Picking winners: An empirical analysis of the determinants of educational outcomes in India

We use data from the Young Lives longitudinal survey to analyse the effect of socioeconomic conditions and gender on the educational performance of young children in India. In particular, we use data for standardised scores on two cognitive tests: the Peabody Picture Vocabulary Test (PPVT) and a maths test. Our results show that there are significant gender differences in the way that household wealth affects the educational performance of children. Specifically, boys born into wealthier households perform significantly better in maths than those from worse-off economic backgrounds. The effect of wealth on the PPVT is stronger for girls than it is for boys. The results are robust across a range of specifications. The effect of household wealth on performance differed between the genders, even when we focused our analysis on the bottom 10% and top 10% of the performance distribution. One possible explanation for these differences is parental aspirations. We tested this hypothesis and found that boys from wealthier households with higher parental educational aspirations are positively and significantly associated with higher maths scores. Further analysis showed that the moderating role of parents’ educational aspirations was more pronounced at the top of the test score distribution, an indication that more able children are associated with wealthier and more ambitious parents. a rich longitudinal cohort study of childhood poverty for low-to-middle-in-come countries. We observed analysed how socioeconomic factors such as household wealth have affected the educational outcomes experienced by children. We focused our attention on performance, as measured by standardised scores on two cognitive tests: the PPVT and maths test. Our results show that household wealth is an important predictor of a child’s performance in both types of cognitive tests: children from wealthier households tend to achieve higher grades in both types of these tests. We also, however, find that there are significant gender differences in the way that household wealth affects the educational performance of children. In nearly all of the estimations, household wealth was found to have a consistently stronger effect for boys, particularly in maths test. The effect of wealth differed between the two genders, even when we focused our analysis on the bottom and top 10% of the performance distribution. In particular, we found clear and persistent gender differences in test performance, with boys tending to systematically perform better in maths than girls. This finding is consistent with suggestions that family background may encourage girls and boys to value different aspect and subjects of education differently (Sullivan and Brown, 2015).


Introduction
This article analyses the effect of gender and socioeconomic conditions on measures of cognitive outcomes of young children in India. Our study follows children at different ages and uses panel estimation to identify how factors that determine the socioeconomic status of these children may affect the educational outcomes that these children experience. Unlike previous studies, our analysis goes beyond the measurement of education as years of schooling. Instead, we consider measures of cognitive performance, which can be seen as proxies of the quality of education.
Educational attainment and outcomes have been at the centre of public debate in India for nearly three decades, as it became evident that the educational framework of the 1990s and early 2000s was unable to support the fast development the country experienced after the post-1990 market liberalisation reform (Lopez et al., 1999). outcomes for individuals-and, by extension, for societies (Hanushek and Wößmann, 2007). The importance of early-life education as a determinant of later-life success is recognised in the literature for both developing and developed countries. It is also understood that socioeconomic and household characteristics have a powerful effect on the educational attainment and educational performance of young children (Darko and Carmichael, 2020), although the ways these characteristics affect the decision-making processes of households may differ between developing and developed countries in significant ways (Carmichael et al., 2019a).
In the context of developed economies, such as the UK and the USA, recent studies have shown that there are associations between educational outcomes and household characteristics-such as household income, the gender of the pupil, class and ethnicity (Strand, 2011;Hampden-Thompson and Galindo, 2015). Household income is often found to be a strong predictor of children's future educational outcomes, with lower incomes often being associated with higher school dropout rates, lower educational attainment and poorer school performance (see e.g. Dearing, 2008).
Moreover, the significance and magnitude of the household income effect varies significantly throughout childhood. Duncan et al.'s (1998) longitudinal study of 5,000 US households shows that household economic conditions experienced before the age of 5 have a stronger effect on children's school outcomes than economic conditions from ages 6-15. Similar results are reported by Votruba-Drzal (2006), who shows the early childhood income of US households to have enduring effects on educational outcomes. Moreover, a number of studies find that adverse economic shocks are likely to have a stronger and more long-lasting effect on schooling outcomes for children in lower-income households compared to their more affluent peers (Lacour and Tissington, 2011).
In most developing countries, family background is often associated with children's success in adult life. Children from wealthier households tend to have a higher probability of being in school, mainly because these children experience few or no constraints during childhood. The direct costs of education (such as books, tuition fees and school uniforms) are less likely to be a concern for wealthier households (Huisman & Smits, 2009). Opportunity costs are also smaller-wealthier households have less or no need for their children to be available to work or help with household chores (Basu, 1999). Furthermore, poorer children can experience economic hardships that affect their ability to achieve better developmental outcomes. It is, therefore, not surprising that the literature often reports household wealth as one of the strongest predictors of educational attainment and performance. The effect of wealth can, however, be complex and non-linear in developing countries. For instance, Woldehanna et al. (2008) show that when household wealth rises beyond a certain level, it may increase the probability of a child combining school with work.
Other socioeconomic characteristics that are often reported as important determinants of early-life academic achievement include parental education, where the evidence overwhelmingly suggests that children of more-educated parents are generally more likely to stay in school longer and perform better than children of less-educated parents (UNESCO, 2005). Mother's education is often found to be an important determinant of girls' school enrolment: more educated mothers are more likely to keep their daughters in school longer, although the effect of mother's education on girls' performance is not always found to be significant-especially when looked at in the context of traditional developing countries, with strong gender stereotypes, such as India (Breen and Goldthorpe, 1997;Emerson and Portela Souza, 2007). Mani et al. (2013) find that having a mother (father) with non-zero schooling raises the probability of a child's enrolment by 3-7% (7-10%).
Further, on the issue of gender inequality, there is extensive empirical evidence to suggest that education in India is gender discriminatory, with boys having a higher chance of staying longer in school (Vecchio and Roy, 1998) and achieving higher literacy rates-82.14% for boys and 62.46% for girls according to 2011 Census of India data (Batra and Reio, 2016). Strong patriarchal norms and labour market discrimination against female workers have been reported to still have an influence on Indian households' decision-making processes, resulting in a biased allocation of household resources for education towards boys (Chada & Sinha, 2013). This is an important issue, with strong societal, developmental and economic connotations. For instance, a number of papers have found that gender inequality in education leads to slower economic growth (Klasen, 2002); lower quality of life (Nussbaum, 2000); and higher mortality and lower fertility rates (Drèze and Murthi, 2001).

Data
Our data was drawn from the Young Lives longitudinal cohort survey of childhood poverty (Young Lives, 2018). Young Lives followed the lives of around 12,000 younger and older children across four low-to-middle-income countries (Ethiopia, India, Peru and Vietnam). Data were collected during five rounds spread over 15 years : 2002, 2006, 2009, 2013 and 2016. The first round of the survey took place when the younger cohort were 1 year old and the older cohort were 8 years old. For both cohorts, the survey collected a rich set of information on household and parental characteristics, as well as detailed information on children's characteristics including educational attainment and measures of cognitive ability. As the survey collects information on children and household characteristics, it is possible to examine how children's development changes over time. The results that we present in this article are based on data for the older cohort for India, as the younger cohort has limited information on the educational outcomes that are the focus of this study. This included a sample of 951 children from three Indian regions: coastal Andhra Pradesh, Rayalaseema and Telangana. 1 We use two measures of cognitive ability for this study, both of which are based on assessments of literacy and mathematical ability. At ages 12 and 15, children's cognitive development was assessed using the Peabody Picture Vocabulary Test (PPVT), a test of receptive vocabulary that has been widely used to measure verbal ability and general cognitive development 2 (Rosenzweig and Wolpin, 1994). The second measure of cognitive ability was the maths test, which required children to solve some maths-based questions. Maths tests were conducted at ages 12, 15 and 19. Both the PPVT and the maths test were collected for all children, regardless of whether they were attending school or not. This unique feature potentially avoids the issues of selection bias, which are often associated with school-based data.
The estimated equations control for a range of household socioeconomic characteristics, including household wealth, parental education and location of the household. Household wealth is measured with a composite variable that combines a set of wealth-related metrics, including proxies for housing quality, access to services and consumption of durable goods. 3 We also control separately for parental education, measured as the highest grade completed by the household head (in years). Since education is positively linked to earnings, the educational attainment of the household head is also likely to have a strong impact on the ability of the household to stock up wealth, which is usually found to be an important determinant of educational attainment (Hannum et al., 2009).
Investment in education may also change with the age of the child. As children grow older, the opportunity cost of education increases. Traditionally, this has resulted in lower enrolment rates at higher grades, as poorer households opt to take their children out of school and bring them into income-generating activities. The Education for All policy reforms of 2002 managed to reduce this trend to an extent by boosting enrolment rates in upper primary, primary and elementary education (Mehrotra, 2006). Table 1 shows summary statistics for the main variables used in our analysis. Boys and girls are represented in nearly equal shares throughout all cohorts. Most children (nearly 70% of our total sample) reside in rural areas and in households with an average size of five family members. As expected, the share of female-headed households is relatively smaller (just over 13%) when compared to male-headed households. Boys perform better, particularly in maths, with an average score of 10.5 compared to girls (8.5). For both tests, the differences between boys and girls were statistically significant. Figure 1 illustrates the distribution of educational outcomes for boys and girls. As shown, girls tend to underperform their male counterparts, especially at the top end of the distribution. The gap is, however, narrower (particularly for PPVT) at both ends of the distribution. Figure 2 presents further evidence of the differences in educational outcomes between boys and girls, this time by taking into consideration the distributional properties of household wealth. In particular, the figure shows the distribution of test scores by wealth quartile, Q. For both measures of cognitive ability, the distribution for boys and girls is similar at lower ends of the household wealth distribution. A test of differences in means for maths, for boys and girls at the bottom end of the distribution, fails to identify any statistically significant differences between genders. At relatively higher levels of household wealth, the figure shows that boys perform better compared to girls. This is confirmed by tests of differences in means between boys and girls at higher quartiles. Similar evidence is found for PPVT scores. Table 2 shows a summary of average test scores at different ages and by gender. There is clear evidence of improved performance for both tests as the child gets older. Boys are shown to achieve systematically higher scores at all ages for both the PPVT and the maths test. As all the biological, socioeconomic and developmental variables in our dataset follow similar distributions for both genders (as one would expect from a representative sample), such differences in performance are likely to be driven by Determinants of educational outcomes in India 5  Determinants of educational outcomes in India 7 societal and cultural norms (Baker & Milligan, 2013), which we explore in further detail later.

Methodology
This section outlines the methodological approach that we are going to follow in the rest of the article, while also summarising some of the key properties of the main variables used in our analysis. The estimation results are then presented and explained in the next section. We base our estimations on a multivariate panel least-squares model. The general form of the basic estimated model is as follows: Subscripts it are used to denote the value of a variable for child i at time period t , whereas α 1 ,α 2 and α 3 are the corresponding coefficient vectors; j and v are time and region dummies, respectively. The dependent variables, Maths it and PPV T it , record performance on each of the two cognitive tests.
To ensure that our dependent variables also capture some element of educational quality, we adjust the test scores to take into account the individual's completed years of schooling. Doing this gives a more accurate measure of the child's ability for their level of completed schooling. We derive this measure by firstly calculating the average test score by the child's year of completed schooling. This is then subtracted from the actual test score. Values greater than the average indicate better performance for the child's level of completed schooling, whereas values below average indicate that the child underperformed. In effect, this variable is taking into account educational quality. The final values are then standardised to have mean 0 and standard deviation 1.
A key limitation of the dependent variable is that test scores are not available for all survey rounds. The maths test was administered in rounds 2, 3 and 4, whereas the PPVT was administered in rounds 2 and 3 only.
The main independent variable is wealth, a composite index that combines a set of wealth-related metrics, including proxies for housing quality, access to services and consumption of durable goods. X is a vector of individual characteristics, including age of the child (in months) and health as measured by body mass index (BMI). Finally, Z is a vector of household characteristics, including the gender and age of the household head, highest grade completed by the household head, household size, caste and religion. All specifications allow for time-fixed effects j ð Þ to capture the effect of time-variant economic trends on educational outcomes. The regional and urban-rural location dummies would account for the effect of unobserved regional policies and location-specific characteristics.

Selectivity bias
There is a possibility that the sample of children who completed the test is a non-random subset of the population. This could result in selection bias (and, therefore, sample-induced endogeneity). For instance, more able children can often afford to stay longer in school (by being enrolled and completing more years of schooling) and consequently achieve more. Similarly, children who are currently enrolled in school would be more likely to complete the exercise and consequently may perform better than children who were not enrolled in school. The data actually supports this, and indicates significant differences in both PPVT and maths scores between children who were enrolled and those who were not enrolled. As such, estimating test scores without empirically accounting for selection into enrolment could bias the estimates. We address this issue of sample selection using the Heckman two-stage formulation. The first-stage enrolment equation is estimated with a probit model and takes the following form: The dependent variable, Enrolled, takes the value of 1 if the child is currently enrolled in school. g i is a variable that is not included in the educational outcomes regressions but satisfies the exclusion restrictions. The restriction requires that this variable should directly affect enrolment but should not have a direct effect on educational outcomes. All other variables are as previously defined. We use the number of children (0-5 years) and the number of children of school-going age (6-18 years) as exclusion restrictions.
The identification strategy is that having more young children and children of school-going age in the household may impact on the education enrolment of other children. For instance, as the number of children of school-going age increases in the household, children will have to compete for resources and therefore parents will be unable to enrol all children in school. Investment in education will fall as a result. Similarly, as the number of young children (0-5 years) increases, the need for older children to help with caring for their younger siblings will also increase, thereby reducing children's likelihood to enrol in school.
To account for the potential bias that may result from non-randomness, we use a second-stage equation which yields a selection parameter, the inverse Mills ratio (IMR). The IMR parameter that is derived from the enrolment Equation (2) is then included as an additional explanatory variable in the second-stage test scores equation, which is as follows: Determinants of educational outcomes in India 9 All other variables are as previously explained.
To reduce further the effect of individual-level heterogeneities, we implemented a propensity score-matching technique (Deheija and Wahba, 2002) to construct a sample of those not enrolled that is comparable to the sample of children who were enrolled. Due to the reduced sample size, we estimated joint regressions and included a female gender dummy and its interaction with household wealth. 4 Table 3 shows the panel ordinary least squares (OLS) estimates for measures of educational outcomes (adjusted test scores) separately for boys and girls. The signs of the reported coefficients are largely as expected, with household wealth having a positive effect on both PPVT and maths scores for boys and girls. Higher household wealth significantly increases both PPVT and maths scores for boys by 46 percentage points, respectively. The effect of wealth on girls' performance is also positive and significant for PPVT (62 percentage points), but not significant for maths. This finding could relate to possible suggestions that family background may encourage girls and boys to value different aspects and subjects of education differently (Mensah and Kiernan, 2010), so that girls rather than boys view themselves more as readers and writers. Moreover, the results show a positive association between the level of schooling of the household head and children's educational outcomes-although the level of significance of this effect differs depending on the gender of the child. The education of the household head has similar effects on cognitive outcomes and increases test scores by 2% on the maths test and PPVT, for girls and boys, respectively. This positive effect suggests that educated households can invest more in their children's education and provide further academic support which enables children to perform better. This result agrees with a number of other papers that report a link between parental education and children's educational development (Davis-Kean, 2005).

OLS estimations
Our measure of household wealth could be susceptible to endogeneity-induced bias if there are differences in the size of households. For instance, larger households may have more income recipients than smaller households because they are more likely to have working adults (we find evidence of this in the data); therefore, these households may be able to afford more assets. We therefore attempt to eliminate any form of bias that can affect the estimate of wealth on children's educational outcomes by adjusting the household wealth variable. We do this by first estimating the average wealth by total household size, and then subtracting actual household wealth from this average value by household size. Households with wealth values that are higher than the size-adjusted wealth average value are better off compared to their peers. Results that use this variable are presented in Table A1 in the Appendix. 5 As seen, adjusting household wealth by total household size does not substantially alter our findings.
It should also be noted that none of the four specifications showed any significant differences in performance for female-headed households and household size (except in column one, where the coefficient on household size was found to be negative and significant at the 10% level). Table 4 presents selectivity-corrected estimates of the effect of household wealth on children's educational outcomes. Starting with the first-stage estimations in columns 1 and 2, the exclusion restriction variables (number of children) are found to have a negative effect on the likelihood of enrolment for both boys and girls, with the effect larger for girls. This is an intuitive result that has been reported in a number of previous studies (see e.g. Ahiakpor et al., 2014), depicting the positive relationship between household expenditure and number of children in developing countries: larger households generally have less money to spend on children's education, leading to lower enrolment rates and school performance. The size of the effect is higher and more strongly significant for younger children (0-5 years). Household wealth has a positive effect on likelihood of enrolment for boys, but not for girls-for whom the Determinants of educational outcomes in India 11 estimated coefficient is positive, albeit much smaller in magnitude and not statistically significant.

Selectivity bias
Columns 3 to 6 show the selectivity-corrected estimates. The direction of the effects of household wealth is consistent with the results presented in Table 3, and shows positive effects of wealth on educational outcomes, although both the size and significance of the estimated coefficient varies depending on gender: boys (girls) in wealthier households tend to perform significantly better in the maths test (PPVT), respectively. The IMR is largely insignificant, especially for boys. However, in terms of maths score, the effect is negative (for girls) and indicates that the joint effect of unobservables is negatively correlated with educational outcomes. The negative sign Columns 3 to 6 include school type, age of child (in months), health of the child, age of the child and age of the household head. Standard errors in parentheses. *p < 0.1. **p < 0.05. ***p < 0.01. 12 C. K. Darko and N. Vasilakos suggests that girls who are more likely to enrol in school perform worse relative to other girls of similar characteristics (after controlling for observed attributes). The negative effect of the selectivity term can be interpreted to suggest that school enrolment is simply not enough to secure better maths scores, perhaps more so for the less advantaged.

Individual-level heterogeneities: matched subsample
Moreover, we examined how observable individual characteristics might differ based on the child's enrolment status, thereby biasing the results, using a propensity scorematching technique. Figure A1 in the Appendix illustrates results from the matching process and shows the kernel distributions of propensity scores before and after the matching procedure. The figure provides sufficient support for good matching. Table A3 in the Appendix presents results using the matched subsample. Similar to earlier results, the interaction term indicates a negative effect on both PPVT and the maths test. This provides further support that the wealth effect we identified in previous estimations does not appear to be biased by the characteristics of individuals.

Effect of household wealth at bottom and top of test scores distribution
In an effort to better understand the effect of household wealth and gender attitudes, we now look at the distributional properties of children's educational outcomes (and how these are or are not affected by wealth) using the unconditional quantile regression (UQR) technique as proposed by Firpo et al. (2009). The underlying principle of this method is to estimate a re-centred influence function (RIF) for the variable of interest (in our case test scores) on a set of regressors, by estimating the partial effects of these covariates on the unconditional quantiles. This influence function can then be used to measure the effect of a particular observation on the distributional statistics of the main variable. 6 Table 5 summarises the main results for the bottom and top 10% of the test scores distribution. It was expected that gender differences should disappear at the bottom and top end of the test scores distribution, as wealth should have no differentiating effect between boys and girls. In other words, if children in the top 10 percentile of the test score distribution are likely to be from wealthier backgrounds, then we should not be able to identify any significant gender differences on the effect of wealth in performance on this part of the distribution (especially so as boys and girls are represented in roughly equal shares in our distribution). The results in columns 3, 4 and 8, 9 indeed show that the effect of wealth on the top quartile of performers was positive for all children. However, the differences in magnitude of the estimated coefficients between the two genders that we identified in previous estimations remain-the effect of wealth on top-performing boys was almost eight (six) times bigger than for top-performing girls in maths (PPVT). In terms of the statistical significance of the effect, we observe again the same pattern as in previous estimations, with wealth being a significant determinant of educational outcomes for boys for maths (but not PPVT). These results tentatively suggest that, even among the bestperforming children in the maths test, top-performing boys are more advantaged Determinants of educational outcomes in India 13  All regressions include school type, age of child (in months), health of the child, age of the child and age of the household head.
Standard errors in parentheses.
*p < 0.1. **p < 0.05. ***p < 0.01. 14 C. K. Darko and N. Vasilakos compared to top-performing girls. The results for the PPVT are generally inconclusive and show a significant effect only for poor-performing girls at the bottom end of the PPVT distribution.

Education aspirations and educational outcomes
Finally, we examine whether parental aspirations can moderate part of the wealth effect on children's educational outcomes. It is possible that part of the effect of household wealth on cognitive development could be shaped by parental expectations and aspirations for the child. The link between aspirations and educational outcomes has been identified before, although the majority of papers we are aware of have focused on pupils' (rather than caregivers') aspirations (Croll and Attwood, 2013;Khattab, 2015;Berrington et al., 2016). All regressions include school type, age of child (in months), health of the child, age of the child and age of the household head. Standard errors in parentheses. *p < 0.1. **p < 0.05. ***p < 0.01.

Determinants of educational outcomes in India 15
The Young Lives survey provides interesting data on caregivers' aspirations and expectations of children's educational attainment. The question on educational aspiration that we use asks the caregiver (usually the mother): 'What level of education would you like your child to complete?' This question was asked in the second round when the child was 12 years old. The responses provided by caregivers were found to be positively correlated with family wealth and also parental education, with a coefficient of 0.18 and 21.2, respectively. There is also some evidence of gender bias in caregivers' response. For instance, 67% of caregivers aspire for boys to complete university, compared with only 43% for girls. This response is similar when the same question was asked to the child in relation to 'the education grade you would like to complete'. In this case, 61% of girls desired to complete university compared to 76% of boys. Even when this was conditioned on household wealth, boys still had higher aspirations than girls. While these findings are not causal, they can be seen as evidence of parents' preference for boys compared to girls. Figure A2 in the Appendix shows the distribution of parents' aspirations by gender of child. Results from these estimations are presented in Table 6.
As with previous results, we find persistent evidence of gender bias. The interaction effect (shown in columns 1 and 2) indicates a significant and positive effect on the maths test for boys-the effect was found to be not significant for girls, although positive. It is possible that the significant effect for boys may be largely driven by parental preference, due to boys being seen as more likely to be the main source of financial support for parents in old age (Kingdon, 1998). There are no significant effects on PPVT scores. Focusing on maths scores, Figure 3 plots the results from a local polynomial regression and shows the estimated conditional mean of the test scores at age 15 and 19, conditional on parents' aspirations and children's aspirations. The figure shows a largely positive relationship between parental aspirations and children's later educational outcomes. The extent to which parental aspirations can affect children's educational outcomes provides further evidence that the existence of a gender bias in our sample (and, in particular, in India) may be beyond parental preference. It is possible that some of these effects are associated with other socio-cultural norms. Two main explanations are often cited for the gender gap. The first associates this gap with labour market discrimination, where employers value women's education less than that of men. This reduces the incentives to invest in girls' education (Kingdon, 1998). The second associates the gender gap with kinship norm, and the notion that because girls leave the house after marriage, any returns to education are enjoyed by their in-laws. This perception reduces investment in children's, especially girls', education-see Chakraborty and Kim (2010) for a more detailed discussion of kinship structure in India. These results provide evidence that girls, rather than boys, remain disadvantaged-even after accounting for a number of family background characteristics.
In further analysis, we examine the interaction effect along the distribution of children's test scores (see Table A2 in the Appendix). The results show that at the top of the distribution, the effect of household wealth and parental educational aspiration is significant for both boys and girls, although the effect is marginally larger for boys than for girls. This finding is a possible indication that while boys are more advantaged than girls, parental aspirations can play a role in moderating this effect, albeit this is more relevant for wealthier children.

Discussion of key findings
The results that we presented earlier in this section (as well as in the accompanying Technical Appendix) leave no doubt that socioeconomic household characteristics (and, in particular, household wealth) are important determinants of educational advancement in India. Indeed, children from poorer households are consistently found to experience educational disadvantages compared to their wealthier peers. This result remains prevalent, even after controlling for factors such as location, school type and other covariates. Although caregiver aspirations are found to compensate this effect, the compensation is only partial, gendered and still strongly influenced by household wealth. This powerful and persistent effect of wealth on educational progression is particularly concerning from a policy perspective-not only because of the existence of gender bias (which, as we show here, remains a pertinent issue), but also because it highlights the limitations of the current education policy to support the development of children from poorer households, who are in turn found to be substantially disadvantaged by the current education system.
There are many reasons why differences in household wealth may matter for educational performance (and for the successful implementation of educational policy reforms). Children from less wealthy backgrounds have access to fewer educational resources (such as textbooks and other reference material), and we do know from Determinants of educational outcomes in India 17 previous research that such resources can have a significantly positive effect on educational performance (Spaull, 2013). Poorer and often less-educated parents may spend less time with their children (Guryan et al., 2008), and they may also be more constrained in their ability to provide support with schoolwork (Cooper, 2010).
In addition, poorer households are likely to be more susceptible to adverse economic shocks (Guarcello et al., 2010;Azam and Imai, 2012), more credit constrained (Menon, 2009) and more vulnerable to the effects of economic uncertainty (Morduch, 1994)-all of which could impact household attitudes towards educational expenditure, and could well explain part of the wealth and gender bias that we find in this article. For instance, liquidity constraints mean that poorer households are less likely to be able to finance educational expenses, which may in turn force them to make choices about which child to send to school (Calero et al., 2009). Poorer households are also more likely to be reliant on their children's income for survival (Jacoby and Skoufias, 1997;Aggarwal, 2018). Such effects can be exacerbated further by social norms and gender-based stereotypes, resulting in further imbalances in educational expenditure allocation between boys and girls for poorer households (Desai et al., 2010).
Finally, another area that is likely to be relevant for some of the results that we report in this study is school quality heterogeneity: children from less wealthy households are more likely to enrol in schools that offer more limited educational resources than their wealthier peers. There are numerous references in the literature to results that link household wealth and quality of schooling (Checchi, 2006;Glewwe and Kremer, 2006;Figlio et al., 2016). Studies such as those of Desai and Kulkarni (2008) and Asadullah et al. (2009) show that despite significant growth in school enrolment in India (Dougherty and Herd, 2008), the widening of wealth inequality that has been observed over the course of the last two decades may have had an effect on the academic performance of poorer children along the lines that we describe in this article. Aspects of school quality such as teacher-pupil ratio (Case and Deaton, 1999) and teacher quality (Rothstein, 2010;Rivkin and Schiman, 2015) could also be contributing to the performance gap between children from poorer and wealthier households-partly because allocation into high-quality schools is influenced by family socioeconomic background.
From a policy perspective, this means that educational policy reforms may not be able to fully achieve their objectives, unless they are accompanied by economic policies that address issues of inequity and inequality. Such policies should aim to economically empower poorer households to reap the benefits of educational reforms by making them less reliant on their children's income for survival (Chamarbagwala, 2008), whilst improving schooling quality, especially in areas where children from poorer households are likely to be over-represented.

Conclusion
India has undergone a long period of fast economic reforms which have changed the development prospects the country faces for the better. As part of these reforms, the country embarked on a long series of policy interventions that aimed to improve the quantity (years of schooling) as well as the quality of education offered, mainly by 18 C. K. Darko and N. Vasilakos public schools. Our article has considered educational outcomes in the period following the start of these reforms, by using data drawn for India from the Young Lives dataset, a rich longitudinal cohort study of childhood poverty for low-to-middle-income countries. We observed and analysed how socioeconomic factors such as household wealth have affected the educational outcomes experienced by children. We focused our attention on performance, as measured by standardised scores on two cognitive tests: the PPVT and maths test.
Our results show that household wealth is an important predictor of a child's performance in both types of cognitive tests: children from wealthier households tend to achieve higher grades in both types of these tests. We also, however, find that there are significant gender differences in the way that household wealth affects the educational performance of children. In nearly all of the estimations, household wealth was found to have a consistently stronger effect for boys, particularly in maths test. The effect of wealth differed between the two genders, even when we focused our analysis on the bottom and top 10% of the performance distribution. In particular, we found clear and persistent gender differences in test performance, with boys tending to systematically perform better in maths than girls. This finding is consistent with suggestions that family background may encourage girls and boys to value different aspect and subjects of education differently (Sullivan and Brown, 2015).
One possible explanation for the difference in performance found between girls and boys may be that it is driven by parental expectations and aspirations for children's future. We put this hypothesis to the test by estimating the effect of caregivers' aspirations on children's performance using information provided directly by the head caregiver (usually the biological mother). We found that high caregiver aspirations are positively and significantly associated with better performance in maths tests for boys but not for girls.
We therefore conclude that, despite the success of recent policy reforms in boosting enrolment rates and improving access to education for boys and girls in Indian households, there are still significant gender-and wealth-driven disparities affecting the educational progression of young children in India. These disparities become more visible when using measures of performance, like the ones we presented in this study. It is possible that some of these differences can be attributed to cultural factors and stereotypes that may be historically entrenched in the way of thinking among local societies (labour market discrimination being a case in point). Policy reforms that aim to support the developmental and economic outcomes of young adults in India need to consider gender differences in access to employment opportunities as well as earlier access to education and children's material living conditions. 7 We did find evidence, after all, that parents' expectations have a significant effect on future cognitive outcomes.
Changes in culture are certainly harder (and slower) to achieve, and possibly require interventions that extend beyond the boundaries of education policy. Policy interventions should, however, aim to foster and monitor such changes by providing information, training and support to caregivers and schoolteachers, and encourage children (irrespective of their gender) to achieve their real potential. Until that happens, the country will be limiting its economic and developmental potential by picking winners based on the wrong criteria. NOTES 1 The survey takes into account regional variations to ensure balanced representation of the three regions in the sample. 2 To elicit a response from the child, a set of four pictures that correspond to a word read out by the examiner (interviewer) is presented to the child. The starting set of items is dependent on the child's age, and the progress (up or down) through the test is determined by performance. This then determines the Basel and Ceiling Item sets. The final scores are computed by subtracting the number of errors from the individual's Ceiling Item score. 3 The housing quality index is computed as the average of the type of flooring, roofing and walls used, as well as the number of bedrooms. Assets are measured as the scaled sum of ownership of consumer durables. The access to services index is defined as the average of access to drinking water, toilet, fuel and electricity. 4 The estimation controlled for gender, years of completed schooling, education of household head, gender of the household head, religion and region. 5 In results not reported here, we further adjust household wealth using the number of adults (rather than total household size). The results were similar to those reported in this study.

SUPPORTING INFORMATION
Additional Supporting Information may be found in the online version of this article: Figure A1. Matched and unsampled samples. Figure A2. Parents' educational aspirations for children. Table A1. Effect of (adjusted) wealth on children's cognitive outcomes. Table A2. Effects of wealth and parental aspirations along test score distribution. Table A3. Gender and wealth effect on children's cognitive outcomes: matched subsample.
Determinants of educational outcomes in India 23