offshoring, unemployment, and wages: the role of labor market institutions

Journal of International Economics 89 (2013) 172–186

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Journal of International Economics

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Offshoring, unemployment, and wages: The role of labor market institutions☆

Priya RanjanUniversity of California, Irvine, United States

☆ I would like to thank Joshua Aizenmann, Gabrielseminar and conference participants at ISI, Delhi, UC-IrvMcKenna College, and especially two anonymous refereextremely helpful and constructive comments.

E-mail address: [email protected].

0022-1996/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.jinteco.2012.06.003

a b s t r a c t
a r t i c l e i n f o
Article history:Received 3 November 2010Received in revised form 20 June 2012Accepted 25 June 2012Available online 6 July 2012

JEL classification:F16J64J50

Keywords:OffshoringUnemploymentCollective bargainingUnionsUnemployment benefitsRecruitment cost

It is shown that whenwages are determined through collective bargaining, there is a non-monotonic relation-ship between the cost of offshoring and unemployment. Starting from a high cost of offshoring, a decrease inthe cost of offshoring reduces unemployment first and then increases it. The non-monotonicity of unemploy-ment in the cost of offshoring does not obtain if wages are determined by individual Nash bargaining insteadof collective bargaining. The non-monotonic relationship between the cost of offshoring and unemployment isverified through a calibration exercise performed using parameters for Sweden. The calibration exercise pre-dicts that a decrease in the cost of offshoring, starting from the present level, would reduce unemployment inSweden. In a two country framework of offshoring (source country and host country) it is shown how changesin the labor market institutions in one country affect labor market outcomes in both countries.

© 2012 Elsevier B.V. All rights reserved.

1 Percentage of workers covered by collective bargaining: Austria:99, Belgium:96,Finland:90, Norway:72, Sweden:92, U.S:13, Japan:16, Canada:32. Source: Venn (2009).

2 Our concept of offshoring includes the procurement of inputs both from a foreign af-

1. Introduction

There has been a resurgence of interest in analyzing the impact ofglobalization on unemployment. Most papers use models of searchunemploymentwherewages are set through individual Nash bargainingbetween the worker and the employer, and therefore, do not take intoaccount the role of collective bargaining in the wage setting process.This is a serious omission because for many European countries collec-tive bargaining plays an important role in the wage setting process.When thinking about the importance of collective bargaining in an econ-omy, people usually think about union density whichmeasures the frac-tion of workforce that is unionized. Union density varied among OECDcountries from a low of 8% in France to a high of 71% in Sweden in2007 (OECD, 2010). However, union density grossly understates the per-centage of workers covered by collective bargaining. This is particularlyso in some countries like Francewhere despite a very low union density,approximately 95% of workers are covered by collective bargaining(Venn, 2009). In general, in many European countries like Austria,Belgium, Finland, Norway, and Sweden a veryhigh percentage ofworkersare covered by collective bargaining, much in excess of union density.However, in countries like the U.S., Canada, and Japan only a small

Felbermayr, Devashish Mitra,ine, UC-Santa Cruz, Claremontes and editor Robert Staiger for

rights reserved.

percentage of employees are covered by collective bargaining.1 This mo-tivates us to study the implications of different wage setting institutionsfor unemployment in a globalized world.

The facet of globalization that we study in this paper is offshoringwhere by offshoringwemean the sourcing of inputs (goods and services)from foreign countries which enables the fragmentation of productionprocess.2 One of the main motivations for fragmenting the productionprocess is the ability to procure these inputs at a lower cost from abroadthan at home.3 When production of these inputs moves to foreign coun-tries, the fear at home is that jobs will be lost, unemployment will rise,andwages will fall, making it a salient public policy issue. It is also fearedthat firms can use the threat of offshoring to force workers to acceptlower wages. Therefore, gaining an upper hand in wage bargainingwith domestic workers could be an additional motivation for offshoring.

This paper constructs a Pissarides style search model of unemploy-ment to study the impact of offshoring on unemployment and wages.While wages are set through individual Nash bargaining in the standard

filiate and a non-affiliate. Sometimes the term foreign outsourcing is used for the latterand the two together are also referred to as “externalization abroad” (see OECD, 2007).

3 Offshoring is quantitatively important as well. According to OECD (2007), the index ofoutsourcing abroad of goods and services (value of goods and services offshored as a shareof domestic demand) in year 2000 was 81% in Belgium, 69% in Netherlands, 61% in bothDenmark and Sweden, and 43% in Finland. UNCTAD in 2004 found that 39 percent of thetop 500 European firms had engaged in offshoring of services (UNCTAD, 2004, 153).

http://dx.doi.org/10.1016/j.jinteco.2012.06.003

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http://dx.doi.org/10.1016/j.jinteco.2012.06.003

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4 In Davis (1998) Europe has a binding minimum wage while the U.S. has no mini-mum wage, while in Moore and Ranjan (2005) Europe has greater unemploymentbenefit than the U.S.

5 Also see Helpman et al. (2010) where trade increases wage inequality but the im-pact on unemployment is ambiguous.

173P. Ranjan / Journal of International Economics 89 (2013) 172–186

Pissarides framework,we postulate an institutional settingwherewagesare set through collective bargaining, and contrast the resultswith thoseobtained using individual bargaining.We also extend themodel to a twocountry setting where the price of the offshored input is determinedendogenously and analyze the implications of offshoring and changesin the labor market institutions on labor market outcomes in both thesource and the host country.

Collective bargaining is modeled using a monopoly union typemodel where unions set wages in the first stage and then firms chooseemployment in the second stage. Looking at the small country casefirst, it is shown that the unemployment of domestic workers could beless in an offshoring equilibrium compared to autarky. The reason isthat the mere possibility of offshoring changes the behavior of unions.Seeing the possibility of jobs moving abroad, unions reduce their wagedemand in the first stage, which induces firms to hire more domesticworkers. More generally, there is a non-monotonic relationship betweenthe cost of offshoring and unemployment. Starting from a cost ofoffshoring close to the autarky cost of obtaining the input domestically,a decrease in the cost of offshoring decreases unemployment first, andwhen the cost of offshoring becomes small unemployment starts rising.In all cases, however,whether comparing the autarky equilibrium to theoffshoring equilibrium or comparative statics with respect to the cost ofoffshoring, more offshoring is always associated with lower wages. Theresult on decreased wages due to a decrease in the cost of offshoring isconsistent with the anecdotal evidence that one of the key motivationsfor offshoring is to reduce the bargaining power of workers/unions.

The result that a mere threat of offshoring can lead to a reduction inwages has important implications for empirical research. The traditionalapproach is to see if greater offshoring in an industry is associated withlower wages. However, our results suggest that what is important isthe offshorability – how easy or hard it is to offshore – of an industryrather than the actual amount of offshoring. Ignoring the threat ofoffshoring as captured in the offshorability of an industry and simply fo-cusing on the actual amount of offshoring, as is done in several empiricalstudies discussed in the survey by Harrison et al. (2011), can lead to anunderestimate of the true impact of offshoring on labor market out-comes. Consistentwith our view, Blinder (2009) finds that, after control-ling for education, most highly offshorable occupations were payingmuch lower wages in 2004. Similarly, Ebenstein et al. (2009) find thatoffshoring had a larger impact on the wages of workers engaged in rou-tine tasks — tasks which are easily offshorable.

In addition to providing analytical results, we also undertake a cali-bration exercise using parameters for a country with pervasive collec-tive agreements, Sweden, and show that the relationship between thecost of offshoring andunemployment is non-monotonic. The calibrationexercise predicts that a decrease in the cost of offshoring, starting fromthe present level, would reduce unemployment in Sweden.

In contrast to the above results, whenwages are set through individ-ual Nash bargaining, we do not obtain the non-monotonicity of unem-ployment in the cost of offshoring. A decrease in the cost of offshoringalways leads to an increase in unemployment. Also, unemployment isalways higher in an offshoring equilibrium compared to autarky.

Next, we extend the model to a two country case where the price ofthe offshored input is determined endogenously. To the best of ourknowledge, this is thefirst attempt to study the implications of offshoringfor unemployment in a two country framework. We introduce a countryForeign (host country for offshoring) that supplies the offshored input toHome (source country for offshoring). Now, the labor market policies ineither country affect the world price of the offshored input and conse-quently the labor market outcomes in both countries. In this setting it isshown that a decrease in the exogenous element of the offshoring costreduces Foreign unemployment but the impact on Home unemploy-ment is similar to that in the small open economy case. That is, thenon-monotonicity of unemployment with respect to the exogenouselement of offshoring cost obtains evenwhen the price of the offshoredinput is determined endogenously.

Looking at the implications of labor market policies, it is shown thatincreases in recruitment costs or unemployment benefits in Foreignlead to an increase in the price of the offshored input. Consequently, theimpact on Home is similar to that of an increase in the offshoring costdiscussed for the small open economy case earlier. That is, Home wagesincrease but the impact on Home unemployment is ambiguous. As faras the Foreign labor market is concerned, in the case of unemploymentbenefits Foreign wages increase unambiguously, but the impact onForeign unemployment is ambiguous. The direct effect of increases in un-employment benefits is to increase unemployment in Foreign but thefeedback effect working through an induced increase in the price of theoffshored input decreases unemployment. Increases in recruitment costsin Foreign have ambiguous effects on Foreign wages and unemployment.

Finally, increases in the recruitment costs or unemployment benefitsin Home increase offshoring by Home. The consequent increase in theprice of the offshored input increases wages and reduces unemploy-ment in Foreign. Homewages increase but the impact on Home unem-ployment is theoretically ambiguous.

To sum up, a key prediction of our model is that the impact ofoffshoring on unemployment in the source country is much more be-nign in the presence of collective bargaining than in the absence of it.An implication is that offshoring is more likely to increase unemploy-ment in the U.S. where wages are mostly negotiated individually com-pared to Europe where wages are mostly set by collective bargaining.This is in contrast to some earlier work on globalization and unemploy-ment (e.g. Davis, 1998; Moore and Ranjan, 2005) where globalization inthe formof tradewith unskilled labor intensive countries is likely to leadto a larger increase in unemployment in Europe with an inflexible labormarket than in the U.S. which has a more flexible labor market.4

1.1. Related literature

While the traditional approach of trade economists has been toworkwith full employment models, in a series of papers Carl Davidson andSteven Matusz studied the implications of introducing unemploymentarising from labor market frictions in trade models. The main focus oftheir work, as discussed in Davidson and Matusz (2004), has been theroles of efficiency in job search, the rate of job destruction and the rateof job turnover in the determination of comparative advantage. Mooreand Ranjan (2005) show how trade liberalization in a skill-abundantcountry can reduce the unemployment of skilled workers and in-crease the unemployment of unskilled workers. Skill-biased techno-logical change on the other hand, can reduce the unemployment ofunskilledworkers. Helpman and Itskhoki (2010) use an imperfectly com-petitive set upwith heterogeneous firms to look at how gains from tradeand comparative advantage depend on labor market rigidities, and howlabor-market policies in a country affect its trading partner. They alsostudy the impact of trade liberalization on unemployment. Trade liberal-ization in their set updoesn't affect sectoral unemployment, however, theaggregate unemployment is affected due to workers moving from onesector to another. Depending on whether the country's comparativeadvantage is in the high unemployment or low unemployment sector,trade liberalization could increase or decrease aggregate unemploy-ment.5 Another related paper, Felbermayr et al. (2011) incorporatessearch unemployment in a one sector model with firm heterogeneityto study the implications of a bilateral reduction in trade cost on unem-ployment. Decreases in trade costs in their setting improve the averageproductivity of firms which in turn reduces the effective cost of post-ing vacancies leading to higher wages and lower unemployment. Thepresent paper differs from these studies in two respects. One, the facet

174 P. Ranjan / Journal of International Economics 89 (2013) 172–186

of globalization studied in these papers is a reduction in the trading costof final goods while we focus on offshoring. Second, none of these pa-pers allows wages to be determined by collective bargaining.6

Mitra and Ranjan (2010) study the impact of offshoring in a twosector model where some jobs in one of the two sectors can beoffshored while all the jobs in the other sector must remain onshore.7

In this setting they show that offshoring could lead to a decrease in un-employment in both sectors if there is sufficient intersectoral mobilityof labor. The key to the unemployment reducing effect of offshoring inthat paper is the positive productivity effect of offshoring due to a com-plementarity between the offshored input and the domestically procuredinput. In contrast, in the present paper, offshored input and domesticlabor are perfect substitutes. Therefore, in the absence of collectivebargaining offshoring is going to increase unemployment. To isolate thenew insight arising from collective bargaining,we have removed the pos-sible productivity effect of offshoring from the model. Bringing in anypositive productivity effect of offshoring simply strengthens its unem-ployment reducing effect. Using a constant elasticity of substitution pro-duction function we verify that our results described above go throughwhen the elasticity of substitution is high. However, for lower elasticityof substitution (complementarity between offshored input and domesticlabor) increased offshoring is associated with reduced unemploymentirrespective of the wage setting mechanism, that is for both collectivebargaining and individual bargaining.

Among the studies on the spillover effects of labor market institu-tions in a country on its trading partners, Felbermayr et al.(2009) con-struct a North–North type model with a single composite good wherecountries export varieties of differentiated intermediate goods to eachother. In that setting, decreases in unemployment benefits in one coun-try reduce unemployment everywhere. In our North–South type modelin contrast, the impact depends on two things: thewage setting institu-tions; and whether the changes in labor market policies originate inHome (the source country for offshoring) or Foreign (the host countryfor offshoring).

Even though Helpman and Itskhoki (2010) is mainly a North–Northmodel focusing on trade between symmetric countries, the paper doesanalyze the impact of changes in labormarket policies in an asymmetriccountry setting where the asymmetry arises due to differences in un-employment benefits in the two countries. In this setting, increases inunemployment benefits in the differentiated goods sector in a countryhave a non-monotonic effect on own unemployment but raise unem-ployment in the trading partner. The mechanism through which theseresults obtain are completely different from our paper. In the countrywhere unemployment benefits increase, the direct effect is to raise un-employment in the differentiated goods sector which happens to be thehigh unemployment sector. However, the loss of competitive edge in thedifferentiated goods sector also means that this sector shrinks and henceworkers move out of this sector. The result is that the first effect domi-nates initially but is outweighed by the second effect for further increasesin unemployment benefits. Since the trading partner gets an edge in thedifferentiated sector, the expansion of the differentiated sector theremeans an increase in aggregate unemployment. In our framework, thetransmission of labormarket policies in one country to its trading partnerworks through changes in the world price of the offshored input.

It is worth mentioning that while the theoretical literature on therelationship between offshoring and unemployment is nascent, thereis now a vast literature on other aspects of offshoring.8 Following

6 In the working paper version, Felbermayr et al. (2008) also look at a case wherewages and employment are chosen through efficient bargaining between the unionand the firm, however, their results for this case are qualitatively similar to thoseobtained using individual bargaining.

7 Davidson et al. (2008) also study the implications of offshoring in a job searchmodel. However, their focus is on the offshoring of high-tech jobs on low and high-skilled workers’ wages, and on overall welfare.

8 See Helpman (2006) for a review of this literature and Grossman and Rossi-Hansberg (2008) for a recent contribution.

the tradition in standard trade theory, these studies assume fullemployment.

While there is not much theoretical work on the impact of globaliza-tion on labor markets characterized by collective bargaining, there is asizeable empirical literature on the subject, but it mainly focuses on theunion wage premium and not on the employment effects of offshoring.Dumont et al. (2006) estimate the impact of globalization on thebargaining power of workers using data from 5 European countriesand find that globalization reduces the bargaining power of workers.Using data from Belgium, Brock and Dobbelaere (2006) do not find ev-idence of trade or inward FDI having an impact on the bargaining powerof workers. They find some evidence of technological change having apositive effect on the bargaining power of workers. Finally, using datafrom Germany, Braun and Scheffel (2007) find that greater internationaloutsourcing reduces the union wage premium of low skilled workers.

The rest of the paper proceeds as follows. In Section 2weprovide thebasic ingredients of the model. Sections 3 and 4 solve for the autarkyand offshoring equilibriums, respectively, for the small open economycasewith collective bargaining. Section 5 discusses the small open econ-omy case with individual bargaining. Section 6 provides the calibrationexercise. The two country model is developed in Sections 7 and8 concludes.

2. The model

We are first going to describe the autarky equilibrium in a countrycalled “Home”. Then we look at the impact of offshoring in Home underthe assumption that Home is a small country, that is, it takes the priceof the offshored input as given. Then we look at a two country worldwhere a country “Foreign” is the source for offshored inputs. In this casethe price of the offshored input is determined endogenously. In the nota-tion below the subscript h under a variable is going to denote its value forHome and the subscript f is going to denote its value for Foreign.

2.1. The goods market

There is a single final good Zwhich can be produced using 3 differenttechnologies. In Home there is a traditional technology that allows oneunit of labor to produce bh amount of the final good. In Foreign the tra-ditional technology allows one unit of labor to produce bf amount of thefinal good. In addition, Home can produce this good using a more so-phisticated technology, which requires some entrepreneurial input,which is in fixed supply, and hence this technology exhibits diminishingreturns to scale. The more sophisticated technology requires producingthefinal good using an intermediate inputwhich can be produced usingeither domestic labor or foreign labor. The production function usingthe sophisticated technology is given by

Z ¼ AXγ;0 b γ b 1 ð1Þ

where X is the amount of the intermediate input used. γ captures thediminishing returns and is useful in making the firm size determinatefor the purposes of union wage setting. We further assume that oneunit of Home labor can produce one unit of the intermediate input. For-eign does not have access to the sophisticated technology, however, itcan produce the intermediate input that goes into the production ofthe final good using sophisticated technology.9

2.2. The labor market

The labor markets in both countries are characterized by a standardPissarides (2000) type search friction. To produce the intermediate

9 This is similar in spirit to the modeling of the South in the Antras and Helpman(2004) model of offshoring where the South cannot produce the varieties of final goodbut can produce the inputs that go into it.


input X, a firm needs to open job vacancies and hire workers. The cost ofvacancy is ci, i=h,f, in terms of the final good. Denote the total size ofwork force by �Li, rate of vacancy by vi, and the rate of unemploymentby ui. Define θi ¼ vi

uias the measure of market tightness where vi�Li is

the total number of vacancies and ui �Li is the number of unemployedworkers searching for jobs. Define mi(vi,ui) as a constant returns toscale matching function given below.

mi vi;uið Þ ¼ μ ivδii u

1−δii ð2Þ

Define qi θið Þ ¼ mi vi ;uið Þvi

, where qi(θi)�t is the probability of a vacancybeing filled during a small interval of time �t. Since mi(vi,ui) is con-

stant returns to scale, q′i(θi)=(δi−1)μiθiδi−2b0. Note that mi vi ;uið Þui

¼θiqi θið Þ where θiqi(θi)�t is the probability of an unemployed workerfinding a job during a small interval of time �t. It follows that 1

qi θið Þ is

the average duration of a vacancy and 1θiqi θið Þ is the average spell of un-

employment. Also, any job can be hit with an idiosyncratic shock withprobability λi and be destroyed.

In steady-state the flow into unemployment must equal the flowout of unemployment:

λi 1−uið Þ ¼ μ iθδii ui ð3Þ

The above implies

ui ¼λi

λi þ μ iθδii

ð4Þ

The above is the standard Beveridge curve in Pissarides type searchmodels where the rate of unemployment is positively related to theprobability of job destruction, λi, and negatively related to the degreeof market tightness θi.

Having introduced the common elements of the labor market, weswitch to a discussion of autarky equilibrium in Home followed by adiscussion of the offshoring equilibriumwhen Home is a small country.We will return to the two country case later.

3. Autarky equilibrium in Home

To save notation assume that there is a unit mass of identical firmsin the economy. Therefore, we do not have to use separate notationsfor the firm specific variables and the economy specific variables. Aswell, there is a unit mass of identical unions each with �Lh membersand a representative union deals with a representative firm. The in-teraction between the representative union and the representativefirm is modeled using a two stage game where the union proposes awage in the first stage and the firm chooses employment in the secondstage. The timing of moves is same as in the standard monopoly unionapproach towardswage setting, however, unlike the standardmonopo-ly union model where the union is very large, the representative unionin our setting is small in the sense that it takes the economywidemarkettightness as given while proposing a wage. This framework is analyti-cally tractable and allows us to obtain several analytical results ratherthan having to rely solely on numerical simulations.10 As argued by

10 Qualitatively similar results obtain using the “right to manage” approach wherewages are set in the first stage through bargaining between unions and firms and em-ployment is determined by firms in the second stage. In this setting, wages depend onthe bargaining power of unions relative to the bargaining power of firms, and whenunions have all the bargaining power in wage setting, the model converges to that ofmonopoly union. The results using the right to manage approach, based on numericalsimulations, were presented in an earlier version of the paper and are available uponrequest. The possibility of offshoring reducing unemployment exists even in the effi-cient bargaining approach where firms and unions simultaneously choose the efficientlevels of employment and wages.

Pissarides (1986), in the context of a search model where firms haveto search for workers and any job can be destroyed due to an idiosyn-cratic shock, letting firms choose the level of employment seems to bea more realistic approach. This is also the approach taken by Delacroix(2006)who studies the implications of unionwage setting and its inter-actions with policies in a multisector matching model.

We solve the model backwards where we first solve the represen-tative firm's problem in the second stage for a given wage, and thenwe solve for the wage in the first stage.

3.1. Firm's problem

Denote the number of vacancies posted by a firm by Vh and thenumber of workers employed at a firm by Lh. Assuming that eachfirm is large enough to employ and hire enough workers to resolvethe uncertainty of job inflows and outflows, the dynamics of employ-ment for a firm is

Lh� tð Þ ¼ μhθh tð Þδh−1Vh tð Þ−λhLh tð Þ ð5Þ

Note that since one unit of Home labor produces one unit of theintermediate good, in autarkyX=Lh and hence Z=AXγ=ALh

y. Denotingthe wage by wh and the rate of discount by ρ, the profit maximizationproblem for the representative firm can be written as

MaxVh sð Þ; Lh sð Þ

∫∞t e

−ρ s−tð Þ A Lh sð Þð Þγ−wh sð ÞLh sð Þ−chVh sð Þ� �ds ð6Þ

The firmmaximizes Eq. (6) subject to Eq. (5), takingwh(s) and θh(s)as given. Denoting the Lagrangian multiplier associated with Eq. (5) byψ and dropping the time notation s to reduce clutter, the current valueHamiltonian for the firm can be written as

H ¼ ALγh−whLh−chVh þ ψ μhθδh−1h Vh−λhLh

h i

The first order conditions for the above maximization are follows.

Vh : ch ¼ ψμhθδh−1h ð7Þ

Lh : wh þ ψλh ¼ γALγ−1h þ _ψ−ρψ ð8Þ

In steady-state _ψ=0, therefore, Eqs. (7) and (8) imply

γALγ−1h ¼ wh þ

ρþ λð Þchμhθ

δh−1h

ð9Þ

The above equation determines employment Lh as a function of wh

and θh. Note that a higher wh demanded by the union results in a loweremployment, Lh.

3.2. Wage determination by unions

Asmentioned earlier,wages are proposed by unions in thefirst stage.Following a common practice in the literature, we assume that unionsmaximize the surplus (or the rent) of their members. While employedworkers get a wage of wh, unemployed workers get bh. Recall from theearlier discussion that workers have access to a traditional technologythat allows them to produce bh amount of final good. Implicitly we areassuming that unemployed workers are able to engage in productionusing this technology. Alternatively, bh can be viewed as the sum of un-employment benefits and themonetary equivalent of the value of leisureof unemployed workers. Later we will use changes in bh to capture thechanges in unemployment benefits.


Denote the asset value of an employed worker by Eh and the assetvalue of an unemployed worker by Uh. These asset values are given inflow terms as follows.

ρEh ¼ wh þ λh Uh−Ehð Þ ð10Þ

ρUh ¼ bh þ μhθδhh Eh−Uhð Þ ð11Þ

The above two imply that

ρEh ¼ρþ μhθ

δhh

� �wh þ λhbh

ρþ λh þ μhθδhh

ð12Þ

ρUh ¼ μhθδhh wh þ ρþ λhð Þbhρþ λh þ μhθ

δhh

ð13Þ

If the total number of union members is �Lh and Lh of them becomeemployed, then the expected welfare of a union member is given by

�Lh−Lh�Lh

� �ρUh þ

Lh�Lh

� �ρEh ð14Þ

If the firm rejects the union's wage offer then all members gettheir unemployment income ρUh. Therefore, the union's objective isto maximize the aggregate surplus or rent of its members given by

�Lh−Lh�Lh

� �ρUh þ

Lh�Lh

� �ρEh−ρUh

� ��Lh ¼ ρ Eh−Uhð ÞLh

¼ ρ wh−bhð ÞLhρþ λh þ μhθ

δhh

ð15Þ

where the last equality follows from Eqs. (12) and (13).11

The subgame perfect equilibrium where the union proposes awage first and then the firm decides on employment can be obtainedby maximizing Eq. (15) subject to Eq. (9). It is shown in Appendix Athat the solution to the above problem yields the following expres-sion for wage.

wh ¼ bh þ γ 1−γð ÞALγ−1h ð16Þ

Next, if the total amount of labor available in Home is �Lh, then itmust be the case that in equilibrium �Lh(1-uh)=Lh. Using the expres-sion for uh in Eq. (4) we get

�Lhμhθ

δhh

λh þ μhθδhh

!¼ Lh ð17Þ

Therefore, the key endogenous variables in an autarky equilibri-um, θh,wh, and Lh are determined by Eqs. (9), (16), and (17). Theexistence and uniqueness of autarky equilibrium is established inAppendix A.

4. Offshoring equilibrium for a small country

Nowassume that the intermediate input canbe imported fromabroadat a price of pf. There are costs associatedwithmaking the imported inputwork in the domestic production process.We can think of it as the cost ofadapting the foreign produced input to the domestic production process.We assume that to use M units of the foreign produced input in thedomestic production process, an amount ϕh(M)M must be imported,where ϕh(M)>1 and h′(M)>0. Therefore, the effective per unit cost ofthe imported input is pfϕh(M). The restriction h′(M)>0 captures in a

11 Effectively the union is maximizing the surplus (or rent) of employed members(as in Felbermayr et al.(2008)) since unemployed members don't earn a rent.

reduced form sense the fact that some inputs may be harder/costlier tooffshore than others as in Grossman and Rossi-Hansberg (2008). In oursetting it ensures that the firm faces an upward sloping supply curve forthe imported input, and yields an interior solution even though domesticand foreign produced inputs are perfect substitutes in efficiency units. Theparameter ϕ captures the general cost of offshoring arising from costsrelated to communications barriers, legal restrictions, cultural differences,trade barriers etc. and will be useful in comparative statics below. Inensuing discussions we will call ϕ the “offshoring cost” and h(M) the“adaptation cost”. In the small country case pf is exogenous, but in the twocountry case discussed later pf is going to be endogenously determined.

We solve the offshoring equilibrium as follows. The representativefirm takes wh, θh, and pf as given and chooses its employment and theextent of offshoring optimally in the second stage. As in autarky, therepresentative union chooses a wage in the first stage.

For givenwh(s), θh(s), and pf, the firmmaximizes the following ob-jective function in the second stage.

MaxVh sð Þ;Lh sð Þ;M sð Þ

∫∞t e

−ρ s−tð Þ A Lh sð Þ þM sð Þð Þγ−wh sð ÞLh sð Þ−pfϕh Mð ÞM sð Þ−chVh sð Þn o

ds

subject to the labor adjustment Eq. (5). Dropping the time notation s,the current value Hamiltonian in this case is given by

H ¼ A Lh þMð Þγ−whLh−pfϕh Mð ÞM−chVh þ ψ μhθδh−1h Vh−λhLh

h i

The first order conditions are

M : γA Lh þMð Þγ−1 ¼ pfϕ h Mð Þ þ h′ Mð ÞM� �

ð18Þ

Vh : ch ¼ ψμhθδh−1h ð19Þ

Lh : wh þ ψλh ¼ γA Lh þMð Þγ−1 þ _ψ−ρψ ð20Þ

Again, in steady-state _ψ=0, and therefore, Eqs. (19) and (20) imply

γA Lh þMð Þγ−1 ¼ wh þρþ λhð Þchμhθ

δh−1h

ð21Þ

Next, Eqs. (18) and (21) imply

Lh ¼ 0 and M > 0 ifγA Mð Þγ−1 ¼ pfϕ h Mð Þ þMh′ Mð Þ� �

bwh

þ ρþ λhð Þchμhθ

δh−1h

ð22Þ

M ¼ 0 and Lh > 0 ifγA Lhð Þγ−1 ¼ wh þρþ λhð Þchμhθ

δh−1h

b pfϕh 0ð Þ ð23Þ

We assume that parameters are such that we always get an interiorsolution. In that case, Eqs. (18) and (21) determine Lh and M for givenvalues of wh, θh, and pf.

4.1. Determination of wage in offshoring equilibrium

The offshoring equilibrium wage is obtained by maximizing theunion's objective function, Eq. (15), subject to Eq. (18) and Eq. (21).It is shown in Appendix A that the equilibrium wage is given by

wh ¼ bh þLh 1−γð ÞγA Lh þMð Þγ−2pfϕ 2h′ Mð Þ þMh′

′Mð Þ

� �� 1−γð ÞγA Lh þMð Þγ−2 þ pfϕ 2h′ Mð Þ þMh′′ Mð Þ

� � ð24Þ

The 4 Eqs. (18), (21), (24) along with Eq. (17) determine the 4 en-dogenous variables – wh, θh, Lh and M – in an offshoring equilibrium.


Comparing autarky with the offshoring equilibrium, we derive the fol-lowing analytical result (proved in the online Appendix B).12

Proposition 1. Offshoring costs that lead equilibrium offshoring to beapproximately zero nonetheless reduce both wages and unemploymentin the offshoring equilibrium relative to autarky.

As mentioned in the Introduction, the mere possibility of offshoringleads to a reduction in the wages demanded by unions which increasesthe hiring of domesticworkers byfirms. An implication is that the actualamount of offshoring may hide the true impact of offshoring on labormarket outcomes.

4.2. Comparative statics with respect to cost of offshoring

A change inϕ in ourmodel captures the exogenous change in the costof offshoring. For a linear adaptation cost, h(M)=d+gM, we prove thefollowing result in the online Appendix B.13

Proposition 2. In an offshoring equilibrium the wage is monotonicallyincreasing and the extent of offshoring is monotonically decreasing inthe cost of offshoring, ϕ. The rate of unemployment is non-monotonicin ϕ. Starting in the vicinity of autarky equilibrium (M≈0), a decreasein ϕ leads to a decrease in unemployment first but beyond a point unem-ployment starts increasing as ϕ decreases further.

The intuition behind the non-monotonicity of unemployment withrespect to the offshoring cost can be understood as follows. Upon a de-crease in the offshoring cost, unions foresee jobs moving abroad, andtherefore, moderate their wage demands. This moderation of wage de-mand leads tomore hiring of domestic workers as long as the offshoringcost is relatively high. That is, firms can do more of both: offshoring andhiring of domestic workers. However, beyond a point the offshoring costbecomes so low that it makes sense to substitute offshored input for do-mestic workers, leading to an increase in domestic unemployment.

Even though the result above is proved analytically for the linearadaptation cost case, numerical calibrations discussed below usingconvex and concave functions provide similar results.

4.3. Comparative statics with respect to labor market policies

As mentioned earlier, a change in bh is used to capture the impactof changes in unemployment benefits. A change ch captures the changein recruitment cost. The following results are proved in the onlineAppendix B.

Proposition 3. Increases in unemployment benefits or recruitment costsincrease offshoring, wages, and unemployment.

Intuitively, a higher bh increases the reservation wages of unionswhich results in higher wage demands and consequently, firms findit profitable to hire less domestic workers and increase offshoring. In-creases in the recruitment costs induce firms to post less vacancies andhire less domestic workers which increases unemployment in additionto increasing offshoring. Higher recruitment costs also result in higherwages. Intuitively, higher recruitment costs lower the sensitivity of hir-ing to wages, and therefore, unions are more willing to trade-off higherwages for lower employment.

The results described in the proposition above are also useful in de-riving the implications of changes in labor market institutions in Homein the 2 country extension discussed below.

12 Theproofs of all thepropositions are gathered in anonlineAppendixB available at http://dx.doi.org/10.1016/j.jinteco.2012.06.003.13 The analytical proof of non-monotonicity of unemployment is given for d=0 case.

Next, we contrast the impact of offshoring when wages are deter-mined through collective bargaining with the case when wages aredetermined through individual bargaining.

5. Offshoring with individual wage bargaining

Assume that instead of wages being determined by unions, firmsenter into individual bargaining with matched workers. It is assumedthat the domestic employment aswell as the amount of inputs offshoredis chosen in the first stage correctly anticipating the wages that will bedetermined through individual bargaining in the second stage.

The representative firm maximizes

MaxV sð Þ;Lh sð Þ;M sð Þ

∫∞t e

−ρ s−tð Þ A Lh sð Þ þM sð ÞÞγ−wh sð ÞLh sð Þ−pfϕh Mð ÞM sð Þ−chV sð Þ� o

dsn

subject to Eq. (5).In doing the firm maximization, an issue to consider is whether the

wages determined in the second stage are taken as given by the firm orwhether the firm recognizes the impact its employment choice willhave on the wages negotiated later. In particular, a relevant issue iswhether the breakdown of bargaining with a worker leads to a renego-tiation of wages with all workers or not. If it does, then the firm takesthis into account while choosing employment in the first stage. In thiscase there is a feedback effect from the marginal product to the wagesetting, first pointed out by Stole and Zwiebel (1996), which results inoverhiring by the firm because it recognizes that hiring an extra workerwill reduce the marginal product of each worker and therefore, reducethewage the firmwill pay to eachworker. Dropping the time notation s,the first order condition for employment choice in this case can bewrit-ten as

γA Lh þMð Þγ−1−Lh ¼ wh þρþ λhð Þchμhθ

δh−1h

ð25Þ

The term dwhdLh

captures the effect identified by Stole and Zwiebel(1996).

Alternatively, one can think of the wages being bargained by eachworker simultaneously with the firm (say a separate representative ofthe firm) without the possibility of renegotiation. Or, the firm couldsimply bemyopic and ignore the consequences of its first stage employ-ment choice on wage bargaining in the second stage. In this case, thefirst order condition for employment choice is given by

γA Lh þMð Þγ−1 ¼ wh þρþ λhð Þchμhθ

δh−1h

ð26Þ

The first order condition for the optimal choice ofM is same as in theunion wage case and is given by

γA Lh þMð Þγ−1 ¼ pfϕ h Mð Þ þMh′ Mð Þ� �

ð27Þ

Denote the bargaining power of workers in Nash bargaining by βh.It is shown in the online Appendix B that the wage equation when thefirm recognizes the effect of employment choice on wage bargainingis given by

wh ¼ 1−βhð Þbh þ βhchθh þ L− 1

βhh γA∫Lh

0 xþMð Þγ−1x1βh−1dx ð28Þ

To obtain the wage in autarky, simply set M=0.Note from Eq. (28) that

Lhdwh

dLh¼ − 1

βhL− 1

βhh γA∫Lh

0 xþMð Þγ−1x1βh−1dxþ γA Lh þMð Þγ−1 ð29Þ

14 In reality, the adaptation cost would vary across industries and would capture theease/difficulty of offshoring inputs/tasks. A convex adaptation cost would capture anindustry where relatively little can be offshored while a concave adaptation cost wouldcapture the opposite case of an industry where it is easy to offshore most inputs.


Using Eq. (29), the first order condition (25) can be written as

1βh

L− 1

βhh γA∫Lh

0 xþMð Þγ−1x1βh−1dx ¼ wh þ

ρþ λhð Þchμhθ

δh−1h

ð30Þ

Eqs. (17), (27), (28), and (30) determine the 4 key endogenousvariables Lh,M,wh, and θh in an offshoring equilibrium with individualbargaining.

It is difficult to obtain analytical results on the impact of offshoringin the case above, therefore, we will rely on numerical calibrations.However, in the other casementioned earlier which obtainswhen eitherthe firm is myopic or there is no possibility of renegotiation, we can ob-tain analytical results. It is shown in the online Appendix B that thewageequation in this case is given by

wh ¼ 1−βð Þbh þ βhchθh þ βhγA Lh þMð Þγ−1 ð31Þ

In this case, Eqs. (17), (26), (27), and (31) determine Lh,M,wh, andθh in an offshoring equilibrium with individual bargaining.

The following results on the impact of offshoring under the re-striction that the adaptation cost function h(M) is not too concave(2 h′(M)+h″(M)>0) are proved in the online Appendix B.

Proposition 4. When wages are determined through individual Nashbargaining, the wages are always lower and the unemployment is alwayshigher in an offshoring equilibrium compared to the autarky equilibrium.Moreover, the offshoring equilibrium wage is monotonically increasingand unemployment is monotonically decreasing in the cost of offshoring,ϕ.

In terms of intuition, the key difference in the individual bargainingcase comes from the fact that when an individual worker bargains witha firm, all that theworker cares about is his ownwage. A decrease in thecost of offshoring does reduce his wage but the worker is not going toaccept a deeper wage cut to increase domestic employment. In thecase of union wage setting on the other hand, seeing a decrease in thecost of offshoring, unions reduce their wage demands to moderate theimpact of offshoring on employment.

6. Numerical calibrations for the small country case

The country chosen for calibration exercise is Sweden because it isone of the countrieswheremost of theworkers are covered by collectivebargaining agreements. According to Venn (2009), 92% of workers inSweden were covered by collective bargaining agreement. Most of theparameters chosen for our calibration exercise for Sweden are takenfrom Albrecht et al. (2006) who conduct a calibration exercise to assessthe labor market effects of the Swedish knowledge lift program. Sincetheyworkwith two different types of workers, low andmedium skilled,while we have only one type of worker in the model, we construct anaggregate rate of job destruction and exit rate from unemploymentbased on their disaggregated numbers. We provide details of this exer-cise as well as the choice of several parameters and their sources inAppendix A. Below we discuss the choice of some crucial parameters.

We obtain an estimate of the exit rate from unemployment, μhθhδh,of 1.948 based on the numbers in Albrecht et al. (2006). No independentestimates of θh are available so, rather than picking θh arbitrarily, we useθh=0.5 from Hall (2005). The most commonly used estimate of theelasticity of matching function, δh, in the literature including that inAlbrecht et al. (2006) is 0.5, which is what we use as well. These valuesof θh and δh pin down the scale parameter in the matching function, μh,at 2.755. Alternative values of θh provide different values of the scaleparameter but results are qualitatively similar. Ekholm and NilssonHakkala (2008) provide several estimates of the extent of offshoringfor Sweden. We use one of their measures called the share of importedinput in total intermediate consumption (narrow) the value of whichfor all industries in 1995 is 0.072. The word narrow refers to the fact

that the input is importedwithin the industry rather than from other in-dustries and may be a more relevant measure for the kind of offshoringwe have in mind where the imported inputs are close substitutesfor domestically produced inputs. Using their alternative measuresof offshoring in our numerical exercise provides qualitatively similarresults. Note that the amount of intermediate input produced domesti-cally in our model is given simply by Lh. Therefore, the ratio of importedinputs to total intermediate consumption in ourmodel is M

LhþM. Our base-line calibration sets M

LhþM ¼ 0:07:We have three remaining parameters: ch,ϕ, and pf to determine.

Recall that ϕ in our model captures the general cost of offshoring arisingfrom costs related to communications barriers, legal restrictions, culturaldifferences, trade barriers etc. A commonly used value of the transporta-tion cost alone in calibration exercises is 1.3 (e.g. Felbermayr et al, 2011).Since ϕ includes more than just transportation cost, we choose a slightlyhigher initial value of ϕ at 1.5. The remaining two parameters ch and pfare chosen tomatch the unemployment rate of 0.077 for 1995 in Swedenand M

LhþM ¼ :07.We are going to try 3 alternative specifications of the ad-

aptation cost function h(M): linear case : h(M)=1+M; convex case:h(M)=(1+M)2; concave case: h Mð Þ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1þMð Þp.14 Depending on the

specification of h(M), we obtain different values of ch and pf. In our com-parative static exercises, for each specification of the adaptation costfunction,we hold the values of ch and pf constant at their respective base-line values.

Fig. 1 shows the results of comparative statics with respect to theoffshoring cost parameter ϕwhen h(M)=1+M. The horizontal line ineach figure shows the hypothetical autarky value of the variable of in-terest. Fig. 1a shows the non-monotonicity of unemployment with re-spect to ϕ. The horizontal line drawn from the right axis at 0.099shows the hypothetical autarky unemployment for the baseline param-eter values (to show the non-monotonicity of unemployment clearly,we have drawn the horizontal line from right axis in Fig. 1a). That is,Fig. 1a says that if Sweden were a closed economy, then with these pa-rameter values its unemployment rate would be 9.9% instead of it being7.7%. The highest value of ϕ in this figure is at 1.75. At this value of ϕ,Mbecomes zero. That is, even though Sweden is notionally open, theoffshoring cost is so high that offshoring becomes zero. The unemploy-ment at this value of ϕ is 7.85%. The fact that the hypothetical autarkyunemployment of 9.9% is greater than the offshoring equilibriumunem-ployment of 7.85%whenϕ=1.75 and consequently,M=0 is consistentwith the result described in Proposition 1with respect to unemployment.Fig. 1b shows that the wage in Sweden decreases as the offshoring costdecreases. The gap between the horizontal line and the downward slop-ing line atϕ=1.75 is consistentwith the result onwages in Proposition 1.

Fig. 1c and d shows the impact of offshoring on unemployment andwages in the case of individual bargaining. These figures are drawnusing a value of workers' bargaining power, βh, of 0.5. Again, the free pa-rameters ch and pf are chosen to yield μh=0.77 and M

LhþM ¼ 0:07 whenϕ=1.5. The horizontal lines capture the hypothetical autarky values. Inboth Fig. 1a and c, the value of unemployment in an offshoring equilibri-um corresponding to ϕ=1.5 is 0.077 by construction. It is easily seenfrom Fig. 1c and d that a decrease in the offshoring cost leads to an in-crease in unemployment and a decrease in wage. As well, offshoringequilibrium unemployment is always higher and wages are lower thanin the autarky equilibrium which is consistent with Proposition 4.

One way to look at the quantitative significance of collectivebargaining in determining labor market outcomes is to note fromFig. 1a and c that an increase in the offshoring cost from ϕ=1.5 toϕ=1.75 increases unemployment by 0.185 percentage points withcollective bargaining, but the same increase in the offshoring cost

15 All the parameters used to draw Fig. 4c and f are the same as in Figs. 1–3, and 4a,b,d,e, except for one: bh. In the baseline case we used a value of bh that gave a replace-ment rate of 67%. It turns out that for this value of bh, the implied ch when σ=2.5 be-comes negative in the collective bargaining case. Therefore, we used a value of bh suchthat the replacement rate is 50%.

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.70.075

0.076

0.077

0.078

.099

offshoring cost (Φ) offshoring cost (Φ)

offshoring cost (Φ) offshoring cost (Φ)

unem

ploy

men

ta) offshoring and unemployment with collective bargaining

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.70.48

0.50

0.52

0.54

0.56

0.58

0.60

wag

e

b) offshoring and wage with collective bargaining

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.70.070

0.075

0.080

0.085

0.090

unem

ploy

men

t

c) offshoring and unemployment with individual bargaining

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.70.65

0.70

0.75

0.80

wag

e

d) offshoring and wage with individual bargaining

Fig. 1. Unemployment, wage, and offshoring (linear adaptation cost).


reduces unemployment by 0.5 percentage points in the case of individ-ual bargaining, a difference of 0.7 percentage points.

Figs. 2 and 3 repeat the same exercise for convex and concaveh(M) functions, respectively. To highlight the non-monotonicity ofunemployment with respect to offshoring costs, depending on thespecification of h(M), we choose different minimum values of ϕ: 0.5in Fig. 2 and 1 in Fig. 3. As well, in Figs. 2a and 3a, again the right axisis used to depict the hypothetical autarky value of unemployment.The qualitative results in Figs. 2 and 3 are similar to those in Fig. 1. Itis worth pointing out that even though offshoring increases in responseto a decrease in ϕ, the reduction in ϕ is partially offset by an increase inthe adaptation cost due to h′(M)>0. This latter effect is stronger themore convex the adaptation cost, and therefore, a given reduction inϕ leads to a smaller increase in offshoring the more convex the adapta-tion cost. An implication is that the range of ϕ over which unemploy-ment decreases is larger the more convex the adaptation cost.

6.1. Numerical results with CES production function

In the baselinemodel it was assumed that the input produced by do-mestic labor and the offshored input were perfect substitutes once thelatter were adapted. However, our results hold more generally whenthe substitutability between domestic labor and offshored input ishigh.We confirm this numerically using the constant elasticity of substi-tution (CES) production function of the following form.

Z ¼ A Lσ−1σ

h þMσ−1σ

� �σ γσ−1

;σ > 0

where σ is the elasticity of substitution between domestic labor and theoffshored input. To conserve space, the equations for the CES productionfunction case are presented in the online Appendix B. The results of thenumerical calibrations using the CES production function are shown in

Fig. 4 which assumes a linear adaptation cost: h(M)=1+M. Fig. 4ashows the relationship between unemployment and offshoring cost, ϕ,for σ=10, when wages are determined through collective bargaining.We again obtain a non-monotonic relationship between unemploymentandϕ similar to the one obtained for the perfect substitute case in Fig. 1a.We have verified that as σ→∞ the results converge to those in Fig. 1a.One difference between Figs. 1a and 4a is that forϕ≥1.75, offshoring be-comes zero (M=0) in Fig. 1a and therefore, unemployment becomesdelinked from the offshoring cost forϕ≥1.75. In the imperfect substitutecase drawn in Fig. 4a, offshoring goes to zero only in the limit as ϕ→∞and therefore, the offshoring unemployment rate keeps increasing andasymptotes a horizontal line as ϕ→∞. Fig. 4b is drawn for the case ofσ=4 where again a non-monotonic relationship obtains between thecost of offshoring and unemployment. Fig. 4d and e are the analoguesof Fig. 4a and b for the individual bargaining case. As was the case inFigs. 1–3, with individual bargaining, a decrease in the cost of offshoringleads to an increase in unemployment.

Itwasmentioned earlier that if there is a high degree of complemen-tarity between the offshored input and domestic labor (as in the modelof Grossman and Rossi-Hansberg (2008)), then greater offshoring canlead to lower unemployment even with individual bargaining. Inour model the complementarity effect becomes stronger as σ de-clines. Fig. 4c plots the relationship between offshoring and unem-ployment for σ=2.5 for the collective bargaining case.15 Due to thecomplementarity, an increase in offshoring (induced by lower ϕ)leads to a decrease in unemployment. And finally, as mentioned in theintroduction, Fig. 4f shows that greater offshoring is associated with

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.073

0.075

0.077

0.079

0.081

0.083

.095

unem

ploy

men

ta) offshoring and unemployment with collective bargaining

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.48

0.50

0.52

0.54

0.56

0.58

0.60

0.62

offshoring cost (Φ)

offshoring cost (Φ)offshoring cost (Φ)


wag

e


0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.07

0.08

0.09

0.10

0.11

unem

ploy

men

t

c) offshoring and unemployment with individual bargaining

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.65

0.70

0.75

0.80

wag

e

d) offshoring and wage with individual bargaining

Fig. 2. Unemployment, wage, and offshoring (convex adaptation cost).

1.0 1.1 1.2 1.3 1.4 1.5 1.6

0.078

0.08

0.082

0.084.102



unem

ploy

men

t

a) offshoring and unemployment with collective bargaining

1.0 1.1 1.2 1.3 1.4 1.5 1.6

0.40

0.45

0.50

0.55

wag

e


c) offshoring and unemployment with individual bargaining d) offshoring and wage with individual bargaining

1.0 1.1 1.2 1.3 1.4 1.5 1.60.07

0.08

0.09

0.10

0.11

unem

ploy

men

t

1.0 1.1 1.2 1.3 1.4 1.5 1.6

0.65

0.70

0.75

0.80

wag

e

Fig. 3. Unemployment, wage, and offshoring (concave adaptation cost).


1.0 1.5 2.0 2.5 3.0 3.5 4.00.075

0.080

0.085

0.090

unem

ploy

men

tun

empl

oym

ent

unem

ploy

men

tun

empl

oym

ent

unem

ploy

men

tun

empl

oym

ent

a) Collective bargaining (σ=10)

1.0 1.5 2.0 2.5 3.0 3.5 4.00.0770

0.0775

0.0780

0.0785

0.0790

0.0795

0.0800

b) Collective bargaining (σ=4) c) Collective bargaining (σ=2.5)

d) Individual bargaining (σ=10) e) Individual bargaining (σ=4) f) Individual bargaining (σ=2.5)

1.0 1.5 2.0 2.5 3.0 3.5 4.00.0762

0.0764

0.0766

0.0768

0.0770

0.0772

0.0774

0.0776

1.0 1.5 2.0 2.5 3.0 3.5 4.0

0.075

0.080

0.085

0.090

1.0 1.5 2.0 2.5 3.0 3.5 4.00.074

0.075

0.076

0.077

0.078

0.079

0.080

1.0 1.5 2.0 2.5 3.0 3.50.0750

0.0755

0.0760

0.0765

0.0770

0.0775

0.0780

0.0785

offshoring cost (Φ) offshoring cost (Φ)offshoring cost (Φ)

offshoring cost (Φ) offshoring cost (Φ)offshoring cost (Φ)

Fig. 4. Offshoring and unemployment with CES production function.


reduced unemployment even in the case of individual bargaining whenσ=2.5.

Therefore, we claim that the result that we derived on the non-monotonic relationship between offshoring and unemployment in thecollective bargaining case when domestic labor and offshored inputare perfect substitutes holdsmore generally for high elasticity of substi-tution between the two inputs.

7. Offshoring in a two country world

Now,wediscuss the two country casewhere the price of the offshoredinput, pf, is determined endogenously. Assume that one unit of Foreignlabor can produce one unit of the intermediate input. The alternativefor Foreign labor is to produce bf units of thefinal good using a traditionaltechnology. We also assume that the wages in the production of the in-termediate good in Foreign are determined through individual Nashbargaining and not collective bargaining.16 Since Foreign does not havethe sophisticated technology to produce the final good, and there is con-stant returns to scale in the production of the intermediate good, there isno loss of generality in assuming that Foreign has one worker firms.

With one worker firms, if the price of the intermediate input is pf,the value of output produced by one unit of labor is pf. Since firmshave to post vacancies and pay workers a wage of wf, free entry in va-cancy creation implies the following.

pf ¼ wf þρþ λf

� �cf

μ f θδf−1f

ð32Þ

Assume the bargaining power of workers to be βf. Followingthe same steps as in the case of Home, it is shown in Appendix

16 It is possible for the wages in Foreign also to be determined by collective bargaining.However, to avoid discussing too many cases, we restrict the wage determination in For-eign to individual bargaining.

A that the wage determined through Nash bargaining in Foreignis

wf ¼ 1−βf

� �bf þ βf pf þ cf θf

� �ð33Þ

The above two equations determine wf and θf for each pf . It can beverified that Eq. (32), which is commonly referred to as the Job Creation(JC) condition in the search literature, implies a downward sloping rela-tionship betweenwf and θf . Eq. (33), referred to as theWage Bargaining(WB) condition, implies anupward sloping relationship betweenwf andθf. The intersection of these two relationships determineswf and θf for agiven pf as is shown in Fig. 5a. Once we know θf we can find out theamount of labor employed in this sector, which also equals the outputof the intermediate good produced by Foreign, from the equation below.

�Lf 1−uf

� �¼ �Lf

μ f θδff

λf þ μ f θδff

0@

1A ¼ Lf ð34Þ

where uf is the rate of unemployment in Foreign. Therefore, for each pfwe obtain the supply of the intermediate input produced in Foreignfrom the 3 equations, Eqs. (32), (33), and (34) above. An increase in pfshifts both the JC and the WB curves up in Fig. 5a. It can be verifiedfrom Eqs. (32) and (33) that the vertical shift in the JC curve is morethan the vertical shift in the WB curve. Therefore, both wf and θf in-crease. An increase in θf, in turn, implies from Eq. (34) that the supplyof the intermediate input from Foreign increases. Therefore, the supplycurve for the intermediate input produced in Foreign is upward sloping.

The demand for the intermediate input produced in Foreign comesfrom Home. The demand curve can be derived from the 4 equations,Eqs. (17), (18), (21), (24), which give Lh, θh, wh, and M for a given pffor Home. Recall that in the small open economy case we had shownthat dM

dϕ b0. Since ϕ and pf are isomorphic in the small open economy

17 The increase in pf in Home is similar to the terms of trade loss arising from a tariffreduction in a large country.

θf

wfWB

JC

a) Labor Market Equilibrium in Foreign

b) Determination of World Price

pf

Quantity of offshored input

D

S

Fig. 5. a: Labor market equilibrium in foreign. 5b: Determination of World Price.


case, it follows that dMdpf b0. Note that when firms in Home useM amountof the offshored input, the amount actually purchased from Foreign isϕh(M)M given that some of the Foreign produced input is lost in the ad-aptation process. Since h′(M)>0, it is easily verified that

d ϕh Mð ÞMð Þdpf

¼ ϕ h Mð Þ þ h′ Mð ÞM� � dM

dpfb0 ð35Þ

Therefore, the demand curve for the gross amount of offshoredinput, ϕh(M)M, is decreasing in pf. Since the demand is downwardsloping and the supply is upward sloping, there exists a price pf thatclears the market for the intermediate input produced in Foreign asshown in Fig. 5b. Algebraically, the price pf is determined by the fol-lowing market clearing condition for the input produced in Foreign:

Lf ¼ ϕh Mð ÞM ð36Þ

The offshoring equilibrium in a two country world is characterizedby the 8 equations, Eqs. (17), (18), (21), (24), (32), (33), (34) and(36), which solve for the 8 endogenous variables of interest: Lh, M, wh,θh, Lf, wf, pf, and θf.

7.1. Comparative statics

7.1.1. Decrease in the cost of offshoringStarting from an offshoring equilibrium, holding the price of the

offshored input constant, a decrease in the cost of offshoring, ϕ,

increases the amount of offshored input used in Home: ∂M∂ϕ b0. What

happens to the price, pf, depends on what happens to the amount ofinput purchased from Foreign, ϕh(M)M:

∂ ϕh Mð ÞMð Þ∂ϕ ¼ h Mð ÞM þ ϕ h Mð Þ þ h′ Mð ÞM

� �∂M∂ϕ ð37Þ

There are two effects of a decrease in the cost of offshoring. Sinceoffshoring becomes more attractive firms want to offshore more.However, a decrease in ϕ also reduces the amount of the Foreign pro-duced input that needs to be purchased for any given amount used inthe production process. A sufficient condition for ∂ ϕh Mð ÞMð Þ

∂ϕ b0 is

ϕM

∂M∂ϕ

> h Mð Þ

h Mð Þ þ h′ Mð ÞM � ð38Þ

Wewill assume that this condition is satisfied, that is, the first effectmentioned above dominates. Numerical simulations using the parame-ters used in Figs. 1–3 confirm that ∂ ϕh Mð ÞMð Þ

∂ϕ b0 for the three cases of theadaptation cost. The results are shown in Fig. 6. When Eq. (38) is satis-fied, we get the reasonable result that a decrease in the offshoring costincreases the demand for the intermediate input produced in Foreign.That is, the demand curve in Fig. 5b shifts to the right. Sincenothinghap-pens to the supply curve, there is an increase in the price, pf. An implica-tion is that Foreign is going to export more of the intermediate input.

An increase in pf implies from Fig. 5a that unemployment decreasesand wages increase in Foreign. The impact on Home labor market de-pends on two effects: a direct effect of a decrease in ϕ which is sameas in the small country case and a feedback effect arising from an in-crease in pf. Whether the feedback effect completely offsets or partiallyoffsets the direct effect depends on the parameters and can be answeredonly in specific cases.17 Fig. 7 provides an illustration of the numericalrelationship between offshoring and unemploymentwhen pf is endoge-nous. To construct Fig. 7 we need to specify parameters for Foreign. Toavoid using too many new parameters in the two country case, we con-tinue to use the parameters for Sweden for Home. For Foreign we arbi-trarily choose the parameters, some of them same as in Sweden, sothat the baseline two country case reproduces the baseline result forSweden. The parameters for Foreign are listed in Appendix A. For all 3cases of the adaptation cost, the results with endogenous pf in Fig. 7 aresimilar to thosewith exogenous pf in Figs. 1a, 2a, and 3a. That is, as is rea-sonable, the feedback effect from pf is not strong enough to offset the di-rect effect of a change in ϕ. We summarize the results in a propositionbelow.

Proposition 5. Decreases in the cost of offshoring in a two county worldincrease offshoring and wages and reduce unemployment in Foreign, thehost country. The impact on Home, the source country, labor market isqualitatively similar to that in the small country case.

It is worth re-iterating that the non-monotonicity of Home unem-ployment in the offshoring cost obtains even in a two country settingwhen the price of the offshored input is endogenously determined.

7.1.2. Changes in Foreign labor market institutionsWe study the impact of changes in unemployment benefits or re-

cruitment costs in Foreign on the labor markets in both Home andForeign. Note that we have described bf as the amount of final goodthat a worker can produce using traditional technology. As with bhdiscussed earlier, we interpret bf broadly to include unemploymentbenefits as well. In that case, an increase in bf can be used to captureincreases in the unemployment benefits. In all these cases, the impacton Home labor market works through changes in pf. Therefore, we

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.70.0

0.1

0.2

0.3

a) Linear adaptation cost

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.1

0.2

0.3

0.4

0.5

b) Convex adaptation cost

1.0 1.1 1.2 1.3 1.4 1.5 1.60.0

0.1

0.2

0.3

0.4

0.5

0.6c) Concave adaptation cost

φ h(

M)

Mφ

h(M

) M

φ h(

M)

M




Fig. 6. Gross offshoring as a function of offshoring cost.

a) Linear adaptation cost

b) Convex adaptation cost

c) Concave adaptation cost

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0760

0.0765

0.0770

0.0775

Une

mpl

oym

ent (

Hom

e)U

nem

ploy

men

t (H

ome)

Une

mpl

oym

ent (

Hom

e)

0.5 1.0 1.5 2.00.0740

0.0745

0.0750

0.0755

0.0760

0.0765

0.0770

1.0 1.2 1.4 1.6 1.8 2.00.0770

0.0771

0.0772

0.0773




Fig. 7. Offshoring and home unemployment with endogenous pf.


need to figure out how the supply of the intermediate input by Foreignchanges in response to changes in its labor market policies.

An increase in bf shifts the upward slopingWB curve to the left leav-ing the downward sloping curve JC curve unaffected in Fig. 5a. Thisleads to a decrease in θf and an increase in wf . A decrease in θf impliesa decrease in the supply of the intermediate input produced by Foreign.Since the demand from Home is unchanged, there is an increase in theprice, pf. Therefore, the impact of an increase in bf on Home is similarto that of an increase in ϕ described in Proposition 2. That is, unemploy-ment may increase in Home in the presence of collective bargaining.18

The impact on Foreign consists of a direct effect and a feedback effectarising from an increase in pf. Since the feedback effect on wages is inthe same direction as the direct effect, wages increase unambiguously.The direct effect of an increase in bf is to increase unemployment, butthe feedback effect from the induced increase in pf reduces unemploy-ment, rendering the net effect theoretically ambiguous. The impact ofan increase in βf, the bargaining power of Foreign workers, is qualita-tively similar to the impact of an increase in βf.

18 In the presence of individual bargaining in Home, however, unemployment de-creases unambiguously.

An increase in the recruitment cost, cf, leads to a leftward shift inboth JC andWBcurves in Fig. 5a. Therefore, θf decreases unambiguously.It is verified in the online Appendix B that wf decreases as well. A de-crease in θf implies a decrease in the supply of the intermediate inputproduced by Foreign leading to an increase in pf. Since pf increases,the impact on Home is same as the result described in Proposition 2.In Foreign the direct effect of an increase in cf is decreasedwages and in-creased unemployment, however, the feedback effects arising from anincrease in pf go in the opposite direction rendering the net effectambiguous.

We summarize the results below.

Proposition 6. Increases in unemployment benefits or recruitment costsin Foreign lead to less offshoring by Home. Home wages increase, but theimpact on Home unemployment is theoretically ambiguous. Foreignwages increase with unemployment benefits, but the impact on Foreignunemployment is ambiguous. Increases in recruitment costs have ambiguouseffects on Foreign wages and unemployment.

7.1.3. Changes in Home labor market institutionsAsmentioned in Proposition 3 for the small country case, increases in

bh or ch increase offshoring for a given pf. That is, they increase the de-mand for the offshored input and therefore, the demand curve in


Fig. 5b shifts to the right. Since the supply curve of Foreign is unchanged,the price, pf, of the Foreignproduced input increases. The consequence forForeign is increased wages and reduced unemployment. The impact onHome labor market consists of a direct effect discussed in Proposition 3and a feedback effect coming from an increase in pf. The impact ofan increase in pf is the same as that of an increase in ϕ discussed inProposition 2. That is, Homewages increase, but Home unemploymentchanges non-montonically with respect to pf. The net result is thatHome wages increase unambiguously, but the impact on Home unem-ployment is ambiguous. The results are summarized below.

Proposition 7. Increases in recruitment costs or unemployment benefits inHome increase offshoring byHome. Foreign experiences increasedwages andreduced unemployment. Home wages increase but the impact on Home un-employment is ambiguous.

The results summarized in Propositions 6 and 7 show the impor-tance of labor market institutions in a globalized world. Lower unem-ployment benefits or recruitment costs in host countries give them anadvantage in producing offshored inputs and therefore lead to greateroffshoring with attendant consequences for the labor markets in sourcecountries. Similarly, higher unemployment benefits or recruitment costsin source countries lead to greater offshoring which improve the labormarket outcomes in host countries, but have ambiguous effects on unem-ployment in source countries.

8. Concluding remarks

This paper shows the crucial role of labor market institutions in de-termining the impact of globalization on unemployment and wages. Inparticular, it shows how the results differ across alternative wage set-ting institutions such as individual bargaining and collective bargaining.While a model with individual bargaining predicts that offshoringwould increase unemployment, we show that it can go down if wagesare determined through collective bargaining. The calibration exerciseusing parameters for Sweden verifies the non-monotonic relationshipbetween the cost of offshoring and unemployment. Moreover, it pre-dicts that a decrease in the cost of offshoring starting from the presentlevel would reduce unemployment in Sweden. Extending the modelto a two country set up allows us to study how labormarket institutionsin one country have spillover effects on its trading partner. In particular,increases in the recruitment costs or unemployment benefits in the hostcountry can increase unemployment in both the host and the sourcecountry. Increases in recruitment costs or unemployment benefits inthe source country, on the other hand, are likely to increase unemploy-ment in the source country, but reduce unemployment in the hostcountry. An implication is thatwhen thinking about labormarket policiesin open economies, the policymakers have to be mindful of the feedbackeffects of policies working through forces of globalization. For example, amore generous unemployment benefit in Home not only increases un-employment in Home directly as would be the case in a closed economy,but also leads to increased offshoring. Increased offshoring leads to an in-crease in the price of imported input, which can lead to further increasesin unemployment if wages are determined by collective bargaining.Therefore, the impact of changes in labor market policies may be magni-fied in a globalized world.

Finally, while we have focused on the competitive threats fromoffshoring in this paper, similar considerations may be present within acountry from its internal geography. For example, the possibility of jobsmoving from a high wage region to a low wage region can have similarconsequences for unemployment in the two regions as in our two coun-try setting.We focus on offshoring for a couple of reasons: One, thewagedifferences within a country are usually smaller than across countries;Two, the impact of offshoring on aggregate unemployment for a countryis likely to be much larger than from the movement of jobs from one

region within a country to another, although in the latter case it couldgive rise to severe inter-regional differences in unemployment rates.

Appendix A

A.1. Wage determination in autarky

The union maximizes ρ wh−bhð ÞLhρþλhþuhθ

δhh

in the first stage, anticipating firms

to choose employment given by the condition (9) in the text. Theproblem is equivalent to maximizing the the following Lagrangian bychoosing wh and Lh.

γ ¼ ρ wh−bhð ÞLhρþ λh þ μhθ

δhh

!þ ξ γALγ−1

h −wh−ρþ λð Þchμhθ

δh−1h

" #ð39Þ

The first order conditions are

wh :ρLh


!¼ ξ ð40Þ

Lh :ρ wh−bhð Þ


!¼ ξ 1−γð ÞγALγ−2

h ð41Þ

Solve the above two to get

wh ¼ bh þ 1−γð ÞγALγ−1h ð42Þ

A.2. Existence and uniqueness of autarky equilibrium

Using Eq. (17) to substitute out Lh in Eqs. (9) and (16) obtain

γA �Lhμhθ

δhh

λh þ μhθδhh

! !γ−1

¼ wh þρþ λhð Þchμhθ

δh−1h

ð43Þ

wh ¼ bh þ γ 1−γð ÞA �Lhμhθ

δhh

λh þ μhθδhh

! !γ−1

ð44Þ

From Eqs. (43) and (44) obtain the following equation determin-ing the autarky equilibrium value of θh.

γA �Lhμhθ

δhh

λh þ μhθδhh

! !γ−1

¼ bh þρþ λhð Þchμhθ

δh−1h

ð45Þ

It is easy to verify that the r.h.s of Eq. (45) is increasing in θh and has avertical intercept at bh. The l.h.s of Eq. (45) is decreasing in θh, asymp-

totes the vertical axis as θh→0 while asymptotes γ2A�L1−γh

as θh→∞M

LhþM ¼ :07. Therefore, there exists a unique θh that solves Eq. (45). It fol-lows from Eq. (43) that there is a unique value of wh in autarky.

A.3. Derivation of wage in the offshoring case

The Lagrangian is given by

γ ¼ ρ wh−bhð ÞLhρþ λh þ μhθ

δhh

!þ ψ γA Lh þMð Þγ−1−wh−

ρþ λhð Þchμhθ

δh−1h

" #

þ φ pfϕ h Mð Þ þMh′ Mð Þ� �

−wh−ρþ λhð Þchμhθ

δh−1h

" #ð46Þ

Parameter Description Value Source

ρ Annual rate of discount 0.05 Albrecht et al.(2006)δh Elasticity of matching function 0.5 Albrecht et al.(2006)λh Annual job destruction rate. 0.165 Based on Albrecht et al

(2006)bh Unemployment benefit

(replacement rate)0.67wh OECD (1999)a

Γ Production function parameter 0.66 OECD (1999)b

μhθhδh Exit Rate from Unemployment 1.948 based on Albrecht et al(2006)

θh Market tightness 0.5 Hall (2005)μh Scale parameter in the

matching function2.755 Obtained from μhθhδh and θh

Φ Offshoring cost 1.5 ArbitraryA Aggregate productivity

parameter1 Normalization

�Lh Size of Labor Force 1 Normalizationch Recruitment cost Free to match uh=0.077 and

MLhþM ¼ 0:07

pf Price of offshored input Free to match uh=0.077 andM

LhþM ¼ 0:07

βh Bargaining power of workers 0.5 Felbermayr et al. (2011)

a: corresponds to a 67% replacement rate in Sweden in 1994–95.b: estimates for Swedenrange from 0.6 (OECD (1999) to 0.72 (Bentolila and Saint-Paul, 2003).We chose the aver-age of these two which also corresponds to the commonly used share of labor for manyOECD countries.


The first order conditions with respect to wh, Lh, and M are givenby

wh :ρLh


!¼ ψþ φ ð47Þ

Lh :ρ wh−bhð Þ


¼ ψ 1−γð ÞγA Lh þMð Þγ−2 ð48Þ

M : ψ 1−γð ÞγA Lh þMð Þγ−2 ¼ φpfϕ 2h′ Mð Þ þMh′′Mð Þ

� �ð49Þ

Next, eliminate ψ and φ from the above 3 equations to get

wh ¼ bh þLh 1−γð ÞγA Lh þMð Þγ−2pfϕ 2h′ Mð Þ þMh′

′Mð Þ

� �� 1−γð ÞγA Lh þMð Þγ−2 þ pfϕ 2h′ Mð Þ þMh′′ Mð Þ

� � ð50Þ

A.4. Determination of wage in foreign

arg maxwf

Ef−Uf

� �βf pf−wf

pþ λf

!1−βf

ð51Þ

where Ef and Uf are defined exactly in the manner in which they weredefined for Home, that is simply by replacing the subscript h by f inEqs. (10) and (11). The first order condition for the above maximiza-tion is given by

1−βf

� �Ef−Uf

� �¼ βf

pf−wf

pþ λf

!ð52Þ

Note from Eq. (10) in the text that Ef−Uf ¼ wf−ρUf

ρþλf. Therefore,

Eq. (52) can be written as

wf ¼ 1−βf

� �ρUf þ βf pf ð53Þ

Next, from Eq. (11) in the text obtain ρUf=bf+μfθf (Ef−Uf). Sub-stitute this in Eq. (52) and use Eq. (32) to obtain

ρUf ¼ bf þβf cf θf1−βf

ð54Þ

Substituting Eq. (54) in Eq. (53) obtain the expression for wagebelow.

wf ¼ 1−βf

� �bf þ βf cf θf þ βf pf ð55Þ

A.5. Calibration parameters for Sweden

Calculation of job destruction rate and exit rate fromunemploymentbased on Albrecht et al (2006).

Using the data on elapsed unemployment duration (AKU Table49) Albrecht et al fit an exponential distribution and estimatethe exit rate out of unemployment for low skilled to be 1.867and for medium skilled to be 2.163. Total unemployment ofthese two groups is.077. The fraction γ1 of the unemployed islow skilled and the fraction γ2 is medium skilled. p1 is thefraction of low skilled in the labor force. p2 is the fraction of medi-um skilled. δ1 is the job destruction rate for low skilled job andδ2 for medium skilled job. ϕ1 is the fraction of vacancies requiringlow skill and ϕ2 is the fraction requiring medium skill. e11: unskilledemployed in unskilled jobs. e21: medium skilled employed inlow skilled jobs; e22: medium skilled employed in medium skilled

jobs. m(θ) exit rate for medium skilled. The data are the follow-ing.

u ¼ :077; p1 ¼ :648;p2 ¼ :352;γ1 ¼ :724;γ2 ¼ :276;u1 ¼ :086;

u2 ¼ :060

Exponential distribution for unemployment duration

m θð Þϕ1 ¼ 1:867;m θð Þ ϕ1 þ ϕ2ð Þ ¼ 2:163 ¼ m θð Þ

The above implies

m θð Þ ¼ 2:163;ϕ1 ¼ :863;ϕ2 ¼ :137

Steady state implies the following three conditions for job creationto equal job destruction.

ϕ1m θð Þγ1u ¼ δ1e11;ϕ1m θð Þγ2u ¼ δ1e21;ϕ2m θð Þγ2u ¼ δ2e22

Now, e11=p1−γ1u=0.592, therefore, δ1=0.176. This impliese21=0.225. Since e11+e21+e22=1−u=0.923, e22=0.106. This inturn implies δ2=0.059. That is

δ1 ¼ 0:176; δ2 ¼ 0:059; e11 ¼ 0:592; e21 ¼ 0:225; e22 ¼ 0:106

We are interested in calculating the average job destruction rate δand the exit rate �m(θ). Summing up the three s–s conditions obtain

ϕ1γ1 þ ϕ1γ2 þ ϕ2ð Þm θð Þu ¼ δ1e11 þ δ1e21 þ δ2e22ϕ1 þ ϕ2γ2ð Þm θð Þu ¼ δ1e11 þ δ1e21 þ δ2e22

Therefore, �m(θ)=(ϕ1+ϕ2γ2)m(θ) is the exit rate from unem-ployment for the two skill types as a whole, and δ ¼ δ1e11þδ1e21þδ2e22

1−u¼e11þe21þe22is

the job destruction rate for the groups combined.

�m θð Þ ¼ ϕ1 þ ϕ2γ2ð Þm θð Þ ¼ :863þ :137 � :276ð Þ2:163 ¼ 1:948;

δ ¼ :1625

These are the two key numbers that we are going to use in our cal-ibration. In our notation δ corresponds to λh and �m (θ) corresponds toμhθhδh.

Table 1Calibration parameter values for Sweden.


A.5.1. Parameters for Foreign in the two country caseParameter values for Foreign in the two country case:�Lf=1, βf=

0.5, bf=0.2;δf=δh=0.5;ρ=0.05; λf=λh=0.165, θf=0.18. μf and cfare the free parameters that are chosen to be consistent with thebaseline values of pf and M obtained for Sweden with ϕ=1.5 andh(M)=1+M. That is, we use the baseline value of parameters under-lying Fig. 1 for Sweden and choose μf and cf for Foreign consistentwith the implied values of pf andM, the two variables that are relevantfor Foreign. One downside of this approach is that since M=0.7 in thebaseline case for Sweden, Foreign employment in the input productionis very small given the normalization �Lf =1. The rest produce the finalgood using home production technology and show up as unemployedin our figures. Therefore, the absolute value of the unemployment ratefor Foreign is not going to be realistic. Only the direction of change inthe unemployment for Foreign is informative.

Appendix B. Supplementary data

Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.jinteco.2012.06.003.

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