Abstract

The aim of this study is to estimate the causal effect of family size on the proximity between older mothers and adult children by using a large administrative data set from Sweden. Our main results show that adult children in Sweden are not constrained by sibship size in choosing where to live: for families with more than one child, sibship size does not affect child-mother proximity. For aging parents, however, having fewer children reduces the probability of having at least one child living nearby, which is likely to have consequences for the intensity of intergenerational contact and eldercare.

Introduction

The geographic proximity between parents and their adult children plays a key role in determining the quality and intensity of intergenerational relationships. It is not only one of the most important factors explaining the provision of care and support in family networks (Couch et al. 1999; Pezzin et al. 2006) but also has implications for the strength of kinship ties (Cheadle et al. 2010; Ermisch 2009; Hank 2007; Shelton and Grundy 2000). Because intergenerational relations are a fundamental part of our social identity, scientists from different disciplines have invested a great deal of effort and thought into identifying the determinants of the geographic distances between generations (see, e.g., Compton and Pollak 2009; Greenwell and Bengston 1997; Konrad et al. 2002; Løken et al. 2012; Malmberg and Pettersson 2007; Pettersson and Malmberg 2009). Much of this research has focused on education, parental health, and socioeconomic status as the main predictors of the distance between adult children and their parents. A growing number of studies have also looked at family size (a term that we use interchangeably with sibship size) and its association with child-parent proximity: Shelton and Grundy (2000), Hank (2007), and Malmberg and Pettersson (2007) found a significant negative association between the number of siblings and proximity to parents.

Understanding how different configurations of family size affect patterns of child-parent proximity is a topic of great concern. Over the last few decades, virtually every industrialized country has witnessed demographic changes that have dramatically reshaped the family. One of the most important trends has been a change in the population structure by age resulting from the increased life expectancy of the average individual (Schoeni and Ofstedal 2010). At the same time, the number of families having a second or third child has declined significantly, with a shift toward single-child families from the previously dominant two-child or three-child family models. The aging of the population and the growing trend toward single-child families place many adult children in an unprecedented situation with respect to parent care. Indeed, more and more adult children are likely to be caught in a “demographic double bind” (Treas 1979): they are increasingly likely both to have at least one parent who survives into old age and to have fewer siblings with whom to share caregiving responsibilities.

What are the likely implications of these demographic trends for the geographic mobility of younger generations? Can we expect adult children to be forced to stay close to their parents because of familial obligations, and will we see a decline in labor mobility? Despite the enormous policy implications (United Nations 2005), we know very little about these issues. An answer to these questions first requires a thorough understanding of whether family size causally affects intergenerational proximity, or whether the patterns observed in the previous studies reflect unobserved characteristics of parents and children that are correlated with sibship size (i.e., a selection effect). If the negative relationship between the number of siblings and proximity found in previous studies is confounded by selection bias, the scope for policy interpretation will be limited, and we will be unable to determine whether the decline in fertility is likely to have implications for the location decisions of young adults.

In this study, we explore the causal effects of family size on the geographic proximity between adult children and older parents. Purging the estimates of selection bias by using quasi-experimental variation in family size resulting from the birth of multiples, our findings reflect children’s responses to sibship size rather than underlying preferences of the family that are also correlated with the number of children. The causal estimates can therefore be expected to provide useful information about the geographic mobility of future generations that will grow up with few siblings, and to make important contributions to the policy debates on both elderly care and labor mobility.

From the adult child’s perspective, sibship size may influence individual location decisions, but this question should also be examined from the aging parents’ viewpoint. From their perspective, it is reasonable to think about the proximity to the closest child as the most important factor in both the frequency of interaction and the intensity of care. We therefore complement our analysis by looking at the effect of family size on the child-parent proximity of the closest child. We also provide graphical evidence of child-parent proximity over time and investigate the extent to which the distance changes in response to maternal aging.

The analysis is based on Swedish register data covering 35 % of cohorts born between 1935 and 1950. A unique feature of our data set is the possibility of using Swedish census information to identify the geographic location of all individuals in the sample. Using the geographic coordinates of the main town or village in each parish along with household identifiers, we calculate the approximate distance between children and their parents. Combining this distance measure with detailed information about family size and birth order allows us to conduct a comprehensive study of the relationship between family size and the geographic mobility of adult children.

Our causal analysis allows us to identify the effects of sibship size for families with two or more children; for these families, the results show that adult Swedish children are not constrained in their location decisions because of family size: sibship size does not affect child-parent proximity.1 For aging parents, however, having fewer children reduces the probability of having at least one child close-by. Recent fertility trends are, thus, not limiting the mobility of young adults but may imply a lower frequency of intergenerational interaction and, potentially, less eldercare provided by children. On the methodological side, our results highlight the importance of accounting for potential problems of omitted variable bias when investigating the relationship between sibship size and intergenerational proximity.

The remainder of this article is organized as follows. The second section provides a conceptual framework and derives hypotheses about the effect of family size on intergenerational proximity. Then we describe the data and descriptive statistics, followed by a presentation of descriptive graphical evidence on intergenerational proximity. Following that, we outline the identification strategy and then present the main results. The penultimate section provides a series of robustness checks and discusses the interpretation of the causal estimates, and we then conclude.

Conceptual Framework and Hypotheses

We are interested in exploring how family size might affect the geographic proximity between adult children and older mothers. Our estimations are based on the distance between Swedish working-age adults (44 years old, on average) and their elderly mothers (73 years old, on average), measured at a single point in time. We take the broad view that proximity at this point in time is the product of numerous individual and joint decisions by family members who have different preferences and face different constraints. First, it involves young adults’ decisions to leave home and their subsequent work- and family-related mobility choices. Second, observed proximity may also reflect intergenerational geographic convergence as a manifestation of child-initiated or parent-initiated return migration to revive an earlier nuclear family arrangement.2 The factors likely to influence residential mobility over a family’s life course are manifold: for example, the socioeconomic characteristics of adult children and their parents, the geographic distribution of labor market opportunities, social norms of the family (e.g., the degree to which family obligation is important), and individual preferences for autonomy in intergenerational relations. Moreover, if children have pro-social preferences (e.g., are motivated by altruism or reciprocity), past family interactions and assessments of parental needs will also shape observed patterns of intergenerational proximity.

Within this broad conceptual framework, family size might affect the geographic proximity between adult children and older mothers for various reasons. Here, we discuss three competing hypotheses. First, a positive relationship might exist between family size and child-parent proximity. This case might arise because parents’ preferences for children and their children’s pro-social preferences are codetermined. For example, some studies suggest that children from larger families are more family oriented (Marini 1985). If this family orientation is shared among siblings, children from large families might cluster close to their parents, resulting in less dispersed networks of siblings. Moreover, the greater the number of siblings who live near their parents, the greater the location-specific social capital (Michielin and Mulder 2007).

A second hypothesis predicts just the opposite: namely, that family size has a negative effect on child-parent proximity. The following perspective can be cited to support this hypothesis: a small family may compel children to live closer to their parents, since there are fewer siblings to help when parents are in need of support or care. By contrast, a large family may enable sharing of responsibility for caregiving among more siblings. Thus, the size of the family might decrease child-parent proximity, since a child who has more siblings is likely to have fewer caregiving obligations and may hence be less reluctant to locate farther away from the parents (Rainer and Siedler 2009, 2012).

Finally, we propose a third hypothesis: family size has no effect on the geographic distance between adult children and their parents. One can argue in favor of this hypothesis with particular reference to the relationship between intergenerational family help and welfare state support. On the one hand, if the public sector plays only a minor role in caring for the elderly, family size might be expected to play an important role in determining the residential choices of adult children. On the other hand, generous provision of welfare state services in support of older people might crowd out family help, with the consequence that the presence of siblings no longer influences choices where to live. Our data set comes from Sweden, a country with a well-developed system of care designed to support older people in need without placing excessively high demands on family members (Shea et al. 2003). One could therefore speculate that such a well-developed modern welfare state nullifies the potential effects of family size on child-parent proximity.

Overall, the hypotheses we have put forward suggest that the effect of family size on the proximity between adult children and their parents is a priori ambiguous and, therefore, an empirical question.

Data and Descriptive Statistics

The data, a 35 % random sample of cohorts born in Sweden from 1935 to 1950, originate from registers administrated by Statistics Sweden. By means of a population register, siblings and biological parents are matched to the individuals in the random sample. A unique feature of the data is that through information in the bidecennial censuses between 1980 and 1990, we can identify the geographic location of all these individuals. The censuses contain information on the parish and municipality in which the individuals lived.3 In addition to information on these geographic units, the data include an indicator for the household to which the individual belongs, which makes it possible to identify cases of coresidence between adult children and their mothers.

Our main outcomes of interests are (1) the logarithm of geographic distance between adult children and their mothers and (2) the logarithm of geographic distance between the mother and the child living in closest proximity. Using the logarithm of the dependent variable allows us to estimate a nonlinear relationship between child-mother geographic distances and the explanatory variables, the so-called semi-elasticity model. For similar specifications in the demographic literature on spatial interactions, see Silverstein (1995) and Michielin and Mulder (2007). In the Robustness section, we also discuss estimates for alternative outcome measures: whether adult children and their mothers live within 10 km of each other and whether they live in the same parish or municipality.

We measure the geographic distance from the last census year in which this information was provided in order to capture geographic distances at a time when mothers are elderly and likely to require some help and support. As a result, 81 % of child-mother distances are measured in 1990; for mothers who had passed away in 1990, we use census information from 1985 (11 %) or 1980 (8 %). Using the geographic coordinates of the main town/village in each parish, we calculate the approximate distance in kilometers, as the crow flies, between the two generations. In 1990, for example, the number of parishes in Sweden was 2,563, with a population ranging from 2 to 56,714 inhabitants. The median parish population was 968. For our graphical analysis, we use intergenerational proximity from censuses including the 1975 census and information on parish of residence from the 1995 and 2000 population registers. For our multivariate analysis, we measure our outcome in the years 1980, 1985, and 1990 because the census information on coresidence is more precise than the register information from 1995 and 2000.

Our measure of geographic distance will be imprecise, for several reasons. First, we do not have exact information on the distance between children and mothers who live in the same parish. We do know whether they coreside, in which case they are assigned a zero distance (for linear specifications) or a distance of 1 meter (for logarithmic specifications). If they do not live in the same household but live in the same parish, we assign for each parish a distance that is one-half of the minimum distance between any other child-mother pair not living in the same parish. Secondly, parishes vary widely in geographic area, and using the coordinates of a parish is more precise for smaller parishes than for larger ones. In unreported regressions, we also explored the effects of family size on the probability that children and mothers live in the same parish or in the same municipality. These alternative outcome measures are unlikely to suffer from measurement error because we do not need to assign a positive distance to mothers and children living in the same parish or municipality. The results from these linear probability models are in line with the present estimates and are available from the authors upon request.

We restrict the sample to adult children aged 30 and older in the year the child-mother geographic distance is measured, and for the majority of the individuals, we should capture the location they choose after completing their studies. For the 1935–1950 cohorts, concentrating on the distance between children and mothers in bidecennial censuses between 1980 and 1990 implies that we lose 10 % of the sample members whose mothers had died before 1980. Issues of sample selection arise because mortality of mothers is likely to vary according to the number of children born. However, when constructing the data set, a trade-off emerges. On the one hand, we want to measure distance when adult children have already entered the labor market; on the other hand, we cannot observe them too late because their parents are then likely to be deceased. We take this trade-off into account when constructing the sample, but unfortunately, we do not have any means of testing for the importance of sample selection with respect to maternal mortality. Paternal mortality will be considered further in the empirical analysis. We also briefly consider the distances between adult children and their mothers at different ages of the mother in our discussion of the main results, which support the use of proximity measures when the mothers are aged 73, on average.

The data also contain information on completed education. For the parents, this information is based on the 1970 census, whereas for the children and their siblings, education is reported in Statistics Sweden’s education register from 2003. The level of education is translated into years of schooling according to the years normally required to complete a degree.4

We restrict the data to full biological siblings and exclude families that experienced the death of a child. The rationale for these sample selections is that we want to disentangle the mechanisms of sibship size in a “clean” setting with a limited set of mechanisms at stake.

Table 1 presents the descriptive statistics of our estimation sample. The first eight rows present the means and standard deviations for the different proximity measures. On average, the adult children in the sample live 83 km from their mothers, and the mothers’ closest child lives, on average, 29 km away. Forty percent of the individuals in the sample live within 10 km, and 29 % live in the same parish as their mother. Sixty-six percent of elderly mothers have at least one child living within 10 km. Moving on to Table 2, reporting the number of children in families of different sizes, we see that most children grew up in families with two or three children: nearly 30 % of the children are from two-child families. Families with six or more children are rare. Finally, in our instrumental variable analysis, we use the event of twin births as an instrument for family size. Twins are identified in the data as full biological siblings born in the same month and year. In our sample, we have 7,163 twins.

Setting the Scene: Intergenerational Proximity and the Family

Child-Mother Geographic Distance Over the Life Course

Before turning to our multivariate analysis, it is worth examining whether the distance between children and their mothers might change over the life course. For instance, parents might decide to move closer to their children to facilitate intergenerational contact and increase the frequency of visits. Alternatively, adult children might move closer to their parents at a time when those parents actually need their children’s help and support. Figure 1 displays the average geographic distance between adult children and their mothers by the age of the mother at the time of the census (solid line) and the average distance between the mother and the child living in closest proximity (dashed line). The figure shows that the average child-parent distance is relatively stable over mother’s age. The average distance between mothers and adult children increases until mothers are approximately 70–75 years old, and decreases slightly thereafter. For example, the average child-parent distance is around 75 km when mothers are 60 years old, and 80 km when they are 73–74 years old. The decrease in child-mother distance when mothers are older might be driven by parents becoming disabled and needing more help and support. Unfortunately, our data do not contain information on maternal disabilities, and we therefore cannot shed more light on this issue. Similarly, the average distance between mothers and the children living in closest proximity is quite stable over time, varying between 35 and 40 km. Figure 1 also exemplifies that most of the changes in child-parent proximity occur when mothers are between 60 and 70 years old, rather than at an older age. These changes are very likely to be driven by adult children leaving home. In summary, the graphical evidence suggests that the geographic distance between adult children and their elderly mothers in Sweden remains relatively stable as mothers are aging. In addition, over the 10 years 1980–1990, 16 % of elderly mothers had moved, while 31 % of adult children had moved, indicating that in Sweden, the elderly are less mobile than their middle-aged children.

Descriptive Evidence on Sibship Size and Child-Parent Proximity

Previous literature has shown that child-parent proximity is associated with various family and socioeconomic characteristics. Linking to this literature, in this study, we present a descriptive analysis of the determinants of child-mother proximity with a particular focus on sibship size. In panel A of Table 3, we present results of ordinary least squares (OLS) regressions of the logarithm of child-mother distance on family size. The regressions can be represented by the following equation:
Table 3

OLS regressions of the effect of family size on last observed child-mother distance

Demographic and Municipality ControlsDemographic and Municipality Controls, Including Child’s Education
(1)(2)(3)(4)
A. Outcome: Log of Child-Mother Distance 
 Number of children 0.04**  0.06**  
 (0.00)  (0.00)  
 2 children  0.21**  0.18** 
  (0.01)  (0.01) 
 3 children  0.28**  0.28** 
  (0.01)  (0.01) 
 4 children  0.31**  0.35** 
  (0.01)  (0.01) 
 5 children  0.28**  0.36** 
  (0.01)  (0.01) 
 6 children  0.30**  0.42** 
  (0.02)  (0.02) 
 7 children  0.25**  0.40** 
  (0.02)  (0.02) 
 8 children  0.29**  0.45** 
  (0.03)  (0.03) 
 9 children  0.28**  0.46** 
  (0.04)  (0.04) 
 10 children  0.39**  0.57** 
  (0.06)  (0.06) 
 Observations 687,681 687,681 687,681 687,681 
 R2 .099 .100 .146 .146 
B. Outcome: Log of Distance to Closest Child 
 Number of children −0.37**  −0.35**  
 (0.01)  (0.01)  
 2 children  −0.71**  −0.76** 
  (0.02)  (0.01) 
 3 children  −1.14**  −1.18** 
  (0.02)  (0.02) 
 4 children  −1.44**  −1.46** 
  (0.03)  (0.03) 
 5 children  −1.73**  −1.71** 
  (0.04)  (0.03) 
 6 children  −2.04**  −1.99** 
  (0.05)  (0.05) 
 7 children  −2.17**  −2.09** 
  (0.07)  (0.07) 
 8 children  −2.40**  −2.32** 
  (0.11)  (0.11) 
 9 children  −2.65**  −2.56** 
  (0.16)  (0.16) 
 10 children  −2.66**  −2.56** 
  (0.23)  (0.23) 
 Observations 286,439 286,439 286,439 286,439 
 R2 .130 .132 .157 .160 
Demographic and Municipality ControlsDemographic and Municipality Controls, Including Child’s Education
(1)(2)(3)(4)
A. Outcome: Log of Child-Mother Distance 
 Number of children 0.04**  0.06**  
 (0.00)  (0.00)  
 2 children  0.21**  0.18** 
  (0.01)  (0.01) 
 3 children  0.28**  0.28** 
  (0.01)  (0.01) 
 4 children  0.31**  0.35** 
  (0.01)  (0.01) 
 5 children  0.28**  0.36** 
  (0.01)  (0.01) 
 6 children  0.30**  0.42** 
  (0.02)  (0.02) 
 7 children  0.25**  0.40** 
  (0.02)  (0.02) 
 8 children  0.29**  0.45** 
  (0.03)  (0.03) 
 9 children  0.28**  0.46** 
  (0.04)  (0.04) 
 10 children  0.39**  0.57** 
  (0.06)  (0.06) 
 Observations 687,681 687,681 687,681 687,681 
 R2 .099 .100 .146 .146 
B. Outcome: Log of Distance to Closest Child 
 Number of children −0.37**  −0.35**  
 (0.01)  (0.01)  
 2 children  −0.71**  −0.76** 
  (0.02)  (0.01) 
 3 children  −1.14**  −1.18** 
  (0.02)  (0.02) 
 4 children  −1.44**  −1.46** 
  (0.03)  (0.03) 
 5 children  −1.73**  −1.71** 
  (0.04)  (0.03) 
 6 children  −2.04**  −1.99** 
  (0.05)  (0.05) 
 7 children  −2.17**  −2.09** 
  (0.07)  (0.07) 
 8 children  −2.40**  −2.32** 
  (0.11)  (0.11) 
 9 children  −2.65**  −2.56** 
  (0.16)  (0.16) 
 10 children  −2.66**  −2.56** 
  (0.23)  (0.23) 
 Observations 286,439 286,439 286,439 286,439 
 R2 .130 .132 .157 .160 

Notes: Robust standard errors, shown in parentheses, are clustered on families. Regressions in panel A include controls for gender, years of schooling of mother and father, birth year, mother’s and father’s age, year of distance observation, presence of grand children, father’s death, and mother’s municipality in 1960. Regressions in panel B include controls for birth years of youngest and oldest child, share of girls and the average presence of grandchildren of all the children, mother’s and father’s age and education, mother’s municipality in 1960, and indicators for year of distance observation and death of father. See Table 6 in the appendix for detailed regression output.

**p < .01

formula
(1)
where log(DISTANCEij) represents the logarithm of child-mother geographic distance in kilometers for adult child i from family j, FAMILYSIZEj indicates the total number of children in family j, the vector xij contains covariates, and represents the disturbance term. Controls included in the vector xij are dummy variables for the child’s birth year and gender, mother’s and father’s age and years of schooling, father deceased, presence of grandchildren, and indicators for year of distance observation and mother’s municipality in 1960. The specifications in columns 3 and 4 also include controls for the child’s own schooling. Mother’s municipality is included for two reasons: first, our distance measure varies in quality by region; second, family size might vary nonrandomly by region. For example, if family size is larger in rural areas, and if mobility is higher for children in rural areas because of labor market (or other) reasons, our estimation strategy will capture a spurious correlation between sibship size and geographic proximity unless we control for region-specific effects.

The effects on child-mother proximity that are not observed by researchers, captured by , may include factors such as adult children’s and their parents’ preferences and risk attitudes. The key parameter of interest—the relationship between family size and child-mother geographic distance—is the coefficient . Estimates of will tell us whether having one more sibling is associated with a higher average geographic distance between adult children and their parents. We also run similar regressions in which the linear variable FAMILYSIZEj is exchanged for dummy variables for each family size.

Panel B of Table 3 reports OLS estimates for the logarithm of child-parent distance only for the sample of adult children living in closest proximity to their mother. As a result, the OLS regressions are estimated on a sample of 286,439 adult children, compared with a sample size of 687,681 in panel A of Table 3. The regressions in panel B include controls for the birth years of the youngest and oldest child, the share of girls and the average presence of grandchildren of all the children, mother’s and father’s age and education, mother’s municipality in 1960, and indicators for year of distance observation and death of father.

Panel A in Table 3 reports the results for the outcome logarithm of child-mother distance in kilometers. The first column in panel A of Table 3 shows that with family size entered as a linear regressor, one more child in the family is related to a 4 % increase in the average distance from the mother, conditional on xij. Using a more flexible specification with dummy variables suggests that in families with two children, the average distance from the mother is 23 % (exp(0.21) – 1) higher than that between an only child and her mother.5 Moving on to families with three to six children, the estimated coefficients represent average distances that are around 32 % to 36 % larger.

The results in the first two columns in Table 3 do not include controls for the child’s education. Location choice and education are likely to be closely linked, but the way in which they are linked is unclear. Choice of location could be the consequence of a certain type of education, but location and education can also be regarded as a joint decision: job opportunities for many types of education are restricted to certain geographic areas, and this is known when the education choice is made. In columns 3 and 4, we therefore include controls for the child’s years of schooling. The estimated coefficient on the number of children in column 3 in panel A (Table 3) suggests that one more child in the family is associated with a 6 % higher child-mother geographic distance. Similarly, the estimated coefficients on the dummy variables for family size in column 4 point to a higher child-mother geographic distance in larger families.

From the perspective of the mother, the distance to the closest child is naturally a key outcome. Panel B of Table 3 presents the estimates for the logarithm of distance to the closest child. Having more children is closely associated with having at least one child closer to home, and the coefficients are remarkably stable across specifications. For example, the results in columns 1 and 3 suggest that one more child reduces the distance to the closest child by around 45 %. Moreover, the estimates on the family size dummy variables in columns 2 and 4 also indicate that having more children is strongly related to having at least one adult child living close-by.

Overall, we therefore conclude that sibship size is positively associated with the geographic distance between individual adult children and their older mothers, but that the estimated association is small. Moreover, the simple OLS regressions suggest that having more children is strongly related to having at least one child living close-by. If we hypothesize that this effect represents a causal mechanism, we can conclude that patterns of lower fertility are likely to limit the geographic mobility of young adults, a finding in line with our second hypothesis presented earlier. The regressions are also revealing in terms of other demographic and socioeconomic factors associated with intergenerational proximity (see Table 6 in the appendix). Adult women live, on average, further from their mothers than do adult men, with an average distance between daughters and mothers that is about 35 % higher than that between sons and mothers. Moreover, both parental and child schooling are negatively related to child-mother proximity. These patterns confirm recent findings by Malmberg and Pettersson (2007) for Sweden.6

Birth Order and Child-Mother Proximity

We next ask whether the observed relationship between family size and child-mother proximity is driven by birth-order effects. Indeed, if the average distance from parents is smaller (or larger) for children of low birth order, this then increases (or reduces) the average child-parent distance in large families. To net out this effect from the association between family size and child-parent proximity, it is important to include birth order controls in the regression analysis. Related to this, Black et al. (2005) showed that family size effects on children’s education are mostly driven by birth-order effects. High-birth-order children emerge with lower education, which lowers the average for large families. After we control for birth order in a regression of education on family size, the effect of family size is negligible. However, when we include birth-order effects in the specifications shown in Table 3, the estimates are virtually unchanged. Thus, the association between family size and child-mother geographic distance appears not to be driven by birth-order effects.

To shed light on the birth-order effects, we regress distance from mother on birth order separately for different family sizes. The results are outlined in Table 4. In the upper panel, the results point to decreasing mobility in birth order for the most common family types. Later-born siblings locate closer to their parents, which is in line with the hypothesis that early-born siblings have a first-mover advantage and are less constrained in their location choice than younger siblings. Note that we omit results for families with more than nine children, for which there are very few observations. When we control for the child’s education, as in the lower panel of Table 4, it is clear that education plays a crucial role for birth-order effects. Controlling for children’s education, we no longer find that distance decreases with birth order for the most common family sizes.

To interpret these findings, we conclude from the previous literature (see, e.g., Black et al. 2005) that higher birth order implies lower education. Now we also know from our results that unconditional on education, higher birth order implies more restricted geographic mobility, but this effect goes away after we control for education. The nature of the education and location decision-making process, however, makes it difficult to extrapolate which mechanisms are at stake. On the one hand, if children are responsive to their parents’ care needs, and if younger siblings know that they will carry the burden of caregiving, the incentive to invest in higher education might be lower if the return to education is low in their home region. In this case, it is the location constraint that determines the birth-order effects for educational outcomes. On the other hand, high birth order may be associated with lower educational outcomes for other reasons, and in this case, the birth-order effects on proximity that we found in Table 4 are spuriously driven by educational choices. Recent research on education and mobility reports a positive causal effect of the length of compulsory years of schooling on regional geographic mobility (Machin et al. 2012). This finding speaks in favor of including adult children’s years of schooling as a control variable in our regressions in order to net out the mobility effect that results from higher education. Thus, in the following regressions, we always control for adult children’s years of schooling. All results, however, are very similar even when we exclude education as a control.

Identification Strategy: Using Multiple Births as an Instrument for Family Size

We now examine whether the observed positive relationship between family size and child-mother geographic distance is causal or instead is a reflection of unobserved family background characteristics and demographics. Many reasons lead us to believe that family size and child-mother geographic distance are correlated but not necessarily causally related. For example, families are traditionally larger in rural areas, and urbanization makes it likely that many children will leave rural areas for cities. Some skepticism regarding a causal interpretation also arises from the recent literature on the intergenerational transmission of preferences and attitudes. For example, growing evidence suggests that attitudes toward risk-taking are transmitted from one generation to the next (Dohmen et al. 2012), and it is also well understood that individuals’ willingness to take risks is positively correlated with their mobility behavior (Jaeger et al. 2010). Thus, if a significant correlation between parents’ risk-taking attitudes and family size exists, and if such attitudes are transmitted from one generation to the next, then a positive link between family size and child-parent geographic distance might not be causal. To the best of our knowledge, this study represents the first attempt to isolate the causal effect of sibship size on child-mother proximity. To do so, we use a source of quasi-experimental variation in family size in an instrumental variables (IV) approach: the unplanned event of a multiple birth (see, e.g., Angrist and Evans 1998; Rosenzweig and Wolpin 1980).

The main idea is that the birth of multiples is unplanned and therefore provides a source of exogenous variation in family size: that is, parents end up with more children than anticipated. It is reasonable to assume that the “surprise” increase in family size is unlikely to be correlated with parents’ unobservable characteristics, which is an important requirement for a multiple birth to be a valid instrument for family size (Angrist and Evans 1998; Angrist et al. 2010; Black et al. 2005; Rosenzweig and Wolpin 1980). Although the prevalence of twin births has been found to increase with maternal age, this can be accounted for by including the mother’s age at childbirth as a control in the regressions. Note also that we use a data set with multiple births among cohorts born between 1935 and 1950:—that is, prior to the existence of fertility techniques (e.g., in vitro fertilization (IVF) or intracytoplasmic sperm injection (ICSI)), which increase the likelihood of multiple births and the correlation with family background characteristics.

In line with recent empirical literature, we argue that the birth of twins (or triplets) results in an increase in family size of two (or three) when only one additional child was originally expected. For example, recent research exploits variation in the number of children induced by multiple births to study the effects of family size on education and earnings (Angrist et al. 2010; Aslund and Grönqvist 2010; Black et al. 2005) and IQ test scores (Black et al. 2010). Together, these studies provide comprehensive evidence that multiple births are likely to constitute a valid exogenous variation in family size.

The second requirement for twin births to constitute a valid instrument for sibship size is that they affect outcomes only through family size: that is, there is no direct effect of twinning on outcomes, conditional on family size. This requirement would be violated, for example, if having twins in the family implies a reallocation of parental investments in children or affects sibling interactions (and proximity) in adulthood. This is an untestable assumption, but following Black et al. (2005), we investigate one mechanism through which this assumption may be violated: spacing. Our focus is on firstborn children who subsequently have two more siblings (who are not twins). If the spacing of the second and third child affects the child-parent proximity of the firstborn, it is possible that the extreme case of close spacing—that is, twins—also affects location decisions through spacing and not only through sibship size. However, in our sample, there are no significant differences in the proximity measures for firstborns that are related to the spacing of subsequent siblings. If this result carries over to twins, a twin birth at parity two should at least not affect the firstborn child because of close spacing of the twins. Naturally, there are many other mechanisms for which we unfortunately cannot test.

Turning to the main analysis, we aim to estimate the impact of family size on the distance between adult children and elderly mothers by two-stage least squares (2SLS), treating family size as endogenous and the other explanatory variables as exogenous. The estimation strategy consists of the following two equations:
formula
(2)
formula
(3)
with the log(DISTANCEij), FAMILYSIZEj, and xij as in Eq. (1). The instrumental variable candidate TWINSj equals 1 if the nth birth of family j is a multiple birth (twins or triplets), and equals 0 if the nth birth is a singleton birth, with n = 2 or n = 3. Equation (3) represents the first stage of the 2SLS procedure, and Eq. (2) denotes the second stage.

We restrict the sample to families with two (or three) and more children when using multiple births as an instrument for family size. Importantly, we estimate 2SLS regressions only for adult children born before the multiple birth in the family (Angrist et al. 2010; Black et al. 2005). Estimations for the n = 2 case, therefore, include only firstborn children, whereas the n = 3 regressions include both first- and second-born children. This sample restriction will increase the likelihood of a comparison between adult children from families with similar preferences for family size at the nth birth. In other words, by focusing on a sample of adult children born before birth n, we circumvent potential selection biases that arise because families that have another child after a multiple birth may differ from families that choose to have another child after a singleton birth. In addition, this helps us to avoid the potential problem that families with more children are more likely to include twins, who themselves might be nonrepresentative of the majority of children. Another advantage of using a sample of adult children born before a possible multiple birth occurs is that we avoid potentially confounding problems of an increase in family size and changes in birth order. As Black et al. (2010) argued, estimates also using adult children born subsequent to a multiple birth would not only increase the number of children in the family but also alter the birth order.

Instrumental Variables Results

Panel A of Table 5 presents the results for the outcome logarithm of child-mother distance for firstborn children in families with two or more children, the instrument being a multiple birth at the second birth. The OLS estimate in the first column indicates that the positive association between family size and child-mother geographic distance also holds for this particular sample. The estimated coefficient suggests that having one more child in the family is associated with an increase in the average child-mother distance by 5 %. Thus, we are not working with a sample here that looks very different from the random sample. Next, the second column shows a strong first stage, with a very high F statistic of 892. This suggests that multiple births provide a strong instrument for family size, and that one important assumption of instrumental variable regressions—namely, that the instrument is strongly correlated with the endogenous variable—holds (Staiger and Stock 1997). Quantitatively, the estimated coefficient in column 2 indicates that a multiple birth increases completed family size by about 0.7, with a standard error of 0.02. This is consistent with previous research. Black et al. (2010), using Norwegian data, reported a similar first-stage coefficient of 0.68 (0.02) when using twin at second birth as an instrument for family size. Finally, the IV estimate of −0.03 (SE = 0.07) suggests that the previously observed positive relationship between sibship size and the geographic distance is not causal and that the OLS estimate in column 1 is upwardly biased.

Panel B in Table 5 reports the corresponding regression results for a sample for first- and second-born children in families with three or more children. The estimates reveal that twins at higher parity have a larger impact on family size, with an estimated first-stage coefficient of 0.76. An intuitive and plausible interpretation is that a multiple birth at higher parity is more likely to push family size above the desired number of children. Again, this finding is consistent with the evidence in Black et al. (2005, 2010) and Angrist (2010). Overall, panel B of Table 5 paints a similar picture when we use multiple births at third birth as an instrument: although the first stage is strong, the random event of a multiple birth does not point to a causal impact on geographic mobility in the family. The estimated IV coefficient of 0.04 is very close to the corresponding OLS estimate, but the effect is imprecisely estimated, and thus we cannot reject the null hypotheses of zero effect.

Panel C of Table 5 reports the estimates for our second outcome measure: the logarithm of the distance to the child living closest to the mother.7 Distance to the closest child is calculated for all siblings, including twins. This would constitute a potential problem if the location decisions of twins were different than those of singletons. In our data, however, for a given family size, there is no statistically significant difference in the distance to the closest child between families with or without twins.

The OLS coefficient in column 1 of panel C suggests that having one more child decreases the distance to the child living in closest proximity by 28 %. Column 4 presents the 2SLS result, where the instrument is the indicator for whether the second birth was a multiple birth. In contrast with the previous IV estimates, the 2SLS estimate is statistically significant at the 1 % level. The IV estimate suggests that increasing family size has a negative effect on the geographic distance of the child living in closest proximity to the parents. On average, having one more child reduces this distance by around 35 %. This result suggests that a larger family size considerably increases the likelihood of having at least one child living in close geographic proximity to the mother. The results when using multiple births at third birth as exogenous variation for family size confirm these findings. The instrumental variable estimates in panel D of Table 5 also point to a causal negative effect of sibship size on the distance between the mother and the child living in closest proximity. The estimated IV coefficient suggests that having one more child decreases the average distance to the closest child by 26 %.

Taken together, the findings from the analysis using multiple births as an instrument are twofold. First, there is no causal effect of sibship size on individual child-mother proximity. Second, from the mother’s perspective, the result remains that having more children decreases the distance to the closest child.8

Sample Selection, Alternative Outcomes, Heterogeneous Effects, and Caveats

Sample Selection

Only 2 % of the children in the sample coreside with their mothers. As a sensitivity test, we omitted these children from the models in Tables 3 and 4. Doing so had no effect on the signs and significance of all coefficients, but the magnitudes on almost all of them declined by at least 50 %. These alternative estimates, however, do not change our conclusions about the validity of the three hypotheses put forward in our second section. The significance and magnitude of the coefficients in Table 5 were robust to the exclusion of children who coreside with their mothers. Our results are robust to estimating Tobit specifications taking into account the left censoring introduced by the coresidents. The log-linear specifications were also stable when we assigned coresidents 0.1 m instead of 1 m. All these results can be obtained from the authors upon request.

Alternative Outcomes

We examined whether sibship size effects are better captured by alternative outcomes. We applied the IV approach, using linear probability models in which the outcome reflects whether the child and mother live within 10 km. The results are reported in Table 7 in the appendix. In line with our previous estimates, we did not find a causal relationship between family size and the average child-parent geographic proximity in families with two or more children. Consistent with our results in Table 5, the IV estimates suggest that the likelihood of having at least one child living within a distance of 10 km increases by around 5–10 percentage points with an additional child in the family. We also estimated OLS and IV regressions for whether children and mothers live in the same parish or in the same municipality, respectively (see also Løken et al. 2012). These specifications confirm our previous findings and are available upon request.

Heterogeneous Effects

If siblings relocate in response to increasing needs for care, and if sibship size plays a role, we expect to find significant results for the oldest mothers in our sample. We have argued that the evidence in Fig. 1 does not support major relocations as care is needed, but further robustness tests are warranted. We found that when we split the sample by the 75th percentile of mothers’ age (around age 78), the results for younger and older mothers do not differ.

Heterogeneity may also be present along many other dimensions related to the family situation. We examined heterogeneity by the presence of grandchildren and a deceased father, finding that the results are stable across these subgroups.

Finally, we looked at whether young adults in rural regions are more likely to face the trade-off between moving to a more prosperous urban area and staying close to the family, whereas children growing up in urban areas already have job opportunities nearby and do not see the need to relocate. To investigate whether there is any heterogeneity in the sample in this respect, we split the sample by urban and rural regions—urban being the counties surrounding the three major cities in Sweden (Stockholm, Gothenborg, and Malmö) and rural corresponding to the rest of the country. These regressions did not alter the picture: we found no significant effect of family size on geographic distance between adult children and their aging mothers. Again, the IV results in both the urban and the rural sample suggest that a larger family size increases the likelihood of having at least one child living nearby.

Caveats

As noted by Moffitt (2005), it is a general feature of IV regressions that they can only estimate the effects for those who are actually affected by the instrument, the so-called local average treatment effects. One limitation of our analysis is that we do not have an instrument that identifies the shift from being an only child to a child with a sibling, which is potentially the most important difference in terms of family size. It might be that the existence of siblings is what matters and not necessarily how many. In the present study, the IV regressions capture an exogenous increase in family size from two to three children and from three to four children. Unfortunately, we do not have an instrument for the variation in family size from one to two children, and therefore cannot investigate whether a causal effect is present in the lower part of the family size distribution.9

Moreover, because of data limitations, we could not investigate heterogeneous effects by the marital status of adult children and by whether mothers had severe health limitations or disabilities.

Conclusions

In this article, we examine the effect of family size on the geographic distance between mothers and adult children. Our empirical analysis is based on register data from Sweden. We find a small positive relationship between sibship size and the geographic distance between adult children and their elderly mothers in cross-sectional estimations. Sibship size, however, is negatively related to the distance between the mother and her closest child, indicating that having more children increases the probability of having at least one child close-by.

Keeping in mind that the number of children in a family is not exogenous, but, for example, reflects parental preferences that might be correlated with our outcome measure, we take our analysis one step further by introducing an instrumental variable approach in which we use multiple births as exogenous variation for family size. This approach is appealing because it controls for unobserved heterogeneity across individuals that potentially confounds simple cross-sectional estimates.

The conclusions from our analysis are twofold. First, there is no causal effect of family size on individual child-mother geographic distance: that is, having more siblings does not influence individual proximity decisions. However, IV estimates identifying the effect of sibship size on mother’s distance to her closest child show a negative and statistically significant effect. Having fewer children therefore reduces the likelihood of having at least one child close-by in old age.

It is important to acknowledge the limits of our analysis. In particular, our instrumental variables estimates have to be interpreted as measures of the local average treatment effects of family size increasing from two to three children or from three to four children. In the next phase of empirical research in this area, it will be important to look for variation that identifies the shift from being an only child to a child with a sibling.

With this limitation in mind, our findings nevertheless suggest that the recent trend toward smaller families in many developed countries may not necessarily result in adult children being constrained in terms of their geographic location decisions, at least not in Sweden. In the Swedish context, having fewer siblings does not seem to limit children’s residential choices. Having fewer children does, however, have a detrimental effect on aging parents, who are less likely to have children close-by. This is likely to have implications for the intensity of intergenerational contact and for the amount of eldercare provided by younger family members. The question of who will care for the elderly thus remains a topic of great policy concern.

Acknowledgments

We gratefully acknowledge financial support from the Economic and Social Research Council under Grant RES-000-22-2684 and through the Research Centre on Micro-Social Change (MiSoC) (Award No. RES-518-28-001). Helena Holmlund would also like to thank the Jan Wallander and Tom Hedelius Foundation for financial support. We also thank seminar participants at the 2007 IZA Workshop on Long-Term Care, the 2009 ESPE conference, and seminar participants at the University St. Gallen.

Notes

1

In the fifth and sixth sections, we discuss the methodology and the interpretation of the estimated effects in more detail.

2

Evidence from the United States suggests that older parents indeed expect to move closer to adult children out of need (Silverstein and Angelelli 1998). In what follows, we provide descriptive evidence showing that the distance between adult children and their parents remains relatively stable over time, suggesting that intergenerational geographic convergence is not a common phenomenon in Sweden.

3

Parishes constitute the smallest administrative unit that is used in Sweden for population censuses. Municipalities are larger service-providing local authorities, of which there were 289 in 1990.

4

A detailed description of how the 2003 education register has been translated into years of education can be found in the working paper version of this article (Holmlund et al. 2009).

5

Throughout the article, we interpret the coefficients in the log-linear models in percentage terms, obtaining the percentage changes using the formula (exp(beta) – 1).

6

The geographic distance between children and mothers might also vary by children’s marital status (Compton and Pollak 2009). Unfortunately, we do not have information on adult children’s marital status in our data set and therefore cannot investigate this issue.

7

The regressions here are run at the level of the mother; that is, we have one observation per family.

8

As mentioned in the fourth section, we controlled for adult children’s education in our IV regressions because recent research suggests that individuals with higher levels of education are geographically more mobile. However, a critic might argue that adult children’s education is likely to be correlated with the error term in Eq. (2), leading to biased estimates of family size on child-parent geographic proximity. In unreported regressions, we therefore estimated the regressions without controlling for adult children’s education, which did not alter our overall conclusions. The results are available from the authors upon request. As we will discuss further in the next section, it is important to keep in mind that these results hold for families with two or more children, and not necessarily for the shift from being an only child to having siblings. Finally, in unreported regressions, we also estimated the preceding regressions separately for women and men. The results did not point to considerable differences in the effect of family size on child-parent geographic distances by gender.

9

Bedard and Deschênes (2004) used the sex of the first child as an exogenous variation for family breakup in order to investigate the causal effect of marital dissolution on the mother’s economic status. However, in our context, the sex of the first child is unlikely to be a valid instrument for family size because gender might have a direct effect on adult children’s location decisions.

Appendix

The text of this article is only available as a PDF.

References

Angrist, J. D., & Evans, W. N. (
1998
).
Children and their parents’ labor supply: Evidence from exogenous variation in family size
.
American Economic Review
,
88
,
450
477
.
Angrist, J. D., Lavy, V., & Schlosser, A. (
2010
).
Multiple experiments for the causal link between the quantity and quality of children
.
Journal of Labor Economics
,
28
,
773
823
. 10.1086/653830
Aslund, O., & Grönqvist, H. (
2010
).
Family size and child outcomes: Is there really no trade-off?
.
Labour Economics
,
17
,
130
139
. 10.1016/j.labeco.2009.05.003
Bedard, K., & Deschênes, O. (
2004
).
Sex preferences, marital dissolution, and the economic status of women
.
Journal of Human Resources
,
40
,
411
434
.
Black, S. E., Devereux, P. J., & Salvanes, K. G. (
2005
).
The more the merrier? The effect of family size and birth order on children’s education
.
Quarterly Journal of Economics
,
120
,
669
700
.
Black, S. E., Devereux, P. J., & Salvanes, K. G. (
2010
).
Small family, smart family? Family size and the IQ scores of young men
.
Journal of Human Resources
,
45
,
33
58
. 10.1353/jhr.2010.0001
Cheadle, J. E., Amato, P. R., & King, V. (
2010
).
Patterns of nonresident father contact
.
Demography
,
47
,
205
225
. 10.1353/dem.0.0084
Compton, J., & Pollak, R. A. (
2009
).
Proximity and coresidence of adult children and their parents: Description and correlates (Working Paper 2009–215)
.
Ann Arbor
:
Michigan Retirement Research Center, University of Michigan
.
Couch, K. A., Douglas, M. C., & Wolf, D. A. (
1999
).
Time? Money? Both? The allocation of resources to older parents
.
Demography
,
36
,
219
232
. 10.2307/2648110
Dohmen, T., Falk, A., Huffman, D., & Sunde, U. (
2012
).
The intergenerational transmission of risk and trust attitudes
.
Review of Economic Studies
,
79
,
645
677
. 10.1093/restud/rdr027
Ermisch, J. (
2009
).
Adult-child parent relationships
. In M. Brynin, & J. Ermisch (Eds.),
Changing relationships
(pp.
111
126
).
New York
:
Routledge
.
Greenwell, L., & Bengston, V. L. (
1997
).
Geographic distance and contact between middle-aged children and their parents: The effects of social class over 20 years
.
Journal of Gerontology: Social Sciences
,
52B
,
S13
S26
. 10.1093/geronb/52B.1.S13
Hank, K. (
2007
).
Proximity and contacts between older parents and their children: A European comparison
.
Journal of Marriage and Family
,
69
,
157
173
. 10.1111/j.1741-3737.2006.00351.x
Holmlund, H., Rainer, H., & Siedler, T. (
2009
).
Meet the parents? The causal effect of family size on the geographic distance between adult children and older parents
(IZA Discussion Paper No. 4398). Bonn,
Germany
:
Institute for the Study of Labor
.
Jaeger, D. A., Bonin, H., Dohmen, T., Falk, A., Huffman, D., & Sunde, U. (
2010
).
Direct evidence on risk attitudes and migration
.
The Review of Economics and Statistics
,
92
,
684
689
. 10.1162/REST_a_00020
Konrad, K. A., Künemund, H., Lommerud, K. E., & Robledo, J. R. (
2002
).
Geography of the family
.
American Economic Review
,
92
,
981
998
. 10.1257/00028280260344551
Løken, K. V., Lommerud, K. E., & Lundberg, S. (
2012
). Your place or mine? On the residence choice of young couples in Norway. Advance online publication.
Demography
. doi:10.1007/s13524-012-0142-8
Machin, S., Pelkonen, P., & Salvanes, K. G. (
2012
).
Education and mobility
.
Journal of the European Economic Association
,
10
,
417
450
. 10.1111/j.1542-4774.2011.01048.x
Malmberg, G., & Pettersson, A. (
2007
).
Distance to elderly parents: Analyses of Swedish register data
.
Demographic Research
,
17
(
23
),
679
704
. 10.4054/DemRes.2007.17.23
Marini, M. M. (
1985
).
Determinants of the timing of adult role entry
.
Social Science Research
,
14
,
309
350
. 10.1016/0049-089X(85)90015-8
Michielin, F., & Mulder, C. H. (
2007
).
Geographical distances between adult children and their parents in the Netherlands
.
Demographic Research
,
17
(
22
),
655
678
. 10.4054/DemRes.2007.17.22
Moffitt, R. (
2005
).
Remarks on the analysis of causal relationships in population research
.
Demography
,
41
,
91
108
. 10.1353/dem.2005.0006
Pettersson, A., & Malmberg, G. (
2009
).
Adult children and elderly parents as mobility attractions in Sweden
.
Population, Space and Place
,
15
,
343
357
. 10.1002/psp.558
Pezzin, L. E., Pollak, R. A., & Schone, B. S. (
2006
).
Efficiency in family bargaining: Living arrangements and caregiving decisions of adult children and disabled elderly parents
.
CESifo Economic Studies
,
53
,
69
96
. 10.1093/cesifo/ifm004
Rainer, H., & Siedler, T. (
2009
).
O brother, where art thou? The effects of having a sibling on geographic mobility and labor market outcomes
.
Economica
,
76
,
528
556
. 10.1111/j.1468-0335.2008.00696.x
Rainer, H., & Siedler, T. (
2012
).
Family location and caregiving patterns from an international perspective
.
Population and Development Review
,
38
,
337
351
. 10.1111/j.1728-4457.2012.00495.x
Rosenzweig, M. R., & Wolpin, K. I. (
1980
).
Testing the quantity-quality fertility model: The use of twins as a natural experiment
.
Econometrica
,
48
,
227
240
. 10.2307/1912026
Schoeni, R. F., & Ofstedal, M. B. (
2010
).
Key themes in research on the demography of aging
.
Demography
,
47
,
S5
S15
. 10.1353/dem.2010.0001
Shea, D., Davey, A., Femia, E. E., Zarit, S. H., Sundström, G., Berg, S., & Smyer, M. A. (
2003
).
Exploring assistance in Sweden and the United States
.
The Gerontologist
,
43
,
712
721
. 10.1093/geront/43.5.712
Shelton, N., & Grundy, E. (
2000
).
Proximity of adult children to their parents in Great Britain
.
International Journal of Population Geography
,
6
,
181
195
. 10.1002/1099-1220(200005/06)6:3<181::AID-IJPG181>3.0.CO;2-U
Silverstein, M. (
1995
).
Stability and change in temporal distance between the elderly and their children
.
Demography
,
32
,
29
45
. 10.2307/2061895
Silverstein, M., & Angelelli, J. J. (
1998
).
Older parents’ expectations of moving closer to their children
.
Journal of Gerontology: Social Sciences
,
53B
,
S153
S163
. 10.1093/geronb/53B.3.S153
Staiger, D., & Stock, J. (
1997
).
Instrumental variables regression with weak instruments
.
Econometrica
,
65
,
557
586
. 10.2307/2171753
Treas, J. (
1979
).
Intergenerational families and social changes
. In P. Ragan (Ed.),
Aging parents
(pp.
58
65
).
Los Angeles
:
Andrus Gerontology Center, University of Southern California
.
United Nations
. (
2005
).
United Nations expert group meeting on social and economic implications of changing population age structures
.
Mexico City, Mexico
:
Department of Economics and Social Affairs, Population Division
.