# Comparing Distributions of Environmental Outcomes for Regulatory Environmental Justice Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Three Fundamental Questions for Regulatory EJ Analysis

#### (1). What is the baseline distribution of the environmental outcome?

#### (2). What is the distribution of the environmental outcome for each regulatory option?

#### (3). How do the policy options being considered improve or worsen the distribution of the environmental outcome with respect to vulnerable subgroups?

## 3. Describing Distributions

#### 3.1. Visual Displays

_{2}trading program across U.S. regions. Results are presented using tables and maps.

#### 3.2. Summary Statistics

#### 3.3. Regression Analysis

## 4. Ranking Distributions

#### 4.1. Visual Ranking Tools

**Lorenz Curves.**If one accepts the ethical premise that it is always desirable to transfer a unit of pollution away from a highly exposed individual to a lesser exposed one, then Lorenz curves provide a means of ranking policy outcomes. Some hypothetical Lorenz curves for distribution of a pollutant are depicted in Figure 1. The horizontal axis of the graph indicates percentiles of the population ranked by pollution exposure: 10 corresponds to the ten percent of the population least exposed to the pollutant, 50 corresponds to the half of the population least exposed to pollution, etc. The vertical axis represents the percent of pollution exposed by percentile. The black diagonal line depicts a perfectly equal distribution of exposure: the lowest 10 percent of the population experience 10 percent of the exposure the lowest 50 percent of the population experience half the exposure, etc.

**Concentration Curves.**Like the Lorenz curve, the vertical axis of the concentration curve displays the share of an outcome variable experienced by a population. The horizontal axis displays the cumulative percent of the population ranked by socio-economic status (typically income). A Lorenz curve, in contrast, would display the population ranked by exposure. The height of the concentration curve indicates the share of the outcome experienced by a given cumulative proportion of the population. Figure 2 displays hypothetical concentration curves. A perfectly equal distribution of outcomes corresponds to a concentration curve along the 45° line. Kakwani [31] first developed this analysis to study income tax progressivity. Wagstaff et al. [32] proposed its use in measuring the equity of health outcomes.

#### 4.2. Inequality Indices

**Gini Coefficient.**The Gini coefficient is the most widely used inequality index. Its popularity is likely due more to the fact that it is easily understood as an increasing function of the area between a Lorenz curve and the diagonal line representing perfect equality than to desirable theoretical properties. The Gini coefficient has the undesirable feature that the effect of a transfer on the index number depends on the individuals’ ranks, not the difference in outcomes. In contrast to the widely accepted principle that an inequality index should place greater weight on transfers among the relatively worse off, for a typical bell-shaped distribution a transfer between individuals in the middle of the distribution will have a higher effect on the Gini coefficient than a transfer between two similarly distanced individuals at either tail [38]. There are ways of modifying the Gini coefficient to introduce flexibility in the weights placed on different segments of the population [39,40]. These techniques are rarely used in practice, however.

_{2}emissions across countries grouped by income. Millimet and Slottje [43] use the Gini coefficient to compare distributions of pollution across states grouped by income class. Since the Gini coefficient does not satisfy consistency in aggregation both of these studies required a group overlap term in addition to between and within group terms. Millimet and Slottje [44] use the Gini coefficient to evaluate the effect of regulatory compliance costs on the distribution of toxics reported in the U.S. Toxic Release Inventory across U.S. states and counties. They combine regression results with Spearman correlations between demographic characteristics and emissions to argue that policies that increase inequality as measured by the Gini coefficient increase racial disparities. In these studies, the Gini coefficient has been used primarily as an ordinal measure of dispersion, without attendant welfare implications.

**Concentration Index.**The concentration index is similar to the Gini coefficient, being an increasing function of the difference between the 45° line and the concentration (rather than Lorenz) curve. For details on the practical use of the concentration index, see [15]. Its value ranges from −1 (the entire outcome is borne by the poorest individual) to 1 (the entire outcome is borne by the wealthiest individual). Since the concentration curve can cross the 45° line, zero either indicates perfect equality or that the area above the curve is exactly equal to the area below it. As with the Gini coefficient, the effect of allocating a unit of the outcome variable to an individual is weighted by the individual’s rank. With the concentration index, the relevant rank is income, rather than the outcome variable.

**Atkinson Index.**The Atkinson index satisfies several desirable theoretical properties lacking in other relative indices [35,36,38]. Among these are that it is a function of individual allocations rather than rank, and it can be disaggregated into subgroups in a consistent manner (see also [48]).

**Kolm-Pollak Index.**The Kolm-Pollak index shares the desirable theoretical properties of the Atkinson index [35,37,48]. It also uses an inequality aversion parameter to specify the relative importance of allocations to different segments of the population. Higher values correspond to greater weight being placed on the worse off and zero indicates complete indifference to the allocation.

## 5. Conclusions

## Acknowledgments

**Disclaimer**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.

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Maguire, K.; Sheriff, G. Comparing Distributions of Environmental Outcomes for Regulatory Environmental Justice Analysis. *Int. J. Environ. Res. Public Health* **2011**, *8*, 1707-1726.
https://doi.org/10.3390/ijerph8051707

**AMA Style**

Maguire K, Sheriff G. Comparing Distributions of Environmental Outcomes for Regulatory Environmental Justice Analysis. *International Journal of Environmental Research and Public Health*. 2011; 8(5):1707-1726.
https://doi.org/10.3390/ijerph8051707

**Chicago/Turabian Style**

Maguire, Kelly, and Glenn Sheriff. 2011. "Comparing Distributions of Environmental Outcomes for Regulatory Environmental Justice Analysis" *International Journal of Environmental Research and Public Health* 8, no. 5: 1707-1726.
https://doi.org/10.3390/ijerph8051707