Transitions to Second Birth and Birth Intervals in France and Spain: Time Squeeze or Social Norms?

: As ﬁ rst births are increasingly postponed across Europe, a strong two-child family norm persists. Past research has examined educational differentials in progressions to second birth, testing various hypotheses but overlooking normative aspects. Comparing fertility surveys from France and Spain, we explore whether late ﬁ rst-time mothers, who have fewer reproductive biological years left to conceive, accelerate the transition to a subsequent child (time squeeze effect). We also consider a normative dimension, i.e., whether women have their ﬁ rst child earlier or later than others in their educational and cohort groups. In both countries, among ﬁ rst-time mothers between 25 and 34 years of age, highly-educated women transitioned to second birth more frequently than less-educated women did. Within the same age group, highly-educated women in Spain had a second child more quickly after the ﬁ rstborn than their less educated counterparts did, while there is no such difference in France. These results hold after controlling for cohort effects, but are only partly explained by a time squeeze effect. Different normative ages at ﬁ rst birth by education and birth cohort explain the educational gap in the likelihood of transitioning to second birth, but not the birth intervals in Spain. In sum, our analysis demonstrates a persistent educational gap in second births in this country that cannot be reduced to biological or normative effects. This suggests that a broad range of economic constraints play a role, such as unfavourable individual economic conditions and lower levels of institutional support for parenthood.


Introduction
Family formation has been delayed in all of Europe, but large variations in total fertility rates persist across countries (Sobotka 2017). These differences depend on how much people delay their fi rst birth and how many children they ultimately have (Beaujouan et al. 2023;Frejka 2008). This has been studied in terms of completed fertility or by parity, with a growing interest in parity progression ratios (PPR) owing to the importance of higher-order births in explaining fertility levels (Brzozowska et al. 2022). In contexts where a two-child family norm is strong (Sobotka/Beaujouan 2014), countries' economic conditions, the friendliness of their institutions towards the family and their surrounding social norms are commonly evoked as factors for cross-country differences. In addition, once the fi rst birth is postponed, people may experience an ensuing time squeeze and respond by accelerating further births (Rendall et al. 2020). Hence, as people have children later in life, questions about the timing of subsequent births also arise. Educational differentials in the transition to second and third births have been identifi ed as crucial factors in analyses of fertility levels (Brzozowska et al. 2022;Klesment et al. 2014;Kreyenfeld 2002;Van Bavel/Różańska-Putek 2010). At the individual level, scholars have been interested in mechanisms that can explain why, in most countries, highly-educated women more commonly transition to another birth when the fi rst one is delayed. This line of research examines whether this phenomenon is explained by income (Baizán 2005), selection (Billari/Borgoni 2005) or partner effects (Kreyenfeld 2002). It has also been proposed that highly-educated women shorten the interval between the fi rst and second child to limit their time out of the labour market (Ekert-Jaffé et al. 2002;Köppen 2006;Ní Bhrolcháin 1986), while others argue that they accelerate the second birth to avoid biological limits after delaying the fi rst one (Castro 2015;Köppen 2006;Kreyenfeld 2002). Previous research also emphasises the role of normative aspects in explaining educational differences in family enlargement, although this remains less studied (Hoem 1996;Klesment et al. 2014;Van Bavel/Nitsche 2013;Van Bavel/Różańska-Putek 2010).
This paper examines the extent and pace with which women who entered motherhood at different ages transition to a second child in France and Spain. We do so by focusing on educational attainment and by taking into account changes across cohorts. We are particularly interested in individual mechanisms and therefore do not address the effect of population composition on countries' fertility levels, which has been studied elsewhere (Brzozowska et al. 2022;Lazzari et al. 2021;Zeman et al. 2018). We focus on two possible dimensions of age (Rennes 2019). The fi rst is chronological age, i.e., the number of years that have elapsed since a person was born, which also indicates when it may become more diffi cult for women to conceive since fecundity decreases with age. The second dimension is normative. The life course is organised into different stages, and social expectations around when transitions should occur vary across social groups and over time. In particular, age at fi rst birth follows very different patterns across educational and cohort groups (Ní Bhrolcháin /Beaujouan 2012;Rendall et al. 2005) and presumably refl ects differences in the appropriate timing of childbearing to which people adhere. We defi ne here a normative age based on the distribution of fi rst-birth schedules by women's characteristics, and we distinguish between whether women had their fi rst child very early, early, late, or very late compared to the other mothers in their educational and cohort group.
We fi rst examine age through its chronological dimension by asking whether educational differentials in progressions to second birth are associated with shorter birth intervals at later ages (time squeeze), especially among higher-educated women who tend to postpone entry into motherhood. Then, we explore whether differences in age standards at fi rst birth explain educational gaps in subsequent family behaviours, by country. Finally, we discuss alternative factors by examining whether higher educational degrees induce greater progressions to second birth and shorter birth intervals. This stems from an assumption according to which highly-educated women are better able to afford expenses related to a second birth and are motivated by return-to-work considerations.

2
Past research on second births in Europe

Postponement of fi rst births and parity progression to second births
The relationship between age at motherhood and completed cohort fertility has received growing attention regarding the extent to which higher-order births are foregone after postponing the fi rst child (Philipov 2017) because delaying entry into parenthood can lead to smaller families (Kohler et al. 2001;Tomkinson 2019). However, this can be offset if women catch up on the delayed entry into motherhood so that cohort completed fertility remains stable despite a rise in age at fi rst birth. This phenomenon, called "fertility recuperation," is also refl ected by the extent to which the decrease in cohort fertility rates at early ages is offset by the increase in fertility rates at later ages (Ciganda/Todd 2019;Goldstein et al. 2009). Evidence for recuperation has been found in some Nordic countries' cohorts born before 1970 (Andersson et al. 2009;Frejka/Calot 2001) and has been projected in France (Toulemon et al. 2008). Similar evidence has not been found in the United Kingdom (Berrington et al. 2015) or any Eastern European countries (Castro 2015). Furthermore, fertility recuperation can also be captured by observing fertility transitions at each parity (Frejka 2008: 201;Frejka/Sardon 2007;Toulemon et al. 2008). Research in some Western European contexts shows that the likelihood of transitioning to a second child declines from around the age of 25-30 at fi rst birth (Kreyenfeld 2002;Tomkinson 2019). However, a thorough examination of parity progression to a second child (PPR2) at different ages and in different contexts is lacking, despite the ongoing tendency to postpone fi rst births to late ages (Beaujouan/Sobotka 2019). Educational differentials in the transition to subsequent births are also crucial in understanding fertility levels across time and space (Brzozowska et al. 2022;Klesment et al. 2014;Kreyenfeld 2002;Van Bavel/Różańska-Putek 2010). Delayed fertility is a general trend among all population groups, but it is particularly prevalent among highly-educated women. This group is also more likely to catch up on delayed fi rst births when compared to their less educated peers, exhibiting higher or similar PPR2 (Klesment et al. 2014;Köppen 2006;Kreyenfeld 2002;Van Bavel/ Różańska-Putek 2010). To deepen our understanding of the patterns observed, we integrate the educational dimension into our study of progressions to second birth.

The selection of family-prone women into parenthood: preferences explaining educational differentials in PPR2
Selection is a primary explanation for why highly-educated mothers are more likely to further enlarge their families. The line of reasoning is that because childlessness rates increase with levels of education, highly-educated fi rst-time mothers may be particularly family-oriented (Kreyenfeld 2002). After having one child, these women may be more likely to continue enlarging their families until the desired size is achieved. Such "family proneness" is rarely measurable and therefore deduced from models that show evidence for selection effects. This has been supported by previous work on West Germany (Kreyenfeld 2002), Italy (Impicciatore/Zuanna 2017) and Norway (Kravdal 2001), but not on Spain, Hungary and Sweden (Bartus et al. 2013;Billari/Borgoni 2005). The lack of evidence for such an effect in some countries can refl ect the diffusion of family preferences towards two-child families among all female educational groups (Heiland et al. 2005;Testa 2014). Furthermore, because families are now relatively small, selection may particularly explain differences in third-birth rates (Brzozowska et al. 2022), as suggested for Austria (Prskawetz/ Zagaglia 2005). Arguably, selection can also be related to factors other than "family proneness," such as health conditions or personality traits.

Running out of time after the postponement of the fi rst birth?
Besides the probability of having a second child, the speed at which this happens is relevant to understanding patterns of family enlargement. An important question to be addressed is whether some of the women who delayed their fi rst birth accelerate the second to avoid having only one child. So far, birth-interval trends have been poorly documented in low fertility countries (Casterline/Odden 2016). For instance, some Eastern European countries have witnessed a lengthening of birth intervals over time (Rutstein 2011), while in other countries, family policies have contributed to shortening intervals between the fi rst and second birth (Berg/Rotkirch 2014;Miranda 2020;Štástná et al. 2020). To complement the study of parity progression ratios, we study birth intervals -defi ned as the time between the fi rst and the second birth among women who have had at least two children -by age at entering motherhood. At the macro level, fertility recuperation has also been described as "the action of compensating for the fewer reproductive years with higher fertility once motherhood begins" (Castro 2015: 276). Therefore, the inter-birth interval may infl uence the number of children achieved. Likewise, at the individual level, this process has been described as a "time squeeze" (Kreyenfeld 2002). Female fertility starts declining around a woman's thirties and accelerates around age 35 (Dunson et al. 2002). Age-specifi c infertility is generally considered to be stable over time and across countries (Menken 1985;Smarr et al. 2017). Consequently, one could expect women who become mothers at age 30 or older to progress to second birth more quickly because they are more constrained by age to achieve their desired family size (Rendall et al. 2020), especially in contexts with a strong two-child family norm (Sobotka/Beaujouan 2014). This mechanism is also expected to apply to highly-educated women, who tend to postpone fi rst motherhood. This "time squeeze" effect has, however, not been found in previous work on Hungary (Bartus et al. 2013), Germany (Bremhorst et al. 2016) and Denmark (Gerster et al. 2007). Conversely, it does hold for Italy, where highly-educated women have a second child more quickly than their lower-educated peers, especially among fi rst-time mothers above age 30 (Impicciatore/Zuanna 2017). In sum, the timing of second births differs by educational attainment, but whether highly or lower-educated women enlarge their families more quickly depends on the context (Matysiak/ Vignoli 2019). Therefore, a study of birth intervals by age at fi rst birth and level of education in two very different contexts may provide insights into this relationship.

Differences in the "proper timing" of fi rst births by education and birth cohort
Although biological factors infl uence fertility decisions, having a second child and having it more quickly after a late fi rstborn are not solely related to fecundity. Some scholars have shown the role that social rather than biological aspects play in fertility behaviours. For instance, in Sweden, school starts in late August and ends in June the following year, therefore women who graduated in one educational cohort are not all the same age. In this setting, Skirbekk et al. (2004) showed that mothers' fertility patterns followed those of their educational peers more closely than those of their birth cohort, confi rming the importance of social age (Skirbekk et al. 2004).
There is also evidence that social age norms, such as the common perception of what the ideal age at fi rst birth is, are correlated with cross-national differences in the progression to second birth. Transitions to second birth are more frequent in normative contexts where perceptions of the "proper timing" of parenthood are at higher ages (Van Bavel/Nitsche 2013) or when fi rst births occur in an age range close to what is seen as "normal" at the society level (Van Bavel/Różańska-Putek 2010). At the individual level, it is also crucial to consider normative dimensions when analysing educational differentials in family enlargement, for instance by looking at a woman's age at fi rst birth relative to the fi rst birth schedule of mothers in her educational group (Hoem 1996;Köppen 2006). For instance, having a fi rst birth at age 30 may have a different meaning from one group to another -presumably being perceived as "late" by lower-educated women and more "normal" by higher-educated women. As actual behaviours to some extent refl ect age norms, the relative age at fi rst birth may capture normative aspects. For example, the average perceived ideal age at fi rst birth is higher in Spain than in France, as is the average age at fi rst birth (Liefbroer/Merz 2009). In addition, as births are increasingly postponed, societal perceptions of the ideal age at fi rst birth have also shifted towards later ages over time (Seiz et al. 2022;Lazzari et al. 2022). Hence, we investigate the role of norms in educational differences in second-birth behaviours by considering a woman's age at fi rst birth relative to the prevailing fi rst-birth schedule within her educational and cohort group.

Economic factors explaining the link between education and fertility: opportunity costs, income, and partner characteristics
Microeconomics also provides interpretations for educational differences in second births. While high opportunity costs theoretically explain fi rst-birth postponement, highly-educated women are also likely to earn more -a fact that may explain why they are more likely to have a second child after the postponement of motherhood.
As regards the timing of second births, shorter intervals after the fi rst birth can be related to return-to-work motivations to limit time spent outside the labour market (Ekert-Jaffé et al. 2002;Köppen 2006;Ní Bhrolcháin 1986). Context may also reinforce educational differences in second-birth behaviours. Patterns of recuperation related to completed fertility have been found for both higher-and lower-educated women in the Nordic countries (Andersson et al. 2009), while differentials in second-birth schedules and progressions are more pronounced in Britain (Berrington et al. 2015). In Western Europe, higher-educated women end up having as many children as the medium-educated group despite delaying entry into motherhood, but still fewer than their lowest-educated counterparts (Klesment et al. 2014). These cross-national variations in educational gap magnitude are often explained by different institutional contexts which can ease the work and family life balance, such as the availability of childcare services and family policies (Klesment et al. 2014; Van Bavel/Różańska-Putek 2010). The role of partners' characteristics has also been increasingly explored by focusing on educational status and couples' homogamy or heterogamy (Nitsche et al. 2018). Following the line of reasoning that people with more economic resources are more likely to transition to second birth, highly-educated women may be more likely to enlarge their family after postponing motherhood because they tend to be partnered with men of the same educational group (Klesment et al. 2014;Kreyenfeld 2002). However, the infl uence of male partners' education varies between contexts (Trimarchi/Van Bavel 2020). Evidence for such an infl uence has been found in West Germany (Köppen 2006;Kreyenfeld 2002) and Austria (Prskawetz/Zagaglia 2007), but not in France (Köppen 2006), Hungary (Bartus et al. 2013), Spain (Bueno/García-Román 2021) or Denmark (Gerster et al. 2007). Finally, although less explored, the partner's age may also play a role, as women who enter motherhood at late ages tend to have a fi rst child with men their age or younger (Compans 2021;Dudel et al. 2020).
Analyses of the quantum and tempo of second births often test a limited number of mechanisms. Here, we disentangle age and educational differences in transitions to second birth and the intervals between fi rst and second birth. Examinations of the infl uence of normative factors on second births have also remained scarce, hence we probe this question by looking at age at fi rst birth relative to women's educational group and birth cohort. By doing so, we investigate to what extent biological factors explain second-birth acceleration and educational differentials at later ages (30 years old and above), or whether they can be challenged by other aspects. We focus on two national contexts, France, and Spain. In the following section, we describe aspects of these countries' fertility regimes relevant to understanding second birth trends.

3
France and Spain: distinct fertility regimes but similar cultural features

France: exceptionally high fertility levels
In France, birth rates before age 25 decreased substantially throughout the 1980s and 1990s (Toulemon et al. 2008). As a result, teenage births became rare -around 2 percent of mothers in the early-1970s cohort had their fi rst child during adolescence (Tomkinson 2019). Fertility in women's thirties has increased accordingly, along with late fertility rates (40+) now close to the European average (Beaujouan/Sobotka 2019). This delay is partly driven by education extension because births occurring while studying are rare, at less than 5 percent (Ní Bhrolcháin/Beaujouan 2012;

Régnier-Loilier 2016).
France is an unusual case among Western European countries, as fertility levels remained close to two children per woman in the past decades despite the postponement of fi rst births (Mazuy et al. 2015;Toulemon et al. 2008). This suggests that fertility postponement and fertility levels developed relatively independently of each other. A long tradition of pronatalist family policies within a generous welfare state explains these comparatively high fertility levels and small educational gaps in fertility behaviours (Toulemon et al. 2008). For instance, maternity leave allowances and family benefi ts can infl uence fi rst and higher-order births. Formal childcare is also widely available and used. In the early 2000s, enrolment rates in formal childcare among children under three years old was 43 percent, higher than the OECD average of 30 percent (OECD 2008). Such policies decrease the opportunity costs associated with having children, especially for highly-educated groups (Van Bavel/Różańska-Putek 2010) and allow women to achieve a more manageable work and family balance. French mothers return to work quickly after birth and often continue working full-time when having young children (Pailhé/Solaz 2006). In the 1990s and 2000s, 65 percent of the active female population were working mothers with children younger than 15 (Beaujouan/Berghammer 2019). The female load of parental and household tasks in France is close to the European average (Aliaga 2006) and the gap between men and women has decreased since the mid-1980s (Champagne et al. 2015).
Moreover, while the two-child family norm is strong (Frejka 2008;Frejka/Sardon 2007;Sobotka/Beaujouan 2014), large families (at least three children) are perceived as an ideal for many people (Ruckdeschel et al. 2018;Sobotka/Beaujouan 2014). Regarding the proper timing for childbearing, in 2006, the average ideal age for fi rst motherhood was slightly above 25 years and the average perceived age deadline for motherhood was 42 years (Liefbroer/Merz 2009).
Hence, in this economic, institutional, and normative context, progressions to second birth are relatively more common than in other Western European countries such as the United Kingdom (Tomkinson 2019) and Southern European countries such as Spain (Frejka 2008).

Spain: strong postponement of births and lowest-low fertility
The postponement of births has been particularly substantial in Spain (Castro Martín/Martín García 2016). While early motherhood has become very rare, this country exhibits one of the highest shares of births occurring over the maternal age of 40 among European countries (6.1 percent; Beaujouan/Sobotka 2019). In line with actual fertility behaviours, perceptions of the normative window for parenthood in 2006 also correspond to higher ages in comparison to France -close to 28 years for the ideal age at fi rst motherhood and 43 years on average for the age limit for female childbearing (Liefbroer/Merz 2009). In contrast to the French context, this substantial postponement has been associated with lowest-low fertility levels, down to 1.3 children per woman in the 1990s (Kohler et al. 2002). This is also visible in the decline in cohort completed fertility (Esteve et al. 2016). This trend is paralleled by the decrease in the desired number of children (Delgado et al. 2008) converging into a two-child family norm (Sobotka/Beaujouan 2014).
This dramatic decline in fertility occurred concurrently with changes in the labour market -unemployment rose tremendously from the 1980s, affecting young people in particular (Adserà 2011b/a;Delgado et al. 2008) -and was combined with a lack of family policies to reconcile motherhood and labour force participation (Esping-Andersen 2009). Indeed, Spain is a familistic welfare state that provides little childcare support. This can partly be explained by cultural norms. Motherhood is mainly seen as a private matter in which the state should not intervene (Alvarez/ Marre 2022), resulting in a reliance on informal childcare by grandparents or other family members (Rutigliano 2020). As a result, preschool enrolment rates are close to the OECD average, but below those observed in France (OECD 2008). Employment rates among women are also much lower compared to France -only 49 percent in 2000-04 (Beaujouan/Berghammer 2019). In the private sphere, the sharing of household tasks remains gendered, which affects women's fertility intentions (Suero 2023). However, the country has progressed into the Second Demographic Transition as far as its neighbouring European countries have (Sobotka 2008). For instance, attitudes are now quite favourable towards "non-traditional" family behaviours such as cohabitation or divorce (Seiz et al. 2022).
Because the economic and policy landscape in Spain has made it diffi cult to seamlessly combine family life and work, highly-educated women still show lower completed fertility than their less-educated counterparts (Klesment et al. 2014). Here, delays in fi rst births seem to have a causal effect on fertility decline and are accompanied by fewer transitions to second birth (Billari/Borgoni 2005;Brodmann et al. 2007). In line with this, previous research has shown an absence of any sign of recuperation (Delgado et al. 2008) and a persistent educational gap in fertility (Requena 2022).
In summary, progression to a second child is less common for women in Spain than in France (Klesment et al. 2014), which may be attributed to the two countries' very different economic and welfare conditions. Despite this, both countries share common cultural traits, such as the two-child family norm. Fertility intentions are more often unmet in Spain than in France, as there seems to be more of a confl ict between fertility desires and the economic context (Beaujouan/Berghammer 2019;Castro-Martín/Martín-García 2016). There is also a negative educational gradient in transitions to second birth, which does not hold after controlling for age at fi rst birth in both countries (Klesment et al. 2014;Matysiak/Vignoli 2019); while information on educational gradients in fi rst and second childbirth intervals is lacking for both countries. By comparing France and Spain's second birth transitions and birth intervals along two dimensions of age (chronological and normative) and educational attainment, we provide new insights into how family enlargement patterns differ within these countries.

Research question and hypotheses
This paper examines, in France and Spain, the extent to which women who become mothers at different ages transition to second birth, at which pace they do so and how this varies by educational attainment. The time squeeze effect posits that later fi rst-time mothers speed up the transition to the second child in anticipation of greater biological constraints with age. Accordingly, we formulate the following hypotheses: 1a. Among mothers with at least two children, we expect women who delayed family formation to have transitioned to second birth more quickly after the fi rstborn. 1b. Assuming that biological constraints remain the same in France and Spain for women born between 1935 and 1974, we expect this time squeeze to be similar across countries and to hold after accounting for cohort effects. 1c. As highly-educated women are more likely to postpone a fi rst birth, at later reproductive ages, we expect them to have a second child more often and more quickly than women of other educational groups.
Rather than biological concerns, the pace and extent of family building may also be driven by the prevalent fertility schedules within one's group, which differ depending on women's characteristics. To test whether this normative dimension of age explains educational differences in family enlargement, we examine transitions to second birth by comparing a woman's age at entry into motherhood with the distribution of fi rst-birth schedules within her educational and cohort group. With this indicator of fi rst birth timing relative to group membership, we formulate the following: 2. If the normative dimension of age holds more explanatory power than chronological age, we would expect there to be no educational differential in second births by relative age at fi rst birth. This would indicate that women of different characteristics behave the same way when they conform or deviate from the standard within their group.  de Fecundidad, INE, 1985, 1999 with observations of women born between 1935 and 1974. These samples were obtained after excluding 203 and 186 multiple fi rst births for France and Spain, respectively. The French survey is conducted about every ten years in conjunction with the census, in a self-completed questionnaire that includes fertility histories. Despite an underestimation of the total number of children across cohorts in the 2011 survey, the quality is good as regards parity distribution (Brée 2017 . Therefore, most women are considered to have reached the end of their reproductive life. However, since some of them may have had a second birth after being surveyed, we discuss possible biases which may exist in the paper. We conduct analyses on different subsamples depending on the birth parity studied. Educational groups are defi ned according to the level attained at the time of the survey and divided into three groups. 2 Following the ISCED classifi cation, a low degree corresponds to no schooling, primary education, and lower secondary education. The medium group comprises upper secondary education and vocational training, while the highest levels include university graduates (Table 1) The degree was not necessarily acquired before the fi rst birth, particularly for the highlyeducated mothers who had a child before age 25. Therefore, it is possible that their studies infl uenced the timing and occurrence of the second birth.

Data and measures
Age at fi rst birth is defi ned in two different ways: in absolute and relative terms. While the fi rst can refl ect a time squeeze effect after a late birth, the second is an indicator of deviation from (or conformity to) the norm in fi rst-birth behaviour within an individual's cohort or educational group. It is computed by comparing the age at which a woman had her fi rst child with the distribution of age at fi rst birth in her educational group and birth cohort, by country. We distinguish between "very early" (below the 25 th percentile, i.e., the ages at which 25 percent of women become mothers), "early" (between P25 and P50), "late" (between P50 and P75) and "very late" fi rst-time mothers (above the 75 th percentile). Note that "very late" births refer to fi rst-time mothers of 30 years old or older for highly-educated women and even to those above age 35 among the most recent cohorts of women in Spain (Table A1). Thus, this category illustrates not only normative aspects of age but also biological ones, since fecundity declines from women's thirties onwards. These cutoffs are also above 30 years old for the medium and lower-educated groups from the 1960s cohort in Spain, but are below 30 for lower-educated women in France.

Methods
First, we report descriptive statistics by education. Our main focus is on parity progression ratios to second births (PPR2), computed as the ratio between the number of women with two children and the number of women with at least one child, generally by age 42 depending on the birth cohort (see above). We also focus on the number of years between the fi rst and second birth, examining closed intervals (Casterline/Odden 2016). Conditional on having at least two children by the end of the reproductive life, birth intervals between the fi rst and second child (BI2) are the differences between each child's birthdate (computed in months, shown in years). We calculate the median age interval within each observed group (e.g., by educational level).
Past research often focused on the occurrence of births after the fi rstborn using event-history models, which combine the analysis of the tempo and the event of  (2011) and Spanish Fertility surveys (1989,1999,2018) using survey weights.
More recently, some studies have used cure models, which allow for the estimation of the share of people who have not experienced a second birth when analysing transition rates (Bremhorst et al. 2019;Matysiak/Vignoli 2019). Instead, we separate the analysis of transition occurrences from that of the timing of second births. This is made possible by examining the birth cohorts of women who are considered to have completed their fertility (these are the same cohorts used in the descriptive analysis): there is no censoring, and we know whether the second birth took place or not. Regarding fertility levels, we estimate the probability of having a second birth through logit models. These models are run among mothers with at least one child (n=120,946 for France, after excluding 7,174 observations due to missing values, and 10,247 minus two observations for Spain). For the analysis of second birth timing after entering motherhood, we use lognormal durations models. Assuming a non-monotonic hazard distribution, they are suitable to estimate duration to the next birth when hazards decrease over time (which is the case for second births) and show good statistical fi t compared to other model specifi cations. We focus on women who have had at least two children by the end of their reproductive life, so the produced estimates refl ect the timing of second births only, not their occurrence. We calculate predicted median birth intervals based on the estimates of the models. The lognormal models were run among a subsample of 92,213 French mothers with at least two children (after excluding 7,511 observations with missing values) and among 7,927 Spanish mothers (after excluding 30 observations with missing values). 3 In all models, we control for the birth cohort and allow the infl uence of age at fi rst birth to vary by level of education, including interaction terms. Finally, we produce a second set of estimates using relative age instead of chronological age.

Differences in occurrence and timing of second birth by age at fi rst birth and education
Before breaking down the analysis by age at fi rst birth, we describe, at the macro level, the different intensities and paces at which educational groups transitioned to motherhood and enlarged their families in France and Spain. We only describe statistically signifi cant results (signifi cance level of 5 percent). For all cohorts , transitions to fi rst birth decrease with the level of education, with a more signifi cant differential in Spain than in France ( Table 2). The higher the woman's degree, the later the fi rst birth is on average. Within the same educational groups, women in Spain postponed fi rst births more than women in France did; this was especially the case for highly-educated women (30.9 vs 28.3 years old on average).
3 Additional analyses including further covariates were conducted when the information was available in the French survey (country of birth, professional category of the respondent's father) and with relevant variables depending on those available in each Spanish fertility survey. Including these controls do not change the education, age at fi rst birth and cohort results substantially.
Among those who did become mothers, lower-educated women in France exhibited the highest progression ratio to a second child (8 out of 10 mothers). For women with medium and high educational attainment, the ratio is lower, but similar between the two groups (0.76-0.77), despite the large educational variations in the fi rst birth schedule. The median birth interval (BI2) was slightly shorter among low-educated women (under three years) than for other groups, but differences by educational degree were slight in France. Conversely, in Spain, transitions to second birth decreased more clearly with the level of education (from 0.79 to 0.70 between the ends of the educational scale). Highly-educated women had a second child more quickly after the fi rstborn than other groups did (though only signifi cant compared to the medium educated). All in all, the relationship between second birth progressions and birth intervals is not straightforward. For instance, fewer highly-educated women in Spain transitioned to second birth, even though they did so more quickly than the other groups. This may be explained by this group's much higher mean age at fi rst birth. To better understand this, we examine women according to their educational level and age at entry into motherhood.

A time squeeze effect?
The top panel of Figure 1 reports predicted probabilities of transitions to second birth and their confi dence intervals, estimated with logit models that include an interaction between age at fi rstborn and level of education, controlling for women's birth cohorts. Progressions to second birth decrease substantially with age for both countries. In France and Spain, young and highly-educated fi rst-time mothers (<25 years) progress to second birth as often as their lower-educated counterparts of the same age at fi rst motherhood do. Between 25 and 34 years old, highly-

Tab. 2:
Levels and timing of progressions to fi rst and second birth by women's educational level in France and Spain ( 146,555 120,946 120,946 92,213 12,451 10,247 10,247 7,927 Note: PPR refers to parity progression ratios to fi rst (PPR1) and second birth (PPR2). MAB1 is the mean age at fi rst birth. BI2 are birth intervals between the fi rst and second births. Source: own calculation based on the French Family and Housing survey (2011) and Spanish Fertility surveys (1989,1999,2018) using survey weights.
educated women are more likely to enlarge their families, while PPR2 are similar between medium and lower-educated groups. In Spain, PPR2 are also higher for higher-educated women after a late fi rstborn (35+), but this result is not signifi cant due to the small sample size (Fig. 1b). The higher PPR2 at most ages for the most qualifi ed group explain why, when controlling for age at fi rst birth in both countries, higher-educated women are more likely to transition to second birth than those with medium educational attainment (see the estimates for second birth occurrence in Table A2 in the Appendix). Despite similar graphs for France and Spain in Figure 1, the age compositions of mothers in the two countries differ, leading to various aggregate fertility outcomes as shown in Table 2.
In France, the median birth interval curves shown in the bottom panel of Figure 1 display a similar BI2 between women with different educational levels. This is after a fi rst birth occurred between 25 and 34 years (Fig. 1c). 4 Longer birth intervals among medium and highly-educated women at young ages can be explained by fi rst births occurring during schooling or entry into the labour market, prompting a second birth postponement. At later ages, the median birth interval is considerably shorter than for younger fi rst-time mothers and equal across groups. This may refl ect the similar effect biological limits have in constraining fertility, regardless of the educational degree. By combining the analysis of PPR2 and BI2 in France, we fi nd that second birth timing is more determined by age at fi rst birth than by the level of education. That is, the time squeeze hypothesis does not explain why highly-educated women in France demonstrate a higher PPR2 between ages 25 and 34, since they do not have their second child faster than other groups do.
In Spain, the picture is different -highly-educated women exhibit shorter birth intervals between the fi rst and second child than their counterparts in any age group do, except for those who became mothers before age 25 (Fig. 1d). 5 Faster family enlargement among highly-educated mothers may explain why they exhibit higher PPR2 than lower-educated women. However, at age 25-29, women are not yet constrained by biological limits. Thus, this correspondence between shorter birth intervals and larger transitions to second birth cannot be entirely attributed to a time squeeze effect.
On the whole, in both countries, women over 30 and even more so over 35 years old at fi rst birth have a second child less frequently. However, when they do, they progress to second birth more quickly than other age groups do. The comparison with men lends support for an interpretation of these fi ndings partly in biological terms (see Appendix A3): compared to later fi rst-time fathers, later fi rsttime mothers either have an only child or accelerate the second birth. In summary, the time squeeze hypothesis helps us understand the variations in progressions to second birth by age at fi rstborn. At the same time, biological constraints do not fully 4 See estimates without interaction in Table A3. 5 There are also strong cohort effects on BI2 in Spain, which are detailed in Appendix 4. Birth intervals increased signifi cantly between women born in 1935 and 1974, especially if the fi rst birth took place at a young age. explain the differences by education. Indeed, in France, education and second birth timing seem disconnected (since patterns by education are different between PPR2 and BI2), while in Spain, higher PPR2 is associated with faster second births but this is not specifi c to late ages.

A refl ection of various norms in fi rst-birth schedules?
Next, we explore age from a normative perspective by estimating the level and timing of second births using ages relative to women's membership in educational groups and birth cohorts. This indicator allows us to examine family enlargement Fig. 1: Predicted progressions to second birth and median intervals between the fi rst and second birth (with confi dence intervals) by chronological age at fi rst child and education in France and Spain Note: Predicted progressions to second birth are estimated with logit models and median BI2 with lognormal duration models. Models control for cohort effects. Results are shown here for the 1950-59 cohort (reference level). They are displayed with confi dence intervals (95%) in grey, which are small for France due to the large sample size. The full models can be found in Tables A2 and A3 in the Appendix. Source: own calculation based on the French Family and Housing survey (2011) and Spanish Fertility surveys (1989,1999,2018). age at first birth median birth interval (years) education high medium low behaviours depending on whether women were deviating from or conforming to the prevailing fi rst-birth schedule within their group.
Switching to relative ages in lieu of chronological age cancels out educational differentials in the occurrence of second births in both countries ( Fig. 2a and 2b). For all educational groups, progressions to second birth decrease slightly between very early and late relative ages at fi rst birth -a less pronounced curve than with absolute age at fi rst birth -and decrease sharply from very late ages only. 6 6 We can note that, among very late mothers at fi rst birth, low-educated women show higher PPR2 ( Fig. 2a and b, though not statistically signifi cant for Spain because of the sample size). This may be explained by the lower age limits for this group (below age 30 in France) compared to highly or medium-educated women (Table A2).

Fig. 2:
Predicted progressions to second birth and median birth intervals between the fi rst and second birth (with confi dence intervals) by relative age at fi rst child and education in France and Spain Note: Predicted progressions to second birth are estimated using logit models and median BI2 with lognormal duration models. Models control for cohort effects. Results are shown here for the 1950-59 cohort (reference level). They are displayed with confi dence intervals (95%) in grey, which are small for France due to the large sample size. Source: own calculation based on the French Family and Housing survey (2011) and Spanish Fertility surveys (1989,1999,2018 Turning to birth intervals (bottom panel of Fig. 2), medium-educated women in France take slightly more time than the other groups to enlarge their families (Fig. 2c). In Spain, despite the lack of an educational gap in PPR2 by relative age, highly-educated women have second births more quickly than their less-educated counterparts in each age group, except for the very early one (Fig. 2d).
Birth intervals across relative age groups are also rather stable within each educational level, suggesting that the timing of a second child is barely infl uenced by the normative dimension of age within one's group. For instance, having a fi rst birth at 27 can be considered late for medium-educated women and close to the norm for highly-educated women ( Table 2), but deviation or conformity to this norm does not infl uence the timing of the second birth strongly (Fig. 2). Notably, the fact that very early fi rst-time mothers do not tend to accelerate their second births suggests that they are not, as a group, more prone to family enlargement (with the exception of low-educated women in France who show slightly shorter birth intervals than their educational counterparts). It is only at very late ages that mothers from all educational groups have second births more quickly, a behaviour that possibly derives from both biological and normative pressures.

Conclusion and discussion
Through a thorough exploration of second birth occurrence and timing among the 1935-74 cohorts in France and Spain, we found that, at most reproductive ages, highly-educated mothers are more likely to have a second child than other groups are. To explain variations by age at fi rst birth and education, we found evidence for the two hypotheses we tested: an age-related time squeeze and the normative infl uence of age. First, as age at fi rst birth increases, there is a parallel decrease in the occurrence of second births and shortening in birth intervals in both countries, which can be interpreted as a time squeeze effect. Especially for those entering motherhood at or above age 35, the shorter birth intervals we observe seem to refl ect a phenomenon in which mothers enlarge their family before it is "too late" by having a second child within a short timeframe. Biological age effects on women's family enlargement are also visible in the comparison with men's fertility (which is less constrained by a decline in fecundity) since late fi rst-time fathers had second births more often and less quickly than late fi rst-time mothers. Furthermore, we showed that the time squeeze is visible in all educational groups, but because highly-educated women tend to have their fi rst child later, the decrease with age in second birth progressions and birth intervals between the fi rst and second child explains some of the educational differences in the aggregate indicators. However, this time squeeze effect does not explain why the highly educated in Spain accelerated the transition to a second child even before age becomes a biological constraint.
Next, we made alternative use of age-at-fi rst birth data by exploring the infl uence of differences in norms between groups on fertility enlargement. Previous work highlights the importance of cultural factors in shaping transitions to second birth (Hoem 1996;Van Bavel/Nitsche 2013;Van Bavel/Różańska-Putek 2010). We considered age a factor that may prevent or encourage women to enlarge their family more or less quickly, depending on the distribution of age at fi rst birth in their educational group and birth cohort. Of fi rst note is that cultural and biological dimensions of age are linked. This link is particularly visible in the "very late fi rst-time mother" category. Findings support the idea that age norms may be turning more fl uid (Lazzari et al. 2022), as early or late fi rst-time mothers do not show substantially different behaviours related to family enlargement. More interestingly, we show that, for both countries, differences in fi rst-birth schedule standards explain the educational gap in second birth progressions. However, like the time squeeze effect, the relative dimension of age is insuffi cient to explain faster transitions to second birth among highly-educated women in Spain.
These conclusions leave room for alternative explanations. It has been assumed that second birth transitions among higher-educated mothers can be explained by a greater family proneness when compared to childless peers (Kreyenfeld 2002). However, there is little support for this selection hypothesis in our analysis and the literature (Bartus et al. 2013;Billari/Borgoni 2005), and selection effects may be more apparent while observing third birth dynamics (Brzozowska et al. 2022).
It can also be expected that, at the same age at fi rst birth, highly-educated women would be more likely to have a second child than less-educated women for fi nancial (because they can better afford to raise an additional child) or work-related reasons (to reduce cumulative time outside the labour market). Such economic factors can also interact with the partner's educational level, a relationship we did not explore here. However, previous work has found no evidence for a partner effect in France (Köppen 2006) and Spain (Bueno/García-Román 2021). Nonetheless, data on women's income or employment pathways or that of their partners would be useful in refi ning the analysis (Baizán 2005). Information on the motivations behind long or short birth intervals would also bring valuable insights.
Finally, fi ndings in Spain suggest that women with a high level of education more often overcome normative and biological barriers to family enlargement by quickly transitioning to second birth. Such an education effect is not found in France, and this could be explained if, in general, fertility decisions are more constrained in Spain than in France. Cross-country variations in family enlargement are often attributed to differences in family policies and economic factors. Compared to France, childcare is less institutionalised and generous in Spain (Delgado et al. 2008), a country where labour market uncertainty has persisted for decades (Adserà 2011a; Bueno/Brinton 2019). Therefore, highly-educated Spanish women may wait to start a family until their professional goals are achieved to limit time spent outside the labour market in order to secure higher salaries and greater stability (Dueñas et al. 2017). After delaying childbearing, they likely fi nd themselves in a better fi nancial position than their lower-educated counterparts and are therefore able to transition to second birth more quickly. All in all, economic factors seem to signifi cantly infl uence family enlargement in Spain more than in France, which could explain the greater educational gap. In addition, as labour conditions among young people in Spain are more uncertain than in France, unemployment rates are particularly high. This could explain why birth intervals for young fi rst-time mothers rose more substantially across cohorts in Spain than in France. In Spain, in addition to improving the reconciliation of work and family, implementing public policies aimed to reduce job precarity may make it more feasible to transition to a second child, especially for women with low levels of education. Such conclusions are in line with recent work on low fertility levels in this country, calling for policies that not only target family behaviours but also increase social equality in education and labour market conditions (Elizalde-San Miguel et al. 2023 Source: own calculation based on the French Family and Housing survey (2011) and Spanish Fertility surveys (1989,1999,2018).

Appendix 3: Comparison between male and female fertility
Family enlargement is often studied by observing female fertility, as data on male fertility by parity are scarcer. One might expect time squeeze effects to have less of an infl uence on fathers' likelihood to progress to second birth than on mothers' because men are less biologically constrained by age when conceiving. The survey data we use allow for some comparison between women's and men's fertility. For France, this analysis was conducted using the same cohorts as those used for women (1935-74, n=74,822 men after excluding multiple fi rst births). For Spain, data on male fertility are only available in the 2018 Spanish Fertility survey (n=1,025). While the comparison to women's fertility is possible, among the cohorts of interest the sample size is too limited to obtain signifi cant results by both men's education and age at fi rst fatherhood. Since men meet fewer biological barriers to conception than women, we expect more transitions to second birth and later completed fertility among fathers than mothers. Indeed, men have a higher probability than women of enlarging their family to two children, and this gender gap increases after age 30 (Fig. A1a). Results (not shown) do not differ by education. Among late-fi rst-time parents, men also tend to have a second child within later and longer timeframes than women (Fig. A1b). Results are similar in both countries, although with large confi dence intervals for Spain due to the small sample size (Fig. A1c and A1d).
In turn, differences in late fertility behaviours by sex provide evidence for a biological age effect on female family enlargement.  Predicted progressions to second birth and median birth intervals between the fi rst and second birth (with confi dence intervals) by age at fi rst child and sex in France and Spain Note: Progressions to second birth are estimated using logit models and median birth intervals with lognormal duration models. They are shown for women and men with medium educational attainment and for the cohort 1950-59 for France, and 1965-69 for Spain (reference levels). They are displayed with confi dence intervals (95%) in grey, which are small for France due to the large sample size. Source: own calculation based on the French Family and Housing survey (2011) and Spanish Fertility surveys (1989,1999,2018).