Employment Duration and Match Quality over theBusiness Cycle∗
Ismail Baydur†

Toshihiko Mukoyama‡

ADA University and CERGE-EI

University of Virginia

October 2015

Abstract
This paper studies the cyclical behavior of employment duration. We estimate
a proportional hazard model with competing risks, distinguishing diﬀerent types ofseparations. A higher unemployment rate at the start of an employment relationshipincreases the probability of job-to-job transitions, while its eﬀect on employment-tounemployment transitions is close to zero. We ﬁnd similar patterns when we distinguishthe separations by diﬀerent reasons and contrast quits and ﬁrings. We then build a
simple job-ladder model to interpret our empirical results. The cyclical behavior ofopportunities for job-to-job transitions plays an important role in the cyclical behaviorof match quality.
Keywords: Business cycles, Match quality, Employment duration
JEL Classifications: E24, E32, J22, J63, J64.

∗

We thank seminar and conference participants at the CEF conference in Taiwan, the Federal Reserve
Bank of St. Louis, the Midwest Macro Meetings in Florida International University, and the SED Meetings in
Warsaw for useful comments. We also thank Nick Embrey for editorial help. Mukoyama thanks the Bankard
Fund for Political Economy and AHSS research support at University of Virginia for ﬁnancial support. Allerrors are our own.
†
Contact information: ibaydur@ada.edu.az‡
Contact information: tm5hs@virginia.edu

1Introduction

In a frictional labor market, ﬁrms and workers may not always be able to ﬁnd their best
match. When a ﬁrm and a worker meet, they have to decide whether to form a match or
keep looking for an alternative partner. If a match is not formed, a result can be “mismatch
unemployment,” that is, a co-existence of vacancy and unemployment because potential
beneﬁt from a match (the “match quality”) is too low.1 Even if a match is formed, the match
quality may not be very high—the match may be formed just because it is too costly for bothparties to keep looking for alternative partners. This type of “mismatch employment,” causedby labor market frictions, is one of the important reasons for misallocation of productive
resources in the macroeconomic context.2
When the quality of a match is not perfect, reallocating workers across ﬁrms can improveoverall economic eﬃciency. Given that a frictional labor market often involves various externalities among market participants, there can be potential gains from government policies.
Therefore, it is of interest to know how newly-formed match qualities can diﬀer depending on
various economic situations. From a macroeconomic viewpoint, since the degree of frictionsin the labor market may vary over diﬀerent phases of the business cycle, it is natural to ask
whether a better-quality match is formed during booms than recessions. We approach thisquestion by analyzing employment durations of workers.
The main idea behind our study is that a worker-ﬁrm match with a higher match quality
would last longer. If a worker has a better match with a particular ﬁrm compared to anotherﬁrm, it is more likely that he would feel better oﬀ working in the former ﬁrm, and thus he isless likely to leave that ﬁrm. From the ﬁrm’s perspective, if a worker is a better match thananother worker, it is less likely that the ﬁrm wants to ﬁre that worker. Especially when amatch is formed eﬃciently from the viewpoint of a worker-ﬁrm pair, a high match quality
implies a high surplus, and it requires a large negative shock to break that match.
The advantage of our approach, compared to the alternative approach of directly measuring productivity and wages from matched employer-employee data, is that we can consider
a broader concept of match quality that does not show up in output or wages, such as theattachment of a worker to a particular ﬁrm or the worker’s geographical preferences.3 Our
approach is in the spirit of the revealed preferences theory—to the extent that what weeventually care about is aggregate welfare, rather than output itself, this is an advantage
1

The issue of mismatch unemployment has received considerable attention recently, in the context of theGreat Recession. See, for example, Şahin et al. (2014).
2
There has been a substantial amount of recent research on misallocation of productive resources in themacroeconomic context, following Restuccia and Rogerson (2008) and Hsieh and Klenow (2009).
3
Nosal and Rupert (2007) and Nunn (2013) emphasize the importance of considering non-wage characteristics in analyzing workers’ job choices.

1rather than a shortcoming.
At the general level, theoretical predictions about how the business cycle aﬀect the newlyformed match quality is ambiguous. In the prototypical Mortensen and Pissarides (1994)
model (modiﬁed so that the initial match quality is allowed to be stochastic), in which thematch is formed eﬃciently from the viewpoint of the individual match, a high aggregate
productivity in booms allows a relatively low-quality match to be formed. If this eﬀect
is strong, the average quality of new matches tends to be countercyclical. However, theresult also depends on the cyclicality of the job arrival rate, and it is also aﬀected by otherelements such as the eﬀectiveness of on-the-job search. When match formation/separation is
not individually eﬃcient, the disagreement between workers and ﬁrms may have conﬂicting
cyclical eﬀects. On the worker side, the unemployment rate is high during recessions, andjobseekers compete for a relatively small number of job openings. Thus the workers may bewilling to accept a job that is not so desirable. On the ﬁrm side, labor market conditions
are favorable for hiring ﬁrms during recessions, because there are a relatively small numberof hiring ﬁrms. Thus the ﬁrm is able to wait until ﬁnding a worker with a high match
quality. In addition, it is also possible to think about situations where the new match
quality distribution itself varies cyclically.
In the following, we ﬁrst empirically study the eﬀects of aggregate labor market conditions
on employment duration using data from the National Longitudinal Survey of Youth (NLSY)1979 cohort. We use the Cox (1972) proportional hazard model for job separations. Our main
innovation is that we estimate the eﬀects of the unemployment rate separately for diﬀerent
types of job separations. We consider two diﬀerent methods for dividing separations into
diﬀerent types. First, we consider the distinction between diﬀerent transition types after the
separation: job-to-job transitions (EE transitions) and separation into unemployment (EUtransitions).4 Second, we separate job spells by reasons for why the job ended; in particular,
separations by quits or by ﬁrings. We ﬁnd that a higher unemployment rate at the formationof the match has contrasting eﬀects on subsequent EE and EU transitions. The distinction
between quits and ﬁrings results in a similar contrasting outcome.
In order to interpret our empirical results, we build a simple job-ladder model to study
the match quality over the business cycle. The model-generated data exhibits a similar
pattern as the empirical results. It turns out that the cyclicality of the opportunities for EEtransitions is essential in generating the observed pattern.
The pioneering work by Bowlus (1995) also studies the employment duration over thebusiness cycle. We ﬁrst replicate her study using our dataset. Our dataset includes a longer
4

In our dataset, there is no distinction between unemployment and not in the labor force. We label all
nonemployment as “unemployment” in this paper.

2

time period, and more importantly, we are able to include prime-aged workers. We show that
Bowlus’ (1995) result, which indicates that the unemployment rate at the start of the job
has a negative eﬀect on employment durations, is substantially weaker in our dataset which
includes a longer time series. In macroeconomic literature, her result has been interpreted
as evidence that matches formed during booms are of higher quality,5 but in our dataset
the result seems more nuanced. The main diﬀerence of our study from Bowlus (1995) isthat we show that once we look at diﬀerent types of job separations separately, we can drawa clearer conclusion on the eﬀect of the business cycle on employment duration. Similarly
to Bowlus (1995), a recent paper by Mustre-del-Rio (2014) also ﬁnds that a match formed
during a boom lasts longer. His methodology is diﬀerent from ours and he focuses on thecontrast between the eﬀect of the unemployment rate at the time of job separation versus theeﬀect of the unemployment rate at the time of match formation. Finally, using a matchedemployer-employee data set, Kahn (2008) also ﬁnds that job spells are shorter when a match
is formed during a recession. However, this relationship reverses after controlling for ﬁrm
ﬁxed eﬀects.
There is an additional reason why it is important that we distinguish the types of job
separations. In the estimation of Bowlus (1995) and Mustre-del-Rio (2014), the current
unemployment rate is included as an independent variable. However, it is well known that
diﬀerent types of job separations can exhibit diﬀerent cyclical properties. For example, theEE transition rate is known to be procyclical and the EU transition rate is countercyclical(similarly, the quit rate is procyclical and the ﬁring rate is countercyclical), and thus the current unemployment rate has the opposite eﬀect on employment duration and these opposing
forces can cancel each other out. In our estimation, we can estimate both eﬀects separately.
The distinction between EE and EU transitions results in strikingly contrasting outcomes: a high unemployment rate at the start of a match increases the probability that itends with an EE transition but it has almost no (or slightly negative) eﬀect on the probability
that it ends with an EU transition. As is expected, an increase in the current unemployment
rate reduces the probability that the job spell ends as an EE transition, but it increases theprobability that it ends with an EU transition. We ﬁnd a similar pattern when we makea distinction by causes—the result for quits is similar to the EE transition and the resultfor ﬁrings (and other reasons) is similar to the EU transition. This is as expected, because
ﬁred workers tend to move to nonemployment after separation, while those who quit tend5

For example, this is an implication of the models by Moscarini (2001) and Barlevy (2002). Thesemodels consider on-the-job search and share some features with our job-ladder model, although our model
is substantially simpler. In Costain and Reiter (2008), this relationship between match quality and businesscycles plays an important role in explaining labor market volatility.

3

to move on to new jobs.6
The contrasting eﬀect on diﬀerent types of separations calls for a theoretical interpretation. To this end, we build a quantitative job-ladder model that features both endogenous
separation and on-the-job search. We estimate the model-generated data in the same way
as we treat the NLSY data. There, EE transitions and EU transitions are both considered
as separations. Theoretically, both types of separations tend to happen for a match with alow match quality. However, there are some important diﬀerences between diﬀerent types ofseparations. The matches that endogenously end as EU transitions are at the bottom of thematch quality distribution; that is, of very small match surplus. In contrast, it is possiblethat the matches that end in EE transitions have a decent match quality—workers quit
because they ﬁnd a job with even higher match quality. The responses of EU transitions aregoverned by variations in the creation of “very bottom” jobs over the cycle. The creationof very bottom jobs are mainly aﬀected by the behavior of the reservation match quality forthe unemployed. For EE transitions, the average level of match quality is more important,and thus the overall distribution matters. During recessions, the improvement of match
quality is slow because there are fewer opportunities to move to a better job. This leads toa lower level of average match quality during recessions. This in turn implies that matches
created by EE transitions during recessions are of lower quality than the ones created during
booms, because they tend to originate from a lower-quality matches. This eﬀect governs thecyclicality of new match quality through EE transitions.
In the next section, we describe the dataset. Section 3 describes the empirical methodology, in particular cause-speciﬁc and subhazard regressions. We present the estimation resultsin Section 4. Section 5 describes the theoretical framework and results. Section 6 concludes.

2

Data description

We use data from the NLSY 1979 cohort in this study. A total of 12,686 individuals born
between 1957 and 1964 participated in this survey. These individuals were interviewed
annually from 1979 through 1994 and biennially thereafter until the survey ended in 2012.
The data set we use in this study covers all the survey years until 2010. The survey collects
detailed information about each job a respondent holds or previously held. We use the
Employer History Roster (Beta Version) for employment histories for all the individuals
participating in the survey. This roster alleviates the more involved linking process across6

See Akerlof, Rose, and Yellen (1989) for a discussion.

4

diﬀerent survey years.7
Our analysis is based on making a diﬀerentiation across job separations. There are twoparticular features of the data that we use to make such a distinction. First, the panel
aspect of the data allows us to keep track of what happens after separating from the current
employer, i.e., whether the worker becomes unemployed or ﬁnds another job immediately.
Second, the data provides detailed information about the reason why a job spell ended.
A detailed description of the reasons for job separations is available in Appendix B. In
particular, we observe whether the job ended due to the worker’s quit decision to take orlook for another job or due to the ﬁrm’s ﬁring decision.
Using these two pieces of information, we make two classiﬁcations for job separations.
In the ﬁrst classiﬁcation, we distinguish employment-to-employment transitions, EE, fromtransitions to unemployment, EU . When a worker loses his job, but is able to ﬁnd a newjob within one month, we call this separation an EE transition.8 An exception is the casewhere the separation is due to an obvious layoﬀ or ﬁring. We check the reason for separationfor each job spell, and if the reason is either “layoﬀ, job eliminated” or “discharged or ﬁred,”
we do not categorize that separation as an EE transition. The reason for this exception isthat, by EE transition, we want to capture the behavior of a worker voluntarily moving to
a new job—this is how the EE transition is modeled in Section 5. We call all separations
that are not EE transitions EU transitions.
The second classiﬁcation is based on the information about the reason why a job spell
ended. We deﬁne three categories for the reasons of job separations: quits, ﬁrings, andother reasons. Our interest in quits partly comes from the intuition that, from a worker’s
perspective, job spells should be shorter for those jobs created during a recession because
workers are willing to take a low match-quality job foreseeing that they will quit to takeor look for a better job. Accordingly, it is natural to categorize quits due to reasons otherthan to take or look for another job into “other reasons.” The ﬁrm-side incentives imply
longer spells for jobs created during a recession, because these matches are expected to behigh quality, and ﬁrms are less likely to ﬁre these workers. Thus, the “ﬁrings” category
includes discharges and layoﬀs. Termination of temporary and seasonal jobs are included
in “other reasons” category, because these jobs are set for a ﬁxed term regardless of match
7

Obtaining some of the job characteristics, e.g., class of worker and union status, still requires linking
across diﬀerent survey years. We describe in detail the construction of our dataset in Appendix A.
8This is in line with the identiﬁcation of EE transitions in the literature. Studies that use Monthly
Current Population Survey, such as Fallick and Fleischman (2004), rely on survey responses that are one
month apart from each other. Tjaden and Wellschmied (2014), who use the Survey of Income and Program
Participation dataset, deﬁne job-to-job transitions as those transitions in which the worker works in two
consecutive months without reporting unemployment in between (in addition to the ones identiﬁed from theoccupational switch).

5

quality. Separations due to closings are also included in “other reasons” category since alljobs regardless of match quality are terminated with this type of job separation.9
Under each classiﬁcation, our sample consists of multiple job spells for each individual.
We measure the duration of a job spell in months. Some of the job spells are right-censored
due to the ﬁnite horizon of the survey and loss of follow-up. We include the unemployment
rate at the start of the job, u0 , to analyze the eﬀect of aggregate labor market conditions
when the job is created. We also include the current unemployment rate, ut , as a timevarying regressor to capture on-going labor market conditions. We obtain data from the
Bureau of Labor Statistics for the national unemployment rate. The time series is notseasonally adjusted so that it is consistent with the data from NLSY. The other explanatory
variables include personal and job characteristics at the start of a job such as age, gender,
race, education, and whether the job is protected by a union.

3

Estimation strategy

The Cox (1972) proportional hazard model is widely applied to duration data when time
to a failure event is of interest. In the analysis of employment duration, the failure eventof interest is job separation. In our analysis, there are multiple types (“causes”) of job
separations, and only the ﬁrst of these causes for job separation, if any, is observed. In
other words, each cause for job separation is a competing risk for the other causes. In thissection, we start with a description of Cox’s proportional hazard model when there is a single
cause for the failure event. Then, we describe two alternative approaches proposed in theliterature when there are competing risks: cause-speciﬁc hazard regressions and regression
on a subhazard function.10

3.1

Cox Proportional Hazard Model

Let the hazard function for job separations be:
P (t ≤ T < t + ∆t|T ≥ t)
.
∆t→0
∆t

h(t) = lim

The hazard function is the instantaneous probability that a job separation occurs at time T
conditional on surviving up to time t. Cox (1972) further imposes that the hazard function
for job separations, conditional on a set of explanatory variables at time t, X(t), takes the9

Inclusion of these type of job separations in the “ﬁrings” category does not change the conclusions.
Both methods have their pros and cons—see, for example, Putter, Fiocco and Geskus (2006) for a general
discussion.
10

6

following proportional form:h(t|X(t)) = h0 (t) exp(X(t)β),(1)where X(t) are time-varying explanatory variables, β is a vector of parameters common
across all job spells, and h0 (t) is the baseline hazard. The baseline hazard is also common
across all job spells, and its form is left unspeciﬁed. Cox (1972) describes a semi-parametricapproach for obtaining estimates of the model parameters, β̂, through the maximization of
the following partial likelihood function:
L =∏i:Ci =1∑∏h(ti |Xi (ti ))exp(Xi (ti )β)∑=,
j:tj ≥ti h(ti |Xj (ti ))j:tj ≥ti exp(Xj (ti )β)
i:C =1(2)iwhere Ci = 0 if the job spell is right-censored. Note that right-censored job spells enter thepartial likelihood function only through the denominator. Further, the baseline hazard can berecovered non-parametrically after obtaining β̂ even though it cancels from the estimating
equation. The proportionality assumption implies that the hazard functions are strictly
parallel and inference is possible solely based on β̂. Speciﬁcally, a positive (negative) valueof β̂ implies that the probability of job separation increases (decreases) with an increase in
the value of the explanatory variable.

3.2

Cause-specific hazard functions

A standard application of the Cox proportional hazard model can be misleading when there
are competing events. The proportional hazard model in equation (1) assumes that the
explanatory variables aﬀect the probability of job separation in the same way regardless of
its cause. However, the model is misspeciﬁed under such a restriction if the eﬀect of one of
the explanatory variables is diﬀerent for each cause-speciﬁc job separation. In this study, an
EE transition and an EU transition (or a quit and a ﬁring) are competing events for job
separations, and the theory predicts that both the starting and current unemployment rateaﬀect the probability of job separation due to these causes in opposite directions.
Taking this issue into account, here we deﬁne a separate hazard function for each causespeciﬁc job separation. Formally, let k denote one of the K possible types of job separations.
The hazard function for a job separation due to type k is:hk (t|X(t)) = h0,k (t) exp(X(t)βk ).

(3)

The speciﬁcation in equation (3) is similar to the standard speciﬁcation in equation (1) except
7

that it is now separately deﬁned for K diﬀerent possible types for job separations. Both thebaseline hazard functions and the parameters are allowed to diﬀer across diﬀerent types ofjob separations. The βk ’s can be estimated separately for each cause-speciﬁc hazard function
by maximizing the partial likelihood function in equation (2). However, the occurrence ofa competing event is treated as right-censored in each of these estimations. While theestimation procedure with cause-speciﬁc hazard functions is the same as with the standard
Cox proportional hazard model without competing risks, the interpretations of the parameter
estimates are diﬀerent. Because the distributions of time to a job separation for each causespeciﬁc event are potentially dependent, the sign of the parameter estimates alone cannot
determine the eﬀect of a covariate on the duration of employment. When the hazard functions
are estimated separately for each cause-speciﬁc job separation, the eﬀect of a change in thevariable of interest on a cause-speciﬁc job separation depends nonlinearly on baseline hazard
functions and parameter estimates of the other cause-speciﬁc hazard functions.
To illustrate this point, let the baseline cumulative cause-speciﬁc hazard function be∫ t
Hk (t) =hk (s)ds.
0Then, the probability of surviving from any event at time t isS(t) = exp(−

K∑

Hk (t)).

k=1

The survival probability now depends on the baseline and parameter estimates not only fromthe hazard regression of the event of interest, but also from the hazard regressions of theother competing events. Further, the probability of failing from cause k before time t is:∫ t
Ik (t) =hk (s)S(s)ds.

(4)0

The probability in equation (4) is called the cumulative incidence function. The cumulative
incidence function represents the probability that failure from cause k occurs before time t.
Since this is an intuitively appealing object, below we measure the eﬀect of a change in thestarting and current unemployment rates on diﬀerent types of separations by constructing
cumulative incidence functions.

8

3.3

Regression on a subhazard function

As an alternative to cause-speciﬁc hazard regressions, Fine and Gray (1999) propose amethodology that allows inference on cumulative incidence functions solely based on estimates of β. They deﬁne a subhazard function for the competing risk k as follows:
P (t ≤ T < t + ∆t|T ≥ t ∪ (T ≤ t ∩ K ̸= k))
.
∆t→0
∆t

h̄k (t) = lim(5)

The subhazard function shows the instantaneous probability of a job ending due to reason
k conditional on surviving up to time t or ending before time t due to a reason other thank. Similarly to Cox’s proportional hazard model, Fine and Gray (1999) assume that thesubhazard function takes the form:h̄k (t|X(t)) = h̄0,k exp(X(t)βk ).

(6)

The subhazard function in equation (6) can be estimated in a way that is analogous toequation (2). The only diﬀerence in the estimation procedure is in the treatment of the risk
set. According to equation (5), job spells that have already ended due to another cause arestill considered to be in the risk set for the competing risk k. Since these observations canpotentially become right-censored and dropped from the risk set (but the censoring cannot
be observed because job spells have already ended), Fine and Gray (1999) weight them using
the Kaplan-Meier estimate of the survivor function for the censoring distribution.
One of the advantages of the estimation strategy proposed by Fine and Gray (1999)
is that inference can now be made solely based on β̂, because the subhazard function is
directly linked to the cumulative incidence function. Note that the baseline cumulative
incidence function and subhazard function for the competing risk k are related as follows:( ∫ t)
Ik (t) = 1 − exp −h̄k (s)ds .
0

The estimates of β have a similar interpretation to the standard Cox proportional hazard
model. A positive (negative) value of β̂k implies that increasing the value of the explanatory
variable increases (decreases) the probability of job separation due to cause k.

9

4

Results

4.1

Sample restrictions

Following Bowlus (1995), we restrict the dataset to include only private sector employment.
Jobs that start before the individual completes all schooling or is younger than 16 years old
are dropped from the sample. Further, jobs with missing information and those lasting lessthan a month are not included in the sample. Unlike Bowlus (1995), we include females inour sample. Bowlus (1995) restricts the sample to only males on the grounds that females
are likely to quit for reasons other than poor match quality, such as marriage, pregnancy,and childcare. We do not make such a restriction on our sample, because it is likely that
distinctions among job separations can control for these diﬀerences.
The original dataset consists of multiple job spells for each individual. If there is anindividual-speciﬁc unobserved component, the job spells for the same individual are potentially correlated and the estimates of β are biased. To address the concerns about unobserved heterogeneity, we follow Bowlus (1995) and randomly select one spell per individual.
Bowlus (1995) argues that such a restriction on the sample (under certain restrictions on
the distribution of unobserved heterogeneity) produces unbiased estimates of β.11 However,
the estimates for the baseline hazard functions are still biased, because longer spells are
now overrepresented in the sample. Since cumulative incidence functions are constructedfrom the estimates of the baseline hazard functions, they are also potentially biased. Whilethe bias in cumulative incidence function calculations is problematic for inference from thecause-speciﬁc hazard regressions, this is not a concern for the subhazard regressions because
inference is possible solely based on the estimates of β.

4.2

Preliminary estimation

As a preliminary step, we ﬁrst repeat Bowlus’s (1995) analysis. First, we run her estimation
with the same time period as hers (from 1979 to 1988). For comparability, we exclude
females from our sample in this section along with other restrictions in the previous section.
Also only in this section, we use the weekly employment status instead of monthly. In thesubsequent sections, we use monthly employment status so that it can be directly comparable
to the model in Section 5.
Table 1 presents the estimation results. The ﬁrst column is from Table 1 in Bowlus(1995), and the second column is from our sample which covers the same time period as hers.
11

See pp. 340-341 of Bowlus (1995) for detailed discussions. She argues that even when the unobservables
do not have the correct distribution, inference is still possible and when a variable has a signiﬁcant impact
on the hazard rate, this indicates that the variable’s impact is real and not due to the misspeciﬁcation bias.

10Variable
u0
ut
u2t
HS
COL
AGE
SQAGE
NWHITE
UNION
Occurrence:# of observations:# of right-censored:

BowlusSampleOur sample(Short Panel)

Our sample(Long Panel).050*(.023)−.460*(.183).028*(.011)−.260**(.066)−.521***(.106)−.152(.112)−.003(.003).090(.068)−.174*(.076).052**(.016)−.321*(.126).018*(.008)−.170***(.045)−.790***(.080)−.027(.085).001(.002).069(.039)−.481***(.048).007(.014).389***(.098)−.025***(.006)−.107*(.045)−.545***(.067).262***(.026)−.005***(.001).171***(.035)−.360***(.043)

1392
2135
743

2873
4330
1457

3456
4073
617

Table 1: Replication of Bowlus (1995). The ﬁrst column is taken from Bowlus (1995, Table 1). The second and third columns are the replication of her results with our samples
from 1979 to 1988 and from 1979 to 2010, respectively. UNION=1 if the job is covered
under a union contract or collective bargaining agreement; NWHITE=1 if the respondent isblack or hispanic; SQAGE=age squared; HS=1 if the respondent is a high school graduate,
and COL=1 if he completed 16 or more years of education. Standard errors are given inparentheses. * indicates signiﬁcant at 5%, ** indicates signiﬁcant at 1%, and *** indicatessigniﬁcant at 0.1%.

11

Despite the retrospective corrections of the samples and randomness in selecting spells, ourresult is qualitatively very similar to hers. In particular, u0 has a signiﬁcantly positive eﬀect
on separation probability, indicating that the match quality is higher for the jobs that are
created in booms.
Next, we extend the sample period to the same as the current analysis (from 1979 to 2010)
and repeat the analysis. We maintain the same sample restrictions as Bowlus (1995). The
third column in Table 1 presents the estimation results from the longer panel. Now the eﬀectof u0 becomes statistically insigniﬁcant. The diﬀerence is likely due to the age of samples—
Bowlus’ (1995) samples consist of very young workers, whose labor market experiences arevery diﬀerent from older workers. To the extent that we are interested in the behavior of
typical worker-ﬁrm match, our samples are more representative of the entire economy thanhers. Below, in our main analysis, we show that the eﬀect of u0 is more transparent once wetake diﬀerent types of separations into account.

4.3

EE and EU transitions

In this section, we treat movement to another job and transition to non-employed status ascompeting risks. Table 2 presents our main estimation results. The ﬁrst two columns show
the estimation results from the cause-speciﬁc hazard regressions for EE transitions and EU
transitions. The last two columns show the results from the subhazard resgressions. The
coeﬃcients of interest are those for the unemployment rate at the start of the job spell, u0 ,and the current unemployment rate, ut , for EE transitions and EU transitions.
The eﬀects of the explanatory variables can be directly inferred from the estimates ofthe subhazard regressions. The eﬀect of u0 is positive and statistically signiﬁcant for EEtransitions. The positive sign implies that a high unemployment rate at the start of a job
spell increases the probability that the worker moves from his current job to another job. In
contrast, for the job separations that results in EU transitions, the sign of the coeﬃcient for
u0 is negative, which implies that a high unemployment rate at the start of a job reduces
the probability that the worker experiences EU transition in the future.
In the aggregate data, the cyclical behavior of the EE and EU ﬂow rates are qualitatively
diﬀerent. While the EE ﬂow rate is strongly procyclical, the EU ﬂow rate is strongly countercyclical. This macro-level observation suggests that they also respond to ut in opposite
directions. The negative coeﬃcient for ut from the subhazard regression for EE transitions
indicates that the probability that a job spell ends with an EE transition is lower during
recessions. In contrast, the coeﬃcient estimate from the subhazard regression for the EU
transitions is positive and statistically signiﬁcant. The positive coeﬃcient implies that the12Cause-Specific Hazard
Variable
u0
ut
HS
COL
AGE
SQAGE
NWHITEGEN
UNION
Occurrence:

EEEU.043**(.015)−.035*(.016).042(.055)−.066(.067).388***(.028)−.007***(.000)−.008(.038)−.191***(.037)−.501***(.050)−.029(.015).096***(.014)−.255***(.046)−1.080***(.078).105***(.022)−.002***(.000).272***(.036).247***(.035)−.366***(.046)

3111

3276

Subhazard
EE

EU.134***−.050**(.020)(.018)−.188*** .086***(.023)(.019).186**−.236***(.055)(.045).419*** −.948***(.066)(.076).263***−.040(.025)(.021)−.005***.000(.000)(.000)−.116**.283***(.038)(.035)−.287*** .309***(.036)(.035)−.226*** −.105*(.048)(.043)
3111

3276# of observations: 7551
# of right-censored observations: 1164
Table 2: Estimation results for hazard functions under EE and EU classiﬁcations.
UNION=1 if the job is covered under a union contract or collective bargaining agreement;
GEN=1 if the respondent is female; NWHITE=1 if the respondent is black or hispanic;
SQAGE=age squared; HS=1 if the respondent is a high school graduate, and COL=1 if
he completed 16 or more years of education. Standard errors are given in parentheses. *indicates signiﬁcant at 5%, ** indicates signiﬁcant at 1%, and *** indicates signiﬁcant at
0.1%

13

probability that a job spell ends with an EU transition is higher during a recession. Bothof these estimates are consistent with the cyclical behavior of EE and EU ﬂows.
The results for the eﬀect of ut are crucial for isolating the eﬀect of u0 , as the duration of a job spell is aﬀected by the current cyclical ﬂuctuations. Both Bowlus (1995) and
Mustre-del-Rio (2014) include the unemployment rate as an explanatory variable for hazard
regressions. However, the model suﬀers from misspeciﬁcation bias if ut has opposite eﬀects
on the decisions of workers and ﬁrms. In both of these papers, the coeﬃcient estimate for
ut is statistically insigniﬁcant when it is added linearly to the model. Bowlus (1995) further adds the squared value of ut to the right-hand side variables, and the estimates forthe explanatory variables involving ut are signiﬁcant in her results. By distinguishing job
separations according to their causes, we separately identify the eﬀects of current cyclicalﬂuctuations on the duration of a job spell ended with EE transitions and EU transitions.
The opposite signs for diﬀerent causes support the discussion about the eﬀect of ut raised in
Bowlus (1995).12
While the estimates from the subhazard regressions provide a direct inference on theeﬀects of u0 and ut on EE transitions and EU transitions, using these estimates to makeinferences about the overall duration of employment can be misleading. The subhazard
functions for diﬀerent reasons of job separations are estimated separately, and the probabilityof job separation can potentially exceed one when the value of one of the explanatory variables
is changed.
To evaluate the overall behavior of employment durations, we use the coeﬃcient estimatesfrom the cause-speciﬁc hazard regressions. Note that the estimates of the coeﬃcients from thecause-speciﬁc regressions alone are not informative about the eﬀects of u0 and ut , although
the signs agree with the estimates from the subhazard regressions. Therefore, we obtainthe cumulative incidence functions for each job separation category using the coeﬃcient andbaseline hazard estimates from the cause-speciﬁc hazard regressions. By construction, theprobability of job separation is less than one at any point in time.
Figure 1 shows the cumulative incidence functions for each cause-speciﬁc job separations.
The cumulative incidence functions are drawn for a 29 year-old high-school graduate whitemale whose job is not protected by a union. The unemployment rate is set equal to theaverage value of the unemployment rate for the survey years, 6.15%, and it is assumed tobe equal to this value for all of the time periods from the start of the job. The plots forboth termination types are stacked so that the diﬀerences show the probability of observing
12

Bowlus’ (1995) motivation for including the current unemployment rate non-linearly in her analysis is
to capture the countercyclicality of ﬁrings. Because we make a distinction across job spells according totransition type and reason, we do not need to maintain this non-linearity assumption. Hence, we drop u2t
from our analysis.

14

0.8

Event
Free

0.7

Probability

0.6EUMovement

0.5
0.4
0.3

EE
Movement

0.2

Median Duration: 10 months
0.1
0
0

5

10

15

20

25

MonthsFigure 1: Cumulative incidence functions for quits, ﬁrings, and other reasons. The cumulative incidence functions are stacked so that the distance between two curves represents theprobabilities of the diﬀerent events.
the corresponding cause-speciﬁc job separation before time t. At any time t, the diﬀerence
between the sum of cumulative incidence functions and one represents the survival probability. From the survival probability, we can calculate that the median duration of a job is
10 months.
Figure 2 shows the eﬀects of a change in u0 on the cumulative incidence functions for EEtransitions and EU transitions. In each plot, the solid curve shows the cumulative incidence
functions when u0 is equal to its sample mean for the period under study, 6.15%. The
dashed and dotted curves correspond to the cumulative incidence functions when u0 is one
standard deviation, 1.71 percentage points, above or below its sample mean. The current
unemployment rate is still kept at its average value for all of the remaining time periods.
It can be seen that the quantitative magnitude of the eﬀect of u0 on the EE transition
probability is signiﬁcantly larger than the eﬀect on the EU transition probability.
Similar results hold for the eﬀects of ut . Figure 3 shows the change in the cumulative
incidence functions for cause-speciﬁc job separations after a change in ut . In each plot, thesolid curves show the cumulative incidence functions when ut is equal to its sample mean.
The dashed and dotted curves correspond to the cumulative incidence functions when ut ispermanently one standard deviation above or below its sample mean for all the periods after
the job spell has started.
Comparing Figures 2 and 3, the eﬀect of u0 on the probability of EE movements isof quantitatively comparable order to the eﬀect of ut . The eﬀect of aggregate economic
15a) EE Movements

0.6

0.5

0.5

high u00.4

Probabilityb) EU Movements

0.6

0.4

low u00.3

0.3

low u00.2

0.2high u0
0.1

0

0.1

0

10

0

20

0

Months1020MonthsFigure 2: Changes in cumulative incidence functions in response to a change in u0 .

a) EE Movements

0.6b) EU Movements

0.6

0.5

0.5

Probability

low ut
0.4

0.4

0.3

0.3

high uthigh ut
0.2

0.2

0.1

0.1

low ut

0

0

10

0

20

Months01020MonthsFigure 3: Changes in cumulative incidence functions in response to a change in ut .

16

conditions (here represented by ut ) on worker ﬂows is well documented and extensively
studied. These ﬁgures show that the eﬀect of u0 on worker ﬂows is also quantitatively
important.

4.4

Quits, firings, and other reasons

In this section, we distinguish job spells based on the reasons for job separation. The ﬁrst
three columns show the estimation results from the cause-speciﬁc hazard regressions for job
separations due to quits, ﬁrings, and other reasons, respectively. The last three columns
show the results from the subhazard regressions.
Table 3 paints a very similar picture as Table 2, with quits corresponding to EE transitions and ﬁrings (and other reasons) corresponding to EU transitions. The unemployment
rate upon match has a positive eﬀect on quits and small negative eﬀect on ﬁrings. The
current unemployment rate has a negative eﬀect on quits and a positive eﬀect on ﬁringsand other reasons. Again, these eﬀects of ut can easily be understood by the procyclicalaggregate quit rate and countercyclical aggregate ﬁring rate.
Figures 4, 5, and 6 correspond to Figures 1, 2, and 3 in the previous subsection. The
results are very similar, with quits corresponding to EE transitions and ﬁring (and otherreasons) corresponding to EU transitions. In the following model analysis, we focus solely
on the EE-and-EU distinction, mainly because of the diﬃculty in deﬁning quits and ﬁrings
at a theoretical level. However, given these direct associations, we believe that the quitsand-ﬁrings distinction can also be interpreted similarly.13

5

Model

In this section, we analyze a simple job-ladder model in order to interpret our empiricalﬁndings in a more formal setting.14 Our model focuses on a worker’s decision of whether toaccept a job with a given match quality. Firms’ decisions are not modeled explicitly—one
interpretation is that ﬁrms’ decisions are implicit in the distribution of oﬀered match quality
13

One alternative interpretation of the diﬀerence in results between quits and ﬁrings is the diﬀerent motivations for workers and ﬁrms. For matches where workers’ decisions are important in the match formation/separation, workers tend to take low-quality jobs in recessions and they tend to quit into another job
in future. For matches where ﬁrms’ decisions are important, the match quality improves during recessions
because the ﬁrms can wait longer until a good match comes along, and they are less likely to end up withﬁrings in the future. This interpretation is not explicitly considered in the model in the next section—weleave it to future research to investigate this (and other potential) interpretation further.
14
Given that the ﬁt of the model to the empirical results turns out to be very good, another possible
interpretation of this paper’s exercise is that we are estimating the job-ladder model with indirect inference(Smith (1993) and Gouriéroux and Monfort (1996)), using the Cox model as the auxiliary model.

17

Cause-Specific Hazard
Variable
u0
ut
HS
COL
AGE
SQAGE
NWHITEGEN
UNION
Occurrence:

Quits

Firings.182***−.065**(.023)(.017)−.131***.161***(.019)(.021).023−.250***(.060)(.069)−.083−1.316***(.074)(.131).646***.089**(.040)(.035)−.012*** −.002***(.001)(.001).084**.286***(.042)(.055)−.083** −.252***(.041)(.056)−.510*** −.156**(.056)(.064)
2536

Subhazard
Other−.175***(.019).135***(.017)−.173**(.055)−.707***(.082).070**(.024)−.002***(.001).114**(.042).313***(.041)−.520***(.056)

1398

2453

Quits

Firings.396***−.123***(.021)(.032)−.423***.179***(.025)(.031).149*−.185**(.061)(.069).382*** −1.028***(.074)(.129).541***−.060(.048)(.034)−.010***.001(.001)(.001).017.236***(.042)(.054)−.130*** −.294***(.040)(.055)−.241***.179**(.054)(.062)
2536

1398

Other
−.272***(.024).174***(.023)−.097(.055)−.454***(.079)−.065**(.023).001(.000).053(.042).341***(.041)−.255***(.053)
2453# of observations: 7551
# of right-censored observations: 1164
Table 3: Estimation results for hazard functions under quits, ﬁring, and other reasons classiﬁcations. UNION=1 if the job is covered under a union contract or collective bargaining
agreement; NWHITE=1 if the respondent is black or hispanic; SQAGE=age squared; HS=1
if the respondent is a high school graduate, and COL=1 if he completed 16 or more yearsof education. Standard errors are given in parentheses. * indicates signiﬁcant at 5%, **indicates signiﬁcant at 1%, and *** indicates signiﬁcant at 0.1%

18

0.8

Event
Free

0.7

Probability

0.6
0.5

Other
reasons

0.4

Firings

0.3

Quits

0.2
Median Duration: 10 months
0.1
0
0

5

10

15

20

25

MonthsFigure 4: Cumulative incidence functions for quits, ﬁrings, and other reasons. The cumulative incidence functions are stacked so that the distance between two curves represents theprobabilities of the diﬀerent events.

a) Quits

0.5

0.5

high u0

0.5

0.45

0.45

0.4

0.4

0.35

0.35

0.35

0.3

0.3

0.3

0.25

0.25

0.25

0.2

0.2

0.45
0.4

Probabilityb) Firings

low u0low u0

0.2

0.15

0.15

0.1

0.1

0.1

0.05

0.05

0.15

0
0

low u010Months2000c) Other Reasonshigh u010Months20high u0

0.05
0
0

10

20

MonthsFigure 5: Changes in cumulative incidence functions in response to a change in u0 .

19

0.5

a) Quits

0.45

0.5

b) Firings

0.5

0.45

0.45

0.4

0.4

0.4

0.35

0.35

0.35

0.3

0.3

0.3

0.25

0.25

0.2

0.2

0.2

0.15

high ut 0.15

0.15

0.1

0.1

0.1

0.05

0.05

c) Other Reasons

Probability

low uthigh uthigh ut

0.25

low ut0.05

low ut0010Months

20

0
0

10

Months

20

0
0

10

20

MonthsFigure 6: Changes in cumulative incidence functions in response to a change in ut .
(the distribution is assumed to be the same over time) and labor market frictions. Anotherinterpretation is that the match formation/separation decision is eﬃcient so that workers’
decisions and ﬁrms’ decisions agree with each other.
As is mentioned in the previous section, there can be interpretations that are not captured
in this simple model. This model should therefore be viewed as a ﬁrst step, and although
it is indeed quite surprising that this model can quantitatively capture the above empiricalpatterns quite well, it does not rule out alternative (possibly more complex) interpretations.

5.1

Setup

The model setup is the standard job-ladder model.15 An inﬁnitely-lived worker is either
employed or unemployed. We assume that his utility is linear and he consumes what hereceives each period. An employed worker receives a wage of zx. The component z is theaggregate productivity and x is the match quality. z follows a Markov process according to
F (z ′ |z), where ′ (prime) represents the next period. We assume that x is constant for a given
job. At the beginning of the following period, an employed worker can receive two diﬀerent
shocks. First, he may receive a job oﬀer from another employer. The probability of this15

Moscarini and Postel-Vinay (2014) use a similar model in their analysis of the Great Recession.

20

shock is λe (z ′ ) ∈ [0, 1]. Note that this probability is a function of the next period aggregate
state z ′ . The match quality of this new job is randomly drawn from a distribution that isconstant over time, G(x). After seeing the match quality, the worker chooses whether tostay in the same job, move to the new job, or move to unemployment. The second shock is aseparation shock with probability δ(z ′ ) ∈ [0, 1] which forces him to move to unemployment.
We assume that λe (z ′ ) + δ(z ′ ) ≤ 1 for all z ′ .
An employed worker’s Bellman equation can be written as
W (x, z) =zx + βEx′ ,z′ [λe (z ′ ) max{W (x′ , z ′ ), W (x, z ′ ), U (z ′ )}+ (1 − λe (z ′ ) − δ(z ′ )) max{W (x, z ′ ), U (z ′ )} + δ(z ′ )U (z ′ )].
Here, W (x, z) is the value function of an employed worker, U (z) is the value function of an
unemployed worker, and β is the discount factor. The operator Ex′ ,z′ [·] takes the expectedvalue with regard to x′ and z ′ .
An unemployed worker receives a job oﬀer with probability λu (z ′ ) ∈ [0, 1]. While unemployed, he receives a ﬂow value of b, which can be interpreted as the combination ofunemployment insurance beneﬁt, home production, and the value of leisure. After observing
the match quality of the oﬀer, he chooses whether to take that job. An unemployed worker’s
Bellman equation is therefore
U (z) = b + βEx′ ,z′ [λu (z ′ ) max{W (x′ , z ′ ), U (z ′ )} + (1 − λu (z ′ ))U (z ′ )] .

5.2

Calibration
1

One period is set as one month. The discount factor is set at β = 0.99 3 , as in Gertler andTrigari (2009). Following Hall and Milgrom (2008), we choose b so that it is 71% of theaverage wage. F (z ′ |z) approximates an AR(1) process:log(zt+1 ) = ρz log(zt ) + ϵt ,1

where ϵt ∼ N (0, σz2 ). We set ρz = 0.95 3 , again following Gertler and Trigari (2009). For σz ,we target the cyclicality of the wages of new hires. This is because it is commonly consideredthat existing workers’ wages tend to be sticky, and here what aﬀects the match formation is
the wages at the time of contact between the worker and the ﬁrm. Shimer (2005b) estimates
the standard deviation of labor productivity to be 2 percent quarterly, after HP-ﬁlteringwith parameter 105 . In Pissarides (2009), the elasticity of job changers’ wages with respect
to labor productivity is estimated to be 1.70. Haefke et al. (2013) estimates this elasticity to21

be 1.31 for new hires from non-employment and 2.02 for job changers, although the standard
errors are large (Table 8). This provides the target of the quarterly standard deviation ofwages for new matches to be from 2.6 percent to 4.0 percent. We set σz to be 0.01, which
gives us 3.1 percent value for this target.
The logarithm of the match quality shock is normally distributed with its mean normalized to zero, log(x) ∼ N (0, σx2 ). The dispersion in x directly aﬀects the gains from switching
to another employer. Tjaden and Wellschmied (2014) estimate the average wage gain upon
job-to-job transition to be 3.3%, and we target this value. This gives us σx = 0.035.
The labor market frictions, λu (z), λe (z), and σ(z), are calibrated using labor market
ﬂows. First, we assume that λe (z) is proportional to λu (z); λe (z) = αλu (z).16 We set
α = 0.27 to target an average job-to-job ﬂow rate of 1.4% per month, again taken fromTjaden and Wellschmied (2014).
We assume that λu (z) and δ(z) take the following form:λu (z) = λ̄u + ϕλ log(z),andδ(z) = δ̄ − ϕδ log(z).
The average values, λ̄u and δ̄, are set so that the model replicates the gross ﬂow rate for
unemployment to employment and employment to unemployment. Krusell et al. (2015)
calculate these values (with adjustments for measurement errors) as 0.235 and 0.014 permonth, using the Current Population Survey dataset.17 The parameter values are λ̄u = 0.242
and δ̄ = 0.014. The parameters governing the ﬂuctuations, ϕλ and ϕδ , are set so that theﬂuctuations of the corresponding ﬂow rates in the model mimics the behavior of the data.
Krusell et al. (2015) calculate the standard deviation of (quarterly averaged, logged, andHP-ﬁltered with parameter 1,600) these ﬂows as 0.085 and 0.085. We obtain ϕλ = 1.10 andϕδ = 0.063. Table 4 summarizes the calibration.

5.3

Results

The model implies the steady-state value of unemployment at 5.6%. The standard deviationof employment and the unemployment rate are 0.009 and 0.136. The corresponding empirical
16
Shimer (2005a), Moscarini and Postel-Vinay (2014), and Mukoyama (2014) employ a similar assumption.
This property comes out naturally from a search and matching model where employed and unemployedworkers compete for the same set of vacancies, but they diﬀer in the eﬃciency of search.
17
The time span that Krusell et al. (2015) analyze is from 1978 to 2009, which is almost identical to ourdata period.

22

Parameter

Description

Target/Source

Value

β

Discount Factor

Gertler and Trigari (2009)

0.99 3b

Value of unemployment

Hall and Milgrom (2008)

0.735

ρz

Persistence of aggregate shocks

Gertler and Trigari (2009)

0.95 3σz

Dispersion of aggregate shocks

cyclicality of new hire’s wages

0.01

σx

Dispersion of match quality

Tjaden and Wellschmied (2014)

0.035

α

λe (z) relative to λu (z)Tjaden and Wellschmied (2014)

0.27

λ̄u

Average value of λu

Krusell et al. (2015)

0.242

δ̄

Average value of δ

Krusell et al. (2015)

0.014

ϕλ

Fluctuation parameter of λu

Krusell et al. (2015)

1.10

ϕδ

Fluctuation parameter of δ

Krusell et al. (2015)

0.063

1

1

Table 4: Calibration
Cause-Specific Hazard
Variableu0
ut
Occurrence:

EE

EU.051***(.002)−.084***(.002)−.005*(.002).090***(.002)

95741

93014

Subhazard
EE

EU.074*** −.085***(.003)(.003)−.141*** .161***(.003)(.003)
95741

93014

# of observations: 188755
Table 5: Regression results from model generated data. Standard errors are given in parentheses. * indicates signiﬁcant at 5%, ** indicates signiﬁcant at 1%, and *** indicates significant at 0.1%
values are 0.010 and 0.113 in the data (Krusell et al. 2015).18 As in the data, the ﬂow rate
for job-to-job transition and U E ﬂow are procyclical and EU ﬂow rate is countercyclical(the corresponding correlation coeﬃcients with the unemployment rate are −0.686, −0.876,
and 0.821). Thus the model represents the aggregate cyclical movement of the labor market
very well.
Now we turn to the micro-level behavior of employment duration. Table 5 presents theresults from running the same estimation as Section 4 on model-generated data. The model
predictions are largely consistent with the empirical result.
18

For all summary statistics below, the variables are quarterly averaged, logged, and HP-ﬁltered withparameter 1,600.

23

1.05

average x of new match

1.045

from another job

1.04
1.035
1.03
1.025
1.02
1.015

from U

1.01
1.005
1
0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

unemployment rate
Figure 7: Average value of new x at each period, plotted against the unemployment rate
5.3.1

Intuitions

Interpreting the coeﬃcients for ut is straightforward. Largely because of the movementsin λe (z) and δ(z), the EE ﬂow rate is procyclical and the EU ﬂow rate is countercyclical.
Interpreting the coeﬃcients on u0 requires more information, as it is a reﬂection of the qualityof matches formed in the past.
The key to understanding these coeﬃcients is what type of matches are created at eachpoint in time. Figure 7 plots the simulated average match quality for new workers, calculated
separately for the matches formed by EE transitions (“from another job”) and the matches
formed by U E transitions (“from U ”). The average match quality is plotted against the
unemployment rate. One can see striking diﬀerences in these two series. First, the average
quality of matches formed by EE transitions is higher than that of matches formed by U Etransitions. This is natural because EE transitions are more selective. Second, they exhibit
a diﬀerent relationship with the unemployment rate. Let us consider them one by one.
For the U E transition, because the distribution of new x is constant over the businesscycle, the average quality in Figure 7 reﬂects the reservation match quality. The reservation
match quality, in relation to the aggregate state z, is plotted in Figure 8.19
There are two properties that are notable in Figure 8. First, the reservation match quality
19

The discreteness of the graph in Figure 8 comes from the grid points we use. This is also reﬂected in
the outcome for U E transitions in Figure 7.

24

0.948threshold value of x

0.946
0.944
0.942
0.94
0.938
0.936
0.934
0.932

0.9

0.95

1

1.05

1.1

z

Figure 8: Reservation match quality for each z
is decreasing in z. This means that more of the “very bottom quality” jobs are created inbooms, and they are destroyed when a recession arrives. This is reﬂected in the (smallbut) negative entry of u0 ’s inﬂuence on EU ﬂow, although the mapping between the average
match quality and the coeﬃcient is not exact.20 The jobs that are created in booms are more
likely to be separated into unemployment. Second, the slope is very small, compared to theﬂuctuations in z. This is because there are multiple eﬀects oﬀsetting each other. First andthe most obvious eﬀect is that when z is high, zx can be high even if x is low, so that evena low x can be accepted. Second, because λu (z) is increasing in z, there are more chancesof obtaining another draw in booms, and this makes the worker more choosy during booms.
This raises the reservation match quality in booms—the exact opposite of the ﬁrst eﬀect.
The third eﬀect is that because λe (z) is increasing in z, the worker is willing to take a low-x
match, thinking that there will soon be another chance on the job. This oﬀsets (a part of)
the second motive of waiting in booms.
The fact that the proﬁle in Figure 8 is close to ﬂat implies that these eﬀects almost
exactly oﬀset each other. This is reﬂected in the small size in the coeﬃcient of u0 for EU
20

Another reason for the negative coeﬃcient on u0 here is that ut does not adjust immediately to thechange in z. For example, when z decreases very rapidly, ut does not increase immediately and thus theterm with ut under-predicts the increase in the EU ﬂow rate. A part of increase in the EU ﬂow rate is thus
attributed to the fact that the recent unemployment rate was low, and to the extent that u0 is a reﬂectionof the recent unemployment rate, this eﬀect can generate a negative coeﬃcient on u0 .

25

1.05
1.045
1.04

average x

1.035
1.03
1.025
1.02
1.015
1.01
1.005
1
0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

unemployment rate
Figure 9: Average value of x, plotted against the unemployment ratetransitions in the cause-speciﬁc hazard regression (although, once again, the mapping is notexact because of the competing risks structure). It is almost statistically insigniﬁcant despite
generating a very large sample. We believe that this is in fact a favorable property of themodel, considering that the corresponding coeﬃcient in Table 2 is insigniﬁcant.
It is relatively straightforward to understand the relationship between the unemployment
rate and the average new match quality for EE transitions in Figure 7. In booms, the average
match quality for existing matches is already good, because of the frequent opportunity for
job-to-job transitions (this can be seen from Figure 9 which plots the average match quality
for all matches). Thus the new match formed by a job-to-job transition in a boom shouldhave a higher match quality compared to the match formed in a recession. The pattern inFigure 7 for EE transitions is reﬂected in the coeﬃcient on u0 for EE in Table 5. Because
the average x of jobs created in recessions by job-to-job transitions are worse, these jobs will
have more opportunity to experience EE transitions in future.
In sum, the model provides theoretical intuitions for our empirical results in earlier sections. It is substantially easier to interpret the outcome by inspecting the mechanism in themodel than directly speculating what is in behind the regression coeﬃcients from the data,
since we can directly observe the match quality in the model.
Finally, going back to the original question of whether a better quality match is createdduring booms or recessions, we provide two answers. First, because the oﬀered match quality

26

1.05

average x of new match

1.045
1.04
1.035
1.03
1.025
1.02
1.015
1.01
1.005
1
0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

unemployment rate
Figure 10: Average value of x for newly formed match, plotted against the unemployment
rate
distributions in the job-ladder model is acyclical and it is still capable of generating theregression coeﬃcients that are empirically relevant, we can conclude that the cyclicality ofoﬀered match quality distribution is not necessary in explaining the pattern of employment
duration. This is important because one possible explanation of Bowlus’ (1995) result is atechnology shock that is cohort-speciﬁc.21 Second, the change in job-to-job transition rate
is an essential driver of the quality distribution of new matches over the business cycle.
Figure 10 plots the overall average quality of new matches, and it is clearly procyclical. In
this sense, Bowlus’ (1995) takeaway that the quality of new matches is procyclical survives,
despite the fact that the coeﬃcient on u0 for her Cox (1972) regression in our extended
samples is not statistically diﬀerent from zero (in Table 1). We reach this conclusion froman entirely diﬀerent route from Bowlus (1995). Our approach is to distinguish diﬀerent typesof separations and to build a model that matches the data properties in order to directly
observe the match quality of newly-formed matches.
21

See, for example, Costain and Reiter (2008).

27

6Conclusion

In this paper, we empirically examined the eﬀects of labor market conditions on the durationof employment. Using data from NLSY 1979 cohort, we estimated a proportional hazard
model under the assumption that diﬀerent causes of job separations are competing risks.
Making a distinction between diﬀerent types of separations is the main contribution of thispaper, because it allowed us to test separately for both of these opposing forces rather thanestimating their net eﬀect on the duration of employment.
Two functions, the cause-speciﬁc hazard function and the subhazard function, have been
widely used in the literature to estimate hazard models when there are competing risks. We
applied both of these in this paper and they produced results that are consistent with eachother. We found that an increase in the unemployment rate at the start of an employment
relation increases the probability that a separation with job-to-job transition occurs, but it
reduces the probability that it ends with the worker moving into unemployment.
The distinction based on reasons for the separation, which divides the separations intoquits, ﬁrings, and other reasons, yielded a similar result. This was as expected because
the majority of quits result in job-to-job transitions and ﬁred workers tend to transit into
unemployment.
There can be several diﬀerent interpretations for the diﬀerent patterns of job-to-job transitions and transitions into unemployment (or quits and ﬁrings) in relation to the aggregate
condition at the time of match formation. In order to examine the mechanism formally,
we built a simple job-ladder model and calibrated it to match the U.S. data. The modeloutcome is largely consistent with the empirical results.
The model allowed us to interpret the results in the empirical part more directly in thecontext of match quality. The model outcome shows that the average quality of new matches
is procyclical. It also clariﬁes that job-to-job transitions play an important role in analyzing
the time-series of the average quality of new matches. Our result suggests that when studying
the issues of “mismatch” in the labor market, it is essential to take job-to-job transitions
into account.22

22
Barlevy (2002) and Mukoyama (2014) emphasize the consequences of this “mismatch employment” onaggregate productivity.

28

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[2] Barlevy, G. (2002): “The Sullying Eﬀect of Recessions,” Review of Economic Studies
69, 65–96.
[3] Bowlus, A. J. (1995): “Matching Workers and Jobs: Cyclical Fluctuations in Match
Quality,” Journal of Labor Economics 13, 335–350.
[4] Costain, J. S., and M. Reiter (2008): “Business Cycles, Unemployment Insurance,
and the Calibration of Matching Models,” Journal of Economic Dynamics and Control
32, 1120-1155.
[5] Cox, D. R. (1972): “Regression Models and Life Tables.”, Journal of Royal StatisticalSociety, 34(2): 187-220.
[6] Fallick, B. and C. A. Fleischman (2004): “Employer-to-Employer Flows in the
U.S. Labor Market: The Complete Picture of Gross Worker Flows,” FEDS Working
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[7] Fine, J. P. and R. J. Gray (1999): “A Proportional Hazard Model for the Subdistribution of a Competing Risk,” Journal of American Statistical Association 94, 496–509.
[8] Gertler, M. and A. Trigari (2009): “Unemployment Fluctuations with Staggered
Nash Wage Bargaining,” Journal of Political Economy 117, 38–86.
[9] Gouriéroux, C. and A. Monfort (1996): Simulation-Based Econometric Methods,
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[10] Haefke, C., M. Sonntag, and T. van Rens (2013): “Wage Rigidity and Job
Creation,” Journal of Monetary Economics 60, 887–899.
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of Recessions,” mimeo. Federal Reserve Bank of Kansas City.
29

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31

Appendix
A

Details of Data Construction and Summary Statistics

We use the Employer History Roster (Beta version) provided by NLYS 1979. This roster
contains information about each of the up to 57 jobs every individual holds. We retrieved
the job start and end dates, employment status, and reason for job separations directly fromthis roster. Class of worker and union status are spread out on a roster created separately
for each survey year. We created these variables by linking the rosters for each survey year.
We removed observations with inconsistent information. We use the job start and end dates
to calculate the duration of the job spells and the information on employment status todetermine censored observations.
Starting from 1980, each survey asks respondents about their school enrollment for eachmonth from the date of the last interview until the date of the current interview. We use
this information in all survey years to determine the last month a respondent was enrolled
in school. For those who did not attend school after 1980, we use the information in theﬁrst survey in 1979 about the last date a respondent attended school. If the year of lastschool enrollment is missing, we drop this individual from our sample. If only the monthof last school enrollment is missing, we insert May as the graduation month, which is themodal month in our sample. For duration analysis, we drop job spells that start before allschooling is completed.
To determine EE and EU transitions for a job spell, we compare the stop date of thatjob spell with the start date of other job spells. If there is less than a month of diﬀerence
and the job did not end with a ﬁring, we label this job as EE. There are some cases wherea respondent holds multiple jobs. For these cases, if the respondent already has another jobat the time the job ended, we labeled it as EE. All the other job spells are labeled as EU .
When creating the sample for the shorter panel, we restrict our dataset to the jobs thatstart before the year 1988. This restriction reduces the maximum number of jobs that anindividual holds to 32. For the jobs that started before 1988, but ended after 1988, we change
the job ending date to the interview date in 1988 for that individual. We also label thesejob spells as censored. Similarly, when we determine the date for last school enrollment, we
restrict our dataset to survey years until 1988. This process overwrites some of the jobs withmissing ending dates and the last school enrollment dates for respondents, which causes a
diﬀerence between the sample sizes of shorter and longer panels. Table 6 shows summary32

statistics from our short and long panel samples after imposing the restriction above.
Variable

Explanation

u0
AGE
HS
COL
NWHITEUNION
GENDER

Unemployment rate at the start of the job
Age of the respondent at the start of the job=1 if obtained high school diploma or equivalent=1 if completed 16 years of schooling=1 if black or Hispanic=1 if covered by union=1 if female

Mean(Short Panel)

Mean(Long Panel)

7.400
22.606
0.659
0.120
0.407
0.218
0.000

7.002
25.231
0.703
0.145
0.389
0.184
0.461

4330
1457
61 weeks

7551
1164
12 months# of Observations:# of right-censored:Median duration:

Table 6: Description and Means for Our Samples. Short panel uses survey years until 1988
and long panel uses survey years until 2010.

B

List of Job Separation Reasons

Employer History Roster (Beta version) in NLSY 1979 provides the following reasons for job
separations. We categorize these reasons as [Q]-quit, [F]-ﬁring, and [O]-other reasons.
1. Layoﬀ, job eliminated [F]2. Company, oﬃce or workplace closed [O]
3. End of temporary or seasonal job [O]
4. Discharged or ﬁred [F]5. Government program ended [O]
6. Quit for pregnancy, childbirth or adoption of a child [O]
7. Quit to look for another job [Q]
8. Quit to take another job [Q]
9. Other (SPECIFY) [O]
10. Quit because of ill health, disability, or medical problems [O]33

11. Moved to another geographic area [O]12. Quit to spend time with or take care of children, spouse, parents, or other family
members [O]
13. Quit because didn’t like job, boss, coworkers, pay or beneﬁts [O]
14. Quit to attend school or training [O]
15. Went to jail, prison, had legal problems [O]
16. Transportation problems [O]
17. Retired [O]
18. No desirable assignments available [O]
19. Job assigned through a temp agency or a contract ﬁrm became permanent [O]
20. Dissatisﬁed with job matching service [O]21. Project completed or job ended [O]
22. Business failed or bankruptcy [O]
23. Sold business to another person or ﬁrm [O]
24. Business temporarily inactive [O]
25. Closed business down or dissolved partnership [O]The last four reasons are related to self-employment jobs. Because we restrict our sample toprivate sector employment only, our sample does not include any job spell that ends due toone of these reasons.
Of our interest is how well quitsmatch with EE transitions. Table 7 shows the crosstabulation of these job separation categories from our sample with the longer panel. About
three-fourths of quits turn out to be an EE transition.

C

Computational Details of the Model

The Bellman equations are computed on discretized grids. We put 31 grid points in log(z)dimension and 51 grid points on log(x) dimension. The upper and lower bounds of the log(z)grid are set at plus and minus three standard deviations of the unconditional distribution
34

Transition Type
Reason

EE

EU

Total

Quits
Firings
Other reasons

1894
0
1217

642
1398
1236

2536
1398
2453

Total

3111

3276

6387

Table 7: Cross tabulation of job separations by transition type and reason from our longer
panel sample.
of log(z). The upper and lower bounds of the log(x) grid are set at plus and minus ﬁve
standard deviations of the log(x) draw. The stochastic processes are approximated with
Markov chains using Tauchen’s (1986) method.
The value functions are computed by the standard value function iteration. Once thevalue functions and the policy function is computed, we simulate the model and generatesamples. The samples are treated in the same way as the NLSY samples, and used for
estimation. In the benchmark case, we simulate 200,000 people for 20,000 periods each. For
each observation, we randomly select one employment spell per person from the ﬁrst 200
spells.

35

Additional References for Appendix[1] Tauchen, G. (1986): “Finite State Markov-Chain Approximations to Univariate andVector Autoregressions,” Economics Letters 20, 177–181.

36