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On-the-Job Search and the Cyclical
Dynamics of the Labor Market

WP 10-12

Michael U. Krause
Deutsche Bundesbank
Thomas A. Lubik
Federal Reserve Bank of Richmond

This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/

On-the-Job Search and the Cyclical Dynamics of the Labor
Market∗
Michael U. Krause
Economic Research Center
Deutsche Bundesbank†

Thomas A. Lubik
Research Department
Federal Reserve Bank of Richmond‡
June 2010

Federal Reserve Bank of Richmond Working Paper No. 10-12

Abstract
We develop a business cycle model with search and matching frictions in the labor
market and show that on-the-job search generates substantial amplification and propagation. Rising search by employed workers in an expansion amplifies the incentives of
firms to post vacancies. By keeping job creation costs low for firms, on-the-job search
amplifies exogenous shocks. In our calibration, this allows the model to generate fluctuations of unemployment, vacancies, and job-to-job transitions whose magnitudes are close
to the data, and leads output to be highly autocorrelated. On-the-job search implies
higher-order serial correlation that is absent from the standard search and matching
model.

JEL CLASSIFICATION:
KEYWORDS:

E24, E32, J64
Search and matching, job-to-job mobility, worker flows,
Beveridge curve, business cycle, propagation.

∗
We are grateful to Sam Henly for expert research assistance. The views expressed in this paper are not
necessarily those of the Federal Reserve Bank of Richmond, the Federal Reserve System or the Deutsche
Bundesbank.
†
Wilhelm-Epstein-Str. 14, D-60431 Frankfurt, Germany. Tel.: +49(0)69 9566-2382. Fax: +49(0)69
9566-3082. Email: michael.u.krause@bundesbank.de
‡
701 East Byrd Street, Richmond, VA 23261. Tel.: +1 804 697-8246. Email: thomas.lubik@rich.frb.org

Introduction

Job-to-job transitions are an important component of labor market dynamics and have
attracted renewed attention in the literature. The movements of workers from one job to the
next without an intermittent unemployment spell can be interpreted as the outcome of onthe-job search of the employed. From the perspective of a search and matching model of the
labor market, this has the attractive feature that it expands the set of potential job seekers
from which firms can draw. In the standard model, it is only the unemployed who search,
while in a framework with on-the-job search they are complemented by already employed
workers. In an economic upturn, rising search activity by employed workers expands the
pool of potential hires for firms, in addition to those searching from unemployment.
We show in this paper that introducing on-the-job search into an otherwise standard
search and matching model aﬀects labor market dynamics in a quantitatively significant
manner. The empirical background for our study is the observation by Hall (2005), Shimer
(2005) and Costain and Reiter (2008) that the search and matching model along the lines of
Mortensen and Pissarides (1994) has diﬃculty explaining the cyclical dynamics of the labor
market. Specifically, the standard framework underpredicts the volatility of vacancies and
unemployment. The mechanism at the root of this shortcoming is that workers’ bargained
share in the returns to job creation depends strongly on labor market tightness, which rises
quickly with falling unemployment in an expansion. We argue that on-the-job search oﬀers
a resolution to this issue because it keeps labor market tightness more stable and thus the
bargaining position of workers low. Thus incentives for firms to post vacancies remain high.1
To develop this argument, we present a general equilibrium business cycle model with
labor market frictions and search by employed and unemployed workers. On-the-job search
is motivated in a straightforward manner by the presence of two types of jobs, which diﬀer
in terms of profitability and thus the returns to working. Workers in low-wage (‘bad’) jobs
search in order to gain employment in high-wage (‘good’) jobs. Good job vacancies can be
matched with employed and unemployed job seekers, whereas firms in the bad job sector
only hire unemployed workers. Wages are determined by Nash bargaining for each matched
job-worker unit and are continuously renegotiated. We calibrate the model to match salient
long-run features of job and worker flows.
Our model can match the observed volatility of the vacancy-unemployment ratio. At the
1

Both Hall (2005) and Shimer (2005) explore real wage rigidity as a solution to this shortcoming. When
wages do not adjust to rising returns in an expansion, firms’ incentives to create new jobs are kept high.
Hagedorn and Manovskii (2008), Fujita and Ramey (2005), and Rotemberg (2006), among others, explore
alternative mechanisms.

same time, the ratio of vacancies to unemployed and employed job seekers is substantially
less volatile. It is the latter that is the determinant of wage dynamics as both firms and
workers take into account that the presence of an expanded set of job seekers, namely the
employed, aﬀects the probability of workers finding a job and firms finding a worker. In
other words, the value of a filled vacancy, and thus the willingness to post more, is higher
the more potential workers there are. This view of the expanded pool of potential hires is
related to the results in Andolfatto (1996). He calibrates the model to an employment rate
of 57%, so that the pool of job searchers is an enormous 43%. The standard calibration in
the literature is usually around a tenth of this number. Andolfatto finds that his model can
match the labor market volatilities remarkably well. In our framework, the counterpart to
this large pool of searchers are employed workers engaging in on-the-job search. The key
insight we oﬀer in this paper is that, irrespective of the exact calibration of the relevant
pools, labor-market participation decisions, be they of employed job seekers or of marginally
attached workers, is crucial for understanding labor market dynamics.
We also show that our framework delivers a strong internal propagation mechanism.
Employed workers’ search activity responds strongly to a positive aggregate shock in order
to take advantage of the increased availability of good employment opportunities. Job-tojob flows increase substantially. But as search on the job rises, and wage and hiring cost
increases are muted, the incentive to create vacancies remains high. The corresponding fall
in unemployment is large. This is achieved even though productivity shocks are of plausible
magnitude and wages are, a priori, fully flexible. Through the channel of replacement
hiring, as workers in bad jobs leave for good jobs, small aggregate impulses engender large
and long-lasting responses of output and employment. We show that this propagation is
intricately linked with the mechanism that keeps job creation high.
Our paper is closely related to recent work that has introduced on-the-job search in
dynamic stochastic general equilibrium models of the business cycle. Tasci (2007) develops a
model where on-the-job search is motivated by uncertainty about the quality of an employerworker match. Workers in low-quality match are motivated to search in order to improve
their joint productivity and thus their wage. In expansions, job-to-job transitions are rising
since there is a larger pool of workers that desire to move on and are also more likely
to be contacted by firms. His model thus delivers the same degree of amplification and
propagation as our benchmark, albeit with a diﬀerent mechanism. We therefore regard
Tasci’s work as highly complementary to ours.
Van Zandweghe (2010) studies the eﬀect of on-the-job search on inflation dynamics in

a two-sector labor market model similar to ours. He finds that the propagation mechanism
engendered by on-the-job search amplifies the output response to monetary policy shocks,
but reduces the variability of the inflation response. His paper uses a diﬀerent timing
assumption for when new matches become productive. Interestingly, the persistence and
volatility pattern in a model with on-the-job search is strongly aﬀected by this, which would
not be the case for the simple search and matching model.
Finally, Krause and Lubik (2006) compare the a simple two-sector model of the labor
market with the standard search and matching model and find that they deliver essentially
identical aggregate dynamics. This pattern is broken by the introduction of on-the-job
search in a similar manner as in this paper. The implication is that on-the-job search
facilitates the creation of high-quality jobs in a cyclical upswing. There is also a substantial
labor literature on on-the-job search that mostly focuses on steady state behavior. We
discuss the relationship of this research to ours in Section 7.
The paper proceeds as follows. The next section gives a brief discussion of the relevant
evidence on the dynamic behavior of the labor market, in particular the quit rate. Section 3
lays out the model and characterizes the steady state. Section 4 gives the calibration details.
The results of the dynamic simulation of the model are presented in section 5. Section 6
contains further discussion of the role of search intensity. We also assess the robustness of
our benchmark model by introducing varying search intensity of the unemployed. Section
7 relates the findings to the literature, while section 8 concludes.

The Empirical Background

This section documents the cyclical behavior of key indicators of labor market activity
in search and matching models, specifically vacancies, unemployment, and labor market
tightness for the U.S. labor market and their relation to productivity, output, employment,
and real wages. While we use labor market data from 1950 until 2009, some series cover
only a shorter period. For instance, the time series on average hourly earnings which we use
as our measure of the real wage (deflated by the CPI) is only available from 1964 on. All
series are available from the website of the U.S. Bureau of Labor Statistics (www.bls.gov),
except the series on quits, which has been compiled from the Employment and Earnings
publication of the BLS. This series, however, is only available up to 1982, when it was
discontinued. For the period from the first quarter of 2001 on we use the quit rate reported
in the Job Openings and Labour Turnover Survey (JOLTS) from the BLS. Vacancies are
constructed from the index of help-wanted advertisements in the 50 largest metropolitan
4

areas, which is compiled by the Conference Board. All variables are quarterly and, where
appropriate, detrended using the HP-filter, with the smoothing parameter set to 1600.
The dynamics of vacancies and unemployment follow a familiar pattern. Figure 1 shows
vacancies that are highly procyclical whereas unemployment is strongly countercyclical;
that is, the two variables exhibit a Beveridge curve with a contemporaneous correlation
of −0.89. This pattern implies that a measure of labor market tightness, the vacancy-

unemployment ratio, is also highly procyclical. Table 1 presents the standard deviations
and cross-correlations of the variables of interest. Real wages are procyclical, the degree
of which depends on the time period considered.2 Particularly the 1970s feature a highly
procyclical real wage, while from the 1980s on it appears almost acyclical. In fact, for
the full sample, the correlation between output and real wages is 0.40, whereas from 1982
onward it is merely 0.19. For consistency with the theoretical model, we take output per
worker as a measure of labor productivity, which has a correlation with output of 0.63.
One of the central variables for the argument considered in this paper is the rate of
job-to-job mobility and quits, which are the outcome of on-the-job search activity. A long
time series on worker mobility and quits is contained in the BLS labor turnover series for the
manufacturing sector from 1926 to 1981, which we use from 1950 on. We follow Blanchard
and Diamond (1990) by making two adjustments based on more recent numbers. First,
quit rates in manufacturing tend to be lower than in the entire economy and therefore need
to be adjusted upwards. We use Fallick and Fleischman’s (2004) results based on the CPS
data. They find an economy-wide average monthly quit rate of 2.6%. Some caution may
be mandated since the data cover only one upswing and one mild downturn. A long-run
average which includes a severe contraction might yield somewhat lower rates. Secondly, not
all quits are job-to-job flows. Fallick and Fleischman (2004) suggest that job-to-job quits
are about half of total quits, while Blanchard and Diamond (1990) postulate 40 percent.
The standard deviation of the adjusted quit series can be found Table 1, based on the
sample up to the end of 1982. It is worth noting that the quit rate is ten times as volatile as
GDP and about 50 percent more volatile than unemployment.3 The correlation of the quit
rate with output is a very high 0.88. Figure 2 shows that the quit rate appears to comove
with the vacancy index, especially between about 1955 and 1975. In fact, the detrended
series of vacancies and the quit rate for the whole period have a correlation of 0.94. Figure
2 also depicts the quit rate available from JOLTS for completeness. The correlation pattern
of the JOLTS-based series is virtually identical to the labor turnover series, but it is much
2
3

These results are not reported, but are available from the authors.
See Petrongolo and Pissarides (2001) for evidence on the relative magnitudes of diﬀerent quit flows.

less volatile. The standard deviation of the JOLTS variable is only 4.96 vs. 10.06. Sample
size may be an issue here, but the discrepancy may also reflect the influence of the Great
Moderation in aggregate volatilities from the mid-1980s. An analysis of the changing pattern
of these statistics over the full sample period is, however, beyond the scope of this paper.

A Business Cycle Model with On-the-Job Search

Time is discrete and infinite, and the economy is populated by a representative household,
homogeneous workers and heterogeneous firms. There are two types of firms, labeled ‘good’
and ‘bad’, which diﬀer in their costs of creating new jobs. In the presence of labor market
frictions, these costs generate rents which give rise to diﬀerences across jobs in the value
of being employed.4 These diﬀerentials motivate workers in low-wage jobs to search for
employment in high-wage jobs. All workers in low-wage jobs search on the job with varying
intensity that is determined endogenously. Unemployed workers direct their search to either
good jobs or bad jobs, according to the respective returns to search. Workers in good jobs
have no incentive to search as it is costly and does not oﬀer any improvements over their
current returns to employment. We first characterize labor and product markets, and the
aggregate household problem. We then discuss the optimal choices by firms and workers in
this environment.

3.1

The Labor Market

The process of matching workers and firms is subject to frictions, represented by a matching
function, which determines the number of per period matches of job searchers and vacancies.
The matching function has constant returns to scale and is homogeneous of degree one. We
assume that the functional form of the matching function is the same for both job types
and searchers.5 For good jobs, the total number of new matches between vacancies and
searching workers each period is given by:
mgt = m(vtg , ugt + et ),

(1)

where vtg is the measure of good job vacancies, ugt the measure of unemployed workers
searching for good jobs, and et = st nbt is the measure of eﬃciency units of search by
employed job seekers nbt , who search with intensity st .
4
In this respect, the model is similar to Pissarides (1994) and Acemoglu (2001). The key elements of the
model are the heterogeneity of jobs and the endogeneity of search intensity by employed workers.
5
This assumption is based on empirical reasoning, e.g., Blanchard and Diamond (1990). However, these
estimates typically ignore the presence of job-to-job flows. For a thorough discussion of the potential biases
see Petrongolo and Pissarides (2001).

Unemployed job seekers are assumed to search with fixed search intensity (equal to
one)6 . For bad jobs, the number of matches between vacancies and unemployed workers is:
mbt = m(vtb , ubt ).

(2)

Note that unemployed workers search in distinct pools for jobs. They have to decide to
which type of job they devote their search eﬀort. Worker mobility implies that the returns
to search for either job type are equalized.
Define θgt = vtg /(ugt + et ) and θbt = vtb /ubt as measures of labor market tightness in the
matching markets for good jobs and bad jobs, respectively. Vacancies are filled with the
¡
¢
corresponding probabilities qtg ≡ mgt /vtg = m (1, 1/θgt ) and qtb ≡ mbt /vtb = m 1, 1/θbt . For

searching workers, the probabilities of finding a good or bad vacancy are given by pgt ≡
¡
¢
mgt /(ugt + et ) = m (θgt , 1) and pbt ≡ mbt /ubt = m θbt , 1 . An employed worker’s probability
of being matched with a good job is st pgt with pgt taken as given by the worker. Note that

employed job seekers and unemployed job seekers cause congestion for each other in the
market for good jobs.7 We will show below that this feature is the main driver of the
business cycle dynamics in the model.
The evolution of employment in good and bad jobs is governed by the equations:
ngt+1 = (1 − ρ)[ngt + mgt ],

nbt+1 = (1 − ρ)[nbt + mbt − pgt st nbt ],

(3)
(4)

where ρ is the exogenous separation rate for new hires and existing employment relationships. It is identical for both types of jobs.8 The separation rate comprises both job destruction events and separations of workers for reasons other than quits to another employer. The
last term in the second equation can also be expressed as pgt st nbt = et /(ugt + et )mgt , which is
the fraction of new good matches that go to employed searchers. Aggregate unemployment
equals ut = ugt + ubt = 1 − ngt − nbt = 1 − nt .

In order to determine wages, we assume that a worker and a firm split the joint surplus

that their match generates in fixed proportions. The surplus of job type i is given by
Sti = Jti − Vti + Wti − Uti , where Jti is the value of a filled job for firms, Vti is the value of a

vacancy, Wti is the return of working to a worker, and Uti is the value of unemployment. The
6

This assumption will be relaxed below. We show that this has no substantive implications for the results.
This observation is consistent with empirical evidence, see, for example, Burgess (1995), but also the
discussion in Petrongolo and Pissarides (2001). In Pissarides’ (1994) model with on-the-job search, workers
cannot direct their search and are randomly matched across good and bad vacancies.
8
Allowing for diﬀering job destruction rates for good jobs would not change the basic mechanism of the
model.
7

wage is such that workers obtain a share Wti − Uti = ηSti , with bargaining weight 0 < η < 1.
Firms receive the remainder Jti = (1 − η)Sti . Wages are determined by taking the search

intensity of workers as given, while search intensity itself is chosen by workers taking as
given the current wage. Contracts are renegotiated each period.

3.2

Firms and Product Markets

The cost of creating a job is represented by a flow cost of posting a vacancy, cg for good
firms, and cb for bad firms, where cg > cb . Production of a (representative) firm of type
i = g, b is given by the constant returns to scale technologies:
yit = At nit ,

(5)

where At is aggregate productivity and nit is employment in sector i. Output of good and
bad firms is combined in a final goods sector according to the aggregator function:
α 1−α
ygt .
yt = ybt

(6)

The two intermediate goods, ygt and ybt , are sold at competitively determined prices, Pgt =
(1−α) (ygt /yt )−1 and Pbt = α (ybt /yt )−1 . The price of aggregate output serves as numeraire.
In the model, both types of jobs coexist in equilibrium.9

3.3

The Aggregate Household

We use a representative household to construct the discount factor that governs intertemporal decisions of workers and firms. We follow Merz (1995) in assuming that workers are
members of a large family which pools income and then redistributes it equally to all members. The family ensures that all workers, employed and unemployed, participate in the
labor market. Thus, the optimization problem of a representative household is:
E0
max
∞

{ct }t=0

∞
X
t=0

βt

c1−τ
−1
t
,
1−τ

(7)

subject to the aggregate resource constraint:
ct = yt − ht ,
9

(8)

A similar product market structure is used by Acemoglu (2001). It can be interpreted as representing
either diﬀerences across industries or diﬀerences across firms within industries. Evidence by Parent (2000),
among others, indicates that a large fraction of job-to-job transitions are within industries. This is suggestive
of intra-industry diﬀerences of jobs motivating worker mobility. Additional evidence comes from Albaek and
Sorensen (1998), who find that flows of workers in upturns typically are from small firms to large firms.

where 0 < β < 1 is the household’s discount factor, and τ > 0 is the inverse of the
intertemporal elasticity of substitution. ct is consumption, yt is aggregate production and
ht = cg vtg + cb vtb are the aggregate hiring (or job creation) costs incurred by firms. From
the household’s problem we can construct the implied stochastic discount factor β t+1 =
−τ
βc−τ
t+1 /ct , which firms and workers use to evaluate their activities.

3.4

Job Creation, Search Intensity, and Wages

The optimal choices by firms and workers are governed by asset values. The asset values of
the two types of jobs filled with a worker are given by the Bellman equations:
£
g
g ¤
+ ρVt+1
,
Jtg = Pgt At − wtg + Et β t+1 (1 − ρ)Jt+1

h
i
b
b
.
+ (ρ + (1 − ρ)pgt st )Vt+1
Jtb = Pbt At − wtb + Et β t+1 (1 − ρ)(1 − pgt st )Jt+1

(9)

(10)

wti , i = g, b are the wages paid, Et is the expectation operator conditional on the information
set at time t. Jobs survive into the next period at the rate (1 − ρ), and are destroyed

otherwise. Bad jobs face the additional risk of workers leaving to good jobs. A higher search
intensity by an employed worker reduces the likelihood (1 − pgt st ) of the job remaining filled
in the next period.

The value Vti of a vacancy for either good or bad jobs, i = g, b, is:
£
¤
i
i
+ (1 − (1 − ρ)qti )Vt+1
.
Vti = −ci + Et β t+1 (1 − ρ)qti Jt+1

(11)

A vacancy is filled and produces in the next period with probability (1 − ρ)qti . It remains

unfilled with probability (1 − (1 − ρ)qti ). Free entry implies that the values of vacancies are
driven to zero at any point in time, i.e., Vtg = Vtb = 0, for all t. Solving the asset equations

for vacancies then yields the two job creation conditions:
cg
g
= (1 − ρ)Et β t Jt+1
,
qtg

and

cb
b
= (1 − ρ)Et β t Jt+1
.
qtb

(12)

The equations relate the cost of a posted vacancy to the expected benefit.
Turning to workers, the asset values of employment in good and bad jobs are, respectively:
£
¤
g
Wtg = wtg + Et β t+1 (1 − ρ)Wt+1
+ ρUt+1 ,

(13)

n
h
io
g
b
Wtb = max wtb − k(st ) + Et β t+1 (1 − ρ)(1 − st pgt )Wt+1
+ (1 − ρ)st pgt Wt+1
+ ρUt+1 (14).
st

k(st ) denotes the strictly convex cost of search intensity st , with k(0) = 0, k0 > 0, and
k00 > 0. The higher the search intensity, the more likely a worker is matched with a good
job. Convexity of the eﬀort function guarantees uniqueness of the optimal search eﬀort.
Search intensity is chosen by the worker, taking the wage as given. We assume that firms
cannot directly observe the search eﬀort of workers. However, firms anticipate the optimal
choice that workers will make in equilibrium.10
The optimal search intensity is:
η g
p
k (st ) =
1−η t
0

cb
cg
−
qtg qtb

(15)

i
i
= (1 − ρ)Et β t [Wt+1
− Ut+1 ](1 − η)/η
where we used the fact that ci /qti = (1 − ρ)Et β t Jt+1

from bargaining (see section 3.1). Search intensity is increasing in the probability of finding
a good job and in the diﬀerence between the value of good and bad jobs. If cg /qtg ≤ cb /qtb

no search on the job would take place. The factor η/(1 − η) reflects the fact that workers
obtain only a share of the value of a job.

The asset values of unemployed search for jobs of type i = g, b are
i
i
+ (1 − (1 − ρ)pit )Ut+1
].
Uti = z + Et β t+1 [(1 − ρ)pit Wt+1

(16)

From worker mobility, we know that Utg = Utb = Ut , for all t. Setting the asset values equal,
g
b . Inserting
= (1 − ρ)pbt Et β t Jt+1
and using the bargaining equations yields (1 − ρ)pgt Et β t Jt+1

the job creation condition results in:
pgt

b
cg
bc
g = pt b
qt
qt

⇐⇒

θgt cg = θbt cb .

(17)

Thus, the relative labor market tightness for both types of jobs are exactly proportional to
the relative costs of job creation. Note that in percentage terms labor market tightness in
both sectors move together perfectly and are, in fact, identical.
Finally, wages paid in good and bad jobs are, respectively:
wtg = ηPgt At + (1 − η)z + ηcg θgt
10

(18)

There is no role for the wage in reducing the likelihood of workers quitting because of the timing structure
of the model and the nature of bargaining. Wages are continuously renegotiated so that current wages have
no implications for wages paid next period, which will be newly negotiated. However, next period’s payments
are what motivates search activity this period. If firms could commit to wages for more than a period, then
adjusting today’s wage would have an eﬀect on search intensity and thus quitting. We exclude this possibility.
This also allows us to determine the wage as an outcome to Nash bargaining, because the bargaining set is
convex. The need to determine the wage as the outcome of bargaining with alternating oﬀers thus does not
arise. See Shimer (2006) for a discussion of the relevant issues.

and
wtb = ηPbt At + (1 − η)(z + k(st )) + η ((1 − st )cg θgt ) .

(19)

The equations are derived from the bargaining relationship (1−η)(Wti −Ut ) = ηJti , using the

respective asset equations and the job creation conditions. The second equation makes use

of equation (17). The wage compensates the worker for the incurred search cost k(st ) and
compensates the firm for the increased likelihood of separation due to the workers’ search
eﬀort st . Note that we assume that wages in previous jobs are not part of the outside
options of a worker.

Calibration and Model Solution

We proceed by linearizing the equation system around the non-stochastic steady state. The
resulting linear rational expectations model is then solved by the method described in Sims
(2002). To evaluate the cyclical properties of the model we assign numerical values to the
structural parameters. The calibration is somewhat more complicated than in the standard
model as some parameters in our model do not have easily identifiable counterparts in
aggregate labor market data. Moreover, since pertinent information is not available for some
parameters, we have to compute these indirectly from the steady-state values of quantifiable
endogenous variables. The calibration is summarized in Table 2.
We choose a separation rate of ρ = 0.1. Following the argument in Den Haan et al.
(2000), this value captures both exogenous job destruction and quits into unemployment
as well as movements out of the labor force. We set the unemployment rate to 12%, i.e.,
u = 0.12. It is chosen higher than that commonly observed in the data to take into account
workers that are only loosely attached to the labor force, such as discouraged workers or
workers that are engaged in home production. Once the opportunity arises, these (potential)
workers participate in the matching market.11
We set the steady-state job-to-job transition rate to 0.06. In our model, this corresponds
to the term epg /n, i.e., the number of workers in bad jobs who move on to good jobs relative
to total employment. This number is derived from the data on average job-to-job quits over
the sample period as reported above. When combined with the dynamics of employment,
this implies a ratio of job-to-job movements to total hires of 54%, which we regard to be at
the high end of the empirically plausible range.
For the matching function, we choose a Cobb-Douglas functional form that is identical
11

This argument is based on Blanchard and Diamond (1990).

in both sectors, so that mg = Mg vg1−μ (ug + e)μ and mb = Mb vg1−μ uμb . Similarly to the
literature, the elasticity parameter is calibrated as μ = 0.4.12 The level parameters Mg ,
Mb are computed to imply an economy-wide firm matching probability of 0.7, which is a
commonly used value in the literature. This leads to Mg = Mb = 0.6. The corresponding
steady state sectoral matching rates, that is, the probability that a firm in the good or bad
sector finds an employee, are 0.77 and 0.63, respectively.
Job heterogeneity is generated by diﬀerences in the job creation costs cg > cb . Crucial as
these parameters are, it is also not trivial to pin them down. We let our choice be motivated
by the following considerations. First, job creation costs consist of costs for recruitment,
training, and unused capital, which are likely to be proportional to the capital intensity. In
fact, Acemoglu (2001) links creation costs to capital intensities in service and manufacturing
sectors. We thus impose that job creation costs for good firms are four times as large as for
bad firms, which is on the order of magnitude of the diﬀerence between the capital intensity
of average high-wage and low-wage jobs. Second, even though job creation costs can be
treated as scale parameters, they should not be out of line with the general steady state
implications of the model. Specifically, they cannot be so large as to substantially reduce
aggregate GDP below production. Setting cg = 0.16 and cb = 0.04 results in 5% of output
used in job creation activities and obeys the first criterion. Furthermore, we impose that
sectoral prices are roughly equal in steady state, which implies a share α = 0.4 of production
derived from bad jobs. Together with the diﬀerential in job creation costs, this implies that
wages are higher in good jobs.
The costs of searching on the job are assumed to be strictly increasing and convex in
the search intensity. We use k(s) = κsσ , where κ > 0, σ > 1. In our benchmark calibration
we choose σ = 1.1. We regard highly elastic search as the most plausible case, based on
the following reasoning. First, there may be increasing returns to search as argued by
Rotemberg (2006). Second, the model tries to explain data generated by search at both
the intensive and extensive margins.13 We also note that Merz (1995) chooses a value of
one. Since this is one of our main parameters of interest, we will present and discuss the
implications of variations in the search elasticity below. The scale parameter κ is not chosen
independently, but is computed implicitly to be consistent with the calibrated steady state.
We find κ = 0.04.
12

Empirical estimates of this elasticity parameter are biased when there is on-the-job search (see Petrongolo
and Pissarides, 2001, for the estimation). We are aware of no empirical study of the matching function that
takes on-the-job search into account.
13
Christensen et al. (2005) estimate a search model with intensive and extensive search on the job and
report a search elasticity of 2.

The parameters describing the household are standard. We choose a coeﬃcient of relative risk aversion τ = 1, and a discount factor β = 0.99. The worker’s share in the surplus of
the match is η = 0.5. This follows the convention in the literature, which is largely agnostic
about this value. Hagedorn and Manovskii (2008) have demonstrated recently that small
values of η are needed for matching the volatilities of unemployment and vacancies. We
do not follow this calibration, however, since we demonstrate in this paper that on-the-job
search alone is suﬃcient for capturing labor dynamics.
Similar reasoning also applies to the value of the outside option of the worker, whereby a
high value of z, close to the marginal product of labor, results in high volatility of tightness
(see Hagedorn and Manovskii, 2008). We partially avoid making a stand on this parameterization since we back out the utility value z from the model’s steady state conditions to
be consistent with our calibrated unemployment rate of 12%. We find that z = 0.39, which
is below wages in both sectors.
Finally, we need to calibrate the shock process. The (logarithm of the) aggregate productivity shock is assumed to follow an AR(1) process with coeﬃcient ρA = 0.90. As is
common in the literature, we choose an innovation variance such that the baseline model’s
predictions match the standard deviation of U.S. GDP, which is 1.62% over the sample
period. Consequently, the standard deviation of technology is set to σ ε = 0.0049.
Based on this calibration, we find that in the non-stochastic steady state equilibrium
about 30% of jobs are in the bad, that is, low-wage sector, and that search intensity s is
about one third. In other words, 10% of the labor force are eﬀectively searching on the
job in any time period. Although we lack independent information on this number, we
regard it as not outlandishly implausible. A relatively low number of unemployed workers
look for good jobs (1.3%), while the remainder of the unemployed (10.7%) search for bad
jobs. This is the result of an endogenous response of the unemployed to the competition
for good jobs that they face with employed seekers. Vacancies relative to the labor force
(which is normalized to one) are 7.5 percent for good jobs, and 15.6 percent for bad jobs.
The resulting match probabilities for workers with, respectively, a good or a bad job are
pg = 0.43 and pb = 0.67. Similarly, the flow of new good matches per period is 0.057 and
for new bad matches, 0.092. The larger amount of bad matches reflects the fact that the
workers moving from bad to good jobs are replaced at the industry level.14 We finally note
that wages for good jobs are slightly higher than for bad jobs, the diﬀerence being roughly
4%.
14

The flows in the bad job sector can be interpreted as either reflecting replacement hiring at the firm
level, or as job destruction in some firms, while others expand, holding total industry employment steady.

Model Analysis

We first discuss the business cycle statistics generated from simulating the model, followed
by a characterization of the economy’s response to a productivity shock. We then analyze
in detail the sources of the model’s propagation and amplification mechanism.

5.1

Business Cycle Properties

We report labor market variables of interest in Table 3. Since the variance of the technology
shock was calibrated to match the standard deviation of U.S. GDP, we only evaluate the
model’s predictions based on relative volatilities. We find that, in general, the variables in
the model are only slightly less volatile than in the data, in particular, vacancies, unemployment, and labor market tightness. This lends support to the assertion that a model
with on-the-job search can explain the Shimer (2005) finding that a standard search and
matching model cannot replicate the observed volatility of unemployment and vacancies.
The volatility of aggregate unemployment ut and vacancies vt , which we compute as
simple sums of the sectoral variables, are roughly as volatile as those in the data, although
both statistics still fall somewhat short of the data. Model-implied labor market tightness
is an order of magnitude more volatile than output and does not quite come close to the
data, but it is a substantial improvement over the standard calibration of the simple search
and matching model. Our model also captures the high volatility of the quit rate in the
data extremely well. We will see below in the robustness section that this is largely the
result of a highly responsive search intensity. The elastic supply of additional searchers
holds the ratio of vacancies to unemployment and employed search relatively stable. At the
same time, it keeps the incentives high for firms to post vacancies.
We also note the large discrepancy between the volatility of the standard measure of
aggregate tightness θt = vt /ut and an alternative measure that includes on-the-job seekers;
to wit, b
θt = vt /(ut + et ). The standard deviation of the latter is an order of magnitude
smaller than that of the standard measure, but still two and a half times more volatile than
output. We do not report a corresponding measure in the actual data, since on-the-job

search activity would be diﬃcult to observe. We can infer it implicitly from the outcome
of on-the-job search, namely job-to-job transitions, but this would require a more elaborate
empirical approach.
This discrepancy highlights the key contribution of the paper: On-the-job search can
explain the observed high variability of the vacancy-unemployment ratio, while at the same
time the tightness variable relevant for wage determination is much less volatile. In other
14

words, the standard tightness measure is misleading in the sense that it does not properly
reflect the variable that is guiding workers’ and firms’ choices. This also suggests that
on-the-job search has a significant eﬀect on the model’s propagation mechanism, when
compared to the standard framework, as tightness is the driving force behind firms’ vacancy
posting decisions and wage setting outcomes. We will discuss this issue in more detail below.
Finally, we find that the aggregate wage, the size-weighted average of the sectoral wages,
is substantially less volatile than in the data (0.19 vs. 0.65). The low volatility of the former
is due to the relative smoothness of the tightness variable which is an important determinant
for wage determination: see Eqs. (18)-(19). We do not want to push this interpretation too
far, but one could interpret this finding as endogenously generated inertia in the absence of
any ad-hoc wage stickiness mechanism.
The simulation also yields strong predictions with respect to contemporaneous correlations. First and foremost is the Beveridge curve, the negative correlation of unemployment
and vacancies over the business cycle. In U.S. data this correlation is −0.95, which we are
able to replicate fairly closely.15 We also match the negative comovement of unemployment

with all other aggregate variables of interest. For instance, the unemployment rate is highly
negatively, though not perfectly, correlated with the job-to-job transition rate. When an
adverse technology shock raises unemployment, search intensity falls due to a declining job
finding probability. Workers are less likely to engage in on-the-job search so that relatively
fewer workers in bad jobs move on to better ones. Interestingly, our two measures of labor
market tightness are perfectly correlated on account of the strong comovement of search
intensity with GDP. We also note the very high procylicality of job-to-job quits in terms of
the correlation with output. A noteworthy exception is the high correlation of wages and
on the job search in the model, in contrast to the data.

5.2

Impulse Responses

We illustrate the influence of on-the-job search on the model dynamics by using the impulse
responses reported in Figures 3 and 4. Consider a positive, one percent shock to aggregate
productivity. On impact, aggregate output rises with productivity, followed by a protracted
hump-shaped increase until peaking three quarters after the initial shock. At the same
time, vacancies and labor market tightness for both job types rise. Since the probability of
finding good jobs is now higher, search intensity, and thus the eﬀective number of on-the-job
searchers, e, increases (see Eq. (15)). Vacancies in the bad jobs sector rise proportionally
15
For their model, Mortensen and Pissarides (1994) report a correlation of only −0.26. See also the
interesting discussion in Shimer (2005).

more than those in the good sector because firms anticipate the future flows of workers to
better jobs, which will then have to be replaced in the next period.
Aggregate unemployment does not move on impact since the timing of the model is
such that new matches become productive only in the period after which they were formed.
Unemployment starts declining persistently in the period after the shock, while it follows the
same hump-shaped pattern as aggregate output. Note that sectoral search activity of the
unemployed does react immediately.16 Unemployed searchers face increased competition
from employed searchers who raise their search intensity. They therefore redirect their
search activity to low quality jobs. The congestion eﬀect from on-the-job search eﬀectively
crowds out unemployed searchers from the good sector. In our benchmark version, we
assume that the unemployed search with fixed intensity. We show below that the results of
the paper go through when the unemployed can also vary their search intensity.
In the periods after the initial shock, good vacancies start to fall quickly from their
impact level, while the adjustment in bad vacancy postings is more pronounced. This is due
to the fact that as employment rises for both job types, more workers leave bad jobs, which
requires rising replacement hiring. Overall, the hiring rate rises for several more quarters.
Furthermore, search intensity continues to rise because the fall in unemployment increases
the chances of the employed to be matched with good jobs even more. Employment in the
good sector rises because the inflow of new workers exceeds the outflow from job destruction.
Even though the standard measure of labor market tightness θ = v/u is highly volatile,
wages rise by much less than without on-the-job search. The reason is that the measures of
labor market tightness relevant for the workers’ outside options that enter wage bargaining,
are substantially less volatile, as can be seen in Figure 3. The wage in bad jobs rises by
less, however, because of higher search intensity. While search has a positive impact on the
present value of the match for workers, it reduces the value of the match to firms.
We see from the impulse responses that changes in productivity have persistent eﬀects,
indicating that search on the job adds substantial propagation to the model. Similarly,
employment has a hump-shaped response. This is not caused per se by the heterogeneity
of jobs in the economy. Analysis of the model without employed search, as in Krause and
Lubik (2006), show that the impulse responses of that model are very similar to those of a
standard one-sector model, such as those by Andolfatto (1996) or Merz (1995).
16

ug and ub are not state variables, but rather jump variables. These variables should not be thought of
as the stock of unemployed searching for jobs in the respective sectors, but rather as the degree of search
activity directed towards each sector.

5.3

Inspecting the Mechanism with On-the-Job Search

We now dig deeper into the mechanism that generates the results of the model. We show
that on-the-job search modifies the standard model both in terms of amplification and
propagation of productivity shocks in a qualitatively and quantitatively significant manner.
The key to understanding the model’s dynamics is the definition of labor market tightness in the good jobs sector when workers can search on the job:
θgt =

vtg
,
ugt + et

(20)

where et = st nbt is the eﬀective number of on-the-job searchers. Without on-the-job search,
tightness is defined as θgt = vtg /ugt . The inclusion of on-the-job searchers expands the pool of
potential hires that a job-posting firm is confronted with. Other things being equal, on-the
job search reduces the responsiveness of tightness to movements in vacancies vtg and sectoral
search ugt , which, in turn, dampens movements in wages, see Eqs. (18)-(19). This keeps
the firm’s incentive to post vacancies up, as less of its surplus is eaten up by corresponding
wage increases. Hence, vacancy posting is more volatile with on-the-job search than in the
standard model.
The key mechanism of the model is as follows. Consider a persistent increase in aggregate
productivity which raises the expected value of a job in both sectors. This stimulates
vacancy creation in a manner identical to the propagation mechanism of shocks in the
search and matching model as encapsulated in the job creation condition:
ci ¡ i ¢μ
i
= (1 − ρ)Et β t Jt+1
, i = g, b.
θ
m t

(21)

What is diﬀerent is how sectoral tightness reacts. Note that on impact neither aggregate nor
sectoral employment moves since they are pre-determined, nor does aggregate unemployment ut . However, the unemployed can alter their direction of search. Figure 3 shows, that
relative to the steady state, the number of the unemployed ugt searching in the good sector
falls substantially, while it rises in the bad sector. This is driven by the competition with
employed searchers for good jobs. Search for low quality jobs is relatively more attractive
since the pool of potential searchers in that sector is smaller.
We now log-linearize the tightness equation around the steady state levels of its variables
(we denote x
et = log xt − log x):

g
eg +
e
θt = ϑ
t

e
(e
ug − eet ) ,
ug + e t
17

(22)

e = veg − u
where we have defined ϑ
egt . Tightness in the good sector can be decomposed into
t
t
eg that takes into account only the search activity of the unemployed
a tightness measure ϑ
t

and a component that captures the congestion eﬀect from on-the-job search. Recall that
ebt . We now assume for sake
et = st nbt , so that in steady state e = snb and eet = set + n

of the argument that search intensity is fixed, i.e. set = 0, and eet = n
ebt . The robustness

section below looks more closely at the importance of time-varying search intensity of the
employed.

egt < 0) drives a wedge between the two measures of
The decline in ugt (and thus u
g
eg . Specifically, on-the-job-search dampens the movements of the
tightness so that e
θt < ϑ
t

inclusive measure θgt . This implies that firm’s incentives for vacancy creation are higher than
they otherwise would be since wages do not increase by as much. Note that the arbitrage
g
b
g
θt and pegt = pebt . Since movements in e
θt are dampened by the
condition (17) implies e
θt = e
b
on-the-job searchers, search activity in the bad sector has to rise (e
θ = veb − u
eb ) to maintain
t

equality between the job-finding probabilities and, by implication, between the expected

i
in both sectors. Furthermore, as those who quit for good jobs will
values of a job Et Jt+1

have to be replaced, additional vacancies are posted, which can be seen from the protracted
response of vetb in Figure 3.

In subsequent periods this mechanism is amplified through the rise in eﬀective search

ebt > 0. This eﬀect can be seen in the
as employment in the bad sector increases, eet = n

lower panel of Figure 4. Tightness increases by even more than on impact resulting in a
characteristic hump-shaped response pattern. The amplification channel is present in the

specification without varying search intensity. Once we allow for an endogenous choice of
g
θ . As tightness rises, so
st , there is additional feedback. Eq. (15) implies that set = 1 e
σ−1 t

g
eg by even more.
does search intensity, which increases the wedge between e
θt and ϑ
t

Our model with on-the-job search also has a striking implication for the labor market

propagation mechanism. This insight is depicted in Figure 5, which shows impulse response
functions of aggregate output for various (nested) specifications of our benchmark model.
The dotted line depicts the case without on-the-job search, that is, a model with a twosector, good job/bad job structure as in Krause and Lubik (2006). The complete lack of
endogenous propagation is clearly evident as the response essentially tracks the dynamic
path of a highly persistent productivity shock.17 The middle (dash-dotted) line shows the
adjustment path in our model with a fixed search intensity, while the solid line replicates
17

It is this inability of the search and matching model that has been widely discussed in the literature
(see, for instance, Den Haan et. al., 2000).

the aggregate output response from Figure 3. In both cases, output exhibits a pronounced
hump-shaped pattern, which is apparently generated by the presence of on-the-job search.
The diﬀerence between the two top responses stems from the endogenous response of search
intensity to rising labor market tightness, as given by the optimality condition for st , Eq.
(15). This diﬀerence, however, only has an amplification eﬀect. Clearly, on-the-job search
changes the model’s propagation mechanism.
In technical terms, the response without on-the-job search follows a typical first-order
autoregressive process, which carries over from the AR(1)-productivity shock.18 Humpshaped dynamics, on the other hand, require autoregressive terms of at least second order.
These are provided by the stock of workers that engage in on-the-job search. The employment equation in the good sector can be linearized as follows:
g
ug
u
eg .
ngt + ρ(1 − μ)e
θt + ρ g
n
egt+1 = (1 − ρ)e
u +e t

(23)

egt = n
ebt +
The definition of tightness θgt implies (assuming set = 0 for simplicity) that u
³
´
g
g
ug +e e
e . Substituting this expression yields:
θt − ϑ
t
e
g

n
egt+1 = (1 − ρ)e
ngt + ρ(1 − μ)e
θt + ρ

ug
ug ³eg eg ´
b
n
e
+
ρ
θt − ϑt .
ug + e t
e

(24)

Good employment has intrinsic dynamics via its own lag, but is also ‘driven’ by endogenous
´
³ g
g
eg , and n
eb .
θ −ϑ
processes e
θ , e
t

The employment equation in the bad sector can be linearized as:

b
ngt + ρ(1 − μ)e
θt + (ρ + (1 − ρ)pg s) u
ebt .
n
ebt+1 = (1 − ρ)(1 − pg s)e

(25)

We can substitute this equation into the employment equation for the good sector and find:
egt − (1 − ρ)2 (1 − pg s)e
ngt−1 +
n
egt+1 = [(1 − ρ)(1 − pg s) + (1 − ρ)] n
´ ³
´
³
g
g
eg and ϑ
eg
+ terms in e
θt and e
θt−1 + terms in ϑ
t
t−1 .

(26)

This semi-reduced form therefore implies that sectoral employment has intrinsic dynamics
through its own lags of second order. Moreover, the driving terms of employment, namely
labor market tightness in the two sectors, are determined by the respective job-creation conditions. These are expectational diﬀerence equations which can be solved out as functions of
18

Lubik (2010) shows that the standard (one-sector) search and matching model with AR(1)-productivity
shocks implies a reduced-form specification for output that is an AR(2). However, because of the lack in
endogenous propagation the second autoregressive root is small. Consequently, the model delivers dynamics
that are very close to an AR(1). It can also be shown that the two-sector model without on-the-job search
easily aggregates to the one-sector set-up, and that, hence, aggregate dynamics are identical (see Krause
and Lubik, 2006).

the exogenous aggregate productivity process, which results in a reduced-form specification
for tightness of autoregressive order one. Consequently, the driving processes would add
even more autoregressive dynamics.
All these elements combined guarantee that employment exhibits higher-order dynamics
that result in hump-shaped adjustment path. The ultimate source of this pattern is the
specification of the employment ladder in our model. Employed searchers enter the matching
function of another sector and thereby provide strong endogenous propagation through this
simple accounting mechanism. In a robustness check below, we show that this mechanism
is still present when we modify the model to include endogenous search intensity of the
unemployed. We therefore conclude that on-the-job search as modeled in this multi-sector
set-up would have to play a central role in explaining aggregate business cycle dynamics.
In order to highlight this argument we compare our model to the autocorrelation patterns in U.S. data. Figure 6 depicts the autocorrelation functions of U.S. GDP growth rates
over the period 1950:1-2009:1 and for the three model specifications discussed above. The
lack of propagation in the model without on-the-job search is well documented by a flat
autocorrelation function around zero. The benchmark model, on the other hand, captures
U.S. output dynamics remarkably well, even slightly overpredicting the first-order autocorrelation. But even when search intensity is constant, the autocorrelation pattern by far
outperforms the standard model without on-the-job search.19

Discussion and Robustness

We now discuss the robustness of the results with respect to aspects of the calibration and to
a number of extensions, specifically the calibration of the search elasticity and endogenous
intensity of unemployed search.

6.1

The Role of Search Intensity

Why does the cyclicality of job-to-job quits change the behavior of the economy so dramatically? On the one hand, rising search eﬀort raises good firms’ incentives to post vacancies.
Without employed searchers, the creation of good jobs is constrained by the fall in the number of unemployed searchers and the strong rise in wages. On the other hand, the increasing
availability of good jobs further encourages on-the-job search. A small rise in productivity
leads to large changes in the incentives to search and to post vacancies, which explains that
19
Inclusion of capital is likely to further increase the autocorrelation of output in addition to that achieved
by on-the-job search.

unemployment falls substantially even though competition with employed job seekers rises.
Only slowly do these incentives fall back to their steady state levels.
The role of search intensity can be illustrated by varying the elasticity of search eﬀort.
The results of this exercise are depicted in Figure 7. We plot the standard deviations of
measures of labor market tightness and the quit rate against the elasticity parameter σ in
the search cost function.
As σ approaches one from above, the quit rate and labor market tightness become
exceedingly volatile. Since the responsiveness of search costs to changing search eﬀort
declines, the volatility of job-to-job quits rises. Even though the standard and our modified
measures of labor market tightness, θ = v/u and b
θ = v/(u + e), are almost perfectly

correlated, their volatility is strikingly diﬀerent. While the former is very responsive to
changes in σ, the latter is barely aﬀected. The reason is that as unemployment falls,

employed search rises, keeping the incentives for vacancy creation high after a favorable
aggregate shock. The theoretical counterpart in our model, vg /(ug + e), behaves similarly.
As is evident from the impulse responses, the presence of time-varying on-the-job search
activity leads to persistent movements of output after shocks to technology. The elasticity of
search is, however, only partially responsible for the propagation mechanism in the model.
Even with fixed search intensity, productivity shocks are still amplified and propagated in
a hump-shaped manner as Figure 5 illustrates.
Figure 7 also shows how our calibration of σ = 1.1 manages to target both the standard
deviation of the quit rate and the observed vacancy-unemployment ratio θ. This comes at
the price of an on-the-job-search inclusive measure of tightness that is not very volatile,
which results in wage movements that are too smooth relative to U.S. data. Moreover,
such a high degree of search elasticity may be empirically doubtful. We regard this issue
therefore far from settled.

6.2

Endogenous Search Intensity of the Unemployed

The key mechanism in our model is the increasing flow and search activity of employed job
seekers. At the same time, the search intensity of unemployed workers is fixed. We show in
this section that this assumption is immaterial for our results. Conceivably, as unemployed
search intensity rises, their incentives to search for good jobs stay high. They would thus
compete more strongly with the employed searchers from the bad sector. In our on-the-job
search framework, however, the mechanism that expands search on the job is the fall in
unemployment. If unemployed workers were to search more intensively, the unemployment

pool would deplete even faster. This would then further amplify the importance of search
for employed workers.
It is fairly straightforward to include endogenous search intensity of the unemployed in
our model. The asset value of unemployment is modified to introduce a search cost which
is convex in search intensity:
i ui
i
i ui
i
Uti = z − k(sui
t ) + Et β t+1 [(1 − ρ)pt st Wt+1 + (1 − (1 − ρ)pt st )Ut+1 ],

(27)

where sui
t denotes the search intensity in sector i. The first order condition for search
intensity is:
k0 (sui
t )=

£ i
¤
η
i
.
(1 − ρ)pit Et β t Wt+1
− Ut+1
1−η

(28)

u
g g
As before, arbitrage between sectors implies that sui
t = st . This also implies that c θ t =

cb θbt . The optimal search intensity of the unemployed can then be written as:
k 0 (sut ) =

η g cg
η g g
pt g =
c θt .
1 − η qt
1−η

(29)

As expected, increases in tightness in either sector would lead the unemployed to search
more intensively, and the probability of finding a job pit increases.
How does this aﬀect the search intensity of the employed? We can use the optimality
condition (15) and divide the two expressions. This yields:
∙
´1−μ ¸
³
k 0 (set )
b g
= 1 − c /c
.
k0 (sut )

(30)

This condition implies that the search intensity of the unemployed and of on-the-job searchers
move in fixed proportions.20 In a somewhat loose sense, employed job seekers respond to
rising search intensity of employed by increasing their intensity as well. Key to the model’s
propagation mechanism via firms’ job posting decision is not how the pool of searchers is
composed, but that it is expanding in upturns. In other words, varying search intensity
of the unemployed does not aﬀect the basic propagation mechanism of the model as highlighted in the previous section. Endogenous search intensity provides an additional feedback
mechanism that can amplify the adjustment pattern but not overturn it.
20

If the cost functions are identical, then obviously shet = shut . For diﬀerent cost functions, we can always
find combinations of the level parameters κi and elasticity parameters σi such that the modified model
produces the same aggregate dynamics as our benchmark model. In the end, it is an empirical question as
to what these parameters are and whether job search of the employed or the unemployed is more costly at
the margin.

Relation to Previous Work

Earliest precursors of our model with on-the-job search are the contributions by Pissarides
(1994) and Mortensen (1994). The former develops a model that shares with our framework
the presence of two diﬀerent job types, ‘good’ and ‘bad’, and features random search for
jobs. The existence of idiosyncratic productivity draws in a match generates heterogeneity
in worker productivities across jobs. This implies a threshold in the tenure of workers above
which workers do not switch jobs, because starting wages in good jobs are lower than the
wage in bad jobs. In this model employed job search reduces the volatility of unemployment
and would therefore not aid in understanding the unemployment and vacancy volatility
found in the data.
Mortensen (1994) simulates a stochastic version of the Mortensen and Pissarides (1994)
model, with the addition of on-the-job search. The presence of employed search helps
in explaining the negative correlation between job creation and destruction. The model
also features a procyclical quit rate, with workers being randomly matched to the most
productive jobs. Both Pissarides and Mortensen do not explore prediction of their models
for the joint dynamics of vacancies, unemployment and job-to-job flows or the eﬀects on
wages. Finally, the two papers have exogenous interest rates and prices, shutting down
general equilibrium eﬀects, which aﬀect the dynamics of vacancies and unemployment.
Neither of these papers considers these dynamics quantitatively.
In many other models in the labor market literature, employed search is mainly varied
at the extensive margin instead of search intensity as in our framework. Search is made
costly, however, through the payment of a lump sum. Pissarides (2000) is an early example
for this modeling strategy. Jobs diﬀer by idiosyncratic productivity levels, drawn from a
continuous distribution. With workers choosing whether to search or not, this implies two
thresholds in terms of productivity. Below the higher threshold workers have an incentive to
search for better employment, participating in the common matching market. New matches
start at the highest possible productivity. Below the second threshold, the joint value of
the match with the firm is below the parties’ outside option, leading to job destruction.
Since all jobs are created at the highest possible productivity level, vacancies are the same
for employed and unemployed workers. The key diﬀerence to our model is the search at
the intensive margin and the persistent diﬀerence between job types. Including persistent
idiosyncratic shocks in a business cycle model of this type comes, however, at considerable
computational costs.

A second class of models with on-the-job search consider the possibility of endogenous
wage distributions arising in the presence of frictions. However, these models are primarily
steady state models, and are based on wage posting. That is, wages do not respond to
shocks and are not renegotiated. Burdett and Mortensen (1998) explore the link with interindustry and firm-size wage diﬀerentials. Cahuc et al. (2006) estimate such a model and
show how it accounts for a steady state distribution of wages. Christensen et al. (2005)
estimate a similar model with endogenous intensity of search. We do not know of any
example in the literature that analyses dynamic stochastic general equilibrium versions of
these models with a focus on business cycle analysis.21
We oﬀer a final thought on the literature that confronts the Mortensen and Pissarides
(1994) model with the data. It typically focuses on the performance of the model along the
dimension it was designed to explain, namely the behavior of job creation and destruction.
For example, Cole and Rogerson (1999) find that the model performs well if the steadystate unemployment rate is high. Den Haan et al. (2000) achieve plausible job flows by
modeling endogenous job destruction along with capital. As mentioned, Hall (2005) and
Shimer (2005) are the first to consider the ability of the search and matching framework to
quantitatively match the cyclical behavior of unemployment and vacancies. In all papers,
the performance of the model is enhanced by an assumption that reduces the cyclicality of
hiring costs or wages. In our model, it is the presence of employed search.

Conclusion

We have presented a model of labor market and aggregate dynamics and in which on-thejob search plays a crucial role. We show that it is possible to explain the joint dynamics
of vacancies, unemployment, and productivity without resorting to any imperfection other
than search and matching frictions. In particular, we do not require wages to be rigid in
order to bring the model closer to the data. Instead, increased search eﬀort by employed
workers is suﬃcient to dampen the movements in labor market tightness and to keep the
costs of job creation more stable for firms. Consequently, wages are less volatile, and
incentives to post vacancies remain high. Unemployed workers’ incentives to direct search
to jobs where they do not compete with employed searchers further amplify these eﬀects.
The model delivers a rich description of the labor market over the business cycle. Booms
are times which allow employed workers to upgrade into better jobs, while opening jobs for
unemployed workers, albeit of lower quality. The reallocation of labor to more productive
21

See also Shimer (2005) who reports that no such analysis has been conducted.

units is facilitated by direct job-to-job transitions, rather than requiring movements of
workers through the unemployment pool. One fundamental reason for worker mobility is
the heterogeneity of jobs which gives rise to persistent diﬀerences in the returns to workers.
The creation of good jobs is amplified by the rising intensity of search by employed workers.
The propagation mechanism that the model implies has important implications for business cycle analysis. In response to a positive productivity shock, output displays a marked
hump-shaped pattern, which is considered a stylized fact in the empirical macroeconomics
literature. A higher match probability induces employed workers to search for better jobs.
This feeds back into the incentives for firms to continue posting vacancies for a protracted
period. Falling unemployment further reduces the competition for good jobs and keeps incentives for search high. Interestingly, we obtain a propagation of shocks that is similar to
Den Haan et al. (2000), even though we do not include capital or a variable job destruction
rate.
However, the findings are not meant to rule out an potentially important role for (real)
wage rigidity. Hall (2005) and Shimer (2005) suggest this as a solution to the empirical
diﬃculties they identified with Mortensen-Pissarides model. Also in our model, wage rigidity
would further amplify the cyclical response of vacancies, unemployment and job-to-job flows.
Hall (2005) has made an interesting advance modeling wage setting based on social norms,
which allows wages even for new hires to be rigid. In previous work, we applied this idea
in a monetary business cycle model with search frictions (Krause and Lubik, 2007). Van
Zandweghe (2010) combines these elements in a model with on-the-job search similar to
ours.

References
[1] Acemoglu, Daron (2001): “Good Jobs versus Bad Jobs”. Journal of Labor Economics,
19(1), 1-21.
[2] Albaek, Karsten, and Bent Sorensen (1998): “Worker Flows and Job Flows in Danish
Manufacturing, 1980-91”. The Economic Journal, 108, 1750-1771.
[3] Andolfatto, David (1996): “Business Cycles and Labor Market Search”. American
Economic Review, 86(1), 112-132.
[4] Blanchard, Olivier, and Peter Diamond (1990): “The Cyclical Behavior of the Gross
Flows of U.S. Workers”. Brookings Papers on Economic Activity, 2, 85-155.

[5] Burdett, Kenneth, and Dale T. Mortensen (1998): “Wage Diﬀerentials, Employer Size
and Unemployment”. International Economic Review, 39, 257-273.
[6] Burgess, Simon M. (1993): “A Model of Competition Between Unemployed and Employed Job Searchers: An Application to the Unemployment Outflow Rate in Britain”.
The Economic Journal, 103, 1190-1204.
[7] Cahuc, Pierre, Fabien Postel-Vinay, and Jean-Marc Robin (2006): “Wage Bargaining
with On-the-Job Search: Theory and Evidence”. Econometrica, 74(2), 323-364.
[8] Christensen, Bent Jesper, Rasmus Lentz, Dale T. Mortensen, George R. Neumann,
Axel Werwatz (2005): “On-the-Job Search and the Wage Distribution”. Journal of
Labor Economics, 23(1), 31-58.
[9] Cole, Harold L., and Richard Rogerson (1999): “Can the Mortensen-Pissarides Matching Model Match the Business Cycle Facts?”. International Economic Review, 40(4),
933-959.
[10] Costain, James S., and Michael Reiter (2008): “Business Cycles, Unemployment Insurance, and the Calibration of Matching Models”. Journal of Economic Dynamics and
Control, 32(4), 1120-1155.
[11] Den Haan, Wouter, Garey Ramey, and Joel Watson (2000): “Job Destruction and
Propagation of Shocks”. American Economic Review, 90(3), 482-98.
[12] Fallick, Bruce, and Charles A. Fleischman (2004): “Employer-to-Employer Flows in
the U.S. Labor Market: The Complete Picture of Gross Worker Flows”. Finance and
Economics Discussion Series, #2004-34, Board of Governors of the Federal Reserve
System.
[13] Hagedorn, Marcus, and Iourii Manovskii (2008): “The Cyclical Behavior of Equilibrium
Unemployment and Vacancies Revisited”. American Economic Review, 98(4), 16921706.
[14] Hall, Robert (2005): “Employment Fluctuations with Equilibrium Wage Stickiness”.
American Economic Review, 95(1), 50-65.
[15] Krause, Michael U., and Thomas A. Lubik (2006): “The Cyclical Upgrading of Labor
and On-the-job Search”. Labour Economics, 13, 459-77.

[16] Krause, Michael U., and Thomas A. Lubik (2007): “The (Ir)relevance of Real Wage
Rigidity in the New Keynesian Model with Search Frictions”. Journal of Monetary
Economics, 54(3), 706-727.
[17] Lubik, Thomas A. (2010): “Identifying the Search and Matching Model of the Labor
Market”. Manuscript.
[18] Merz, Monika (1995): “Search in the Labor Market and the Real Business Cycle”.
Journal of Monetary Economics, 36, 269-300.
[19] Mortensen, Dale T. (1994): “The Cyclical Behavior of Job and Worker Flows”. Journal
of Economic Dynamics and Control, 18, 1121-42.
[20] Mortensen, Dale T. and Christopher Pissarides (1994): “Job Creation and Job Destruction in the Theory of Unemployment”. Review of Economic Studies, 61, 397-415.
[21] Parent, Daniel (2000): “Industry-specific Human Capital: Evidence from Displaced
Workers”. Journal of Labor Economics, 6(4), 306-323.
[22] Petrongolo, Barbara, and Christopher Pissarides (2001): “Looking into the Black Box:
A Survey of the Matching Function”. Journal of Economic Literature, 39(2), 390-431.
[23] Pissarides, Christopher (1994): “Search Unemployment with on the Job Search”. Review of Economic Studies, 61, 457-476.
[24] Pissarides, Christopher (2000): Equilibrium Unemployment Theory. Second edition,
MIT Press.
[25] Rotemberg, Julio (2006): “Cyclical Wages in a Search and Bargaining Model with
Large Firms”. NBER International Seminar on Macroeconomics, 65-114.
[26] Shimer, Robert (2005): “The Cyclical Behavior of Equilibrium Unemployment and
Vacancies”. American Economic Review, 95(1), 25-49.
[27] Shimer, Robert (2006): “On-the-Job Search and Strategic Bargaining”. European Economic Review, 50, 811-30.
[28] Sims, Christopher A. (2002): “Solving Linear Rational Expectations Models”. Computational Economics, 20 (1-2), 1-20.
[29] Tasci, Murat (2007): “On-the-Job Search and Labor Market Reallocation”. Federal
Reserve Bank of Cleveland Working Paper No. 0725.
27

[30] Van Zandweghe, Willem (2010): “On-the-Job Search, Sticky Prices, and Persistence”.
Journal of Economic Dynamics and Control, 34(3), 437-455.

Appendix: The Equation System
1. Job creation conditions:
cg
qtg
cb
qtb

∙
¸
c−τ
cg
g
t+1
= (1 − ρ)Et β −τ Pg,t+1 At+1 − wt+1 + g
,
qt+1
ct
"
#
b
c−τ
c
g
t+1
b
= (1 − ρ)Et β −τ Pb,t+1 At+1 − wt+1
+ (1 − pt+1 st+1 ) b
.
qt+1
ct

2. Wage determination:
wtg = ηPg,t At + (1 − η)z + ηpgt

cg
,
qtg

wtb = ηPb,t At + (1 − η)(z + κsσt ) + η(1 − st )pgt

cg
.
qtg

3. Optimal search intensity:
κσsσ−1
t

η g
p
=
1−η t

cg
cb
g − b
qt
qt

4. Evolution of employment:
ngt+1 = (1 − ρ) (ngt + mgt ) ,
´
³
nbt+1 = (1 − ρ) nbt + mbt − pgt st nbt .
5. Unemployment:
ut = ugt + ubt = 1 − ngt − nbt .
6. Employed searchers:
et = st nbt .
7. Matching functions:
mgt = m(vtg , ugt + et ) = Mg (vtg )1−μ (ugt + et )μ ,
mbt = m(vtb , ubt ) = Mb (vtb )1−μ (ubt )μ .
8. Firm and worker match probabilities:
qtg = mgt /vtg , qtb = mbt /vtb ,
pgt = mgt /(ugt + et ), pbt = mbt /ubt .
29

9. Arbitrage condition:
pgt

b
cg
bc
g = pt b .
qt
qt

10. Sectoral and aggregate output:
yg,t = At ngt , yb,t = At nbt ,
α 1−α
yg,t .
yt = yb,t

11. Prices:
Pg,t = (1 − α)
Pb,t = α

yb,t
yt

yg,t
yt

¶−1

12. Aggregate consumption:
ct = yt − cg vg,t − cb vb,t .
13. Tightness:
θgt =

vtg
g
ut +et

, θbt =

vtb
ubt

14. Aggregate technology:
log At = ρA log At−1 + εAt .

Table 1: U.S. Business Cycle Statistics

Standard Deviation
Y
1.68

W
0.65

N
0.88

Y
N

0.80

U
8.71

V
8.39

θ
15.99

QR
10.06

Cross-Correlations
Y
Y
W
N
Y /N
U
V
θ
QR

1
—
—
—
—
—
—
—

Y
N

0.40
1
—
—
—
—
—
—

0.82
0.11
1
—
—
—
—
—

0.63
0.57
0.11
1
—
—
—
—

-0.87
-0.25
-0.90
-0.31
1
—
—
—

0.88
0.32
0.84
0.41
-0.89
1
—
—

0.88
0.29
0.87
0.37
-0.95
0.98
1
—

0.88
0.45
0.86
0.40
-0.90
0.88
0.89
1

Notes: The statistics are computed from HP-filtered data with a smoothing parameter of 1,600. The standard deviations are measured relative to that of GDP.

Table 2: Model Parameters and Calibration

Parameter

Value

Description

μ
Mg
Mb
cg
cb
ρ
σ
η
α
β
τ
u
ζ
z
κ

0.4
0.6
0.6
0.16
0.04
0.1
1.1
0.5
0.4
0.99
1
0.12
0.06
0.39
0.04

Match Elasticity
Level Parameter
Level Parameter
Good Job Creation Cost
Bad Job Creation Cost
Separation Rate
Search Elasticity
Nash Bargaining Share
Output Aggregator Elasticity
Discount Factor
Intertemporal Substitution Elasticity
Steady State Unemployment Rate
Steady State Quit Rate
Unemployment Benefit
Search Cost Function Parameter

Table 3: Benchmark Simulation

Standard Deviations
Y
1.62

W
0.19

N
0.56

Y
N

0.27

U
6.09

V
5.43

θ
11.17

θn
2.57

QR
10.05

Cross-Correlations
Y
Y
W
N
Y /N
U
V
θ
QR

1
-

Y
N

0.83
1
-

0.99
0.81
1
-

0.97
0.86
0.54
1
-

-0.99
-0.75
-1.0
-0.54
1
-

0.93
0.97
0.87
0.84
-0.87
1
-

0.99
0.88
0.97
0.87
-0.97
0.96
1
-

0.96
0.94
0.92
0.96
-0.92
0.99
0.98
1

Notes: The statistics were computed as follows. We simulated the model 500 times
by drawing realizations from the innovation of the productivity shock. The sample
length was 200 periods. We then computed the statistics above for each simulation
and averaged. The standard deviations are measured relative to that of GDP.

120

Unemployment and Vacancies

100
Unemployment Rate
Vacancy Index

t
n
e
cr 6
e
P

0
1950

0
1960

1970

1980

1990

Figure 1: Unemployment and Vacancies

2000

2010

x
e
d
In

Quit Rate and Unemployment

t
n
e
cr 6
e
P

2
Unemployment Rate
JOLTS Quarterly Quit Rate
Employment and Earnings Quarterly Quit Rate
0
1950

1960

1970

1980

1990

Figure 2: The Quit Rate and Unemployment

2000

2010

Output and Aggregate Real Wage

Quit Rate and On−the−Job Searchers
10
y
w
A

1.5
1
0.5
0

5
10
15
20
Unemployment and Vacancies

5
0
−5
0

10
15
20
Sectoral Searchers

10
15
20
Tightness Measures

θ
θ

5
0

10
15
20
Sectoral Vacancies

8
% Deviation

% Deviation

50
0
ug
ub

−50
−100

15
u
v

% Deviation

−10

qr
e

% Deviation

vg
vb

6
4
2
0

Figure 3: Impulse Response Functions to a 1% Productivity Shock

Good Jobs Employment

Bad Jobs Employment

1
g

n
% Deviation

% Deviation

0.5

10
15
Good Matches

0.5

10
15
Bad Matches

8
mb
% Deviation

% Deviation

mg
4
2
0

10
15
20
Good Jobs Tightness

6
4
2
0

10
15
20
Bad Jobs Tightness
θb

% Deviation

4
θg

2
1
0

3
2
1
0

Figure 4: Impulse Response Functions to a 1% Productivity Shock

1.5
Benchmark
Constant Search Effort
No On−the−Job Search

Percent Deviation

0.5

Time

Figure 5: Impulse Responses of Output to a 1% Productivity Shock

0.4

0.35

0.3
U.S. Data
Autocorrelation Coefficient

0.25

0.2

0.15

0.1
Constant Search Effort
Benchmark

0.05

−0.05
No On−the−Job Search
−0.1

3
Lag

Figure 6: Autocorrelations of Output Growth Rates

Search Elasticity and Volatility
14
θ
quit rate
θn

(Rel.) Standard Deviation

1.2

1.4

1.6

1.8

2
σ

2.2

2.4

2.6

Figure 7: Search Elasticity and Aggregate Volatilities

2.8

Full text of Working Papers (Federal Reserve Bank of Richmond) : On-The-Job Search and the Cyclical Dynamics of the Labor Market, Working Paper 10-12

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