A Matching Model on the Use of Immigrant Social Networks and Referral Hiring

doi:10.4236/tel.2012.24070

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Theoretical Economics Letters, 2012, 2, 379-384

http://dx.doi.org/10.4236/tel.2012.24070 Published Online October 2012 (http://www.SciRP.org/journal/tel)

A Matching Model on the Use of Immigrant Social

Networks and Referral Hiring

Mónica García-Pérez

Department of Economics, St. Cloud State University, St. Cloud, USA

Email: migarciape[email protected]

Received August 8, 2012; revised September 7, 2012; accepted October 9, 2012

ABSTRACT

Using a simple search model, with urn-ball derived matching function, this paper investigates the effect of firm owner’s

and coworkers’ nativity on hiring patterns and wages. In the model, social networks reduce search frictions and wages

are derived endogenously as a function of the efficiency of the social ties of current employees. As a result, individuals

with more efficient connections tend to receive higher wages and lower unemployment rate. However, because this ef-

ficiency depends on matching with same-type owners and coworkers, there is also a differential effect among workers’

wages in the same firm. This analysis highlights the potential importance of social connections and social capital for

understanding employment opportunities and wage differentials between these groups.

Keywords: Immigration; Search Models; Social Networks; Wage Differential; Hiring Process

1. Introduction

Previous work has studied the effects of networks in the

labor market to explain labor market inequalities as a

function of differential social capital (social resources,

network structures, network resources). Minority indi-

viduals are generally connected to other minority-group

workers who can only provide them with limited oppor-

tunities to change their employment outcomes. In this

context, personal networks are then considered an addi-

tional determinant of inequality [1]. For instance, His-

panics and blacks are disadvantaged because they are

likely to match with same-kind job contacts, and end up

working in lower wage workplaces where other Hispan-

ics and blacks work (see [2]).

This paper intends to model the interconnection be-

tween owner’s and coworkers’ nativity and workers’

hiring patterns and wages. We use a simple search model

where social networks reduce search frictions to develop

the theoretical implications o f social ties between owners

and workers for individual labor outcomes. In the model,

wages are derived endogenously as a function of the effi-

ciency of the social ties of current employees. Firms can

fill their vacancies either by posting their offers or by

using their current workers’ connections. However, em-

ployers may use this mechanism differently for different

worker types, depending on their ability to take advan-

tage of their workers’ connections. Given their cultural,

linguistic, and social backgrounds, immigrant employers

have an advantage, compared to natives, in exploiting

their immigrant workers’ social connections. As a result,

individuals with better connections—a combination of

owner type and coworkers type—tend to have higher

wages. Two forces drive that result. First, current work-

ers provide a costless recruitment mechanism to the firm.

Second, workers will produce more new hires in the fu-

ture and for those unemployed, a better social connection

would result in more job offers.

The rest of the paper is arranged as follows: Section 2

provides a background on the discussion on the use of

networks in the labor market, particularly by minority

groups; Section 3 provides reasoning behind the assump-

tions in the model; Section 4 presents the model; and

Section 5 off ers concluding re marks.

2. Background

2.1. On the Effect of Firm Owners and

Coworkers

Both employers and employees may make use of their

contacts to find each other. On the job seeker side, for

instance, three direct beneficial effects can be related to

the use of contacts. First, contacts can provide job op-

portunities that may not be widely known by the public.

Also, contacts can increase the chances of getting a par-

ticular job by being a referred candidate. Third, contacts

may offer additional information about the job environ-

ment (i.e. internal structure and boss-employee relation)1.

1See [3,4], among others.

M. GARCÍA-PÉREZ

380

The potential benefits of the use of this mechan ism by

employers are also documented. The personnel literature

has discussed the employers hiring procedures, with spe-

cial attention to certain informal methods of recruitment,

such as those which rely on current employees for dis-

semination of information (see [5,6]). Also the role of

employee referrals in the understanding of ethnic divi-

sions of labor and allocation of jobs has been considered

(see [2]).

Current workers may increase the number of appli-

cants by spreading the words about a new opening. This

process is generally costless for the firm. Furthermore, in

the labor market generally employers have imperfect

information about the candidate unobserved ability. To

correct for this, firms could use employee referrals as a

useful screening device. Personal contacts might transmit

information about productivity of applicants that other-

wise would be difficult to obtain from a simple evalua-

tion of the candidate Current workers give information

for future candidates, because workers tend to refer indi-

viduals with similar characteristics to themselves ([6]

called “inbreeding bias”), or tend to refer high-qualified

candidates given that their reputation would depend on

this new candidates performances. Therefore, current work-

ers’ information may reduce uncertainty about future w o r k -

ers’ productivity.

Additionally, employers can obtain more information

about candidate qualities such as work ethic and leader-

ship, providing a higher chance of a “better match”. Fi-

nally, employers can also benefit from the potential co-

operation among coworkers in the workplace. On-the-job

training can be provided by older employees at zero cost

for the firm, generating a faster assimilation for new com-

ers.

On wage effects, previous research has suggested that

much of the unexplained variation in wages among em-

ployees is linked to characteristics of their firms, such as

size and industry2. Not only individual characteristics

explain wage differentials between immigrants and na-

tives, but potentially so do other characteristics, such as

the birthplace or ethnicity of em ployers and coworke rs.

2.2. Social Networks, Ethnic/Racial Groups and

Immigrant Segregation

Empirical literature has also discussed the racial an d eth-

nic differences in informal job matching (see [2,5]). These

differences arise because informal channels permit race

and other characteristics in the network to play a more

prominent role in the hiring process than it does when

formal mechanisms are used. As noted by [2], one of the

puzzles during 1980s and 1990s was the worsening of

less educated blacks in the labor markets while the same

markets were absorbing thousands of new immigrant

workers. Surprisingly, these new workers had, on aver-

age, similar characteristics to blacks: low formal educa-

tion and high geographic segregation. So the question of

job distribution became to be a first order issue, espe-

cially in the topics of immigration and immigrant as-

similation. According to [10], the answer for this puzzle

has been focused in the use of social networks by differ-

ent groups for fi n di n g em ployment.

Meanwhile the role of prospective employers in the

use of these mechanisms has been ignored. The differen-

tial use of job referral by the employers is also relevant

when we examine who is hired and how the benefits are

distributed in the firm. For instance, immigrants will be

hired most likely by immigrant firms with high share of

immigrant workers than by native firms with high share

of immigrant workers. This tendency promotes the crea-

tion of what [1] called immigrant economies.

3. Modeling the Importance of Social

Networks and Labor Outcomes

[5] is the first theoretical discussion of firms’ hiring pro-

cedures. However, no implications for wages were ana-

lyzed. The hypothesis is that networks may reduce costs

and the uncertainty about workers’ productivity. Since

screening workers, negotiating wages, supervising, and

enforcing contracts are all part of the administrative costs

of a firm, firm owners may improve efficiency by using

network connections available to workers with similar

social backgrounds. We can think then that information

networks may work better within groups (ethnic/race of

employers and employees) than between them.

A second group of studies consider job information

networks as exogenous and investigate the impact of

networks on wages (see [6]). Networks solve the infor-

mational problem that employers face when they cannot

observe the underlying ability of potential workers. In

these models, the equilibrium wage distribution increases

with the probability that an offer comes from a contact.

These works further evaluate the link between wages and

the strength of social ties (strong versus weak). Their

models assume that firms post wages above or below the

market wage based on the distribution of skill across in-

dividuals, and then workers decide whether to accept the

offer or do otherwise. Because there is not a reservation

wage developed in the model, individuals who reject

offers or do not receive any offer must find employment

in the anonymous market, so there is not employment

differential across worker types.

More recent studies have explicitly modeled the struc-

ture of networks to analyze the effect of network dynam-

ics on wages and unemployment (see [11,12]). In these

models, the topology of the social ties is defined and

built with detail and networks also work as instruments

2See [7-9].

M. GARCÍA-PÉREZ 381

to dissipate information imperfections. Workers face a

cost of obtaining information on vacancies, or need to

join networks that provide them with the best informa-

tion. However, these models only focus on the supply

side of the market; the role of firms or any type of nego-

tiation are ignored. They treat labor markets as a black

box. Therefore, the origin of the vacancy and the partici-

pation of firms in the job search are ignored.

4. A Simple Search Model

We consider a model similar to [5] where firms choose

hiring procedures and workers sear ch for jobs, and, then,

include the importance of social contacts by assuming

that firms take into account their current workers’ social

connections in their decision process. We include differ-

ent types of firms and multiple networks. Firms can

choose to fill their vacancies either by posting offers or

by using their current workers’ connections—a costless

process—considering the capacity of their employees to

find candidates for the position.

There are two types of firms () denoted as na-

tive-owned (n) and immigrant-owned (

),d two types

of workers (i) denote as native (n) and immigrant (

The number of each type of worker is exogenously given

by i

L, and the number of type i workers among the un-

employed is i

Workers and firms are risk neutral, live infinitely and

have a common discount rate . There is free-entry, and



represents the number of type firms in steady

state. Only unmatched workers engage in search. Unem-

ployed workers receive a value of leisure b, and workers

are separated from jobs at the exogenous rate

. Jobs

are vacant or occupied.

4.1. The Matching Function

Like [13], the matching function is derived from an urn-

ball process3. This process provides a microfoundation

for the matching process and considers the coordination

failure that arises from congestion externalities4.

Then, as in [6] we include workers in the search proc-

ess and the idea of job referral as a screening device. So,

the efficiency of the social networks is also a function of

the capacity of current workers to replicate themselves

through the new candidate (“inbreeding bias”), together

with employers’ capacity of obtaining the best informa-

tion from the worker about the new comer.

Each existing worker generates applicants for the em-

ployer at an exogenous rateio



, which depends on work-

er (i) and employer (o) types. This factor is common to

all firms with type ond worker i. Here, io



ays the

role of the network efficiency variable con sidered in [13].

Network efficiency depends on the number of workers of

type i in the firm and their social ties with same-type

unemployed workers in steady state, and of the employer

o’s ability to ue his employees’ (type i) connections.

Unemployed

workers receive offers from two sources:

from posted vacancies and from similar-type current

workers in the firm. 1u is the chance that any unem-

ployed worker receiven offer from a posted vacancy

and s a

1iu is a type-i unemployed worker’s probability of

receiving an offer from social ties to a particular existing

worker at the firm. Given the randomness of vacancies

offered to unemployed workers, the probability that no

firms’ offers reach an unemployed worker of type i is

given by



1111 io io

onf







.

We assume that the levels of vacancies and unemploy-

derive the probability

ent are very high, which result in a constant ratio (mar-

ket tightness). Therefore, the urn-ball matching function

exhibits constant returns to scale.

With this in mind, we can then

at an unemployed worker from group i receives at least

one offer.



11111

io io

onf





 

 u (1)

where represents the probability that an un employed

worker receives at least one job offer. This distribution

can be approximated by a Poisson distribution.



1exp







3In the typical urn-ball process, there are U unemployed workers and V

vacancies. Each unemployed worker submits an application.These

applications are randomly distributed across the V vacancies with the

restriction that any particular worker send at most one application to

any particular vacancy. Each vacancy then chooses one application at

random and offers that applicant a job. A worker may get more than

one offer. In that c ase, the worker accepts one of the offers at rando m.

Urn-

all process introduces a new coordination problem, because there

could be multiple applications of job seekers but only one firm will

hire the individual.

4This failure arises when workers apply to some vacancies without

knowing where other workers applied, so that as a result there are

multiple applications to some vacancies and zero to others. Therefore,

the group of vacancies without applicants remains unfilled. For more

detail refer to [14]. Here the case is reversed. Unemployed workers are

considered the urns and job offers the balls. These workers received

multiple offers depending on the conditions in the model.

(2)

where

i oioio

pv L











 (3)

and

 (4)

The probability that an offer is matched to an unem-

ployed worker of type i is given by the matching function

M. GARCÍA-PÉREZ

382



muC



 (5)

iiiioio io

pv L







This function exhibits constan t returns to scale. An in-

crease of io



will translate into an increase in the num-

ber of offers to a particular worker in group i. We can

rewrite Equation (5) as

 



11exp



 (6)

where







i. It canis the expected number of workers hired

of type be shown that







.

  





1 expi

exp













 (7)

which is negative as long as



1exp



exp i





 .

when , then 0

. The

ofi

0x

tive of

 



1xexp xexp x

ction is negative with respec



deriva this funt to x

for 0x (i.e. the tighter the market, the harder for

firmst nd a worker).

Additionally,





represents the exit rate from

unoemployment fividual i. The total number of

matches is the sum of the contact rates within each social

group.

r an ind



ioio ioi

MpvLm









 (8)

4.2. Workers: Unemployed and Employed

t dis-On the workers’ side, we denote i

U as the presen

counted utility of an unemployed worker and io

W as the

present discounted value of an employed workolding

a job, with io

w being the wage rate for worker type i in

firm type o.

er h











iiiio

rUbmE WU





(9)





ioioi io

rWws UW

Workers receive offers from formal an

group

(10)

d informal chan-

ls, but only accept one offer. Therefore, an increment

in the probability of finding a candidate through current

workers increases the number of offers received by un-

employed workers through informal channels.

4.3. Firms: Vacancy and Filled-Job Value

To simplify the model, an employee of a given

transfers job offers only to unemployed workers belong-

ing to the same group. If he doesn’t find an unemployed

worker from his group, the job offer is lost. All types of

employed worke rs prod uce

In addition to relying on coworker referrals, firms can

advertise a job vacancy at coa st c. These posted offers

are sent randomly to u unemployed workers. i



repre-

sents market tightness for workers of group i. o

v is the

number of vacancies posted by firm of type o.

Firms choose o

v taking into account that eployees

also produce applicants. Therefore, employers

face the

foallowing profit mximization problem:













0vo

oioio ioio

VLMaxyLwLcvrVL

o io

















oioiooi

LLvm







 s.t

LL



(11)

The firm is interested in g io

Liven io







VL is

the firm expected profit. si Kuhn-Solving the Bellman Equation and ungTucker

conditions we obtain:





 0









 (12)



. 0

io o

iioi

mrsm









 (13)

Firms will post a vacancy if and only if th

posting the vacancy is equal to the value of filling the

ith this we endogenize labor market out-

ording to the Nash solution of

e cost of

cancy. If o

v different to zero, in each period a firm o

would choose the number of advertised vacancies, so it

controls the increment of its total number of employees.

In this way, the firm indirectly influences the number of

applicants the social network will produce. Therefore,

social connections may be used by the firms to find new

workers in a costless way and as a mechanism for scr een -

ing workers.

Wages are a result of bargaining between workers and

employers. W

mes (wages and vacancies) but assume an exogenous

job information network5.

Wages are subject to a bargaining process. The surplus

of each match is shared acc

e bargaining problem, with





0,1



 representing the

bargaining weight of firms.







io i

WU



 (14)

type

where is the expected value of a

worker i for a firm o. An individu

filled job with a

al will accept an

offer ifis above the bargained wage. Using Equations

(9)-(11) and Equation (14) we derive the wage implied

by Nash bargaining.

5Other models fully describe the topology of the networks. However,

in the framework of this paper, trying to endogenize networks would

make it impossible to find a closed form solution. The simplicity of the

model presented here allows us to draw strong implications without

losing the relevant characteristics of the process.

M. GARCÍA-PÉREZ 383









io rs

wb yb







 



(15)

1io i













where









 .

rival rate of The arjob offers from a firm o to an un-

ed worker of i is directly proportional to the employ type

number of people in the network (group i) who are em-

ployed in firm o. An interpretation for io



is that it

represents the capacity of workers and employers to take

advantage of the groups’ social connections. We could

think io



consists of two exogenous components





io i





. (16)

where i



i hais the set of connections that current workers

of typeve, and o



represents the employer’s ability

to take ntage of his current employees’ social ties.

Proposition 1: In partial equilibrium, taking i

adva



given, and for a given y, c, b, and s, wages are an in-

creasing function of the efficiency of the social network



. A higher network efficiency induces a higher job

matching rate for the firm with no additional cost.

Proof: Using Equation (15) we compute the derivative

of wages with respect to social network efficiency:









myb

rs mm



 







 (17)

ii ioi



The incr ease on the eff iciency of n etworks for a w

er type i in a firm o generates a higher number of ex-

ork-

cted matches for workers of typ e i, given them a better

bargaining position in the firm. Therefore, we would

expect the probability of hiring an immigrant worker to

be higher the larger the amount of immigrant workers

already employed by a firm. We could call this the “co-

worker effect”. Additionally, when group i has more ef-

ficient social ties, and the owner is also more efficient in

taking advantage of these social ties to find new workers,

the use of current employees’ connections to find candi-

dates becomes less costly. Workers of type i would pro-

vide more candidates to the firm, therefore, the probabil-

ity of this group being hired by the firm will be higher

than otherwise, and the wage of those particular candi-

dates would be higher compared to those with less effi-

cient social networks in the firm.

There are two forces generated by any increment in



. On one side, it increases the job offers using infor-

able to exploit their employ-

al channels, more candidates are searched by owners

ing current workers. On the other side, it decreases the

number of vacancies advertised because firms find more

costly to post a vacancy compared to using informal

channels. This substitution effect guarantees the unique-

ness of the equilibrium.

Because of lack of familiarity with their employees’

cultural background, language, and social patterns, own-

ers may not necessarily be

s’ social ties. Within a firm, workers of different

groups are paid differently because their social ties differ

in their level of efficiency. That is, foreign-born and na-

tive workers receive different wages when working for

an immigrant firm because links between immigrant em-

ployers and immigrant workers result in more worker

referrals. Additionally, workers with higher offer arrival

rates earn more in equilibrium. For instance, if we as-

sume a distribution of network efficiency as follows:

nnfffn nf



, there would be a distribution of

wages in which natives are paid higher wages when

working for native firms, but are paid lower when they

owned businesses. Similarly, immi-

grants are paid better when working for immigrant em-

ployers, but still obtaining lower wages overall in the

market.

Proposition 2: In equilibrium, labor market tightness

adjusts so that the expected cost of an advertised vacancy

equals the

work for immigrant-

expected profit of a filled position.

Proof: Using results from the firm’s problem, Equation

(11), with 0

v, and wage bargaining results from

Equation (15), we obtain:









mrsm m



iioi



 



 (18)

The solution is defined only when the right ha

of Equation (18) is positive, that is, when the

value of a filled position is positive. This holds provided

nd side

marginal











ii ioi

rs mm

 



 .

As i



, such that : suming











ii ioi

rs mm

 



 

th s

en for valueof ,













 , the expression is in-

creasing in i



r, so that the marginal value of a filled

vacancy is deceasing with respect to i



, whilost

ncreases wite the c

of a filling vacancy ih higher values of i



Unemployent rate in equilibrium is obtained by

equating the flow out of employment to the flow into the

unemployment for each type i and is a function of the

market tightness and the exit rate.



usm



 (19)

Recall that







n (19), as

is the unemploym

Using Equatioent exit rate.



increas

exit rate es, the equilibrium







increases, reducing .

imple misaper explores

the potential mechanisms explaining the interconnection

5. Concluding Remarks

Using a satching framework, th p

M. GARCÍA-PÉREZ

384

’ nativity and workers’ 6. Acknowledgements

My espe

between owner’s and coworkers

hiring patterns and wage.

The model has implications on the effect of social in-

teractions on market wages. Among subgroups with the

same y, h, s, firm-group combinations with higher

cial thanks to all comments fro m SEA and WEA I

om CeMent Fellowship

[1] I. Light, “Deflecting Immigration,” Sage Publications,

New York, 20

[2] J. R. Elliot, “nically Homogene-

arch, Vol. 94, No. 3, 2001, pp. 426-

urtis and J. T. Warner, “Matchmaker, Matchmaker:

participants and my colleagues fr

2011. All errors are my own.



will have higher wages and a lower unem ployment rate.

There would be a distribution of wages in which work-

ers are paid higher when working for same-type owners.

Within a firm, workers of different groups are paid dif-

fer

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10, No. 3, 1992, pp. 306-330. doi:10.1086/298289

[5] H. Holzer, “Hiring Procedures in the Firm: Their Eco-

nomic Determinants and Outcomes,” NBER working pa-

per series, 1987. http://www.nber.org/papers/w2185

worker replication. The better the employer can get

information from its current employees, in this case the

better immigrant firms obtain information from its cur-

rent immigrant employees, the lower the uncertainty on

the expected productivity, the lower the informational

cost, and the lower the recruitment cost. The informal

mechanism would be relatively more efficient than the

use of formal recruitment processes.

In this framework, there are two effects generated by

any increment of social connection’s efficiency. On one

side, it increases the job offers using informal channels;

0020

[6] J. Montgomery, “Social Networks and Labor Market Out-

comes: Toward an Economic Analysis,” American Eco-

nomic Review, Vol. 81, No. 5, 1991, pp. 408-418.

[7] J. M. Abowd, F. Kramarz and D. N. Margolis. “Hi gh Wage

Workers and High Wage Firms,” Econometrica, Vol. 67,

No. 2, 1999, pp. 251-333. doi:10.1111/1468-0262.0

[8] E. L. Groshen, “Five Reasons Why Wages Vary among

Employers,” Industrial Relations, Vol. 30, No. 3, 1991,

pp. 350-381. doi:10.1111/j.1468-232X.1991.tb00793.x

re candidates are found using current workers. On the

other side, it decreases the number of vacancies adver-

tised because firms find more costly to post a vacancy

compared to use informal channels.

In the model, wages are derived endogenously as a

function of the efficiency of the social ties of current

employees. There are two types of owners and workers:

[9] E. L. Groshen, “Sources of Intra-Industry Wage Disper-

sion: How Much Do Employers Matter?” Quarterly Jour-

nal of Economics, Vol. 106, No. 3, August 1991, pp. 869-

884. doi:10.2307/2937931

[10] R. Waldinger, “Black-Immigrant Competition Re-Assessed:

New Evidence from Los Angeles,” Sociological Perspec-

tives, Vol. 40, No. 3, 1997, pp. 365-386.

4, pp. 426-454.

tive and immigrant. Owners can choose to fill their

vacancies either by posting offers or by using their cur-

rent workers’ connections. As a result, individuals with

better connections have higher wages. Individual with

more ties would find more candidates for the firm, but he

would have more opportunities when he becomes unem-

ployed.

This analysis highlights the potential importance of

social connections and social capital for understanding

the disparity of employment opportunities and wage dif-

fer

[11] A. Calvo-Armengol and M. O. Jackson, “The Effects of

Social Networks on Employment and Inequality,” Ameri-

can Economic Review, Vol. 94, No. 3, 200

doi:10.1257/0002828041464542

[12] A. Calvo-Armengol and M. O. Jackson, “Networks in

Labor Markets: Wage and Employment Dynamics and In-

equality,” Journal of Economic Theory, Vol. 132, No. 1,

2007, pp. 27-46. doi:10.1016/j.jet.2005.07.007

[13] F. Fontaine, “A Simple Matching Model with Social Net-

works,” Economic Letters, Vol. 32, No. 4, 2006, pp. 1667-

1717.

entials between native and foreign bor n w or ker s .

Notice that we assume exogenous network efficiency.

Trying to endogenize and define the topology of net-

works could make more challenging the solution of the

model.

[14] J. W. Albrecht, G. Pieter and S. B. Vroman, “Matching

with Multiple Applications,” Economic Letters, Vol. 78,

No. 1, 20 03, pp. 67-70.

doi:10.1016/S0165-1765(02)00178-7