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Defining health inequality: why Rawls succeeds where social welfare theory fails
Journal of Health Economics 21 (2002) 497–513
Defining health inequality: why Rawls succeeds where social welfare theory fails Antoine Bommier a , Guy Stecklov b,∗ b
a Institut National d’etudes Démographiques (INED), INRA-Jourdan, Paris, France Department of Population Studies, Department of Sociology and Anthropology, Mount Scopus Campus, Hebrew University of Jerusalem, 91905 Jerusalem, Israel
Received 12 May 2000; received in revised form 7 November 2001; accepted 7 December 2001
Abstract While there has been an important increase in methodological and empirical studies on health inequality, not much has been written on the theoretical foundation of health inequality measurement We discuss several reasons why the classic welfare approach, which is the foundation of income inequality analysis, fails to provide a satisfactory foundation for health inequality analysis. We propose an alternative approach which is more closely linked to the WHO concept of equity in health and is also consistent with the ethical principles espoused by Rawls [A Theory of Justice. Harvard University Press, Cambridge, MA, 1971]. This approach in its simplest form, is shown to be closely related to the concentration curve when health and income are positively related. Thus, the criteria presented in our paper provide an important theoretical foundation for empirical analysis using the concentration curve. We explore the properties of these approaches by developing policy scenarios and examining how various ethical criteria affect government strategies for targeting health interventions. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Health inequality; Social welfare; Concentration curve
1. Introduction Increasing interest in health inequality has intensified efforts to provide the tools to measure and analyze the distribution of health. Most of this research is empirically related and is aimed at measurement and evaluation of changes in health inequality. In particular, economists have become increasingly involved in research on health inequality and— borrowing heavily from related research on income inequality—have produced a number of ∗ Corresponding author. Tel.: +972-2-588-3320; fax: +972-2-532-4339. E-mail address: [email protected] (G. Stecklov).
0167-6296/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 6 2 9 6 ( 0 1 ) 0 0 1 3 8 - 2
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important methodological and substantive contributions to this research (recent review by Wagstaff and van Doorslaer, 2000). These contributions include statistical tests of health inequality indicators (Kakwani et al., 1997) and empirical analyses of health inequality trends in developed and developing countries (van Doorslaer et al., 1997; Wagstaff et al., 1991). Despite these important empirical and methodological advances in the field of health inequality, there is not general agreement on the definition and meaning of health inequality. Wagstaff and van Doorslaer (2000) discuss two contrasting approaches: pure inequalities in health and socioeconomic inequalities in health. The pure inequalities in health approach focuses entirely on the distribution of the health variable itself within the population (see Murray et al., 1999, 2000; Le Grand and Rabin, 1986). The socioeconomic inequalities in health approach focuses on the distribution of health across social and economic groups (Wagstaff et al., 1991; Braverman et al., 2000). The former approach leads to usage of standard income inequality measures such as the Lorenz curve and Gini coefficients but where the unit of measure is in terms of health rather than income. The theoretical bases for understanding measures of pure health inequality basically mirror the approaches developed for analysis of income inequality. Widespread interest in the second approach, analysis of the distribution of health across social and economic groups, has led to the development of other tools such as the concentration curve and concentration index. Yet, there has been very little research on the theoretical foundations of these health inequality measures and we believe this partly explains the divergence in opinion on the measurement of health inequality. In this article, we explore the different approaches for defining and measuring both pure and socioeconomic health inequalities. We begin by recalling how the social welfare definition of inequality, which is widely used to study income inequality, can be extended to define a concept of multi-dimensional inequality. We show how this notion of multidimensional inequality may be used to define health inequality. However, our discussion will show why this approach, which is a natural extension of the theory of income inequality, fails to provide an acceptable definition of health inequality. This leads us to consider a new definition of socioeconomic health inequality that captures both the distribution of health and the association between health and income and which is consistent with Rawls’ definition of equity. We show that this approach provides a theoretical basis for the use of the concentration curve as well as a direction for continued theoretical research towards defining health inequality. Finally, we develop a series of policy scenarios to highlight the differences between the various ethical approaches to health inequality.
2. From single to multi-dimensional inequality The theoretical foundations of inequality analysis have primarily focused on developing criteria and empirical tools which allow us to consistently rank distributions with respect to their level of inequality. For the most part, this line of research has proven highly successful and has generated wide acceptance of empirical tools such as the Lorenz curve and Gini coefficient. At the same time, the emphasis has been almost entirely on inequality in a single dimensional factor. As economists have become increasingly concerned with evaluating inequality in more than one dimension—for example, income and health—they have naturally sought to extend the classical theory.
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In fact, the social welfare (SW) approach for income inequality analysis turns out to be quite adaptable to multi-dimensional inequality analysis. Basically, the SW approach developed in Dalton’s seminal article of 1920 suggests that one society can be said to be less unequal than another if, for the same mean income level, it provides a larger social welfare level. Obviously, a precise notion of welfare is central to this definition. Since any definition of SW can be disputed, ranking in terms of inequality is only considered conclusive if the SW criterion gives the same ranking for a wide class of SW functions. Dalton focused on additive SW functions: N
W =
1 U (yi ) N
(1)
i=1
where the social welfare function is the average utility level in society and where the utility of person i is an increasing and concave function of income, yi . It has been shown that this additive SW function can be extended to the more general case where W is symmetric, continuous, monotonic and quasi-concave (Dasgupta et al., 1973; Rotshchild and Stiglitz, 1973). Typically, inequality is measured with respect to a single dimension such as income. However, when another dimension is introduced, such as health, education, or another outcome, Eq. (1) can be easily modified. Instead of having only one argument in the utility function, such as income, one might include two arguments, xi and yi , so that the SW function becomes N
W =
1 U (xi , yi ) N
(2)
i=1
This is the approach developed by Atkinson and Bourguignon (1982) and which they illustrate with an analysis of inequality in income and life expectancy across countries. It is worth noting that in addition to generalizing from one to two dimensions, Atkinson and Bourguignon’s approach also differs from the pure utilitarian approach of Dalton in that they assume that the function U can be derived from the preferences of a social planner or decision maker and not necessarily from individual preferences. As in the single dimensional case, the shape of the U function is important, and economists look for inequality rankings that are valid for the widest possible set of SW functions. Obviously, restrictions on the utility function make it easier to conclude whether one distribution is more or less unequal than another distribution. However, imposing restrictions also reduces the generality of the results. The most common assumptions are that the U function is increasing and concave in both arguments. What is left is deciding on the association between the two variables. Atkinson and Bourguignon propose various assumptions on the cross derivatives. We present four cases: • • • •
Case A: No assumption is made on the cross derivatives. = 0. Case B: The cross derivatives are assumed to equal zero, Uxy Case C: The two factors are assumed to be substitutes, Uxy < 0. > 0. Case D: The two factors are assumed to be complements, Uxy
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Determining the appropriate restrictions will depend on the variables that are to be analyzed. In the following section, we focus on the analysis of inequality in income and health, and we examine the appropriateness of each of these cases for the definition of health inequality. We will ignore measurement issues for now, particularly with respect to the health variable, and simply assume that the income (y) and health (h) variables are both continuously measurable. We consider the problem of measurement of the health variable in Section 4.
3. A social welfare approach to health inequality Atkinson and Bourguignon’s approach allows us to define a bi-dimensional notion of inequality that depends on the distribution of both health and income. However, our interest is not in a fully two-dimensional measure of inequality, but rather in providing a definition and measure of health inequality that is responsive to the degree of fairness in the distribution of health but is relatively insensitive to the degree of inequality in the existing income distribution. One solution involves using the bi-dimensional SW definition of inequality to compare societies with identical income distributions. Where income distributions are the same, differences in bi-dimensional inequality reflect differences in the distribution of health or in its association with income. In practice, societies have very different income distributions. However, income variations can be rescaled in a way such that the new income distribution fits some common reference income distribution and bi-dimensional inequality measures can then be used to define health inequality. 1 Health inequality in country A will be said to be greater than in country B with the same income distribution, if the bi-dimensional health inequality as defined by Atkinson and Bourguignon is greater in A than in B. Health inequality measures based on such a definition encompass two distinct components of health inequality. The first is simply a function of the distribution of health itself within the population and is taken into account by the second derivative of U with respect to health ). The second is due to the association between income and health and has an impact (Uhh . The second component may be accounted for in on SW through the cross derivative Uhy , as proposed by Atkinson and different ways by specifying additional assumptions on Uhy Bourguignon. Of the four cases presented above, Case A is obviously the most appealing and least restrictive since no assumption is made on the cross derivative of the utility function. At the same time, due to its greater generality, we are unable to rank most societies under Case A. Class B makes the strongest assumption about the relationship between income and health since it assumes that the change in utility from income is independent of health and vice versa. The independence between health and income means that the general utility function can be rewritten as, U (y, h) = U (h) + U (y). The independence assumption leads to a situation where bi-dimensional measures of health inequality correspond to the definition 1 Rescaling in this case involves fitting the actual income distribution with an income distribution of reference. In practice, this can be done by using individual ranks in the real income distribution to assign fictive incomes whose distribution will correspond to the reference distribution.
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of health inequality in a single dimension. Thus, the same classical tools developed for the analysis of income inequality, such as the Lorenz curve or Gini coefficient, can be applied to the health variable to compare health inequality across societies. However, such an approach leaves us unable to differentiate between a situation where all health is distributed to the poor, to the rich, or randomly throughout the population. Class C assumes that health and income are substitutes—an assumption consistent with the mainstream politics of health inequality. It is consistent with stated health inequality policies of international organizations that focus on averting undue concentration of ill-health among the poor. It suggests that concentrating ill-health among the poor is less equitable than not concentrating ill-health among the poor. Inequality in income may be compensated through inverse inequality in health. Of course, the extent to which poor health should be distributed towards the rich will depend on the distribution of income and on the exact shape of the utility function. Class D assumes that income and health are complements. This is the opposite of Case C. Under this scenario, the social planner should prefer to concentrate ill-health among the poor. We ignore this case because it leads to social preference of health inequality distributions where the poorest are the sickest—a situation which conflicts with most social goals for health. The above discussion suggests that Class B and Class C are the main focuses of interest with respect to health inequality. Among others, Class A does not allow any ranking in practice while Class D leads us to prefer a society where the rich also enjoy better health than the poor. The next section considers several consequences of defining health inequality using this bi-dimensional SW approach.
4. Weaknesses in the SW definition of health inequality We have shown that the SW approach appears to provide a useful framework for defining and analyzing health inequality, but that its benefits depend on our ability to place restrictions on the evaluation of welfare derived by the combination of given income and health levels. Furthermore, we should consider a series of methodological issues that arise when we try to apply the above concept of health inequality. The first of these issues concerns the measurement of the health variable. The theory of income inequality has been developed under the assumption that income can be measured on a linear scale and that the measure of income inequality should be scale-independent (Atkinson, 1970). The SW criterion does not formally allow income inequality to be ranked between societies with different mean income levels. When researchers are faced with this situation, the problem is typically resolved by rescaling income so both societies have identical mean income levels. Health, however, is more difficult to measure. Health is sometimes measured on a linear scale using anthropometric measures on child height-for-age or weight-for-height z-scores, blood pressure measures on adults, or life expectancy or related measures such as quality-adjusted or disability-adjusted life years (QALYs and DALYs). There is no difficulty in such cases since the health variable can be easily rescaled. However, health data are often also based on ordinal categories, such as self-assessed health status, which are
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impossible to rescale. Health inequality should then only be compared between societies having the same marginal distributions of health, although not necessarily the same joint distribution of health and income. When health is measured by a dichotomous variable, such as child stunting or living status (dead/alive), the mean level is obviously defined. However, equal means imply identical distributions for dichotomous variables. Thus, the problem is essentially the same and, de facto, comparison is only appropriate between societies with identical health distributions. 2 This limitation also highlights the importance of further research on possible health measures. Wagstaff and van Doorslaer (1994) propose a method to translate categorical health indicators to continuous measures and their approach has been applied in van Doorslaer et al. (1997) to analyze health inequality based on self-reported health data from several industrialized countries. Furthermore, their method is supported by results from a validation study conducted on Swedish data (Gerdtham et al., 1999). These are important efforts and continued research in these directions will provide us with more tools to analyze health inequality. The difficulties of measuring health variables are a key concern but they are common to both the SW approach and the Rawlsian approach to be presented below. However, we now turn to the fundamental weakness of the SW approach. This weakness is due to the inconsistency of the SW approach with the basic notion of a just or equitable distribution of health. The literature on health inequality suggests that a fair health distribution does not imply equal health status for all individuals since individuals may differ in their health endowments (Culyer and Wagstaff, 1993). Instead, this ideal rests on the notion that avoidable differences should be reduced or eliminated. This is implicit in the Global Strategy for Health for All resolution (WHA32.30) adopted by the World Health Assembly in 1979 and WHO Health for All. As Whitehead notes (1990), “Equity is . . . concerned with creating equal opportunities for health and with bringing health differentials down to the lowest level possible.” More generally, these aims are consistent with a social justice approach to health (Wagstaff and van Doorslaer, 2000). We believe it is useful to define the health distribution in the ideal equitable society as one where access to health has not been determined by socioeconomic status or income. Why then is the SW approach inconsistent with a social justice approach to health inequality? This is because, regardless of the assumptions that are made on the cross derivatives of the utility function, the sum of utility functions depending on two arguments, health and income, cannot provide an indication of the level of unfairness in the health distribution. Whatever restrictions we place on the cross derivatives of the utility function, the SW approach is unable to reject income-based discrimination in access to health. In Case B income-based discrimination does not matter. On the other hand, in Case C, society will choose discrimination in favor of the poor, even if health is not related to income. In Case D, society will choose discrimination in favor of the rich. Only Case A avoids this pitfall, but we already know Case A is not helpful since it is unable to rank most societies. In fact, the failure of the SW approach is due to the fact that it gives symmetric roles to income 2 We should also note that another measurement problem arises from the fact that we only observe the health of survivors. Nonetheless, the expected utility should be measured by the average destiny of all people and not only from the average destiny of survivors.
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and health. Thus, the SW approach will always opt for conditioning health access on the distribution of income, even if income is not a source of discrimination in access to health. Thus, the SW approach cannot provide a definition of the ideal equitable health distribution or with the basis for a measure of the gap between the ideal and the actual health distribution. Instead, we turn to a different approach which is related to Rawls’ Theory of Justice and helps us provide a definition of both the ideal health distribution in the equitable society and a measure of the distance from this ideal.
5. A Rawlsian approach to health inequality measurement Our goal is to offer a definition of health inequality that is consistent with prevailing egalitarian principles with respect to health inequality. Our approach follows from Rawls’ First Principle of Justice (1971). According to Rawls’ First Principle of Justice, basic freedoms must be distributed equally throughout society. However, we must address the fact that the First Principle cannot be directly applied to health. Rawls himself labels health a natural good and explicitly rules out health as a basic freedom (Rawls, 1982). We argue nonetheless that Rawl’s first principle can be used as a basis for defining health inequality once we recognize that the actual health of individuals depends on both individual health endowments as well as on how health endowments are transformed into actual health through access to health resources. We agree with Rawls’ perspective that it makes little sense to include actual health status itself as a basic freedom since individuals differ in their health endowments and it would be absurd to define the ideal society as the one where all individuals were genetically identical. Instead, we propose that access to health resources is a basic freedom and therefore that health access should be distributed equally in the ideal society. Thus, all individuals should have the same opportunity to achieve their potential health levels. This means we should expect two individuals with equivalent health endowments to reach the same health level, regardless of their socioeconomic status. A society where some individuals have limited access to health, relative to others, is to be considered unfair, regardless of the source of the discrimination. Once we recognize health access (a) as a basic freedom, Rawls’ First Principle of Justice provides a natural step towards defining the concept of health inequality. Rawls’ First Principle then indicates that health access should be equally distributed. In this case, the ideal measure of health inequality might appear to be a simple unidimensional measure such as the Gini coefficient applied to a health access measure. The problem is that access to health is not observed. We can measure the actual health status (h) of individuals but we have no information on their health endowments (e) and therefore the gap between the two is unmeasurable. However, if we assume that e is distributed independently of one variable, y, and a is identical for the entire population, actual health, h, should then also be independent of y. Any existing relationship between h and y is proof of health inequality and stronger association between y and h indicates higher levels of health inequality. Thus, by examining the association between y and h we can assess one component of inequality in access to health, even if access to health is not directly measurable. This is why we propose to measure health inequality by measuring the association between observed health, h, and another variable, y, which is unrelated to the health endowment and is discussed below.
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Our approach bears resemblance to a similar definition Roemer (1998) has offered for equality of opportunity. However, Roemer’s approach and ours are focused on rather different philosophical concerns. Roemer is primarily concerned by the fact that individuals may not invest equal levels of effort in the production of their own health. He argues that unequal effort should not be confused with inequality per se. His definition for the perfectly equal society is the one that provides the same level of outcome (health in this case) for all those who invest the same degree of effort. Our work is less concerned by variations in the effort levels of individuals in the production of health, and more concerned by heterogeneity in health resulting from unobservable natural factors (something we label “natural endowments” but may simply be “luck”, etc.). There is definitely a difference between Roemer’s concern and ours, or in other words between “degree of effort” and “luck”, but since both of these factors are unobservable, the two definitions lead to similar definitions of health inequality. In fact, the unobservability of degree of effort in Roemer’s work, and of natural endowment in our work, makes it necessary to add similar additional independence assumptions (Roemer, 1998, p.15). Obviously, the association between h and y may not account for the entire variation in a. Indeed, it may be possible that a is not equally distributed but that the variation in a is orthogonal with the variation in y. Our approach is therefore conditional on the appropriate choice of a variable y. Such a variable should be: (i) independent of health endowments and (ii) likely to reflect a major cause of discrimination in access to health. There is no obvious choice for such a variable. Discrimination in access to health is likely to be based on socioeconomic-status and income seems a good choice with respect to the second point. However, it does not fully satisfy condition (i) since a poor health endowment may be a cause of low income. Better candidates may be parental socioeconomic status which may be more consistent with point (i) or an instrumented socioeconomic status measure. For simplicity, we will thereafter refer to income as the y variable even though we recognize that such a variable does not fulfill requirement (i). In practical applications, more thought should be given to the choice of this variable according to the characteristics of the data that are used and to the socioeconomic environment of the population under study. Once we choose a measure of y, such as income, our concept of health inequality simply focuses on the association between the health and income distributions. Unfortunately, there is no universal method for measurement of the association between two distributions. Obvious and simple candidates include the covariance, the correlation, and the Spearman correlation. However, each of these measures relies on an implicit value judgement. For example, the correlation is appropriate for detecting a monotonic trend between two variables and weights each observation according to its distance from the mean. The Spearman correlation is based solely on the rank of the observations and thus is only affected by relative positions in both the health and income distributions. This means that measures of health inequality based on the covariance implicitly assume that only the relative income and health levels matter, while measures based on the Spearman correlation depend only on positioning along the income and health scales. The two criteria clearly rely on different conceptions of health inequality. The Relative Index of Inequality is another common indicator which is closely related to the Concentration Index and is obtained by regressing the relative health level on the ranking in the income distribution (Kakwani et al., 1997). In fact, the relative index of Inequality reflects properties of both the covariance and
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the Spearman correlation since it focuses on how positioning on the economic scale affects the relative level of health. It is impossible to choose among the many potential measures of bivariate association without first introducing some social value judgement. This problem is identical to trying to choose among the many measures of income inequality such as the Gini coefficient, Theil coefficient, or the variance of the logarithm. For this reason, economists prefer to use inequality criteria that are based on a class of inequality measures, as illustrated with the SW approach to income inequality. Here, we propose a parallel approach and offer criteria that can be used with a wide class of health inequality measures. Following the theoretical approach of Rawls and including our assumption that health access is a basic freedom, we argue that the expectation of actual health given income, E(hi |yi ), should be equal to the average health level in the society, E(hi ), and therefore independent of income. Analysis of the variation of E(hi |yi ) within societies provides a useful criterion for assessing health inequality. Yet, we have not specified how this variation should be measured-a problem that depends on how one weights minor variations compared to large variations but our challenge is now reduced to the more traditional one of measuring inequality in one dimension: inequality in E(hi |yi ). Thus, we suggest one simple indicator of health N
1 W1 = U (E(hi |yi )) N
(3)
i=1
where U is an increasing and strictly concave function. Such indicators share certain important properties with the SW function defined by Eq. (2). In particular, they have an additive structure which makes it relatively easy to compute society’s “willingness” to improve one person’s health relative to another or, in other words, to define a health policy. However, W1 type indicators are also quite different since they do not assume separability between the health and income of different individuals. This means it is generally impossible to define intervention priorities between any two individuals without having more information on the health and income distributions within the population. Clearly, for any concave function, U, for a given average health level, the W1 indicator will lead us to prefer the situation where there is no association between hi and yi . The shape of the function U will determine the tradeoff between inequality and the average health level. Strict adherence to the priority for health based on the First Principle would require us to assume an infinitely concave U function that would imply the equalization of expected health across society. Indicators defined by Eq. (3) lead us to our first general criterion of health inequality, the W1 criterion, which states that health inequality in society A can be said to be greater than in society B, if W1 is always larger in B than in A, for all functions U which are increasing and concave. 3 This health inequality criterion is based on a class of unidimensional inequality measures. Thus, it can be easily interpreted using a graphical representation by drawing the Lorenz curve for the variable E(hi |yi ). One particular case is when E(hi |yi ) is an increasing 3 Like in the Social Welfare case, such a criterion can not rank all societies. As illustrated in the literature on income inequality, additional restrictions may be imposed on the function U, and this makes it possible to increase the number of societies that may be ranked. However, this possibility must be balanced by our interest and willingness to make specific ethical assumptions on inequality at different health levels.
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function of income. Then ranking in terms of E(hi |yi ) and ranking in terms of income are identical and the Lorenz Curve exactly corresponds to the concentration curve. In fact, our proposed W1 criterion is closely related to the concentration curve, which is probably the most widely used measure of health inequality. However, there has been very little effort geared towards developing the theoretical foundations of the concentration curve. Our results suggest that the extensive use of concentration curves for comparisons of health inequality, evident in both theoretical (Contoyannis and Forster, 1999) and empirical research (e.g. van Doorslaer et al., 1997) is consistent with the Rawlsian approach. One drawback to the above function, W1 , is that it does not depend on the distribution of health within income groups. However, according to a Rawlsian approach to health inequality, the full distribution of health conditional on income, rather than simply its average, should be independent of income. Therefore, an improved measure of health inequality might also depend on the distribution of health within income groups. This can be easily resolved by assuming decreasing returns to health in the objective function. That is, N
W2 =
1 U (E(v(hi )|yi )) N
(4)
i=1
with U and v being increasing and concave. In Eq. (4), concavity in the function U still reflects aversion to inequality across income groups while concavity in the function v represents aversion to inequality within income groups. Measures like W2 appear to be simple extensions of W1 measures. Such inequality measures will obviously depend on the particular shapes of the functions U and ν, but again a general inequality criterion can be defined considering the classes of increasing and concave functions. Such a criterion is closer to the Rawlsian concept of health inequality, but it no longer has a direct relationship to the concentration curve. While this clearly reduces its immediate relevance in relation to the current literature, an indicator such as W2 has the advantage of encompassing both a unidimensional and bi-dimensional approach to defining and measuring health inequality. In the next section, we further examine the properties of both measures using policy scenarios and we also contrast their implications with those obtained from alternative ethical criteria to health inequality.
6. Implications for the design of health intervention policies We illustrate here the implications of various ethical approaches to health care intervention. We assume that governments accept a particular tradeoff between equity and efficiency and we consider a series of simple scenarios where the health technology remains constant while the ethical goals of the government are varied. We assume the public sector has the opportunity to distribute a new health treatment to the population but that the cost of the treatment makes universal coverage impossible. Thus, the government must decide on a strategy for targeting the new treatment. Whatever strategy is adopted, there will be a trade-off between equity and efficiency and the final decision will depend on the government’s aversion to health inequality. Our goal is to highlight how the equity component will be valued differently according to the inequality measure that is used.
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Fig. 1. Equity-efficiency tradeoff: targeting when only health equality matters.
A number of simplifying assumptions are introduced. We assume that the health (h) and income (y) variables are continuous and measurable. We assume that the health intervention produces only a marginal effect on individual health levels and thus an infinitesimally small impact on the health distribution. We assume that this health impact depends on the health and income levels of those treated. The health impact of the treatment is assumed to be larger for persons at lower initial health levels or higher income levels. 4 This means that program efficiency may be increased by targeting interventions towards less healthy or more wealthy persons. This is implicit in the positive slope of the iso-technology lines (see dashed lines) shown in Figs. 1–4. Each iso-technology line represents persons along the joint health and income continuum for whom the treatment will produce the same change in health for a given investment in the health sector. Efficiency is increased as we move the treatment towards lines that lie in the southeasterly direction. Each subsequent line 4 These assumptions are not essential but serve to simplify our example. They are also reasonable. Treating less healthy individuals is often more efficient than treating the more healthy which explains the first part of our assumption. For a given level of health, treating the richer may also be more efficient since they are typically more educated and more efficient in the use of medical care. Furthermore, the wealthier are also more likely to pay for treatment. This may further raise the efficiency of per capita public health expenditures on the rich.
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Fig. 2. Equity-efficiency tradeoff: targeting using the social welfare criteria.
represents intervention possibilities that are α times more efficient than interventions on the previous line. The government policy will depend on technological constraints represented by the iso-technology lines and their intersection with welfare and equity principles. We consider several different ethical criteria: health egalitarianism, SW as well as the Rawlsian measures we have proposed and we show how each of these leads to a different government targeting strategy. Ethical criteria may be represented by government indifference curves (see dotted lines) as shown in Figs. 1–4. The indifference curves in each graph represent an equal gain in the government’s objective for a given improvement in health. The scenario shown in Fig. 1 represents the case where the government is solely concerned with reducing health inequality by raising health levels of the least healthy, regardless of their income levels. This leads to the horizontal indifference curves in Fig. 1 since the government’s objective is assumed to depend solely on the health levels of those that are treated. The gain is larger when improving health of individuals at lower health levels and each consecutive curve represents gains in government’s objective that are α times larger. Thus, the distance between the curves measures the level of the government’s aversion to health inequality: the smaller the distance the higher the aversion to inequality.
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Fig. 3. Equity-efficiency tradeoff: targeting based on Rawlsian criteria W1 .
Combining the technological constraints and government preferences on the same figure enables us to see their tradeoff and provides a tool to target health interventions. Turning again to Fig. 1, position b and c represent equivalent equity levels since they lie on the same indifference curve while a and b represent similar efficiency levels because they lie on the same iso-technology line. Positions c and d lie on the line that represents α percent greater health returns than positions a and b for every dollar invested while a lies on the indifference curve representing α percent greater return in terms of equity for every unit of health improvement than positions b and c. Furthermore, positions a and c are equally desirable in terms of targeting. Although, a is α times preferable relative to c in terms of equity, c is also α times preferable in terms of efficiency. A series of iso-targeting lines may be drawn (see solid lines) to reflect interventions that provide equal gain in the government’s objective for a given dollar investment. Positions a and b lie on different iso-targeting lines and it is easy to see why a is a preferable investment from the government’s perspective since it is on the same iso-technology line but offers a higher return in terms of equity. The simplified geometry underlying these scenarios allows them to help us identify how a government with limited resources might use the iso-targeting lines as boundaries for
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Fig. 4. Equity-efficiency tradeoff: targeting based on Rawlsian criteria W1 .
health interventions. Of course, all the above conclusions depend on the assumption that is made on the equity-efficiency tradeoff of the government. A government more averse to inequality would have indifferences curves much closer together resulting in almost horizontal iso-targeting lines and meaning that intervention a would be preferred to almost any other intervention. In contrast, a government little concerned by inequality will have its policy mainly driven by efficiency goals, which would result in iso-targeting lines having almost the same slope as the iso-efficiency lines. In any case, the slope of the iso-targeting lines will lie somewhere between the slope of the indifference curves (horizontal in this case) and the slope of the iso-technology curves—depending on the extent to which the government is ready to trade efficiency for equity. In contrast to the pure health inequality case, we now consider cases where the government priority includes both the distribution of health as well as the association between health and income. Fig. 2 presents the first such case where the technological relationship is the same as Fig. 1 but the government’s aim is to maximize SW (see Eq. (2)) and views health < 0). Because of the acceptability of the tradeoff between and income as substitutes (Uhy health and income in SW, the indifference curves are negatively sloped. Fig. 2 shows that the
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tradeoff between efficiency and welfare will lead the government to choose to compensate the poor with additional health, as compared to the health egalitarianism case illustrated in Fig. 1. If the government were to view health and income as complements (Case D), the slope of the indifference curves would reverse and become positive (not shown). We would then expect the slope of the iso-targeting lines to be steeper than in Fig. 1 to reflect a greater likelihood of focusing treatment towards better off individuals (both in terms of income and health). We now examine W1 , which is the first of our proposed Rawlsian measures. Instead of assuming a tradeoff between health and income, the government is assumed to be primarily concerned with avoiding differences in expected health levels across income groups. Thus, the indifference curves are drawn as vertical lines since there is no stated preference to help individuals at different health levels within an income category. In the first case (Fig. 3), we assume that health and income are strongly and positively correlated and this leads us to draw the indifference curves relatively close together. In the next case (Fig. 4), we consider the consequences of maintaining a similar level of inequality aversion but assuming a weaker association between health and income. This leads to greater spacing between the indifference curves. In both cases, indifference curves to the left imply greater gains in term of equity since they concern income groups who have on average lower health levels. The slope of the iso-targeting line is greater in Fig. 4 than in Fig. 3, although the only change that has been introduced is the statistical correlation between health and income in the population (aversion to inequality and government preferences are the same). Had we introduced a second figure for the SW scenario to represent the difference between weak and strong correlations with no other differences, the targeting line in Fig. 2 would have remained the same, as a consequence of the assumption of additive separability underlying the SW function (Eq. (2)). This last point leads us to stress a fundamental difference between the SW and Rawlsian approaches. In the case of the SW approach, the government targets health interventions towards people with lower utility levels. This means it targets interventions towards the poor if income and health are viewed as substitutes and this targeting is independent of any existing association between income and health. According to the Rawlsian approach, health interventions should be targeted towards the poor for ethical reasons only when there is a positive correlation between health and income. Stronger correlations lead to greater targeting. Thus, the SW approach targets health interventions towards the poor in order to diminish welfare inequality that is due to inequality in both income and health levels. This means that it may be advisable to apply discriminatory health policies even when all individuals have the same health levels in order to compensate for inequality in income. On the other hand, according to W1 , targeting health interventions towards the poor is only advised if low income is statistically found to negatively affect health, since this targeting aims to correct for income-based discriminations in health access. Restricting the indifference curves in Figs. 3 and 4 to be vertical may seem rather inconsistent with common ethical criteria since it means entirely ignoring any preferences to treat the less healthy individuals within income groups. In fact, this is the fundamental advantage of our second proposed measure of health inequality, W2 , which provides the basis for discriminatory health interventions within income groups as well as across income groups. This measure considers both the full distribution as well as the mean level of health within
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each income group. Certain assumptions on the form of the function v would allow us to draw the indifference curves for this case as well. In fact, the indifference curves would be identical to those for W1 except for a slight counterclockwise rotation of the curves leading to a similar slight rotation in the iso-targeting lines (not shown). The extent of the counterclockwise rotation would depend on both the government’s aversion to health inequality within income groups and how within inequality varies between income groups.
7. Conclusion There is widespread interest in reducing health inequality. Economists and other social scientists have engaged in this effort by providing analytical tools and empirical assessments aimed at facilitating the measurement and reduction of health inequality. However, there has yet been very little research on the theoretical foundations underlying the analysis of health inequality. Our paper evaluates the appropriateness of the classic social welfare (SW) approach to the development of a conceptual definition of health inequality. We discuss several measurement and ethical criticisms related to the analysis of health inequality that reduce the desirability of the classic approach. In particular, the SW approach treats income and health as comparable variables—an important drawback in terms of ethical considerations. We propose an alternative approach which appears to be more closely linked to the WHO concept of equity in health and is also consistent with the ethical principles espoused by Rawls (1971). This concept, in its simplest form, is shown to be closely related to the concentration curve as soon as we assume that health and income are positively related. Thus, the criteria presented in our paper provide an important theoretical foundation for empirical analysis using the concentration curve. In addition, we have presented an additional measure which is theoretically more appealing but further study is need in order to determine its usefulness in empirical research on health inequality.
Acknowledgements We thank Shlomo Yitzhaki for critiques and suggestions on an earlier version of this paper. We also benefited from comments from two anonymous reviewers. References Atkinson, A.B., 1970. On the measurement of inequality. Journal of Economic Theory 2 (3), 244–263. Atkinson, A.B., Bourguignon, F., 1982. The comparison of multidimensional distribution of economic status. Review of Economic Studies 49 (2), 183–201. Braverman, P., Krieger, N., Lynch, J., 2000. Health inequalities. Health Inequalities and Social Inequalities in Health. Bulletin of the World Health Organization 78 (2), 232–234. Contoyannis, P., Forster, M., 1999. The distribution of health and income: a theoretical framework. Journal of Health Economics 18, 605–622. Culyer, A.J., Wagstaff, A., 1993. Equity and equality in health and health care. Journal of Health Economics 12 (4), 431–457.
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Dalton, H., 1920. The measurement of the inequality of incomes. Economic Journal 30, 348–361. Dasgupta, P., Sen, A., Starrett, D., 1973. Notes on the measurement of inequality. Journal of Economic Theory 6, 180–187. Gerdtham, U.G., Johannesson, M., Lundberg, L., et al. 1999. A note on validating Wagstaff and van Doorslaer’s health measure in the analysis of inequalities of health. Journal of Health Economics. Kakwani, N., Wagstaff, A., van Doorslaer, E., 1997. Socioeconomic inequalities in health: measurement, computation, and statistical inference. Journal of Econometrics 77, 87–103. Le Grand, J., Rabin, M., 1986. Trends in British health inequality, 1931–1983, In: Culyer, A.J., Bengt, Jonsson (Eds.), Public and Private Health Services. Blackwell, Oxford. Murray, C.J.L., Gakidou, E.E., Frenk, J., 1999. Health inequalities and social group differences: what should we measure? Bulletin of the World Health Organization 77 (2), 537–543. Murray, C.J.L., Gakidou, E.E., Frenk, J., 2000. Reply to Braverman et al on health inequalities and social inequalities in health. Bulletin of the World Health Organization 78 (2), 234–235. Rawls, J., 1982. Social unity and primary goods, In: Sen, A., Williams, B. (Eds.), Utilitarianism and Beyond. Cambridge University Press, Cambridge, MA. Rawls, J., A Theory of Justice. Harvard University Press, Cambridge, MA, 1971 Roemer, J.E., Equality of Opportunity. Harvard University Press, Cambridge, MA, 1998. Rotshchild, M., Stiglitz, J.E., 1973. Some further results on the measurement of inequality. Journal of Economic Theory 6 (2), 188–204. van Doorslaer, E., Wagstaff, A., Bleichrodt, H., Calonge, S., Gerdtham, U.-G., Gerfin, M., Geurts, J., Gross, L., Häkkinen, U., Leu, R.E., O’Donnell, O., Propper, C., Puffer, F., Rodr´ıguez, M., Sundberg, G., Winkelhake, O., 1997. Income-related inequalities in health: some international comparisons. Journal of Health Economics 16, 93–112. Wagstaff, A., Paci, P., van Doorslaer, E., 1991. On the measurement of inequalities in health. Social Science and Medicine 33, 545–557. Wagstaff, A., van Doorslaer, E., 1994. Measuring inequalities in health in the presence of multiple-category morbidity indicators. Health Economics 3, 281–291. Wagstaff, A., van Doorslaer, E., 2000. Equity in health care finance and delivery. In: Culyer, A.J., Newhouse, J.P. (Eds.), Handbook of Health Economics. Elsevier, Amsterdam. Whitehead, M., 1990. The Concepts and Principles of Equity and Health. Discussion Paper prepared by the Programme on Health Policies and Planning of the WHO Regional Office for Europe, 1990.
Defining health inequality: why Rawls succeeds where social welfare theory fails Antoine Bommier a , Guy Stecklov b,∗ b
a Institut National d’etudes Démographiques (INED), INRA-Jourdan, Paris, France Department of Population Studies, Department of Sociology and Anthropology, Mount Scopus Campus, Hebrew University of Jerusalem, 91905 Jerusalem, Israel
Received 12 May 2000; received in revised form 7 November 2001; accepted 7 December 2001
Abstract While there has been an important increase in methodological and empirical studies on health inequality, not much has been written on the theoretical foundation of health inequality measurement We discuss several reasons why the classic welfare approach, which is the foundation of income inequality analysis, fails to provide a satisfactory foundation for health inequality analysis. We propose an alternative approach which is more closely linked to the WHO concept of equity in health and is also consistent with the ethical principles espoused by Rawls [A Theory of Justice. Harvard University Press, Cambridge, MA, 1971]. This approach in its simplest form, is shown to be closely related to the concentration curve when health and income are positively related. Thus, the criteria presented in our paper provide an important theoretical foundation for empirical analysis using the concentration curve. We explore the properties of these approaches by developing policy scenarios and examining how various ethical criteria affect government strategies for targeting health interventions. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Health inequality; Social welfare; Concentration curve
1. Introduction Increasing interest in health inequality has intensified efforts to provide the tools to measure and analyze the distribution of health. Most of this research is empirically related and is aimed at measurement and evaluation of changes in health inequality. In particular, economists have become increasingly involved in research on health inequality and— borrowing heavily from related research on income inequality—have produced a number of ∗ Corresponding author. Tel.: +972-2-588-3320; fax: +972-2-532-4339. E-mail address: [email protected] (G. Stecklov).
0167-6296/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 6 2 9 6 ( 0 1 ) 0 0 1 3 8 - 2
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important methodological and substantive contributions to this research (recent review by Wagstaff and van Doorslaer, 2000). These contributions include statistical tests of health inequality indicators (Kakwani et al., 1997) and empirical analyses of health inequality trends in developed and developing countries (van Doorslaer et al., 1997; Wagstaff et al., 1991). Despite these important empirical and methodological advances in the field of health inequality, there is not general agreement on the definition and meaning of health inequality. Wagstaff and van Doorslaer (2000) discuss two contrasting approaches: pure inequalities in health and socioeconomic inequalities in health. The pure inequalities in health approach focuses entirely on the distribution of the health variable itself within the population (see Murray et al., 1999, 2000; Le Grand and Rabin, 1986). The socioeconomic inequalities in health approach focuses on the distribution of health across social and economic groups (Wagstaff et al., 1991; Braverman et al., 2000). The former approach leads to usage of standard income inequality measures such as the Lorenz curve and Gini coefficients but where the unit of measure is in terms of health rather than income. The theoretical bases for understanding measures of pure health inequality basically mirror the approaches developed for analysis of income inequality. Widespread interest in the second approach, analysis of the distribution of health across social and economic groups, has led to the development of other tools such as the concentration curve and concentration index. Yet, there has been very little research on the theoretical foundations of these health inequality measures and we believe this partly explains the divergence in opinion on the measurement of health inequality. In this article, we explore the different approaches for defining and measuring both pure and socioeconomic health inequalities. We begin by recalling how the social welfare definition of inequality, which is widely used to study income inequality, can be extended to define a concept of multi-dimensional inequality. We show how this notion of multidimensional inequality may be used to define health inequality. However, our discussion will show why this approach, which is a natural extension of the theory of income inequality, fails to provide an acceptable definition of health inequality. This leads us to consider a new definition of socioeconomic health inequality that captures both the distribution of health and the association between health and income and which is consistent with Rawls’ definition of equity. We show that this approach provides a theoretical basis for the use of the concentration curve as well as a direction for continued theoretical research towards defining health inequality. Finally, we develop a series of policy scenarios to highlight the differences between the various ethical approaches to health inequality.
2. From single to multi-dimensional inequality The theoretical foundations of inequality analysis have primarily focused on developing criteria and empirical tools which allow us to consistently rank distributions with respect to their level of inequality. For the most part, this line of research has proven highly successful and has generated wide acceptance of empirical tools such as the Lorenz curve and Gini coefficient. At the same time, the emphasis has been almost entirely on inequality in a single dimensional factor. As economists have become increasingly concerned with evaluating inequality in more than one dimension—for example, income and health—they have naturally sought to extend the classical theory.
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In fact, the social welfare (SW) approach for income inequality analysis turns out to be quite adaptable to multi-dimensional inequality analysis. Basically, the SW approach developed in Dalton’s seminal article of 1920 suggests that one society can be said to be less unequal than another if, for the same mean income level, it provides a larger social welfare level. Obviously, a precise notion of welfare is central to this definition. Since any definition of SW can be disputed, ranking in terms of inequality is only considered conclusive if the SW criterion gives the same ranking for a wide class of SW functions. Dalton focused on additive SW functions: N
W =
1 U (yi ) N
(1)
i=1
where the social welfare function is the average utility level in society and where the utility of person i is an increasing and concave function of income, yi . It has been shown that this additive SW function can be extended to the more general case where W is symmetric, continuous, monotonic and quasi-concave (Dasgupta et al., 1973; Rotshchild and Stiglitz, 1973). Typically, inequality is measured with respect to a single dimension such as income. However, when another dimension is introduced, such as health, education, or another outcome, Eq. (1) can be easily modified. Instead of having only one argument in the utility function, such as income, one might include two arguments, xi and yi , so that the SW function becomes N
W =
1 U (xi , yi ) N
(2)
i=1
This is the approach developed by Atkinson and Bourguignon (1982) and which they illustrate with an analysis of inequality in income and life expectancy across countries. It is worth noting that in addition to generalizing from one to two dimensions, Atkinson and Bourguignon’s approach also differs from the pure utilitarian approach of Dalton in that they assume that the function U can be derived from the preferences of a social planner or decision maker and not necessarily from individual preferences. As in the single dimensional case, the shape of the U function is important, and economists look for inequality rankings that are valid for the widest possible set of SW functions. Obviously, restrictions on the utility function make it easier to conclude whether one distribution is more or less unequal than another distribution. However, imposing restrictions also reduces the generality of the results. The most common assumptions are that the U function is increasing and concave in both arguments. What is left is deciding on the association between the two variables. Atkinson and Bourguignon propose various assumptions on the cross derivatives. We present four cases: • • • •
Case A: No assumption is made on the cross derivatives. = 0. Case B: The cross derivatives are assumed to equal zero, Uxy Case C: The two factors are assumed to be substitutes, Uxy < 0. > 0. Case D: The two factors are assumed to be complements, Uxy
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Determining the appropriate restrictions will depend on the variables that are to be analyzed. In the following section, we focus on the analysis of inequality in income and health, and we examine the appropriateness of each of these cases for the definition of health inequality. We will ignore measurement issues for now, particularly with respect to the health variable, and simply assume that the income (y) and health (h) variables are both continuously measurable. We consider the problem of measurement of the health variable in Section 4.
3. A social welfare approach to health inequality Atkinson and Bourguignon’s approach allows us to define a bi-dimensional notion of inequality that depends on the distribution of both health and income. However, our interest is not in a fully two-dimensional measure of inequality, but rather in providing a definition and measure of health inequality that is responsive to the degree of fairness in the distribution of health but is relatively insensitive to the degree of inequality in the existing income distribution. One solution involves using the bi-dimensional SW definition of inequality to compare societies with identical income distributions. Where income distributions are the same, differences in bi-dimensional inequality reflect differences in the distribution of health or in its association with income. In practice, societies have very different income distributions. However, income variations can be rescaled in a way such that the new income distribution fits some common reference income distribution and bi-dimensional inequality measures can then be used to define health inequality. 1 Health inequality in country A will be said to be greater than in country B with the same income distribution, if the bi-dimensional health inequality as defined by Atkinson and Bourguignon is greater in A than in B. Health inequality measures based on such a definition encompass two distinct components of health inequality. The first is simply a function of the distribution of health itself within the population and is taken into account by the second derivative of U with respect to health ). The second is due to the association between income and health and has an impact (Uhh . The second component may be accounted for in on SW through the cross derivative Uhy , as proposed by Atkinson and different ways by specifying additional assumptions on Uhy Bourguignon. Of the four cases presented above, Case A is obviously the most appealing and least restrictive since no assumption is made on the cross derivative of the utility function. At the same time, due to its greater generality, we are unable to rank most societies under Case A. Class B makes the strongest assumption about the relationship between income and health since it assumes that the change in utility from income is independent of health and vice versa. The independence between health and income means that the general utility function can be rewritten as, U (y, h) = U (h) + U (y). The independence assumption leads to a situation where bi-dimensional measures of health inequality correspond to the definition 1 Rescaling in this case involves fitting the actual income distribution with an income distribution of reference. In practice, this can be done by using individual ranks in the real income distribution to assign fictive incomes whose distribution will correspond to the reference distribution.
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of health inequality in a single dimension. Thus, the same classical tools developed for the analysis of income inequality, such as the Lorenz curve or Gini coefficient, can be applied to the health variable to compare health inequality across societies. However, such an approach leaves us unable to differentiate between a situation where all health is distributed to the poor, to the rich, or randomly throughout the population. Class C assumes that health and income are substitutes—an assumption consistent with the mainstream politics of health inequality. It is consistent with stated health inequality policies of international organizations that focus on averting undue concentration of ill-health among the poor. It suggests that concentrating ill-health among the poor is less equitable than not concentrating ill-health among the poor. Inequality in income may be compensated through inverse inequality in health. Of course, the extent to which poor health should be distributed towards the rich will depend on the distribution of income and on the exact shape of the utility function. Class D assumes that income and health are complements. This is the opposite of Case C. Under this scenario, the social planner should prefer to concentrate ill-health among the poor. We ignore this case because it leads to social preference of health inequality distributions where the poorest are the sickest—a situation which conflicts with most social goals for health. The above discussion suggests that Class B and Class C are the main focuses of interest with respect to health inequality. Among others, Class A does not allow any ranking in practice while Class D leads us to prefer a society where the rich also enjoy better health than the poor. The next section considers several consequences of defining health inequality using this bi-dimensional SW approach.
4. Weaknesses in the SW definition of health inequality We have shown that the SW approach appears to provide a useful framework for defining and analyzing health inequality, but that its benefits depend on our ability to place restrictions on the evaluation of welfare derived by the combination of given income and health levels. Furthermore, we should consider a series of methodological issues that arise when we try to apply the above concept of health inequality. The first of these issues concerns the measurement of the health variable. The theory of income inequality has been developed under the assumption that income can be measured on a linear scale and that the measure of income inequality should be scale-independent (Atkinson, 1970). The SW criterion does not formally allow income inequality to be ranked between societies with different mean income levels. When researchers are faced with this situation, the problem is typically resolved by rescaling income so both societies have identical mean income levels. Health, however, is more difficult to measure. Health is sometimes measured on a linear scale using anthropometric measures on child height-for-age or weight-for-height z-scores, blood pressure measures on adults, or life expectancy or related measures such as quality-adjusted or disability-adjusted life years (QALYs and DALYs). There is no difficulty in such cases since the health variable can be easily rescaled. However, health data are often also based on ordinal categories, such as self-assessed health status, which are
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impossible to rescale. Health inequality should then only be compared between societies having the same marginal distributions of health, although not necessarily the same joint distribution of health and income. When health is measured by a dichotomous variable, such as child stunting or living status (dead/alive), the mean level is obviously defined. However, equal means imply identical distributions for dichotomous variables. Thus, the problem is essentially the same and, de facto, comparison is only appropriate between societies with identical health distributions. 2 This limitation also highlights the importance of further research on possible health measures. Wagstaff and van Doorslaer (1994) propose a method to translate categorical health indicators to continuous measures and their approach has been applied in van Doorslaer et al. (1997) to analyze health inequality based on self-reported health data from several industrialized countries. Furthermore, their method is supported by results from a validation study conducted on Swedish data (Gerdtham et al., 1999). These are important efforts and continued research in these directions will provide us with more tools to analyze health inequality. The difficulties of measuring health variables are a key concern but they are common to both the SW approach and the Rawlsian approach to be presented below. However, we now turn to the fundamental weakness of the SW approach. This weakness is due to the inconsistency of the SW approach with the basic notion of a just or equitable distribution of health. The literature on health inequality suggests that a fair health distribution does not imply equal health status for all individuals since individuals may differ in their health endowments (Culyer and Wagstaff, 1993). Instead, this ideal rests on the notion that avoidable differences should be reduced or eliminated. This is implicit in the Global Strategy for Health for All resolution (WHA32.30) adopted by the World Health Assembly in 1979 and WHO Health for All. As Whitehead notes (1990), “Equity is . . . concerned with creating equal opportunities for health and with bringing health differentials down to the lowest level possible.” More generally, these aims are consistent with a social justice approach to health (Wagstaff and van Doorslaer, 2000). We believe it is useful to define the health distribution in the ideal equitable society as one where access to health has not been determined by socioeconomic status or income. Why then is the SW approach inconsistent with a social justice approach to health inequality? This is because, regardless of the assumptions that are made on the cross derivatives of the utility function, the sum of utility functions depending on two arguments, health and income, cannot provide an indication of the level of unfairness in the health distribution. Whatever restrictions we place on the cross derivatives of the utility function, the SW approach is unable to reject income-based discrimination in access to health. In Case B income-based discrimination does not matter. On the other hand, in Case C, society will choose discrimination in favor of the poor, even if health is not related to income. In Case D, society will choose discrimination in favor of the rich. Only Case A avoids this pitfall, but we already know Case A is not helpful since it is unable to rank most societies. In fact, the failure of the SW approach is due to the fact that it gives symmetric roles to income 2 We should also note that another measurement problem arises from the fact that we only observe the health of survivors. Nonetheless, the expected utility should be measured by the average destiny of all people and not only from the average destiny of survivors.
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and health. Thus, the SW approach will always opt for conditioning health access on the distribution of income, even if income is not a source of discrimination in access to health. Thus, the SW approach cannot provide a definition of the ideal equitable health distribution or with the basis for a measure of the gap between the ideal and the actual health distribution. Instead, we turn to a different approach which is related to Rawls’ Theory of Justice and helps us provide a definition of both the ideal health distribution in the equitable society and a measure of the distance from this ideal.
5. A Rawlsian approach to health inequality measurement Our goal is to offer a definition of health inequality that is consistent with prevailing egalitarian principles with respect to health inequality. Our approach follows from Rawls’ First Principle of Justice (1971). According to Rawls’ First Principle of Justice, basic freedoms must be distributed equally throughout society. However, we must address the fact that the First Principle cannot be directly applied to health. Rawls himself labels health a natural good and explicitly rules out health as a basic freedom (Rawls, 1982). We argue nonetheless that Rawl’s first principle can be used as a basis for defining health inequality once we recognize that the actual health of individuals depends on both individual health endowments as well as on how health endowments are transformed into actual health through access to health resources. We agree with Rawls’ perspective that it makes little sense to include actual health status itself as a basic freedom since individuals differ in their health endowments and it would be absurd to define the ideal society as the one where all individuals were genetically identical. Instead, we propose that access to health resources is a basic freedom and therefore that health access should be distributed equally in the ideal society. Thus, all individuals should have the same opportunity to achieve their potential health levels. This means we should expect two individuals with equivalent health endowments to reach the same health level, regardless of their socioeconomic status. A society where some individuals have limited access to health, relative to others, is to be considered unfair, regardless of the source of the discrimination. Once we recognize health access (a) as a basic freedom, Rawls’ First Principle of Justice provides a natural step towards defining the concept of health inequality. Rawls’ First Principle then indicates that health access should be equally distributed. In this case, the ideal measure of health inequality might appear to be a simple unidimensional measure such as the Gini coefficient applied to a health access measure. The problem is that access to health is not observed. We can measure the actual health status (h) of individuals but we have no information on their health endowments (e) and therefore the gap between the two is unmeasurable. However, if we assume that e is distributed independently of one variable, y, and a is identical for the entire population, actual health, h, should then also be independent of y. Any existing relationship between h and y is proof of health inequality and stronger association between y and h indicates higher levels of health inequality. Thus, by examining the association between y and h we can assess one component of inequality in access to health, even if access to health is not directly measurable. This is why we propose to measure health inequality by measuring the association between observed health, h, and another variable, y, which is unrelated to the health endowment and is discussed below.
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Our approach bears resemblance to a similar definition Roemer (1998) has offered for equality of opportunity. However, Roemer’s approach and ours are focused on rather different philosophical concerns. Roemer is primarily concerned by the fact that individuals may not invest equal levels of effort in the production of their own health. He argues that unequal effort should not be confused with inequality per se. His definition for the perfectly equal society is the one that provides the same level of outcome (health in this case) for all those who invest the same degree of effort. Our work is less concerned by variations in the effort levels of individuals in the production of health, and more concerned by heterogeneity in health resulting from unobservable natural factors (something we label “natural endowments” but may simply be “luck”, etc.). There is definitely a difference between Roemer’s concern and ours, or in other words between “degree of effort” and “luck”, but since both of these factors are unobservable, the two definitions lead to similar definitions of health inequality. In fact, the unobservability of degree of effort in Roemer’s work, and of natural endowment in our work, makes it necessary to add similar additional independence assumptions (Roemer, 1998, p.15). Obviously, the association between h and y may not account for the entire variation in a. Indeed, it may be possible that a is not equally distributed but that the variation in a is orthogonal with the variation in y. Our approach is therefore conditional on the appropriate choice of a variable y. Such a variable should be: (i) independent of health endowments and (ii) likely to reflect a major cause of discrimination in access to health. There is no obvious choice for such a variable. Discrimination in access to health is likely to be based on socioeconomic-status and income seems a good choice with respect to the second point. However, it does not fully satisfy condition (i) since a poor health endowment may be a cause of low income. Better candidates may be parental socioeconomic status which may be more consistent with point (i) or an instrumented socioeconomic status measure. For simplicity, we will thereafter refer to income as the y variable even though we recognize that such a variable does not fulfill requirement (i). In practical applications, more thought should be given to the choice of this variable according to the characteristics of the data that are used and to the socioeconomic environment of the population under study. Once we choose a measure of y, such as income, our concept of health inequality simply focuses on the association between the health and income distributions. Unfortunately, there is no universal method for measurement of the association between two distributions. Obvious and simple candidates include the covariance, the correlation, and the Spearman correlation. However, each of these measures relies on an implicit value judgement. For example, the correlation is appropriate for detecting a monotonic trend between two variables and weights each observation according to its distance from the mean. The Spearman correlation is based solely on the rank of the observations and thus is only affected by relative positions in both the health and income distributions. This means that measures of health inequality based on the covariance implicitly assume that only the relative income and health levels matter, while measures based on the Spearman correlation depend only on positioning along the income and health scales. The two criteria clearly rely on different conceptions of health inequality. The Relative Index of Inequality is another common indicator which is closely related to the Concentration Index and is obtained by regressing the relative health level on the ranking in the income distribution (Kakwani et al., 1997). In fact, the relative index of Inequality reflects properties of both the covariance and
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the Spearman correlation since it focuses on how positioning on the economic scale affects the relative level of health. It is impossible to choose among the many potential measures of bivariate association without first introducing some social value judgement. This problem is identical to trying to choose among the many measures of income inequality such as the Gini coefficient, Theil coefficient, or the variance of the logarithm. For this reason, economists prefer to use inequality criteria that are based on a class of inequality measures, as illustrated with the SW approach to income inequality. Here, we propose a parallel approach and offer criteria that can be used with a wide class of health inequality measures. Following the theoretical approach of Rawls and including our assumption that health access is a basic freedom, we argue that the expectation of actual health given income, E(hi |yi ), should be equal to the average health level in the society, E(hi ), and therefore independent of income. Analysis of the variation of E(hi |yi ) within societies provides a useful criterion for assessing health inequality. Yet, we have not specified how this variation should be measured-a problem that depends on how one weights minor variations compared to large variations but our challenge is now reduced to the more traditional one of measuring inequality in one dimension: inequality in E(hi |yi ). Thus, we suggest one simple indicator of health N
1 W1 = U (E(hi |yi )) N
(3)
i=1
where U is an increasing and strictly concave function. Such indicators share certain important properties with the SW function defined by Eq. (2). In particular, they have an additive structure which makes it relatively easy to compute society’s “willingness” to improve one person’s health relative to another or, in other words, to define a health policy. However, W1 type indicators are also quite different since they do not assume separability between the health and income of different individuals. This means it is generally impossible to define intervention priorities between any two individuals without having more information on the health and income distributions within the population. Clearly, for any concave function, U, for a given average health level, the W1 indicator will lead us to prefer the situation where there is no association between hi and yi . The shape of the function U will determine the tradeoff between inequality and the average health level. Strict adherence to the priority for health based on the First Principle would require us to assume an infinitely concave U function that would imply the equalization of expected health across society. Indicators defined by Eq. (3) lead us to our first general criterion of health inequality, the W1 criterion, which states that health inequality in society A can be said to be greater than in society B, if W1 is always larger in B than in A, for all functions U which are increasing and concave. 3 This health inequality criterion is based on a class of unidimensional inequality measures. Thus, it can be easily interpreted using a graphical representation by drawing the Lorenz curve for the variable E(hi |yi ). One particular case is when E(hi |yi ) is an increasing 3 Like in the Social Welfare case, such a criterion can not rank all societies. As illustrated in the literature on income inequality, additional restrictions may be imposed on the function U, and this makes it possible to increase the number of societies that may be ranked. However, this possibility must be balanced by our interest and willingness to make specific ethical assumptions on inequality at different health levels.
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function of income. Then ranking in terms of E(hi |yi ) and ranking in terms of income are identical and the Lorenz Curve exactly corresponds to the concentration curve. In fact, our proposed W1 criterion is closely related to the concentration curve, which is probably the most widely used measure of health inequality. However, there has been very little effort geared towards developing the theoretical foundations of the concentration curve. Our results suggest that the extensive use of concentration curves for comparisons of health inequality, evident in both theoretical (Contoyannis and Forster, 1999) and empirical research (e.g. van Doorslaer et al., 1997) is consistent with the Rawlsian approach. One drawback to the above function, W1 , is that it does not depend on the distribution of health within income groups. However, according to a Rawlsian approach to health inequality, the full distribution of health conditional on income, rather than simply its average, should be independent of income. Therefore, an improved measure of health inequality might also depend on the distribution of health within income groups. This can be easily resolved by assuming decreasing returns to health in the objective function. That is, N
W2 =
1 U (E(v(hi )|yi )) N
(4)
i=1
with U and v being increasing and concave. In Eq. (4), concavity in the function U still reflects aversion to inequality across income groups while concavity in the function v represents aversion to inequality within income groups. Measures like W2 appear to be simple extensions of W1 measures. Such inequality measures will obviously depend on the particular shapes of the functions U and ν, but again a general inequality criterion can be defined considering the classes of increasing and concave functions. Such a criterion is closer to the Rawlsian concept of health inequality, but it no longer has a direct relationship to the concentration curve. While this clearly reduces its immediate relevance in relation to the current literature, an indicator such as W2 has the advantage of encompassing both a unidimensional and bi-dimensional approach to defining and measuring health inequality. In the next section, we further examine the properties of both measures using policy scenarios and we also contrast their implications with those obtained from alternative ethical criteria to health inequality.
6. Implications for the design of health intervention policies We illustrate here the implications of various ethical approaches to health care intervention. We assume that governments accept a particular tradeoff between equity and efficiency and we consider a series of simple scenarios where the health technology remains constant while the ethical goals of the government are varied. We assume the public sector has the opportunity to distribute a new health treatment to the population but that the cost of the treatment makes universal coverage impossible. Thus, the government must decide on a strategy for targeting the new treatment. Whatever strategy is adopted, there will be a trade-off between equity and efficiency and the final decision will depend on the government’s aversion to health inequality. Our goal is to highlight how the equity component will be valued differently according to the inequality measure that is used.
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Fig. 1. Equity-efficiency tradeoff: targeting when only health equality matters.
A number of simplifying assumptions are introduced. We assume that the health (h) and income (y) variables are continuous and measurable. We assume that the health intervention produces only a marginal effect on individual health levels and thus an infinitesimally small impact on the health distribution. We assume that this health impact depends on the health and income levels of those treated. The health impact of the treatment is assumed to be larger for persons at lower initial health levels or higher income levels. 4 This means that program efficiency may be increased by targeting interventions towards less healthy or more wealthy persons. This is implicit in the positive slope of the iso-technology lines (see dashed lines) shown in Figs. 1–4. Each iso-technology line represents persons along the joint health and income continuum for whom the treatment will produce the same change in health for a given investment in the health sector. Efficiency is increased as we move the treatment towards lines that lie in the southeasterly direction. Each subsequent line 4 These assumptions are not essential but serve to simplify our example. They are also reasonable. Treating less healthy individuals is often more efficient than treating the more healthy which explains the first part of our assumption. For a given level of health, treating the richer may also be more efficient since they are typically more educated and more efficient in the use of medical care. Furthermore, the wealthier are also more likely to pay for treatment. This may further raise the efficiency of per capita public health expenditures on the rich.
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Fig. 2. Equity-efficiency tradeoff: targeting using the social welfare criteria.
represents intervention possibilities that are α times more efficient than interventions on the previous line. The government policy will depend on technological constraints represented by the iso-technology lines and their intersection with welfare and equity principles. We consider several different ethical criteria: health egalitarianism, SW as well as the Rawlsian measures we have proposed and we show how each of these leads to a different government targeting strategy. Ethical criteria may be represented by government indifference curves (see dotted lines) as shown in Figs. 1–4. The indifference curves in each graph represent an equal gain in the government’s objective for a given improvement in health. The scenario shown in Fig. 1 represents the case where the government is solely concerned with reducing health inequality by raising health levels of the least healthy, regardless of their income levels. This leads to the horizontal indifference curves in Fig. 1 since the government’s objective is assumed to depend solely on the health levels of those that are treated. The gain is larger when improving health of individuals at lower health levels and each consecutive curve represents gains in government’s objective that are α times larger. Thus, the distance between the curves measures the level of the government’s aversion to health inequality: the smaller the distance the higher the aversion to inequality.
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Fig. 3. Equity-efficiency tradeoff: targeting based on Rawlsian criteria W1 .
Combining the technological constraints and government preferences on the same figure enables us to see their tradeoff and provides a tool to target health interventions. Turning again to Fig. 1, position b and c represent equivalent equity levels since they lie on the same indifference curve while a and b represent similar efficiency levels because they lie on the same iso-technology line. Positions c and d lie on the line that represents α percent greater health returns than positions a and b for every dollar invested while a lies on the indifference curve representing α percent greater return in terms of equity for every unit of health improvement than positions b and c. Furthermore, positions a and c are equally desirable in terms of targeting. Although, a is α times preferable relative to c in terms of equity, c is also α times preferable in terms of efficiency. A series of iso-targeting lines may be drawn (see solid lines) to reflect interventions that provide equal gain in the government’s objective for a given dollar investment. Positions a and b lie on different iso-targeting lines and it is easy to see why a is a preferable investment from the government’s perspective since it is on the same iso-technology line but offers a higher return in terms of equity. The simplified geometry underlying these scenarios allows them to help us identify how a government with limited resources might use the iso-targeting lines as boundaries for
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Fig. 4. Equity-efficiency tradeoff: targeting based on Rawlsian criteria W1 .
health interventions. Of course, all the above conclusions depend on the assumption that is made on the equity-efficiency tradeoff of the government. A government more averse to inequality would have indifferences curves much closer together resulting in almost horizontal iso-targeting lines and meaning that intervention a would be preferred to almost any other intervention. In contrast, a government little concerned by inequality will have its policy mainly driven by efficiency goals, which would result in iso-targeting lines having almost the same slope as the iso-efficiency lines. In any case, the slope of the iso-targeting lines will lie somewhere between the slope of the indifference curves (horizontal in this case) and the slope of the iso-technology curves—depending on the extent to which the government is ready to trade efficiency for equity. In contrast to the pure health inequality case, we now consider cases where the government priority includes both the distribution of health as well as the association between health and income. Fig. 2 presents the first such case where the technological relationship is the same as Fig. 1 but the government’s aim is to maximize SW (see Eq. (2)) and views health < 0). Because of the acceptability of the tradeoff between and income as substitutes (Uhy health and income in SW, the indifference curves are negatively sloped. Fig. 2 shows that the
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tradeoff between efficiency and welfare will lead the government to choose to compensate the poor with additional health, as compared to the health egalitarianism case illustrated in Fig. 1. If the government were to view health and income as complements (Case D), the slope of the indifference curves would reverse and become positive (not shown). We would then expect the slope of the iso-targeting lines to be steeper than in Fig. 1 to reflect a greater likelihood of focusing treatment towards better off individuals (both in terms of income and health). We now examine W1 , which is the first of our proposed Rawlsian measures. Instead of assuming a tradeoff between health and income, the government is assumed to be primarily concerned with avoiding differences in expected health levels across income groups. Thus, the indifference curves are drawn as vertical lines since there is no stated preference to help individuals at different health levels within an income category. In the first case (Fig. 3), we assume that health and income are strongly and positively correlated and this leads us to draw the indifference curves relatively close together. In the next case (Fig. 4), we consider the consequences of maintaining a similar level of inequality aversion but assuming a weaker association between health and income. This leads to greater spacing between the indifference curves. In both cases, indifference curves to the left imply greater gains in term of equity since they concern income groups who have on average lower health levels. The slope of the iso-targeting line is greater in Fig. 4 than in Fig. 3, although the only change that has been introduced is the statistical correlation between health and income in the population (aversion to inequality and government preferences are the same). Had we introduced a second figure for the SW scenario to represent the difference between weak and strong correlations with no other differences, the targeting line in Fig. 2 would have remained the same, as a consequence of the assumption of additive separability underlying the SW function (Eq. (2)). This last point leads us to stress a fundamental difference between the SW and Rawlsian approaches. In the case of the SW approach, the government targets health interventions towards people with lower utility levels. This means it targets interventions towards the poor if income and health are viewed as substitutes and this targeting is independent of any existing association between income and health. According to the Rawlsian approach, health interventions should be targeted towards the poor for ethical reasons only when there is a positive correlation between health and income. Stronger correlations lead to greater targeting. Thus, the SW approach targets health interventions towards the poor in order to diminish welfare inequality that is due to inequality in both income and health levels. This means that it may be advisable to apply discriminatory health policies even when all individuals have the same health levels in order to compensate for inequality in income. On the other hand, according to W1 , targeting health interventions towards the poor is only advised if low income is statistically found to negatively affect health, since this targeting aims to correct for income-based discriminations in health access. Restricting the indifference curves in Figs. 3 and 4 to be vertical may seem rather inconsistent with common ethical criteria since it means entirely ignoring any preferences to treat the less healthy individuals within income groups. In fact, this is the fundamental advantage of our second proposed measure of health inequality, W2 , which provides the basis for discriminatory health interventions within income groups as well as across income groups. This measure considers both the full distribution as well as the mean level of health within
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each income group. Certain assumptions on the form of the function v would allow us to draw the indifference curves for this case as well. In fact, the indifference curves would be identical to those for W1 except for a slight counterclockwise rotation of the curves leading to a similar slight rotation in the iso-targeting lines (not shown). The extent of the counterclockwise rotation would depend on both the government’s aversion to health inequality within income groups and how within inequality varies between income groups.
7. Conclusion There is widespread interest in reducing health inequality. Economists and other social scientists have engaged in this effort by providing analytical tools and empirical assessments aimed at facilitating the measurement and reduction of health inequality. However, there has yet been very little research on the theoretical foundations underlying the analysis of health inequality. Our paper evaluates the appropriateness of the classic social welfare (SW) approach to the development of a conceptual definition of health inequality. We discuss several measurement and ethical criticisms related to the analysis of health inequality that reduce the desirability of the classic approach. In particular, the SW approach treats income and health as comparable variables—an important drawback in terms of ethical considerations. We propose an alternative approach which appears to be more closely linked to the WHO concept of equity in health and is also consistent with the ethical principles espoused by Rawls (1971). This concept, in its simplest form, is shown to be closely related to the concentration curve as soon as we assume that health and income are positively related. Thus, the criteria presented in our paper provide an important theoretical foundation for empirical analysis using the concentration curve. In addition, we have presented an additional measure which is theoretically more appealing but further study is need in order to determine its usefulness in empirical research on health inequality.
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