Early Cognitive Development and Educational Assimilation of
Migrant Children
Colm Harmon, Anita Staneva*, Deborah Cobb-Clark, Garry Barret
School of Economics, University of Sydney, Australia
Working Draft
October 2016
Abstract
In this paper we use data from the five sweeps of the UK Millennium Cohort study to examine the
dynamic relationship between migration and early cognitive development amongst children. The model
follows children from age of 3 until 11 years, and tests the role of self-productivity in cognitive skills
development. We show that migrant children lag behind the native children at age of 3 but they catch
up by the time they are 5 years old by which time any ‘migrant’ penalty has disappeared. Moreover,
migrant children have higher cognitive development scores by age 7. Parental investment is found to
significantly increase the cognitive ability of children, but this declines as children enter formal
schooling. The paper suggests that efforts to promote the assimilation of migrant children should
concentrate towards the home environment in the early years.
Keywords: cognitive skills production function, structural equation model, latent cognitive skills
*
Corresponding Address: Anita V Staneva, School of Economics, Faculty of Arts and Social
Sciences,Rm 479, Merewether Building H04, The University of Sydney, NSW, 2006.
E-mail: [email protected].
1
1. Introduction
Economists have argued that development of cognitive and non-cognitive skills
is vital for long-term education and labour market outcomes of individuals.1 Less is
known, however about the formation of these skills, which starts very early in life and
depends on the initial level of human capital as well as investment made by parents.2
The early years are extremely important, both because events during these years seem
to have very long-run consequences and because young children are vulnerable to
negative environmental factors and different types of shocks (Attanasio, 2015). What
kinds of investments are most effective has been subject to a debate (Fiorini and
Keane, 2014)3 and we still do not know the details of how the production function of
human capital evolves in the early years. The work of Heckman and several coauthors has been particularly forceful in this respect.
In a very general sense, cognitive outcomes can be conceptualised as deriving
from a genetic endowment and the cumulative effect of inputs in a skill production
function. The Bell Curve by Herrnstein and Murray (2010) assigned a primary role to
genetics in explaining the origins of differences in human cognitive ability and a
primary role to cognitive ability in shaping adult outcomes. Recent research
establishes the power of socio-emotional abilities and environmental influences in
creating and fostering abilities. Inputs may be thought as investments in skills
acquisition, or in the case of very young children, home investments by parents
(Leibowitz, 1974). In this context, language is considered as a key instrument for
human capital formation and it is a central to the process of immigrant assimilation.
Early life language acquisition is linked to better performance at later stages of
1
See Heckman et al. (2006), Borghans et al. (2008), Cobb-Clark and Tan (2011), Mendolia and Walker
(2015).
2
From economics point of view early test score measures are important becuase they have been shown
to be strongly related to measures of later adults success. Cameron and Heckman (1993), Carneiro
(2007), Keane and Wolpin (1997), Currie and Thomas (1999), Conti and Heckman (2014) and
Dustman et al. (2013) all provide empiricla evidence on the importance of early child development in
explaining differences in schooling and adult labour market outcomes in the U.S. and the UK.
3
There is a lack of consensus in the schooling quality literature over whether schooling inputs, such as
class-size, teacher education and experience matter in improving cognitive skills in children. For
instance, Coleman (1967) find small effects of school resources on student achievement tests. There are
similar disagreements in the child development research that examine the question of whether maternal
employment in the early years of a child's life is determental to children's cognitive and social
development. Even when studies are based on the same data source, estimates range from maternal
employment being detrimental (Belsky and Eggebeen, 1991) to its having no effect (Blau and
Grossberg, 1992) or being beneficial (Vandell and Ramanan, 1992).
2
schooling (Kamhofer, 2014) and higher returns in adult life (Clifton, 2015).4 Bleakley
and Chin (2004) demonstrate the role of language proficiency, as an input to the
human capital is far more important than the direct effect of language on the marginal
product of labour. For both social and economic reasons, language is a barrier that
separates many immigrants from natives.
Interest in the language of immigrants has increased in part by the recent
upsurge in immigration to the United Kingdom. The 2011 UK Census shows that a
13% of the UK population is foreign born, up from 7% in 1991.5 Most of these recent
immigrants are from non-English speaking countries.6 With this increasing number of
immigrants families in the UK, concern has increased over the impact that growing up
in a non-English speaking home environment may have on children's cognitive
development and education performance.7 Little is known about the adaptation
process that migrant children must navigate and educational consequences that
emerge as they learn a new culture and language.
Over the past few decades, technological advances have allowed researchers to
investigate how bilingualism interacts with, and possibly changes the cognitive and
neurological systems. To maintain the relative balance between two languages, the
bilingual brain relies on executive functions, a regulatory system of general cognitive
abilities. Because bilingual person's language systems are always active and
competing, that person uses these control mechanisms every time she or he speaks or
listens. This constant practice strengthens the control mechanisms and changes the
associated brain regions (Bialystok et al., 2012). It is an argument in the literature,
therefore, that by exposing children to two different languages early on, parents may
increase their productive skills and enable them to learn more efficiently in the future,
hence, giving them an advantage over their peers.8 At the same time, some other
studies warn that bilingualism could be deterious to learning and can put a child at a
4
Numerous empirical studies suggest a positive association between English-language ability and
earnings (Bleakley and Chin, 2004; Chiswick, 1991).
5
In the 2011 Census there were 7.5 million people born abroad; this compares to 4.6 million in 2001
and 3.6 million in 1991 (UK Office for National Statistics (ONS), 2011 Census).
6
India was top of this list with 694,000 usual residents, followed by Poland with 579,000 and Pakistan
with 482,000. The Polish-born population in England and Wales increased nine-fold between 2001 and
2011, more than any other country (ONS, UK, 2011 Census).
7
Bilingualism refers to the ability to use two languages and involves both understanding and speaking.
8
Because a bilingual child switches between languages, the theory goes, he develops enhanced
executive control, or the ability to effectively manage so called 'higher cognitive processes', such as
problem-solving, memory and thought, or it is a phenomenon that researchers call the bilingual
advantage.
3
disadvantage and slow down cognitive ageing (see Bhatia and Ritchie (2008), Hakuta
(1986)). These early studies conclude that native speaker students outperformed
immigrant students on a range of cognitive tasks. Bilingual children initially possess a
smaller vocabulary in each of their languages, and in general they come from families
where at least one parent is foreign immigrant and this may be considered as a
disadvantage (Oller and Eilers, 2002). In addition, families with two foreign parents
may be less proficient in the native language and may lack location-specific
knowledge being essential for a child's development. These differences may play an
additional role in children's skill formation and later life outcomes. It is also
theoretically ambiguous as to what the effect of growing up in a bilingual
environment on early cognitive skills formation is.9
To economists, the issue is to what extent do bilingualism matters in early
cognitive development or put it differently is the cumulative effect of 'inputs' in a skill
production function different for children being exposed to two different languages
early in their life.10 Understanding the source of the gap between native and nonEnglish-speaking origin children may help inform future education policy.
Furthermore, to design effective policy interventions it is necessary to understand the
complex dynamic development and differences between native and non-English
speaking children's abilities. The motivation for this paper stems that child
development is a multi-dimensional process, and it is important to establish whether
the family inputs that foreign and native parents have access to are associated with
different cognitive development outcomes. Building on the theoretical analyses of
Cunha et al. (2006), Cunha and Heckman (2008) and Cunha and Schennach (2010),
we estimate the cognitive skills production functions of immigrant and native children
in the very early years of their lives using the UK Millennium Cohort Study (MSC).
We test the notations of self-productivity, more skills accumulated in the present
period leads to more skills accumulated in the next period, in the transition from early
to mid childhood (ages 3 to 11) by considering immigrant families are bound to be
different in many respects. The emphasis is also on the importance of parental inputs
and home environment defined in terms of the quality of stimulation and support
9
Beyond differences in neuronal activation, bilingualism is found to affect the brain's structure. Higher
proficiency in a second language, as well as earlier acquisition of that language, correlates with a high
gray matter volume in the left inferior parietal cortex (Mechelli et al., 2004).
10
In contrast, there are some studies suggesting that cognitive skills remain unaffected by being
exposed to two different languages (Baker, 2011).
4
available to the child. Following the input hypothesis, we consider spoken language at
home as an additional input into the cognitive skills production function. The English
language is acquired when children are exposed to that comprehensible input which is
sufficient condition for language acquisition to take place and requires no effort on
the part of the learner. We adopt a value-added plus lagged inputs model of skill
formation (Todd and Wolpin, 2003), whereby a child's current cognitive ability
depends on their previous ability and the past parental home environment inputs,
socio-economic status and persistent poverty status. We estimate children's
production functions in a more complex structural approach that attempts to estimate
the entire dynamic process of child development.11 A central problem with the
production function approach is accounting for the endogeneity of parental inputs and
endogeneity of language acquisition as language spoken at home is an endogenous
decision made by each household. Language skills are often correlated with other
attributes that cannot be measured, such as innate ability and the motivation to learn a
new language. In our estimation framework we account for the potential endogenity
of the parental home learning environment and language inputs considering that
linguistic distance between migrant's origin and destination country language is
expected to affect the efficiency of language learning and to raise the cost of human
capital investment. The argument is that immigrants face very different costs of
language acquisition, associated with their linguistic origin and immigrant children
learn a new language easier and faster the linguistically closer their mother tongue is
(Isphording, 2015).12 We also incorporate into the analysis year of arrival in the UK
and the identifying instrument is an interaction of year of arrival and linguistic
distance.
The rest of the paper is organized as follows. Section 2 discuses the relevant
literature and Section 3 outlines a dynamic model of child development. Section 4
discusses in detail the dataset and variables used in the analysis. Section 5 presents the
results and section 6 concludes.
11
One limitation of the static, cross-sectional estimates of the production function is that it overstates
the importance of contemporaneous inputs measures because of their correlation with omitted historical
inputs.
12
Isphording (2015) shows that linguistic barriers raised by language differences play a crucial role in
the determination of the destination-country language proficiency of immigrants.
5
2. Background Literature
There is growing evidence across various disciplines that home and school
environment in the early years of a child's life has a significant influence on cognitive
skill formation (Knudsen et al., 2006). Family characteristics such as income and
education, time spent in educational activities (reading and writing) may all influence
children's cognitive and non-cognitive performance.13
The role of family background and culture on children's outcomes has been
recognised in migration studies. Dustmann (2008) shows a gap in performance for
first generation immigrants, relative to the native population. A lack of English
proficiency is cited as a primary reason for a poor school performance among many
first- and second- generation children (Rosenthal et al., 1983). Macnamara (1967)
claims that the lower verbal performance among bilingual children is a result of a
'balance effect' whereby proficiency in a second language necessitated a loss in
proficiency in one's first language. Thus, it is proposed that foreign speakers never
reach comparable levels of linguistic proficiency as native speakers. Lambert (1977)
claims that when ethno-linguistic minority children reject their own cultural values
and practices for those of the prestigious, dominant group, the second language
eventually replaces their native language. In contrast, immigrant ethno-linguistic
minority children often do not fully develop their cognitive abilities in their native
language while they must confront instruction in another language at school.14 Studies
on older immigrant youth find them to be at an academic disadvantage when
compared to their native-born peers and the question of why this pattern occurs is an
area of debate among researchers (Rong and Brown (2001)). Considering the
extensive challenges immigrant families face while navigating a new social
environment, it is not surprising that many immigrant youth struggle academically
(Perreira et al., 2006).
13
See Ermisch (2008), Blanden et al. (2007), Melhuish et al., (2008), Fiorini adn Keane (2014).
Lambert (1977) distinguishes between an additive and a subtractive form of bilingualism. An
additive form involves both languages and cultures being complementary positive influences on overall
development, which results from valuing the languages and cultures of families and communities.
Thus, an additive approach to bilingualism involves acquisition of a second language at the same time
that all abilities in the first language are maintained, as is the case of children from a dominant social
group learning a minority language within school. A subtractive form of bilingualism, on the other
hand, occurs when two languages are competing.
14
6
The other strand of the literature thus strongly supports the cognitive
advantages of bilingualism, particularly with regard to metalinguistic awareness.
Research has found that both foreign-born and native-born youth with immigrant
parents show better academic, behavioural, emotional, and health outcomes than
youth with native-born parents (Garcia Coll and Marks, 2012). This is paradoxical
because the superior outcomes of the children of immigrants counter what would be
predicted, given their lower SES.
Bilingual children also show other enhancements in their mental development.
The relationship between bilingualism and concept formation is illustrative in some
early studies. For instance, Bain (1974) findings support the bilingual children's
superior performance on concept formation tasks. The extent of the observed
difference, however, depends crucially on the age at arrival in the country (Bohlmark,
2008) as well as the length of stay before the gap is measured (Glick and HohmannMarriott, 2007). The divide is also visible for second-generation immigrants but
varies across countries. Dustmann et al. (2012) compare the educational attainment of
second-generation immigrants with that of children born to native parents in several
OECD countries and show that the average gap in test scores of children of
immigrants and natives differs widely across countries, and is strongly related to
achievement differences in the parent generation. The disadvantages faced by
immigrant children reduces, and even disappears for some countries, once parental
background characteristics are controlled for. A foreign language spoken at home is
the single most important factor associated with the achievement gap. Studying
second generation immigrants from minority groups in Britain, Dustmann et al.
(2011) find that British born ethnic minorities, despite their initial education
disadvantage, perform well in terms of their educational achievements, catching up
continuously throughout the British compulsory school system, and achieving higher
shares of college education than their British born white peers. We should note,
however that there is a considerable heterogeneity between the different minority
groups. Duncan and Trejo (2011) compare the outcomes of children from mixednationality and foreign families, but do not answer a question as to how early, if at all,
potential performance gap emerges.
These studies however, consider outcomes of growing up second-generation
immigrants and past the early childhood stage. Reardon and Galindo (2009) look at
development of cognitive and non-cognitive skills of Latino pre-schoolers in the U.S.,
7
and find that students with Mexican and Central American origins, particularly first
and second-generation immigrants and those from homes where English is not
spoken, have the lowest maths and reading skill levels at nursery entry but show the
greatest achievement gains in the early years of schooling. Clifton-Sprigg (2015)
presents evidence of early life performance gaps between children in foreign/bilingual
and native families, using data for Scotland. Overall, children perform comparably on
an array of measures, including cognitive (picture similarities), non-cognitive
(strength and difficulties questionnaire) and motor development. Where the difference
do emerge (vocabulary naming, speech assessment), the outcomes are likely to be
related to speech and linguistic skills. The author highlights that bilingual families are
heterogeneous group and children with two foreign-born parents are at a particular
disadvantage at this early age. Clifton-Sprigg (2015), however, does not show a
causal effects and the implications are more likely qualitative. Given the unobserved
heterogeneity among children, which is crucial for their performance and correlated
with the included covariates, a caution is needed when drawing conclusions. Further,
there is a potential to selection issues. Amongst those who emigrate, there is a
propensity to intermarry, thus forming mixed families. This positive selection may
lead to bias as children of more educated parents are likely to perform better, which
would close the gap between the mixed and native children.
An important contribution of this research is the connection between the level
of household income, child development (Blau (1999), Dahl and Lochner (2012)) and
foreign family structure. Hart and Risley (1995) measure the language environment
children were exposed to up to age 36 months and document that children of
professional parents exhibited superior language development throughout the period
of study. Specifically, the authors find that the children of welfare parents heard about
600 words per hour, whereas the children of professional parents heard almost twice
as many words in the same amount of time. Rowe (2008) concludes that poor and
uneducated women were simply unaware that it was important to talk to their
babies.15 This is persuasive evidence that beliefs about the technology of skill
formation are correlated with investment choices (Cunha, 2013). Dickerson and Popli
(2016) use the UK Millennium Cohort study data and find that the cognitive
15
The study indicates that child-directed speech relates to socio-economic status as measured by
income and education, and the relation between socio-economic status and child-directed speech is
mediated by parental knowledge of child development.
8
development test scores at age 7 years are almost 2 percentile ranks lower for children
who are persistently in poverty throughout their early years, when compared to
children who have never experienced poverty.16
However, a higher level of family income does not necessarily indicate a
higher level of family resources being devoted to children (Del Boca et al., 2014).
Differences in human capital at birth may lead to different investment by parents
(Cuhna and Heckman, 2010). Cuhna and Heckman (2010) quantify the importance of
four main determinants of early investment in children, namely the budget constraints
that parents face, differences in the child's characteristics, differences in beliefs about
the technology of skill formation, and differences in preferences. The authors argue
that this quantification is important because the different channels have distinct
implications about what public interventions should be implemented to foster human
capital formation. They find that heterogeneity in parental preferences and beliefs
plays an important role in explaining the gap in early investment. In the UK, a number
of other studies using the Millennium Cohort Study have shown that parental inputs
plays a significant role in explaining child development.17 Ermisch (2008), for
example, shows that much of the difference in child development (at age of 3) by
parent's socio-economic status can be explained by parental style and educational
activities.
Our paper differs from reviewed studies in some important aspects. First, in
our analysis we focus on the early years of children's development, as reflected in
their cognitive development by addressing some key empirical issues such as
measurement error and endogeneity of home environmental parental and English
language inputs. Second, we estimate the production functions of the child in a more
complex structural approach that attempts to estimate the entire dynamic process of
child development. We consider a longer time horizons by examine children's
cognitive development at age of 3, 5, 7 and 11 years. This allows us to include a
period when the children have been attending school. To facilitate the presentation
and discussion, those years are divided into two broad periods: early childhood (ages
3 to 7) and middle childhood (age of 11). Children’s cognitive development during
both periods is driven by different inputs.
16
It has been documented in the literature, however, that poverty alone does not explain variation in
educational outcomes or behavioural patterns of immigrant children (Rumbaut, 1995).
17
See Ermisch (2008), Kiernan and Huerta (2008), Hernandez Alava and Popli (2013), Schoon et al.
(2012).
9
Furthermore, skill formation is a dynamic process with some important features
such as self-productivity; the skills produced at one stage augment the skills attained
at later stages (Cuhna and Heckman, 2008). We test the notions of self-productivity in
the transition from early to middle childhood. It is also highlighted that bilingualism
on its own is unlikely to fully explain the differences in performance between native
and non-English origin children.18 Immigrant families differ from each other and, it is
expected that performance of bilingual children to differ from monolingual children
partly because of the different environment they are growing up in.
3. The Development of child Cognitive skills
This section develops the model that serves as the basis of our empirical
analysis. Building on the theoretical work proposed by Cunha (2013), Cunha and
Heckman (2008), Cuhna et al. (2006), Cinha and Schennach (2010), Attanasio (2015),
and Attanasio et al. (2015), we consider human capital formation (production
function) as a multi-dimensional process that starts very early in life with the birth of
a child. We consider migrant families are bound to be different in many respects, not
just the fact that two languages are spoken at home.19
To set up the idea we define the child life cycle as constituting of distinct time
periods indexed by t, not necessarily equivalent to a year. More formally, let ��
represents a stock of latent cognitive developmental of the child in period t.
18
Baker (2011) provides an extensive overview of the impact of bilingualism on cognitive outcomes in
children reflecting mainly ideas from sociological and linguistic literature. However, the linguistic
studies are usually based on experimental runs on relatively selected samples since participation is
voluntary.
19
With the respect of the mechanism through which the bilingualism operates in child cognitive skills
formation, it could be both different levels of family language inputs that are combined with different
production functions. These two alternatives are not mutually exclusive and it is not possible to
separately identify them in a model in which both were allowed. We expect that the migrant children
have particular environments that may be associated with low SES, constrained early learning
opportunities, parents who have experienced their own educational difficulties and this limits responses
to the cognitive skill tests assessment. Immigrants also differ in their ability or efficiency in acquiring
the destination language. This ability is shaped by cognitive ability, education that might be influenced
by selection processes in migration. A major factor influencing the ability to learn new languages is the
age at arrival, given that this determines the ability to acquire the new language according to the
linguistically based critical period hypothesis discussed earlier. Immigrants arriving in young ages
before this critical period in early adolescence pick up the destination language almost effortlessly and
reach a near native level of proficiency (Isphording, 2014). Some early studies have documented that
mother tongue development facilitates the acquisition of second language, and thus argue that the first
step in learning English should be mastery of the mother tongue (Cropley, 1983). These authors explain
that poor immigrant children are more likely to receive limited linguistic support at home, and
therefore need more support in school to acquire the mother tongue.
10
Childhood developmental state evolves over time according to the following dynamic
process:
t=1,2,…T-1
�!!! = �! �! + �� �! + �! �! + �� �� + �!
(1)
where �! is a (�×1) latent vector representing the parental investment at time t
towards the development of the child. The model allows for the possibility that more
than one latent factor underlines parental investment. Parental investment
encompasses any activities parents involve in with the children related to home
environment and stimulation - educational, physical and social.20 This investment may
be result of conscious choices parents make to ensure a child's development. Parents
make investments in child development from the first period, t=1, through the last
development period t+1. Specifically, investment at age 9 months is measured using
the mother's attitudes toward child rearing. Responses to four questions about the
importance for development of talking to the baby, cuddling the baby, stimulating the
baby and having regular sleeping and eating time are used. Investment at age 3 is
measured using a series of activities providing learning opportunities at that age:
frequencies of reading to the child, visits to the library, help with the alphabet,
numbers/counting, learning songs, poems and rhymes, drawing and painting. At ages
5 and 7, they are asked similar questions but the wording of some questions changes
in order to reflect the developmental stage of the child. �! , �! , �! , and �� contain
time-varying coefficients to be estimated; �� is a matrix of observed variables
representing the child's current socio-economic environment, poverty being one such
covariate; and �! is the error term assumed to be independent over time for the same
individual with the contemporaneous matrix
!
!!
The relationship in equation (1) allows for a cumulative effect of parental
investment, with past investment accumulated into the current development period
and new investment affecting development into the next period. The latent vector of
parental investment at time t is also a function of a matrix of observable covariates �!! :
�! = �!! �!! + �!! , t=1,2,…T-2
20
Certain skills, such a socio-emotional skills, accumulated in the first five years of life are found to be
key to the accumulation of cognitive skills in subsequent periods (see for instance, Duckworth and
Selingman (2005)).
11
where �!! �!! is matrix of coefficients and �!! are random errors independent across
individuals and over time. The following equation for the initial period is assumed:
�! = �! �! + �
�! = �!! �!! + �!!
where the matrices �! and �!! include variables representing family background and
circumstances. These two matrices do not necessarily contain the same set of
covariates; � is the random error with covariance matrix
!!.
An important feature
of the model is the self-productivity - the skills produced at one stage augment the
skills attained at later stages (Cunha, 2010).21
Specifically, anticipating the structure of the data available for the MCS, children
observed at ages 3, 5, 7 and 11, for a child i at period t=1 equation (1) will be as:
�! = �!! �! + �!" �! + �!" �! + �!" ��� + �! . In our data we do not have specific
measures to identify separately the initial endowments �! and initial parental inputs in
the child i, �! , and hence we assume that these together depend in a linear fashion on
a set of covariates �! . Therefore, for time t=1 we estimate the following model:
�! = �!! �! + �!" ��� + �!
Between any two periods, the child's cognitive skills will change as a result of several
main inputs: initial starting developmental conditions �!,! 22; the current language
home environment �! ; the past stock of cognitive skills �!!! , the past parental
investment �!!! , which depends on some exogenous covariates �!! .23
21
The presence of lagged values of the factors in the human capital production function makes the
process dynamic and, in the presence of complementarities among different arguments, can create
opportunities for investment in certain periods particularly important for future development. Todd and
Wolpin (2003) propose to take the first differences of a linear specification (1) in order to capture the
unobserved genetic endowment with which a child is born.
22
To control for differences in the starting developmental position of children, we use child’s birth
weight, the age of the mother at birth and mother’s level of education. Parental stock of human capital
is assumed to be fixed at the first period levels.
23
Cunha (2013) proposes the importance of four determinants of early child investments, defined as
heterogeneity in family budget constraints, differences in maternal preferences, heterogeneity in beliefs
about the technology of skill formation, and heterogeneity in human capital at birth.
12
Measurement model
As both child ability and parental investment are latent variables and cannot be
observed directly, we have a measurement error (Cunha and Heckman, 2008).24 We
try to reduce the array of observable measures to low dimensional constructs using
factor models.25 In this way, the model takes into account measurement error and does
not impose an ad hoc combination of the measures; it rather allows the parameters to
be freely estimated (Hernandez Alava and Popli, 2013).26 The measurement system is
given as:
!
!
!
!
= �!,!
+ �!,!
�! + �!,!
�!,!
!
!
!
�!,!! = �!,!
+ �!,!
�! + �!,!
!
where �!,!
for � ∈ �, � and � ∈ 1, … �!! are the measures that are available for the
latent cognitive ability and latent parental input at time t; �!! are numbers of measures
!
that are available, such as �!! ≥ 2; �!,!
are the factor loadings which can be
!
interpreted as the amount of information that the measures �!,!
contain about the latent
variables �! and �! , and their relative magnitude allows to understand to what extent
!
an observed indicator is driven by the latent factor; �!,!
are the measurement errors,
which capture the difference between the observed measures and the unobserved
!
latent variables; �!,!
can depend on regressors as long as they are independent of the
!
latent variables �! and �! and the error term �!,!
.
Endogeneity
Enodgeneity of speaking a foreign language and parental inputs are issues, which
clearly pose a problem for the empirical identification of the parameters. We can think
of reverse causation where parents observe some aspect of child's current ability and
this would affect their investment decision, so that �! can be expected to impact �! .
24
What we observe are child's test scores which are correlated with latent cognitive ability, and
measured with an error.
25
To mitigate the problem we can use multiple tests at each age to estimate the latent cognitive ability
of the child, and in a similar way numerous proxies are available in our data which are related to the
latent parental investment in the child.
26
In the literature, the observed indicators are often combined in indices. For example, the Home
Learning Environment index designed by (Bradley and Caldway, 1980), obtained from a summation of
a series of activities has been used extensively in the literature; see Todd and Wolpin (2003). However,
the indicators are often measured with error.
13
Parental decision-making is a complex process, and several factors, such as available
resources, mother labour supply possibilities and beliefs about optimal parental
practices, interact to determine them. Importantly, parents often have to make
decisions to allocate resources among several children (Del Boca et al., 2014). In
equation (1) using lagged parental investment, �!!! , to explain child's current
cognitive ability, �! , should solve the issue of reverse causation. We have a dynamic
model where �!!! impacts �! and, if the inputs are endogenous, then �!!! can also
impact �!!! , which will then violate the assumption that �! is independent of �! . $. To
address the issue of endogeneity of inputs we specify a parental investment function:
�! = �!! �! + �!! �!! + �!! �! + �!
where �! is the normal error term that is orthogonal to (�! , �!! , �! ) and we assume that
there is at least one such variable �! that impacts parental investment but not the
ability of the child. One possible way to interpret �! is that it reflects the family
resources or constraints that limit the ability of the parents to invest in their children
but do not have a direct effect on a child's ability, although we recognize that it may
be difficult to find a variable which satisfies this exclusion restriction. Cuhna et al.
(2010) discuss in details the justification of the investment function given by the last
equation; they further suggest that to estimate that equation we can use two-stage least
squares where the past values of �! are used as proxies for �! .
To address the issue of endogeneity of language spoken at home, a two stage
least square (2SLS) estimation approach is applied.27 We instrument for our measure
of non-Englsih language spoken at home by exploiting variation in the immigrant’s
language distance to the UK. Following Dustman and Fabbri (2003), we highlight that
the cost of acquiring the host country language depends on the distance of the
migrants’ mother tongue from the dominant majority language, in our case English.
We use a measure of linguistic proximity between country of origin and the UK as
developed in Adserà and Pytliková (2015) and based on information from the
27
Assume for the moment that the language variable is measured without error. Then the problem is
that those individuals who have chosen to obtain proficiency in the English language and speak it at
home may differ from those individuals who have chosen not to do so. If these differences affect
outcomes (in our case, children’s cognitive skills) other than through language, a comparison in
outcomes of the two groups does not produce an unbiased estimate of the causal effect of the language.
14
encyclopaedia of languages Ethnologue (Lewis, 2009) to capture this variation. In our
sample, the index ranges from 0 (when the two languages are the same) to a
maximum of 0.99 (for the distance between Arabic and English languages).28
Moreover, those parents who migrate at younger age should have a higher incentive to
acquire language capital; therefore year of arrival is a relevant variable included in all
specifications. The first stage equation in the 2SLS approach has a non-English
language spoken at home as the dependent variable for a child i:
�! = �! + �! �! + �! �! + �!!
where �! is exogenous instrument, defined as an interaction effect between the year in
which child’s parent arrived in the UK and the linguistic distance index, �! is a vector
of individual characteristics.
4. The Data and Descriptive analysis
The data used in this analysis come from the UK Millennium Cohort Study
(MCS) following a large sample of around 19,000 babies born in 2000-2001. The
study has been tracking the Millennium children through their early childhood years
and collects information on diverse aspects of their lives, including behaviour,
cognitive development, health, schooling, housing and parents’ employment and
education, income and poverty; housing, neighbourhood and residential mobility; and
social capital and ethnicity.29 The five surveys of cohort members conducted so far –
at ages 9 months and 3, 5, 7 and 11 years – have built up a uniquely detailed portrait
of children's development.30
Identify migrant children
We use information on parents’ place of birth and language in the home to categorize
children at each wave into the following three mutually exclusive language
categories: non-English speaking children that use mainly foreign language at home
and at least one parent born in a foreign country; children who speak about half
28
We have information on the language spoken at home.
The data are collected via both direct interview and by self-completion. For the sample analysed in
this paper, 98% of the main respondents are biological mothers or fathers of the children.
30
The first sweep took place in 2001-2002 when these babies were, on average, around 9 months old.
The second sweep took place when the children were around 3 years old, whereas the third sweep was
administered when the children had reached age 5 years and had started school. Finally, the forth and
the fifth sweeps were undertaken in 2008 and 2012 when the children were 7 and 11 years old
respectively. The sample sizes at each sweep of data collection are presented in Appendix Table 1.
29
15
English and half other language at home and at least one parent born in a foreign
country; and all co-resident parents are native-born and the children speak the official
language English at home (native speakers). The first category is our 'treatment' group
and the second is our 'control' group. The last category is omitted from the OLS and
2SLS analysis, because these children are not exposed to the language setting.
Cognitive test scores
A wide range of cognitive ability tests are used in the MCS data and the measures
described below correspond to Yt as defined in our theoretical model. Cognitive
ability is assumed to be latent, and the test scores defined bellows are used as
measures for it. Cognitive ability of a child at age 9 months is captured using the
Denver Development Screening Test (DDST), which is an assessment widely used for
examining the development of children from birth until age 6 years (Frankenburg and
Dodds, 1967).31 The test assesses children on 125 items grouped into four different
areas. The MCS uses a subset of the items covering three areas: Fine motor
functioning: eye/hand co-ordination, and manipulation of small objects; Gross motor
functioning: motor control, e.g. sitting, walking, standing and other movements; and
Communicative gestures: (Dex and Joshi, 2004). Following Dickerson and Popli
(2016) we classify a child as having a delay in a particular functioning if he or she
cannot perform a task that 90% of the children of their age can do. The classification
is based on answers from the main respondent of the survey.
The data also records several standard tests of cognitive development at ages 3,
5, 7 and 11 years, administrated to the children themselves. We focus on the children's
performance across all of these tests since each of them reflect different cognitive
abilities and educational performance. The British Ability Scales (BAS) are a set of
standard age-appropriate individually administered tests of cognitive abilities and
educational achievements suitable for use with children and adolescents aged from 2
years 6 months to 7 years 11 months.32 Six different BAS tests have been
administrated across the MCS sweeps. The BAS Naming Vocabulary (BAS-NV) is a
31
It is difficult to measure cognitive development at that early age since there are no tests for cognitive
ability for children that young (Dickerson and Popli, 2016). We can only measure their development,
i.e. the physiological and psychological functioning, and whether they have reached particular agespecific development that most children at that age can do. However, it might be argued that the items
in the DDST might be capturing other concepts, not just cognitive development.
32
Hansen (2010) provides the relevant information on this subsection.
16
verbal scale, which assesses spoken vocabulary.33 This test was administrated to the
children at ages 3 and 5 years. In the BAS Pattern Construction test (BAS-PC), the
child constructs a design by putting together flat squares or solid cubes with black and
yellow patterns to each side. The child score is based on both speed and accuracy in
the task. All the raw scores are adjusted using a set of standard adjustment tables to
take account of the age of the child and the difficulty of the item set administrated.
This test was carried out at ages 5 and 7 years. The BAS Picture Similarity test (BASPS) measures children’s pictorial reasoning and problem solving abilities. In the BAS
Word Reading test (BAS-WR), children read aloud a series of words presented on a
card, and this assessment was administrated to the children when they were 7 years
old. In addition to the six BAS-based tests, two further tests were administrated. First,
the Bracken School Readiness Assessment (BSRA) is used to assess the conceptual
development of young children across a wide range of categories (see Bracken, 2002)
Second, at age 7, children's numerical and analytical skills were assessed using a
variant of the National Foundation for Educational Research standard Progress in
Maths (PiM) test in which a range of tasks covering number, shape, space, measures
and data are assessed.
Following Dickerson and Popli (2016), for each of these tests, we use the agestandardized scores and construct the child's percentile ranking across all children in
the MCS who completed the test and we consider the differences in scale and
dispersion between the tests. The percentile rankings record on a scale of 0-100 the
percentage of children in the sample completing the test who are ranked below the
child's score. Thus a child's ranking of 90 on a particular test indicates that 90% of
children scored lower in the test; the child is thus in the top 10% of the specific test
score distribution. Percentile rankings provide a convenient metric against which to
record the influence of being bilingual on the different cognitive skills that are
assessed in each of the tests. Descriptive Table 1 in Appendix shows the average
scores for children defined as native and non-English speaker across these tests.
At age 11, new measures of memory, strategic thinking, decision making and
risk taking were introduced. Combined, these measures provide a comprehensive
33
The Naming Vocabulary scores reflect expressive language skills; vocabulary knowledge of nouns;
ability to attach verbal labels to pictures; general knowledge; general language development; retrieval
of names from long-term memory; and level of language stimulation.
17
picture of the children’s cognitive development at this age.34 The Cambridge
Gambling Task (CGT) measures risk-taking behaviour and decision-making under
uncertainty.35 They were given scores for the quality of their decisions (that is, how
often they chose the more likely option); for the time taken them to choose a colour;
for their impulsiveness in bets placing; for their risk aversion and risk adjustment (that
is, whether they adjusted their bets based on the likelihood they would be right).
Specifically, we focus on the deliberation time taken to perform the test as a measure
of risk taking indicating the children's latencies in making a choice response on which
colour to bet upon; delay aversion, risk adjustment and risk taking. Children's
memory and problem-solving ability were tested for the first time adapting
Cambridge Neuropsychological Test Automated Battery (CANTAB) Spatial Working
Memory Task (SWM). In this computer-based assessment, the child is asked to find
tokens hidden in boxes, and scored on their ability to do so quickly, strategically and
without error.36 Although it is sensitive to spatial working memory capacity it is also
thought to be measure executive functioning. The key outcomes of this test used in
this paper are the total errors, time taken until last response and strategy. In the case of
these tree variables, higher scores are indicative of worse performance.
Home input measures and parental investment
Parental investment at 9 months is measured using the mother's attitudes toward child
rearing. Responses to four questions about the importance for development of talking
to the baby, cuddling the baby, stimulating the baby and having regular sleeping and
eating time for the baby are used. To obtain a measure of parental home environment
investment, we follow Melhuish et al. (2008)37 and compute a summative index 34
Specifically, the cohort members completed an assessment of their verbal reasoning and knowledge.
They were read sets of words and asked to say how the words were related. Each child was given a
total score based on how many questions he or she answered correctly. The scores took into account
their age and the difficulty of the set of questions they answered. Their scores ranged from 20 to 80
points.
35
Children were asked to bet points on whether a yellow token was under a red or blue box.
36
There are 12 trials, starting off with four boxes, progressing to six and finally eight boxes. Each trial
consists of a number of turns (four, six or eight – depending on the number of boxes). Within each trial
the token is hidden under a different box at each turn. During each turn, the child must remember not to
open a box they have previously found to be empty. Over the course of each trial, the child must
remember not open a box in which they found a token on a previous turn. The children were given
scores based on how many mistakes they made, their use of strategy to find the tokens, and how long it
took them to complete each trial.
37
This measure originates in the work of Bradley and Caldwell (1984), Bradley and Caldwell (1980)
and is used to describe child's home environment. Cuhna (2013) and Todd and Wolpin (2003) use the
18
Home Learning Environment Index (HLI) that categorises some home activities
providing learning opportunities at age of 3, 5 and 7 years.
Other covariates
To control for differences in the starting developmental position of children, we use
birth weight, the age of the mother at birth, level of education of the mother, mother's
locus of control and self-esteem and poverty status.38 The measurement error model
equations for cognitive ability include the age of the child at the time assessment was
made in all time periods. Other variables included in the cognitive measurement
equation at 3, 5 and 7 years are ethnic background.
Descriptive Analysis
We start by comparing performance of the two groups without conditioning on any
covariates, to identify whether their outcomes differ. Appendix Table 1 provides the
descriptive statistics of the measures of cognitive skills and investments used in this
paper for the treatment and control groups. Children who do not speak English at
home score much lower than children who speak half English in Bracken school
readiness test and Naming Vocabulary exercise at both age 3 and 5, and the same can
be said about the Picture Similarities scores measured at age 5. The gap between these
two groups is significant at the age of 3 but the outcomes tend to equalise with age.
5. Results
We start the analysis comparing the cognitive outcomes of migrant with the native
children and further narrow the analysis by comparing the outcomes of children who
do not speak English at home (treatment group) with those who speak half English
and half other language (control group). Finally, we present the results of the main
structural dynamic latent variable equation models and addressing the issue of
measurement error assuming that both children’s cognitive ability and parental
components of the 'Home Score' measure to proxy parental investment. Dearden et al. (2011) construct
a similar index and divide the HLE index into five equally-sized quintiles.
38
Birth weight is included as a proxy for genetic endowment (Del Bono et al., 2012), and mother's age
and education are included to capture any disadvantage that the child might face (Hernandez Alava and
Popli, 2013).
19
investment in the child are latent variables. The results from the OLS regression of
various outcomes on the language and family composition, controlling for poverty
status, parental activity, ethnicity of the child are reported in Appendix tables 2 to 5.
Mother’s education at birth is included to capture the finding in the literature that
educated parents, especially mothers, tend to systematically spend more time with
their child (Guryan et al. 2005). Table 6 presents the parameters of the structural
dynamic equation model.
5.1. OLS and 2SLS
In Tables 2 and 3, columns 1 and 4 show the results using OLS, and columns 3 and 5
show the results using 2SLS. The OLS results suggest that at age of 3, compared to a
child who speaks half English and half other language, a child who does not speak
English at home on average tend to score lower in both School Readiness and BASNaming Vocabulary tests. In particular, the child’s School Readiness and BASNaming Vocabulary at age of 3 years is expected to be 0.058 standard deviations
(SDs) and 0.079-SDs, respectively below the cognitive scores of a child who speaks
half English and half other language. A child who has been in poverty at birth can be
expected to be 0.085-SDs below the School Readiness score of the child who has
never been in poverty. Also, higher mother’s age at the time of birth, having mother
with higher qualification, and being white are all associated with higher development
at age of 3 years. At age of 5, children who do not speak English at home continue to
score on average lower in the BAS-Naming Vocabulary test than children who speak
half English and half other language at home. The results suggest that a child from
non-English language spoken at home scores 0.057 lower in the test than a child who
speaks half English and half other language (Table 3). This may be suggestive that
these children continue to fall behind at age of 5. We find evidence of selfproductivity - cognitive skill at age of 5, as measured by the BAS-Naming
Vocabulary test, is predicted significantly by cognitive skills accumulated up to the
age of 3. This finding is consistent with Cunha and Heckman (2008) and Dickerson
and Popli (2016). The magnitude of the self-productivity coefficients remains
virtually unchanged in the other cognitive outcomes – BAS-Picture Similarity and
Pattern Construction. However, the coefficient on English language dummy indicator
became insignificant in the Picture similarities and Pattern Construction tests
20
measured at age of 5. At age of 7 and 11 we only report the OLS estimates as the
Durbin-Watson test statistics are found insignificant; we fail to reject the null
hypothesis and consider the OLS estimates as consistent.
The coefficient of linguistic distance interacted with the year of arrival in the
model with non-English spoken at home as an outcome in Tables 2 and 3 column (2),
our first-stage specification for the rest of the article, is positive and it is highly
significant at 1%. It implies that emigration flows to the UK with the most distant
language should be more likely to speak language other than English.
5.2. Structural latent development variable equations
Table 6 presents the parameter estimates of �� , �� and �� of the dynamic equation (1).
At age 3 years, a child who is exposed to two languages is found to lag behind in
cognitive development when compared to native children. Specifically, a migrant
child is expected to be 0.124-SDs below the latent cognitive ability score of a native
speaker child. Interesting, the parameter of interest has changed to a positive and
significant effect on a child’s latent cognitive ability at all ages after. At age of 5, a
migrant child can be expected to be 0.0405-SDs above the latent cognitive
development of a native speaker child and the effect tends to increase gradually with
age. There is a significant autoregressive effect in children’s cognitive development –
higher levels of cognitive development foster higher levels of development in future
periods. For instance, a 1-SD higher latent cognitive ability at age of 3 years is
associated with 0.853-SD higher latent ability at age of 7 years, equivalent to 22
percentile ranks.39 Lagged parental investment �!!! is a significant determinant of
future cognitive development. From Table 3, if latent parental investment at age of 3
years increases by 1-SD, then the child’s cognitive ability at age 5 years would
increase by 0.4362-SDs, which is equivalent to an increase of 11 percentile ranks.
Interestingly, the parental investment diminishes with child’s age (if parental
investment at age of 5 years increases by 1-SD, then child’s cognitive ability at age 7
years would increase by 0.1446-SDs (equivalent to an increase of 4 percentile ranks).
39
The percentile rank changes are calculated by multiplying the observed SD changes in the latent
variable by the SD of the underlying measures; all the test scores have an SD of around 26 (see
Appendix descriptive table).
21
This might be due to the fact that children start school and the value of school
dominates the parental efforts.
5.3. Measurement equation- parental investment
Table 7 reports the parameters of the latent parental investment measurement
equations at different ages. The signs are as expected. The probability of strongly
agreeing with the importance of talking, stimulating, cuddling and having regular
sleeping and feeding times increase for higher levels of the underlying latent
variable.40 The largest loading is on the importance of talking to the baby. At age of 3
and 5 years old, we control more fully for parental investment. We find that at age of
3, the largest factor loading is in the frequency with which mother reads to the chid.
By the age of 5, the frequency the mother reads to the child is much smaller in relative
terms and the two largest factor loadings were the frequency in helping with writing
and maths.
6. Conclusion
This paper uses longitudinal data from the Millennium Cohort Study to estimate a
dynamic structural model of migrant child development in the UK using the
framework of Cuhna and Heckman (2008). We show that migrant children lag behind
the native children at age of 3 but they catch up by the time they are 5 years old and
by age of 7 they actually have higher cognitive development scores. We find
significant evidence of self-productive effect in children’s cognitive development –
higher levels of cognitive development at time t foster higher levels of cognitive
development at age t+1. Parental investment is found to significantly increase the
cognitive ability of children, but this declines as children enter formal schooling.41
This finding suggests that efforts to promote assimilation of migrant children should
concentrate towards the home environment in the very early years and in particular to
concentrate on the changes in parental investment at different development stages.
40
We reversed the attitudes variables measured at 9 months and coded as discrete values ranging from
0=strongly disagree to 4 = strongly agree.
41
The first year of compulsory education in the UK is form the age of 5.
22
23
Table 1: Unweighted descriptive statistics for the variable used in the analysis
Non-English at home
Mean
SD
Half English& half other
Mean
Measures of cognitive ability:
Gross motor development (=1 if delay)
0.211
0.408
0.153
Fine motor development delay (=1 if delay)
0.194
0.396
0.142
Communicative gestures develop (=1 if delay)
0.423
0.494
0.406
Bracken school readiness, age of 3
27.070
26.431
38.531
BAS-Naming Vocabulary, age of 3
15.820
20.027
28.671
BAS-Naming Vocabulary, age of 5
20.228
22.853
29.071
BAS-Picture Similarity, age of 5
44.820
29.983
46.498
BAS-Pattern Construction, age of 5
40.890
27.947
42.229
BAS-Pattern Construction, age of 7
38.676
28.146
43.089
BAS-Word Reading ability score, age of 7
49.399
29.538
53.563
Math score, age of 7
41.875
29.793
46.699
Verbal Sims standard score, age of 11
55.865
10.700
57.323
Deliberate time, age11
53.474
21.156
55.047
Risk taking, age 11
0.569
0.164
0.546
Risk adjustment, age 11
0.477
0.929
0.560
Delay aversion, age 11
0.289
0.263
0.289
SWM: Total error, age 11
40.259
20.309
35.998
SWM: Strategy, age 11
35.226
5.562
34.551
SWM time, age 11
500.678
127.777
486.194
Measure of parental investment and style:
Importance of simulating the baby
0.583
0.616
0.495
Importance of talking to baby
0.343
0.494
0.268
Importance of cuddling baby
0.299
0.478
0.228
Importance of regular sleeping/eating for baby
0.785
0.855
0.697
Home learning environment index (HLE) age of 3
22.374
9.206
25.519
Home learning environment index (HLE) age of 5
24.155
12.696
23.695
Initial conditions measured at age of 9 months:
Child ethnic background (=1 if white)
0.178
0.383
0.235
Birth weight (kg)
1.953
1.126
1.743
Mother's age at birth
27.785
5.534
28.655
Mother's highest academic qualification measured at child's birth
Higher degree
0.026
0.159
0.065
First degree
0.093
0.290
0.131
Diplomas in higher education
0.033
0.178
0.059
A- level ( A / AS / S levels)
0.074
0.261
0.087
O - level (GCSE grades A-G)
0.187
0.390
0.249
Other academic qualifications
0.129
0.336
0.115
No qualification
0.459
0.499
0.294
Mother in work, measured at age of 7
0.340
0.474
0.478
Partner in work, measured at age of 7
0.711
0.454
0.766
Below 60% of the median UK household income:
At 9 months
0.651
0.477
0.488
At age of 3
0.609
0.488
0.477
At age of 5
0.623
0.485
0.481
At age of 7
0.620
0.486
0.462
SD
0.360
0.349
0.491
30.192
27.073
26.240
29.328
27.851
29.188
28.591
30.473
11.298
21.511
0.173
0.989
0.262
19.071
6.164
97.383
0.623
0.502
0.501
0.762
8.797
12.076
0.424
1.087
5.592
0.246
0.338
0.236
0.282
0.432
0.319
0.456
0.500
0.423
0.500
0.500
0.500
0.499
24
Table 2: Cognitive abilities at age 3 and non-English language spoken at home
Non-English spoken at home
Gross motor development delayt-1
Fine motor development delayt-1
Communication gesture delayt-1
White
Birth weight
Child's age in months
Mother's age at birth
Number of siblings
Higher degree
First degree
Higher Diploma
A-level
O-level
Other qualification
Importance of stimulating babyt-1
Importance of talking to babyt-1
Importance of cuddling babyt-1
Importance of regular sleep/feed t-1
Poverty t-1
Poverty t
Year of arrival
School Readiness
(OLS)
First-stage
School Readiness
(IV)
BAS-NV
(OLS)
BAS-NV
(IV)
-0.057***
(-3.61)
-0.083***
(-4.55)
0.025
(1.13)
-0.005
(-0.35)
0.070***
(4.00)
-0.006
(-0.93)
0.001
(1.11)
0.006***
(4.15)
-0.034***
(-4.80)
0.151***
(4.61)
0.154***
(5.86)
0.126***
(3.81)
0.041
(1.60)
0.029
(1.44)
0.064**
(2.43)
-0.006
(-0.50)
0.023
(1.36)
0.015
(0.92)
-0.026***
(-2.67)
-0.085***
(-4.95)
-0.025
(-1.49)
-0.000
(-1.61)
-
0.001
(0.01)
-0.086***
(-4.41)
0.023
(1.08)
-0.005
(-0.36)
0.065***
(3.15)
-0.007
(-1.00)
0.001
(1.25)
0.006***
(3.80)
-0.034***
(-4.69)
0.157***
(4.66)
0.155***
(6.19)
0.132***
(3.82)
0.044
(1.58)
0.035
(1.46)
0.071**
(2.32)
-0.008
(-0.59)
0.022
(1.27)
0.012
(0.62)
-0.026***
(-2.74)
-0.087***
(-4.88)
-0.028
(-1.48)
-0.000*
(-1.65)
-0.079***
(-5.87)
-0.058***
(-4.08)
-0.013
(-0.81)
-0.020
(-1.61)
0.155***
(9.35)
-0.012**
(-2.12)
-0.000
(-0.02)
0.005***
(3.73)
-0.015**
(-2.44)
0.142***
(4.80)
0.130***
(6.13)
0.159***
(5.52)
0.089***
(4.03)
0.047***
(3.01)
0.052**
(2.55)
0.005
(0.47)
0.012
(0.82)
-0.018
(-1.27)
-0.014*
(-1.72)
-0.031**
(-2.09)
-0.010
(-0.63)
-0.000**
(-2.57)
-0.105
(-0.93)
-0.057***
(-3.33)
-0.012
(-0.68)
-0.020
(-1.62)
0.157***
(8.68)
-0.012**
(-2.04)
-0.000
(-0.06)
0.005***
(3.14)
-0.015**
(-2.36)
0.140***
(4.70)
0.130***
(5.90)
0.156***
(5.13)
0.088***
(3.60)
0.044**
(2.06)
0.049*
(1.82)
0.006
(0.51)
0.012
(0.80)
-0.016
(-0.99)
-0.015*
(-1.75)
-0.031**
(-1.96)
-0.008
(-0.49)
-0.000**
(-2.31)
1566
0.2454
1566
0.2828
1566
0.2812
Year of arrival*Linguistic distance
N
R2
1566
0.2513
0.041
(1.48)
0.031
(1.01)
0.002
(0.1)
0.086***
(3.33)
0.011
(1.07)
-0.001
(-0.84)
-0.006***
(-2.71)
0.003
(0.23)
-0.077
(-1.65)
0.022
(0.58)
-0.082*
(-1.72)
-0.023
(-0.57)
-0.071*
(-2.32)
-0.115***
(-2.91)
0.038**
(1.99)
0.004
(0.15)
0.040
(1.54)
-0.008
(-0.57)
0.013
(0.47)
0.048*
(1.83)
0.000
(0.29)
0.0002***
(5.16)
1566
0.259
Notes: ***, ** and * denote significance at the 1%, 5% and 10% level respectively. (i) The 2SLS estimates are obtained using the interaction of year of
arrival and linguistic distance as instrument for the endogenous regressor non-English speaking at home. (ii) A test on excluding our potential
instrument from the reduced form equations yields an F-statistics of 26.66*** and partial R2 of 0.0170. (iii) The DWH test is 0.057, p-value=0.810, so
we do not reject the null hypothesis; Parental investment latent variables measured at 9 months are coded as discrete values ranging from 0=strongly
agree; 1=agree; 2=neither agree nor disagree; 3=disagree; 4=strongly disagree;
25
Table 3: Cognitive abilities at age 5 and non-English language spoken at home
Non-English spoken
School readiness t-1
BAS-NV t-1
White
Birth weight
Child's age in months
Mother's age at birth
Number of siblings
Higher degree
First degree
Higher Diploma
A-level
O-level
Other qualification
HLE t-1
Parental style
Poverty t-1
Poverty t
Year of arrival
BAS-NV
(OLS)
First-stage
BAS-NV
(IV)
BAS-PS
(OLS)
BAS-PS
(IV)
BAS-PC
(OLS)
BAS-PC
(IV)
-0.058***
(-3.19)
0.196***
(5.98)
0.317***
(8.80)
0.003
(0.19)
-0.017***
(-2.58)
-0.001*
(-1.85)
0.003
(1.62)
-0.006
(-0.78)
0.136***
(4.49)
0.058**
(2.31)
0.077**
(2.50)
0.081***
(3.32)
0.036*
(1.94)
0.014
(0.60)
0.001
(0.72)
0.015
(0.95)
-0.027
(-1.60)
-0.003
(-0.18)
0.000
(0.43)
-
-0.246
(-1.52)
0.211***
(6.33)
0.293***
(7.41)
0.004
(0.21)
-0.016**
(-2.31)
-0.001*
(-1.88)
0.003*
(1.70)
-0.007
(-0.81)
0.108***
(2.67)
0.038
(1.20)
0.047
(1.11)
0.056
(1.54)
0.003
(0.09)
-0.012
(-0.32)
0.000
(0.12)
-0.024
(-0.65)
-0.036*
(-1.67)
0.006
(0.27)
0.000
(0.62)
0.012
(0.51)
0.194***
(5.00)
-0.040
(-0.96)
0.061***
(2.88)
0.014*
(1.73)
-0.001**
(-2.07)
-0.005***
(-2.60)
0.013
(1.19)
0.053
(1.38)
0.034
(1.06)
0.010
(0.22)
-0.011
(-0.33)
0.026
(0.94)
0.071**
(2.22)
0.003***
(2.86)
0.011
(0.58)
-0.038
(-1.52)
-0.010
(-0.39)
0.000*
(1.73)
-0.245
(-1.21)
0.214***
(5.17)
-0.071
(-1.45)
0.062***
(2.76)
0.016*
(1.85)
-0.001**
(-2.17)
-0.005**
(-2.45)
0.012
(1.13)
0.014
(0.28)
0.006
(0.15)
-0.032
(-0.60)
-0.046
(-1.03)
-0.019
(-0.42)
0.037
(0.82)
0.002*
(1.95)
-0.042
(-0.92)
-0.049*
(-1.87)
0.003
(0.10)
0.000*
(1.90)
0.005
(0.23)
0.230***
(6.49)
0.038
(0.94)
0.066***
(3.02)
0.018**
(2.45)
0.001
(1.04)
-0.004**
(-2.43)
0.023**
(2.23)
0.030
(0.78)
0.069**
(2.11)
0.070*
(1.68)
0.109***
(3.16)
0.087***
(3.24)
0.076**
(2.34)
0.001
(1.01)
0.045**
(2.39)
0.013
(0.56)
-0.018
(-0.75)
0.000***
(2.95)
-0.087
(-0.45)
0.237***
(6.03)
0.026
(0.56)
0.066***
(3.13)
0.019**
(2.30)
0.000
(0.84)
-0.004**
(-2.26)
0.023**
(2.22)
0.016
(0.34)
0.059
(1.56)
0.055
(1.09)
0.096**
(2.26)
0.071*
(1.69)
0.064
(1.49)
0.001
(0.70)
0.026
(0.60)
0.009
(0.37)
-0.014
(-0.56)
0.000***
(2.99)
1090
0.359
1090
0.096
1090
0.160
1090
0.136
1090
0.160
Year*Distance
N
R2
1090
0.410
0.062
(1.33)
-0.1056**
(-2.06)
0.001
(0.03)
0.007
(0.66)
-0.001
(-0.96)
0.001
(0.43)
-0.006
(-0.46)
-0.121**
(-2.49)
-0.081**
(-1.99)
-0.144***
(-2.83)
-0.109***
(-2.55)
-0.142***
(-4.21)
-0.124***
(-2.89)
-0.0026**
(-1.97)
-0.206***
(-9.07)
-0.041
(-1.37)
0.039
(1.32)
0.000
(0.29)
0.00016***
(4.12)
1090
0.160
Notes: ***, ** and * denote significance at the 1%, 5% and 10% level respectively. (i) The 2SLS estimates are obtained using the
interaction of year of arrival and linguistic distance as instrument for the endogenous regressor non-English speaking at home. (ii) A
test on excluding our potential instrument from the reduced form equations yields an F-statistics of 17.00*** and partial R2 of 0.0156.
(iii) The DWH test is 0.239, p-value=0.624, so we do not reject the null hypothesis; Parental investment is measured with Home
Learning Environment index measured at age of 3;
26
Table 4: Cognitive abilities at age 7 and non-English language spoken at home
Non-English spoken at home
BAS-PC t-1
BAS-PS t-1
BAS-NV t-1
White
Birth weight
Child's age in months
Mother's age at birth
Number of siblings
Higher degree
First degree
Higher Diploma
A-level
O-level
Other qualification
HLE t-1
Self regulation
Poverty t-1
Poverty t
Year of arrival
N
R2
BAS-PC
(OLS)
0.070***
(4.91)
0.418***
(17.99)
0.121***
(5.38)
0.160***
(5.91)
0.037**
(2.45)
0.004
(0.69)
0.000
(1.26)
0.000
(0.18)
-0.003
(-0.55)
0.075**
(2.57)
0.085***
(3.60)
0.029
(0.95)
0.081***
(3.47)
0.064***
(3.70)
0.000
(0.02)
0.001
(1.06)
0.051***
(2.96)
0.017
(1.02)
-0.021
(-1.24)
0.000**
(2.25)
1593
0.3696
BAS-WR
(OLS)
0.035**
(2.36)
0.193***
(7.88)
0.054**
(2.25)
0.215***
(7.63)
-0.165***
(-10.03)
0.010
(1.62)
0.001*
(1.65)
0.001
(0.76)
-0.017**
(-2.50)
0.142***
(4.83)
0.053**
(2.14)
0.013
(0.44)
0.094***
(3.98)
0.023
(1.26)
0.086***
(3.47)
0.002***
(3.56)
0.097***
(5.48)
-0.058***
(-3.24)
-0.012
(-0.68)
0.000***
(3.67)
1593
0.2608
Maths
(OLS)
0.056***
(3.72)
0.197***
(7.64)
0.206***
(8.30)
0.212***
(7.20)
-0.054***
(-3.11)
0.016***
(2.60)
-0.000
(-0.44)
0.003**
(2.21)
-0.022***
(-3.18)
0.055*
(1.88)
0.033
(1.27)
0.045
(1.44)
0.104***
(4.23)
0.035*
(1.81)
0.035
(1.48)
0.000
(0.26)
0.056***
(3.20)
-0.001
(-0.06)
-0.060***
(-3.41)
0.000
(0.61)
1593
0.2725
Notes: ***, ** and * denote significance at the 1%, 5% and 10% level respectively.
27
Table 5: Cognitive abilities at age 11 and non-English language spoken at home
Non-Englsih spoken at home
BAS-PC t-1
BAS-WR t-1
Maths t-1
White
Birth weight
Child's age in months
Mother's age at birth
Number of siblings
Higher degree
First degree
Higher Diploma
A-level
O-level
Other qualification
HLE index
Behaviour problem
Support at school
Teacher’s hours spent in Englsih
Poverty t-1
Poverty t
Year of arrival
N
R2
Verbal similarity
(OLS)
0.008
(0.37)
0.098***
(2.63)
0.072*
(1.78)
0.219***
(5.58)
-0.000
(-0.01)
-0.008
(-0.95)
0.000
(0.06)
0.007***
(3.37)
-0.033***
(-3.18)
0.086**
(2.02)
0.083**
(2.19)
0.095*
(1.83)
0.016
(0.42)
-0.013
(-0.50)
0.036
(1.15)
0.001
(0.45)
0.111
(1.22)
-0.072
(-1.53)
0.005*
(1.71)
0.018
(0.73)
-0.111***
(-4.26)
-0.000
(-0.23)
874
0.2856
Risk Adjustment
(OLS)
-0.136*
(-1.76)
0.392***
(2.75)
0.066
(0.42)
0.089
(0.56)
0.017
(0.14)
-0.008
(-0.23)
-0.002
(-1.03)
0.004
(0.55)
-0.037
(-1.01)
0.309*
(1.76)
-0.056
(-0.35)
0.021
(0.11)
0.089
(0.69)
0.083
(0.84)
0.152
(1.08)
0.007
(1.15)
-0.235
(-1.08)
-0.164
(-1.14)
-0.012
(-1.11)
-0.069
(-0.79)
-0.036
(-0.39)
0.000
(0.04)
874
0.0586
Risk Taking
(OLS)
0.029**
(2.00)
0.001
(0.05)
-0.006
(-0.25)
-0.073***
(-2.85)
-0.014
(-0.63)
0.002
(0.30)
0.000
(0.86)
0.001
(0.39)
-0.003
(-0.53)
-0.020
(-0.61)
0.002
(0.10)
-0.008
(-0.26)
-0.008
(-0.34)
-0.015
(-0.91)
-0.007
(-0.34)
-0.001
(-0.97)
0.045
(0.89)
-0.017
(-0.68)
0.002
(1.24)
0.016
(1.11)
0.012
(0.77)
0.000
(0.47)
874
0.0456
Notes: ***, ** and * denote significance at the 1%, 5% and 10% level respectively.
28
Table 6: Parameters estimates of the development dynamic equations
3 years
Migrant child
�!!!
�!!!
�!
�!!!
-0.124***
(0.011)
0.163***
(0.015)
0.125***
(0.011)
-0.212***
(0.010)
-0.195***
(0.010)
Latent Cognitive Development �!
Age of the child
5 years
7 years
11 years
0.0405***
(0.006)
0.8531***
(0.0094)
0.4362***
(0.017)
0.005
(0.0061)
-0.0119*
(0.0062)
0.0902***
(0.0043)
0.9617***
(0.0020)
0.1446***
(0.0073)
-0.0289***
(0.0044)
-0.0173***
(0.0043)
0.112***
(0.012)
0.9434***
(0.0211)
0.1486***
(0.019)
-0.048***
(0.0113)
-0.0211***
(0.0111)
Notes: The table gives the estimates of the structural parameters in equation (1), where latent ability at time
t, �! , is determined by being exposed to two languages early in life, past latent ability �!!! , past parental
investment �!!! , poverty at time t and t-1, and ethnicity of the child. All reported coefficients are
standardized. For the continuous independent variable, the coefficient represents the change in the
dependent variable associated with a 1-SD change in the independent variable. For the binary independent
variables the coefficient represents the change associated with a shift in the variable from 0 to 1. ***, **
and * denote significance at the 1%, 5% and 10% level respectively; standard errors in brackets.
29
Table 7: Estimated parameters of the parental investment measurement equations
Importance of stimulating the baby
Importance of talking to the baby
Importance of cuddling the baby
Importance of regular sleep/feeding time
Frequency mother reads to the child
Frequency child paints/draws at home
Frequency child helped with counting/maths
Frequency child sing songs
Frequency child helped with the alphabet
Frequency child taken to the library
Frequency child helped with writing
Frequency child helped with reading
Frequency mother tell stories to the child
Latent parental investment �!
Age of the child
9 months
3 years
5 years
0.773***
(0.005)
0.785***
(0.005)
0.688***
(0.005)
0.585***
(0.006)
0.966***
0.413***
(0.001)
(0.0104)
0.915***
0.419***
(0.0016)
(0.009)
0.924***
0.620***
(0.002)
(0.008)
0.946***
(0.0011)
0.773***
(0.004)
0.573***
(0.006)
0.688***
(0.008)
0.655***
(0.006)
0.362***
(0.010)
Notes: ***, ** and * denote significance at the 1%, 5% and 10% level respectively; standard errors in brackets.
30
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