Introduction

1The role of social norms in shaping family and fertility during the fertility transition has been heavily commented upon in light of the spatial patterns of decline in marital fertility observed in Europe during the late 19^th and early 20^th century (Watkins, 1986). Interpreting this diffusion pattern relies on the idea that people who live near each other know each other, and through social interactions they create and diffuse new norms about family and fertility, which made people strive for smaller families (Knodel & van de Walle, 1979; Lesthaeghe & Surkyn, 1988; Watkins, 1986; Szreter, 1996). However, the precise mechanisms of this diffusion process are still unknown. On the one hand, social interactions might contribute to disseminate new attitudes and behaviours (Watkins, 1990; Goldstein & Klüsener, 2014; Klüsener et al., 2019). On the other hand, it could be that similar individuals, especially in terms of social and economic characteristics, could be living nearby (Barnes & Guinnane, 2012; Brown & Guinnane, 2007; McPherson et al., 2001; Palloni, 2001). In this study, I address this question by measuring diffusion effects at a much smaller geographical scale than previous studies. To do so, I use longitudinal demographic data from the Skellefteå region in northern Sweden from 1850 to 1950.

2Specifically, I investigate whether the fertility behaviours of married couples were influenced by the reproductive behaviours of their married neighbours and its evolution over time. The relationship is explored at two geographical levels: between neighbourhoods and between couples within and across neighbourhoods. Neighbourhood diffusion effects refer to couples in adjacent neighbourhoods displaying similar behaviours independently of other similarities, such as age or occupation. A high spatial autocorrelation of fertility behaviours would indicate spatial diffusion effect at a neighbourhood level. At a couple level, effects between neighbours occur, as birth control decisions of a couple are influenced by the attitudes and behaviours of their neighbours. To explore this effect, I measure how the fertility of neighbours change for a given couple over their reproductive life course and how that couple, in turn, responded to these changes. Additionally, I measure how couples respond to long-term and short-term changes in neighbour fertility. By measuring neighbour effects over different time scales and geographical levels, it is possible to separate the role of different diffusion mechanisms and how they evolved, before, during, and after the fertility transition.

3In the first section, I discuss the potential mechanisms of spatial fertility patterns. The next section presents the hypothesis tested and the research design applied in this study. Then, I present the results, first between neighbourhoods; second between couples.

Explanations of spatial fertility patterns

4The spatial patterns in fertility decline have been argued to be explained either by the diffusion of reproductive behaviour through social interactions or by the spatial clustering of similar people in the same location. The diffusion hypothesis asserts that fertility change is not solely an adaptation to economic, demographic or social structural changes but also a reflection of the spread of attitudes and behaviours (Palloni, 2001). Diffusion was most notably identified as important for the historical fertility transition by the conclusions of the European fertility project (EFP) which found that the variations in fertility followed linguistic and cultural boundaries rather than economic or demographic developments (Knodel & van de Walle, 1979; Watkins, 1986). Cleland (1987) draws the conclusions of the EFP even further, dismissing all economic determinants of fertility in place of diffusion of birth control. Casterline and collaborators (Montgomery & Casterline, 1993; Rosero-Bixby & Casterline, 1993) have a more inclusive perspective in their analysis, arguing that diffusion mechanisms work to spread both ideational and economic effects in Taiwan. Bongaarts and Watkins (1996) research on high-fertility regions follows in line with these conclusions, how fertility decline was dependent on the diffusion of knowledge, more specifically how social interactions within network spread knowledge about birth control and attitude towards smaller families.

5On an individual level, Palloni (2001) argues that fertility decisions change due to an alteration of preferences. While economic and social structural effects would affect individuals through their social position, diffusion would affect decisions as people reevaluate their behaviours in light of others’ attitudes and behaviours and adopt new birth control practices. New attitudes and behaviours are thus assumed to be diffused through social interactions. Studies of post-industrialised populations have shown that people’s fertility practices are affected by social interactions (Bernardi, 2003; Keim, 2011; Bernardi & Klärner, 2014). People’s decision to become a parent (Balbo & Barban, 2014) or have another child (Keim, Klärner & Bernardi, 2009) is associated with the fertility behaviours of friends and peers.

6Social interactions would also create spatial fertility patterns, for example, by neighbours learning from each other or conforming to social pressures in one’s local community. This is based on the assumption that proximity increases the probability that individuals have faceto-face meetings (Hedström, 1994; Marsden & Friedkin, 1994). Although long-distance interactions became increasingly common over time, distance is still one of the best predictors of whether or not individuals know each other (Marsden & Friedkin, 1994; Bongaarts & Watkins, 1996; Zhang & Pang, 2015). A number of studies find spatial diffusion effects on a crossnational macro level while controlling for economic structural effects. Spatial analyses of the transitions in Brazil (Schmertmann, Potter & Cavenaghi, 2008), Egypt (Bonneuil & Dassouki, 2006) and Great Britain (Bocquet-Appel & Jakobi, 1997; Garrett et al., 2001) have all provided evidence for diffusion effects. In an analysis of the European transition, Watkins (1990) argues that differences in the geographical extent of social networks influenced the diffusion of fertility decline. As these networks grew from local communities to national ones, the geographic homogeneity of fertility behaviours increased.

7The alternative hypothesis is that spatial patterns are caused by the clustering of people who are similar in the same location. Brown (2007) argues that the EFP results were biased by the high aggregation level, missing economic effects, which work at a disaggregated level, leading to an ecological fallacy. This literature draws upon microeconomic theory, which asserts that the socio-economic differences are caused by a substitution effect. Becker (1960) theorises that the cost of child quality decreases, for example, because the benefits and availability of education increased, therefore parents will invest more time and resources in child-raising instead of having more children (Guinnane, 2011). Socio-economic differences were created because the higher classes were the first to gain from larger investments in children. A number of studies have shown the importance of structural economic changes, primarily through an increase in differences between socio-economic groups (Dribe et al., 2014; Dribe & Scalone, 2014). Galloway (1994) argues that the Prussian fertility decline was driven by structural economic changes rather than ideational and diffusion mechanisms. However, an updated analysis of the Prussian transition by Goldstein and Klüsener (2014) has shown substantial spatial patterns. Fertility levels within a district were more likely to decline if they were near a district where fertility decline had already started.

8In his analysis of the British fertility decline, Szreter (1996) argues that reproductive practices were shared within communication communities during the demographic transition. Within the nexus of class, gender and community, the perceived relative cost of childrearing, was created, diffused and reproduced to be a part of individuals identities, shaping family formation. By communication communities, Szreter refers to social networks who share the same “sociocultural environment of language, values, and roles” (Szreter, 2015, 177), often created from a combination of class and neighbourhood. However, contrary to Szreter’s results, Barnes and Guinnane (2012) have shown that socio-economic differences rather than spatial ones can explain the majority of the variations in fertility during the decline. Dribe et al. (2015) come to the same conclusions in their analysis of the Swedish fertility transition.

9Importantly, these analyses are limited to cross-sectional data, thus measuring spatial patterns of fertility at specific points in time, rather than across time over the reproductive life courses of couples. The pattern can also be an effect of social network homophily (Bras, 2014). Homophily refers to the tendency of individuals to associate with others who are similar to themselves. It is easier for people who share some form of characteristics such as age, class or attitudes, to form relationships (McPherson et al., 2001) and thus, they would be more likely to live near each other. People who live near each other would, therefore, display similar reproductive behaviours because of their attitudes and values which were independent of the attitudes of others (Palloni, 2001). The hypothesis is that they only live near each other because they already were similar, not that they became similar because they lived near each other.

10The current study contributes by analysing neighbour effects explicitly on a much smaller scale and over time using longitudinal data. By specifically studying correlations in fertility within and across neighbourhoods, rather than within communication communities, I can adjust the measurements for both structural conditions, such as the socioeconomic composition or proportion of migrants, and individual-level factors, such as socio-economic status and migration experiences. Furthermore, the temporal ordering of events in the longitudinal data makes it possible to separate the fertility behaviour of couples from the past behaviours of their neighbours. This makes it possible to estimate the independent effect of neighbourlevel social interactions on fertility behaviour.

Research design

11The overarching hypothesis is that couples’ decision to limit their fertility during the transition was influenced by the attitudes and behaviours of their neighbours. Thus, couples who lived in proximity to other couples who practised fertility limitation would be more likely to limit their fertility themselves, as they would be influenced by the action of their neighbours. The initial hypotheses in this study are: (1) that there were spatial correlations in marital fertility between adjacent neighbourhoods and (2) that a couples’ fertility was affected by the fertility of their neighbours. Additionally, the spatial diffusion effect would likely be stronger as more people adopted new fertility behaviours; thus, another hypothesis is (3) that these effects varied over time.

12The spatial patterns could be confounded by local, social and economic differences between locations or by people migration decisions. Thus, there could be similarities in the fertility outcomes of neighbours without any effects of social interaction. The research design mobilised in this study aims to take into account contextual differences and selection bias by separating the effect of social and economic similarities from geographical proximity. This is done by adjusting the estimated neighbourhood and neighbourhood effects for social and economic factors at neighbourhood – and couple – levels using event history regression models. Any remaining associations in fertility between neighbours and neighbourhoods, once controlled for these confounders, would reflect the role of other factors, such as the diffusion of norms and values through social interactions.

13The overall strategy in this study is to estimate separately the actions of other actors – e.g. neighbours or couples within adjacent neighbourhoods – and their effects on the fertility outcomes of couples. As neighbourhood-level effects and neighbour effects work at different geographical levels, they are investigated in two separate analyses. Similarities in fertility for couples in adjacent neighbourhoods are measured by subdividing each parish into smaller areas, or neighbourhoods, consisting of adjacent villages and towns. Neighbourhood-level fertility differences are then estimated as random-effects in Cox regressions, and similarities between adjacent neighbourhoods are measured as spatial autocorrelation of the neighbourhood hazard ratios. By using couple-level data, it is possible to estimate neighbourhood-level spatial autocorrelations while controlling for both individual and neighbourhood-level confounding factors.

14The temporal ordering of events in the longitudinal data is used to estimate how the past reproductive practices of neighbours affected the fertility of couples. The analysis is performed in two steps. The first one is to estimate changes in the fertility of the neighbours of each couple across their reproductive life courses. Guinnane et al. (1994, 3) define the fertility transition as “a sustained increase in the use of birth control methods”. Thus, diffusion effects during the transition are usually measured at a decade timescale (Watkins, 1986; Goldstein & Klüsener, 2014; Dribe et al., 2015), which is more suitable when trying to capture sustained changes rather than short-term fluctuations. However, diffusion effects between individuals in post-transitional societies have been shown to have a bell-shaped pattern over time, where the effect of the behaviours of others increases in the first few years and then decreases over time (Balbo & Barban, 2014). Short-term changes are often associated with social interaction effects influencing the timing of births rather than a sustained change in practices (McDonald, 2000; Keim et al., 2009; Balbo & Barban, 2014; Bernardi & Klaerner, 2014). To separate these two kinds of effect, I measure changes in neighbour fertility within two different timescales – a long-term change, ten years, and a short-term change, five years. In the second step of the analysis, the neighbour fertility changes are incorporated as couple-level features into a Cox proportional hazard regression model. In these models, I estimate how a change in the fertility of neighbours was associated with the risk for a couple to have an additional birth while controlling for both individual and neighbourhood-level confounding factors.

Data and setting

15The data come from the longitudinal database POPLINK, which contains longitudinal individual-level data for the Skellefteå region from the mid-18^th century until the 1960s (Westberg et al., 2016). The Skellefteå region consists of parishes which were once a part of the original Skellefteå parish up until 1810, shown in Figure 1. By 1950 the region had been subdivided into eight parishes, six of which are included in the database: Skellefteå lands, Skellefteå stads, Byske, Bureå, Norjsö and Jörn (Westberg et al., 2016). The region did not experience the same rapid industrialisation as other coastal regions in Northern Sweden such as Sundsvall. The only town, Skellefteå, at the mouth of the Skellefteå river on the shores of the Bothnian Bay, served primarily as an administrative centre. This was a small town with a population of less than 2,000 until the 1910s. Until 1940 the majority of the population worked in agriculture, and industrialisation was limited to a few sawmills, established from the 1870s primarily at the coast near the rivers. However, the level of industrialisation was relatively low until the mining industry took off in the 1930s (Gaunitz et al., 2002).

Fig. 1

Neighbourhood division of the six parishes in the Skellefteå region

Neighbourhood division of the six parishes in the Skellefteå region

16In comparison to Sweden as a whole, fertility started to decline in the region relatively late. Period fertility rates started to decline continuously after 1900 in Västerbotten county, which the Skellefteå region was a part of, as seen by the total fertility rates in Fig. 2. In addition, fertility rates in the region were higher than the average Swedish rates, both before and after the transition.

Fig. 2

Total fertility rates (TFR) in the Skellefteå region, 1850-1950

Total fertility rates (TFR) in the Skellefteå region, 1850-1950

17POPLINK contains information on births, deaths, marriages and migration linked at an individual-level across parishes within the region. It also has linked information gathered from the cathechetical examinations, containing recurrent information on who lived in each household, their occupation, and place of residence. Using linked information makes it possible to follow individuals across their lifetime as their lives change, such as when and where they move between locations, marry, change occupations, have children or experience the death of their spouse.

18The dataset contains reliable information on the onset of risk which in historical Sweden can be set to the beginning of marriage (Carlsson, 1966; Coale & Watkins, 1986), and the end of their reproductive careers, either emigration from the region, the death of the husband or menopause, set to age 50. For this analysis, the sample consists of all married women who had at least one child, who married between 1850 and 1950, a sample of 20,439 married women within 706 places of residence.

19The places of residence have been geocoded, and due to the detailed information on migration, I could determine who live near each other at each moment in time. To ensure the anonymity of individuals living in the smallest villages some places of residence are aggregated: each time a place had a population smaller than ten individuals the place is combined with the closest village or town; the procedure was iterated over the whole dataset until all places of residence had a population larger than ten individuals for each year.

20Socioeconomic status is derived from occupational information. Occupational data were recorded at most of these life events for men, and more infrequently for women, even rarer for married women. However, during the study period married women’s social position was dependent on their husband’s position. Thus, the husband’s occupation is used as a proxy for the couples’ social position. These occupations have been coded into HISCO codes (Van Leeuwen et al., 2004; Mandemakers et al., 2013) which in turn is used to classify occupations using the HISCLASS scheme (Van de Putte & Miles, 2005). HISCO is an international standard for coding occupations and is used here to classify occupational titles into HISCLASS groups. Although occupational titles can hide large variations in education and wealth, HISCO codes and HISCLASS have been shown to capture large socioeconomic variations in fertility during the Swedish fertility transition (Dribe & Scalone, 2015). As the sample population was relatively homogenous in terms of socioeconomic status, the 12 classes in the scheme are condensed into six.

Neighbourhood level correlations

Method

21Both before and during the fertility transition, fertility control within marriage was primarily limited to higher-order parities. Thus, deliberate fertility limitation, if any, should be observed only after the first child. Whether or not limitation was achieved by waiting longer until the next child or by stopping having children altogether, the practice would affect the timing of another birth, which is the outcome of interest in this study. Fertility is measured as the risk of having another birth and estimated using Cox proportional hazard regressions.

22On an aggregate level, diffusion effects would create correlations in fertility for couples in adjacent neighbourhoods. A neighbourhood (a “small area”) consists of all married couples who live near each other in adjacent villages and towns within a parish. On average, these couples were more likely to have regular face-to-face meetings with each other than with more distant couples. Ideally, the boundaries of a neighbourhood would be based on people’s perceptions of community (Diez Roux, 2001). However, such perceptions are unattainable for this historical population. Instead, neighbourhoods are identified by dividing the space within parishes into smaller areas based on the proximity of places of residence. The POPLINK data contains geographical information at two levels, parish and place of residence, which refers to the village or town in which the couple resides. The six parishes in the Skellefteå region are large, up to 1,935 km², and an average village was too small for calculations of neighbourhood level fertility risks. Instead, neighbourhoods are created by subdividing each parish into smaller areas consisting of adjacent villages and towns, and the area surrounding them.

23The six parishes in the Skellefteå region are partitioned into smaller subareas. The procedure is visualised in Figure 3 for the Bureå parish. The first step is to split the land of a parish into smaller areas consisting of the land surrounding each unique village or town, here referred to as a place. This is done by calculating the Voronoi tessellation based on the coordinates of all places within the parish. The tessellation algorithm assigns each point within the space of the parish to the place which it was closest to (Lee & Schachter, 1980). This results in a partition of the parish into N smaller areas, where N is equal to the number of unique places within the parish (Fig. 3 A).

24The next step is to cluster the places into larger groups of locations which are close to each other. The number of clusters depends on the average yearly married population in a parish. In the parish with the highest population density, Skellefteå stad, the ratio of clusters was 0.5 per 1000 married couple, and in the other parishes, it was 4 per 1000. Each place is allocated into a subregion through K-means clustering, hence maximising the geographical distance between groups while minimising the distance within each group (Fig. 3 B). The final step is to combine each area created by the Voronoi tessellation according to its cluster assignment, into one neighbourhood (Fig. 3 C). The process results in a spatial partition of the region (Fig. 1) that make it possible to measure differences between neighbourhood fertility risks while controlling for both individuallevel and neighbourhood level characteristics over the whole study period, 1850-1950.

25The variation in fertility at neighbourhood-level and the spatial correlations in fertility between adjacent neighbourhoods are estimated in two steps. The first step is to estimate differences in fertility between neighbourhoods using event history analysis, namely mixed-effects Cox proportional hazard regressions. The outcome of interest is the timing of another birth, estimated as differences in hazard of having another birth for couples in different neighbourhoods. The neighbourhood effects are modelled as random effects, assumed to be drawn from a Gaussian probability distribution (Therneau, 2019). As the analysis includes all higher-order parities, the risk of having a child is stratified by parity, to ensure that the risk group is restricted to couples who had experienced a similar number of births (Prentice et al. 1981). The full model includes both fixed effects, such as the age of the wife, and a neighbourhood random-effect.

26

27The risk λ(t) of an event at time t is determined by the baseline hazard function λ_o(t), stratified by parity g and the exponentiated predictors e^βX+Zb. Within the predictors, X is a model matrix, and β is the corresponding matrix of fixed effect coefficients, Z is a model matrix of random effect variables and b a matrix of random effects. The models were computed using R (R Core Team, 2019) and the package coxme: Mixed-effects Cox models (Therneau, 2019; Therneau, 2012).

28The second step of the analysis is to estimate how these neighbourhood-level random-effects correlated between adjacent neighbourhoods. If couples were affected by the behaviour of the couples living in adjacent neighbourhoods, the hazard ratios for these neighbourhoods would be similar, even after adjusting for confounding factors. These spatial correlations are measured and tested for using Moran’s I, an index of spatial autocorrelation. To assess how the autocorrelations change over time, the sample is divided into four periods, 1850-1874, 1875-1899, 1900-1924 and 1925-1950. The first period is before the transition, whereas the second one captures the initial fertility decline of vanguard groups. The majority of the decline occurred during the third period while the last period is the end of the fertility transition.

29The neighbourhood level effects are estimated while controlling for couple-level and neighbourhood-level characteristics. At a neighbourhood level, it is possible to compute yearly population density and migration rates, which are being used as proxies for urbanisation. Socioeconomic structural differences are controlled for by calculating how the population was distributed according to the social status scheme for each year and then clustering the neighbourhoods into four groups with similar socioeconomic distributions using K-means clustering. In this way, it was possible to differentiate between neighbourhoods with a predominant farmer population from those with a working-class population. A number of couple-level characteristics are used as controls: age of the wife, migration status of the husband and the wife, socioeconomic status of the husband and calendar time.

Results

30The spatial patterns of fertility are visualised by extracting the neighbourhood random-effects for each period and drawing them as a series of maps. The hazard ratios are estimated using Cox proportional hazard models, without any controls. As can be seen on the maps in Figure 4 there were substantial spatial differences, and they increase over time. This is clear in the increase in the standard deviation of the neighbourhood hazard ratios (Table 1). The map also indicates some spatial clustering of hazard ratios, as adjacent neighbourhoods displayed similar hazards. This clustering is measured by calculating Moran’s I for spatial autocorrelation. Moran’s I describes how close similar locations reside to each other on a scale from −1 to 1. A positive correlation (>0) indicates that neighbouring areas were similar to each other while a negative correlation (<0) indicates that neighbouring areas were dissimilar to each other, and a correlation close to 0 indicates that there were no relationship between the fertility of neighbouring areas.

Tabl. 1

Moran’s I tests for spatial autocorrelation of neighbourhood random-effects

Moran’s I tests for spatial autocorrelation of neighbourhood random-effects

31Table 1 shows that there are positive autocorrelations in all periods, and the highest correlations are found in 1875-1899. These measurements are tested against the expected values of Moran’s I without any spatial autocorrelations. Couples in adjacent neighbourhoods had similar fertility behaviours before, during and after the fertility transition. However, this does not mean that fertility practices were shared between neighbourhoods through social interactions. These spatial patterns could be an effect of correlations in structural characteristics. For instance, urbanisation, industrialisation, and socioeconomic development were seldom spatially independent.

32To investigate the spatial patterns of socio-economic structures, the distribution of socio-economic status of married couples by neighbourhoods each year is grouped into four groups with similar distributions. As the elite group is very small, they are merged with the middleclass group in this part of the analysis. Figure 5 shows the average proportions of couples by socio-economic status within each cluster and their spatial distribution over time. The four clusters had distinct socio-economic structures. However, two distinct patterns are visible. Farmers dominated cluster three and four, while cluster one and two had a low proportion of farmers. Although the two farmer clusters are similar, neighbourhoods in cluster four had a higher proportion of unskilled worker families. Neighbourhoods in both cluster one and two represent urban and industrialised areas: a majority of couples in cluster one were unskilled worker families, while the couples in cluster two show a much more diverse socio-economic structure.

33Figure 5 also shows the spatial distribution of these clusters. Until 1924 the region consisted primarily of neighbourhoods dominated by farmers (clusters three and four). Only the town of Skellefteå and a few neighbourhoods with larger settlements showed a shift from the farmer clusters to the urban and industrial clusters prior to 1925. Cluster one and two are found in a few inland neighbourhoods and the coastal area. After 1925 the socio-economic structure of the region was transformed, much more neighbourhoods display socio-economic structures representative of an urban or industrialised area.

Fig. 3

Spatial partitioning process for Bureå parish

Spatial partitioning process for Bureå parish

34The spatial distribution of socioeconomic structure over time also appeared to correlate with fertility differences, when comparing the maps in Figure 4 and 5. It is easy to deduce that some amount of the spatial patterns could be caused by differences in socio-economic structure rather than diffusion. In addition to differences in social structure, the spatial pattern could also have been affected by population density, migration rate, individual socio-economic status, age and migration history.

Fig. 4

Spatial distribution of hazard of another birth from estimated neighbourhood-level random effects from a Cox proportional hazard model, 1850-1950

Spatial distribution of hazard of another birth from estimated neighbourhood-level random effects from a Cox proportional hazard model, 1850-1950

Fig. 5

Social class distribution by neighbourhood 1850-1950

Social class distribution by neighbourhood 1850-1950

35By controlling for these confounding factors, it is possible to estimate adjusted neighbourhood hazard ratios (the full regression model is reported in Table 3 in Appendix). Even after controlling for confounders, substantial spatial differences remain. The regression models indicated that a proportion of the variation between neighbourhoods could be explained by similarities in neighbourhood-level and couple-level characteristics, as the variance in neighbourhood effects are smaller in all periods. The adjusted model shows that the variation between neighbourhoods was largest in 1900-1924. The model also indicates that the autocorrelations between adjacent neighbourhoods before (1850-1874) and after (1925-1950) the transition is related to structural similarities, as Moran’s I is close to zero and not statistically significant (Figure 6). Additionally, a portion of the autocorrelations in the period 1875-1899, the onset of the transition, is also related to structural similarities. However, significant autocorrelations remain after controlling for confounding factors: the level of autocorrelation stays approximately the same for the period 1900-1924, as Moran’s I is similar in size in both the adjusted and the unadjusted models, and the autocorrelations are statistically significant.

Fig. 6

Moran’s I of neighbourhood hazard ratios by period, with and without controls

Moran’s I of neighbourhood hazard ratios by period, with and without controls

36The results of this analysis suggest that fertility practices were shared between couples in adjacent neighbourhoods through social interactions at the onset of the fertility transition and during the transition, but not before or after. However, these differences could be caused by selection effects by network homophily. It is possible that individuals who had already started to adopt low fertility behaviours were more likely to move near others where this behaviour was accepted and promoted (Palloni, 2001), which in turn would lead to spatial autocorrelations that were independent of any social interaction effects. To account for this reverse causation, the next section presents an analysis that separates the timing of practices of couples from that of their neighbours, i.e., the time lag between events.

Between neighbour effects

Method

37To test whether neighbours fertility practices had an effect on couples’ risk of having a child, I first estimate changes in fertility of neighbours for each couple for every year in their reproductive life course and then estimate the effect of these changes on the couple’s risk of having a child.

38Neighbours of a married couple consist of all other couples who lived within five kilometres, which is about an hour of walking (Himann et al., 1988). Within this distance, people had a high likelihood of regular face-to-face interactions. Changes in neighbour fertility are measured for each year in a couples’ life course; this makes it possible to measure how fertility changed as new couples moved into the neighbourhood and as a couple changed places of residence within the region. As discussed in the research design section, to separate long-term and shortterm changes in neighbour fertility, fertility change is measured over two time periods, over five and ten years.

39Long-term and short-term changes in neighbour fertility of a couple at a given time is measured by selecting all other couples within five kilometres, and estimating the average yearly change in the risk of having another child compared with the past five and ten years for these neighbours, using Cox proportional hazard regression. Similarly to previous models, the analysis is limited to higherorder births, and the onset of risk of having another birth is set nine months after the previous birth, to account for amenorrhea. Additionally, the strength of the relationship between couples and neighbours might depend on the distance between them; thus, the effect of each neighbour is weighted by the distance between them and the couple. The weight is assumed to be linear in relation to distance: for example neighbours who live in the same location have a weight of 1 and neighbours who live 2 km from the couple have a weight of 0.8.

40How the risk of having a child changed over the time period is obtained by calculating the predicted relative risk (RR) of having a child for neighbours at the end of the period compared to the risk at the beginning of the period, 5 or 10 years ago. Thus long-term changes in neighbour fertility for a couple in 1880 is measured as:

41

42The process is repeated for each year in the reproductive life course of a couple, creating a couple-level time series of changes in neighbour fertility. The long-term change in neighbour fertility for one individual is illustrated in Figure 7. As the individuals move between locations, their neighbour groups change and therefore, their neighbour fertility shifts. Even though neighbour fertility varies a lot, the overall trend is stable and reflects the fertility transition (Fig. 8). Averages in both long-term and short-term changes in neighbour fertility continuously decline after 1915. Also, one can see the large variations in short-term neighbour fertility before the transition, most notably the reactions to the hunger crisis in the late 1860s.

Fig. 7

Example of long-term neighbour fertility change over the course of one couple’s reproductive life course

Example of long-term neighbour fertility change over the course of one couple’s reproductive life course

43The effect of changes in neighbour fertility on couples’ risks of having a birth is estimated using mixed-effects Cox proportional hazard regressions, similar to equation 1. Once again the outcome of interest is the average risk of having a birth across couples’ reproductive life courses, and the analysis includes all birth intervals after the first birth. The model includes a random effect for each neighbourhood to control for unobserved heterogeneity for couples in the same neighbourhood, caused by unmeasured ideational, social or economic differences. Also, as the analysis is based on multiple births per couple, the risk of having a birth is stratified by parity (Prentice et al., 1981). To ascertain how the effects change over time, the sample is split into four time periods, 1850-1874, 1875.1899, 1900-1924 and 1925-1950, similarly to the previous analysis. To disentangle selection effects and contextual effects from diffusion effects the models control for a number of couple-level and neighbourhood level confounders.

44Although the analysis was made possible by separately estimating changes in neighbour fertility and the effect of these changes on couples’ fertility, the research design underestimates the variation in neighbour fertility. Neighbour fertility change is only based on the predicted relative risk, which is an average change; the total variation in neighbours’ fertility is not included in the estimation of couples’ responses to these changes. However, some of this variation is captured in aggregate across the whole population, as the accuracy of the estimation is in itself prone to variation. This becomes evident when looking at the distribution of changes in neighbour fertility (Fig. 8). The total variation is large enough that it always includes changes in neighbour fertility, both positive and negative, even though the trend is negative after 1915.

Fig. 8

Distribution of 5-year and 10-year neighbour fertility change

Distribution of 5-year and 10-year neighbour fertility change

Results

45As mentioned previously, neighbour fertility change is measured as the predicted relative risk of having a child for neighbours compared to 10 or 5 years earlier. To capture an average change in neighbour fertility, the measurement is standardised by dividing it by the negative standard deviation of the log of the total variance of neighbour fertility. This means that a one unit change in neighbour fertility reflects a decrease in neighbour fertility as large as one standard deviation (Tab. 2). The SD of the log of neighbour relative risk (RR) is just above 0.5, which is equivalent to approximately 45 % lower risk of having a child. A change of one SD is also relatively common, 72.9 % of couples experienced a long-term change in neighbour fertility of this size, and 79.3 % a one SD change in short-term neighbour fertility change. However, as the relationship is assumed to be linear, any association to a change in neighbour fertility could be both positive and negative. Thus, a significant effect could indicate that couples postpone having another child when neighbour fertility declines by one unit or are more likely to have another child when fertility increases by one unit. During the fertility decline, one can assume that in most cases, any significant relationship between the hazard of having another birth and neighbour fertility is negative.

Tabl. 2

Descriptive statistics of neighbourhood fertility change measured as standard deviations (SD) of relative risks (RR), and the proportion of all couples who experienced a change of one SD

Descriptive statistics of neighbourhood fertility change measured as standard deviations (SD) of relative risks (RR), and the proportion of all couples who experienced a change of one SD

46Figure 9 shows the unadjusted effect of a one SD decline in neighbour fertility on the risk of having a birth for couples during the four different time periods. The effect is estimated using Cox proportional hazard regression and was stratified by parity; however, no other controls are used in these models. The unadjusted hazard ratios show a Ushaped pattern for long-term changes in neighbour fertility. There is no significant effect before 1875, the effect is negative in the period 1875-1899, and even more so in 1900-1924. Finally, the effect is again close to zero in the last period (1925-1950). The opposite pattern can be seen for short-term changes in neighbour fertility. There is a significant negative effect before and after the transition and not during the transition (1875-1899 and 1900-1924); however, the size of these effects is much smaller. Additionally, these patterns are also affected by underlying differences in confounders, seen by the adjusted models.

Fig. 9

Unadjusted differences in hazard of having another birth when neighbours’ fertility declines by one standard deviation over the past 10 or 5 years. Hazard ratios and 95% confidence intervals from Cox proportional hazard regressions, seen in Table 4 in Appendix

Unadjusted differences in hazard of having another birth when neighbours’ fertility declines by one standard deviation over the past 10 or 5 years. Hazard ratios and 95% confidence intervals from Cox proportional hazard regressions, seen in Table 4 in Appendix

47Figure 10 shows the adjusted hazard ratios of having another birth. These effects are estimated using Cox proportional hazard regressions while controlling for both neighbourhood level and couple-level characteristics, and unobserved heterogeneity at a neighbourhood-level through the introduction of random-effects. Some of the effects are related to underlying factors, as the size of the effect of longterm neighbour fertility is smaller than in the unadjusted models. However, the pattern is similar, long-term changes in neighbour fertility affected couples’ risks of having a child during the transition, and the effect grew over time, while short-term changes only affected fertility before and after the transition.

Fig. 10

Adjusted differences in hazard of having another birth when neighbours’ fertility declines by one standard deviation over the past 10 or 5 years. Hazard ratios and 95 % confidence intervals from mixed-effects Cox proportional hazard regressions, seen in Table 5 in the Appendix

Adjusted differences in hazard of having another birth when neighbours’ fertility declines by one standard deviation over the past 10 or 5 years. Hazard ratios and 95 % confidence intervals from mixed-effects Cox proportional hazard regressions, seen in Table 5 in the Appendix

48The main difference between the adjusted and unadjusted models comes from the control for calendar time (as seen on the models without calendar time in Table 3 and 4 in Appendix). Additionally, the impact of calendar time is most substantial for long-term changes in neighbour fertility in 1900-1924, during which the majority of the fertility decline occurred. This is expected since this was the period when fertility declined in most areas. Therefore, a majority of couples would have experienced declines in neighbour fertility. However, even when adjusting for the overall decline in fertility through the control for calendar time, there remains an effect of neighbour fertility in 1875-1924. In other words, couples who have neighbours who limit their fertility more than average are more likely to limit their fertility. The pattern of response to long-term neighbour fertility is similar to that of the correlations between neighbourhoods. It is visible just at the onset of the transition and continuous during the decline and then disappears again after the transition.

49Interestingly, the opposite pattern is seen for short-term changes; the effect is only visible before and after the transition. These responses to short-term changes in neighbour fertility are not an effect of a sustained increase in the use of birth control. Rather it indicates that couples were influenced by their neighbours in the timing of having another birth. This could be in the form of the diffusion of knowledge on future economic hardship, which was shown to incentivise a postponement of another birth in the form of a lengthening of birth intervals in response to changes in the prices of crops or fluctuations in wages, prior to the fertility transition (Hammel & Galloway, 2000; Van Bavel, 2004; Bengtsson & Dribe, 2006; Cinnirella et al., 2019). This could also reflect the efforts of couples to draw upon the social and emotional support which one can gain from having small children at the same time, which has been shown to influence the timing of births in post-transitional societies (McDonald, 2000; Keim et al., 2009; Balbo & Barban, 2014). Overall, the results suggest that fertility responses to neighbours fertility over the short-term is not only a part of a post-transitional demographic regime but a pattern distinct for stable demographic-regimes in general.

50In addition, the hazard of having another birth is not only associated with social interaction effect but with structural differences. This is evident by the larger differences in hazard ratios between socioeconomic groups, shown in Table 3. Before the transition, it was the higher social groups (elite and middle class) who showed the highest fertility, but during the transition, the relationship was reversed. After 1900 the middle class had the lowest fertility, followed by the skilled working class and the elite. These findings are in line with what can be observed across world populations (Skirbekk, 2008). Additionally, couples in neighbourhoods with a low population density, a low proportion of migrant or with a population dominated by farmers had higher fertility than more densely populated and socially diverse neighbourhoods. This suggests that the fertility decline was associated with overall social and economic development during the transition.

Conclusions

51The results of this study suggest that patterns in spatial marital fertility can be explained by both social interaction effects and social and economic structural differences between places. I find spatial autocorrelations at neighbourhood-level in the Skellefteå region from 1850-1950. But these effects vary over time. Before the transition (1850-1874) and after it (1925-1950), the spatial patterns are associated with social and economic structural differences. Just before and during the transition (1875-1924), the autocorrelations in fertility of adjacent neighbourhoods are independent of confounding factors. Similar patterns are found for the effect of long-term changes (over ten years) of neighbour fertility on couples’ fertility behaviours. Between 1875 and 1924, couples’ risk of having another child is associated with the past behaviours of their neighbours. This is not the case for the period before 1875 and for the period after 1924. The opposite pattern is found for the effect of short-term neighbour fertility change (over five years). Couple’s fertility is associated with that of their neighbour only before 1875 and after 1924. This supports previous research showing spatial correlations at provincial or country level during the European fertility transition (Watkins, 1990; Goldstein & Klüsener, 2014; Klüsener et al., 2019). The findings of the current study suggest that spatial diffusion mechanisms were also in effect at a smaller geographical scale and were not limited to periods when fertility declined.

52The three different forms of social interaction effects, between neighbourhoods, long-term neighbour effects and short-term neighbour effects, are themselves related to different social interaction mechanisms and the difference between strong and weak social ties (Granovetter, 1983). Couples would be more likely to form strong social ties to other couples who live in their neighbourhood rather than couples who live in other neighbourhoods. Strong social ties are, in turn, associated with stronger social pressures to conform to communal norms. The results of this study suggest that the effect on a couples’ reproductive practices grew stronger as more and more couples in their surrounding changed their behaviour. As more people adopted fertility limitation the social pressure to conform to these practices and norms increased, and individuals were, therefore, more inclined to adopt new behaviours to gain approval or to avoid sanctions from their neighbours (Bernardi & Klärner, 2014). This would explain that the effect of long-term neighbour fertility change increase over time. Additionally, as this effect is already present before 1900, the results suggest that social pressure mechanisms were part of the diffusion of new fertility behaviours already at the onset of fertility transition, spreading birth control practices from vanguard groups to their neighbours.

53Another explanation is the increased opportunities for social learning. This relates to the idea that as a greater share of neighbours adopted new behaviours, the opportunities to observe these practices by others increased. By observing others and evaluating the perceived net benefits of the outcome, a couple would reject or adopt the behaviour (Palloni, 2001). Social learning could, through social interactions, spread the perceived benefits of low fertility incentivised by social and economic structural changes (Montgomery & Casterline, 1993; Kohler, 2001). Although industrialisation and urbanisation were relatively modest in the Skellefteå region, intraregional migration and industrialisation did increase during the period 1875-1925 (Gaunitz et al., 2002). Increased mobility would lead to an increase in social connections with weak ties (Watkins, 1990). Granovetter (1983) argues that weak ties, in turn, create potential bridges between social groups, and with the increase in the number of weak ties, the diffusion of new ideas becomes easier. According to Granovetter, over time, new networks stabilise and create strong transitive ties, which are less suitable for social learning; instead, these networks enable stronger effects of social pressure and social support. This could explain the sudden increase in spatial correlations just before the transition: the diffusion of low fertility practices was enabled by many weak ties between neighbourhoods. As spatial mobility increased in the region, the number of weak ties in people’s social networks increased, this strengthens social learning and led to the diffusion of new fertility behaviours. Over time, people started to form more stable networks and fitting into a community became increasingly important. What was considered appropriate behaviour within one’s community became more important as the ties to that community grew stronger, and birth control practices became a mean to conform to community ideals. At the same time, the results indicate that social interactions also perpetuated existing behaviours, creating resistance to fertility change in some neighbourhoods, which could explain why the difference between neighbourhoods peaked when fertility declined most rapidly.

54This interpretation is also in line with Watkins and Danzi (1995) who argue for the importance of the strength of weak ties for the low fertility of Jewish women in the US in the early 19^th century. Socially diverse networks are more inclined to adopt new practices than others. In a later study, Bongaarts and Watkins (1996) argue that the networks would become more and more homogenous, across the nation, through the creation of imagined communities via mass media. Thus, the effect of social interaction between neighbours would decrease over the course of the transition. The results of the current study do find that the autocorrelations related to social interaction effects between neighbourhoods are no longer present after the transition; however, at the couple-level, short-term social interaction effect is visible after the transition.

55This suggests that the social interaction effects were not only related to the spread of new norms about family and fertility, leading to an increased use of birth control. Effects of short-term changes are a reflection of social relations that function as channels of diffusion of information in response to shortterm economic changes (Bengtsson & Dribe, 2006; Cinnirella et al., 2019). Another possible mechanism is that social relations provide social support where couples synchronise childbirth with their neighbours to gain access to social support that arises when neighbours have children at the same time, in line with results of studies on contemporary populations (Balbo & Barban, 2014; Keim et al., 2009; McDonald, 2000). In these cases the response to short-term changes would not be a consequence of the spread of new norms but rather an adaptation of individuals to the behaviours of neighbours within stable demographic regimes.

56Although this study has measured spatial diffusion effect at a much more detailed geographic scale than previous studies, at both a neighbourhood- and a couple-level, the research design has some limitations. Because of this more detailed scale, the current study cannot account for the diffusion process that operates on national or regional levels. The spatial patterns of the European fertility decline were not only local but primarily worked on a macro-level, creating a relatively uniform and simultaneous transition across Western Europe. It is not self-evident that the same social interaction mechanisms were of importance on these scales as on a local level. At a macro-scale, it has been argued that new communication networks and increase long-distance migration were of greater importance (Bongaarts & Watkins, 1996). However, the current study suggests that this was accompanied by local-level social interaction mechanisms to diffuse new behaviours between neighbours. On an individual level, the observed spatial patterns could be caused by individual perceptions of birth control use such as personal preferences or religious views, that were independent of socioeconomic status or place of residence. Although the current study has tried to account for this self-selection process by measuring neighbour fertility change as people migrate from neighbourhoods with different fertility levels, the study lacks data on individual preferences prior to the start of family formation.

57Another issue is that communities were not necessarily spatially dependent during that period, as the landscape of social relations evolved, and social relations did not depend solely on geographic proximity (Watkins, 1990). Although other forms of demographic behaviours such as marriage partner selection were often limited to spatial proximity in the Skellefteå region, the spatial patterns were not always spatially uniform (Brändström, 2002). Fertility has also been shown to be dependent on social interactions external to spatial communities. Becoming a member of a temperance association, a union or a free church affected fertility behaviours during the transition (Junkka & Edvinsson, 2016; Junkka, 2018a, 2018b). Finally, estimating separately the neighbour effects means that the total variance in neighbour behaviours was underestimated, and the effect of this underestimation is uncertain. This is a limitation which could be overcome in future studies by incorporating neighbour effects as time-lagged spatial autocorrelation in a joint probability model. Developments in Bayesian spatial survival models could be extended to fit these forms of problems (Zhou & Hanson, 2017).

58Despite these limitations, the current study provides evidence in support for spatial diffusion of fertility behaviours through social interactions. This suggests that fertility decline was not solely related to structural changes but was also affected by the diffusion of new norms about family and fertility. Or, rather, the combination of these factors: structural ideational, economic, demographic and social changes shifted the incentives for having another child, while social interactions diffused these new ideas, creating spatial fertility patterns.