Theoretical Economics Letters, 2012, 2, 379-384 Published Online October 2012 (
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
Received August 8, 2012; revised September 7, 2012; accepted October 9, 2012
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
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.
opyright © 2012 SciRes. TEL
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-
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].
Copyright © 2012 SciRes. TEL
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.
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
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.
io io
 
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.
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.
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.
i oioio
pv L
The probability that an offer is matched to an unem-
ployed worker of type i is given by the matching function
Copyright © 2012 SciRes. TEL
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
 
 (6)
i. It canis the expected number of workers hired
of type be shown that
  
1 expi
which is negative as long as
exp i
 .
when , then 0
. The
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).
represents the exit rate from
unoemployment fividual i. The total number of
matches is the sum of the contact rates within each social
r an ind
ioio ioi
 (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
rUbmE WU
ioioi io
rWws UW
Workers receive offers from formal an
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
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:
oioio ioio
o io
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:
 (12)
. 0
io o
 (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
representing the
bargaining weight of firms.
io i
 (14)
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.
Copyright © 2012 SciRes. TEL
io rs
wb yb
 
1io i
 .
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
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:
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-
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
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
 
 (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
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.
Recall that
n (19), as
is the unemploym
Using Equatioent exit rate.
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
Copyright © 2012 SciRes. TEL
Copyright © 2012 SciRes. TEL
’ 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-
Referral Hiring and Eth
ently because their social ties differ in their level of
efficiency. That is, foreign-born and native workers re-
ceive different wages when working for an immigrant
firm because links between immigrant employers and
immigrant work ers result in more w orker referrals. Add i-
tionally, workers with higher offer arrival rates earn more
in equilibrium.
Even an immigrant firm with a low level of skilled
workers could be able to generate a more efficient con-
nection with its current workers if it can exploit the rate
ous Jobs: How Prevalent Is the Connection and for Whom?”
Social Science Rese
[3] M. Granovetter, “Getting a Job: A Study of Contacts and
Careers,” The University of Chicago Press, Chicago, 1995.
[4] S. J. C
The Effect of Old Boy Networks on Job Match Quality,
Earnings, and Tenure,” Journal of Labor Economics, Vol.
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.
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;
[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-
This analysis highlights the potential importance of
social connections and social capital for understanding
the disparity of employment opportunities and wage dif-
[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
[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-
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
[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.