Fertility progression in Germany: An analysis using flexible nonparametric cure survival models

Parental Leave and Fertility: Individual-Level Responses in the Tempo and Quantum of Second and Third Births

Previous studies have documented varying fertility responses to changes in parental leave provisions. We contribute to this literature by investigating the effects on the transition to second and third births of a policy reform that introduced generous earnings-dependent parental leave benefit in Estonia in 2004. Our study employs a mixture cure model, a model with some useful properties that has been seldom applied in fertility research. The advantage of the cure model over conventional event history models is the ability to distinguish the effect of the covariates on the propensity to have a next child from their effect on the tempo of childbearing. The results show that the transition to next birth accelerated as parents responded to so-called speed premium, a feature that allowed them to avoid a reduction in benefits caused by a reduction of earned income between births, through the closer spacing of births. Furthermore, the findings suggest that the introduction of generous earning-related parental leave was associated with a substantial increase in the progression to both second and third births.

Grandparental childcare and second births in China

China has low birth rates at higher parities and intensive grandparental childcare. Despite this, there has been little empirical research into the role of intergenerational support in the transition to second birth. This study examines whether grandparental childcare increases the likelihood and speed of a transition to second birth in the context of relaxations in Chinese family planning policy and whether this differs for working and non-working mothers. Using data from the China Family Panel Studies (2010-2016), the association between grandparental childcare, mother's working status and second childbirth are explored using split-population survival models to distinguish between the impact on the timing of fertility and ultimate parity progression. The odds of having a second child are four times higher for those who use grandparental childcare than those that don't. Amongst those who have a second child, grandparental childcare leads to 30% lower odds of transition to second birth than those without grandparental care, each month. Grandparental childcare is also associated with maternal employment, which is itself associated with a sharp decrease in the transition to second birth. At the micro-level, grandparental childcare helps mothers continue working, which in turn defers a second birth. The results emphasise the importance of work-life balance strategies, such as grandparental care, in enabling women of childbearing age to realize their fertility intentions in combination with work.

Second Birth Fertility in Germany: Social Class, Gender, and the Role of Economic Uncertainty

Building on a thick strand of the literature on the determinants of higher-order births, this study uses a gender and class perspective to analyse second birth progression rates in Germany. Using data from the German Socio-Economic Panel from 1990 to 2020, individuals are classified based on their occupation into: upper service, lower service, skilled manual/higher-grade routine nonmanual, and semi-/unskilled manual/lower-grade routine nonmanual classes. Results highlight the "economic advantage" of men and women in service classes who experience strongly elevated second birth rates. Finally, we demonstrate that upward career mobility post-first birth is associated with higher second birth rates, particularly among men.

Fitting parametric cure models in R using the packages cuRe and rstpm2

BACKGROUND AND OBJECTIVE

Within medical research, cure models are useful for analyzing time-to-event data in the scenario where a proportion of the analyzed individuals are expected to never experience the event of interest. Cure models are also useful for modelling the relative survival in scenarios where a proportion of the individuals are expected to eventually experience a mortality rate similar to that of the general population. Here we present two R packages, cuRe and rstpm2, that provide researchers with several tools for performing statistical inference using parametric cure models.

METHODS

Cure models are commonly used to estimate 1) the proportion of individuals that are cured and 2) the event-time distribution of individuals who are not cured. This can be done using simple parametric distributions for the event-time distribution of the uncured, but our implementations also enable fitting of more flexible spline-based cure models. The parametric framework of both packages ensures that cure models for the relative survival can easily be used.

RESULTS

The cuRe package contains two main functions for estimating parametric mixture cure models; one based on simple parametric distributions (e.g. Weibull or exponential) and one utilizing a spline-based formulation of the cure model. The rstpm2 package enables estimation of spline-based latent cure models, i.e., cure models with no explicit parameters modelling the proportion of cured individuals.

CONCLUSIONS

Through the R-packages cuRe and rstpm2, a wide range of different parametric cure models can be fitted. The cuRe package also contains a number of useful post-estimation procedures for computing the time to statistical cure and conditional probability of cure, which may spread the use of cure models in medical research.

Nativity differentials in first births in the United States: Patterns by race and ethnicity

BACKGROUND

While recent decades have seen gradual convergence in ethno-racial disparities in completed fertility in the United States, differences in the age pattern of first births remain. The role of nativity has not been fully understood.

OBJECTIVE

This paper examines how first births vary by nativity, and how this variation contributes to more significant racial and ethnic differentials.

METHODS

Using data from the National Survey of Family Growth (1997-2017), we jointly estimate the correlates of the timing of first births and childlessness. We assess differences between immigrants and US-born and child-migrant women across ethno-racial groups.

RESULTS

The unique first-birth patterns among foreign-born women have a notable impact on Hispanics, reducing differences from Whites in the average age at first birth and contributing to more significant differentials in childlessness. The impact of immigrant women on White and Black first births is more modest in scope.

CONTRIBUTION

Our work shows the importance of nativity for ethnic/racial disparities in the timing and quantum of fertility in the United States. We demonstrate how the migrant population is more determinant for Hispanic fertility patterns than for Black or White. We conclude by elaborating on the implications of these results for future research as the immigrant population in the United States becomes ethnically and racially more diverse.

Stop! Go! What Can We Learn About Family Planning From Birth Timing in Settler South Africa, 1835-1950?

We revisit the discussion on family limitation through stopping and spacing behavior before and during the fertility transition with a sample of 12,800 settler women's birth histories in nineteenth- and twentieth-century South Africa. Using cure models that allow us to separate those who stop childbearing from those who continue, we find no evidence of parity-specific spacing before the transition. We do find evidence of non-parity-based birth postponement before the transition. Increased stopping and parity-independent postponement characterized the beginning of the fertility transition, with increased parity-specific spacing following later in the transition phase.

Height and marital outcomes in the Netherlands, birth years 1841-1900

Adult body height appears to be significantly associated with marital outcomes: taller men across contexts have been found to be more likely to be married, and more likely to be married at younger ages. We are interested in exploring both outcomes individually and simultaneously, while using an unique, individual-level dataset of Dutch men and their brothers born between 1841 and 1900. To do so, we exploit survival models and cure models. While survival models yield a single estimate for the hazard (or age at) marriage, cure models yield two: one for the likelihood of marriage, and one for the hazard of first marriage. Cure models thus account for selection into marriage, while survival models do not. We find that, in the survival analyses, being in the shortest 20 % of heights is associated with later ages of marriage, relative to being average height. However, when we account for selection into marriage with cure models, we find that height is no longer associated with age at marriage. Instead, we see that height is associated with the likelihood of being married, with being in the bottom 20 % of heights associated with a 56.1 % decreased likelihood of being married, relative to being average height. We therefore conclude that height may be a gatekeeper for access to marriage, but it appears that other factors - likely related to the ability to set up an independent household - are more important in determining the timing of marriage for our research population.

Survival and sex composition of offspring: Individual-level responses in the quantum and tempo of childbearing during the demographic transition

Previous studies have documented varying fertility responses to childhood mortality and to the sex composition of the surviving offspring during the demographic transition. We contribute to this literature by applying a mixture cure model to reproductive histories of Estonian women born 1850-99. This model, unlike standard event history models, is capable of separating the effect of the covariates on the propensity of having another birth from their effect on its timing. Child fatalities, not having sons, and to a smaller extent, not having daughters, increased the propensity to have another child and decreased the interval to it. The response was stronger among later cohorts, but only with respect to parity progression. By contrast, the accelerated childbearing response diminished over time. Our findings suggest that behavioural responses in the quantum and tempo of childbearing can occur relatively independently.

Generalized parametric cure models for relative survival

Cure models are used in time-to-event analysis when not all individuals are expected to experience the event of interest, or when the survival of the considered individuals reaches the same level as the general population. These scenarios correspond to a plateau in the survival and relative survival function, respectively. The main parameters of interest in cure models are the proportion of individuals who are cured, termed the cure proportion, and the survival function of the uncured individuals. Although numerous cure models have been proposed in the statistical literature, there is no consensus on how to formulate these. We introduce a general parametric formulation of mixture cure models and a new class of cure models, termed latent cure models, together with a general estimation framework and software, which enable fitting of a wide range of different models. Through simulations, we assess the statistical properties of the models with respect to the cure proportion and the survival of the uncured individuals. Finally, we illustrate the models using survival data on colon cancer, which typically display a plateau in the relative survival. As demonstrated in the simulations, mixture cure models which are not guaranteed to be constant after a finite time point, tend to produce accurate estimates of the cure proportion and the survival of the uncured. However, these models are very unstable in certain cases due to identifiability issues, whereas LC models generally provide stable results at the price of more biased estimates.

Does broadband Internet affect fertility?

The spread of high-speed (broadband) Internet epitomizes the digital revolution. Using German panel data, we test whether the availability of broadband influences fertility choices in a low-fertility setting well known for the difficulty in combining work and family life. We exploit a strategy devised by Falck and colleagues to obtain causal estimates of the impact of broadband on fertility. We find positive effects of broadband availability on the fertility of highly educated women aged 25-45. We further confirm this result using county-level data on total fertility. We show that broadband access significantly increases the share of women reporting home- or part-time working. Furthermore, we find positive effects on time spent with children and overall life satisfaction. Our findings are consistent with the hypothesis that access to broadband allows highly educated women, but not the less educated, to reconcile career and motherhood, which may promote a 'digital divide' in fertility.

Estimation and identification issues in the promotion time cure model when the same covariates influence long- and short-term survival

The promotion time cure model is a survival model acknowledging that an unidentified proportion of subjects will never experience the event of interest whatever the duration of the follow-up. We focus our interest on the challenges raised by the strong posterior correlation between some of the regression parameters when the same covariates influence long- and short-term survival. Then, the regression parameters of shared covariates are strongly correlated with, in addition, identification issues when the maximum follow-up duration is insufficiently long to identify the cured fraction. We investigate how, despite this, plausible values for these parameters can be obtained in a computationally efficient way. The theoretical properties of our strategy will be investigated by simulation and illustrated on clinical data. Practical recommendations will also be made for the analysis of survival data known to include an unidentified cured fraction.

Nonparametric double additive cure survival models: An application to the estimation of the non-linear effect of age at first parenthood on fertility progression

This article introduces double additive models to describe the effect of continuous covariates in cure survival models, thereby relaxing the traditional linearity assumption in the two regression parts. This class of models extends the classical event history models when an unknown proportion of the population under study will never experience the event of interest. They are used on data from the German Socio-Economic Panel (GSOEP) to examine how age at first birth relates to the timing and quantum of fertility for given education levels of the respondents. It is shown that the conditional probability of having further children decreases with the mother's age at first birth. While the effect of age at first birth in the third birth's probability model is fairly linear, this is not the case for the second child with an accelerating decline detected for women that had their first kid beyond age 30.