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Holdup and hiring discrimination with search friction
Sheng Bi, Yuanyuan Li
To cite this version:
Sheng Bi, Yuanyuan Li. Holdup and hiring discrimination with search friction. 2016. �halshs-
01277548�
Documents de Travail du
Centre d’Economie de la Sorbonne
Holdup and hiring discrimination with search friction
Sheng BI, Yuanyuan LI
2016.02
Maison des Sciences Économiques, 106-112 boulevard de L'Hôpital, 75647 Paris Cedex 13
http://centredeconomiesorbonne.univ-paris1.fr/
ISSN : 1955-611X
Holdup and hiring discrimination with search friction
∗
BI Sheng
†
, LI Yuanyuan
‡
30th, December
Abstract
A holdup problem on workers' skill investment can arise when employers adopt discriminatory hir-
ing norm to extract higher than socially optimal prot. When hiring priority is determined by both
productivity-dependent (skill level) and -independent characteristics (discrimination), skill investment
decision becomes strategic between the discriminated and favored group. We consider frictional markets
with either posted or bargained wage (xed sharing rule). With posted wage, depending on market tight-
ness there may be equilibrium or multiple equilibria on skill investment. With discriminatory hiring, if
in equilibrium both groups stay high skilled, both are worse o and rms better o; In any equilibrium
where one group underinvest, the other group remain high skilled and are better o, while rms are worse
o with discrimination. With bargained wage, similar equilibrium where the favored group underinvest
exists, and rms incur cost for an intermediate range of bargaining power when they discriminate.
JEL Classications:
J7, J42
Key words:
Discrimination; Directed Search; Pre-matching Investment
∗
We are very grateful for the discussions and encouragement from Professor Bernhard Eckwert, Professor François Langot,
Professor Anna Zaharieva, Professor Bertrand Wignoille, Nikolai Brandt, Dr. Andreas Szczutkowski, as well as participants in
BIGSEM Colloquium, BIGSEM Workshop, EDEEM Annual meeting, and GAINS seminar. Yuanyuan LI would like to thank
the EDEEM program for the nancial support, and BI would like to thank for the nancial sponsorship from University of
Paris 1 and University of Bielefeld, and Deutsch-Französishe Hoshschule.
†
University of Paris 1, and University of Bielefeld; E-mail: brbisheng@gmail.com
‡
University of Bielefeld, and University of Paris 1
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Documents de travail du Centre d'Economie de la Sorbonne - 2016.02
1 Introduction
A holdup problem arises when some investment is sunk ex ante by one party, and the payo is shared
with that one party's trading partner. Since cost has no other use once sunk, that trading partner will have
every incentive to squeeze the prot at the ex post stage. In an important study on such a problem in a
labor market with search friction, Acemoglu and Shimer (1999b) show that with rms' sinking capital and
ex post wage bargaining, the equilibrium is always inecient, since wages paid ex post can be so high such
that rms' ex ante incentive of investment is harmed; while if rms are able to post wages to direct workers'
search, then the holdup problem to rms' investment no longer appears; the eciency can be achieved,
because wage posting allows workers to observe oers and choose where to apply, and it induces workers
to optimize their expected payo from application by making trade-o between every wage they observe
and the probability of obtaining it. Within conventional wage posting framework, we spot another source of
ineciency in a holdup problem where workers sink skill investment cost: when the market is crowded for the
rms, by adopting a discriminatory hiring norm rms are able to expropriate higher than socially optimal
level of prot, and this has the consequence of discouraging the investment incentives for both the favored
and discriminated groups. We analyze the impact of such rent seeking behavior of rms on the structure of
market segmentation, and on the workers' skill investment incentives.
When discrimination is absent, the wage posting economy with workers' ex ante skill investment attains
eciency in the equilibria, and we show which equilibrium emerges depends on the rivalry between the
log return to skill and the market tightness (workers/rms ratio) which measures the degree of market
competition. The fundamental reason behind this eciency result is that skill achievement is a quality which
can be legally written into the wage contracts. It is a dierent story when other (binary) characteristics which
are not closely related to productivity, such as gender, race, height, origin etc. enter also into rms' preference.
Under equal pay legislation, posted wages can not be conditioned explicitly on these characteristics; however,
if rms still select workers according to their preference on these characteristics, a separating equilibrium
can result where separate rms post dierent levels of wages, and workers of dierent groups sort themselves
and apply to dierent wages: the market is then endogenously segregated. On the side of rms, they have
incentive to adopt such discriminatory hiring norm, when workers' return to skill investment is suciently
high; in that case discrimination allows them to grasp higher than the socially optimal level of operating
prot. On the side of the workers, it proves that both the discriminated group and favored group are worse
o: for the former, it is because discrimination discretely reduces the labor market opportunity of these
workers, who anticipate discrimination, then demand lower wages, which makes them cheaper to hire; for
the latter, it is so because when rms are able to hire the discriminated workers cheaply, it is as if rms
enjoy larger market power, which allows them to suppress further the undiscriminated workers' expected
payo. Naturally, anticipating discrimination, all groups expect lower payo from search, jeopardizing their
skill investment incentives.
A key feature of our study is the multidimensionality of characteristics based on which workers are
ranked. On one hand, there is ranking by productivity-dependent type identity: workers are either high
skilled (type
H
) or low skilled (type
L
); high skilled have priority to low skilled simply because such ranking
gives rms higher prot. On the other hand, there is ranking by productivity-independent group identity:
workers belong either to the favored (group
a
) or the discriminated group (group
b
). The resulting ranking
schedule has the following order:
aH bH aL bL
. It reads: given any skill level, group
a
are preferred
to group
b
; the high skilled are always preferred to low skilled. Under such an intertwined ranking order,
the skill investment decision for dierent groups becomes strategically interdependent. Focusing on Nash
2
Documents de travail du Centre d'Economie de la Sorbonne - 2016.02
pure strategy equilibrium on skill investment, in the wage posting economy, we nd that depending on the
value of market tightness there can be equilibrium or multiple equilibria on skill investment due to that
interdependence. Compared to the case without discrimination, when the market is very crowded (market
tightness is small) for the rms, discrimination is protable for rms and all the workers are worse o;
as the tightness further increases, both group can choose low skill and in equilibrium whenever one group
underinvest, the other group remain high skilled and are better o, while the rms are worse o with
discrimination. In particular, the equilibrium where the favored group underinvest, while the discriminated
group choose to remain high skilled exists; And in this case rms' prots drop since workers' underinvestment
in skill leads to lower average productivity in the economy compared to the case where discrimination is
absent.
In the economy where wages are bargained (determined according to a xed sharing rule) after matching
hence do not direct search, we nd similar equilibrium where the favored group underinvest, hence earn lower
expected payo compared to the case without discrimination within a certain region of bargaining power;
in such an equilibrium, surplus is transferred from rms and favored group to discriminated group. Firms'
prots are piecewise monotone, because increase of workers' bargaining power can increase workers' incentive
of skill investment, hence discretely improves the market skill composition and average productivity. We
also nd that there is an intermediate range of workers' bargaining power for values of which rms are
worse o by discriminating, due to discouraged skill investment from discriminated group. All in all, the
key dierence between wage posting and wage bargaining is that the actual wage now exogenously pegs on
the productivity, and rms can no longer manipulate their market power by translating their discriminatory
preference into constantly lower wages.
1.1 Relation to the literature
Job search process is an important channel through which discrimination keeps functioning in the labor
market. Several papers have highlighted the impact of discrimination through job search channel to the
wages gaps. To name a few, Pendakur and Woodcock (2010) show that the existent glass ceilings for the
immigrant and minority workers may be attributed by large measure to their poor access to the jobs in
high-wage rms; As well, in an important article from Ritter and Taylor (2011), they show that most of
the disparity in unemployment rate could not be explained by cognitive skills that emerge at an early stage,
although for wage gap it could be the case. This result concerning the unemployment disparity is conrmed
by the nding that this disparity is still signicant even for workers of similar skill levels.
Our work is most closely related to the directed search literature
1
. In this literature, search frictions
are derived endogenously through agents' sequential strategic interactions. Taking into account strategic
interaction allows search externality to be internalized. The resulting economy remains competitive, albeit
with a non-Walrasian market structure, and prices play an allocative role to achieve eciency. To the best
of our knowledge, among the discrimination literature with search friction, only two of them are built upon
wage posting context. Lang, Manove, and Dickens (2005, hereafter LMD) show that a discriminatory hiring
rule could lead to labor market segmentation and signicant wage gap with even a negligible dierence in
productivity; however, the discriminated group turn out to have lower unemployment rate, which is in sharp
contrast with evidence. Merlino (2012) aims at improving the result of LMD (2005). He considers further the
1
This literature is sometimes also termed as wage posting game with coordination friction
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Documents de travail du Centre d'Economie de la Sorbonne - 2016.02