In Population 69(3), 2014, Gustavo De Santis, Sven Drefahl, and Daniele Vignoli presented the EU Statistics on Income and Living Conditions (EU-SILC) as an invaluable source of data to analyse fertility by sociodemographic characteristics. These surveys, though, have biases that require an adjustment in observed fertility. In this article, Angela Greulich and Aurélien Dasré examine these very biases by comparing the number of children born by mother’s age with unbiased estimates from the Human Fertility Database. They explore the limits of these surveys for each birth order and measure, in the case of France, the extent of this bias according to the mother’s sociodemographic characteristics.
1Covering 32 European countries, the European Union Statistics on Income and Living Conditions (EU-SILC) provides a large set of harmonized socioeconomic measures at both the individual and household levels. EU-SILC users can address a wide range of topics. Originally designed for socioeconomic analysis, EU-SILC is also attractive for sociodemographic analysis. It provides information not only about employment, income, and social transfers but also childcare attendance, health, education, and housing. The extensive country coverage facilitates multilevel analyses, and household members can be merged. Besides a nationally representative probability sample for each country (cross-section samples), short rotational panels are available (with a follow-up period of a maximum of four years).
2Despite EU-SILC’s many advantages and increasing use, one should beware of a major pitfall. Children of respondents are only observed when living permanently in their parents’ household. To obtain information about these children, the researcher has to link them to their parents by merging their register files. EU-SILC contains register files for all household members of all ages, which provide basic demographic information (age, sex, residential status, etc.). It also provides personal files for household members aged 15 and over, with information on education, labour market participation, and income. Merging children’s register files with those of their parents is possible because of the identifiers they contain (for household, father, mother, and spouse/partner). Researchers can thus observe the number of children in a household at a given period and reconstruct fertility behaviour (for example, by retrospectively calculating maternal age at first birth). No distinction can be made, however, between biological parents, adoptive parents, foster parents, and step-parents (Eurostat, 2010). Because EU-SILC was mainly designed to analyse household income and living conditions, the questionnaire does not ask about the number of children women and men ever had, leaving unobserved those children who live outside the household. Information about fertility behaviour in EU-SILC is thus distorted by the progressive departure of children from the parental household. Consequently, the downward bias in the number of children reported by EU-SILC increases with age. This downward bias is also likely to vary according to other demographic and socioeconomic characteristics of individuals and households, as the number of children living outside the household and the age at departure from the family home depend on an ensemble of micro- and macro-level conditions: labour and housing markets, sociological and societal norms (such as allowing unmarried children to live outside the parental household), education and income of children and parents, maternal age at first birth, number and spacing of children, family configuration (divorce, second union, stepchildren), etc.
3To circumvent the problem of unobserved information about children living outside the household in demographic analysis, researchers tend to limit the sample to younger ages. Baizan, Arpino, and Delclos (2016), for example, analyse the impact of education on the number of children of women under the age of 40. D’Albis, Gobbi, and Greulich (2017) concentrate on the number of children of women aged 38–44 to identify the birth order most responsible for fertility differences between European countries.
4EU-SILC’s lack of information about children living outside the household poses a problem not only for demographic analysis. When research seeks to explain income and living conditions for individuals of a certain age, missing information about fertility history may lead to serious biases that cannot be neglected. For example, in explaining the career advancement of a 50-year-old woman, it would be unfortunate not to know that she had her first child at the age of 20. One could argue that most research based on EU-SILC aims to describe current income and living conditions of households, which justifies observing only those children who are living in them (i.e. for whom one can calculate consumption units). However, the growing number of divorces, higher-order unions, and “patchwork” families in Europe go hand in hand with a rising number of children who do not live permanently with both biological parents but who represent important cost factors for them. With prolonged education and later (increasingly uncertain) access to steady financial independence, children’s departures from the family home and attainment of financial independence are no longer events that necessarily coincide (Villeneuve-Gokalp, 1997). Young adults may leave the household while remaining dependent on their parents, especially while in training or seeking employment. Castell et al. (2016) find that in France almost 50% of young adults aged 18–24 live on their own, but not even 20% are financially self-sufficient. The argument that children living outside the household do not represent significant cost factors for parents and that these children are thus irrelevant when studying economic conditions of households seems problematic. Furthermore, because this bias has far-reaching consequences for all fields of research, caution is advised when interpreting results. To sensitize users to this issue, we offer a systematic analysis of the quality of the measure of the number of children in EU-SILC. For reasons of comparability, we focus on the number of children observed for women.
5While systematic work has evaluated the quality of fertility measures in other important datasets, such as the Generations and Gender Survey (Vergauwen et al., 2015), few studies have addressed the issue of measurement bias regarding fertility in EU-SILC. The quantifications of the bias are not systematic, and the available studies only focus on one country (De Santis et al., 2014, for example, for Italy). Other studies, for example by Iacovou et al. (2012), discuss the quality of EU-SILC data in general but do not provide a detailed analysis of the quality of fertility measures.
6Our article analyses the bias in the number of children reported by EU-SILC by providing two important, complementary pieces of information.  A first, descriptive part quantifies the bias in the number of children reported by EU-SILC by age and birth order, and measures the phenomenon of child departure. A second, analytical part identifies the demographic and socioeconomic profiles that are most subject to biased measures. In this systematic approach, we compare EU-SILC data with two different data sources. To differentiate the bias by age and birth order, we compare EU-SILC measures with unbiased measures from the Human Fertility Database (HFD), the international scope of which allows us to cover a set of European countries. To analyse the bias by demographic and socioeconomic characteristics, we use the French version of EU-SILC (Statistiques sur les ressources et les conditions de vie, SRCV), which includes a question about the number of children in and outside the household. Apart from this difference regarding the question about children, the French EU-SILC sample and the SRCV are almost identical.  We can therefore use the SRCV to identify the socioeconomic profiles in EU-SILC for which fertility measures are most biased due to unobserved children living outside the household.
I – Number of children by age and birth order
7To analyse the measurement bias in the number of children by mother’s age and by birth order, we compare the EU-SILC measures with those of the HFD. Information by age and birth order is available for ten countries in the HFD (Bulgaria, Estonia, Hungary, Lithuania, the Netherlands, Norway, Portugal, the Czech Republic, Slovakia, and Sweden). At the time we conducted the analysis, the latest available year was 2009 (HFD). We first focus on the measurement bias in the number of children by mother’s age. We therefore use the age-specific fertility rates by HFD cohort. By applying a longitudinal approach, we calculate the sum of age-specific fertility rates until 2009 for each cohort between 1959 and 1994 (cumulative fertility rate). We approximate this measure with EU-SILC data (cross-section database of 2009) by observing the average number of children living with their mothers by the mothers’ age in 2009 (cohorts 1959 to 1994).
8The EU-SILC and HFD fertility measures differ by construction, due not only to unobserved children living outside the household in EU-SILC. To provide fertility rates, the HFD combines vital registration data (to obtain information about births) and census and/or register data (to obtain information about the number of women). The HFD measures focus on children ever born, while those of EU-SILC focus on children living in the household and, unlike the HFD measures, do not consider children who have already died, which may yield lower measurements than those of the HFD. But given the relatively low levels of infant, child, and adolescent mortality in Europe,  this construction bias should be relatively minimal. In addition, unlike the EU-SILC measures of fertility, HFD fertility rates do not take into account foreign births of immigrant women, whose higher fertility rates compared to native women might inflate the EU-SILC measures, relative to those of the HFD (assuming that the children born abroad were living with their mother at the time of the survey). Finally, if women residing abroad return to the country at the time of their child’s birth (for example, expatriate women who wish to return to their place of origin at the time of birth), these births are counted by vital registration data, but the women are not counted by census and/or register data (Davie and Mazuy, 2010). In EU-SILC measures, neither these births nor these women are taken into account.
9Figure 1 compares the EU-SILC and HFD measures of the average number of children by age for women of cohorts 1959 to 1994, observed in 2009 for ten European countries. EU-SILC reports a lower number of children for all ages of women, but its measure is within the confidence interval for all ten countries until around the age of 40. This is the case for small countries with large confidence intervals (e.g. Lithuania) but also for larger countries (e.g. the Czech Republic or Bulgaria). In all countries, the bias increases with age and is significant from age 40 onwards.
10To shed more light on the issue of unobserved children in EU-SILC, we now distinguish between children of different birth orders. We therefore observe with EU-SILC data the proportion of women by age and birth order (x% of women of age y in 2009 have z children). To obtain a comparable measure with the HFD, we use the age-specific fertility rates by birth order. The sum of these rates yields the proportion of women having at least z children, and the differences between these proportions yield the proportion of women having exactly z children. Figure 2 illustrates these proportions for Sweden (the proportions of the other nine countries do not differ much and can be found in Appendix Figure A.1). Figure 2 shows that EU-SILC overestimates the proportion of childless women of all ages. However, the differences become significant only from the age of 40 onwards, suggesting that the departure of children, and notably of those who have no siblings, underlies this bias. Women who had children at comparatively early ages are, at age 40, particularly subject to an underestimation of their number of children because the latter then start leaving the parental household.
11As a result, firstborn children (birth order 1) begin to be overestimated from age 40 onwards, and children of birth orders 2 and higher are under-represented from age 40 onwards. These biases are the logical consequence of the first child’s departure because few women have three or more children. A two-child family is identified as having only one child after the first child departs, which causes the proportion of women having one child to be overestimated and the proportion of those having two children to be underestimated. If there were a large proportion of three-child families, departure of the first child would lead to an overestimation of women having two children. That the proportion of women having two children is under-instead of overestimated means that two-child families outnumber those with three or more. There are more two-child families that end up with one child or zero children (for mothers aged between 40 and 50) than families with three or more children that end up with two or fewer.
Number of children by women’s age (EU-SILC vs HFD), 2009
Number of children by women’s age (EU-SILC vs HFD), 2009
12The extent of the measurement bias by birth order depends, however, not only on a country’s fertility level but also on various other factors, such as the child’s age at departure from the household, the birth interval between siblings, and maternal age at first birth. The interplay of these factors might explain why, on average, there are no important differences in the measurement bias by birth order among the ten European countries under study. In any case, the analysis shows that the non-observation of children who already left the household leads both to an underestimation of completed family size and to an incorrect attribution of birth orders for those siblings still living with their parents.
Proportion of women in Sweden who have 0, 1, 2, and 3+ children by age (EU-SILC vs HFD), 2009
Proportion of women in Sweden who have 0, 1, 2, and 3+ children by age (EU-SILC vs HFD), 2009Coverage: Women of cohorts 1959 to 1994, year 2009.
13We now calculate the absolute contribution of the over-/under-representation of each birth order to the downward bias in the number of children by age. The order among the children living in the household is determined using information about the age of the children in the household reported by EU-SILC. With the data from the HFD, we calculate, for each birth order z, the sum of age-specific fertility rates until age y, which gives us the proportion of women having at least z children at age y. The sum of these proportions gives the fertility rate at age y. The difference in the fertility rate at age y between EU-SILC and the HFD is obtained by summing the differences between the proportions of women having at least z children. The following is a breakdown of the calculation of the absolute contribution of the over-/under-representation of each birth order in EU-SILC to the downward bias in the number of children by age:
15For all ten countries, we find that the higher the age, the larger the underestimation of the number of children due in particular to unobserved children of birth order 2. For younger ages up to age 30, however, EU-SILC slightly underestimates the number of children mainly because children of birth order 1 are unobserved.
16To facilitate the comparison between countries, we now focus on women aged 49. Table 1 presents the number of children of women aged 49 obtained from EU-SILC and the HFD. For this same group of women, Figure 3 illustrates the relative contribution of the over-/under-representation of children of birth orders 1, 2, and 3 or more to the downward bias in the number of children. For all countries except Slovakia, unobserved children of birth order 2 contribute most to underestimating the number of children of women aged 49 in EU-SILC, compared with the HFD data. Differences among countries for birth order 2 are relatively small. In all ten countries, having two children is the norm for women aged 49, which explains the large contribution of children of birth order 2. The departure of the first child leads to the second child being observed as a first child in EU-SILC; the second child is thus “missing”.
Number of children of women aged 49
Number of children of women aged 49Coverage: Women of cohort 1960, year 2009.
Relative weight of the over-/under-representation of children of birth order z to the downward bias in the number of children, for women aged 49
Relative weight of the over-/under-representation of children of birth order z to the downward bias in the number of children, for women aged 49Coverage: Women of cohort 1960, year 2009.
17The erroneous attribution of birth orders also explains two further observations. First, the greater the number of children of women aged 49 (HFD), the greater the contribution of missing children of birth order 3 or higher to the downward bias in EU-SILC. Second, the fewer the real number of children of women aged 49, the greater the contribution of missing children of birth order 1 to the downward bias in EU-SILC.
II – Child departure
18The age at which children tend to leave their parents’ household also influences the downward bias under study. To address this issue, we observe child departure in the EU-SILC longitudinal database and focus on women observed for at least two consecutive waves from 2009 onwards. The selected women all had at least one observed child in 2009. We identify a child as having left the parental household when he or she disappears from one wave to the next, while the parental household continues to be observed. Table 2 presents (for each country) the average age of mothers in the year of child departure and the average age of the child in the year of departure. 
19We observe all children here, independent of birth order because we cannot be certain of it; we may observe households that some children had already left before the period of observation. We also consider cases in which the younger child left the parents’ household before the older child, so the observed maternal age at child departure is not necessarily the age at which the oldest child leaves the household.
20Women’s age at child departure reported by EU-SILC depends on several factors, all of which influence the bias in its reported completed fertility:
- maternal age at first childbirth
- number of children ever born to the woman
- age at birth of any other children (higher birth orders)
- age at which children leave the parental household
21Table 2 shows that the highest age of mothers at child departure (above age 46) is observed in the Netherlands, France, and Greece, followed by Luxembourg, Romania, Slovenia, Finland, Sweden, Italy, Spain, and Denmark. This is a heterogeneous group of countries. In the Nordic countries, France, the Netherlands, and Luxembourg, the high age of mothers at child departure is likely due to relatively late ages at first childbirth and to high fertility levels, which implies that we observe departures of children of higher birth orders. Departure ages of children are lowest in the Nordic and Baltic countries, followed by continental European countries. For Greece, Italy, Spain, Romania, and Slovenia, long cohabitation most likely explains the high ages of mothers at child departure, as the relatively high age of children at departure suggests. With EU-SILC, we identify the same countries as Eurostat (2015), Prioux (2006), Macura and Beets (2002), and Kiernan (2002) as ones with traditionally long cohabitation of parents and children (except Portugal, Cyprus, and Slovakia, which are identified as countries with late child departures by Eurostat, 2015). Mothers are youngest at child departure in Portugal, the Czech Republic, Estonia, and Latvia, where fertility and the women’s age at first childbirth are relatively low, and where children leave their parents’ household relatively early. In Portugal, the low age of children at departure suggests a data-collection problem: children tend to exit the survey at age 15; from then on, parents are supposed to fill out a personal file for their children, including information about income, education, labour market status, etc. Besides the heterogeneity across countries illustrated in Table 2, there exist within each European country significant differences in ages at child departure among socioeconomic groups (see, for example, Castell et al., 2016, for France).
Average age of mothers and children in the year when children leave the parental household
Average age of mothers and children in the year when children leave the parental household
22Though the determinants of mothers’ ages at child departure are various, descriptive analysis helps to identify from which age the measure of the number of children in EU-SILC is no longer reliable. To choose the optimal age at which to observe women’s final number of children, one has to balance child departures and childbirths: the higher the age, the higher the risk of underestimating the number of children due to child departures. The younger the age, the higher the risk of underestimating the number of children, due to incomplete fertility.
23The HFD reports that taking into account childbirths for women aged 40 and over increases the average number of children per women by 0.1 to 0.2 children, depending on the country in Europe. To enlarge country coverage, we calculate total fertility rates for women aged 40 and over with EU-SILC (by applying a method that minimizes measurement bias caused by attrition ). EU-SILC reports that the number of births for these women is greater in those countries where women tend to delay first childbirth and where fertility is relatively high. This is particularly the case in the Nordic countries, France, and anglophone countries. The lowest fertility rates for women aged 40 and over are found in Eastern European countries with low fertility and relatively low ages at first childbirth. Continental and Mediterranean countries are intermediate cases with late first childbirth and low or intermediate fertility levels.
24To determine the age at which the underestimation bias in the number of children is minimized, we calculate, for every country, the age beginning at which child departures exceed entries of children (births, adoptions, and returns of older children are considered) in EU-SILC, again based on its longitudinal database (2009–2012). Therefore, for each woman aged between 25 and 60 having at least one child, we count the number of child departures from and entries into the parental household. On average, child departures increase linearly from age 35 to 39, and exponentially so from age 40 on. Consequently, birth orders may be incorrectly attributed for women aged 35 and over on average. Child entries decrease continuously until age 45 and then increase slightly due to some adult children moving back into their parents’ household. For most countries, the average critical maternal age from which child departures exceed child entries varies between 39 and 42 years. Countries with outstanding early critical ages are Bulgaria and Portugal. Countries with outstanding late critical ages are Italy and the Netherlands.
25As the critical maternal age from which child departures exceed child entries does not vary much between countries, the optimal way to approximate completed fertility in EU-SILC is to observe the number of women around age 40. For country-specific analyses, it is prudent to take into account additional ages around 40 to avoid fluctuations due to cohort effects and small sample sizes (for example, by grouping together ages 38 to 44, as we do in the following section).
III – Evaluating the impact of children living outside the maternal household
26To measure the extent to which the number of children living outside households differs between socioeconomic groups, we use the French version of the Statistics on Income and Living Conditions (SRCV, cross-sectional wave of 2011). This national version contains a question about the number of children living in and outside the household. We can thus link this information to education, labour market status, and income characteristics.
27To compare measures of “approximate” completed fertility for France from the international and French modules, we calculate the number of children of women aged 38 to 44 (cohorts 1967–1973, observed in 2011) using both the French EU-SILC sample and the SRCV. With the SRCV, which directly asks respondents for the number of children in and outside the household, we obtain a weighted average total number of children of 2.00. This total is composed of 1.69 children living in the household and 0.31 children living outside the household. With the EU-SILC sample for France, we obtain a weighted average number of children within the household of 1.67. The difference of 0.02 children between the SRCV and the French EU-SILC sample is not significant and results from a small number of children not having register files in the French EU-SILC sample. 
28In comparison to other European countries, the proportion of children living outside the household is likely to be high in France. Children leave the parental household early, especially compared to Southern Europe (Eurostat, 2015), and fertility levels are high relative to other European countries (HFD, 2012). The higher number of unobserved children living outside the household in France is thus likely to be an essential explanatory factor of the considerable underestimation bias in approximate completed fertility rates, as illustrated in Appendix Figure A.2, which covers all European countries (which is possible because we are not analysing by birth order here). The measurement bias in the number of children of women aged 38–44 (year 2011) in the international EU-SILC sample (without children living outside the household) is −14% for France versus −11% on average for all 27 countries presented.
29However, the unbiased measure of the number of children for cohorts 1967–1973 observed in the beginning of 2011 is 1.93 for France (calculations based on the HFD and census data),  whereas the SRCV reports 2.0 children for these cohorts. The SRCV thus obtains a somewhat higher number of children than the HFD, even though the SRCV only observes living children, while the HFD data report all children ever born. The survey’s overestimation of the number of children compared to the census data is likely due to (besides migration, mortality, and non-response or under-reporting of children in the census) the number of children in and outside the household being observed for households, not on an individual basis.  The SRCV therefore does not provide a mother ID for children living outside the household. Consequently, the reported number of children living outside the household cannot be attributed to an individual respondent but only to the household as a whole, which means that we might attribute some children to women who are not their biological mothers.
30To limit the overestimation of women’s number of children living outside the household due to this problem, we exclude households with women aged 38–44 who are themselves registered as “children of the household” in the survey. This exclusion avoids counting siblings and grandchildren as children. To further avoid counting nephews and nieces (for example) as children, we also exclude households with more than one woman aged 30 and over, which concerns only a small minority of households in the sample (0.3%). With this reduced sample, the total number of children reported by the SRCV is 1.99, or 1.71 children in the household and 0.28 children living outside the household. The overestimation in the SRCV compared to the HFD is therefore only slightly reduced.
31The problem remaining is that children living outside the household cannot be attributed to their biological parents, so there is some risk that children with step-parents are counted twice in a representative survey like the SRCV. Children living with a stepmother count once as a child of her household and once as a child living outside the biological mother’s household.  Children not living with their fathers can also be counted twice: once as a child of the mother’s household and once as a child outside the household if the father lives with another woman. Although the majority of children of separated couples still live with their mothers, shared custody is more common, and thus some children have more than one residence, which also increases the risk of counting them twice. Toulemon and Pennec (2010) calculate that in the SRCV of 2006, 10.1% of households have at least one family member (including students) living elsewhere. On an individual basis, around 2% of very young children (0–3 years old) and around 12% of young adults reside in more than one place. Of respondents aged 0–18, 7% are counted twice in the survey, i.e. the number of children in the 2006 SRCV is overestimated by 3.5% due to double counting. With an average number of two children per woman, this would correspond to 0.07 children.
32In the SRCV, the double counting of children residing in multiple places is not corrected by individual or household weights. However, the overestimation due to double-counts is likely to be offset by women’s tendency in surveys to under-report their children slightly, at least from a certain age on. This trend is identified by Ní Bhrolcháin et al. (2011), for example, who find that in the British household survey, the under-reporting of children increases with age (due to ageing, conflicts between parents and children, etc.). Régnier-Loilier (2014) confirms for the French sample of the Generations and Gender Survey that parents tend to under-declare their children if they are not on good terms, or at least not in permanent contact, with them.
33To determine the number of stepchildren living in and outside the household of women aged 38 to 44 in 2011 in France, we use the Family and Housing Survey (Enquête Famille et Logements, EFL) of 2011. Although this survey is not directly comparable with EU-SILC and the SRCV, it does ask, on an individual basis, for biological and stepchildren (total and within the household). Table 3 presents measures of the number of children of women aged 38 to 44 in 2011 in France, using data from the French EU-SILC sample, the SRCV, the HFD, and the EFL.
Number of children of women aged 38 to 44 in 2011 in France
Number of children of women aged 38 to 44 in 2011 in France* Number of children outside the household / total number of children.
Coverage: Women aged 38 to 44 in 2011 (cohorts 1967 to 1973) in France.
34The EFL data confirm observations from the SRCV, with 14% of children living outside households of women aged 38 to 44, and almost two-thirds of these children are stepchildren. The large majority of biological children live in their mother’s household, while only 6% of biological children live outside the household (0.11 out of 1.88 children). The comparison with the EFL reveals that the French sample of EU-SILC and the SRCV both underestimate the number of children in the household to a non-negligible extent. However, a comparison of EU-SILC and SRCV data shows that the non-observation of children living outside the household strongly contributes to underestimating fertility in the French sample of EU-SILC.
35This downward bias increases with age. Figure 4 presents the number of children living outside the household by woman’s age (observed in the 2011 wave of the cross-sectional SRCV database; three-year moving average). Consistent with our finding that in the longitudinal database in EU-SILC, child departure rises significantly, on average, from age 40 in EU countries, the French SRCV reports that in France the number of children living outside the household increases exponentially from age 40 onwards.
Number of children living outside the household by woman’s age in France
Number of children living outside the household by woman’s age in FranceCoverage: Women aged 30 to 50.
Socioeconomic characteristics of women with children living outside the household
36We now test the effect of women’s demographic and socioeconomic characteristics on the downward bias in EU-SILC fertility data due to unobserved children living outside the household. Table 4 presents descriptive statistics of the number of children in and outside the household by women’s demographic and socioeconomic characteristics (SRCV cross-sectional wave 2011, women aged 38 to 44).
37The demographic characteristics are civil and marital status as well as nationality. The selected socioeconomic categories are education and labour market status, which serve as proxies for women’s access to collectively desired resources, such as material goods, income, influence, networks, healthcare, etc. Although there is no consensus in socioeconomic research on which indicators signal access to which resources and on whether there is a clear correlation between these indicators and the desired outcomes (Oakes and Rossi, 2003), education and labour market status do provide important information about women’s potential in procuring economic resources and financial independence. All categories combined, we recall that in our sample, 0.28 out of 1.99 children (or 14%) live outside their mother’s household (SRCV).
Number of children in and outside the household by socioeconomic categories, France, women aged 38–44
Number of children in and outside the household by socioeconomic categories, France, women aged 38–44* Number of children outside the household / total number of children.
Coverage: Women of cohorts 1967–1973; N = 1,271.
38Low-educated women (pre-primary, primary, or lower secondary) have the highest number of children in and outside the household compared to middle-educated (upper secondary or post-secondary) and high-educated (tertiary) women. On average, for low-educated women, 0.51 children out of
392.51 children (20%) are not living with their mothers. When considering the distribution of women over education categories, we find that 0.08 out of the average number of 0.28 children living outside the household are children of low-educated women (i.e. 28%). Around 47% of children living outside the household are children of middle-educated women and 25% of high-educated women. 
40When comparing women of different civil statuses, we observe that divorced women have the highest absolute number of children living outside the household (0.60), followed by widowed women (0.28), while the number is lowest for women living in a consensual, legal union (marriage and civil partnerships called “PACS” in France) (0.27). However, children of these (currently) married women represent 51% of all children living outside the household. Women cohabiting with their partner (i.e. de facto partners) have a greater number of children living outside the household than married and single women. Unfortunately, retrospective information on partnership status is not available in the SRCV.
41Regarding nationality, the absolute number of children living outside the household is by far the highest for non-European/OECD women (0.68), while the difference between French women and those of other high-income countries is smaller (0.27 for French and 0.39 for European/OECD women). By considering women’s distribution over nationalities, we find that 88% of children living outside their mothers’ household have a mother whose nationality is French.
42Finally, disabled and full-time self-employed women have the highest absolute numbers of children living outside the household compared to women of other activity statuses. However, as these women only represent small minorities, their children living outside the household do not contribute much to explaining the overall number of children living outside the household. A large share of children living outside the maternal household (41%) have mothers in full-time employment.
43These statistics must be interpreted with caution. No inference about causality can be made at this stage for two reasons. First, endogeneity is an issue: Does a woman’s child live elsewhere because she works full-time? Or can she work full-time because her child lives elsewhere? Second, the different characteristics presented in Table 4 are likely to be correlated with each other, just as they are correlated with other demographic characteristics, such as the number of children, the age at first childbirth, the age difference between children, etc.
44To disentangle the impacts of the different categories in Table 4, we estimate women’s absolute number of children living outside the household as a function of education, marital status, nationality, and employment status; we also control for the number of children currently living in the household (linear regression). We cannot control for the mother’s age at first childbirth, nor for the ages and age differences of the children because the SRCV does not contain register files for children living outside the household.
45Table 5 presents the results of the regressions. The number of children living outside the household decreases with the number of children inside the household. Highly educated women have a significantly lower number of children living outside the household compared with middle- and low-educated women. The number of children living outside the household is highest for low-educated women. While certain observable characteristics are controlled for, these results do not allow a comprehensive interpretation of the educational gradient, as we lack information about age at first childbirth, the history and stability of partnerships, etc.
46We further see that the number of children living outside the household is significantly higher in cohabiting women than married women.  At the observed ages (around 40), cohabiting women are often in second unions, which might explain the greater number of children living outside the household. But without retrospective information on partnerships, a cohabiting partnership cannot be interpreted as less stable or more recent.
47Differences between French and other European women are not significant, but non-European/OECD women have a significantly greater number of children living outside the household than French women. This might be linked to higher fertility and younger ages at childbirth, but it could also be due to specific behaviour related to child departure. Some of these children might be born outside France (and thus are also not counted by fertility statistics based on civil registration data) and/or live outside France. Since non-European/ OECD women represent only a minority of women living in France (see Table 3), these unobserved children do not contribute much to the underestimation bias in the international module.
Estimation of the absolute number of children living outside the household France, women aged 38–44
Estimation of the absolute number of children living outside the household France, women aged 38–44Coverage: Women of cohorts 1967–1973.
48Finally, the number of children living outside the household is significantly higher for disabled and full-time self-employed women compared with full-time employed women, while differences with the other activity statuses are not significant. The coefficient for economically inactive women is positive and significant at the 10% level, suggesting that economically inactive women tend to have a higher number of children living outside the household than women employed full-time.
49This paper sheds light on the quality of measures of the number of children in EU-SILC. The downward bias affecting these measures increases with maternal age mainly because children living outside the household are not observed.
50On average, the number of child departures outnumbers that of births when women are in their early 40s. From that age, birth orders are no longer correctly attributed, resulting in an overestimation of children of birth order 1 and an underestimation of children of birth order 2 (and higher). The downward bias is quite heterogeneous among European countries, as the number of children living outside the household depends on multiple factors (fertility levels, age at first childbirth, age interval between children, age at which children leave the parental household, etc.). France and several other continental countries such as Belgium, Luxembourg, the UK, and several Nordic countries are most concerned, while the downward bias is lower in most Eastern and Southern European countries.
51Our analysis based on the French SRCV, which contains a question on the number of children living outside the household but is otherwise identical to the French EU-SILC, points to significant socioeconomic differentials in this measurement bias. While we do not observe all potential determinants of the number of children living outside the household (age at first childbirth, stability of relationships, characteristics of the child, etc.), our regression analysis clearly indicates that the number of children living outside the household is not randomly distributed among women in France. The downward bias is lower for women with tertiary education as well as for married, part-time employed, and economically inactive women. It is higher for women with a non-European nationality. Our analysis suggests that the underestimation of family size from a certain age onwards in the international EU-SILC module concerns in particular women who are low educated; who have a migration background; neither married nor single but cohabiting; disabled; and full-time self-employed. This is likely to be the case not only for France.
52Our finding that the downward bias in the number of children differs significantly between socioeconomic groups in EU-SILC is problematic not only for demographic but also for economic analysis. For analyses modelling the number of children as an endogenous or exogenous variable, it seems reasonable to limit the sample to women not older than 40. For socioeconomic analyses, which go beyond describing current household situations, it seems problematic not to have information about fertility history, which is an important determinant of income and living conditions. In addition, some children living outside the parental household may still represent an important cost factor for parents (alimony, students, unemployed, etc.).
53How to define a “household” or a “family” is a highly relevant question, and statistical methods are urged to adapt to changing concepts. The concept “housing unit = household = family” emerged at a time when the stable, nuclear, “mono-located” and resource-sharing family could pass as a quasi-general model. However, over the last three decades, European societies have experienced important changes in family patterns (Johnson-Hanks et al., 2011), which has far-reaching consequences, both culturally and socioeconomically. Enabling researchers to document these family transitions represents a major challenge for statistical offices and other data providers.
54Adding a question on the number of children living outside the household in the EU-SILC questionnaire may therefore be an effective investment. It is important to add this question to the individual and not (only) to the household questionnaire. Furthermore, a distinction between biological and stepchildren would be helpful, in particular for demographic analysis. Finally, socioeconomic analysis would greatly benefit from having personal files for children living outside the household, which provide information on education, labour market participation, and income. These files would enable researchers to evaluate the financial burden of families in a much more comprehensive way.
Proportion of women with 0, 1, 2, and 3+ children by age, EU-SILC vs HFD
Proportion of women with 0, 1, 2, and 3+ children by age, EU-SILC vs HFDCoverage: Women of cohorts 1959 to 1994, year 2009.
Measurement bias in ‘approximate’ completed fertility rates in EU-SILC (women aged 38–44)
Measurement bias in ‘approximate’ completed fertility rates in EU-SILC (women aged 38–44)
Number of children in and outside the household by educational categories of French women, aged 38–44
Number of children in and outside the household by educational categories of French women, aged 38–44* Number of children outside the household / total number of children.
Coverage: Women of cohorts 1967–1973 (N = 29,955).
For a comprehensive analysis of the quality of measures of periodic fertility in EU-SILC, see Greulich and Dasré (2017). From a cross-sectional perspective, the authors compare period fertility measures obtained with EU-SILC to unbiased measures from the Human Fertility Database for several European countries. They show that EU-SILC measures of period fertility are biased downward, mainly due to attrition, while births of order 1 for ages 20–29 are particularly under-reported. However, they find no evidence of socioeconomic differentials in attrition, suggesting that EU-SILC can be used to analyse socioeconomic determinants and consequences of childbearing behaviour.
Both contain a nine-year follow-up of individual households. Besides the question on the number of children living outside the household, the French version includes additional questions concerning financial transfers with family members living outside the household and with other households. The SRCV data file is available for research purposes via the Réseau Quetelet at http://bdq.quetelet.progedo.fr/fr/Details_d_une_serie_d_enquete/28
For example, the under-five mortality rate is below 5 per 1,000 live births in all European countries except Slovakia (7.3), Hungary (5.9), and Poland (5.2) (WHO, 2015). The European WHO region thus has the lowest under-five mortality rate worldwide (i.e. compared to the other WHO regions: Africa, the Americas, Southeast Asia, Eastern Mediterranean, and Western Pacific). The WHO also reports that adolescent mortality is lowest in Europe. For example, the under-20 mortality rate in France in 2014 was 5.11 per 1,000 inhabitants.
These averages are calculated based on the subsample of child departures (women who have experienced at least one child departure; children who left the parental household) during the observed period (arithmetic means).
TFR for women aged 40 and over is calculated with the cross-sectional wave of 2012, retrospectively for years 2008–2010. This approach reduces the downward bias due to attrition. Women and their children are observed a couple years after childbirth, not around childbirth. Childbirth often coincides with change of residence, which is why Greulich and Dasré (2017) find that in EU-SILC, measures of TFR are less downward biased when childbirths are observed with some time delay (own child method). The combination of three waves (2008, 2009, 2010) also allows us to obtain sufficiently large sample sizes for each country.
The difference is due to a higher proportion of childless women in the international EU-SILC sample. These women reported a certain number of children when asked directly about their children (SRCV) but did not fill out the register files for them. As in the French EU-SILC sample, we use the register files to reconstruct the number of children; these women are observed childless.
Authors’ calculation: average number of children of the different cohorts in 2011 (HFD) weighted by the number of women in each of these cohorts (French population census).
The concrete question in the SRCV questionnaire is (for households with more than one member): “Do you or another member of the household have children who do not live here? Yes/No. If yes, how many?”
It is also possible that children enter the panel due to household separations, as individuals who move together with a person followed-up by EU-SILC (co-residents) are covered by the survey (Burricand and Lorgnet, 2014), albeit weighted with zero in the longitudinal database.
As the SRCV does not allow distinguishing between biological and stepchildren, we test the robustness of our findings with EFL data. Appendix Table A.1 presents the number of biological and stepchildren living in and outside the household by level of education. The share of children living outside the household (biological + stepchildren) by level of education is the same as that reported by the SRCV (Table 4).
This category includes women living in a registered civil partnership, or PACS, which is a legal substitute for marriage.