Given these definitions, although efficiency is incorporated into any health benefits analysis, equity and related distributional issues are often omitted (Yitzhaki 2003). Most regulatory impact analyses have focused exclusively on aggregate benefits [U.S. Environmental Protection Agency (EPA) 1999a, 1999b] without formally considering the geographic or demographic distributions of these benefits. In parallel, many studies of equity or environmental justice did not quantify health risks, instead focusing on proximity to sources (Burke 1993; Pollack and Vittas 1995; Sheppard et al. 1999), emissions (Millimet and Slottje 2002a, 2002b; Perlin et al. 1995), or concentrations (Lopez 2002). Studies that quantified risk inequality (Apelberg et al. 2005; Morello-Frosch and Jesdale 2006) or proposed a framework to do so (Finkel 1990, 1997) focused on characterizing baseline distributions of risk rather than the benefits of control strategies, and the appropriate methodology may differ in this context. The lack of a systematic framework to simultaneously consider efficiency and equity in a decision context may imply that decisions are based largely on maximization of societal benefits without formal consideration of equity implications.

To address these limitations, we developed a framework by which risk inequality could be formally quantified within health benefits analysis (Levy et al. 2006). Briefly, we proposed that quantitative indicators of inequality, similar to those used to measure income inequality, could allow decision makers to construct an optimal efficiency–equality frontier and avoid policies that are dominated across both dimensions. Based on an axiomatic approach, we selected the Atkinson index (Atkinson 1970) as the most appropriate indicator for health benefits analysis, focusing on the change in this indicator under different control scenarios. Other indicators were considered useful for sensitivity analyses (the Gini coefficient, mean log deviation, and the Theil entropy index).

Quantitative measures of risk-based efficiency and equality may be useful in many contexts, including the evaluation of national-level policies to control emissions from power plants in the United States. In theory these policies could involve site-specific control requirements or cap-and-trade programs. Cap-and-trade programs are designed primarily for economic efficiency but operate under the presumption that health benefits would be similar regardless of the distribution of emissions (Farrell and Lave 2004). However, given differences in atmospheric conditions and population patterns, how emission controls are distributed geographically could influence the magnitude and distribution of benefits. Sulfur dioxide (SO₂) emission trading related to the Title IV Acid Rain Program (U.S. EPA 2007) resulted in greater health benefits than a hypothetical program without trading, based on the geographic distribution of controls (Burtraw and Mansur 1999).

Regardless of efficiency claims, environmental justice advocates and communities housing power plants have expressed concern that unrestricted emission trading does not decrease and may exacerbate environmental inequities (Solomon and Lee 2000). Previous analyses (Corburn 2001; Swift 2001) focused on the possibility of emissions hot spots associated with Title IV and whether low-income or minority populations tended to have lesser emission reductions in proximate facilities. While these studies concluded that there were no hot spots, they used a procedural rather than an outcome-based concept of equity and therefore did not address the question of changing patterns of health risks. The benefits analysis of Title IV (Burtraw and Mansur 1999) indicated that certain geographic areas received health benefits while others had health disbenefits. However, without a more formal analysis, it is difficult to determine whether health inequality increased, decreased, or stayed the same, or to ascertain the potential impacts of future policies. Given the framing of the debate about national power plant controls, an outcome-based focus implies that an evaluation of how various distributions of emission controls correspond to changes in health benefits and in the spatial inequality of health risk would be informative for the design of future emission control programs.

We first consider the scenarios to simultaneously control SO₂, NO_x, and primary PM_2.5, and apply the Atkinson index with = 0.75, calculating inequality based on changes in mortality risk from a baseline of PM_2.5-related mortality. As indicated in Figure 2, the estimated public health benefits of the policies range from approximately 17,000 to 21,000 fewer premature deaths per year across control scenarios. Of this total, approximately 14,000–17,000 are associated with secondary sulfate particles. Given this, it is not surprising that the scenario with the greatest benefits (scenario C) involves controlling the plants with the highest health benefits per ton of SO₂ emissions first. Policies requiring uniform emission reductions or for each plant to reach a target emission rate tend to fall in the middle of the efficiency spectrum, similar to the intermediate control scenarios.

As the y-axis in Figure 2 represents the Atkinson index for postcontrol conditions subtracted from the Atkinson index for precontrol conditions, positive values indicate reductions in inequality and points toward the upper right represent more efficient and more equitable outcomes. Scenarios with greater health benefits generally also most reduce spatial inequality (Figure 2). This is because the power plants with maximum population exposure reductions per unit emissions of SO₂ tend to be in the areas with highest ambient PM_2.5 concentrations (Figure 3). The two policies on the optimal frontier involve controlling the plants with the highest health benefits per ton of SO₂ emissions first (scenario C) or controlling the plants with the highest background PM_2.5 concentration first (scenario I)—whether one prefers one policy over another depends on one’s willingness to trade efficiency for equality. All other policies are strictly dominated.

Within our sensitivity analyses, we first considered the application of the Atkinson index with different values of as well as the other inequality indicators, holding other assumptions as in Figure 2. Of note, comparing the absolute values of the different inequality indicators to one another is not directly interpretable; the key question is whether the optimal policies are robust to the choice of indicator. Although there was some modest reordering of control strategies, the general conclusions remained robust, with only scenarios C and I on the optimal frontier (Figure 4). We present results for ranging from 0.25 to 3 (the range generally used in the literature), but conclusions are similar for higher values as well.

Considering the influence of the choice of baseline highlights some important issues (Figure 5). Although the optimal strategies are identical for different mortality-related baselines, the Atkinson index changes to a greater extent for power plant PM_2.5-related mortality. Postcontrol power plant-related PM_2.5 mortality is close to zero in some locations, and the Atkinson index and other indicators are sensitive to near-zero values. Of greater significance is the fact that ignoring baseline conditions leads to substantially different conclusions, in which the scenarios previously considered to most improve equality are now considered to be least equitable. This is because scenarios such as C and I focus controls in geographic areas that have elevated baseline exposures and risks, so that the benefits are spread less uniformly but serve to reduce existing inequalities.

We additionally examined whether the conclusions differed when considering concentrations rather than health effects (with population-weighted concentration change as the efficiency measure and inequality in concentrations as the equity measure), with no significant difference in the findings (results not shown). Omission of primary PM_2.5 emissions from the analysis, which more closely mirrors some of the proposed national cap-and-trade programs, led to similar conclusions (Figure 6). Not surprisingly, the optimal policies differed if only single pollutants were considered (i.e., controlling only NO_x emissions), but the findings similarly illustrated bounding estimates for efficiency by controlling the maximum/minimum health benefits per unit emissions and bounding estimates for equality by controlling the power plants in high/low ambient PM_2.5 settings first.

We also demonstrated within our analysis that these conclusions were robust across numerous model configurations as long as baseline conditions are appropriately incorporated. In particular, the optimal policy choices did not vary with ; if the conclusions were sensitive to , follow-up studies would be needed to determine the values that best capture priorities of stakeholders and decision makers.

Another interesting finding is that the difference in health benefits across the control scenarios is small in relative terms, with only a 22% difference between the minimum and maximum benefits. This can be attributed to the fact that the emission reductions are substantial enough to require controls at many facilities, reducing the variation between scenarios in spite of larger variations in plant-specific benefits (Figure 3). That being said, a 22% difference does reflect an absolute difference of nearly 4,000 deaths per year, which could be significant in determining optimal policies. In addition, if not all power plants were controlled at the same time, the differences between the scenarios would increase if discount rates were applied to benefits in future years.

Although our findings are generally robust, a number of limitations are important to recognize. First, we have only addressed one dimension of equity, by focusing on spatial variability in county-level mortality risks with a national focus. More conventionally, equity considerations in an environmental justice context consider racial and ethnic disparities, which are omitted from this analysis. Inclusion of effect modifiers such as educational attainment (Pope et al. 2002) or evaluation of morbidity outcomes with known demographic patterning could significantly influence spatial patterns of risk (Levy et al. 2002) and any conclusions about equity, especially if methods are used to decompose inequality between and within different subpopulations (Levy et al. 2006). Although these factors are clearly important, much of the outcome-based debate related to national power plant control strategies has revolved around spatial equity. In general, the equity measure utilized should be the one most informative to the decision-maker within the context of the policy question. In applications in which other dimensions of equity are central, particularly those involving mobile sources (where the spatial extent of impact is lesser and local socioeconomic and demographic factors may be more influential), other measures should be used.

In addition, for our results to be useful for decision making, the costs of control need to be included, with realistic control strategies rather than bounding values and randomly-generated scenarios. With plant-specific control costs, we could compare net monetized benefits with changes in the spatial inequality of risk (noting that cost information cannot be used directly in our inequality indicator). Considering other dimensions of equity, such as the distribution of costs across power plant companies or consumers, would lead to a more comprehensive and relevant analysis, and methods should be developed to synthesize these elements into a single decision framework.

Our findings are also dependent on the validity of S-R matrix. Although S-R matrix is simplified relative to state-of-the-science dispersion models, it has yielded similar health impact estimates as more advanced models (Abt Associates et al. 2000; Levy et al. 2003). It also has the benefit of explicit calibration with ambient monitoring data. Moreover, given the numerous sources and control scenarios in our analysis, a more intensive model would have been infeasible. We can corroborate our modeling to a limited extent by comparison with similar analyses of the benefits of national cap-and-trade programs. For example, the U.S. EPA analysis of CAIR used CMAQ to estimate benefits of 17,000 fewer premature deaths per year, with population-weighted PM_2.5 concentration reductions of about 1.2 μg/m³ (U.S. EPA 2005d). Our corresponding estimates (for SO₂ and NO_x control only) of 15,000–18,000 fewer premature deaths and 1.3–1.6 μg/m³, for a slightly more stringent emissions cap, compare favorably with these estimates, although this validates our efficiency measures to a greater degree than our equity measures (which rely on spatial concentration patterns). S-R matrix also does not include the influence of NO_x emissions on ozone formation. Including ozone-related health benefits could theoretically influence our findings, although previous studies have shown that PM_2.5 dominates monetized benefits (U.S. EPA 2005d).

In addition, although we conducted multiple sensitivity analyses, some alternative assumptions could have significantly influenced our findings. In particular, if definitive information were available about the relative toxicity of different particle constituents, our conclusions could differ. That being said, Figure 6 demonstrates that control scenario I is on the optimal frontier for all pollutants and therefore would be robust across different toxicity assumptions. Alternative assumptions about concentration–response function nonlinearities or regional differences in concentration–response functions could also have important effects. In particular, thresholds in the concentration–response function would reduce the benefits outside the Midwest, potentially enhancing the differences between control scenarios but likely not changing the optimal control scenarios. Nonlinearities and large variations in baseline risks would also lead to greater differences between concentration-based conclusions and risk-based conclusions, thereby enhancing the importance of risk-based indicators. As the epidemiologic evidence did not provide strong support for any of these factors, we did not formally incorporate them into sensitivity analyses, but they could be considered in future analyses as the evidence base evolves. Of note, other uncertain parameters (like the magnitude of the concentration–response relationship) would not influence the core conclusions about optimal control strategies. More generally, formal uncertainty analysis related to both efficiency and equity measures would be required for any future decision making in this setting.

A final concern is related to the inequality indicators themselves. Although the indicators we used agree with an axiomatic approach proposed previously (Levy et al. 2006), there are some limitations. The parameter in the Atkinson index most influences sensitivity to low values, but in a health risk inequality context, we are more concerned about high values, so this represents an indirect mechanism for expressing concern about different segments of the risk distribution. We also observed the sensitivity of all indicators to values near zero, which can be influential given certain definitions of baseline. Because of these issues, development of novel inequality indicators specific to health benefits analysis may be warranted, although our conclusions were not sensitive to the statistical formulation of the inequality indicator.

More generally, although our framework helped to identify policies on the optimal frontier and policies that were strictly dominated, it is difficult to know to what extent decision-makers should be willing to trade off a given increase in health benefits for a given decrease in an inequality indicator. Further research is needed into the interpretation of small changes in inequality.