1

December 2012

Vertical Offshoring with

Heterogeneous Firms:

a Story of Employment

Inequality

in Europe

Marco Antonielli

Fondazione Luigi Einaudi

Abstract

This paper shows how in a two-countries model with

heterogeneous firms vertical offshoring can raise employment

inequality within sectors. The model matches the empirical

findings of the heterogeneous firms’ literature as well as

characteristics of the offshoring waves occurred between

Western Europe and Central and Eastern Europe in the 2000s.

I would like to thank Fondazione Einaudi for the unique opportunity of writing

this work. I also wish to thank Prof. Gino Gancia, Prof. Rosario Crinò, Prof.

Alessandra Bonfiglioli and Prof. Giorgio Ricchiuti for their precious suggestions

2

to the making of this work during my studies at Barcelona GSE. I would also like

to thank Alexander Ballantyne for his accurate feedbacks to the introduction. All

errors remain mine.

1 Introduction

In the last thirty years the world economy has experienced economic

integration between different regions and a contemporaneous increase of within-

country inequality in many countries. These phenomena have been criticized under

the presumption that the benefits of economic integration are not evenly distributed

among citizens. While skill-biased technological change has been recognized as the

main driver of rising wage inequality in advanced countries, international trade and

offshoring are lately gaining more attention. The focus has often been towards the

liberalization of world trade, like the constitution of NAFTA in 1994 and of Mercosur

in 1992. More recently, the integration of several Central and Eastern European

countries into the European economy, fostered by accession to the European Union

in the 2000s, also raises questions regarding the distribution of its benefits.

Since the Hecksher-Ohlin-Samuelson theorem, the economic literature has

attempted to explain how the relative wages of skilled versus unskilled labor, or the

wage gap for short, could be linked across economies heterogeneous in productivity

and the relative endowment of skills. In this abundant literature, a recent challenge

has been posed by data regarding the performance of firms engaging in international

trade and offshoring: we discovered that the heterogeneity in characteristics and

dynamic behavior of firms, which are ultimately the agents trading in the real

economy, can modify the predictions over the movement of the wage gap resulting

from trade liberalization. Indeed, heterogeneity in productivity and skill

composition of the workforce turn out to be determinants.

How can offshoring within Europe be a cause of rising wage and employment

inequality in all the EU countries? In this paper I develop a model matching the

existing evidence on the offshoring waves of the 2000s to find an innovative answer

to this question. The fundamental finding of this model is that when firms start to

offshore they also expand their headquarters activities in the home country: since

offshoring firms use relatively skill-intensive technologies, the demand of skills can

rise in both the home and the host country. In order to guide the theoretical work, in

Paragraph 1.1 I analyze the available evidence on the extent of offshoring and wages

differentials in several countries within the two zones, as well as recent studies on

firm-level data and behavior. The model is framed in the literature on wage

inequality in Paragraph 1.2.

3

1.1 Firm-level productivity, wage gaps and offshoring in Europe

The offshoring wave from Western to Eastern Europe started in the late 1980s

but it reached a substantial dimension in the 2000s. In particular, over the late 1990s

and 2000s the EU10 countries1 attracted substantial foreign direct investment,

especially from EU15 countries2. As shown in Graph 1, the stock of FDI in Poland,

Hungary and Czech Republic, the three biggest EU10 economies, more than doubled

over the period 1998-2003 and more than tripled over the period 2003-2008. The

EU15 countries’ firms contributed for most of the new FDI in the 1998-2008 period,

respectively 83% of the total in Poland and Czech Republic and 55% for Hungary.3

Graph 1 – Inward FDI stock in EU10 selected countries

OECD data – own composition

The offshoring wave towards Eastern Europe was also significant from the

perspective of Western European economies: while the total outward FDI stock of

the EU15 soared between 2000 and 2008 by 2.7 times, the share of FDI stock in

Poland, Hungary, Czech Republic and Slovakia rose from 2% to 5% (OECD data).

The advantages of offshoring production in Central and Eastern Europe were

geographical closeness, low labor costs and the presence of educated workforce

(Gausellman, Kneel and Stephan, 2011).

While the boom of FDI crucially characterizes an offshoring wave, the

“identity” of the offshoring firms could be crucial to evaluate its implications on the

1 Cyprus, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Malta, Poland, Slovakia, and

Slovenia. 2 Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxemburg,

Netherlands, Portugal, Spain, Sweden, and UK. 3 Similar trends are observed for other EU10 countries: the FDI stock originated in the EU15

countries increased by 11 times in the Slovak Republic over the period 2000-2008 and by 2.5 times in

Estonia over the 2003-2008 period (OECD …).

0

50

100

150

200

250

300

World Total EU15 World Total EU15 World Total EU15

Poland Hungary Czech Republic

FDI

sto

ck in

$, b

illio

ns

1998

2003

2008

4

labor market (Yeaple, 2005, Altomonte, Barba Navaretti, di Mauro and Ottaviano,

2011, Pflüger, Blien, Möller and Moritz, 2012). The basic intuition is that trade and

offshoring liberalizations lead to labor reallocations across firms of the same

industry. As different firms may operate under different skill intensities, the relative

demand for skills could shift. In literature the identity of firms is often associated

with the intrinsic productivity of the firm, to which many other dimensions of firm

performance are associated (e.g., size, skill and capital intensity). With respect to

internationalization, the empirical literature has established that within sectors only

the most productive firms engage in international trade and offshoring (see e.g.

Mayer and Ottaviano, 2007). The motive is that internationalizing the firm means

higher variable costs – i.e. tariffs and transportation costs – and higher fixed costs –

i.e. start up and integration costs – that can be sustained only by the most productive

firms (see e.g. Helpman, 2006, Antras, 2003, Greenaway and Kneller, 2007,

Hayakawa, Machikita and Kimura, 2011).

Starting from this fundamental observation, the performance of the offshoring

firms has been empirically studied under other key dimensions: Hayakawa et al.

(2011) review recent papers drawing attention to the selection into

internationalization, learning (broadly defined as the ‘causal effects of globalizing

activities on productivity’, p.336), and the impact of trade and investment

liberalization. For the present context, the survey shows that offshoring firms tend to

increase their productivity in Italy (Navaretti and Castellani, 2006) but not in France

(Navaretti, Castellani and Disdier, 2010); when vertical and horizontal types of

offshoring are considered separately, the results show that horizontal offshoring

helps French firms ‘learning’, but vertical offshoring does not (Navaretti et al., 2010,

and Hijzen, Jean and Mayer, 2006). This is the opposite of what is predicted in

theory: on the one hand, vertical offshoring should decrease the total cost of

production by locating tasks in countries owning a comparative advantage; on the

other hand, horizontal offshoring should have an ambiguous effect as it also implies

a loss of economies of scale.

In addition, Castellani et al. (2008) and Hijzen et al. (2006) do not find a

positive link between skill-upgrading and vertical offshoring. This result is also

shared with Wagner (2011), which analyses data collected in different years (2001-

2006) from surveys about German firms in the manufacturing industry. Again, the

prediction is different: by offshoring unskilled tasks, the skill-intensity of the home

production should increase. Another important finding of Wagner (2011) is that the

offshoring firms are more skill-intensive than the non-offshoring firms. Therefore at

present we cannot infer that offshoring spurs within firm skill-upgrading.

5

1.2 Wage and employment inequality in Europe

The rise in wage and employment inequalities is common trend for several

advanced and emerging countries in the recent past (for recent surveys, see Van

Reenen, 2011, and Chusseau and Dumont, 2012). From a review of several empirical

papers concerning advanced countries, Crinò (2009) concluded that the shift in the

relative skilled labor demand has taken place within industries. Following this trend,

skill-upgrading occurred within sectors, or even within firms. In addition, Crinò

(2009) concluded that material offshoring represented one of the main causes of

rising wage inequality in advanced countries in the recent past.4 Also, integration of

developing countries into the world economy has often coincided with widening

wage gaps (Goldberg and Pavcnik, 2007).

There is a point in which these trends show an inconsistency with the firm-

level evidence described above: we have seen that only the most skill-intensive firms

offshore and within-firm skill-intensity and productivity dynamics appear not to be

linked to offshoring activities. This is apparently puzzling as skill premium and

employment inequality in an advanced country should respond negatively to the

offshoring of the most skill-intensive production in each manufacturing towards low

wage countries. Indeed, the firms keeping production at home are relatively low

skilled in respect to the offshoring firms. A possible explanation could be that firms

engaging in offshoring go on to skill-upgrading the activities they keep at home.

However, at present no empirical study concerning European firms finds that

within-firm skill-upgrading takes place in offshoring firms.5

To explain this apparent puzzle we can compare the new evidence with the

literature providing justification for the wage gap increase as caused by offshoring.

The most convincing explanations follow the pioneering contribution of Feenstra

and Hanson (1999).6 In their model the final good is produced with a continuum of

inputs ranked according to skill intensity; when offshoring inputs’ production is not

prohibitively costly, the high-skilled inputs are produced in the skill-abundant

country, labeled as North, and the low-skilled inputs are produced in the skill-scarce

country, labeled as South. If production capacity increases in the South, also

offshoring opportunities expand and new inputs in the middle of the range are

relocated to the South; however, these inputs are low-skilled for the North

4 The other great cause was skill-biased technological change. 5 Bustos (2011, 2012) shows that in Argentina trade liberalization stimulated within firm skill-

upgrading by firms trading with abroad. 6 Notice that offshoring can raise low skilled wages in real terms, as highlighted by Grossman

and Rossi-Hansberg (2006; 2008). Their analysis shows that outsourcing unskilled tasks improves the

productivity of home skilled tasks to which they are complementary in production of the final good.

6

standards, but high-skilled for South standards, so that the wage gap rises in both

countries.

Whereas this is a convincing proof of how within industry wage inequality

can be fostered by offshoring, the Feenstra-Hanson mechanism is rather

unsatisfactory in solving our puzzle. The main reason is that in the Feentra-Hanson

world the expanding offshoring opportunities affect all firms the same way while we

now know that heterogeneous firms respond differently to cheaper offshoring

opportunities: virtually all firms should transfer some input production abroad in

the Feenstra-Hanson world, but in reality only the most productive can sustain the

fixed costs of offshoring activities abroad.7 This makes a difference for our puzzle

which is based on different ex-ante skill-intensity between offshoring and non-

offshoring firms. In the original form, the Feenstra-Hanson mechanism only

highlights skill-intensity across inputs and is thus silent on the solution of our

puzzle.

The Feenstra-Hanson mechanism could be strong enough to offset a possible

downward pressure to wage inequality arising from the offshoring of skill-intensive

production. Nonetheless, the within industry labor reallocations characterizing an

heterogeneous firms world could still move up the relative demand of skills:

competitive pressure from offshoring firms would force the least productive firms to

exit, and resources would move towards the new offshoring firms, which run skill-

biased technologies with respect to the least productive firms.8 In this work I

develop a theoretical mechanism that displays this result: firms from an advanced

country engage in offshoring keeping at home the production of fixed services like

headquarters, research & development, legal services, marketing services, while

relocating the production task in a low wage emerging country. To distinguish from

the Feenstra-Hanson world, the model runs under two simplifying hypotheses: first,

skill intensity is correlated with firm-level productivity and not with the inputs/tasks

performed (within each firm, the skill intensity is the same across fixed cost and

variable cost production, as in Bernard, Redding and Schott, 2007); second, wages

are exogenously determined so that the wage gap is identical in the two countries,

but the advanced country has higher skilled and unskilled wages. This is the only

source of ex-ante asymmetry between the two countries.9

7 The Melitz model, as for example used in Grossman, Helpman, Szeidl (2006), can account

for this feature. 8 In consistency with the empirical findings, within the set of surviving firms the fraction of 9 In a general equilibrium model with endogenous wages, the asymmetry between advanced

and emerging countries could arise from ex-ante technological backwardness of emerging countries’

7

With firms heterogeneous in productivity, only the most productive make

enough operating profits to sustain the fixed costs of offshoring. This way, an

offshoring wave takes place from a reduction in offshoring fixed costs:10 more firms

in the advanced country decide to locate production in the emerging market in order

to save on labor cost. These firms run skill-biased technology with respect to the

other firms operating in the emerging country.11 Thus, the relative demand of skills

in the emerging country shifts up. As wages are given, within-industry skill-

intensity increases in the emerging country.

In the advanced country three factors contribute to the movement of the

relative demand of skills: firstly, offshoring skill-biased production tends to decrease

the relative demand of skills, that would be a formalization of our puzzle; secondly,

also the reduction in fixed cost production by already offshoring firms tends to

decrease the relative demand of skills; thirdly, the new offshoring firms get more

labor to work in the fixed cost production, thus boosting up the relative demand of

skills. I show that the third component can offset the other two and lead to an

increase in the demand of skills, and thus also the within-industry skill-intensity.

Notice that offshoring does not cause the share of firms using skill-biased technology

to rise.

The attention towards micro-mechanisms influencing wage and employment

inequality is a promising avenue for research, as pointed out by Chausseau and

Dumont (2012), and Burstein and Vogel (2010). The most closely related paper is

Bustos (2011a) which studies how skill-upgrading raises the wage gap in Argentina

as a result of trade liberalization. From that work, I borrow the idea that firms

introduce a skill-biased technology because it augments firm level productivity; this

way the share of firms using a skill-biased technology is endogenously determined.

In Bustos (2011a) this share increases, while in my model it does not change with a

reduction of the offshoring costs.

firms. With identical relative endowments of skilled versus unskilled labor, also the wage gaps would

be identical, and the working of the model would be maintained (Bernard, Redding, and Schott,

2007). 10 In the light of the European case, these lower costs can be interpreted as savings in

managerial, legal and financial costs as well as reduction in the riskiness of investing in Central and

Eastern Europe country. The process of accession to the EU permitted to Western Europe firms to

spread in an investment-friendly Eastern Europe. 11 Notice that firms born in the emerging country never offshore as they would incur in

higher variable cost, i.e. labor, whilst paying higher fixed costs.

8

2 Model

This section presents a model that explains how a reduction in offshoring

costs can raise relative demand for skills in both advanced and emerging economies.

Two asymmetric countries trade differentiated goods on the same industry at no

cost. At the same time, an exogenous wage differential motivates offshoring of

production from the high wage country to the low wage country.

2.1 Setup

I consider a world with two asymmetric countries, two factors of production

(skilled and unskilled labor), and a continuum of heterogeneous firms competing in

one industry. Firms from both countries produce differentiated goods under

increasing returns to scale à la Krugman (1979) in a monopolistically competitive

market. Production entails a fixed cost and a variable cost for which firms have

heterogeneous productivities. In addition, as for production technology firms face

two choices: firstly, they can upgrade their default low productivity technology by

introducing a high productivity skill-biased one which entails higher fixed costs as

in Bustos (2011a, 2011b); secondly, they can offshore the variable cost production to

the other country by paying a higher fixed cost as in Helpman, Melitz and Yeaple

(2004).

In both countries the wage rates are exogenously determined, i.e. at the given

wages the supplies of skilled and unskilled labor are unlimited. These exogenous

wages are higher in one country, hereafter labeled as advanced, and lower in the

other one, hereafter labeled as emerging. This is the only source of ex-ante

asymmetry. In addition, the model features a common market for goods, i.e. costless

international trade.

Demand structure

Consumers have preferences over a continuum of horizontally-differentiated

varieties within the industry. Consumers’ utility takes the usual CES form

[∫ ( )

]

with an elasticity of substitution ( ) , and being

the measure of existing varieties. The demand for each variety generated by these

preferences is ( ) ( ) where [∫ ( )

]

is the price of the

aggregate consumption good defined as , and is the aggregate level of

spending in the integrated economy12.

12 As international trade is costless, firms sell their products in the international market,

which includes consumers from both countries

9

Entry

Each firm is the monopolistic producer of one variety within the industry and

uses a technology with increasing returns to scale. In order to enter the industry,

firms have to pay a fixed cost which is thereafter sunk. The entry cost uses skilled

and unskilled labor under the skill intensity of the default technology, following

Cobb-Douglas specification:

(

)

where , identifies the sunk cost ( ), is the wage of skilled labor

and is the wage of unskilled labor in the country of entry.

The “nationality” of firms is defined before entry. Instead, upon entry each

firm draws its productivity level from a Pareto cumulative distribution function

( ) with . The distribution’s shape and parameter are the same in

the two countries.

Technology and offshoring

Once new entrants have learnt about their productivity level, they can decide

either to exit either to stay and produce. Firms can operate at the default technology l

or upgrade to a skill-biased and more productive one h. In addition, firms can

offshore production to the other country, where they can, in theory, operate with

technology l or h. Accordingly, each firm faces a choice over four production

strategies.

The default technology consists of a variable cost and a fixed cost which use

skilled and unskilled work as in Bernard et al. (2007). The idiosyncratic productivity

level affects the variable cost but not the fixed cost. The resulting total cost

function is:

( ( )) ( ( )

) (

)

where identifies the fixed cost, ( ) are the produced quantities and and are

the wages of skilled and unskilled labor in the country of entry. Accordingly, the

constant marginal cost is

.

10

Firms have the option of decreasing their marginal cost by adopting a skill-

biased technology. At the same time upgrading entails higher fixed costs13. Thus the

total cost function of the skill-biased technology is:

( ( )) ( ( )

) (

)

where , , and ( ). The constant marginal cost of the

skill-intensive technology is

.

In addition, firms have the opportunity of offshoring variable cost production

in the other country. Doing so entails higher fixed costs. The total cost functions of

offshoring technology l and h are respectively:

( ( )) (

)

( )

(

)

( ( )) (

) ( )

(

)

where , and and are the wage of skilled labor and the wage of unskilled

labor in the other country. Such a cost structure reflects the fact that offshoring firms

maintain headquarters’ activities in the home country14.

Labor market

Wages are exogenously determined outside the model. The emerging country

has low skilled and unskilled wages ( and ) while the advanced country has

high skilled and unskilled wages ( and ):

and

As for wage gaps, i.e. relative wage of skilled versus unskilled labor, I assume

these are the same across countries (

).15 Thus, to evaluate the effects of

offshoring waves at given wage structure we can look at the relative demand of

13 Skill intensity in variable and fixed cost production is identical, as in Bernard et al. (2007).

This assumption does not alter the results. 14 These activities normally include firms’ departments like direction, R&D, marketing etc. 15 Whereas normally the wage gap is thought to be lower in advanced countries, in this

specific model this assumption is founded on three facts. 1) In Europe wage gaps are so diverse

within the group of advanced countries as well as within the group of emerging country that it is not

possible to establish a valid comparison. 2) If the wage gaps were different, offshoring technology l

and offshoring technology h would bring different advantages on wages, while we know from the

data that vertical offshoring is mostly motivated by wage differentials across countries and not within

countries. 3) The simplification does not alter the results that are drawn on the relative demand of

skills in each country.

11

skilled versus unskilled labor (

)

, which is defined at the country level. An

increase in the relative demand of skills implies better employment conditions for

skilled with respect to the unskilled.16

Industry equilibrium

To solve for the industry equilibrium it is sufficient to find the equilibrium in

the goods market, which rules entry and exit of firms. Indeed, with exogenous

wages the labor market is automatically in equilibrium, and in this sense the model

delivers a partial equilibrium. Firstly, I show the pricing behavior of firms, which are

the same for firms in the advanced and in the emerging country. Secondly, I derive

firms’ behavior and industry equilibrium in the advanced country. Finally, I derive

firms’ behavior and industry equilibrium in the emerging country.

Pricing behavior

When consumers have CES preferences, profit maximizing firms set a price

equal to a constant markup over marginal cost. With costless trade all firms are also

exporters. Then, a firm using the default technology sets a price equal to ( )

, which depends on its productivity . Instead, if the firm adopts

technology h, its price will be ( ) ( ) , where (

) is the

marginal cost advantage of technology h in respect to technology l. Similarly,

offshoring firms set prices equal to ( ) ( ) if using technology l, and

( ) ( ) if using the technology h, where

. Accordingly, in

respect to running technology l in the country of entry, offshoring the technology l

has a cost advantage of , while offshoring the technology h has a cost advantage of

.

Since wages are different in the two countries, and wages affect pricing

behavior, two ex-ante identical firms born in different countries may operate

different strategies and adopt different prices. The strategy adopted by a firm is

therefore affected by the country of entry. For this reason I describe firms’ behavior

and equilibrium conditions in the two countries separately.

2.2 Firms’ behavior and industry equilibrium in the advanced economy

The relative profitability of the four strategies determines firms’ behavior.

Profits if using technology in the advanced country are:

16 Wages are not perfectly flexible in the real world. Focusing on relative demand of skills

allows ascertaining from this issue, while acknowledging that a rise in relative demand of skills can

both cause higher unemployment rates for the unskilled workers and reinforce wage inequality.

12

( )

( )

(

) ( )

where ( ) ( ) (

) are revenues. Profits if using technology

in the developed country are:

( )

( )

(

) ( )

where is the constant marginal advantage of the high technology in the

advanced country. Profits if offshoring technology are

( )

( )

(

)

where is the wage differential between advanced and emerging country. Finally,

profits if running technology in the emerging country are:

( )

( )

(

) ( )

For each productivity level, the strategies attaining the highest profits are

depicted in Figure 1. The equilibrium represented in the figure mirrors the findings

outlined in the introduction: within the industry firms sort in four different groups.

The least productive firms ( ) cannot cover the fixed costs and exit the market.

Low productivity firms (

) produce under the default technology in the

home country; medium productivity firms (

) choose to upgrade their

technology but still produce in the home country. Finally, highly productive firms

( ) produce in the host country and use the skill-biased technology. The

cutoffs separating the four intervals are defined as follows:

Exit cutoff: (

)

Technology adoption cutoff: (

) (

)

Offshoring cutoff: (

) (

)

Figure 1 – Firms’ self selection – Advanced country

The marginal offshoring firm uses technology , consistently with data. For

this order of cutoffs to apply in equilibrium, I need to state the conditions under

which:

13

-

, and

- Offshoring technology l is always dominated by some other strategy.

Exit

The exit cutoff identifies the firm making zero profits. Revenues are just high

enough to cover the fixed cost of the default technology.

(

)

( ) (

)

( ) (

)

Using this definition we can obtain the following expression for revenues

( ):

( ) (

) (

)

( )

Technology adoption

The technology adoption cutoff is defined by

(

) (

) ( ) (

) (

)

( (

) (

))

Adopting technology provides firms a marginal cost advantage with

respect to technology l. Thus, with elastic demand, revenues rise: the total benefit is

expressed on the left-hand side of the equation above. However, upgrading

technology requires higher fixed costs (the term on the right-hand side of the

equation). In fact, while the fixed cost is the same for all firms, the benefit of the high

technology increases with productivity. As a result, only firms with intrinsic

productivity over the cutoff adopt the high technology.

Using (4) and rearranging terms we can express the adoption cutoff as17:

( )

( (

)

)

( )

Offshoring

The offshoring cutoff is defined as

(

) (

)

17 In order to have firms adopting the technology we need to assume that that (

)

.

14

(

) (

) (

)

(

)( )

The opportunity to offshore variable production cost to the low wage

emerging country provides firms a marginal cost advantage . Alike the

technology adoption choice, exploiting a cost advantage raises revenues as demand

is elastic (total benefit appears on the left-hand side of the equation above).

However, offshoring production has higher fixed costs (on the right-hand side of the

equation). While these fixed costs are the same for every firm, the benefit rises with

productivity. Therefore, among the producers using technology , the most

productive ones offshore production to the emerging country.

Rearranging terms we obtain:

( (

))

( (

)

( ))

( )

Notice that in order to have

, we need the following parameter

restriction, obtained from the comparison of equation (5) with equation (6).

( (

)

( )

(

)

(

)

)

Once the order of cutoffs depicted is justified, I need to give further

conditions to establish that advanced country’s firms do not perform technology l

abroad in equilibrium. Lemma 1 states these conditions.

Lemma 1 – Advanced country’s firms do not offshore the default technology

under the following conditions:

- If (

) (

), then (

)

( )

- If (

) (

), then ( )

(

)

(

)

Proof – see the Appendix.

Industry equilibrium

In an equilibrium featuring free entry in the industry, the expected value of

entry must equal the sunk entry cost. The expected value of entry is the expected

profitability of producing the good until death, so that the free entry condition is

stated as

15

( )

(

) ( )

where ( ) is the probability of survival, are per period expected profits

conditional on survival and is the per period probability of exit. Expected profits

are the sum of the average profitability of each strategy multiplied by the

probability of implementing the strategy:

( )

where

( ) (

)

( )

is the fraction of firms running technology l and are their

average profits,

( ) (

)

( )

is the fraction of firms running technology h and

are their average profits, and

(

)

( )

is the fraction of firms offshoring

technology h in and are their average profits. Next, in order to solve for the free

entry condition, we need to derive expected profits , which is done in the

appendix:

(

)

( (

)

)

( )

( (

)

( ))

(

)

The model displays positive expected profits only if , assumption

that is made hereafter. Plugging the solution expected profits in the free entry

condition and solving for we obtain:

(

)

( )

From the definitions of the technology adoption cutoff and offshoring cutoffs

in equations (5) and (6) we obtain:

(

)

( (

)

)

( )

( )

(

)

( (

)

( ))

( (

))

( )

16

2.3 Firms’ behavior and industry equilibrium in the emerging country

Firms in the emerging economy are confronted with the same set of strategies

and select the one bringing about the highest profits. Profits if adopting technology

in the emerging country are:

( )

( )

(

)

where ( ) ( ) (

) are revenues. Profits if using technology

are:

( )

( )

(

)

where is the constant marginal cost advantage of technology h.

Firms in the emerging country can decide to offshore production but in

equilibrium they never do so. Indeed, offshoring to the advanced country would

increase the marginal cost of each technology, while leading to higher fixed costs.

Consequently, the strategy choice of firms born in the emerging country is pretty

simple: exit, use technology l or use technology h. The best strategy according to

productivity level is reported in Figure 2.

Figure 2 – Firms’ self selection – Emerging country

Least productive firms (

) do not make enough revenues to cover the

fixed costs and exit the market. Medium productivity firms (

) use the

low technology, while high productivity firms use the high technology. Such cutoffs

are defined as

Exit cutoff: (

)

Technology adoption cutoff: (

) (

)

For this order of cutoffs to apply in equilibrium, I only need to state the

condition under which

. To find the exit and the technology adoption

cutoffs we can apply the same procedures used above.

Exit

The exit cutoff identifies the firm making zero profits. Revenues are just high

enough to cover the fixed cost of the default technology.

17

(

)

( ) (

)

( ) (

)

Using this definition we can express revenues ( ) in a comfortable form:

( ) (

) (

)

Technology adoption

The technology adoption cutoff is defined by

(

) (

) ( ) (

) (

)

( (

) (

))

Using technology grants firms a marginal cost advantage with respect to

the default technology, while increasing its fixed costs. Exactly like for firms in the

advanced country, this leads only firms with intrinsic productivity over the cutoff

adopt the high technology.

Rearranging terms we get to the following expression of the adoption cutoff:18

( )

( (

)

)

( )

Industry equilibrium

The definition of the equilibrium is parallel to the one given for the developed

country’s firms: in a free entry industry, the expected profitability of entering the

market equals the sunk entry cost. The condition is stated as:

( )

(

) ( )

where ( ) is the probability of survival, are per period expected profits

conditional on survival. Expected profits are the sum of the average profitability

of each strategy multiplied by the probability of implementing the strategy:

where

( ) (

)

( )

is the fraction of firms using the default technology and

are their average profits,

( )

( )

is the fraction of firms using technology h and

are their average profits.

18 In order to have firms adopting technology we need to assume that (

)

.

18

To solve for the free entry condition it is necessary to find a solution for the

expected profits. Derivations are very similar to the ones detailed for the advanced

country case in the appendix.

(

) ( )

( (

)

)

( )

Plugging the solution expected profits in the free entry condition and solving

for we obtain:

(

)

From the definitions of the technology adoption cutoff (12) we obtain:

(

)

(

(

)

)

2.4 Offshoring waves: effects on productivity and the labor market

With the stated equilibrium cutoffs levels, I can now focus on the impact of a

decline in offshoring costs on firms’ strategies and on the labor market. The first

thing to notice is that as emerging country’s firms do not engage in offshoring

activities, a reduction of its costs do not alter their strategy choice.19

2.4.1 Advanced economy’s firms

With declining offshoring fixed costs, we have two immediate effects on the

advanced economy’s firms: first, offshoring firms make higher profits as production

levels remain constant while the fixed costs decrease; second, the profitability of the

offshoring opportunity rises with respect to the other options, so that more firms

choose to exploit the unaltered offshoring benefits paying the lower fixed cost.

Together, these two considerations mean that expected profits upon entry are

higher. Starting from this result, we can display all consequences of a reduction in

offshoring costs, which is done in Proposition 1.

19 The missing feedback relies on the fact that profitability of entry as firm in the emerging

country does not change.

19

All the effects stemming from a decline in offshoring costs are summarized in

Proposition 1.

Proposition 1. As result of a reduction in offshoring costs

a) the share of high technology firms decreases

b) the share of low technology firms remains equal

c) the share of offshoring firms increases

d) expected profits upon entry rise

e) the entry cutoff increases

f) the technology adoption cutoff increases

g) the offshoring cutoff drops

.

Proof – See appendix.

Discussion – Figure 3 below displays cutoff’s movements caused by a fall in

offshoring fixed costs. To analyze how firms’ behavior changes we can look at how

cutoffs move. First, the exit cutoff rises because expected profits upon entry increase

(

in the figure). Given a sunk entry cost and rising expected profits from

successful entry, the probability to exit must increase, hence the exit cutoff must

move up20. Second, the technology adoption cutoff follows the movement of the exit

cutoffs (see equation (7)), and shifts up(

in the figure). Third, the offshoring

cutoff shrinks: while the exit cutoff tends to increase it (see equation (6)), the fall in

the offshoring cost implies that some firms choose to switch from using technology

to offshoring technology (

in the figure). Firms switching to an

offshoring strategy maintain the skill-biased technology, consistently with existing

data.

20 This can be interpreted as an increase in competition for entry.

20

Figure 3 – Firms’ reaction to easier offshoring opportunity

As the technology adoption cutoff moves exactly as the exit cutoff, the share

of firms using the default technology remains constant. As a consequence, the share

of firms operating the skill-biased technology, either at home or offshore, also

remains constant.21 In fact, within this group the firms below the threshold start

to offshore: while remains constant, the increase in

is mirrored by a

symmetric fall in .

2.4.2 Labor markets’ effects

The change in firms’ behavior in the advanced country causes the relative

demand of skills to move in both countries. Indeed, the firms who start to offshore

now employ workers in the emerging country to produce the variable cost, while

they keep employing workers in the advanced country to produce the fixed cost.

Given that the skill intensity of offshorers differs from the average skill intensity in

both countries, the relative demand of skills must shift in both countries. Intuitively

one would say that it goes down in the advanced country and goes up in the

emerging one. I shall show that this is not always the case and we can have relative

demand of skills rising in both countries.

In order to retrieve these movements, we can start decomposing the demand

of skilled and unskilled labor as sums of demands of high and low technology firms,

respectively and , where , , and are the demands of

unskilled and skilled labor employed by low and high technology producers, which

are obtained as sums of firm-level demands. Notice that as for employer status high

21 With respect to Bustos (2011 both) the marginal user of the skill-biased technology is an

international firm (exporter). In fact, her results rest on rising share of firms using the skill-biased

technology.

21

technology firms in one country can be domestic non-offshoring firms (fixed and

variable cost production), domestic offshorers (fixed cost production) or foreign

offshorers (variable cost production). Instead low technology firms do not offshore

so that we only observe national non-offshoring firms.

Using Shephard’s lemma we can derive the demands of skilled and unskilled

labor at the firm-level by differentiating the total cost functions. For low technology

firms these are respectively ( ) and ( ):

( ( ))

( ) ( ) (

( )

)(

)

( )

( ( ))

( ) (

( )

)(

)

( )

Hence, the relative demand of skills is constant for all low technology firms, ( )

( ) (

)

. Similarly, high technology firms (but not offshoring) demand

functions are ( ) for unskilled labor and ( ) for skilled labor:

( ( ))

( ) ( ) (

( )

)(

)

( )

( ( ))

( ) ( ) (

( )

)(

)

( )

The skill intensity is also fixed for firms of this type, ( )

( ) (

)

.

Offshoring firms demand labor in both countries. Demands of skilled and

unskilled labor in the home country are ( ) and ( ):

( ( ))

( ) ( ) (

)

( )

( ( ))

( ) (

)

( )

Demands of skilled and unskilled labor in the host country are ( ) and

( )

( ( ))

( ) ( ) ( )

(

)

( )

( ( ))

( ) ( )

(

)

( )

22

Therefore, the skill intensity in the home country is ( )

( ) (

)

while in the host country is ( )

( )

(

)

. Comparing the relative

demands by different types of firms, we re-discover that the skill intensity is

attached to a technology as it does not change with production level ( ), but it does

change with the wage gap

and the intrinsic skill bias ( and ). All high

technology firms, irrespectively of the offshoring status and the kind of cost

produced, operate under the same skill intensity (

)

=(

) .

To sum up, in each country the relative demand of skills for the firms using

the high technology is

(

) , and for low technology firms is

(

)

22. Thus,

the aggregate relative demand of skills is a weighted average of the skill intensities

(

) and (

) , where the weights are given by the share of unskilled employment in

the low and high technology firms versus total unskilled employment:

(

)

(

)

(

)

The formula above shows that, at given skill intensities23, when the share of

employment in high technology firms ⁄ rises, the relative demand of skill shifts

upwards because the high technology is skill-biased. As in Bustos (2011a), this

structure of the relative demand of skill reminds the H-O framework, where skilled

and unskilled labor is employed in skill-intensive and unskill-intensive sectors and

goods are traded between two countries. In our case the unskill-intensive sector is

represented by the low technology firms whereas the skill-intensive sector is

represented by the high technology firms, within the same industry. In addition,

with costless trade, it is the offshoring activity to move the demand of labor.

In next paragraphs I use changes in the ratio

at the country level to explain

how the relative demand of labor moves. The positive relationship can be

established using eq above and skill intensities:

(

)

[

]

[

]

Deriving with respect

to we obtain

22 These are effectively skill intensities since wages are exogenous. 23 Skill intensities are fixed in this model because the wages are exogenous.

23

(

)

(

)

[

]

Advanced country’s labor market effects.

Workers in the advanced country are employed under the skill-biased

technology by high technology firms and by offshoring firms which keep the fixed

cost production at home. Thus, to obtain the demand of unemployed workers we

can sum firm-level demands from all high technology firms that can be grouped

according to firm’s strategy. Similarly, the demand of unemployed workers can

be found summing up the firm-level demands from low technology firms.

∫ ( )

( ) (

)

∫

( )

( ) (

)

∫ ( )

( ) (

)

where ( )

( ) and ( ) are the firm-level demands of unskilled

workers according to firm’s strategy. Using expressions (15) (17) (19), and the

equilibrium quantities we obtain the resulting relative demand of unskilled workers

(derivations are detailed in the Appendix):

(

)

(

)

( ) (

)

( )

((

)

(

)

)

( (

)

) ( )

( (

)

)

( )

When offshoring costs fall, some high technology firms start to offshore

variable cost production, which tends to decrease the relative demand of skill; at the

same time, the fixed cost production of these firms increase, which tends to increase

the relative demand of skill. Proposition 2 states that both the movements can

actually take place, depending on the model’s parameters.

Proposition 2. A reduction in offshoring costs causes the relative demand of

skill in the advanced country

- to rise if ( ) [(

)

(

)

]

- to fall if [(

)

(

)

] ( ).

24

Proof – See Appendix.

Emerging country’s labor market

In the emerging country, workers are employed under the skill-biased

technology by domestic high technology firms and by advanced country’s offshoring

firms. Thus, to obtain the demand of unskilled workers by high technology firms ,

we can sum the firm-level demands of the two groups. Similarly, the low technology

firms’ demand of unskilled workers is the sum of all firm-level demands by firms

of this type. Hence

∫ ( )

( ) (

)

∫

( )

( ) (

)

∫ ( )

( ) (

)

where ( ) and

( ) are the firm-level demands of unskilled workers according

to firm’s strategy. Using expressions (15) (21), we obtain the resulting relative

demand of unskilled workers (derivations are detailed in the Appendix):

( ) (

)

( (

)

( )

(

)

( )

(

)

)

( ) (

)

( (

)

( )

( (

)

))

( )

When offshoring costs fall, new advanced country’s firms start to offshore

variable cost production, which increases the relative demand of skill in the

emerging country. This result is stated in Proposition 3.

Proposition 3. A reduction in offshoring costs implies higher relative demand

of skill in the emerging country.

Proof – See Appendix.

3 Conclusions

Despite its potential benefits, economic integration between different areas

can also create winners and losers. A debated topic concerns the presumption that

the most skilled and educated workers in each country have more to gain in the

process. In the recent past, a special focus has been given to economic integration

25

within Europe, especially to the offshoring waves between Western and Central and

Eastern Europe occurred in the 2000s. In this paper it is argued that systematic

differences between offshoring and non-offshoring firms can be a cause of rising

inequality in both the areas. Crucially, the empirical literature has discovered that

the offshoring firms operate relatively skill-intensive technologies, but also that they

are not induced to upgrade skill.

To match these empirical facts of the offshoring waves and illustrate the

point, we have seen how, at given wages, sectoral relative employment of skilled

versus unskilled workers can shift up in both an advanced country and an emerging

country when vertical offshoring takes place between them. At first sight, relative

employment should decrease as offshoring firms use skill-intensive production also in

respect to advanced country firms. However, it is argued here that the expansion of

headquarters, R&D, legal and marketing services taking place within the new

offshoring firms can offset this factor and lead to an increase of the demand of skills.

This expansion reflects an increase in fixed costs due to offshoring.

The mechanism complements the Feenstra-Hanson’s view that the relocated

input productions are skill-intensive both for the advanced and the emerging

country. In this work skill intensity does not vary across tasks performed within the

industry but only across firms producing differentiated goods within the industry.

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APPENDIX.

Proof of Lemma 1.

Offshoring the low technology is the best strategy for some firms if for a range

of values of it attains the highest profits. Therefore, it is sufficient to show under

which parameter restrictions this strategy attains lower profits with respect to the

best equilibrium strategy for any value of , as depicted in Figure 1. The comparison

with using technology is only meaningful if

(

) (

)

28

In this case we need that where ( )

( ) also ( )

( ).

( )

( )

( )

(

) (

)

( )

( )

( )

(

)( )

Therefore, ( )

( ) ( )

( ) if and only if

(

)

( )

The comparison with offshoring technology is only meaningful if

(

) (

)

In this case we need that where ( )

( ) also ( )

( )

( )

( )

( )

(

)( )

(

)

( )

( )

( )

(

) (

)

Therefore, ( )

( ) ( )

( ) if and only if

( )

(

)

( )

Solution for expected profits .

Starting from eq (x), expected profits can be rewritten as

∫ ( )

( )

( )

∫

( )

( )

( )

∫

( )

( )

(

) [ (

) [ (

)

] [ (

)

( )]]

where are average revenues over the surviving firms and are their

average fixed costs. The expressions for is obtained exploiting the fact that

(

).

29

Then, in order to simplify average revenues , we can exploit the zero profit

condition in (t) and rearrange terms to obtain:

(

) [(

)

(

) [ (

)

] (

)

[ (

)

( )] (

)

]

where (∫ ( )

( )

)

( )

for .

Next, we can plug expressions for average revenues and fixed cost in the

average profit function:

(

) [[(

)

] (

) [ (

)

] [(

)

]

[ (

)

( )] [(

)

]]

From this equation we can obtain (u) using the fact that under a Pareto

distribution with shape parameter k, (

)

.

Proof of Proposition 1.

a) Using the productivities distribution ( ) , we can express

(

)

(

)

. Next, using equation (5) and (6) and deriving

with respect to

(

)

[

(

) ]

The sign of the derivative is given by

(

):

(

)

( (

))

( (

)

( ))

(

)

b) Similarly, we know that (

)

. The derivative is of course zero

using (5) does not depend on .

c) Again, we can define (

)

, and using (6) we see

30

(

)

[

(

) ] (

)

(

( )( ))

d) Deriving expected profits on we obtain

(

)

(

)

(

)

e) Deriving the exit cutoff (9) on we obtain

(

)

[ (

) [ (

)

]

[ (

)

( )]]

(

[ (

)

]

(

)

(

)

)

The first and the second terms under brackets are positive. Therefore the sign

is given by the sum in the third brackets. Using the expression for

found at point

c), we can simplify the third term into

(

)

( ) (

)

( )( )

Which is always negative for .

f) Exploiting the fact that

and using the expressions for

in

and

above (equations (9) and (6)), we get to

(

)

[(

)

(

)

[ (

)

] [ (

)

( )]]

31

(

)

(

) [(

)

(

)

[ (

)

]

[ (

)

( )]]

(

(

)

(

)

[ (

)

] (

)

)

The sign is given by the third bracket. It is easy to see that

and

, so that all terms are positive.

g) The adoption technology cutoff follows the exit cutoff.

Demand of unskilled workers in the advanced country

Starting from equations (15) (17) (19) and using the equilibrium quantities, we

obtain that the firm-level demands of unskilled are

( ) ( ) ( ( ) (

)

)(

)

( ) ( ) (

( ) (

)

)(

)

( ) ( )

Using these definitions we can find that

∫ ( ) ( ( ) (

)

) (

) ( )

( )

∫ ( ) (

)

( ) (

)

∫ ( ) ( ( ) (

)

) (

) ( )

( )

We reach equation (a1) rearranging terms as in the Solution for expected

profits.

Proof of Proposition 2.

32

Taking the derivative of

(see eq (23)) with respect to we obtain

(

)

(

)

[

(

)

]

( (

)

) ( )

( (

)

)

The derivative is negative as long as condition 1 in Proposition 2 is satisfied.

The derivative is positive as long as condition 2 in Proposition 2 is satisfied.

Demand of unskilled workers in the emerging country

The firm-level demands of unskilled labor are (following equations (15) (17)

(21))

( ) ( ) ( ( ) (

)

)(

)

( ) ( ) (

( ) (

)

) (

)

( ) ( )

( ) (

)

(

)

Using these definitions we can find that

∫ ( ) ( ( ) (

)

)(

) ( ) (

)

( )

( ) (

)

(

)

( )

( )

∫ ( ) ( ( ) (

)

) (

) ( ) (

)

Proof of Proposition 3.

The derivative of equation (b1) with respect to takes the sign of

( ) (

)

( ) (

)

(

)

( )

( (

)

)

(

(

)

)