Is there a Causal Effect of Working Part-time on Today’s and
Future Wages?
Marie Paul
(née Waller, University of Duisburg-Essen)
Preliminary draft! Please do not circulate!
This version: October 17, 2011
Abstract: This paper studies the causal effects of working part-time on wages using data on women in Germany. The causal effect of current part-time employment
is disentangled from the effect of part-time employment in the past. Furthermore,
long-run wage effects of typical female employment patterns are estimated. A simultaneous bivariate correlated random effects model with a wage equation flexibly
capturing the employment history and a dynamic employment equation modeling
the decision between non-employment, part-time employment, and full-time employment is used. This econometric approach accounts for unobserved heterogeneity, selectivity and contemporaneous endogeneity of the current employment status
and experience. Exclusion restrictions from the institutional context are used to
support identification. The model is estimated using Markov Chain Monte Carlo
(MCMC) methods. Results suggest that, while there is a considerable wage differential between part-time and full-time workers just conditioning on observable
characteristics, there exists no causal effect of working part-time on current wages.
However, there is a negative long-term wage effect of part-time employment.
Keywords: part-time employment, female employment patterns, panel data models, MCMC
JEL: J31, J16, C33, C11, J24
Contents
1 Introduction
1
2 Econometric Approach
5
2.1
Econometric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.2
Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.3
Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
3 Data and Institutional Background
9
3.1
Data and Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
3.2
Employment Patterns of Females in Germany . . . . . . . . . . . . . 10
3.3
Model Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Results
14
5 Conclusion
17
References
19
1
Introduction
The employment rate of women has increased over the last decades in many countries
and this increase is often achieved through part-time work. In the European Union,
71% of women in the core working age engage in market work but 27% of them work
part-time.1 On the one hand, part-time employment may be a good way to combine
market work and family responsibilities, in particular during the child caring years
but also when caring for the elderly. On the other hand, recently, part-time work
is increasingly perceived as a “trap”. The fear is that part-time work is less paid
and that it also leads to lower wages in the long-run.2 Yet, it is an open question if
employees do receive lower wages due to working part-time and if there is a long-term
wage effect of sequences in part-time work.
This paper provides evidence on the causal effect of current part-time work and
on how part-time work in the past influences current wages, to understand how
working part-time today influences today’s and future wages. Furthermore, typical
female employment patterns involving part-time (PT) employment, full-time (FT)
employment as well as non-employment (NE) spells are compared to uninterrupted
FT careers and to long interruptions with regard to their long-term wage effects. I
use panel data from Germany, a country in which PT work plays an important role,
with a PT share of 39% among the working females and a high female employment
rate (75%).3
To estimate the causal wage effect of currently working PT (conditional on the
employment history), it is necessary to take into account: first, unobserved heterogeneity and selection into PT and into employment based on this, second contemporaneous endogeneity of PT work and of employment, third differences in histories of
PT and FT workers (like interruptions and prior PT work) and fourth, endogeneity
of the history with regard to selection based on unobserved heterogeneity and with
regard to contemporaneous endogeneity.4 From the latter, one can also identify the
1
OECD Stat Extracts, own calculations, age group 25-54, year 2009.
2
Evidence for this perception are for example newspaper articles like “Frauen in der Teilzeitfalle”
(Women in the Part-time Trap), F.A.Z. (04.05.2010) or “Arbeitszeit: Raus aus der Teilzeitfalle”
(Working Time: Leave the Part-time Trap), Stern (10.08.2008).
3
OECD StatExtracts, own calculations, age group 25-54, year 2009.
4
If one is solely interested in the wage effect of current PT work and has a suitable identification
strategy, the two latter points do not necessarily have to be taken into account.
1
causal effect of PT in the past on current wages. Most prior studies have taken into
account part of these issues. To the best of my knowledge, the present study is the
first to estimate the causal wage effect of PT work taking into account unobserved
heterogeneity, selectivity, as well as endogeneity of the PT status and employment
for females in a broad age range. The only paper in the PT literature taking unobserved heterogeneity, selectivity and contemporaneous endogeneity into account is
the paper by Aaronson and French, 2004, who provide the causal effect of working
PT for older workers in the US. Aaronson and French are also the only ones in the
PT literature to use instruments from the institutional context for identification. I
am not aware of any study which disentangles the effect of differences in experience
in PT from the effect of current PT work while fully endogenizing experience.
Descriptive evidence seems to support the fear that PT work goes along with lower
wages – almost all studies on the wage differential between PT and FT workers
(the so called PT penalty) find that PT workers earn substantially less than PT
workers, as long as one conditions only on standard observable characteristics.5 An
important part or even all of the wage gap vanishes when conditioning on the sort of
job.6 But - though rendering important insights in understanding the wage patterns
- this does not answer the question if there is a causal wage effect of working PT.
Job characteristics may be an outcome of the PT decision (not all sorts of jobs are
available to PT workers) and furthermore working in a less favorable job and working
PT may both be driven by third factors (e.g. a change in the family situation) that
may have a direct wage effect (e.g. restrictions in mobility and working schedule).
As Manning and Petrongolo, 2008, state: "the true PT pay penalty probably lies
between those two numbers." (p. F28).
Evidence on the causal effect of PT work is still scarce. On the one hand, there exist a
few recent studies taking unobserved heterogeneity into account and considering the
role of employment history when estimating the PT/FT wage differential (Connolly
and Gregory, 2009; Hirsch, 2005; and Fernandez Kranz, Paul, and Rodriguez-Planas,
2011).7 Connolly and Gregory, 2009, consider the effect of history and identify the
5
See for example Blank, 1990, and Hirsch, 2005, for the US; Ermisch and Wright, 1993, Manning and Petrongolo, 2008, and Connolly and Gregory, 2008, for the UK; Fernandez Kranz and
Rodriguez-Planas, 2011, for Spain and Wolf, 2002, for Germany.
6
Like conditioning on occupation (Manning and Petrongolo, 2008), on occupation and workplace
characteristics (Mumford and Smith, 2008), on job characteristics and skill requirements (Hirsch,
2005), or on type of contract (Fernandez Kranz and Rodriguez-Planas, 2011).
7
Focussing on the effect of current PT work, also Booth and Wood, 2008, and Fernandez Kranz
2
effect of current PT status and experience using switches employing a fixed-effects
approach on UK data. They find that much of the PT wage gap can be attributed
to occupational downgrading when switching to PT and changes of employer accompanying the switches as well as lower returns to experience in these PT jobs,
especially if these are low skill jobs.8 Hirsch, 2005, uses two period panels from the
US and identifies wage effects from switches and from the wage changes of switchers relative to those of non switchers. As a way to study long-term dynamics, in
addition to short-term dynamics, Hirsch allows the returns to potential experience
to vary by the current PT status supposing that current PT workers are likely to
have worked more in PT before and he finds that the PT penalty increases with
potential experience, but having no information on actual experience his analysis of
this issue is limited. He stresses that an important part of the PT wage disadvantage is likely to be due to PT workers having accumulated less human capital due
to different employment histories. Fernandez Kranz, Paul, and Rodriguez-Planas,
2011, study wage differentials and wage returns of working under different flexible
work arrangements in Spain employing a trivariate random effects model. With
regard to PT work they find that there is a substantial PT/FT wage differential at
least under fixed term contracts conditional on work history and that experience in
PT work is less rewarded than in standard FT work. None of the aforementioned
studies deals with contemporaneous endogeneity of the PT status and employment
for the current period or earlier periods.9
On the other hand, there are several – less recent – studies which take contemporaneous endogeneity of PT and employment into account, modeling the selection
into employment and PT in a cross-sectional approach (e.g. Beblo and Wolf, 2002,
Blank, 1990, Ermisch and Wright, 1993, and Wolf, 2002). Beblo and Wolf, 2002, like
and Rodriguez-Planas, 2011, take unobserved heterogeneity into account and stress the importance
of doing so.
8
Furthermore, there are several studies that focus on returns to experience in PT work (e.g.
Ferber and Waldvogel, 1998, Fouarge and Muffels, 2009, and Green and Ferber, 2005). These
studies estimate wage functions including experience and experience squared in PT work using OLS
(and in some cases FE and RE models) assuming (contemporaneous) exogeneity of experience, the
current PT status and employment.
9
On the wage returns to employment in general, there exists a large literature (see for example
Light and Ureta, 1995, Hotchkiss and Pitts, 2005, and Spivey, 2005) with a strand of papers
focussing on career particular career interruptions, like for example maternity leave (for example
Beblo and Wolf, 2003, Kunze, 2002, Buligescu et. al., 2009, and Schönberg and Ludsteck, 2007).
While this literature does focus on patterns specific to female employment biographies, it does not
focus on PT work.
3
the present study, estimate long-term wage effects of PT work and non-employment
spells using data from Germany. Beblo and Wolf find that the timing of the interruptions matter and that the depreciation of human capital is less severe in PT
work than in non-employment. The aforementioned studies assume exogeneity of
experience with regard to time-constant and contemporaneous selectivity and do
not deal with individual specific unobserved heterogeneity in general. As it was
standard at the time of these studies, to be able to deal with contemporaneous endogeneity these studies use instruments from the family context, like young children
and marital status. Such instruments may be invalid as these variables are likely
to have a direct effect on wages, because they may go along with restrictions in,
for example, flexibility or regional mobility, which may in turn influence wages or
these variables may even have a direct effect on productivity (for a discussion see for
example Aaronson and French, 2004). To my knowledge, only one study, Aaronson
and French, 2004, uses instruments from the institutional context (in there study
work disincentives from the social security system). Aaronson and French study the
PT/FT wage differential for males and females aged 50 to 70. They use an IV approach that allows for individual fixed effects and thus they additionally account for
unobserved heterogeneity. They do not disentangle the effect of currently working
PT from the effects of the employment history - for older workers it is not an issue
how experience will be rewarded.
The econometric approach employed in this paper is a bivariate simultaneous correlated random effects model with a wage equation and a reduced form employment
equation. The wage equation incorporates a highly flexible specification for the
work history. The employment equation is a dynamic ordered probit model on the
decision between NE, PT and FE in each period. In this approach experience in
FT and PT employment and interruptions are fully endogenized, because experience
consists of the employment decisions in each prior period. Thus, the model accounts
for potential selection biases that may evolve from employment decisions in current
and past periods and allows to consistently estimate the returns to different employment patterns. Individual specific random effects in both equations and their
potential correlation across equations serve to capture time-constant unobserved
heterogeneity and selection based on it. The idiosyncratic random components are
allowed to be contemporaneously correlated to capture a potential dependence of
exogenous shocks. The model is estimated using Markov Chain Monte Carlo Meth-
4
ods (MCMC). This approach is methodologically similar to the approach Buchinsky,
Fougère, Kramarz, and Tchernis (2010) (BFKT, hereafter) use to study the returns
to seniority in the U.S and it also borrows from the literature on dynamic treatment
effects (for example Heckman and Navarro, 2007). Changes in the institutional settings which affect different individuals at different times during their working live
along with time-varying covariates are exploited for identification. In addition to
this, functional form assumptions are needed. This approach allows to obtain the
wage effect of current PT status, the (long-run) wage returns to PT work, and to
compare typical employment patterns involving PT employment, FT employment
and NE spells to un-interrupted FT careers and intermittent behavior with regard
to their wage returns. Furthermore, information on the direction and strength of
selectivity is available and it is possible to simulate the total effect of a switch to
PT as state dependence is modeled.
The results of this paper suggest that, while there is a considerable wage differential
between part-time and full-time workers just conditioning on observable characteristics, there is no causal wage effect of currently working PT given the employment
history. Thus, working PT does not have an immediate negative wage effect. However, an hourly wage disadvantage continues to accumulate with an increased number
of years in PT. Nevertheless, the negative effect of PT employment in the past is
much lower than the wage effect of employment interruptions.
The remainder of this paper is structured as follows. Section 2 presents the methodological approach, section 3 describes the data, the institutional context and the
specification. Section 4 discusses the results and section 5 concludes.
2
2.1
Econometric Approach
Econometric Model
To study the causal effect of PT work, this paper uses a bivariate simultaneous
equation model with a wage equation and an employment equation. The wage
equation is a linear equation of the log hourly wage implementing a flexible specification for the work history distinguishing FT employment, PT employment and
non-employment. The employment equation is a reduced form dynamic ordered pro-
5
bit model on the decision between NE, PT and FE in each period. In this approach
not only the current employment status is endogenized, but also experience in FT
and PT is fully endogenized, as it consists of the employment decisions in the past
and these are modeled. Thus, the approach allows to disentangle the causal effect of
PT work on current wages and the causal effect of different employment histories.
The econometric model accounts for potential selection biases that may evolve from
the employment decisions in current and past periods and allows to consistently
estimate the returns to different employment patterns. The approach deals with
unobserved heterogeneity, selectivity and contemporaneous endogeneity. Individual
specific random effects in both equations and their potential correlation across equations serve to capture time-constant unobserved heterogeneity and selection based
on it. The idiosyncratic random components are allowed to be contemporaneously
correlated, to capture a potential dependence of exogenous shocks. This approach is
methodologically similar to the approach BFKT use to study the returns to seniority
in the U.S.10
The wage equation builds on the work history specification suggested by Light and
Ureta, 1995.11 The employment history is captured by a function H W which collects
the employment status each year from the year before the current period as far back
as the sample allows. In the present model, an array of dummies for FT employment
(FT[t-1] to FT[t-24]) and for PT employment (PT[t-1] to PT[t-24]) are used to
capture the employment status at the annual interview in the most flexible way.
The dummies for very remote periods with few observations are summarized in one
variable by summing them up. A dummy can equal zero for two reasons, either
if the woman is not in that state in the current year (if both the FT and the PT
dummy equal zero the woman is in NE) or if the dummy refers to a year which is
before the individual is observed in the sample. To distinguish these two reasons,
an array of dummies is defined, which equals one if the respective period is not yet
observed in the sample. As standard in the literature, the outcome variable is the
natural logarithm of the deflated hourly wage.
10
BFKT use a model with three equations to model wages, employment and mobility. They
incorporate some additional flexibility by allowing for heteroscedasticity in the variance of the
random effects. Their specification does not involve an ordered probit model, as PT is not an
issue. BFKT also use MCMC estimation but apply a different blocking scheme.
11
Light and Ureta in their model capture the intensive margin by using the share of weeks worked
in each year but not the distinction between PT and FT work
6
The wage is only observed if the individual i works in period t (i.e. if her employment
status in t is either PT or FT):
(1)
lnWit = lnWit∗ · 1(Eit > 0)
W
W
lnWit∗ = β1W P Tit + β2W HitW + β3W xW
it + αi + ²it
where 1 is the indicator function, Eit gives the employment status (2 for FT, 1 for
PT and 0 for NE), HitW captures the employment history as described above and xW
is a vector of observable covariates. The error term consists of an individual specific
correlated random effect αiW and a contemporaneous idiosyncratic error term ²W
it .
The reduced form employment equation is a dynamic correlated random effects
ordered probit model given by
Eit = 0 if E ∗ ≤ 0, Eit = 1 if 0 < E ∗ ≤ µ ,Eit = 2 if E ∗ > µ
(2)
E E
E E
E
E
Eit∗ = β0E + β1E xE
it + β2 Hit + β3 zit + αi + ²it
where xE is a vector of observable covariates, HitE is the employment history, capturing state dependence and duration dependence, and z E is a vector of exclusion
restrictions. Again, the error term consists of an individual specific correlated random effect αiE , and ²E
it is a contemporaneous idiosyncratic error term. The initial
condition is model as suggested by Wooldridge (2005), so the initial employment
status is included among the regressors for each period.
The individual specific effects αiW and αiE are allowed to be correlated to accommodate potential correlation of the unobserved individual heterogeneity in the wage
equation with the unobserved individual specific employment propensity. αiW and
αiE are assumed to follow a joint normal distribution N (f (x), Σ). f (x) denotes a
function which could depend on the exogenous variables in all periods, in practice
this function is specified using a Mundlak approach, i.e. the sample averages of
time-varying regressors are included into the equations. The individual specific effects are assumed to be independent of the idiosyncratic shocks. The idiosyncratic
E
error components ²W
it and ²it are allowed to be contemporaneously correlated and are
assumed to follow a joint normal distribution N (0, Ω) where the variance parameter
for the probit equation is set to one.
7
2.2
Identification
Identification of this model depends on functional form restrictions, time-varying
covariates and exclusion restrictions (Hyslop 1999, see also BFKT for a discussion
on identification of a methodologically comparable model). Identification comes
from both the cross-sectional and the time-series dimensions. In the present application it is possible to use the time-series dimension for identification, because many
women switch between states during the observation period and the cross sectional
differences, because different women follow different employment patterns over their
working life. In a dynamic context it is particularly difficult to find suitable exclusion restrictions because the variable or its effect has to change over the individuals
and the time periods (Heckman and Navarro, 2007 and Troske and Voicu, 2010).
The exclusion restrictions imposed in this paper exploit changes in the institutional
setting over time. In particular, I use changes in parental job protection rules, the
introduction of a parental benefit, the introduction of a law that introduces a right
to switch to PT employment, proxies for alimentary transfers, the introduction of
care reform, and the introduction of care leave. Details are given in section 3.3.
2.3
Estimation
To estimate the model, I use Bayesian Markov Chain Monte Carlo (MCMC) techniques. This approach avoids simulating multivariate normal integrals and allow
a numerically robust estimation of the flexible model specification.12 The goal of
this technique is to obtain a sample from the posterior distribution of the model
parameters. From a classical perspective, the mean of the posterior distribution
converges to the point estimator from a maximum likelihood estimation and the
variance of the posterior distribution converges to the asymptotic variance of the
point estimator in a maximum likelihood estimation. Thus, the standard deviation
of the draws may be interpreted as standard errors from the classical perspective
(see Train, 2003, for an overview over important properties of MCMC estimators).
To simplify the sampling from a complex joint distribution of the model parameters,
the Gibbs sampler forms blocks of model parameters and samples recursively from
12
See Chib (2008) for an introduction into the use of MCMC methods for panel data models
and for recent applications in labor economics see BFKT, Fitzenberger et. al. (2010), Horny et al.
(2009), and Troske and Voicu (2010).
8
the distribution of one block conditional on the current values of the re-maining parameters. The resulting sequence of simulated parameters is a Markov Chain whose
invariant distribution is the desired posterior distribution. The Gibbs sampling algorithm used in this paper builds on several sources in the literature: the key ideas
are to draw the random effects (Zeger and Karim, 1991) as well as the latent variables and the threshold parameter needed for the estimation of the ordered probit
(Albert and Chib, 1993) as steps of the algorithm. Chib and Carlin (1999) suggest
improved blocking schemes for random effects models, one of which is used here.
The algorithm for binary endogenous regressors presented by Chib (2008) accommodates most of these points and features a structure with two equations and an
endogenous regressor. In addition, for periods in non-employment the unobserved
wages have to be drawn as one step of the algorithm. The implementation of this
builds on Hasselt (2009) who proposes an algorithm for selection models in which
the outcome variable is only partially observed. I implemented the Gibbs sampler
in Stata using its matrix language Mata. Conjugate but very diffuse priors are used.
Convergence is monitored by comparing the means at different stages of the chains.
The first 5,000 iterations are discarded (the burn-in phase).
3
Data and Institutional Background
3.1
Data and Sample
This study uses data from the German Socio-Economic Panel (SOEP), version 25,
SOEP, 2010. The SOEP is a yearly household panel which was started in 1984 for
West Germany and includes East Germany after reunification (for information on
the SOEP see Wagner et al., 2007).13 The sample used in this study is based on all
subsamples of the SOEP, except those oversampling foreigners, and uses all available
years (1984 to 2009). It includes women of age 25 to 55 who are observed for at least
five consecutive years. The sample of analysis is chosen to start in the year in which
the woman turns 25 years old or the year in which she is first interviewed. Those
women who become civil servants or self-employed are censored from this period on.
13
The data used in this paper was extracted using the ADD-On package PanelWhiz for
Stata. PanelWhiz (http://www.PanelWhiz.eu) was written by Dr. John P. Haisken-DeNew
(john@PanelWhiz.eu). See Haiksen-DeNew and Hahn (2006) for details. The PanelWhiz generated DO file to retrieve the data used here is available from me upon request. Any data or
computational errors in this paper are my own.
9
In this study, FT employment is defined as working at least 35 hours and a woman
is defined to work PT if she worked at least 5 hours per week but less than 35
hours. To measure the hours worked the information on contractual hours is used
due to the potential measurement error of using actual hours in the week before the
interview together with monthly earnings (Buligescu et al., 2009). Mothers who are
taking maternity leave but have an employment contract are observed to have zero
contractual hours. The hourly wage is defined as the gross monthly wage in Euros
of 2005 divided by the contractual hours.14
The sample used for the estimation consists of 45,906 person-periods. It includes
5016 women for whom 4 to 25 years plus the initial period are observed. On average
9 years are used (median 8 years) for the estimation. In addition information of the
first year in the sample is used to construct the information on the initial period
(t=0). Furthermore, information relating to the time before the woman turns 25
years old or retrospective information relating to the time before the women is first
interviewed is used to construct covariates on pre-sample experience. For 30% of
the women the estimation starts before the year 1991. Table 1 provides summary
statistics over all person-periods used in the model for some important variables. The
average wage in the sample is 12.71 Euros of 2005. On average the individuals are
40 years old and 30% of the observations refer to a woman living in East Germany.
The number of children the woman has ever born is 1.52 on average over all periods
and the youngest child is on average 12.75 years. For those who have a partner
who is earning a wage his monthly gross wage is on average 2,969 Euros of 2005
per month. More than half of the observations relate to women holding a middle
vocations degree and 16% to those holding a university degree, either from a general
or an applied university. 5% of the individuals in the sample are single mothers.
— Table 1 about here. —
3.2
Employment Patterns of Females in Germany
In Germany, women typically work FT until they have children. After giving birth
to a first child, employment histories diverge with the following stylized patterns
14
There are a few cases for which the monthly wage is almost the same as in the year before,
but hours almost half or double; these observations are dropped as well as the few cases for which
the information on hours is missing.
10
being typical: 1) an interruption of several years followed by several years of PT
work, 2) short interruption(s) interchanging with spells of PT work and / or FT
work, and 3) continuous FT work with very short interruption(s). These patterns
go hand in hand with German institutions, like long periods of job protection for
parents who interrupt market work, day care being available for a limited share of
small children only, many schools and kindergartens finishing in the early afternoon,
and incentive effects of the tax and social security systems. After their children are
grown up, many women return to FT work.15 Apart from raising children, also
caring for the elderly may be a reason to reduce working hours. As Schneider et.
al., 2001, show, this task is often taken by women and often leads to a reduction
in market work. If women start caring for an older family member, an important
number of those who worked FT before reduces their labor market attachment to
PT work or even interrupts market work and also some of those women working PT
before temporarily leave the labor force.
— Table 2 about here. —
— Table 3 about here. —
These patterns are reflected in the sample of analysis. Out of 5016 women, 849
women are non-employed in every period observed, 491 women are always observed
to work PT and 1115 women are always observed to work FT. The other 2561
women experience at least one switch between different employment states within
the observation period. Table 2 gives the probability of the employment status in the
sample given a particular employment status in the last year; and table 3 indicates
the probability a particular employment status given a particular employment status
in the year before and given that a switch occurs. For those women who are currently
not employment, it is much more likely that they start PT work than FT work.
Those who currently work PT are more likely to switch to non-employment than to
FT and those who are working FT are much more likely to switch to non-employment
than to PT work. This table is congruent with the pattern that women typically
switch from FT to non-employment and then from non-employment to PT and
maybe back to non-employment and only eventually part of them goes back to FT.
Counting all switches, unconditional of the employment status in the last period,
15
For a description of typical female employment patterns in Germany see Dressler et.al. 2005.
11
the most frequent switch is from non-employment to PT employment, it amounts
to 26.25% of all switches. The second is the switch from FT to NE (24.30%). The
fewest switches occur from PT to FT (11.20%) and from FT to PT (12.06%).
— Table 4 about here. —
— Table 5 about here. —
Table 4 and table 5 show descriptive statistics by employment status. As one would
expect, FT workers have on average less children and are less likely to be married.
Table 6 gives the employment status by broad categories of the age of the youngest
child and shows that the numbers are in line with the above mentioned employment
patterns with regard to motherhood. PT work occurs in all groups but is most
frequent for those women with children in school. Non-employment is the most
frequent labor market state for those women with young children. FT work is by
far the most frequent labor market state for those who do not (yet) have children
and is again the most important labor market state when children are grown up.
Although not many women with small children work FT, a non negligible number
of women does though, even when having a baby at home.
— Table 6 about here. —
3.3
Model Specification
The following section summarizes how the two equations of the econometric model
are specified. Details are shown in the result table 7. Both equations include a
flexible specification of the employment history, as described in section 2.1 and
standard covariates like age categories, education (coded in dummies for actual
degrees) and nationality. Due to the richness of the SOEP data, several variables
may be added that are less standard but have a considerable effect on wage and
/ or employment decisions, like the education of the parents of the woman and
the husband’s earnings in the year before the current year. Furthermore, the data
allows to include very detailed information on the family status of the woman, like
the age of the youngest child in monthly precision, the number of children, if the
woman is married, and if she is living together with a partner. Information on the
12
industry, the firm size, or the reported health status of the women are not included,
as they may be an outcome of labor market states in the past. For identification it
is important to include time-varying covariates. Many of the variables used in the
current model have some variation over time, as for example the family variables,
the wage of the husband and the region the woman lives in.
The employment equation includes several variables that are not included in the
wage equation and thus serve as exclusion restrictions. In a dynamic context identification comes from the changes in the variables used as exclusion restriction. Changes
in their values have to be uncorrelated to the error terms of the wage equation. The
exclusion restrictions imposed in this paper exploit changes in the institutional setting over time. I use changes in parental job protection rules, the introduction of
a parental benefit, the introduction of a law strengthening the right to request PT
employment, proxies for alimentary transfers, the introduction of a care reform and
the introduction of a care leave. All these variables change over individuals (or their
effect changes) and over time, each of them is relevant for some, but not all women,
at different times in their working life. Note that a full set of dummies for the calendar years is included as control variables and that also the age of the youngest child
is controlled for by using dummy variables for detailed age categories. The first
exclusion restriction exploits changes in job protection rules. While in the whole
time period used in this study mothers in Germany are entitled to paid maternity
leave six weeks before and eight weeks after giving birth, there exists in addition
a job protection period which has been changing over time, in January 1986 it has
been extended from 6 to 10 months, to 18 months in July 1990 and finally to three
years in January 1992 (see Schönberg and Ludsteck, 2007, for a description of these
reforms). Schönberg and Ludsteck find that each of these reforms induces women to
delay their return to work. I construct a dummy variable if a woman is (potentially)
subject to parental job protection in the current period, calculated from the age
of the youngest child in the respective month and the institution under which it
was born. Being subject to job protection induces a significant negative effect on
employment. Second, the introduction of a new parental leave benefit (Elterngeld)
is exploited. Parents of children born from 2007 on receive a parental benefit for
the time they take parental leave (up to 14 months). This reform implies a strong
increase in transfer payments for those who worked in the year before the child was
born and just created an incentive for a non-employment spell for this group. I
13
create a dummy if the woman is entitled for this increased transfer. Third, I use the
introduction of a law that strongly enhanced the rights of employees to require a
reduction of hours from FT work to PT work in 2001 (“Teilzeitbefristungsgesetz”).
These rights are not restricted to women with children, but are often used by women
who want to come back to work after parental leave but only in PT. I make use of
this law by constructing a dummy if a woman has been in parental leave in the last
year and if she is subject to this PT law. Under the law she has a significantly
higher probability to return to work - but in PT. Fourth, I use information if the
woman is divorced or widowed (controlling for being single, having a partner and
being a single mother in both equations). Having been married in the past is a
proxy of being eligible to some alimentary or widow-pension and it has a significant
negative employment effect. Fourth, the introduction of care insurance as part of
social security system is used. From 1996 on, those older persons who need care
receive a payment which allows them to pay for external care or to keep it in the
family if a family member does the care work. This provides additional income that
allows women who care for the elderly to reduce market work (Schneider et. al.,
2001). Also the dummy capturing if this law is in place and a women has worked in
the last period has a significant effect.
4
Results
Preliminary!
I will begin by discussing my results on the wage effect of currently working PT and
the returns to PT work in a past year and then discuss the effects of typical female
employment patterns and finally the results for other model parameters. Table 7
provides means and standard deviations (SD) of the posterior distribution of the
model parameters that can be interpreted as coefficients and standard errors from
a Maximum Likelihood estimation.
The Effect of Currently Working Part-time
The first line in table 7 gives the estimate of the causal wage effect of currently
working PT. The estimated effect is positive (0.03), but rather insignificant (SE:
14
0.018). It thus indicates that, on average, there is no pay reduction of working
part-time, probably there is even a small premium. Note that this effect is given
the work history, thus this results suggests that females do not suffer from a wage
reduction due to currently working PT given their work history. If, in a thought
experiment, one chose any woman and made her work either PT or FT, this would
not have an (immediate) negative wage effect. This suggest that in the short-run,
there tend to be – ceteris paribus – no worse opportunities with regard to wages in
PT jobs and those working PT do not take away lower wages.
As discussed in the introduction, existing studies in the PT literature take part
of the selection issues into account and most of them do not estimate an effect of
current PT work given the work history. Thus, it is instructive to see how the results
evolve. The raw PT/FT wage differential in my sample is -10.17% (SE: 0.01), this
controls already for a dummy for East Germany. Controlling for all covariates of
the wage equation but not the employment history gives a similar coefficient on the
PT dummy (-0.11, SE: 0.01). Thus my sample supports the finding of most studies
on the PT/FT wage differentials, that PT workers earn substantially less than PT
workers, as long as one conditions only on standard observable characteristics.16 But
this effect vanishes when controlling for the work history and endogenizing it.
The Marginal Effect of Part-time work in a Past Year
The second and following lines of table 7 provide the effect of PT work in the past
on current wages by giving the parameter estimates for PT work one year ago PT[t25
P
1], two years ago PT[t-2] until ten to 25 years ago
P T [t − j]. These can be
j=10
interpreted as marginal effect, i.e. they give the causal effect of PT in that specific
year as opposed to FT in that specific year given the rest of the work history. These
parameter estimates are almost all negative, meaning that the return to PT work
tends to be lower than to FT work; but they are insignificant. Reasons for lower
returns to working PT (than for FT) may for example be, that less experience is
collected when working PT due to working fewer hours, less valuable experience
might be collected if PT workers do different tasks on the job, PT workers may be
less likely to be considered for promotions or managerial positions or it might be
16
See for example Blank, 1990 and Hirsch, 2005, for the US; Ermisch and Wright, 1993, Manning and Petrongolo, 2008 and Connolly and Gregory, 2008, for the UK; Fernandez Kranz and
Rodriguez-Planas, 2011, for Spain and Wolf, 2002, for Germany.
15
the case that PT workers get less on-the-job training. Results suggest that while
this seems to be true to some extend, the effect is on average not very strong.
25
P
Considering the effects of non-employment in the past (NE[t-1] to
N E[t − j]),
j=10
puts the returns to PT work into perspective. The effects of NE in the past are
all significantly negative (except the lag referring to NE nine years ago, which has
no significant effect) and about five times as high as the estimates to PT in the
past, suggesting that an interruption of work goes along with a much higher wage
reduction than PT work.17
The Causal Effect of Typical Employment Patterns
As discussed in section 3.2, there exist several stylized patterns which are typical
for women in Germany. In the following the causal effects of such employment
patterns on the current wage are presented. To study the effect of different stylized
employment patterns, consider a woman who is currently 35 years old. If she has
always worked FT (and entered the labor market at the age of, say, 25 years), she
currently has obtained FT experience of 10 years. This FT career is the benchmark
case. If this woman had not worked during the last ten years, i.e. until she was
25, the model estimates a wage reduction of 46% (SE 0.03). Not surprisingly such
a long career interruption has a strong negative effect. But what if the woman
worked PT instead of interrupting in those ten years? If, during these 10 years, she
had worked PT, this would imply a wage reduction of 8.1% (SE 0.02), thus having
worked PT for a very long time period involves a considerable negative wage effect
which is though much less severe than the effect of an interruption. Having worked
FT but PT only the last three years involves a negative wage effect of 4.4% (SE
0.01). As discussed before, a typical female wage pattern is to combine periods of
interruptions with periods of PT work. If the woman in the example had a three
years long non-employment spell followed by seven years of PT, this would reduce
her current wage by 14.67% (SE 0.02) as compared to not interrupting. If she had
interrupted these three years and than immediately returned to FT, the current
wage reductions would be less strong (7.9%, SE 0.02). In sum, this exercise suggests
that there is clearly a penalty of interrupting FT work, but it is much smaller if the
woman engages in PT work in at least part of these years as if she does not work
17
When estimating the wage equation using a standard fixed-effects or random effects estimator,
the coefficients to PT or NE in the past are also negative, but the size is about double as large.
16
for many years.
Variance Parameters
Table 7 indicates that an important part of the variance is on the individual level
in both equations (55% in the wage equation and 22% in the employment equation), suggesting that unobserved individual heterogeneity is important both for the
wage and for the employment decisions. The correlation between the individual
specific effects αiW and αiE is 31% and highly significant. Since higher labor market
involvement leads to more experience which involves positive wage returns, the positive correlation of the individual effects implies that those workers with unobserved
characteristics favorable to wages tend to be the ones with a higher employment
propensity. Thus, if one omitted the individual specific effect αiW from the estimation, one would expect an upward bias in the returns to experience. In contrast,
failing to endogenize the employment history would lead to a downward bias in the
returns to experience (see BFKT for a similar discussion in a different economic
E
context). The correlation between the idiosyncratic errors ²W
i and ²i is negative
(-3%) and not significant, suggesting that exogenous shocks influencing employment
decisions are on average not (or slightly negatively) related to wages.
— Table 7 about here. —
Exclusion Restrictions and State Dependence
The variables used as exclusion restriction all have a significant effect (except for the
right for a care leave) on employment and they have the expected sign (see last lines
referring to the employment equation in table 7). The parameter estimates of the
exclusion restrictions are also jointly highly significant (F-value: 55.07). Turning to
state dependence and duration dependence, table 7 shows that these are strong, the
parameter estimates of lagged PT and NE are highly significant.
5
Conclusion
In the present paper I have estimated the causal effects of PT work on wages using
data on women in Germany. The causal effect of current PT work is disentangled
17
from the effect of PT work in the past. Furthermore, long-run wage effects of typical female employment patterns involving PT employment, FT employment and
non-employment are compared to uninterrupted FT careers with regard to their
wage returns. Using a simultaneous bivariate correlated random effects model with
a wage equation flexibly capturing the employment history and a dynamic employment equation modeling the decision between non-employment, PT employment and
FT employment, the econometric approach accounts for unobserved heterogeneity,
selectivity and contemporaneous endogeneity of the current employment status and
experience. Exclusion restrictions from the institutional context are used to support
identification. The model is estimated using Markov Chain Monte Carlo (MCMC)
methods.
First results suggest that there is no negative causal wage effect of currently working
PT given the employment history. Thus, PT work instead of FT does not have an
immediate wage effect but an hourly wage disadvantage accumulates in the long
run through PT work being less rewarded. In a next step, I will investigate effect
heterogeneity of these results and analyse which channels may lead to PT work
being less rewarded. Furthermore, as state dependence and duration dependence
have turned out to be important, I will simulate the total long-term effect of a
switch from FT to PT in a certain period.
18
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Tables
Table 1: Summary Statistics
All person-time periods
Variable
Mean
SD
N
wage
12.712 5.935
30039
lnwage
2.447
0.444
30039
hours
21.27
17.215 45906
age
40.213 8.152
45906
living in East Germany
0.296
0.457
45906
no German nationality
0.02
0.138
45906
born abroad
0.054
0.225
45906
no adequate schooling information
0.013
0.114
45906
highest degree: general elementary
0.124
0.329
45906
highest degree: middle vocational
0.568
0.495
45906
highest degree: Abitur plus vocational 0.059
0.236
45906
highest degree: higher vocational
0.076
0.266
45906
highest degree: tech. / appl. university 0.093
0.291
45906
0.067
0.249
45906
highest degree: university
number of children
1.52
1.11
45906
age youngest child
12.75
8.542
36122
married
0.741
0.438
45906
0.118
0.323
45906
separated, divorced or widowed
partner in household (not married)
0.088
0.283
45906
24.329 4.473
36122
age when first child was born
0.053
0.225
45906
single mother
at least one parent with university
0.06
0.238
45906
0.296
45906
no parent holds at least a vocat. degree 0.097
monthly wage husband / partner
2969.262 1804.466 32360
21
Last period in sample
Mean
SD
N
13.496 7.609
3303
2.486
0.484
3303
20.313 16.791 5016
44.198 8.449
501 6
0.284
0.451
5016
0.024
0.154
5016
0.062
0.241
5016
0.013
0.111
5016
0.126
0.332
5016
0.557
0.497
5016
0.069
0.253
5016
0.075
0.264
5016
0.086
0.28
5016
0.075
0.263
5016
1.626
1.114
5016
15.705 9.433
4110
0.741
0.438
5016
0.137
0.344
5016
0.077
0.267
5016
24.776 4.677
4110
0.053
0.224
5016
0.066
0.248
5016
0.096
0.295
5016
3187.332 1861.907 3233
Table 2: Probability of Employment Status in Current Year Given Employment
Status in Year Before (in Percent)
NE in t-1
84.97
9.81
5.22
NE in t
PT in t
FT in t
PT in t-1
9.73
83.92
6.35
FT in t-1
7.64
3.70
88.66
Table 3: Probability of Direction of a Switch Given a Switch of Employment Status
Occurs (in Percent)
NE in t-1
67.58
32.42
NE in t
PT in t
FT in t
PT in t-1
61.90
38.10
FT in t-1
66.83
33.17
-
Table 7: Means and Standard Deviations of Parameters
from MCMC Estimation
Name
Mean
SD
0.0322
-0.0187
-0.0141
-0.0088
-0.0035
-0.0103
-0.0101
0.0005
-0.0129
0.0044
0.0175
0.0114
0.0075
0.0079
0.0082
0.0087
0.0093
0.0103
0.0113
0.0113
Wage Equation
PT
PT[t-1]
PT[t-2]
PT[t-3]
PT[t-4]
PT[t-5]
PT[t-6]
PT[t-7]
PT[t-8]
PT[t-9]
25
P
P T [t − j]
-0.0053 0.0024
j=10
NE[t-1]
NE[t-2]
NE[t-3]
NE[t-4]
NE[t-5]
NE[t-6]
NE[t-7]
NE[t-8]
NE[t-9]
25
P
N E[t − j]
-0.0944
-0.0758
-0.0446
-0.0489
-0.0537
-0.0383
-0.0356
-0.0301
-0.0134
0.0175
0.0089
0.0084
0.0086
0.0090
0.0094
0.0100
0.0108
0.0112
-0.0196 0.0028
j=10
NE in t = 0
PT in t = 0
Experience in FT in t = 0
-0.1492 0.0191
-0.0532 0.0155
0.0099 0.0023
<continued on next page>
22
Means and Standard deviations of Parameters from
MCMC Estimation <continued>
Name
Experience Sq in FT in t = 0
Experience in PT in t = 0
Experience Sq in PT in t = 0
lag 2 not in model
lag 3 not in model
lag 4 not in model
lag 5 not in model
lag 6 not in model
lag 7 not in model
lag 8 not in model
lag 9 not in model
lag 10 to 25 not in model
25 to 29 years old
30 to 34 years old
40 to 44 years old
45 to 49 years old
50 to 55 years old
living in East Germany
born abroad
no German nationality
year 1985
year 1986
year 1987
year 1988
year 1989
year 1990
year 1991
year 1992
year 1993
year 1994
year 1995
year 1996
year 1997
year 1998
year 2000
year 2001
year 2002
year 2003
year 2004
year 2005
year 2006
year 2007
year 2008
<continued on next page>
23
Mean
-0.0002
-0.0022
0.0001
-0.0615
-0.0358
-0.0217
-0.0165
-0.0208
-0.0697
0.0205
0.0243
-0.0408
-0.0340
-0.0286
0.0041
-0.0050
-0.0117
-0.3009
-0.1264
-0.1232
-0.1986
-0.2102
-0.2049
-0.1867
-0.1695
-0.1643
-0.3385
-0.1935
-0.1095
-0.0663
-0.0469
-0.0247
-0.0471
-0.0336
0.0027
0.0276
0.0381
0.0418
0.0283
0.0099
-0.0204
-0.0450
-0.0557
SD
0.0001
0.0034
0.0002
0.0086
0.0086
0.0084
0.0090
0.0093
0.0096
0.0102
0.0099
0.0123
0.0115
0.0076
0.0070
0.0097
0.0129
0.0124
0.0247
0.0325
0.0187
0.0178
0.0173
0.0167
0.0165
0.0158
0.0133
0.0133
0.0125
0.0125
0.0121
0.0119
0.0118
0.0121
0.0113
0.0106
0.0110
0.0111
0.0112
0.0117
0.0118
0.0123
0.0130
Means and Standard deviations of Parameters from
MCMC Estimation <continued>
Name
year 2009
no adequat schooling information
highest degree: general elementary
highest degree: Abitur plus vocational
highest degree: higher vocational
highest degree: technical or applied university
highest degree: university
married
living with a partner but not married
single mother
no children (yet)
youngest child younger than 1
youngest child one year old
youngest child two years old
youngest child 8 to 12 years old
youngest child 13 to 16 years old
youngest child older than 16
three or more children
at least one parent with university degree
no parent has at least a vocational degree
monthly wage of partner / husband last year /1000
wage of partner / husband last year: not applicable or missing
partner / husband had no labor earnings last year
average number of children in sample period
average of married dummy in sample period
average of partner dummy in sample period
average monthly wage of partner / husband last year /1000
average of dummy for no earnigs of husband
Constant
Employment Equation
PT[t-1]
PT[t-2]
PT[t-3]
9
P
P T [t − j]
j=4
25
P
P T [t − j]
Mean
-0.0120
-0.0822
-0.0378
0.1001
0.0605
0.2070
0.4186
-0.0473
-0.0090
0.0078
0.0380
-0.2206
-0.0741
-0.0069
-0.0092
0.0079
0.0127
-0.0316
0.0771
-0.0691
0.0061
0.0387
0.0260
-0.0094
-0.0614
-0.1071
0.0461
0.0372
2.6167
SD
0.0132
0.0401
0.0124
0.0176
0.0131
0.0164
0.0195
0.0106
0.0106
0.0126
0.0146
0.0295
0.0160
0.0130
0.0074
0.0090
0.0095
0.0184
0.0216
0.0194
0.0020
0.0129
0.0090
0.0084
0.0217
0.0278
0.0046
0.0306
0.0278
-1.1939 0.0290
-0.2424 0.0326
-0.0819 0.0313
-0.0188 0.0084
0.0161
0.0092
j=10
NE[t-1]
NE[t-2]
NE[t-3]
9
P
N E[t − j]
-2.1753 0.0384
-0.5298 0.0316
-0.2114 0.0313
-0.0320 0.0091
j=4
<continued on next page>
24
Means and Standard deviations of Parameters from
MCMC Estimation <continued>
Name
25
P
N E[t − j]
Mean
SD
0.0339
0.0085
-0.7084
-0.2440
0.0211
0.0175
-0.1094
-0.1567
-0.1791
0.1375
0.1711
0.0654
-0.0942
-0.2267
-0.4460
0.0391
-0.1560
-0.4308
-0.2179
-0.3094
-0.3452
-0.2201
-0.1420
-0.1499
-0.2303
-0.2870
-0.3448
-0.2989
-0.1583
-0.1517
-0.1476
-0.0375
-0.0446
-0.0077
-0.0891
-0.0568
-0.1078
-0.0116
0.0842
0.0773
0.1998
-0.1589
-0.0604
0.0415
0.0361
0.0024
0.0034
0.0417
0.0359
0.0424
0.0484
0.0402
0.0282
0.0266
0.0345
0.0422
0.0278
0.0701
0.0685
0.0727
0.0714
0.0690
0.0648
0.0654
0.0601
0.0609
0.0598
0.0582
0.0585
0.0523
0.0544
0.0552
0.0545
0.0500
0.0502
0.0484
0.0500
0.0503
0.0510
0.0511
0.0545
0.0940
0.0867
0.0322
j=10
FT in t = 0
PT in t = 0
Experience in FT in t = 0
Experience in PT in t = 0
lag 2 not in model
lag 3 not in model
lag 49 not in model
lag 10 to 25 not in model
25 to 29 years old
30 to 34 years old
40 to 44 years old
45 to 49 years old
50 to 55 years old
living in East Germany
no German nationality
year 1985
year 1986
year 1987
year 1988
year 1989
year 1990
year 1991
year 1992
year 1993
year 1994
year 1995
year 1996
year 1997
year 1998
year 2000
year 2001
year 2002
year 2003
year 2004
year 2005
year 2006
year 2007
year 2008
year 2009
no adequat schooling information
highest degree: general elementary
<continued on next page>
25
Means and Standard deviations of Parameters from
MCMC Estimation <continued>
Name
highest degree: Abitur plus vocational
highest degree: higher vocational
highest degree: technical or applied university
highest degree: university
married
living with a partner but not married
single mother
no children (yet)
youngest child younger than 1
youngest child 12 to 18 months
youngest child 18 to 24 months
youngest child two years old
youngest child 18 to 12 years old
youngest child 13 to 16 years old
youngest child older than 16
three or more children
at least one parent with university degree
no parent has at least a vocational degree
monthly wage of partner / husband last year /1000
partner / husband had no labor earnings last year
average of partner / husband wage missing
average number of children in sample period
average of married dummy in sample period
average monthly wage of partner / husband last year /1000
potentially under job protection
separated, divorced or widowed
right to come back to work part-time
care reform applicable
right for care leave
parental benefit
Constant
Variance and Covariance Parameters
W
Var(α )
Var(αE )
Cov(αW , αE )
Var(²E )
Cov(²W , ²E )
Var(αW )/(Var(αE ) + Var(²W )
Var(αE )/(Var(αE ) + 1)
Corr(αW , αE )
Corr(²W , ²E )
26
Mean
0.0941
0.0388
0.3719
0.3791
-0.4267
-0.1332
-0.1879
0.4494
-2.4772
-0.9035
-0.4615
-0.1640
0.0435
0.1673
0.2127
-0.1338
-0.0842
-0.0730
-0.0156
0.0540
-0.1215
0.0141
0.0674
-0.0198
-0.1887
-0.1208
0.1669
-0.1412
-0.1120
-0.5405
2.9409
SD
0.0436
0.0378
0.0389
0.0453
0.0551
0.0446
0.0489
0.0442
0.0800
0.0744
0.0702
0.0567
0.0273
0.0331
0.0338
0.0426
0.0458
0.0362
0.0081
0.0344
0.0514
0.0191
0.0486
0.0101
0.0610
0.0422
0.0504
0.0383
0.0970
0.1794
0.0917
0.0776
0.2789
0.0456
0.0637
-0.0072
0.5489
0.2179
0.3098
-0.0285
0.0021
0.0179
0.0051
0.0008
0.0080
0.0076
0.0109
0.0297
0.0318
Table 4: Summary Statistics by Employment Status
Variable
log hourly wage
Emp. Status p25 p50 p75
PT
2.15 2.45 2.70
FT
2.22 2.50 2.74
hourly wage
PT
8.59 11.62 14.95
FT
9.20 11.19 15.50
weekly hours
PT
19
20
29
FT
38
40
40
age
NE
33
39
47
PT
36
42
48
FT
32
40
47
number of children NE
1
2
3
PT
1
2
2
FT
0
1
2
age youngest child NE
2.42 7.33 15.75
PT
6.58 12.33 18.92
FT
10.67 16.75 22.42
Table 5: Summary Statistics by Employment Status (Dummy Variables)
Variable
Emp. Status Mean
living in east Germany NE
0.212
PT
0.226
FT
0.414
born abroad
NE
0.064
PT
0.052
FT
0.046
married
NE
0.847
PT
0.831
FT
0.591
single mother
NE
0.059
PT
0.058
FT
0.045
Table 6: Share of Observations in NE, PT, and FT by Age of Youngest Child
Age Youngest Child
no child
0 years
1 to 2 years
3 to 6 years
7 to 15 years
older 15 years
all
FT
0.775
0.049
0.099
0.182
0.302
0.439
0.399
PT
0.114
0.063
0.201
0.330
0.349
0.287
0.255
27
NE
0.111
0.888
0.700
0.488
0.350
0.274
0.346