Inequality of educational opportunity in India: Changes over time and across states

(Comments most welcome; please don t cite without permission) Inequality of educational opportunity in India: Changes over time and across states Niaz Asadullah University of Reading, IZA and University of Oxford Gaston Yalonetzky OPHI, University of Oxford This draft: September 2009 Abstract This paper documents the extent of inequality of educational opportunity in India spanning the period 1983-2004 using National Sample Survey (NSS) data. We build on recent developments in the literature that has operationalized concepts in the inequality of opportunity theory (including Roemer s) and construct two indices of inequality of educational opportunity using data on an adult sample. Irrespective of the index used, the state of Kerala stands out as the least unequal in terms of educational opportunities. However, even after excluding Kerala, significant inter-state divergence remains amongst the remaining states. Transition matrix analysis confirms substantial inter-temporal mobility in inequality of opportunity across India states. Rajasthan and Gujarat in the West and Uttar Pradesh and Bihar in the Centre experienced large-scale fall in the ranking of inequality of opportunities. However, despite being poor, Eastern states of West Bengal and Orissa made significant progress in reducing inequality of opportunity. At a region level, Southern, North-eastern and Eastern regions on average experienced upward mobility in terms of decline in inequality of opportunity whilst Central region experienced downward mobility. We conclude by examining the link between progress towards equality of opportunity and poverty reduction, growth and a selection of pro-poor policies. Key words: Schooling mobility; Dissimilarity index, Gini index.!" # 1

1. Introduction Between-group income inequality is a common phenomenon in mutli-ethnic societies. Such inequalities often reflect persistent differences in the capacity of the individuals from different social groups to exploit market opportunities either because of discrimination or market constraints (Roemer, 1998). A society with unequal opportunities is said to be characterized by a low degree of social mobility, in that individuals economic success/status is largely predictable in terms of family background such as caste and religion. Such social immobility leads to intergenerational persistence in poverty and consequently has serious implications for the process of development. A popular policy instrument to secure socio-economic mobility across generations is equalization of individuals opportunities to acquire human capital. The existing literature on determinants of schooling in developing countries, exhibits large and significant influence of parental background on children s school attainment (Haveman and Wolfe, 1995). Given substantial returns to education in the labour market in these countries, educational immobility has serious implications for economic mobility in adult life. Greater crossgenerational persistence in schooling and higher returns to education sees less earnings mobility (Solon, 2002). Mere reduction in education inequality does not yield greater economic mobility either. It simply compresses the income distribution and stunts returns to education, which in turn limits income mobility. For example, Cheechi et al. (2000) find that Italy has greater educational equality but less mobility compared to the USA. Thus what is needed is to promote a distribution of human capital where schooling varies along with individuals level of effort instead of family background and other characteristics for which they cannot be held responsible (Roemer, 1998). There is a rich literature examining the question of educational mobility in developed countries. Among recent studies, Chevalier et al. (2003) look at educational mobility across twenty OECD countries, while Wößmann (2004) examines the effect of family background in student achievement in Europe and the USA using PISA data. The empirical evidence indicates substantial cross-country variation in the degree of equality of opportunities within the developed world. Similarly, Wößmann (2005) uses Third International Mathematics and Science Study (TIMSS) data for five high performing Asian countries - Japan, South Korea, Taiwan, Thailand and Singapore - to study the effect of family background on test scores. In contrast to these studies, relatively little is known on this topic for developing countries: indepth evidence about the impact of family background on educational production using comparable data is very limited (Hanushek, 2002). A relevant comprehensive multi-country study on schooling enrolment and attainment is Filmer and Pritchett s (1999) which uses comparable household survey data from 35 developing countries. But their study is purely descriptive: they do not directly measure the extent of equality of educational opportunity or mobility in schooling attainment. Such dearth of research is despite the fact that inequality in educational attainment is much larger in developing countries, particularly so in South Asia: educational Gini coefficient for India is one of the largest in the world (Thomas et al., 2000). In the recent past, attempts were made to measure schooling mobility using comparable household datasets with information on family background. Estimates of educational mobility have traditionally remained limited only to countries for which household data with complete information on schooling of adult children and their parents are available. Such information usually has a panel/retrospective dimension and hence is usually unavailable in comparable developing country cross-sectional datasets. However, two studies Dahan and Gaviria 2

(2002) and Behrman, Birdsall and Székely (2001) $ adopt a regression-model-based approach to measure schooling mobility using data on children s schooling from Latin America. Educational mobility in these studies is modelled in terms of inter-generational persistence in schooling. Similarly, Schütz, Ursprung and Wößmann (2008) use comparable data on students from the TIMSS survey and develop an index of the inequality of educational opportunity in 54 countries. However, once again, their index is defined in terms of regression estimates of the effect of family background (measured in terms of the number of books in the students home) on students educational performance. Given the strong relationship between education and earnings, intergenerational correlations in education are argued to be a valid index of the inequality of opportunity later in life for children from different family backgrounds. However, even if we focus exclusively on the instrumental value of education as productivity enhancer, % intergenerational correlations serve as imperfect indices of the inequality of educational opportunity for at least two reasons. Firstly, they relate a limited set of circumstances beyond the individual s control to his/her welfare outcome (usually the father s or mother s value for that outcome) thereby, by construction, attributing too much of welfare inequality to characteristics for which individuals should be held accountable. In the inequality of opportunity literature the idea is to account for as many circumstances beyond the individual s control as possible. Secondly if dissimilarities across distributions of well-begin conditioned by circumstances beyond individuals control are deemed to contribute to inequality of opportunity then intergenerational correlations are inappropriate to measure inequality of opportunity even in hypothetical societies where just one single parental attribute constitutes the set of circumstances beyond the individual s control. & As Yalonetzky (2009a) shows, several joint distributions of parental and offspring s well-being (e.g. education) can produce the same intergenerational correlations. By contrast studies like those of Gasparini (2002), Checci and Peragine (2005), Lefranc et al. (2008), Ferreira and Gignoux (2008) and Barros et al. (2009) have developed and implemented indices of inequality of opportunity which handle multivariate sets of circumstances, which is a minimum requirement for a methodology aimed at quantifying inequality of opportunity. Ferreira and Gignoux (2008), for instance, estimate an index for a large number of Latin American countries using comparable data on adults. In this study, we follow a similar approach: we measure inequality of opportunity with two indices, a Gini index of inequality of opportunities (Lefranc et al., 2008) and a dissimilarity index of inequality of opportunity (Yalonetzky, 2009b). Both are suited to handle multidimensional $ ' ($))*+,! $-.%$ # /0 123.,(.+ 4.!! 5!.. 6 7 6, 8! # 6 #!! #! $-3, 9!4 %!" :! ; ( + (%--$+ < /.! 0 <! (%--*+ & " 1!!!! 1!.!!= ( = 7$))*7%--+ " ;!! 1 3

circumstances beyond the individual s control and outcomes of interest measured with discrete variables. To the best of our knowledge, this is the first attempt to measure the extent of inequality of educational opportunities, in terms of schooling level completion of adults, in India. India provides an ideal setting to empirically investigate this issue. Significant progress has been made in increasing enrolment and school completion. Enrolment in primary schools has increased from 19.2 million in 1950-51 to 113.6 million in 2001. Gross primary school enrolment is nearing 100%. In an overall sense, enrolment of children in all stages of education in India has improved over the years. Such increase in school participation has been also associated with a significant jump in the literacy rate which rose from 18% in 1951 to 65% in 2001 (Dougherty and Herd, 2008). The growth in enrolment has been accompanied by large scale increase in the number of schools. For instance, between 1950 and 1990, the number of schools increased more than three-fold, outpacing the growth of the school age population. This era has also seen a number of other major programmes and large-scale interventions such as mid-day Meals (Dougherty and Herd, 2008). School participation may have also responded to educational interventions that have been in place since the 1990s. This latter growth in schooling has coincided with the era of economic reform and liberalization which also saw high rates of economic growth by historical standards. Between 1983 and 2004, rural poverty declined from 46.9% to 28.4%, at a rate of one percentage point a year (Lanjouw and Murgai, 2009). Economic growth may have enabled previously poorer families to enrol children in school thereby reducing inequalities in educational opportunities. Indeed the post-reform era of the nineties has been a period of fairly rapid increase in literacy and school participation (Dougherty and Herd, 2008). In general, educational inequality in India is not only one of the highest in the world; it has not declined much in the last three decades (Thomas et al., 2000). An additional motivation to focus on India is in the striking gaps in educational outcomes across gender, caste, religion and between urban and rural inhabitants (Wu, Goldschmidt, Azam and Boscardin, 2006), which altogether explains a large part of the overall educational inequalities. Gender discrimination within households contributes to such gender deficit in the region. A significant part of the disparity is also an unintended consequence of sex preference (Jensen, 2002). Consequently, one would expect limited educational mobility of girls in India. The gender disparity aside, widespread caste and religion inequality in socio-economic outcomes in India is a well-documented phenomenon. Recent research using multiple-rounds of nationally representative data clearly documents persistence of gender, caste and religion gaps in school participation and attainment (Asadullah, Kambhampati and Lopez-Boo, 2009). A comparison of 1983 data with 2004 data reveals that even the later years of (1991 s) liberalization have not been accompanied by a complete closure of social gaps in schooling, an important pre-market factor: these gaps remain substantial for most states. By 2004, education outcomes for the majority of women continue to be low, with substantial interreligion (and caste) disparity, although there is an increase in school participation and completion for all social groups between the two rounds of NSS data. Even then, analysis of more recent data from the 1990s reveal that intergenerational persistence in schooling is higher for Hindus compared to Muslims (Bhalotra, Langer, Stewart and Zamora, 2008). Similarly, whilst there has been some narrowing of the rural-urban gap in school participation in the past decades suggesting a weakening of the disadvantage associated with one s rural background, significant inter-region gaps in educational outcomes remain. Therefore, it is not known to what extent the recent progress in the field of education reflects equalization of educational opportunities. 4

These trends in inequality of educational outcomes are not conclusive of a reduction in inequalities of educational opportunities. For instance, there is evidence of continued importance of other circumstance factors such as parental wealth and education which is suggestive of persistent inequality in educational opportunities. Indeed, India hosts a large part of the world s out-of-the-school children, most of whom belong to poor households (Filmer and Pritchett, 1999). To this end, considerable educational investment has been made in past decades in some states which coincide with significant growth in school enrolment. However, this experience of educational progress was not equally shared across states. There exist large disparities in educational achievement across states in India about two-thirds of the children who do not attend school are in five of the poorest states: Bihar, Uttar Pradesh, West Bengal, Madhya Pradesh, and Rajasthan (Dougherty and Herd, 2008). Persistence of schooling inequalities in some states raises concern regarding the extent to which such investment has translated into greater equality of educational opportunities. Dreze and Sen (1995) attribute existing inequality in educational achievement to variation in efforts to expand basic education in different states. If inequality in the access to education continues to restrict the benefit of (public) investment in education to children from higher social class and the majority (religious) group, it is unlikely to equalize educational opportunities. Therefore, it is of policy interest to study the degree of inequality of educational opportunity across Indian states. According to Roemer s theory, in an unequal society, human capital accumulation is significantly influenced by family background (such as caste and religion). The key challenge in operationalizing this notion of equality of opportunity is to find data on exogenous circumstance factor for adults and their parents. The most widely referred circumstance factor is that of parental education. However, no nationally representative large scale datasets for India provides this information for the adults (i.e. individuals for whom schooling data is not censored). In the absence of such data, our study focuses on two other commonly studied circumstance factors, namely, gender and religion of the individual. Allied with the data on caste, gender and religion, the objective of this paper is to look at the interplay between social origins and gender in the determination of educational opportunity in contemporary India. The key questions that we wish to address are as follows: (a) Are educational opportunities in India becoming more equal? (b) Is there intra- and inter-regional disparity in educational opportunities? (c) If so, how much mobility is there over time do states that were less equal in the past have remained so today? To explore the Indian experience of progress in equalizing educational opportunities, we use NSS data spanning the time period 1983-2004. Our study differs from Ferreira and Gignoux (2008) in that we calculate two indices a dissimilarity index and a special Gini index to measure inequality of educational opportunity across Indian states. Ferreira and Gignoux (2008) normalize between-group inequality by total inequality which is both conceptually appealing and methodologically problematic it is possible for both between-group inequality (the numerator) and total " 1 ( 1 + 1( 1! 7 +, >!.! 1! 7,!! 1!? 1.!.!! #!,! 1!"!!! 1 1 5

inequality to worsen (the denominator) at the same time. But if the latter grows more it will give the false impression that inequality of opportunity decreased. Alternatively, one could use just a between-group inequality indicator as an indicator of inequality of opportunity. However, the resultant index only has a lower bound (a zero) but not an upper bound. To circumvent this problem, Elbers et al. (2008) devised a different normalization method called the ELMO which was used by Lanjouw and Rao (2008) on an application to caste inequality in two thoroughly studied Indian villages. Their method divides between-group inequality as measured by mean log deviation by the maximum inequality that such measurement could yield giving the groups sizes and the total sample size. However the method is computationally intensive for it requires testing for several possible allocations of the sample across the number (and sizes) of partitions as defined by the sizes and number of the original social groups. Notwithstanding the merits of these indices, an additional reason for our opting for different indices is in the next section. We use a dissimilarity index based on one of Roemer s definitions of equality of opportunity. It takes the value of zero if and only if conditional distributions of well-being are identical across social groups and it takes its maximum value of one if and only if there is perfect association between social group partitions and non-overlapping subsets of the outcome. In addition, we estimate Lefranc et al. s Gini of opportunity. It is an interesting index based on a definition of inequality of opportunity different to Roemer s. It measures instead Giniinequality of Sen s welfare metrics (1976) across social groups. The personal distribution of schooling described in this paper is based on a representative sample of households drawn from two periods which span the year when the Indian economy was formally liberalized. The two time periods of the NSS chosen mark the pre- and postliberalization era in India. This presents an interesting setting to study equality of opportunity to acquire education, an important pre-market factor @. Market liberalization has brought important changes in the distribution of background factors that matter for schooling success. The liberalisation of the Indian economy in 1991 was followed by significant growth and fall in poverty. However, growth patterns in the nineties are characterised by major regional imbalances. As a matter of fact, regional disparities increased in the 1990s, with the southern and western regions doing much better than the northern and eastern regions. Broadly speaking, western and southern states (Andhra Pradesh excluded) have tended to do comparatively well. The low growth states, on the other hand, form a large contiguous region in the north and east. This is a matter of concern, since the northern and eastern regions were poorer to start with. In some of the poorer states, notably Assam and Orissa, there has been very little reduction between the 90s (Deaton and Dreze, 2002). These patterns have implications for equality of educational opportunity at the state level. For another reason, it is useful to study inequality of opportunity across states in India. There are well-known regional divides in norms and culture within India. Whilst stories of genderexclusion are common in the North, research using data from the South report almost no evidence of gender gaps in social outcomes (Dreze and Sen, 1995). For instance, in an insightful study, Jejeebhoy and Sathar (2001) compare the lives of women and explore dimensions of their autonomy in different regions of South Asia-Punjab in Pakistan, and @ #!! < 7A 97: (%--)+!' #!. 7'7' 79B ($))*+, C" 6

Uttar Pradesh in north India and Tamil Nadu in south India. They find that while women s autonomy is constrained in all three settings, women in Tamil Nadu fare considerably better than other women, irrespective of religion. If true, the origin of cross-state differences in educational opportunities may lie in regional differences in norms and educational preferences within India, amongst other factors. Attaining equality of educational opportunity is a universally accepted social principle. Yet, because of lack of a statistical measure, it has not been possible to assess progress made in equalization of educational opportunities in India. Neither has it been possible to study the conditions that are necessary for an equalization of educational opportunity. To the best of our knowledge, this is the first study that attempts to empirically investigate the extent and correlates of equality of educational opportunity across states in India. Therefore, our study fills an important gap in the otherwise rich literature on the between-region differences in human development in India. Because the study is based on household datasets, we are able to describe the trends in inequality of opportunity between states and regions. In addition, we study mobility of Indian states and regions in terms of decline in inequality of educational opportunity over time. Irrespective of the index used, the state of Kerala stands out as the least unequal in terms of educational opportunities. However, even after excluding Kerala, significant inter-state divergence remains amongst the remaining states. Transition matrix analysis confirms substantial mobility in inequality of opportunity across India states. Rajasthan and Gujarat in the West and Uttar Pradesh and Bihar in the Centre experienced large-scale fall in the ranking of inequality of opportunities. However, despite being home to a large number of poor people, Eastern states of West Bengal and Orissa made significant progress in reducing inequality of opportunity whilst the situation worsened in Bihar. At a region level, Southern, North-eastern and Eastern regions experienced upward mobility in terms of decline in inequality of opportunity, whereas the Central region experienced downward mobility. The rest of the paper is organized as follows. Section 2 explains the methodology and the data. Section 3 discusses state rankings in terms of inequality of educational opportunity and presents some potential explanation for divergent experience across the states. Section 4 is conclusion. 2. Methodology and Data In this section we briefly introduce the two indices used in tracking changes in inequality of opportunity of education in India from 1983 to 2004. We first present the general framework of circumstances and outcomes. We then explain the dissimilarity index of multidimensional inequality of opportunity and the Gini index of inequality of opportunity. General framework We assume that societies can be partitioned into a set of individuals types, following Roemer (1998). Each type itself is defined by a special combination of values taken by a vector of circumstances, i.e. factors over which the individual does not exert control, like parental education, ethnicity or gender. For instance, imagine a society with two circumstances: gender (male or female) and parental education ( low or high ). In such a society type 1 individuals could be those who are male (meaning arbitrarily a value of 1 in the gender entry) and whose parents had low education (meaning arbitrarily a value of 1 in the 7

parental education entry). By combining the difference categories within each and every circumstance, four types are defined in this example. Following the notation in Yalonetzky (2009b), in general z circumstances are considered, each of which is partitioned into g i categories (for i=1,2, z), making every circumstance a vector, V i, with gi elements. (For instance, a gender vector would have just two elements). By combining all the possible values in the vectors of circumstances a vector of types is defined. Formally, types are generated by a function f that transforms combinations of circumstance values into a natural number representing the ensuing type: T f : V1 V2... V z + The ensuing vector of types, G { 1,2,...,T } =, has T = z i= 1 g i elements. * All individuals having the same set of circumstances are said to be of the same type (e.g. in the U.S. context assuming z=4, one set determining a type could be being an adult Asian male whose two parents had achieved complete secondary education). Empirically, the absolute frequency of t people in a society belonging to type t, such that t G, is denoted by N. Similarly outcomes or advantages can be considered in a multidimensional way. All possible combinations of outcomes (e.g. health status with education achievement and earnings and so on) are in the vector O = { 1,2,..., A}. Assuming that there are b outcome vectors, V j, each having m j elements (for j=1,2,,b), then multidimensional outcomes are generated by a function q that transforms combinations of individual outcomes into multidimensional outcomes: 1 2 b A q : V V... V + O has elements, each of which represents a combination of outcomes, each one partitioned in the aforementioned m j elements or categories. For instance an element α O and equal to 1 might stand for having tertiary education, excellent health status and the highest earning capacity (i.e. the categories can represent intervals too). Finally, the probability of attaining a given combination of advantages (e.g. α =k) conditional on being of type t is: p. The corresponding absolute frequency of people being of type t and attaining a k t combination k is b A = m j= 1 j t N k. In the one-dimensional case the number of outcomes is A=m 1. The mean of the welfare measure over the whole population is denoted by µ while µ i is the respective mean for type i. G i is the Gini coefficient for type i. The dissimilarity index of inequality of opportunity Recent operationalizations of Roemer s (1998) definition of inequality of opportunity follow his definitions of circumstances, efforts and advantages. In Roemer s definition of equality of * D! 7 1 9, ) #!. E 9 (%--)!+ 8

opportunity the distribution of an advantage across the population should be independent of sets of circumstances. That is, circumstances should not affect the advantage either directly or indirectly through effort or random shocks. An implication of this definition is that, under a situation of equality of opportunity, any measure of between-group inequality of outcomes (i.e. Roemer s advantages) should be nil. The dissimilarity index used in this paper relates to the definitions of Roemer (1998), Checci and Peragine (2005) and Ferreira and Gignoux (2008) in which equality of opportunity is achieved when the conditional distributions of outcomes/advantages are equal across circumstance sets. The types approach and the tranches approach, both implemented by Checci and Peragine (2005), emphasize the connection between inequality of opportunity and traditional measurement of between-group inequality of outcomes using path-independent decomposition techniques for the mean log deviation index. $- We do not use the mean log deviation index in this paper because our variables for education are discrete. $$ We also do not follow the types approach of Checci and Peragine (2005) because it assumes that inequality of opportunity vanishes if and only if the means of the conditional distributions are identical. Even though this is a legitimate definition we prefer to allow for more distributional differences in the analysis of inequality of opportunity. The dissimilarity index that we use in this paper is closer to the tranches approach in that both declare inequality of opportunity if and only if conditional distributions of well-being are identical across social groups. $% However the latter is normalized by total inequality and requires continuous variables for implementation. Therefore we opt for the dissimilarity index in this paper. By contrast, the dissimilarity index of inequality of opportunity highlights the association between sets of circumstances, so-called types in Roemer s terminology, and sets or values of advantages/outcomes. In fact the index achieves its maximum value, with which it signals maximum inequality of opportunity, whenever there is perfect or maximum association between circumstances and advantage. On the other hand the index achieves its minimum value when the conditional distributions of outcomes are all identical, i.e. homogeneous, which implies that the conditioning factors are irrelevant in determining the advantages. The index therefore measures a concept of inequality of opportunity based on the degree of dissimilarity of multinomial distributions, in turn captured by the metric of a Pearson goodness-of-fit statistic used to test homogeneity of such distributions. $ The index is based on a test of homogeneity among multinomial distributions (e.g. see Hogg and Tanis, 1997). The formula of the index is equal to the statistic of the test divided by its maximum possible value (which was originally found by Cramer, 1946): ( ) 2 T A t * X p t α pα ($+ H = = 2 w * X max t = 1 α = 1 min{ T 1, A 1} pα 2 $- F. 1 1,! #, 1,!# < (%---+ $$ G!! $% <! E 9 (%--)!+ $ <,!. 1 E 9 (%--)!+ 9

Where w t is the relative weight of the population belonging to type t, t w = t N T *, and p α is a k N weighted average of all the sample or group-specific probabilities for state α in which the * weights are given by the share of each sample size on the total sum of them: p α is calculated the following way: t t N T α * t N t= 1 (%+ pα = pα = T T t= 1 t t N N t= 1 t= 1 The weighted average probability performs the comparison of the probabilities across the different type samples. The closer the respective probabilities across samples then the more the weighted average probability resembles each and every of its constituting probabilities (in (2)) and therefore the closer to zero the statistic in (1) is. Notice that an advantage of the dissimilarity index based on the statistic in (1) is that it can be used to assess inequality of opportunity with multiple outcomes. The index fulfils axioms of population invariance $& and scale invariance. $ It is also normalized in order to take the value of 0 when the samples under comparison (i.e. the conditional probability vectors) are identical, which would reflect equality of opportunity, at least in terms of the types considered. And it takes the value of 1 with maximum association between circumstances and outcomes. In the context of the dissimilarity index (and in general, of contingency tables analysis) maximum association means that for any arbitrary partition of the sets G and O into non-overlapping subgroups then: H k G, O O : O k k T k O1 O2... OT = O where O k is a subset of O made of all those outcome elements attained by type k with positive probability. Maximum or perfect association means that for every type there is a vector of outcomes which is a subgroup of the outcome vector and is only attainable by that type. For instance, if type t 1 is associated with outcomes α 3 and α 4 (i.e. that there exists a positive probability of being in outcomes α 3 or α 4 conditional on being type t 1 ), then no other type is associated with those categories, and similarly if type t 2 is associated with outcomes α 5 and α 6 then type t 1 is not associated with those latter outcomes. The concept of maximum association is not a concept of perfect predictability because if a type is associated with more than one outcome grids (as in the aforementioned examples) then one cannot perfectly predict the final outcome (e.g. it could be either α 3 or α 4 if the type is t 1 ) although one can accurately predict that someone with type t 1 never attains outcomes α 5 or α 6. $& #7 7, $ #7 ( +! (! αi+7,6 k = 1 10

H α O, G G : G α G1 G2... GA = G Where G α is a subset of G made of all those types who attain outcome α with positive probability. Maximum or perfect association means in this case that for every outcome state there is a vector formed by all and only the types that attain that specific outcome state. Any other subgroup of types cannot attain that outcome and/or any other outcome is associated with a different, non-overlapping subgroup of types. #I"H α O, k G : k α That is, every outcome state is associated exclusively with only one type. This concept of maximum inequality of opportunity as perfect association is suitable when there are multiple circumstances and outcomes since the latter do not exhibit any natural ordering across all its possible values due to their multidimensionality. The Gini index of inequality of opportunity α α In order to propose their Gini index of inequality of opportunity Lefranc et al. (2008) follow a similar reasoning to that of Roemer in terms of the impact of circumstances on outcomes. But they depart from Roemer (1998) when they propose an alternative definition of equality of opportunity according to which the latter is achieved when there are no sets of circumstances which are second-order dominated within a society. Guided by concerns over return and risk of the outcome from different circumstance sets, in the definition of Lefranc et al. (2008) circumstances may actually affect advantages differentially but equality of opportunity is still deemed to exist as long as individuals can not rank any circumstances according to second-order stochastic dominance among their respective outcome distributions. Hence in their definition of equality of opportunity the properties of the outcome lottery (e.g. average return and risk) faced by people with different circumstances matter in the sense that people may find some circumstances more appealing than others in terms of their related outcome or advantage lotteries. If people could choose their circumstance before being born on the grounds of such appeal (formally using a second-order stochastic dominance criterion) and in turn they happened to be indifferent between circumstances, based on that criterion, then their society could be deemed as showing equality of opportunity. In the framework of Lefranc et al. second-order stochastic dominance may help to ascertain equality of opportunity but, as with any other partial ordering criterion, it is not useful to rank societies in terms of their degree of inequality of opportunity, i.e. their level of departure from perfect equality. Therefore they propose the Gini index of inequality of opportunity, which is related to Sen s welfare metric: W ( x ) = µ ( x ) 1 I ( x ), where the mean of the variable x is multiplied by one minus an inequality index applied to the distribution of x. Such metric is related to second-order stochastic dominance in that whenever society A second- 11

order stochastically dominates society B, then. (However, the opposite is not true). The Gini of inequality of opportunity of Lefranc et al. is based on Sen s metric and is defined as: T T 1 (+ GO = wi wj µ i ( 1 Gi ) µ j ( 1 G j ) 2µ i = 1 j = 1 Note that when comparing GO against Roemer s definition it is easy to verify that whenever a society is opportunity-equal according to Roemer s criterion, and according to the dissimilarity index, GO is zero, thereby measuring equality of opportunity according to Roemer s definition. However the reverse is not true. GO may be zero even when distributions of the advantage/outcome are not equal. For instance, let T=2, it is not difficult to find values for the two types means and Gini coefficients such that µ 1 > µ 2 and G 1 > G 2, which imply dissimilarity in the two distributions of the advantage and inequality of opportunity according to Roemer, $ and GO=0, which implies equality of opportunity according to Lefranc et al. $@ Data B ( ) > ( ) A W x W x The data used come from the NSS 1983 and 2004 rounds. Our analysis is based on individual s school completion $*. Since this data is censored for children, we restrict our analysis to adults aged at least 25 years old. The dissimilarity index relates data on school completion to a variety of circumstances such as caste, religion, gender and location (ruralurban) $). Because for certain states, sample size was too small, we further restricted our data to 25 states %-. This yields a total of six comparable circumstance sets: Hindu male, Hindu female, non-hindu male, non-hindu female. 3. Results Appendix Figure A reports the indices for the whole India over adults 25 years or older. In all cases, the point estimates are surrounded by narrow confidence intervals as is to be expected from the large sample size. This confirms the statistically significant difference of our estimates of Inequality of opportunity indices from 1983 to 2004. This is also the case for the two bootstrapping techniques used. The plot of the dissimilarity index suggests a modest decline in inequality of opportunity whilst the opposite is true for estimate of Gini index. $"!!, $@ <!,? E 9 (%--)!+ $* H.-$7 HG?J<GDJ"GD.-%7 #CD.-7.-& H!.-7.-7.-@7.-*7.$-7 J.$$7.$%7!.$ $) " 7!! %- ' $)*%--&7! " >F%--&>F> ; %--&! >F> 12

National averages of the dissimilarity index and the Gini index can mask important betweenstate differences in educational opportunities. This is confirmed by Table 1 which reports rankings of states according to inequality of opportunity indices. Also reported is the fraction of population with primary and secondary education. Several patterns are noteworthy from the Table. First: In the case of primary and secondary education, significant progress has been made between 1983 and 2004. In 1983, none of the states (except Delhi and Nagaland) had more than 20% of the population with up to or above secondary level education. By 2004, this increased by 2-3 folds in all states except Andhra Pradesh, Rajasthan, Orissa and Tripura. Because of low base, the fraction of population with secondary education increased by more than 100% in Northern state of Uttar Pradesh as well as Southern state of Kerala. Similarly, the fraction of population with primary education almost doubled in almost all states between 1983 and 2004. Once again Northern states such as Uttar Pradesh and Bihar saw 100% increase in the percentage of primary educated population. States that had invested heavily in primary education in the past (such as Kerala, Karnataka and West Bengal) also saw modest growth in primary educated population. Second: there is considerable disagreement between the Gini and dissimilarity indices over the ranking of states in 1983. This is evident from the low value of the rank correlation coefficient. However, the two indices correlate highly for 2004 data (with a rank correlation coefficient value of 0.95). The differences on the indices between the two years are statistically significant which is unsurprising given the large sample size. However the difference may not be large enough to be economically significant. In addition, the opposing trends espoused by each index are possible given that they do not measure the same concept of inequality of opportunity. The dissimilarity index measures inequality as distance across multinomial distributions which in turn is related to the degree of association between population groups (or types in Roemer s words) and outcomes. By contrast the Gini of inequality of opportunity is a Gini index of Sen s metrics, W x, for each group in which I ( x) Third: is estimated using the intra-group Gini coefficient. In general, there is a negative link between level of educational attainment in the population (i.e. mean school primary/secondary completion) and inequality of opportunity. For instance, in the year 2004, 76% of the population completed primary schooling in the least unequal state of Kerala whilst the figure for Uttar Pradesh, the most unequal state, was 44%. The rank correlation coefficients reported at the bottom of Table 1 are always positive highlighting the fact that all states that succeeded in increasing primary and secondary education did so by reducing inequality of opportunity. This therefore highlights the value added of the indices for ranking purposes. However, the correlation is far from perfect and seldom significant at 5% level. ( ) 13

Table 1: Estimates of Inequality of educational opportunity indices by state and year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otes: (a) Figures on indices are ranks. (b) Ranks: 1=most unequal; 25= least unequal. (c) p-values in parenthesis. -- ($+ -& (%+ -$ (--+ -%- (-%+ 14

Fourth: The pace of improvement in inequality of opportunity has been quite uneven between states within India. To highlight the extent and direction of movement of states in terms of inequality of opportunity, we plot state ranks in Figure 1. The Y-axis corresponds to position in 1983 whilst the X-axis indicates position in 2004. If a state is above and further from the 45 degree line, it indicates increasing inequality of opportunity. Reassuringly, irrespective of the index used, Uttar Pradesh and Bihar are located above the 45 degree line and experienced significant decline in their original rank in 1983. Figure 1: Scatter plot of ranking of states by Gini index and Dissimilarity index, 1983-2004 1983 (Gini Index) 0 5 10 15 20 25 Rajasthan Nagaland Sikkim Kerala Himachal Pradesh Uttar Pradesh Bihar Andhra Pradesh Meghalaya Orissa Karnataka Haryana Madhya Pradesh Gujarat Delhi Punjab Jammu and Kashmir Arunachal Pradesh Assam Maharashtra Tripura Tamil Nadu West Bengal Manipur Goa 0 5 10 15 20 25 2004 (Gini Index) 1983 (Heterogeneity Index) 0 5 10 15 20 25 Kerala Delhi Gujarat Punjab Himachal Pradesh Karnataka Meghalaya Andhra Pradesh Rajasthan Arunachal Pradesh Uttar Pradesh Haryana Maharashtra Assam Sikkim Tamil Nadu Bihar Nagaland Tripura Madhya Pradesh West Bengal Orissa Manipur Jammu and Kashmir Goa 0 5 10 15 20 25 2004 (Heterogeneity Index) Notes: (a) Dashed line is the 45 degree line. (b) The solid line represents the linear regression trend. (c) Increase in ranks implies higher inequality. 15

Figure 2: Scatter plot of ranking of states across regions by Gini index and Dissimilarity index, 1983-2004 1983 (Gini Index) 0 5 10 15 20 25 West North_East North_East South North Central Central South North_East East South Central Central West Central North North North_East North_East West North_East South East North_East West 0 5 10 15 20 25 2004 (Gini Index) 1983 (Heterogeneity Index) 0 5 10 15 20 25 South Central West North North South North_East South West North_East Central Central West North_East North_East South Central North_East North_East Central East East North_East North West 0 5 10 15 20 25 2004 (Heterogeneity Index) Notes: (a) Dashed line is the 45 degree line. (b) The solid line represents the linear regression trend. (c) Increase in ranks implies higher inequality. To examine movement in inequality of opportunity rankings more formally, we construct transition (quartile) matrix of dissimilarity index for 25 Indian states (see Appendix Table 1). The calculated value of the underlying immobility, as measured by the trace index %$ is close to unity (i.e. 0.91) implying substantial mobility in inequality of opportunity across India states. A problem in transition matrix analysis is that with only 25 observations, some cells have no observations at all. To partially circumvent the problem, we disaggregate state data by rural and urban areas and re-calculate the transition matrices using the resultant dataset which now contains 50 observations in total (see Appendix Table 2). Once again, the %$ #,,3. 4J3.$4 7:,! J 16

calculated value of the trace index remains high (i.e. 0.87) confirming that several states changed ranks so that many of those with relatively high inequality of opportunities in 1983 are not in the same (relative) category by 2004 %%. To what extent is observed inter-state differences in inequality of opportunity mirroring between-region inequality in educational opportunity? To answer this question, we reproduce the scatter-plot of state rankings showing the region of each state in the plot (see Figure 2). Western states were equally divided above and below the 45 degree line Rajasthan and Gujarat saw a worsening of equality of opportunity whilst Maharashtra and Goa an improvement. Eastern states (West Bengal and Orissa) rank consistently amongst states that have succeeded in reducing inequality of opportunity. Southern states (Andhra Pradesh, Karnataka, Kerala, Tamil Nadu) all gained in terms of ranks (when assessed using the Gini index). However, when assessed in terms of the dissimilarity index, 2 states (Kerala and Andhra Pradesh) fell below the 45 degree line but both remained very close to the line. North/North-Eastern states have equal share above and below the 45 degree line Central (Bihar, Uttar Pradesh, Haryana) states are mostly above the 45 degree line (irrespective of the index used). Once again, to formally examine how much mobility there is across regions, we compute quartile transition matrix and immobility indices (see Appendix Table 4). Given only 6 regions in India, we further disaggregated the data by rural/urban location of the households to enlarge the sample size. The calculated value of trace index is once again close to unity (i.e. 0.87) implying substantial mobility in inequality of opportunity across India regions. The Pearson chi-square statistic however is only marginally significant (p-value 0.11) which is likely to be owing to the small number observations. To better understand the movements in the position of regions across the distribution of inequality of opportunity, we plot region-specific values of Dissimilarity and Gini index in Figure 3 by year. Looking at Figure 3, therefore, it is easy to trace changes in equality of opportunity in education across Indian regions. Several patterns are noteworthy here: (a) irrespective of the index used, the central region saw a rise in inequality of opportunities; (b) irrespective of the index used, the southern, eastern and north-eastern regions saw a decrease in inequality of opportunities; (c) compared to the Gini index, there is more movements across regions in terms of the dissimilarity index. Figure 3: Changes in inequality of opportunity in education according to the Dissimilarity index and Gini index across Indian regions %%! 7 F.1 (. ---%- + 17

Notes: Estimates based on data on adults 25 years old and older. What could explain the diverging experience of Uttar Pradesh and Kerala in equalizing educational opportunities? Fortunately, a good deal of research has been carried out that not only documents the difference in human development between the states but also traces the observed differences in human development outcomes to differences in policy chosen by the states. For instance, Dreze and Sen (1995) attribute differences in entitlement to basic services between Uttar Pradesh and Kerala to differences in the scope and quality of public services such as school facilities which in Uttar Pradesh are often non-existent. Relevant factors, among others, are the importance of social movement and public action, and the lack of political power of socially disadvantaged group (or agency of scheduled tribe/scheduled caste/muslim population). In order to shed light on some of these possibilities, we present descriptive evidence in the following section. Policy origin of inequality of opportunity What can explain the large-scalee fall in the ranking of Rajasthan and Gujarat in the West and Uttar Pradesh and Bihar in the Centre? On the other hand, what explanationn is there for reduction in inequality of opportunity in the Eastern states of Orissa and West Bengal that are much poorer? These questions are interesting because in the last two decades, India has experienced significant economic growth at a sustained rate. The decade of the 1990s saw significant fall in poverty, a significant source of disadvantage for children born into Muslim and other minority social groups (e.g. scheduled caste, scheduled tribe). Overbearing poverty has been a significant cause of withdrawal of children from schools. GDP growth and poverty reduction has been achieved in the backdrop of 1990s market liberalization which has also led to changes in economic structure and organization. These changes may have relaxed household credit constraints and altered household returns to investment in education.

However, gains in poverty reduction following economic growth have not been equally divided across states. In general, in a federal state like India, provision of public goods is the responsibility of individual states. Therefore, it is expected that socio-economic outcomes would differ across states because of between-state differences in macro policies and micro-institutions. Certain states may have affirmative action policies that attenuate the adverse effect of discriminatory factors such as caste and religion. Therefore the internal diversities within India are of much interest. Independently of policy differences, inter-state comparisons are useful because states in India also differ in terms of social norms. Certain states in India have historically displayed a poor record in terms of gender inequality. For instance, the northern Indian state of Uttar Pradesh has a long history of oppressive gender relations. On the other hand, women s economic participation has been active in the Southern state of Kerala for a long time which is arguably responsible for a wide range of social achievements. Whilst stories of genderexclusion are common in the North, research using data from the South report almost no evidence of gender gaps in social outcomes (Dreze and Sen, 1995). Therefore, it is of policy interest to document how inequality of educational opportunity varies across states. In order to delve a little deeper into the state-level policy factors and experiences with economic growth and poverty reduction, we build on Besley et al. (2007). Table 3 connects the policy analysis above to the earlier discussion of the link between economic growth and educational opportunity. It ranks Indian states by inequality of opportunity and their growth elasticity of poverty, GDP growth rates, rates of poverty reduction, and performance in each of the four areas of policy discussed above. All variables relating to economic growth, poverty and policies are in lagged form. The table thus allows an informal look at how policy performance such as gains in GDP growth and poverty reduction are linked to the level of and changes in inequality of educational opportunity. The first four columns in Table 3 present rankings in terms of (level and changes in) inequality of opportunity indices. The next column identifies the states that have been most effective at securing economic growth and reducing poverty. These states have tended to have high growth elasticities of poverty and fast growth rates (rankings are in columns 5 and 6). Poverty reduction is greatest in states like Kerala, Punjab, and Andhra Pradesh (states with significant reduction of inequality of educational opportunity) whilst it is lowest in states like Bihar, Assam, and Madhya Pradesh (states with poor record of equality of educational opportunity). On the whole, there is a very high positive correlation (rank correlation coefficient of 0.70-0.71) between inequality of opportunity and poverty reduction. States that have reduced poverty are also those who have low inequality of opportunity in 2004. Most assuring is the finding that states that have succeeded in reducing poverty are also those that made significant gains in reducing inequality of opportunity between 1983 and 2004. This is confirmed by the positive correlation between rankings based on poverty reduction and inequality of indices. A similar positive correlation also exists with respect to growth rate. However, the rank correlation coefficient is smaller in size suggesting the relative importance of poverty reduction over economic growth in equalizing educational opportunity. 19