de05_Article1 11/16/05 3:53 PM Page 959

Journal of Economic LiteratureVol. XLIII (December 2005), pp. 959–988

Search-Theoretic Models of the Labor
Market: A Survey
RICHARD ROGERSON, ROBERT SHIMER, and RANDALL WRIGHT∗
We survey the literature on search-theoretic models of the labor market. We show
how this approach addresses many issues, including the following: Why do workers
sometimes choose to remain unemployed? What determines the lengths of employment and unemployment spells? How can there simultaneously exist unemployedworkers and unfilled vacancies? What determines aggregate unemployment andvacancies? How can homogeneous workers earn different wages? What are the tradeoffs firms face from different wages? How do wages and turnover interact? What
determines efficient turnover? We discuss various modeling choices concerning wage
determination and the meeting process, including recent models of directed search.

1. IntroductionT

he economic fortunes of most individuals are largely determined by their labormarket experiences—that is, by paths fortheir wages, their employers, and theirintervening spells of unemployment or nonemployment. Hence, economists are naturally interested in documenting theempirical behavior of wages, employment,
and unemployment, and also in building
models to help us understand the forces thatshape these outcomes and using the models
to assess the consequences of changes inpolicies or institutions.
∗ Rogerson: Arizona State University. Shimer: Universityof Chicago. Wright: University of Pennsylvania. We thank
Daron Acemoglu, Ken Burdett, Zvi Eckstein, Roger
Gordon, Iourii Manovskii, Derek Laing, John McMillan,
Dale Mortensen, Peter Rupert, Martin Schindler, Gerard
van den Berg, two anonymous referees, and many students
for their input. We also thank the Federal Reserve Bank of
Cleveland, the National Science Foundation, and the Sloan
Foundation for research support.

While the usual paradigm of supply anddemand in a frictionless labor market isuseful for discussing some issues, many
important questions are not easily
addressed with this approach. Why do
unemployed workers sometimes choose toremain unemployed, say by turning down
job offers? What determines the lengths of
employment and unemployment spells?
How can we simultaneously have unemployed workers and unfilled vacancies?
What factors determine the aggregate
unemployment and vacancy rates? How canapparently homogeneous workers in similarjobs end up earning different wages? What
are the trade-offs faced by firms in paying
different wages? How do wages and turnoverinteract? What determines the efficientamount of turnover?
From its inception, search theory has
provided a rigorous yet tractable framework that can be used to address these andrelated questions. Central to the approach959

de05_Article1 11/16/05 3:53 PM Page 960

960

Journal of Economic Literature, Vol. XLIII (December 2005)

is the notion that trading frictions areimportant. It takes time and otherresources for a worker to land a job, especially a good job at a good wage, and for afirm to fill a vacancy. There is simply nosuch thing as a centralized market wherebuyers and sellers of labor meet and trade
at a single price, as assumed in classicalequilibrium theory. Of course, economic
models do not have to be realistic to be
useful, and the supply-and-demand paradigm is obviously useful for studying many
issues in labor economics. But it is equallyclear that the simple supply-and-demand
approach is ill suited for discussing questions such as those raised in the previous
paragraph.
We argue that even the earliest searchmodels, with their focus on a single worker,
enhance our ability to organize observations on employment histories. We thenexamine more recent research that embeds
the decision-theoretic model into an equilibrium framework. Although there areseveral important modeling decisions inequilibrium search theory, we argue thattwo questions are paramount. First, how
do agents meet? In particular, is searchrandom, so that unemployed workers areequally likely to locate any job opening, ordirected, so that for example firms canattract more applicants by offering higher
wages? Second, exactly how are wages
determined? Do matched workers andfirms bargain, or are wages posted unilaterally before they meet? We consider various alternative sets of assumptions andindicate how the choice affects predictions.
We also emphasize how a common set of
methods and ideas are used in all of thedifferent approaches.
Before proceeding, we mention thatsearch theory constitutes a very large field.
In addition to labor, it has been used inmonetary theory, industrial organization,
finance, the economics of the marriage
market, and other areas, all of which wemust neglect lest this survey becomes

unmanageable.1 Search has been used inmuch fairly technical theoretical research,and has also been a workhorse for empiricaleconomics, but we can neither delve into
pure theory nor pay attention to all of theeconometric issues and empirical findings
here.2 Also, while we strive to be rigorous,
we emphasize issues rather models or
methods per se. Hence the presentation
revolves around the ways in which theframework helps us think about substantive
questions like those mentioned above.
The logical structure of the paper is as follows. We begin in section 2 with the problem
of a single agent looking for a job, not only
because this is the way the literature started,but because it is a building block for theequilibrium analysis to follow. Even thisrudimentary model is consistent with twofacts that do not come out of frictionlessmodels: it takes time to find an acceptablejob; and what one ends up with is at least partially a matter of luck, which means similar
agents may end up with different wages. In
section 3, we describe some generalizationsof this model designed to help understandturnover and labor market transitions. Thissection also introduces tools and techniques
needed for equilibrium search theory.
We also spend some time here discussing
the logical transition between decision theory and equilibrium theory. We first argue
that one can reinterpret the single-agent
1
Examples in monetary economics include Nobuhiro
Kiyotaki and Randall Wright (1993), Shouyong Shi (1995),
and Alberto Trejos and Wright (1995); examples in themarriage literature include Dale T. Mortensen (1988),
Kenneth Burdett and Melvyn G. Coles (1997, 1999), andRobert Shimer and Lones Smith (2000); examples in IO
include Steven C. Salop (1977), Boyan Jovanovic (1982),
and Jovanovic and Glenn M. MacDonald (1994); examples
in finance include Darrell Duffie, Nicolae Garleanu, andLasse Pedersen (2002) and Pierre-Olivier Weill (2004).
2
Examples of theoretical work studying the question ofwhether frictionless competitive equilibrium is the limit ofsearch equilibrium as the frictions get small include Ariel
Rubinstein and Asher Wolinsky (1985, 1990), Douglas
Gale (1987), and Mortensen and Wright (2002). Theresa J.
Devine and Nicholas M. Kiefer (1991), Kenneth I. Wolpin(1995), and Zvi Eckstein and Gerard J. van den Berg
(forthcoming) survey empirical work.

de05_Article1 11/16/05 3:53 PM Page 961

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
model as an equilibrium of a simple economy. But in such a model several key variables, including the arrival rate anddistribution of wage offers, are essentially
fixed exogenously. For some issues, one may
want to know how these are determined inequilibrium, and in particular how they areaffected by labor market conditions or labormarket policy. There is no single way to proceed, but any approach requires us to confront the two questions mentioned above:
how do workers and firms meet; and how dothey determine wages?
In section 4, we present a class of equilibrium models built on two main ingredients:
the matching function, which determines
how workers and firms get together, and thebargaining solution, which determines
wages once they do. The matching function
helps us in analyzing transitions from unemployment to employment as a function of, ingeneral, the behavior of all the workers andfirms in the market. Bargaining is one of themore popular approaches to wage determination in the literature, and since it is a key
ingredient in many models we take sometime to explain how the generalized Nashsolution works and how to interpret it interms of strategic bargaining theory.
In section 5, we consider an environment
where wages are posted ex ante, rather thanbargained after agents meet, and in addition
where search is directed—i.e., workers do
not encounter firms completely at random
but try to locate those posting attractive
terms of trade. Models with the combinationof wage posting and directed search, called
competitive search models, behave quite differently from those in section 4, although
they can be used to analyze similar issues. In
section 6, we consider models where wages
are posted but search is once again purely
random. This class of models has been widely used in research on wage dispersion andthe distribution of individual employment/
unemployment spells.
In section 7, we discuss efficiency. This isimportant because, to the extent that one

961

wants to analyze policy, one would like toknow whether the models rationalize a rolefor intervention in a decentralized economy.
It is fine to say, for example, that a change insome variable reduces unemployment, but
it is obviously relevant to know whether thisimproves welfare. We derive conditions
under which equilibrium with bargaining isefficient. We also show that the combinationof wage posting and directed search generates efficiency under quite general assumptions, providing a version of the first welfare
theorem for economies with frictions.
Finally, we finish in section 8 with a few
concluding remarks.3
2. Basic Job Search
We begin here with the familiar discretetime formulation of the basic job searchmodel, and then derive its continuous-timeanalogue, which is used for the remainder ofthe paper. We then use the framework to discuss some issues relating to unemployment
duration and wages.
2.1 Discrete Time
Consider an individual searching for a job
in discrete time, taking market conditions asgiven.4 He seeks to maximize E t=0β txt ,3
Earlier surveys of search theory as applied to labormarkets include Steven A. Lippman and John J. McCall(1976a), Mortensen (1986), and Mortensen andChristopher A. Pissarides (1999a, 1999b). While there isnaturally some overlap, there are important differences in
our approach. We build equilibrium models up from thedecision problem, focusing on the role of random versus
directed search and the role of bargaining versus wage
posting. In particular, previous surveys do not examine
directed search models, or explicitly discuss the efficiency
properties of different models, as we do.
4 While it is often said that the economics of searchbegan with George Stigler (1961), his formulation was static. The sequential job search model in this section wasdeveloped first by McCall (1970), Mortensen (1970), andReuben Gronau (1971), although others had analyzed
related problems, including Herbert A. Simon (1955), who
discussed the housing market, and Samuel Karlin (1962),
who discussed asset markets. The presentation in this andthe next section is based on some lecture notes that contain many more details, examples and exercises, and can befound at http://www.ssc.upenn.edu/~rwright/courses/
courses.html.

de05_Article1 11/16/05 3:53 PM Page 962

962

Journal of Economic Literature, Vol. XLIII (December 2005)

where β ∈ (0,1) is the discount factor, x t isincome at t, and E denotes the expectation.
Income is x = w if employed at wage w andx = b if unemployed. Although we refer to w
as the wage, more generally it could capturesome measure of the desirability of the job,
depending on benefits, location, prestige,etc., and although we refer to b > 0 as unemployment insurance (UI), it can also include
the value of leisure or home production.5
We begin with the case where an unemployed individual samples one independently and identically distributed (i.i.d.) offer
each period from a known distribution F(w).
If an offer is rejected, the agent remains
unemployed that period. Assume previously
rejected offers cannot be recalled, although
this is actually not restrictive because theproblem is stationary, so an offer that is not
acceptable today will not be acceptable
tomorrow. For now we assume that if a job isaccepted the worker keeps it forever. Hence,
we have the Bellman equations(1)

W (w) = w + β W (w)(2) U = b + β ∫ max {U , W (w)} dF(w) ,0where W(w) is the payoff from accepting a
wage w (W stands for working) and U is thepayoff from rejecting a wage offer, earning b,
and sampling again next period (U stands for
unemployed).
Since W(w)  w/(1 − β) is strictly increasing, there is a unique wR, called the reservation wage, such that W(wR)  U, with theproperty that the worker should reject5
Our worker is interested in maximizing expected discounted income. This is the same as maximizing expectedutility if he is risk neutral, but also if he is risk averse andconsumption markets are complete, since then he canmaximize utility by first maximizing income and thensmoothing consumption. The case of a risk averse agent
facing incomplete markets is more difficult. Early analyses
include John P. Danforth (1979) and John R. Hall,
Lippman, and McCall (1979); more recent studies include
Victor Valdivia (1996), James Costain (1997), Daron
Acemoglu and Shimer (1999b, 2000), Martin Browning,
Thomas F. Crossley, and Eric Smith (2003), and Rasmus
Lentz and Torben Tranaes (forthcoming).

−R(we adopt thew< wR and accept w ≥1w
max{U , W (w)}dF(w) +U.
convention
that he accepts0
1 + r when indifferent). Substituting U = wR /(1 − β) andW(w) = w/(1 − β) into (2), we have(3)wR = T (wR ) (1 − β )b + β ∫ max {w , wR }dF(w).
0

The function T is easily shown to be a contraction, so there is a unique solution towR = T(wR). This implies that if one fixes w0
and recursively defines wN+1 = T (wN), thesequence converges to wR as N → . If theinitial wage is w0 = b, the worker’s reservation wage in the final period of a finite horizon problem, wN has the interpretation of
being the reservation wage when N periodsof search remain, after which the worker
receives either b or the accepted wage w
forever.
The optimal search strategy is completely
characterized by (3), but we also present
some alternative representations that areoften seen in the literature. First, subtracting β wR from both sides of (3) and simplifying gives the standard reservation wage
equationβ(w − wR )dF(w).
(4) wR = b +∫1 − β wR
Using integration by parts, we can also write
this asβ(5) wR = b +[1 − F(w)]dw ,∫1 − β wR
which, as we shall see, is handy in some of
the applications below.66Note that in the above analysis, as in most of what we
do here, it is assumed that the worker knows F. If he has
to learn about F while searching, the problem gets harderand a reservation strategy may not even be optimal. For
example suppose we know either: (a) w = w0 with prob 1;or (b) w = w1 with prob π and w = w2 with prob 1 − π. If
w2 > w1 > w0 and π is small, it can be optimal to accept w0
but not w1 since an offer of w1 signals that there is a goodchance of getting w2. Michael Rothschild (1974) gives
conditions that guarantee a reservation strategy is optimal.
See Burdett and Tara Vishwanath (1988a) for additional
discussion and references.

de05_Article1 11/16/05 3:53 PM Page 963

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
2.2 Continuous TimeWe now derive continuous-time versionsof the above results. First, generalize thediscrete-time model to allow the length of aperiod to be ∆. Let β = _1_1_r_ and assume
that the worker gets a wage offer with probability ∆ in each period.7 Then the payoffs
to working and unemployment satisfy thefollowing versions of (1) and (2)
(6)

(7)

W (w) = w +U = b +1W (w)
1 + r


1 + r ∫1 − 
U.
× ∫ max{U , W (w)}dF(w) +0
1 + r


Algebra implies(8)rW (w) = (1 + r  ) w(9)rU = (1 + r  ) b+  ∫ max {0 , W (w) − U }dF(w).

that he gets an offer , times the expected
increase in value associated with the offer,
noting that the offer can be rejected.
The reservation wage wR satisfies
W(wR) = U, so equation (10) implies W(w) −U = (w − wR)/r. Substituting this into (11)gives the continuous time reservation wage
equation(12) wR = b +Bellman equations(10) rW (w) = w (w − wR )dF(w).
r ∫ wR

Again one can integrate by parts to get(13) wR = b + [1 − F(w)]dw.
r ∫ wR

Although most of the models that we discuss assume fixed search intensity, it can beendogenized. Suppose a worker can affectthe arrival rate of offers , at cost g(), whereg > 0 and g > 0. Unemployed workers
choose  to maximize rUwR, where (w − wR )dF(w).
r ∫ wR
The first order condition for an interior
solution is(14) wR = b − g() +0When ∆ → 0, we obtain the continuous time

963

(15)



∫ (w − w )dF(w) = rg().
wR

R

Worker behavior is characterized by a pair(wR, ) solving (14) and (15). It easy to showthat an increase in b, e.g., raises wR andreduces .

(11) rU = b +  ∫ max {0 , W (w) − U }dF(w).

2.3 Discussion

Intuitively, while U is the value of being
unemployed, rU is the flow (per period)
value. This equals the sum of the instantaneous payoff b, plus the expected value ofany changes in the value of the worker’s
state, which in this case is the probability

Traditional frictionless models assume thata worker can costlessly and immediately
choose to work for as many hours as he wants
at the market wage. By relaxing these
extreme assumptions, search models allow us
to think about unemployment and wages in adifferent light. Consider unemployment
duration. The probability that the worker has
not found a job after a spell of length t is e−Ht,
where H =  [1 − F(wR)] is called the hazard
rate and equals the product of the contact
rate  and the probability of accepting

07
Alternatively, we may assume that the number of wage
offers per period is a Poisson random variable with mean
. When the time period is short, the probability ofreceiving multiple offers within a single period is negligible.
See Mortensen (1986) for details.

de05_Article1 11/16/05 3:53 PM Page 964

964

Journal of Economic Literature, Vol. XLIII (December 2005)

1 − F(wR).8 The average duration of an
unemployment spell is therefore1(16) D = ∫ tHe− Ht dt = .
0
H
Also, the observed distribution of wages paidis G(w = F(w⏐w ≥ wR).
Consider the impact of an increase in b,
say more generous UI, assuming for simplicity here that search intensity and hence  are
fixed. From (12), the immediate effect is toincrease wR, which has two secondary
effects: the distribution of observed wages
G(w) is higher in the sense of first order stochastic dominance, since more low wage
offers are rejected; and the hazard rate H islower, which increases average unemployment duration. Hence, even this elementarymodel makes predictions about variables
that would be difficult to generate using atheory without frictions.9
3. Worker Turnover
Although the model in the previous section is interesting, there are important issues
that it cannot address. For instance, we
8

Because this simple model is stationary, H does notchange with the duration of unemployment. Several generalizations would overturn this, the simplest being toassume a finite horizon. More interestingly, Burdett (1979)
and Mortensen (1977) allow UI to vary over time.
Lippman and McCall (1976b) and Lippman and John W.
Mamer (1989) allow wage offers to vary over time. Salop(1973) studies systematic search where a worker first looks
for opportunities that are best according to some prior andthen, if unsuccessful, proceeds to other locations, typicallylowering his reservation wage over time. The models discussed earlier in which the worker learns about the wage
distribution also predict wR and hence H vary over time.
Bruce D. Meyer (1990) and Wolpin (1987) are examples ofa large body of empirical work on hazard rates.
9
We can also study changes in F or . As pointed out
by Burdett (1981), for some experiments it is useful toassume F is log-concave. Suppose we increase every w inF either by a constant or proportionally. Perhaps surprisingly, E[w⏐w ≥ wR] may actually decrease, but it can be
guaranteed to increase under log-concavity; seeMortensen (1986) or Wright and Janine Loberg (1987).
Suppose we increase the arrival rate. One might expectthat this must raise the hazard, but since it increases wR,
the net effect is ambiguous. One can show H/ > 0 underlog-concavity; see Christopher J. Flinn and James J.
Heckman (1983), Burdett and Jan Ondrich (1985), or van
den Berg (1994).

assumed above that when a worker accepts a
job he keeps it forever. Yet according to
Bruce Fallick and Charles A. Fleischman(2004), in the United States from 1994 to
2004, 6.6 percent of employment relationships ended in a given month (of these, forty
percent of workers switched employers
while the rest either became unemployed orleft the labor force). We now generalize theframework to capture such transitions.
3.1 Transitions to Unemployment
The simplest way of generating transitions
from employment into unemployment is to
assume that jobs end for some exogenous
reason; sometimes in the literature this isinterpreted by saying that workers face layoff risk. A tractable formulation is to assume
that this occurs according to a Poissonprocess with parameter λ, which for now is
an exogenous constant.10
Introducing exogenous separations does
not affect the Bellman equation for U,
which is still given by (11), but now we haveto generalize (10) to(17) rW (w) = w + λ[U − W (w)].
The reservation wage still satisfies W(wR)U,
and the methods leading to (13) yield[1 − F(w)]dw.
(18) wR = b +∫r + λ wR
Notice that λ affects wR only by changing theeffective discount rate to r + λ . However, aworker now goes through repeated spells of
employment and unemployment: whenunemployed, he gets a job at rate
H =  [1 − F( wR)], and while an employed
he loses the job at rate λ.
A simple way to endogenize transitions tounemployment is to allow w to change at agiven job. Suppose that this happens according to a Poisson process with parameter λ,and that in the event of a wage change a new10

An interesting extension of the basic model is to letvary across jobs, which implies the reservation strategy
generally depends on the pair (w, ); see Burdett andMortensen (1980) or Wright (1987).

de05_Article1 11/16/05 3:53 PM Page 965

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Marketw is drawn from F(w⏐w). When the wagechanges the worker can stay employed at w
or quit to unemployment. The exogenous
layoff model discussed above is a special casewhere w= 0 with probability 1, so that at
rate λ the job effectively disappears. In thismore general model,(19) rW (w) = w + λ ∫ max {W (w)0

− W (w) ,U − W (w)} dF(w | w).
A natural assumption is that F(w⏐w2) firstorder stochastically dominates F(w⏐w1)
whenever w2 > w1. This implies W(w) is
increasing, and there is a reservation wage
wR such that unemployed workers accept ifw ≥ wR and employed workers quit if theirwage falls to w⏐wR. Hence separations are
decreasing in w. In the simplest case whereF(w|w) = F(w) (independence), we have−λ 
(w − wR )dF(w).
r + λ ∫ wR
Notice that λ >  implies wR < b; in this case,workers accept a job paying less than unemployment income and wait for the wage tochange, rather than searching while unemployed. In any case the usual comparative
static results, such as ∂ wR /∂ b > 0, are similar
to what we found earlier.
(20) wR = b +3.2 Job-to-Job Transitions
To explain how workers change employers
without an intervening spell of unemployment, we need to consider on-the-job
search.11 Suppose new offers arrive at rate
0 while unemployed and 1 while
employed. Each offer is an i.i.d. draw fromF. Assume that employed workers also lose
their job exogenously at rate λ. The Bellman
equations are965(22) rW (w) = w + 1 ∫ max {W (w) −0− W (w) ,0} dF(w) + λ[U − W (w)].
The second term in (22) represents theevent that an employed worker gets an offer
above his current wage.
It is easy to see that W is increasing,
implying that unemployed workers use areservation wage satisfying W(wR) = U,
and employed workers switch jobs whenever w> w. Evaluating (22) at w = wR andcombining it with (21), we get(23) wR = b+ (0 − 1 ) ∫ [W (w) − W (wR )]dF(w).
wR

Observe that wR > b if and only if  0 > 1.
Thus, if a worker gets offers more frequently when employed than when unemployed,
he is willing to accept wages below b.
To eliminate W from (23), use integration
by parts and insert W(w) = {r + λ +  1 [1 −F(w)]}−1, which we get by differentiating(22), to yield(24) wR = b+ (0 − 1 ) ∫1 − F ( w)
⎡
⎤
dw.
⎢
wR r + λ +  [1 − F ( w ) ] ⎥
⎣
⎦
1



If 1 = 0, this reduces to the earlier reservation wage equation (13). Many results, like
∂ wR /∂ b > 0, are similar to what we foundabove, but we also have some new predictions. For instance, when wR is higher, workers are less likely to accept a low w, so they
are less likely to experience job-to-job transitions. Thus, an increase in UI reduces
turnover.12(21) rU = b + 0 ∫ [W (w) − U ]dF(w)wR

11
The on-the-job search model was introduced by
Burdett (1978). The presentation here follows Mortensen
and George R. Neumann (1984).

12
As in the basic model, we can endogenize searchintensity here. Let g0() be the cost of achieving  for an
unemployed worker and g1() the cost for an employedworker. If g0 () ≤ g1() for all , unemployed workers
search harder than employed workers. In any case, searchintensity decreases with w for employed workers.

de05_Article1 11/16/05 3:53 PM Page 966

966

Journal of Economic Literature, Vol. XLIII (December 2005)

3.3 Discussion
The model of the last subsection is a natural framework in which to analyze individualtransitions between employment and unemployment, and between employers. It makes
predictions about the relationships between
wages, tenure, and separation rates. For
example, workers typically move up thewage distribution during an employment
spell, so the time since a worker was last
unemployed is positively correlated with his
wage. Also, workers who earn higher wages
are less likely to get better opportunities,
generating a negative correlation between
wages and separation rates. And the fact thata worker has held a job for a long time typically means that he is unlikely to obtain abetter one, generating a negative relationship between job tenure and separation
rates. All of these features are consistent
with the empirical evidence on turnover andwage dynamics summarized in, e.g., Henry
Farber (1999).13
With a slight reinterpretation, the framework can also be used to discuss aggregate
variables. Suppose there are many workers,
each solving a problem like the one discussed above, with the various stochastic
events (like offer arrivals) i.i.d. across workers. Each unemployed worker becomes
employed at rate H =  0[1 − F(wR)] and each
employed worker loses his job at rate λ, so
the aggregate unemployment rate u evolves
according to
13
Other extensions can also deliver similar prediction.
One such class of models is the learning models in
Jovanovic (1979a, 1979b) and Louis L. Wilde (1979). In
these models, workers have to learn about how good they
are at a job, and those with longer tenure have less to learn
and hence are less likely to leave. Another class of models
introduces human capital. Since we do not have space todo justice to this topic, we refer the reader to recent workby Gueorgui Kambourov and Iourii Manovskii (2004,
2005) that studies human capital within a search framework very similar to what is presented here. Other searchbased models with human capital include Acemoglu(1996), Lars Ljungqvist and Thomas J. Sargent (1998),
Adrian M. Masters (1999), Coles and Masters (2000),
Burdett and Smith (2001), and Laing, Theodore Palivos,
and Ping Wang (1995, 2003).

u̇ = λ (1 − u) − 0[1 − F(wR)]u.
Over time, this converges to the steady state(25) u∗ =λ.
λ + 0 [1 − F ( wR )]One can also calculate the cross-sectional
distribution of observed wages for employedworkers, denoted by G(w), given any offer
distribution F(w). For all w ≥ wR, the flow of
workers into employment at a wage nogreater than w is u0[F(w) − F(wR)], equal to
the number of unemployed workers times therate at which they find a job paying between
wR and w. The flow of workers out of thisstate is (1 − u)G(w){λ + 1[1 − F(w)]}, equal
to the number of workers employed at w orless, times the rate at which they leave either
for exogenous reasons or because they get anoffer above w. In steady state, these flows areequal. Using (25) and rearranging, we have(26) G ( w) =λ [ F(w) − F(wR )].
[1 − F(wR )]{λ + 1 [1 − F(w)]}

We can now compute the steady state job-tojob transition rate,(27) 1 ∫ [1 − F(w)]dG(w).
wR

This type of model has been used in a variety of applications. For example, Wright(1986) uses a version with learning to discussmacro aggregates, showing how the combination of search and learning generates considerable persistence in the unemployment rate.
Under the interpretation that the learning
comes from a signal-extraction problem,
where workers see nominal wages and have tolearn the real wage, the model also generates
a Phillips curve relation between inflation andunemployment. Unlike previous signal-extraction models, such as Robert E. Lucas (1972),
unemployment is persistent because search
provides a natural propagation mechanism.
Jovanovic (1987) considers a variation thatallows workers who are not satisfied with

de05_Article1 11/16/05 3:53 PM Page 967

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
their current wage to either search for a better one, or to rest and return to work whenw increases. This model can generate procyclical quits and productivity, along withcountercyclical unemployment, as in thedata. Wright and Loberg (1987) use anothervariation to analyze the impact of changes intaxes on unemployment and wages of workers at different points in the skill distribution. Ljungqvist and Sargent (1998) add
human capital accumulation during employment and deaccumulation during unemployment and study the effects of policy.
Kambourov and Manovskii (2005) use a version of the model to study life-cycle earnings
profiles.
Although these applications all seeminteresting, there is an old critique of theframework—which is that it is partial equilibrium because the distribution F is exogenous (Rothschild 1973). From a logical pointof view, this critique is not compelling, as
there are various ways to embed the model
into an equilibrium context without changing the results. For instance, one can imagine workers looking for wages as fishermen
looking for lakes. Then F is simply the distribution of fish across lakes, which is something we can logically take as fixed withrespect to most policy interventions.
Another approach that involves only asmall change in interpretation is to invoke
the island metaphor often used in searchtheory. Imagine workers searching acrossislands, on each of which there are many
firms with a constant returns to scale technology using only labor. The productivity ofa randomly selected island is distributed
according to F. If the labor market on eachisland is competitive, a worker on an islandwith productivity w is paid w. This triviallymakes the equilibrium wage distribution thesame as the productivity distribution, F. In
fact, this is the Lucas and Edward C.
Prescott (1974) equilibrium search model,
aside from some minor details—e.g., they
allow for decreasing returns to scale, which
complicates the algebra but does not change967

the idea.14
In summary, we think it is silly to criticize
the framework as being partial equilibrium
per se, since it is trivial to recast it as an equilibrium model without changing the essence.
The more pertinent question is, do we missanything of substance with these stories
about lakes and islands? The models that we
present below introduce firms and equilibrium considerations using more economics
and less geography.
4. Random Matching and Bargaining
This section introduces a popular line ofresearch, emanating from Pissarides (1985,
2000), used to study the determinants ofarrival rates, match formation, match dissolution, and wages. We present a sequence ofmodels that emphasize different margins,
including entry, the decision to consummate
matches, and the decision to terminate
matches. Before we begin, there are twoissues that need to be addressed: how doworkers and firms meet, and how are wages
determined. These models assume meetings
are determined through a matching function
and wages through bargaining.
4.1 Matching
Suppose that at some point in time there
are v vacancies posted by firms looking forworkers and u unemployed workers looking
for jobs. Building on ideas in Peter A.
Diamond (1981, 1982a, 1982b), Mortensen(1982a, 1982b), Pissarides (1984, 1985), andelsewhere, assume the flow of contacts
between firms and workers is given by amatching technology m = m(u,v). Assuming
all workers are the same and all firms are thesame, the arrival rates for unemployed workers and employers with vacancies are thengiven by14

We do not discuss the Lucas–Prescott model indetail, since it can be found in standard textbooks (Nancy
Stokey, Lucas, and Prescott 1989, chapter 13; Ljungqvist
and Sargent 2004, chapter 26). Applications include
Jeremy Greenwood, MacDonald, and Guang-Jia Zhang(1996), Joao Gomes, Greenwood, and Sergio Rebelo(2001), Fernando Alvarez and Marcelo Veracierto (1999),
and Kambourov and Manovskii (2004).

de05_Article1 11/16/05 3:53 PM Page 968

968

Journal of Economic Literature, Vol. XLIII (December 2005)

m(u , v)m(u , v)and e =.
uv
It is standard to assume the function m iscontinuous, nonnegative, increasing inboth arguments and concave, withm(u,0) = m(0,v) = 0 for all (u,v). It is also
convenient to assume m displays constantreturns to scale, i.e., m(u,v)  m( u, v).
While alternative assumptions are interesting—e.g., Diamond emphasizes that
increasing returns can generate multiple
equilibria—constant returns is consistent
with much empirical work.15 Also, constantreturns generates a big gain in tractability, as
it implies w and e depend only on the ratio
v/u, referred to as a measure of market tightness. Thus, w is an increasing and e adecreasing function of v/u, and there is acontinuous, decreasing, 1 to 1 relationshipbetween w and e.
The matching technology is meant to represent in a simple, if reduced-form, fashion
the notion that it takes time for workers andfirms to get together. Just as a production
function maps labor and capital into output,
m maps search by workers and firms into
matches. There are papers that model thismore deeply, some of which we discuss
below, but starting with an exogenous
matching function allows us to be agnostic
about the actual mechanics of the process bywhich agents make contact. An advantage isthat this is a flexible way to incorporate features that seem desirable—e.g., more searchby either side of the market yields more
matches—and one can regard the exact
specification as an empirical issue. Thismight make matching a bit of a black box,
but it is a common and useful approach.16(28)  w =15
Early empirical work on matching goes back to
Pissarides (1986) and Olivier J. Blanchard and Diamond(1989); see Barbara Petrongolo and Pissarides (2001) for a
recent survey.
16
An interesting alternative is to assume the number ofmatches depends on both the flows of newly unmatchedworkers and firms and the stocks of existing unemployment and vacancies, as in Coles and Smith (1996, 1998).
See Ricardo Lagos (2000) for another approach.

4.2 Bargaining
Consider the situation of a worker and afirm who have met and have an opportunity
to produce a flow of output y. Suppose that
if the worker gets a wage w, his expected
lifetime utility is W(w) while the firm earns
expected discounted profit J(π), whereπ = y − w. Again W stands for the value ofworking, and now J stands for the value tothe firm of a job that is filled. If they fail toreach agreement, the worker’s payoff falls to
U and the firm’s to V. Again U stands for thevalue of unemployment, and now V stands
for the value to the firm of a vacancy. We willsoon determine U and V endogenously, but
for now take them as given. We are of course
interested in situations where W(w) > U andJ(y − w) > V for some w, so that there issomething to bargain over.
A standard approach is to assume that w isdetermined by the generalized Nash bargaining solution with threat points U and V,(29) w ∈ arg max [W (w) − U ]θ1−θ×× [J(y − w) − V ] ,where ∈(0,1) is the worker’s bargaining
power. The solution to the maximization
problem satisfies(30) θ [J ( y − w) − V ]W(w)= (1 − θ )[W (w) − U ]J(y − w) ,which can be solved for w. Since it is an
important building block in this class ofmodels, and since wage determination is oneof the main themes of this essay, we want todiscuss Nash bargaining carefully.
John Nash (1950) did not actually analyze
the bargaining process, but took as given
four simple axioms and showed that his solution is the unique outcome satisfying theseaxioms.17 The solution, while elegant and17
Nash actually showed that the unique outcome consistent with his axioms has = 1/2. Relaxing his symmetry
axiom, (R-Nash) with any∈(0,1) satisfies the otheraxioms, and this is what is called the generalized Nashsolution. See, e.g., Martin J. Osborne and Rubinstein(1990).

de05_Article1 11/16/05 3:53 PM Page 969

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
practical, is again a black box. However, one
can provide a game-theoretic description of
the bargaining process, along the lines of
Rubinstein (1982), that has a unique subgame perfect equilibrium with the following
property: as the time between counteroffers
in the game becomes small, the equilibriumoutcome converges to the prediction of the
Nash solution for particular choices of thethreat points and bargaining power that
depend on details of the underlying game;see e.g., Osborne and Rubinstein (1990).
For instance, suppose that each agent has agiven probability of proposing an offer (asopposed to responding) in each round of
bargaining; everything else equal, this gamegenerates the same outcome as the Nashsolution in which the bargaining power
equals that probability.
Of course this only pushes θ back one
level—where does that probability comefrom? One position is to say that the natureof bargaining may well differ across industries, countries, and so on, and varying θ is
one way to try and capture this. Also, at leastin simple models, as we vary θ between 0
and 1 we trace out the set of bilaterally efficient and incentive compatible employment
relationships, which would seem to cover thecases of interest. Just as the matching function is not the last word on how people meet,
Nash bargaining is not the last word on wage
determination, but it is a useful approach.
To proceed, suppose as usual that workers
and firms are risk neutral, infinitely lived, anddiscount future payoffs in continuous time atrate r, and that matches end exogenously atrate λ. Then we have(31) rW(w) = w + λ [U − W(w)](32) rJ(π) = π + λ[V − J(π)].
This implies W(w) = J(π ) = r +1λ . Insertingthese into (30) and rearranging gives(33) W(w) = U+ θ [J(y − w) − V − W(w) − U].

969

This says that in terms of total lifetime
expected utility, the worker receives histhreat point U plus a share of the surplus,
denoted S and defined by(34) S = J(y − w) − V + W (w) − U
y − rU − rV,r+λwhere the last equality is derived by using(31) and (32).18
From (31) and (32) we have W(w) − U =_w__w_ and J(π) − V = ____ where w and π
r
r
R
R
are reservation wage and profit levels for theworker and firm. Then (29) reduces to=RR(35) w ∈ arg max [w − wR ]θ [y − w − π R ]1−θ ,which has solution(36) w = wR + θ (y − π R − wR ).
Hence, in this model the Nash solution also
splits the surplus in terms of the current
period utility. Notice that w ≥ wR if and only
if y ≥ yR = πR + wR. Similarly, π = y − w ≥ πR if
and only if y ≥ yR. Hence, workers and firms
agree to consummate relationships if andonly if y ≥ yR.
4.3 Equilibrium
We now combine matching and bargaining in a model where a firm’s decision to posta vacancy is endogenized using a free entry
condition. There is a unit mass of homogeneous workers, and unmatched workers
search costlessly while matched workers
cannot search. We focus here on steadystates, and let u and v represent unemployment and vacancies. The steady-state unemployment rate is u = λ /(λ + w), where w = m(u,v)/u and m is the matching technology. As we discussed above, assuming
constant returns, once we know  w we knowe since both are functions of u/v.
18
Notice that S is independent of the wage. Intuitively,
S corresponds to the joint payoff available in the match,while w simply divides this among the agents.

de05_Article1 11/16/05 3:53 PM Page 970

970

Journal of Economic Literature, Vol. XLIII (December 2005)

They valueof(ypostinga vacancy is− yR )dF).
(37) rV = − k + e [J(π ) − V ],where k is a flow cost (e.g., recruiting costs).
As free entry drives V to 0, we need not keep
track of V, and we can rewrite (37) as(38) e J(π ) = k.
The value of unemployment satisfies(39) rU = b +  w [W (w) − U ],while the equations for W and J are
unchanged from (31) and (32). Formally, anequilibrium includes the value functions(J,W,U), the wage w, and the unemployment
and vacancy rates (u,v), satisfying the
Bellman equations, the bargaining solution,
free entry, and the steady-state condition.19
In terms of solving this model, one
approach would be to try to find the equilibrium wage. Start with some arbitrary w,
solve (32) for J(π), and then use (38) to solvefor e and w. This determines W and U.
This w is an equilibrium if and only if theimplied values for J, W, and U are such thatthe bargaining condition holds. While thisworks, here we bypass w by working directlywith the surplus, which from (34) is(40) (r + λ )S = y − rU .
Now (33) allows us to rewrite (39) as
rU = b + w S, and (40) gives(41) (r + λ +  wθ )S = y − b.
The next step generally in this method is
to obtain expressions that characterize optimal choices for each of the decisions made19
Rather than having entry, one can assume a fixed number of firms and then equilibrium determines V endogenously. Also, although we focus on steady states, dynamics
here are straightforward. The key observation is that thefree entry condition pins down e and therefore w. Hence,
given any initial unemployment rate, vacancies adjust so thatu/v jumps to the steady state level, which implies all othervariables are constant along the path as u and v converge totheir steady state levels. See Mortensen (1989, 1999), e.g.,
for related models with more complicated dynamics.

outside of a match, given S. Here the only
such decision is whether to post a vacancy.
Using (38) and the fact that bargaining
implies J(π) = (1 − θ)S, we have(42) k = e (1 − θ )S.
Equilibrium is completely characterized by(41) and (42). Indeed, we can combine
them asr + λ +  wθ y − b.
=(43)(1 − θ )ek
Under standard regularity conditions, aunique solution for w exists. From this we
can recover the wage,(44) w = y − (r + λ )(1 − θ )S .
Finally, the steady state unemployment ratesatisfies an equation analogous to (25),accounting for the fact that all meetings
result in matches:λu∗ =.
λ + w
A number of results now follow easily. For
example, an increase in b reduces the rate at
which workers contact firms w, raises therate at which firms contact workers e,
reduces S, and raises w. The conclusion thatunemployment duration and wages increase
with UI is similar to what we found earlier,but here the mechanism is different. In the
single-agent model, an increase in b induced
the worker to raise his reservation wage, andto reduce search intensity if it is endogenous. Now an increase in b raises the bargained wage, which discourages job
creation, thereby increasing unemployment
duration.
4.4 Match-Specific Productivity
In the above model, it takes time for workers and firms to get together, but every contact leads to a match and w is the same inevery match. This seems quite special whencompared to what we did in sections 2–3, as
it corresponds to workers sampling from ade05_Article1 11/16/05 3:53 PM Page 971

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
degenerate distribution. Moreover, in applications, changes in the probability that acontact leads to a match may be important.
Here we extend the model so that not every
contact results in a match and not every
match has the same w. The easiest way toproceed is to assume that when a worker andfirm meet they draw match-specific productivity y from a distribution F, where y isobserved by both and constant for the duration of the match. From section 4.2, workers
and firms agree to match if and only if y ≥ yR,
where yR is characterized below.
In equilibrium, workers in a match withproductivity y earn wage w(y) satisfying
the Nash bargaining solution. Let Wy(w)be the value for an employed worker of amatch with productivity y earning w,
Jy(y − w) the value for a firm with a filled
job at productivity y earning profits y − w,
and Sy the surplus in a job with productivity
y. Generalizing (40) gives(45) (r + λ )Sy = y − rU .
Only the Bellman equations for an unemployed worker and the free entry conditionchange appreciably, becoming∞(46) rU = b +  w ∫ {Wy [w(y)] − U }dF(y)yR∞= b +  wθ ∫ Sy dF(y)yR∞(47) k = e ∫ J y [y − w(y)]dF(y)yR∞= e (1 − θ ) ∫ Sy dF(y).
yR

To solve this model, combine (46) and (47)αw k— and substitute into (45):to get rU = b + α—e (1 − ) wθ k.
(48) (r + λ )Sy = y − b −e (1 − θ )In particular, yR satisfies SyR = 0, or(49) yR = b + wθ k.
e (1 − θ )Since Sy is linear in y, this implies
Sy = (y − yR)/(r + λ), so (47) can be written

971(50) (r + λ )k = e (1 − θ ) ∫ y (y − yR )dF(y).
R

We can now solve for yR and w from (49)and (50). The first of these equations
describes an increasing relationship between
 w and yR (when it is easier for a worker tofind a job, he is more willing to turn down apotential match with low productivity). The
second gives a decreasing relationshipbetween yR and w (when yR is higher,
matches are less profitable for firms so they
post fewer vacancies). There exists a uniqueequilibrium under standard conditions. One
can again recover the wage function: sincew(yR) = yR and w(y) = υ if y > yR, we havew(y) = yR + θ(y − yR).
Equilibrium also determines theobserved distribution of productivity acrossexisting relationships, or equivalently, given
w(y), the observed wage distribution G(w).
Since the distribution of match productivity
is F(y) truncated at yR, the equilibrium wage
distribution G(w) is determined by yR, F(y),and w(y).
It is easy to discuss turnover and wages.
For example, an increase in b shifts (49) but
not (50), resulting in an increase in yR, areduction in w, and a reduction in
H =  w[1 − F(yR)]. From a worker’s perspective, this closely resembles the singleagent problem, in the sense that he receives
offers at rate w from a given distribution,and needs to decide which to accept, except
now the arrival rate and distribution are
endogenous.
4.5 Endogenous Separations
Mortensen and Pissarides (1994) endogenize the separation rate by incorporating onthe-job wage changes.20 The resulting
framework captures endogenously both the20This section mimics what we did in the single-agent
problem in section 3. Other extensions discussed there canalso be added, including on-the-job search (Pissarides
1984, 1994), and learning (Michael J. Pries 2004,
Giuseppe Moscarini 2005, and Pries and Richard
Rogerson 2005).

de05_Article1 11/16/05 3:53 PM Page 972

972

Journal of Economic Literature, Vol. XLIII (December 2005)

flows into and out of unemployment. Given
that these flows vary a lot across countries
and over time, it allows one to begin thinking
formally about factors that may account forthese differences. To proceed, let y be current productivity in a match, and assume
that at rate λ we get a new draw fromF(y|y), where F(y|y2) first order stochastically dominates F(y|y1) whenever y2 > y1. It
remains to specify the level of productivity in
new matches. One can assume they start at a
random y, but we assume all new matches
begin with the same y0.
An equilibrium is defined as the naturalextension of the previous model, and we canjump directly to the equation for the surplus(51) (r + λ )Sy = y − rUy+ λ ∫ Sy dF(y | y).
yR

Since rU = b +  w Sy0, this can be rewritten(52) (r + λ )Sy = y − b −  wθ Sy0y+ λ ∫ Sy dF(y | y).
yR

To close the model we again use free entry,(53) k = βe (1 − θ )Sy0 .
Finding equilibrium amounts to solving (53)and (52) for yR and w.
The solution is more complicated here
because we are now looking for a fixed point
in a system of functional equations—(52)defines both yR and Sy as functions of w.
Nevertheless, an increase in w reduces Sy
for all y and hence raises the reservation
wage yR. Thus, (52) describes an increasing
relationship between w and yR. At the sametime, (53) indicates that when w is higher
Sy0 must be higher, so from (52) yR must be
lower, and this defines a decreasing relationship between w and yR. The intersection of these curves gives steady-state
equilibrium, which exists uniquely understandard conditions. See Mortensen and
Pissarides (1994, 1999b) for details of theargument.
4.6 Discussion
There are many applications and extensions of this framework. David Andolfatto(1996), Monika Merz (1995, 1999), Harold
L. Cole and Rogerson (1999), Wouter J. den
Haan, Gary Ramey, and Joel Watson (2000),
Costain and Michael Reiter (2003), Shimer(2005), and Robert E. Hall (2005) all study
versions of the model quantitatively. Thereis a literature that uses versions of themodel to study the behavior of worker andjob flows across countries as well as over thebusiness cycle, including Stephen P. Millard
and Mortensen (1997), Alain Delacroix(2003), Blanchard and Pedro Portugal(2001), and Pries and Rogerson (2005).
There is also a literature that introduces
heterogeneous workers and firms, including
Acemoglu (1999, 2001), James Albrecht andSusan Vroman (2002), Mortensen and
Pissarides (1999c), Shimer (1999), andShimer and Smith (2000). Ricardo J.
Caballero and Mohamad L. Hammour(1994, 1996) and Gadi Barlevy (2002) study
whether recessions are cleansing or sullying
in terms of the distribution of match quality(do they lead to more good jobs or badjobs). Moscarini (2001) also studies thenature of match quality over the businesscycle. We do not have space to do justice toall the work, but this illustrates that it is anactive and productive area.
5. Directed Search and Posting
We now move to models where someagents can post wage offers, and otheragents direct their search to the most
attractive alternatives. Following Espen R.
Moen (1997) and Shimer (1996), the combination of posting and directed search isreferred to as competitive search. Note that
it is the combination of these features thatis important; in section 6 we consider wage

de05_Article1 11/16/05 3:53 PM Page 973

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market

973

posting with random search, which is quite
different.
The literature has proposed several equivalent approaches. One posits a group ofagents called market makers who set up submarkets, with the property that any match
consummated in a submarket must be at theposted wage. Within each submarket there isa constant returns matching function m(u,v),
so that the arrival rates w and e are determined by q = u/v, which is called the queue
length (the inverse of market tightness).
Each unemployed worker and each firmwith a vacancy take as given w and q in every
submarket, and go to the one offering thehighest expected utility. In equilibrium, q ineach submarket is consistent with agents’
expectations and no market maker can post adifferent wage and attract both workers andemployers.21
Another approach supposes that employers themselves post wages, and unemployedworkers direct their search to the most
attractive firms. A high posted w attracts
more applicants, which reduces workers’
contact rate w and raises the employer’s
contact rate e. In equilibrium, workers are
indifferent about where to apply, at least
among posted wages that attract some workers. Firms choose wages to maximize expected profit. Still another approach assumes
that workers post wages, and firms direct
their search to them. As we said, theseapproaches are equivalent, in the sense thatthey give rise to identical equilibrium conditions. For brevity we consider only the casewhere firms post wages.

must pay cost k, and we can either assume
free entry (making v endogenous) or fix thenumber of vacancies. Any match within the
period produces output y, which is divided
between the worker and firm according to
the posted wage. At the end of the period,
unmatched workers get b, while unmatchedvacancies get 0. Then the model ends.
Consider a worker facing a menu of different wages. Let U denote the highest valuethat he can get by applying for a job at somefirm. Then a worker is willing to apply to aparticular job offering a wage w ≥ b only if
he believes the queue length q at that job—i.e., the number of workers who apply—issufficiently small. In fact, he is willing toapply only if w(q) is sufficiently large, in thesense that

5.1 A One-Shot Model(56) V = max − k

We first discuss the basic mechanism in astatic setting. At the beginning of the period,
there are large numbers u and v of unemployed workers and vacancies, and q∗ = u/v isthe queue length. Each firm with a vacancy
21

The idea here is that market makers compete to
attract workers and firms to their submarkets since they
can charge them an entrance fee, but in equilibrium thisfee is 0 due to free entry into market making.

(54) U ≤  w (q)w + [1 −  w (q)]b.
If this inequality is strict, all workers would
want to apply to this firm, reducing the righthand side. Therefore, in equilibrium, if any
workers apply to a particular job, q adjusts tosatisfy (54) with equality.
To an employer, (54) describes how achange in his wage w affects his queue lengthq. Therefore he chooses w to maximize(55) V = max − k + e (q)(y − w) ,w ,qtaking (54) as a constraint. Note that each
employer assumes he cannot affect U,
although this is an endogenous variable to be
determined in equilibrium. Eliminating w
using (54) at equality, and also using
e(q) = qw(q), we getq+ e (q)(y − b) − q(U − b).
The necessary and sufficient first ordercondition is(57) e (q)(y − b) = U − b.
In particular, (57) implies all employers
choose the same q, which in equilibrium
must equal the economywide q∗. Hence (57)de05_Article1 11/16/05 3:53 PM Page 974

974

Journal of Economic Literature, Vol. XLIII (December 2005)

pins down the equilibrium value of U. Then
(54) at equality determines the market wage(58) w∗ = b + ε (q∗ )(y − b),where ε(q∗) ≡ _q∗__ee(_(q∗_q∗)_) is the elasticity of e(q∗),
which is in (0,1) by our assumptions on thematching function m. Comparing (58) withthe results in section 4.2, notice that thiswage rule operates as if the worker and firmbargained over the gains from trade, withthe workers’ share θ given by the elasticity
(q∗); this has important implications for theefficiency of competitive search, as we discuss below.
Substituting (58) into (55) pins down(59) V = − k+ [e(q∗) − q∗e(q∗)](y − b).
If the number of vacancies v is fixed thisgives profit; or we can use free entry V = 0 to
endogenize v and hence q∗. In either case,the model is simple to use. Indeed, thismodel looks a lot like a one-shot version of
the random search and bargaining model.
There is a key difference, however: here thesurplus share is endogenously determined.
5.2 Directed Matching
Before generalizing to a dynamic setting,
we digress to discuss some related literature.
James D. Montgomery (1991) studies a nascent version of the above model (see also
Michael Peters 1984, 1991). He starts with
two unemployed workers and two firms.
First firms post wages, then each worker
applies to one of them (possibly randomly).
A firm receiving at least one application
hires at the posted w; if more than one
applies the firm selects at random.22
Suppose both firms offer the same w > 0.
Then there are three equilibria in the application subgame: worker 1 applies to firm 1
22
By assumption here firms post wages rather thanmore general mechanisms. Coles and Jan Eeckhout (2003)
relax this (e.g., they allow w to be contingent on the number of applicants who turn up) and show it does not affectthe main conclusions.

and worker 2 to firm 2; worker 1 applies tofirm 2 and worker 2 to firm 1; and both
workers use identical mixed strategies,
applying to each firm with probability 1/2.
One can argue that the coordination impliedby the first two equilibria is implausible, atleast in large labor markets, and so themixed-strategy equilibrium is the natural
outcome. This introduces a coordination
friction, as more than one worker may apply
for the same job.
Generalizing this reasoning, suppose
there are u unemployed workers and v
vacancies, for any u and v. If each worker
applies to each firm with equal probability,
any firm gets a worker with probability
1 − (1 − 1_v)u. Taking the limit of this expression as u and v go to infinity with q = u/v
fixed, in a large market a fraction e(q)= 1 − e q of firms get a worker. This is a standard result in statistics. Suppose there are uballs independently placed with equal probability into each of v urns. Then for large u
and v, the number of balls per urn is a
Poisson random variable with mean u/v, so afraction e u/v of the urns do not get any balls.
For this reason, this process is often called
an urn–ball matching function.
Because the urn–ball matching processprovides an explicit microeconomic story of
both meetings (a ball is put in a particularurn) and matches (a ball is chosen from thaturn), it is suitable for environments with heterogeneous workers (not all balls are thesame). For instance, suppose there are u1
type 1 workers and u2 inferior type 2 workers, with u = u1 + u2. Firms hire type 1 workers over type 2 workers when both apply;
hence they hire a type 1 worker with probability 1 − e u /v and a type 2 worker with probability e u /v(1 − e u /v). They hire someworker with probability 1 − e u/v.23
There are several generalizations of thismatching process. Burdett, Shi, and Wright
1

1

2

23
Therefore an increase in the number of undesirable
type 2 workers does not affect the matching rate for type 1
workers, but an increase in the number of desirable workers adversely affects undesirable workers.

de05_Article1 11/16/05 3:53 PM Page 975

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market(2001) let some vacancies hire multiple
workers. Albrecht, Pieter Gautier, andVroman (2003), and Albrecht, Gautier,Serene Tan, and Vroman (2004) let workers
make multiple applications. If workers cansimultaneously apply for every job, thiseffectively flips the urn–ball problem
around, so a worker is employed if at least
one firm offers him a job; see Benoit Julien,
John Kennes, and Ian King (2000). Theintermediate case in which workers canapply for a subset of jobs delivers additional
possibilities. In general, these directed
search models provide a way to get inside
the black box of the matching process.24
5.3 A Dynamic Model
To get something like the basic Pissarides
model with directed search, start with an
unemployed worker. Suppose he anticipates
an unemployment–vacancy ratio q and awage w. Then(60) rU = b +  w (q)[W (w) − U ](61) rW (w) = w + λ[U − W (w)].
It is convenient to combine these into
 (q)(w − rU ).
(62) rU = b + w
r+λSimilarly, for firms(63) rV = − k + e(q)[J(y − w) − V](64) rJ(y − w) = y − w + λ [V − J(y − w)].
Free entry yields

 (q)(y − w).
(65) k = er+λ24
In these models, generally, one has to be somewhat
careful about strategic interaction between firms. In theprevious section, in maximizing (55) subject to (54), thefirm takes as given that a worker’s market payoff is U. But,in general, if a firm changes its wage then U will change.
Burdett, Shi, and Wright (2001) solve the model with finite
numbers of agents, where each firm must compute theeffect of a change in its w on workers’ strategies and on theimplied U. In the limit as u and v grow, they show that the
problem is equivalent to one where each firm treats U
parametrically, as we assumed above.

975

Now suppose firms choose w and q to maximize rV, or equivalently by free entry, to maximize e(q)(y − w). They take (62) as given.
Eliminating w using this constraint and again
using e(q) = qw(q), this reduces to(66) max e (q)qy − rU− q(rU − b).
r+λThe necessary and sufficient first ordercondition,y − rUq)= rU − b ,(67) (er+λhas a unique solution, so all firms choose thesame q. Eliminating U and w from (62), (65),and (67) we get an implicit expression for q,
r + λ + e (q)y−b(68)  (q) − q (q) = k .
eeThis pins down the equilibrium q, or
equivalently the arrival rates w and e.
Under standard conditions the solution is
unique. We can again perform standard
exercises, such as changing b, with similar
results: here this raises the u/v ratio, which
reduces w, raises e, and increases w. But
although the conclusions are similar to thosereached in the previous section, the mechanism is quite different. An increase in b inthis model makes workers more willing toaccept an increase in the risk of unemployment in return for an increase in w. Firms
respond by offering workers what theywant—fewer jobs at higher wages.
5.4 Discussion
Competitive search equilibrium theory
provides arguably a more explicit explanation of the matching process and of wage
determination than the bargaining models in
section 4. Nash bargaining says w divides thesurplus into exogenous shares; here workers
face a trade-off between a higher wage and alower probability of getting a job, while firms
face a trade-off between profit and the probability of hiring. Competition among wage
setters, whether these be firms, workers, orde05_Article1 11/16/05 3:53 PM Page 976

976

Journal of Economic Literature, Vol. XLIII (December 2005)

market makers, leads to a point along theindifference curves of agents trading off
wages and arrival rates.25
However, a potential disadvantage ofthese models—indeed, of any model thatassumes posting—is that it is a strong
assumption to say that agents commit to theposted terms of trade. If the markets is really decentralized, what prevents them fromtrying to bargain for a different w after they
meet? Again, this comes up in any postingmodel. In the context of the wage postingmodel in the next section, Coles (2001)shows explicitly how to prevent firms from
reneging on their posted wage using reputational considerations, but there is more work
to be done on the issue.
In terms of other extensions, Coles andEeckhout (2000), Shi (2001, 2002), andShimer (forthcoming) add heterogeneity,
which introduces wage dispersion among
heterogeneous workers, and among identicalworkers at different firms. Acemoglu andShimer (1999b) allow workers to be riskaverse, which means it is no longer possible
to solve the model explicitly. They show thatan increase in risk aversion reduces wages,
while an increase in b raises it. Building on
this, Acemoglu and Shimer (2000) show that
UI can enhance productivity. Much more
research is currently being done on directed
search models. Again, while we cannot dojustice to all of the work in the area, we wantto say that it appears to have great potential.
6. Random Matching and Posting
We now combine random matching, as insection 4, with posting, as in section 5.26
This class of models has been used extensively in the literature on the pure theory of
25

In section 7, we show that competitive search equilibrium achieves the optimal trade-off between thesefactors.
26
The remaining combination—directed search andbargaining—is not so interesting, at least if firms are homogeneous, since there is nothing for workers to direct theirsearch toward. Lawrence Uren (2004) studies directed
search and bargaining with heterogeneous firms.

wage dispersion, which tries to understand
how workers with identical productivity canbe paid different wages. Note that the models in the previous two sections generate
wage dispersion only if workers are either exante or ex post heterogeneous. A pure theory of wage dispersion is of interest for a couple of reasons. First, the early literaturesuggested that search is relevant only if the
distribution from which you are sampling is
nondegenerate, so theorists were naturally
led to study models of endogenous dispersion. Second, many people see dispersion asa fact of life, and for them the issue isempirical rather than theoretical.
As Mortensen (2003, p. 1) reports,“Although hundreds if not thousands ofempirical studies that estimate so-called
human capital wage equations verify thatworker characteristics that one could view as
indicators of labor productivity are positively
related to wages earned, the theory is woefully incomplete in its explanatory power.
Observable worker characteristics that aresupposed to account for productivity differences typically explain no more that 30 percent of the variation in compensation.”
Eckstein and van den Berg (forthcoming)argue that “equilibrium search models provide a framework to empirically analyze thesources of wage dispersion: (a) workers heterogeneity (observed and unobserved); (b)firm productivity heterogeneity (observed
and unobserved); (c) market frictions. The
equilibrium framework can . . . empiricallymeasure the quantitative importance of eachsource.” 27
Diamond (1971) is an early attempt toconstruct a model of dispersion, andalthough it did not work, it is useful tounderstand why. Consider an economy
where homogeneous workers each face a27
As they report, van den Berg and Geert Ridder(1998) estimate that up to 25 percent of wage variability is
attributable to frictions, in the sense that this is what would
emerge from a posting model that ignored heterogeneity,
while Fabien Postel-Vinay and Jean-Marc Robin (2002)
estimate up to 50 percent.

de05_Article1 11/16/05 3:53 PM Page 977

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
standard search problem. We do not give all
the particulars, since the model is a special
case of what is described in detail below, but
the key is that the offer distribution F is generated by wage-posting firms, each of which
has a constant returns technology with laboras the only input, with productivity y. A firmhires any worker it contacts who is willing toaccept its posted w. Consider an individual
firm. Letting F be the distribution of wages
posted by other firms, he wants to maximize
expected profit taking F as given. An equilibrium is defined as a distribution such thatevery wage posted with positive probability
earns the same profit, and no other wage
earns greater profit.
Diamond provides a rather striking result:
there is a unique equilibrium, and in it all
employers set the same wage, w = b. The
proof is simple. Given any F, since workers
are homogeneous they all choose the same
reservation wage wR. Clearly, no firm posts
w < wR as this would mean it cannot hire,
and no firm posts w > wR as it can hire every
worker it contacts at w = wR. To see why itturns out that w = b, consider an individual
firm when all firms are posting w > b. If it
deviates and offers a wage slightly less thanw, it still hires every worker it meets. Since
this is true for any w > b, we must have w = b
in equilibrium. The model not only fails torationalize wage dispersion, it fails to explain
why workers are searching in the first place!
6.1 Heterogeneous Leisure
Why might one expect to find pure wage
dispersion? One answer is that search frictions produce a natural trade-off for a firm:
while posting higher wages lowers your profit per worker, it could allow you to hire workers faster, and so, in the long run, you get
more of them. In Diamond’s model, thistrade-off is nonexistent, since when you
increase your wage above wR there is no
increase in your hiring rate. Albrecht and Bo
Axell (1984) allow for heterogeneity in workers—not in productivity but in their value of

977

leisure—which leads to heterogeneity inreservation wages and this makes the above
trade-off operational.
Consider two types of workers, some withb = b1 and others with b = b2 > b1. For any
wage distribution F there are two reservation wages, w1 and w2 > w1. If Wi(w) is thevalue of a type i worker who is employed atwage w and Ui is the value of an unemployed type i worker, these wages satisfy
W1(w1) = U1 and W2(w2) = U2. Generalizing
our logic from the Diamond model, no firm
posts a wage other than w1 or w2. It is possible that these two wages could yield equal
profit, however, since low-wage firms canhire only workers with b = b1 while highwage firms can hire everyone they contact.
In the Albrecht–Axell model, equal profits at
two different wages can occur in equilibrium
for a large set of parameters.28
To see how this works, normalize themeasure of firms to 1, and let the measure ofworkers be L = L1 + L2 where Lj is the measure with bj. Let  be the endogenous fraction of firms posting w2. Any candidate
equilibrium wage distribution is completely
summarized by w1, w2, and . Observe firstthat the reservation wage of type 2 workers is
w2 = b2. It is clear that their reservation wage
cannot be any lower, since otherwise theywould prefer to remain unemployed. On theother hand, if their reservation wage exceeds
b2, an argument like the one we used for the
Diamond model ensures that a firm could
reduce w2 and still attract these workers.
To determine w1, note that type 1 workers
accept both w = w1 and w = w2, and so given
the arrival rate w their value functions satisfy(69) rU1b1w(1 )[W1(w1) U1]
w[W1(w2) U1](70) rW1(w1)w1λ[U1 W1(w1)]28
Albrect and Axell do not actually have firms earning
equal profit, but allow y to vary across firms and look for acutoff y∗ such that firms with y > y∗ pay w = w1 and thosewith y > y∗ pay w = w2 ; the economic implications are basically the same.

de05_Article1 11/16/05 3:53 PM Page 978

978

Journal of Economic Literature, Vol. XLIII (December 2005)(71) rW1(w2)w2λ[U1 W1(w2)].
Note that although type 1 workers accept
w1, they get no capital gain from doing so
and suffer no capital loss when laid off,
since W1(w1) = U1. Then using w2 = b2, we
can simplify and solve for w1 in terms of ,(r + λ )b1 +  w b2.
(72) w1 =r + λ +  wUnemployment rates for the two types areλλ——and u2 = α—.
u1 = α—w+ λw + λFor firms, the expected value of contacting a worker is the probability he accepts
times the profit conditional on acceptance.
The acceptance probability is _L_1L_u11u_1_L2__u2 forfirms paying w1 and 1 for firms paying w2,
y w
while discounted profit is __r ___i_ . So expecteddiscounted profits from the two wages are(73) 1 = e

L1 u1y − w1L1 u1 + L2 u2 r + λ(74)  2 = ey − b2,r+λwhere for now we are taking e as given.29
Inserting u1, u2, and w1, after some algebra,
we see that 2 − 1 is proportional to(75) T ( ) = (r + λ +  w ) {(y − b2 ) ×× [ λ L1 + ( w + λ )L2 ] − (y − b1 )λ L1 }− r w L1 (b2 − b1 ).
For an equilibrium, we need(76)  = 0 and T(0) < 0;  = 1
and T(1) > 0; or  ∈(0,1) and T() = 0.
It is easy to show there exists a unique solution to_ (76), and 0 <  < 1 if and only if_y < y < y where29
An alternative to having firms maximize expecteddiscounted profit is to maximize the value of posting avacancy, which is more in line with sections 4 and 5; seeMortensen (2000). We adopt the criterion in the text
because it facilitates comparison with the model in thenext subsection.

(77) y = b2 +_y = y+

λ L1 (b2 − b1 )and( w + λ )L2r w L1 (b2 − b1 ).
(r +  w + λ )( w + λ )L2

When productivity is low all firms pay
w 1 = b 1, when it is high all firms pay
w2  b2, and when it is intermediate there
is wage dispersion. When  ∈(0,1), we cansolve T() = 0 for  and use (72) to solve
for w1 and the distribution of paid wages
explicitly.30
Of course, all of this is for given arrival
rates, and the value of  that solves (76)depends on w. Using the matching function,
we can endogenize(78)  w =m(L1 u1 + L2 u2 ,1),L1 u1 + L2 u2

where L1u1 + L2u2 is the number of unemployed workers and we assume that all firms
are always freely posting a vacancy, so thatv = 1, with the idea being that each one willhire as many workers as it can get. Since u2
depends on , so does w. An equilibrium isa pair (w,) satisfying (76) and (78).31
6.2 On-the-Job Search
In the previous section, firms may pay higher
wages to increase the inflow of workers. Therealso exist models where firms may pay higher
wages to reduce the outflow of workers (e.g.,
Burdett, Lagos, and Wright 2003). In Burdett
and Mortensen (1998), both margins are atwork, and firms that pay higher wages bothincrease the inflow and reduce the outflow of
30
Clearly, we get at most two wages here, but the argument can be generalized to many types of workers(Eckstein and Wolpin 1990).
31
See Damien Gaumont, Martin Schindler, and Wright(forthcoming) for details, and for several other variations
on the general theme of Albrecht–Axell models. They also
discuss a problem with models based on ex ante heterogeneity: Given type 2 workers get no surplus, if there is any
search cost ε > 0, they drop out of the market, leaving only
type 1 workers. Then we are back to Diamond and the distribution collapses (and of course the problem applies withany number of types). Gaumont, Schindler, and Wrightalso discuss models that avoid this problem.

de05_Article1 11/16/05 3:53 PM Page 979

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
workers. We now present this model in detail,which is relatively easy here, because it isbased on on-the-job search, and we can makesubstantial use of results derived in section 3.
The arrival rates are 0 and 1 while
unemployed and employed, and every offer
is a random draw from F(w). For ease ofpresentation, we begin with the case
0 = 1 = , which implies wR = b by (24), andreturn to the general case later. Since all
unemployed workers use a common reservation wage, and clearly no firm posts w < wR,
the unemployed accept all offers and wehave u = λ /(λ + ) as a special case of (25).
Also, the distribution of paid wages is(79) G(w) =λ F(w),λ +  [1 − F(w)]a special case of (26).
If a firm posts w ≥ wR, a worker he contacts accepts if he is currently unemployedor currently employed but at a lower wage,
which occurs with probability u +(1 − u)G(w). The employment relationshipthen yields flow profit y − w until the worker leaves either due to an exogenous separation or a better offer, which occurs at rate
λ +  [1 − F(w)]. Therefore, after simplification, the expected profit from w is(80) (w) =λ (y − w){λ +  [1 − F ( w)]} {r + λ +  [1 − F(w)]}.

Again, equilibrium requires that any posted
wage yields the same profit, which is at least
as large as profit from any other wage.
Clearly no firm posts w < wR = b or w > y. In
fact,_ one can show
_ that the support of F is[b,w] for some w  y, and there are neither
gaps nor mass points on the support.32
32
Suppose there were a mass point at some w.
c Then a
firm posting w
c +ε would be able to hire away any worker it
contacts working from a w
c firm, increasing its revenue discretely with only an ε increase in cost, which means w
c doesnot maximize profit. Suppose there were a gap in F, say
between w
c and w.
t Then a firm postingwt could lower its wage
and reduce cost without reducing its inflow or increasing its
outflow of workers, and again w
t could not maximize profit.

979

We now construct F explicitly. The key
observation is that firms earn equal profits
from all posted wages, including the lowest
w = b: (w) = (b) for all w ∈ [b,⎯w]. Since
F(b) = 0, (b) = λ(yb) / ( + λ)(r +  + λ).
Combining this and (80) gives an equationthat can easily be solved for F(w). In thesimplest case where r ≈ 0, the result is(81) F(w) =y− w⎞
λ + ⎛1−.
⎜ ⎝y − b ⎟⎠

We know the lower bound is b, and theupper bound⎯w can easily be found by solving F(⎯w) = 1. This yields the unique distribution consistent with equal profit for all
wages posted.
In words, the outcome is as follows. All
unemployed workers accept the first offer
they receive, and move up the wage laddereach time a better offer comes along, butalso return to unemployment periodically
due to exogenous layoffs. There is a nondegenerate distribution of wages posted byfirms F given by (81), and of wages earned
by workers G, given by inserting F into (79).
The model is consistent with many observations concerning worker turnover, and also
concerning firms, including, e.g., the factthat high wage firms are bigger. See
Mortensen (2003) for details.
There are many interesting extensions.
First, with 0 ≠ 1 the same methods lead to(82) F(w) =λ + 1 ⎛
y−w ⎞
1−
,
⎜
1 ⎝
y − wR ⎟⎠where now wR is endogenous (with 0 = 1
we knew wR = b). To determine wR, integrate(24) to get( λ + 1 ) b + (0 − 1 ) 1 y.
2
( λ + 1 ) + (0 − 1 ) 12(83) wR =One
can check that in the limit as 1 → 0,_
w = wR, which means there is a single wage,
w = wR = b. This is the Diamond result as a
special case when there is no on-the-job_
search. Also, in the limit as 1 → , w = y andde05_Article1 11/16/05 3:53 PM Page 980

980

Journal of Economic Literature, Vol. XLIII (December 2005)

G(w) = 0 for all w < y; hence all workers earn
w = y. Moreover, as 1 → , clearly u → 0.
Hence, the competitive solution also emerges
as a special case when 0 and 1 get large.
One can let firms be heterogeneous withrespect to y. In equilibrium there is a distribution of wages paid by each type of firm,
and all firms with productivity y2 pay morethan all firms with y1 < y2. Thus, higher productivity firms are more likely to hire andless likely to lose any worker. With heterogeneous firms, van den Berg (2003) shows
there may be multiple equilibria. Perhaps
more significantly, firm heterogeneity isimportant empirically, because with homogeneous firms the equilibrium wage distribution (81) has an increasing density, which
is not in the data. With heterogeneity F canhave a decreasing density. Another very
important extension is to allow firms whose
workers contact rivals to make counteroffers,
as in Postel-Vinay and Robin (2002).
Margaret Stevens (2004) allows firms topost wage–tenure contracts, rather than simply a constant wage. She shows firms have an
incentive to back load wages to reduceturnover. If workers can make an up-front
payment for a job, an optimal contract
extracts an initial fee and then pays w = y. If
firms are homogeneous this contract eliminates all voluntary quits. In equilibrium all
firms demand the same initial fee, and thisleaves unemployed workers indifferent
about accepting the position. Stevens also
shows that if initial payments are impossible,
say because of liquidity constraints, there isan equilibrium where all firms offer a contract that pays the worker 0 for a fixed period and then pays w = y. If firms arehomogeneous, they extract all of the surplus,
there are no job-to-job transitions, and allcontracts are identical.
However Burdett and Coles (2003) showthat Stevens’s results can be overturned if
workers desire smooth consumption. They
allow firms to commit to wage–tenure contracts, but assume workers are risk-averse anddo not have access to financial markets (theymust consume w each period). They provethat all equilibrium wage–tenure contracts aredescribed by a common baseline salary scale,
which is an increasing, continuous relationshipbetween the wage and tenure. Firms offer different contracts in the sense that they start
workers at different point on the scale. Thus,
consumption smoothing reintroduces wage
dispersion, both in the sense that workers get
different wages depending on their tenure,and in the more fundamental sense that firms
offer different contracts.
6.3 Discussion
The two models of wage dispersion we
have presented are based on worker heterogeneity and on-the-job-search, respectively.
Of course, one can integrate them. This isimportant empirically, because although onthe-job-search models (with heterogeneousfirms) do a good job accounting for wages,
they do less well accounting for individual
employment histories, especially the factthat hazard rates tend to decrease with thelength of unemployment spells. Models withworker heterogeneity do better at accounting for this, but less well for wages. An integrated model can potentially account for
both; see Christian Bontemps, Robin, andvan den Berg (1999). Many other extensions
and applications are possible, and this is a
productive area for both theoretical andempirical research.33
7. Efficiency
We now move on to efficiency. Of course,
in an economy with many agents there aremany Pareto optimal allocations. Here wefocus on those that maximize the sum of
agents’ utility, or equivalently, that maximize
33
We mention some related work. Masters (1999) studies a wage-posting model and uses it to analyze changes in
the minimum wage. Delacroix and Shi (forthcoming) consider directed search in an environment similar to
Burdett–Mortensen and show it also gives rise to wage dispersion, although for different reasons. Finally, some people consider as an alternative to random search models
where workers are more likely to meet large firms, as in
Burdett and Vishnawath (1988b).

de05_Article1 11/16/05 3:53 PM Page 981

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
the present discounted value of output netof the disutility of work and search costs.
7.1 A One-Shot Model
Initially, u workers are unmatched. Firms
decide how many vacancies v to post, each atcost k, and then m(u,v) matches form. Let
q = u/v and assume constant returns, som(u,v) = vm(q,1) = v e(q). Each match produces y at an opportunity cost b to each worker. Assume provisionally that wages are
determined by bargaining, w = θ y + (1 − θ)b.
Then the economy ends. Firms post vacancies
until the free entry condition(84) e (q)(1 − θ )(y − b) = k
holds. This is a static version of the basic
Pissarides model.
Now consider a planner who posts vacancies to maximize output, net of workers’
opportunity cost and the cost of postingvacancies. Equivalently, he chooses q = u/v,
knowing that each worker will contact avacancy with probability w(q), to maximize(85) u w (q)(y − b) − vku
= [e (q)(y − b) − k ] .
q
The necessary and sufficient condition for asolution is(86) [e(q) − qe(q)](y − b) = k.
∗

Denote the planner’s solution by q .
The following is immediate from (84)and (86): the planner’s solution and thedecentralized solution coincide if and only if(87) θ ∗ = ε (q∗ ) ,q α e (q )where ε(q∗) = —
α e—
(q ∗—
) was defined in section 5
as the elasticity of e(q). This is the Hosios
condition (Arthur J. Hosios 1990), determining the share of the surplus that must go toworkers for bargaining to be efficient.34
Alternatively, in terms of wages,
equilibrium is efficient if w = w∗ = θ∗y∗∗qα e′ (q)

′
qα w
(q)

Because e(q) = qw(q), we have α e (q) + α w (q) = 1 ;hence the condition can equivalently be stated as firms’
bargaining power 1 − must equal the elasticity of w(q).
34981+ (1 − θ ∗)b. If
is too high, for example,
then w > w∗ and v is too low.
Now consider the competitive searchmodel from section 5. From (58), in competitive search equilibrium w = w∗, andequilibrium is necessarily efficient. That is,
the Hosios condition holds endogenously—
although agents do not bargain, the surplus
is still being split, and the equilibrium split
implies efficiency. To understand why, it isuseful to think in terms of competition
between market makers, as discussed above.
With free entry, market makers effectively
maximize workers’ expected utility,w(q)(w − b), recognizing that firms must
break even to participate, e(q)(y − w) = k.
Using the constraint to eliminate w, this is
identical to the planner’s problem.
Now consider extending the model toendogenize workers’ search _intensity. The_
total number of matches is m(s u,v), where s
is average intensity. Assuming constantreturns,a _ firm hires with probability_e(s q) = m(s q,1), while a worker with searchintensitys gets__ _hired with probabilitysw(s q) = s e(s q) / s q. An unemployed worker chooses s to maximize(88) b − g(s) +se (sq)θ (y − b).
sq

In equilibrium
all workers choose the same_s = s , where(89) g(s ) =e (sq)θ (y − b),sq

and free entry by firms implies(90) k = e (sq)(1 − θ )(y − b).
The planner solves(91) max b − g(s ) +q, se (sq)(y − b) − ku,qwhich has necessary and sufficient conditions(92) g(s ) = e (sq)(y − b)(93) k[e(s–q) –s qe(s–q)](y b).

de05_Article1 11/16/05 3:53 PM Page 982

982

Journal of Economic Literature, Vol. XLIII (December 2005)

Notice something interesting: (89) and (92)_coincide if the Hosios condition θ = ε (s q)holds, while (90) and (93) coincide under thesame condition. That is, bargaining equilibrium achieves efficient search intensity andentry under the Hosios condition. This
seems genuinely surprising,_as there are twovariables to be determined, s and v, and only
one parameter, υ.
Since we have already shown that in competitive search equilibrium we get the
Hosios condition endogenously, competitive
search equilibrium achieves efficient searchintensity and entry. As suggested above,
market makers effectively choose the termsof trade to ensure that both workers andfirms behave optimally. There is nothing
special about endogenous entry decisions or
search intensity. We could consider various
other extensions (e.g., match-specific productivity with the reservation match value yR
determined endogenously), and we wouldfind the same result: bargaining equilibriumis efficient if and only if the Hosios condition
holds, and competitive search equilibrium
generates this condition endogenously.
Rather than go through these exercises wenow move to dynamics.
7.2 A Dynamic Model
Here we formulate the planner’s problem
for the benchmark Pissarides model recursively. The state variable is the measure ofmatched workers, or the employment rate, e.
The current payoff is y for each of the eemployed workers, b for each of the 1 − eunemployed workers, and − k for each of thev = (1 = e)/q vacancies. The employment rate
follows a law of motion ė = α__eq_(q_) (1 − e) − λ e.
Putting this together, the planner’s problem is(94) rY(e) = max ye + b(1 − e)q−k(1 − e)⎡  (q)(1 − e)⎤
− λ e⎥ .
+ Y(e) ⎢ eqq⎣⎦

One can show that Y(e) is affine; i.e.,
Y(e) = a0 + a1e for some constants a0 and a1,

where a0 can be interpreted as the value ofan unemployed worker and a1 the surplus
from a match.35
The first order condition from (94) simplifies to(95) k = a1 [e (q) − qe (q)] .
Using the fact that Y(e) = a0 + a1e and theenvelope theorem, we can differentiate bothsides of (94) to getk⎡  (q)⎤(96) ra1 = y − b + − a1 ⎢ e + λ ⎥ .
q⎣ q⎦
Combining (95) and (96) to eliminate a1, wearrive atr + λ + e (q) y − b
=
.
(97)
k
e (q) − qe (q)This completely characterizes the optimal
policy q = q(e); notice that in fact q does notdepend on the state e, only on exogenous
parameters.
How does this compare with equilibrium?
Recall that equilibrium in section 4.3 satisfies (43). It is easy to see that the solutions
are the same, and hence bargaining equilibrium coincides with the planner’s solution, if
and only if = ε(q). Now looking at (68)from the competitive search version of themodel, we see that competitive search equilibrium is necessarily efficient. Hence theresults from the static model generalize
directly, and again carry over to more general models with endogenous search intensity,
match-specific productivity, and so on.
7.3 Discussion
We have demonstrated in several contexts
that competitive search is efficient, whilebargaining is efficient if and only if the
Hosios condition holds. Although theseresults are in some sense general, it would be
35
The mapping defined by (94) is a contraction andtakes affine functions into affine functions. Since the set ofsuch functions is closed, the result follows immediately.
This method also works and is especially useful when there
is a distribution of productivity across matches.

de05_Article1 11/16/05 3:53 PM Page 983

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
misleading to suggest that we can get efficient equilibria in all search models. A general understanding of the nature ofefficiency in these models is still being developed. Mortensen and Wright (2002) provide
some results, but only for constant returns
matching functions; without this, equilibria
are unlikely to be efficient. Shimer andSmith (2001) show that in some models withheterogeneity, even with constant returns,
the efficient outcome may not even be compatible with a steady state, but exhibits
cycles.
The efficiency of search equilibria with exante investments is an interesting topic. For
example, in Acemoglu (1996) and Masters(1998), agents decide on how much capitalto acquire prior to searching. Genericallythere is no θ that makes the equilibrium outcome under bargaining efficient—the valueof θ that provides the right incentive forinvestment in human capital by workers isdifferent from the value of that provides theright incentive for firms (whether firms
choose the number of vacancies, the types ofjobs to create, or physical capital). However,Acemoglu and Shimer (1999a) show competitive search equilibrium with ex ante
investments is efficient. Another case where
there is no θ such that bargaining yields theefficient outcome is discussed by Smith(1999), who assumes firms have concave
production functions and hire a large number of workers, but bargain with each one
individually.
One can also ask about the efficiency of thewage-posting models in section 6. In general,
if firms commit to pay the same w no matterthe circumstances, it is unlikely to yield efficient outcomes. In Albrecht and Axell (1984),
e.g., a planner would want all meetings toresult in matches, which does not happen. In
the simplest Burdett and Mortensen (1998)
model, with 0 = 1, efficiency does result
because all meetings involving unemployedworkers result in matches and other meetings are irrelevant from the planner’s perspective. In extended versions, however,983

there is no reason to necessarily expect efficiency (Mortensen 2000). In general, there ismuch more work to be done on this topic.
8. Conclusion
In contrast to standard supply-anddemand models, search theory emphasizes
frictions inherent in the exchange process.
Although there is no one canonical searchmodel, and versions differ in terms of wage
determination, the matching process, andother assumptions, we have tried to showthat there is a common framework underlying all of the specifications. We have usedthe different models to discuss several
issues, mainly related to worker turnover
and wages. We have also used them to discuss some simple policy experiments, suchan increase in UI. Different models emphasize different margins along which such policies work, including the choice ofreservation wage, search intensity, entry, andso on.
The approach, as we have seen, is consistent with many interesting observations. Fora start it predicts the unemployment rate is
not zero, which is perhaps a low hurdle but
not one that can be met by many alternative
theories. The reason the model predicts thisis obvious, but also obviously correct—ittakes time for workers to find jobs. It also
takes time for firms to fill vacancies, and anice property of these models is that there
can be coexistence of unemployed workers
and unfilled vacancies. The framework canbe used to organize thinking about individualtransitions between unemployment andemployment, as well as job-to-job transitions.
Different search-based models can beused to help explain the relationships
between tenure, wages, and turnover,including versions that incorporate on-thejob search, learning, or human capital.
Several models can be used to discuss the
distribution of wages, and some of the models are consistent with observations such as
the fact that high wage firms tend to havede05_Article1 11/16/05 3:53 PM Page 984

984

Journal of Economic Literature, Vol. XLIII (December 2005)

more workers, or high productivity firms
tend to pay more. We also discussed the welfare properties of the models. Bargaining
models achieve efficiency if and only if thebargaining weights satisfy a condition related
to the matching technology, while in competitive search models, this condition
emerges endogenously.
We have only scratched the surface, but
hopefully we have conveyed the main ideas.
The goal was never to claim that search theorists fully understand all of the issues, andindeed there are many interesting directions
for future research. One involves further
quantifying the models, using both micro
and aggregate data. On a more conceptual
front, the models we have presented do notoffer a cogent theory of the firm, and do not
distinguish between worker and job flows.
The welfare results are incomplete. Finally,
we have emphasized the importance of bothwage determination and the matching function. What is the right model of wages? What
are the mechanics that determine matching?
Perhaps this survey will stimulate additional
research on these important questions.
REFERENCES
Acemoglu, Daron. 1996. “A Microfoundation for Social
Increasing Returns in Human Capital Accumulation.”
Quarterly Journal of Economics, 111(3): 779–804.
Acemoglu, Daron. 1999. “Changes in Unemployment
and Wage Inequality: An Alternative Theory andSome Evidence.” American Economic Review, 89(5):1259–78.
Acemoglu, Daron. 2001. “Good Jobs Versus Bad Jobs.”
Journal of Labor Economics, 19(1): 1–21.
Acemoglu, Daron, and Robert Shimer. 1999a.
“Holdups and Efficiency with Search Frictions.”
International Economic Review, 40(4): 827–49.
Acemoglu, Daron, and Robert Shimer. 1999b.
“Efficient Unemployment Insurance.” Journal of
Political Economy, 107(5): 893–928.
Acemoglu, Daron, and Robert Shimer. 2000.
“Productivity Gains from Unemployment Insurance.”
European Economic Review, 44(7): 1195–1224.
Albrecht, James W., and Bo Axell. 1984. “An
Equilibrium Model of Search Unemployment.”
Journal of Political Economy, 92(5): 824–40.
Albrecht, James W., and Susan B. Vroman. 2002.
“A Matching Model with Endogenous Skill
Requirements.” International Economic Review,
43(1): 283–305.
Albrecht, James W., Pieter A. Gautier, and Susan B.

Vroman. 2003. “Matching with Multiple
Applications.” Economics Letters, 78(1): 67–70.
Albrecht, James W., Pieter A. Gautier, Serene Tan, andSusan B. Vroman. 2004. “Matching with Multiple
Applications Revisited.” Economics Letters, 84(3):311–14.
Alvarez, Fernando, and Marcelo Veracierto. 2000.
“Labor-Market Policies in an Equilibrium Search
Model,” in NBER Macroeconomics Annual 1999,
Volume 14. Ben S. Bernanke and Julio J. Rotemberg,
eds. Cambridge and London: MIT Press, 265–304.
Andolfatto, David. 1996. “Business Cycles and LaborMarket Search.” American Economic Review, 86(1):
112–32.
Barlevy, Gadi. 2002. “The Sullying Effect ofRecessions.” Review of Economic Studies, 69(1):65–96.
van den Berg, Gerard J. 1994. “The Effects of Changesof the Job Offer Arrival Rate on the Duration of
Unemployment.” Journal of Labor Economics, 12(3):478–98.
van den Berg, Gerard J. 2003. “Multiple Equilibria andMinimum Wages in Labor Markets with
Informational Frictions and Heterogeneous
Production Technologies.” International Economic
Review, 44(4): 1337–57.
van den Berg, Gerard J., and Geert Ridder. 1998. “AnEmpirical Equilibrium Search Model of the Labor
Market.” Econometrica, 66(5): 1183–1221.
Blanchard, Olivier, and Peter Diamond. 1989. “TheBeveridge Curve.” Brookings Papers on Economic
Activity, 1: 1–60.
Blanchard, Olivier, and Pedro Portugal. 2001. “WhatHides Behind an Unemployment Rate: Comparing
Portuguese and U.S. Labor Markets.” American
Economic Review, 91(1): 187–207.
Bontemps, Christian, Jean-Marc Robin, and Gerard J.
van den Berg. 1999. “An Empirical Equilibrium Job
Search Model with Search on the Job andHeterogeneous Workers and Firms.” International
Economic Review, 40(4): 1039–74.
Browning, Martin, Thomas Crossley, and Eric Smith.
1999. “Asset Accumulation and Short Term
Employment.” University of Essex. Mimeo.
Burdett, Kenneth. 1978. “A Theory of Employee Job
Search and Quit Rates.” American Economic
Review, 68(1): 212–20.
Burdett, Kenneth. 1979. “Unemployment Insurance
Payments as a Search Subsidy: A Theoretical
Analysis.” Economic Inquiry, 17(3): 333–43.
Burdett, Kenneth. 1981. “A Useful Restriction on theOffer Distribution in Job Search Models,” in Gunnar
Eliasson, Bertil Holmlund, and Frank P. Stafford, eds.
Studies in Labor Market Behavior: Sweden and theUnited States. Stockholm: IUI Conference Report.
Burdett, Kenneth, and Melvyn G. Coles. 1997.
“Marriage and Class.” Quarterly Journal of
Economics, 112(1): 141–68.
Burdett, Kenneth, and Melvyn G. Coles. 1999. “LongTerm Partnership Formation: Marriage and Employment.” Economic Journal, 109(456): F307–34.
Burdett, Kenneth, and Melvyn G. Coles. 2003.
“Equilibrium Wage–Tenure Contracts.” Econometrica, 71(5): 1377–1404.

de05_Article1 11/16/05 3:53 PM Page 985

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
Burdett, Kenneth, Ryoichi Imai, and Randall Wright.
2004. “Unstable Relationships.” Frontiers ofMacroeconomics, 1(1): Article 1.
Burdett, Kenneth, Ricardo Lagos, and Randall Wright.
2003. “Crime, Inequality, and Unemployment.”
American Economic Review, 93(5): 1764–77.
Burdett, Kenneth, Ricardo Lagos, and Randall Wright.
2004. “An On-the-Job Search Model of Crime,
Inequality, and Unemployment.” International
Economic Review, 45(3): 681–706.
Burdett, Kenneth, and Dale T. Mortensen. 1980.
“Search, Layoffs, and Labor Market Equilibrium.”
Journal of Political Economy, 88(4): 652–72.
Burdett, Kenneth, and Dale T. Mortensen. 1998. “Wage
Differentials, Employer Size, and Unemployment.”
International Economic Review, 39(2): 257–73.
Burdett, Kenneth, and Jan I. Ondrich. 1985. “How
Changes in Labor Demand Affect Unemployed
Workers.” Journal of Labor Economics, 3(1): 1–10.
Burdett, Kenneth, Shouyong Shi, and Randall Wright.
2001. “Pricing and Matching with Frictions.” Journalof Political Economy, 109(5): 1060–85.
Burdett, Ken, and Eric Smith. 2001. “The Low Skill
Trap.” European Economic Review, 46(8): 1439–51.
Burdett, Kenneth, and Tara Vishwanath. 1988a.
“Declining Reservation Wages and Learning.”
Review of Economic Studies, 55(4): 655–65.
Burdett, Kenneth, and Tara Vishwanath. 1988b.
“Balanced Matching and Labor Market Equilibrium.”
Journal of Political Economy, 96(5): 1048–65.
Caballero, Ricardo J., and Mohamad L. Hammour.
1994. “The Cleansing Effect of Recessions.”
American Economic Review, 84(5): 1350–68.
Caballero, Ricardo J., and Mohamad L. Hammour.
1996. “On the Timing and Efficiency of Creative
Destruction.” Quarterly Journal of Economics,
111(3): 805–52.
Cole, Harold L., and Richard Rogerson. 1999. “Can the
Mortensen–Pissarides Matching Model Match theBusiness-Cycle Facts?” International Economic
Review, 40(4): 933–59.
Coles, Melvyn G. 2001. “Equilibrium Wage
Dispersion, Firm Size, and Growth.” Review of
Economic Dynamics, 4(1): 159–87.
Coles, Melvyn G., and Jan Eeckhout. 2000.
“Heterogeneity as a Coordination Device.” Mimeo.
Coles, Melvyn G., and Jan Eeckhout. 2003.
“Indeterminacy and Directed Search.” Journal of
Economic Theory, 111(2): 265–76.
Coles, Melvyn G., and Adrian Masters. 2000.
“Retraining and Long-Term Unemployment in a
Model of Unlearning by Not Doing.” European
Economic Review, 44(9): 1801–22.
Coles, Melvyn G., and Eric Smith. 1996. “Cross-Section
Estimation of the Matching Function: Evidence fromEngland and Wales.” Economica, 63(252): 589–97.
Coles, Melvyn G, and Eric Smith. 1998. “Marketplaces
and Matching.” International Economic Review,
39(1): 239–54.
Costain, James. 1997. “Unemployment Insurance in a
General Equilibrium Model of Job Search andPrecautionary Savings.” University of Chicago Ph.D.
Dissertation.
Costain, James, and Michael Reiter. 2003. “Business

985

Cycles, Unemployment Insurance, and theCalibration of Matching Models.” Universidad
Carlos III. Mimeo.
Danforth, John P. 1979. “On the Role of Consumption
and Decreasing Absolute Risk Aversion in the
Theory of Job Search,” in Studies in the Economics of
Search. S. Lippman and J. McCall, eds. Amsterdam:
North Holland, 109–31.
Delacroix, Alain. 1999. “Firing Costs, Minimum Wageand the Outside Option Principle.” Purdue
University. Mimeo.
Delacroix,
Alain.
2003.
“Transitions
into
Unemployment and the Nature of Firing Costs.”
Review of Economic Dynamics, 6(3): 651–71.
Delacroix, Alain, and Shouyong Shi. Forthcoming.
“Directed Search on the Job and the Wage Ladder.”International Economic Review.
den Haan, Wouter J., Garey Ramey, and Joel Watson.
2000. “Job Destruction and Propagation of Shocks.”
American Economic Review, 90(3): 482–98.
Devine, Theresa J., and Nicholas M. Kiefer. 1991.
Empirical Labor Economics: The Search Approach.
Oxford: Oxford University Press.
Diamond, Peter A. 1971. “A Model of Price
Adjustment.” Journal of Economic Theory, 3(2):156–68.
Diamond, Peter A. 1981. “Mobility Costs, Frictional
Unemployment, and Efficiency.” Journal of Political
Economy, 89(4): 798–812.
Diamond, Peter A. 1982a. “Aggregate Demand
Management in Search Equilibrium.” Journal of
Political Economy, 90(5): 881–94.
Diamond, Peter A. 1982b. “Wage Determination andEfficiency in Search Equilibrium.” Review of
Economic Studies, 49(2): 217–27.
Duffie, Darrell, Nicolae Garleanu, and Lasse Heje
Pedersen. 2002. “Securities Lending, Shorting, andPricing.” Journal of Financial Economics, 66(2–3):
307–39.
Eckstein, Zvi, and Gerard van den Berg. Forthcoming.
“Empirical Labor Search: A Survey.” Journal of
Econometrics.
Eckstein, Zvi, and Kenneth I. Wolpin. 1990. “Estimatinga Market Equilibrium Search Model from Panel Dataon Individuals.” Econometrica, 58(4): 783–808.
Fallick, Bruce, and Charles A. Fleischman. 2004.
“Employer-to-Employer Flows in the U.S. Labor
Market: The Complete Picture of Gross Worker
Flows.” Federal Reserve Board of Governors
Working Paper 2004-34.
Farber, Henry. 1999. “Mobility and Stability: The
Dynamics of Job Change in Labor Markets,” in The
Handbook of Labor Economics. O. Ashenfelter and
D. Cards, eds. Amsterdam: Elsevier, 2439–83.
Flinn, Christopher J., and James J. Heckman. 1983.
“Are Unemployment and out of the Labor Force
Behaviorally Distinct Labor Force States?” Journalof Labor Economics, 1(1): 28–42.
Gale, Douglas M. 1987. “Limit Theorems for Markets
with Sequential Bargaining.” Journal of Economic
Theory, 43(1): 20–54.
Gaumont, Damien, Martin Schindler, and Randall
Wright. Forthcoming. “Alternative Models of Wage
Dispersion,” in Structural Models of Wage andde05_Article1 11/16/05 3:53 PM Page 986

986

Journal of Economic Literature, Vol. XLIII (December 2005)

Employment Dynamics. Henning Bunzel, Bent J.
Christensen, George R. Neumann, and Jan-Marc
Robin, eds. Amsterdam: Elsevier.
Gomes, Joao, Jeremy Greenwood, and Sergio Rebelo.
2001. “Equilibrium Unemployment.” Journal of
Monetary Economics, 48(1): 109–52.
Greenwood, Jeremy, Glenn M. MacDonald, andGuang Jia Zhang. 1996. “The Cyclical Behavior of
Job Creation and Job Destruction: A Sectoral
Model.” Economic Theory, 7(1): 95–112.
Gronau, Reuben. 1971. “Information and Frictional
Unemployment.” American Economic Review,61(3): 290–301.
Hall, Robert E. 2005. “Employment Fluctuations with
Equilibrium Wage Stickiness.” American Economic
Review, 95(1): 50–65.
Hall, John R., Steven A. Lippman, and John J. McCall.
1979. “Expected Utility Maximizing Job Search,” inStudies in the Economics of Search. S. Lippman and
J. McCall, eds. Amsterdam: North-Holland, 133–56.
Hosios, Arthur J. 1990. “On the Efficiency of Matching
and Related Models of Search and Unemployment.”
Review of Economic Studies, 57(2): 279–98.
Howitt, Peter. 1988. “Business Cycles with Costly
Search and Recruiting.” Quarterly Journal of
Economics, 103(1): 147–65.
Howitt, Peter, and R. Preston McAfee. 1987. “Costly
Search and Recruiting.” International Economic
Review, 28(1): 89–107.
Jovanovic, Boyan. 1979a. “Job Matching and theTheory of Turnover.” Journal of Political Economy,
87(5): 972–90.
Jovanovic, Boyan. 1979b. “Firm-Specific Capital andTurnover.” Journal of Political Economy, 87(6):1246–60.
Jovanovic, Boyan. 1982. “Selection and the Evolutionof Industry.” Econometrica, 50(3): 649–70.
Jovanovic, Boyan. 1987. “Work, Rest, and Search:
Unemployment, Turnover, and the Cycle.” Journal ofLabor Economics, 5(2): 131–48.
Jovanovic, Boyan, and Glenn M. MacDonald. 1994.
“Competitive Diffusion.” Journal of Political
Economy, 102(1): 24–52.
Julien, Benoit, John Kennes, and Ian King. 2000.
“Bidding for Labor.” Review of Economic Dynamics,
3(4): 619–49.
Kambourov, Gueorgui, and Iourii Manovskii. 2004.
“Occupational Mobility and Wage Inequality.” PIER
Working Paper 04-026.
Kambourov, Gueorgui, and Iourii Manovskii. 2005.
“Accounting for the Changing Life-Cycle Profile ofEarnings.” University of Pennsylvania. Mimeo.
Karlin, Samuel. 1962. “Stochastic Models and Optimal
Policy for Selling an Asset,” in Studies in Applied
Probability and Management Science. K. J. Arrow, S.
Karlin, and H. Scarf, eds. Stanford: Stanford
University Press, 148–58.
Kiyotaki, Nobuhiro, and Randall Wright. 1993. “A
Search-Theoretic Approach to Monetary Economics.” American Economic Review, 83(1): 63–77.
Lagos, Ricardo. 2000. “An Alternative Approach to
Search Frictions.” Journal of Political Economy,
108(5): 851–73.
Laing, Derek, Theodore Palivos, and Ping Wang. 1995.

“Learning, Matching and Growth.” Review of
Economic Studies, 62(1): 115–29.
Laing, Derek, Theodore Palivos, and Ping Wang. 2003.
“The Economics of ‘New Blood.’” Journal of
Economic Theory, 112(1): 106–56.
Lentz, Rasmus, and Torben Tranaes. Forthcoming.
“Job Search and Savings: Wealth Effects andDuration Dependence.” Journal of Labor
Economics.
Lippman, Steven A., and John J. McCall. 1976a. “TheEconomics of Job Search: A Survey.” Economic
Inquiry, 14(2): 155–89, 347–68.
Lippman, Steven A., and John J. McCall. 1976b. “Job
Search in a Dynamic Economy.” Journal of
Economic Theory, 12(3): 365–90.
Lippman, Steven A., and John W. Mamer. 1989. “A
Simple Search Model with Procyclical Quits.” Journalof Economic Dynamics and Control, 13(2): 247–53.
Ljungqvist, Lars, and Thomas J. Sargent. 1998. “TheEuropean Unemployment Dilemma.” Journal of
Political Economy, 106(3): 514–50.
Ljungqvist, Lars, and Thomas J. Sargent. 2004.
Recursive Macroeconomics Theory. Cambridge:
MIT Press.
Lucas, Robert E., Jr. 1972. “Expectations and the
Neutrality of Money.” Journal of Economic Theory,
4(2): 103–24.
Lucas, Robert E., Jr., and Edward C. Prescott. 1974.
“Equilibrium Search and Unemployment.” Journalof Economic Theory, 7(2): 188–209.
Masters, Adrian M. 1998. “Efficiency of Investment in
Human and Physical Capital in a Model of Bilateral
Search and Bargaining.” International Economic
Review, 39(2): 477–94.
Masters, Adrian M. 1999. “Wage Posting in Two-Sided
Search and the Minimum Wage.” International
Economic Review, 40(4): 809–26.
McCall, John J. 1970. “Economics of Information and
Job Search.” Quarterly Journal of Economics, 84(1):
113–26.
Merz, Monika. 1995. “Search in the Labor Market andthe Real Business Cycle.” Journal of Monetary
Economics, 36(2): 269–300.
Merz, Monika. 1999. “Heterogeneous Job-Matches
and the Cyclical Behavior of Labor Turnover.”
Journal of Monetary Economics, 43(1): 91–124.
Meyer, Bruce D. 1990. “Unemployment Insurance andUnemployment Spells.” Econometrica, 58(4): 757–82.
Millard, Stephen P., and Dale T. Mortensen. 1997.
“The Unemployment and Welfare Effects of LabourMarket Policy: A Comparison of the USA and theUK,” in Unemployment Policy: Government
Opposition for the Labour Market. D. J. Snower and
G. de la Dehesa, eds. New York: Cambridge
University Press, 545–72.
Moen, Espen R. 1997. “Competitive Search
Equilibrium.” Journal of Political Economy, 105(2):385–411.
Montgomery, James D. 1991. “Equilibrium Wage
Dispersion and Interindustry Wage Differentials.”
Quarterly Journal of Economics, 106(1): 163–79.
Mortensen, Dale T. 1970. “A Theory of Wage and
Employment Dynamics,” in Microeconomic
Foundations of Employment and Inflation Theory.

de05_Article1 11/16/05 3:53 PM Page 987

Rogerson, Shimer, and Wright: Search-Theoretic Models of the Labor Market
E. S. Phelps et al., eds. New York: W. W. Norton,
124–66.
Mortensen, Dale T. 1977. “Unemployment Insurance
and Job Search Decisions.” Industrial and Labor
Relations Review, 30(4): 505–17.
Mortensen, Dale T. 1982a. “The Matching Process as a
Noncooperative Bargaining Game,” in The
Economics of Information and Uncertainty. John J.
McCall, ed. Chicago: University of Chicago Press,
233–54.
Mortensen, Dale T. 1982b. “Property Rights andEfficiency in Mating, Racing, and Related Games.”
American Economic Review, 72(5): 968–79.
Mortensen, Dale T. 1986. “Job Search and Labor
Market Analysis,” in Handbook of Labor Economics.
O. Ashenfelter and R. Layard, eds. Amsterdam:
North Holland, 849–920.
Mortensen, Dale T. 1988. “Matching: Finding a
Partner for Life or Otherwise.” American Journal of
Sociology, 94(Supplement): S215–40.
Mortensen, Dale T. 1989. “The Persistence andIndeterminancy of Unemployment in Search
Equilibrium.” Scandinavian Journal of Economics,
91(2): 347–70.
Mortensen, Dale T. 1999. “Equilibrium Unemployment Dynamics.” International Economic Review,
40(4): 889–914.
Mortensen, Dale T. 2000. “Equilibrium Unemployment with Wage Posting: Burdett–Mortensen Meets
Pissarides,” in Panel Data and Structural Labor
Market Models. H. Bunzel, B. J. Christianesen, N.
M. Keifer, and D. T. Mortensen, eds. Amsterdam:
Elsevier, 281–92.
Mortensen, Dale T. 2003. Wage Dispersion. Cambridge: MIT Press.
Mortensen, Dale T., and George R. Neumann. 1984.
“Choice or Chance? A Structural Interpretation ofIndividual Labor Market Histories,” in Studies inLabor Market Dynamics. G. R. Neumann and W.
Westergaard-Neilsen, eds. Heidelberg: SpringerVerlag, 98–131.
Mortensen, Dale T., and Christopher A. Pissarides.
1994. “Job Creation and Job Destruction in the
Theory of Unemployment.” Review of Economic
Studies, 61(3): 397–415.
Mortensen, Dale T., and Christopher A. Pissarides.
1999a. “New Developments in Models of Search in
the Labor Market,” in Handbook of Labor
Economics. O. Ashenfelter and D. Card, eds.
Amsterdam: North Holland, 2567–2627.
Mortensen, Dale T., and Christopher A. Pissarides.
1999b. “Job Reallocation, Employment Fluctuations,and Unemployment Differences,” in Handbook of
Macroeconomics. M. Woodford and J. Taylor, eds.
Amsterdam: North Holland, 1171–1228.
Mortensen, Dale T., and Christopher A. Pissarides.
1999c. “Unemployment Responses to ‘Skill-Biased’
Technology Shocks: The Role of Labour Market
Policy.” Economic Journal, 109(455): 242–65.
Mortensen, Dale T., and Randall Wright. 2002.
“Competitive Pricing and Efficiency in Search
Equilibrium.” International Economic Review,
43(1): 1–20.
Moscarini, Giuseppe. 2001. “Excess Worker

987

Reallocation.” Review of Economic Studies, 68(3):593–612.
Moscarini, Giuseppe. 2005. “Job Matching and theWage Distribution.” Econometrica, 73(2): 481–516.
Nash, John. 1950. “The Bargaining Problem.”Econometrica, 18(1): 155–62.
Osborne, Martin J., and Ariel Rubinstein. 1990.
Bargaining and Markets. London: Academic Press.
Peters, Michael. 1984. “Bertrand Equilibrium with
Capacity Constraints and Restricted Mobility.”
Econometrica, 52(5): 1117–27.
Peters, Michael. 1991. “Ex Ante Price Offers in
Matching Games Non-Steady States.” Econometrica,
59(5): 1425–54.
Petrongolo, Barbara, and Christopher A. Pissarides.
2001. “Looking into the Black Box: A Survey of the
Matching Function.” Journal of Economic
Literature, 39(2): 390–431.
Pissarides, Christopher A. 1984. “Search Intensity, Job
Advertising, and Efficiency.” Journal of Labor
Economics, 2(1): 128–43.
Pissarides, Christopher A. 1985. “Short-Run
Equilibrium Dynamics of Unemployment Vacancies,
and Real Wages.” American Economic Review, 75(4):676–90.
Pissarides, Christopher A. 1986. “Unemployment and
Vacancies in Britain.” Economic Policy, 3(3): 499–559.
Pissarides,
Christopher
A.
1994.
“SearchUnemployment with On-the-Job Search.” Review of
Economic Studies, 61(3): 457–75.
Pissarides, Christopher A. 2000. Equilibrium
Unemployment Theory. Cambridge: MIT Press.
Postel-Vinay, Fabien, and Jean-Marc Robin. 2002.
“The Distribution of Earnings in an Equilibrium
Search Model with State-Dependent Offers andCounteroffers.” International Economic Review,
43(4): 989–1016.
Postel-Vinay, Fabien, and Jean-Marc Robin. 2002.
“Equilibrium Wage Dispersion with Worker and
Employer Heterogeneity.” Econometrica, 70(6):2295–2350.
Pries, Michael J. 2004. “Persistence of Employment
Fluctuations: A Model of Recurring Job Loss.”
Review of Economic Studies, 71(1): 193–215.
Pries, Michael J., and Richard Rogerson. 2005. “Hiring
Policies, Labor Market Institutions and Labor
Market Flows.” Journal of Political Economy, 113(4):811–39.
Robin, Jean-Marc, and Sebastien Roux. 1998.
“Equilibrium Search with Decreasing Returns to
Scale and Hiring Costs: Theory and Estimation.”
Mimeo.
Rothschild, Michael. 1973. “Models of Market
Organization with Imperfect Information: A Survey.”
Journal of Political Economy, 81(6): 1283–1308.
Rothschild, Michael. 1974. “Searching for the Lowest
Price When the Distribution of Prices Is Unknown.”
Journal of Political Economy, 82(4): 689–711.
Rubinstein, Ariel. 1982. “Perfect Equilibrium in a
Bargaining Model.” Econometrica, 50(1): 97–109.
Rubinstein, Ariel, and Asher Wolinsky. 1985.
“Equilibrium in a Market with Sequential
Bargaining.” Econometrica, 53(5): 1133–50.
Rubinstein, Ariel, and Asher Wolinsky. 1990.

de05_Article1 11/16/05 3:53 PM Page 988

988

Journal of Economic Literature, Vol. XLIII (December 2005)“Decentralized Trading, Strategic Behaviour and theWalrasian Outcome.” Review of Economic Studies,57(1): 63–78.
Salop, Steven C. 1973. “Wage Differentials in a
Dynamic Theory of the Firm.” Journal of Economic
Theory, 6(4): 321–44.
Salop, Steven C. 1977. “The Noisy Monopolist:
Imperfect Information, Price Dispersion and Price
Discrimination.” Review of Economic Studies, 44(3):393–406.
Shi, Shouyong. 1995. “Money and Prices: A Model of
Search and Bargaining.” Journal of Economic
Theory, 67(2): 467–96.
Shi, Shouyong. 2001. “Frictional Assignment: I:
Efficiency.” Journal of Economic Theory, 98(2):232–60.
Shi, Shouyong. 2002. “A Directed Search Model of
Inequality with Heterogeneous Skills and SkillBased Technology.” Review of Economic Studies,69(2): 467–91.
Shimer, Robert. 1996. “Contracts in Frictional Labor
Markets.” MIT. Mimeo.
Shimer, Robert. 1999. “Job Auctions.” Princeton
University. Mimeo.
Shimer, Robert. 2005. “The Cyclical Behavior of
Equilibrium Unemployment and Vacancies.”
American Economic Review, 95(1): 25–49.
Shimer, Robert. Forthcoming. “The Assignment ofWorkers to Jobs in an Economy with Coordination
Frictions.” Journal of Political Economy.
Shimer, Robert, and Lones Smith. 2000. “Assortative
Matching and Search.” Econometrica, 68(2): 343–69.
Shimer, Robert, and Lones Smith. 2001.
“Nonstationary Search.” Princeton University.
Mimeo.
Simon, Herbert A. 1955. “A Behavioral Model ofRational Choice.” Quarterly Journal of Economics,
69(1): 99–118.
Smith, Eric. 1999. “Search, Concave Production, andOptimal Firm Size.” Review of Economic Dynamics,

2(2): 456–71.
Stevens, Margaret. 2004. “Wage–Tenure Contracts in a
Frictional Labour Market: Firms’ Strategies for
Recruitment and Retention.” Review of Economic
Studies, 71(2): 535–51.
Stigler, George. 1961. “The Economics ofInformation.” Journal of Political Economy, 69(3):213–25.
Stokey, Nancy, Robert E. Lucas Jr., and Edward
Prescott. 1989. Recursive Methods in Economic
Dynamics. Cambridge: Harvard University Press.
Trejos, Alberto, and Randall Wright. 1995. “Search,
Bargaining, Money, and Prices.” Journal of Political
Economy, 103(1): 118–41.
Uren, Lawrence. 2004. “The Allocation of Labor andEndogenous Search Decisions.” Mimeo.
Valdivia, Victor. 1995. “Evaluating the Welfare Benefitsof Unemployment Insurance.” Mimeo.
Weill, Pierre-Olivier. 2003. “Leaning Against theWind.” Stanford University. Mimeo.
Wilde, Louis L. 1979. “An Information-Theoretic
Approach to Job Quits,” in Studies in the Economics
of Search. S. A. Lippman and J. J. McCall, eds.
Amsterdam: North Holland, 35–52.
Wolpin, Kenneth I. 1987. “Estimating a Structural
Search Model: The Transition from School to Work.”
Econometrica, 55(4): 801–17.
Wolpin, Kenneth I. 1995. Empirical Methods for the
Study of Labor Force Dynamics. Luxembourg:
Harwood Academic Publishers.
Wright, Randall D. 1986. “Job Search and Cyclical
Unemployment.” Journal of Political Economy,
94(1): 38–55.
Wright, Randall D. 1987. “Search, Layoffs, andReservation Wages.” Journal of Labor Economics,
5(3): 354–65.
Wright, Randall D., and Janine Loberg. 1987.
“Unemployment
Insurance,
Taxes,
andUnemployment.” Canadian Journal of Economics,
20(1): 36–54.