Trade, wages, and ‘superstars’

Journal of International Economics 54 (2001) 97–117www.elsevier.nl / locate /econbase

Trade, wages, and ‘superstars’a , b*Paolo Manasse , Alessandro Turrini

aUniversity of Milan-Bicocca and IGIER-Bocconi. Dipartimento di Economia Politica,`Universita degli Studi di Milano-Bicocca. V. le Sarca, 202, 20126 Milan, Italy

b `University of Bergamo and CEPR. Departimento di Scienze Economiche, Universita di Bergamo,Piazza Rosate 2, 24100 Bergamo, Italy

Received 2 February 1999; received in revised form 20 October 1999; accepted 28 February 2000

Abstract

We study the effects of ‘globalization’ on income inequality in an economy where sellerswith higher skills enjoy larger market shares and higher earnings. In our ‘global’ economy:(a) innovations in production and communication technologies enable suppliers to reach alarger mass of consumers and to improve the (perceived) quality of their products, and (b)trade barriers fall. When transport costs fall, income is redistributed away from thenon-exporting to the exporting sector of the economy. As the latter turns out to employworkers of higher skill and pay, the effect is to raise wage inequality. Whether the leastskilled stand to lose or gain from improved production or communication technologies, incontrast, depends on how technological change relates with skills. The model provides anintuitive explanation for why changes in wage premia are significantly associated with theexport status of firms in recent firm-level empirical investigations. 2001 ElsevierScience B.V. All rights reserved.

Keywords: International trade; Income inequality; Technological change

JEL classification: F12; F16; J31

1. Introduction

‘Globalization’, ‘Internet economy’, ‘Electronic trade’ are the buzzwords of the

*Corresponding author. Tel.: 139-2-6448-6594; fax: 139-2-6437-8845.E-mail address: [email protected] (P. Manasse).

0022-1996/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved.PI I : S0022-1996( 00 )00090-8

98 P. Manasse, A. Turrini / Journal of International Economics 54 (2001) 97 –117

day. The enthusiasm for the opportunities offered by new markets and tech-nologies, however, is often cooled down by worries concerning their possibleconsequences on income distribution. Will a ‘globalized’ society be more or less‘equal’? Who will be the winners and the losers? In spite of abundant empiricalwork aimed at assessing the causes of increasing wage inequality, the distributiveimplications of globalization are not yet fully understood.

‘New’ trade theory based on imperfect competition, while accounting for thefailure of international convergence in factor prices, is, in general, silent about the

1implications of trade integration on within-countries inequality. A generalprediction is that intra-industry trade has a small effect on income distribution, andis likely to lead to higher welfare for all agents.

Traditional trade theory predicts that trade integration between developed andless developed countries will benefit skilled workers in the former, and manualworkers in the latter (assuming these are the relatively abundant factors in the twoareas). This view is generally refuted by the data. The actual changes in productprices generated by trade integration are hardly sufficient to explain the observed

2deterioration of the relative position of the unskilled. In addition, the Stolper–Samuelson theorem cannot account for the fact that inequality has risen dramati-cally within narrowly defined segments of the labor market (Juhn et al., 1993) i.e.between workers of similar occupations, education levels, and, in general,belonging to similar ‘skill’ categories.

The conventional view is that the most part of the rise in wage inequality duringthe last two decades is not due to changes in relative product demand associatedwith trade. The culprit is more often identified in shifts in labor demand, awayfrom the unskilled, induced by technological change within most industries (see,e.g., Lawrence and Slaughter, 1993). The empirical work aimed at assessing theeffect of trade on wage inequality has only recently shifted from industry tofirm-level analysis. A number of studies, conducted at firm or establishment level,have found robust empirical links between exporting activity, firms’ performance,and wages. Bernard and Wagner (1998), in a study on export decision of Germanfirms in Saxony, find evidence that ‘successful plants, measured by size orproductivity, are more likely to become exporters, as plants with greater shares of

3skilled labor’. Bernard and Jensen (1997), in a plant-level study for the US, findthat the skilled /unskilled wage premia has been rising during the 1980s especiallydue to between-plants changes, with the greater part of these changes explained byplants’ export growth. This new ‘micro’ evidence seems to suggest that changes in

1See, for instance, Helpman and Krugman (1985).2See Freeman (1995), Rodrik (1997) and Slaughter and Swagel (1997) among recent surveys on the

empirical literature concerning the trade and wages debate.3Bernard and Jensen (1999) find consistent evidence: larger and faster growing firms are more likely

to start exporting.

P. Manasse, A. Turrini / Journal of International Economics 54 (2001) 97 –117 99

the goods market, and those related to trade in particular, have indeed a role inexplaining the rise of wage inequality.

This paper studies the ‘effects globalization’ on income inequality in a modelthat accounts for the positive association between exporting, market size, and wagepremia.

Our description of a ‘global economy’ is based on three crucial ingredients. Thefirst is increasing returns in production. Market size matters. This is the basictenets of ‘new’ trade theory. The second is the role of technology in productionand communication. Technological improvements enable suppliers to improve thequality of their products and allow firms to reach a larger mass of consumers. Thethird ingredient is transport costs and market access costs that segment theinternational market. As globalization proceeds, barriers to trade tend to fall.Combining these ingredients into a simple trade model, we obtain a representationof the ‘global’ economy that is reminiscent of Rosen’s (1981) ‘Economics of

4Superstar’.In his seminal paper, Rosen discussed the role that non-convexities in

production may exert on income distribution. Some products and services are likenon-rival public goods: singing on a satellite-broadcast TV program or in a small

`cafe requires approximately the same effort. For products where these non-convexities are particular important and where ‘talents’ are particularly appreciatedby consumers, even small differences in ‘skills’ are associated with disproportion-ate differences in incomes (think of the show-biz, sport, science, etc.).

The recent bestseller by Frank and Cook (1995) has popularized the idea of‘winner-take-all’ markets. To the extent that the earnings of executives and staffworkers are increasingly tied to firm performance, the tendency towards increasingdifferentials in earnings is likely to spread from professionals and executivestowards salaries and wages (as shown, for instance, in Hall and Liebman, 1998).

In this paper we take an admittedly extreme view of the labor market.Individuals derive their income from the rents associated with their specific skills.As in Rosen, the income distribution is shaped by the distribution of rentsgenerated by individual abilities. To that we add a fully-fledged general equilib-rium model, where the interaction between the distribution of wages, the size offirms and exporting decisions can be analyzed.

We consider a monopolistic competition trade model (Krugman, 1980), whereworkers differ in their abilities. Firms supply different product varieties, and thisgenerates demand ‘niches’ and market power for all sellers. However, the usualsymmetry that characterizes monopolistic competition models does not hold in ourformulation because those firms that employ better workers also manage toproduce goods of better quality, to capture larger market shares and to enjoy

4See also Grossman and Maggi (1998) for a representation of an open ‘Superstars’ economy basedon the use of submodular production functions.


higher profits. Due to the presence of a fixed cost to access foreign markets, onlyfirms employing a ‘high-level staff’ benefit from exporting. In such a setting, thedecision to export is explicitly modelled, so that the economy’s degree of opennessand the distribution of income are jointly determined.

As barriers to trade fall, more firms will benefit from exporting and will haveaccess to a larger market. Competition for skills boost skill premia in exportingfirms. Hence, trade integration unambiguously leads to a redistribution of incomefrom the workers employed in non-exporting firms to those employed in the exportsector. Since the latter employs workers of greater skills, trade integration raiseswage inequality. Even if aggregate welfare unambiguously rises following areduction in trade barriers, low-skilled workers may end up losing in nominal andeven in real terms.

The introduction of new technologies allows firms to improve the quality oftheir products, and enables them to better communicate the characteristics of thesegoods to consumers. Hence, consumers everywhere start discriminating more andmore among products, placing increasing weight on their (perceived) quality. Asin the case of reduced trade barriers, consumers will concentrate their purchases onbest-sellers products. Once general equilibrium effects are taken into account, itemerges that the redistributive effects of technological progress crucially dependon how the new technologies interact with skills at the margin. The high skilledgain at the expense of the low skilled only if technological progress expandsproportionally more the capabilities of sellers with higher skills. Moreover,contrary to trade integration, technical change has ambiguous effects on the shareof exporting firms in the economy and on the relative skill rents between exportingand non-exporting sellers.

These findings may be useful in disentangling trade and technology wheninterpreting empirical evidence. Increasing income inequality is unambiguouslyassociated with export growth only when globalization takes place via reducedtrade barriers. Furthermore, only in this case will we always observe a redistribu-tion of income in favor of exporting sellers.

The remainder of the paper is organized as follows. In Section 2 we present themodel. Consumers’ and firms’ problems are solved in Section 3, while Section 4presents the general equilibrium solution. Some comparative statics exercises areperformed in Section 5. Section 6 summarizes the main conclusions.

2. The model

The world consists of two symmetric countries. We focus on the domestic one.Firms produce differentiated goods under imperfect competition and free-entry.Consumers like variety, according with the Dixit–Stiglitz formulation. Productionrequires two factors of production: skill (‘talent’), whose total endowment is


denoted by S, and raw inputs, M (unskilled labor, raw materials). The market forproduction factors is competitive. The economy is populated by a unit-masscontinuum of households–workers, indexed by h, h [ 0, 1 . Household h isf g

h 1 hendowed with the amount raw inputs M , e M dh 5 M. Skills are measured by0

the index s. More talented workers are characterized by higher s. Households are]distributed over the interval s, s , according to an everywhere continuousf g]

cumulative distribution whose associated density is denoted by f(s). Necessarily,]s 5e f(s)s ds 5 S. Production requires one skilled worker and an amount ofs]

composite input proportional to output. Raw inputs provide standardized servicesfor production. Workers’ skills improve the quality of the product. As aconsequence, products are differentiated both along a horizontal dimension(variety) and a vertical one (quality).

Shipping entails a iceberg transport cost plus a fixed market access cost (setting6up a network of distributors abroad, covering legal expenses, etc.). Because of the

fixed export costs, some firms prefer not to export their output at all. On the otherhand, because of iceberg transport costs, no firm is willing to sell its production onthe foreign market only. As a result, firms may either sell only on the domesticmarket, or in both domestic and foreign markets.

2.1. Production technology

There is one consumption good, X, which can be differentiated along acontinuum of varieties i, i [ R. Each variety i is produced out of raw inputs, M,and skill, S. Each worker can employ her skills in the production of at most onevariety of good X. The size of firms is normalized in such a way that one firmemploys the skill of one worker. Each firm thus supplies only one variety. Rawinputs requirements are proportional to output. Let w(s) and v denote, respectively,the return to skills of a worker endowed with ‘talent’ s and that of raw inputs M.The cost of producing X units of variety i, when a type-s(i) worker is involved is:

iC(s(i), i) 5 w(s(i)) 1 vbX(i) 1 d vg. (1)

The parameter b represents the inverse of marginal productivity of raw inputs(units of inputs required for producing one unit of the variety i). The third term onthe right hand side has the following interpretation. If the firm also sells in theforeign market it has to incur a fixed costs g, which represents the extra units of

5We could have instead specified a distribution of skills across individuals, s(i), assuming that eachagent is endowed with a share e(i) of total skills, s(i) 5 e(i)S. We choose the former specification fornotational convenience.

6Market access costs have been modelled as fixed costs in other papers. See, for instance, Smith andVenables (1991). Empirically, fixed (sunk) costs seem to play a crucial role in affecting exportdecisions (see, for instance, Bernard and Wagner (1988) and Roberts and Tybout (1997)).


7raw inputs that are required to export. We denote the set of all existing varietiese eby N, and the subset of traded goods by N . If the variety i belongs to N , then

id 5 1 and the firms sells at home and abroad. If the variety is not exported,

e ii [⁄ N , d 5 0, and no cost is incurred.Firms are atomistic profit-maximizers. They produce goods which are imperfect

substitutes and set their price, taking as given other firms’ choices (the ‘largegroup’ Chamberlinian hypothesis holds). Consumers’ utility increases with theextent of variety in consumption. As it is standard in monopolistic competitionmodels, love for variety plus increasing returns in production insure that no firm iswilling to supply the same variant offered by a rival. While in standardmonopolistic competition models the condition of free-entry determines thenumber of firms and varieties, in our set up N is exogenous. Since each firmrequires the skill of one worker, and all factors are fully employed from free-entry,then the number of firms is given by uNu 5 1. In turn, the condition of free-entryensures that skilled workers perceive all the operating profits realized by firms.Note that under this formulation each worker can be equally interpreted as theentrepreneur who runs the firm and earns operating profits. In the followinganalysis we leave this interpretation open, and we use interchangeably the termsskilled workers, sellers, entrepreneurs. Households’ income is thus constituted ofthe sum of earnings from their endowment of raw inputs (sold on a competitivemarket) and skill rents associated with firms’ operating profits. This is a firstanalogy of our model with Rosen (1981).

2.2. Preferences

All households have identical tastes, but different incomes, depending on theirendowments of production factors. The income of household h, endowed with

hskills s and raw inputs M , is thus

h hI 5 vM 1 w(s) (2)

Consumers like variety, in the sense that their utility is increasing in the number ofvarieties consumed, according to the Dixit–Stiglitz formulation. A distinguishingfeature of our formulation is that more talented entrepreneurs produce betterquality of each variety, and better quality is appreciated by consumers. Householdsderive utility from a combination of the quantity, X, and the ‘quality’, indexed byT(.), of each good. In this sense, a commodity is assimilated to a bundle of a

7The choice of units of measurement for fixed market access costs does not affect our qualitativeresults. As will be clear in the following analysis, all comparative statics results would be confirmedhad we expressed market access costs in terms of the final good.


physical good, X (the silk in tie, a physical CD) and of an intangible good, T(.)(the griffe of a fashionable tailor, the sound of a particular pop group), that isincorporated in the tangible commodity. For simplicity, we adopt a Cobb–Douglas

hspecification to nest T(.) and X , while we use the standard CES specification fordifferent varieties:

1 /rrh h12rU 5 E T(s(i), a) X (i) di . (3)s ds dF G

hi[N

hThe set N is the set of varieties consumed by individual h; as usual, theparameter r [ (0, 1) is related to the elasticity of substitution between differentvarieties s 5 1/(1 2 r) . 1. This coincides with the price elasticity of the demandfor each variety and therefore (inversely) measures the degree of market power ofindividual firms. T(.) is a function that matches the particular skill of theentrepreneur, s, and the state-of-the-art technology, a, into the appreciated qualityof the good. A product ‘quality’ thus depends on two factors: the skill of theentrepreneur producing the good, s, and the existing stock of technical knowledgea. This element reflects the cumulated stock of know-how in production and incommunication. A technological break-through enables firms to improve theirproduct quality or to market their products more effectively, raising consumers’satisfaction. Here a plays the role of a shift parameter. We assume that T(s, a) is atwice-differentiable continuous function satisfying some intuitiverequirements. First, quality improves with technical progress, so that T (s, a) . 0a

for all s, a. Second, more talented entrepreneurs produce ‘better’ goods, so thatT (s, a)) . 0, for all s and a. Finally, we add structure to this function assumings

that the elasticity of T(.) with respect to s, q(s, a) ; T (s, a)s /T(s, a), is monotonics

in a. We say that technology is marginally skill-neutral, marginally skill-comple-ment or marginally skill-substitute depending on whether q (s, a) is equal to,a

higher or lower than zero. Note that this concept of skill substitutability /com-plementarity of technological progress is different from the one normally used inthe literature. Here what matters is how new technologies interact with skills at themargin.

Our production and consumption technologies capture two important asymmet-ries between the role of primary inputs and skills in production. First, while costsrelated to primary inputs increase with output, the same expenditure for talent isrequired in serving a large or a small market. Second, even if both factors arerequired for production of a ‘standardized ’ variety, X (i.e., a good of qualityT(.) 5 1), only workers’ (‘entrepreneurial’) talent can add ‘quality’, according tothe technology T(s, a). These particular features of our model — namely,non-convexities in production and consumers valuing the characteristics associatedwith talented producers — give it its Rosen-type flavor.


3. Firms’ and households’ equilibrium

3.1. Demand, exports and imports

The results of our model depart in some aspects from the standard monopolisticcompetition trade models (Helpman and Krugman, 1985). Like the standardmodel, due to love for variety, consumers will try to spread their purchases acrossall available goods, produced either domestically or in the foreign country.However, not all firms will find it convenient to supply foreign consumers,because of the presence of fixed market access costs. In the standard model allfirms sell abroad and their number is determined by the zero profit condition. Here,the total number of firms (entrepreneurs) is given, while the mass of exportingfirms is endogenously determined.

We denote by an asterisk variables referring to the foreign country. Recall that,from the assumption of symmetry, all firms and workers abroad have access to thesame technology as domestic workers and firms, defined by Eq. (1) and by thefunction T(s, a). Let N and N* denote, respectively, the mass of distinct varietiesof the consumption good produced under free-trade at home and abroad. Denote

e e*further by N and N the subset of, respectively, home and foreign goods that arealso exported. In addition to the fixed market access costs g (see (1)), there isanother impediment to trade, namely transport costs of the iceberg type. For oneunit shipped abroad, 1 2 t is lost in transit, and only a fraction 0 , t , 1 arrives toforeign consumers. Hence t inversely measures the extent of transport costs.

Consider the home country. Household h maximizes utility (3) subject to thebudget constraint (2). Domestic demand for home goods is given by

2sI p(s(i), i)] ]]]S DX(s(i), a, i) 5 T(s(i), a) (4)P P

where I is total domestic income]s

I 5 nM 1 E f(s)w(s) ds (5)s5s

]

and P is the CES cost-of-living index that must also take into account importedgoods

12sP 5 E T(s(i), a)p(s(i), i) diFi[N

1 / (12s )12s1 E T(s(i*), a*) p(s(i*), i*) /t di* . (6)s d G

ei*[N *

Note from (4) that demand for variety i has unit elasticity with respect to quality


and real households’ income, and decreases with the relative price of good i with*elasticity s. Demand for imports, X (s(i*), i*), is instead as followsm

2sI p(s(i*), i*) s 21] ]]]* S DX (s(i*), a*, i*) 5 T(s(i*), a*) t . (7)m P P

The lower the transport cost, the lower the relative import price of foreignvarieties, the higher imports. Moreover, as the domestic price index falls, realdomestic income rises, so that domestic demand for imports rises both for asubstitution and for an income effect.

We choose domestic raw inputs as a numeraire, so that v 5 1. Given the perfectsymmetry of the model, it must also be v* 5 1 at equilibrium.

Denote the firm’s exports (foreign demand for its goods) by X . Depending onm*

whether firm i is only selling on the domestic market or is also exporting, herprofits will differ:

i i ip(s(i), i) 5 p(.)X(.) 1 d p*(.)X (.) 2 w(.) 1 b X(.) 1 d X (.) 1 d g . (8)f s d gm* m*

Profit maximization leads to mark-up pricing. Since the elasticity of demand is thesame for each ‘quality’, all firms will set the same mark-up over marginal costs.Moreover, since all firms share the same technology, all varieties will sell for the

8same (‘free-on-board’) price, in both countries

s]]p(s(i), i) 5 p*(s(i), i) 5 b ; p for all i, s(i). (9)s 2 1

As a result, the product quality will only show up in the quantities consumed byhouseholds, who will buy more units of better goods. Using this condition ofsymmetric pricing (9), the domestic and foreign demand for home goods can be

9rewritten as follows:2sX(s, a) 5 p Y T(s, a) (10)

2s s 21X s, a 5 p Y*T(s, a) t (11)s dm*

wheres 21 s 21Y ; I P , Y* ; I*P* (12)

denote the domestic and foreign demands for a good of unitary price and‘standard’ quality (T(.) 5 1). Because this variables enter multiplicatively indomestic and foreign sales, they can be interpreted as a measure of the scale of a‘standard’ firm.

Two (endogenous) variables affect the magnitude of Y: aggregate income, I, andthe price index, P. Given M, the distribution of skill earnings w(s) determines

8Consistently, we can omit henceforth the index i.9 2s s 21*Similarly the domestic demand for foreign goods (imports) is X s, a*, M 5 p Y(M)T(s, a*)t .s dm


aggregate income I. Other things being equal, higher households’ income raisesthe demand for a firm’s product. Note also that the real income elasticity ofdemand is unity, while the relative price elasticity is s . 1. Therefore a higher P— a higher average price of competitors — raises the demand for each individualproducer.

3.2. Income distribution, trade, and technology

We now study the interaction between the distribution of entrepreneurial rentsand firms’ choice to export. Suppose that a firm, run by a type-s entrepreneur,decides not to export. Free entry entails that the earnings of entrepreneurscoincides with firms’ operating profits. From (8) and (9) we see that

T(s, a)i 12s n e]]w (s, a) 5 ( p 2 b )X(s, a) 5 p Y ; w (s, a), i [⁄ N (13)s

In the non-export sector, the earnings of a worker /entrepreneur with skill s ispositively related to the scale of the representative firm on the domestic market, Y,and to the firm’s market power, measured by the mark-up p 2 b (which isinversely related to the price elasticity of demand, s). Notice that the en-trepreneurial rent rises linearly with quality, T(s, a). The elasticity of skill earningswith respect to the level of skill, s, coincides with the elasticity of the qualityindex T, q(s, a) ; T s /T. Whenever the quality of the product rises more thans

proportionately with the skill of the producer, q(s, a) . 1, even small differencesin skills may result in a large earnings premia and in a skewed income distribution,as in Rosen (1981).

Assume now that a firm employing a type-s entrepreneur decides to export.Recalling that an exporting firm must incur a fixed cost g to access the foreignmarket, and imposing a 5 a*, and M 5 M*, the earnings of type-s worker /entrepreneur is

iw (s, a) 5 ( p 2 b ) X(s, a) 1 X (s, a ) 2 gs dm*

(14)T(s, a) Y*12s s 21 e e]] ]S D5 p Y 1 1 t 2 g ; w (s, a), i [ Ns Y

Comparing (13) and (14) we see that the skill premium increases even more withs if the firm is exporting, see Fig. 1.

The intuition is simple. Each additional unit of talent in exporting firms allowsfor larger sales in both home and foreign markets. This difference in the demand

s 21of the representative firm, Y*/Yt , is translated in earnings differentials. As in


Fig. 1. Wage structure when technology is skill-complement.

10Rosen (1981), are the more talented that gain more from market size. Note thatthe elasticity of the skill premium with respect to skills is larger in the exporting

e esector, w (s) 1 g ) /w (s) q(s, a) . q(s, a), a feature which is consistent withs dempirical evidence concerning the wage premium paid by exporting firms(Bernard and Jensen, 1997).

From (13) and (14) it is clear that, for given representative firm’s demandY, trade integration due to lower transport cost (higher t) or lower access cost g,boosts the earnings of workers employed in the export sector, while leavingunaffected those in non-exporting firms. Since, as we shall see, the export sectoremploys workers of higher skills than the non-export sector, this tends to raiseincome concentration.

It is now easy to see under what conditions a type-s entrepreneur will be willingto venture on the export market. She will do so provided this raises the firm’s

e noperating profits, i.e. w (s) $ w (s). Since the access cost to foreign markets g isindependent of sales, while sales increase with talent, only firms employingsufficiently skilled workers will sell on the foreign market, from (13) and (14)

10‘ . . . no wonder that the best economists tend to be theorists and methodologists rather than narrowfield specialists, that the best artists sell their work in the great market of New York and Paris, not inCincinnati, . . . ’ Rosen (1981).


s 21gp s]]]T(s, a) $ , (15)s 21Y*t

or1s 21

gp sS D]]] ¯s $ z ; Z , a (16)s 21Y*t

21 11where Z(., a) ; T (., a).Consistently with the evidence previously discussed, firms in the export sector

tend to employ workers with higher skill and, consequently, to pay them more.The ‘degree of openness’ of the economy is measured by the share of exporting

]sfirms, e f(s) ds. This is endogenously determined. The share of exporting firm isz

negatively related to the cut-off skill level z, that is, it is larger the lower thiscut-off. Hence openness rises with the scale of the representative firm on theforeign market, Y*, since this boosts the skill premium and induces moreentrepreneurs to venture abroad. Holding constant Y*, technological change, asmeasured by changes in a, reduces the cut-off skill level z, and fosters openness,because workers with lower skills start producing the threshold quality (checkfrom (16), recalling that Z 5 2 1/T , 0.) Clearly, the model generates tradea a

provided]s , z #s, (17)

]

a condition that we assume to be satisfied in the following analysis.Trade and technology shocks affect the cut-off skill level z and the representa-

tive firm’ s demand Y* simultaneously, so that the implications for the wagedistribution requires a joint solution for these variables.

4. Model solution

Invoking symmetry, we can set Y 5 Y*, and z 5 z*, and concentrate on the case12of balanced trade. Next we exploit the fact that each worker /firm produces a

single variety of the good. The space of goods can consistently be mapped intothat of skills, and the CES price index (6) can be rewritten in terms of thes-distribution,

] ] 21 / (s 21)s s

12s s 21P 5 p E T(s, a)f(s) ds 1 t E T(s, a)f(s) ds (18)3 1 24s z]

11Hence, Z 5 1/T . 0; Z 5 2 1/T , 0.1 s a a12 *By symmetry, N 5 N*; N 5 N is required for trade to balance.m* m


Note that the price level P depends on openness, inversely measured by z. Theprice index falls whenever z falls, because more firms decide to venture abroad.Due to ‘love for variety’, a larger mass of varieties available through importsraises indirect utility, thus reducing the true price index (which is dual to it). Inorder to derive an expression for Y which only depends upon z, integrate acrossskill rents (13) and (14) and substitute the resulting expressions into aggregateincome (5). This yields

] ]s s12sp Ys 21 s 21]]Y 5 P M 1 E T(s, a)f(s)s ds 1 t E T(s, a)f(s)s dss3 1 2

s z]

]s

2 g E f(s) ds (19)4z

Substituting the expression for P (18) into (19), gives

]s

M 2 g E f(s) dsz

]]]]]]]]]]]]]]]]]Y 5 (20)] ]s sss 2 1 12s s 21]]S D b E T(s, a)f(s) ds 1 t E T(s, a)f(s) ds

s 3 4s z]

The numerator of expression (20) represents the total income of primary inputsemployed in manufacturing, M, net of the income earned in export services.Clearly, the more resources are used up in market-access services, the lower theamount of resources that are left for production, and the lower the demand of astandard firm, Y. The denominator is inversely related to the price index. Sinceelasticity of demand to the firm relative price exceeds unity (see (4)), thesubstitution effect prevails on the income effect. Hence when the general priceindex rises (the denominator falls), the individual producer becomes morecompetitive and her sales rise. It is immediate to check that this expressiondepends positively on z, Y . 0. Two effects are at work in the same direction.z

First, when z rises, the number of exporting firms falls, less resources are used formarket access, and consequently the mass of production factors employable inproduction increases, together with firms’ scale. Second, as imports fall, the CESprice index rises (see (18)), and this makes domestic firms more competitive.

Eqs. (16) and (20) jointly determine the cut-off skill level, z, and the size of astandard firm in the domestic market, Y. The equilibrium can be represented on a


Fig. 2. Equilibrium degree of openness (z) and firms’ scale (Y).

simple diagram. Fig. 2 depicts Eq. (20), the YY curve, and Eq. (16), the ZZ curve,13in the z, Y space.s d

The properties of the two curves imply that there exists an unique equilibrium,represented by the intersection of the two loci. This diagram will help the analysisof next sections, where we perform comparative statics on the system.

5. Trade integration

Our aim in this section is to assess the implications of trade integration onincome distribution. From our diagram and from (16) we see that a reduction intransport costs (a rise in t) shifts the ZZ curve down to the left (see Fig. 3). Astransport costs fall, the price set abroad by domestic firms is reduced, foreigndemand increases, and the mass of exporters rises (z falls). From (20) we see thatthe YY locus shifts up to the left. Lower transport costs increase competition fromabroad, thus reducing demand for each firm, at given z. In the new equilibrium, Yunambiguously falls. Even if total sales are boosted by increased exports, each

13 ]Note that since we consider an equilibrium with trade, s , z #s must hold. Consistently, the range]] ]s 21of admissible values for market size must satisfy Y , Y #Y, where Y ; sg sb /(s 2 1)t /T(s, a)s d

] ]]s 21and Y ; sg sb /(s 2 1)t /T(s, a).s d

]


Fig. 3. The effect of reduced trade barriers.

firm operates on a smaller scale. The degree of openness is subject to twoconflicting forces. One the one hand, lower transport costs boost the demand forexports through a direct price effect. This raises the mass of firms willing to export(see (16)), and z falls. On the other hand, lower transport costs have a negativeeffect on foreign demand through a scale effect (Y* falls), and this reduces themass of export-oriented firms (z rises). It can be shown that the price effect alwaysdominates, so that the economy becomes more open when transport costs falls,dz /dt , 0, confirming partial equilibrium intuitions.

From this result we can derive the effects on the distribution of income. Eq. (13)nshows that skill premia in the non-exporting sector, w (s), must fall proportionate-

ly to the contraction the representative firm’s scale, Y. Conversely, from (14) weesee that all earnings in the export sector, w (s), may either fall, if the negative

effect of the shrinking firm’s scale Y prevails, or rise, if the positive price effect14due to lower transport costs prevails . What is clear from the expression above is

that, following the reduction in transport costs, all rents of export sector move inthe same direction. In particular even if they fall, they will fall by less than they doin the non export sector.

Take any one worker in the export sector, indexed by skill s9 $ z and any one in

14This second effect dominates provided demand is sufficiently elastic (s high).


the non export sector, s0 , z. It is easy to show that their relative earnings,e n 15w (s9) /w (s0), widens with trade integration. Given that lower transport costs

tend to raise the share of the export sector (dz /dt , 0), a reduction in transportcosts unambiguously implies a redistribution of income from the non-export to theexport sector of the economy.

It is easy to work out the distributional effects between skilled workers, S onone hand, and owners of primary inputs, M. Denote the aggregate (average) skill

]z n s nrent by D ; e w (s)f(s) ds 1 e w (s)f(s) ds. From (20) one can show thats z]

]s

M gs]] ]]D 5 2 E f(s) ds. (21)s 2 1 s 2 1

z

Differentiating expression (21) yields

dD gs dz] ]] ]5 f(s) , 0, (22)dt s 2 1 dt

since dz /dt , 0. A reduction in transport costs tilts the income distribution infavor of primary inputs. This result follows immediately by recalling thatexporting requires a fixed access cost in term of these inputs. As more firmsventure abroad, more primary commodities are demanded for export services,while the same number of entrepreneurs is required. Hence the share of wage rentsmust fall.

Finally, the effect of trade integration on total welfare can be assessed bylooking at changes in the utilitarian indicator W ; I /P 5 D /P 1 M /P. First noticethat a fall in transport costs reduces the price level. From (18), we see that this isdue to two reasons. First, a direct positive effect via lower price of imported good.Second, an indirect effect through the reduction of the threshold z, which raisesaverage quality. As a consequence, the ‘real’ earnings of primary inputs, M /P,unambiguously rises. As for the average real skill earnings, D /P, the effects areambiguous, since D is reduced by higher t. Comparative statics show that theoverall effect of lower transport is to increase total welfare, as measured by I /P.

The above findings are summarized in the following Proposition (a formal proofis available upon request).

Proposition 1. Trade integration via lower transport costs (higher t) has thefollowing effects: (i) openness rises (i.e., z falls) and the scale of the standard firmon the domestic market Y shrinks; (ii) skill earnings in non-exporting firms arereduced, skill earnings in exporting firms may rise or fall, and their ratio,

e nw (s9) /w (s0), rises; (iii) there is a redistribution from skill to raw inputs: D falls;(iv) total welfare W rises.

15This result is contained in an Appendix available by request from the authors.


Some remarks are in order. First, whether trade integration occurs as a result oflower transport cost or because of a reduction in the fixed cost of exporting, g,does somewhat affects the results. Again, it can be shown that when tradeintegration occurs via lower market access cost, income is redistributed towardsthe exporting sector, the share of traded goods rises and welfare improves.However the effects on aggregate skill rents and upon the firms’ scale become

16ambiguous. Second, even if welfare rises when transport costs fall, this does notimply that trade integration leads to a Pareto improvement. In other words, someagents may end up worse off when transport costs fall. Intuitively, if a worker isemployed in the non-export sector (has low skill) and has a small endowment of

17raw inputs, it is likely to suffer an income loss when trade barrier fall.

6. Technological progress

Now consider what happens when, as a result of a rise in technical knowledge,a, the quality of all products improves. Clearly, this means that a lower skillendowment is now required for achieving any given quality standard. Thus, from(16) the ZZ curve shifts down to the left in Fig. 2 (recall that Z 5 2 1/T , 0.) Aa a

higher fraction of firms can benefit from exporting, at any given scale Y. In turn,from (20), the YY curve shifts up to the left, since the price index falls whenaverage quality improves. Hence, each firm’s output becomes relatively moreexpensive compared with that of competitors, and demand falls. In the newequilibrium, a technology shock reduces the firm’s size, Y, but, differently fromtrade integration, has an ambiguous effect on the cut-off skill level, z.

The implications for entrepreneurial rents can be assessed as follows. Denotethe elasticity of product quality and of firm scale with respect to a, respectively, byh(s, a) 5 T (s, a)a /T(s, a), and j(a) 5 2 (dY /da)a /Y . 0. Differentiating the wagea

equations (13), (14) with respect to a we find

dw(s)]]$ 0⇔h(s, a) 2 j(a) $ 0 (25)da

16A proof of this result is available from the authors upon request.17For example, consider a worker employed in the non-exporting sector, who has zero endowment of

hraw inputs, M 5 0 Her skill rent, deflated by the CES price index is

T(s, a) Yn 12s ]] ]v (s) 5 p . (23)s P

(s 21) nApplying the definition Y ; IP and totally differentiating v (s) with respect to t yieldsn

≠v (s) T(s, a) ≠I ≠P12s (s 22) (s 23)]] ]] ] ]5 p F P 1 (s 2 2)P G. (24)≠t s ≠t ≠t

nSince ≠P/≠t , 0 and ≠I /≠t 5 ≠D /≠t , 0, s $ 2 is sufficient to imply ≠v (s) /≠t , 0.


in both the export and non-export sector.A technology shock exerts two contrasting forces on skill earnings: a positive,

firm-specific effect, h(s, a), and a negative effect, j(a), that is common to all firms.The first one reflects the fact that better quality directly raises firms’ demand, thusboosting operating profits. The second effect works through increased competition.As the general price level falls due to better average quality, the product of eachfirm becomes relatively more expensive, and this lowers the standard firm’s size Y.As a consequence, the effects on skill earnings and income distribution are ingeneral ambiguous.

A useful benchmark is the case of a linear technology T(s, a) 5 as. It is easy toshow that in this case h(s, a) 5 j(a) 5 1. The idiosyncratic effect is completelyoffset by the common effect, so that nominal earnings are unaffected by the shock.It follows that, in this linear example, the cut-off skill level z and the average skillearnings D (see from (21)) are not affected by technology shocks. Hence, whentechnological improvements are skill-neutral at the margin, they simply reduce theprice level, thereby raising welfare, W.

In order to generalize the analysis, remember that all firms experience lowersales via the common competition effect, j(a), while the positive ‘quality’ effect,h(s, a), varies across firms. For some s, the difference in (25) may be positive:these firms will benefit from technical progress. For some other, the opposite mayhold, h(s, a) , j(a), implying a loss. Of course, results crucially depend on howh(s, a) changes with s. Suppose, for instance, that technology is marginallyskill-complement, that is T (s, a) is ‘sufficiently’ large, so that entrepreneurs withas

high skill can exploit the technical innovation better than less talented18entrepreneurs. Then the ‘quality’ effect will tend to dominate for more skilled

workers, who will benefit from the innovation, while the ‘competition’ effect maydominate for the less skilled, who will lose. It is possible to show that there always

19]˜ ˜exists a skill level s [ s, s such that the two effect cancel out: h(s, a) 5 j(a).f g]Provided technological progress and skill are complement at the margin, a

˜technological shock boosts the earnings of a worker with skill s . s and reduces˜ ˜those of workers of type s , s. It is important to note that the value of s has no

relation with z; it might equally be higher or lower. Results on the degree of trade20openness are therefore ambiguous. Non neutral technological change also has

18A simple example of skill-complement technology is T(s, a) 5 as 1 c, c . 0. The product’squality depends on a common ‘state of the art’ component, c, and on an idiosyncratic one, proportionalto the level of skills.

19 ]˜The argument runs as follows. Assume that s [ s, s does not exist, and that there is marginallyf g]skill-complement technological progress. Necessarily, either a) all rents are raised, or b) all are lowered.However, in the first (resp., second) case, z, and then D (check from (21)) must fall (resp., rise), whichyields a contradiction. A symmetric reasoning applies to the case of marginally skill-substitutetechnological progress.

20It can be shown that when technological change is skill-complement (resp., substitute) at the˜ ˜margin, a technological shock raises openness only if z , s (resp., z . s ).


ambiguous implications on the income distribution between raw inputs and skilledworkers. This can be seen by differentiating D in (21) with respect to a andrecalling that the sign of ≠z /≠a is ambiguous. Finally, similarly to trade shocks,technological progress raises welfare, as measured by the change in our utilitarianindicator W. Results are summarized as follows (a formal proof is available uponrequest).

Proposition 2. Technological progress (an increase in a) has the following effects:(i) openness may rise or fall, while firms’ scale Y unambiguously falls; (ii) iftechnology is skill-complement (skill-substitute) at the margin, workers endowed

˜with talent s , s experience a fall (rise) in their earnings; (iii) the average skillpremium, D, may either rise or fall; (iv) total welfare, W, rises.

There are two main differences with respect to trade integration. First, whilelower trade barriers raise the share of exporting firms, technological progress hasan ambiguous effect on openness. Second, while trade shocks unambiguouslyredistribute income from the firms in the non-export to firms in the export sector,technology shocks may redistribute among firms belonging to the same sector.Moreover, following a technology shock, when technology is complement to skillsat the margin, some firms in the export sector may be hurt more than some firms in

21the non-export sector.

7. Conclusions

We have studied the effects ‘globalization’ on income inequality. Manydifferent things are generally meant by ‘global economy’. We have discussed two:trade integration in the form of lower transport cost, and technological change thatenables suppliers to improve the (perceived) quality of their products and raiseconsumers’ satisfaction.

If globalization takes place in terms of reduced trade barriers, then we find thatincome is redistributed from non-exporting to exporting firms, and that more firmschoose to export. Since non-exporting firms generally employ workers of lowerskill and pay, the effect is to raise wage inequality, although welfare, as measuredby real GDP, rises. This result differs from the conclusions of much of the existingtrade theory. Income redistribution in favor of the export sector is a well-knownfeature of ‘specific-factor’ models (Jones, 1971). In our model, however, trade isintra-industry, and wage differentials widen even among exporting firms. Con-versely, the new trade theories typically imply that (intra-industry) trade does notproduce victims. In our setting, trade-related gains are guaranteed only to those

21 e n˜Assume that s . z. Taken any two skill levels s9 , z and s0 . z, ≠(w (s0) /w (s9)) /≠a $ 0 requirese e0 . h(s0, a) 2 j(a) (w (s0) 1 g/w (s0)) $ h(s9, a) 2 j(a) , a condition that may or may not be satisfied.f g f g


sellers that do better than their average competitor. The conclusion that tradeintegration harms firms that do not sell abroad depends somehow on the Dixit–Stiglitz specification for preferences. Under this specification, all varieties have thesame substitution elasticity with all the others, irrespective of quality. Under amore general specification, however, we can expect a stronger substitution relationamong varieties with close quality level. In such a case, trade integration may leadto increased competition especially for firms supplying goods at the top of thequality ladder. The effect of trade on skill inequality may thus be dampened.

In addition, our conclusion that trade integration reduces the average skill rent(D), is somehow at odds with the common wisdom. This result is due to the factthat trade, in our model, is entirely intra-industry, so that integration leads to moreintense competition. This necessarily translates into lower profits and skillearnings. In a broader set-up with both intra- and inter-industry trade, the usualStolper–Samuelson result of rising returns to skill in the skill-abundant countrywould be restored.

If globalization takes place in terms of improved production or communicationtechnologies, then we find more ambiguous effect. The less skilled may either loseor gain, depending on whether technology is skill-complement or substitute at themargin. Income inequality rises only if the innovations can be exploited to a largerextent by firms employing the more skilled workers. Moreover, technologicalimprovements may raise as well as lower the share of exporting firms, and haveambiguous effects on the distribution of income across exporting and non-exporting firms.

Clearly, all our results derive from an extreme view of the labor market, wherewage earnings are associated with skill-specific rents. Yet these findings mayprovide a useful criterion for disentangling empirically trade from technologyshocks. In our set-up, the export status of firms is a sufficient criterion forpredicting if a firm stands to gain or loose if a trade shock occur, but not if atechnology shock occurs. Our story is therefore consistent with the empirical

22evidence found in Bernard and Jensen (1997)).The main policy implication of the analysis is that globalization, although

welfare improving, is likely to raise inequality, and to foster demand forprotection, in particular by firms in the non traded sector. Redistribution, ratherthan protection, should be the answer. The implications for redistribution,however, may be more complex than the traditional skilled /unskilled distinctionwould suggest. Globalization entails income transfers even among those workersthat appear to be skilled. The export status of firms and plants may guide policyaction to target the sectors who stand to loose more.

22Bernard and Jensen (1997) are cautious in attributing wage inequality changes to export demandalone, in that export status and technology status appear to be strongly correlated.


Acknowledgements

We would like to thank participants to seminars at IGIER-Bocconi, and HebrewUniversity. The usual disclaimer applies. Alessandro Turrini acknowledges afinancial contribution from CNR.

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