Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods

Geographical variations in fertility and the diffusion of fertility across space and social networks are central topics in demographic research. Less is known, however, about the role of neighborhoods and neighbors with regard to geographical variations in fertility. This paper investigates spatial variations in family size by analyzing third births in a neighborhood context. Using unique geo-data on neighbors and neighborhoods, this paper introduces a new geographical dimension of fertility variation and contributes to our understanding of geographical variations in fertility. Flexible, ego-centered neighborhoods are constructed using longitudinal geodata taken from administrative registers (2000-2014). Data on inhabitants’ residential address, their housing, family situation and fi xed effects for statistical tracts are used to account for sorting into housing and urban versus rural districts. The analysis shows that the likelihood of two-child couples having another child increases with the share of families in the neighborhood that have three or more children. This relationship remains unchanged, even after controlling for the sociodemographic characteristics of couples, the educational level attained by neighboring women as well as time-constant characteristics of neighborhoods. Results are consistent across various neighborhood defi nitions ranging from the 12 to the 500 nearest neighbors. However, the association between neighbors’ fertility becomes stronger as the number of neighbors increases, suggesting that selective residential sorting is an important driver. Consequently, this study indicates that transitions to third birth may be linked to social interaction effects among neighbors, in addition to well-known processes of selective residential sorting.


Introduction
Declining family sizes and, in particular, fewer women having a third child, are principal causes of overall fertility decline worldwide (Zeman et al. 2018). Research on higher parity birth progressions is thus once more a focus of attention in several countries, such as France (Breton et al. 2005), Germany (Diabaté/Ruckdeschel 2016), and Turkey (Greulich et al. 2016). The link between the declining number of three-child families and declining total fertility rates has traditionally been considered important in Norway (Kravdal 1992), and while the number of large families is falling, almost half of the Norwegian ISSP respondents in 2012 continue to regard three or more children as the ideal number for a family (ISSP Research Group 2016). Young people's fertility preferences have been shown to vary considerably by their regional childbearing context (Testa/Grilli 2006), and research on local geographical patterns of childbearing highlight potential normative (Ruckdeschel et al. 2018) and cultural infl uences (Fulda 2015). The spatial diffusion of fertility behavior is an inherent part of demographic transition theories (Bongaarts/Watkins 1996;Lesthaeghe/Neels 2002), and the importance of compositional and contextual factors in shaping fertility variation is increasingly acknowledged .
Geographical variations in fertility are well recognized at the level of regions, nation states, and along the urban-rural dimension. For instance, they are documented for the Nordic countries (Kulu et al. 2007), the Netherlands (de Beer/Deerenberg 2007), Austria, Switzerland, and Germany (Basten et al. 2011), Italy (Vitali/ Billari 2015), Great Britain (Fiori et al. 2014), and Australia (Gray/Evans 2018). However, there is little research that considers the importance of different geographical scales or focuses on neighborhoods (Logan 2012). Neighborhoods can form arenas where neighbors interact and infl uence each other's childbearing behavior through emotional contagion, social learning and social pressure (Bernardi/Klarner 2014), and studies have shown that neighbors become more important for couples' networks when entering parenthood (Rözer et al. 2017;Kalmijn 2012). However, because neighborhoods are important contexts of childrearing, couples may also sort geographically based on their fertility preferences.
Using unique geo-data drawn from Norwegian registers, this study aims to provide an insight into spatial variations in family sizes by analyzing third births in neighborhood context. In order to acknowledge the dimensionality and complexity of neighborhood defi nitions (Sharkey/Faber 2014), it also analyzes how the correlation of neighbors' fertility varies depending on the chosen neighborhood scale. In this paper, neighborhoods are defi ned as networks of neighbors using k-nearest neighbor measures and are couple-centered and scalable (Östh et al. 2015). While other fi elds increasingly use individualized neighborhoods to capture the residents' environment (Türk/Östh 2019), fertility research focusing on families' immediate residential context is sparse (but see Malmberg/Andersson 2019). Given that there is considerable interest in geographical variations in fertility and the diffusion of fertility across space and social networks, neighborhoods and neighbors are potentially important but understudied drivers of the observed larger geographical variations. Furthermore, comparing results for individualized neighborhoods of different sizes has the potential to shed light on the explanatory importance of neighborhood context, residential sorting and social infl uence among neighbors and might therefore increase our knowledge on the spatial diffusion of fertility behavior (Logan 2012).
At the same time, family transitions and residential relocations remain highly interrelated (Kulu/Steele 2013;Wagner/Mulder 2015). This means that geographical clustering of fertility, even at small scales and net of many important area-level infl uences, may refl ect both residential sorting and social interaction (Manski 1993). The present analyses use detailed longitudinal data from Norway (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014), covering inhabitants' residential address, their housing, family situation and fi xed effects for statistical tracts, thus accounting for central sorting mechanisms related to housing and sorting into urban districts or villages. The questions posed are: (i) Are couples in neighborhoods with many large families more likely to also have a third child? (ii ) At what neighborhood scale do we observe the strongest association? (iii) To what degree is the association weakened when controls for other individual and arealevel infl uences are included?

The case of Norway
In the European low-fertility context, Norway and the other Nordic countries are known for relatively high birth rates. In 2014, the last year of observation in the current study, the total fertility rate (TFR) for Norway was 1.76, but it has since declined to 1.53. As is the case in many European countries, there seems to be a two-child family ideal (Frejka 2008;Sobotka/Beaujouan 2014), and 40 percent of all Norwegian women above the age of 45 had given birth to two children (Dommermuth et al. 2015). In stark contrast to other European countries, a deviation from the twochild norm results in women having more than two children, rather than fewer children. In 2014, 14 percent of all women aged 45 were childless, another 14 percent had one child, and 32 percent had three or more children (Dommermuth et al. 2015). However, across Norway this pattern is not evenly distributed geographically. Figure 1 illustrates the distribution of large families across Norway in 2014, by plotting the proportion of women aged 20-44 with three or more children. Primarily, an east-west divide regarding family sizes is visible. The number of women in the southwestern parts of Norway, also called the Norwegian Bible Belt, having at least three children is greater than that in the more metropolitan southeast. This fi nding is consistent with regional variations that have been documented for previous decades (Lappegård 1999), and reveals persisting regional fertility cultures. Besides these regional patterns, fertility rates also differ between neighborhoods. For example, within the capital city of Oslo, the difference in total fertility rates between urban districts stood at 0.8 children in 2015 (TFR of 2.08 in Bjerke versus 1.29 in St. Hanshaugen) (Syse et al. 2016). In contrast, the difference between counties is 0.3 children (Syse et al. 2016). While the association between sociodemographic characteristics and third births in Norway is relatively well-studied (Kravdal /Rindfuss 2008;Hart et al. 2015), the origin of the uneven spatial distribution of large families is less explored. Source: Map from the Geodatabase at Statistics Norway. Data from Norwegian administrative registers.

3
Third births: why should the context matter?
As for all parity transitions, having a third child depends on having the resources, the partner, and the ability to continue childbearing (see also Balbo et al. 2013). Whereas a woman's education is less important for completed fertility in relatively high-fertility countries such as the Nordic nations and France, becoming a mother at a later age is well known to lower a woman's probability of having many children (Breton et al. 2005;Andersson et al. 2009). Beyond individual determinants, in post-transitional societies too recent studies also relate the number of children in families to social interaction, e.g. social pressure from network members (Balbo/ Mills 2011) or social infl uence by role models (Ruckdeschel et al. 2018 To the extent that socially embedded preferences drive third birth probabilities, one may expect to see geographical clusters of large families. This could emerge because neighbors sort residentially by lifestyle and fertility preferences, and/or because neighbors infl uence each other's fertility preferences. Empirically, several studies corroborate such geographical clustering, e.g. Meggiolaro's (2011) study of Milanese neighborhoods.
Moreover, fertility intentions have been shown to vary with regional fertility contexts in Europe (Testa/Grilli 2006). However, planning or having many children is also often linked to intergenerational transmission and rather stable religious values (Adsera 2006;Cools/Hart 2017). These are factors known to be unevenly distributed across space (Mönkediek et al. 2017). At the same time, early internalized family values and religious orientations are less likely to change with contemporary living contexts, or if so, rather slowly.
So, why might we observe similar fertility behavior among neighbors? Correlated fertility behavior within neighborhoods and variations in the number of children between neighborhoods may emerge through similar channels as for other geographical aggregates. Theoretical divisions are often made between explanations focusing on: (i) population composition and residential sorting; (ii) contextual effects; and (iii) social interaction and diffusion, although these often prove diffi cult to distinguish empirically.
(i) Population composition and residential sorting National, regional, and local fertility dynamics can, in part, be understood through the compositions of the inhabitants and the residential sorting of individuals into 1 In the contemporary Norwegian context, there is broad access to contraception and early medical abortion. Unintended pregnancies are therefore assumed to be a minor issue and are not discussed further. Also, this paper makes no strict distinction between the desired or intended number of children versus the actual number, because desires and intentions are interrelated and subsequently revised to match possibilities and constraints (e.g. Iacovou/Tavares 2011). places (Hank 2002;Dribe et al. 2017). With regard to population composition, one typical notion is that cities have a TFR below the national TFR because of the overrepresentation of highly educated women in urban areas, who are more likely to remain childless (Kulu/Washbrook 2014). However, this relation could likewise emerge from a so-called contextual effect if the cities' universities and labour markets not only attract highly educated individuals but also foster a career-oriented culturealso resulting in lower fertility rates, not only for highly-educated women.
The migration patterns of families additionally infl uence the population composition. Importantly, families do not move at random, and residential relocations often coincide with family expansion (Kulu/Steele 2013). Couples who intend to have many (more than two) children may tend to favor the same residential areas, either because these provide playmates for their children or offer other goods preferred by families. Such residential sorting tends to be empirically diffi cult to disentangle from contextual effects, but in most cases, population composition and residential sorting alone is not a suffi cient explanation for spatial patterns in fertility (de Beer/ Deerenberg 2007;Kulu/Washbrook 2014;Kulu et al. 2007;Kulu/Boyle 2009;Fiori et al. 2014;Basten et al. 2011; Gray/Evans 2018).

(ii) Contextual factors
Different places provide unique economic and social conditions for families which may infl uence moving and childbearing patterns and may be particularly salient and important to families with many children. In the Norwegian context, the propensity of having a third child has previously been associated with contextual factors such as settlement size or opportunity structures for families in a municipality. For instance, living in a rural area or a smaller town increases the probability of a third birth compared to living in larger cities (Kulu et al. 2007), whereas aggregate unemployment decreases the number of higher-order births (Kravdal 2002). Childcare availability has shown positive effects on all parities (Rindfuss et al. 2010), highlighting opportunities for having a large family as an important contextual factor. Within neighborhoods, proper and affordable housing is another crucial aspect (Clark 2012). Usually, home ownership and/or living in a single-family house is seen as the best option for families, but what is perceived as proper housing varies within and between countries (Mulder 2013). In addition to a family-friendly infrastructure and housing opportunities, broader cultural differences related to place-specifi c traditions or local social norms may play a role in the existence and persistence of local fertility patterns (de Beer/Deerenberg 2007;Fulda 2015). Several studies examine the relationship between local social norms and fertility, including linkages between neighborhood disadvantage and early childbearing (Lupton/Kneale 2012) as well as living in elite neighborhoods and late childbearing (Malmberg/Andersson 2019).

(iii) Social interaction and diffusion
The pace and spread of new fertility behaviors, such as nonmarital births, has led to the recognition of fertility diffusion as an important mechanism (Bongaarts/Watkins 1996;Casterline 2001). Such diffusion of fertility behavior between neighboring regions has been documented in several European contexts, for instance in France, Belgium, and Switzerland (Lesthaeghe/Neels 2002), Italy (Vitali/Billari 2015), historical Prussia (Goldstein/Klüsener 2014), and Norway . As family dynamics are found to spread across regions, it can be expected that they also spread within neighborhoods. Neighborhoods can form arenas where neighbors interact and infl uence each other's childbearing behavior through mechanisms such as emotional contagion, social learning, and social pressure (Bernardi/Klarner 2014). This may be especially true for parents, as couples' networks have been shown to shift to more local ties after becoming parents (Rözer et al. 2017;Kalmijn 2012). Parents have many opportunities to interact with neighbors in a similar family situation, and such interaction might be particularly relevant. In line with this, results from a Swiss panel study show that after having a child, respondents feel closer to more neighbors and report more neighborly contact and support than before the childbirth (Kalmijn 2012).
Neighboring families may infl uence each other's fertility through similar channels as other networks (Bernardi/Klarner 2014). They may share knowledge, provide information, and behavioral examples, and social contagion may be apparent. Social contagion among neighbors has been documented among welfare recipients for instance (Mood 2010a;Markussen/Røed 2015). Previous studies fi nd fertility contagion among friends (Balbo/Barban 2014), siblings (Lyngstad/Prskawetz 2010), and colleagues (Pink et al. 2014), though these tend to be potentially confounded by self-selection and contextual effects. Furthermore, the likelihood of becoming a parent has been found to be greater among individuals in cases where many network members have young children (Lois/Becker 2014). Drawing on similar mechanisms, neighbors' fertility (ideals) have been associated with family sizes and fertility limitation in several high-fertility contexts, for example in Nepal (Axinn/Yabiku 2001;Jennings/Barber 2013) and Cairo . In low-fertility countries, however, theneighborhood dimension appears to be understudied when it comes to fertility behavior.
In summary, geographical variations in family size might be rooted in different opportunity structures of places, but they may also refl ect local culture and/ or norms. These contextual drivers may infl uence local fertility patterns through attracting certain couples or through infl uencing those already living there. Above that, social interaction may reinforce existing patterns. Hence, the phenomenon that couples with many children tend to live in similar neighborhoods may emerge due to a combination of compositional effects and residential sorting, specifi c characteristics of the residential context, and possibly social interaction.

Hypotheses
Based on the theoretical background and previous research, a strong association between the share of neighbors with more than two children and the probability of two-child couples of having another child is expected (Hypothesis 1). However, because of residential sorting, it is also expected that this relationship will be moderated and in part explained by individual characteristics of couples (Hypothesis 2a), and by enduring observed and unobserved characteristics of the residential context (Hypothesis 2b). More specifi cally, the following individual characteristics are considered: age, global region of birth, union status, education, employment and income. Other factors that are also taken into consideration are housing, time since the last move, and neighborhood characteristics such as the share of highly educated women, centrality and region. Lastly, unobserved characteristics of administrative neighborhoods are captured using fi xed effects for statistical tracts. Next, the relationship between neighbors' family sizes and a couple's probability of having another child depends on and varies with the chosen scale of the neighborhood fertility measure (Hypothesis 3). Spatial analysis always suffers from the modifi able areal unit problem (MAUP) where decisions about unit scaling and zoning infl uence the results one obtains (Openshaw 1984). The question is therefore not only whether neighbors' fertility behavior is related (Sharkey/Faber 2014), but also at what scale neighborhoods are relevant. In previous studies, regions, municipalities and census tracts have most commonly been examined as fertility contexts beyond the nation state (Petrović et al. 2018). Weeks (2004: 389) says: "The only real solution to both aspects of the MAUP is to begin with individual level data that are geocoded to specifi c locations, and thus, be able to aggregate the data to any scale that the researcher desires, and delimit any set of boundaries that the researcher believes is appropriate to the data." The neighborhood scales that this study considers range from the closest 12 to the closest 500 households and may represent families' local activity spaces. With fewer neighbors, each neighbor's family size is given more weight. Andersson and Musterd (2010) argue that a grid of 100 x 100 metres, comprising on average 30-40 neighbors, is most relevant if social interaction among neighbors is of interest. Restricting the focus to very few neighbors increases the possibility of relevant neighbors being excluded, with the risk that couples' perception of their neighborhood is not captured. At the same time, it is common to attribute correlated behavior at small scales to social interaction among neighbors (e.g. Andersson/Musterd 2010), while the infl uence of unmeasured confounding characteristics and self-selection grows with neighborhood scale. Consequently, comparing the association at different scales might also indicate the relative importance of social interaction versus residential sorting and other contextual effects.

Data and measures
This study uses high-quality longitudinal data from several Norwegian administrative registers covering the entire population of Norway in the years 2000 to 2014.
Using universal personal identifi cation numbers and detailed address codes, time series on individual information from registers were linked and connected to individuals' residential information, the nationwide housing stock, and other geocoded information. Geographical coordinates for each inhabitant's place of residence were used to fi nd couples' (k-)nearest neighbors in each year of observation.
The study sample consists of 257,527 married and unmarried co-residential couples. To identify them, information from Norwegian population registers was used and women who gave birth to their second child in the study period were selected, provided they were aged between 20 and 44 when their second child was born and lived in the same household as the child's father. Selection was based on the woman's parity since she is most involved with childbearing and childrearing. For almost 10 percent of couples, the birth of the second child represented the couples' fi rst joint child. Whether the father or mother had children from previous partners was included as a control variable. Couples were censored when they moved abroad, one partner died, the woman turned 44 or the observation period exceeded 10 years. As periods in which couples did not share an address were excluded, separation also led to their removal from the risk set. Quarters of years are the time units, and process time (time since second childbirth) was included in the models using linear and quadratic terms. Thus, 5,413,443 couple-quarter observations were included in the regression analysis.
Outcome: The event under study is a woman's third childbirth, backdated to the start of pregnancy 2 A range of individual and couple characteristics that are known to impact childbearing and that are unevenly distributed across neighborhoods were included as control variables in the models. They were measured yearly and for both partners, if relevant. All couples in the study sample were registered at the same address and were therefore co-residential. Whether they were married is included as a timevarying measure for their union status. Stepchildren were documented using the following categories: (i) No children from previous partners; (ii) Both partners had children from previous partners; (iii) Only the woman had children from previous partners; (iv) Only the man had children with previous partners; and lastly (v) Couples had more complicated prehistories or missing information. Global region of birth was measured for both partners, distinguishing between those born in Asia, Africa, South, and Central America, and those born in any other region, including Norway. Furthermore, both partners' age when entering the risk set was included.
2 Originally, the event of interest is a couple's decision to have a third child. Because register data do not provide information about when that decision was taken, I use the fi rst trimester of the pregnancy leading to the live birth of the female partner's third child. The analyses thus capture individual and neighborhood circumstances at the time the female partner becomes pregnant with her third child. Note that abortions and miscarriages are not captured by these data.
Next, a woman's employment status was defi ned as active if her annual income exceeds the social security base income. Educational enrollment was documented for both partners using a dummy measure that is updated annually. Each partner's highest educational level was measured using the following categories: (i) Primary education (≤ 10 years); (ii) Secondary education (11-13 years); (iii) Short university education (14-17 years); and (iv) Long university education (≥ 18 years). Moreover, the annual household income from wages and salaries (infl ation-adjusted to 2013-NOK) was included using fi ve categories: (i) No income; (ii) < 600,000 NOK; (iii) 600,000-800,000 NOK; (iv) 800,000-1,000,000 NOK; and (v) > 1,000,000 NOK.
Housing: To indicate whether couples' current housing had room for another child, a variable combining the number of rooms and dwelling type in six different categories was used; distinguishing between single-family houses, terraced/ row houses, and apartments, and comparing whether each house type had up to 4 rooms, or 5 rooms and more.
Residential relocations: Addresses and dates on residential relocations exist for the whole study period and couples continued to be followed even after moving. The point at which the couple moved to the current neighborhood was measured as a time-varying covariate with the following categories: (i) Moved to the neighborhood during the last year; (ii) Lived in the neighborhood for up to 5 years; (iii) Up to 10 years; or (iv) More than 10 years.
Neighborhood defi nition: The geographical coordinates of a couple's residential address form the center of their individual neighborhood. Through calculating straight-line distances to surrounding residents using the Modeclus procedure in SAS, the geographically nearest neighbors were selected up to the desired number (K = 12, 25, 50, 100, 250, and 500). Since population density varies across Norway and perceptions of personal neighborhoods are spatially limited, maximum distances between neighbors were defi ned (ranging between 15 and 100 km, respectively, see Appendix Table A1). Consequently, couples residing in remote places were given smaller numbers of potential neighboring peers. Neighborhoods were defi ned at 31 December for each study year.
Neighborhood fertility: This is the percentage of female neighbors with at least three children out of all female neighbors aged between 20 and 44. The neighbor's number of children was obtained from individual-level population registers and, for each year, aggregated at the defi ned scales. Clear overrepresentation or underrepresentation of large families in the neighborhood may have had greater impact on couples' further childbearing. To detect such nonlinearity or thresholds, the measure was divided into fi ve categories: (i) < 10 percent; (ii) 10 up to 15 percent; (iii) 15 up to 20 percent; (iv) 20 up to 25 percent; (v) ≥ 25 percent. Neighboring women's educational level: Using the same strategy, the percentage of neighboring women with a university education was calculated for each study year and included as a continuous control variable.
Municipal centrality: The centrality of a couple's residential municipality was included in the models without fi xed effects since the rural, urban, and suburban dimensions have been emphasized in previous studies. Centrality describes a municipality's geographical position in relation to urban settlements and the popu-lation size of these settlements (see Statistics Norway Standard Classifi cation of Centrality at http://stabas.ssb.no/, 2014 classifi cations). This study used the following fi ve categories: (i) Municipality with a regional center; (ii) Municipality within 35 minutes' commuting time to a regional center; (iii) Municipality within 36 to 75 minutes' commuting time to a regional center; (iv) Relatively central municipalities; and (v) Less and least central municipalities.
Regions: To catch dynamics at higher spatial levels ("regional cultures"), dummies for the seven main regions in Norway were included. These are: Oslo and Akershus (Capital region), South Eastern Norway, Hedmark and Oppland, Agder and Rogaland, Western Norway, Trøndelag, and Northern Norway.

Statistical models
Linear probability models (LPM) were implemented with robust standard errors, adjusting for potential heteroscedasticity due to the binary dependent variable, and the correlation of observations over time or within units (Mood 2010b;Snijders/ Bosker 2012: 197). 3 Results from discrete-time hazard regression models produced similar conclusions and can be found in Appendix Table A5 and Figure A1. In the fi rst part of the analysis, the following models are estimated: where Y it is a couple's predicted probability of becoming pregnant with the third child during a certain quarter of the year and the subscripts denote the i th couple in the t th quarter of the year. X Nbors,it represents the percentage of neighbors with at least three children among couple i's k-nearest neighbors in year t in intervals (0-10, 10-15, 15-20, 20-25 and 25+ percent). Z Time,it is a continuous counter variable (process time) where the fi rst couple-quarter for each couple is coded as 0, and each subsequent quarter of year incremented by 1. Model 2 additionally includes sociodemographic characteristics of couples, where Z Sociodem,i represents time-constant couple-characteristics as the woman's and man's age at second childbirth, the presence of stepchildren and global region of birth, while Z Sociodem,it represents time-varying characteristics such as the cou-3 Mood (2010b: 78f.) presents the use of LPM as a valid solution to avoiding comparability issues in logistic regression. According to Mood, main reservations against using linear regression with binary dependent variables stem from the fear of: (1) getting predicted probabilities out of range; (2) heteroscedastic and non-normal residuals which could lead to invalid standard errors; and (3) a misspecifi ed functional form. While (1) is not a problem here, (2) is solved by using robust standard errors, and (3) is of minor relevance because nearest neighbors' fertility is measured in categories. Hence, no continuous probability function is modeled but discrete probabilities associated with each neighborhood fertility category. LPM coeffi cients are closely related to the often-used average marginal effects from logit models (Breen et al. 2018: 50).
(Model 1) ple's union status, the woman's employment status, educational enrolment, highest educational level and annual household income: The next model adds covariates measuring residential characteristics (Z ResidChar,it ) such as housing, time since last move and neighboring women's educational level, all of which are time-varying: In model 4, Z Region,it denotes dummies for region of country and Z Centrality,it the centrality of the municipality where the couple lived using fi ve categories. Both varied over time only if the couple had relocated during the observation period.
With the k-nearest neighbor approach the "neighborhoods" of interest were egocentered and thus, in essence, a characteristic of the couple. As a result, clustering observations within neighborhoods was neither possible nor needed in this study. 4 However, the risk remained that the main estimates capture other unmeasured neighborhood characteristics which had infl uenced predominant family sizes. Additional models with fi xed effects based on administrative neighborhood boundaries were therefore utilized in model 5. Fixed effects take account of all time-constant features of these neighborhoods, which may be the built environment, childcare facilities, and other opportunity structures for families that were shared at this or a higher neighborhood level and that remained constant over the observation period, including relatively time-stable values or norms.
Because observations over time are nested within couples, but not necessarily nested within one (higher level) geographical unit, the data are non-hierarchical or cross-classifi ed when it comes to neighborhoods. This makes them less suitable for multilevel models, which would become computationally demanding (Snijders/Bosker 2012: 207). Hence, the infl uence of other neighborhood factors besides the nearest neighbors' fertility is treated as "disturbance" rather than the phenomenon to be studied in this paper.

(Model 5)
As the data cover the whole country -containing both densely populated cities and sparsely populated rural regions -the chosen administrative unit was statistical tracts. Z StatTract,it are dummies for the approximately 1,550 statistical tracts in Norway (statistical tract fi xed effects). Statistical tracts represent a level between the smallest statistical unit and municipalities and were constructed to comprise naturally coherent units of communication and space. In urban areas they ideally comprise 3,000-6,000 inhabitants, in rural areas around 1,000-3,000 inhabitants. 5 In the models with statistical tract fi xed effects, associations at lower scales will be better identifi ed. To the extent that associations are found, these capture how individual neighborhoods deviate from the statistical tract where the couple lived.

Descriptive statistics
In total, 29.5 percent of the 257,527 couples in the study sample got pregnant with their third child during the years 2000 to 2014 (see Appendix Table A2). The average spacing between a second childbirth and the pregnancy was 10.6 quarters of years, which corresponds to 2.7 years; the whole study sample was observed for 4.6 years on average. Men and women in couples who conceived a third child were, on average, 1.6 years younger than the sample average when the second child was born and were more often found among those who were born abroad and who were married. In addition, when the woman's fi rst child was from a previous relationship, couples more often had another child (see Appendix Table A2). Table 1 gives descriptive statistics about couples' residential contexts. Two-child families in Norway most commonly lived in relatively spacious single-family houses, regardless of whether they were expecting another child or not. Over 40 percent of all fi nal observations were on couples who lived in a single-family house with 5 rooms or more. Furthermore, in the last year of observation, most of the families (40.3 percent) had lived in their respective neighborhood for up to 5 years; couples expecting a third child were overrepresented among those with shorter residencies. As previously shown (Fig. 1), descriptive statistics confi rm that couples conceiving their third child more often lived in the least central municipalities and were overrepresented in certain regions of Norway. Also, the share of neighboring women with a university education was somewhat lower among women expecting their third child.
Looking at neighbors' family sizes, we see from Table 2 that among most couples, 10 to 20 percent of the nearest neighbors had three or more children. As expected for neighborhoods which referred to the 50 nearest neighbors or fewer, observations are more dispersed and are more often found in the lower, but also in the highest categories. However, irrespective of whether the neighborhood fertility measure refers to the 12 or the 500 nearest neighbors, third births are most com-

Tab. 1:
Descriptive statistics of residential context variables (last coupleobservation) Sample total Couples with a 3rd birth N ( t o t a l ) M e a n N ( t o t a l ) M e a n mon among two-child couples who live in neighborhoods with the greatest proportion of (25+ percent) large families. This is consistent with the fi rst hypothesis claiming that there is a positive relationship between the percentage of neighbors with more than two children and the probability among two-child couples of having another child. So far, the more neighbors the neighborhood fertility measure refers to, the clearer the pattern.

Results from the regression models
To address the research questions and test the previously posed hypotheses, several regression models as described in chapter 6 were estimated where the outcome is a third birth and the predictor of interest is the share of women with three or more children among each couple's 250 nearest neighbors. First, a basic model including the neighbors' fertility and process time (model 1) is shown. Then, sociodemographic characteristics of couples are included (model 2). Next, a model with individual residential characteristics, such as housing (model 3), and a model including observed area-level characteristics (model 4) is discussed, before unobserved neighborhood characteristics at the level of statistical tracts are held constant (model 5). Finally, to analyze the impact of neighborhood scaling (MAUP) and to test Hypothesis 3, results for neighborhood measures referring to couples' 12, 25, 50, 100, and 500 nearest neighbors are compared.

Stepwise models
Results from the fi rst models with stepwise inclusion of sociodemographic, residential and area-level variables, as well as fi xed effects, are illustrated in Figure 2 and shown in Appendix Table A3. As seen in the fi rst baseline model, including only the neighborhood fertility measure and process time, having a third child was most likely among couples who lived in neighborhoods with many other large families (25+ percent). The predicted probability of being pregnant with a third child three years after the second childbirth was about 66 percent higher for these couples compared to couples who lived in neighborhoods where the proportion of large families was less than 10 percent. This is consistent with Hypothesis 1. However, Hypothesis 2a states that this association exists either partly or fully because couples with initially different probabilities of giving birth to a third child sort into different neighborhoods. Comparing couples living in different neighborhoods, while controlling for partners' age, global region of origin, union status, the presence of stepchildren, the man's or woman's level of education and educational enrolment, the woman's labor force participation and household income (model 2), the positive association between neighbors' family sizes and a couple's likelihood of having another child persisted. In fact, the predicted probabilities do not appear to be substantially different from the previous model (see Fig. 2).
Surprisingly, adding residential characteristics such as couples' dwelling type and size, residential time in the neighborhood, and the share of neighboring women with a university education (model 3) did not impact the main relationship either. Usually, housing as well as women's average education represent important sorting dimensions and are assumed to explain much spatial correlation of fertility behavior (e.g. Kulu/Boyle 2009). Indeed, families who lived in apartments, row houses, or in houses with four rooms or less were less likely to increase their family size than couples who lived in spacious single-family houses (see Appendix Table A3). It is also evident that couples who had remained in place for a while were less likely to have a third child than couples who had relocated during the last year. Hence, the fi ndings confi rm that anticipatory moves and appropriate housing were important predictors of third births. However, including these variables did not alter the relationship between neighbors' family size and third births. Taken together, results from model

Fig. 2:
Model comparison using predicted probabilities with 95 percent CIs for being in the 1st trimester of pregnancy with the subsequent live-born 3rd child, at the time the 2nd child turns 3 years of age, by neighborhood fertility (250 nearest  Note: All models include process time and process time squared. Additional covariates included in models 2 to 5 are: both partners' age at start, global region of birth, union status, stepchildren, both partners' educational attainment and enrolment, the woman's employment status and household income. Models 3 to 5 additionally include measures for housing, residential time in current neighborhood and neighboring women's education. Model 4 includes dummies for country region and municipal centrality, while Model 5 includes fi xed effects for statistical tracts (see also chapter 6).
Source: Data from Norwegian registers on a quarterly/yearly basis 2000-2014.
2 and 3 therefore consolidate Hypothesis 1 but provide only limited support for Hypothesis 2a, claiming that parts of the association between neighbors' family sizes are moderated and explained by individual characteristics of couples that were included in these models. The main relationship appeared noticeably different fi rst when indicators for the centrality of a couple's municipality and country region dummies were added (model 4). As the share of neighboring women with three or more children increases, the variance in the predicted probability of having a third birth was less when these area characteristics were taken into account (see Fig. 2). Consequently, results from the fourth model support Hypothesis 2b, stating that parts of the association between neighbors' family sizes and a couple's probability of having another child were explained by other characteristics of the residential context. However, note that area variables had more impact on the relationship of interest than individual measures such as housing and the education of couples' nearest neighbors. Moreover, the characteristics that could be included in model 4 were limited to those available in the dataset. Introducing neighborhood fi xed effects at the level of statistical tracts, the fi fth model controls for unobserved variation between these tracts.
The model with fi xed effects replaces the controls for municipal centrality and region with a fi xed term that captures all time-constant features at the level of statistical tracts and higher levels. Consequently, residential sorting at larger scales, into regions and larger "neighborhoods", is accounted for, and the main estimates capture remaining variation in third birth probabilities between the smaller individual neighborhoods. When applying these fi xed effects, the predicted probability of having a third child for couples living among many large families (25+ percent) was reduced in particular. In this model, their predicted probability of being pregnant with a third child three years after the second childbirth was only about 20 percent higher compared to couples who lived in neighborhoods where the share of large families was less than 10 percent. Generally, the remaining variation between the different neighborhood categories was much lower. The fi fth model therefore also supports Hypothesis 2b and shows that parts of the association between neighbors' family sizes and a couple's probability of having another child were explained by unobserved characteristics of the neighborhoods.
Nonetheless, results from the regression models using neighborhoods which refer to couples' 250 nearest neighbors still support the fi rst hypothesis claiming that the family size of neighbors was positively related to a couple's propensity to have a third child. Parts of this relationship were (slightly) moderated by individual characteristics of couples and their housing situation, but even more so by observed and unobserved characteristics of the broader residential context. These fi ndings support Hypothesis 2b in particular and indicate that residential sorting at larger spatial scales is important for the spatial clustering of fertility. However, the relationship of interest remained, even after controlling for these characteristics of couples and their larger neighborhoods, and was thus relatively consistent.

Scale comparison
To show how sensitive results are for the scaling of the individual neighborhoods, results for fertility measures of a couple's nearest 12, 25, 50, 100, 250, and 500 neighbors are presented in Figure 3 (see also Appendix Table A4). Overall, the association between the share of neighbors with more than two children and the probability of two-child couples having another child was weaker as the number of neighbors to which the neighborhood fertility measure referred decreases. This was especially true for the predicted probability of third births among couples who were surrounded by a high percentage of large families (25+ percent). On the other hand, for couples living in neighborhoods where large families were scarce (0-10 percent), the predicted probabilities for third births were relatively similar regardless of how many neighbors the measure referred to.

Fig. 3:
Neighborhood scale comparison using predicted probabilities with 95 percent CIs for being in the 1st trimester of pregnancy with the subsequent live-born 3rd child, at the time the 2nd child turns 3 years of age, models 4 and 5  Note: Covariates included are: process time, both partners' age at start, global region of birth, union status, stepchildren, both partners' educational attainment and enrolment, the woman's employment status, household income, housing, residential time, neighbors' education, centrality and region (last two only in model 4). Model 5 additionally includes fi xed effects for statistical tracts. For k-12, few observations fell in the categories 10-15 and 20-25 percent (see also Table 2).
Source: Data from Norwegian registers on a quarterly/yearly basis 2000-2014.
From Figure 3, we also notice that the estimates with increasing neighborhood scale also differ more between model 4, which includes all previously mentioned control variables, and model 5, which uses fi xed effects for statistical tracts. 6 This confi rms that the infl uence of unmeasured confounding neighborhood characteristics grows with neighborhood scale. Meanwhile, with decreasing numbers of neighbors, the variation in predicted third birth probabilities by neighborhood fertility generally decreased.
Given the observed variation, the results confi rm the previously discussed MAUP and thus support the third hypothesis, which states that (the strength of) the relationship between neighbors' family sizes varies with the chosen neighborhood scale. Specifi cally, the strength of the relationship between neighbors' fertility increased with neighborhood scale, which might emphasize the relative importance of other contextual effects over social interaction effects. Nevertheless, a correlation between the percentage of neighboring families with many (3+) children and a couple's transition to having a third child is apparent, even if only the twelve nearest neighbors were considered.

Conclusion and discussion
Previous research has found that couples' decisions about fertility behavior are infl uenced by their social context, in which immediate neighborhoods and neighbors may also play a signifi cant role. Neighborhoods are important contexts of childrearing. Families may therefore sort geographically based on their fertility preferences, but they may also increasingly interact with neighboring families (Kalmijn 2012). Even so, with few exceptions (e.g. Malmberg/Andersson 2019), neighborhoods and neighbor networks have to date been severely understudied in fertility research. This study indicates that fertility behavior is sociogeographically situated through potential social interaction effects among neighbors as well as well-known processes of selective moves. The analyses showed that two-child couples who lived in neighborhoods with a higher share of families with more than two children were more likely to have a third child than were other two-child couples. Conversely, two-child couples who lived in neighborhoods where families with at least three children were scarce were less likely to have a third child.
In previous studies, spatial variations in fertility have often been explained by population composition and residential sorting, regional cultures and specifi c characteristics of the residential context, such as housing and centrality (Hank 2002;Kulu et al. 2007;de Beer/Deerenberg 2007;Fulda 2015). In this study, observed and unobserved characteristics of the residential context and, to a lesser degree, sociodemographic characteristics of couples, moderated the relationship between fertility in the neighborhood and a couple's probability of continued childbearing. Accounting for broader area-level variables had more impact on the relationship of interest than individual measures such as housing and the education of couples' nearest neighbors. This indicates that residential sorting at larger spatial scales is important for the spatial clustering of fertility, aligns well with regional variations that have been documented for previous decades (Lappegård 1999), and underlines the persistent regional fertility cultures. Moreover, the results also confi rmed previous fi ndings that the propensity to have many children is highest among couples living in spacious single-family houses in rural regions. But beyond these characteristics, the fertility of nearest neighbors also seems to matter. This correlation has never been shown at such a small scale.
The neighborhood scales that were considered in this study range from the nearest 12 to the nearest 500 neighbors and may all reasonably represent families' everyday activity spaces. The more neighbors referred to in the neighborhood measure, however, the stronger the correlation between neighbors' family size and couples' continued childbearing became. This was especially true for couples living in neighborhoods where large families were overrepresented. The analyses also revealed that the infl uence of unmeasured confounding neighborhood characteristics grew with neighborhood scale. In sum, these results might emphasize the relative importance of other contextual effects and selection over social interaction effects. Family events and residential relocations are highly intertwined processes. The positive association that was found between third births and recent residential relocations may also point towards selective or anticipatory relocations, or perhaps towards new neighborhoods and neighbors stimulating couples' child desires. While the latter is not completely unlikely if one assumes that desired family size is subject to change (Thomson 2015), the mechanisms cannot be distinguished empirically.

Limitations and strengths
The aim of this paper was to gain more insight into spatial variations in family sizes by ascertaining the importance of the family behavior of couples' nearest neighbors relative to those of other neighborhood characteristics. It is notoriously difficult to distinguish between self-selection into neighborhoods and causal effects of neighborhood contexts, and studies rarely succeed in this endeavour. Importantly, families do not move at random, and couples who intend to have many (3+) children may tend to favor the same residential areas. Even if very small neighborhood scales were used and a range of traits and fi xed effects could be included in the models, shared unmeasured confounders among neighbors are likely to remain.
In future studies, it might be interesting to elaborate further on the residential segregation of families, including by dimensions such as country of origin and socioeconomic status. Such segregation is particularly prevalent in larger cities and is most likely important because contact with neighbors might depend on more commonalities than simply sharing the children's playground. The study was also limited to current neighborhoods and thus did not address couples' neighborhood histories. There could be cumulative (or contradictory) effects over the life course, which call for an inclusion in future studies of time lags, the upbringing context, and the family of origin (Miltenburg/van der Meer 2018). To test whether there are any discrepancies or changes over the life course, it would also be interesting to analyze how fertility ideals, and not only actual fertility behavior, are interrelated among neighbors and within neighborhoods. Unfortunately, such data are not available for Norway.
Source: Data from Norwegian registers on a quarterly/yearly basis 2000-2014.
Linking Neighbors' Fertility: Third Births in Norwegian Neighborhoods • 393

Fig. A1:
Results from discrete-time hazard regression models for being in the 1st trimester of pregnancy with the subsequent, live-born 3rd child. Neighborhood scale comparison using average marginal effects with 95 percent CIs at all observation points, 2000-2014 Note: Neighborhoods with 15-20 percent neighboring women with 3 or more children serve as reference. Covariates included are: Both partners' age at start, global region of birth, union status, stepchildren, both partners' educational attainment and enrolment, the woman's employment status, household income, housing, residential time, neighbors' education, centrality and region. Comparable to results from linear probability model 4. Source: Data from Norwegian registers on a quarterly/yearly basis 2000-2014. Share of neighboring women with 3+ children