## Abstract

Research has indicated that fertility spreads through social networks and attributed this phenomenon to social interaction effects. It remains unclear, however, whether the findings of previous studies reflect the direct influence of network partners or contextual and selection factors, such as shared environment and common background characteristics. The present study uses instrumental variables to improve the identification of social interaction effects on fertility. Using data from the System of social statistical data sets (SSD) of Statistics Netherlands, we identify two networks—the network of colleagues at the workplace and the network of siblings in the family—to examine the influence of network partners on individual fertility decisions. Discrete-time event-history models with random effects provide evidence for social interaction effects, showing that colleagues’ and siblings’ fertility have direct consequences for an individual’s fertility. Moreover, colleague effects are concentrated in female-female interactions, and women are more strongly influenced by their siblings, regardless of siblings’ gender. These results are the first to demonstrate spillover effects across network boundaries, suggesting that fertility effects accumulate through social ties not only within but also across different domains of interaction.

## Introduction

Recent studies have suggested that individual fertility behavior is profoundly influenced by network partners. This literature has focused on networks, such as siblings (Cools and Kaldager 2017; Kotte and Ludwig 2011; Kuziemko 2006; Lyngstad and Prskawetz 2010), colleagues (Asphjell et al. 2013; Ciliberto et al. 2016; Pink et al. 2014), and friends (Balbo and Barban 2014). Most findings have indicated that the fertility behavior of interaction partners in these networks is positively correlated (e.g., Balbo and Barban 2014; Lyngstad and Prskawetz 2010; Pink et al. 2014). These findings support interaction theories, suggesting that mechanisms such as social learning and social pressure lead to a contagious spread of fertility through social networks.

It is not clear, however, whether the effects documented in previous research reflect the direct influence of network partners or contextual and selection factors, such as shared environment and common background characteristics. Social contacts considered in previous studies (i.e., siblings, colleagues, and friends) are similar in various factors associated with fertility. Although analysts have included controls for some of these factors, important determinants of fertility—such as family norms, neighborhood characteristics, or workplace policies—are often unobserved in survey data or register data. Despite their merits, extant studies still leave the possibility that the associations found are due to contextual factors rather than the direct influence of network partners.

Understanding the direct influence of network partners on fertility is important because social interaction effects trigger social multipliers, whereas contextual effects do not (Manski 1993). If individuals’ behaviors are influenced by contextual factors, it is not clear whether their actions also have consequences for others. In the presence of social interaction effects,1 however, influential behaviors of network partners may lead to chain reactions and thus spill over to other domain-specific networks. For instance, a colleague’s transition to parenthood may influence an individual’s fertility decision, which in turn may influence a sibling’s fertility. In the presence of such spillover effects, small differences in initial conditions can lead to large differences between groups as the effects of individual fertility accumulate through social ties (Montgomery and Casterline 1996).

This study provides new empirical evidence on social interaction effects and social spillover effects on fertility. Our main contribution is twofold. First, we use instrumental variables to improve the identification of social interaction effects and to distinguish social interaction effects from contextual effects and selection effects. Second, we offer the first direct test for social spillover effects, considering two central domains that previous research has identified as important contexts for social interaction effects on fertility: the family and the workplace. Our data include information about social ties not only within but also between both domains, allowing us to examine social spillover effects and chain reactions in fertility spreading from one domain to the other. On the basis of these data, we addressed three questions. First, do colleagues influence each other’s fertility decisions? Second, do siblings influence each other’s fertility decisions? Third, if direct social interaction effects exist, do they lead to social spillover effects?

To disentangle social interaction effects from contextual and selection effects, we used an instrumental variable design. To assess colleague effects on fertility, we used information on the fertility of colleagues’ siblings as an instrument. Specifically, we examined the impact of colleagues’ siblings’ fertility on a focal person’s transition to parenthood. Conversely, we used siblings’ colleagues’ fertility as an instrument to identify sibling effects on fertility. The key idea behind these instruments is that if a colleague’s sibling affects a focal person’s fertility, then this effect should run through the colleague’s fertility; conversely, if a sibling’s colleague affects a focal person’s fertility, then this effect should run through the sibling’s fertility. This approach allowed us not only to disentangle social interaction effects from other effects but also to examine social spillover effects in fertility from the family to the workplace and from the workplace to the family.

We draw on data from the System of social statistical data sets (SSD), which is an integrated longitudinal database of various registers provided by Statistics Netherlands (Bakker et al. 2014). This database holds information on the entire Dutch population, and individuals can be linked to family members and colleagues through unique individual and workplace identifiers. This information allowed us to link different networks and individuals as well as to test for colleague, sibling, and social spillover effects on fertility.

## The Mechanisms Behind Social Interaction Effects on Fertility

The seminal work of Coale and Watkins (1986) and Bongaarts and Watkins (1996) has shown that fertility is influenced not only by individuals’ own characteristics but also by the behavior of interaction partners. Knowledge about the mechanisms behind social interaction effects on fertility is mainly based on qualitative studies conducted in Italy and Germany (Bernardi 2003; Keim et al. 2013). These studies have focused on different interaction domains—including family, friends, colleagues, and neighbors—and listed four main mechanisms underlying social interaction effects on fertility: social learning, social contagion, social support, and social pressure.

Social learning refers to individuals learning from others through observation, imitation, and modeling (Bandura 1977). Individual perceptions about certain events are altered as individuals learn about the consequences of these events or reinterpret their knowledge based on other’s behavior and experiences (Bongaarts and Watkins 1996). Particularly at the transition to parenthood, colleagues may influence each other’s fertility decisions through social learning. Individuals can learn from a colleague about the consequences of becoming a parent and how parenthood influences work and family life (Keim et al. 2013). Given that colleagues share the context of the workplace, they are a particularly relevant source of social learning about the work-family interface (Bernardi 2003). This is supported by the psychological concept of self-efficacy, which posits that social learning is fostered by (perceived) similarity among interaction partners (Bandura 1994).

Because brothers and sisters are important role models and behavioral examples (Axinn et al. 1994), the information obtained from siblings is also likely to influence important life course transitions, such as becoming a parent (Lois and Becker 2014). Social learning from siblings is relevant especially before the initial transition to parenthood, reducing uncertainty about the challenges and joys of having a child.

Social contagion refers to changing emotional reactions while interacting with relevant others. Individuals may “catch” their social contacts’ emotions, even without being aware of it. Applied to fertility, this mechanism mainly operates through contact with a newborn prompting the desire to have a child (Bernardi 2003). Given that ties to colleagues are usually weaker than ties to siblings, direct contact with a colleague’s baby occurs less frequently than direct contact with a sibling’s baby. Qualitative research has shown that the contagious influence of a sibling’s newborn starts with birth and continues throughout family gatherings and day-to-day interactions (Bernardi 2003; Keim et al. 2013).

A third potential mechanism underlying social interaction effects on fertility is social support. Opportunities for receiving financial, instrumental, and emotional support reduce the (anticipated) costs of childbearing (Keim 2011). Similar to the contagion mechanism, these types of support can be expected to occur more frequently in stronger sibling ties and less frequently in weaker colleague ties. Some studies have argued that siblings might even synchronize their fertility to benefit from the cost-reducing effects of joint childrearing, coordinated childcare, sharing of material expenses, and emotional support (Kuziemko 2006).

The fourth mechanism, social pressure, refers to individuals changing their attitudes and behavior to conform to social norms (Festinger 1954). Social pressure influences individuals’ decision-making through sanctions and/or rewards. Colleagues’ fertility may exert normative pressure especially if fertility is common at the workplace (Keim et al. 2013). Among siblings, social pressure can also operate through parental expectations: (prospective) grandparents often express the wish to have a grandchild and/or to adhere to the normative rhythm of the adult life course. If siblings fulfill these expectations, pressure may rise to follow suit (Keim et al. 2013).

We expect that these social interaction mechanisms affecting fertility behavior are more relevant for women compared with men, for a number of reasons. First, the costs of childbearing will be higher for women, and consequently, the importance of social support associated with the transition to parenthood will also be greater for women. A large share of women who want to work or have to work rely on childcare support provided by network partners, including siblings (Keim et al. 2013).

Second, qualitative research has indicated that the social learning mechanism is more important in women’s decisions regarding reconciling work and family life (Bernardi 2003; Keim et al. 2013). Although the fraction of Dutch women who returned to pre-motherhood work hours after childbearing increased from 40% to 60% between 2007 and 2017, the Netherlands still leads Europe in terms of part-time jobs (Centraal Bureau voor de Statistiek n.d.-b). Information obtained from colleagues or siblings who became parents appears to be more relevant for women than for men. On the one hand, this information may trigger or accelerate women’s transition to parenthood as uncertainty about balancing work-family life after childbearing is reduced. On the other hand, the acquired knowledge from relevant others’ childbearing may deter women from childbearing. If network partners reduce their working hours or change into part-time jobs after motherhood, career-oriented women may refrain from childbearing.

Moreover, it is plausible that the emotional contagion mechanism operates differently for mothers who have unique childbearing experiences not shared by fathers. Bernardi (2003) and Keim (2011) showed that women report emotional arousal when they are in direct contact with the babies of their network partners. Brase and Brase (2012:1144) further supported these findings by showing that emotional contagion of parenthood and the average rates of feeling “a bodily desire for the feel, sight, and smell of an infant” is higher for women than men.

Last, the qualitative literature has also indicated that the social pressure mechanism is more influential for women than for men (Bernardi and Klärner 2014; Keim et al. 2013). In qualitative studies, men reported pressure exerted only through strong ties, such as parents and friends, after relevant others became parents. The social pressure on women to become mothers was not limited to strong ties. Women additionally reported social pressure through weak ties. Keim et al. (2013), for instance, showed two ways of social pressure exerted on childless women. The first type of social pressure exerted by weak ties was primarily driven by biological reasons. A respondent reported that her doubts about the postponement of motherhood increased when younger acquaintances asked her about the risk of having a disabled child by postponing childbearing. In the second case, weak ties’ social pressure on women were linked with institutional norms and gender roles. Two respondents from Germany declared that they were feeling under pressure when they declared to remain childless, and they were expected to become mothers. This was because their acquaintances were thinking that childless women denounced the intergenerational solidarity of the German pension system through not giving birth to pension payers of the next generation.

Network partners’ gender might also be important in the social interaction effects on fertility. Regarding sibling effects, knowledge acquired from a sister who became a mother might be more informative than knowledge obtained from a brother who became a father. In the same vein, the social contagion of fertility might be stronger in sister-sister relationships. Social pressure and comparison are also reinforced by the similarity between network partners (Festinger 1954). Consequently, a sister’s transition to parenthood might exert more pressure on a woman than a brother’s childbearing. Yet, these three mechanisms might also be relevant in opposite-sex relationships, given that siblings are often close and serve as role models to one another (Axinn et al. 1994). Regardless of the gender composition of the sibling dyad, siblings may learn from each other about the consequences of childbearing, share emotions, and feel pressure following the birth of a niece or nephew. Moreover, there is no obvious reason why sharing the costs of childbearing would be influenced by sibling gender.

The gender of a colleague, however, might be more relevant in fertility behavior than sibling gender. As discussed earlier, we expect that fertility behavior spreads among colleagues through the mechanisms of social learning and social pressure. Colleagues are important sources of learning about the work-family interface (Bernardi 2003). This type of information would be more relevant for women when it is provided by female colleagues who share relatively similar conditions. We also expect that the social pressure mechanism is more influential among women working at the same firm because individuals assess their well-being and needs by comparison with benchmarks provided by the behavior of similar others (Festinger 1954). Consequently, a female colleague’s parenthood is likely to be more important for women than a male colleague’s parenthood.

## The Identification of Social Interaction Effects on Fertility

The challenging nature of identifying social interaction effects—the direct influence of network partners on an individual’s behavior—has been discussed extensively in the literature (e.g., Manski 1993, 1999). Similarities in fertility behavior may not be driven by the network partners’ direct influence but by group characteristics. For example, siblings’ fertility preferences may be shaped by their parents. In the same vein, workplace characteristics may have consequences for colleagues’ fertility preferences. These effects are referred to as contextual or exogenous effects. Second, individuals may behave in similar ways because of correlated effects, which emerge from group-level unobservable characteristics that influence the behavior of all members simultaneously. For instance, individuals working at the same workplace or siblings who experienced similar socialization may be independently affected by unobserved factors, such as sorting into family-friendly jobs that would in turn lead to similarities in their timing of fertility.

Studies have adopted different approaches to identify social interaction effects on fertility. Coale and Watkins (1986) used the term social interaction to explain regional differences in aggregate levels of fertility. After their seminal work, numerous studies used social interaction theories to explain temporal and regional fertility differences at the macro level (e.g., Bongaarts and Watkins 1996; Montgomery and Casterline 1996). More recently, researchers have shown an increased interest in micro-level networks to identify social interaction effects on fertility. To identify direct colleague effects on fertility, Pink et al. (2014) included random effects at the firm level, whereas Asphjell et al. (2013) used placebo peer groups to test whether the positive correlations in fertility decisions found among colleagues also existed for unrelated groups. In studies of sibling effects on fertility, Kuziemko (2006) and Lyngstad and Prskawetz (2010) used random effects at the family level, and Cools and Kaldager (2017) attempted to exploit twin births and the sex composition of children as random shocks. Kotte and Ludwig (2011) used various controls to separate direct sibling effects from contextual and selection effects.

Although the inclusion of random effects may capture spurious correlations found within networks, such an approach cannot fully disentangle contextual effects from direct effects even in the presence of various group-level controls. In the same vein, placebo peer groups and falsification tests may indicate associations in fertility behavior that are not due to similar institutional environments, but whether these are driven by contextual factors or by social interaction effects is not clear. Consequently, the evidence for direct social interaction effects on fertility behavior remains inconclusive.

A potential solution to the problem of separating social interaction effects from contextual and correlated effects is the use of instruments. A suitable instrument is a factor that influences the network partner’s fertility but not the focal person’s fertility. If this instrument shows an effect on the focal person’s fertility, this effect can operate only through the network partner’s fertility. Consequently, the instrument can separate direct effects from contextual and correlated effects.

Two previous studies used instruments to identify social interaction effects on fertility. Cools and Kaldager (2017) attempted to identify these effects by using twinning at second birth and having two children of the same sex as instruments. Although both occurrences are random and predictive of subsequent fertility (lower subsequent fertility following twins, and higher subsequent fertility following same-sex siblings), these instruments have crucial limitations. Most important, both instruments can be used to examine only transitions to higher parities. Social interaction effects on fertility, however, are expected to be most relevant at the first transition to parenthood because the mechanisms of social contagion, social pressure, and particularly social learning are much more likely to operate before parenthood than after having children (Bernardi and Klärner 2014; Lyngstad and Prskawetz 2010).

Ciliberto et al. (2016) used the fertility of colleagues’ siblings as an instrument in their analysis of social interaction effects at the workplace. Although this study did not focus on the transition to parenthood and took the workplace rather than social ties within the workplace as a unit of analysis, the instrumental variable represents an important improvement because it allows separating social interaction effects from contextual and correlated effects.2 We build on this approach to identify the effects of interest based on appropriate exclusion restrictions. Our design also links two interaction domains—the workplace and the family—to test for spillover effects.

## Identification of Colleague Effects and Sibling Effects

To identify colleague and sibling effects, we used information about the fertility of colleagues’ siblings and the fertility of siblings’ colleagues. This approach improves the identification of direct effects and tests for social spillover effects. Positive associations between siblings’ fertility (Kuziemko 2006; Lyngstad and Prskawetz 2010) and colleagues’ fertility (Asphjell et al. 2013; Ciliberto et al. 2016; Pink et al. 2014) are well established in the literature. Thus, the instruments were correlated with the endogenous variables of interest (i.e., the colleague’s and the sibling’s fertility). The exclusion restriction for the identification of colleague effects was that the fertility of a colleague’s sibling influences a focal person’s fertility not directly but only through the colleague’s fertility, as shown in panel a of Fig. 1; the exclusion restriction for the identification of sibling effects was that the fertility of a sibling’s colleague influences a focal person’s fertility not directly but only through the sibling’s fertility, as shown in panel b of Fig. 1. Thus, we assessed the impact of a colleague’s sibling’s fertility and of a sibling’s colleague’s fertility on a focal person’s transition to parenthood. Such effects would indicate direct influence of colleagues and siblings on fertility behavior: if a colleague’s sibling affects a focal person’s fertility, then this effect should run through the colleague’s fertility. Conversely, if a sibling’s colleague affects a focal person’s fertility, then this effect should run through the sibling’s fertility. Furthermore, as shown in Fig. 1, this strategy connected both interaction domains, allowing us to examine spillover effects from the family to the workplace and vice versa.

## Data and Sample Selection

### Data

The SSD of Statistics Netherlands is an integrated longitudinal database comprising various registers and surveys provided by Statistics Netherlands. The central unit types included in the database are individuals, households, buildings, and organizations (Bakker et al. 2014). To link each unit to different types of data sets, all units are identified with linkage keys. In our analyses, we focused mainly on registers. Our central database includes person identification numbers (PIN; i.e., anonymized citizen service numbers) of the entire Dutch population, year and month of birth, gender, education, and parental PINs.

The registers allowed us to identify each individual’s siblings (via parental PINs), children, marital history, education, income, workplace, and current place of residence. In addition, the data allowed us to link individuals to their colleagues using the firm and workplace identifiers. The standard business classification (SBI) and firm size of each workplace were identified using the unique workplace identifiers. Network partners’ (colleagues’ and siblings’) fertility histories were obtained by the same approach.

### Sample Selection

Given that SSD holds information on the entire Dutch population, we made a number of selections to create an appropriate sample for the analyses. First, we selected as our anchor sample the Dutch population born between 1970 and 1979. The main reason for this selection was the comprehensive set of data available for these cohorts, owing to an expansion of the SSD with detailed information on jobs, firms, and wages (de Vuijst et al. 2017). Another reason concerns the parent-child linkage quality, which is best for relatively young cohorts: it is nearly perfect for all offspring of parents born in 1945 or later. All steps of our sample selection are illustrated in Fig. 2.

### Sample Selection for Colleague Effects

We first linked our anchor sample to their workplaces and used the information on colleagues, colleagues’ fertility history, workplace size, industry, and wages. As in other studies on colleague effects (e.g., Asphjell et al. 2013; Ciliberto et al. 2016), our sample was restricted to workplaces with 10–50 employees. This restriction was important to establish a well-defined network of colleagues at the workplace who are likely to interact on a regular basis. Furthermore, considering workplaces with fewer than 10 employees could be problematic because they are likely to be a more homogenous group. Additionally, we restricted the sample to firms in which at least two colleagues aged 20–45 were present. We also excluded loosely attached workers (i.e., if the relative working time of the job in relation to a full-time job in the same company was smaller than 0.5) and firms with more than one location to assure that individuals identified within a firm were located at the same workplace.

One problem with identifying the colleagues of our anchor sample was the dynamic structure of workplaces. Within any period, there may be workers leaving a firm as well as new hires. To keep the data set manageable, we used workplace information of every September between the years 2006 and 2015. Based on the unique person and workplace identifiers, our anchor sample’s colleagues were determined for each period. Colleagues’ influence on fertility was examined for all individuals aged 20–45 in a given period.

Each period lasted one year, ending in the month of data collection.3 For example, a childless individual observed in a firm with 10–50 employees in September 2006 and in September 2011 was defined to be at risk within the periods of October 2005–September 2006 and October 2010–September 2011, respectively. If individuals were working in multiple firms, their main job (based on wages) was considered in the analyses. Individuals were considered at risk during any month between October 2005 and September 2015 as long as they were observed at the workplace or until the month of their (or their partner’s) first conception that led to a live birth. Based on these restrictions, we identified on average 175,600 workers per period. In the interest of computation time, we reduced the sample size by randomly selecting one-third of the whole sample from each period.

To distinguish social interaction effects from contextual effects, we used the birth history of colleagues’ siblings as an instrumental variable. One drawback of linking colleagues to their siblings was that they could be identified only if one of the siblings was born in the 1970s. Thus, if neither the colleague nor the sibling was born between 1970 and 1979, the information was missing in the analyses.4 Despite this drawback, a considerable share of individuals in the prime age range of transitions to first birth were included in the sample. For example, the youngest and oldest cohorts born in the 1970s were aged 26–35 in October 2005. According to the birth statistics of the Netherlands, more than 70% of all first births fall into this interval (Centraal Bureau voor de Statistiek n.d.-a). Furthermore, this percentage will likely be even higher for two reasons. First, the birth events of men were also considered, and more births fall into this interval for men than for women. Second, the birth information of all siblings was available if one sibling was born in the 1970s, which allowed us to consider a considerable number of births from cohorts outside our focus group.

A small number of firms in which no colleague had any siblings were also excluded from the analysis. The final sample for the analyses of colleague effects on fertility consisted of 609,949 persons. As shown in panel a of Fig. 2, the average age of our final sample was younger than the initial sample because only childless individuals at risk of parenthood were considered. Furthermore, the share of men was larger than in the initial sample, mainly due to the exclusion of loosely attached workers, most of whom were women. Two robustness checks in which we (1) considered only firms with relatively equal gender distribution and (2) also considered loosely attached workers yielded similar findings.

### Sample Selection for Sibling Effects

Like previous studies (Lyngstad and Prskawetz 2010), we restricted our sample to men and women with one brother or sister because the inclusion of more siblings would lead to many complications in data handling and analysis. We linked members of our focal group to their full siblings (i.e., individuals who share father and mother) and excluded other types of sibship formations, such as half-siblings. The year of birth interval of the siblings was not restricted to a birth year interval of the anchor sample. Yet, we restricted the age difference between the sibling dyads to a maximum of 15 years. Dyads aged 20–45 were defined to be under the risk of transition to parenthood, and the full sample consisted of 1,227,764 sibling dyads.

As noted earlier, we used siblings’ colleagues’ fertility as an instrument to investigate sibling effects on fertility. Two additional restrictions were required to use this instrument. First, we restricted our analyses to the period October 2005–September 2015 because workplace data were available only for this period. Our sample restriction to dyads with at least one sibling born in the 1970s led to a selective exclusion of younger parents who had their first child before October 2005. As a result, the mean age at first birth was about three years higher for the restricted sample than for the full sibling sample. After all restrictions, our final sample for the analyses of sibling effects included 72,703 individuals. Because individuals who (or whose partner) conceived before October 2005 were not included in the analysis, our final sample was younger than the initial sample, and the share of men was larger because the mean age at first birth is higher for men than for women (see panel b of Fig. 2). We addressed this selection problem with a Heckman model (Heckman 1979), as explained in detail in the next section.

### Analytical Strategy

For the analyses, we created person-month files separately for colleague and sibling effects. The outcome variable used in both models was a binary measure for conception, taking the value 1 in the month of conception and 0 in all preceding months. The timing of conception/partner’s conception was measured by subtracting nine months from the birth month of the first child. We focused only on first births of the focal persons and network partners. We did not consider recurrent events because it is hard to identify whether multiple births are influenced by network partners or whether they reflect only the focal person’s behavior.

We estimated a series of discrete-time logit event-history models with random effects at the individual level. We proceeded in four steps. First, we estimated reference models in which we used dummy variables indicating the past childbearing behavior of colleagues and siblings respectively, similar to the specification used by other studies on social interaction effects on fertility (e.g., Lyngstad and Prskawetz 2010; Pink et al. 2014). In the second step, we included various controls to assess the extent to which social interaction effects can be explained by contextual factors, such as industry or parental income. Third, we employed an exclusion restriction and replaced the conventional dummy variables by the instruments without the control variables. Fourth, we re-added the controls to examine the reliability of the instruments because the instruments were expected to be uncorrelated with the controls. The complete set of controls for colleague effects and sibling effects are located, respectively, in Tables A1 and A2 of the online appendix.

Instrumental variable estimations have different characterizations depending on the endogenous main predictors and choice of instruments in panel data models (Wooldridge 2005). In our models, the main predictors were time-varying dummy variables taking the value 1 within the intervals of 0–11 months, 12–23 months, and 24–35 months after a network partner became a parent. In other words, network partners’ transitions to parenthood reflected the occurrence of events. Therefore, we could not apply the standard two-stage least squares (2SLS) instrumental variables estimation in which the endogenous main predictors are regressed on the instrumental variables at the first stage.

Instead, we followed the strategy of Ciliberto and Tamer (2009:1802, theorem 2) and Ciliberto et al. (2016), who showed that the parameters of interest can be identified in the present setup with the direct inclusion of instrumental variables. This means that we directly assessed the impact of our instruments (i.e., a colleague’s sibling’s fertility and a sibling’s colleague’s fertility) on the outcome (i.e., focal person’s risk of transition to parenthood). This strategy had two advantages. First, it enabled us to test for the presence of direct social interaction effects. Finding effects of the instruments would indicate a direct influence of social contacts on fertility decisions because the effects of the instruments can operate only through network partners.5 Second, this analytical setup also provided direct evidence on spillover effects from one interaction domain to another.

### Model for Colleague Effects

The primary empirical specification of colleague effects with random effects at the individual-level model takes the following form:
$loghit1−hit=αDit+∑s=13δc′Ccti+β1′Xi+β2′Zit+ηi.$
1

The hazard of conception/partner’s conception for individual i at time t is represented by hi(t). Di(t) is the baseline hazard specified as a quadratic function of individual i’s age at time t: Di(t) = α0 + α1(agei) + α2(agei)2. To capture dynamic patterns of colleagues’ fertility, we created three time-varying dummy variables (i.e., Cc) taking the value 1 if any colleague became a parent in the last 11 months, 12–23 months, and 24–35 months, respectively. If a colleague became a parent in September 2007, for instance, the dummy variable referring to a colleague’s childbearing within the last 0–11 months takes the value 1 between the period September 2007 and August 2008, and 0 in all other months unless another colleague became a parent. Thus,$δC′$, the main parameter of interest, indicates whether colleagues’ fertility was correlated with the focal persons’ fertility. Xi and Zi represent time-constant and time-varying controls, respectively. ηi denotes unobserved time-constant characteristics of individual i.

Next, we replaced the dummy variables for colleagues’ fertility by our instruments: namely, the dummy variables for the fertility of colleagues’ siblings. Cc indicates whether any sibling of any colleague became a parent within the last 0–11, 12–23, and 24–35 months. These dummy variables take the value 1 if any colleague’s sibling became a parent within the mentioned period. Descriptive statistics on the main predictors are shown in panel A of Table 1.

### Model for Sibling Effects

Similar to the analysis of colleague effects, we focused on the period October 2005 and September 2015 to examine sibling effects on fertility. As noted earlier, this approach may leave us with a selective sample because individuals who (or whose partner) conceived before October 2005 were not included in the analysis. To reduce bias arising from this selection, we estimated the probability of conceiving (or partner’s conceiving) before October 2005 and calculated the inverse mills ratio (Heckman 1979). Subsequently, the selection variable λ was included in the main model. The two-step equations for the primary sibling effects model take the following form:
$loghit1−hit=αDit+β1λi+∑s=13δs′Csti+β1′Xi+β2′Zit+ηi.$
2
$Prgi=1=αDi+β1′Xi′+εi.$
3

In Eq. (2), hi(t) represents the hazard of conceiving/partner’s conceiving for individual i at time t. Cs denotes time-varying indicators for whether the sibling became a parent in the past 11 months, 12 to 23 months, or 24 to 35 months. $δs′$ denotes the corresponding coefficients and the main parameter of interest in the model. To illustrate, if a sibling became a parent in March 2010, the dummy variable referring to a sibling’s childbearing within the last 12–23 months takes the value 1 between March 2011 and February 2012, and 0 in all other months. λi represents the inverse mills ratio obtained in Eq. (3) to account for selection bias. Time-constant (Xi) and time-varying controls (Zi) are also included in the model. Time-constant unobserved individual-specific factors are captured by ηi.

In Eq. (3), Pr(gi = 1) is the probability of being included in the main model (i.e., no conceiving/no partner’s conceiving before October 2005) and is estimated using a probit model. Individual i’s age in October 2005 is specified as Di = α0 + α1(agei) + α2(agei)2 if individual i had not conceived yet, and it refers to the timing of (partner’s) conception for individuals who (whose partner) conceived before October 2005. $Xi′$ denotes a set of control variables: education, gender, parental status, house ownership of parents, and the total fertility rate of the place of birth in 2010. εi represents the individual error term.

After estimating the basic sibling effects model, we replaced the main parameter of interest (i.e., siblings’ fertility) by our instruments for siblings’ colleagues’ fertility to empirically distinguish direct sibling effects from contextual effects and correlated effects. Again, two-step equations are estimated to account for selection. The main parameters of interest are three dummy variables (Cs) indicating whether any colleague of the sibling became a parent in the past 11 months, 12–23 months, or 24–35 months. Descriptive statistics on the main predictors are illustrated in panel B of Table 1.

## Results

### Results on Colleague Effects

Results on colleague effects are shown in Fig. 3 (full estimates are located in Table A3, online appendix). In line with previous studies (Asphjell et al. 2013; Pink et al. 2014), panel a shows significant positive effects of a colleague’s fertility on an individual’s transition to parenthood. The temporal shape of colleague effects follows an inverse U-shaped pattern and peaked within the second year after a colleague had a child. We further included various controls and random effects at the firm level. As shown in Panel a of Fig. 3, the positive effect of a colleague’s fertility remains significant and positive, but the inclusion of these factors accounts for approximately 40% of the observed effects. This reduction shows that a substantial part of the initial associations is due to contextual and selection factors captured by the controls. Whether all relevant controls were included in the model, however, remains unclear. Although these results suggest that fertility decisions spread among colleagues, it remains unclear whether the observed effects represent social interaction effects or the effects of unobserved contextual and selection factors.

To identify social interaction effects, we introduced the instruments for colleagues’ siblings’ fertility. Panel b of Fig. 3 illustrates the results. Estimated coefficients are insignificant for the first two years following a colleague’s sibling’s birth event. After the second year, however, a highly significant positive effect is observed. Considering that these effects first spread from a colleague’s sibling to the colleague and then to the focal person through the colleague, this temporal shape of the effect is in line with theoretical expectations and previous findings. Including controls does not lead to any substantive changes in the coefficients of the instrumental variables, which further supports the reliability of the instruments given that they were not expected to be influenced by the inclusion of controls. A comparison between the strongest effects found in panel a (i.e., 0.115) and the magnitude of the instrument coefficient (i.e., 0.069) indicates that at least 60% of the colleague effects represent direct social interaction effects. This suggests that the controls included in panel a account for a significant share of the relevant contextual and selection factors. Furthermore, this finding is the first to demonstrate spillover effects from the (colleagues’) family to the workplace.

### Results on Sibling Effects

The estimated coefficients for sibling effects on fertility are shown in Fig. 4 (full estimates are located in Table A4, online appendix). The coefficients shown in these models are based on simultaneous equations in which the selection model (i.e., the probability of being included in the restricted sample) is estimated jointly with the main model. The results of the selection equation are shown in Table A5 (online appendix). The effects of siblings’ fertility on the transition to parenthood are significant for all social interaction dummy variables. Similar to the findings of Lyngstad and Prskawetz (2010), the short-term effect is strongest. Sibling effects on the transition to parenthood become weaker with the inclusion of various controls, such as parental status and random effects at the family level, suggesting that the relationship is partly driven by confounders. This reduction shows that a substantial part of the initial associations is due to contextual and selection factors captured by the controls. Whether all relevant controls were included in the model, however, remains unclear. Thus, although these results suggest that fertility decisions spread among siblings, it remains unclear whether the observed effects represented social interaction effects.

To identify social interaction effects, we introduced the instruments for sibling’s colleague’s fertility. The results are shown in panel b of Fig. 4 and in Models 3 and 4 in Table A4 (online appendix). Similar to the findings on colleague effects, the transition rate to (partner’s) pregnancy increased after the second year following a sibling’s colleague’s transition to parenthood. Accordingly, the temporal shape and strength of the instrument indicated direct sibling effects as well as spillover effects of fertility from the workplace to the family. Consistent with theoretical considerations, the validity of the instruments is further corroborated: the substantive findings presented without controls are reproduced after the inclusion of the controls. A comparison between the strongest effects observed in the conventional models (i.e., 0.201) and the respective effects of the instrument (i.e., 0.076) indicate that at least 38% of the fertility behavior associations observed between siblings is due to social interaction effects. Moreover, this also suggests that the controls included in panel a of Fig. 4 are insufficient to distinguish direct social interaction effects from contextual effects and selection effects.

### Gender Differences

In Fig. 5, we present analyses separated by focal person’s and network partner’s gender (full estimates are located in Table A6, online appendix). Significant colleague effects are observed only in female-female dyads, indicating that the transition rate to pregnancy increased after the second year following a female colleague’s sibling’s transition to parenthood. This indicates that colleague effects on fertility behavior are mainly relevant to female-female interactions.

Sibling effects separated by the focal person’s and the sibling’s gender are illustrated in Fig. 6 (full estimates are located in Table A7, online appendix). Similar to the gender differences found for colleague effects, men were influenced by neither their female nor their male sibling’s colleague’s fertility. For women, estimated coefficients are significant after the second year following not only a female sibling’s colleague’s but also a male sibling’s colleague’s birth event. These results are in line with Kuziemko’s (2006) study finding cross-gender sibling effects on fertility behavior.

### How Important Are Social Interaction Effects on Fertility?

To gain more insight into the importance of social interaction effects and social spillover effects on fertility, we considered exposure to network partners’ fertility as well as the magnitude of the estimated effects. For instance, even if colleague effects may be weaker than sibling effects, people are exposed to more birth events of colleagues than of siblings. We constructed a scenario in which exposure to the fertility of interaction partners in both domains was examined. The consequences of these effects were determined not only by the size of the estimated coefficients but also by the total amount of exposure. We calculated how transition rates to (partner’s) pregnancy increased in a month with exposure to each main predictor used in the models and multiplied it by the total months of exposure. Accordingly, we assessed how the number of births would change if the effects were set to 0.

As shown in Table 2, we observed 19,863 instances of (partner’s) conception in the analysis of colleague effects and 20,068 instances of (partner’s) conception in the analysis of sibling effects during the study period. The findings suggest that this number of pregnancies would drop considerably if interaction effects were set to 0. The estimated number of pregnancies would drop by 1,151 (5.8%) in the absence of colleague effects and by 315 (1.5%) in the absence of sibling effects. This illustrates that although sibling effects are larger in magnitude than colleague effects, the higher exposure to colleagues’ fertility render this interaction domain more relevant for the total number of conceptions. These findings demonstrate the importance of considering effect size as well as exposure.

We also used the scenario to illustrate the importance of spillover effects from one domain to another. If spillover effects from the family to the workplace were absent, the number of pregnancies would drop by 699 (3.5%). Conversely, if spillover effects from the workplace to the family were absent, the number of pregnancies would drop by 249 (1.2%). Taken together, these results further emphasize that small changes and seemingly trivial sizes of direct effects can lead to large differences through the amount of exposure.

To assess the reliability of our findings, we conducted robustness checks. First, we conducted falsification tests to assert that our main conclusions about workplace and family effects were not spurious. We assigned individuals to “unrelated firms” based on industry sector and a four-category measure of firm size (i.e., firm size <20, 20–29, 30–39, and 40–50). Subsequently, we assessed whether unrelated colleagues’ and unrelated colleagues’ siblings’ fertility influenced the risk of becoming a parent (full estimates are located in Models 1 and 2 of Table A8, online appendix).

In a similar vein, we matched individuals with “unrelated siblings” based on their birth order, a four-category measure of mother’s age at first birth (younger than 20, 20–24, 25–34, and older than 34), a four-category measure of parental income (low, lower-middle, upper-middle, and high), and gender of the sibling to assess the validity of our sibling effects models. Subsequently, we estimated the impact of unrelated sibling’s and unrelated sibling’s colleague’s fertility on the risk of parenthood (full estimates are located in Model 1 and 2 of Table A9, online appendix).6 As presented in panels a and b of Fig. 7, none of the effects within the workplace or family networks are significant, suggesting that the associations found in the main models are unlikely to be chance effects or effects driven by the contextual variables used for matching.

We further took a random 30% of the samples included in the main models to test whether the significant effects found in the main models were driven by the large sample sizes (the estimates with the random samples for colleague and sibling effects are located in, respectively, Model 3 of Table A8 and Model 3 of Table A9 in the online appendix). The results obtained from these analyses with reduced sample sizes are significant and very similar to the main findings.

A further robustness check concerned our exclusion restriction. Specifically, we assumed that focal persons are not directly affected by their colleagues’ siblings and siblings’ colleagues, respectively. Because this assumption is more likely to be met in the more anonymous context of larger cities, we stratified the sample by the size of the city in which focal persons resided and considered only larger cities (i.e., cities with more than 5,000 inhabitants).7 Findings for colleague and sibling effects are presented in Model 4 of Tables A8 and A9, respectively, showing that the main findings are not altered when we focus only on larger cities.

As an alternative robustness check for our exclusion restriction, we considered the distance between siblings given by the geographic coordinates of the siblings’ places of residence. We divided siblings into tertiles, created three distance groups, and replicated the analyses. Even for siblings living distant from each other, the effects remain significant (results not shown).8 However, effect sizes are weaker when we look at distant siblings, a plausible result given that some of the hypothesized mechanisms (emotional contagion and social support) are less likely to operate between distant siblings.

In additional robustness checks, we first replicated the analyses for our anchor group rather than all colleagues in a firm and included additional controls, such as marital status, education, and parental background, because these controls were available for only the anchor group. This allowed us to test whether the findings were robust to potential confounders that were likely to influence the association among colleagues’ fertility behavior. Second, we changed the upper bound (i.e., 50 to 40) and the lower bound (i.e., 10 to 20) of firm size because both social interaction between colleagues and fertility preferences might be influenced by firm size. Third, we tested whether the findings on colleague effects were robust to the inclusion of all workers. We examined an alternative period between 2005 and 2010, using all identified colleagues rather than considering a random sample of colleagues from each calendric period. Moreover, considering that the share of women was lower in our colleague effects sample (women are more likely to be loosely attached to their jobs), we made two additional robustness checks. First, we examined only workplaces with a more relatively equal gender distribution (i.e., at least 30% of the colleagues at the workplace were female). Second, we also included loosely attached workers in the analyses. The results obtained from these checks are very similar to those shown in Fig. 3.

Furthermore, we assessed sibling effects for dyads who were defined to be under risk of becoming a parent after their twentieth birthday with the consideration of various controls to further test whether the selectivity of our sample influenced our conclusions (results not shown). To keep the data set manageable, a random 30% of sibling dyads were included in these models. To understand whether findings on sibling effects were influenced by focusing only on sibling dyads, we replicated our analyses by considering individuals with two or more siblings. The results from these robustness checks are almost identical to those presented in Fig. 4. We further included period dummy variables to test for common shocks both for colleague and sibling effects. In both analyses, our findings are robust to the inclusion of period dummy variables.

## Conclusion

There has been a rapid growth of studies on social interaction effects on fertility. The evidence suggests that fertility decisions are positively correlated within interaction domains, such as the friendship circle (Balbo and Barban 2014), the family (Lyngstad and Prskawetz 2010), and the workplace (Asphjell et al. 2013; Pink et al. 2014). A major reason behind this research interest is that interaction effects are multipliers of individual decisions, both within and across different domains of social interaction. Despite the importance of studying these effects, evidence for direct social interaction effects and social spillover effects has remained inconclusive.

The main contribution of the present study is twofold. First, we provide a better test for social interaction effects using instrumental variables that yield more robust evidence for the presence of such effects than previous research has offered. Our findings on the strength and temporal shape of social interaction effects show that colleagues’ and siblings’ fertility have direct consequences for an individual’s fertility. Positive effects of a colleague’s sibling’s fertility as well as a sibling’s colleague’s fertility on a person’s transition to parenthood are observed after the second year following these events. These findings are in line with our expectations: the instruments first influence the focal person’s network partners and then the focal person through the network partners. These findings are further supported by several additional robustness checks. Considering the focal person’s and network partner’s gender shows that social interaction effects on fertility are more relevant for women in both network domains. This is in line with our expectations that mechanisms such as social learning and social support are more relevant for women than for men. The second main contribution of our study is that we provide the first direct test for social spillover effects across interaction domains, showing how fertility spreads from the workplace to the family and vice versa.

The literature on social interaction effects and fertility has emphasized the importance of identifying social interaction effects and how these may lead to social multiplier effects (Balbo and Barban 2014; Kohler et al. 2002; Lyngstad and Prskawetz 2010). However, these ideas had not been sufficiently supported by empirical evidence. The present study fills this gap.

We conclude with limitations and suggestions for further study. One limitation is that there may be similarities in fertility behavior among colleagues and siblings because of the influence of intergenerational factors. On the one hand, siblings may be influenced by their parents’ own fertility preferences and by their parents’ preferences regarding their children’s fertility (Axinn et al. 1994). On the other hand, intergenerational factors may also influence individuals’ transition to parenthood by guiding them on different career pathways (Barber 2000). Similar intergenerational factors may create significant associations between a colleague’s and a sibling’s fertility through education and career or firm choices. Furthermore, direct effects may run between the workplace and family networks as colleagues and siblings may be aware of each other through social media or other communication channels. Although we cannot rule out these intergenerational factors and social ties, our identification strategy for social interaction effects is based on much weaker assumptions than previous studies that attempted to identify these effects. In addition, the temporal shape of effects and insignificant placebo tests provide further support to our strategy: one would expect to find significant relationships between a colleague’s and a sibling’s fertility not only after the second year but also within the first two years if this relationship was driven by intergenerational factors.

Another limitation is that our sample is limited to individuals who had siblings. This introduces some sample selectivity given that the Dutch population is characterized by relatively low fertility. Yet, as shown by Fokkema et al. (2008), low fertility trends in the Netherlands are mainly driven by declines in larger families (i.e., families with four or more children) and increases in childlessness. Only 12.5% of individuals in the target group of our sample selection have no siblings. Additional checks also show that the intention to have a child of the excluded group does not differ significantly from that of the individuals with siblings in our study cohort. Our identification strategy, however, does not cover this group, reducing the generalizability of our key estimates to people with siblings.

Despite the benefits of our data for identifying social interaction effects, we lacked direct information about the fertility preferences of individuals and relied on their fertility behavior instead. We were also not able to identify whether individuals within an interaction domain did, in fact, interact. However, given our focus on smaller firms as well as the rarity of estranged sibling relationships, it is clear that the large majority of the sample were aware of birth events within their social networks, although we were unable to model interaction frequency and intensity in more detail. Furthermore, we were unable to examine the mechanisms that we expected to give rise to interdependencies among colleagues and siblings in the process of the transition to parenthood. As a result, it remains unclear whether and to what extent the social interaction effects observed in our data are due to social learning, social contagion, social support, and/or social pressure (Bernardi and Klärner 2014).

Increasing availability of register data in various countries (e.g., Denmark, Finland, Norway, and Sweden) will enable researchers to extend our study design to other national contexts and to other networks, such as neighbors. Furthermore, our understanding of social influence on childbearing practices will benefit from collecting survey data that can be linked to these registers given that detailed information such as childbearing intentions is available only in survey data. Last, given that recent research has shown that social interaction effects extend to other domains of demographic behavior, such as divorce (e.g., de Vuijst et al. 2017), it would be interesting to test for direct influence and social spillover effects on demographic behaviors other than fertility.

## Acknowledgments

This study was supported by the German Research Foundation (Grant Number EN 424/10-1) and the NORFACE DIAL project EQUALLIVES.

## Notes

1

In this study, the term social interaction effects refers to the direct influence of network partners on an individual.

2

Ciliberto et al. (2016) used a dummy variable indicating whether any colleague’s sibling had a baby within the last two years and examined the impact of this variable on total number of children that women in a workplace had. Because this instrument should first influence the colleague’s fertility and then the focal person’s fertility through the colleague, it is likely that the effects are not captured within a two-year period.

3

Extending the risk period to more than one year would increase the risk of unidentified workers who left the workplace before September. Our restrictions ensured that people identified as colleagues were working at the firm in a given period.

4

Using a colleague’s sibling’s fertility as an instrument restricted the sample to only colleagues with siblings, who account for 87.5% of our target group. Accordingly, we additionally checked whether the fertility intentions of the excluded group differed from the individuals with siblings. Analyses using the Netherlands Kinship Panel Study (NKPS; Dykstra et al. 2012) showed that the intention to have a child—regardless of having a child or not—did not differ significantly between singletons and individuals with siblings in our study cohort. The only significant difference observed was that the desire to have three children was higher for individuals with two or three siblings compared with singletons.

5

Similar to Ciliberto and Tamer (2009) and Ciliberto et al. (2016), this strategy allowed us to identify the effects of interest but not to precisely quantify these effects.

6

We alternatively relaxed the matching criteria by excluding mother’s age at first birth and using a three-category measure of parental income to increase the number of matches. The findings are very similar to those presented in Fig. 4.

7

The findings are robust to increasing the threshold to 10,000 and 15,000 respectively.

8

We were not able to replicate these analyses for colleague effects because of colleagues with siblings living distant and also colleagues with siblings living close present within the same firm.

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