Manajemen | Fakultas Ekonomi Universitas Maritim Raja Ali Haji 073500104000000299
Journal of Business & Economic Statistics
ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20
Job Turnover and the Returns to Seniority
Benoit Dostie
To cite this article: Benoit Dostie (2005) Job Turnover and the Returns to Seniority, Journal of
Business & Economic Statistics, 23:2, 192-199, DOI: 10.1198/073500104000000299
To link to this article: http://dx.doi.org/10.1198/073500104000000299
Published online: 01 Jan 2012.
Submit your article to this journal
Article views: 59
View related articles
Citing articles: 1 View citing articles
Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=ubes20
Download by: [Universitas Maritim Raja Ali Haji]
Date: 12 January 2016, At: 23:47
Job Turnover and the Returns to Seniority
Benoit D OSTIE
Institute of Applied Economics, HEC Montréal, Montréal, Québec, Canada (benoit.dostie@hec.ca)
In this article, we match firm data to individual work history files to simultaneously estimate the wage
and employment duration processes of a longitudinal sample of 2 million French workers employed in
roughly 1 million firms and followed over 20 years. The particular structure of the dataset allows us to
distinguish between the impact of job search and labor demand indicators on wages and employment at
the job level. The model allows for correlated individual and job unobserved heterogeneity. Controlling
for job matching, we find that returns to seniority are close to zero.
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
KEY WORDS: Endogeneity; Job duration; Linked employer–employee data; Maximum likelihood; Unobserved heterogeneity; Wage determination.
1. INTRODUCTION
2. ANALYTICS
The question of how earnings change with seniority is a classic one in labor economics. This relationship is typically rationalized with one of two theories. It is explained either by
the existence of implicit contracts in which a worker’s effort is
motivated through delayed compensation (see, e.g., Hutchens
1989) or by an optimal life-cycle policy for human capital investment: Workers forego potential earnings during their initial
years of employment at a firm to augment earnings capacity
through investments in employer-specific human capital.
In this article, we present estimates of the magnitude of
the returns to seniority in France using a longitudinal linked
employer–employee dataset that was previously analyzed by
Abowd, Kramarz, and Margolis (1999). Those authors found
that the average return to a year of seniority is just over 1%. The
main contribution of this article is that it models job turnover,
which Abowd et al. (1999) assumed to be exogenous. There
are good reasons to suspect that job mobility is endogenous,
because we observe only “self-selected” wages, namely wages
that are above an individual’s reservation wage. This potential
endogeneity may be due to the effects of unmeasured factors
that influence both job turnover and the level or growth rate of
wages. Failure to take this sample selection problem into account will lead to biased estimates of the returns to seniority.
The approach that we use to deal with endogenous seniority
is to simultaneously estimate the wage and employment duration processes in the spirit of Lillard (1999) while explicitly
modeling the correlation between unobserved factors affecting
both wage and job turnover. This can be done because the linked
nature of the dataset allows us to control for both firms’ and
workers’ unobserved heterogeneity. Moreover, we are able to
go one step further than Lillard (1999) by exploiting the firm
information present in the linked data to better identify unobserved job heterogeneity and proxy for labor demand. We can
thus account for the firm side and the match component more
effectively than can be done with work history data alone. In
the process, we also obtain estimates of the impact of firm attributes in the wage and mobility equations, something that has
not been done before.
The rest of the article proceeds as follows. We first review
the wage seniority literature, especially the modeling issues that
must be taken into account to estimate the returns to seniority.
We then describe the statistical model and derive the likelihood
function that we use for estimation. In Section 3 we describe the
data and consider sample construction issues. We present the
estimation results in Section 4, and provide a brief conclusion
in Section 5.
Returns to seniority are usually estimated using specifications of the form
ln wiJ(i,t)t = β0 seniJ(i,t)t + β1 expit + β2 timet + ǫiJ(i,t)t ,
(1)
where ln wiJ(i,t)t is the log real wage of person i with employer
J(i, t) in period t, expit is total labor market experience of individual i at time t, seniJ(i,t)t is seniority of individual i with
employer J(i, t) at time t, and timet is a time trend. The parameter of interest is, of course, β0 .
The traditional approach has been to estimate (1) via ordinary
least squarest (OLS). For example, Topel (1991) reported that
10 years of seniority raises the log wage by .30. However, using
OLS to estimate β0 and β1 is inappropriate, because correlation
between seniority and the error term ǫiJ(i,t)t leads to biased estimates of β0 and β1 . Recognizing this fact, most of the focus
of the wage-seniority literature has been on controlling for the
endogeneity of seniority in the wage equation.
To illustrate this correlation further, we can decompose the
error term as
ǫiJ(i,t)t = θi + φJ(i,t) + ηiJ(i,t) + υiJ(i,t)t ,
(2)
where θi is an individual-specific error component, φJ(i,t) is
a firm-specific error component, ηiJ(i,t) is an employer–employee match error component, and υiJ(i,t)t is a time-varying
error term. If seniority is correlated with unobserved individual (θi ), firm (φJ(i,t) ), and job match (ηiJ(i,t)t ) heterogeneity,
then estimated returns to job-specific training will clearly be
biased by the decisions that generate job mobility.
The job search literature suggests at least three reasons to
believe that these correlations might be important. First, jobchanging decisions could be the outcome of a career process
by which workers are sorted into more stable and productive
jobs. Second, it is possible that more productive or able workers change jobs less often. This would be the case if more loyal
employees were also more productive. Finally, some employers may choose to pay higher wages than others, so that workers are less inclined to shirk or to quit. In these three cases,
high-wage jobs tend to survive, which means that workers with
higher seniority will be observed to be earning a higher wage,
192
© 2005 American Statistical Association
Journal of Business & Economic Statistics
April 2005, Vol. 23, No. 2
DOI 10.1198/073500104000000299
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
Dostie: Job Turnover and the Returns to Seniority
193
not because of high returns to seniority, but rather because of
matching in the job market.
Many studies, including those of Topel (1986, 1991),
Abraham and Farber (1987), Altonji and Shakotko (1987), and
Altonji and Williams (1997), attempt to deal with these types of
correlation problems. However, full estimation of (1) with (2)
has not been undertaken, because information about J(i, t) is
rarely available. In fact, most of the previous studies define
J(i, t) to be a job identifier instead of a firm identifier. Abraham
and Farber (1987) focused only on ηiJ(i,t) and defined it as
person/job-specific error term representing the excess of earnings enjoyed by person i on job J(i, t) over and above the earnings that could be expected by a randomly selected person/job
combination. Topel (1991) and Altonji and Williams (1997) incorporated θi in their estimation procedure but did not account
for firm heterogeneity. Abowd et al. (1999) had information on
employers and estimate a version of (1) with both employer
and employee effects but did not consider job match heterogeneity, ηiJ(i,t) . Overall, studies that do take the endogeneity of
seniority into account in various ways find returns to seniority
to be very low, except for the study of Topel (1991) (or see
also Buchinsky, Fougère, Kramarz, and Tchernis 2003), which
obtained returns to seniority similar to those arrived at through
OLS estimation.
Theoretically, linked employer–employee data uniquely permit the estimation of the full error decomposition in (2).
However, in the following statistical model, we restrict our
attention to the endogeneity caused by the individual (θ ) and
job (η) heterogeneity components. This is because introducing
both individual and firm heterogeneity components in a nonlinear framework is intractable. Although there is a vast literature
on the inclusion of random effects in linear models (see, e.g.,
Searle, Casella, and McCulloch 1992), the same cannot be said
for nonlinear models. Nonlinear models with more than one
variance component are very hard to estimate due to their high
dimensionality, especially if the random effects are not nested,
which is the case with firm and individual heterogeneity. Many
methods have been proposed to overcome such numerical difficulties (see Lee and Nelder 1996; Jiang 1998), but unfortunately, it turns out that none are sufficiently robust to deal with
datasets of the size that we use in this analysis. However, we
argue that our match heterogeneity component comprises the
firm heterogeneity component, and thus this omission is unlikely to significantly affect our results about the endogeneity
of seniority and the impact of firm-demand indicators.
To estimate the simultaneous model, we also need a model
of employment duration. As emphasized earlier, the mobility
problem can be seen as a sample selection problem. Only acceptable new job offers are observed. In other words, we observe wage paths only for which ln wijt was higher than some
reservation wage rit . To illustrate this approach, suppose that
a worker receives a new wage offer w0ij t from a firm j′ with
probability π in each period, where the natural log of the real
wage offered is given by
ln w0ij′ t = y0ijt = f1 (expit ) + θi + ηij′ .
(3)
In more general models, the probability π could be made endogenous to reflect a different search effort. (Recent evidence
of endogenous job search was given in Anderson and Burgess
2000.) Within-job wage growth could take the form
yijt = ln wijt = yijt−1 + f2 (expit , senijt ) + ǫijt .
We assume that the functional form for the log real reservation
wage is
rijt = yijt + f3 (expit , senijt ).
An individual will move if
y0ijt
(4)
> rijt , or if
ηij′ > yijt + f3 (expit , senijt ) − f1 (expit ) − θi ≡ M.
(5)
Therefore, the probability of observing a job separation (or the
hazard rate), conditional on the wage, can be written as
h( yijt , expit , senijt ) = π{1 − F(M)},
(6)
where F(·) is the cumulative distribution of the job match heterogeneity component ηij′ .
Obviously, demographic characteristics of individuals will be
important in the mobility decision, especially through their effect on yijt . However, firm characteristics also should be important, for at least two reasons. First, external considerations
could lead to the firm’s decision to terminate a job. Second,
firm characteristics may also influence an individual job termination decision directly. Using linked employer–employee data
permits us to investigate these influences for the first time.
3. STATISTICAL MODEL
Taking into account observations from the previous section,
the particular form that we use for the wage equation is
ln wiJ(i,t)t
= β0 + β ′1 Xi + β ′2 ZiJ(i,t) + β ′3 FJ(i,t)t + θ1i + η1iJ(i,t)
+ 1 + η2iJ(i,t) γ ′ seniJ(i,t)t + (1 + β ′4 Xi + θi2 )β ′5 expit
+ β ′6 timet + ǫiJ(i,t)t ,
(7)
where θ1i and θ2i are typical random person effects, η1iJ(i,t)
and η2iJ(i,t) are job random effects, and ǫiJ(i,t)t is the error term.
We use two individual random effects to allow for both higher
wages at the beginning of an individual’s career and superior
wage growth related to unobservable characteristics throughout
the career. In a similar fashion, we specify two job-specific heterogeneity components to allow for both higher initial wages
and higher wage growth throughout the job. Regressors include
basic demographic characteristics (Xi ), such as education and
gender. We distinguish between job characteristics and timevarying firm-level variables. The former, included in ZiJ(i,t) , are
usually part of work history surveys such as the location of the
job. We use a dummy variable that indicates whether the job is
located in Paris. The latter, included in FJ(i,t)t , are time-varying
firm variables, such as the first difference in the log of sales and
first difference in the log of capital stock.
We also add experience (expit ), time (timet ), and seniority
(seniJ(i,t) ) as piecewise-linear splines. For a duration spline T(s)
with P nodes, we have
min[s, p1 ]
max[0, min[s − p1 , p2 − p1 ]]
T(s) =
(8)
···
,
max[0, min[s − pP−1 , pP − pP−1 ]]
max[0, s − pP ]
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
194
Journal of Business & Economic Statistics, April 2005
where p1 , . . . , pP represent the nodes. The experience and seniority profiles are represented by piecewise-linear splines with
nodes at 5, 10, 20, and 30 years for experience and nodes at 2,
5, and 10 years for seniority. The time spline has no node and
can be interpreted as a linear trend on calendar time. The use
of splines is crucial for an application such as this one, where
the effect of seniority may not be linear. It is important to note
that the numbers and positions of these nodes were determined
in such a way as to provide the best fit for the data.
Identification of the seniority effects is made easier because
we observe multiple jobs per person. For those persons, their
seniority clock turns to zero when they change jobs, but their
experience clock continues to increase. A separate coefficient
for a time trend can be estimated because workers begin their
jobs at different calendar times. The interaction term in experience allows the wage profile to vary according to the gender of
the individual through β 4 .
Finally, we assume that all of the random effects have
mean 0. The job heterogeneity components follow a normal
distribution,
η1iJ(i,t) , η2iJ(i,t) ∼ N(0, η,η ),
and we do not impose any restrictions on the variance–
covariance matrix η,η . The error term has a within-job transitory autoregressive structure of the form AR(1),
ǫiJ(i,t)t = κ1 ǫiJ(i,t)t−1 + uiJ(i,t)t .
(9)
This autoregressive process implies correlation among all wage
values for a person as a function of the amount of time in years
between the wage values.
To model employment duration, we use a proportional hazard
of the form:
ln hiJ(i,t)t (s) = δ0 + δ ′1 Xi + δ ′2 ZiJ(i,t) + δ ′3 FJ(i,t)t
+ δ ′4 seniJ(i,t)t + δ ′5 expit + δ6′ timet
+ θ3i + λ1 η1iJ(i,t) + λ2 η2iJ(i,t) ,
(10)
where θ3i is a random person effect, the load factors λ1 and λ2
are the coefficients of the job effects η1iJ(i,t)t and η2iJ(i,t)t
[defined in (7)], and where Xi , ZiJ(i,t) , and FJ(i,t)t are as defined earlier. The baseline hazard duration dependence is a
piecewise-linear spline also known as generalized Gompertz.
Note that three sources of time dependence are incorporated in
the model through seniority (seniJ(i,t)t ), experience (expit ), and
a time trend (timet ).
To derive the survivor function, suppose for the moment that
we use a simpler hazard of the form
ln hi (s) = α ′ T(s) + δ ′ Xi + θ3i .
(11)
In the absence of time-varying covariates, the survivor function
can be written as
s
h(τ ) dτ
Si (s) = exp −
0
s
exp{δ′ Xi +θ3i }
′
= exp −
expα T(τ ) dτ
(12)
0
or
′
Si (s) = S0i (s)exp{δ Xi +θ3i } ,
(13)
where
s
h0i (τ ) dτ
S0i (s) = exp −
(14)
0
and ln h0 (s) = α ′ T(s).
When we add time-varying covariates, the survivor function
is slightly more complicated,
′
n
S0i (si ) exp{δ Xi +θ3i }
Si (s) =
.
(15)
S0i (si−1 )
i=1
The period between the beginning of the spell and duration s is
divided into n intervals within which time-varying covariates
are constant.
The simultaneity in the model is introduced throught the hypothesis that the individual heterogeneity components in the
wage and hazard equations are jointly normally distributed
[(θ1i , θ2i , θ3i ) ∼ N(0, θ,θ )], and through the introduction of
load factors (λ1 and λ2 ) on the job heterogeneity components
from the wage equation in the hazard equation. Testing the exogeneity of seniority in the wage equation is equivalent to testing
that the correlations between θ3i and each of (θ1i , θ2i ) equal 0
and that the load factors λ1 and λ2 also equal 0.
We allow for correlation between θ1i , θ2i , and θ3i to take
into account possible correlation between wage and seniority
through the classic movers/stayers phenomenon. Similarly, if
λ1 and λ2 are negative, then this would mean that good job
matches last longer, either through the initial wage offers or
through superior wage growth, giving credence to job-matching
theories of job mobility.
3.1 Estimation
Given the nested structure of the problem, we can derive the
likelihood function at the individual level following the work
of Lillard (1999). Assuming that the individual likelihoods are
independent conditional on job and individual heterogeneity,
we can take the product to get the sample likelihood. The full
joint marginal likelihood for the ith person is given by
−1/2
Li = (2π)−Ti /2 ζ i ,ζ i
1
′ −1
× exp − (Wi − i ) ζ i ,ζ i (Wi − i )
2
∞
−1/2
1 θ3 − µθ3 |Wi 2
2
×
exp −
2πσθ3 |Wi
2
σθ3 |Wi
−∞
∗
1 ηiJ − µηiJ∗ |Wi 2
2 −1/2
2πση∗
exp −
×
iJ
∗
2
σηiJ∗ |Wi
ηiJ
D
∗
× hθ3i ,ηiJ∗ (τiJ ) J Sθ3i ,ηiJ∗ (τiJ ) dηiJ
×
j
i −1
j=1
∗
1 ηiJ − µηiJ∗ |Wi 2
2 −1/2
2πση∗
exp −
iJ
∗
2
σηiJ∗ |Wi
ηiJ
∗
× hθ3i ,ηiJ∗ (τiJ )Sθ3i ,ηiJ∗ (τiJ ) dηiJ dθ3 ,
where Dj = 1 if the last job has ended and 0 otherwise, and
Wi is the vector of Ti observed wage values wit for person i
Dostie: Job Turnover and the Returns to Seniority
195
organized in order of jobs and calendar time within a job, which
we decompose as
Wi = i + ζ i .
(16)
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
Thus the vector Wi includes a vector of ji subvectors with elements representing the jth job, where ji is the total number
ji
TiJ(i,t) . The job-specific
of jobs for individual i and Ti = j=1
mean subvectors are given by the regression equations
′
β0 β 1′
1
′
′
iJ(i,t) = 1TiJ(i,t) , β 5 expit , β 6 timet
1 β4
Xi
1
0
1
0 β′ β′
′
2
3
+ 1TiJ(i,t) , γ seniJ(i,t)t
ZiJ(i,t) ,
1 0
0
FJ(i,t)t
The joint likelihood is obtained by numerically integrating out
the heterogeneity components from the product of the conditional likelihoods of the individuals, assuming joint normality
of the heterogeneity components and of the innovations to the
autoregressive components. Because a closed-form solution to
the integral does not exist, the likelihood was computed by approximating the normal integral by a weighted sum over “conditional likelihoods,” that is, likelihoods conditional on certain
well-chosen values of the residual.
4. DATA
Our main data source is the “Déclarations Annuelles des
Salaire” (DADS), a large-scale administrative database of
matched employer–employee information collected by INSEE
and the job-specific residual subvectors are given by
(Institut National de la Statistique et des Études Économiques)
θ1i
and maintained by the Division des Revenus. The data are based
′
ζij = 1TiJ(i,t) , β 5 expit
on mandatory employer reports of the gross earnings of each
θ2i
employee subject to French payroll taxes. These taxes apply
η1iJ(i,t)
+ ǫiJ(i,t) , to all “declared” employees and to all self-employed people—
+ 1TiJ(i,t) , γ ′ seniJ(i,t)t
η2iJ(i,t)
essentially, all employed people in the economy.
The Division des Revenus prepares an extract of the DADS
where ǫ iJ(i,t) is the vector of the ǫiJ(i,t)t corresponding to the job
for scientific analysis, covering all individuals employed in
match iJ(i, t).
The residual covariance matrix for the full vector of Ti ob- French enterprises who were born in October of even-numbered
years, excluding civil servants. Meron (1988) showed that indiserved wage values is given by
viduals employed in the civil service move almost exclusively
′
ζ i ,ζ i = 1Ti , β ′5 expit θ,θ 1Ti , β ′5 expit
to other positions within the civil service. Thus the exclusion
′
′
= + diagji 1TiJ(i,t) , γ seniJ(i,t)t η,η 1TiJ(i,t) , γ seniJ(i,t)t of civil servants should not affect our estimation of a worker’s
market wage and employment duration equation. Employees of
+ ǫ i ,ǫ i ,
state-owned firms are, however, present in our sample. We have
where diagJi {·} denotes a block diagonal matrix with Ji blocks. longitudinal work histories running from 1976 to 1996, but are
The mean and variance of the job duration person-specific missing wage data from 1981, 1983, and 1990, because the uncomponent, conditional on the observed wage series, are derlying administrative data were not collected in these years.
The initial dataset contained 15,425,746 annual wage obgiven by
servations for 1,951,333 individuals, 1,142,738 firms, and
µθ3i |Wi = θ3i ,ζ i −1
5,913,042 employment spells. Limiting the sample to full-time
ζ i ,ζ i (Wi − i )
jobs in the goods and services sector yields 3,622,090 employand
ment spells. Firm data are obtained through the EAE (Enquête
.
σθ23i |Wi = σθ23i − θ3i ,ζ i −1
Annuelle d’Entreprises), an annual survey of firms. The EAE
ζ
,θ
ζ i ,ζ i
i 3i
data are available only from 1978 to 1996. After further restrictThe covariance matrix between the wage residuals ζ i and the
ing the sample to people age 16 years or older and who started
person-specific job duration residual θ3i is given by
a new job in 1978 or later, we are left with 2,795,419 job spells.
We deleted an additional 59 job spells because of inconsistent
σθ1i ,θ3i
.
(17)
ζ i ,θ3i = 1Ti , β ′5 expit
starting and ending dates.
σθ2i ,θ3i
Each employment spell identified from the DADS has a firm
The mean and variance of each of the ji job-specific job duration
identifier that we match to the EAE to get information about
components conditional on the observed wage series for the job
firm characteristics such as sales, number of employees, and
are given by
capital stock. Some 65% of the employment spells occur in
−1
′
a firm covered by the EAE. However, we do not have a com∗
µηiJ(i,t)
|Wi = λ ηiJ(i,t) ,ζ i ζ i ,ζ i (Wi − i )
plete set of time-varying firm characteristics for each job spell.
and
We effectively discard job spells that have one or more missing
values in their firm characteristics histories. We obtain com−1
′
2
ση∗ |Wi = λ ηiJ(i,t) ,ǫiJ(i,t) − ηiJ(i,t) ,ζ i ζ i ,ζ i ζ i ,ηiJ(i,t) λ.
iJ(i,t)
plete histories for 989,215 job spells, or 35.4% of the original
The covariance matrix between the wage residuals ζ i and the sample. We performed estimation with both the full dataset and
∗
the smaller sample with firm characteristics. Because results did
is given by
job-specific job duration residuals ηiJ(i,t)
not vary significantly between the two samples, we present only
∗
ζ i ,ηiJ(i,t)
(18) results from the dataset with firm covariates.
= 1Tij γ ′ seniJ(i,t)t J ηη λ.
i
196
Journal of Business & Economic Statistics, April 2005
Table 1. Summary Statistics at the Individual Level
Years of schooling
n = 620,078
Table 2. Summary Statistics for Employment Duration (in years)
Men (65%)
Mean
SD
Women (35%)
Mean
SD
12.38
12.19
1.73
1.72
Mean
SD
Min
Q25
Q50
Q75
Max
2.12
3.12
n = 989,215
.08
.25
.83
2.58
19.00
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
Table 3. Summary Statistics at the Job Level
Summary statistics for our sample are divided into four
tables. Table 1 presents summary statistics for individual
characteristics including schooling and gender. The average
employment duration in our sample is 2.07 years (Table 2). This
is lower than is usually seen in work history surveys, probably
due to the administrative nature of the data. Table 3 reports
summary statistics at the job level. Job description variables include identifiers for whether the job was located in the Paris
metropolitan area (called “Île de France”); 32% of the employment spells took place in Paris, and 15% are right censored at
1996. The dependent variable in our wage rate analysis is the
logarithm of real annualized total compensation cost for the
employee. Table 4 shows that men earn on average 29% more
than women. Average experience at the beginning of the job
spell is 12.4 years. A worker’s experience is computed as the
difference between current age and school-leaving age. Finally,
Table 4 also includes summary statistics for time-varying firm
characteristics.
Men (68%)
Mean
SD
Censored
Lives in Île de France
Experience in years
(when spell begins)
n = 989,215
Women (32%)
Mean
SD
.15
.30
.36
.46
.13
.35
.34
.48
12.40
10.40
10.86
9.86
Table 4. Summary Statistics of Annual Data
(log) Wage
Capital stock (million FF)
Number of employees (thousand)
Total sales (million FF)
First difference in log-capital stock
First difference in log-sales
n = 2,484,039
Men (69%)
Mean
SD
Women (31%)
Mean
SD
4.37
15.70
7.88
7.85
.09
.07
4.11
10.95
5.56
5.29
.10
.08
.66
92.97
30.29
27.59
.51
.33
.69
74.16
23.93
21.06
.50
.33
Table 5. Estimation Results, Hazard Equation
5. RESULTS
The discussion of the results is organized as follows. Section 5.1 presents results of the estimation of the employment
duration equation, and Section 5.2 discusses the results for the
wage equation. Table 5 reports various estimates of the coefficients for the employment duration model, Table 6 does the
same for the wage equation, and Table 7 presents estimates
for the variance–covariance matrix of the various heterogeneity components included in the statistical model.
Constant
Male
Years of schooling
Lives in Île de France
Seniority spline
0–2nd year
2–5th year
5.1 Employment Duration
The first and second columns of Table 5 report estimates
of the coefficient on gender, schooling, job location, seniority,
experience, a time trend, and various time-varying firm variables for the basic and mixed duration models. As is typical
with duration analysis, positive coefficients indicate a higher
probability of employment termination or, conversely, shorter
job duration. Standard errors, reported in parentheses, were
computed using the covariance matrix of estimated model parameters given by the inverse of minus the Hessian matrix.
Estimates of the basic (the “Base” column in Table 5), mixed
(“Mixed”) and simultaneous (“SIM”) models tell very similar stories about the determinants of employment duration in
France. Males keep their job longer, education is associated
with a lower probability of job termination, and employment
relationships are less stable in the metropolitan area of Paris.
For the latter, the magnitude of the coefficients indicates that
the probability of losing a job in any year is about 20% higher
in Paris.
5–10th year
10th year +
Experience spline
0–5th year
5–10th year
10–20th year
20–30th year
30th year +
Time trend
Base
Mixed
SIM
1.249
(.017)
−.069
(.003)
−.045
(.001)
.192
(.003)
1.268
(.017)
−.069
(.001)
−.045
(.001)
.191
(.003)
1.089
(.018)
−.061
(.003)
−.045
(.001)
.210
(.003)
−.763
(.002)
−.093
(.002)
−.059
(.002)
−.054
(.003)
−.576
(.003)
−.071
(.002)
−.024
(.002)
−.037
(.004)
−.573
(.003)
−.069
(.002)
−.024
(.002)
−.035
(.004)
−.105
(.001)
−.061
(.001)
−.016
(.001)
−.021
(.001)
.061
(.001)
.024
(.000)
−.110
(.001)
−.074
(.001)
−.020
(.001)
−.025
(.001)
.060
(.001)
.023
(.001)
−.106
(.001)
−.069
(.001)
−.017
(.000)
−.021
(.000)
.057
(.000)
.025
(.000)
−.065
(.000)
−.064
(.000)
−.146
(.003)
−.145
(.003)
First difference
in log-capital stock
First difference
in log-sales
n = 989,215
NOTE:
Standard errors are in parentheses.
Dostie: Job Turnover and the Returns to Seniority
197
Table 6. Estimation Results, Wage Equation
Constant
Male
Years of schooling
Lives in Île de France
Seniority spline
0–2nd year
2–5th year
5–10th year
10th year +
OLS1
OLS2
Mixed
SIM
2.961
(.002)
.229
(.001)
.039
(.000)
.216
(.001)
3.125
(.003)
−.012
(.002)
.038
(.000)
.216
(.001)
3.186
(.015)
−.024
(.003)
.041
(.001)
.142
(.001)
2.782
(.016)
−.031
(.003)
.040
(.001)
.140
(.001)
.042
(.001)
.020
(.001)
−.002
(.000)
−.002
(.000)
.042
(.001)
.020
(.001)
−.002
(.000)
−.003
(.000)
.936
(.010)
−.008
(.001)
.008
(.000)
−.008
(.000)
−.008
(.000)
.895
(.018)
−.053
(.001)
.005
(.000)
−.008
(.000)
−.005
(.000)
.858
(.031)
.050
(.002)
.035
(.001)
.016
(.000)
.005
(.000)
−.007
(.000)
.008
(.000)
.031
(.000)
.022
(.000)
.010
(.000)
.003
(.000)
−.004
(.000)
.009
(.000)
.034
(.002)
.019
(.001)
.010
(.000)
.003
(.000)
.003
(.000)
.008
(.000)
.038
(.002)
.019
(.001)
.009
(.001)
.003
(.001)
.000
(.000)
.008
(.000)
−.004
(.001)
.008
(.001)
.008
(.001)
.010
(.001)
.020
(.001)
.020
(.001)
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
Male × experience
Experience spline
0–5th year
5–10th year
10–20th year
20–30th year
30th year +
Time trend
Table 7. Variance Components Parameter Estimates
First difference
in log-sales
First difference
in log-capital stock
n = 989,215
NOTE:
Standard errors are in parentheses.
The impact of seniority and experience is also as expected.
Taking into account individual unobserved heterogeneity flattens the seniority profile, as can be seen by comparing the coefficients on the seniority spline in the “Base” and “Mixed”
columns in Table 5, but the interpretation remains the same.
The first 2 years on a job are associated with an important reduction in the probability of job termination (−.576 for “0–2nd
year” in the “Mixed” column). This indicates that the probability of job termination is cut in half in each of the first 2 years on
a job. This probability keeps falling as seniority increases, but
at a much lower rate in the following years. The story is similar with experience. Results show that individuals are sorted in
more stable employment relationship as they gain labor market experience. The effect is again stronger for the first 2 years
and gradually dies off after 20 years on the job market. We see
the opposite effect after 30 years of experience, due to people
getting out of the job market.
Time-varying firm characteristics are found to be important.
Increases in both sales and the size of the firm as measured by
its capital stock are associated with a lower probability of job
termination. Finally, unobserved individual heterogeneity in the
job duration equation is found to be significant, although its
impact on other coefficients is not dramatic (σθ3 = .546 in the
“Mixed” column of Table 7).
BASE
Mixed
Individual heterogeneity variance components, θ ,θ
.159
(.001)
σθ2
.989
(.029)
σθ3
.546
(.003)
ρθ1 ,θ2
−.734
(.004)
σθ1
ρθ1 ,θ3
ρθ2 ,θ3
Job heterogeneity variance components, η,η
ση1
.378
(.000)
ση2
30.345
(2.583)
ρη1 ,η2
.458
(.002)
λ1
λ2
SIM
.219
(.002)
1.136
(.045)
.563
(.003)
−.747
(.004)
−.013
(.011)
−.345
(.006)
.370
(.005)
6.167
(.117)
.456
(.002)
−.020
(.008)
.013
(.001)
Autoregressive error structure
κ1
σu
NOTE:
.630
(.000)
.202
(.001)
.441
(.000)
.180
(.001)
.398
(.000)
Standard errors are in parentheses.
5.2 Wage Determination
The first two columns of Table 6 report results of an OLS
estimation of the wage equation, first in its conventional form
and then with additional covariates related to labor demand.
We also add a gender interaction to experience, to take into
account different life-cycle returns to experience between men
and women in the second specification. Typical results are obtained for gender, returns to education, and job location for both
sets of results. Not surprisingly, men are found to earn more
than women, as indicated in the “OLS1” column. However,
as shown by the positive interaction term between gender and
experience in the other columns, the gap grows wider as individuals gain experience. Looking at the “SIM” column, the interpretation is that although returns to experience for women are
about 3.8% for their first 5 years on the job market, returns for
men are moderately higher at 7.1% (1.858 × .038). The returns
to an additional year of education are about 4%, and salaries
are found to be higher in the Paris metropolitan area. The coefficient on the time trend is stable across different specifications
and indicates that real wages grew on average by 1% a year
between 1978 and 1996. Note that all results for other parameters are robust to the inclusion of time dummies instead of a
time trend.
Now turning to the returns to specific and general human
capital, we find that returns to 10 years of seniority are a little less than 15% in the OLS regression. The first striking result
is obtained by observing how these returns collapse when unobserved heterogeneity is included in the wage equation. Taking
into account individual and job unobserved heterogeneity reduces the returns to seniority to close to zero. When we estimate
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
198
Journal of Business & Economic Statistics, April 2005
the model simultaneously to take into account the endogeneity
of seniority, returns to seniority are in fact negative for the first
2 years on a job. This is in stark contrast to returns to experience, which, although diminishing somewhat after taking into
account unobserved heterogeneity, still average 4% a year for
the first 5 years on the labor market and 2% for the following
5 years in the simultaneous model. It is well known that returns
to seniority are pretty low in France (see Abowd et al. 1999),
but our estimates are even lower than those reported in previous
studies.
Turning to the coefficients on time-varying firm variables,
we report in Table 6 that positive changes in sales lower the
probability that workers will quit their current job. This is the
first time it has been possible to assess the influence of labor
demand indicators on employment at the employer–employee
match level. As discussed earlier, one interpretation of this result is that these positive changes in sales are indicative of firm
labor demand. But one could also argue that these factors are
taken into account in the workers’ mobility decisions; positive
changes in sales could be used to predict a higher future wage,
or a higher probability of promotion within the firm. At this
stage one cannot distinguish between these two hypotheses.
However, another striking result is that those changes in sales
have almost no impact on the wage level.
Finally, in Table 7 we present parameter estimates for the
unobserved heterogeneity components. We first note that individual and job unobserved heterogeneity components are significant. Significant unobserved job heterogeneity in returns to
seniority was also reported by Abowd et al. (1999) and Lillard
(1999). The relatively high parameter estimate for ση2 indicates that although average returns to seniority are close to
zero, actual ranges for those returns are much wider. More interestingly, we report in the “SIM” column that both correlations between unobserved individual heterogeneity components
from the wage equation and those from the hazard equation
(ρθ1 ,θ3 and ρθ2 ,θ3 ) are significantly different from 0. Both are
negative, which suggests that both high-wage and high-wage–
growth workers tend to have longer job duration. Also note that
both λ1 and λ2 are statistically significant. This indicates that
good job matches, through either higher starting wage or superior wage growth throughout the job, also last longer. Based
on these significant correlations, we can reject exogeneity of
seniority in the wage equation.
job market in which most wage growth comes from switching
to higher-paying jobs, especially early in one’s career.
Overall, the foregoing results lend credence to theories that
accord greater importance to job search and job matching as
determinant of wage level and wage growth, because returns
to seniority are found to be very small, even negative. Firmspecific capital does not seem to be important, and human capital would be easily transferable from firm to firm. It remains
to be seen what applying our methodology on similar U.S. data
would yield. In fact, there is no reason for the returns to seniority to be the same in Europe as in the U.S. (Wasmer 2003).
Finally, we find that changes in sales have an important effect in reducing the hazard rate in the mobility equation and
a somewhat smaller impact on wages. Therefore, the mobility
decision depends on more factors besides demographic characteristics and unobserved heterogeneity. We plan on exploring
this decision even further in future research by disaggregating
our sales data along product lines. It should also be interesting to decompose sales shocks into its permanent and temporary components. However, as we noted in our discussion of the
results, interpretation of the coefficients on firm-side variables
would be helped by the development of theoretical models of
the firm linking its employment and wage policies to events on
the product market at the micro level. We expect the development of such models to be spurred by the availability of linked
employer–employee datasets.
Another avenue for future research is to decompose the unobserved job-match heterogeneity component into its firm and
“pure” job-match components. It would be interesting to get
posterior expectations for the firm and individual random effects and aggregate these at the industry level, especially for
the job duration equation.
ACKNOWLEDGMENTS
The author acknowledges financial support from the National Science Foundation (grant SES 99-78093 to Cornell University). The author thanks John Abowd, Robert Clark, Gary
Fields, Robert Hutchens, George Jakubson, Raji Jayaraman,
Joan Moriarty, and three anonymous referees for very helpful
comments. All remaining errors are the author’s alone.
[Received May 2002. Revised February 2004.]
6. CONCLUSION
REFERENCES
In this article we estimate simultaneously the wage and job
duration processes for a longitudinal sample of French workers
from 1978 to 1996 to obtain estimates of the returns to seniority
that are not potentially biased by the endogeneity of seniority in
the wage equation. We find that taking into account unobserved
individual and job heterogeneity considerably lowers the returns to seniority estimates. Moreover, these unobservables are
significantly correlated across the wage and employment duration equations. Taking this correlation into account actually
causes the returns to seniority to become negative in the first
few years on a job, a result corroborated by a recent study also
on French data by Kramarz (2003). Negative returns to seniority
for the first few years on a job are consistent with a view of the
Abowd, J. M., Kramarz, F., and Margolis, D. N. (1999), “High-Wage Workers
and High-Wage Firms,” Econometrica, 67, 251–333.
Abraham, K., and Farber, H. (1987), “Job Duration, Seniority, and Earnings,”
American Economic Review, 77, 278–297.
Altonji, J., and Shakotko, R. A. (1987), “Do Wages Rise With Job Seniority?”
Review of Economic Studies, 54, 437–459.
Altonji, J., and Williams, N. (1997), “Do Wages Rise With Job Seniority? A Reassessment,” Working Paper 6010, National Bureau of Economic Research.
Anderson, P. M., and Burgess, S. M. (2000), “Empirical Matching Function:
Estimation and Interpretation Using State-Level Data,” Review of Economics
and Statistics, 82, 93–102.
Buchinsky, M., Fougère, D., Kramarz, F., and Tchernis, R. (2003), “Interfirm
Mobility, Wages, and the Returns to Seniority and Experience in the U.S.,”
mimeo, UCLA.
Hutchens, R. M. (1989), “Seniority, Wages and Productivity: A Turbulent
Decade,” Journal of Economic Perspectives, 2, 49–64.
Dostie: Job Turnover and the Returns to Seniority
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
Jiang, J. (1998), “Consistent Estimators in Generalized Linear Mixed Models,”
Journal of the American Statistical Association, 93, 720–729.
Kramarz, F. (2003), “Wages and International Trade,” Discussion Paper DP3936, Center for Economic Policy Research.
Lee, Y., and Nelder, J. (1996), “Hierarchical Generalized Linear Models,”
Journal of the Royal Statistical Society, Ser. B, 58, 619–678.
Lillard, L. A. (1999), “Job Turnover Heterogeneity and Person-Job-Specific
Time-Series Wages,” Annales d’Économie et de Statistique, 55–56, 183–210.
Meron, M. (1988), “Les Migrations des Salariés de l’État: Plus Loin de Paris,
Plus Près du Soleil,” Économie et Statistique, 214, 3–18.
199
Searle, S. R., Casella, G., and McCulloch, C. E. (1992), Variance Components,
New York: Wiley.
Topel, R. (1986), “Job Mobility, Search, and Earnings Growth: A Reinterpretation of Human Capital Earnings Functions,” in Research in Labor Economics, Vol. 8, ed. R. Ehrenbrerg, Greenwich, CT: JAI Press, pp. 199–233.
(1991), “Specific Capital Mobility and Wages: Wages Rise With Job
Seniority,” Journal of Political Economy, 99, 145–176.
Wasmer, E. (2003), “Interpreting European and U.S. Labour Market Differences: The Specificity of Human Capital Investments,” Discussion Paper DP3780, Center for Economic Policy Research.
ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20
Job Turnover and the Returns to Seniority
Benoit Dostie
To cite this article: Benoit Dostie (2005) Job Turnover and the Returns to Seniority, Journal of
Business & Economic Statistics, 23:2, 192-199, DOI: 10.1198/073500104000000299
To link to this article: http://dx.doi.org/10.1198/073500104000000299
Published online: 01 Jan 2012.
Submit your article to this journal
Article views: 59
View related articles
Citing articles: 1 View citing articles
Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=ubes20
Download by: [Universitas Maritim Raja Ali Haji]
Date: 12 January 2016, At: 23:47
Job Turnover and the Returns to Seniority
Benoit D OSTIE
Institute of Applied Economics, HEC Montréal, Montréal, Québec, Canada (benoit.dostie@hec.ca)
In this article, we match firm data to individual work history files to simultaneously estimate the wage
and employment duration processes of a longitudinal sample of 2 million French workers employed in
roughly 1 million firms and followed over 20 years. The particular structure of the dataset allows us to
distinguish between the impact of job search and labor demand indicators on wages and employment at
the job level. The model allows for correlated individual and job unobserved heterogeneity. Controlling
for job matching, we find that returns to seniority are close to zero.
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
KEY WORDS: Endogeneity; Job duration; Linked employer–employee data; Maximum likelihood; Unobserved heterogeneity; Wage determination.
1. INTRODUCTION
2. ANALYTICS
The question of how earnings change with seniority is a classic one in labor economics. This relationship is typically rationalized with one of two theories. It is explained either by
the existence of implicit contracts in which a worker’s effort is
motivated through delayed compensation (see, e.g., Hutchens
1989) or by an optimal life-cycle policy for human capital investment: Workers forego potential earnings during their initial
years of employment at a firm to augment earnings capacity
through investments in employer-specific human capital.
In this article, we present estimates of the magnitude of
the returns to seniority in France using a longitudinal linked
employer–employee dataset that was previously analyzed by
Abowd, Kramarz, and Margolis (1999). Those authors found
that the average return to a year of seniority is just over 1%. The
main contribution of this article is that it models job turnover,
which Abowd et al. (1999) assumed to be exogenous. There
are good reasons to suspect that job mobility is endogenous,
because we observe only “self-selected” wages, namely wages
that are above an individual’s reservation wage. This potential
endogeneity may be due to the effects of unmeasured factors
that influence both job turnover and the level or growth rate of
wages. Failure to take this sample selection problem into account will lead to biased estimates of the returns to seniority.
The approach that we use to deal with endogenous seniority
is to simultaneously estimate the wage and employment duration processes in the spirit of Lillard (1999) while explicitly
modeling the correlation between unobserved factors affecting
both wage and job turnover. This can be done because the linked
nature of the dataset allows us to control for both firms’ and
workers’ unobserved heterogeneity. Moreover, we are able to
go one step further than Lillard (1999) by exploiting the firm
information present in the linked data to better identify unobserved job heterogeneity and proxy for labor demand. We can
thus account for the firm side and the match component more
effectively than can be done with work history data alone. In
the process, we also obtain estimates of the impact of firm attributes in the wage and mobility equations, something that has
not been done before.
The rest of the article proceeds as follows. We first review
the wage seniority literature, especially the modeling issues that
must be taken into account to estimate the returns to seniority.
We then describe the statistical model and derive the likelihood
function that we use for estimation. In Section 3 we describe the
data and consider sample construction issues. We present the
estimation results in Section 4, and provide a brief conclusion
in Section 5.
Returns to seniority are usually estimated using specifications of the form
ln wiJ(i,t)t = β0 seniJ(i,t)t + β1 expit + β2 timet + ǫiJ(i,t)t ,
(1)
where ln wiJ(i,t)t is the log real wage of person i with employer
J(i, t) in period t, expit is total labor market experience of individual i at time t, seniJ(i,t)t is seniority of individual i with
employer J(i, t) at time t, and timet is a time trend. The parameter of interest is, of course, β0 .
The traditional approach has been to estimate (1) via ordinary
least squarest (OLS). For example, Topel (1991) reported that
10 years of seniority raises the log wage by .30. However, using
OLS to estimate β0 and β1 is inappropriate, because correlation
between seniority and the error term ǫiJ(i,t)t leads to biased estimates of β0 and β1 . Recognizing this fact, most of the focus
of the wage-seniority literature has been on controlling for the
endogeneity of seniority in the wage equation.
To illustrate this correlation further, we can decompose the
error term as
ǫiJ(i,t)t = θi + φJ(i,t) + ηiJ(i,t) + υiJ(i,t)t ,
(2)
where θi is an individual-specific error component, φJ(i,t) is
a firm-specific error component, ηiJ(i,t) is an employer–employee match error component, and υiJ(i,t)t is a time-varying
error term. If seniority is correlated with unobserved individual (θi ), firm (φJ(i,t) ), and job match (ηiJ(i,t)t ) heterogeneity,
then estimated returns to job-specific training will clearly be
biased by the decisions that generate job mobility.
The job search literature suggests at least three reasons to
believe that these correlations might be important. First, jobchanging decisions could be the outcome of a career process
by which workers are sorted into more stable and productive
jobs. Second, it is possible that more productive or able workers change jobs less often. This would be the case if more loyal
employees were also more productive. Finally, some employers may choose to pay higher wages than others, so that workers are less inclined to shirk or to quit. In these three cases,
high-wage jobs tend to survive, which means that workers with
higher seniority will be observed to be earning a higher wage,
192
© 2005 American Statistical Association
Journal of Business & Economic Statistics
April 2005, Vol. 23, No. 2
DOI 10.1198/073500104000000299
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
Dostie: Job Turnover and the Returns to Seniority
193
not because of high returns to seniority, but rather because of
matching in the job market.
Many studies, including those of Topel (1986, 1991),
Abraham and Farber (1987), Altonji and Shakotko (1987), and
Altonji and Williams (1997), attempt to deal with these types of
correlation problems. However, full estimation of (1) with (2)
has not been undertaken, because information about J(i, t) is
rarely available. In fact, most of the previous studies define
J(i, t) to be a job identifier instead of a firm identifier. Abraham
and Farber (1987) focused only on ηiJ(i,t) and defined it as
person/job-specific error term representing the excess of earnings enjoyed by person i on job J(i, t) over and above the earnings that could be expected by a randomly selected person/job
combination. Topel (1991) and Altonji and Williams (1997) incorporated θi in their estimation procedure but did not account
for firm heterogeneity. Abowd et al. (1999) had information on
employers and estimate a version of (1) with both employer
and employee effects but did not consider job match heterogeneity, ηiJ(i,t) . Overall, studies that do take the endogeneity of
seniority into account in various ways find returns to seniority
to be very low, except for the study of Topel (1991) (or see
also Buchinsky, Fougère, Kramarz, and Tchernis 2003), which
obtained returns to seniority similar to those arrived at through
OLS estimation.
Theoretically, linked employer–employee data uniquely permit the estimation of the full error decomposition in (2).
However, in the following statistical model, we restrict our
attention to the endogeneity caused by the individual (θ ) and
job (η) heterogeneity components. This is because introducing
both individual and firm heterogeneity components in a nonlinear framework is intractable. Although there is a vast literature
on the inclusion of random effects in linear models (see, e.g.,
Searle, Casella, and McCulloch 1992), the same cannot be said
for nonlinear models. Nonlinear models with more than one
variance component are very hard to estimate due to their high
dimensionality, especially if the random effects are not nested,
which is the case with firm and individual heterogeneity. Many
methods have been proposed to overcome such numerical difficulties (see Lee and Nelder 1996; Jiang 1998), but unfortunately, it turns out that none are sufficiently robust to deal with
datasets of the size that we use in this analysis. However, we
argue that our match heterogeneity component comprises the
firm heterogeneity component, and thus this omission is unlikely to significantly affect our results about the endogeneity
of seniority and the impact of firm-demand indicators.
To estimate the simultaneous model, we also need a model
of employment duration. As emphasized earlier, the mobility
problem can be seen as a sample selection problem. Only acceptable new job offers are observed. In other words, we observe wage paths only for which ln wijt was higher than some
reservation wage rit . To illustrate this approach, suppose that
a worker receives a new wage offer w0ij t from a firm j′ with
probability π in each period, where the natural log of the real
wage offered is given by
ln w0ij′ t = y0ijt = f1 (expit ) + θi + ηij′ .
(3)
In more general models, the probability π could be made endogenous to reflect a different search effort. (Recent evidence
of endogenous job search was given in Anderson and Burgess
2000.) Within-job wage growth could take the form
yijt = ln wijt = yijt−1 + f2 (expit , senijt ) + ǫijt .
We assume that the functional form for the log real reservation
wage is
rijt = yijt + f3 (expit , senijt ).
An individual will move if
y0ijt
(4)
> rijt , or if
ηij′ > yijt + f3 (expit , senijt ) − f1 (expit ) − θi ≡ M.
(5)
Therefore, the probability of observing a job separation (or the
hazard rate), conditional on the wage, can be written as
h( yijt , expit , senijt ) = π{1 − F(M)},
(6)
where F(·) is the cumulative distribution of the job match heterogeneity component ηij′ .
Obviously, demographic characteristics of individuals will be
important in the mobility decision, especially through their effect on yijt . However, firm characteristics also should be important, for at least two reasons. First, external considerations
could lead to the firm’s decision to terminate a job. Second,
firm characteristics may also influence an individual job termination decision directly. Using linked employer–employee data
permits us to investigate these influences for the first time.
3. STATISTICAL MODEL
Taking into account observations from the previous section,
the particular form that we use for the wage equation is
ln wiJ(i,t)t
= β0 + β ′1 Xi + β ′2 ZiJ(i,t) + β ′3 FJ(i,t)t + θ1i + η1iJ(i,t)
+ 1 + η2iJ(i,t) γ ′ seniJ(i,t)t + (1 + β ′4 Xi + θi2 )β ′5 expit
+ β ′6 timet + ǫiJ(i,t)t ,
(7)
where θ1i and θ2i are typical random person effects, η1iJ(i,t)
and η2iJ(i,t) are job random effects, and ǫiJ(i,t)t is the error term.
We use two individual random effects to allow for both higher
wages at the beginning of an individual’s career and superior
wage growth related to unobservable characteristics throughout
the career. In a similar fashion, we specify two job-specific heterogeneity components to allow for both higher initial wages
and higher wage growth throughout the job. Regressors include
basic demographic characteristics (Xi ), such as education and
gender. We distinguish between job characteristics and timevarying firm-level variables. The former, included in ZiJ(i,t) , are
usually part of work history surveys such as the location of the
job. We use a dummy variable that indicates whether the job is
located in Paris. The latter, included in FJ(i,t)t , are time-varying
firm variables, such as the first difference in the log of sales and
first difference in the log of capital stock.
We also add experience (expit ), time (timet ), and seniority
(seniJ(i,t) ) as piecewise-linear splines. For a duration spline T(s)
with P nodes, we have
min[s, p1 ]
max[0, min[s − p1 , p2 − p1 ]]
T(s) =
(8)
···
,
max[0, min[s − pP−1 , pP − pP−1 ]]
max[0, s − pP ]
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
194
Journal of Business & Economic Statistics, April 2005
where p1 , . . . , pP represent the nodes. The experience and seniority profiles are represented by piecewise-linear splines with
nodes at 5, 10, 20, and 30 years for experience and nodes at 2,
5, and 10 years for seniority. The time spline has no node and
can be interpreted as a linear trend on calendar time. The use
of splines is crucial for an application such as this one, where
the effect of seniority may not be linear. It is important to note
that the numbers and positions of these nodes were determined
in such a way as to provide the best fit for the data.
Identification of the seniority effects is made easier because
we observe multiple jobs per person. For those persons, their
seniority clock turns to zero when they change jobs, but their
experience clock continues to increase. A separate coefficient
for a time trend can be estimated because workers begin their
jobs at different calendar times. The interaction term in experience allows the wage profile to vary according to the gender of
the individual through β 4 .
Finally, we assume that all of the random effects have
mean 0. The job heterogeneity components follow a normal
distribution,
η1iJ(i,t) , η2iJ(i,t) ∼ N(0, η,η ),
and we do not impose any restrictions on the variance–
covariance matrix η,η . The error term has a within-job transitory autoregressive structure of the form AR(1),
ǫiJ(i,t)t = κ1 ǫiJ(i,t)t−1 + uiJ(i,t)t .
(9)
This autoregressive process implies correlation among all wage
values for a person as a function of the amount of time in years
between the wage values.
To model employment duration, we use a proportional hazard
of the form:
ln hiJ(i,t)t (s) = δ0 + δ ′1 Xi + δ ′2 ZiJ(i,t) + δ ′3 FJ(i,t)t
+ δ ′4 seniJ(i,t)t + δ ′5 expit + δ6′ timet
+ θ3i + λ1 η1iJ(i,t) + λ2 η2iJ(i,t) ,
(10)
where θ3i is a random person effect, the load factors λ1 and λ2
are the coefficients of the job effects η1iJ(i,t)t and η2iJ(i,t)t
[defined in (7)], and where Xi , ZiJ(i,t) , and FJ(i,t)t are as defined earlier. The baseline hazard duration dependence is a
piecewise-linear spline also known as generalized Gompertz.
Note that three sources of time dependence are incorporated in
the model through seniority (seniJ(i,t)t ), experience (expit ), and
a time trend (timet ).
To derive the survivor function, suppose for the moment that
we use a simpler hazard of the form
ln hi (s) = α ′ T(s) + δ ′ Xi + θ3i .
(11)
In the absence of time-varying covariates, the survivor function
can be written as
s
h(τ ) dτ
Si (s) = exp −
0
s
exp{δ′ Xi +θ3i }
′
= exp −
expα T(τ ) dτ
(12)
0
or
′
Si (s) = S0i (s)exp{δ Xi +θ3i } ,
(13)
where
s
h0i (τ ) dτ
S0i (s) = exp −
(14)
0
and ln h0 (s) = α ′ T(s).
When we add time-varying covariates, the survivor function
is slightly more complicated,
′
n
S0i (si ) exp{δ Xi +θ3i }
Si (s) =
.
(15)
S0i (si−1 )
i=1
The period between the beginning of the spell and duration s is
divided into n intervals within which time-varying covariates
are constant.
The simultaneity in the model is introduced throught the hypothesis that the individual heterogeneity components in the
wage and hazard equations are jointly normally distributed
[(θ1i , θ2i , θ3i ) ∼ N(0, θ,θ )], and through the introduction of
load factors (λ1 and λ2 ) on the job heterogeneity components
from the wage equation in the hazard equation. Testing the exogeneity of seniority in the wage equation is equivalent to testing
that the correlations between θ3i and each of (θ1i , θ2i ) equal 0
and that the load factors λ1 and λ2 also equal 0.
We allow for correlation between θ1i , θ2i , and θ3i to take
into account possible correlation between wage and seniority
through the classic movers/stayers phenomenon. Similarly, if
λ1 and λ2 are negative, then this would mean that good job
matches last longer, either through the initial wage offers or
through superior wage growth, giving credence to job-matching
theories of job mobility.
3.1 Estimation
Given the nested structure of the problem, we can derive the
likelihood function at the individual level following the work
of Lillard (1999). Assuming that the individual likelihoods are
independent conditional on job and individual heterogeneity,
we can take the product to get the sample likelihood. The full
joint marginal likelihood for the ith person is given by
−1/2
Li = (2π)−Ti /2 ζ i ,ζ i
1
′ −1
× exp − (Wi − i ) ζ i ,ζ i (Wi − i )
2
∞
−1/2
1 θ3 − µθ3 |Wi 2
2
×
exp −
2πσθ3 |Wi
2
σθ3 |Wi
−∞
∗
1 ηiJ − µηiJ∗ |Wi 2
2 −1/2
2πση∗
exp −
×
iJ
∗
2
σηiJ∗ |Wi
ηiJ
D
∗
× hθ3i ,ηiJ∗ (τiJ ) J Sθ3i ,ηiJ∗ (τiJ ) dηiJ
×
j
i −1
j=1
∗
1 ηiJ − µηiJ∗ |Wi 2
2 −1/2
2πση∗
exp −
iJ
∗
2
σηiJ∗ |Wi
ηiJ
∗
× hθ3i ,ηiJ∗ (τiJ )Sθ3i ,ηiJ∗ (τiJ ) dηiJ dθ3 ,
where Dj = 1 if the last job has ended and 0 otherwise, and
Wi is the vector of Ti observed wage values wit for person i
Dostie: Job Turnover and the Returns to Seniority
195
organized in order of jobs and calendar time within a job, which
we decompose as
Wi = i + ζ i .
(16)
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
Thus the vector Wi includes a vector of ji subvectors with elements representing the jth job, where ji is the total number
ji
TiJ(i,t) . The job-specific
of jobs for individual i and Ti = j=1
mean subvectors are given by the regression equations
′
β0 β 1′
1
′
′
iJ(i,t) = 1TiJ(i,t) , β 5 expit , β 6 timet
1 β4
Xi
1
0
1
0 β′ β′
′
2
3
+ 1TiJ(i,t) , γ seniJ(i,t)t
ZiJ(i,t) ,
1 0
0
FJ(i,t)t
The joint likelihood is obtained by numerically integrating out
the heterogeneity components from the product of the conditional likelihoods of the individuals, assuming joint normality
of the heterogeneity components and of the innovations to the
autoregressive components. Because a closed-form solution to
the integral does not exist, the likelihood was computed by approximating the normal integral by a weighted sum over “conditional likelihoods,” that is, likelihoods conditional on certain
well-chosen values of the residual.
4. DATA
Our main data source is the “Déclarations Annuelles des
Salaire” (DADS), a large-scale administrative database of
matched employer–employee information collected by INSEE
and the job-specific residual subvectors are given by
(Institut National de la Statistique et des Études Économiques)
θ1i
and maintained by the Division des Revenus. The data are based
′
ζij = 1TiJ(i,t) , β 5 expit
on mandatory employer reports of the gross earnings of each
θ2i
employee subject to French payroll taxes. These taxes apply
η1iJ(i,t)
+ ǫiJ(i,t) , to all “declared” employees and to all self-employed people—
+ 1TiJ(i,t) , γ ′ seniJ(i,t)t
η2iJ(i,t)
essentially, all employed people in the economy.
The Division des Revenus prepares an extract of the DADS
where ǫ iJ(i,t) is the vector of the ǫiJ(i,t)t corresponding to the job
for scientific analysis, covering all individuals employed in
match iJ(i, t).
The residual covariance matrix for the full vector of Ti ob- French enterprises who were born in October of even-numbered
years, excluding civil servants. Meron (1988) showed that indiserved wage values is given by
viduals employed in the civil service move almost exclusively
′
ζ i ,ζ i = 1Ti , β ′5 expit θ,θ 1Ti , β ′5 expit
to other positions within the civil service. Thus the exclusion
′
′
= + diagji 1TiJ(i,t) , γ seniJ(i,t)t η,η 1TiJ(i,t) , γ seniJ(i,t)t of civil servants should not affect our estimation of a worker’s
market wage and employment duration equation. Employees of
+ ǫ i ,ǫ i ,
state-owned firms are, however, present in our sample. We have
where diagJi {·} denotes a block diagonal matrix with Ji blocks. longitudinal work histories running from 1976 to 1996, but are
The mean and variance of the job duration person-specific missing wage data from 1981, 1983, and 1990, because the uncomponent, conditional on the observed wage series, are derlying administrative data were not collected in these years.
The initial dataset contained 15,425,746 annual wage obgiven by
servations for 1,951,333 individuals, 1,142,738 firms, and
µθ3i |Wi = θ3i ,ζ i −1
5,913,042 employment spells. Limiting the sample to full-time
ζ i ,ζ i (Wi − i )
jobs in the goods and services sector yields 3,622,090 employand
ment spells. Firm data are obtained through the EAE (Enquête
.
σθ23i |Wi = σθ23i − θ3i ,ζ i −1
Annuelle d’Entreprises), an annual survey of firms. The EAE
ζ
,θ
ζ i ,ζ i
i 3i
data are available only from 1978 to 1996. After further restrictThe covariance matrix between the wage residuals ζ i and the
ing the sample to people age 16 years or older and who started
person-specific job duration residual θ3i is given by
a new job in 1978 or later, we are left with 2,795,419 job spells.
We deleted an additional 59 job spells because of inconsistent
σθ1i ,θ3i
.
(17)
ζ i ,θ3i = 1Ti , β ′5 expit
starting and ending dates.
σθ2i ,θ3i
Each employment spell identified from the DADS has a firm
The mean and variance of each of the ji job-specific job duration
identifier that we match to the EAE to get information about
components conditional on the observed wage series for the job
firm characteristics such as sales, number of employees, and
are given by
capital stock. Some 65% of the employment spells occur in
−1
′
a firm covered by the EAE. However, we do not have a com∗
µηiJ(i,t)
|Wi = λ ηiJ(i,t) ,ζ i ζ i ,ζ i (Wi − i )
plete set of time-varying firm characteristics for each job spell.
and
We effectively discard job spells that have one or more missing
values in their firm characteristics histories. We obtain com−1
′
2
ση∗ |Wi = λ ηiJ(i,t) ,ǫiJ(i,t) − ηiJ(i,t) ,ζ i ζ i ,ζ i ζ i ,ηiJ(i,t) λ.
iJ(i,t)
plete histories for 989,215 job spells, or 35.4% of the original
The covariance matrix between the wage residuals ζ i and the sample. We performed estimation with both the full dataset and
∗
the smaller sample with firm characteristics. Because results did
is given by
job-specific job duration residuals ηiJ(i,t)
not vary significantly between the two samples, we present only
∗
ζ i ,ηiJ(i,t)
(18) results from the dataset with firm covariates.
= 1Tij γ ′ seniJ(i,t)t J ηη λ.
i
196
Journal of Business & Economic Statistics, April 2005
Table 1. Summary Statistics at the Individual Level
Years of schooling
n = 620,078
Table 2. Summary Statistics for Employment Duration (in years)
Men (65%)
Mean
SD
Women (35%)
Mean
SD
12.38
12.19
1.73
1.72
Mean
SD
Min
Q25
Q50
Q75
Max
2.12
3.12
n = 989,215
.08
.25
.83
2.58
19.00
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
Table 3. Summary Statistics at the Job Level
Summary statistics for our sample are divided into four
tables. Table 1 presents summary statistics for individual
characteristics including schooling and gender. The average
employment duration in our sample is 2.07 years (Table 2). This
is lower than is usually seen in work history surveys, probably
due to the administrative nature of the data. Table 3 reports
summary statistics at the job level. Job description variables include identifiers for whether the job was located in the Paris
metropolitan area (called “Île de France”); 32% of the employment spells took place in Paris, and 15% are right censored at
1996. The dependent variable in our wage rate analysis is the
logarithm of real annualized total compensation cost for the
employee. Table 4 shows that men earn on average 29% more
than women. Average experience at the beginning of the job
spell is 12.4 years. A worker’s experience is computed as the
difference between current age and school-leaving age. Finally,
Table 4 also includes summary statistics for time-varying firm
characteristics.
Men (68%)
Mean
SD
Censored
Lives in Île de France
Experience in years
(when spell begins)
n = 989,215
Women (32%)
Mean
SD
.15
.30
.36
.46
.13
.35
.34
.48
12.40
10.40
10.86
9.86
Table 4. Summary Statistics of Annual Data
(log) Wage
Capital stock (million FF)
Number of employees (thousand)
Total sales (million FF)
First difference in log-capital stock
First difference in log-sales
n = 2,484,039
Men (69%)
Mean
SD
Women (31%)
Mean
SD
4.37
15.70
7.88
7.85
.09
.07
4.11
10.95
5.56
5.29
.10
.08
.66
92.97
30.29
27.59
.51
.33
.69
74.16
23.93
21.06
.50
.33
Table 5. Estimation Results, Hazard Equation
5. RESULTS
The discussion of the results is organized as follows. Section 5.1 presents results of the estimation of the employment
duration equation, and Section 5.2 discusses the results for the
wage equation. Table 5 reports various estimates of the coefficients for the employment duration model, Table 6 does the
same for the wage equation, and Table 7 presents estimates
for the variance–covariance matrix of the various heterogeneity components included in the statistical model.
Constant
Male
Years of schooling
Lives in Île de France
Seniority spline
0–2nd year
2–5th year
5.1 Employment Duration
The first and second columns of Table 5 report estimates
of the coefficient on gender, schooling, job location, seniority,
experience, a time trend, and various time-varying firm variables for the basic and mixed duration models. As is typical
with duration analysis, positive coefficients indicate a higher
probability of employment termination or, conversely, shorter
job duration. Standard errors, reported in parentheses, were
computed using the covariance matrix of estimated model parameters given by the inverse of minus the Hessian matrix.
Estimates of the basic (the “Base” column in Table 5), mixed
(“Mixed”) and simultaneous (“SIM”) models tell very similar stories about the determinants of employment duration in
France. Males keep their job longer, education is associated
with a lower probability of job termination, and employment
relationships are less stable in the metropolitan area of Paris.
For the latter, the magnitude of the coefficients indicates that
the probability of losing a job in any year is about 20% higher
in Paris.
5–10th year
10th year +
Experience spline
0–5th year
5–10th year
10–20th year
20–30th year
30th year +
Time trend
Base
Mixed
SIM
1.249
(.017)
−.069
(.003)
−.045
(.001)
.192
(.003)
1.268
(.017)
−.069
(.001)
−.045
(.001)
.191
(.003)
1.089
(.018)
−.061
(.003)
−.045
(.001)
.210
(.003)
−.763
(.002)
−.093
(.002)
−.059
(.002)
−.054
(.003)
−.576
(.003)
−.071
(.002)
−.024
(.002)
−.037
(.004)
−.573
(.003)
−.069
(.002)
−.024
(.002)
−.035
(.004)
−.105
(.001)
−.061
(.001)
−.016
(.001)
−.021
(.001)
.061
(.001)
.024
(.000)
−.110
(.001)
−.074
(.001)
−.020
(.001)
−.025
(.001)
.060
(.001)
.023
(.001)
−.106
(.001)
−.069
(.001)
−.017
(.000)
−.021
(.000)
.057
(.000)
.025
(.000)
−.065
(.000)
−.064
(.000)
−.146
(.003)
−.145
(.003)
First difference
in log-capital stock
First difference
in log-sales
n = 989,215
NOTE:
Standard errors are in parentheses.
Dostie: Job Turnover and the Returns to Seniority
197
Table 6. Estimation Results, Wage Equation
Constant
Male
Years of schooling
Lives in Île de France
Seniority spline
0–2nd year
2–5th year
5–10th year
10th year +
OLS1
OLS2
Mixed
SIM
2.961
(.002)
.229
(.001)
.039
(.000)
.216
(.001)
3.125
(.003)
−.012
(.002)
.038
(.000)
.216
(.001)
3.186
(.015)
−.024
(.003)
.041
(.001)
.142
(.001)
2.782
(.016)
−.031
(.003)
.040
(.001)
.140
(.001)
.042
(.001)
.020
(.001)
−.002
(.000)
−.002
(.000)
.042
(.001)
.020
(.001)
−.002
(.000)
−.003
(.000)
.936
(.010)
−.008
(.001)
.008
(.000)
−.008
(.000)
−.008
(.000)
.895
(.018)
−.053
(.001)
.005
(.000)
−.008
(.000)
−.005
(.000)
.858
(.031)
.050
(.002)
.035
(.001)
.016
(.000)
.005
(.000)
−.007
(.000)
.008
(.000)
.031
(.000)
.022
(.000)
.010
(.000)
.003
(.000)
−.004
(.000)
.009
(.000)
.034
(.002)
.019
(.001)
.010
(.000)
.003
(.000)
.003
(.000)
.008
(.000)
.038
(.002)
.019
(.001)
.009
(.001)
.003
(.001)
.000
(.000)
.008
(.000)
−.004
(.001)
.008
(.001)
.008
(.001)
.010
(.001)
.020
(.001)
.020
(.001)
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
Male × experience
Experience spline
0–5th year
5–10th year
10–20th year
20–30th year
30th year +
Time trend
Table 7. Variance Components Parameter Estimates
First difference
in log-sales
First difference
in log-capital stock
n = 989,215
NOTE:
Standard errors are in parentheses.
The impact of seniority and experience is also as expected.
Taking into account individual unobserved heterogeneity flattens the seniority profile, as can be seen by comparing the coefficients on the seniority spline in the “Base” and “Mixed”
columns in Table 5, but the interpretation remains the same.
The first 2 years on a job are associated with an important reduction in the probability of job termination (−.576 for “0–2nd
year” in the “Mixed” column). This indicates that the probability of job termination is cut in half in each of the first 2 years on
a job. This probability keeps falling as seniority increases, but
at a much lower rate in the following years. The story is similar with experience. Results show that individuals are sorted in
more stable employment relationship as they gain labor market experience. The effect is again stronger for the first 2 years
and gradually dies off after 20 years on the job market. We see
the opposite effect after 30 years of experience, due to people
getting out of the job market.
Time-varying firm characteristics are found to be important.
Increases in both sales and the size of the firm as measured by
its capital stock are associated with a lower probability of job
termination. Finally, unobserved individual heterogeneity in the
job duration equation is found to be significant, although its
impact on other coefficients is not dramatic (σθ3 = .546 in the
“Mixed” column of Table 7).
BASE
Mixed
Individual heterogeneity variance components, θ ,θ
.159
(.001)
σθ2
.989
(.029)
σθ3
.546
(.003)
ρθ1 ,θ2
−.734
(.004)
σθ1
ρθ1 ,θ3
ρθ2 ,θ3
Job heterogeneity variance components, η,η
ση1
.378
(.000)
ση2
30.345
(2.583)
ρη1 ,η2
.458
(.002)
λ1
λ2
SIM
.219
(.002)
1.136
(.045)
.563
(.003)
−.747
(.004)
−.013
(.011)
−.345
(.006)
.370
(.005)
6.167
(.117)
.456
(.002)
−.020
(.008)
.013
(.001)
Autoregressive error structure
κ1
σu
NOTE:
.630
(.000)
.202
(.001)
.441
(.000)
.180
(.001)
.398
(.000)
Standard errors are in parentheses.
5.2 Wage Determination
The first two columns of Table 6 report results of an OLS
estimation of the wage equation, first in its conventional form
and then with additional covariates related to labor demand.
We also add a gender interaction to experience, to take into
account different life-cycle returns to experience between men
and women in the second specification. Typical results are obtained for gender, returns to education, and job location for both
sets of results. Not surprisingly, men are found to earn more
than women, as indicated in the “OLS1” column. However,
as shown by the positive interaction term between gender and
experience in the other columns, the gap grows wider as individuals gain experience. Looking at the “SIM” column, the interpretation is that although returns to experience for women are
about 3.8% for their first 5 years on the job market, returns for
men are moderately higher at 7.1% (1.858 × .038). The returns
to an additional year of education are about 4%, and salaries
are found to be higher in the Paris metropolitan area. The coefficient on the time trend is stable across different specifications
and indicates that real wages grew on average by 1% a year
between 1978 and 1996. Note that all results for other parameters are robust to the inclusion of time dummies instead of a
time trend.
Now turning to the returns to specific and general human
capital, we find that returns to 10 years of seniority are a little less than 15% in the OLS regression. The first striking result
is obtained by observing how these returns collapse when unobserved heterogeneity is included in the wage equation. Taking
into account individual and job unobserved heterogeneity reduces the returns to seniority to close to zero. When we estimate
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
198
Journal of Business & Economic Statistics, April 2005
the model simultaneously to take into account the endogeneity
of seniority, returns to seniority are in fact negative for the first
2 years on a job. This is in stark contrast to returns to experience, which, although diminishing somewhat after taking into
account unobserved heterogeneity, still average 4% a year for
the first 5 years on the labor market and 2% for the following
5 years in the simultaneous model. It is well known that returns
to seniority are pretty low in France (see Abowd et al. 1999),
but our estimates are even lower than those reported in previous
studies.
Turning to the coefficients on time-varying firm variables,
we report in Table 6 that positive changes in sales lower the
probability that workers will quit their current job. This is the
first time it has been possible to assess the influence of labor
demand indicators on employment at the employer–employee
match level. As discussed earlier, one interpretation of this result is that these positive changes in sales are indicative of firm
labor demand. But one could also argue that these factors are
taken into account in the workers’ mobility decisions; positive
changes in sales could be used to predict a higher future wage,
or a higher probability of promotion within the firm. At this
stage one cannot distinguish between these two hypotheses.
However, another striking result is that those changes in sales
have almost no impact on the wage level.
Finally, in Table 7 we present parameter estimates for the
unobserved heterogeneity components. We first note that individual and job unobserved heterogeneity components are significant. Significant unobserved job heterogeneity in returns to
seniority was also reported by Abowd et al. (1999) and Lillard
(1999). The relatively high parameter estimate for ση2 indicates that although average returns to seniority are close to
zero, actual ranges for those returns are much wider. More interestingly, we report in the “SIM” column that both correlations between unobserved individual heterogeneity components
from the wage equation and those from the hazard equation
(ρθ1 ,θ3 and ρθ2 ,θ3 ) are significantly different from 0. Both are
negative, which suggests that both high-wage and high-wage–
growth workers tend to have longer job duration. Also note that
both λ1 and λ2 are statistically significant. This indicates that
good job matches, through either higher starting wage or superior wage growth throughout the job, also last longer. Based
on these significant correlations, we can reject exogeneity of
seniority in the wage equation.
job market in which most wage growth comes from switching
to higher-paying jobs, especially early in one’s career.
Overall, the foregoing results lend credence to theories that
accord greater importance to job search and job matching as
determinant of wage level and wage growth, because returns
to seniority are found to be very small, even negative. Firmspecific capital does not seem to be important, and human capital would be easily transferable from firm to firm. It remains
to be seen what applying our methodology on similar U.S. data
would yield. In fact, there is no reason for the returns to seniority to be the same in Europe as in the U.S. (Wasmer 2003).
Finally, we find that changes in sales have an important effect in reducing the hazard rate in the mobility equation and
a somewhat smaller impact on wages. Therefore, the mobility
decision depends on more factors besides demographic characteristics and unobserved heterogeneity. We plan on exploring
this decision even further in future research by disaggregating
our sales data along product lines. It should also be interesting to decompose sales shocks into its permanent and temporary components. However, as we noted in our discussion of the
results, interpretation of the coefficients on firm-side variables
would be helped by the development of theoretical models of
the firm linking its employment and wage policies to events on
the product market at the micro level. We expect the development of such models to be spurred by the availability of linked
employer–employee datasets.
Another avenue for future research is to decompose the unobserved job-match heterogeneity component into its firm and
“pure” job-match components. It would be interesting to get
posterior expectations for the firm and individual random effects and aggregate these at the industry level, especially for
the job duration equation.
ACKNOWLEDGMENTS
The author acknowledges financial support from the National Science Foundation (grant SES 99-78093 to Cornell University). The author thanks John Abowd, Robert Clark, Gary
Fields, Robert Hutchens, George Jakubson, Raji Jayaraman,
Joan Moriarty, and three anonymous referees for very helpful
comments. All remaining errors are the author’s alone.
[Received May 2002. Revised February 2004.]
6. CONCLUSION
REFERENCES
In this article we estimate simultaneously the wage and job
duration processes for a longitudinal sample of French workers
from 1978 to 1996 to obtain estimates of the returns to seniority
that are not potentially biased by the endogeneity of seniority in
the wage equation. We find that taking into account unobserved
individual and job heterogeneity considerably lowers the returns to seniority estimates. Moreover, these unobservables are
significantly correlated across the wage and employment duration equations. Taking this correlation into account actually
causes the returns to seniority to become negative in the first
few years on a job, a result corroborated by a recent study also
on French data by Kramarz (2003). Negative returns to seniority
for the first few years on a job are consistent with a view of the
Abowd, J. M., Kramarz, F., and Margolis, D. N. (1999), “High-Wage Workers
and High-Wage Firms,” Econometrica, 67, 251–333.
Abraham, K., and Farber, H. (1987), “Job Duration, Seniority, and Earnings,”
American Economic Review, 77, 278–297.
Altonji, J., and Shakotko, R. A. (1987), “Do Wages Rise With Job Seniority?”
Review of Economic Studies, 54, 437–459.
Altonji, J., and Williams, N. (1997), “Do Wages Rise With Job Seniority? A Reassessment,” Working Paper 6010, National Bureau of Economic Research.
Anderson, P. M., and Burgess, S. M. (2000), “Empirical Matching Function:
Estimation and Interpretation Using State-Level Data,” Review of Economics
and Statistics, 82, 93–102.
Buchinsky, M., Fougère, D., Kramarz, F., and Tchernis, R. (2003), “Interfirm
Mobility, Wages, and the Returns to Seniority and Experience in the U.S.,”
mimeo, UCLA.
Hutchens, R. M. (1989), “Seniority, Wages and Productivity: A Turbulent
Decade,” Journal of Economic Perspectives, 2, 49–64.
Dostie: Job Turnover and the Returns to Seniority
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:47 12 January 2016
Jiang, J. (1998), “Consistent Estimators in Generalized Linear Mixed Models,”
Journal of the American Statistical Association, 93, 720–729.
Kramarz, F. (2003), “Wages and International Trade,” Discussion Paper DP3936, Center for Economic Policy Research.
Lee, Y., and Nelder, J. (1996), “Hierarchical Generalized Linear Models,”
Journal of the Royal Statistical Society, Ser. B, 58, 619–678.
Lillard, L. A. (1999), “Job Turnover Heterogeneity and Person-Job-Specific
Time-Series Wages,” Annales d’Économie et de Statistique, 55–56, 183–210.
Meron, M. (1988), “Les Migrations des Salariés de l’État: Plus Loin de Paris,
Plus Près du Soleil,” Économie et Statistique, 214, 3–18.
199
Searle, S. R., Casella, G., and McCulloch, C. E. (1992), Variance Components,
New York: Wiley.
Topel, R. (1986), “Job Mobility, Search, and Earnings Growth: A Reinterpretation of Human Capital Earnings Functions,” in Research in Labor Economics, Vol. 8, ed. R. Ehrenbrerg, Greenwich, CT: JAI Press, pp. 199–233.
(1991), “Specific Capital Mobility and Wages: Wages Rise With Job
Seniority,” Journal of Political Economy, 99, 145–176.
Wasmer, E. (2003), “Interpreting European and U.S. Labour Market Differences: The Specificity of Human Capital Investments,” Discussion Paper DP3780, Center for Economic Policy Research.