Does coresidence with grandparents reduce the negative association between sibship size and reading
test scores? Evidence from 40 countries.
Abstract
This paper investigates the effect of coresidence with grandparents in three-generation households
on the nature and size of the association between sibship size and reading test scores. It also
explores whether this interaction changes with the level of socioeconomic development of a society.
We argue that coresidence in traditional three-generation households has a protective effect
against resource dilution and thus decreases the magnitude of the negative association between
family size and test scores. We also suggest that coresidence in more modern contexts magnifies the
degree of this negative association, since modern families form three-generation households only
when severely destabilized. We apply 3-level regression models to the PISA 2000 data to examine our
hypotheses and use the Human Development Index as a measure of development. We find that the
negative association between family size and test scores increases at higher levels of development
and does so more strongly when students coreside with grandparents. We, however, find no context,
in which coresidence would erase the negative consequences of having many brothers and sisters on
one’s own school test scores. These findings hold even when controlling statistically for the
effects of public expenditure on education, public social security expenditure, and crude divorce
rate as well as for the interactions of these variables with sibship size.
Keywords: sibship size; school achievement; reading literacy; development; three-generation
households; coresidence
1. Introduction: family size and educational achievement
The number of siblings (or family size, which is often used as a synonym for number of siblings),
has traditionally been one of the exogenous variables in the status attainment model. While various
aspects of the sibship configuration have attracted scholarly attention at least since the late
19^th century (see examples provided by Steelman et al., 2002), family size was not standard part
of research on social stratification and mobility until the field entered its ‘second generation’
(Ganzeboom, Treiman, & Ultee, 1991). Blau and Duncan’s classic study The American Occupational
Structure (1967) showed that men from smaller families attained, on average, more education than
men from larger families, presumably due to the dilution of parental resources. A number of later
studies (Featherman & Carter, 1976; Featherman & Hauser, 1978; Hauser & Featherman, 1977) were
consistent in revealing a negative association between number of siblings and educational
attainment and attributed this to resource dilution.
The reasons for the negative association between family size and educational achievement are,
however, a frequently-debated issue in current sociological research (Guo & VanWey, 1999; Jaeger,
2008, 2009; Steelman et al., 2002). The literature offers four alternative explanations. First, the
confluence model posits that each additional birth into a family changes the interpersonal dynamics
and intellectual level of the family environment. Each child, then, is exposed to more or less
advantageous environments for shorter or longer periods of his/her life, which cumulatively
produces different cognitive as well as school outcomes (Guo & VanWey, 1999; Jaeger, 2009;
Steelman, 1985; Zajonc & Marcus, 1975). Second, the resource dilution model assumes that the family
has only a limited amount of economic and non-economic resources that can be used for the benefit
of the children. Therefore, the more children there are in the family, the lower the share of
available resources each child can claim and the less education he/she obtains (Downey, 1995;
Jaeger, 2008, 2009; van Eijck & de Graaf, 1995). Third, the economic literature postulates that
both the number of children and the investment per child are chosen by parents and, as a
consequence, there is a trade-off between the quality and quantity of children resulting in the
observed negative association between sibship size and school outcomes (Angrist et al., 2010;
Becker & Lewis, 1973; Becker &Tomes, 1976). Fourth, some authors propose that the association
between family size and schooling is spurious and does not reflect a true causal link, since
fertility and children’s schooling may be jointly determined by some third variable(s) (Guo &
VanWey, 1999). As summarized by Jaeger (2008, p. 217), “it might be that sibship size captures the
influence of (…) socio-economic or other unmeasured family characteristics indirectly rather than
having an independent causal effect on schooling outcomes”. Although many different analytical
strategies–including fixed-effect models (Guo & VanWey, 1999; Lindert, 1977; Olneck & Bills, 1979)
and random-effect models (de Graaf & Huinink, 1992; Sandefur & Wells, 1999; Sieben et al., 2001)
applied to sibling data and/or panel data as well as instrumental variable estimators applied to
(quasi)-experimental data on twin-births (Black et al., 2005; Cáceras-Delpiano, 2006) or sibship
sex composition (Angrist et al., 2010; Conley & Glauber, 2006)–have been employed to assess the
validity of this last claim, the literature is still somewhat inconclusive with regards to whether
there is indeed a causal effect of family size on school outcomes (Jaeger, 2008).
A further dispute is related to the role of socioeconomic context in shaping the nature and size of
the association between number of siblings and socioeconomic outcomes. The existence of this
negative association has been robustly and convincingly documented in many populations of Europe
and North America (see also Booth & Kee, 2005; Heer, 1985, 1986; Jaeger, 2008; Hirschová & Kreidl,
2012; Kuo & Hauser, 1997; Olneck & Bills, 1979; Park, 2008; van Eijck & de Graaf, 1995; Steelman et
al., 2002 offer a comprehensive review of this literature).
The empirical evidence is far less consistent and persuasive when we look beyond the advanced
industrialized democracies or look at specific subpopulations. For instance Shavit and Pierce
(1991) found that number of siblings has a negative effect on the educational attainment of Jews in
Israel, but has no effect on education among the Arabs. The authors argued that, among other
things, the Arabs can rely on the help of the extended family (the hamula) to share in the cost of
child rearing and thus prevent undesirable resource dilution. Then, family size has no detrimental
consequences for the child’s education. Also Lu (2009) found a negative effect of the number of
siblings among whites in South Africa, but no similar effect among the blacks. She offered
differences in kin systems and family organization as an explanation. Similarly, Sudha (1997)
reported a negative effect of sibship size among the Chinese and Indians in Malaysia, but no effect
among the Malays, whose education, as the author pointed out, was subsidized by the state for
several decades. Anh et al. (1998) found a negative association only in very large families (with
at least 6 children) in Vietnam. Gomes (1984) found a positive effect of family size (particularly
among the largest families with 7 or more kids) in Kenya, where parents maintain control over the
earnings of the eldest child and can use it for the benefit of the younger siblings (see also
Buchmann, 2000). Positive consequences of family size have been similarly reported in Botswana
(Chernichovsky, 1985).
The effect of the number of siblings often varies across cohorts within a single society. Maralani
(2008), for example, reported a strong positive association between family size and schooling in
early urban cohorts in Indonesia, but negative associations in more recent urban cohorts. Moreover,
her analysis revealed no association between family size and children’s schooling for any cohort of
rural children. Similarly, Lu and Treiman (2008) also identified variations in the association
between family size and education across cohorts in China.
In this paper, we extend the literature on the varying association between sibship size and
educational achievement by comparing 40 countries participating in the 2000 PISA survey of
15-year-old students. After reviewing arguments explaining this cross-country variation, we propose
a specific measure: coresidence with a grandparent in a three-generation household that shall
modify the relationship between sibship size and standardized test scores. We argue that the
association between sibship size and test scores changes in a predictable way with level of
socioeconomic development being more negative in the more advanced nations. Furthermore, we propose
that there is a three-way interaction between sibship size, three-generation coresidence, and level
of development. We suggest that coresidence with grandparents may serve as a buffer against
resource dilution in more traditional societies, but does not have this protective effect in more
socioeconomically advanced societies, where three-generation households are not formed out of
tradition, but out of necessity in response to some serious problem such as teenage pregnancy,
criminal activity, drug addiction, and poor health. In doing so, we link two important recent
streams of population research–literature on sibship size effects (Steelman et al., 2002; Jaeger,
2008) and literature on social stratification across multiple generations (Mare, 2011), which has
recently been attracting increasing attention (see e.g. Chan & Boliver, 2013; Hällsten, 2013;
Hertel & Groh-Samberg, 2013; Jaeger, 2012; Mare, 2014; Pfeffer, 2014; Sharkey & Elwert, 2011; Zeng
& Xie, 2011).
2. Explaining the variation in the association between family size and educational achievement
Many explanations have been proposed to account for the variability in the association between
sibship size and stratification variables across contexts reaching from family organization,
cultural roles, and intergenerational wealth flows, to the cost of education, demand for education,
and mode of production in a given society/historical period (Maralani, 2008; Sudha, 1997).
Generally, the list of explananda consists of factors that “influence both the availability of
resources and their internal allocation within a family” (Lu & Treiman, 2008, p. 813).
Family organization and cultural roles that influence the amount and/or direction of wealth flows
between the generations are particularly interesting to study, since they determine “whether the
burden of child rearing is limited to the nuclear family or extended across broader kin networks,
whether and how much school-aged children work inside and outside the home” (Maralani, 2008, p.
694). Maralani (2008, p. 695) concludes that “(i)n societies where parents bear most of the cost of
schooling and where the costs are high, we might expect a negative relationship between family size
and educational attainment. In societies with extended kinship networks and lower schooling costs,
the relationship may be neutral or positive”.
Sudha (1997) claims that resource-distribution and family-planning processes occur at higher levels
of development as a consequence of the rising importance of schooling for socioeconomic
achievement. Hence, a negative association between family size and schooling emerges in the course
of socioeconomic development and strengthens with continuing modernization. Desai (1995) similarly
proposed that variations in the negative correlation between parental resources (and their
increasing dilution with growing family size) and child development (measured as height-for-age)
are linked to level of development. She argued that this correlation is magnified as countries move
from very low to moderate levels of socioeconomic development, since community resources and
infrastructure (such as access to drinking water) matter much more than family resources at the
lowest levels of development.
While there are many arguments operating with macro-level explanatory variables, there is
surprisingly little empirical comparative research in this area. Most published papers are
single-country studies. These sometimes make comparisons across cohorts or historical periods
(e.g., Lu & Treiman, 2008; Maralani, 2008), or across various segments of one society (Lu &
Treiman, 2008; Maralani, 2008; Shavit & Pierce, 1991). Comparisons across societies are very
uncommon, which is surprising since the persisting theoretical puzzles in this area call for more
comprehensive comparative designs. Moreover, proposed explanatory macro-variables are seldom
measured explicitly. Rather, speculative statements about the sources and nature of the differences
between contexts are offered. These tentative interpretations, while often very enlightening and
instructive, are not explicit empirical tests. More rigorous investigations would require finding
measures of key explanatory variables, finding contexts with sufficient variation of these
variables, and identifying interactions between sibship size and these other predictors. Given the
enormous importance of family and family organization for social stratification, this lack of
explicit tests and larger-scale quantitative comparisons is striking.
There are, nevertheless, a few exceptions to this rule. Wolter (2003) used PISA 2000 data from six
countries (Belgium, Germany, Switzerland, Canada, Finland, and France) to explore the size of the
effect of sibship size on reading literacy test scores. While this effect turned out to be negative
in all countries, its size varied significantly: it was strongest and very pervasive in Belgium and
weakest in Finland, where only children from very large families faced any disadvantages. In a post
hoc interpretation, Wolter attributed cross-country differences to differing policies. Park (2008)
took this issue a step further and included several country-level quantitative measures of public
welfare provisions for families with children and public spending on family policies and education
into his multi-level model of reading literacy test scores across 20 OECD countries selected from
the PISA 2000 database. He found that the negative effect of sibship size was indeed lessened by
strong and deepened by weak public (family-oriented) policies.
3. The effect of coresidence with grandparents on school outcomes
There has been little effort to systematically explore and describe the circumstances that lead to,
and the consequences of, coresidence of grandparents and grandchildren for school outcomes in an
international comparative perspective. There are two different approaches to the issue. Some
studies explore three-generation households (grandparents, parents, grandchildren), whereas other
emphasize skipped-generation households (grandparents plus grandchildren). The former coresidence
pattern is more common in less developed societies today and typically becomes less prevalent as
the society and economy modernize (Glazer et al., 2006; Pong & Chen, 2007; Popenoe, 1987; Ruggles &
Heggeness, 2008; Shah et al., 2011; Japan is often pointed out as an exception with relatively high
rates of three-generation coresidence, but even there three-generation households are declining,
see Ruggles & Heggeness, 2008; Takagi et al., 2007). The latter type seems to be increasingly
common in some mostly advanced industrialized societies due to the increasing incidence of specific
problem behaviors such as drug addiction, teenage pregnancy, HIV infection, and divorce
(Albuquerque, 2008; Bryson & Casper, 1999; Caputo, 2001; Hayslip & Kaminski, 2005; Kelch-Oliver,
2011; Minkler, 1999; Pong & Chen, 2007).
Studies of skipped-generation households are more common than investigations of three-generation
coresidence, which have been almost completely absent in the field until recent years (Pong & Chen,
2007; but see Zeng & Xie, 2011). Three-generation households are more often researched in
non-western societies, where they are more prevalent (Pong & Chen, 2007, 2010; Pong, Frick, & Moyi,
2004). In Europe, multigenerational households can be found in Southern European countries (such as
Italy) and in Central European countries (such as Hungary). But even there the situation is more
likely to develop as a reaction to the needs of the offspring (de Jong Gierveld, de Valk, &
Blommesteijn, 1999; Pong et al., 2004). Elsewhere in Europe three-generation households are very
rare, perhaps because most Europeans value privacy and emphasize the nuclear family and independent
living (Glaser et al., 2010; de Jong Gierveld et al., 1999; Pong et al., 2004).
Living with a grandparent (or several grandparents) can either be the result of tradition, or of
necessity (Pilkauskas, 2012). While traditional coresidence may be beneficial for the kids,
necessity often indicates trouble and social disorder. Necessity may result from the situation in
either of the generations, but coresidence for the sake of the younger generation seems to be more
common (Albuquerque, 2008; de Jong Gierveld et al., 1999; Park, 2005; Pilkauskas, 2012; Pong &
Chen, 2007; Pong et al., 2004), since grandparents are typically rather reluctant to interfere with
the lives of their children or grandchildren unless the intervention is absolutely unavoidable
(Jendrek, 1994; Shore & Hayslip, 1994), and most grandparents strongly prefer independent
households (de Jong Gierveld et al., 1999). Hence, grandparental coresidence is less and less
common and typically indicates a highly destabilized and vulnerable family situation (Bengston,
2001; Cherlin & Furstenberg, 1992; Glaser et al., 2010; Park, 2005; Pebley & Rudkin, 1999).
Coresidence of three generations may have both positive and negative consequences for the
grandchildren and its effects may be direct or indirect (Denham & Smith, 1989). Grandparents may
directly contribute to the pool of the available financial resources, or their incomes may increase
the diversity of available financial sources and thus partially shield the household from economic
turbulence and labor market insecurities (Dunifon & Kowaleski-Jones, 2007; Mutchler & Baker, 2009;
Pong et al., 2004). Grandparents can also function as role models, shaping the child’s educational
and occupational aspirations, and may “provide support for academic achievement in the form of help
with homework, encouragement of intellectually oriented hobbies and activities” (Dunifon &
Kowaleski-Jones, 2007, p. 467). Children can learn to plan their future, or can develop more
effective relationships with adults through regular interaction with grandparents (Denham & Smith,
1989; Hayslip & Kaminski, 2005). Similarly, grandchildren can benefit from the grandparent doing a
part of the housework, so the parent is left with greater amount of time to spend with the
offspring (Pong & Chen, 2010). Grandparents can supervise the child, and thus help prevent and
detect problematic behavior that may require intervention (Pong & Chen, 2010; Pong et al., 2004).
The presence of the grandparent can also alleviate parental stress (i.e. in singe-mother families),
which in turn can improve parenting (Dunifon & Kowaleski-Jones, 2007), or lessen a child’s stress
from “overly critical or demanding parents” (Denham & Smith, 1989, p. 347).
However, three-generation coresidence may also be harmful to the child. The coresident grandparent
can contribute to increased levels of stress. Since “grandparents, and especially grandmothers,
often assume a substantial role in taking care of grandchildren” (Pebley & Rudkin, 1999, pp.
220-221), their high degree of involvement may result in disputes over the education or upbringing
of the grandchild. Parenting practices and standards may be directly questioned or undermined. In
general, grandparent’s inability to maintain the right distance can create conflict (Attias-Donfut
& Segalen, 2002). Such conflict-laden environment can then have a negative impact on the offspring,
since the child does not know who the primary authority is, and/or suffers stress as a consequence
(Dunifon & Kowaleski-Jones, 2007; Pong & Chen, 2010). Furthermore, grandchildren may be deprived of
a certain proportion of family resources that are redirected to the grandparent–be these resources
monetary (e.g. the cost of health care), material (such as own room to study and do homework in
quiet), or other (parental time, attention etc.) (de Jong Gierveld et al., 2001; Pong & Chen, 2007,
2010).
The negative effect of coresidence identified in the regression-type model (a typical analytical
tool for most studies) may result from non-random selection into coresidence: “it is hypothesised
that the children’s difficulties may be due to the family difficulties which led to the
grandparent’s involvement” (Glaser et al., 2010, p. 33; see also Cherlin &Furstenberg, 1992;
McLanahan & Sandefur, 1994; Pong & Chen, 2007). Moreover, there seems to be selection into
coresidence on socioeconomic status. More highly-educated grandparents prefer independent living
and more highly-educated parents prefer non-familial care for their children (Pong & Chen, 2007;
Pong et al., 2004). Hence coresidence may be more common among the lower classes and the negative
effect of low SES may be confounded with the effect of coresidence. Indeed, the estimated effect of
coresidence in these studies is frequently negative (see also Monserud & Elder, 2010).
A net positive effect of three-generation coresidence on behavioral or educational outcomes has
been shown in single-mother families in the USA (Deleire & Kalil, 2002; Dunifon & Kowaleski-Jones,
2007). Aquilino (1996) reported a net positive effect of coresidence in households headed by
child’s parent on the chances of graduating from high school and getting into college. A positive
effect of coresidence in intact families was documented by the Taiwanese data (Pong & Chen, 2007,
2010). Parker and Short (2009) found a positive effect of a coresident grandmother on school
enrolment of children of absent (dead or non-coresident) mothers in Lesotho, South Africa.
An educational disadvantage for children in skipped-generation households was found by Monserud and
Elder (2010). Bryson and Casper (1999) documented that children in skipped-generation households
are more likely to be poor, receive public assistance, and have no health insurance. Mutcher and
Baker (2009), however, pointed out that children from mother-only families with coresident
grandparent are less likely to live below or at the poverty line compared to the same household
type without the grandparent present, since they are more likely to receive wider array of
financial aid (from the coresident grandparent, or from other sources). Working with international
data, Pong, Frick, and Moyi (2004) found a negative effect of grandparental coresidence on the test
scores of 3^rd and 4^th grade students. Yet they also found that this effect is weaker in countries
where living with grandparents is more common (the strongest negative effect was found in the USA
and England). Moreover, they attributed some of the variation in this effect to family
structure–with children from guardian families (but not from other family types) actually
benefiting from having a grandparent in the household.
So, as summarized by Denham and Smith (1989, p. 348), “it is obvious that the influence of
grandparents upon grandchildren depends upon a variety of individual, family, and cultural
factors”. In the next section of this paper we will develop hypotheses linking family size,
coresidence with grandparents, and selected macro-level variables based on this assessment.
4. Hypotheses linking family size, coresidence, and level of development
Both sibship size effects and coresidence effects appear to be context-dependent. The contexts, in
which they matter the most can be identified both at the family level and at the societal level. In
this paper we link the literature on sibship size and coresidence with grandparents into one
analytical context; we study how the association between sibship size and reading test scores may
depend on coresidence, and how this correlation may change with socioeconomic development.
We argue that coresidence with grandparents can be used as an explicit indicator of how each family
works and is organized. Grandparental coresidence in less developed societies is likely to have
positive consequences for the child’s school outcomes, and is likely to alleviate some potentially
negative consequences of the lack of resources in the family (such as low socioeconomic status, or
larger family size). Coresiding grandparents are more likely to serve as resource providers in more
traditional societies. At higher levels of development, however, coresidence is more likely to
indicate social dislocation and hence would be negatively associated with school outcomes.
Furthermore, the negative impact of coresidence is likely to be larger if combined with other
disadvantages such as larger sibship or low SES. Coresiding grandparents are likely to be
dependents/resource consumers in more modern societies. So overall, the (main) effect of
coresidence is likely to turn from positive to negative with increasing development. Similarly, the
protective effect of coresidence (against the dilution of resources) is likely to change to
detrimental with continuing development.
5. Data, variables, and method
We use data from the first wave of OECD “Programme for International Student Assessment” (PISA
2000) combined with macro-level indicators of the level of development, public spending on welfare
and education, and family destabilization. PISA “is a collaborative effort among OECD Member
countries to measure how well 15-year-old young adults (...) are prepared to meet the challenges of
today’s knowledge societies” (Adams & Wu, 2002, p. 15). PISA assesses reading, mathematical, and
scientific literacy, while also collecting additional school- and student-level information. We
elected to use the 2000 wave of the survey, since it contains richer information on the composition
of the student’s household (namely information about siblings and coresidence with grandparents)
than more recent waves.
PISA 2000 was primarily aimed at the reading literacy (Adams & Wu, 2002) of randomly chosen
students born between 1983 and 1987. Reading literacy was defined as an individual’s ability to
retrieve, understand, use, interpret, and evaluate information in order to achieve one’s goals and
to develop one’s knowledge (OECD 2001). We are working with data from the student questionnaire,
which (apart from the reading literacy variables) collects information about siblings, structure of
a student’s family, and about education and occupation of a student’s parents.
The PISA 2000 dataset contains information collected in 43 countries (data were collected in 32
countries–28 OECD and 4 non-OECD–in the year 2000; the rest was collected in 2002). The data
collection was organized to maximize its international comparability (Adams & Wu, 2002). Our
analysis excludes three of the original countries (Japan, Netherlands, and Lichtenstein) due to
various problems with the data (missing information about parental education in the Japanese data,
very low school participation rate in the Netherlands, and very small sample size in Lichtenstein;
see Adams & Wu, 2002, p. 186 for additional details). Further reductions in the sample size reflect
our decision not to study skipped-generation households (since somewhat different mechanisms lead
to the establishment of three-generation and skipped-generation households, and we want to focus
our analysis on the former type) and elimination of data with missing values on one or more
covariates (we deleted observations with missing values on any explanatory variable). Thus we base
our investigation on 151377 cases from 40 countries.
Our analysis employs the reading literacy scale in the position of the dependent variable. PISA
reports five plausible values of reading literacy for each student. “The plausible values represent
a set of random values for each student selected at random from an estimated ability distribution
of students with similar item response patterns and background. They are intended to provide good
estimates of parameters of student populations (for example, country mean scores), rather than
estimates of individual student proficiency” (OECD, 2002, p. 22). We used STATA’s mi package (STATA
Corp., 2011b) to work with plausible values, since plausible values and imputed values (or latent
variables and missing data) are conceptually and computationally synonymous and require, as stated
by Lee and Cai (2012, p. 1), “the same analytical tools”. The overall mean on the reading test is
485 in our analytical sample (see Table 1); reading test scores by country are reported in Table
A.1 in the Appendix.
The student questionnaire asked, “How many brothers and sisters do you have?” Students reported the
number of younger, older, and same-age siblings by ticking the relevant box ranging from “none” to
“four or more” in each category. The final number of siblings was then obtained by adding responses
to each item. The scale ranges from 0 to 12 in our analytical sample. The questionnaire did not
differentiate among biological, half-, or step-siblings. Respondents in the analytical sample have
on average 1.9 brothers and sisters (see Table 1). Several country means fall significantly below
the overall mean, with the lowest values recorded in Bulgaria (1.0), Italy (1.3), and Korea (1.3).
The highest means are found in Peru (3.0), Indonesia (2.9), Israel (2.9), and Mexico (2.9; see
Table A.1 in the Appendix).
Students were further asked, “Who usually lives at home with you?” They were offered eight possible
yes/no questions. One of these questions related to grandparent(s). Based on the data we are able
to ascertain whether the student coresided with a grandparent (grandparents), but we can neither
determine the number of coresiding grandparents, nor their characteristics. Hence, coresidence is
measured by a dichotomous variable, with category 1 denoting coresidence with a grandparent (or
several grandparents) and 0 meaning no coresidence. Overall, about 20 % of students in the
analytical sample coreside with a grandparent (see Table 1). About 2 % of students coreside in
Finland, 4 % in Iceland and Sweden. At the other extreme, we find 50 % coresiding students in
Bulgaria, and 48 % in Indonesia and Thailand (see Table A.2 in the Appendix).
We also used student questionnaire data on household composition to differentiate among 3 types of
parental constellations: the student lives with either (1) two biological parents, or (2) one
biological (single) parent, or (3) one biological parent and his/her opposite sex partner who is
not biologically related to the child (note that our classification differs from the family
structure variable provided in the PISA database). In our sample, about 80 % of students lived with
two biological parents, 13 % with a single parent, and about 7 % with a biological parent and a
step-parent (see Table 1). The share of students living in intact families ranges from a low of 65
% in the USA and 69 % in Latvia, to a high of 94 % in Macedonia, 93 % in Korea and Indonesia (see
Table A.2 in the Appendix). The lowest percentage living with a single parent is recorded in
Indonesia (4 %), Macedonia (5 %), and Korea and Greece (6 %). The highest share of students from
single-parent families is found in Latvia (20 %), Chile and New Zealand (19 %), and in the USA,
Peru, Russia and Brazil (18 %; see Table A.2 in the Appendix). Coresidence is somewhat less common
in families with one biological parent and one step-parent (about 14 % students in step-families
coreside with grandparents), while about 20 % of students in two-biological parent and
single-parent families coreside with their grandparents (see Table 2; coresidence by family
structure within individual countries is shown in Table A.3 in the Appendix).
Parental education is measured using ISCED categories (we combine categories 1 and 2, since the
former has only few cases in many countries). We use the higher of the mother’s and father’s
education and dichotomize the resulting variable into four contrast variables in the analysis.
Parental occupation was measured with an open-ended question about the characteristics of the
parents’ main job. The answer was coded using ISCO codes and then transformed into ISEI (Ganzeboom
& Treiman, 1996). Again, we use the higher of both parents’ ISEI (variable “HISEI” provided in the
original PISA 2000 dataset). The average ISEI in the analytical sample is 47.9 (see Table 1); we
center ISEI on its grand mean to render the intercept in the model equation more interpretable
(Hox, 2002, pp. 54-58). A dichotomous variable indicating that student’s mother was employed around
the time of the interview was also utilized (66 % of mothers were employed, see Table 1; the
variable was dichotomized from students’ reports on their mothers’ employment situation – the
original question differentiated full-time employed, part-employed, and unemployed mothers looking
for a job as well as other non-employed mothers). We also control for respondents’ gender in the
analysis (coded 1-male, 0-female). There are 51 % girls in the analytical sample (see Table 1).
We use several macro-level variables in our analysis. We employ a single composite macro-level
indicator of the level of development/modernization of each individual country, the so-called Human
Development Index (HDI). We understand modernization as movement towards democracy, a national and
welfare state, and higher levels of education, equality, industrialization, social mobility,
wealth, general social tolerance, individualism, secularism (Divale & Seda, 2000; Ciftci, 2010;
Marks, 2009), and towards the nuclear family (Popenoe, 1987).
Gross Domestic Product (GDP) has often been used as an indicator of modernization. This practice,
however, has been criticized at least since the 1970s, as GDP was not designed to measure
development/progress and does not measure it adequately (Eurostat, 2010; Afsa et al., 2008; Boarini
et al., 2006; United Nations Development Programme, 1990). As summarized by Afsa et al. (2008, p.
1), GDP “is essentially a measure of economic activity, and more specifically of economic
activities leading to monetary transactions. As a result, GDP suffers from two major weaknesses:
(a) being a monetary aggregate, it pays little or no attention to distributional issues and to
elements of human activity or well-being for which no direct or indirect market valuation is
available; (b) it is measuring productive flows and, as such, ignores the impact of productive
activities on stock, including stock of natural resources.” The advocates of alternative measures
of development put it succinctly in stating that “income is not the sum total of human life”
(United Nations Development Programme, 1990, p. 9). Human development is then defined as a general
(beneficial) movement towards better-quality life, linked to forming and using capabilities. It is
a way of enlarging people’s choices (be it in the matters of education, health, living standard, or
politics) and enhancing well-being. Income, measured by the GDP, is only partially a proxy for such
choices. It may be necessary, but not sufficient for human development: “there is no automatic link
between income growth and human progress” (United Nations Development Programme, 1990, p. 10). It
is argued that using GDP as a proxy for development has shifted attention away from the ends
(benefits for people) toward means.
Some authors have advocated using alternative measures, be they adjusted or extended versions of
GDP itself, sets of indicators (which reflect multidimensionality of progress), or composite
indexes (which acknowledge multidimensionality of progress while answering the need for a single,
easily used measure; Afsa et al., 2008; Boarini et al., 2006). So far no single preferred
alternative has emerged. UNDP’s Human Development Index (HDI) is one of the well-known composite
indexes. Presented in the 1990 Human Development Report, it was set to replace GDP as a measure of
human development, capturing what are claimed to be three main elements of human life – longevity,
knowledge, and standard of living (United Nations Development Programme, 1990). Despite still being
rather imperfect (it has been criticized for not working with enough dimensions of human
development and for being arbitrary, even redundant, see McGillivray & White, 1993; Cahill, 2005;
Ranis et al., 2006; Afsa et al., 2008), it “remains one of the few indexes that are regularly
compiled and widely disseminated by international organizations to allow systematic cross-country
comparisons” (Afsa et al., 2008, p. 1). We use the HDI as a way of addressing the issue of GDP
inadequacy when it comes to measuring development/modernization/progress.
HDI consists of three dimensions: health, education, and living standards. HDI utilizes a set of
four variables to cover these three dimensions: health is measured by life expectancy at birth;
education by combining mean years of schooling of adults above 25 and expected years of schooling
of children of school entering age; and Gross National Income (GNI) per capita measures living
standard (income is adjusted for variations in purchasing power across countries). The inclusion of
health and educational achievement into HDI along with an indicator of economic performance was
guided by the idea that both education and health are “regarded as two major ingredients of
development and progress” (Afsa et al., 2008, p. 13). The HDI is measured on a scale ranging from 0
to 1; higher values reflect higher level of development (Cahill, 2005).
Our analysis employs HDI values taken from the 2011 Human Development Report (United Nations
Development Programme, 2011, pp. 131-134). We use values for the year 2000, which–within selected
PISA countries–range from 0.543 in Indonesia to 0.913 in Norway. For the purposes of our analysis
we categorized the HDI into four categories using the values of 25^th, 50^th, and 75^th percentile
(0.7405; 0.8275; 0.8635, respectively). We categorized HDI in order for its interactions with
sibship size (a continuous variable) to be more readily interpretable. There were, then, ten
countries in each category (1^st quartile consists of Albania, Brazil, Bulgaria, Indonesia, Latvia,
Mexico, Peru, Romania, Russia, Thailand, 2^nd quartile Argentina, Chile, Czech Republic, Greece,
Hong Kong, Hungary, Italy, Macedonia, Poland, Portugal, 3^rd quartile Austria, Denmark, Finland,
France, Iceland, Israel, Korea, Luxemburg, Spain, United Kingdom, and finally the 4^th quartile
Australia, Belgium, Canada, Germany, Ireland, New Zealand, Norway, Sweden, Switzerland, and the
United States). Values of HDI and assignment of countries into quartiles are presented in Table A.1
in the Appendix).
We employ three macro-level variables as controls in our analyses: total public expenditure on
education, total public social expenditure, and crude divorce rate. The first two variables follow
the logic of Park’s analysis (Park, 2008), which postulated that public financial support for
education and/or families may reduce resource dilution and protect children against the negative
consequences of having many brothers and sisters. We do not, however, use the same context-level
variables, mostly for practical reasons: our analysis covers countries not included in Park’s
models. Park’s macro-level measures of public investment into education and public transfers
towards families were not available for all countries in our sample. Instead we use public
expenditure on education and total public social security spending, which are clearly related both
conceptually and empirically. Total public expenditure on education is defined as “the total public
expenditure (current and capital) on education expressed as a percentage of the Gross Domestic
Product (GDP) in a given year … includ[ing] government spending on educational institutions (both
public and private), education administration, and transfers/subsidies for private entities” (World
Bank, 2013). Similarly to Park (2008) we are using a 10-year average for years 1991-2000. The data
on public expenditure on education come from World Bank’s World Development Indicators database
(World Bank, 2013). We also use total public social security expenditure as a percentage of GDP,
which is defined as “the sum of expenditure (including benefit expenditure and administration
costs) of all existing public social security/social protection schemes or programmes in the
country” (International Labour Office, 2010, p. 261) including spending on health in the year 2000.
The data came from ILO’s World Social Security Report (International Labour Office, 2010, pp.
258-261). The missing data point for Peru was taken from the Restoring Fiscal Discipline for
Poverty Reduction in Peru publication (World Bank, 2003, p. 33).
We further expand the list of macro-level indicators to include crude divorce rate (CDR) in 2000 as
a rough indicator of the destabilization of the family system at the time of the PISA survey. Crude
divorce rate refers to the annual number of divorces per thousand individuals in the population.
The information was taken from UN 2003 Demographic Yearbook (United Nations, 2006). CDR was missing
for Chile in the source database, since divorce was not made legally possible in Chile until 2004.
Zero was substituted for this missing data point. The correlations and descriptive statistics
(computed in the sample of 40 countries) of all macro-level variables are presented in Table 3. We
see that the country-level variables are relatively highly correlated with Pearson’s correlation
coefficients ranging from 0.30 to 0.66.
Since the dependent variable is a test score, i.e. a numeric variable, regression analysis seems to
be an appropriate analytical tool. Yet, one has to deal with a nested data structure that includes
schools nested within countries and students nested within schools. Therefore, we decided to use a
multi-level version of regression analysis to take this clustering structure into account. We
decided to use three-level hierarchical linear models, in which students (level-1, N = 151377) are
nested within schools (level-2, N = 8218) and schools are nested within countries (level-3, N = 40)
with explanatory variables measured at level-1 and level-3.[1] We estimated all models using
xtmixed procedure in STATA 13 MP (STATA Corp., 2011a).
We estimated and present five multi-level models. The first model uses only two level-1 predictors
(family size and coresidence), one level-3 predictor (HDI), and their three-way interaction (along
with all lower-order interaction effects required by the marginality principle). The second model
adds individual-level controls (respondent’s gender, parental education, family structure, mother’s
employment status, parental ISEI). We decided to present these two sets of results because the
structure of the relationships between explanatory variables is very complex and endogeneity is not
easily determined. We believe that comparing the two sets of results would both capture the overall
picture of the interrelatedness of family size, coresidence, and level of development, and would
also depict the degree to which these patterns may be due to correlations with other variables such
as family structure, socioeconomic status, mother’s employment and so on. Furthermore, we expand
Model 2 by adding other macro-level controls (total public social security expenditure, total
public expenditure on education, crude divorce rate). We add these additional control variables one
by one to form Model 3 (controlling for total public social security expenditure on top of
variables contained in Model 2), Model 4 (similarly controlling for total public expenditure on
education), and Model 5 (controlling for crude divorce rate). Each of Models 3, 4, and 5 also
interacts the newly added country-level variable with sibship size.
6. Results
We present results of the first two estimated models of determinants of reading test scores in
Table 4 and begin our interpretation with the simpler one. We see that there is a negative
association between family size and reading test scores in countries with the lowest HDI (the first
quartile). This is equally so with and without coresidence with grandparents. Among students not
coresiding with grandparents, the estimated coefficient for sibship size is -3.555, while it is
-3.305 (= -3.555+0.250) among coresiding students. The difference between these two slopes is not
statistically significant at the 0.05 level (s.e. = 0.250, t = 0.48, p = 0.630). It seems that the
disadvantage in reading test scores associated with larger sibship size is unrelated to coresidence
status in the least developed countries in our sample (i.e. in countries with HDI between 0.543 and
0.732).
Table 4 shows that the negative association between sibship size and reading test scores increases
at higher levels of development. For instance, among students who do not coreside with their
grandparents, the estimated associations are -3.555, -3.499, -4.289, and -4.684 in the 1^st, 2^nd,
3^rd, and 4^th quartiles of the distribution of HDI values, respectively. An even stronger trend
also applies to students in three-generation households, where the associations are -3.305, -6.111,
-7.883, and -8.468 going from the first to the fourth HDI quartile (see Model 1 in Table 4).
Even more interesting is the changing difference between the sibship size slopes estimated for
coresiding and non-coresiding students. We have observed already that these slopes do not differ in
the least developed countries in our sample. Yet, the situation changes as we move toward more
developed societal contexts. For instance, in the second quarter of the distribution of HDI values
the two slopes differ by -2.862, which turns out to be statistically significant at the
conventional 0.05 level (t-statistic testing the equality of the slopes is -2.92, which implies
p = 0.004). The two slopes further diverge in the third and fourth quartiles of HDI distribution,
the differences being -3.844 and -4.034, respectively (see Table 4, Model 1).
Clearly, the estimated association between sibship size and reading test scores depends both on
three-generation coresidence and level of development: the association becomes more negative as we
move from moderate to high levels of development. The interaction is best portrayed in a graph (see
Figure 1), which depicts the growing difference in the slopes of the sibship size across levels of
development as well as the divergence of the two slopes with increasing development.
Model 2 adds statistical controls measured at level-1 (individual students) into Model 1. These
controls do not change the overall picture to any significant degree, yet the estimated effects are
somewhat weaker. For instance, the main estimated effect of the number of siblings is -2.622 (among
students who do not coreside) in Model 2, i.e. it is reduced by approximately 25 % in comparison to
its size in Model 1 (see Table 4). The estimated negative effect of the number of siblings (among
students who are not coresiding) tends to increase with development. In the second quartile of HDI
it is -2.795 (= -2.622-0.173), in the third quartile it is -3.559 (= -2.662-0.937), and in the
highest quartile it grows to -4.077 (= -2.622-1.455; see Table 4 for the respective interaction
terms that produce these point estimates). Similarly, the estimated association between sibship
size and reading test scores increases with development among students who do coreside with their
grandparents. While it is -2.910 (= -2.622-0.288) in the 1^st quartile of HDI (see Model 2 in Table
4), it grows to -5.415 (= -2.622-0.288-0.173-2.332), -6.934 (= -2.662-0.288-0.937-3.087), and
-7.510 (= -2.662-0.288-1.455-3.145) in the 2^nd, 3^rd, and 4^th quartiles, respectively.
The difference between the two sibship size slopes (defined by coresidence status) increases from
the negligible value of -0.288 (HDI in the 1^st quartile) to the more substantial -3.145 (HDI in
the 4^th quartile). Evidently, Models 1 and 2 support the same story: the absolute value of the
estimated sibship size slope tends to increase with development and this growth is more pronounced
if the student lives in a three-generation household with at least one of his/her grandparents.
These tendencies in the net associations are displayed graphically in Figure 2.
The main effect of coresidence is -14.824 in Model 1 indicating that coresidence is associated with
poorer test scores at lower levels of HDI and no siblings present in the same household. The effect
of coresidence on test scores seems to change with HDI in a non-linear fashion (see Table 4). While
it always stays negative, we only find a significantly more negative effect of coresidence at the
highest HDI level, i.e. in the most advanced societies. Hence, we can conclude that coresidence is,
net of other factors, always associated with lower reading test scores in our sample of countries.
Now we pause briefly to comment on the estimated effects of other explanatory variables. We see
that boys score almost 25 points lower on the reading test scale than girls. Students from intact
families perform better than students from single-parent or step-parent family environments. The
mean net difference between a student from a two-parent and a single-parent family is -2.652, and
between two-parent and a step-parent family it is -4.836 (all these effects are highly
statistically significant (the respective p-values are lower than 0.0005).
Model 2 also indicates strong positive and significant net effects of parental education on test
scores. For instance, a student whose parents have tertiary education is expected to score 21
points higher on the reading test than a student whose parents have only primary education,
disregarding other variables in the model. Similarly, parental occupational status has a strong
positive effect on reading literacy. Net of other factors, each additional point on the ISEI scale
increases expected test score by 0.817 points. Hence, the expected net difference between the child
of a secondary school teacher (ISEI = 71) and a farm worker (ISEI = 16) in the reading literacy
test is approximately 45 points (0.817*(71-16) = 44.935). Moreover, the mother’s employment tends
to be associated with poorer performance on the reading test (net of other factors in the
model)–the difference is 1.074 points, which seems to be of relatively little substantive
importance.
Models 3, 4, and 5 represent essential theory-motivated extensions of Model 2 presented above. Each
of these models includes one additional country-level control variable – namely total public social
security expenditure (TPSE), total public expenditure on education (TPEE), and crude divorce rate
(CDR) – and its interaction with sibship size. The inclusion of TPSE and TPEE into the model
follows the logic of Park’s paper (Park 2008) to see if public resources directed towards schooling
and/or welfare transfers reduce the disadvantage stemming from larger sibships and if this happens
differently by three-generation coresidence. The third of these additional macro-level variables
(CDR) then reacts to our assumption that it might be growing family instability (and not
socioeconomic development per se) that is responsible for increasing negative effects of
coresidence and increasing negative effects of sibship size in more advanced societies.
Estimated parameters of these models are presented in Table 5. Clearly, only some additional
level-3 controls have a significant net effect on reading literacy. More specifically, TPSE and
TPEE have little net effect on reading literacy. Furthermore, their interactions seem to be of
negligible substantive importance. For instance, the interaction between TPSE and sibship size is
statistically significant (t=-4.78, p<0.0005), but it is substantively uninteresting (the point
estimate is -0.155 with the TPSE scale ranging from 2.32 to 28.5). CDR, on the other hand, has a
positive net effect on reading literacy (see Table 5). This positive association may reflect
declining average levels of pre-divorce conflict at higher divorce rates (see e.g. Amato &
Hohmann-Marriott, 2007).
Furthermore, once we add these level-3 controls (and their interactions) into our models, we see
little change in the effects of other variables. One of the more salient modifications is found in
Model 3. It suggests that the effect of sibship size (among not-coresiding students) does not
change with development – it is between -3.984 and -3.706 in the lowest and highest categories of
HDI (with somewhat lower values in the middle two categories, see Table 6). The effect of sibship
size does, however, change with HDI among students who coreside with their grandparents and it
becomes more negative at higher development levels (see Table 6): for instance the effect of
sibship size is -4.405, -5.273, -6.446, and -7.164 in the 1^st, 2^nd, 3^rd, and 4^th HDI
quartiles, respectively (see Table 6, Model 3). Hence, sibship size effect increases with HDI when
we look at students living in three-generation households and its slope is significantly steeper
than among students not living in three-generation households.
Also Models 4 and 5 document that the effect of sibship size changes more dramatically (i.e.
becomes more negative) with HDI levels in three-generation households than in two-generation
households. For instance, Model 4, which controls for TPEE and its interaction with sibship size,
gives the following point estimates of the sibship size effect in three-generation households:
-2.867, -5.399, -6.945, and -7.537 in the 1^st, 2^nd, 3dr, and 4^th quartiles of development (see
Table 6). The sibship size effect grows only relatively moderately with HDI in two-generation
households, from -2.585 in the lowest HDI quartile to -4.103 n the highest HDI quartile (see Table
6). Model 5 (which controls for CDR at level-3) confirms the same story. The sibship size effect
among coresiding students grows from -2.955 at the lowest HDI level to -7.455 at the highest HDI
level, while it increases from -2.668 to -4.023 only, when we look at students who are not
coresiding with their grandparents (see Table 6). Hence, even Models 3, 4, and 5 confirm that the
effect of sibship size changes to a significant degree with HDI levels when we look at
three-generation households, whereas it changes comparatively little (or not at all) when we
investigate two-generation households only.[2]
7. Conclusions and discussion
We have documented that the estimated associations between number of siblings and reading test
scores among 15-year-old students vary systematically with grandparental coresidence and with the
level of development as measured by the Human Development Index in a sample of 40 countries. The
negative association between sibship size and reading scores was relatively modest, and did not
differ by coresidence, in the least developed nations in our sample. Yet, these associations tend
to be more negative at higher levels of HDI. Furthermore, the increase is greater among students
who coreside with grandparents and relatively smaller (but still significantly different from zero)
among students who live separately from their grandparents. Hence, three-generation coresidence
magnifies the disadvantage stemming from large sibships and does so more strongly in the most
advanced societies. The main findings are rather robust vis-à-vis partial model re-specifications
including adding new macro-level covariates (and their interactions with sibship size) such as
public spending on education, public spending on social security, and crude divorce rate.
Our findings do not fully confirm our initial hypotheses that grandparental coresidence would
protect students from the negative effects of resource scarcity resulting from a larger sibship at
lower levels of social development. It is possible that coresidence with grandparents has this
protective effect, but it might only be detectible at much lower levels of development. Our
analysis was based on a sample of 40 relatively advanced societies that included OECD countries and
a handful of other, comparatively advanced nations. The lowest value of the Human Development Index
in our sample was 0.543 (in Indonesia), with the average value being 0.80; i.e. it is possible that
our data did not represent social contexts where the anticipated protective effect would play out
fully. We therefore believe that our hypothesis should also be examined in other, less advanced
societies in order to be subjected to a more complete test.
The results do, however, provide evidence that coresidence of three generations is associated–on
average–with a significant socio-economic disadvantage at higher levels of development. Indeed,
this disadvantage increases at higher levels of modernization. We interpret this as an indication
that grandparents tend to coreside as dependents (rather than as providers) more often in more
advanced socio-economic contexts. While three-generation households are less and less common, they
are associated with growing socio-economic disadvantage. To the extent that cross-sectional data
may hint at future developments, one would anticipate that the harmful effects of
three-generational coresidence would magnify in the coming decades if the modernization process
continues. If this development takes place, it would further highlight the need to include multiple
generations in status attainment models (see e.g. Chan & Boliver, 2013; Hällsten, 2013; Hertel &
Groh-Samberg, 2013; Jaeger, 2012; Mare, 2011, 2014; Pfeffer, 2014).
Furthermore, our results suggest that a larger sibship and three-generation coresidence represent
two particular dimensions of disadvantage. When they are combined, children’s tests scores are
particularly strongly impacted; more so than one would expect on the basis of each of these
circumstances alone. This interaction also suggests that the disadvantages associated with
coresidence and sibship size do not reflect one underlying scale (e.g. household density), because
this argument would imply that – in the context of a multivariate statistical model – both
coresidence and sibship size should affect test scores additively.
This paper illustrates further the heterogeneity of sibship size effects. Other authors have shown
that the sibship size effect may vary according to help coming from outside of the nuclear family,
e.g. from the extended family (Shavit & Pierce, 1991), religious communities (Blake, 1989), or the
state (Park, 2008). We have shown that the sibship size effect also varies by level of overall
socioeconomic development, being relatively weak in less advanced societies and quite stronger in
more advanced societal contexts. Furthermore, we have shown that the sibship size effect interacts
with three-generation coresidence: the sibship size effect is significantly stronger in
three-generation households than in two generation households. This finding, however, is only
limited to the more advanced societies in our sample.
The purpose of this text was not to adjudicate the three competing interpretations of the
repeatedly reported associations between sibship size and educational achievement (Booth & Kee,
2005; Jaeger, 2008; Kuo & Hauser, 1997; Park, 2008; van Eijck & de Graaf, 1995). On the contrary,
our data make such adjudication unfeasible and we interpreted our results as purely descriptive,
making no assertions regarding the nature of causality. We believe that our results are in
principle consistent with all three explanations of sibship size effects: resource dilution, the
dynamics of intellectual environment in the family, as well as the possibility of a joint
determination of both parental fertility and children’s schooling are all likely to change with
socioeconomic development. Similarly, these processes are equally likely to interact with
three-generation coresidence.
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9. Appendix
Tables and Figures
Table 1: Descriptive statistics of level-1 variables used in the analysis. 15-year-old students in
selected countries in 2000. Number of level-1 observations (students) = 151377.
Reading literacy score (mean)
485
Female
50.7 %
Parental HISEI (mean, before centering)
47.9
Education of the better educated parent (ISCED)
Level 1 or less (primary education or less)
9.9 %
Level 2 (lower secondary)
12.3 %
Level 3B or 3C (upper secondary)
13.0 %
Level 3A (upper secondary)
26.3 %
Level 5A, 5B, or 6 (tertiary)
38.5 %
Number of siblings (mean)
1.9
Mother is employed (proportion)
66.3 %
Family structure (proportion):
Two biological parents
80.3 %
Single biological parent
13.0 %
One biological parent and their partner
6.8 %
Co-resident grandparent(s) (proportion)
19.8 %
Table 2: Per cent co-residing with grandparents by family type. 15-year-old students in selected
countries in 2000. Number of level-1 observations (students) = 151377.
Family type
% co-residing
Intact family (two biological parents)
20.3 %
Single parent
19.7 %
Biological parent and a step-parent
13.6 %
Table 3: Correlations and descriptive statistics of macro-level variables used in the analysis.
Number of level-3 observations (countries) = 40.
HDI
TPEE
TPSE
CDR
HDI
1.00
Total public expenditure on education (TPEE)
0.66
1.00
Total public social expenditure (TPSE)
0.64
0.63
1.00
Crude divorce rate (CDR)
0.44
0.37
0.30
1.00
Mean
0.80
4.69
16.87
1.84
s.d.
0.09
1.39
7.03
0.98
Minimum
0.543
1.1
2.32
0.00
Maximum
0.913
7.7
28.5
4.31
Table 4: Estimated parameters and standard errors (in parentheses) of three-level hierarchical
linear models of reading literacy. Number of level-1 observations (students) = 151377, number of
level-2 observations (schools) = 8218, number of level-3 observations (countries) = 40.
Model 1
Model 2
Co-residence with grandparent(s)
-14.824
(1.400)
-12.483
(1.365)
Sibship size
-3.555
(0.350)
-2.622
(0.344)
HDI quartile (1^st quartile is ref. category)
HDI 2^nd quartile
48.935
(14.894)
47.775
(14.749)
HDI 3^rd quartile
94.656
(14.918)
89.684
(14.768)
HDI 4^th quartile
111.794
(14.877)
103.301
(14.736)
Male
-24.568
(0.425)
Family structure (intact family is ref. category)
Single parent
-2.652
(0.602)
Parent and step-parent
-4.836
(0.808)
Education (ISCED level 1 or lower is ref. category)
ISCED 2
3.783
(0.898)
ISCED 3B, or 3C
15.748
(0.956)
ISCED 3A
19.324
(0.895)
ISCED 5A, or 5B, or 6
21.270
(0.981)
Socioeconomic status of parental occupation (ISEI)
0.817
(0.017)
Mother employed
-1.074
(0.466)
Table 4: continued
Interactions
Sibship size*co-residence
0.250
(0.519)
-0.288
(0.507)
HDI 2^nd quartile*co-residence
8.248
(2.271)
7.157
(2.221)
HDI 3^rd quartile*co-residence
3.664
(2.57)
3.024
(2.508)
HDI 4^th quartile*co-residence
-13.217
(2.582)
-12.739
(2.519)
HDI 2^nd quartile*sibship size
0.056
(0.562)
-0.173
(0.549)
HDI 3^rd quartile*sibship size
-0.734
(0.549)
-0.937
(0.536)
HDI 4^th quarter*sibship size
-1.129
(0.485)
-1.455
(0.472)
HDI 2^nd quartile*sibship size*co-residence
-2.862
(0.982)
-2.332
(0.96)
HDI 3^rd quartile*sibship size*co-residence
-3.844
(1.109)
-3.087
(1.083)
HDI 4^th quartile*sibship size*co-residence
-4.034
(1.018)
-3.145
(0.993)
Intercept
420.256
(10.521)
421.662
(10.45)
Table 5: Estimated parameters and standard errors (in parentheses) of three-level hierarchical
linear models of reading literacy. Number of level-1 observations (students) = 151377, number of
level-2 observations (schools) = 8218, number of level-3 observations (countries) = 40.
Model 3
Model 4
Model 5
Co-residence with grandparent(s)
-12.189
(1.364)
-12.493
(1.365)
-12.476
(1.364)
Sibship size
-3.984
(0.427)
-2.585
(0.390)
-2.668
(0.351)
HDI quartile (1^st quartile is ref. category)
HDI 2^nd quartile
50.236
(16.375)
45.735
(14.907)
46.148
(13.114)
HDI 3^rd quartile
92.759
(17.641)
82.862
(17.312)
75.668
(13.808)
HDI 4^th quartile
106.834
(17.604)
96.097
(17.574)
86.739
(14.029)
Male
-24.555
(0.425)
-24.568
(0.425)
-24.566
(0.425)
Family structure (intact family is ref. category)
Single parent
-2.648
(0.602)
-2.653
(0.602)
-2.652
(0.602)
Parent and step-parent
-4.806
(0.808)
-4.841
(0.807)
-4.828
(0.809)
Education (ISCED level 1 or lower is ref. category)
ISCED 2
3.829
(0.898)
3.778
(0.897)
3.788
(0.897)
ISCED 3B or 3C
15.815
(0.955)
15.742
(0.956)
15.749
(0.956)
ISCED 3A
19.370
(0.895)
19.318
(0.895)
19.318
(0.895)
ISCED 5A, 5B, 6
21.343
(0.981)
21.264
(0.981)
21.266
(0.981)
Socioeconomic status of parental occupation (ISEI)
0.816
(0.017)
0.817
(0.017)
0.817
(0.017)
Mother employed
-1.139
(0.466)
-1.076
(0.466)
-1.079
(0.466)
Total public social security expenditure
-0.348
(0.942)
Total public social security expenditure*sibship size
-0.155
(0.032)
Total public expenditure on education
(10-year average)
3.590
(4.832)
Total public expenditure on education*sibship size
(10-year average)
0.026
(0.157)
Crude divorce rate
17.491
(5.318)
Crude divorce rate*sibship size
-0.111
(0.178)
Table 5: continued
Interactions
Sibship size*co-residence
-0.421
(0.508)
-0.282
(0.508)
-0.287
(0.507)
HDI 2^nd quartile*co-residence
6.660
(2.233)
7.167
(2.230)
7.190
(2.220)
HDI 3^rd quartile*co-residence
3.024
( 2.508)
3.017
(2.504)
3.057
(2.507)
HDI 4^th quartile*co-residence
-12.986
(2.520)
-12.732
(2.522)
-12.749
(2.518)
HDI 2^nd quartile*sibship size
1.189
(0.600)
-0.194
(0.553)
-0.172
(0.549)
HDI 3^rd quartile*sibship size
1.096
(0.653)
-0.999
(0.623)
-0.853
(0.548)
HDI 4^th quarter*sibship size
0.278
(0.591)
-1.518
(0.590)
-1.355
(0.515)
HDI 2^nd quartile*sibship size*co-residence
-2.057
(0.967)
-2.338
(0.965)
-2.357
(0.958)
HDI 3^rd quartile*sibship size*co-residence
-3.137
(1.083)
-3.079
(1.081)
-3.103
(1.084)
HDI 4^th quartile*sibship size*co-residence
-3.037
(0.994)
-3.149
(0.994)
-3.145
(0.992)
Intercept
419.431
(12.322)
426.043
(11.939)
430.791
(9.700)
Table 6: Estimated net effects of sibship size from selected three-level hierarchical linear models
of reading literacy. Number of level-1 observations (students) = 151377, number of level-2
observations (schools) = 8218, number of level-3 observations (countries) = 40.
Net effect of sibship size
Model 3
No co-residence
Co-residence
1^st HDI quartile
-3.984
-4.405
2^nd HDI quartile
-2.795
-5.273
3^rd HDI quartile
-2.888
-6.446
4^th HDI quartile
-3.706
-7.164
Model 4
No co-residence
Co-residence
1^st HDI quartile
-2.585
-2.867
2^nd HDI quartile
-2.779
-5.399
3^rd HDI quartile
-3.584
-6.945
4^th HDI quartile
-4.103
-7.534
Model 5
No co-residence
Co-residence
1^st HDI quartile
-2.668
-2.955
2^nd HDI quartile
-2.840
-5.484
3^rd HDI quartile
-3.521
-6.911
4^th HDI quartile
-4.023
-7.455
Table A.1: Descriptive statistics of selected variables used in the analysis by country.
15-year-old students in 2000. Number of level-1 observations (students) = 151377.
Country
Reading literacy score (mean)
Number of siblings (mean)
HDI
HDI quartile
Number of level-1 cases
Albania
366.6
2.0
0.691
1^st
3967
Argentina
432.4
2.6
0.749
2^nd
2546
Australia
534.9
2.0
0.906
4^th
4650
Austria
507.1
1.6
0.839
3^rd
3406
Belgium
528.4
1.7
0.876
4^th
4943
Brazil
389.3
2.4
0.665
1^st
3446
Bulgaria
432.4
1.0
0.715
1^st
3056
Canada
528.3
1.9
0.879
4^th
18811
Chile
422.0
2.2
0.749
2^nd
3500
Czech Republic
502.7
1.5
0.816
2^nd
4539
Denmark
509.4
1.9
0.861
3^rd
3099
Finland
552.0
2.0
0.837
3^rd
4355
France
512.4
1.8
0.846
3^rd
2986
Germany
509.3
1.5
0.864
4^th
4232
Greece
480.7
1.4
0.802
2^nd
2749
Hong Kong
533.2
1.5
0.824
2^nd
3331
Hungary
490.3
1.4
0.775
2^nd
3944
Iceland
512.1
2.5
0.863
3^rd
2482
Indonesia
369.8
2.9
0.543
1^st
4664
Ireland
540.5
2.6
0.869
4^th
1796
Israel
482.3
2.9
0.856
3^rd
2712
Italy
496.2
1.3
0.825
2^nd
3720
Korea
524.7
1.3
0.830
3^rd
2840
Latvia
469.4
1.6
0.732
1^st
3086
Luxembourg
460.0
1.6
0.854
3^rd
2358
Macedonia
383.7
1.4
0.772
2^nd
3089
Mexico
434.9
2.9
0.718
1^st
3231
New Zealand
544.7
2.2
0.878
4^th
2299
Norway
520.8
2.0
0.913
4^th
2404
Peru
342.8
3.0
0.674
1^st
3634
Poland
479.6
1.8
0.770
2^nd
2959
Portugal
484.6
1.4
0.778
2^nd
2638
Romania
453.9
1.4
0.704
1^st
3357
Russia
468.7
1.7
0.691
1^st
4441
Spain
499.7
1.4
0.839
3^rd
4220
Sweden
524.2
2.2
0.894
4^th
2629
Switzerland
504.3
1.6
0.873
4^th
4389
Thailand
443.3
2.1
0.626
1^st
3801
UK
545.5
2.0
0.833
3^rd
4682
USA
519.2
2.4
0.897
4^th
2386
Table A.2: Per cent co-residing with grandparents and per cent living in various family types by
country. 15-year-old students in 2000. Number of level-1 observations (students) = 151377.
Family type
Country
% co-residing with grandparents
% in intact families
% in single parent families
% in step-parent families
Albania
32.2
91.7
7.4
0.9
Argentina
29.0
76.7
17.5
5.8
Australia
5.3
74.5
16.0
9.5
Austria
25.0
80.1
12.9
7.1
Belgium
6.7
79.9
11.5
8.7
Brazil
26.2
73.3
18.1
8.6
Bulgaria
50.3
85.5
12.1
2.3
Canada
9.5
76.3
13.7
10.0
Chile
22.0
71.4
19.2
9.4
Czech Republic
19.1
79.8
10.6
9.6
Denmark
4.5
75.5
13.9
10.6
Finland
2.4
76.4
16.6
7.1
France
7.4
76.6
14.4
9.1
Germany
19.7
77.8
14.6
7.7
Greece
24.4
92.1
6.3
1.5
Hong Kong
12.6
89.7
8.9
1.4
Hungary
13.4
76.5
15.6
7.9
Iceland
3.8
73.2
13.3
13.5
Indonesia
48.2
92.8
4.3
2.9
Ireland
10.9
87.4
10.1
2.5
Israel
14.3
89.9
8.0
2.0
Italy
32.0
84.0
14.0
2.0
Korea
27.9
92.8
5.9
1.3
Latvia
30.8
68.5
20.0
11.6
Luxembourg
16.2
83.0
9.2
7.9
Macedonia
46.6
93.8
5.4
0.8
Mexico
28.6
82.6
13.8
3.6
New Zealand
6.4
70.9
18.8
10.4
Norway
9.3
77.0
12.9
10.1
Peru
21.8
79.1
17.6
3.4
Poland
18.9
89.2
8.1
2.7
Portugal
25.3
84.3
10.6
5.1
Romania
31.4
86.2
10.1
3.7
Russia
32.7
73.8
18.2
8.1
Spain
26.2
86.7
11.6
1.7
Sweden
3.7
72.2
17.3
10.5
Switzerland
11.7
80.5
13.1
6.4
Thailand
48.0
85.7
10.4
4.0
UK
6.9
76.1
14.3
9.7
USA
16.2
64.8
18.3
16.9
Table A.3: Per cent co-residing with grandparents by family type and by country. 15-year-old
students in 2000. Number of level-1 observations (students) = 151377.
Country
Two biological parents
Single parent
One biological parent, one step-parent
Albania
32.5
29.0
30.6
Argentina
28.4
33.7
22.3
Australia
5.3
5.9
4.3
Austria
26.8
17.6
17.1
Belgium
6.5
7.8
7.0
Brazil
25.4
30.1
24.6
Bulgaria
50.0
53.8
41.4
Canada
9.5
10.1
8.3
Chile
17.9
37.0
22.8
Czech Republic
20.1
17.0
12.4
Denmark
4.8
3.9
3.4
Finland
2.7
1.7
0.7
France
6.8
10.5
7.4
Germany
21.4
15.6
10.8
Greece
23.7
35.1
23.8
Hong Kong
12.1
15.8
28.9
Hungary
13.2
16.6
9.0
Iceland
3.4
6.1
3.3
Indonesia
48.1
45.0
56.6
Ireland
10.9
11.5
9.1
Israel
14.1
18.4
9.1
Italy
33.3
26.3
19.2
Korea
27.8
30.5
21.1
Latvia
29.8
34.6
29.7
Luxembourg
16.8
13.4
14.1
Macedonia
46.6
47.6
34.6
Mexico
27.5
34.7
31.9
New Zealand
6.3
7.2
5.4
Norway
9.3
10.0
8.3
Peru
20.6
25.2
32.0
Poland
18.8
21.8
13.6
Portugal
24.8
30.7
22.2
Romania
31.1
32.9
33.9
Russia
31.7
39.4
27.1
Spain
26.5
25.4
20.6
Sweden
3.6
4.0
4.0
Switzerland
12.7
7.0
8.5
Thailand
48.0
46.5
52.7
UK
7.1
6.9
4.9
USA
17.2
15.4
13.2
Figure 1: Estimated total effects (from Model 1) of the number of siblings on reading test scores
by quartiles of the Human Development Index and co-residence with grandparents from a three-level
linear regression model. PISA 2000, number of level-1 observations (students) = 151377, number of
level-2 observations (schools) = 8218, number of level-3 observations (countries) = 40.
Figure 2: Estimated net effects (from Model 2) of the number of siblings on reading test scores by
quartiles of the Human Development Index and co-residence with grandparents from a three-level
linear regression model. PISA 2000, number of level-1 observations (students) = 151377, number of
level-2 observations (schools) = 8218, number of level-3 observations (countries) = 40.
________________________________
[1] Our model specification may inspire the conclusion that the second level (schools) is redundant
in our analysis, since there are no explanatory variables measured at the school level. The reason
why the second level is nevertheless kept in the model relates to the use of schools as sampling
units in the complex sample designs that were implemented in all countries. If the complexities of
the sampling design were ignored, we would face the risk of obtaining biased point estimates of
model parameters as well as underestimated standard errors (Kreuter & Valliant, 2007). While PISA
is distributed with a set of replicate weights that reflect the sampling structure and many PISA
users seem to prefer the use of replicate weights in their own work, replication is not generally
considered to outperform direct incorporation of design information into the analysis (Kreuter &
Valliant, 2007). Indeed some scholars recommend that incorporating elements of multi-stage sampling
directly into a multi-level analysis design is the obvious choice as it adequately reflects the
uncertainty due to sampling in the analysis and has also other favorable properties (see e.g.
Treiman 2009: ch. 9).
[2] Countries at the lower two levels of development (as measured by HDI) appear to be particularly
diverse with respect to culture and history; most notably post-communist societies stand out as a
distinct group. Therefore, we also experimented with other control variables to capture this
apparent diversity and included a dichotomous indicator of post-communism into our models. This
additional covariate does not change other effects in Models 1-5 to any significant degree
(practically not at all).