Estimating an Equilibrium Job Search Model for
the German Labour Market
Maximilian J. Blömer1) , Nicole Guertzgen2) ,
Laura J. Pohlan1) , Holger Stichnoth1) , and Gerard J. van den Berg2)
1)
2)
Centre for European Economic Research, Mannheim
Centre for European Economic Research, University of Mannheim∗
February 2015
PRELIMINARY - DO NOT CITE OR CIRCULATE
Abstract
In this study, we estimate an econometric structural equilibrium search
model to ex-ante simulate the introduction of a uniform minimum wage in
the German labour market. We use the model to gain a better understanding
about the magnitude of search frictions and, thus, the extent of employers
market power in the German low-wage sector. To accommodate a wide range
of employment responses, we estimate the model by Bontemps et al. (1999),
which allows for negative, zero or positive employment effects. We take the
model to large-scale administrative German data, and validate our estimations
by comparing our predictions to the results from quasi-experimental studies
on the introduction and changes in sectoral minimum wages. We then use
the model to conduct a variety of policy simulations, including the systematic
variation of general minimum wages over a large range of values.
Keywords: minimum wage, job search, Germany
JEL-Code: J31; J51; J64
∗
Address of correspondence: Nicole Guertzgen, Holger Stichnoth, Centre for European Economic Research, Department of Labour Markets, Human Resources and Social Policy, L 7.1, 68161
Mannheim, Germany, E-Mail: [email protected], [email protected].
1
Introduction
Job search models have long been used to provide a structural framework to study
labour markets in the presence of search frictions. These frictions may create a
certain amount of market power for employers, enabling them to have some influence
over wages. Understanding the empirical relevance of search frictions may therefore
provide important insights into which of the two fundamentally different frameworks,
the neoclassical or the monopsonistic case, represent the more appropriate view of
the labour market. From a policy perspective, knowledge about the “true” labour
market structure is of key importance, as the predicted consequences of certain
economic policies, such as the imposition of a minimum wage, may substantially
differ from those derived from the neoclassical competitive case (Manning, 2003).
In this paper, we estimate an equilibrium job search model for the German labour
market. The German labour market is particularly interesting as it only recently
experienced the introduction of a statutory uniform minimum wage of 8.50 Euro per
hour. The imposition of a uniform minimum wage is unprecedented in Germany,
as prior to its introduction in the year 2015 minimum wages had been implemented
only in selected industries.1 Even though monopsonistic labour market structures
have been frequently invoked by policy makers to justify a wage floor, there is
surprisingly little structural empirical evidence on the relevance of search frictions
in the German labour market. Given the importance of frictions in determining the
sign of the expected employment effects, this clearly constitutes a major research
gap that our present study aims to overcome. By estimating an equilibrium job
search model, our analysis not only seeks to gain a better understanding about the
relevance of search frictions, but also aims at quantifying the expected labour market
effects of a uniform minimum wage.
1
While a number of transitional measures shall respect existing collective agreements and those
signed in the meantime, the uniform minimum will apply to all industries at the latest by 2017.
A further transitory exception will be given to those industries where industry-specific minimum
wages had already been introduced prior to 2015 via the Posting of Workers Act (Arbeitnehmerentsendegesetz ). The bargaining parties of an industry subject to this legislation may request that
the Federal Ministry of Labour declares its (minimum wage) agreement to be generally binding for
their whole industry.
1
To analyse the labour market effects, we estimate the wage-posting model by
Bontemps, Robin, and Van den Berg (1999). The model is particularly suited for
our purposes as it accommodates a wide range of employment responses, by allowing
both for heterogeneity in firms’ productivity and workers’ reservation wages. This
is a particularly attractive feature of the model, as models that only allow for heterogeneity in employers productivity typically restrict the employment effects to be
negative or zero. In contrast, additionally accounting for heterogeneous reservation
wages may also predict positive employment effects.
The data we use to estimate the model stem from an administrative data source,
the IAB Sample of Integrated Labour Market Biographies (SIAB); for detailed information see vom Berge et al. (2013). The data set is a two per cent random sample
of individuals subject to social security contributions during the time period 1975
to 2010. The SIAB data provide an ideal basis for estimating a structural equilibrium search model for several reasons: First and most importantly, the data permit
us to precisely measure the duration of different labour market states and transitions between them, notably job-to-job as well as employment-to-unemployment
transitions. These transitions are crucial to the identification of the model’s central
parameters, such as job arrival and destruction rates. Second, as the data are based
on employers’ notifications to the social security authorities, they are less prone to
measurement error than comparable information from survey data. Additional advantages over survey data include the larger sample size and a much lower extent of
panel attrition.
In addressing the labour market effects of the recent introduction of a uniform
minimum wage, our study contributes to the empirical literature on the labour market effects of minimum wages in Germany. Much of the evidence deals with ex-post
evaluations of industry-specific minimum wages using difference-in-differences designs. In what is probably the first quasi-experimental study for Germany, König
and Möller (2009) analyse the introduction of a minimum wage in the construction industry. The authors find no significant employment effects in West Germany
and small negative effects in the East, where the minimum wage has greater bite.
2
In 2011, the German Federal Ministry of Labour commissioned an evaluation of
minimum wages in several industries. In general, these studies also tend to find
little employment effects (e.g., Boockmann et al. (2013); Frings (2013) ), with the
exception of the roofing industry (Aretz et al., 2013). While these ex-post form approaches provide valuable insights into the labour market effects of industry-specific
policies, they are neither informative about the underlying transmission mechanisms
nor are they able to assess the economic impacts of different minimum wage levels.
The few available structural studies for Germany have relied on estimates of labour
demand function under the assumption of perfect competition (Ragnitz and Thum,
2008; Bauer et al., 2009; Knabe and Schöb, 2009). In this framework, the effects
of a minimum wage can by construction only be zero (if the minimum wage is not
binding) or negative (see the critique by Fitzenberger 2009). The strong negative
effects reported by some of these studies appear at odds with the quasi-experimental
evidence, which underscores the need for a richer structural model that allows for a
wide range of employment effects.
The remainder of the paper is laid out as follows: Sections 2 and 3 start by giving
a brief overview of the model. Section 4 provides a description of the data set and
the construction of our variables of main interest, and Section 5 shows descriptive
statistics. Section 6 outlines the estimation procedure, Section 7 presents the results,
and Section 8 concludes. Note that the paper is still very much work in progress
and that as a result, the existing findings and the conclusion are still preliminary.
2
Theoretical Overview
Equilibrium job search models provide a framework in which the wage offer distribution that workers face in their search emerges as the equilibrium of a non-cooperative
wage search and wage posting game between workers and employers. A minimum
wage policy alters the wage offer distribution, thereby affecting the number of firms
that continue to operate in the market and increasing the average wage offer that an
3
unemployed person can expect to receive. A number of studies have estimated different variants of equilibrium job search models building on the Burdett-Mortensen
framework with on-the-job search (e.g. Bowlus et al., 1995, 2001; Van den Berg and
Ridder, 1998).
A drawback of the Burdett-Mortensen model is that it generates a strictly increasing wage offer density. This has led researchers to shift the emphasis towards
models incorporating heterogeneity in firm productivity. Firm heterogeneity has
been shown to improve the fit of the wage distribution and has been modelled in
different ways in the literature: While Eckstein and Wolpin (1990) assume a lognormal distribution, Bowlus et al. (1995, 2001) and Bunzel et al. (2001) allow for
a discrete number of firm types. Bontemps, Robin, and van den Berg (2000) allow
for a continuous distribution but estimate it non-parametrically. In the context of
a minimum wage policy, heterogeneity in firm productivity is of key importance,
as a minimum wage with homogeneous firms would create a knife-edge impact on
employment, with all firms either leaving or staying in the market. In addition to
incorporating heterogeneity in firm productivity, the model by Bontemps, Robin,
and Van den Berg (1999) also allows for heterogeneity in workers reservation wages.
While this comes at the expense of assuming equal job arrival rates for the unemployed and those searching on the job, it creates more flexibility in terms of the
predicted employment effects. In particular, it implies that the minimum wage can,
in principle, even have a positive effect on employment. This may be driven by a
higher acceptance rate of job offers: as the minimum wage precludes low wage offers, it draws more unemployed workers with high reservation wages into the market.
In the absence of a minimum wage, these workers have to wait longer for a wage
offer that is acceptable to them, as firms by assumption cannot make wage offers
conditional on individuals’ reservation wages.
4
3
Model Description
In this section, we provide a brief description of the main features of the model
by Bontemps, Robin, and Van den Berg (1999). We start by describing firms’ and
individuals’ strategies. Individuals maximise their expected steady-state discounted
future income. They are characterised by heterogeneous opportunity costs of employment denoted by b, which may include search costs and unemployment benefits.
The distribution of b is denoted by H, assumed to be continuous over its support
[b, b]. Job offers accrue at the constant rate λ > 0 and are characterised by a
drawing from a wage offer distribution F with support [w, w]. Layoffs accrue at
the constant rate δ. Unemployed individuals searching for a job face an optimal
stopping problem, whose solution consists in accepting any wage offer w such that
w > b. Employed individuals, in contrast, accept any wage offers strictly greater
than the present wage contract. Because job offers accrue at the same rate whatever
the state of workers, the reservation wage is explicit and equal to the opportunity
cost of employment.
Equating equilibrium flows into and out of unemployment, the fraction of unemployed with a reservation wage no larger than b for b ≤ w is given by
u · Hu (b) =
1
· H(w).
1+κ
(1)
For b > w the fraction is given by
κ
u · Hu (b) =
· H(w) +
1+κ
Zb
dH(x)
.
(1 + κ)F (x))
(2)
w
Moreover, Bontemps, Robin, and Van den Berg (1999) show that in steady-state
there exists a unique relationship between the unobserved offer and the observed
5
earnings distribution functions, represented by
1
H(w) +
H(w) − [1 + κ · F (w)][ (1+κ)
G(w) =
Rw
w
[1 + κ · F (w)](1 − u)
1
dH(x)]
1+κ·F (x)
.
(3)
Each firm offers only one wage and incurs a flow p of marginal revenue per worker.
A firm seeks to maximise its steady-state profit flow, π(p, w) = (p − w) · l(w), with
l(w) denoting the size of a firm’s labour force. The amount of workers, l, attracted
by a firm that offers wage w is given by
l(w) =
κ · H(w)
,
[1 + κ · F (w)]2
(4)
where l(w) is an increasing function of the offered wage.
Firms are heterogeneous in p. The distribution of p across active firms is denoted
by Γ(p), and is assumed to be continuous over its support [p, p]. Under the additional
assumption that H(b) is log concave, Bontemps et al. (1999) show that there exists
a unique single valued, monotone and continuous function w = K(p), which maps
the support of the productivity distribution Γ into the support of the wage offer
distribution F . Secondly, they demonstrate that more productive firms offer higher
wages. These two facts imply that F (w) = Γ(K −1 (w)). The solution to the optimal
wage setting problem of a p-type firm is given by


p


Z
 p−w
 [1 + κ · Γ(x)]2
H(K(x))
K(p) = p −
·
H(w)
+
·
dx
·
,
2


H(K(p))
[1 + κ · Γ(x)]2
 [1 − κ]

(5)
p
which completes the steady-state solution of the model.
4
Data
The data used in the empirical analysis are taken from German register data, the
IAB Sample of Integrated Labour Market Biographies (SIAB). This administrative
6
data set, which is described in more detail by vom Berge et al. (2013), is a two per
cent random sample of all individuals who have at least one entry in their social
security records between 1975 and 2010 in West Germany and 1992 and 2010 in East
Germany, respectively. The data cover approximately 80 per cent of the German
workforce and provide longitudinal information on the employment biographies of
1.6 million individuals. Self-employed workers, civil servants, and individuals doing
their military service are not included in the data set.
The data provide an ideal basis for estimating a structural equilibrium search
model for several reasons: First and most importantly, the data contain daily information on employment records subject to social security contributions, unemployment records with transfer receipt as well as periods of job search. This permits us
to precisely measure the duration of different labour market states and transitions
between them, notably job-to-job transitions as well as transitions between employment and unemployment (with and without transfer receipt). Second, due to their
administrative nature the data are less prone to measurement error than comparable
information from survey data. Additional advantages over survey data include the
larger sample size and a much lower extent of panel attrition.
For our sample selection, we restrict the sample to individuals from the working
age population aged 20 to 65. In a first step, we exploit the full time dimension
of the data spanning the time period 1975–2010, in order to measure the duration
of different labour market states. Because the model shall be used for an ex-ante
evaluation of a policy starting in 2015, we then restrict the sample to the most
recent available years 2007 to 2010. In particular, we construct a stock sample, by
retrieving all spells of employment and unemployment spanning the set date 1st of
January 2007. From these spells we exclude all those individuals who exhibit at
least one part-time and/or non-employment spell during the time period of consideration. Overall, this leads to an exclusion of 323,192 out of 707,657 individuals.
Restricting the sample to the period 2007-2010 has the advantage that it permits us
to include unemployment spells for individuals receiving means-tested welfare benefits, which were not recorded in the data prior to 2007. While this comes at the cost
7
of including left-censored unemployment spells, it enables us to adopt a consistent
definition of unemployment for the sample period considered (see also Table A2 in
the Appendix). Next to information on different labour market states, we retrieve
individual information on (daily) wage records and a number of individual characteristics such as age, education, nationality and occupational status. To address
missing information on the educational status, we use the imputation rules proposed
by Fitzenberger et al. (2005). Dropping individuals who still have missing values
in the relevant observables (such as daily wages, the educational and occupational
status as well as the regional and sectoral affiliation) leads to an additional exclusion
of 67,807 individuals.
Apart from their virtues, the administrative data have some disadvantages as
well. First, while we observe an individual’s full-time or part-time status (defined
as working less than 30 hours per week), the data lack explicit information on the
number of hours worked. For this reason, we complement the administrative data
by the German Microcensus. We use this survey data set to assign average weekly
working time information based on industry-occupation cells. Second, the wage
information in the IAB data is censored since there is an upper contribution limit
to the social security system. To address this issue we follow Gartner (2005), by
replacing right-censored observations by imputed wages. The latter are randomly
drawn from a truncated normal distribution whose moments are constructed by the
predicted values from Tobit regressions and whose (lower) truncation point is given
by the contribution limit to the social security system.
Finally, the data do not allow a distinction between involuntarily unemployed
individuals without transfer receipt and individuals who left the labour force or
who became self-employed or civil servants. To distinguish more precisely between
voluntary and involuntary unemployment, we follow the assumptions proposed by
Lee and Wilke (2009) about when the state of unemployment is reached. A full
description of the variables used in our analysis can be found in Tables A1 and A2
in the Appendix.
8
5
Descriptives
This analysis exploits information on 316,656 individuals who are either unemployed
(6%) or regularly employed (94%) on January 1st 2007 and fit the sample selection
criteria described in the previous section. Given that the spell ends within the
observation period, the subsequent labor market status can be observed. While
an unemployed person either finds a job or stays unemployed, an employed person
can become unemployed, change his job or stay in his current position. Table 4
to Table 6 present some sample statistics of selected labor market variables. In
particular, we provide information on labor market transitions, survival rates and
wage distributions for the whole sample, separately by sex and separately by sectors.
Looking at labor market transitions, we find that 64% of the unemployment spells
end with a transition into regular employment. The actual starting date of 19% of
the unemployment spells is unknown due to left-censoring. Unemployment benefit
histories from some data sources are not completely observable as recording has
started at a fixed date which does not necessarily correspond with the beginning of
the unemployment spell (see Appendix, table A2). 21% of the initially employed
move from job-to-job and 13% move from employment-to-unemployment during
the time window 2007–2010. 6% of the employment spells are left-censored which
implicates employment without interruption at the same firm since January, 1st
1975.
Moreover, Table 4 shows descriptive statistics separately by sex. About 68 %
of the individuals in the sample are men and 32 % are women. The distribution
of unemployment and employment spells across gender is nearly equal. However,
the fraction of unemployed persons exiting to employment within the observation
window is larger for men than for women. Looking at transitions of employed
individuals, the data reveal a similar pattern for both groups.
Table 5 shows non-parametric Kaplan-Meier estimates of the survivor function
which gives the probability of staying in the initial state which can be employment
or unemployment on a daily basis. The plots of the survivor functions reveal the
9
following pattern: the probability of still being unemployed after one year is around
50% while it is around 25% after three years. Hence, the figures suggest that the
risk of transition to employment is especially high during the first 12 months of
unemployment. A possible explanation is the expiration of unemployment benefits
coming along with an increased incentive to search for a new job. The survivor
function flattens after two years of unemployment which might be an indicator of
discouragement and stigma effects. Both fewer job offers and reduced job search
hinder exit from unemployment as time evolves. We do observe a steeper downward movement of the survivor function for men: after one year about 40% of the
males and about 55% of the females are still unemployed. Thus women more likely
stay unemployed for a longer period, indicating that it might be more difficult for
unemployed women to find a job again.
With regard to employment-to-employment transitions, the probability of being
still employed at the current employer is around 70% after fifteen years with regard to job-to-job transitions while it is over 80% after fifteen years in the case of
employment-to-unemployment transitions, respectively. This pattern holds true for
both genders.
The plots show that the maximal duration of an unemployment spell is about 6
years while an employment spell can last over the whole observation period covering
35 years. Note that spells might be subject to censoring and hence the durations
stated above could be longer.
The distribution of wages in the sample is based on the following hourly wage
specification: hourly wages are calculated by dividing the daily wages by 40 hours.
Moreover, the wage information used is based on a weighted average of wages earned
in the last observed year of the first employment spell and the first observed year
of the subsequent employment spell (see Appendix, table A.2, assignment of wages,
variant 4). In the current specification wages over the upper contribution limit are
not replaced by imputed wages. First, we investigate the wage structure in our
sample before a transition to unemployment or employment takes place. The plots
10
reveal that wages of individuals that change their job are on average higher and
more workers touch the upper contribution limit than those who become unemployed. Individuals moving from unemployment-to-employment accept wages that
are comparatively low which is in line with our theoretical considerations. One notable aspect is that a sizable fraction of unemployed move to jobs paying less than
8.50 Euro per hour. This number corresponds to the uniform minimum wage which
was introduced in Germany only recently, on January 1st 2015, and hence was not
an active institution during our sampling period. Considering job-to-job transitions,
the wages earned in the new job are slightly higher than the wages earned in the
old position. Looking at right-censored employment spells, we find that the wage
distribution has a symmetric and not a right-skewed shape.
Table 6 shows pronounced gender differences in earnings. Men earn more on
average, hit more often the upper contribution limit and the uniform minimum wage
bits in fewer cases compared to women. These findings point to gender differences
in pay. In Germany the average gross hourly earnings of women are 22% lower
than the earnings of men in 2013 (Statistisches Bundesamt, 2013). At the European
level, Germany belongs to the states with the highest gender differences in payment
(Eurostat, 2012). High female labor market participation and a large fraction of
women working part-time might be reasons for the large wage gap in Germany.
Table 8 displays the descriptives of the total number of 316,656 observed spells
cross-tabulated by 14 industries.2 . The number of observations differs considerably
across industries, but due to our large sample size the smallest industry (agriculture)
has still 5,590 observations.
Overall, Table 9 shows that employment and unemployment durations exhibit
substantial cross-industry variation. Most notably, manufacturing (metal industry,
electrical/optical/vehicles, consumption goods) as well as construction and the public sector are characterized by long lasting employment spells with a large fraction
of employment spells being right censored.
2
Following the German Classification of Economic Activities, Edition 1993 (WZ93)
11
Moreover, in manufacturing and the public sector over 75% of the employment
durations are longer than 35 years. Employment durations prior to an unemployment spell are on average shortest in hotels/restaurants as well as in construction.
In these two sectors, the probability of still being employed (without interruption
by unemployment) falls relatively sharp in the first three years and is below 75%
after ten years.
At the same time, however, the same industries (along with agriculture) exhibit
below-average probabilities of long lasting unemployment spells, with around 75%
of unemployment spells being shorter than one year. In the remaining industries,
the probability of staying unemployed is much higher and the risk of long term
unemployment (after more three years) amounts to more than 25%. Employment-toemployment transitions have similar patterns across all industries. The probability
of working at the same employer stays above 70% after 15 years.
Table 10 documents substantial cross-industry variation in hourly wages. The
distributions illustrate that wages are on average lower in agriculture, hotels/restaurants,
construction sector as well as retail/wholesale, whereas the chemical and metal industry, the electrical/optical/vehicle industry and the public sector pay on average
higher wages. In these industries, hourly wages also reach more often the upper
social security contribution threshold at around 30 EUR per hour.
Comparing the distributions across different transitions several patterns stand
out: First, over all industries wages are higher for employments that end because
employees find a new job at a different firm and for right censored employment spells.
This is in line with our theoretical considerations. These patterns are especially
significant in the chemical and metal industry, and in the electrical/optical/vehicle
industry but also in the services sectors.
Second, hourly wages in all industries are on average consistently higher during employment spells that precede an employer change as compared to those that
precede an unemployment spell. This pattern holds especially true for services. In
contrast, in the chemical and metal as well as in the electrical/optical/vehicle in-
12
dustry the differences in the distributions across transitions are less pronounced, by
showing a substantial mass at higher wages even prior to transitions to unemployment.
Finally, across all industries the wage distributions of employment spells following an unemployment spell are dominated by the wage distributions of employment
spells prior to employer changes and those of right-censored employment spells.
Table 11 shows the degree to which different sectors are affected by the introduction of the minimum wage of 8.50 EUR in 2010 prices. There is considerable
variation accross industries and by the type of labour market transition: The minimum wage has the strongest bite in the sectors agriculture, hotels/restaurants3 , and
the services sectors. In these sectors around 10% to 15% of the wages before and
after a job change are still below the minimum wage whereas 30% to 50% of the
jobs before or after unemployment are affected. In contrast, in the chemical and
metal industry, in the electrical/optical/vehicle industry, and in the construction
sector fewer individuals are affected by the introduction of the minimum wage and
the bite is also considerably weaker for jobs after or before unemployment. This
is because these sectors are more often covered by collective agreements or already
existing sector specific minimum wages.
6
Estimation
As shown by Bontemps, Robin, and van den Berg (2000), the likelihood contribution
for an individual who is initially unemployed is given as4
2−d −d
λ0 0b 0f
exp[−λ0 (t0b + t0f )]f (w0 )1−d0f .
1 + κ0
3
(6)
Note that the hotels/restaurants sector might be also an outlier because the measured wages
do not include tips.
4
The current, preliminary version of the paper does not yet estimate the model with both firm
and worker heterogeneity outlined in the theoretical section above. Instead, we currently follow
Bontemps et al. (2000) and assume that the opportunity cost of employment b is homogenous
across individuals. In exchange, we allow for separate job arrival rates while unemployed (λ0 ) and
employed (λ1 ). Future versions of the paper will allow for heterogeneity in b.
13
The probability of sampling an unemployed individual is given by 1/(1 + κ0 ). The
likelihood contribution reflects that unemployment durations are exponentially distributed with exit rate λ0 . In a flow sample, where the elapsed (”backward”) duration t0b is zero by definition5 , the density of the residual (”forward”) duration
t0f is given as h(t0f ) = λ0 exp(−λ0 t0f ). In a stock sample, we need to consider
the total duration t0b + t0f , conditional on the elapsed duration t0b . The latter
has the density h(t0b ) = λ0 exp(−λ0 t0b ). It can be shown that the conditional
density h(t0f |t0b ) is given as λ0 exp(−λ0 t0f ). For the joint density we then obtain
h(t0b , t0f ) = h(t0f |t0b )h(t0b ) = λ20 exp[−λ0 (t0b + t0f )], which is the term that figures
in the likelihood expression above. The term in front of the exponential function
is adjusted if either the elapsed or the residual duration is censored (d0b = 1 or
d0f = 1).
f (w0 ) is the density function of wage offers evaluated at the offer that we observe
as the initially unobserved person transits into employment. If the unemployment
duration is right-censored (d0f = 1), this term drops out of the likelihood function.
For individuals who are initially employed, the likelihood contribution is
κ0
g(w)[δ + λ1 F̄ (w1 )]1−d1b × exp{−[δ + λ1 F̄ (w1 )](t1b + t1f )}{δ v [λ1 F̄ (w1 )]1−v }1−d1f
1 + κ0
(7)
The probability of sampling such an individual is given by the first term, κ0 /(1 +
κ0 ). There are now two ways in which the job spell can end: through a transition
into unemployment (v = 1) and through a job-to-job transition (v = 0). Both
durations are again exponentially distributed. The exit rate into unemployment is
given by δ, while exit into another job happens with rate λ1 F̄ (w1 ). t1b denotes the
elapsed (“backward”) duration (equal to zero in a flow sample), t1f is the residual
(“forward”) duration of the current job. d1b equals 1 if the elapsed duration is leftcensored, while d1f = 1 means that the residual duration is right-censored, i.e. the
individual does not change his job during the observation period.
5
In the SIAB data there is an exception to this rule, however, as some unemployment spells
that began in the past were recoded to begin on January 1st, 2007. We therefore have to treat
them as left-censored in both the stock and the flow sample.
14
Maximum likelihood estimation of the model is numerically cumbersome as the
expressions that are related to the wage offer and earnings distributions (i.e., f , g,
and F̄ ) are highly non-linear functions of the productivity distribution Γ. Optimization therefore involves the numerical computation of the inverse K −1 , further
complicated by the fact that K contains an integral that has to be evaluated numerically as well. Beyond these numerical concerns, there is the issue that most
distributions for Γ imply wage and wage offer distributions that do not fit the data
well.
As an alternative, Bontemps, Robin, and van den Berg (2000) therefore propose
a three-step procedure in which the distributions of wages, wages offers, and productivities is estimated non-parametrically. They show parametric assumptions about
Γ are not needed to identify (Γ, λ0 , λ1 , δ, b) as long as the minimum wage is higher
than the reservation wage and the rate ρ at which workers discount their future
income is known.
The three-step procedure works as follows:
1. In a first step, estimate G and g, i.e., the cdf and pdf of the wage distribution,
using kernel density estimators. Use the estimates Ĝ and ĝ to obtain consistent
estimates of F̄ and f (conditional on κ1 ), namely
1 − Ĝ(w)
F̄ˆ =
1 + κ1 Ĝ(w)
(8)
and
fˆ(w) =
1 + κ1
[1 + κ1 Ĝ(w)]2
ĝ(w).
(9)
2. The estimates from Step 1 are plugged into likelihood function. The likelihood
is then maximized with respect to κ0 , κ1 , and δ.
3. Once these parameters are known, the productivity can be expressed as a
15
function of the wage:
p = K −1 (w) = w +
1 + κ1 G(w)
.
2κ1 g(w)
(10)
An estimate of the productivity distribution is given as
γ(p) =
2κ1 (1 + κ1 )g(w)3
.
3κ1 g(w)2 [1 + κ1 G(w)]2 − g 0 (w)[1 + κ1 G(w)]3
(11)
Note that γ is only a well-specified density function if the denominator is
greater than zero, i.e. if 3κ1 g(w)2 − g 0 (w)[1 + κ1 G(w)] > 0. We test for this
condition below.
Standard errors are obtained by bootstrapping the three estimation stages.
7
Results
7.1
Whole sample
As noted above, the paper is still work in progress. In particular, the estimation does
not yet incorporate the heterogeneity in the opportunity cost of employment that
is part of the theoretical section above. For this reason, we keep the results section
deliberately short, reporting the results for the stock sample only and focussing
on the estimates for the frictional parameters, with only a brief discussion of the
distributions of f , g, and γ. By the time of the conference, full results for the richer
model will be available.
Table 1 shows our estimates of δ, κ0 , and κ1 . The estimation is based on a
stock sample with more than 300,000 observations, allowing fairly precise estimates.6
Bootstrapped standard errors (based on 100 runs) are shown in parentheses. These
6
For comparison, Bontemps et al. (2000) use about 10,000 observations, while Holzner and
Launov (2010) estimate their model on less than 4000 observations. However, we are currently not
making full use of the large sample. To reduce computation time for the bootstrap, the preliminary
results have been estimated on a random subsample of 10,000 observations.
16
Table 1: Estimation results for the frictional parameters
N
δ
κ0
κ1
Whole sample
316656
Men
215383
Women
101273
0.0071
(0.0001)
0.0071
(0.0001)
0.0080
(0.0001)
14.1
(0.47)
17.6
(0.73)
11.6
(0.35)
1.6
(0.04)
1.6
(0.04)
1.4
(0.04)
Standard errors based on 100 bootstrap runs in parentheses. N refers to the total number of available observations.
estimations were carried out on a random subsample of 10,000 observations in each case.
The
take into account the sampling variation in both the non-parametric estimation of
the wage and wage offer distributions and in the maximum likelihood estimation.
We estimate the job destruction rate δ to be 0.0071. The number that we find
for Germany is of the same order of magnitude as in the study by Bontemps et al.
(2000); they report a δ of 0.0061 for France in the early 1990s. Holzner and Launov
(2010), who use data from the German Socio-Economic Panel 1984–2001, estimate
δ to be 0.0047. The higher value that we find for the years 2007–2010 is consistent
with the well-documented increase in labour market dynamics in Germany since
the mid-2000s, and with the fact that our sampling period spans the recession of
2008/2009.
As in the estimation by Bontemps et al. (2000), κ, i.e., the ratio of the job
arrival over the job destruction rate, is much greater for the unemployed than for
the employed. We estimate κ0 to be 14.6 and κ1 to be 1.6. Bontemps et al. also
find that κ1 is greater than κ0 by a factor of about 10. In both cases, this reflects
that continental European labour markets are characterized by relatively little jobto-job mobility compared with the United States. Holzner and Launov’s results fit
this basic pattern, but show a slightly smaller difference: they estimate κ1 to be
2.2, while their three values of κ for the unemployed (they assume that individuals
search on skill-specific labour markets) range between 5.6 and 17.1.
Figure 1 summarizes the results from the first and third stages of the estimation
procedure. The density of the wage distribution g is estimated using the corrected
17
Figure 1: Wages and productivity
(a) Wages and wage offers
(b) Productivity
Note: The vertical lines correspond to the 5th, 25th, 50th, 75th, and 95th percentiles of the wage
and productivity distributions, respectively.
kernel estimator proposed by Bontemps et al.:
"
n
1 X
ĝ(w) =
ϕ
nh i=1
w − wi
h
# −1
w − ŵ
Φ
h
(12)
where Φ and ϕ are the cdf and the density of the standard normal distribution and
ŵ is the smallest wage observed in our sample. To find the wage offer distribution f
and the productivity distribution γ, the non-parametric estimate of g is combined
with the maximum likelihood estimates for the frictional parameters, as outlined
in Section 6 above. As our results are still preliminary, we do not discuss these
distributions in detail here. The main point to take away from the figure is probably the straight line that is apparent between the 5th and 95th percentiles of the
productivity distributions in the log-log diagram – such a straight line is a feature
of a Pareto density, which is often assumed in equilibrium job search models that
rely on a parametric specification of the productivity distribution.
7.2
Analysis by gender and by sector
As noted, a key advantage of the administrative data that we use over the survey
datasets used by Bontemps et al. and by Holzner and Launov is the much bigger
18
Table 2: Estimation results by sector
N
Agriculture
Rubber and Plastic
Chemical Industry
Metal Industry
Electrical/Optical/Vehicles
Consumption Goods
Hotels/Restaurants
Construction
Retail/Wholesale
Transportation
Services I
Services II
Public Sector I
Public Sector II
5590
7717
6032
30075
26531
22772
7653
22705
45378
20293
57776
16133
32904
15097
δ
0.0087
0.0064
0.0054
0.0057
0.0052
0.0064
0.0131
0.0099
0.0078
0.0088
0.0095
0.0071
0.0068
0.0053
(0.0001)
(0.0001)
(0.0001)
(0.0001)
(0.0000)
(0.0001)
(0.0002)
(0.0001)
(0.0001)
(0.0001)
(0.0001)
(0.0001)
(0.0001)
(0.0000)
κ0
16.5
19.4
18.6
22.3
22.9
16.1
8.4
14.4
12.9
16.0
12.0
13.4
12.8
22.6
(0.81)
(0.92)
(1.19)
(0.84)
(1.43)
(0.54)
(0.27)
(0.58)
(0.47)
(0.56)
(0.37)
(0.46)
(0.38)
(1.03)
κ1
1.2
1.3
1.6
1.5
1.7
1.4
1.4
1.2
1.6
1.8
1.9
1.4
1.6
1.6
(0.05)
(0.04)
(0.05)
(0.04)
(0.04)
(0.03)
(0.04)
(0.03)
(0.04)
(0.05)
(0.04)
(0.04)
(0.04)
(0.04)
Standard errors based on 100 bootstrap runs in parentheses. N refers to the total number of available observations.
estimations were carried out on a random subsample of 10,000 observations in each case.
The
sample size. We can therefore estimate the model for various subsamples. In this
preliminary version, we report results by gender and by sector. In later versions, we
will also interact these two dimensions and will distinguish by region.
Table 1 shows that the frictional parameters differ between men and women,
in particular with respect to unemployment. We find that the ratio of the job
arrival rate over the job destruction rate is 17.6 for men, but only 11.6 for women,
a difference that is both statistically significant and sizeable. The difference for the
people who are currently employed is less pronounced (1.6 vs. 1.4).
There are also sizeable differences in both job offer and job destruction rates
between sectors (cf. Table 2). Three groups can be distinguished. First, some
sectors such as the chemical industry, the metal industry, parts of the public sector
or the sector comprised of the electrical, optical and car industries have low job
destruction rates and a high κ0 for the unemployed, consistent with relatively short
unemployment spells. In these sectors, κ1 tends to be close to the overall average of
1.6.
19
A second group of sectors (retail/wholesale, transportation, services I) stand out
for having both high job destruction rates and a high rate of job-to-job transitions.
The latter are reflected in high values of κ1 , and this despite the high δ in the
denominator. κ0 tends to be on the lower end for these sectors.
Finally, a third group consists of hotels/restaurants, construction, and, to a lesser
degree, agriculture. Job destruction rates are particularly high here (reaching 0.0131
for hotels and restaurants, almost twice the value for the overall sample), while both
κ0 and κ1 tend to be low or very low.
These inter-sectoral differences are potentially relevant for the design of the new
statutory minimum wage in Germany. After a transition period, the new rate will
be uniform for all workers. The table suggests that the uniform rate applies to
sectors that differ in the extent of search frictions and thus in employee’s monopsony
power on the labour market. While this may be prima facie evidence in favour of
a more disaggregated rate (akin to the existing sectoral agreements), drawing firm
conclusions would be premature at this stage.
Among the things that are still in flux is the treatment of the restriction that
follows from Equation 11. In the estimation above (for the entire sample), the
restriction is violated for slightly less than 16 percent of workers. We are currently
investigating whether this is due to the right-censoring of observed wages introduced
by the threshold for social security contributions. If the violations remain in the
same order of magnitude, we will consider imposing the constraint in the maximum
likelihood estimation.
7.3
Robustness checks
As the estimation is still preliminary, we have run only a few robustness checks
so far. First, we measured the hourly wage for the employment spells at different
points in time. This is necessary because we observe wage variation for the same
individual at the same employer. The theoretical model abstracts away from this by
20
Table 3: Robustness checks: different wage measurements
SSC
threshold
Censored
Censored
Censored
Censored
Censored
Censored
Censored
Imputed
Imputed
Imputed
Imputed
Imputed
Imputed
Imputed
Hours
Wage
Old spell
Wage
New spell
40
40
40
40
Imputed
Imputed
Imputed
40
40
40
40
Imputed
Imputed
Imputed
Avg last year
Last observed
Average
First observed
Avg last year
Last observed
Average
Avg last year
Last observed
Average
First observed
Avg last year
Last observed
Average
Avg 1st year
First observed
Average
First observed
Avg 1st year
First observed
Average
Avg 1st year
First observed
Average
First observed
Avg 1st year
First observed
Average
N
δ
κ0
κ1
316656
314835
330875
310065
316127
314563
324683
312332
310257
330302
309110
312113
310327
322007
0.0071
0.0072
0.0069
0.0069
0.0072
0.0073
0.0072
0.0073
0.0072
0.0071
0.0070
0.0073
0.0073
0.0072
14.1
14.8
15.6
15.5
15.3
14.7
14.9
15.4
14.8
15.5
15.8
14.8
14.6
16.0
1.6
1.6
1.7
1.6
1.7
1.6
1.6
1.6
1.6
1.5
1.5
1.6
1.6
1.6
N refers to the total number of available observations. The estimations were carried out on a random subsample of 10,000
observations in each case.
assuming that jobs are characterized by a single, immutable wage. In our empirical
implementation we experimented with different measurements. The results reported
so far are based on average wages in the last year observed in the old new and, if
we observe a transition, the first year of the new job. In a slight variant of this
approach, we chose the last wage observed in the old job and the first wage observed
in the new job. As two other alternatives, we took the average over the entire spells,
or the first wage observed in each job.
Second, we have varied the way in which we treat wages that are censored at the
threshold. While in the results reported so far we left out these censored observations, we alternatively imputed them, as outlined in the data section above.7 The
final robustness check so far concerns the construction of the hourly wage variable.
The results above rely on a data preparation in which we assumed full-time work
to correspond to 40 hours per week. Alternatively, we imputed the hours based on
7
We also estimated a variant in which we include the imputed wages in the non-parametric
estimation of the wage distribution and left them out only in estimation of the frictional parameters.
The results change very little.
21
information from the Mikrozensus (see the data section for details).
Table 3 shows the results for all these different ways of measuring wages.8 The
main message of the table is that the results are very robust to these different ways
of measuring wages. The job destruction rates are always close to 0.007, while κ0 is
near 14.0 and κ1 tends to be around 1.6.
In another robustness check we left out individuals with wages below the existing
sectoral minimum wages.9 Identifying these observations is complicated in some
cases because the sectoral classification in the SIAB data do not always coincide
with the definitions used in the sectoral wage agreements. We follow a conservative
approach and leave out only those individuals for which we are reasonably certain
(based on information on sector, region and, in some cases, occupation) that they
are covered by a sectoral minimum wage agreement but earn less than the hourly
minimum stipulated in the agreement. We find this to be the case for about 10% of
all individuals who we can assign to a sectoral minimum wage agreement. When we
exclude these observations, our estimates for the frictional parameters change very
little (δ = 0.0074, κ0 = 14.6, κ1 = 1.6).
8
Conclusion
The paper is still work in progress. We have currently presented first estimation
results for an equilibrium job search model with firm heterogeneity. Our large administrative dataset has allowed us to distinguish by both gender and sectors. We
have uncovered sizeable differences in both job offer and job destruction rates. If
these results are confirmed in later estimations, they might suggest that the design
of the new statutory minimum wage in Germany (which, after a transition period,
8
The only exception is that we leave out combinations in which we impute weekly hours based
on the Mikrozensus and at the same time measure wages in the first year of the current employment
spell. These combinations greatly reduce the number of observations as the information from the
Mikrozensus is only available for recent years. We therefore lose all employment spells that have
been running for more than a couple of years.
9
Such minimum wages exist in about a dozen industries or occupations. See Möller (2012) for
an overview.
22
will be at a uniform rate for all workers) could be improved upon. However, this
conclusion will depend on the extent to which the minimum rate of 8.50 euros will
be relevant for the different sectors, so differences in the search frictions alone need
not be sufficient cause for deviating from a uniform rate.
Moreover, we consider the current findings preliminary for several reasons. First,
while the theoretical part of the paper follows Bontemps, Robin, and Van den Berg
(1999) and allows for heterogeneity in the opportunity cost of employment, the
estimation currently assumes that all individuals are identical in this respect (as
in Bontemps, Robin, and van den Berg (2000)). We will relax this assumption
in the next estimation round. A second, longer-term extension will be the use
of linked employer-employee data. These will allow to better distinguish whether
firm or worker characteristics drive the observed wage differences. Finally, we will
extend the model to simulate the employment effects of the new German minimum
wage. Our framework is well-suited for this as it does not impose any a-priori
restrictions on the sign of these effects. Whether a trade-off exists between wage
gains and employment losses is therefore an empirical question, and will depend on
how important the search frictions are that individuals face.
23
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26
Appendix
Table 4: Observations by Sex, stock sample
Spells
Unemployment
→ Employment
right censored
Total
Men
Women
316,656
215,383
101,273
19,264
11,995
7,269
12,376
6,888
8,671
3,324
3,705
3,564
3,630
2,065
1,565
297,392
203,388
94,004
62,394
37,091
197,907
43,232
24,945
135,211
19,162
12,146
62,696
1,834
1,424
410
left censored
Employment
→ Employment
→ Unemployment
right censored
left censored
Sample for wage variable wage cens h40 aly afy
Table 5: Durations by Sex, stock sample
Total
Men
Women
Survival rate
Unemployment
→ Employment
1.00
0.75
0.50
0.25
0.00
0
Employment
→ Employment
1000
2000
0
1000
2000
0
1000
2000
1.00
0.75
0.50
0.25
0.00
0
Employment
→ Unemployment
6000
12000
0
6000
12000
0
6000
12000
6000
12000
0
6000
12000
0
6000
12000
1.00
0.75
0.50
0.25
0.00
0
Sample for wage variable wage cens h40 aly afy
27
Table 6: Wages by Sex, stock sample
Total
Men
Women
Wage before transition (wage cens h40 aly afy)
Employment
→ Employment
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
Employment
→ Unemployment
Wage after transition (wage cens h40 aly afy)
Employment
→ Employment
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
Unemployment
→ Employment
Wage of right censored spells, (wage cens h40 aly afy)
Employment
right censored
0
10
20
30
0
10
20
30
Wage of left censored spells, (wage cens h40 aly afy)
Employment
left censored
0
10
20
30
0
10
Sample for wage variable wage cens h40 aly afy
28
20
30
Table 7: Observations and Fractions by Sex, stock sample
Total
Men
Women
316,656
215,383
101,273
19,264
11,995
7,269
12,376
6,888
8,671
3,324
3,705
3,564
3,630
2,065
1,565
297,392
203,388
94,004
62,394
37,091
197,907
43,232
24,945
135,211
19,162
12,146
62,696
1,834
1,424
410
1.000
1.000
1.000
0.061
0.056
0.072
→ Employment
right censored
0.039
0.022
0.040
0.015
0.037
0.035
left censored
0.011
0.010
0.015
0.939
0.944
0.928
→ Employment
→ Unemployment
right censored
0.197
0.117
0.625
0.201
0.116
0.628
0.189
0.120
0.619
left censored
0.006
0.007
0.004
Spells
Unemployment
→ Employment
right censored
left censored
Employment
→ Employment
→ Unemployment
right censored
left censored
Spells
Unemployment
Employment
Sample for wage variable wage cens h40 aly afy
29
Table 8: Observations by Sector, stock sample
Spells
Total
Agric.
Plastic
Chem.
Metal
Elect.
Cons.
Hotel
Const.
Retail
Transp.
Serv. I
Serv. II
Publ. I
Publ. II
316,656
5,590
7,717
6,032
30,075
26,531
22,772
7,653
22,705
45,378
20,293
57,776
16,133
32,904
15,097
19,264
844
307
160
786
588
1,256
1,044
2,605
2,798
1,128
4,303
1,046
1,940
459
12,376
6,888
721
123
199
108
67
93
482
304
317
271
787
469
687
357
2,131
474
1,561
1,237
774
354
2,839
1,464
567
479
976
964
268
191
3,630
97
42
26
114
69
178
289
279
539
231
1,081
249
359
77
297,392
4,746
7,410
5,872
29,289
25,943
21,516
6,609
20,100
42,580
19,165
53,473
15,087
30,964
14,638
62,394
37,091
197,907
714
900
3,132
1,136
832
5,442
904
330
4,638
4,490
2,377
22,422
4,418
1,463
20,062
3,476
2,768
15,272
1,697
1,825
3,087
3,672
4,721
11,707
9,692
5,852
27,036
5,194
2,497
11,474
16,590
8,130
28,753
2,650
1,877
10,560
5,631
2,942
22,391
2,130
577
11,931
1,834
13
48
68
340
291
194
8
88
200
51
188
73
112
160
Unemployment
→ Employment
right censored
left censored
Employment
→ Employment
→ Unemployment
right censored
left censored
Sector Abbreviations: Agriculture, Rubber and Plastic, Chemical Industry, Metal Industry, Electrical/Optical/Vehicles, Consumption Goods, Hotels/Restaurants,
Construction, Retail/Wholesale, Transportation, Services I, Services II, Public Sector I, Public Sector II. Sample for wage variable wage cens h40 aly afy.
Table 9: Durations by Sector, stock sample
Total
Agric.
Plastic
Chem.
Metal
Elect.
Cons.
Hotel
Const.
Retail
Transp.
Serv. I
Serv. II
Publ. I
Publ. II
Survival rate
Unemployment
→ Employment
1.00
0.75
0.50
0.25
0.00
0
Employment
→ Employment
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
0
1000
2000
1.00
0.75
0.50
0.25
0.00
0
Employment
→ Unemployment
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
0
6000
12000
1.00
0.75
0.50
0.25
0.00
0
Sector Abbreviations: Agriculture, Rubber and Plastic, Chemical Industry, Metal Industry, Electrical/Optical/Vehicles, Consumption Goods, Hotels/Restaurants, Construction,
Retail/Wholesale, Transportation, Services I, Services II, Public Sector I, Public Sector II. Sample for wage variable wage cens h40 aly afy.
Table 10: Wages by Sector, stock sample
Total
Agric.
Plastic
Chem.
Metal
Elect.
Cons.
Hotel
Const.
Retail
Transp.
Serv. I
Serv. II
Publ. I
Publ. II
Wage before transition (wage cens h40 aly afy)
Employment
→ Employment
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
Employment
→ Unemployment
Wage after transition (wage cens h40 aly afy)
Employment
→ Employment
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
0
10
20
30
Unemployment
→ Employment
Wage of right censored spells, (wage cens h40 aly afy)
Employment
right censored
0
10
20
30
0
10
20
30
0
10
20
Wage of left censored spells, (wage cens h40 aly afy)
Employment
left censored
0
10
20
30
0
10
20
30
0
10
20
Sector Abbreviations: Agriculture, Rubber and Plastic, Chemical Industry, Metal Industry, Electrical/Optical/Vehicles, Consumption Goods, Hotels/Restaurants, Construction,
Retail/Wholesale, Transportation, Services I, Services II, Public Sector I, Public Sector II. Sample for wage variable wage cens h40 aly afy.
Table 11: Observations and Fractions of Wages below 7.97 EUR by Sector, stock sample
Total
Agric.
Plastic
Chem.
Metal
Elect.
Cons.
Hotel
Const.
Retail
Transp.
Serv. I
Serv. II
Publ. I
Publ. II
10
11
7
8
43
0
103
216
116
64
378
1
72
132
57
35
283
0
285
575
243
168
1,321
8
600
1,003
487
373
1,166
3
180
453
142
188
610
0
787
1,268
660
362
2,598
7
473
547
442
193
755
0
2,307
3,026
1,493
2,016
2,215
2
457
779
361
230
1,093
4
580
824
433
324
1,667
2
28
117
19
30
75
0
0.01
0.03
0.01
0.12
0.01
0.00
0.02
0.09
0.03
0.13
0.02
0.00
0.02
0.09
0.01
0.11
0.01
0.00
0.08
0.21
0.07
0.21
0.09
0.04
0.35
0.55
0.29
0.54
0.38
0.38
0.05
0.10
0.04
0.09
0.05
0.00
0.08
0.22
0.07
0.23
0.10
0.04
0.09
0.22
0.09
0.25
0.07
0.00
0.14
0.37
0.09
0.71
0.08
0.01
0.17
0.42
0.14
0.41
0.10
0.05
0.10
0.28
0.08
0.33
0.07
0.02
0.01
0.20
0.01
0.11
0.01
0.00
Employment Spells with Wage below 7.97 EUR, Observations
before Job change
before Unemployment
after Job change
after Unemployment
right censored
left censored
6,038
9,316
4,589
4,249
12,938
27
103
277
97
224
526
0
53
88
32
34
208
0
Employment Spells with Wage below 7.97 EUR, Fractions
before Job change
before Unemployment
after Job change
after Unemployment
right censored
left censored
0.10
0.25
0.07
0.34
0.07
0.01
0.14
0.31
0.14
0.31
0.17
0.00
0.05
0.11
0.03
0.17
0.04
0.00
Sector Abbreviations: Agriculture, Rubber and Plastic, Chemical Industry, Metal Industry, Electrical/Optical/Vehicles, Consumption Goods, Hotels/Restaurants,
Construction, Retail/Wholesale, Transportation, Services I, Services II, Public Sector I, Public Sector II. Sample for wage variable wage cens h40 aly afy. The
minimum wage of 7.97 EUR is the wage of 8.50 EUR in 2010 prices.
Variable
Definition/Categories
Educational Status
Low skilled : No degree or highschool degree (Reference category)
Medium skilled : Completed vocational training
High skilled : Technical college degree or university degree
Imputation Education
Missing and inconsistent data on education are corrected according to
the imputation procedure described in Fitzenberger et al. (2005). This
procedure relies, roughly speaking, on the assumption that individuals
cannot lose their educational degrees.
Daily Wages
Gross daily wages are right-censored due to the upper social security contribution limit. To address this problem, we construct cells based on
gender, year and region (East and West Germany). For each cell, a Tobit regression is estimated with log daily wages as the dependent variable
and age, tenure, age squared, tenure squared, two skill dummies, occupational, sectoral as well as regional (Federal State) dummies as explanatory
variables. As described in Gartner (2005), right-censored observations are
replaced by wages randomly drawn from a truncated normal distribution
whose moments are constructed by the predicted values from the Tobit
regressions and whose (lower) truncation point is given by the contribution limit to the social security system. After this imputation procedure,
nominal wages are deflated by the Consumer Price Index of the Federal
Statistical Office Germany normalised to 1 in 2010.
Table A1: Description of individual characteristics
33
Definition of Labour Market States and Assignment of Wages
Employment: Employment spells include continuous periods of employment (allowing gaps of up to four weeks) subject to social security contributions and (after 1998) marginal employment. For parallel spells of
employment and unemployment (e.g. for those individuals who in addition
to their earnings receive supplementary benefits), we treat employment as
the dominant labour market state.
Unemployment Unemployment spells include periods of job search as
well as periods with transfer receipt. Prior to 2005, the latter include benefits such as unemployment insurance and means-tested unemployment assistance benefits. Those (employable) individuals who were not entitled to
unemployment insurance or assistance benefits could claim means-tested
social assistance benefits. However, prior to 2005, spells with social assistance receipt may be observed in the data only if the job seekers’ history
records social assistance recipients as searching for a job. After 2004,
means-tested unemployment and social assistance benefits were merged
into one unified benefit, also known as ‘unemployment benefit II’ (ALG
II). Unemployment spells with receipt of ALG II are recorded in the data
from 2007 onwards, such that the data provide a consistent definition of
unemployment only for the period 2007-2010.
Distinction between Un- and Non-Employment Extending the procedure proposed by Lee and Wilke (2009), involuntary unemployment is
defined as comprising all continuous periods of registered job search and/or
transfer receipt. Gaps between such unemployment periods or gaps between transfer receipt or job search and a new employment spell may
not exceed four weeks, otherwise these periods are considered as nonemployment spells (involving voluntary unemployment or an exit out of
the social security labour force). Similarly, gaps between periods of employment and transfer receipt or job search are treated as involuntary
unemployment as long as the gap does not exceed six weeks, otherwise
the gap is treated as non-employment.
Assignment of Wages In our data, continuous employment spells may
consist of a sequence of different spells with time-varying information of
daily wages. To address this issue, we adopt four different variants to
assign wages to one continuous employment spell. (1) The first observed
wage information is assigned to each employment spell. (2) The last observed wage is assigned to the first employment spell, whereas the first observed wage information is assigned to the subsequent employment spell.
(3) Using the wage information over the entire employment spell, we compute a (duration) weighted average of daily wages over all full-time employment spells. (4) The weighted average is confined to the last observed
year for the first employment spell and to the first observed year for the
subsequent employment spell.
Assignment of Full/Parttime-Status Consistent with the wage assignment rules spelled out above, the assignment of the part and full-time
status is as follows. (1) The first part/fulltime status is assigned to each
employment spell. (2) The last part/fulltime status is assigned to the first
employment spell, whereas the first part/fulltime status is assigned to any
subsequent employment spell. (3, 4) An individual is considered mainly
fulltime employed, if the weighted average duration of fulltime spells (either over the entire spell (3) or one year (4)) exceeds 50 %).
Table A2: Description of labour market states
34