The Journal of Socio-Economics 38 (2009) 456–463

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The Journal of Socio-Economics

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Low wages and high unemployment rates: The role of social interactionsin hiring discrimination�

Jean-Francois Jacquesa,∗, Emmanuelle Walkowiakb

a LEDA, Paris-Dauphine, Place du Marechal de Lattre de Tassigny, 75775 Paris Cedex 16, Franceb ERUDITE1, Université Paris-Est and Centre d’Etudes de l’emploi (CEE2), TEPP (FR n◦ 3126, CNRS), France

a r t i c l e i n f o

Article history:Received 29 May 2007Received in revised form14 November 2008Accepted 12 December 2008

JEL classification:J41J82D23Z13

a b s t r a c t

The purpose of this paper is to explain why low-wage workers with identical qualifications to higher-wage workers are more exposed to unemployment. Each worker is considered to belong to a social group(defined according to his/her gender, age, and nationality). We assume that workers experience both pro-ductive interdependencies and social interactions within the firm. Also inter- and intra-group interactionsdetermine worker productivity, and frictions on the labor market limit the hiring of the most productiveworkers. Consequently, externalities acting both within the firm and in the labor market can lead to ahigher rate of unemployment for low-wage workers.

© 2008 Elsevier Inc. All rights reserved.

Keywords:DiscriminationSU

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ocial interactionsnemployment rate

. Introduction

Despite notable improvements in their qualification levelsnd/or professional experience, workers who are socially catego-ized as young, old, female, or foreign continue to experience higherates of unemployment and receive lower wages (OECD, 2003).hese gaps can clearly be seen in trends in participation rates,

nemployment rates, and wage differentials from the 1970s to theresent.

Numerous laws against sexual discrimination notwithstanding,nemployment rates for women are generally higher than those

� We are particularly indebted to J. Scheinkman for his constructive remarks dur-ng the construction of our model. We would like to thank C. Aubert, A. Clark, N.reenan, M. Gurgand, J. Gautié, R. Kierzenkowski, B. Kukla, E. Lavery, T. Weitzen-lum, B. Burgess and the participants of the REMMI seminar of the Centre d’Etudese l’Emploi and EURiSCO-Dauphine. We also thank C. Sofer for valuable commentsn an earlier version of this paper which was presented at the LIIIth Congrès of theFSE (2004). Finally we are grateful to the anonymous referees for their stimulatingomments. We retain full responsibility for any remaining errors.∗ Corresponding author. Tel.: +33 1 44 05 44 60.

E-mail addresses: jacques@dauphine.fr (J.-F. Jacques),mmanuelle.walkowiak@univ-paris12.fr (E. Walkowiak).

1 Université Paris Est, 61, avenue du Général de Gaulle, 94010 Créteil Cedex, France.2 «Le Descartes I» - 29, promenade Michel Simon, 93166 Noisy-le-Grand Cedex,

rance. Tél.: +33 1 45 92 68 00.

053-5357/$ – see front matter © 2008 Elsevier Inc. All rights reserved.oi:10.1016/j.socec.2008.12.008

for men, and their average wages are lower. For example, in Spain,the European country with the greatest unemployment gender gapafter Greece (4.5 points), the mean wage for women is 82 percent ofthat for men in 2007. Similarly, Portuguese female unemploymentrates are 3 points higher than those for men, and their wages are 8percent lower. In 2007, these kinds of gaps were typical in the EUas well as for most other developed countries. As shown in Fig. 1below, there are only a few exceptions to this general trend, witha gender employment gap favorable for women (Romania, Latvia,Ireland and Estonia) or unemployment rates almost at parity formen and women (Japan, United States, United Kingdom, Germany,Lithuania).

Foreign workers are also under-represented in the labor mar-ket (OECD, 2003). In OECD countries, from 1999 to 2000, theemployment-rate gap between non-citizens and citizens was 4 per-cent for men and 8 percent for women. According to the EuropeanLabor Force Survey in 1998, this gap was the largest in Belgium,Sweden and France, where the unemployment rate of foreigners(non-EU members) was more than 20 points higher than that forthe local population.

These observations suggest substantial inequalities in employ-ment outcomes between social groups. Any cumulation of thesedifferent social characteristics reinforces the negative effects onoutcomes (OECD, 2003). For example, the French Labor Force Sur-vey from 1998 calculates an unemployment rate for non-EU foreign

J.-F. Jacques, E. Walkowiak / The Journal of Socio-Economics 38 (2009) 456–463 457

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Fig. 1. Gap in the unemployment r

omen between the ages of 15 and 24 of 55 percent. Different the-ries have been developed to explain these inequalities amongstndividuals with the same qualifications.

Mortensen (2003) focuses on wage inequalities, and suggestshat these result from job-search frictions, which are the direct con-equence of asymmetric information regarding wages. Mortensenoncludes that these inequalities do not, therefore, result fromiscrimination. In our paper, we use this standard assumption of

abor-market frictions as part of our explanation why similar work-rs have unequal access to employment.

In contrast to Mortensen, economic theories of discrimina-ion (Becker, 1971; Phelps, 1972; Arrow, 1973) explain inequalitiesn employment access for equally qualified workers. However,hese theories do not explain why discrimination persists in theong run. To simplify, we can classify theories of discriminationnto two groups.3 The first brings together papers in the Becker1971) tradition, where discrimination is considered to result fromiscriminatory preferences. As a result of this preference for dis-rimination among employers, employees and/or consumers, firmshat discriminate will not employ the most productive workers.herefore, in the long run, discriminatory firms are less efficienthan non-discriminatory firms. In theory, competition should elim-nate these firms from the market and hence discrimination shouldrogressively disappear. However, this is not the case. Phelps (1972)nd Arrow (1973) developed a second approach known as statis-ical discrimination. Employers statistically discriminate becausehey lack information regarding the productivity and turnover ofheir applicants. While the individual productivity of an applicants unknown, the productivity of his/her reference group is com-

on knowledge. Due to the inaccuracy of imprecise observationsf individual productivity, employers tend to assess an applicant’sroductivity according to their reference group. When referenceroups differ in average productivity, statistical discrimination

3 A third approach considers that institutions shape behaviors or keep some socialroups out of certain professions. As this paper focus on firm behavior, this approachill not be developed here. See Altonji and Blank (1999) for a survey of theoretical

nd empirical papers using this approach.

tween females and males in 2006.

implies that some categories of workers, for example women, arepaid less than their marginal productivity. During the 1970s womenwere generally less educated than men, so that such statisticaldiscrimination could be explained. Today employers are proba-bly aware that in developed countries men and women receivethe same level of education, and therefore that this kind of dis-crimination is groundless. Our paper offers an alternative way ofunderstanding both kinds of discrimination. In contrast to the Beck-erian view, we show the persistence of discrimination in the longrun; and in contrast to the statistical discrimination model, we con-sider the productivity of each individual applicant to be perfectlyknown, but endogenous as it depends on work organization.

Explaining the persistence of long-run discriminatory behaviorrequires an understanding of how employers assess the quali-fications of the workers they choose to hire. The nature of thediscrimination problem suggests that the abilities of certain minori-ties are systematically underestimated given their qualifications ordiplomas. Why are qualifications or diplomas assessed differentlyfor different groups of workers? When considering the criteria thatdetermine worker selection, it is crucial to understand why workerqualifications are differentiated from their abilities.

We appeal to the socio-economic status of the worker to explainthe persistence of discrimination. The main objective is to illus-trate how the worker’s individual socio-economic characteristicscombined with the social composition of the workforce can affectindividual productivity via social interactions. That is, by com-municating with other workers (who are similar to or differentfrom themselves), workers improve their problem-solving abilities.The worker’s qualifications and their ability to resolve problemsthrough worker interactions jointly determine their productivity.This assumption may be particularly relevant in innovative firmsor firms facing complex and unstable environments. Mintzberg(1981) has shown that informal communication is an efficientcoordination mechanism that enhances productivity in such envi-

ronments. Empirically, Gant et al. (2003) analyze differences ininformation sharing and connections between workers across theworkplace with traditional and innovative HRM systems in sev-eral production lines in the Steel industry. They show that firmsfavor workplace communication between employees in innovative

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58 J.-F. Jacques, E. Walkowiak / The Journ

roduction lines. All workers communicate more extensively toolve operating problems on these production lines, which achievereater productivity levels than do lines where there is less com-unication.Our approach follows recent research, which has investigated

he effects of worker diversity on productivity. Work on diversityithin teams has however produced contrasting results. The case

tudies in Kochan et al. (2003) on diversity within teams show thatontext is crucial in determining the impact of diversity on perfor-ance. In Hamilton et al. (2006) teams with more age diversityere less productive, while those composed of only one ethnic

roup were more productive. However, these findings depend onhe model specification. Greenan and Walkowiak (2005), usingrench data, show that a worker’s ability to communicate dependstrongly on diversity in qualifications, age, gender and citizenshipn the firm.

By analyzing the role of social interactions in the productionrocess, three dimensions of problem-solving abilities4 are iden-ified: individual, collective and social. Abilities are deemed toe individual when based on the qualifications of the worker,hereas they are collective or social when they rely on inter- and

ntra-group social interactions. From an efficiency point of view,s inter- and intra-group communications will not be the sameor all workers, both the social characteristics of workers and theocio-demographic composition of the firm’s workforce affect theirbilities to solve problems and therefore their individual productiv-ty, as in Gant et al. (2003).

The paper is organized as follows. Section 2 introduces the con-epts used here, and puts them into perspective by comparinghem to discrimination theories. Section 3 outlines the model, andection 4 analyses the equilibrium of the model. Last, Section 5oncludes.

. Social interactions and productive activity: someheoretical concepts

We focus on one aspect of the labor process to understand theay in which employers assess abilities: the interdependenciesetween workers. In economics, interdependencies at work areormalized as productive complementarities. Two tasks are com-lementary in a production function if the effort involved in the firstositively affects the marginal productivity of the second (Alchiannd Demsetz, 1972). As a result, the production contribution of eachndividual task cannot be fully identified.

One of the basic assumptions of our model is that workers are insituation of both productive interdependencies and social interac-

ions. The quality of the social interactions can affect the productionrocess. Also, productive activity may contribute to the develop-ent of social interactions. We now consider the consequences of

aking social interactions into account on the economic analysis ofroduction.

Social interactions first lead to a process of categorizationmong workers. Reference groups are categories resulting fromsocial process of categorization, much like those described by

ryer and Jackson (2003). This process explains how the struc-ure of social interaction draws distinctions between employees

ue to their socio-demographic characteristics. When interactionsccur, employees class others into categories based on observableharacteristics. This type of behavior occurs for efficiency rea-ons: workers cannot remember every detail about every person

4 We do not cover all of the relevant debates, particularly in sociology, over theoncept of ability, but consider this concept in the light of human-capital theory.n the latter, abilities are attached to individuals, whatever their nature (general orpecific, transferable or not transferable).

ocio-Economics 38 (2009) 456–463

they meet, and this kind of broad classification allows individu-als to store and retrieve salient features quickly and efficiently.Fryer and Jackson show that for a fixed number of categories,an individual looks for cognitive efficiency by minimizing thevariance of socio-demographic characteristics within categories.Consequently, individuals in the same category tend to have similarsocio-demographic characteristics. We consider the characteristicson which these categories are based (age, gender, citizenship, etc.)to be socio-demographic, as they are observable by all employees.These characteristics could also be cultural (for example, languageor religion).

The survey in Williams and O’Reilly (1998) reveals the effects ofsocio-economic diversity on labor efficiency and firm performance.The work surveyed there has shown that the socio-economic com-position of the workforce plays a role in both social interactionsand the process of group formation. This composition modifiescommunication, cohesion and conflict within the firm, as wellas decision-making style, which affects overall performance. Assuch, the socio-demographic composition of employees can playan important role in worker productivity. In our model, the refer-ence group is translated into vectors of norms where values providea common language.

When the employees run into problems at work, they interactby communicating; this improves their problem-solving abilities.Models formalizing social interactions generally consider a utilityfunction that depends on the agent’s actions and also on the meanaction of the reference group to which the agent belongs (Glaeserand Scheinkman, 2002, and Becker and Murphy, 2000). We fol-low this tradition, and assume that the ability to solve problemsdepends on both the individual’s own qualifications and the meanqualification level among other workers in the firm.

When a worker interacts with other workers, he/she draws onthe human capital of the other workers in the firm to solve theproblem at hand, and this will increase his/her own social capital(i.e. the human capital associated with the interactions). This socialcapital in turn, improves the collective problem-solving ability ofall of the workers. Finally, as in Glaeser et al. (2000), we considerthat social interactions lead to the accumulation of social capital,and that social capital is a component of human capital. Whereasthese authors introduce social capital into the utility function, wehere introduce it into the production function.

Furthermore, following Leana and Van Buren (1999), we sup-pose that social capital has two components: one emotional and theother based on qualifications. The emotional component of socialcapital reflects the fact that the worker is not just required to carryout certain tasks, but also to be a certain type of person. We proposeto distinguish the sociability of workers from different communitiesas a function of their reference group.

We also assume that the efficiency of communication dependson each worker’s reference group. In this respect, we formalize twohypotheses discussed in the social capital literature. For Bourdieu(1980) and Coleman (1990), closed social networks, where indi-viduals are in close proximity, favor the development of socialcapital because the flows of information and trust are stronger.In this view, workers in the same reference group may com-municate more efficiently than workers in different referencegroups. But the opposite may also hold. Proximity between work-ers may lead to an excess of information and to lower efficiency(Burt, 1992). Here the interaction between different workers mayfavor the accumulation of social capital in a close proximity set-ting.

The integration of social interactions into a production functionhighlights the collective and social nature of abilities. The external-ities created by the interactions between workers inside the firmare added to the externalities generated by competition betweenthe unemployed in the labor market.

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into account both productive interdependencies and social interac-

J.-F. Jacques, E. Walkowiak / The Journ

. The model

In this section, we propose a new production function thatncludes social interactions. This production function renders therganization of labor within the firm endogenous due to the search-ased labor market.

We assume that the economy is populated by N agents denoted i.e consider two exogenous sources of worker heterogeneity: qual-

fications denoted by a, and the reference group denoted by g. Toimplify, we assume that the human capital of an agent is given byis/her qualifications and we assume that there are two referenceroups, g = 1, 2. Each agent belongs to only one reference group,hich indicates his/her type. Belonging to this group defines socialroximity between individuals. This social proximity provides aommon language and conveys norms and collective values. Theseeference groups imply a similar language, which is not necessar-ly efficient. We do not assume, a priori, any ranking for the relativefficiency of intra- and inter-group communication. We do howeverssume that all of the workers interact.

.1. The production function when workers interact

Let N1 and N2 denote the number of workers of type-1 and 2ithin the firm. The total number of workers is denoted by N (with= N1 + N2). Total production Ytot is the sum of the individual out-uts. Letting yg

idenotes the output of the worker i of type g, total

roduction is equal to:

tot =N1∑i=1

y1i +

N2∑j=1

y2j (1)

Individual output depends on both an externality denoted E andndividual problem-solving ability denoted m as follows:

gi

= mgi

× E for i = 1, . . . , N and g = 1, 2 (2)

As in Rosen (1982), E is a positive organizational externality thatas a symmetrical effect on the production of all workers. Thiselates to the indivisibility of managerial choices. Whereas in theodel of Rosen (1982) the positive scale effect associated with the

ierarchical organization of labor comes from the manager, herehis effect arises from the horizontal interdependencies betweenosts formalized via an O-Ring function (Kremer, 1993). This scaleffect does not allow for substitution between “quantities” andquality” in the chain of production. We have:

=

⎛⎝ N1∏

i=1

m1i ·

N2∏j=1

m2j

⎞⎠

1/N

(3)

In the models of Rosen and Kremer, the match between workersnd firms relies on the workers’ abilities, which are exogenous. Herebilities are endogenous, depending on the worker’s qualificationsa) and his/her level of social capital (b). For the worker i of type g,his ability is:

gi

= agi

× bgi

for g = 1, 2 (4)

In this paper we focus on inequalities which are not explainedy qualification differentials. Wage residual inequality increasedteadily throughout the 1970s and 1980s, and continued to increaseharply in the 1990s (Acemoglu, 2002 and Lemieux, 2006). For thiseason, we assume that qualifications are exogenous and identicalmong workers, ag

i= a whatever their type, in order to focus on

nequalities in the access to employment that do not result from

ocio-Economics 38 (2009) 456–463 459

differences in qualifications.5 According to Eq. (4), differences inproblem-solving ability do not only come from worker qualifica-tions. The social capital of each worker is endogenous. As mentionedabove, we consider two hypotheses about social-capital accumula-tion: a closed group of homogenous individuals, or an open groupof heterogeneous individuals. We formulate these via a peer effect,denoted S, which is assumed to be the same for the two referencegroups. Denoting the proportion of workers of type-1 in the firm asp, and that of workers of type-2 as (1 − p), the social capital levels bof the workers i of type-1, and of the workers j of type-2 are writtenas

b1i

= b1 = a(Sp + (1 − p)) for workers of type 1b2

j= b2 = a((1 − p)S + p) for workers of type 2 (5)

The parameter S can be greater or less than one. In the first case(S > 1), at a given qualification level, the exchange of knowledgefrom social interactions is greater between workers of the sametype (the Bourdieu–Coleman hypothesis). The communication in agroup of homogenous workers in terms of their type (intra-groupinteractions) is more efficient than the communication betweenheterogeneous individuals (inter-group interactions). In the secondcase (S < 1), inter-group interactions are more efficient than intra-group interactions (the Burt hypothesis). Inter- and intra-groupcommunication is equally efficient when there is no peer effect(S = 1). We exclude the extreme cases where S = 0 or S = +∞, whichcorrespond, respectively to no effect of communication betweenmembers of the same group or members of different groups. Implic-itly, everybody communicates.

In Eq. (5), all workers belonging to group 1 (respectively group2) own the same level of social capital. Individual indices could thenbe omitted. However, workers of type-1 and 2 differ in their level ofsocial capital. The variable b then depends on the peer effect, andconsequently on the socio-demographic composition of the work-ers (p) in addition to the influence of the qualifications of the otherworkers in the firm. We obtain mg

i= ag

i× bg by combining Eqs. (4)

and (5), and we directly see the individual, collective and socialdimensions of the ability to solve problems.

Regarding the individual dimension, ability (mgi) increases with

the individual human capital of the worker (agi). The collec-

tive dimension of abilities raises the question of the effect ofthe socio-demographic diversity/homogeneity of the workforcewithin organizations. Social capital (bg) depends on the socio-demographic composition of the workforce (since p and 1 − prepresent the proportions of each group). Communication will bemore efficient with higher qualification levels, given the socio-demographic composition of the workforce. Finally, the thirddimension is social, as the value of bg depends on the referencegroup to which the worker belongs. This means that the social cap-ital of a worker depends on both his/her reference group and thepercentage of the workforce who are of the same type as her. Thisview of abilities fits the empirical evidence (Hamilton et al., 2006;

5 This assumption makes the question of worker segregation by skill irrelevant,since there is no skill variance in our model. Some papers have shown that duringthe 1990s, the correlation between the wages (and also seniority) of workers withinfirms has increased in the US, UK and France (for instance Kremer and Maskin, 1996).The explanation of skill segregation is beyond the scope of our paper. We focus onother forms of segregation like gender, ethnicity, and age, as highlighted in a numberof papers (see for instance Bayard et al., 2003).

460 J.-F. Jacques, E. Walkowiak / The Journal of S

t

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3

fitodriAfahnt2

stO

a

ber of positions in the economy, K, is fixed. Eq. (9) indicates the

7 In this article wages are exogenous: workers in group 1 are paid at a constantwage w1, and workers of group 2 are paid w2. The scope of this paper is not to explainthis difference in wages. Different theories explain wage inequalities associated withsocial characteristics: discrimination theory, age-biased technological or organiza-tional change, obsolescence of human capital for older workers, and the importanceof domestic work for women associated with a lower reservation wage. Alternativesociological views highlight the role of social representation in the persistence ofwage inequalities: “old people are rigid” so they can not adapt easily to new stan-

Fig. 2. The production function.

ions between workers. This can be written as follows6:

tot = E

⎡⎣ N1∑

i

a(a(Sp + (1 − p)) +N2∑j

a(a(S(1 − p) + p))

⎤⎦ (6)

Fig. 2 below shows total output as the proportion of workersf type-1 varies, with the same number of workers. When intra-roup communication is the more efficient (S > 1), and when therere fewer workers of type-1 (p < 1/2), it is not efficient to increaseheir proportion. On the contrary, if type-1 workers are in the major-ty (p > 1/2), productivity rises with their group size. So, when S > 1,he output curve is U-shaped. This representation of aggregate out-ut is fairly similar to the empirical finding of Goldin (2002), whoonsidered gender segregation in the US. The firm thus always hasn interest in increasing the proportion of the majority group. Onhe contrary, when inter-group communication is the more efficientS < 1), the curve is hump-shaped. The firm would be better off inncouraging a mix of workers, i.e. in increasing the proportion ofhe minority group.

.2. Labor-market equilibrium

To determine the market equilibrium, we assume that all therms have the same production function given by (6) and focus onhe symmetric equilibrium. Each group has its own labor marketut of which a dual market emerges, as in Saint-Paul (1996). Even ifiscrimination is illegal in hiring announcements, the pre-selectionound (in which costs for both workers and the firm are negligible,.e. submitting a CV) leads to a segmentation of the labor market.fter this first selection, only workers of type g continue to compete

or the job catering to group g. Both the vacancies and the workersre directed towards a specific labor market. The number of workersired Hg in segment g of the labor market depends positively on theumber of unemployed Ug and on the number of vacancies openo that category of workers Vg. The matching function (Pissarides,000) of workers with vacancies is Hg = m(Ug, Vg).

If there is no friction in the labor market, and if S > 1, the firmhould hire only workers of type-1 or 2, depending on their respec-ive productivity. However, frictions prevent such corner equilibria.n the contrary, if S < 1, the firm hires just as many workers of type-

6 As E depends on the proportion of each category of worker in the firm, we onlynalyze the symmetric equilibrium.

ocio-Economics 38 (2009) 456–463

1 as workers of type-2. As in Saint-Paul’s model, the equilibriumdepends on the conditions in the labor market, which are exoge-nous: wages (w1, w2),7 the labor supply of each category (L1, L2),and the efficiency of the matching process. In contrast to Saint-Paul,the gains the firm obtains for each post are endogenously deter-mined, and depend on the socio-demographic composition of thefirm (Eqs. (1)–(5)). Individual productivity yg depends on the orga-nizational externality E, which is linked to the socio-demographicorganization of the workers inside the firm. As a consequence, thegain from hiring a worker of type g is endogenously determined bythe matching outside the firm and the interactions inside the firm.

Mathematically, at the market level, two equations determinethe stationary equilibrium. The first relates to the externali-ties inside the firm resulting from productive interdependenciesand social interactions between workers. The second relates tolabor-market externalities, which stem from the bilateral searchprocesses of job-hunting and employee-searching.

The first equation reflects the trade-off of the firm when itdecides to post a vacancy of type-1 or 2. Let �g,t denote the prob-ability per unit of time of finding a worker of type g, and Jg,t thepresent discounted value of a job held by a worker of type g, r theinterest rate, and dt an infinitesimal interval of time. Knowing thatemployees leave the firm at an exogenous rate of q, the value of avacancy of type g follows a Markov process:

VACg,t = (1 − rdt)[�g,tdtJg,t+dt + (1 − �g,tdt)VACg,t+dt]

with Jg,t = yg,t−wg,t+(1 − rdt)[qdtVACg,t+dt+(1 − qdt)Jg,t+dt] (7)

At the stationary equilibrium (VACg,t = VACg,t+dt and Jg,t =Jg,t+dt),the firm has no particular preference for one or the other kind of jobg (VAC1t = VAC2t). Eq. (8) formalizes the trade-off between vacanciesof types 1 and 2:

�2 = �1(r + q)((y2 − w2)/(y1 − w1))(r + �1 + q) − �1

(8)

Except for the asymptote, the graph of Eq. (8) is a continuouscurve, denoted A, on the (�1, �2) locus. It is upward-sloping underspecific conditions8 (see Appendix A): a greater probability of fill-ing a job must be compensated by a greater probability of fillingthe other type of job. Its position depends on the ratio of individ-ual profit made from both types of workers (y2 − w2)/(y1 − w1) =G2/G1, making its position dependent on the social interactionsinside the firm (see Fig. 3).

The second equation of the model, which relates to the labor-market externalities, represents the flow equilibrium in the labormarket. Following Saint-Paul (1996), we assume that the total num-

dards of production, women find low-paid work which is similar to the “domestictask” etc. (Garner-Moyer, 2003). In our model it is possible to endogenize wages bylinking them to productivity, or by formalizing a wage bargaining process, as in SaintPaul.

8 To obtain an upward-sloping curve, it is necessary for the instantaneous gainG2 to be upper-bounded following an infinitesimal increase in �1 or �2. Curve Arepresents the equality of expected gains in the two segments of the labor mar-ket. Curve A falls below the first 45-degree line if y2 − w2 > y1 − w1, and above ifthe reverse holds. Some numerical simulations show that these conditions can berelaxed (Jacques and Walkowiak, 2005).

J.-F. Jacques, E. Walkowiak / The Journal of S

c

�swofia

((tu

u

4

thiwfittTitaiEew

�

probability of providing this type of vacancy. Secondly, when S > 1,an increase in S raises segregation and the unemployment rate ofthe minority employees inside the firm. In our model, the impact ofthe peer group S leads to this kind of inertia and helps to explain thedifference in unemployment rates between the different groups of

Fig. 3. The equilibrium.

onnection between the two segments of the labor market:

L1�(�1) + L2�(�2) = K

where �(�i) = �i + q

�i + h(�i)qand h(�g) = m

(1,

Ug

Vg

)−1(9)

Curve B illustrates Eq. (9). It is downward-sloping on the (�1,2) locus (see Fig. 3). If the number of vacancies is constant at theteady state, a rise in �1 (the probability of obtaining a job for aorker of type-1) means that the number of unemployed workers

f type-1 is greater, as the total number of jobs in the economy isxed (K). This implies that fewer type-2 workers are unemployed,nd so the probability of getting a type-2 job (�2) is lower.

The stationary equilibrium is the solution of the system of Eqs.8) and (9). Graphically, curve A intersects curve B. The solution�*1, �*2) determines the proportion of each type of worker withinhe firm (p and 1 − p), and their respective rate of unemploymentg, which increases with respect to �g:

g = qh(�g)qh(�g) + �g

= h(�g)h(�g) + �g/q

(10)

. The properties of the equilibrium

In this model, even if the wage of a type-1 worker is lower thanhat of a type-2 worker (w1 < w2), type-1 workers can experience aigher rate of unemployment.9 For example, if S > 1 and p < 1/2, hir-

ng a type-2 worker greatly increases the social capital of the type-2orkers, who already represent the majority group within therm. The improvement of their problem-solving abilities increasesheir productivity. This implies that their productivity differen-ial exceeds their wage differential relative to workers of type-1.herefore, when intra-group communication is more efficient thannter-group communication, there is a segregation process withinhe firm. Despite equal qualifications, the lower-paid workers arelso less in demand because their collective problem-solving abil-

ty is lower. The opposite conclusion pertains when S < 1 and p > 1/2.ven if w1 < w2, the firm can have an interest in hiring type-2 work-rs. In fact, when type-1 workers are in the majority, hiring a type-1orker causes a substantial deterioration in their overall social cap-

9 If y1 − w1 < y2 − w2 then the equilibrium is established for values such that1 > �2 (see Eq. (8)) and u1 > u2 (see Eq. (10)).

ocio-Economics 38 (2009) 456–463 461

ital and also of their problem-solving abilities. A firm should thenchoose to post vacancies of type-2 and hire this category of workerin order to gain from the positive consequences of a mix in workerabilities. Finally, in underlining the collective and social nature ofabilities, this model can help to explain why, with equal qualifi-cation levels, and lower wages, certain categories of workers mayexperience a greater risk of unemployment. In addition, the firm isnot on its production efficiency frontier because it does not con-trol the peer group effect (S is exogenous) and there are frictionsin the labor market. In terms of X-efficiency (Liebenstein, 1979),“the degree of X-inefficiency” comes from externalities inside thefirm (social interactions) and outside the firm (labor-market fric-tions).

We now turn to comparative statics. Several shocks may affectthe equilibrium. We distinguish between movements in the curve A(which relates to the trade-off between the two types of vacancieschosen by the firm) and movements in the curve B (which repre-sents the equilibrium of job flows between the two segments of thelabor market).

Curve A is parameterized by the interest rate r, the quit rate q,and the ratio of gains. We focus on the determinants of relativegains (G2/G1). Any exogenous increase in this ratio implies a down-ward movement in curve A (see Fig. 4). When the gains associatedwith the hiring of a type-2 worker are relatively higher than thosefrom hiring a type-1 worker, the firm prefers to post vacancies oftype-2. It is then necessary that the probability of filling a type-1vacancy increase, to compensate for this differential in gains. At theequilibrium, the firm remains indifferent between the two types ofvacancies.

What are the determinants of G2/G1? Two parameters are key:wages and the peer group effect (S). They both affect the unem-ployment rate and the segregation process within the firm. First,when labor supply and wages are exogenous, any change in relativewages will affect G2/G1. For example, a fall in type-2 wages (dw2 < 0)raises the firm’s gain from a type-2 worker compared to a type-1worker. Firms then post more type-2 vacancies and fewer type-1vacancies. As labor supply remains unchanged, the probability ofproviding a type-2 vacancy and the unemployment rate of this cat-egory decreases. A contrario, the scarcity of type-1 vacancies impliesan increase in the unemployment rate of these workers and in the

Fig. 4. The effect of a shock on the curve A.

462 J.-F. Jacques, E. Walkowiak / The Journal of S

wi

tbgIvuststbr

5

mlctatmswTcafcttdioipc

f

Fig. 5. Effect of the increase in the number of jobs in the economy.

orkers. The peer group effect produces a hysteresis phenomenonn segregation, which does not disappear.

Two shocks may impact the balance of job flows between thewo segments of the labor market. The first is a change in the num-er of jobs in the economy (K). The effects are unambiguous: thereater the number of jobs, the greater the number of vacancies.f labor supply remains constant, the probability of filling theseacancies falls, and curve B moves downward. Consequently, thenemployment rates of both types of workers fall (see Fig. 5). Theecond shock is an exogenous change in the “social” composition ofhe labor supply. This implies a rotation of B. By leaving total laborupply unchanged, a larger proportion of type-1 workers increaseshe slope of B. It becomes more difficult to provide a type-2 vacancy,ecause there are fewer workers of this type. The unemploymentate of type-2 workers falls and that of type-1 workers rises.

. Conclusion

In the job-search model developed in this paper, workers areatched to a job according to their problem-solving ability. The

atter is not only individual, as is generally assumed in human-apital theory, but also mostly depends on social interactionshat generate collective learning. The efficiency of these inter-ctions depends on the worker’s reference group. Consequently,he socio-demographic composition of the firm’s workforce deter-

ines aggregate productivity. Taking into account the individual,ocial and collective dimensions of abilities helps us to understandhy there is greater unemployment among low-wage workers.

heir productivity may be low because the socio-demographicomposition of the workforce does not favor them: they cannotccumulate collective problem-solving abilities. As it is rationalrom an employer’s point of view to hire people who communi-ate more easily to solve problems, discrimination can persist inhe long run. When intra-group communication is more efficienthan inter-group communication, employers prefer perfect socio-emographic homogeneity in their workforce. However, frictions

n the labor market prevent employers from hiring only one typef worker. By way of contrast, when intra-group communications less efficient than inter-group communication, employers prefer

erfect socio-demographic heterogeneity in their workforce, andonsequently discrimination should disappear.

The key role of the socio-demographic composition of the work-orce underlines that it is important to distinguish the effects of

ocio-Economics 38 (2009) 456–463

segregation from those linked to discrimination. Segregation anddiscrimination both lead to unequal opportunities for workers asa function of their social characteristics (gender, ethnicity, age,etc.). The policies implemented to counter these inequalities arenot, however, the same. In our model, an affirmative-action policyis not efficient if communication between communities of work-ers is not improved. In this case, such a policy could generatecounter-productive effects and aggregate productivity might fall.The key question raised is to understand how to favor communica-tion between communities in order to encourage a transition fromsegregation to integration.

The efficiency of communication between workers is socially,culturally and historically determined. However, economic factorsalso play a role in improving inter-group interactions. Firstly, byequipping all workers with new communication technologies, firmscould improve their inter-group communication. The communica-tion network of a worker depends to a large extent on the use ofinformation technologies (Gant et al., 2002). Secondly, as shownin the IBM case analyzed by Thomas (2004), the heterogeneity ofthe consumer base requires an innovative spirit within the firmthat could be boosted by worker heterogeneity. Better access tothe right market could potentially provide incentives to firms toincrease the diversity of their teams, and consequently to improvecommunications between the communities inside the firm.

Appendix A. Existence of the equilibrium

Let the curve A be defined by the equation:

�2 = �1(r + q)R(r + q + �1) − �1

where R is equal to the ratio of the gain of type-2 workers G2 andtype-1 workers G1:

R = a(S(1 − p) + p) − w2

a(Sp + (1 − p)) − w1.

This curve passes through the origin and has an asymptote:

If R > 1 lim�1→∞�2 = r + q

R − 1

If R < 1 lim�2→∞�1 = R(r + q)1 − R

B is a downward-sloping curve with two asymptotes repre-sented by the following implicit equations:

L1 1 + �1/q

�1/q + h(�1)= K and L2 1 + �2/q

�2/q + h(�2)= K

In order to obtain an equilibrium, the asymptote of the curve Amust be above the asymptote of curve B.

In the particular case where wages are identical and both popu-lations are of the same size, p = 1/2 is an equilibrium. Consequentlythe slope of curve A is positive and equal to 1. We can conclude thatin the neighborhood of the equality of wages the curve is upward-sloping by continuity and the equilibrium is locally stable.

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