1 Introduction

F

The system of intergovernmental fiscal transfers as it has evolved in India over the years has come under attack on the ground that it has created perverse incentives by putting a premium on equity to the neglect of efficiency and led to fiscal profligacy at lower levels of government, although, sharp regional disparities persist and have grown sharper, particularly, in recent years (Bagchi 2001).

A number of studies on the issue of “convergence” across states have come up since the end of the first decade of reforms. A very recently published study based on panel data for 16 I ndian states from 1978-79 to 2002-03 finds that there is an i ncrease in the dispersion of per capita incomes across states over time, and the states are not converging to identical levels of per capita income in the steady-state. The author notes that “this is indicative of I ndian states converging to increasingly d ivergent steady-states, which may be attributed to increasing inter-state disparities in levels of private and public investment and an insignificant equalising impact of centre-state government transfers” (Nayyar 2008). Thus, in any discussion on i nter-state disparity, the role of centre-state transfers comes u nder the scanner.

Interestingly, India’s experience is not unique as far as growing regional disparity is concerned. In most developing and transition economies there is a sense that regional inequality of incomes and social indicators are on the rise (Kanbur and Venables 2005). However, in an increasingly globalising world, the policy responses to this trend are far from clear. The core of the economist’s perspective on inequality is interpersonal inequality in economic circumstances as indicated by income or wealth, and the moral arguments against inequality in their distribution among people are well known. However, it is not obvious how those arguments could be extended to inequality between r egions. While the notion of equity refers to certain notions of equality or inequality, the two are not the same. Any notion of equity must confront the question: equality of what? While the

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inequality in per capita state domestic product in India has i ncreased over time, state-level indicators of human development show decreasing dispersion for the obvious reason that indicators of health or education are fundamentally different from income in one very important respect. As the average value of an indicator like the literacy rate or “average lifespan” for the whole population increases, i nequality among subgroups of population d ecreases. This happens because, unlike income, all these indicators have a natural upper limit. Does it then mean that instead of worrying about disparity in social indicators, we should focus only on disparity in per capita income? We argue in this paper that there are relevant aspects of disparity across and within states as far as non-income dimensions of well-being are concerned. But before that, we try to come to terms with various n otions of equity and equality and their relevance in the context of inter-regional resource allocation. In the process, we look at the data on distribution of certain indicators of human development across space and try to relate them to resource allocation priorities as revealed by the actual distribution of certain publicly provided resources.

In the next section, we deal with interpretations of equity and equality in the specific context of inter-regional resource allocation. In Section 3 we introduce, in a more formal way, some a xioms and relate them to certain well-known resource allocation rules. Even though this analysis does not give us a magic formula to solve the perennial tension between so-called efficiency and equity, it aims to clarify the normative implications of alternative ways of redistributing resources among regions. In Section 4, we illustrate, with data on literacy and primary school infrastructure, certain perverse patterns of resource allocation between and within states. In Section 5, we conclude.

2 Equity, Inequality and All That

One of the major normative concerns of policymaking in general is equity. Even though at the abstract level the definitions of vertical and horizontal equity are well understood, in the specific context of resource allocation by a federal government among subnational entities, the interpretation of equity can take a variety of forms depending on the way one seeks to capture empirically the equity consequences of an allocation mechanism. In the context of the recommendations of successive finance commissions, it has been observed that over the years there has been a move t owards assigning greater weight to redistributive factors in the formula for transfer to the states. The 12th Finance Commission, which submitted its report for 2005-10 on 30 November 2004, however, slightly reversed this trend by increasing the weight a ttached to income-neutral factors such as population and area, thereby decreasing the weight for redistributive factors. As a r esult, the non-tax grants do not show the expected inverse relationship with per capita gross state domestic product (GSDP) across states (Rajaraman and Majumdar 2005). This is of course one of the possible interpretations of vertical equity which s uggests that states with lower per capita GSDP should receive relatively larger shares of non-tax grants.

While the principle of horizontal equity in the context of individuals says that individuals who are essentially identical should

180 be treated the same, the principle of vertical equity says that dissimilar individuals should be treated differently. But here we are concerned with regions or spatial entities rather than individuals, and therefore the notions of equity become more complex. However, there is a connection between the two types of inequality. As we mentioned at the beginning, there is a good deal of e vidence that inequality in income/consumption has increased in India in the post-reform period, and there is also evidence that the inequality in per capita GSDP across states has increased. Given this, it would be interesting to know how much of the i ncrease in overall inequality could be accounted for by the i ncrease in the between-state component. Empirical studies on the nature of spatial inequality in a variety of countries show that a key determinant of household well-being in a region, over and above household specific characteristics, is the quantity and quality of infrastructure in that region. One is then naturally inclined to think that reducing inequality between regions is an important way of reducing overall inequality.

There can be an independent moral argument for policies that aim to reduce inter-state inequality apart from their instrumental role in bringing down overall inequality. There is no reason to believe that the distribution of individual attributes, such as ability, is markedly different in different states. Any disparity in average outcomes across states then must be considered iniquitous and has to be corrected. When there is a high degree of correspondence between inter-regional disparity and the feeling of discrimination among groups of people who identify themselves with the culture and language of a particular region – as we see in India – the inequalities take on greater significance than their contribution to overall interpersonal inequality.

The normative force of any notion of equity depends on the analysis of the underlying causes of inequality. If we lived in a neoclassical frictionless world, there would be no inequality across different regions even though inequality in interpersonal distribution of income might be very high as different individuals would choose to specialise in different activities, and the relative productivity of their efforts together with the relative prices of their endowments and outputs would determine the distribution of income. Since the final distribution of income is entirely the result of voluntary transactions in an ideal frictionless market, the normative space for equity is narrowed down to the initial distribution of endowments. The Second Welfare Theorem states that a society can attain through market exchange any particular “desired” (which the society may consider “just”) outcome among all the alternative attainable Pareto efficient outcomes, provided the initial endowments of individuals are suitably reallocated. However, the space for equity widens as soon as we recognise the pervasive nature of market failure. Market failures of various kinds may lead to different kinds of inequality, some of which are morally more significant than others from the equity point of view. It is often argued that the poor cannot get out of the poverty trap because of the failure of the loan and credit market to fi nance investment in human capital. In this analytical framework, most of the ethical justifications for pro-poor policies are redundant as those policies can very well be justified in terms of correcting market failure and hence enhancing efficiency.

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3 An Axiomatic Approach to the Allocation Problem

As the allocation of grants-in-aid the ostensibly addresses e quity issues, it would be worthwhile to explore a set of ethical conditions that an allocation rule is reasonably expected to satisfy. In this exploration, we draw heavily on Roemer (1993). For an allocation decision of this kind, two kinds of data for each state are needed: the data on the indicator that is supposed to improve after resource allocation and a kind of “production function” that tells us about the efficiency with which a given amount of resource produces the outcome. Let the outcome indicator be some indicator of human development (HD), and let the per capita resource allocated to a state be denoted by x and the production function by q(x). One state may be more efficient than another in converting resources into outcome. This will be reflected by the differences in q(x). If there are n states, then the set of relevant information that the Centre starts with is S = [M, (q1, N1), (q2, N2)…, (qn, Nn)], where M is the total resource to be distributed and Ni is the population of the i-th state. However, this information set may not be adequate if we recognise the ethical importance of “circumstances” vis-à-vis “effort”. The value of q(x) subsumes the differences that two states may have even when they have the same production function, that is, qi(.) = qj(.). The first state, for example, may have a favourable climate and a good natural source of drinking water but its government may be inept in implementing and managing intervention programmes, while in the second, the climate may be unfavourable but its government tries hard to improve things. Two states may have the same effective production function, but if the allocation rule must take into account the kind of differences we have just mentioned, the information set should contain those additional pieces of information. Let us denote the set of all the relevant information for the i-th state by Ωi. The information set S that the centre should have is S = [M, (q1, N1, Ω1), (q2, N2, Ω2) …, (qn, Nn, Ωn)].

Let the allocation rule be specified by R(S) = (x1, x2, …, xn), where Σ xi = M. Thus, after the i-th state receives xi, it is expected to produce HD= qi(xi/ Ni). We can now state a set of conditions that may be considered “reasonable”:

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does not matter. This may be contentious since we argued above that differences between states in terms of Ω should matter in an allocation decision. The implication of assuming this will soon be clear once we state the allocation rule that satisfies this.

We can now explore the possible allocation rules that would satisfy all or some of the conditions stated above.

Theorem (Roemer): If the allocation rule R satisfies axioms A1 through A6, then R is leximin.

Under leximin rule, resources are allocated in such a way that they are first allocated to the state with the lowest HD until its HD is raised to the HD of the second lowest state, and so on. An interesting corollary of this characterisation is that utilitarianism, which may be considered as an important alternative to leximin, satisfies all the axioms except A2 (monotonicity). Therefore, in a practical context like centre-to-state resource allocation, it would be interesting to note if monotonicity is satisfied or not. What would be a utilitarian rule, or a refined version of the rule, that is, population-weighted utilitarianism, in this context? The population-weighted utilitarian rule would assign the largest fraction of the total resources to the state that is able to make the maximum improvement. Utilitarianism would be insensitive to the initial level of HD, as it compares the rates at which the levels improve. While in modern ethical theory utilitarianism as applied to individuals is much criticised for its insensitivity to individual rights, there is a certain peculiarity about the doctrine. Most people with egalitarian concerns would not hold the view. Yet, for a wide range of people, it is the view towards which they find themselves pressed when they try to give a theoretical account of their moral beliefs. In the passage quoted from Bagchi (2001) at the beginning, those who attack the system of inter-governmental transfer for “putting a premium on equity to the neglect of efficiency” are essentially drawing on the utilitarian logic of maximising the aggregate.

On the contrary, even though leximin rule in abstract may have some appeal to the egalitarians, in the context of resource allocation for human development it can lead to a situation where all the scarce resources are poured into the state that might be a “hopeless” case.

Egalitarianism with respect to resources may imply egalitarianism with respect to well-being or human development, provided resources are interpreted sufficiently broadly to enable d ifferences in the “production functions” between entities to be ascribed to different endowments of “internal” resources. Different sub-national units have different capacities to translate c ertain financial resources into well-being outcome. The “internal”

INTER AND INTRA-STATE DISPARITIES

r esources may include favorable or constraining factors of a natural or institutional kind. One state may be particularly efficient at using resources because it already has a well-organised network of rural clinics or schools in place. Another state might make less effective use of the resources allocated, maybe because it c hannels too large a fraction of the resources to uses not directly benefiting the target groups of people.

We have examined two well-known allocation rules, populationweighted utilitarianism and leximin, whose axiomatic properties are well-discussed in the social choice literature. As populationweighted utilitarianism basically gives the weight to efficiency, it may lead to a situation where Punjab receives more than Bihar, which is what has been observed in the context of 12th Finance Commission. The normative implications of this, however, are not the same across evaluative spaces. While population-weighted utilitarianism in the space of income may lead to such a disturbing consequence, the same rule in the space of infant mortality, for example, may not be so. It seems that saving infant lives would be valuable irrespective of where the infants are situated, and the boundaries between the states may not be morally too relevant. What seems to be important is that the maximum number of lives be saved with the given resources. This takes us to the following important questions: When are the boundaries of states morally relevant, when are they not? Is it not more i mportant to save the maximum number of infants irrespective of where they occur? If minimising premature death is all we care about and state A could save more lives than state B could with a certain sum of money, could one reasonably argue that A should get more than B?

Let us put it a bit more formally. Suppose the central government is considering the division of x million rupees between two regions, A and B. Let the fraction to be allocated to A be denoted by e and the fraction to be allocated to B be denoted by (1-e). Each state has z children at risk, who will die in the absence of extra resources. For each million rupees allocated to A, the number of children saved will be az and the corresponding number for B will be bz. Assume that a > b since the government in A is more efficient in utilising resources to save the children’s lives.

If, out of x million rupees A receives ex and B receives (1-e)x, then the number of children saved in A will be aexz and the number of children saved in B will be b(1-e)xz. It is clear that if the centre wants to save the maximum number of children, it should allocate the entire sum to A, that is, e should be 1 (assuming that even when it allocates the entire sum to A, there will still be some children who will die there because of a lack of resources). Is this an ethically compelling reason to have e = 1? We believe there are strong arguments in favour of giving more to B rather than A. They come from the ethical concern for fairness.

Assume that when the number of children saved in a given region is w, each of the z children at risk in that area has the same responsible for the efficiency or inefficiency of the governments in the region where they happen to be born. Nor did they choose where they were to be born. Given this, is the outcome that gives more to A fair to the children in region B?

We have taken an extreme example to emphasise the point here. Quite a few restrictive features in our example can be relaxed without changing the basic intuitive point. Incidentally, not much will be changed if we replace the children at risk by adults at risk, or any other kind of risk, such as the “risk” of remaining illiterate.

It now seems that if we accept fairness as the most important ethical goal to which societies should give priority, the thing to be equalised should be the probabilities of survival. But it leads to a related question: At what level of “society” should we try to equalise these probabilities? I, as an Indian, share the same life expectancy with other Indians (which means with a Malayali too). But as a Bengali I share a life expectancy with other Bengalis that is different from the life expectancy of a Malayali. Similarly, a Kolkatan has a different life expectancy than a person living in Purulia district. Maybe it would require a kind of iterative process. However, there is no easy answer to the question that we have raised above.

From the discussion, it is obvious that equalising per capita transfer to the states is not sufficient to provide equal opportunity for all-round development in all of them. However, even though B, whose “production function” is less efficient than A, has good reason to claim more resources, as we argued above, we must distinguish between the circumstances beyond a state’s control that influence its ability to effectively utilise resources for development, and the effort that the state makes to utilise r esources. Equalising opportunity would require distributing r esources in such a way that the lower abilities of states to turn resources into HD achievement are compensated for. Here by “ability” we mean circumstances beyond the control of the state. There is no compelling argument as to why differential achievements due to the application of insufficient effort should be compensated for. However, in practice it may be extremely difficult to separate the relative roles that circumstances and effort play in the achievement or non-achievement of a state. In the next s ection we show that the existing within-state distribution of r esources in most states is hard to justify in the light of our c onceptual discussion.

4 Some Aspects of Inequality in Non-income Dimensions

While the inequality in per capita state domestic product in India has increased over time, state-level indicators of human development show decreasing dispersion for the obvious reason that

Figure 1: Literacy Rates for States and Inter-District Disparity

100

90

chance of being saved. So the probability of each child (at risk)

being saved is w/z. In that case, when we give all the resources to

A, that is, when e = 1, the probability of survival of each of the z

Literacy Rates 80 70 60 50

0.000 0.050 0.100 0.150 0.200 0.250

probability of survival of each of the z children at risk in B will

Coefficient of Variation across Districts

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i ndicators of health or education are fundamentally different from income in one very important respect. It is always true that as the average value of an indicator like literacy rate, mean years of schooling, or “average lifespan” for the whole population i ncreases, inequality among subgroups of population decreases.

Table 1: Composite Index of School Infrastructure at Primary Level for States (2005-06)

In Table 1 we present data on a select number of indicators of school infrastructure at the primary level across the states. Studies conducted in different countries have generally found that a key determinant of household well-being in a region, over and above household specific characteristics, is the quantity and quality of infrastructure in that region (Kanbur and Venables 2005). Even though we generally believe that good school infrastructure leads to better outcome, we do not know the extent of the effect that a particular school input has on enrolment, dropping

Figure 2: Literacy Rates and Index of Primary School Infrastructure for States

100

90

Literacy Rates

80

70

60

Manipur 2.9 3.7 20.1 21 2.5 21 0.82

50

Tamil Nadu 2.7 7.6 4.7 26 4.3 30 0.81 Karnataka 2.0 18.8 16.9 24 4.1 24 0.81

40

0.0 0.2 0.4 0.6 0.8 1.0

Delhi 1.7 0.2 0.5 47 4.9 43 0.80

out, or learning achievement. Nevertheless, it is worthwhile to

The ratio indicates the opportunities for further education avail-

Rajasthan 2.5 5.3 40.8 31 6.1 37 0.69

able to students who complete primary education. The percent-

Goa 3.0 31.7 42.8 21 1.2 22 0.68

age of single-classroom schools, student-classroom ratio, per-

Arunachal Pradesh 3.1 25.2 62.2 19 2.1 25 0.63

centage of single-teacher schools, pupil-teacher ratio – all these

Madhya Pradesh 2.8 11.5 32.1 50 15.6 41 0.61

indicators are believed to have a direct influence on educational

Uttar Pradesh 3.0 1.2 5.2 57 44.2 60 0.56

outcome. Clearly, different indicators show wide variations.

Jharkhand 4.0 6.4 33.1 69 19.7 48 0.50 West Bengal 5.3 17.9 6.1 52 35.2 48 0.48

Table 2: Correlation between Literacy (2001) and Different Indicators of Primary

Assam 3.2 64.1 21.9 59 37.1 34 0.43

School Infrastructure (2005-06)

Bihar 3.2 12.6 10.7 91 66.4 63 0.37

natural upper limit. It is therefore not surprising that we find a

Assam -0.17 -0.29 -0.60 -0.65

strong negative relationship between the literacy rate of a state

Bihar 0.48 0.44 -0.51 0.01

and inter-district disparity in literacy within the state (Figure 1,

Chhattisgarh 0.08 -0.65 0.39 0.39

p 182). The value of the correlation coefficient is -0.78.

Gujarat -0.29 0.05 -0.55 -0.28

Almost always disparities in health or education refer to

Haryana -0.05 0.40 -0.41 0.18

inequality in outcomes. Yet, equalising outcome can hardly be a

Himachal Pradesh -0.17 -0.41 0.22 0.13

practical goal of any egalitarian policy. An objective to attain

Maharashtra -0.08 -0.17 0.41 0.14

probability of remaining illiterate is the same as in region B, then

Orissa -0.30 -0.19 0.27 0.37

it can be argued that both A and B should have the same level of

Punjab 0.33 0.54 -0.63 -0.71

resources. Alternatively, if in region A the probability of remain-

Rajasthan -0.33 -0.58 -0.01 -0.14

ing illiterate is higher than in B, the allocation priority should be

Tamil Nadu 0.01 -0.22 0.18 -0.34

such that the quality of primary school infrastructure in A is not

Uttar Pradesh 0.05 -0.36 -0.65 -0.67

worse than in B. We checked this basic intuition of ours with data

Uttarakhand 0.57 0.60 -0.59 -0.41

provided by the District Information System for Education (DISE)

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While the percentage of single-teacher schools is as high as 62.2 in Arunachal Pradesh, it is only 0.1 in Kerala. Similarly, 64% of all primary schools in Assam are single-classroom schools, whereas in Nagaland there are only 0.2% such schools. In the last column, we have presented the values of a composite index of primary school infrastructure, which range from 0.34 to 0.94.

Since the infrastructure data correspond to the year 2005-06, it would be interesting to see to what extent the infrastructure responded to the literacy status of a state as it prevailed in 2001. Given that the Sarva Siksha Abhiyan, the largest ever intervention programme in elementary education in India, was in full swing between 2001 and 2006, it would be reasonable to expect that there were attempts to correct an imbalance in the distribution of infrastructure, if any. We find a very high positive relationship b etween the composite index of infrastructure and literacy rate (Figure 2, p 183). The value of the correlation coefficient is 0.64.

We now focus on the distribution of resources within states. Table 2 (p 183) is indeed revealing. We present in the table a number of correlation coefficients – between literacy rates at the district level and each of the four indicators of infrastructure, namely, percentage of single-classroom schools, percentage of single-teacher schools, percentage of schools with a studentclassroom ratio exceeding 60, and pupil-teacher ratio. A high negative number signifies perverse distribution. For example, a correlation coefficient of -0.81 between the literacy rate and percentage of single-teacher schools in Arunachal Pradesh implies that the worse a district was in terms of literacy in 2001, the higher the percentage of single-teacher schools even in 2005-06. Table 2 shows that in most of the states the inter-district distribution of all or some of the resources is rather perverse, going against any reasonable ethical criteria.

The District Primary Education Programme (DPEP) was d esigned to target areas in which female literacy was low. Under the DPEP, districts were given a high degree of discretion in developing strategies to provide access to primary education for all children and reduce primary dropout rates, equalise enrolment across gender and social strata, and improve learning achievement. However, it has been observed that the first districts chosen for intervention were selected on the basis of their ability to show success in a reasonable time frame, and within districts, the areas with the lowest female literacy were avoided (Pandey 2000). This is an interesting instance of how an ethically sound policy based on a certain fairness principle can degenerate into a perverse outcome in practice.

5 Conclusions

In this paper we have discussed the notions of equity and fairness and related them to well-known allocation rules such as leximin and population-weighted utilitarianism, in the context of resource allocation from the national to sub-national governments. After clarifying a variety of conceptual issues, we turn to the practical instance of distribution of primary school infrastructure across and within states. We find that the distribution is highly perverse, in the sense that areas that had high rates of illiteracy are the ones which have poorer infrastructure even in 2005-06, after several years of the Sarva Siksha Abhiyan, the massive intervention programme in elementary education.

References

Bagchi, Amaresh (2001): “Fifty Years of Fiscal Federalism in India: An Appraisal”, Kale Memorial lecture delivered at Gokhale Institute of Politics and Economics, Pune, 8 December.

Kanbur, R and A J Venables, ed. (2005): Spatial Inequality and Development ( Oxford: Oxford University Press).

Nayyar, Gaurav (2008): “Economic Growth and Regional Inequality in India”, E conomic & Political Weekly, 43(6): 58-67.

Pandey, R S (2000): “Going to Scale with Education Reform: India’s District Primary Education Programme, 1995-99”, World Bank Country Studies, Education Reform and Management Publication Series, 1(4).

Rajaraman, Indira and Debdatta Majumdar (2005): “Equity and Consistency Properties of TFC Recommendations”, Economic & Political Weekly, 40(31): 3413-20.

Roemer, John (1993): “Distributing Health: The Allocation of Resources by an I nternational Agency” in Sen, Amartya and Martha Nussbaum (ed.), The Q uality of Life (Oxford: Clarendon Press), 339-57.

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