Causal Modelling in Fertility Research: A Review of the Literature and an Application to a Parental Leave Policy Reform


Causal Modelling in Fertility Research: A Review of the 
Literature and an Application to a Parental Leave Policy Reform*

Michaela Kreyenfeld

Abstract: This paper reviews empirical studies that have examined the causal 
determinants of fertility behaviour. In particular, we compare the approaches adopted 
in the different disciplines to improve our understanding of how birth dynamics are 
infl uenced by changes in female employment and changes in family policies. The 
wide array of panel data that have become available in recent years provide great 
potential for advanced causal modelling in this fi eld. Event history modelling has 
been a dominant approach in sociology and demography. However, researchers 
are increasingly turning to other methods to unravel causal effects, such as fi xed-
effects modelling, the regression discontinuity approach, and statistical matching. 
We summarise selected studies, and discuss the advantages and the shortcomings 
of the different approaches. In an empirical section, we analyse the impact of the 
German 2007 policy reform on birth behaviour to illustrate the diffi culties involved 
in isolating policy effects. The fi nal chapter concludes by underscoring that even 
simple modelling strategies may be benefi cial for improving our understanding of 
how policy effects shape demographic behaviour, and for laying the groundwork for 
more fi ne-grained causal investigations.

Keywords: Family policy · Event history · Fertility · Causation

1 Introduction

While most Western governments may shy away from formulating any clear-cut 
pro-natalist policy goals, they nevertheless have a vested interest in understanding 
the effects that family policies can have on birth dynamics. Scholars have 
approached this topic from different perspectives. Thus, the modelling strategies 

Comparative Population Studies
Vol. 46 (2021): 269-302 (Date of release: 26.07.2021)

Federal Institute for Population Research 2021 URL: www.comparativepopulationstudies.de
      DOI: https://doi.org/10.12765/CPoS-2021-10
      URN: urn:nbn:de:bib-cpos-2021-10en7
    

* This article belongs to a special issue on “Identifi cation of causal mechanisms in demographic 
research: The contribution of panel data”.

http://www.comparativepopulationstudies.de
https://doi.org/10.12765/CPoS-2021-10


•    Michaela Kreyenfeld270

which researchers use and the importance they attach to issues of causality have 
clearly been shaped by their respective disciplinary standpoints. The comparative 
welfare state approach has been among the most prominent concepts used to shed 
light on the interplay of family policies, female employment, and fertility behaviour 
– despite being the least committed to questions of causal modelling. Based on 
the simple assumption that women now “demand economic independence and 
permanent integration in working life”, it was argued that “familialistic regimes” 
would be punished by low national fertility rates (Esping-Andersen 1999: 69). 
Esping-Andersen has remained the most cited proponent of this line of thought, 
although similar ideas were developed contemporaneously by scholars from other 
disciplines (see e.g. McDonald 2000; Rindfuss/Brewster 1996). 

The empirical evidence that Esping-Andersen (1999) generated in his seminal 
work relied on rather simple OLS regressions, whereby the outcome variable was 
the change in the national total fertility rate (TFR), while the independent variables 
were crude measures that depicted female employment rates and the degree 
to which social policies at the national level supported the compatibility of work 
and family life. Obviously, the strength of this concept did not emanate from its 
methodological rigour. Instead, it had fi lled a void that was left by other theories 
that failed to adequately address the pivotal role of family policies in infl uencing 
birth dynamics. Numerous studies followed that used more refi ned estimation 
techniques or employed more sophisticated measures that mapped the extent 
to which national policies help to achieve a work-family balance (Ahn/Mira 2002; 
Castles 2003; Engelhardt/Prskawetz 2004; Luci-Greulich/Thévenon 2013; Thévenon/
Gauthier 2011).

Overall, the evidence from macro-level data remained inconclusive and 
unsatisfactory (Gauthier 2007). As the unit of analysis is the country, only a few 
observations could be included in such investigations, which resulted in unstable 
results that relied on a set of rather heterogeneous countries. Most importantly, 
concerns were raised about the outcome variables, which were often restricted 
to simple summary indicators, such as the national total fertility rate (TFR). The 
conventional TFR confl ates different birth parities. But even if vital statistics contain 
a parity-specifi c TFR, these data are still limited as they only rarely include real 
“exposure data” that relate births to the population at risk of a certain birth parity. 
Furthermore, these types of data do not allow researchers to conduct fi ne-grained 
analysis; for example, to examine how different subpopulations react to a policy 
change. Longitudinal micro-level analyses were deemed to be a more promising 
avenue in this area of research as they were less prone to the well-known problems 
associated with ecological fallacies, and they opened up new possibilities for 
unravelling the causal effects behind birth behaviour. 

This paper discusses the contribution of longitudinal micro-level analysis to the 
understanding of fertility dynamics. We provide an overview of two broad streams of 
literature in this area. First, we discuss studies that have examined the causal impact 
of women’s work on fertility behaviour. Second, we draw attention to studies that 
have explored how national policies have infl uenced birth dynamics. The third part 
of the paper takes the German 2007 policy reform as an example to illustrate the 



Causal Modelling in Fertility Research    • 271

diffi culties researchers face when seeking to isolate policy effects in an empirical 
investigation. The fi nal section summarises and evaluates the pros and cons of 
the different approaches. Such an overview can never be complete. It is limited to 
the two abovementioned broad research streams, and is restricted to studies that 
use the potential of longitudinal micro-level data to unravel causal effects, which 
may be panel surveys, retrospective surveys, or process-produced administrative 
data.1 Furthermore, most of the literature we discuss below addresses behaviour in 
European countries since the 1990s. 

2 Female employment and fertility

2.1 Contributions and limitations of event history modelling

Despite claims that the heyday of regression analysis has long since passed 
(Morgan/Winship 2015), event history modelling has remained a dominant method 
for studying fertility behaviour, at least in demographic and sociological research. 
Unlike in simple cross-sectional OLS regression, “time” is at the heart of these 
methods. Through its use of time-varying covariates, event history analysis lives 
up to one of the main principles of causal analysis, namely that the cause should 
always precede the effect (Bhrolcháin/Dyson 2007). Thus, a large body of literature 
emerged that examined how women’s work – operationalised by a time-varying 
covariate distinguishing between different employment states – is related to fi rst-
order and higher-order birth risks (for a meta-analysis, see Alderotti et al. 2021; 
Matysiak/Vignoli 2008). Because the moment of childbirth is not equivalent to the 
decision to become a parent, these studies conventionally predated the date of 
childbirth by several months. Important policy-relevant results were generated from 
this type of research, which illustrated that the links between female employment 
and fertility can vary greatly across policy contexts, socio-economic statuses, birth 
parities, cohorts, and time periods (Andersson et al. 2014; Matysiak/Vignoli 2008, 
2013; Schröder/Brüderl 2008; Wood/Neels 2017). 

Micro-level investigations also opened up the opportunity to operationalise 
employment status in a more sophisticated manner. While most of the macro-
level studies were confi ned to simple summary indicators, such as the female 
employment rate, micro-level studies could operationalise women’s work over a 
fi ne-grained measure that differentiated between various employment categories, 
including educational participation, gainful employment, unemployment, and other 
activities. While this level of granularity enabled researchers to cast a more nuanced 

1 This overview is limited to studies that employed longitudinal data. However, we must pay 
tribute to the earlier empirical studies that tried to unravel causal effects, even though they 
relied mostly on cross-sectional datasets only (Cramer 1980; Stolzenberg/Waite 1977; Thomson 
1984; Waite/Stolzenberg 1976). In addition to laying the groundwork for conceptualising the 
association between female employment and fertility, these studies motivated much of the 
later collection of longitudinal data.



•    Michaela Kreyenfeld272

light on the micro-level correlations between female employment and fertility, it 
also raised broader questions about the meaning of women’s employment status. 
This was particularly evident for the category of “housewife” that was included in 
some of the datasets. It was deemed obvious that housewives would experience 
elevated fi rst birth rates, based on the assumption that their life course concept 
was closely intertwined with the idea of having a family. Although the time-varying 
modelling of women’s employment status guaranteed a correct ordering of cause 
and effect, it was also evident that it did not entirely eliminate reverse causality. 
People plan their lives ahead and they base their current actions on their anticipated 
future behaviour (Hoem/Kreyenfeld 2006). An individual’s current employment 
status is therefore more than just an indicator of his/her present circumstances. 
Instead, it is the product of choices that factor in anticipated future behaviour and 
thus the individual’s “personal imaginaries” or “narratives of the future” (Bazzani et 
al. 2020; Vignoli et al. 2020a/b). 

Another source of bias in event history modelling comes from the modelling of 
employment as a time-varying covariate. In such cases, endogenous selection bias 
may bias the coeffi cient for past employment status, if past employment affects the 
confounders of current employment (Elwert 2013; Elwert/Winship 2014; Sharkey/
Elwert 2011). Multi-process models or simultaneous equation event history models 
have been proposed in an effort to address endogeneity (Lillard 1993). The advances 
in such methods have been closely connected to the development of the software 
package aML (Lillard/Panis 2000), which led to an upsurge in the use of these methods 
in family research, particularly in the early and mid-2000s (e.g. Aassve et al. 2006; 
Upchurch et al. 2002; Kravdal 2001; Kulu/Steele 2013; Schnor 2014). This modelling 
approach is based on the premise that partnership formation, marriage, educational 
attainment, and fertility behaviour are transitions that may infl uence each other as 
these processes unfold. Multi-process modelling tries to capture this endogeneity 
by letting the outcome of one process (such as the formation of a partnership) 
infl uence the other process (such as educational attainment), and by including 
heterogeneity components in each process. These heterogeneity components are 
usually assumed to follow a joint normal distribution. A methodological limitation 
of these models is that they hinge on this underlying distributional assumption.2 
While this assumption may be relaxed, employing alternative ones often leads 
to practical problems, such as the models failing to converge (see e.g. Kravdal 
2001: 198). A more substantive limitation of these models is that the unobserved 
heterogeneity components remain a black box, with researchers being unable to 
pinpoint the exact mechanisms that lead to a particular behaviour. Furthermore, 
even if employment and fertility can be modelled as mutually related processes, 
such efforts will not eliminate the bias that arises because people are acting on their 
anticipated behaviour in the future (the abovementioned “personal imaginaries”). 

2 Additionally, the model assumes that the source of unobserved heterogeneity is constant 
across time, which may also be a strong assumption.



Causal Modelling in Fertility Research    • 273

Endogenous selection bias is conceptually different from the more widely known 
problem of common-cause confounding, whereby the bias comes from having 
failed to include a variable that causes both the variable of interest (employment) 
and the outcome variable (fertility) (Elwert 2013; Elwert/Winship 2014; Hernán 
et al. 2002). A typical example would be the omission of migration background, 
which may affect both fertility behaviour and employment. Standard regression 
analysis usually tries to combat this problem by including additional variables in 
the model. Thus, the main strategy for assessing causality in regression models 
is to eliminate “alternative effects” by controlling for confounders. This strategy 
has several implications. It hinges on the availability of variables, whereas some 
variables may simply not be available in a given dataset. In addition, the results 
may vary depending on the number and the type of variables that are included in 
the regression. This is also one of the main conclusions reached by Matysiak and 
Vignoli (2008) in their meta-analysis of 30 journal articles that used event history 
modelling to assess the effects of female employment on fertility. The authors 
concluded that the prior results were often unstable and heavily infl uenced by the 
inclusion of available covariates. While this is undoubtedly a valid conclusion to 
draw from this meta-analysis, it can leave researchers in some despair. Scholars 
may be torn between including further covariates and ending up with a grossly 
over-specifi ed model, or choosing a parsimonious modelling strategy while running 
the risk of being accused that the model does not suffi ciently account for all possible 
confounders. 

2.2 Fixed-effects modelling for fertility research?

The self-selection into “treatment” is one of the main reasons why observational 
studies will always remain limited in their ambitions to make causal claims. While 
experimental designs, such as randomised controlled trials, are usually considered 
the gold standard for causal analysis, conducting them remains an elusive goal 
for most demographic and sociological researchers, as ethical reasons generally 
prohibit the use of such designs (Bhrolcháin/Dyson 2007). Nonetheless, most of 
the progress made in recent decades in the development of sociological research 
methods has been geared towards mimicking an experimental design approach 
(Gangl 2010). The terminology of a “control group” and a “treatment group” clearly 
signals such a commitment. The rise of the use of fi xed-effects regression modelling 
has been informed by this broader aim (Brüderl/Ludwig 2015; Hill et al. 2020). 
Fixed-effects modelling is based on the idea that a person can be used as his/her 
“own control group” if longitudinal data are available (Allison 2009; Brüderl/Ludwig 
2015). Thus, fi xed-effects panel regressions make causal claims by exploiting the 
variations that exist within a person over time. A classical demographic example 
that demonstrates the power of this method is the investigation of the relationship 
between marriage and life satisfaction (Brüderl/Ludwig 2015). In contrast to a 
standard regression approach that compares the life satisfaction of married and 
unmarried people, this method follows a person throughout his/her life course, and 
assesses how the individual’s life satisfaction changes when s/he experiences the 



•    Michaela Kreyenfeld274

event of marriage. In this context, marriage is considered the “treatment”, while the 
“control group” is the individual before s/he experienced the event. Technically, this 
method eliminates all time-constant heterogeneity that commonly distorts standard 
regression analysis (Brüderl/Ludwig 2015). 

Many studies have employed fi xed-effects panel regression to study different 
demographic and sociological themes, such as the demographic determinants of 
life satisfaction and other dimensions of well-being. Moreover, childbirth has been 
used regularly as an independent variable in these models (e.g. Myrskylä/Margolis 
2014). It is noticeable, however, that only a few studies have employed this method 
to examine childbearing behaviour as an outcome variable. In the few cases in which 
the method was employed for fertility research, the results were mainly published 
in economic journals (Boca et al. 2005; Huttunen/Kellokumpu 2016; Michaud/
Tatsiramos 2011).3 Have demographers and sociologists been too slow to catch up 
with this methodological innovation? Or are there sound reasons why this method 
has not yet been widely adopted in fertility research?

A possible answer to these questions is that, the study of fertility from a parity-
specifi c point of view is almost an imperative in demographic and sociological 
research. The decision to have a fi rst child is regarded as a distinct choice that is 
determined by factors that are different to those that result in higher-order births. If 
we subscribe to this idea, we need to model the transition to fi rst parenthood as a 
unique event. Fixed-effects panel regression runs into a problem in such cases, as 
it is based on the premise that the event (i.e. the birth) should be observed before 
and after a treatment (e.g. a change of employment status). If an event is observed 
only once in a lifetime, there is a fundamental fl aw in the logic as there is no before 
and after. If the event of the fi rst birth occurred before the “treatment”, it cannot be 
repeated afterwards. 

To get around this problem, some researchers have treated the number of 
children as a continuous variable (see e.g. Boca et al. 2005; Huttunen/Kellokumpu 
2016; Michaud/Tatsiramos 2011). Obviously, this approach confl ates different 
birth parities. But there are other concerns as well. Births are infrequent events in 
contemporary European societies, and people rarely have more than two or three 
children. As such, there is little variation in the outcome variable, and some of the 
variation comes from the more “unusual” cases of people with larger families. 
Moreover, employment and fertility are events that strongly infl uence each other. 
The birth of a fi rst child often results in drastic changes in a woman’s work pattern. A 
large share of women do not work shortly after giving birth, but re-enter the labour 
market at some later point in time. In other instances, women may space their fi rst 
and second children closely together to minimise their family-related employment 
interruptions. The complex interplay that exists between fertility and women’s 
employment gets completely lost in these models, such that it ultimately becomes 

3 This observation pertains to panel fi xed-effects modelling. Fixed-effects modelling has been 
regularly used with macro-level fertility data in sociological and demographic fertility research; 
for example, to account for regional-specifi c effects (e.g. Schneider 2015).



Causal Modelling in Fertility Research    • 275

diffi cult to grasp the meaning of the underlying behavioural patterns. Thus, the use 
of fi xed-effects panel regression is not a panacea for causal analysis (Collischon/
Eberl 2020; Hill et al. 2020) and it is clearly not the best way to move forward in the 
analysis of fertility behaviour.4

2.3 Fertility intentions and panel data

While fi xed-effects modelling may not be the preferred method for examining 
fertility behaviour, it can be applied more effectively to the analysis of fertility 
preferences. The opportunities to analyse fertility preferences with European panel 
data accelerated in the early 2000s, when data became available from sources such 
as the Generations and Gender Survey, the British Understanding Society study, 
and the German Family Panel, which included recurrent items on the respondents’ 
fertility desires, ideals, and intentions.5 Kuhnt, Kreyenfeld, and Trappe (2017) used 
data from the German family panel (pairfam) to study changes in the ideal number 
of children across the life course by means of fi xed-effects modelling. The authors 
did not fi nd any association between women’s employment status and their ideal 
number of children. The only variable that was shown to have a substantial effect 
was “having (further) children”, which suggests that the respondents were adjusting 
their ideals to align them with their behaviour. Kuhnt, Minkus, and Buhr (2020) 
employed the same data, but used the intention to have a child (within the next two 
years) as an outcome variable in a multinomial fi xed-effects regression model (with 
the categories “certainly yes”, “uncertain”, and “certainly no”). While the authors 
did not fi nd that a woman’s employment status affected her fertility intentions, 
the model showed that men’s worries about fi nding a suitable job increased the 
likelihood of being uncertain about the plans for having a child within the next two 
years. A non-trivial problem that tends to arise in this type of investigation is that 
some respondents may realise their fertility intentions and have a child during the 
study period. As such, there is selective drop out from the study population.6 

Other studies have focused more specifi cally on the link between intentions 
and fertility behaviour. Berrington and Pattaro (2014) used data from the UK data 

4 Schröder and Brüderl (2008) used an event history model to study fi rst birth rates. Instead of 
controlling for employment status, they controlled for whether a person had changed his/her 
employment status (i.e. moved from non-employment to employment). In doing so, the authors 
used standard event history analysis, but also exploited the within-variation.

5 The collection of large-scale longitudinal data that included items that measured fertility 
desires, intentions, and ideals was initiated in the US as far back as the 1970s. Much of the 
work on fertility intentions was motivated by studies based on US data (see e.g. Hayford 2009; 
Thomson 1997).

6 A downturn in these investigations is that all birth parities were pooled in this investigation, 
Thus, the fertility intentions of a particular woman that is observed across time may refer to 
different birth parities. Furthermore, problems of selectivity may arise, because women who 
did not state a preference, or who were pregnant at the time of the interview, are excluded 
from the sample. In a similar vein, the realisation of an intention (childbirth) is not adequately 
accounted for in this model.



•    Michaela Kreyenfeld276

“Understanding Society” to compare women’s fertility intentions at age 23 with 
their actual number of children at age 46. This study found that highly educated 
women were less likely to realise their intentions. However, the results also showed 
that a woman’s employment status at age 23 did not seem to be related to her 
chances of realising her early fertility intentions. Other studies examined how a 
woman’s fertility intentions as measured in a given year determined the probability 
of the woman realising those intentions by the next year or the next round of 
data collection (e.g. Hanappi et al. 2017; Kuhnt/Trappe 2016; Riederer et al. 2019; 
Spéder/Kapitány 2009). These studies have greatly advanced our understanding 
of the obstacles women face in realising their fertility plans. Ultimately, however, 
these models do not solve the problem that a woman may self-select into a certain 
employment status across her life course. 

2.4 Natural experiments 

Our interest in understanding the causal effects of female employment on fertility 
stems from the fact that in economic and demographic theories of fertility, women’s 
labour market participation has been seen as one of the prime factors contributing 
to declining or low fertility rates. Refuting the hypothesis that women’s employment 
leads to lower fertility not only challenges the predictions from conventional 
theories; indeed, in the narrow economic sense, it means that the “income effect” 
has ultimately trumped the “substitution effect”. More broadly, it implies that 
women’s role in society, the meaning of female work, and the economic foundations 
of the family have all shifted. As these are strong implications, it is imperative that we 
rule out the possibility that selection into employment has produced the observed 
outcomes. 

A standard approach used in economics to establish causality is to search 
for natural experiments; i.e. events that affect the variable of interest (female 
employment, non-employment, or unemployment), but that are beyond the 
control of the individual. Examples of such natural experiments are large-scale 
lay-offs, bankruptcies, and fi rm closures. These events have been used previously 
in labour market research to examine how unemployment, operationalised over 
these exogenous unemployment shocks, alters people’s behaviour and well-being. 
However, this approach has seldom been used in fertility research (see, however, 
Del Bono et al. 2015; Hofmann et al. 2017; Huttunen/Kellokumpu 2016). 

With regard to the small number of existing studies that adopted this approach, 
most were conducted by labour economists who employed matching techniques. 
The underlying idea of this approach is that true causal analysis requires a comparison 
of a control group and a treatment group. Standard observational studies suffer from 
the problem that the comparison group may be select, and is thus not comparable 
with the treatment group. To ensure comparability, matching techniques start with 
the sample of “treated” individuals and search the pool of the control group for 
those units that best correspond to the treatment group. This “search procedure” 
has been refi ned in recent years by employing sophisticated algorithms, most 
recently from machine learning operations (Lee et al. 2010). However, despite recent 



Causal Modelling in Fertility Research    • 277

refi nements in these approaches, researchers using matching techniques struggle 
with problems similar to those faced by researchers using conventional regression 
models. To ensure a good match, they need a suffi cient number of covariates. 
If these covariates are not included, the matching techniques will result in poor 
matches – and, by extension, in biased results. 

In addition, matching techniques are not always easy to apply to demographic 
processes. Hofmann and colleagues (2017) examined, for example, the causal effects 
of unemployment on fi rst birth risks. The paper compared the subsequent birth 
risks of individuals who lost their jobs after having been laid off by a fi rm with those 
of a control group of women who were not subject to a fi rm closing. To make the 
control and the treatment groups comparable, fi rm-level information was required. 
As a result, the sample was limited to respondents who had been employed with the 
same fi rm for at least 1.5 years. Women who had been working at fi rms with more 
than 2,000 employees or at very small fi rms had to be excluded as well, because it 
would have been diffi cult to fi nd suitable matches for these women. In the end, after 
the restrictions were imposed, the original sample of 101,910 individuals shrank to 
3,286 treated and 17,836 untreated women. Although the sample restrictions were 
clearly spelled out and clear justifi cation given for them, the results from such an 
analysis are inevitably limited to a restricted subpopulation. In this case, one of the 
restrictions required by the sample was that the women were employed with the 
same fi rm for at least 1.5 years. This limited the results to women who were fi rmly 
established in the labour market. Thus, while this model may have generated careful 
causal effects, the external validity of the results was limited.

2.5 Narratives of the future

A new impetus for understanding the causal link of the “female employment 
and fertility nexus” comes from studies that have tried to integrate future 
uncertainties into models of rational decision-making. These models break from 
the presumption that many decisions, including the decision to have children, are 
long-term commitments. It is therefore argued that actors need to take into account 
the uncertainties regarding the future implications of their choices. Some future 
states of the world may be extrapolated from the “shadow of the past” (i.e. it may 
be assumed that a woman’s husband will continue to have a high income if he is 
currently earning well). Other states of the world are more diffi cult to predict, and 
actors may “play” with imaginaries to deal with these uncertainties (Beckert/Bronk 
2018). 

“Narratives” are standard concepts in psychology and sociology, and have 
recently also been employed in economics (Bènabou et al. 2018; Shiller 2020) 
and demographic research (Vignoli et al. 2020a). It has been argued that while 
conventional fertility models have primarily dealt with the effects of present states, 
fertility choices are governed by narratives of the future, which stem from the 
“human capacity to place oneself in an imagined situation that cannot be deduced 
from present conditions” (Vignoli et al. 2020b). In other words, the decision to have 



•    Michaela Kreyenfeld278

a child depends on how a woman visualises the future; for example, whether she 
can imagine being a “working mother”, or whether she can only imagine being 
a “homemaker”. This area of research is still evolving, and among the major 
challenges scholars have faced is that of generating suitable item sets that can 
capture these “narratives of the future” (Vignoli et al. 2020b) or “images of the future 
self” (Bachrach/Morgan 2016: 466). What is interesting about this debate is that 
it shifts attention away from developing sophisticated econometric techniques for 
studying the causal effect of employment on fertility, and instead focuses on fi nding 
appropriate item sets to measure future “models” or “narratives” of the world. It has 
also been proposed that more qualitative research should be conducted, including 
longitudinal qualitative research that helps to elucidate how these “narratives” are 
formed and altered across time (Bernardi 2021; Vignoli et al. 2020b). 

The concept of “future narratives” resonates well with the considerations 
developed by Friedman, Hechter, and Kanazawa (1994). They provided a rationale 
for why some women may decide to have children in a seemingly unstable und 
insecure economic situation, and why this decision may still be regarded as 
rational. On the one hand, childbirth tends to block biographical “alternatives”. 
Thus, having children while unemployed may limit a woman’s chances of swiftly 
returning to the labour market and fi nding a job with good career prospects. On the 
other hand, this limitation may be perceived as a relief and a source of “uncertainty 
reduction”, as it structures a woman’s otherwise uncertain life course.7 For women 
who foresee that they will not be able to succeed in the labour market, taking on 
the role of a homemaker may be regarded as a meaningful and socially accepted 
“biographical alternative” to an uncertain labour market trajectory. Clearly, the 
societal context matters here because it defi nes the available “narratives” or 
“biographical alternative”. For example, policies may encourage or discourage 
a certain earner model; or the normative fabric of a society may defi ne gender 
roles, attitudes towards non-parental care, and, more generally, attitudes towards 
parents’ roles as earners and carers.

3 Policy change and fertility

3.1 Isolating policy effects 

In response to declining and low birth rates in European countries, policy-makers 
have become increasingly interested in the question of whether policies could halt 
the downward trend in period fertility and reduce childlessness, particularly among 
highly educated and work-oriented women. In this debate, it was argued that the 
expansion of publicly fi nanced child care and the implementation of earnings-
related parental leave benefi ts are key measures that can simultaneously support 

7 Lehrer et al. (1996: 133) criticised this argument for the assumption that the risks “emanating 
from parenthood are more controllable than those associated with labor force participation”. 



Causal Modelling in Fertility Research    • 279

higher levels of gender equality and fertility. Against this background, the European 
Commission issued recommendations to expand public day care and to implement 
suitable parental leave regulations (Annesley 2007). Although many national 
governments followed their own agenda and did not necessarily comply with the 
EU recommendations, most European governments have scaled up their public day 
care services and implemented parental leave regulations since the 1990s (Daly/
Ferragina 2018). Child care services have been gradually expanded, and the speed 
of this expansion has depended in part on the capacities and conditions at local 
municipality level. Researchers have thus been able to use the regional variations 
in these child care expansion efforts to isolate the possible policy effects (e.g. 
Bauernschuster et al. 2016; Hank/Kreyenfeld 2003; Krapf 2014; Kravdal 1996).8 
However, as parental leave benefi t regulations were generally implemented at the 
national level, scholars had to use other strategies to examine the impact of these 
measures on birth behaviour.

Much of the early demographic research into the causal impact of policy changes 
on fertility behaviour has dealt with developing economies, and thus with high-
fertility settings. For these regions, randomised controlled trials have been regularly 
employed to evaluate the effectiveness of family planning programmes (Mwaikambo 
et al. 2011). For advanced economies, these methods are applied less commonly in 
the area of fertility behaviour. There have, however, been investigations of how 
sexual education (and other “moderate” interventions) have affected teenage 
pregnancy rates (for an overview, see Bennett/Assefi  2005). Ethical issues, including 
concerns about equal access to public services, often prevent the implementation 
of randomised control trials to evaluate the impact of more coercive policies on 
fertility behaviour (Bhrolcháin/Dyson 2007). 

However, the programme evaluation literature offers a battery of techniques for 
isolating policy effects with observational data (LaLonde 1986). A standard method 
that is often used is the difference-in-difference (DiD) approach, which is commonly 
combined with the abovementioned matching techniques. This approach suffers 
from the same drawbacks as fi xed-effects modelling (see Section 2). The DiD 
requires an observation before and after the intervention to isolate the causal effect 
of a policy. As the fi rst childbirth is an absorbing event, DiD cannot be employed 
to study fi rst birth processes. Researchers could combine all birth orders so that 
they would be able to observe events before and after treatment (a policy reform). 
However, this would violate a basic understanding of demographic research: namely 
that fi rst and higher-order births are distinct processes. 

In light of these challenges, researchers have increasingly turned to the regression 
discontinuity approach to examine how policy reforms impact behaviour. The 
regression discontinuity approach is based on the idea that causal inference can 

8 The assumption here is that regional and temporal differences in child care slots depend on the 
capacities and willingness of local actors to increase child care services. If municipalities offer 
child care services based on expected demand, regional changes in provision rates cannot be 
used as a suitable exogenous policy measure, as they already refl ect the usage of care services.



•    Michaela Kreyenfeld280

be generated by comparing the behaviour of individuals immediately before and 
after a cut-off date of a policy reform. This method has, for example, been used to 
examine how changes in parental leave regulations have affected labour supply 
(Ginja et al. 2020), living arrangements (Cygan-Rehm et al. 2018), as well as childbirth 
(e.g. Cygan-Rehm 2016; Farré/González 2019; Tamm 2013). While these models are 
central to the fi eld of policy evaluation, they have high data demands. In order to 
generate signifi cant results, large sample sizes that include reasonable numbers of 
events that are observed immediately before and after a policy reform are needed. 
While this need for large amounts of data is a general concern when using these 
types of models, it is a particularly pressing problem in fertility research as births 
are rare events. Therefore, most survey data will not provide a suitable basis for 
applying the regression discontinuity approach to birth behaviour. Consequently, 
this method can mainly be used in fertility research if large-scale register data are 
available.

3.2 Criteria and considerations for the analysis of policy effects

In order to study policy effects, suitable counterfactuals are needed. The Nordic 
countries have been ideal for the counterfactual approach. These countries are at 
the vanguard of progressive parental leave regulations, having already overhauled 
their family policies in the 1970s and 1980s. Furthermore, as these countries have 
large-scale register data suitable for individual-level fertility analysis, studies 
conducted in these countries were among the fi rst to generate solid evidence of how 
parental leave policies could alter fertility patterns (Andersson 1999; Andersson 
et al. 2006; Björklund 2006; Neyer/Andersson 2008). A stylised fi nding from this 
body of research is that the introduction of the so-called “speed-premium”9 in 
the Swedish parental leave system led to an increase in second birth rates, and a 
shortening of birth intervals. This evidence was generated based on simple parity-
specifi c birth rates (i.e. from event history models) for Sweden that were compared 
with patterns in other Nordic countries. In the Nordic context, where there are only 
minor differences in the cultural and economic developments between countries, it 
seems straightforward to analyse Swedish fertility and to use neighbouring Norway 
or Denmark as counterfactuals. Other European countries often lack such clear-cut 
comparison groups, because the data are often less comparable across countries; 
and because countries differ on multiple dimensions, including in their cultural and 
economic conditions, and in their fertility patterns prior to a reform. 

In addition to the challenge of guaranteeing similar prior conditions, Bhrolcháin 
and Dyson (2007) have listed further criteria for performing meaningful causal analysis 
of demographic outcomes. In particular, they have emphasised the importance of 

9 Parental leave benefi ts in Sweden cover roughly 80 percent of prior income. If the fi rst and 
second births are spaced closely apart, women will receive the same parental leave benefi t for 
the second child as for the fi rst one, even if they had reduced their employment and earnings 
between the two births. The same applies to higher-order births (Andersson et al. 2006).



Causal Modelling in Fertility Research    • 281

contiguity: i.e. that the effect should follow shortly after the cause (Bhrolcháin/Dyson 
2007: 8). Moreover, the regression discontinuity approach (see above) capitalises 
on the idea that a policy reform can be regarded as a sudden external shock that 
leads to an immediate reaction. Sharp cut-off dates for eligibility for certain benefi ts 
are very important tools in understanding how policies operate. However, not all 
policy reforms are implemented in a clear-cut fashion. Furthermore, there may be 
a mismatch between the de jure regulations and the de facto implementation of a 
policy. Some groups may be eligible for a service or payment, but may not be able 
to take advantage of it, either because they are simply not aware of their eligibility 
or because they are unable to master the bureaucratic hurdles involved in applying 
for a state benefi t. Moreover, in family law, there is often a “margin of appreciation” 
of how legal texts are interpreted and enforced in practice. This is most evident in 
the regulation of child custody or alimony, in which judges have a certain leeway 
in their rulings. There is only a small margin of appreciation in the case of parental 
leave regulations, as eligibility is clearly defi ned in law. However, for some families, 
bureaucratic hurdles may have indeed been a barrier to taking advantage of these 
programmes. The abovementioned parental leave benefi t reform requires parents 
to document their earnings of the last 12 months. The German Family Ministry has 
only recently intensifi ed efforts to make the procedure easier (by retrieving the 
earnings information automatically from the pension registers). Returning to the 
abovementioned principle of contiguity, we observe that this principle seems to 
confl ict at least somewhat with the ways in which some policies play out in practice. 
Thus, there may not be an immediate “reform effect” because it can take time for 
the knowledge of how to apply for certain benefi ts to trickle down to all layers of 
society. In addition, governments may need time not only to optimise their systems 
and thus remove bureaucratic hurdles, but also to make the application procedure 
easier so that access is guaranteed even for hard-to-reach populations, such as 
those who do not speak the native language. 

Also relevant in this context is the policy process. From the ministerial draft, 
to the discussion in parliament, to the enactment of the law, and to its ultimate 
implementation; this process can easily stretch across several months, or even 
years. Depending on the magnitude and relevance of the reform, this debate may 
receive media coverage. As a result, even if we are able to pin-point the exact date 
when a policy reform came into force, the reform may have increased levels of 
public awareness much earlier. For example, Germany drastically curbed ex-spousal 
maintenance after divorce in 2008 (Radenacker 2020). As this policy process was 
covered in the media, it is likely that women who foresaw that they would get 
divorced had altered their employment behaviour well in advance of the actual date 
of the implementation of that reform. The parental leave benefi t reform, which will 
be analysed below, came into force on 1 January 2007. The reform bill was passed 
on 20 June 2006.10 It is possible that some couples foresaw that this policy would 

10 http://dip21.bundestag.de/dip21/btd/16/018/1601889.pdf

http://dip21.bundestag.de/dip21/btd/16/018/1601889.pdf


•    Michaela Kreyenfeld282

come into effect, and acted accordingly. Thus, births in January 2007 may have 
been planned in anticipation of the implementation of the reform. Therefore, an 
immediate reaction to the reform may have been observed. However, given that 
births are not that easy to time for most couples, a more realistic scenario is that 
there was a certain time lag between the implementation of this reform and its 
effects on fertility. 

Policies are rarely formulated in a vacuum, and how they operate also depends 
on the context. In some cases, a policy may not succeed because people do not 
use it. Levels of policy usage may vary for different reasons. For example, eligible 
individuals may not consider applying for a transfer for fear of being stigmatised if 
they collected the benefi t. Similarly, parents may not take advantage of an available 
child care slot because societal norms sanction the use of day care at young ages. 
Neyer and Andersson (2008: 702) argued that certain policies may be deemed to 
have failed as a result of a lack of coherence and a mismatch with the broader societal 
system. For example, the German parental leave benefi t reform was basically copied 
from the Swedish system. Unlike Sweden, which had already abolished individual 
taxation in the 1970s, Germany retained its system of joint taxation. The German 
system continues to provide tax relief if the “second earner” (usually the woman) 
has worked less. Thus, the system does not provide a clear commitment to the “dual 
earner model”, but instead provides strong incentives to opt for the single earner 
model. Kalwij (2010: 704) concluded that researchers should never analyse policies 
in isolation, nor should they “simply sum up the various family policies”. Instead, 
researchers should consider the interplay of the different measures and how they 
align and resonate with the overall logic of the system. 

Neyer and Andersson (2008) introduced the concept of critical junctures into 
this debate. This terminology was originally used in the political economy literature 
to depict turning points in institutional developments. Critical junctures are policy 
reforms that have a lasting effect on the entire welfare state framework because 
they determine its future pathway and can “lock” the system into moving in a 
certain direction (Pierson 2000; Thelen 1999). It also follows that the constellation 
of different policies generates a unique and separate dimension. In addition to 
pointing to this idiosyncratic nature of policies, the authors suggested to analyse 
possible interaction effects between the existing policy measures and the newly 
introduced ones. For example, it is conceivable that parental leave policies would 
only be effective if they were combined with an increase in the provision of child 
care. While child care policies could be integrated by exploiting regional variations, 
other policies are more diffi cult to integrate (such as the effects that come from 
the tax and transfer system). The use of large-scale cross-national data, combined 
with information on the features of the different welfare states, could provide some 
important insights into how policies operate in different contexts (Wesolowski et al. 
2020).



Causal Modelling in Fertility Research    • 283

4 How did the German parental leave benefi t reform affect fi rst birth 
behaviour? 

4.1 The 2007 parental leave benefi t reform

Below, we use the German parental leave benefi t reform of 2007 to illustrate the 
diffi culties involved in isolating policy effects. The German parental leave benefi t 
reform came into force on 1 January 2007. The reform, which was copied from the 
parental leave benefi t programmes of the Swedish system, was regarded in the 
academic community as marking a major departure from the previous system in 
Germany (Fleckenstein 2011; Spieß/Wrohlich 2008). The prior regulations provided 
a fl at-rate benefi t of 300 euros per month for the duration of two years, while the new 
regulations provided a shorter term of parental leave of only 12 months. Moreover, 
the benefi t was now earnings-related, with the net earnings in the year prior to 
childbirth serving as the basis for the calculation of the benefi t.11 Although the term 
during which benefi ts were received was shortened, the new regulations generally 
led to an increase in monthly payments, one exception being the unemployed and 
persons who were not integrated into the labour market. The benefi ts of these 
individuals were often lower under the new system. 

Some scholars characterised the reform as a major and radical shift and a clear 
departure from the logic of the previous system, which was often classifi ed as a 
conservative and familialistic welfare state regime (Fleckenstein 2011). In addition, 
the new regulations provided strong incentives for women to become established 
in the labour market before having children. Thus, a clear-cut hypothesis follows 
from these observations: namely, that the association between female employment 
status and earnings should have changed after the reform, with women becoming 
more likely to postpone childbearing until they were fi rmly established in the labour 
market. This hypothesis will be tested below based on large-scale register data.

4.2 Data and variables

Data for this investigation come from the German Pension Registers. We use the 
“VSKT 2015”, which is a sample drawn from the registers and which includes 
persons with German citizenship who had an active pension account in 2015, i.e. 
persons who were not yet retired (Stegmann 2018). The main benefi ts of using this 
dataset are its large sample size and its detailed and reliable employment, earnings, 
and fertility biographies (for a validation of the fertility histories, see Kreyenfeld/
Mika 2006). There are, however, several disadvantages to using this dataset. First, 
the pension data cover only about 90 percent of the resident population in Germany, 
as opposed to the total population. People in certain professions (farmers, civil 
servants) are not included in the registers. An additional drawback is that it contains 

11 There is an earnings cap for the calculation of the benefi t (currently 1,800 euros). 



•    Michaela Kreyenfeld284

only a few variables that can be employed for the investigation. For example, 
partner information or information at the household level are not available in the 
dataset. Thus, the analyses must rely on a “sparse model” with a limited number of 
covariates. Another drawback is that the data only include individuals born between 
1948 and 1985. This means that coverage of younger ages for the very recent time 
period is poor.

The data have been transferred into a person-month dataset, and have been 
restricted to women aged between 20 and 40 in the years 2005 to 2010. We do 
not analyse earlier years because unemployment is one of our main covariates, 
and because measures of unemployment are not fully comparable for longer time 
periods due to a major policy reform of the unemployment benefi t scheme that 
came into force in 2004 (the so-called Hartz IV reforms). We do not analyse later 
years because coverage of very young women for the period after 2010 is poor. 
Sensitivity analyses were conducted that cover longer time periods for older women 
(see Fig. A2 in the appendix). 

The main outcome variable is the fi rst childbirth, which was pre-dated by nine 
months. Women who had a child before the observation window are not part of 
this investigation. Cases are censored at “last clearance”, which is the date when 
the German pension fund contacts a person to verify the information provided in 
the registers. The total number of women in the analytical sample is 48,843, which 
corresponds to 2,833,078 person-months. These women gave birth to 13,913 fi rst 
children in the observation window (see Table A1 in the appendix for the sample 
statistics).

The main covariate is the employment status. Employment status is available on 
a monthly basis in the registers. We distinguish between women who were in (1) 
schooling, (2) employment, (3) unemployment, and (4) others. Schooling includes 
any educational episode, including school attendance, vocational training, and 
university education. Not all educational episodes are equally relevant for pension 
payments. For this reason, university education (as well as further education) is 
not fully recorded in the registers.12 Thus, some educational episodes cannot be 
identifi ed, and they will appear in the “other” category (see below). Employment 
includes “regular” employment. It does not include any form of informal or marginal 
employment.13 Unemployment includes periods of registered unemployment 
(including ALG II). The “other” category is heterogeneous. It comprises some 
episodes of university education, marginal employment, or other episodes in which 
a person was out of the labour market for other reasons.

12 Vocational training generates “pension points”, while university education is not immediately 
“pension-relevant”. Although an individual does not acquire any “pension points” while in 
university education, these periods count as “pension-relevant periods”. An individual needs a 
certain minimum of pension-relevant periods before s/he can claim a pension. The maximum 
duration of time that can be claimed was reduced to 96 months in 1992. 

13 Marginal employment is partially or fully exempt from social security contributions and income 
tax. Since 1999, the marginally employed are required to pay contributions to the public pension 
fund, but they are still exempt from other social security payments (such as contributions to the 
unemployment insurance system).



Causal Modelling in Fertility Research    • 285

In order to capture the effect of the policy reform, we control for the time period. 
Even with large register data, the sample sizes are too small to conduct the analysis 
by single years, ages, and employment status and earnings. For that reason, we 
have grouped the calendar years into the following three broad categories: the 
years 2005-2006, 2007-2008, and 2009-2010. Our aim is not to measure precisely the 
effects of the reform; instead, we seek to map the time trends around the reform. 
We will return to this limitation later on. 

We control for major socio-demographic characteristics. We include a binary 
variable that indicates whether a person was living in eastern or western Germany. 
This variable is a time-constant variable and denotes whether the person was living 
in eastern Germany (including East Berlin) or western Germany at the time at which 
they were last contacted by the German pension fund. Age is the baseline hazard 
in the event history model. It is included as a categorical variable in the model that 
distinguishes between ages 20-24, 25-29, 30-34, and 35-40. These cut-points have 
been chosen arbitrarily, but the results remain largely unchanged if more fi ne-
grained ones are used. Moreover, other model specifi cations that do not make any 
parametric assumption regarding the baseline hazard, like the Cox model, lead to 
similar results.

A considerable disadvantage of this dataset is the lack of variables that could be 
used as control variables. While the data include information on level of education, 
this information is incomplete since it is provided by the employer on a voluntary 
basis only. However, a signifi cant advantage of the register data is that they provide 
very detailed monthly earning histories. Earnings information is stored in terms 
of pension points, with one pension point constituting the average earnings in 
a given year. Based on this information, we have generated a variable that gives 
information on each individual’s monthly earnings, distinguishing between low 
earnings (up to 50 percent of average earnings), medium earnings (50 percent to 
less than 100 percent of average earnings), and high earnings (100 percent or more 
of average earnings). This variable is a time-varying covariate that changes its value 
as people progress through time. As earnings generally increase with age, this 
variable is strongly correlated with age. We control for age, but we also provide 
analyses by age group.

4.2.1 Modelling strategies

The empirical investigation we conduct below relies on conventional event history 
modelling. In order to specify the baseline hazard, we use a piecewise constant 
model. Compared to the more widely used Cox model, there are several benefi ts 
to using the piecewise constant model. Most importantly, it generates estimates 
for the baseline hazard, which means that it provides straightforward measures 
for the effect of the main process time (age).14 We start with a simple model that 

14 In the Cox-Model, this is only possible in a post-estimation strategy.



•    Michaela Kreyenfeld286

controls for the main socio-demographic covariates (age, year, employment, 
earnings, region). In the next step, we examine the effect of the policy reform by 
including an interaction term of the calendar year and the main covariate of interest 
(women’s employment and earnings). The policy reform provides strong incentives 
to postpone childbearing until an individual’s earnings are reasonably high. Thus, 
we assume that the association between women’s employment and earnings is 
different before and after reform, i.e. it is assumed that stable employment and high 
earnings have become a prerequisite for family formation in recent years. 

4.3 Results

4.3.1 Determinants of fi rst birth risks

Table 1 displays the results from the event history models, with employment 
(Model 1) and earnings (Model 2) as the major covariates, and fi rst birth (or rather 
fi rst pregnancy) as the outcome variable. All results are provided as relative risks. 
The models show that birth risks were lower at younger (20-24) and older ages (35-
40), but were fairly similar at ages 25-29 and 30-34. The models also indicate that 
the fi rst birth rates were higher in eastern than in western Germany, refl ecting the 
earlier family formation tendencies among eastern German women. Turning our 
attention to the effects of calendar time, the model suggests that the fi rst birth 
rates had increased somewhat since 2005-2006. Model 1 shows that educational 
participation lowered the fi rst birth rates by about 65 percent, which is in line with 
earlier evidence for Germany (e.g. Andersson et al. 2014; Blossfeld/Huinink 1991; 
Schmitt 2012). Unemployment (versus employment) does not seem to infl uence 
birth behaviour. It should, however, be noted that this effect varied by region, with 
eastern German women being more likely than their western German counterparts 
to postpone parenthood during unemployment (see Table A1 in the appendix). 

Model 2 includes a combination factor of earnings and employment, and shows 
a positive gradient; i.e. that higher earnings increased the fi rst birth transition rates. 
However, we cannot rule out the possibility that the strong positive effects we 
observe are attributable to an acceleration of birth intensities among high income 
earners at advanced ages. This would mean that the proportionality assumption of 
the model was violated, and that the effects of earnings on the birth rates varied by 
age. It is therefore possible that there were interaction effects of earnings and age. 
This aspect will be addressed in the next step of the analysis, which also focuses 
more narrowly on how the effects of earnings change over time.

4.3.2 Effect heterogeneity

The next step of the analysis contains more refi ned analyses by age group and 
calendar year. For that purpose, we have split the sample into a group of younger 
(ages 20-29) and older persons (ages 30-39). Furthermore, we have used the 
calendar year in interaction with women’s earnings/employment. While an 
alternative strategy would be to use a three-way interaction, this would be more 



Causal Modelling in Fertility Research    • 287

diffi cult to display. Figure 1 visualises the results separately for the younger and 
the older age groups (for the regression table, see Table A3 in the Appendix). The 
model corroborates earlier fi ndings (see e.g. Andersson et al. 2014) showing that 
unemployment is positively associated with having the fi rst birth at younger ages 
(below age 30), but is negatively associated with having children later in the life 
course. An important fi nding from the results is that the association between female 

Tab. 1: Results from piecewise constant model, fi rst birth risks

Model 1 Model 2

Age
20-24 Ref. Ref.
25-29 1.48*** 1.46***
30-34 1.89*** 1.84***
35-40 1.04 1.01***

Region
Western Germany Ref. Ref.
Eastern Germany 1.18*** 1.20***

Years
2005-06 Ref. Ref.
2007-08 1.05*** 1.05***
2009-10 1.05*** 1.05***

Employment status
Education 0.34*** 0.37***
Unemployment 0.96 1.08*
Other 0.60*** 0.68***
Employment Ref. --
Earnings: low -- Ref.
Earnings: medium -- 1.11***
Earnings: high -- 1.20***

Constant (absolute risk) 0.004*** 0.003***

Model fi t
LL initial model -15,575 -15,575
Final model -14,473 -14,454

Sample size
Persons 48,843 48,843
Events (fi rst births) 13,913 13,913
Person-months 2,833,078 2,833,078

Note: Date of childbirth was backdated by nine months. 
* p<0.05; ** p<0.01; *** p<0.001
Source: VSKT 2015, own estimates



•    Michaela Kreyenfeld288

employment, earnings, and fi rst birth rates changed over time. After 2007, when the 
parental leave benefi t reform came into force, the fi rst birth rates increased among 
women with high earnings, while they declined or stagnated among women with 
lower earnings. Furthermore, the fertility pattern of unemployed women changed 
dramatically, with the fi rst birth rates of younger unemployed women decreasing by 
27 percent from 2005-2006 to 2009-10. While unemployment had been conducive 
to childbearing at younger ages before the parental leave reform came into force, 
it appears that this was no longer the case. We also see a change in patterns at 
older ages. In this age group, the fi rst birth rates of unemployed women had 
dropped by 16 percent over the same time period. The results of the model provide 
strong evidence that the prerequisites of family formation have shifted over time in 
Germany. It has become increasingly important for women to have decent earnings 
and regular employment before starting a family. 

4.3.3 Convincing evidence?

Can we attribute the pattern we observed to the parental leave benefi t reform? 
While the fi ndings allude to a decisive societal change, clearly attributing that shift 
to the parental leave regulations is more cumbersome. Causal modelling requires 
that “all reasonable alternative explanations (including confounders) must be ruled 
out” (Bhrolcháin/Dyson 2007: 9). We obviously cannot rule out the possibility that 
other policies – such as the increase in day care services for children that was 
initiated in 2005 – are the more important drivers of the changes in behavioural 

Fig. 1: Results from the piecewise constant model. Relative fi rst birth risk by 
calendar year, age category, and female earnings

0

1

2

2005-06 2007-08 2009-10

Calendar year

Unemployment

Earnings: Low (0-49%)

Earnings: Medium (50-99%)

Earnings: High (100% and more)

Age 20-29
Relative first birth risk

0

1

2

2005-06 2007-08 2009-10

Calendar year

Age 30-40
Relative first birth risk

Note: Date of childbirth was backdated by nine months. Further covariates in the model 
are region (east/west), age (categorised and time-varying), educational participation, and 
other employment status in interaction with the time period.
Source: VSKT 2015, own estimates



Causal Modelling in Fertility Research    • 289

patterns. An alternative explanation may also be the effects of the global fi nancial 
crisis, which hit Europe at almost the same time as Germany enacted new parental 
leave regulations. The growing sense of economic insecurity in the wake of the 
crisis could have sharpened people’s awareness that the single-earner model is a 
fragile family model – which may, in turn, have led to a reduction in fi rst birth risks 
among unemployed women. 

Would a more causal modelling strategy be better able to discern causal effects? 
A model that mapped the monthly birth rates shortly before and after the reform 
could provide more convincing support for the claim that there was a true “reform 
effect”. Indeed, these kinds of analyses have been conducted using data from the 
German birth registers. The results showed that there was an immediate increase 
in births at the cut-off date of 1 January 2007 (Tamm 2013). Despite the beauty of 
such set-ups, these fi ndings remain limited. They may not even provide clear-cut 
evidence that prospective parents acted in response to the reform. Instead, they 
probably indicate that medical doctors and midwives have some limited leeway to 
infl uence the dates of childbirth. Thus, given that the mechanisms at the cut-off date 
were likely to have been very specifi c, these results may not be generalisable. While 
intricate identifi cation strategies can easily “throw the baby out with the bathwater” 
(for the same analogy, see Hill et al. 2020: 363), the simple event history modelling 
approach – as illustrated above – fails to provide clear-cut causal effects, but delivers 
more accessible and generalisable results.

5 Conclusions

The aim of this paper was to provide an overview of recent attempts to perform 
causal fertility modelling based on longitudinal data. In particular, we focused on 
research that had tried to investigate the causal effects of female employment 
and family policies on birth behaviour in European countries since the 1990s. The 
empirical section of the paper paid special attention to the German policy reform 
of 2007, and raised the question of how this reform affected fi rst birth patterns. 
The “reform effect” was modelled over a time-varying variable that depicted the 
calendar year. A main fi nding from this investigation was that birth rates during 
unemployment declined over time, whereas fi rst birth risks increased at higher 
earnings levels. These results provide important insights into fertility dynamics in 
Germany, as they illustrate that the prerequisites of family formation have shifted 
rather dramatically in recent years. These shifts may be attributed to the parental 
leave policy reform. However, the analysis also revealed how diffi cult it is to rule out 
“alternative explanations” with simple methods, considering that the expansion of 
day care as well as the global fi nancial crisis occurred around the same time as the 
policy was implemented, and could have caused a similar pattern. 

Event history analysis is a concept that has evolved partially from demographic 
research, in which the aim is to portray the fertility behaviour of a given population. 
Event history modelling also shares the general understanding of sociological 
life course research (i.e. Elder 1985) that vital events must be situated in time 



•    Michaela Kreyenfeld290

and studied along major life course dimensions (i.e. by age when fi rst births are 
analysed, and by duration since the last birth when higher order births are the focus 
of attention). A commitment to the life course approach is often absent from many 
of the more causal modelling strategies. Thus, standard event history models are 
better able to deliver on the “life course dimension”, and to provide more accessible 
“descriptions of the social world” (Brüderl/Ludwig 2015: 353). These descriptions 
are of considerable value, and should probably be used as the basis before moving 
to the next step of analysing causal effects. But what are the reasonable next steps 
for causal fertility research? 

The literature overview demonstrated that causal modelling approaches, and 
fi xed-effects methods in particular, have increasingly seeped into sociological and 
demographic research. The wide array of European panel data, such as data from 
the Generations and Gender Survey, the British Understanding Society study, 
or the German Family Panel, have clearly fuelled this development. However, 
demographic and sociological scholars have been very careful when applying 
fi xed-effects methods to fertility processes. While these methods have been 
regularly used to study the question of how demographic events infl uence other 
determinants, such as life satisfaction and well-being, they have rarely been used to 
examine birth dynamics as outcome variables. This is because in family sociology 
and demography, taking a parity-specifi c view is almost an imperative. This includes 
the notion that a fi rst birth is a unique event. The analysis of fi rst births is therefore 
not amenable to fi xed-effects modelling since a requirement of this method is that 
the behaviour being studied can be repeated by the same individual under different 
conditions. 

Other econometric methods from the programme evaluation literature, such 
as the regression discontinuity approach, have been employed to examine the 
causal effects of policy reforms on fertility behaviour. While this technique may be 
highly valuable in terms of advancing causal modelling in demographic research, 
some caution seems warranted when considering its use. It is important to keep in 
mind that these methods have been developed mainly for the evaluation of labour 
market programmes in which the outcome variables are usually frequent events, 
such as entering employment or receiving welfare benefi ts. This is clearly not the 
case for demographic events, which are rare. Thus, there may be only a few birth 
events around a cut-off date available in the survey data, which makes it diffi cult to 
generate signifi cant results. We may intuitively prefer statistically insignifi cant, but 
well-specifi ed results over signifi cant and biased ones. However, an underpowered 
model can also raise concerns. After all, model results that are nowhere near 
conventional levels of signifi cance will be diffi cult to interpret and hard to publish, 
despite all discussions and complaints about the publication bias in peer-reviewed 
journals. While conventional models jump to conclusions too quickly, these types 
of models may be characterised as being too cautious. Hill et al. (2020) pointed out 
that a “no-effect result”, which is based on a seemingly solid causal investigation, 
can be harmful if it leads to the discontinuation of a potentially meaningful policy 
measure, for instance. What seems like a trivial and purely data-driven concern is 



Causal Modelling in Fertility Research    • 291

often of considerable practical relevance, because the sample size can be a serious 
constraint, and because vital events are rare events. 

While acknowledging that a causal perspective is important for arriving at 
meaningful conclusions, the paper also emphasised that the choice of method 
should be carefully considered when studying demographic processes. We argued 
that fertility research can be moved forward through more careful refl ection on the 
origins of the bias. The observation that people act on their anticipated behaviour 
was regarded as a core reason why simple models that study the relationship 
between women’s work and birth behaviour often cannot be interpreted in a causal 
manner. As we noted, several scholars have proposed considering the role of 
“narratives”, which also currently seem to be gaining ground in economic research 
(e.g. Bènabou et al. 2018; Shiller 2020). Instead of applying ever more sophisticated 
econometric modelling techniques, the future of causal fertility research in this area 
may lay in a careful refl ection of how suitable item sets could be developed to map 
these “imaginaries of the future self”.

This overview paper has many limitations. It was restricted to fertility research 
based on studies that relied on longitudinal, prospective, or retrospective surveys, 
as well as on administrative data that were mostly collected in European countries. 
The paper discussed common-cause confounding and endogenous selection 
bias as prime sources of bias in studies that dealt with the relationship between 
female employment and fertility. In terms of the isolation of policy effects, several 
reasons were cited as to why standard tools from the programme evaluation 
literature cannot be used for studying fertility behaviour. Beyond the concerns listed 
in this paper, there are other reasons why an investigation may result in biased 
results. In particular, data quality may affect model results. We addressed the 
limitations related to small sample sizes when vital events are investigated based 
on survey data. However, there are numerous other aspects that revolve around 
the topic of “data quality”. For example, recall bias in retrospective surveys can 
lead to biased models if events in the distant past are not remembered with the 
same precision as events that happened more recently. Furthermore, more salient 
events (childbirth) may be easier to remember than less salient ones (like events in 
a person’s employment biography). While retrospective surveys suffer from recall 
bias and related problems, prospective studies suffer from attrition, which raises 
concerns about the selectivity of the drop-outs. Administrative data can have other 
problems depending on the registration system in a given country. For example, a 
problem of Nordic register data is that most of the information, such as information 
on employment status or childbirth, is only available on a yearly basis. For other 
countries, administrative data may not include the entire resident population. Data 
quality has not been addressed in this overview, but it is certainly an important 
additional and often overlooked aspect that warrants more attention. 

Acknowledgment
For his critical feedback on an earlier version of this paper, I am thankful to Daniele 
Vignoli (University of Florence). I am very grateful to Felix Elwert (University of 



•    Michaela Kreyenfeld292

Wisconsin) for his support in helping me to wrap my head around endogenous 
selection bias. Thanks also to Kai Baron (WZB) for his suggestions to engage with the 
economic literature on “narrative economics”. For valuable comments on matching 
techniques in demographic research, I would also like to thank Daniel Brüggmann 
(German Pension Fund). Many thanks must also go to Tatjana Mika for sharing her 
expertise and knowledge on the German pension data. For language editing I would 
like to thank Miriam Hils. All remaining errors are my own.

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Date of submission: 14.12.2020 Date of acceptance: 31.05.2021

Prof. Dr. Michaela Kreyenfeld (). Hertie School. Berlin. Germany. 
E-mail: Kreyenfeld@hertie-school.org
URL: https://www.hertie-school.org/de/ueber-uns/profi l/person/kreyenfeld

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https://www.hertie-school.org/de/ueber-uns/profil/person/kreyenfeld


•    Michaela Kreyenfeld298

Appendix

Tab. A1: Occurrence (Occ.) and exposures (Exp.) by age group

Ages 20-29 Ages 30-39
Exp. (in %) Occ. Exp. (in %) Occ.

Age
20-24 38 1,964 -- --
25-29 62 5,573 -- --
30-34 -- -- 61 4,747
35-40 -- -- 39 1,629

Region
Western Germany 80 5,639 84 5,371
Eastern Germany 20 1,898 16 1,005

Years
2005-06 44 2,972 32 1,904
2007-08 33 2,586 33 2,176
2009-10 23 1,979 35 2,296

Employment status
Education 11 290 1 45
Unemployment 7 779 7 273
Other 27 1,206 29 1,499
Earnings: low 13 1,201 9 477
Earnings: medium 30 2,998 26 1,700
Earnings: high 12 1,063 29 2,382

Person-months 1,704,821 7,537 1,128,257 6,376

Source: VSKT 2015, own estimates



Causal Modelling in Fertility Research    • 299

Tab. A2: Results from piecewise constant model, fi rst birth risks by eastern and 
western Germany

Western Germany Eastern Germany

Age
20-24 Ref. Ref.
25-29 1.55*** 1.34***
30-34 2.10*** 1.39***
35-40 1.18*** 0.66***

Years
1990-94 Ref. Ref.
1995-99 1.06*** 1.02
2000-06 1.07*** 0.98

Employment status
Education 0.33*** 0.38***
Employment Ref. Ref.
Unemployment 1.01 0.86***
Other 0.63 0.49***

Constant (absolute risk) 0.004*** 0.006***

Model fi t
LL initial model -11,549 -3,098
Final model -48,801 -2,864

Sample size
Persons 39,689 9,154
Events (fi rst births) 11,010 2,903
Person-months 2,309,983 523,095

Note: Date of childbirth was backdated by nine months. 
* p<0.05; ** p<0.01; *** p<0.001
Source: VSKT 2015, own estimates



•    Michaela Kreyenfeld300

Tab. A3: Results from piecewise constant model, fi rst birth risks by age, 
employment status, earnings and time period

Model 1 Model 2
Age 20-29 Age 30-40

Years: 2005-06
Unemployment 1.42*** 0.98
Employment: Low earnings (0-49%) Ref. Ref.
Employment: Medium earnings (50-99%) 1.00 1.29***
Employment: High earnings (100% and more) 0.89 1.59***

Years: 2007-08
Unemployment 1.06 0.70***
Employment: Low earnings (0-49%) Ref. Ref.
Employment: Medium earnings (50-99%) 1.03 1.20***
Employment: High earnings (100% and more) 0.82** 1.57***

Years: 2009-10
Unemployment 1.18 0.75***
Employment: Low earnings (0-49%) Ref. Ref.
Employment: Medium earnings (50-99%) 1.19*** 1.30***
Employment: High earnings (100% and more) 1.11 1.68***

Note: Date of childbirth was backdated by nine months. Two separate models for younger 
ages (age 20-29) and older ages (age 30-40) were estimated. Furthermore, employment 
status was used in interaction with calendar year. The interaction model was re-estimated 
with different references categories, so that the effect of unemployment (versus low 
income) could more easily be compared for a given year. Further covariates in the model 
are region (East/West), age (categorised and time-varying) and educational participation 
and other employment status in interaction with the time period. 
* p<0.05; ** p<0.01; *** p<0.001
Source: VSKT 2015, own estimates



Causal Modelling in Fertility Research    • 301

Fig. A2: Results from piecewise constant model. Relative fi rst birth risk by single 
calendar year and earnings/employment status, only ages 30-40

0

1

2

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

Calendar year

Unemployment

Earnings: Low (0-49%)

Earnings: Medium (50-99%)

Earnings: High (100% and more)

Relative first birth risk

Note: Date of childbirth was backdated by nine months. Further covariates in the model 
are region (East/West), age (categorised and time-varying), educational participation, and 
other employment status in interaction with the time period.
Source: VSKT 2015, own estimates



Published by
Prof. Dr. Norbert F. Schneider

Federal Institute for Population Research 
D-65180 Wiesbaden / Germany

 2021

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