These authors contributed equally to this work.

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Formally evaluating how specific policy measures influence environmental justice is challenging, especially in the context of regulatory analyses in which quantitative comparisons are the norm. However, there is a large literature on developing and applying quantitative measures of health inequality in other settings, and these measures may be applicable to environmental regulatory analyses. In this paper, we provide information to assist policy decision makers in determining the viability of using measures of health inequality in the context of environmental regulatory analyses. We conclude that quantification of the distribution of inequalities in health outcomes across social groups of concern, considering both within-group and between-group comparisons, would be consistent with both the structure of regulatory analysis and the core definition of environmental justice. Appropriate application of inequality indicators requires thorough characterization of the baseline distribution of exposures and risks, leveraging data generally available within regulatory analyses. Multiple inequality indicators may be applicable to regulatory analyses, and the choice among indicators should be based on explicit value judgments regarding the dimensions of environmental justice of greatest interest.

Regulatory analyses, which focus on quantifying the health and environmental benefits of alternative policy measures, are required for major environmental regulations in the United States and elsewhere. While regulatory analyses often include some discussion about environmental justice implications, they rarely engage in formal quantitative analyses to compare how alternative policy measures could differentially influence environmental justice.

Whether it is viable to conduct such analyses depends on a number of factors, including whether “justice” is something that can be analyzed or quantified. As discussed elsewhere [

Inequality is a relative (

In contrast to the concept of inequality, the term “inequity” refers specifically to a subset of measured inequalities that are judged to be unfair or unjust. Judgments concerning inequity rely on social, political and ethical discourse about what a society believes is unfair, and are thus considerably more difficult to quantify [

The implication is that quantitative metrics can be used to measure inequality in health outcomes, paralleling the structure of the regulatory analyses, but that a determination of inequity or injustice would be beyond the scope of such analyses. In other words, the tools of regulatory analysis are not well suited for determining which inequalities are unjust and unfair, or whether the processes that led to the status quo situation occurred fairly and reasonably. Nevertheless, given the core definition of environmental justice used by the federal government in the United States [

The question is therefore whether between-group inequality in environmental health risk could be reasonably characterized within regulatory analyses and, if so, what the most logical approaches are for doing so. In this paper, we provide an overview intended to help environmental regulatory analysts understand how health inequality can be measured and how inequality measures can be applied in a new context. We first review the literature on income and health inequality indicators to determine the viability of quantitative measures of environmental health inequality within regulatory analyses. Given these insights, we propose four fundamental attributes of health inequality measures that should be explicitly evaluated before selecting an indicator. We then focus on health inequality measures that provide between-group comparisons consistent with environmental justice concepts, and we conclude by providing a logical approach by which policy decision makers could select among candidate indicators.

We are primarily concerned with characterizing the degree of inequality across social groups in defined health outcomes and how that inequality changes as a function of regulatory measures targeting environmental exposures. While this has not been done to date within regulatory analyses, similar questions have been addressed in the realm of income inequality through the development of numerous indicators with various attributes over the last century [

Income is different from health in some fundamental ways, raising the question of whether and how the income inequality indicator literature can be leveraged to inform understanding of health inequality. As has been argued elsewhere [

Although these are important observations, the differences are not as stark as they may appear [

Given this, health inequality has been characterized in the peer-reviewed literature and in policy analyses for decades, and there are numerous examples of quantitative metrics of inequality being applied to health outcomes. Relatively simple summary metrics have been used to characterize health inequality, comparing levels of health across different pre-defined groups [

First, because the goal of these measures would be to address environmental justice concerns, they should be able to provide comparisons between socioeconomic or racial/ethnic groups of concern. However, this does not necessarily imply that only between-group comparisons are germane. For example, if a pollutant displays significant spatial variability with local “hot spots,” it could be important to target the high-risk individuals within a minority or low-income population to improve environmental justice, rather than reducing risks uniformly across the minority or low-income population, even if the between-group differences are reduced identically. More generally, understanding whether differences in risk are more strongly driven by geography, demographics, or other factors (e.g., behaviors, co-exposures) is important in designing optimal interventions.

Second, because regulatory analyses focus on characterizing health benefits/harms from regulatory measures, any indicators of environmental inequality should be based on the corresponding distribution of health outcomes. Or, if data are lacking to characterize the distribution of health benefits corresponding to a regulatory measure, indicators should be based on the distribution of exposures to health-relevant pollutants, determining how that distribution changes as a result of the regulatory measure. The general point is that the outcomes used in the inequality indicator should aim to be consistent with those outcomes used to characterize aggregate benefits within the regulatory analysis [

Third, inequality measures themselves often have little meaning absent a context for interpretation, but are useful for comparative purposes. This aligns well with the structure of regulatory analyses, which involve comparing a defined set of policy options with the status quo or baseline, to determine the benefits of the regulation (often in comparison with the costs). Inequality measures will therefore be most meaningful when multiple policy options are under consideration and analyses consider the degree to which inequalities change as a result of the policy options.

Finally, inequality measures will also be interpretable only when they take account of baseline inequality and are evaluated in conjunction with health benefits. To illustrate the importance of baseline values, suppose that two different low-income populations could be targeted for risk-reduction measures. The magnitude of risk reduction would be the same for both measures, but one group has elevated baseline health risks in comparison to higher-income populations, while the second group does not differ in its baseline health risks. Clearly, the option targeting the first population would be preferable from an environmental justice perspective, all else being equal, but this difference would be masked if the baseline distribution were not incorporated into the analysis. Including health benefits data is critical because, without measures of the magnitude of health benefits, inequality metrics could be used to argue for “leveling down,” in which environmental justice concerns could be met by increasing exposures among high-income or non-minority populations [

In summary, health inequality has been characterized in the peer-reviewed literature and in policy contexts for decades. Approaches to characterize health inequality have ranged from simple summary measures to more complex statistical formulations, but there is a strong consensus in the literature that it is appropriate to develop and implement health inequality measures. Although such measures have had limited application in the context of environmental regulatory analysis, the prior applications in the health literature suggest inequality analyses are feasible for assessments of environmental justice.

While inequality measures can be described by a number of attributes, including adherence to various mathematical axioms common within the income inequality literature, we focus in this paper on four choices that we consider to be fundamental for developing interpretable measures of health inequality—reference points, scale, social group ordering, and explicit value judgments [

Any inequality measure reflects a comparison between a reference group and other members of the population (or, in the case of between-group comparisons, members of another population group). For example, each individual might be considered relative to the average member of the population, where the degree of inequality is an aggregation of the differences between each individual and the average. As discussed elsewhere [

One could also consider each individual relative to the best-off person or social group in society [

A third formulation involves comparing health risks of an individual or group to all those who are better off, rather than just the single best-off group or person. This provides a greater characterization of the full range of health risks across the population in relation to one another, and is less dependent on the experience of the best-off individual or group [

While these reference points are the most common by far, multiple variants could be considered. For example, various points along the distribution could be selected rather than the average (e.g., the median), although this is rarely done because of the challenges in constructing a single equation that could be clearly presented, as would be needed for interpretable inequality measures. For health risks (as opposed to positive health states), it could be argued that comparison with the worst-off or worst-off person/group whose condition is not anomalous would have value, but it is more typical to consider inequality in the context of the positive steps that could be taken to move individuals to a preferred state.

Regardless, it is important to recognize that each statistical formulation has an implicit or explicit reference group defined, and that the choice of reference group needs to be consistent with the priorities and beliefs of decision makers. It is also important to recognize that this choice has some significant implications. Consider a simple example, in which there are 4 people in the world, with initial health status of 10, 8, 4, and 2, respectively (on a scale from 1 to 10, where 10 is perfect health). Suppose that a policy measure would lead the distribution of health status to change to be 9, 9, 4, and 2—effectively, a one-unit transfer from the healthiest to the second-healthiest. If each individual is compared to the best off, the situation is unequivocally better with respect to inequality—the gaps have changed from (2, 6, 8) to (0, 5, 7), so each person is closer to the ideal. However, if each individual is compared to the average, it is no longer the case that the situation is unequivocally better with respect to inequality—if all differences were equally weighted, inequality would be unchanged. If the individual with health status of 10 is considered “anomalous”, then the policy measure would increase inequality by widening the gap between the two worst off (4, 2) and the second-best-off individual (9). The choice of reference group and form of statistical comparison should be consistent with how decision makers would perceive alternative scenarios.

Another one of the fundamental questions for any inequality measure is whether it is capturing relative or absolute comparisons among the population [

Further complicating this issue is the fact that for all-or-none health states (e.g., presence or absence of disease) the magnitude of relative inequality will depend on whether one considers inequality in the presence or absence of disease [

Whether relative or absolute inequality measures are more appropriate for health inequality in the context of regulatory analysis is not immediately obvious. On the one hand, environmental regulatory analyses typically apply results from epidemiological studies that generally calculate and report uncertainty on a relative scale. It is appealing to have an inequality indicator be insensitive to these relative uncertainties [

When making this decision, it is important to recognize that the inequality measure in a regulatory analysis is not being used in a vacuum, and does not need to both capture environmental justice and overall health issues. In other words, a situation in which health status in a 4-person world changed from (10, 10, 8, 8) to (5, 5, 4, 4) is a much worse situation all things considered, even if relative health inequality had not changed. An absolute inequality measure may most appropriately reflect the priorities and perspectives of decision makers, but it should not be selected solely because the amount of health risk matters as a separate decision parameter. However, some decision makers might determine that (10, 10, 8, 8) is a more unequal situation independent of the risk level, because more societal resources are required to attain equality (transferring two “units” rather than one “unit” of health). Others focusing only on relative inequality would be indifferent with respect to these two choices, and those more concerned with inequality among those below a certain level of baseline health might find (5, 5, 4, 4) to be a less desirable situation. As above, the choice of the scale of the inequality measure has important implications for evidence and policy on health inequalities.

Another potential criterion for choosing a measure of health inequality is the type of the social groups under consideration [

In some cases one could, for example, create an ordinal-type measure using nominal characteristics across geographic units. For example, by ordering neighborhoods or census tracts by the proportion of minority population, it becomes possible to utilize measures of inequality designed for ordinal comparisons. However, it should be noted that doing so makes an important assumption that the ranking of areas by proportion of minority population is unambiguously associated with increasing disadvantage. Such an assumption may not be tenable if, for example, there are well-off areas with large proportions of minority populations. In addition, assigning the same value to all residents of the neighborhood may mask important within-neighborhood patterns for analyses with geographically resolved exposure information. Such assumptions could be tested or overcome in cases where individual-level data are available on both exposures and social status. But keeping such assumptions and data limitations in mind in the context of group-level data is crucial for a thorough and detailed analysis of inequality.

Any inequality measure involves an implicit or explicit weighting scheme that considers transfers/changes in some parts of the distribution more or less significant than transfers/changes in other parts of the distribution. Even those measures without explicit weights involve an implicit decision about weights (

One way of addressing this concern is to use multiple inequality measures deemed suitable, and to determine if the policy choices are sensitive to the measure selected. Some inequality measures have an explicit weighting parameter, where the value of this parameter influences the relative weights across the distribution. Typically, these parameters can be considered as reflecting the degree of societal aversion toward inequality, or more formally, the amount of weight placed on differences at various points in the distribution [

Numerous inequality measures have been developed and applied to characterize inequality in health, income, or other attributes. Harper and Lynch [

Candidate inequality measures and their key attributes. Derived from Harper and Lynch [

Inequality measure | Reference group | Absolute or relative inequality | Explicit inequality aversion parameter | Ordered social groups |
---|---|---|---|---|

Absolute Difference | Best off | Absolute | No | Yes |

Relative Difference | Best off | Relative | No | Yes |

Regression-Based Relative Effect | Best off | Relative | No | Yes |

Regression-Based Absolute Effect | Best off | Absolute | No | Yes |

Slope Index of Inequality | Average | Absolute | No | Yes |

Relative Index of Inequality | Average | Relative | No | Yes |

Index of Disparity | Best off | Relative | No | No |

Population Attributable Risk | Best off | Absolute | No | No |

Population Attributable Risk% | Best off | Relative | No | No |

Index of Dissimilarity | Average | Absolute | No | No |

Index of Dissimilarity% | Average | Relative | No | No |

Average | Relative | Yes | Yes | |

Average | Absolute | Yes | Yes | |

Average | Absolute | No | No | |

Squared Coefficient of Variation | Average | Relative | No | No |

Average | Relative | Yes | No | |

Gini Coefficient | Average/All those better off | Relative | No | No |

Average | Relative | No | No | |

Average | Relative | No | No | |

Variance of Logarithms | Average | Relative | No | No |

As discussed above, between-group comparisons are fundamental to being able to interpret measures of health inequality in the context of environmental justice. Such comparisons can be conducted using straightforward comparisons of distributions between population groups, both before and after a potential policy change. This could involve simple statistical comparisons of mean levels of pollutants or health outcomes, or the fraction of the population above a certain threshold of exposure or risk (e.g., exceeding the 95th percentile of a distribution). While these simple comparisons have the benefit of generally being more transparent and familiar to analysts and policy makers, they have some serious limitations that should be recognized and considered in the context of regulatory analysis. Pairwise comparisons are of diminishing utility as the number of groups, outcomes, or comparisons increases, particularly in the context of evaluating counterfactual exposure scenarios. With a large number of pairwise comparisons, the information may be difficult to present in a straightforward manner, and decision makers may not be able to readily answer the overarching question about whether or not a policy decision will affect broadly defined health inequalities. And in some cases policy decisions may identify social inequalities in health, broadly defined, as the outcome of interest. For example, US policy targets for health inequalities are framed in overall terms (

We therefore focus on quantitative measures of inequality that can provide insight about between-group differences while also characterizing overall (or within-group) inequality. Because overall health inequality and social inequalities in health may measure different aspects of distributions of health [

Below we describe in detail some selected measures of inequality that may be used to measure both overall and between-group inequality. More exhaustive reviews and technical details of other measures can be found elsewhere [

Multiple inequality measures in ^{2}). The Variance is also widely recognized and easy to communicate to decision makers and others familiar with basic statistics. We therefore briefly discuss key aspects of the Variance.

The generic formula for the total variance of a distribution is:
_{i}

The Variance can also be easily decomposed into between-group and within-group components. For a simple two-group decomposition (e.g., for rich and poor), the total variance can be written as a function of two parts. The between-group part is calculated by assigning rich and poor individuals the average health of their respective groups, and taking the variance of that distribution of groups (this is essentially equivalent to what the variance would be were there no inequality within social groups); and the within-group part is calculated by calculating the variance separately for rich and poor and taking a weighted average of those two variances, with the weights equal to the share of total observations in each group [_{B}_{W}_{j}_{rich}_{poor}_{rich}_{poor}

In the context of analyses focused only on estimating the magnitude of inequality between groups, the first bracketed term on the right-hand side of Equation (2) may be used to measure inequality between groups and is sometimes called the Between Group Variance [

The Variance does not have an explicit inequality aversion parameter, but it does incorporate an implicit weighting by squaring differences and therefore placing a greater weight on large differences from the average. Thus, any decision maker using this measure should be comfortable with the interpretation that a large difference for a small number of people could outweigh a small difference for a large number of people.

Some of the modified forms of the Variance, such as ^{2}^{2} are also additively decomposable inequality measures, but require adjustments to the weighting scheme for the within-group inequality component [

Measures of general entropy may also be used in the context of measuring within- and between-group inequality in health [_{i}_{i}_{i}/_{B}_{i}_{W}_{j}_{j}_{i}/_{j}_{j}_{T}_{j}_{i}/

As with many other common inequality measures, the Theil index involves a comparison with the average and is a relative rather than an absolute measure (_{B}_{j}_{i}/

Another entropy-based measure that is additively decomposable is the Mean Log Deviation (_{i}_{T}_{B}_{W}_{j}

The main difference between _{i}/_{j}

The Atkinson index has been used in a number of income and health inequality applications, in part because it has many desirable features, including sub-group decomposability and an explicit inequality aversion parameter. The overall index may be written as:
_{i}

In contrast to the class of general entropy measures above, the Atkinson index is not strictly additively decomposable. However, it may be usefully decomposed into a between-group component, a within-group component, and a residual term that is minus the product of the between and within components [_{j}

The explicit inequality aversion parameter is an appealing feature of the Atkinson index in the context of an environmental regulatory analysis where it is important to make transparent any assumptions about how different populations have been weighted. However, one concern that has been raised is the fact that an increase in the inequality aversion parameter places increasing weight at the bottom of the distribution, whereas one would prefer increasing weight at the top of the distribution if characterizing adverse health outcomes. This can be addressed by characterizing health as a “good” when theoretically appropriate, by applying basic transformations to the health measure (

The Concentration Index (_{j}_{j}_{j}_{γ}_{j}_{j}

While the formula for the

The

We would consider as plausible candidate indicators to incorporate environmental justice into regulatory analyses any quantitative measures that adhere to basic rules for inequality indicators, and that allow for decomposition of inequality into between-group and within-group components. All of the indicators listed in

The first two of these questions are policy decisions to be made at the level of regulatory decision makers. As discussed above, there are compelling arguments to be made for both relative and absolute concepts of health inequality. Decision makers could conclude that one construct is more suitable given their understanding of environmental justice, or could determine that either concept is reasonable and evaluate the sensitivity of policy conclusions to this choice. The desire for an explicit inequality aversion parameter would be a preference that decision makers might express given the objective to minimize implicit policy decisions within the inequality indicator calculations, although this same preference could be met by using multiple alternative indicators (e.g., multiple generalized entropy measures). The third question may be influenced by the application and subset of environmental justice questions under consideration – socioeconomic status may be the more pertinent measure for some policies, while race/ethnicity may be the more pertinent measure for others.

After choosing a decomposable measure of inequality and assembling the requisite health/exposure data, analysis and decomposition of inequalities is relatively straightforward. All of the equations listed above can be readily implemented in spreadsheets or statistical analysis software [

At times, regulatory analyses (or environmental justice analyses in other contexts) will involve examining baseline trends over time to determine whether circumstances have been improving or getting worse. While this analysis is computationally straightforward, interpreting changes over time in between-group inequality may be complicated, especially over longer periods. One potential complication is that changes in relative and absolute inequality may diverge, leading to potentially opposing conclusions about the effect of the policy on health inequalities. A second complication occurs because changes in the value of between-group inequality are a function of two quantities: changing social group proportions and changing health status among social groups. Differentiating between these two components of change may be important from an environmental justice perspective. If between-group inequality is increasing but the main reason for the observed change is that the share of the population among groups at the tails of the health distribution has increased, it simply demonstrates that the inequality increase is primarily due to the movement into and out-of different social groups and may not be the result of differential changes in health within those groups. This explanation would not necessarily imply that between-group inequality would not be a growing concern, but would emphasize that demographic patterns and other societal factors explain the trends better than changing environmental exposures. On the other hand, if we find that population shares have remained relatively constant over time (likely in the case of shorter periods of observation) but between-group inequality has increased because of changes in the health status of social groups, this implicates differential sources of changes in health status and may imply a need to address the causes of differential health change.

In this paper, we have provided both theoretical and empirical arguments that measurement of health inequality is feasible in the context of environmental justice analyses conducted for evaluating regulatory policy. Health inequality has been characterized in numerous prior investigations following well-established approaches. The questions from the perspective of environmental justice relate to the context in which an inequality measure would be used, the data required for a meaningful measure of health inequality, the criteria for selecting inequality measures to apply in regulatory analyses, and the ultimate application and interpretability of the results.

The regulatory analysis application implies an orientation around health outcomes and how they are distributed, both at present and after a potential policy change. In addition, conceptions of environmental justice suggest that pre-defined social groups are to be given direct consideration. These two contexts emphasize how inequality measures should be applied within regulatory analyses—with characterization of both baseline inequality and how inequality would change given a policy change, and utilizing between-group comparisons while also considering within-group inequality. To make this characterization meaningful, the health risk models must have sufficient resolution to allow for between-group and within-group variation in exposure and susceptibility. The geographic resolution would need to be consistent with both available demographic data and the anticipated spatial contrasts of the exposure—the resolution required to characterize a near-roadway environment would be different from the resolution required for regional air pollution. Ideally, data on differential baseline disease rates or effect modification by demographics relevant to environmental justice analyses would also be available. Absent information of this sort, even the most theoretically desirable inequality measure will not yield meaningful insights. That said, most regulatory analyses involve spatially resolved characterizations of exposure and/or health risk, at baseline and after proposed regulations. So, the analytical foundation is generally in place for health inequality assessments, with the need to ensure that sociodemographic information is considered wherever possible.

Given sufficient information to characterize health risks at baseline and after proposed regulations, decision makers and analysts must choose among candidate inequality measures. In this paper, we do not recommend a specific inequality measure, largely because this is a policy choice. However, we do outline the questions that decision makers would need to ask and answer in order to focus on the subset of indicators best representing their values. Specifically, a decision is necessary regarding whether relative or absolute concepts of inequality are more appropriate; whether a selected indicator must have an explicit inequality aversion parameter (and, if so, the degree of aversion); and whether any environmental justice analyses would involve comparisons only among inherently ordered population groups (

Quantitative measures of inequality cannot represent all dimensions of environmental justice, and analysts should be clear about this point. That said, inequality measures provide important insight into how patterns of health risks are changing over time and space, and if selected and presented appropriately, can make meaningful contributions to regulatory analyses of environmental justice.

Support for this work was provided by the U.S. Environmental Protection Agency (EPA) under contract EP-W-10-002 to Industrial Economics, Inc.

We declare that we have no conflict of interest.

The views expressed in this article are those of the authors and do not necessarily represent those of the U.S. Environmental Protection Agency. No official Agency endorsement should be inferred.