The bilingual gap in children's language, emotional, and pro-social development

Bilingualism is a multifaceted phenomenon with no commonly accepted definition. We adopt the perspective proposed by Kohnert (2010), who views bilinguals as “individuals who receive regular input in two or more languages during the most dynamic period of communication development - somewhere between birth and adolescence” (p. 457). We use information pertaining to the language spoken at home to construct a measure of bilingual status.

We assume that a bilingual child who attends full-time school, is given adequate exposure to both English and their other language. Research indicates that when children divide their learning time equally between the two languages, this results in 50% exposure to one language and 50% to the other; thus, the two languages develop like that of monolingual children (Genesee et al., 2004).

Information about the language status of the children constituting our sample is depicted in Figure 1. At age three, 56% of the children are exposed to a foreign language at home; however, by age 14, less than 30% of children continue to be bilingual.

Figure 1

Given our research interests, we focus on a sub-sample of UK born children, for each of whom at least one parent is foreign-born; these are the children most likely to be exposed to multiple languages at home.

Since the entirety of the MCS sample children are born in the UK, all children in our sample are exposed to broadly the same institutional and cultural environment outside of the home. Moreover, restricting the sample to children with at least one foreign-born parent is helpful in reducing any heterogeneity associated with the fact that foreign-born parents may differ from native-born parents in ways that are non-random.

We begin with an analysis by age group that exploits information for these children at every age in relation to which they are observed. We subsequently estimate dynamic models that rely on an unbalanced panel of 9,532 child-wave observations for those children aged three to fourteen for whom we have complete information on the key development measures and additional controls of interest.

To maintain statistical power, in the analysis performed by child's age, we do not restrict our sample to children with non-missing information on all co-variates across all waves. Our unbalanced panel of 9,532 child-wave observations is further reduced to 6,310 observations due to the lag instrumental structure utilized in the GMM approach.

The MCS provides a range of cognitive ability measures which are intended to be administered directly to children. We use age appropriate tests that come from the British Ability Scales (BAS). Our measure of language development comes from a series of tests of verbal reasoning and knowledge, and is constructed using the following assessments: the BAS naming vocabulary test taken at ages three and five; the BAS word reading test taken at age seven; the BAS verbal similarity test taken at age 11; and the BAS word activities test taken at age 14. The naming vocabulary score reflects expressive language skills, vocabulary (knowledge of nouns), ability to attach verbal labels to pictures, retrieval of names from long-term memory, and general level of language development (Hansen et al., 2012). The word reading score assesses English reading ability, while the verbal similarity score assesses verbal reasoning and verbal knowledge. Finally, the word activities assessment score measures the ability of children to understand the meaning of words. For each of these verbal reasoning tests, we use the age-standardized scores. To facilitate interpretation of the results, we transform the outcomes into z-scores. We are unable to consider cognitive outcomes on other cognitive tests (i.e., the school readiness and mathematical reasoning tests) since there are no consistent measures available over time.

The emotional development of children is assessed using the Strength and Difficulties Questionnaire (SDQ) (Goodman, 2001), which is completed by both the main respondents and their partners. It comprises 25 questions encompassing five domains of behavior, namely: i) emotional issues: child complains of headaches, stomach aches/sickness, often seems worried, unhappy, nervous, or clingy in new situations; ii) conduct problems: child often has temper tantrums, fights with or bullies other children, and is often argumentative with adults; iii) hyperactivity: child is restless, over-active, cannot stay still for long, is constantly fidgeting, and is easily distracted; iv) peer problems: child tends to play alone, does not have at least one good friend, is not generally liked by other children, is picked on or bullied by other children, and gets on better with adults; and v) pro-social behavior: child is considerate of others’ feelings, shares readily with others, is helpful if someone is hurt, upset, or ill, and is kind to younger children. Respondents indicate whether each item is “not true”, “somewhat true”, or “certainly true”. Scores from the conduct problems, hyperactivity, emotional symptoms, and peer problems sub-scales are summed to construct a total SDQ score which varies between 0 and 40, with higher scores being indicative of more behavioral and emotional difficulties. Note that we exclude the pro-social behavior from the SDQ index since it is a positive trait and will be examined separately. The absence of pro-social behaviors is conceptually different from the presence of psychological difficulties (Goodman, 2001). Scores of the pro-social sub-scales range from 0 to 10 with a higher score indicating more engagement in pro-social behavior. The SDQ and pro-social scores are expressed as a normalized z-score.

A major advantage of the MCS data is that they include detailed information about socioeconomic characteristics, migration background, and parental inputs. Our socio-economic controls include the child's age, gender, ethnicity, birth weight, number of siblings, and the question of whether their biological mother lives in the household; also included are the mother's age and marital status, parental education levels, region of residence, and the family's poverty status (i.e., income being less than 60% of the median UK income).

This is the official measure of poverty that is reported in the official Households Below Average Income Report (Department for Work and Pension, 2018), and is defined as living in a household with net equivalent income less than 60% of the UK median household income.

There is evidence that the language proficiency of one family member is positively associated with that of other family members, and that children's language proficiency is more highly correlated with maternal, rather than paternal, proficiency (Chiswick et al., 2005). Unfortunately, the MCS does not include measures of parental fluency in English. It does, however, provide information about migrant status, age at (UK) arrival, and country of origin, which may all be correlated with parental language proficiency and, consequently, with the children's propensity to speak English at home. In particular, we control for whether mothers and fathers come from a non-English-speaking country.

We used The World Almanac and Book of Facts (Park, 2005) to determine whether English was an official or predominant language in each country of origin. We classify the following as English-speaking countries: Australia, Canada, Barbados, Bermuda, Dominica, Ethiopia, Ghana, Guyana, Hong Kong, India, Ireland, U.S., Jamaica, Kenya, New Zealand, Nigeria, Saint Lucia, Saint Vincent and the Grenadines, Seychelles, Singapore, Trinidad and Tobago, and Zambia.

In addition, given that the survey provides information on the specific language used at home, such as Cantonese and Arabic, we experiment in constructing a measure indicating the language distance between the home language and English (see Isphording and Otten, 2014 and Isphording, 2015).

Isphording (2015) shows that linguistic barriers caused by language differences play a crucial role in the determination of the destination-country language proficiency of immigrants. The argument is that immigrants face very different costs of language acquisition associated with their linguistic origin. Immigrant children learn English easier and faster if their language of origin is linguistically closer to that of the host country (Isphording and Otten, 2014). Hence, 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 (Dustmann et al., 2003).

Finally, parents’ investments in their children's development are captured in responses to detailed questions regarding the interactions that parents have with their children. Specifically, when children were nine months old, the main respondent was asked how important: i) talking; ii) cuddling; iii) stimulating; and iv) establishing regular sleeping and eating times were for the development of the child. The responses to these questions provide us with an insight into parents’ approach to child rearing in infancy, and we control for this in our cross-sectional analysis at age three. We measure parental investments at older ages using information about how often parents read to their children or take them to the library.

The level and quality of parental investments are usually proxied by the Home Observation Measurement of the Environment (HOME) scores that have been shown to be significantly correlated with later cognitive, health, and non-cognitive development (Todd and Wolpin, 2007; Cunha and Heckman, 2008). Similar constructs are available in our data but they are inconsistently measured over waves and therefore are not used in our analysis.

Table 1 reports the summary statistics of our unstandardized measures of development outcomes, along with other characteristics.

Corresponding information for native-born children is available upon request. Note that the scaling of the unstandardized verbal measure changes across waves, thereby making it not directly comparable across time.

Parental investment at nine months, as measured by mother's attitudes toward child rearing, is significantly different between bilingual and monolingual mothers. Mothers of bilingual infants are more likely to believe that talking to, cuddling, and stimulating their babies and ensuring regular sleeping and feeding habits for infants are important. When bilingual children are aged three to five, mothers score lower on our parental activity measures, whereas, in contrast, when bilingual children are aged seven, parents tend to spend more time reading to their child and visiting the library. These results suggest that there is some variation in parental practices over time.

We first investigate how the bilingual gap evolves from early childhood to adolescence by estimating Eq. (1) separately by age group. These results provide evidence of the way in which the bilingual gap in development evolves as children mature. We report the estimated bilingual gap separately by age, for language, emotional development, and pro-social behavior as measured by the standardized verbal reasoning test scores (Table 2), the SDQ score (Table 3), and the pro-social score (Table 4). We consider three specifications: Panel (A) in Tables 2–4 includes only basic controls (child's age in months, mother's age at birth, and gender and ethnicity); Panel (B) in Tables 2–4 includes the full set of controls, but omits measures of lagged language and emotional development, or pro-social behavior; and Panel (C) in Tables 2–4 reports the results of our cumulative value-added specification that includes lagged development measures along with our full set of controls.

The full set of controls included in Panels (B) and (C) at each age are slightly different depending on data availability but tend to include child's age in months, gender, ethnicity and birth weight, mother's age and marital status, mother's and father's highest qualification measured when the child is nine months old, an indicator for young migrants, non-English speaking background, whether the biological mother present in the household, number of siblings, frequency of reading to the child or library visits, poverty indicator, regional controls, along with time-varying characteristics measured at period a − 1, such as poverty indicator, number of siblings, marital status, and presence of biological mother.

The estimates reported in Table 2, clearly point to a strong negative correlation between language spoken at home during early childhood and subsequent language development. We find that three-year-old children whose parents speak a foreign language at home have significantly lower verbal reasoning test scores than their monolingual peers. Other things being equal in a very basic specification (Panel (A) in Tables 2–4), speaking a foreign language at home when the child was nine months old reduced the child's language development, measured at age three, by 0.63 standard deviations. Adding a comprehensive set of controls reduces the estimated bilingual deficit in language development relative to that of an otherwise similar monolingual child to 0.35 standard deviations (see Panels (B) and (C) in Tables 2–4). In comparison, the negative impact of bilingualism on language is greater than the effect of low socio-economic background – a nine-month-old child who is living in poverty can be expected to have a verbal reasoning score that is 0.14 standard deviations below that of a non-poor child at age three.

The full set of estimated coefficients are available upon request. These estimates additionally reveal that the education of the mother and father, measured at the time of the child's birth, has a significant and positive association with language development at age three. For example, having a mother with a higher education degree is associated with a 0.19 standard deviation increase in the verbal reasoning score, as opposed to having a mother with a lower qualification. Children with gross, fine motor development and communication delays measured at nine months have not caught up developmentally by age three. The effect of having parents who arrived in the UK at younger ages results in a significant positive increase in verbal development at age three by around 0.13 standard deviations. Parental inputs, as measured by the frequency with which the mother or father reads to the child and/or visits the library, significantly impacts the verbal outcomes of five-year-old children. Overall, adding a comprehensive set of controls reduces the estimated coefficient on current bilingual status, and in some specifications, the effect is rendered statistically insignificant at the conventional levels.

The penalty for not speaking English exclusively at home is reduced at age five, once we fully control for the observable characteristics and past developmental outcomes; however, bilingual children continue to score lower on average in comparison to their monolingual counterparts even if we control for past development levels. The gap is statistically significant at the 1% level. Other things being equal, the results suggest that, on average, bilingual children's verbal reasoning scores are 0.20 standard deviations below that of monolingual children. This provides suggestive evidence that five-year-old bilingual children continue to fall behind in their expressive language and knowledge of names. Consistent with the results of the literature available from Cunha and Heckman (2008) and Dickerson and Popli (2016), past language endowment has a positive and significant effect on language development as measured at a later age. For example, an increase of one standard deviation in the verbal reasoning test score at age three is associated with greater language development (0.40 of a standard deviation) at age five.

Language development in bilingual children, at the age of seven, in the basic specification, is found to be statistically equivalent to that in monolingual children in specifications that omit the prior developmental outcomes (see Panels (A) and (B) in Table 2). However, once we control for the measures of prior language and emotional development, we find that seven year olds who were bilingual at age five have significantly higher language development (0.22 standard deviations) than monolingual children, whether or not they continue to be bilingual themselves at age seven.

Recall that in the verbal reasoning test taken at age seven (the BAS-Word reading test), the child must correctly pronounce words within locally accepted standards, with emphasis on the correct syllable or syllables.

These results reported at the age of seven are consistent with Mumtaz and Humphreys (2001), who show that bilingual children are better at reading as compared to their monolingual counterparts. This suggests a possible “transfer” of first language literacy skills to the development of reading in a second language. It also supports the view that bilingual reading development may aid the acquisition of certain literacy skills such as phonological awareness and memory, and the regular word-reading ability that accumulates over time.

Mumtaz and Humphreys (2001) investigate the impact of Urdu as a first language on learning to read in English as a second language. All students were tested individually over a period of eight weeks. Bilingual children were also found to have an advantage in phonological awareness at the earliest stages of reading, as compared to monolingual children.

At age 11, the advantage in the verbal reasoning tests for children who were bilingual at the age of seven (measured via the one-period lag of bilingualism) is not statistically significant once we fully control for child characteristics, parental characteristics, and children's past developmental outcomes. These results are mirrored for bilingual children at age 14 with a decrease in verbal reasoning scores of 0.09 of a standard deviation, and the effect is insignificant. There is a statistically significant persistence in language development over time. Interestingly, the persistence in language development diminishes as children age; also, the negative association between having emotional difficulties and language development – as measured by the SDQ scores – which is observed at early ages is no longer evident once children reach adolescence.

Our results for emotional development, as measured by the standardized SDQ, are presented in Table 3. We find that the discrepancies in SDQ scores between bilingual and monolingual children, originally explained in Table 1, are insignificant once we fully control for observable characteristics and past endowments (see Panels (B) and (C) in Table 1). In other words, being bilingual has no significant impact on the emotional development of children, regardless of their age. Children's past language development is found to be associated with their emotional development, however. An increase of one standard deviation in the past language score is associated with a reduction of 0.11 of a standard deviation in emotional difficulties at age eleven (see Panel (C) in Table 3). There is a strong persistence in emotional development over time; lagged SDQ scores are highly predictive of current SDQ scores. For example, a one standard deviation increase in emotional difficulties at age five is associated with a 0.56 standard deviation increase in emotional difficulties at age seven.

We observe similar results for pro-social development (see Table 4). The pro-social development of bilingual children is statistically equivalent to monolingual children in the specification that controls for past endowments of pro-sociality (see Panel (C) in Table 4). The persistence in pro-social behavior is significant and stable over time. Specifically, other things being equal, a one standard deviation increase in the lagged pro-social score increases current pro-social behavior by 0.30–0.40 standard deviations.

In summary, results in Tables 2–4 reveal several important findings. First, there is a negative relationship between bilingualism and early language development. The magnitude of this early disadvantage is significant, and consistent with some previous studies. In a more general context, Lang and Sepulveda (2007) find a black–white gap in cognitive tests, ranging from 0.20 to 0.50 of a standard deviation after controlling for a myriad of mother and family controls. The start of schooling, however, appears to attenuate the language gap and by age 14 the difference in early language development is insignificant. We find that there are no significant differences in children's emotional development and pro-social behavior. Finally, our estimates emphasize that prior language and socio-emotional inputs have a noticeable influence on child development.

Results from the cumulative value-added models which were estimated via OLS and dynamic GMM on our unbalanced panel of 9,532 child-wave observations are presented in Table 5. Columns (1) and (2) in Table 5 report the OLS estimates of Eq. (1), without and with past language and emotional endowments, respectively. Column (3) in Table 5 shows the system GMM estimator that combines the levels and the first difference equation.

The specifications also control for the differences in the survey time by including dummies for waves in regressions.

Omitting the previous language and emotional development and pooling all ages together (Column (1)), it is discovered that the lagged bilingual status is associated with a decrease in children's verbal language scores (0.10 of a standard deviation), other things being equal.

In a specification that includes mother fixed-effects (not reported, but available upon request), the estimates are of a similar order of magnitude as those from the OLS model. This suggests that bilingual differences are not simply the product of unobserved variation in time-invariant family characteristics (see De Haan et al., 2014 for similar discussion.).

The system GMM estimates in Column (3) allow for the possibility of detecting the presence of endogenous feedback effects, i.e., parents may adjust their behavior and resource decisions, as governed by feedback on children's outcomes. In the presence of such feedback effects, we expect to observe both a reduction in the persistence parameter, λ, and an increase in the bilingual coefficients (see Andrabi et al., 2011 and Del Bono et al., 2016). We do not find evidence which suggests that feedback effects may be present. The point estimates of the coefficient on past language skills increases from 0.28 in the OLS (Column (2)) to 0.60 in the GMM specification (Column (3)). The coefficient which is associated with past bilingual status increases in absolute value; however, it remains insignificantly different from zero. The system GMM standard errors are much higher than their OLS counterpart.

In terms of precision, this estimator appears much more satisfactory than difference-GMM. This is because lagged differences are stronger instruments for lagged levels (whereas lagged levels are weak instruments for lagged differences).

Consistent with our age-specific results, using the dynamic GMM model, we find no effect of bilingualism on the emotional and pro-social development of children. The point estimate of z-SDQ score_a−1 is 0.27 of a standard deviation in the system GMM specification, representing a decrease with respect to the OLS results reported in Column (2). Similarly, the coefficient on past pro-social behavior decreases from 0.34 in the OLS specification (Column (2)) to 0.29 in the system GMM (Column (3)).

The consistency of the GMM estimates hinges upon the assumption that there is no serial correlation in the unobserved individual level, time-varying determinants. The p-values of the Sargan–Hansen test statistic of over-identifying restrictions indicate that we cannot reject the null hypothesis that the instruments as a group are valid. This constitutes evidence that the models are well specified. The subsequent p-values of the Arelllano–Bond AR(2) test, reported in the bottom of Column (3) in Table 5, are in the range 0.15–0.75 for the three outcomes, showing little evidence for existence in serial correlation; hence, second order lags are likely to be appropriate instruments in the dynamic specifications.

Consistent with previous results, the dynamic specification also illustrates a significant persistence in language, emotional, and pro-social behavior over time. In particular, about 30% of pro-social development persists over time – a one standard deviation increase in the lagged pro-social score increases the current pro-social behavior by 0.29 of a standard deviation (Panel (C)) – while more than 0.60 of a standard deviation of verbal reasoning skills persists across ages. This finding, which is also emphasized by Del Bono et al. (2016) and Fiorini and Keane (2014), is in line with the idea that production functions for cognitive and non-cognitive skills are very different (Cunha et al., 2006).

We assess the sensitivity of our results by re-estimating our dynamic and child age-specific models using a balanced panel of children, with no missing information in the main family background variables over the five observed waves; that leaves us with 926 children, from whom 4,630 child-year observations could be gathered. We do not observe any substantive change in our bilingual coefficients. The results are available on request.

Next, we explore whether there is any heterogeneity in the bilingual effects reported so far. First, we consider whether the effects of bilingualism on language, emotional, and pro-scoial development differ by the children's gender. This additional information is important for identifying whether, for example, gender-specific strategies might be more effective in reducing language difficulties that arise from the language spoken at home.

Previous research shows a gender gap in children's performance. For example, boys’ attitudes towards reading and writing, the amount of time they spend in reading, and their achievement in literacy are all poorer than of the corresponding values for girls (All-Party Parliamentary Literacy Group Commission, 2012). The literature also suggests that gender differences do exist in the maintenance of home language. While girls are more likely to possess higher social skills and academic competence, boys often have more problem behaviors (Margetts, 2005). Furthermore, our estimates, not reported but available on request, consistently suggest that boys are more likely to experience emotional difficulties and that their verbal language development is well below the language development of girls.

In the case of emotional development, it is mainly boys that are found to benefit from their bilingual background, though the effect varies by age. Specifically, at ages five and eleven, the advantage in emotional development for boys is statistically significant when compared to girls. Other things being equal, speaking a foreign language at home when the child was seven years old reduces the total difficulties score by 0.19 of a standard deviation. No significant gap in the emotional development of girls is evident. To gain a better understanding of the domains underlying the emotional development result, we focus on the role of bilingualism by looking at the five SDQ domains separately, rather than at the single SDQ score. Results, available upon request, indicate a significant difference in conduct problems and hyperactivity for boys. Specifically, lagged bilingual status reduces conduct problems and hyperactivity outcomes by 0.18 and 0.26 of a standard deviation, respectively. Finally, for both boys and girls, speaking a foreign language at home does not associate with significantly different pro-social behavior. Although these results should be interpreted with caution due to the low sample sizes, explaining why the emotional development of boys benefits from bilingual status deserves more investigation. It could be hypothesized that the environmental and cultural background may influence children's social competence differently among boys and girls. We leave gender differences in emotional development between bilingual boys and girls to a potential future research.

Furthermore, in Table 7, we report additional results by distinguishing two groups of children based on their mother's education – those whose mother attained a high school qualification, first degree, or diploma, and all the other children (mothers with A-level, GCSE/O-level, or below). We do find evidence of heterogeneous production functions in the development outcomes across children of mothers with different educational qualifications. The early language disadvantage is greater for children whose mothers have a higher educational qualification, but is insignificant by age five. In contrast, the negative association between bilingualism and language development is still evident at age five for children whose mothers have an A-level or lower qualifications; however, the effect size is similar in magnitude for children whose mothers have an A-level or lower qualification. Surprisingly, at the age of seven, a greater positive bilingual effect is evident for children of mothers having a low education. This may be driven by selection, i.e., mothers less educated and less proficient in the English language are more likely to speak a foreign language, and they may invest more heavily in home activities to enhance the learning environment of their children (and possibly try to compensate the early bilingual cognitive disadvantage). We cannot disentangle this explanation since our data do not allow us to pin down the language proficiency level.

Motivated by our findings that bilingual differences in language assessments appear as early as the age of three and that the gap narrows over time, we investigate whether there are corresponding patterns of disparities in maternal behavior and home environment that can explain these early deficits in child development. We hypothesize that potential improvement in children's language development could arise from differences in parent–child interactions, and that a relatively high level of material education and time spent with the child has a positive effect on language development. In addition, it is well established that adverse circumstances such as poverty may create a stressful home environment, which contributes to psychological distress in parents and children (Holmes and Kiernan, 2013). This distress may filter into parenting practices, which tend to be punitive, inconsistent, and less nurturing. For example, persistent maternal mental health problems have been most strongly associated with child behavioral issues (Noonan et al., 2018). A leading potential explanation in our analysis is that, in general, immigrant parents foster higher growth rates in learning skills relative to native parents, which could result from different attitudes or parenting behaviors (see Hull and Norris, 2018).

For this part of the analysis, we use dependent variables that indicate the mother's home activities and well-being behaviors: (i) the time she spends with the child; (ii) the frequency of reading to the child; (iii) whether she is in a good relationship with her partner; (iv) whether a doctor has ever diagnosed her with depression or anxiety; (v) her life satisfaction; and (vi) whether she is currently at work.

Specifically, as part of self-completion module, the main respondent (usually biological mother) is asked about the quantum of time she usually spends with the child, and the possible responses are: “plenty of time”, “just enough”, “not quite enough”, and “nowhere near enough”, the higher scores corresponding to a lower quantum of time spent with the child. The variable “frequency reading” is measured on a 5-point scare, with a score of 5 indicating that the mother reads every day and a score of 1 corresponding to “not reading at all”. The variable “good relationship with partner” takes on the value 1 if the mother were to “strongly agree” or “agree” on the question, “Your partner is usually sensitive to and aware of your needs. Do you agree?”, and is asked in waves 1, 2, and 3. In each wave, respondents were asked whether a doctor had ever diagnosed them with depression or anxiety. If they respond positively, the variable “depressive symptoms” is assigned a 1; otherwise the value is 0. The life satisfaction is measured on an 11-point scale, with a higher score corresponding to a better outcome.

In Table 8, we report our estimates of bilingual maternal behavior toward children from age three to fourteen. We find evidence that mothers who were identified as bilinguals are more likely to spend time with their child; they are more likely to be in a good relationship with their partner and to have higher life satisfaction. They are also less likely to experience depressive symptoms. Overall, the evidence on healthy maternal investments and home environment suggest that children of bilingual families may allow them to “catch up” and develop comparative levels of skills relative to monolingual peers, which is in line with our findings.

The differences between bilingual and monolingual samples, found in Table 1, highlight the challenge which is involved in deriving an empirical method that effectively controls for unobserved child characteristics. Given that we have no experimental design, it is crucial to show that our results are robust to different sample restrictions. Firstly, we expect children whose parents are both foreign to be exposed to foreign languages in a more consistent way than are those with at least one native-born parent. Given this, we restrict the sample to children with two foreign-born parents. For instance, at age three we exclude 607 children on account of having a native-born parent. Table A2 in Appendix shows that results classified on the basis of age group and accounting for child characteristics and past endowments, are robust to this sample restriction. The estimated bilingual effect is very similar to those reported previously in Panel (C) in Tables 2–4, and maintains the result that language disadvantage fades with age. The differences in the SDQ and pro-social outcomes are not significantly different from our main results. The coefficient on past language development is in the range of ≈0.44–0.19, indicating that there is a significant loss of language skills over time.

Secondly, we exclude children whose parents arrived in the UK between 1997 and 2002 (this results in 585 children being dropped from the sample). The estimates, which are reported in Table A3 in Appendix, generally show similar results. We also test the robustness of our sample restriction by re-estimating our model on an expanded sample that includes those who report speaking Welsh (n = 196) or Gaelic (n = 2) in wave 1. This allows us to consider a notion of bilingualism that is not based solely on the language spoken at home. The estimates, available on request, are qualitatively similar. If anything, the magnitude of the estimates increases slightly in absolute value after the inclusion of the Welsh speakers.

Another potential concern is that any misclassification error induced by the categorical assignment of the language spoken at home may potentially cause a bias in our estimates.

See Dustmann and Van Soest (2004) for an analysis of speaking fluency of immigrants using ordered response models with classification errors.

We further consider a propensity score matching (PSM) analysis.

Propensity score matching may be thought of as assuming the selection problem way because it relies on conditional independence that implies no selection of the unobservable conditional on the observable.

The PSM estimates, performed by age group, are generally consistent with those reported from OLS models, Panel (B) (without past endowments), with slightly larger effects, on average, being reported from the PSM estimator (see Table A4 in Appendix). In most cases, where the OLS estimates are statistically significant, the corresponding PSM estimates are typically insignificantly different, suggesting that the degree to which PSM tightens the OLS bound is small, and that OLS seems to perform a reasonable job despite our reservations. Regardless of the matching algorithm used, results are consistent with our main findings.

To examine the potential role of unobserved heterogeneity, we also use recently developed tests that explore the stability of the coefficients of interest while increasing the set of control variables. We report estimates of the parameter δ, developed by Oster (2019), that indicates the level of selection on unobserved variables, as a proportion of the level of selection on observed variables, required to drive the treatment effect to zero. The assumptions underlying the calculation of δ can be varied. In our case, we vary the assumed value of R − max and the R² from a hypothetical regression of the outcomes of interest on treatment (bilingual status) and both observed and unobserved controls. If language, emotional, and pro-social outcomes are fully explained by the language spoken at home and full controls are set in the specification, then R − max = 1.

The suggested cut-off to define an “acceptable” level of selection is an estimate of δ (calculated using (R − max = 1.3^* R̃) that exceeds 1, with a higher value indicating increased robustness to selection on unobservables (see Oster, 2019 for details).

The estimates of δ, which are reported in Table A5 in Appendix, correspond to the bilingual coefficients which are estimated with full controls and past endowments. Results from these tests all exceed 1 in absolute value, aside from the estimates for emotional development at age five.

One potential concern is possible non-random attrition in the MCS, between waves. In Table A6 in Appendix, we compare selective descriptive statistics for individuals who attrite from the sample for any of the three outcomes and those who remain in the sample in wave 6 (age 14). In general, the verbal reasoning scores of children who attrite are slightly lower on average than those of children who do not. Even if attrition is not random, it is important to note that if attrition were attributable to fixed individual characteristics, our use of a first-difference estimator in the GMM implies that our estimates remain unbiased.

We also test whether attrition in any of the three outcomes is random using the approach of Fitzgerald et al. (1998). This approach is based on the assumption that all determinants of attrition can be controlled for (when selection is based on observables). Specifically, we implement a probit model where our dependent variable takes the value of 1 for individuals who drop out of the sample in wave 6 due to non-response in each of the three outcomes, and the value of zero for individuals who remain in the sample. Results reported in Table A7 in Appendix correspond to three separate probit models for the verbal, emotional, and pro-social development on the attrition. The Pseudo R - squared results from our attrition probits suggest that baseline variables explain less than 3% of attrition in verbal reasoning, emotional, and pro-social development outcomes between waves 2 and 6.

The results are available on request.

We then use the inverse of the fitted probabilities from these probit models to construct weights and adjust our main dynamic estimates, as reported in Table 5. The results, available on request, show that the inverse probability weighted estimates are numerically similar, and qualitatively identical, to the original estimates; therefore, we conclude that the attrition in the main outcomes is not likely to affect our estimates. Since our weights take into account important observable information, including baseline cognitive scores, we conclude that it is unlikely for unobservable factors to drive an attrition process which may substantially change our results.

Finally, in Appendix, we provide quantitative evidence on the importance of missing data and ensure that this unavailability is, in our case, unlikely to cause bias. We test whether attrition in any of the three outcomes is random using the approach of Fitzgerald et al. (1998) and show that attrition is not likely to affect our results.