Trade impacts on skill acquisition via variety expansion Yasuhiro Satoy

Kazuhiro Yamamoto

z

June 13, 2011

Abstract We show that trade enhances skill formation through gains from trade via variety expansion à la Krugman [25]. Although workers are identical as unskilled labor, they di¤er in their productivity as skilled labor. Workers become skilled by incurring training costs. By introducing these settings into a trade model with monopolistic competition, we show that, although trade makes all agents better o¤, its e¤ect is stronger for skilled workers than for unskilled workers, which stimulates skill acquisition. As a result of less productive workers becoming skilled, the wage dispersion among skilled workers increases.

JEL Classi…cation: F12, F16 Key words: trade, skill formation, variety expansion, wage dispersion, monopolistic competition

1

Introduction

Over the past several decades, increases in the percentage of skilled labor have been observed worldwide. For instance, from 1983 to 2002, the U.S. manufacturing sector experienced a 37percent increase in employment in high-skill occupations regardless of its contraction during that We thank Taiji Furusawa and two anonymous referees for their constructive comments and suggestions. We are also grateful to Hiroshi Aiura, Kenzo Abe, Kristian Behrens, Masahiro Endo, Masahisa Fujita, Koichi Futagami, Yuzo Honda, Ryoichi Imai, Jota Ishikawa, Michihiro Kandori, Toru Kikuchi, Fukunari Kimura, Hiroki Kondo, Kazuo Mino, Tomoya Mori, Se-il Mun, Toru Naito, Makoto Nirei, Ryoji Ohdoi, Daisuke Oyama, Dan Sasaki, Takashi Shimizu, Takatoshi Tabuchi, Toshiaki Tachibanaki, Takaaki Takahashi, Noriyuki Yanagawa, and Dao-Zhi Zeng for their helpful comments. Of course, we are responsible for any remaining errors. We acknowledge the …nancial support by the JSPS Grants-in-Aid for Scienti…c Research (S, A, B and C) and the MEXT Grant-in-Aid for Young Scientists (B). y Graduate School of Economics, Osaka University (Japan); E-mail: [email protected] z Graduate School of Economics, Osaka University (Japan); E-mail: [email protected]

1

period (Federal Reserve Bank of New York [16]). This trend has also been con…rmed with respect to many countries by Barro and Lee [8]. Whereas possible explanations for this trend have been widely investigated from the viewpoint of skill-biased technological progress (see Acemoglu [1]), several studies have uncovered possible important roles of trade in the enhancement of skill formation given the recent dramatic progress of globalization.

12

Conventional wisdom in trade theory provides the explanation based on the

Stolper-Samuelson e¤ect: international trade between developed and developing countries enhances skill formation in the developed country because trade with a relatively skill-scarce developing country raises the relative price of skill-intensive goods and the demand for skilled labor in the developed country and increases the skilled labor share there. More recently, Acemoglu [2] suggested that international trade, via the Stolper-Samuelson e¤ect, enhances the skill-biased technical change (i.e., technological progress in the skill-intensive sector) and increases further the demand for skilled labor to accelerate skill formation.3 Ishikawa [24] developed a Heckscher-Ohlin-Samuelson model with increasing returns in skill formation, in which scale economies in human capital enable a large country to specialize in the production of a skilled-labor-intensive good and trade with a small country that specializes in the production of an unskilled-labor-intensive good. In principle, trade has e¤ects on skill formation by a¤ecting the di¤erence in utility between skilled and unskilled workers. Changes in the utility can be decomposed into changes in the nominal income of workers and changes in the real income for given nominal income via variety expansion. International trade in‡uences relative wages (nominal income) of skilled and unskilled labor through Stolper-Samuelson e¤ect. The existing studies mentioned above focused on the former channel, 1

Skill-biased technical progress raises the demand for skilled labor and skilled worker wages. As pointed out by Krugman [27] (p. 66-68), even after the rapid proliferation of trade, trade constitutes only a certain part of the total spending in some developed countries, such as the United Sates. This suggests that the direct e¤ects of trade on the domestic labor market are limited and not dominant in such countries. Studies that include that by Borjas et al. [13] support this view by demonstrating that the e¤ects of trade on the wage structure diminished during the late 1980s in the United States. However, if we consider other factors, such as technological changes or changes in skill formation behavior that amplify the trade e¤ects, the overall trade e¤ects on the labor market can be signi…cant. In fact, some researchers have found empirical evidence to consider trade as a signi…cant candidate for the basis of income distribution. Richardson [35] (p. 36) surveyed quite a few empirical studies and concluded regarding the impacts of trade on income inequality that ”...Taken together, they [recent empirical contributions] suggest to me an important role for trade, close to or larger than its 10-15 percent share of U.S. output: not tiny, but not overwhelming either...” Moreover, Feenstra [17] enumerated more recent studies that support this view. Finally, for many European and Asian developed countries, trade occupies a signi…cant part of the total spending, and, hence, the e¤ects of trade on the labor market would be far from negligible. 3 In relation to this, Matsuyama [32] pointed out that, if the technology of the transportation sector is skill-intensive, technical progress in this sector enlarges the trade amounts and enhances skill formation. 2

2

implying that they rely primarily on the Stolper-Samuelson e¤ect in explaining the trade e¤ect on skill formation. We show that the latter channel works in bilateral trade models with monopolistic competition. In a model of this type, trade enlarges the varieties of available goods for people in trading countries. This consumption variety expansion raises the real income of trading countries. This type of gains from trade is well established in the literature of trade theory and plays a key role in our analysis. Of course, we do not intend to determine which channel is more important. We would rather argue that a more balanced treatment is necessary.4 In this paper, we present a trade model with monopolistic competition à la Dixit and Stiglitz [15] and skill acquisition. In our model, although workers are identical as unskilled labor, their productivity as skilled labor di¤ers from worker to worker, i.e., they are vertically heterogeneous. If a worker trains herself/himself, she/he becomes skilled. Thus, we embed vertical labor heterogeneity within the Krugman [25] model of trade under monopolistic competition and increasing returns5 . Using this model, we investigate the possible e¤ects of trade opening on the skill composition, the wage structure and the welfare. In our model, trade enables people to consume wider varieties of goods and lowers the price index of consumption goods, which leads to the higher welfare of all agents. However, it increases the di¤erence in utility between skilled and unskilled workers for a given wage income inequality between them. This encourages even less productive workers to become skilled, which enlarges the wage dispersion among skilled workers. Thus, our model shows that trade induces skill formation via increases in consumption variety. In models of New Economic Geography, like Krugman [26], utility of agents rises when the number of varieties of consumption goods increases. Krugman [26] showed that this e¤ect of variety expansion can cause migration of agents from the periphery regions to the core regions where they can enjoy higher utility for a given nominal income. Such migration mechanism is similar to the 4 In our paper, there are not any traditional Stolper-Samuelson forces, and all workers gain from international trade. However, if there are skill-intensive goods as well as labor-intensive goods and trade takes place between North and South countries, high ability agents may gains from trade whereas low ability agents lose from trade in the North. In the South, some agents may stop to acquire skill under trade liberalization. 5 Yeaple [36] focused on the interaction among monopolistic competition, (exogeneous) skill distribution of workers, and …rm technological choice and showed that a reduction in trade costs bene…ts …rms that choose relatively more skill-biased technology, which increases the share of such …rms accompanied by increases in wage rates for highly skilled workers. Hence, this model cannot investigate whether trade a¤ects skill composition. Amiti and Pissarides [3] constructed a trade model with monopolistic competition, horizontally heterogeneous workers, and skill formation. They examined the relationship between a skill mismatch parameter and the agglomeration of …rms. They showed that decreases in transportation costs and skill mismatch parameters induce skill formation and the agglomeration of …rms.

3

mechanism of skill acquisition in our model. @@People obtain higher real income and incur some costs by migrating from the periphery to the core.@@ Then, migration behavior can be interpreted as a kind of investment. Therefore, both Krugman [26] and our paper present the mechanism in which variety expansion induces investment by agents to obtain high income.6 Anderson [4], Costinot and Vogel [12], and Blanchard and Willmann [11], investigated the relationship between international trade and wage inequality in models with heterogenous workers who sort into industries with varying skill intensity. Anderson [4] constructed a model of continuum of di¤erentiated goods which are produced with continuum of di¤erentiated skills, and showed that globalization necessarily increases the ex post dispersion of wage of heterogenous workers and productivity shocks. Costinot and Vogel [12] examined the relationship between trade and wage inequality in competitive assignment models. They showed that North-South trade induces a pervasive rise in inequality in the North and a pervasive fall in inequality in the South, while North-North trade may either increase or decrease the relative wage between high- and low-skilled workers. Blanchard and Willmann [11] is a paper which has similar spirits to our paper. They constructed a model in which international trade in‡uences on skill acquisition of heterogenous workers. They focus on how the bene…ts of education rise and fall for di¤erent parts of the ability distribution. In their model, there is one homogenous consumption goods which are produced with di¤erentiated intermediate goods. Each intermediate sector uses a specialized type of labor and produces under constant returns to scale and perfect competition. In such an environment, trade openness in‡uences relative wages of labor through Stolper-Samuelson-type channel. On the other hand, in the present paper, skilled labor is necessary for producing di¤erentiated consumption goods which are produced with increasing returns to scale and monopolistic competition whereas skill acquisition reduces time for leisure. In this environment, trade openness enlarges the consumption variety, which in‡uences the importance of consumption relative to leisure. Anderson [4], Costinot and Vogel [12], and Blanchard and Willmann [11] focus on the real returns to skill acquisition via Stolper-Samuelson-type channel. This paper, in contrast, looks at 6

Moreover, it is well known that the university advancement rate is the highest in Tokyo among Japanese prefectures. In Tokyo, people can consume the widest variety of consumption goods, which is considered to raise the value of income. This correlation between the availability of varieties and the incentive of education might be a partial support to our mechanism.

4

the real costs of education via a labor/leisure trade-o¤, where leisure becomes less valuable with trade openness, via the consumption variety expansion. Helpman, Itskhoki, and Redding [23] introduced search and matching frictions and ex post match-speci…c heterogeneity in a workers’ability into a monopolistic competition model a la Melitz [33]. They showed that trade opening raises wage inequality, and once the economy is open to trade, the wage inequality …rst increases then declines as trade costs decrease. Anderson [4], Costinot and Vogel [12], and Helpman, Itskhoki, and Redding [23] showed that international trade has large impacts on relative wages of high- and low-skilled workers, although there is no decision regarding skill acquisition by agents. On the other hand, in our paper, there is endogenous decision of skill acquisition by agents. Our analysis is also related to the recent literature of trade models of monopolistic competition. In the face of new established facts regarding di¤erences in the performance of …rms in the trade environment (see Bernard and Jensen [9][10], among others), the impact of trade in the presence of heterogeneous …rms has been intensively investigated by studies such as those by Melitz [33], Helpman et al. [22], Melitz and Ottaviano [34], and Antras and Helpman [5].78 These scholars developed monopolistic competition models with heterogeneous …rms and showed trade impacts on the industrial structure and …rms, which include the fact that trade in the presence of …rm heterogeneity leads to the self-selection of …rms: e¢ cient …rms sell goods both domestically and internationally, whereas ine¢ cient …rms sell goods only domestically. In their models, workers are identical, and their focus is on di¤erences in the heterogeneity of …rms. In contrast, in our model, although …rms are identical, workers are heterogeneous. Our results and the results of existing studies are complementary in showing that trade is in favor of more e¢ cient agents in the presence of agents’heterogeneity, which is irrespective of which agents are heterogeneous. This paper is organized as follows. In Section 2, we present a basic model and analyze the autarky economy. Section 3 introduces trade and shows how trade a¤ects skill formation and wage structure. Section 4 is the conclusion. 7

Mannase and Turrini [30] considered a model in which the heterogeneity of …rms arises from di¤erences in the skills of entrepreneurs and obtained results regarding industrial changes due to trade openness that were similar to those of Melitz [33]. 8 For recent surveys, see Baldwin [6], Greenaway and Kneller [19], and Helpman [21].

5

2

The model

In this section, we introduce the basic structure of the model and explore its equilibrium. In doing so, we …rst construct a closed economy model and extend it to an open economy model in the next section.

2.1

Consumption

Consider a country in which there is a continuum of (immobile) workers of which measure is one. Each worker is endowed with one unit of labor, which she/he supplies inelastically. Workers are either skilled or unskilled. In this paper, a subscript u (respectively, s) describes that a variable is associated to unskilled (respectively, skilled) workers. We assume that each worker has an identical utility function Ui = U (Q; ci ), where Q stands for an index of the consumption of the di¤erentiated goods. Each worker must train herself/himself by incurring a …xed training cost before she/he starts working. The training cost for worker i (i = s; u) is represented by ci . @@One possible interpretation for this training cost is as follows: Training takes time from leisure rather than time in the workplace, i.e., training decreases leisure. In this interpretation, ci represents the decreased utility from leisure relative to consumption.@@ Skilled and unskilled workers di¤er in two ways. First, the training cost is higher when workers become skilled than when they work as unskilled workers. Without loss of generality, we assume that cu = 0 and cs = c (> 0). Second, as presented in detail later, when workers work as skilled workers, they are heterogeneous in productivity.9 We further specify the utility function in a way that a part representing the utility from the consumption of di¤erentiated goods takes the CES form and the disutility from training comes into the utility function additively: Ui = where

Z

1=

q( ) d

ci ;

(1)

2

is the index of di¤erentiated goods and the measure of the set

available goods. q( ) is the consumption of good .

represents the mass of

is a positive constant satisfying 0 <

< 1.

This implies that the di¤erentiated goods are substitutes and that the elasticity of substitution 9

Blanchard and Willman [11] assumed that the nominal cost of skill acquisition is constant and not in‡uenced by trade liberalization, while the real cost and return to skill acquisition are chnaged with trade liberalziation.

6

between two di¤erentiated goods is

= 1=(1

) > 1. The demands and utility level are given as

Ii ; i = s; u; p( ) P 1 Iu Is Uu = ; Us = c; P P

q( ) =

(2)

where Ii represents the wage income. p( ) is the price of variety , and P is the price index de…ned as P =

2.2

Z

1=(1

p( )1

d

)

:

(3)

2

Production

We normalize the unskilled wage rate to one: wu = 1. Di¤erentiated goods are produced in a monopolistic competitive market. Each …rm supplies one variety, and, in order to begin production, it must employ one unit of skilled labor in e¢ ciency units. Such a skilled labor is considered as a manager or CEO, which is necessary to run the …rm. The payment for skilled labor, ws , represents the …xed cost for production. For the production of one unit of output,

units of unskilled labor

are necessary, which represents that the unskilled workers are actual employees. Hence,

describes

the marginal cost, and we also normalize it to one for expositional simplicity.10 A pro…t-maximizing …rm sets a price equal to p=

1

:

(4)

Note that all …rms set an equal price under the constant markup pricing rule. Therefore, the price index (3) becomes P = n1=(1

)

p;

(5)

where n is the number of varieties (i.e., the number of …rms). As seen in standard monopolistic competition models à la Dixit and Stiglitz [15], a larger number of varieties lead to a lower price index, which improves the indirect utility of workers for a given income level. Using (4) and (5), 10

This production structure is standard in the new economic geography literature. See Baldwin et al. [7] and Fujita and Thisse [18].

7

the pro…t of a …rm becomes

= (p

1)

AI p P1

ws =

AI n

ws :

AI describes the aggregate income. We assume the free entry and exit of …rms, which drives the …rm’s pro…t to zero: ws =

2.3

AI : n

(6)

Skill formation

We assume that a worker can become skilled by incurring a training cost cs (= c) and works as unskilled with no training cost (cu = 0). Because a training cost directly appears in the utility function as described in (1), this assumption implies that a skilled worker must bear larger training disutility than an unskilled worker. Amiti and Pissarides [3] also assume that the training cost is expressed in terms of utility, and we follow this view. Let us imagine a person who wants to obtain a certain degree of education. For that purpose, she/he has to bear the burden of losing time for leisure and making an e¤ort as well as covering the monetary costs of education, which include the opportunity costs. c captures such non-monetary costs, the burden of which is not a¤ected by trade. This irrelevance of the burden of training costs to trade plays a key role in enabling trade to a¤ect the skill acquisition by workers. In fact, as is evident in Section 3, trade has impacts on the skill acquisition only via the price index. Therefore, if we consider only the monetary costs, the bene…ts (the wage premium) and the costs of becoming skilled change reciprocally to the price index, and trade has no impact on the incentive of being skilled. Put di¤erently, even if we consider the monetary costs of training as well, the results do not change, whereas if we consider only the monetary costs, we observe no e¤ect of trade on skill formation. For this reason, we explicitly introduce only the non-monetary costs.11 All workers start as unskilled, but can become skilled after going through training. When each worker is unskilled, she/he is endowed with one unit of labor that she/he supplies inelastically. Hence, the income Iu of an unskilled worker is one. When workers are skilled, they are assumed to 11

Alternatively, we can assume that the training service is produced by using di¤erentiated goods and the …xed amount c of training services is required to become skilled. Under this assumption, the training costs become P c, Z 1=" q( )" d . where c =

8

be heterogeneous in productivity: the productivity of a worker v is denoted by b(v) 2 [0; 1]. b(v) represents the skilled labor supply in e¢ ciency units, which determines the income Is of each skilled worker as b(v)ws . We assume that the distribution of b(v) is given by the distribution function G( ). G( ) is assumed to be de…ned over [0; 1] and continuously di¤erentiable, which implies that the density function g( ) is continuous. It is noteworthy here that the wage income is identical to the wage rate because workers supply one unit of labor.12 Each worker compares the (indirect) utility when she/he becomes skilled with that when she/he is unskilled and chooses to become skilled if the former is larger than the latter. Therefore, there is a cuto¤ level of productivity br 2 [0; 1], under which the utility of being skilled (see (2)) is lower than the utility of being unskilled. br is determined by the arbitrage behavior of workers, which is given by 1 br ws = + c: P P

(7)

This represents the supply of the skilled labor, and we call this the skill-formation condition. Behind this condition, we assume that when making their decisions, workers precisely know their personal productivity level before deciding whether to train or not. Furthermore, the productivity level of each skilled worker is perfectly observable to …rms. Although these are quite strong assumptions, they greatly make the analysis tractable. Of course, we can assume the information structure in a di¤erent way. A worker may know her/his skill type (when there is heterogeneity in skill) or productivity after training or after meeting with a …rm (Amiti and Pissarides [3]; Helpman et al [23]). Because our focus is not on the e¤ects of information structure, we adopt the most simple assumption on this. Because the number of total workers is normalized to one, 1

G(br ) workers are skilled, and R1 G(br ) workers are unskilled. Because b represents the productivity of a skilled worker, br bg(b)db

describes the total skilled labor supply. Moreover, since one unit of skilled labor is necessary for

12 This does not hold with respect to the wage rate in e¢ ciency units, which is one for the unemployed and ws for the employed.

9

the production of one variety, the number of varieties n is given by Z

n = n(br )

1

bg(b)db;

(8)

br

dn(br ) = dbr

br g(br ) < 0;

where n(br ) is positive for br 2 (0; 1). As the skilled worker ratio increases, the number of varieties available in the economy increases as well, leading to a lower price index: substituting (8) into (5), we have P = n(br )1=(1 dP pn(br ) = dbr

)

p;

=(1

(9)

) dn(b

r )=dbr

1

> 0:

Using (4) and (9), (7) can be rewritten as

ws =

2.4

1 1+ br

c 1

n(br )1=(1

)

:

(10)

Zero-pro…t condition

Aggregate income AI is given as

AI = ws

Z

1

bg(b)db + wu G(br ) = ws n(br ) + G(br ).

br

Substituting this into (6) and solving it with respect to ws , we obtain

ws =

(

G(br ) ; 1) n(br )

(11)

which describes the demand of skilled labor, and we call this the zero-pro…t condition.

2.5

Existence and uniqueness of equilibrium

An equilibrium is summarized by a pair (bar ; wsa ) that satis…es (10) and (11). The superscript a represents variables that are related to the closed economy (autarky) case. In this subsection, we show that when

> 2, there is a unique equilibrium. 10

[Please insert Figure 1 around here]

In the br

ws plane, the zero-pro…t condition (11) increases in br and reaches in…nity (zero) as

br approaches one (zero). When the skilled labor supply is small, the economy has fewer varieties, which yields higher revenue for each …rm. Free entry drives the pro…t of each …rm to zero, which implies that the skilled wage rate is high. Hence, the zero-pro…t condition is depicted as an upwardsloping curve. In the skill-formation condition (10), when br converges to zero, the arbitrage of workers requires that the skilled wage increase to in…nity. When br converges to one, no variety is available, and the price index increases to in…nity, which eliminates the relative attractiveness of being skilled for a given skilled wage rate. Thus, in order for the skill-formation condition to be satis…ed, the skilled wage must also increase to in…nity. In fact, because limbr !0 n(br ) > 0 and limbr !1 n(br ) = 0, we can easily see that the skill-formation condition diverges to in…nity as br goes to either zero or one. We now de…ne

as ( RHS of (10) = RHS of (11)

Therefore, if

1)n(br ) + cn(br )( br G(br )

2)=(

1)

:

> 2, lim

br !1

= 0 < 1;

which suggests that the RHS of (11) is larger than the RHS of (10) in the neighborhood of br = 1. From the above arguments, we know that (10) and (11) have at least one intersection in the br plane when

ws

> 2 (see Figure 1 for the illustration).

Moreover, by taking the derivatives of the RHSs of (10) and (11) with respect to br and evaluating them at equilibrium, it is readily veri…ed that, in the br

br g(br )ws g(br )ws ( 1)n(br ) G(br ) br g(br )ws g(br )ws = + : n(br ) G(br )

the slope of (10)jequilibrium = the slope of (11)jequilibrium Hence, we know that, when

ws plane, ws ; br

> 2, the slope of (11) is always larger than that of (10) at an

intersection of the two curves. These facts prove that there exists a unique equilibrium of the model 11

when

> 2.

Summarizing the above arguments, we obtain the following proposition: Proposition 1 The model has a unique equilibrium when

> 2.

Hereafter, we assume that this inequality holds, which is consistent with the markup rate estimated by Hall [20].13 As

becomes smaller, the monopoly power of each …rm becomes stronger, and the

price p goes up (see (4)). This increases the price index, which, in turn, reduces the real income and the incentive to become skilled. Moreover, no workers become skilled when one. @@When

comes very close to

converges to one, the price p, and hence the price index P become in…nite. In such

a case, the real income becomes zero and no workers have incentive to acquire skills.@@ In order for the model to have an interior solution, the …rm’s monopoly power must not be very strong.

2.6

Welfare properties at the equilibrium

Before moving to the analysis of trade, it is worth examining the welfare properties of skill formation in this model. In this paper, we adopt the Benthamite welfare function as a welfare criterion:

W =

Z

1

br

bws P

c g(b)db +

1 G(br ) G(br ) = P ( 1)P

c [1

G(br )] ;

(12)

where we used (11) in the derivation. Note here that the skilled worker fraction increases as br decreases. Di¤erentiating (12) with respect to br and evaluating it at equilibrium (substituting (7) and (11) into it), we have dW dbr

= equilibrium

cg(br ) < 0: ( 1)

(13)

Proposition 2 The equilibrium level of the skilled worker fraction is ine¢ ciently low. Equilibrium number of variety of di¤erentiated goods rises with skill formation of agents, which suggests that skill formation exhibits pecuniary externality. If the training cost c is positive, workers have the incentive to becomes skilled workers if and only if bws > 1+[ c=(

1)] n(br )1=(1

),

while

an increase in the number of skilled workers raises social welfare if and only if bws > 1. Thus, in 13

Hall [20] showed that many industries in the United States have a markup rate =( 1) between 1.5 and 3 (see Table 5). Given his warning regarding overestimation (see p.939), this range of the markup rate is consistent with our assumption.

12

this case, skill formation is ine¢ ciently low. In our model, the e¢ cient and equilibrium outcomes coincide only as c approaches 0. If c is 0, it is socially desirable to increase the number of skilled workers if and only if bws > 1, whereas workers have the incentive to become skilled if and only if bws > 1. Thus, the private and social incentives coincide with each other in this case, and skill formation is socially optimal.

3

Trade impacts

We will now assume that the economy is open and consider a world (or a trade bloc) that is composed of 1 + m countries whose economies are of the type described in the previous section. We assume that the di¤erentiated goods are traded with the standard iceberg trade cost. Hence, T > 1 units of a good must be shipped in order for one unit to arrive at its destination.14 This modi…cation does not change the number of varieties (8) produced in one country for a given br . Here, we consider a symmetric equilibrium in which all countries have the same number of varieties, the same price index, and the same skilled worker share. In this open economy, the price index (3) becomes P = n(br )p1

1=(1

1 + mT 1

)

:

(14)

Using (4), (8), and (14), the skill formation condition (7) can be written as

ws =

1 br

1+

c 1

1=(1

n(br ) 1 + mT 1

)

:

(15)

The pro…t of a …rm now becomes

= (p

1)

(1 + mT 1 p P1

)AI

ws ;

(16)

leading to the fact that the pricing behavior of …rms and zero-pro…t condition are unaltered and X given by (4) and (11), respectively.15 An equilibrium is summarized by the pair (bX r ; ws ) that 14

We can introduce the …xed costs of exporting as in Melitz [33] without changing any results. For expositional simplicity, we assume no …xed costs of exporting, which implies that …rms always choose to export. 15 Trade openness has two e¤ects on …rms’pro…ts. One is that trade openness enables …rms to access to the foreign markets, which raises …rms’pro…ts. This e¤ect is refrected in the term (1 + mT 1 ) in (16). The other is that with trade openness, …rms must compete with foreign …rms, which lowers …rms’ pro…ts. This e¤ects is expressed in the term (1 + mT 1 ) in (14). In this model, these two e¤ects are cannceld out with each other, which is due to the

13

satis…es (11) and (15). The superscript X represents the case of the trading economy.

[Please insert Figure 2 around here]

The closed-economy equilibrium is described by (10) and (11), whereas the open-economy equilibrium is determined by (15) and (11). Since the zero-pro…t condition is the same for the two cases, the di¤erence in the result comes from the di¤erence in the locus of the skill-formation condition. A simple comparison between (10) and (15) shows that, in the br

ws plane, trade opening

shifts the skill-formation condition downward, as described in Figure 2. We can see from this …gure that trade opening enhances skill formation. Under trade, people can consume wider varieties of di¤erentiated goods and enjoy lower price indices than under autarky, which is the only one force driving skill acquisition choices following trade liberalization. @@This implies that people enjoy higher utilities from the same income under trade than under autarky. Hence, trade increases the relative importance of nominal income to loss in utility from leisure caused by training, leading to the downward shift of the skill-formation condition. Because the incentive to be skilled and obtain a higher income becomes stronger, more workers train themselves to become skilled, i.e., br decreases, and the skilled worker fraction 1

G(br ) increases. Increasing consumption possibilities

makes consumption more important relative to leisure, which means that increasing globalization will lead to a more consumptive workforce.@@ This result has a signi…cant welfare implication. Because the price index declines, the utility of unskilled workers increases by trade opening. Among skilled workers, some become skilled after trade opening, whereas others are already skilled under autarky. Equation (7) shows that ws =P increases as a result of trade openness. Therefore, the utility of already skilled workers rises. From (7), it is evident that the utility of a marginal worker (i.e., a worker with productivity br ) increases and, hence, that of newly skilled workers also increases. Thus, trade opening pro…ts everyone. Of course, the national welfare also increases: because the zero-pro…t condition is unaltered by trade, (12) still applies to the economy under trade. In addition, the larger utility of unskilled and marginal workers under trade than under autarky readily veri…es that trade increases the national welfare. The following proposition summarizes the above arguments. Dixit-Stiglitz type monopolistc competition.

14

Proposition 3 Trade opening enhances skill formation and increases the utility of all workers, which also increases the wage income dispersion among skilled workers. Because people who are less productive as skilled workers choose to become skilled ones, wage income dispersion among skilled workers increases. We can con…rm this by examining the highest to lowest income ratio among skilled workers: the di¤erence between this ratio under trade and X that under autarky is wsX =(bX r ws )

1=bar > 0.16

wsa =(bar wsa ) = 1=bX r

Lemieux [29] showed the trends in the variance of wages unexplained by observed characteristics, which measures the inequality within groups in the United States over the past three decades and showed that the inequality for groups with higher education increased more than that for groups with lower education. Given the rapid proliferation of trade, the result of Proposition 3 indicates that trade may have played a certain role in generating the stylized facts shown in Lemieux [29]. The results shown in Proposition 3 are very similar to the trade e¤ects on income dispersion shown in Manasse and Turrini [30]. In their model, each worker is endowed with skilled labor as well as unskilled labor and simultaneously plays the role of an entrepreneur to supply skilled labor and that of an employed worker to supply unskilled labor. Workers are heterogeneous in 16 We can also obtain this result by using other indices of dispersion. In such cases, it is often the case that we must specify the distribution function G(br ). For example, we can employ the coe¢ cient of variation as an index of dispersion. The coe¢ cient of variation CVs is de…ned as the ratio of the standard deviation Ss to the mean Bs ws =P :

CVs = where Ss is given as Ss =

Z

1

(bws

Ss ; Bs ws =P

Bs ws )2

br

1=2

g(b) db 1 G(br )

:

After some (tedious) calculations, we have CVs =

( R1

b2 g(b)db

br Bs2 [1

G(br )]

)1=2

1

:

Whether or not dCVs =dbr is positive depends on the type of distribution G(br ). Here, we specify G(br ) as the uniform distribution. Under the uniform distribution, CVs can be rewritten as CVs =

1 br p : (1 + br ) 3

Di¤erentiating this with respect to br , we …nd dCVs = dbr

2 p < 0: (1 + br )2 3

As shown in Figure 1, trade opening induces less productive workers to become skilled and, hence, raises the skilled wage income dispersion:

15

their talent as entrepreneurs. Hence, a …rm associated with a very talented entrepreneur enjoys high productivity. Given this environment, trade causes self-selection of …rms: high-productivity …rms sell their products domestically and internationally, whereas low-productivity …rms sell their products only domestically. Behind this selection, trade a¤ects …rms’pro…ts asymmetrically. Highproductivity …rms earn more and low-productivity …rms earn less under trade than under autarky, which increases the rewards to very talented skilled labor and decreases the rewards to less talented skilled labor. Thus, trade enlarges the dispersion in the rewards to skilled labor. In contrast, our key mechanism is the e¤ect of trade on skill formation: trade creates incentives for less productive workers to become skilled, which widens the dispersion of skilled wage income. Put di¤erently, Manasse and Turrini [30] proved that trade a¤ects the labor demand side and changes the nominal values of working whereas we uncover the impacts of trade on the supply side of labor. Therefore, the underlying mechanism in our model is quite di¤erent from that in the model developed in Manasse and Turrini [30], although the obtained results regarding wage dispersion are quite similar in these two models.17 Although the utility of all workers rises by trade opening, it is not clear that workers are equally better o¤. In particular, it is possible that there is asymmetry in gains from trade between skilled and unskilled workers. To evaluate this, we consider a worker who chooses to be skilled and a worker who remains unskilled both under autarky and under trade. Let us consider a skilled worker a b with productivity bb. We assume that bX r < br < b so that this worker is skilled both under autarky

and under trade. Her/his utility is given by bbwsa =P a under autarky and bbwsX =P X under trade. Changes bb(wsX =P X

wsa =P a ) in the utility are larger for higher bb. This implies that, among skilled

workers, workers with high productivity gain more from trade than workers with low productivity. The utility of an unskilled worker is 1=P a under autarky and 1=P X under trade. Using (7), we can 17 See also Dinopoulos et al. [14], Kurokawa [28] and Helpman et al. [23] for analysis on the relationship between trade and inequality. In these studies, trade has primarily a¤ects the labor demand side and then changes the features of inequality.

16

examine the di¤erence in changes in the utility level as follows: bbwX s PX

bbwa s Pa

1 PX

1 Pa

bb 1 + cP X bb 1 + cP a 1 1 + a X X a a X P br P br P P 1 1 1 1 > bb X X + a br P bar P a PX P ! bb 1 1 > >0 1 a X br P Pa

=

The last inequality comes from the result that the price index P also declines (i.e., P X < P a ) when trade opens and new goods become available. We can con…rm this by the following two facts: (i) the price index under trade P X is lower than the price index under autarky P a for a given br ; and a 18 (ii) P declines as br decreases (i.e., bX r < br ).

From this, we can readily observe that, whereas trade opening bene…ts unskilled workers, skilled workers enjoy trade bene…ts more than unskilled workers do. This widening of the utility gap gives less productive workers an incentive to become skilled. Proposition 4 Trade opening bene…ts skilled workers more than unskilled workers. Among skilled workers, the higher the productivity, the more the gains from trade. Under trade, people may feel that society becomes more unequal because of this increase in the utility gap between skilled and unskilled workers or that among skilled workers, and they may see it as a social problem. We do not intend to argue the pros and cons of this view. However, it would be worth mentioning that, behind the changes in inequality, people may become better o¤ via trade. Once the economy is open, the trade environment a¤ects skill formation. An increase in the number m of trading countries and a decline in the trade cost T shift the skill-formation condition downward, leading to decreases in bX r (i.e., increases in the skilled worker fraction), and enlarge the wage income dispersion among skilled workers. It also lowers the price index and, hence, makes all people better o¤, whereas skilled workers gain more than unskilled workers and such gains are larger for a worker with higher productivity. Corollary An increase in the number m of trading countries or a decline in the trade cost T enhances skill formation and has similar e¤ ects on the market structure to trade opening. 18

See (9) and (14).

17

4

Concluding remarks

In this paper, we revealed the possible impacts of international trade on a worker’s skill formation and the wage structure. We showed that trade can change the incentive of being skilled and enhance skill acquisition for a given nominal wage inequality, leading to increases in the wage income dispersion among skilled workers. Although these changes make all workers better o¤, skilled workers gain more than unskilled workers, and such gains are larger for workers with higher productivity. Thus, we demonstrated the possible important role of trade on skill composition. An interesting implication of our framework is to shed light on the fact that globalization can bene…t all people via skill formation. It is of value to report some possible extensions. First, we considered only symmetric countries. However, trade between countries of di¤erent sizes should also be investigated. The importance of this issue is suggested by the fact that we often observe regional trade agreements (RTA)s between large and small countries (such as the RTA between the United States and Morocco or that between Japan and Singapore). Because of the possibility of the home market e¤ect, international trade may work in favor of skill formation in a large country but may harm skill formation in a small country.

19

However, it is still possible that the small country will become better o¤ due

to the availability of a wider range of varieties. Second, foreign direct investment (FDI) should be considered. The importance of multinational …rms has recently increased, and these …rms are now the key players in the world economy. Moreover, Markusen [31] pointed out that skilled labor endowments are strongly and positively related to FDI, which suggests the interdependence of FDI and skill formation. Third, incorporating the framework developed in this paper into a model with heterogeneous …rms (Melitz [33]) may give us implications that can be compared with empirical results regarding trade e¤ects on heterogeneous …rms. It would be particularly interesting to explore how the interaction between trade and skill formation a¤ects the allocations of heterogeneous workers to heterogeneous …rms.

19

Because of the home market e¤ect, agglomeration of …rms is progressed with trade liberalization. Thus, some …rms switch their location from the small country to the large country. With this movement, there is possibility that international trade reduce the number of …rms and harm skill formation in the small country.

18

References [1] Acemoglu, D., Technical change, inequality, and the labor market, Journal of Economic Literature 40, 7-72 (2002). [2] Acemoglu, D., Patterns of skill premia, Review of Economic Studies 70, 199-230 (2003). [3] Amiti, M., and C. A. Pissarides, Trade and industrial location with heterogeneous labor, Journal of International Economics 67, 392-412 (2005). [4] Anderson, J. Globalization and income distribution: A speci…c factors continuum approach, Boston College Working Paper (2009). [5] Antras, P., and E. Helpman, Global sorting, Journal of Political Economy 112, 552-580 (2004). [6] Baldwin, R., Heterogeneous …rms and trade: Testable and untestable properties of the Melitz model, NBER Working Paper No.11471 (2005). [7] Baldwin, R., R. Forslid, P. Martin, G. Ottaviano, and F. Robert-Nicoud, Economic geography and public policy, Princeton, Princeton University Press (2003). [8] Barro, R. J., and J. W. Lee, International data on educational attainment: Updates and implications, Oxford Economic Papers 3, 541-563 (2001). [9] Bernard, A. B., and J. B. Jensen, Exceptional exporter performance: Cause, e¤ect, or both? Journal of International Economics 47, 1-25 (1999). [10] Bernard, A. B., and J. B. Jensen, Exporting and productivity in the USA, Oxford Review of Economic Policy 20, 343-357 (2004). [11] Blanchard, E., and Willmann, G. Trade, education, and the shrinking middle class, Mimeo (2009). [12] Costinot, A., and Vogel, J. Matching and inequality in the world economy, Journal of Political Economy 118, 747-786 (2010). [13] Borjas, G., R. B. Freeman, and L. F. Katz, On the Labor Market E¤ects of Immigration and Trade, NBER Working Papers No.3761 (1991). 19

[14] Dinopoulos, E., C. Syropoulos, and B. Xu, Intraindustry Trade and Wage-Income Inequality, mimeo, University of Florida (2009). [15] Dixit, A., and J. Stiglitz, Monopolistic competition and optimum product variety, American Economic Review 67, 297-308 (1977). [16] Federal Reserve Bank of New York, Current Issues in Economics and Finance, vol.12-2 (2006). [17] Feenstra, R. C., ed. The Impact of International Trade on Wages, Chicago, University of Chicago Press (2000). [18] Fujita, M., and J.-F. Thisse, Economics of Agglomeration: Cities, Industrial Location, and Regional Growth, Cambridge University Press (2002). [19] Greenaway, D., and R. Kneller, Firm heterogeneity, exporting, and foreign direct investment, Economic Journal 117, F134-F161 (2007). [20] Hall, R. E., The relation between price and marginal cost in U.S. industry, Journal of Political Economy 96, 921-947 (1988). [21] Helpman, E., Trade, FDI, and the organization of …rms, Journal of Economic Literature 44, 589-630 (2006). [22] Helpman, E., M. J. Melitz, and S. R. Yeaple, Export versus FDI with heterogeneous …rms, American Economic Review 94, 300-316 (2004). [23] Helpman, H., O. Itskhoki, and S. Redding, Inequality and unemployment in a global economy, Econometrica 78, 1239-1283, (2010). [24] Ishikawa, J., Scale economies in factor supplies, international trade, and migration, Canadian Journal of Economics 29, 573-594 (1996). [25] Krugman, P., Scale economies, product di¤erentiation, and the pattern of trade, American Economic Review 70, 950-959 (1980). [26] Krugman, P., Increasing returns and economic geography, Journal of Political Economy 99, 483-499 (1991). 20

[27] Krugman, P., International Economics: Theory and policy, 7th edition (2005). [28] Kurokawa, Y., Trade and variety-skill complementarity: A simple theoretical resolution of trade-wage inequality anomaly, mimeo, University of Minnesota (2006). [29] Lemieux, T., Increasing residual wage inequality: Composition e¤ects, noisy data, or rising demand for skill? American Economic Review 96, 461-498 (2006). [30] Manasse, P., and A. Turrini, Trade, wages, and “superstars,’ Journal of International Economics 54, 97-117 (2001). [31] Markusen, J. R., Multinational …rms and the theory of international trade, Cambridge: MIT Press (2002). [32] Matsuyama, K., Beyond icebergs: Toward a theory of biased globalization, Review of Economic Studies 74, 237-253 (2007). [33] Melitz, M. J., The impact of trade on intra-industry reallocations and aggregate industry productivity, Econometrica 71, 1695-1725 (2003). [34] Melitz, M. J., and Ottaviano, G. I. P., Market size, trade, and productivity, Review of Economic Studies 75, 295-316 (2008). [35] Richardson, J. D., Income inequality and trade: How to think, what to conclude, Journal of Economic Perspective 9, 33-55 (1995). [36] Yeaple, S. R., A simple model of …rm heterogeneity, international trade, and wages, Journal of International Economics 65, 1-20 (2005).

21

ws

Zero profit condition Skill formation condition

wsa

bra

0

unskilled workers

Figure1. Equilibrium

1 skilled workers

br

ws Zero profit condition

wsa Skill formation condition

wsX 0

brX

bra

1

Figure 2. Impact of trade on skill formation

br