe ‘sorting up’for Home’s high-skill workers. Put di¤erently, under trade, Home workers ‡ee the middle-range industries. An interpretation is that Foreign’s educational costs discourage Foreign’s high-ability workers from pursuing the high-skill industries, so a disproportionate number of Foreign’s high-ability workers wind up in middle-range industries (a pattern exacerbated by trade with Home, which will lower the price of high-skill products). This pushes down the prices of middle-range goods compared to what would have been observed in Home under autarky, causing Home middleability workers to ‡ee the middle, with upper-middle-ability workers ‡eeing upward and lowermiddle-ability workers downward. Thus, in Home, trade ‘hollows out the middle class.’ In addition, the e¤ect of trade on welfare is non-monotonic: Low-ability and high-ability Home workers bene...t from trade, but due to the crash in the prices of medium-level goods, a range of middle-ability Home workers is hurt. Obviously, none of this discussion would have been 20
possible in a model limited to ‘high-skill’and ‘low-skill’workers.

A closely related paper is Costinot and Vogel (2010), who also look at a model with a continuum of goods, each of which is produced with labor alone and which di¤er in their skill intensities. Precisely, the output of an industry with skill-intensivity index � is equal to A(s; �) per worker, for a worker of skill level s, where A(s; �) is increasing in s and satis...es: for any s; s<sup>0</sup> ; �; �<sup>0</sup> such that s<sup>0</sup> > s and �<sup>0</sup> > �, so that skill is disproportionally valuable in high-skill-intensive industries. This assumption is called ‘complementarities in production.’ There is an exogenous supply of each of a continuum of di¤erent skill levels in each country, represented by the function V (s) for Home and V<sup>�</sup> (s) for Foreign. Equilibrium is again a schedule of prices such that the way workers choose to sort themselves across industries given that price schedule creates supply that matches with consumer demand for each good. Condition (7) ensures that each skill level chooses one and only one industry, and that higherskill workers match themselves in equilibrium to higher-skill-intensive industries.

With this framework, the authors are able to look at a number of interesting possible e¤ects of trade on income distribution. First, they have a simple and elegant generalization of StolperSamuelson. If Home is skill-abundant relative to Foreign, which means that V (s<sup>0</sup> )=V (s) > V<sup>�</sup> (s<sup>0</sup> )=V<sup>�</sup> (s) whenever s<sup>0</sup> > s, then trade increases income inequality in Home, meaning that whenever s<sup>0</sup> > s, where w(s) denotes the wage paid to a Home worker of skill level s under autarky and w<sup>0</sup> (s) is the corresponding wage under free trade. The opposite e¤ect is found in Foreign. In addition, they analyze a simple concept of o¤shoring: Suppose that technology in Home is superior to the technology in Foreign, in that the A(s; �) function in Home is a scalar 21
multiple of the function in Foreign. Suppose that under free trade, workers produce in Home with Home’s technology and workers in Foreign produce with Foreign’s technology. However, when o¤shoring is allowed, a producer in Home can hire workers in Foreign to produce output using Home’s superior technology. Costinot and Vogel show that this is equivalent to increasing the labor supply of Foreign across the board, and as a result it pushes down the wages of lowskill workers in both countries, pushing up the wages of high-skill workers in both countries, and raising income inequality in both countries in the sense of inequality (8). This is, of course, an interpretation of o¤shoring that is very close to the Feenstra-Hanson view.

These are both generalizations of earlier results on North-South trade. Perhaps the most interesting point, however, involves ...ndings on North-North trade. Suppose that the Home economy is more diverse than Foreign, in the sense that there is a cuto¤ skill level s<sup>0</sup> such that among skill levels less than s<sup>0</sup> Home is low-skill abundant relative to Foreign but among skill levels above s<sup>0</sup> Home is high-skill abundant relative to Foreign. In other words, compared to Foreign, Home has fatter tails in its skill distribution, rather than a di¤erence in average skill abundance. Then when we let the two countries trade, low-skill Home workers sort down; high-skill workers sort up; and wages of middle-income Home workers fall relative to workers at both ends of the spectrum. In other words, this is the ‘hollowing out of the middle class’ studied by Blanchard and Willmann, arrived at by a somewhat di¤erent mechanism.

# 2.4 Labor market frictions.

A number of recent papers explore trades’ impact on income distribution in the presence of labor market frictions. Mitra and Ranjan (2007), for example, apply models of search unemployment to examine the impact of o¤shoring. For reasons similar to the mechanism in Grossman and Rossi-Hansberg (2008), they ...nd that o¤shoring in a given industry can lower domestic unemployment in that industry. The point is, once again, that o¤shoring can create a productivity bene...t for domestic labor, and that induces domestic ...rms to increase the 22
rate at which they create vacancies for domestic employment. In the long run, this reduces unemployment. Anderson (2009) studies a model in which workers must choose in which sector to acquire skills, becoming a speci...c factor after that choice is made; opening up trade increases income inequality by increasing income di¤erentials across industries.

A di¤erent approach to labor market frictions is pursued in Artuç, Chaudhuri, and McLaren (2008, 2010). In those papers, a worker is assumed to be able to switch industries at any time, but must incur two costs. The ...rst is a common cost, a parameter constant across time and the same for all workers. The second is idiosyncratic and time-varying, and can be negative. For example, a worker may become bored of her work, or have an altercation with a supervisor, or need to move geographically for personal reasons to a part of the country where the industry she was in does not exist. On the other hand, the worker may be at the moment really enjoying her work, or have children who are attached to their school friends, making a move costly. These idiosyncratic, time-varying costs are important because they allow for a model that generates a very important fact in the data: Gross ‡ows of workers across industries are an order of magnitude greater than net ‡ows. At any given moment, between any two industries, one tends to see large numbers of workers moving in opposite directions at the same time.

Building these features into a rational-expectations model, one ...nds a number of implications for trade and income inequality. (i) The e¤ect of trade on the distribution of wages can be very di¤erent from the e¤ect of trade on the distribution of lifetime incomes. It is easy to construct an example, and with realistic parameter values, of a trade liberalization that lowers real wages for the import competing industry in the short run and the long run, but that increases the expected lifetime utility of all workers in the import-competing sector. This is because of option value: Each worker in the import-competing sector knows that there is a positive probability that in a given number of years she will choose to move to one of the other sectors. Since trade liberalization raises the real wage in those industries, the value of 23
that option has now gone up. (Similar issues arise in the search literature, as discussed at length in Davidson, Martin and Matusz (1999); see Davidson and Matusz (2009, Ch. 8) for an applied example.) (ii) Announcing trade liberalization in advance tends to soften the blow for workers in the import-competing industry and also reduce the bene...t to workers in the export industry. This is because of anticipatory movement of workers out of the import-competing industry, pulling up wages there before the liberalization occurs, and pulling wages down in the export sector. In the limit, with enough advance warning, all workers are guaranteed to have the same sign of net bene...t from the liberalization, but this could be positive or negative.

# 2.5 Consumer e¤ects and incomplete contracts.

We now look at two strands that have not been explored much but could capture important pieces of the relationship between trade and inequality.

## 2.5.1 A consumer-side approach.

A very di¤erent and potentially very promising approach is taken by Fajgelbaum, Grossman and Helpman (2009). They focus on consumer-side e¤ects of trade on income inequality. The model is built on two sectors, a competitive numeraire sector producing a homogeneous good and a monopolistically-competitive sector in which products are di¤erentiated horizontally (as in standard monopolistic competition models) but also vertically, so that consumers can choose di¤erent varieties and also di¤erent qualities of di¤erentiated product. Both sectors use only labor to produce output. Workers di¤er in their productivity according to an exogenous distribution. They all have the same utility function, which is non-homothetic: consumers with higher income demand higher-quality goods. If two economies open to trade, not only will the number of ...rms in each country and the product diversity available to each consumer be a¤ected as in standard monopolistic competition models, but the quality composition of goods 24
will also be a¤ected in complicated ways that depend on income inequality. The authors study an example with two countries that are identical except that one of them has more productive workers on average. When the cost of transporting high-quality goods falls, the number of high-quality ...rms rises, bene...tting a- uent consumers in both countries. This draws resources away from low-quality goods, reducing the product diversity available to low-income consumers and, for some parameter values, lowering their welfare.

The novelty in this model is that trade does not a¤ect the distribution of income at all, in terms of the numeraire. That is ...xed in each country by the exogenous distribution of worker productivities. It does, however, a¤ect the distribution of real incomes, because consumers at di¤erent income levels consume di¤erent goods. In this sense, it is a consumer-side account of trade and income distribution, while previous approaches work through the factor markets. Since in truth the rich and the poor certainly do consume di¤erent bundles of commodities and di¤erent qualities of goods, this channel may be a very important one to explore in the future.

# 2.5.2 Implicit contracts.

For people who do not live in an Arrow-Debreu economy, good luck can translate into high income and bad luck can lead to poverty. For this reason, risk-sharing institutions can have an enormous e¤ect on income inequality, and to the extent that trade a¤ects those institutions they can be an additional channel through which trade a¤ects inequality. An early exploration of this idea is found in Matusz (1985), who incorporates a simple form of incomplete contracting from the macroeconomics literature into a Heckscher-Ohlin model. In that model, ...rms in one industry su¤er random, idiosyncratic productivity shocks. Employers are risk neutral and workers are risk averse. Employers would like to be able to o¤er employment contracts to workers that put the workers to work in a high-productivity state and lay them o¤ in a low-productivity state, with a payment to the worker that does not depend on the state, but 25
they are prevented from doing so because employers cannot credibly commit to paying the worker anything in a state in which the worker is not producing output. As a result, the low-productivity state has (ine¢ cient) positive employment with a positive probability, with a positive wage paid only when the worker is employed. The fact that the wage will be zero in the event of a layo¤ implies that ...rms must pay a risk premium to workers, which lowers expected pro...ts. Matusz shows that in this sort of model a weakened Stolper-Samuelson theorem holds –over a signi...cant portion of the parameter space, trade raises the welfare of workers and lowers the returns to capital if the economy is labor-abundant (and vice-versa if it is labor scarce). However, even when that familiar relationship holds, it is possible that trade increases the unemployment rate in the implicit contracts sector, with the wage for employed workers rising enough to give an increase in expected utility to workers. It is further possible that the aggregate unemployment rate rises even when the industry’s unemployment rate does not, because a larger fraction of workers is drawn out of the full-employment sector and into the sector with implicit contracts and positive unemployment. In both cases, the point is that although the average worker’s welfare is increased by trade, because of implicit contracts, both unemployment and wage inequality can rise.

The idea has been extended to the ‘invisible handshake’ studied by labor economists, the idea that a risk-neutral employer may o¤er wages smoothed over states of nature to a risk-averse worker, in e¤ect selling insurance at the same time as it buys labor. However, since these arrangements are implicit contracts and based on shocks that are not observable to third parties, they depend upon reputation built out of repeated interactions. The only punishment available to deter an employer from reneging on its wage commitment today is the loss of the worker tomorrow. Consequently, if employers are not su¢ ciently patient, only imperfect insurance can credibly be o¤ered, and in that case an employer will cut wages in lean times. The upshot is that the more impatient an employer is, the more volatile individual workers’wages will be, and the more variance will be observed in the cross section among 26
observationally identical workers.

Bertrand (2004) follows the implications of this thinking in the context of international trade, showing that where ...rms face liquidity constraints and can exit due to bankruptcy, an import shock can make employers e¤ectively less patient by raising the probability of bankruptcy and raising their e¤ective discount rates. Thus, a rise in imports in a given industry can increase wage inequality within that industry (and by the same token opening up an export opportunity can reduce it). Karabay and McLaren (2010) examine invisible handshakes in a two-country general-equilibrium model with both goods trade and o¤shoring of tasks (in the primitive sense that they look at autarky versus free goods trade, and free goods trade versus complete integration of world goods and factor markets). Even though there is no bankruptcy in the model, trade has large e¤ects on wage volatility through implicit contracts. An exporting sector sees a rise in its output price due to trade, which raises the amount it loses if the worker walks away due to a wage dispute. Therefore, the penalty to reneging on a wage promise is steeper, allowing the employer to make promises of stable wages with more credibility. Consequently, wage inequality falls within an export sector, with the opposite e¤ect in an import-competing sector. On the other hand, o¤shoring from a labor-scarce economy to a labor-abundant one makes it easy for an employer to ...nd a new worker to replace one it has lost, thus reducing the punishment to reneging and making it harder for employers to promise stable wages credibly. As a result, an o¤shoring industry sees an increase in wage inequality, ceteris paribus. Putting these together, the model predicts that implicit contract e¤ects produce a net increase in wage inequality in a labor-scarce economy due to both forms of globalization together, and the opposite e¤ect in a labor-abundant economy. (Of course, in practice these e¤ects are combined with all of the other e¤ects on wage inequality highlighted above, so it could be di¢ cult to disentangle the e¤ect empirically.) 27
## 2.6 Summary of Theory Developments.

A summary of the main thrusts of the theory can be put as follows. The older theory o¤ered two stories: Trade a¤ects inequality either by a¤ecting the skill premium (in the StolperSamuelson theorem), or by a¤ecting industry premia (in the speci...c-factors model). It was hard to rationalize how trade could raise inequality everywhere in the world at the same time, or inequality within any group of similarly-skilled workers all doing the same job. It was also hard to see how North-North trade could a¤ect inequality at all. But now, we have stories that predict rising skill premia across countries as a result of North-South trade in tasks, and even as a result of North-North trade in goods due to R&D e¤ects or the skill bias of the transport sector. We have high-dimensional models that go beyond the skill premium to analyze the e¤ect of trade on the ‘middle class,’and distinguish between wage inequality and inequality in lifetime consumption through explicitly dynamic models of labor adjustment. We are also able to analyze the e¤ects of trade on inequality among observationally identical workers doing the same job in the same industry, through heterogeneous-...rms models or implicit contracts models. This rich set of stories helps in describing the e¤ects of trade on income distribution in the real world.

# 3 Empirical Work.

An immense empirical literature exists on the possible linkages between trade and inequality. Most of this literature predates the ‘new’trade models and focuses on testing the implications of the Heckscher-Ohlin framework for trade-inequality linkages. A number of literature surveys also review this work. See for example, Feenstra and Hanson (2001), and Goldberg and Pavcnik (2004, 2007). As in Section 2, we begin in Section 3 with only a brief review of the empirical literature associated with the ‘older’trade models, and then move on to review empirical papers that test the newer theories linking trade to inequality described in Section 28
2.

# 3.1 Earlier Work: Tests of the Heckscher-Ohlin and Speci...c Factor Models.

An excellent summary of the literature on trade and wages is provided by Robert Feenstra in the introduction to his 2000 volume, The Impact of International Trade on Wages. Feenstra begins by documenting a sharp increase in the ratio of the wages of non-production workers to production workers between 1982 and 1994. Summarizing the papers in the volume, Feenstra concludes that there is some role for international trade in a¤ecting the wages earned by American workers. Goldberg and Pacvnik (2007), Feenstra (2008), and others conclude that stylized facts on the evolution of inequality within developing countries as they open up to trade are not consistent with a na¬ve view of the HO model. Donald R. Davis and Prachi Mishra (2007) go further and argue that “Stolper-Samuelson is dead.” They write that use of trade theory to suggest that liberalization will raise the wages of the unskilled in unskilled labor abundant countries is “worse than wrong— it is dangerous.” Davis and Mishra show that such arguments are based on a very narrow interpretation of the Stolper-Samuelson (SS) theorem. In particular, SS holds only if all countries produce all goods, if the goods imported from abroad and produced domestically are close substitutes, or if comparative advantage can be ...xed vis-a-vis all trading partners. As an illustration, a poor country in a world with many factors and many goods may no longer have a comparative advantage in producing low-skill goods. This is easy to understand in the context of three countries; consider, for example, the United States, Mexico, and China. Although Mexico might have a comparative advantage in producing low-skill goods in trade with the United States, its comparative advantage switches vis-a-vis trade with China.

In part to address these and other shortcomings of the HO framework for explaining the rise in inequality within both developing and developed countries, as well as within industries, 29
empirical investigations have branched out into a number of directions, including ...rm-level analysis, new approaches to trade in tasks and o¤shoring, and, to a limited degree, implicit contracts.

# 3.2 Empirical Work on Heterogeneous Firms and Bargaining.

In part because the literature on ...rm heterogeneity is so new, and in part because the data demands for testing these theories are quite high, not many studies are available in this area. To take ...rm and/or worker heterogeneity into account properly, information at both the ...rm and individual employee level is typically required, suggesting the need for matched employeeemployer datasets. In this section, we review several recent papers that have succeeded in contributing to this literature.

The pioneering work on trade and income inequality with heterogeneous ...rms actually predates the theory. Bernard and Jensen (1997) study the Annual Survey of Manufactures from the US Census Bureau to decompose the large rise in average skilled wage premia that occurred over the 1980’s. They show that a substantial fraction of the increase occurred between plants, in other words, by intra-industry shifts in the allocation of workers from plants with lower skill premia to ...rms with higher premia. This between-plant e¤ect is larger than the within-plant e¤ect (which is merely a rise in the skill premium for any one ...rm over time). Indeed, by some measures, the between-plant e¤ect is completely dominant (Table 5). Further, it occurs entirely among ...rms that export, and vanishes when the sample is restricted to ...rms with only domestic sales. This was an early indicator that trade might cause an increase in wage inequality through within-industry e¤ects, a mechanism very di¤erent from HeckscherOhlin, and alerted the ...eld that ...rm heterogeneity may have something important to do with the e¤ect of trade on inequality.

More recently, Menezes-Filho and Muendler (2007) combine insights from the Melitz (2003) model with worker heterogeneity to provide a compelling empirical example of the importance 30
of some of the more recent theoretical breakthroughs. These authors link worker-level panel data with ...rm-level and industry-level data to obtain a rich dataset that allows them to test many implications of the most advanced trade models (e.g. heterogeneous-...rm models that incorporate heterogeneous labor) for Brazil. In so doing, the authors are able to assess the impact on jobs of Brazil’s trade liberalization during the 1990s while controlling for a number of worker-speci...c, ...rm-speci...c, industry-speci...c, and economy-wide structural reforms. Menezes-Filho and Muendler’s dataset allows them to follow workers throughout the liberalization period and observe the path of their employment histories in greater detail than previous studies. They are particularly interested in the e¤ects of trade liberalization on employment status, type of employment (formal or informal), and job reallocations.

Menezes-Filho and Muendler’s results show that exporting ...rms and ...rms in industries with a “comparative advantage" shed workers more frequently. Moreover, these same ...rms also hire workers less frequently than the average ...rm. Thus, on net, trade liberalization leads to net employment losses in these ...rms. This is surprising given the standard predictions of international trade models that would indicate that these sectors and ...rms would potentially hire more workers when liberalization occurs. Menezes-Filho and Muendler also show that tari¤ reductions and increased import penetration are associated with an increase in the likelihood of a worker transitioning into informality and unemployment, as well as with a lower probability of a transition from informality back to formal employment. Furthermore, they ...nd that trade liberalization in Brazil has been associated with longer reallocation times for workers moving from one formal-sector job to another formal-sector job. Their results are robust to di¤erent levels of exposure to trade, ...rm-level productivity, worker heterogeneity, as well as other general trends that occurred in the country during the period studied–such as skill-biased technological change and labor market reforms.

Kaplan and Verhoogen (2009) use matched employer-employee data from Mexico to examine the wage premia paid by exporters in the Mexican manufacturing sector. Wage premia are 31
de...ned as wages above what workers would earn elsewhere in the labor market. Because of the nature of their data, Kaplan and Verhoogen are able to decompose plant level wages into a component that re‡ects skill composition and a component that re‡ects wage premia. Their identi...cation strategy is based on the peso devaluation of 1994 that they argue di¤erentially a¤ected incentives to export within industries. Comparing across plants within industries, they ...nd that roughly two thirds of the higher level of wages in larger, more productive plants are explained by wage premia and that nearly the entire di¤erential within industry wage changes induced by the shock to exports is explained by wage premia and not by skills. The authors conclude that sorting on individual ability is not responsible for the well-documented correlation between exporting and wages.

As the ...rst contribution in the literature to account for both ...rm heterogeneity and intermediate trade in their analyses, Amiti and Davis (2008) o¤er a theoretical and empirical examination of the impact of tari¤ cuts on workers’wages that accounts for the extent of a ...rm’s engagement in international trade. Using Indoneisan manufacturing census data for 1991-2000, a period that encompasses Indonesian trade liberalization, the authors develop a general equilibrium model to estimate this relationship. They ...nd that the impact of a given tari¤ change on a ...rm’s workers’wages is dependent upon that ...rm’s role in the global economy. That is, a 10 percentage point decrease in output tari¤s will lower wages of importcompeting ...rms by 3 percent but will raise wages at exporting ...rms by 3 percent. Likewise, a decrease in input tari¤s by 10 percentage points will increase wages by 12 percent at ...rms that rely on imports but will have an insigni...cant impact on the wages of ...rms that rely on a domestic supply.

As Amiti and Davis (2008) summarize, their ...ndings show that trade liberalization raises wages for workers at ...rms that are most globalized and lowers wages at those ...rms that are either marginalized in the global economy and/or oriented toward the domestic market. This provides some con...rmation for the ideas in theoretical work such as Egger and Kreickemeier 32
(2009) and Helpman, Istkhoki and Redding (2010) that hypothesizes a relationship between ...rm-speci...c wages and how the ...rm responds to globalization.

Bustos (2007) posits that an examination of wage inequality that examines the interaction between trade and technology— as opposed to selecting one explanation in preference over the other— will o¤er a better explanation of the relationship between global trade and inequality. Bustos therefore presents a model of the relationship between trade liberalization and demand for technology and skill among ...rms in developing countries that accounts for ...rm heterogeneity. She tests this model using panel data from Argentine manufacturing ...rms. The dataset spans 1992-1996 and therefore captures a period of trade and capital account liberalization in Argentina.

Bustos ...nds a strong relationship between exporting and increases in technology investment and skill upgrading. Speci...cally she ...nds that, prior to trade liberalization, continuing exporters and foreign owned ...rms employed higher skilled labor than those ...rms that were domestically owned and that had never exported. Those ...rms that began exporting after liberalization upgraded worker skill more quickly than those ...rms that remained exclusively in the domestic market; they also upgraded technology more quickly than all other ...rms. Further, after trade liberalization, new and continuing exporters as well as foreign owned ...rms spent 53-69 percent more on technology than their domestic non-exporting counterparts. Those ...rms that invested more in technology upgrading also realized a faster increase in skilled labor. Bustos concludes that, due to the consequences of rising demand for technological investment, trade liberalization can have a strong impact on worker skill upgrading.

While much of the literature (for example, Verhoogen (2008) and Bustos (2007)) looks at the impact of the act of exporting on ...rm behavior, Brambilla, Lederman, and Porto (2010) focus on how the destination of those exports explains ...rm behavior. Brambilla et al develop and then test an integrated theory of export destinations and skills. Exploring the linkages among exports, export destinations, and the use of skilled labor by ...rms, Brambilla 33
et al theorize that ...rms exporting to high income destinations will hire a higher proportion of high skilled workers and will pay them higher wages than ...rms that either export to low or middle income countries or sell their products domestically. They test their theory with 1998-2000 panel data from Argentine manufacturing ...rms. Their ...ndings show that Argentine ...rms exporting to high-income countries are associated with higher skilled workers and higher average wages than ...rms that either do not export or export to middle income countries. However, they ...nd no signi...cant di¤erence in ...rms’use of skilled labor between those ...rms selling their product domestically and those exporting to low and middle income countries. The authors reason that these results are due to the similarities in the domestic and export markets among low and middle income countries. Their theory and results are in line with Verhoogen’s (2008) ...ndings on the quality upgrades of exporting ...rms and Bustos’ (2007, 2009) work on technology and skill upgrading behavior of exporting ...rms. The results further suggest that non-homotheticities in demand are important for income distribution (as suggested in theory, though not with the same mechanism, by Fajgelbaum, Grossman and Helpman (2009)).

To sum up, the emerging work on trade and inequality with ...rm-level data appears to be con...rming a central role for between-...rm e¤ects in governing the relationship between trade and inequality, and the available results seem to support the thrust of theoretical models in Section 2.2 that predict a rise in inequality with more openness.

# 3.3 New Empirical Work on Trade in Tasks.

Much new empirical work focuses on the fragmentation of the production process, or o¤shoring. Recall from Section 2.3.1 that one of the pioneering theory models in this area was provided by Feenstra and Hanson (1996); not surprisingly, they also pioneered the empirical work (Feenstra and Hanson (1996, 1997, and 1999)). Recall that in that model, o¤shoring increases the relative demand for skilled labor in both countries involved because the o¤shored 34
tasks are more skill-intensive than those previously performed in the country to which they were o¤shored, but they are less skill-intensive than those in the country that is doing the o¤shoring.

Feenstra and Hanson (1999) test whether their explanation for the increase in the demand for skill, based on more o¤shoring, is consistent with the pattern of increasing wage inequality in the United States. They consider the alternative hypothesis that skill-biased technological change accounted for the observed increase in wage inequality. They proxy for technical change with the fraction of high-technology equipment in each industry’s capital stock and they measure o¤shoring with the intermediate inputs imported by each industry. They use a two-step procedure, ...rst to identify the impact of o¤shoring and high technology investments on productivity and prices, and then to trace through the induced productivity and price changes to calculate production and non-production wages.

Using data for the U.S. manufacturing sector between 1979 and 1990, Feenstra and Hanson (1999) ...nd that 25 percent of the increase in the relative wage of nonproduction workers was explained by o¤shoring and about 30 percent by technological change. They conclude that both o¤shoring and the increased use of high-tech capital are important in explaining the increase in the relative wage of skilled workers. They also examine the impact on real wages as distinct from relative wages, which are the focus of measures of inequality. They ...nd that the real wages of production workers were probably una¤ected by o¤shoring activities while the real wages of non-production workers increased by 1 to 2 percentage points. Sitchinava (2008) updates the Feenstra and Hanson (1999) paper to 1996 and also takes into account the possibility of services o¤shoring. Sitchinava ...nds that most of the increase in the relative wages of nonproduction relative to production workers can be explained by technical change, which is proxied with the share of high-technology equipment in the capital stock.

Adapting Feenstra and Hanson (1999) to measure service o¤shoring, Amiti and Wei (2009) provide evidence for the e¤ects of both service and material o¤shoring on domestic productiv35
ity growth. Using US Bureau of Labor Statistics data from 1992-2000, they ...nd that service o¤shoring has a signi...cant positive e¤ect on labor productivity growth, accounting for approximately 10 percent of average growth in this factor. While material o¤shoring also has a positive e¤ect, it is smaller in magnitude— accounting for 5 percent of average growth in labor productivity— and not signi...cant across all speci...cations. They conclude that service o¤shoring does have a positive impact on labor productivity growth in the US and speculate that the smaller and less signi...cant values for material o¤shoring may be due to possible decreasing returns from scale and over time from this sector.

Liu and Tre‡er (2008) analyze the impact of not only o¤shoring but also inshoring— the sale of service produced in the US to una¢ liated buyers in China and India— across several indicators: workers’change of occupation and industry; weeks spent unemployed as a share of total weeks in the labor force; and earnings. They ...nd that the total net e¤ect of inshoring and o¤shoring is positive. However, for those workers in industries exposed to o¤shoring and those workers who are less educated the e¤ect is either less positive or negative.

A di¤erent approach is explored by Ebenstein, Harrison, McMillan, and Phillips (2009), who focus on the e¤ects of trade across di¤erent types of task, as measured by the routineness of di¤erent occupations. Typically, highly routine occupations are associated with workers who have lower educational attainment, while less routine occupations are associated with higher skills and educational attainment.

Why should routineness matter? Grossman and Rossi-Hansberg (2008) posit that improvements in technology make o¤shoring less costly. Cost reductions are much more likely for routine tasks, which are more easily codi...ed and can be communicated and consequently transferred to overseas a¢ liates. Ebenstein et al test this hypothesis by assessing the empirical relationship between the routine nature of a task and o¤shoring. Their measure of routine is based on Autor, Levy, and Murnane (2003) who describe routine jobs as “tasks that can be expressed using procedural or ‘rules-based’logic, that is codi...ed in a fully speci...ed sequence 36
of logical programming commands (“If-Then-Do”statements) that designate unambiguously what actions the machine will perform and in what sequence at each contingency to achieve the desired result.”While Autor et al (2003) use routineness to designate which jobs can be easily performed by computers, the jobs that are classi...ed as routine also include the jobs in manufacturing that we typically think of as being o¤shorable. These jobs include: attaching hands to faces of watches, sewing fasteners and decorative trimming to articles and, though not mentioned explicitly in their paper, include services tasks that we think of as o¤shorable such as answering telephones.

We can contrast this occupation-based approach to a well-known alternative, which is to examine the changes in import penetration across industries (what Goldberg and Pacvnik refer to as the “di¤erential exposure approach”). A di¢ culty with that approach is that, in the event that workers can change industries more easily than occupations, such an approach will miss the main e¤ect; industry premia will be largely arbitraged away, but premia to each occupation can be large and very much a¤ected by trade. Ebenstein et al address this problem by calculating an occupation-speci...c measure of o¤shoring, import competition, and export activity, and show that although international trade has not had large e¤ects on industry premia, it has had large, signi...cant e¤ects on occupation-speci...c wages for routine workers.

Ebenstein et al merge Current Population Survey (CPS) data on US wage earners from 1983 through 2002 with data on import competition, export activity, and o¤shoring employment of U.S. multinational ...rms to show that the impact of o¤shoring on labor-market outcomes depends both on the location of o¤shore activity and on the routineness of the task performed by the worker. Expansion in o¤shore employment in low-income locations is associated with wage reductions for routine workers. However, o¤shore activity in highincome locations is positively correlated with routine wages. These associations, which are signi...cantly stronger in the 1990s relative to the previous decade, parallel earlier ...ndings by Bernard, Jensen and Schott (2006), who show that US manufacturing plants whose dominant 37
industry is one in which low-wage-country imports are large are more likely to exit and less likely to expand, and these di¤erences are more pronounced for more labor-intensive plants; imports from other countries have a much smaller e¤ect, and sometimes the opposite sign. These two studies suggest that the e¤ect on US income distribution of import competition from, and o¤shoring to, low-wage countries seems to be qualitatively di¤erent from the e¤ect of high-wage countries.

Ebenstein et al also ...nd signi...cant e¤ects of import competition on employment reallocation, ...nding that the largest e¤ect of globalization on low-skilled workers’income comes from movement from higher-wage industries to lower-wage ones. This parallels earlier ...ndings by Bernard and Jensen (1999), who found that between-industry e¤ects were a large component of increases in the average skill-premium in the 1980’s, although they were not able to pin down globalization as the cause.

Ebenstein et al also ...nd much stronger e¤ects of o¤shore activities on domestic wages in the later part of the sample period, between 1997 through 2002. Occupation-speci...c changes in o¤shoring and trade are associated with signi...cant wage e¤ects, particularly for workers who are in routine occupations. For these workers, a 1 percentage point increase in low-income o¤shore a¢ liate employment is associated with a 0.11 percent fall in wages. For these same workers, however, increasing a¢ liate activity in high-income locations is associated with a 0.1 percent increase in wages. A 1 percent increase in export shares is associated with a 1 percent increase in wages while a 1 percent increase in import penetration is associated with a 0.46 percent decline in wages. The e¤ects of these globalization measures are generally small in magnitude and insigni...cant for individuals who are in the least routine occupations.

Ebenstein et al also ...nd that the net impact of o¤shoring on wages is a function of the nature of the job: workers who perform more routine tasks have experienced wage declines as a result of o¤shoring, while workers who perform non-routine tasks have experienced wage increases. For routine occupations, which are more easily transferred o¤shore, the net e¤ect 38
on wages is negative but for the least routine (skilled) occupations, the net e¤ects are positive. Recalling the Grossman and Rossi-Hansberg (2008) model of Section 2.3.1, one might interpret these ...ndings roughly as implying that the labor-supply e¤ect of o¤shoring exceeds the productivity e¤ect for the lower-skill workers who specialize in the more-easily-o¤shored routine tasks.

Hummels, Jorgensen, Munch, and Xiang (2010) analyze the relationship between o¤shoring and workers’wages and employment opportunities. They use a matched worker-...rm data set that encompasses the Danish labor force from 1995-2006 as well as a data set on o¤shoring at the ...rm level. They estimate the impact of exogenous shocks to o¤shoring and exporting on ...rm characteristics and on the wages of individual workers. Further, they assess the dependency of these estimates on the education and occupational characteristics of the workers so as to understand the relative sensitivity of types of workers and occupations to o¤shoring. They ...nd that exogenous import shocks will have signi...cant and opposite e¤ects on skilled and unskilled labor wages: skilled labor wages will increase by 8.5 percent while unskilled labor wages will decrease by 7.3 percent. In contrast, shocks to exporting will increase both skilled and unskilled labor wages but low and medium skill workers will see a greater increase.

The examination by Hummels et al of the role of occupational characteristics in wage inequality reveals that workers who are exposed to unsafe working conditions and workers in the natural sciences and engineering will see their wages fall in the case of o¤shoring shocks while those workers in the social sciences and language industries will be less a¤ected by those shocks.

Hummels et al also consider the relationship between displaced workers and o¤shoring, ...nding that those workers displaced by o¤shoring generally experience greater and more persistent wage and earnings loss than workers displaced for other reasons. While initially both low and high skill displaced workers experience wage loss, this loss is smaller and less persistent for high skill workers. A year after losing their jobs to o¤shoring, skilled workers will 39
have lost 19 percent of their predisplacement earnings (which accounts for both lost hours and lowered wages once the worker has re-entered the workforce) as compared to the 28 percent loss experienced by unskilled workers. Additionally, Hummels et al ...nd that it is essential to control for endogeniety of trade events in such an analysis.

An additional ...rm-level study by Sethupathy (2009) shows that over the period in which the North American Free Trade Agreement (NAFTA) came into force, lowering costs of o¤shoring within North America, US ...rms that already o¤shored to Mexico signi...cantly increased: (i) their o¤shoring to Mexico; (ii) their operating pro...ts per US worker; and (iii) the wages they paid to their US workers –without, apparently, reducing their US workforce. This suggests that some of the productivity bene...ts of the Grossman and Rossi-Hansberg (2008) model have been realized by those ...rms, and bene...tted those workers, but it should be noted that this ...nding does not imply any bene...t to workers outside of those ...rms (unlike the Grossman/Rossi-Hansberg model).

In sum, recalling the account in Section 2.3.1, there are two main stories that have emerged from the theoretical literature, ...rst, that o¤shoring can raise wage inequality in both countries as in Feenstra and Hanson (1996); and second, that o¤shoring can raise the real wages of unskilled workers by enhancing their e¤ective productivity, as in Grossman and Rossi-Hansberg (2008). These two predictions are distinct, but not mutually exclusive. There is now fairly strong evidence for the ...rst story, the income-distribution e¤ect, from multiple data sets and approaches. The second story has done less well when confronted with data, at least when the focus is on o¤shoring to low-wage-countries.<sup>5</sup>

# 3.4 Implicit Contracts.

Empirical tests of implicit-contract models with trade are rare. Bertrand (2004) points out that if implicit contracts are very e¤ective, then a workers’wages will be a¤ected by labor-

> 5It is worth noting that in the Bernard, Jensen and Schott (2006) and Ebenstein et al (2009) papers, Mexico is not classi...ed as a low-wage country.

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market conditions such as local unemployment rates at the time the worker joined the ...rm, but not by subsequent labor-market conditions. The reason is that the worker and ...rm will bargain for their optimal implicit contract at the beginning of their relationship, at which point the current unemployment rate will have an e¤ect on workers’bargaining power and hence on the wage agreed to; but if implicit contracts are strong and provide good insurance to the worker, for the remainder of the job, wages will simply follow the agreed-upon wage regardless of subsequent labor-market conditions. She ...nds that (i) a workers’current wage is a¤ected by initial conditions at the time of beginning of the job, independently of current labor-market conditions; and (ii) in industries hit by a rise in import penetration, the current wage is much more dependent on the current labor-market conditions compared with other industries. Together, these ...ndings suggest that (i) implicit contracts are important, and (ii) import competition indeed weakens them, as predicted by her model.

# 3.5 Labor Market Frictions.

Krishna and Senses (2009) o¤er an empirical study of the impact of openness to trade on domestic income. Whereas previous studies examine the impact on wage growth or wage premia, Kirshna and Senses examine the impact on wage volatility. Using longitudinal earnings data on workers from three panels (spanning 1993-2003) of the Survey of Income and Program Participation, they estimate the relationship between labor income risk (de...ned as the variance of unpredictable changes in earnings) and import penetration, a measure of industry exposure to international trade. They ...nd that a 10 percent increase in import penetration will increase the standard deviation in persistent (as opposed to transitory) income shocks by 20 to 25 percent for all workers. Their results are both statistically and economically signi...cant.

Krishna and Senses (2009) also estimate subsets of their data to identify the impact of openness to trade on particular industries and on workers who have changed employment from one industry to another; they ...nd higher income risk among workers who have switched from 41
one industry to another. Among those who switched, income risk was higher among those who moved to non-manufacturing sectors than those who switched within manufacturing sectors. In light of their ...ndings, Krishna and Senses (2009) conclude that the impact on labor income risk needs to be taken into account when calculating the costs of openness to international trade.

Robustness tests by Krishna and Senses (2009) reveal that controlling for o¤shoring causes the coe¢ cient on import penetration to increase. In addition, the o¤shoring variable is negative and signi...cant, suggesting that an increase in o¤shoring in a particular industry is associated with a decrease in income risk in that industry.

Artuç, Chaudhuri, and McLaren (2010) and Artuç and McLaren (2010) estimate and simulate the dynamic model of labor adjustment developed in Cameron, Chaudhuri, and McLaren (2007) and Chaudhuri and McLaren (2007) to assess the distributional e¤ects of trade shocks. The former study uses the US CPS data and the latter uses 2004-2006 data from the Household Employment Survey of the Turkish Statistical Institute. The studies estimate both the average cost of switching industries and the variance of idiosyncratic switching costs, and use the estimates to simulate a trade shock to the manufacturing sector. In both cases, the authors ...nd that, due to the high the costs of switching from one industry to another, the economy takes a decade to reach the new steady state after liberalization. During this time, workers move from the manufacturing sector to other sectors, wages in the manufacturing sector ...rst drop then rise as labor supply to that sector falls, and wages in other sectors at ...rst rise and then fall as labor supply to those sectors rises. However, throughout these ‡uctuations, the real wage of the manufacturing sector remains below that of the tari¤ steady state while the non-manufacturing sector real wage remains above it.

Importantly, the distributional e¤ects of the trade shock on lifetime expected utility are much smaller than the e¤ects on wages, once each worker’s future possible mobility and option value are taken into account. In particular, in many speci...cations import-competing 42
workers’ lifetime welfare rises despite a drop in their wages, because each manufacturing worker understands that there is a probability each year that she will choose to enter the expanding export sector and bene...t from the increased real wages there. A dynamic approach with a full accounting of option value therefore complicates the welfare analysis of income inequality. For example, recall that Ebenstein et al (2009) have argued that o¤shoring to lowwage countries has pushed large numbers of US workers from high-wage manufacturing jobs into lower-wage service-sector jobs. In a dynamic model, these workers may nonetheless bene...t from such o¤shoring, because each manufacturing worker knows that with some probability each year she will move into the service sector anyway; the value of this option is enhanced by any measure that raises the real wage in that sector.

# 4 Directions for Future Research.

Research in the 1990’s undermined the simple Hecksher-Ohlin theory linking trade and inequality, and economists pointed at non-trade factors, such as technology and labor institutions or laws, to explain rising inequality. However, now a number of other channels have been discovered that have led to a vigorous resurgence of the idea that trade can lead to a rise in inequality –with the new features that it can do so through North-North trade; in countries of the South; and within each industry and within each class of workers. These theoretical developments have been in important respects fed by empirical work, and are now in turn giving rise to a rich new empirical literature, partly due to the increasing access to ...rm-level data across an increasing range of countries.

A number of natural directions for future work suggest themselves. The new ideas on consumer-side e¤ects (Fajgelbaum, Grossman and Helpman (2009)) and on higher-dimensional income-inequality e¤ects (Section 2.3.2) await empirical exploration (with the exception of Broda and Romalis (2009) for the former), while the interactions of trade with imperfect contracting have had very little empirical attention. Most empirical work still focuses on 43
the manufacturing sector, which for most countries covers a minority of the workforce, while major e¤ects of globalization may make themselves felt in the remaining sectors (Ebenstein et al (2009)). Most work on inequality has been less focussed on whether real incomes have increased or fallen due to trade than on the the variance of incomes, and it is still di¢ cult to disentangle trade e¤ects from technology shocks. There has been very little attention in theory or in the data to the e¤ects of trade on income inequality across age categories (Artuç (2009)), and the empirical analysis of unemployment lags far behind the theory (Davidson and Matusz (2009)). All of these can usefully be placed on the agenda for the coming years.

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