Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods Janna Bergsvik Abstract: 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 fam- ily size by analyzing third births in a neighborhood context. Using unique geo-data on neighbors and neighborhoods, this paper introduces a new geographical dimen- sion of fertility variation and contributes to our understanding of geographical vari- ations in fertility. Flexible, ego-centered neighborhoods are constructed using longitudinal geo- data taken from administrative registers (2000-2014). Data on inhabitants’ residen- tial 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 socio- demographic characteristics of couples, the educational level attained by neighbor- ing 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. Keywords: Spatial fertility · k-nearest neighbors · Fertility diffusion · Family size · Third births Comparative Population Studies Vol. 45 (2020): 359-394 (Date of release: 27.10.2020) Federal Institute for Population Research 2020 URL: www.comparativepopulationstudies.de DOI: https://doi.org/10.12765/CPoS-2020-21 URN: urn:nbn:de:bib-cpos-2020-21en4 • Janna Bergsvik360 1 Introduction Declining family sizes and, in particular, fewer women having a third child, are prin- cipal 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 sever- al 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 consid- ered 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 geo- graphical patterns of childbearing highlight potential normative (Ruckdeschel et al. 2018) and cultural infl uences (Fulda 2015). The spatial diffusion of fertility behav- ior is an inherent part of demographic transition theories (Bongaarts/Watkins 1996; Lesthaeghe/Neels 2002), and the importance of compositional and contextual fac- tors in shaping fertility variation is increasingly acknowledged (Vitali et al. 2015). Geographical variations in fertility are well recognized at the level of regions, nation states, and along the urban-rural dimension. For instance, they are docu- mented for the Nordic countries (Kulu et al. 2007), the Netherlands (de Beer/Deer- enberg 2007), Austria, Switzerland, and Germany (Basten et al. 2011), Italy (Vitali/ Billari 2015), Great Britain (Fiori et al. 2014), and Australia (Gray/Evans 2018). How- ever, 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’ net- works when entering parenthood (Rözer et al. 2017; Kalmijn 2012). However, be- cause 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 correla- tion 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 res- idential context is sparse (but see Malmberg/Andersson 2019). Given that there is considerable interest in geographical variations in fertility and the diffusion of fertil- ity 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 Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 361 has the potential to shed light on the explanatory importance of neighborhood con- text, 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 u- ences, may refl ect both residential sorting and social interaction (Manski 1993). The present analyses use detailed longitudinal data from Norway (2000-2014), 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 area- level infl uences are included? 2 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 cur- rent 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 Norwe- gian 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 two- child norm results in women having more than two children, rather than fewer chil- dren. 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 nd- ing 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 ex- ample, 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 char- acteristics 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. • Janna Bergsvik362 Fig. 1: Map of regional variations in third births in Norway, 2014. Basic statistical units (N=14,000) N few obs. Source: Map from the Geodatabase at Statistics Norway. Data from Norwegian adminis- trative registers. Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 363 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 chil- dren (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). In line with this, couples alter their family size intentions during the life course due to changing circumstances, new information, reference groups, and perceived norms (Iacovou/ Tavares 2011; Clay/Zuiches 1980; Thomson 2015; Liefbroer 2009).1 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 con- texts 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? Corre- lated fertility behavior within neighborhoods and variations in the number of chil- dren between neighborhoods may emerge through similar channels as for other geographical aggregates. Theoretical divisions are often made between explana- tions 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 medi- cal 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). • Janna Bergsvik364 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 over- representation of highly educated women in urban areas, who are more likely to re- main 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 culture – also resulting in lower fertility rates, not only for highly-educated women. The migration patterns of families additionally infl uence the population compo- sition. Importantly, families do not move at random, and residential relocations of- ten 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 propen- sity 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 un- employment decreases the number of higher-order births (Kravdal 2002). Childcare availability has shown positive effects on all parities (Rindfuss et al. 2010), highlight- ing opportunities for having a large family as an important contextual factor. With- in 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 tradi- tions 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). Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 365 (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/Wat- kins 1996; Casterline 2001). Such diffusion of fertility behavior between neighbor- ing 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 (Vitali et al. 2015). As fam- ily 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 situ- ation, 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 chan- nels as other networks (Bernardi/Klarner 2014). They may share knowledge, provide information, and behavioral examples, and social contagion may be apparent. So- cial 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 par- ent 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 limi- tation in several high-fertility contexts, for example in Nepal (Axinn/Yabiku 2001; Jennings/Barber 2013) and Cairo (Weeks et al. 2004). In low-fertility countries, how- ever, theneighborhood dimension appears to be understudied when it comes to fertility behavior. In summary, geographical variations in family size might be rooted in differ- ent 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 char- acteristics of the residential context, and possibly social interaction. • Janna Bergsvik366 4 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 mod- erated 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 ad- ministrative 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 neigh- borhood fertility measure (Hypothesis 3). Spatial analysis always suffers from the modifi able areal unit problem (MAUP) where decisions about unit scaling and zon- ing 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, munici- palities 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. Re- stricting the focus to very few neighbors increases the possibility of relevant neigh- bors 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 dif- ferent scales might also indicate the relative importance of social interaction versus residential sorting and other contextual effects. Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 367 5 Data and measures This study uses high-quality longitudinal data from several Norwegian administra- tive 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 indi- viduals’ 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 cou- ples. 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 cou- ples’ fi rst joint child. Whether the father or mother had children from previous part- ners 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 pregnancy2 A range of individual and couple characteristics that are known to impact child- bearing 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 time- varying 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) Cou- ples 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. • Janna Bergsvik368 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 differ- ent 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 neighbor- hood 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 residen- tial 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 distanc- es between neighbors were defi ned (ranging between 15 and 100 km, respectively, see Appendix Table A1). Consequently, couples residing in remote places were giv- en 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 underrep- resentation of large families in the neighborhood may have had greater impact on couples’ further childbearing. To detect such nonlinearity or thresholds, the meas- ure 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 percent- age 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 mu- nicipality’s geographical position in relation to urban settlements and the popu- Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 369 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 follow- ing 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”), dum- mies for the seven main regions in Norway were included. These are: Oslo and Ak- ershus (Capital region), South Eastern Norway, Hedmark and Oppland, Agder and Rogaland, Western Norway, Trøndelag, and Northern Norway. 6 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: Y it = β 0 + β Nbors X Nbors,it + β Time Z Time,it + β TimeSq (Z Time,it x Z Time,it ) + ε it where Yit 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 ith couple in the tth quarter of the year. XNbors,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). ZTime,it is a continuous counter variable (pro- cess 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 ZSociodem,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 ZSociodem,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) • Janna Bergsvik370 ple’s union status, the woman’s employment status, educational enrolment, highest educational level and annual household income: Y it = β 0 + β Nbors X Nbors,it + β Time Z Time,it + β TimeSq (Z Time,it x Z Time,it ) + β Sociodem Z Sociodem,it + β Sociodem Z Sociodem,i + ε it The next model adds covariates measuring residential characteristics (ZResidChar,it) such as housing, time since last move and neighboring women’s educational level, all of which are time-varying: Y it = β 0 + β Nbors X Nbors,it + β Time Z Time,it + β TimeSq (Z Time,it x Z Time,it ) + β Sociodem Z Sociodem,it + β Sociodem Z Sociodem,i + β ResidChar Z ResidChar,it + ε it In model 4, ZRegion,it denotes dummies for region of country and ZCentrality,it the centrality of the municipality where the couple lived using fi ve categories. Both var- ied over time only if the couple had relocated during the observation period. Y it = β 0 + β Nbors X Nbors,it + β Time Z Time,it + β TimeSq (Z Time,it x Z Time,it ) + β Sociodem Z Sociodem,it + β Sociodem Z Sociodem,i + β ResidChar Z ResidChar,it + β Region Z Region,it + β Centrality Z Centrality,it + ε it With the k-nearest neighbor approach the “neighborhoods” of interest were ego- centered 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. Addi- tional 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. Y it = β 0 + β Nbors X Nbors,it + β Time Z Time,it + β TimeSq (Z Time,it x Z Time,it ) + β Sociodem Z Sociodem,it + β Sociodem Z Sociodem,i + β ResidChar Z ResidChar,it + β StatTract Z StatTract,it + ε it (Model 2) (Model 3) (Model 4) 4 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) Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 371 As the data cover the whole country – containing both densely populated cities and sparsely populated rural regions – the chosen administrative unit was statisti- cal tracts. ZStatTract,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. 7 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 aver- age 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 hous- es, 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 over- represented 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 cou- ples, 10 to 20 percent of the nearest neighbors had three or more children. As ex- pected for neighborhoods which referred to the 50 nearest neighbors or fewer, ob- servations 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- 5 Consequently, in rural regions in particular, statistical tracts may overlap with a neighborhood size of 500 neighbors. • Janna Bergsvik372 Tab. 1: Descriptive statistics of residential context variables (last couple- observation) Sample total Couples with a 3rd birth N (total) Mean N (total) Mean Neighbor women with a university education % of 500 nearest neighbors 257,527 43.0 75,847 39.2 250 nearest neighbors 257,527 43.0 75,847 39.1 100 nearest neighbors 257,527 43.3 75,847 39.2 50 nearest neighbors 257,527 43.6 75,847 39.4 25 nearest neighbors 257,527 43.9 75,847 39.5 12 nearest neighbors 257,526 44.2 75,846 39.7 N (cell) Pct (col) N (cell) Pct (row) Dwelling type and number of rooms single-family house, 5 rooms or more 109,203 42.4 30,593 28.0 single-family house, 4 rooms or less 73,845 28.7 20,062 27.2 terraced/row house, 5 rooms or more 11,388 4.4 2,974 26.1 terraced/row house, 4 rooms or less 18,739 7.3 5,275 28.1 apartment, 5 rooms or more 1,691 0.7 514 30.4 apartment, 4 rooms or less 20,253 7.9 6,621 32.7 missing housing information 22,408 8.7 9,808 43.8 Residential time in current neighborhood moved during the last year 35,701 13.9 16,658 46.7 last relocation up to 5 years ago 103,746 40.3 39,243 37.8 last relocation up to 10 years ago 75,646 29.4 17,487 23.1 last relocation more than 10 years ago 42,434 16.5 2,459 5.8 Centrality of residential municipality municipality with regional center 67,620 26.3 19,605 29.0 travel time to regional center < 36 min 69,825 27.1 19,011 27.2 travel time to regional center 36-75 min 43,648 17.0 11,965 27.4 relatively central 41,544 16.1 12,344 29.7 less and least central 34,890 13.6 12,922 37.0 Region of Norway Oslo and Akershus (Capital region) 63,887 24.8 16,107 25.2 Hedmark and Oppland 17,173 6.7 4,505 26.2 South Eastern Norway 46,310 18.0 11,277 24.4 Agder and Rogaland 41,373 16.1 14,424 34.9 Western Norway 45,148 17.5 16,067 35.6 Trøndelag 22,522 8.8 6,652 29.5 Northern Norway 21,114 8.2 6,815 32.3 Total 257,527 100 75,847 29.5 Source: Data from Norwegian registers on a quarterly/yearly basis 2000-2014. Descriptive statistics for the last year of observation for each couple. Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 373 Tab. 2: Descriptive statistics of the independent variable (last couple- observation) Sample total Couples with a 3rd birth N (cell) Pct (col) N (cell) Pct (row) Neighbors with at least 3 children out of 500 nearest neighbors 0-10% 33,788 13.1 7,454 22.1 10-15% 94,597 36.7 19,253 20.4 15-20% 72,579 28.2 22,208 30.6 20-25% 39,281 15.3 15,643 39.8 25+% 17,282 6.7 11,289 65.3 250 nearest neighbors 0-10% 37,102 14.4 7,941 21.4 10-15% 88,831 34.5 18,999 21.4 15-20% 70,077 27.2 20,637 29.4 20-25% 40,365 15.7 15,707 38.9 25+% 21,152 8.2 12,563 59.4 100 nearest neighbors 0-10% 44,815 17.4 9,678 21.6 10-15% 72,399 28.1 16,330 22.6 15-20% 68,175 26.5 19,194 28.2 20-25% 41,515 16.1 14,885 35.9 25+% 30,623 11.9 15,760 51.5 50 nearest neighbors 0-10% 51,335 19.9 11,582 22.6 10-15% 74,634 29.0 17,891 24.0 15-20% 48,740 18.9 13,917 28.6 20-25% 47,460 18.4 15,998 33.7 25+% 35,358 13.7 16,459 46.5 25 nearest neighbors 0-10% 75,642 29.4 17,727 23.4 10-15% 44,586 17.3 11,406 25.6 15-20% 41,970 16.3 11,791 28.1 20-25% 35,932 14.0 11,297 31.4 25+% 59,397 23.1 23,626 39.8 12 nearest neighbors 0-10% 116,797 45.4 29,546 25.3 10-15% 1,997 0.8 700 35.1 15-20% 62,676 24.3 18,063 28.8 20-25% 1,778 0.7 680 38.2 25+% 74,278 28.8 26,857 36.2 Total 257,527 100 75,846 29.5 Source: Data from Norwegian registers on a quarterly/yearly basis 2000-2014. Neighbors updated yearly. Descriptive statistics for the last year of observation for each cou- ple. • Janna Bergsvik374 mon among two-child couples who live in neighborhoods with the greatest pro- portion 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. 8 Results from the regression models To address the research questions and test the previously posed hypotheses, sev- eral regression models as described in chapter 6 were estimated where the out- come 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, so- ciodemographic 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 unob- served neighborhood characteristics at the level of statistical tracts are held con- stant (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. 8.1 Stepwise models Results from the fi rst models with stepwise inclusion of sociodemographic, resi- dential 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 neighbor- hoods, 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 Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 375 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 cou- ples 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 predic- tors 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 neighbors) .0 15 .0 17 5 .0 2 .0 22 5 .0 25 .0 27 5 0-10% 10-15% 15-20% 20-25% 25+% Share of neighboring women with 3+ children M1: Base M2: Sociodem. M3: Context M4: All controls M5: FE 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 educa- tion. 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. • Janna Bergsvik376 2 and 3 therefore consolidate Hypothesis 1 but provide only limited support for Hy- pothesis 2a, claiming that parts of the association between neighbors’ family sizes are moderated and explained by individual characteristics of couples that were in- cluded 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 (mod- el 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 ex- plained 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 sta- tistical 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 individ- ual 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 neigh- bors’ 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 re- fer 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 charac- teristics of couples and their housing situation, but even more so by observed and unobserved characteristics of the broader residential context. These fi ndings sup- port 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. Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 377 8.2 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 neigh- bors 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 espe- cially 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 .0 16 .0 18 .0 2 .0 22 .0 24 .0 26 .0 16 .0 18 .0 2 .0 22 .0 24 .0 26 .0 16 .0 18 .0 2 .0 22 .0 24 .0 26 .0 16 .0 18 .0 2 .0 22 .0 24 .0 26 0-10 10-15 15-20 20-25 25+ .0 16 .0 18 .0 2 .0 22 .0 24 .0 26 0-10 10-15 15-20 20-25 25+ .0 16 .0 18 .0 2 .0 22 .0 24 .0 26 0-10 10-15 15-20 20-25 25+ Model 4 Model 5 0-10 10-15 15-20 20-25 25+ 0-10 10-15 15-20 20-25 25+ 0-10 10-15 15-20 20-25 25+ 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. • Janna Bergsvik378 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 characteris- tics grows with neighborhood scale. Meanwhile, with decreasing numbers of neigh- bors, 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 in- creased with neighborhood scale, which might emphasize the relative importance of other contextual effects over social interaction effects. Nevertheless, a correla- tion 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. 9 Conclusion and discussion Previous research has found that couples’ decisions about fertility behavior are in- fl uenced by their social context, in which immediate neighborhoods and neighbors may also play a signifi cant role. Neighborhoods are important contexts of childrear- ing. 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. Converse- ly, 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 char- acteristics 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 6 Because the fi xed effects are at the level of statistical tracts regardless of the scale of the indi- vidual neighbourhood, they might impact individual neighbourhoods differently, as discussed earlier (e.g. note 2). As a result, it may not be the ideal model for a scale comparison. However, because the fi xed effect model remains a stronger model than model 4, both are presented. Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 379 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 previ- ous 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 charac- teristics, 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 near- est 12 to the nearest 500 neighbors and may all reasonably represent families’ every- day 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 neigh- borhoods 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 impor- tance of other contextual effects and selection over social interaction effects. Fam- ily 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. 9.1 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 neigh- bors relative to those of other neighborhood characteristics. It is notoriously diffi - cult 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+) chil- dren 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 so- cioeconomic 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, • Janna Bergsvik380 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. Nevertheless, this study brought together both the spatial and social context by introducing small-scale neighborhoods using k-nearest neighbor measures. By defi ning individual neighborhoods of different sizes, this study introduced a new di- mension of spatial fertility variation and has contributed to an emerging awareness of scale sensitivity. The correlation between neighbors’ fertility behavior could be shown even at the very small scale of the 12 nearest neighbors. As such, this paper contributes to a broadening of spatial and network thinking in fertility research to include neighborhoods and neighbors. 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In: Geographical Analysis 47,1: 34-49. https://doi.org/10.1111/gean.12053 Date of submission: 20.12.2019 Date of acceptance: 30.07.2020 Janna Bergsvik (). Statistics Norway, Research Department. Oslo, Norway. E-mail: Janna.Bergsvik@ssb.no URL: https://www.ssb.no/en/forskning/ansatte/janna-bergsvik • Janna Bergsvik386 Appendix Tab. A1: Distances and number of neighbors included after different choices of neighborhood size Defi ned neighborhood size (k-nearest neighbors): k= 500 250 100 50 25 12 Number of neighbors actually included† Minimum 499 66 66 1 1 1 Maximum 890 645 500 416 416 416 Mean 500 250 100 50 25 12 SD 3 3 3 3 3 3 Max. distance to a neighbor (in meters) Defi ned max. 100,000 50,000 50,000 25,000 20,000 15,000 Final max. 98,830 50,000 49,978 25,000 19,999 14,980 Mean 3,497 2,154 1,149 710 444 265 SD 6,237 3,888 2,266 1,474 988 614 Median distance to neighbors (in meters) Mean 2,077 1,349 721 457 290 177 SD 3,840 2,579 1,513 1,008 670 426 † Values above the defi ned “k” are due to housing block coordinates making it impos- sible to identify exactly the desired number of nearest neighbors. Values below the defi ned “k” stem from the distance cut-off. Source: Data from Norwegian registers on a quarterly/yearly basis 2000-2014. Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 387 Tab. A2: Descriptive statistics of sociodemographic control variables (last couple-observation) Sample total Couples with a 3rd birth N (total) Mean N (total) Mean Process time: quarters of years (max. 40) 257,527 18.2 75,847 10.6 Age at 2nd childbirth woman (min. 20, max. 44) 257,527 31.1 75,847 29.4 man (min. 17, max. 77) 257,527 33.9 75,847 32.3 N (cell) Pct (col) N (cell) Pct (row) Country of birth: Asia, Africa, South or Central America female partner 23,406 9.1 7,941 33.9 male partner 19,695 7.7 7,510 38.1 Marital status (married) 182,313 70.8 59,390 32.6 Children from previous partners neither of the partners 211,150 82.0 60,776 28.8 both partners 5,936 2.3 1,813 30.5 only woman 16,952 6.6 7,997 47.2 only man 18,593 7.2 3,756 20.2 complex/missing 4,896 1.9 1,505 30.7 Highest educational level attained, woman Compulsory or unknown 37,395 14.5 12,717 34.0 High school 77,800 30.2 21,729 27.9 Short university 107,962 41.9 32,272 29.9 Long university 34,370 13.4 9,129 26.6 Highest educational level attained, man Compulsory or unknown 39,395 15.3 12,199 31.0 High school 112,695 43.8 32,179 28.6 Short university 67,659 26.3 20,123 29.7 Long university 37,778 14.7 11,346 30.0 Women in education 19,329 7.5 5,164 26.7 Man in education 11,072 4.3 4,095 37.0 Woman in labor force† 234,697 91.1 66,385 28.3 Annual household income‡ None 1,294 0.5 583 45.1 up to 600,000 NOK 37,192 14.5 17,792 47.8 600,000 – 800,000 NOK 52,551 20.4 20,451 38.9 800,000 – 1,000,000 NOK 65,599 25.5 17,738 27.0 1,000,000 + NOK 100,706 39.1 19,282 19.1 Total 257,527 100 75,846 29.5 Note: Means are given for continuous measures, percentages are given for categories. † Defi ned as active if annual income exceeds social security base income. ‡ From wages and salaries, infl ation-adjusted to 2013-NOK, NOK 1000 ~ € 135 (in 2013). Source: Data from Norwegian registers on a quarterly/yearly basis 2000-2014. Descriptive statistics for the last year of observation for each couple. • Janna Bergsvik388 T a b . A 3: C o m p a ri n g M o d e l 1 t o 5 : L in e a r p ro b a b ili ty m o d e ls f o r h av in g a t h ir d c h ild , 2 0 0 0 -2 01 4 M o d e l 1 M o d e l 2 M o d e l 3 M o d e l 4 M o d e l 5 N e ig h b o rs w it h a t le a st 3 c h il d re n 0 -1 0 % o f 2 5 0 n e a re st -0 .0 0 16 * * * -0 .0 0 17 * * * -0 .0 0 18 * * * -0 .0 0 12 * * * -0 .0 0 15 * * * 10 -1 5 % o f 2 5 0 n e a re st -0 .0 0 19 ** * -0 .0 0 16 ** * -0 .0 0 17 ** * -0 .0 0 10 ** * -0 .0 0 0 6 ** * 15 -2 0 % o f 2 5 0 n e a re st re f. re f. re f. re f. re f. 2 0 -2 5 % o f 2 5 0 n e a re st 0 .0 0 3 3 * * * 0 .0 0 3 0 * * * 0 .0 0 3 0 * * * 0 .0 0 16 * * * 0 .0 0 0 4 * 2 5 + % o f 2 5 0 n e a re st 0 .0 0 8 9 * * * 0 .0 0 8 1 * * * 0 .0 0 8 2 * * * 0 .0 0 6 0 * * * 0 .0 0 2 3 * * * P ro ce ss t im e ( q u a rt e rs o f y e a rs )† 0 .0 0 11 * * * 0 .0 0 12 * * * 0 .0 0 13 * * * 0 .0 0 13 * * * 0 .0 0 14 * * * D w e ll in g t yp e a n d n u m b e r o f ro o m s si n g le -f a m ily h o u se , 5 r o o m s o r m o re re f. re f. re f. si n g le -f a m ily h o u se , 4 r o o m s o r le ss -0 .0 0 12 * * * -0 .0 0 12 * * * -0 .0 0 11 * * * te rr a ce d /r o w h o u se , 5 r o o m s o r m o re -0 .0 0 18 ** * -0 .0 0 2 0 ** * -0 .0 0 17 ** * te rr a ce d /r o w h o u se , 4 r o o m s o r le ss -0 .0 0 2 1 ** * -0 .0 0 2 4 ** * -0 .0 0 2 2 ** * a p a rt m e n t, 5 r o o m s o r m o re -0 .0 0 0 1 -0 .0 0 0 1 -0 .0 0 11 a p a rt m e n t, 4 r o o m s o r le ss -0 .0 0 0 7 ** -0 .0 0 10 * * * -0 .0 0 19 * * * m is si n g h o u si n g i n fo rm a ti o n 0 .0 0 0 6 ** 0 .0 0 0 4 * 0 .0 0 0 1 R e si d e n ti a l ti m e i n c u rr e n t n e ig h b o rh o o d m o v e d d u ri n g t h e l a st y e a r re f. re f. re f. la st r e lo c a ti o n u p t o 5 y e a rs a g o -0 .0 0 0 9 ** * -0 .0 0 0 9 ** * -0 .0 0 10 ** * la st r e lo c a ti o n u p t o 1 0 y e a rs a g o -0 .0 0 4 5 ** * -0 .0 0 4 5 ** * -0 .0 0 4 5 ** * la st r e lo c a ti o n > 1 0 y e a rs a g o -0 .0 0 41 * * * -0 .0 0 4 2 * * * -0 .0 0 4 3 * * * N e ig h b o ri n g w o m e n w it h a u n iv e rs it y e d u ca ti o n % o f 2 5 0 n e a re st n e ig h b o rs 0 .0 0 0 0 ** * 0 .0 0 0 0 -0 .0 0 0 2 ** * C e n tr a li ty o f re si d e n ti a l m u n ic ip a li ty m u n ic ip a li ty w it h r e g io n a l c e n te r -0 .0 0 2 4 * * * - tr a v e l t im e t o r e g io n a l c e n te r < 3 6 m in -0 .0 0 3 0 * * * - tr a v e l t im e t o r e g io n a l c e n te r 3 6 -7 5 m in -0 .0 0 3 0 * * * - re la ti v e ly c e n tr a l -0 .0 0 2 8 * * * - le ss a n d l e a st c e n tr a l re f. - Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 389 T a b . A 3: C o n ti n u a ti o n M o d e l 1 M o d e l 2 M o d e l 3 M o d e l 4 M o d e l 5 R e g io n o f N o rw a y O sl o a n d A ke rs h u s (C a p it a l r e g io n ) re f. - H e d m a rk a n d O p p la n d -0 .0 0 0 3 - S o u th E a st e rn N o rw a y -0 .0 0 14 * * * A g d e r a n d R o g a la n d 0 .0 0 2 1 * * * - W e st e rn N o rw a y 0 .0 0 2 4 * * * - T rø n d e la g -0 .0 0 0 6 ** - N o rt h e rn N o rw a y -0 .0 0 0 1 - In d iv id u a l a n d c o u p le c o va ri a te s N o Y e s Y e s Y e s Y e s F ix e d e ff e ct s fo r st a ti st ic a l tr a ct s N o N o N o N o Y e s F -v a lu e 51 5 3 .0 15 4 3 .2 11 5 8 .9 9 2 7. 1 10 7 8 .3 C o u p le -q u a rt e r o b se rv a ti o n s 5 ,4 13 ,4 4 3 N o te : Ta b le s h o w s b e ta c o e ffi c ie n ts a n d s ig n ifi c an ce le v e ls : * p < 0 .0 5 ; ** p < 0 .0 1 ; ** * p < 0 .0 0 1 . C o v ar ia te s in cl u d e d in m o d e ls 2 t o 5 ar e : b o th p ar tn e rs ’ a g e a t st ar t, g lo b al r e g io n o f b ir th , u n io n s ta tu s, s te p ch ild re n , b o th p ar tn e rs ’ e d u ca ti o n al a tt ai n m e n t an d e n ro lm e n t, th e w o m an ’s e m p lo y m e n t st at u s an d h o u se h o ld in co m e . † P ro ce ss t im e s q u ar e d ( n o t sh o w n ) w as in cl u d e d a n d n e g at iv e b u t cl o se t o z e ro in a ll m o d e ls . S o u rc e : D at a fr o m N o rw e g ia n r e g is te rs o n a q u ar te rl y /y e ar ly b as is 2 0 0 0 -2 0 1 4 . • Janna Bergsvik390 Tab. A4: Comparing different neighborhood scales: Linear probability models for having a third child, 2000-2014 k=12† k=25 k=50 k=100 k= 250 k=500 Model 4 with covariates Neighbors with 3+ children 0-10 % -0.0006*** -0.0008*** -0.0010*** -0.0011*** -0.0012*** -0.0007*** 10-15 % 0.0005 -0.0004** -0.0006*** -0.0008*** -0.0010*** -0.0013*** 15-20 % ref. ref. ref. ref. ref. ref. 20-25 % 0.0013 0.0006** 0.0007*** 0.0012*** 0.0016*** 0.0022*** 25 + % 0.0015*** 0.0022*** 0.0033*** 0.0043*** 0.0060*** 0.0069*** F-value 921.5 923.0 924.1 925.4 927.1 928.5 Model 5 with tract fi xed effects Neighbors with 3+ children 0-10% -0.0004*** -0.0007*** -0.0010*** -0.0013*** -0.0015*** -0.0013*** 10-15% 0.0004 -0.0003 -0.0004** -0.0005*** -0.0006*** -0.0010*** 15-20% ref. ref. ref. ref. ref. ref. 20-25% 0.0010 0.0004* 0.0003 0.0005** 0.0004* 0.0012*** 25+% 0.0008*** 0.0010*** 0.0012*** 0.0016*** 0.0023*** 0.0038*** F-value 1073.5 1074.6 1075.3 1076.2 1078.3 1077.5 Couple-quarter observations 5,413,443 Note: Table shows beta coeffi cients and signifi cance levels: * p<0.05; ** p<0.01; *** p<0.001. Covariates included but not shown are: process time, both partners’ age at start, global region of birth, union status, stepchildren, both partners’ educational at- tainment and enrolment, the woman’s employment status, household income, housing, residential time, neighbors’ education, centrality and region (last two only in model 4). Source: Data from Norwegian registers on a quarterly/yearly basis 2000-2014. Linking Neighbors’ Fertility: Third Births in Norwegian Neighborhoods • 391 T a b . A 5: D is cr e te t im e e v e n t- h is to ry m o d e ls o n h av in g a t h ir d b ir th , 2 0 0 0 -2 01 4 M o d e l 1 M o d e l 2 M o d e l 3 M o d e l 4 M o d e l 5 N e ig h b o rs w it h a t le a st 3 c h il d re n 0 -1 0 % o f 2 5 0 n e a re st -0 .1 2 5 ** * -0 .1 3 9 ** * -0 .1 5 4 ** * -0 .1 10 ** * -0 .1 41 ** * 10 -1 5 % o f 2 5 0 n e a re st -0 .1 5 5 * * * -0 .1 4 0 * * * -0 .1 4 3 * * * -0 .0 9 4 * * * -0 .0 6 3 * * * 15 -2 0 % o f 2 5 0 n e a re st re f. re f. re f. re f. re f. 2 0 -2 5 % o f 2 5 0 n e a re st 0 .2 2 5 * * * 0 .2 0 2 * * * 0 .2 0 4 * * * 0 .1 0 9 * * * 0 .0 2 7 * 2 5 + % o f 2 5 0 n e a re st 0 .5 0 8 * * * 0 .4 5 4 * * * 0 .4 5 9 * * * 0 .3 10 * * * 0 .0 9 8 * * * P ro ce ss t im e ( q u a rt e rs o f y e a rs ) 0 .1 5 8 * * * 0 .1 6 6 * * * 0 .1 7 0 * * * 0 .1 71 * * * 0 .1 74 * * * P ro ce ss t im e s q u a re d -0 .0 0 7 ** * -0 .0 0 7 ** * -0 .0 0 7 ** * -0 .0 0 7 ** * -0 .0 0 7 ** * D w e ll in g t yp e & n u m b e r o f ro o m s si n g le -f a m ily h o u se , 5 r o o m s o r m o re re f. re f. re f. si n g le -f a m ily h o u se , 4 r o o m s o r le ss -0 .0 8 5 * * * -0 .0 8 4 * * * -0 .0 7 7 * * * te rr a ce d /r o w h o u se , 5 r o o m s o r m o re -0 .1 3 9 * * * -0 .1 51 * * * -0 .1 2 8 * * * te rr a ce d /r o w h o u se , 4 r o o m s o r le ss -0 .1 6 3 * * * -0 .1 7 9 * * * -0 .1 6 6 * * * a p a rt m e n t, 5 r o o m s o r m o re -0 .0 17 - 0 .0 15 -0 .0 7 8 a p a rt m e n t, 4 r o o m s o r le ss -0 .0 4 0 * - 0 .0 5 3 ** -0 .1 2 5 ** * m is si n g h o u si n g i n fo rm a ti o n 0 .0 3 4 ** 0 .0 2 3 * 0 .0 0 0 R e si d e n ti a l ti m e i n c u rr e n t n e ig h b o rh o o d m o v e d d u ri n g t h e l a st y e a r re f. re f. re f. la st r e lo c a ti o n u p t o 5 y e a rs a g o -0 .0 5 8 ** * -0 .0 5 9 ** * -0 .0 6 0 ** * la st r e lo c a ti o n u p t o 1 0 y e a rs a g o -0 .2 71 * * * -0 .2 7 3 * * * -0 .2 7 9 * * * la st r e lo c a ti o n > 1 0 y e a rs a g o -0 .5 2 1 * * * -0 .5 3 0 * * * -0 .5 4 4 * * * N e ig h b o ri n g w o m e n w it h a u n iv e rs it y e d u ca ti o n % o u t o f 2 5 0 n e a re st n e ig h b o rs 0 .0 0 2 ** * -0 .0 0 1 ** * -0 .0 11 ** * C e n tr a li ty o f re si d e n ti a l m u n ic ip a li ty m u n ic ip a li ty w it h r e g io n a l c e n te r 0 .0 3 2 * - tr a v e l t im e t o r e g io n a l c e n te r < 3 6 m in -0 .0 19 - tr a v e l t im e t o r e g io n a l c e n te r 3 6 -7 5 m in -0 .0 10 - re la ti v e ly c e n tr a l re f. - le ss c e n tr a l 0 .1 7 7 * * * - • Janna Bergsvik392 T a b . A 5: C o n ti n u a ti o n M o d e l 1 M o d e l 2 M o d e l 3 M o d e l 4 M o d e l 5 R e g io n o f N o rw a y O sl o a n d A ke rs h u s (C a p it a l r e g io n ) 0 .0 15 - H e d m a rk a n d O p p la n d re f. - S o u th E a st e rn N o rw a y -0 .0 9 9 * * * - A g d e r a n d R o g a la n d 0 .1 7 0 * * * - W e st e rn N o rw a y 0 .1 8 3 * * * - T rø n d e la g -0 .0 0 4 - N o rt h e rn N o rw a y 0 .0 3 2 - In te rc e p t -4 .7 9 3 -1 .7 15 -1 .8 8 9 -1 .9 11 - In d iv id u a l a n d c o u p le c o va ri a te s N o Y e s Y e s Y e s Y e s F ix e d e ff e ct s fo r st a ti st ic a l tr a ct s N o N o N o N o Y e s C o u p le -q u a rt e r o b se rv a ti o n s 5 ,4 14 ,4 4 3 N o te : Ta b le s h o w s b e ta c o e ffi c ie n ts f ro m a lo g is ti c re g re ss io n a n d s ig n ifi ca n ce le v e ls : * p < 0 .0 5 ; ** p < 0 .0 1 ; ** * p < 0 .0 0 1 . C o v ar ia te s in cl u d e d b u t n o t sh o w n in m o d e l 2 t o 5 a re : b o th p ar tn e rs ’ a g e a t st ar t, g lo b al r e g io n o f b ir th , u n io n s ta tu s, s te p ch ild re n , b o th p ar tn e rs ’ e d u ca ti o n al a tt ai n m e n t an d e n ro lm e n t, t h e w o m an ’s e m p lo y m e n t st at u s, h o u se h o ld in co m e . S o u rc e : D at a fr o m N o rw e g ia n r e g is te rs o n a q u ar te rl y /y e ar ly b as is 2 0 0 0 -2 0 1 4 . 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. 500 nearest neighbors -.0 05 0 .0 05 .0 1 4 8 12 16 20 24 28 32 36 40 250 nearest neighbors -.0 05 0 .0 05 .0 1 4 8 12 16 20 24 28 32 36 40 100 nearest neighbors -.0 05 0 .0 05 .0 1 4 8 12 16 20 24 28 32 36 40 50 nearest neighbors -.0 05 0 .0 05 .0 1 4 8 12 16 20 24 28 32 36 40 25 nearest neighbors -.0 05 0 .0 05 .0 1 4 8 12 16 20 24 28 32 36 40 Quarters of years since 2nd birth 12 nearest neighbors -.0 05 0 .0 05 .0 1 4 8 12 16 20 24 28 32 36 40 0-10% 10-15% 20-25% 25+% Share of neighboring women with 3+ children Published by Prof. Dr. Norbert F. Schneider Federal Institute for Population Research D-65180 Wiesbaden / Germany 2020 Managing Editor Prof. Dr. Johannes Huinink Dr. Katrin Schiefer Editorial Assistant Beatriz Feiler-Fuchs Wiebke Hamann Layout Beatriz Feiler-Fuchs E-mail: cpos@bib.bund.de Scientifi c Advisory Board Karsten Hank (Cologne) Michaela Kreyenfeld (Berlin) Marc Luy (Vienna) Natalie Nitsche (Rostock) Zsolt Spéder (Budapest) Rainer Wehrhahn (Kiel) Comparative Population Studies www.comparativepopulationstudies.de ISSN: 1869-8980 (Print) – 1869-8999 (Internet) Board of Reviewers Bruno Arpino (Barcelona) Kieron Barclay (Rostock) Laura Bernardi (Lausanne) Gabriele Doblhammer (Rostock) Anette Eva Fasang (Berlin) Michael Feldhaus (Oldenburg) Tomas Frejka (Sanibel) Alexia Fürnkranz-Prskawetz (Vienna) Birgit Glorius (Chemnitz) Fanny Janssen (Groningen) Frank Kalter (Mannheim) Stefanie Kley (Hamburg) Bernhard Köppen (Koblenz) Anne-Kristin Kuhnt (Duisburg) Hill Kulu (St Andrews) Nadja Milewski (Rostock) Roland Rau (Rostock) Thorsten Schneider (Leipzig) Tomas Sobotka (Vienna) Jeroen J. A. Spijker (Barcelona) Heike Trappe (Rostock) Helga de Valk (The Hague) Sergi Vidal (Barcelona) Michael Wagner (Cologne)