By Lauren Hartel

Few topics are as challenging to the study of economics as healthcare. Health is double-counted as a commodity and a human right and fails the main conditions of a perfectly competitive market. It is also intimately entwined with philosophical questions that economists are frequently unable to answer satisfyingly, such as how to value a life (see note one). As unappealing as this makes health to economists, they cannot help but encounter it in their studies. Not only is health a crucial element of individual and population welfare, but it also has direct impacts on local and national economies by affecting labor efficiency and consumer market participation.

In the past half-century, health economics as a subject has grown substantially. Yet, economic analysis of health distribution in and of itself—particularly in developing countries—remains nascent. The few studies that exist tie health to other socioeconomic variables such as income or income inequality, confounding the examination of health distribution. The United Nations’s health-related Millennium Development Goals (MDGs) also neglect health inequality (see note two). Instead of recognizing health equality as a means to eradicating extreme poverty, the goals focus on increasing specific health outcomes, such as child and maternal mortality, and the spread of communicable diseases. While these measures are certainly useful, they are not sufficient on their own.

When Max Lorenz created the first curve measuring income inequality, he argued that no matter how income distribution is valued, the importance of knowing the distribution in the first place is undeniable. This logic easily extends to healthcare: no matter one’s view on the benefits of equal health distribution, it must be agreed that the distribution itself is worth examining. The proposed Sustainable Development Goals (SDGs), should therefore include measures of health distribution in addition to absolute health measures. One such measure can be created in the form of a Health Inequality Index (HII), presented herein– the first attempt at directly quantifying inequality of health burden. The HII uses World Health Organization (WHO) indicators to calculate Gini coefficients for health burden inequality, and to create modified Lorenz Curves to be combined into Overlaid Health Lorenz Curves (OHL curves).

To better understand the meaning of a health burden distribution, it is helpful to follow an approach similar to that of data scientists at the University of South Florida (see note three), who build upon the work of inequality measurement by Hayward Alker and Bruce Russett (see note four). Equation 1 illustrates a nation-state’s population N, with fi denoting the number of citizens of the nation-state. It illustrates the overall health burden of a nation H as a sum of each individual’s share of the health burden hi.

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In a nation-state experiencing perfect equality, each individual would bear an equal share of the health burden (Equation 2). Often this equal share is the expectation ei of an individual (Equation 3). Therefore, the inequality I is the difference between the expected health burden and the actual health burden (Equation 4).

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Alker’s work on inequality focused on the distribution of a single value. Health, however, is extremely multifaceted, and must be dissected into smaller pieces. Here, six global health indicators published by the WHO are used as a proxy for the composite nature of health. The indicators describe overall health burden H as a function of life expectancy and mortality L, cause-specific mortality and morbidity M, selected infectious diseases D, health service coverage C, risk factors R and health systems S (Equation 5; Table 1).

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In reality, it is impossible to define the function f describing how these variables together produce an individual’s overall health. Herein, overall health is defined as the summation of the six factors at the population level in Equation 6 (and at the individual level in Equation 7). While this is an approximation of the true relationship, it provides a useful starting point for analysis, and allows us to see potential relationships between these variables that would otherwise be hidden.

Combining the original definition of a nation’s health burden (Equation 2) with its dissection at the individual level (Equation 7), it can be rewritten as Equation 8. This final equation is the foundation from which to create a national OHL Curve that illustrates national health burden distribution.

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The purpose of a Lorenz Curve is to visualize the difference between the ideal distribution and the actual distribution of a given value or commodity across a population.  In the case of the OHL Curves, a 45 degree line indicates an equally distributed health burde (a), while a second line shows the actual distribution of the health burden (b).


Turning to an example of how the HII can be utilized, Figure 1, displays a model of OHL curves for Western Africa (see note five). It immediately reveals some overarching characteristics of the regional health status. The most equally distributed health indicators are easily identifiable as those closest to the line of equality. Health Service Coverage, for example, has the smallest area of inequality, with the lower 50 percent of the population having only a mildly disproportionate share (58 percent) of the births unattended by skilled health personnel. Conversely, Selected Infectious Diseases has the most unequal distribution with the lower 50 percent of the population carrying approximately 80 percent of the disease burden.


The OHL Curves also highlight where in the population inequality is highest. For example, there is a slight “bump” in inequality between the 50th and 60th percentiles of the population for Health Systems and Selected Infectious Diseases. This raises important research and policy questions: What is it about Health Service Coverage, Risk Factors, and Life Expectancy & Mortality that cause their distributions to be so similar? What causes the middle class to be at increased risk for unequal Health Systems and Selected Infectious Diseases burdens? What programs are being implemented or have been implemented in the recent past that may affect these distributions?

Such questions are essential in working towards the eradication of extreme poverty and the HII produces the data practitioners need to raise and address them. Moreover, by providing Gini coefficients for each indicator, the HII also facilitates goal-setting and cross-population comparisons. Since the data collection of the WHO provides the opportunity to calculate Lorenz Curves and Gini coefficients for each of over 80 health metrics that comprise the six global health indicators, the HII can present a detailed hierarchy of metrics covering all aspects of health.

Because these measurements are anonymous and exhibit scale and population independence, the Health Inequality Index remains accurate and applicable to any health distribution in any size economy or population. Therefore OHL curves and Gini coefficients are particularly useful in evaluating developing countries, where health communities vary in size from multinational regions (such as malaria hot zones) to villages and neighborhoods, and where geographical barriers often prevent the implementation of health programs over a large population.

Of course, the methodology has limitations. In order for the health inequality index to be fully functional, a large amount of data is needed, however collection is often challenging in developing countries. Additionally, even though the data in the health inequality index can be viewed in real-time, certain health outcomes (such as malnutrition) take years, even generations, to manifest in the data. The index’s potentially greatest limitations, however, are the distortion produced in the aggregation process, and the approximation of the health burden function in Equation 7. This Health Inequality Index proposal should therefore not be considered complete. Instead, it forms a basis upon which other researchers may expand. Future studies should focus on enhancing the formula for health burden measures, and optimizing the use of data, and explore the possibility of reintroducing socioeconomic factors to see how inequality of health impacts other aspects of life.

Too often health equality is excluded from the study of health economics. This is unfortunate because it is not until the distribution of health across a population is thoroughly examined and understood that it becomes possible to identify and execute efficient policies. For this reason, the proposed HII could significantly strengthen the utility of the SDG framework, and would help bridge the gap between scholarly research and application by practitioners. If the HII was incorporated into the SDGs, academics could continue to question and refine the theoretical framework behind the index while practitioners developed the application of the index into something truly relevant to fieldwork. Through this dual evolution, major strides can be made in the analysis of causes, characteristics, and implications of health inequality.


NOTE ONE: Many economists have been criticized for attempting to quantify life. In the Affordable Care Act in the United States, cost-effectiveness analysis using quality-adjusted life years (QALYs) is forbidden because of the political sensitivity to assigning monetary values to health outcomes (Health Affairs, 2010).

NOTE TWOUnited Nations. “Millennium Development Goals Indicators,” Effective January 15, 2008.

NOTE THREEBerndt, Donald J., John W. Fisher, and Rama V. Rajendrabab. “Measuring Healthcare Inequities using the Gini Index.” Presented at the 36th Hawaii International Conference on System Sciences, Waikoloa Village January 6-9, 2003.

NOTE FOURAlker, Hayward R. and Bruce M. Russett. “On Measuring Inequality.” Behavioral Science 9(3) (1964): 207-218.

NOTE FIVEThis is used solely to show the abilities of the overlaid curves, and not to assess the health trends of Western Africa, as at present the poor data quality does not permit this. Data comes from the World Health Organization’s Data Repository World Health Statistics. The model includes data from 2005-2007, although due to lack of availability, some data dates back as far as 2003. Western Africa is defined as Benin, Gambia, Ghana, Guinea, Guinea-Bissau, Ivory Coast, Liberia, Senegal, Sierra Leone, and Togo.