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

Abstract

(ProQuest: ... denotes formulae omitted.)1.IntroductionEvent history models have a long tradition in demographic research. They represent a bridge between the classical life table methods and modern regression techniques (Hoem 1993). Unlike OLS regression, they are able to account for censoring and allow for a flexible specification of the baseline intensity and the integration of time-varying covariates into the analysis (Rizopoulos 2012). In fertility research, the most commonly used models are proportional hazard specifications, such as the piecewise exponential or the Cox model. Although they are widely used, these models have a serious shortcoming: They are unable to separate the impact of the covariates on the timing of births from the factors that influence the ultimate parity progression. As they cannot differentiate between timing and quantum, they often produce misleading results.An example of this shortcoming is that models which try to unravel the impact of female education on second and third birth progressions tend to generate confusing estimates. For western European countries, these models have often shown that highly educated women have relatively high second and third birth rates (Berinde 1999; Kravdal 2001; Kreyenfeld 2002; Olah 2003; Prskawetz and Zagaglia 2005; Gerster et al. 2007). There is, however, considerable ambivalence among demographers about how these results should be interpreted. A positive coefficient for a high level of education may indicate that highly educated women are more likely than less educated women to have a second or a third child. This is plausible, as a highly educated woman (or her partner) may be expected to have the earning power to afford a larger family. However, the results may also be indicative of differences in the timing of births among women of different educational levels. This is also a very plausible interpretation. As Ni Bhrolchain (1986) has suggested, a highly educated woman may space her births relatively closely together to minimize interruptions of her employment career. This 'work-accelerated childbearing' leads to narrow birth intervals among the highly educated, but these women do not necessarily have a greater likelihood of progressing to births of higher order. While this may be the case, conventional event history models are unable to provide an unambiguous answer to the question of whether highly educated women are more likely to progress to higher order births, or whether they simply space their births closer together than other women. Our paper addresses the call for more real-world justifications (Ni Bhrolchain 2011: 850) that show that it is worthwhile to separate the level and timing of fertility.Data for this analysis come from the German-Socio-Economic Panel for the years 1984-2013 (version 31.0). Event history models have shown that in Germany, as in most other western European countries, women with higher levels of education have elevated second and third birth rates (Huinink 1989; Kreyenfeld 2002). In this paper, we try to cast new light on these findings by employing cure survival models - and, more precisely, promotion time models - in the analysis of second- and third-birth fertility. Cure survival models are increasingly used in the statistical literature and in epidemiological studies. However, as Alter, Oris, and Tyurin (2007) have pointed out, these families of models are, surprisingly, rarely used in fertility studies. One of the first studies that applied cure survival models in the realm of fertility research was performed by Yamaguchi and Ferguson (1995), who studied the role of education in the transition to second and third births in the US. Their results suggested that the probability of having a second child was significantly greater for highly educated women than for less educated women, but that less educated women spaced their births closer together than highly educated women. Furthermore, highly educated women were found to be significantly more likely to have been 'cured' of a third pregnancy. …