Risk equity: A new proposal

Harvard Environmental Law Review

Volumn 32, Issue 1, 2008, Pages 1-47

  Adler, Matthew D ^a  

^a UNIVERSITY OF PENNSYLVANIA LAW SCHOOL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENVIRONMENTAL JUSTICE; ENVIRONMENTAL LEGISLATION; HEALTH AND SAFETY; PROBABILITY; UNCERTAINTY ANALYSIS; WELFARE PROVISION;

EID: 42949088446     PISSN: 01478257     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (252)

1. For citations to the scholarly literature on risk assessment, and to descriptions of the use of risk assessment by governmental bodies, see Matthew D. Adler, Against "Individual Risk": A Sympathetic Critique of Risk Assessment, 153 U. PA. L. REV. 1121, 1128-29 nn.28-29 (2005) [hereinafter Adler, Against "Individual Risk"].
2. On cost-benefit scholarship, see, for example, A. MYRICK FREEMAN III, THE MEASUREMENT OF ENVIRONMENTAL AND RESOURCE VALUES (2d ed. 2003).
3. On the use of cost-benefit analysis in the federal government, see generally MATTHEW D. ADLER & ERIC A. POSNER, NEW FOUNDATIONS OF COST-BENEFIT ANALYSIS 1-4, 101-23 (2006), and sources cited therein.
4. Exec. Order No. 12,866 § 1(a), 58 Fed. Reg. 51,735, 51,735 (Oct. 4, 1993).
5. The recent amendments to Executive Order 12,866, by Executive Order 13,422, do not change the substantive requirements imposed on agency rules by Executive Order 12,866 and, in particular, do not change its content regarding "distributive impacts" and "equity." Exec. Order. No. 13,422, 72 Fed. Reg. 2763 (Jan. 23, 2007).
6. See Circular A-4, Off. Mgmt. & Budget (Sept. 17, 2003), available at http://www.whitehouse.gov/omb/circulars/a004/a-4.pdf.
7. Exec. Order No. 12,898 § 1-101, 59 Fed. Reg. 7629, 7629 (Feb. 11, 1994).
8. Id.
9. A number of these empirical studies are cited in William Bowen, An Analytical Review of Environmental Justice Research: What Do We Really Know?, 29 ENVTL. MGMT. 3, 13-15 (2002)
10. and in Evan J. Ringquist, Assessing Evidence of Environmental Inequities: A Meta-Analysis, 24 J. POL'Y ANAL. & MGMT. 223, 245-47 (2005).
11. Other scholarship about environmental justice is cited or excerpted in CLIFFORD RECHTSCHAFFEN & EILEEN GAUNA, ENVIRONMENTAL JUSTICE: LAW, POLICY, AND REGULATION (2002);
12. Sheila R. Foster, Meeting the Environmental Justice Challenge: Evolving Norms in Environmental Decisionmaking, 30 ENVTL L. REP. 10992 (2000);
13. and Robert Kuehn, A Taxonomy of Environmental Justice, 30 ENVTL. L. REP. 10681 (2000).
14. On environmental justice tools, see, for example, EPA, SCIENCE ADVISORY BOARD: REVIEW OF DISPROPORTIONATE IMPACT METHODOLOGIES (1998);
15. FENG LIU, ENVIRONMENTAL JUSTICE ANALYSIS: THEORIES, METHODS, AND PRACTICE (2001);
16. TRANSPORTATION RESEARCH BOARD OF THE NAT'L ACADEMIES, EFFECTIVE METHODS FOR ENVIRONMENTAL JUSTICE ASSESSMENT (2004).
17. As discussed below, there are close parallels between the environmental justice and health equity literatures, see infra text accompanying notes 15-19;
18. and that latter literature has developed a variety of metrics for quantifying social skews in health. See, e.g., Johan P. Mackenbach & Anton E. Kunst, Measuring the Magnitude of Socio-economic Inequalities in Health: An Overview of Available Measures Illustrated with Two Examples from Europe, 44 SOC. SCI. MED. 757 (1997).
19. For a critical review of environmental justice policy at EPA, see EPA, OFFICE OF THE INSPECTOR GENERAL, EPA NEEDS TO CONSISTENTLY IMPLEMENT THE INTENT OF THE EXECUTIVE ORDER ON ENVIRONMENTAL JUSTICE, REPORT No. 2004-P-00007 (2004).
20. See also Richard J. Lazarus & Stephanie Tai, Integrating Environmental Justice into EPA Permitting Authority, 26 ECOLOGY L.Q. 617 (1999);
21. Bradford C. Mank, The Draft Title VI Recipient and Revised Investigation Guidances: Too Much Discretion for EPA and a More Difficult Standard for Complaints?, 30 ENVTL. L. REP. 11144 (2000) [hereinafter Mank, The Draft Title VI Recipient];
22. Bradford C. Mank, Executive Order 12,898, in THE LAW OF ENVIRONMENTAL JUSTICE 107-14, 125-29 (Michael B. Gerrard ed., 1999) [hereinafter Mank, Executive Order 12,898].
23. On environmental justice policy at other federal agencies, see Denis Binder et al., A Survey of Federal Agency Response to President Clinton's Executive Order No. 12898 on Environmental Justice, 31 ENVTL. L. REP. 11133 (2001);
24. Mank, Executive Order 12,898, supra, at 114-23, 129-31.
25. On risk assessment at EPA, see, e.g., Adler, Against "Individual Risk," supra note 1, at 1149-64;
26. id. at 1148 n.91 (citing sources).
27. On cost-benefit analysis, see, for example, ECONONIC ANALYSES AT EPA (Richard D. Morgenstern ed., 1997).
28. See EPA, OFFICE OF THE INSPECTOR GENERAL, supra note 8, at 19-26 (discussing differing approaches to identifying disparate impacts on low-income and minority communities employed by EPA regional offices and EPA's failure to establish a single approach). EPA's guidance on incorporating distributional concerns into cost-benefit analysis is lengthier than OMB's in Circular A-4, see supra note 3;
29. but it still fails to recommend specific policy metrics for quantifying the degree of distributional skew or balancing distributive concerns with efficiency/overall welfare. See EPA, GUIDELINES FOR PREPARING ECONOMIC ANALYSES 139-74 (2000).
30. See infra Part I.C.
31. See infra Parts I.D, I.F.
32. See infra Part I.B.
33. For non-economists, what this formula means is that we assign the individual's health state and income state in each period a value. We next multiply these two numbers, arriving at a total value for each period. These period values are then summed to determine lifetime utility.
34. On this conception within the environmental justice literature, see, e.g., Kuehn, supra note 6, at 10683-84.
35. The recent EPA Inspector General report claims that EPA itself is resistant to the social-gradient conception of risk equity. See EPA, OFFICE OF THE INSPECTOR GENERAL, supra note 8, at 10-11.
36. EPA, however, has officially adopted this conception in various documents. See, e.g., EPA, EPA GUIDANCE FOR CONSIDERATION OF ENVIRONMENTAL JUSTICE IN CLEAN AIR ACT SECTION 309 REVIEWS (1999);
37. Mank, The Draft Title VI Recipient, supra note 8, at § 1.3.
38. Scott Farrow has proposed a related approach to equity - namely that a policy not only pass the test of Kaldor-Hicks efficiency, but that actual compensation be provided to members of a "sensitive group," such as low-income or minority groups. Scott Farrow, Environmental Equity and Sustainability: Rejecting the Kaldor-Hicks Criteria, 27 ECOLOGICAL ECON. 183, 185-86 (1998).
39. This proposal, like the disparate-impact tests considered in the text, is vulnerable to the objection that it ignores inequalities among individuals who do not belong to the sensitive group."
40. See Washington v. Davis, 426 U.S. 229 (1976).
41. See, e.g., 42 U.S.C. 2000e-2(k) (2006).
42. I say "arguably" because it is plausible (although certainly not uncontroversial) to take the view that federal prohibitions on practices with a disparate impact are grounded in Congress's power to enforce the Equal Protection Clause, under Section 5 of the Fourteenth Amendment. See, e.g., Richard A. Primus, Equal Protection and Disparate Impact: Round Three, 117 HARV. L. REV. 493, 494-95 & n.4 (2003).
43. See, e.g., Sudhir Anand, The Concern for Equity in Health, in PUBLC HEALTH, ETHICS, AND EQUITY 15, 19-20 (Sudhir Anand et al. eds., 2004);
44. Paula Braveman, Health Disparities and Health Equity: Concepts and Measurement, 27 ANN. REV. PUB. HEALTH 167, 169-70 (2006);
45. C.J.L. Murray et al., Health Inequalities and Social Group Differences: What Should We Measure?, 77 BULL. WORLD HEALTH ORG. 537, 537-38 (1999);
46. Adam Wagstaff & Eddy van Doorslaer, Overall Versus Socioeconomic Health Inequality: A Measurement Framework and Two Empirical Illustrations, 13 HEALTH ECON. 297, 297 (2004);
47. WHO Task Force on Research Priorities for Equity in Health & The WHO Equity Team, Priorities for Research to Take Forward the Health Equity Policy Agenda, 83 BULL. WORLD HEALTH ORG. 948, 948 (2005).
48. See LIU, supra note 7, at 95-96;
49. TRANSPORTATION RESEARCH BOARD, supra note 7, at 19.
50. See supra sources cited in note 7.
51. Paula Braveman & Sofia Gruskin, Defining Equity in Health, 57 J. EPIDEMIOLOGY & CMTY. HEALTH 254, 254 (2003) (emphasis removed).
52. For a similar analysis, see Braveman, supra note 19, at 180-82.
53. See Braveman & Gruskin, supra note 22, at 256;
54. Braveman, supra note 19, at 180-88.
55. Iris Marion Young, Equality of Whom? Social Groups and Judgments of Injustice, 9 J. POL. PHIL. 1, 7 (2001).
56. Id. at 8.
57. Id. at 16.
58. Id. at 15 (emphasis omitted).
59. Id. at 16.
60. Much of the recent philosophical literature on equality has tried to articulate a conception of equality that is sensitive to individual responsibility - a concern triggered by Ronald Dworkin's famous work on equality of resources, which distinguishes between "brute luck" and "option luck." See, e.g., Richard J. Arneson, Welfare Should be the Currency of Justice, 30 CAN. J. PHIL. 497 (2000)
61. (citing Ronald Dworkin, What is Equality? Part 1: Equality of Welfare, 10 PHIL. & PUB. AFF. 189 (1981);
62. Ronald Dworkin, What is Equality? Part 2: Equalily of Resources, 10 PHIL. & PUB. AFF. 283 (1981);
63. Ronald Dworkin, What is Equality? Part 3: The Place of Liberty, 73 IOWA L. REV. 1 (1987)).
64. See, e.g., Derek Parfit, Equality or Priority?, in THE IDEAL OF EQUALITY 81, 95-97 (Matthew Clayton & Andrew Williams eds., 2000) (discussing egalitarian views that do not object to natural inequality).
65. See Adler, Against "Individual Risk," supra note 1, at 1149-79.
66. See id. at 1155-58.
67. More precisely, FDA takes this approach for carcinogens exempt from the Delaney Clause. See id. at 1164-69.
68. See id. at 1150-52.
69. See id. at 1169-71.
70. See id. at 1173-78.
71. See, e.g., Adam M. Finkel, Comparing Risks Thoughtfully, 7 RISK: HEALTH, SAFETY & ENV'T 325, 342-44 (1996);
72. John D. Graham, Making Sense of Risk: An Agenda for Congress, in RISKS, COSTS, AND LIVES SAVED 183, 190-91 (Robert W. Hahn ed., 1996).
73. See also Matthew D. Adler, Risk, Death and Harm: The Normative Foundations of Risk Regulation, 87 MINN. L. REV. 1293, 1423-31 (2003) (discussing environmental-justice account that attends to skews with respect to "individual risk" levels).
74. For overviews of the literature on measuring the inequality of income, see HILDE BOJER, DISTRIBUTIONAL JUSTICE: THEORY AND MEASUREMENT 63-134 (2003);
75. PETER LAMBERT, THE DISTRIBUTION AND REDISTRIBUTION OF INCOME 13-132 (3d ed. 2001);
76. AMARTYA SEN, ON ECONOMIC INEQUALITY 24-46 (expanded ed. 1997);
77. F.A. Cowell, Measurement of Inequality, in 1 HANDBOOK OF INCOME DISTRIBUTION 87 (A.B. Atkinson & F. Bourguignon eds., 2000).
78. As I explain in Part II of the Article, my position is that risk regulation policies should be evaluated with reference to an Atkinsonian social welfare function, which can in turn be decomposed into an Atkinsonian measure of inequality and overall welfare. See infra Part II.C.
79. Shortly before publication of this Article, I became aware of empirical work by Jonathan Levy and collaborators that does precisely this. See Jonathan I. Levy et al., Quantifying the Efficiency and Equity Implications of Power Plant Air Pollution Control Strategies in the United States, 115 ENVTL. HEALTH PERSP. 743 (2007).
80. The approach (which the authors see as applicable to health as well as mortality risks) is also described in Jonathan I. Levy et al., Incorporating Concepts of Inequality and Inequity into Health Benefits Analysis, 5 INT'L, J. EQUITY IN HEALTH 2 (2006).
81. Although I argue for a different approach here, Levy and his collaborators are to be commended for analyzing the equity implications of air pollution policies in a rigorous and novel way, focusing on population-wide inequality rather than social gradients, and applying inequality metrics developed in the income-inequality literature to risk regulation.
82. See W. Kip Viscusi, Risk Equity, in COST-BENEFIT ANALYSIS: LEGAL, ECONOMIC, AND PHILOSOPHICAL PERSPECTIVES 7, 25-31 (Matthew D. Adler & Eric A. Posner eds., 2001) (criticizing conception of risk equity that focuses on incremental risk).
83. There are different ways to define the incremental fatality risk to person P from toxins of type X during period T. (1) the risk that X-type toxins cause P's death during T; (2) the difference in the risk that P dies during T, conditional on his exposure to X-type toxins, and the risk that P dies during T, conditional on non-exposure; and (3) the difference in the risk that P dies in the manner characteristic of deaths caused by X-type toxins (e.g., dies from cancer), conditional on his exposure to X-type toxins, and the risk that P dies in that manner conditional on non-exposure. If T is less than a full lifetime, all three definitions are possibilities. If T is a full lifetime, the first and third are. My critique of an approach to risk equity that focuses on incremental fatality risks does not depend on which precise definition of incremental risk is adopted.
84. See Matthew D. Adler, Well-Being, Inequality, and Time: The Time-Slice Problem and its Policy Implications (Univ. of Pa. Inst. for Law & Econ., Research Paper No. 07-17, 2007), available at http://ssm.com/abstract = 100687 1;
85. see also infra text accompanying note 82.
86. See Matthew D. Adler & Chris William Sanchirico, Inequality and Uncertainty: Theory and Legal Applications, 155 U. PA. L. REV. 279 (2006).
87. This particular variant of the "individual risk" approach is chosen simply for the sake of illustration. Other holistic variants of the "individual risk" approach also involve an ex ante conception of equality under uncertainty - for example, measuring the distribution of the risk of death during some time period other than a year, or measuring the distribution of the lifetime risk of death in a particular manner (e.g., cancer), or measuring the distribution of life expectancy.
88. See Adler & Sanchrico, supra note 43, at 304-34.
89. See id. at 334-50.
90. i,t,), as in the additive-across-periods /multiplicative-within-periods representation of lifetime utility as a function of health and income, see infra text accompanying notes 105-107, because it is an open question what the connection is between the l function, i.e., the zero-to-one scaling of health states elicited through QALY surveys, and the q function.
91. See generally Matthew D. Adler, QALYs and Policy Evaluation: A New Perspective, 6 YALE J. HEALTH POL'Y L. & ETHICS 1, 1-16 (2006) (describing QALY metric, discussing current governmental use, and reviewing and citing scholarship).
92. See generally Franco Sassi et al., Equity and the Economic Evaluation of Healthcare, 5 HEALTH TECH. ASSESSMENT 1, 16-28 (2001) (summarizing this literature).
93. See Emmanuela Gakidou et al., Defining and Measuring Health Inequality: An Approach Based on the Distribution of Health Expectancy, 78 BULL. WORLD HEALTH ORG. 42 (2000).
94. See, e.g., Paul Dolan, The Measurement of Individual Utility and Social Welfare, 17 J. HEALTH ECON. 39 (1998);
95. Lars Lindholm & Måns Rosén, On the Measurement of the Nation's Equity Adjusted Health, 7 HEALTH ECON. 621 (1998);
96. Lars Peter Østerdal, Axioms for Health Care Resource Allocation, 24 J. HEALTH ECON. 679 (2005);
97. Adam Wagstaff, QALYs and the Equity-Efficiency Trade-Off, 10 J. HEALTH ECON. 21, 35-38 (1991);
98. Alan Williams, Intergenerational Equity: An Exploration of the 'Fair Innings' Argument, 6 HEALTH ECON. 117 (1997).
99. See Sassi, supra note 49, at 19-21.
100. See, e.g., Gakidou et al., supra note 50, at 43-44;
101. Magnus Johannesson, Should We Aggregate Relative or Absolute Changes in QALYs?, 10 HEALTH ECON. 573, 574-75 (2001);
102. Williams, supra note 51, at 120-21.
103. Namely, a policy might reduce the expected value of a given social welfare function taking individual lifetime QALYs as its arguments, but increase the expected value of that same social welfare function now taking individual utility as a function of individual longevity, health, and income as its arguments. This latter approach is just PPPA.
104. More precisely, the decision rule compares the incremental cost-effectiveness of policies with cutoff ratios. See Adler, supra note 48, at 8-9, 85-88.
105. See DON FULLERTON & DIANE LIM ROGERS, WHO BEARS THE LIFETIME TAX BURDEN? 1-17 (1993).
106. See generally Ian W.H. Parry et al., The Incidence of Pollution Control Policies 10-19 (Resources for the Future, Discussion Paper 05-24, June 2005) (reviewing literature), available at http:// www.rff.org/rff/Documents/RFF-DP-05-24.pdf.
107. See id. at 5-6, 14.
108. See id. at 25.
109. See infra Part I.E.
110. See supra text accompanying note 50.
111. See infra Part II.B.2.
112. See Louis Kaplow, Why Measure Inequality? 5-6 (Harvard Law Sch. Olin Discussion Paper No. 386, 2002).
113. See infra Part II.C.
114. See ADLER & POSNER, supra note 1, at 1-5.
115. See Olof Johansson-Stenman, Distributional Weights in Cost-Benefit Analysis - Should We Forget About Them?, 81 LAND ECON. 337 (2005).
116. See H.M. TREASURY, THE GREEN BOOK: APPRAISAL AND EVALUATION IN CENTRAL GOVERNMENT 24-25, 91-96 (2003), available at http:// www.hm-treasury.gov.uk/media/3/F/green_book_260907.pdf;
117. Jean Drèze, Distribution Matters in Cost-Benefit Analysis: Comment on K.A. Brekke, 70 J. PUB. ECON. 485, 486 (1998).
118. These are the changes in annual income amounts in the policy outcome that make the individual indifferent between the status quo and the policy. Strictly speaking, these changes are not WTP/WTA amounts - since an individual's WTP/WTA is usually understood as a present, one-time payment sufficient to make her indifferent between the policy and the status quo. To calculate WTP/WTA amounts in this standard sense, we would need to know how long the individuals live and what the discount rate is. For simplicity, then, my example uses WTP/WTA defined as compensating changes to annual income. The point of the example - namely, that large changes in individual incomes pose difficulties for the specification of weights - is unaffected by the choice of annual versus one-time compensation measures.
119. See Johansson-Stenman, supra note 66, at 337-38, 340-42;
120. Parry, supra note 57, at 26-29.
121. See also Liqun Liu, Combining Distributional Weights and the Marginal Cost of Funds: The Concept of Person-Specific Marginal Cost of Funds, 34 PUB. FIN. REV. 60, 63-64 (2006) (discussing use of SWF to set the marginal cost of funds).
122. See Adler, Against "Individual Risk," supra note 1, at 1197-98, 1198 n.300.
123. See also James K. Hammitt & Nicolas Treich, Statistical Versus Identified Lives in Benefit-Cost Analysis, 35 J. RISK & UNCERTAINTY 45 (2005) (showing that CBA, using the VSL method, may deviate from a utilitarian SWF that maximizes the sum of expected utilities because that method is sensitive to information about the distribution of individual fatality risks that the utilitarian SAT would ignore).
124. N). However these weights are set, weighted CBA can deviate from an SWF applied in an ex post manner.
125. For that matter, a utilitarian SWF which is applied in an ex post or ex ante manner will treat the two cases as identical. From the ex post perspective, the two cases are identical; and a utilitarian SWF always reaches the same verdicts whether applied ex post or ex ante. See Adler and Sanchirico, supra note 43, at 307. Only a distributively-sensitive SWF applied in an ex ante manner might treat the two cases as different.
126. To be sure, this is only true if the amount and distribution of fear in the two cases are the same. See generally Matthew D. Adler, Fear Assessment: Cost-Benefit Analysis and the Pricing of Fear and Anxiety, 79 CHI-KENT L. REV. 977 (2004). The hypothetical should therefore be structured so that no individual experiences a different fear state in the status quo in the first case than in the second case, and so that no individual experiences a different fear state with the policy in the first case than in the second case. In particular, it might be assumed that the exposed populations in the two cases are unaware of their exposures.
127. See ROBIN BOADWAY & NEIL BRUCE, WELFARE ECONOMICS 137-69 (1984).
128. See MATTI TUOMALA, OPTIMAL INCOME TAX AND REDISTRIBUTION 1-14 (1990);
129. Nicholas Stern, The Theory of Optimal Commodity and Income Taxation: An Introduction, in THE THEORY OF TAXATION FOR DEVELOPING COUNTRIES 22 (David Newberry & Nicholas Stern eds., 1987).
130. See Parry et al., supra note 57, at 26-28. A recent article by Marc Fleurbaey addresses issues of health equity using the SWF framework.
131. See Marc Fleurbaey, Health Equity and Social Welfare, 83/84 ANNALES D'ECONOMIE ET DE STATISTIQUE 21 (2006). Unfortunately, I became aware of Fleurbaey's article as this Article was going to press and was not able to revise the Article to discuss how it bears on my analysis.
132. See ADLER & POSNER, supra note 1, at 25-39;
133. Matthew D. Adler, Welfare Polls: A Synthesis, 81 N.Y.U. L. REV. 1875, 1904-05, 1959-68 (2006).
134. By "outcome," I mean a set of possible worlds that is homogenous with respect to each individual's well-being. A possible world is a completely specified possible history of the universe. A different definition of outcome is also conceivable: one might just define an outcome as a single possible world and conceptualize SWFs as operating on utility vectors corresponding to each possible world. But this definition unnecessarily inflates the number of outcomes, since every possible world within each set of possible worlds homogeneous with respect to each individual's well-being would have the same utility vector.
135. See Adler & Sanchirico, supra note 43, at 296-304.
136. See infra Part II.B.3.
137. See Adler, supra note 42.
138. See Adler & Sanchirico, supra note 43.
139. Variable-population issues pose a difficult set of problems for social choice theory which I will not attempt to engage here. See generally CHARLES BLACKORBY ET AL., POPULATION ISSUES IN SOCIAL CHOICE THEORY, WELFARE ECONOMICS, AND ETHICS (2005). Extending PPPA to the variable-population case is a topic for further research.
140. To be sure, there is a burgeoning literature on the measurement of happiness, but I take it that data on the current population distribution of happiness, and on how policies perturb that, is still thinner than data on health and income. In any event, as mentioned immediately below, PPPA certainly could be modified to incorporate happiness data and have lifetime utilities be partly determined by happiness. Crucially, however, happiness is not the sole component of well-being. For citations to the happiness literature and a discussion of the connection between happiness and well-being, see Matthew D. Adler & Eric A. Posner, Happiness Research and Cost-Benefit Analysis (Univ. of Pa. Inst. for Law & Econ., Research Paper No. 07-15, 2007), available at http://ssrn.com/abstract=999928.
141. Our best-developed policy-analytic tools, such as CBA, provide rigorous guidance in choosing among a given set of options, not in identifying the initial choice set. See Matthew D. Adler, Rational Choice, Rational Agenda-Setting, and Constitutional Law: Does the Constitution Require Basic or Strengthened Public Rationality?, in LINKING POLITICS AND LAW 109, 113-14 (Christoph Engel & Adrienne Héritier eds., 2003). PPPA is similar to CBA in this regard.
142. See EPA, GUIDELINES FOR PREPARING ECONOMIC ANALYSES 126-30 (2000).
143. See id.; Parry, supra note 57; Klaus Conrad, Computable General Equilibrium Models in Environmental and Resource Economics, in THE INTERNATIONAL YEARBOOK OF ENVIRONMENTAL AND RESOURCE ECONOMICS 2002/2003 66, 66 (Torn Tietenberg & Henk Folmer eds., 2002).
144. FULLERTON & ROGERS, supra note 56, at 4-5.
145. Another example of the use of simulation models to estimate policy effects on lifetime incomes is Jan H.M. Nelissen, Annual Versus Lifetime Income Redistribution by Social Security, 68 J. PUB. ECON. 223 (1998).
146. Further examples are discussed id. at 224-25.
147. See generally SUMMARY MEASURES OF POPULATION HEALTH (Christopher J.L. Murray et al. eds., 2002).
148. See generally sources cited supra note 1.
149. See Michael Wolfson & Geoff Rowe, On Measuring Inequalities in Health, 79 BULL. WORLD HEALTH ORG. 553, 557-58 (2001) (describing use of microsimulation modeling to estimate population health inequality and stating that existing modeling methods are "more than adequate").
150. On tobacco policy, see, for example, Sajad Ahmad & John Billimek, Estimating the Health Impacts of Tobacco Harm Reduction Policies: A Simulation Modeling Approach, 25 RISK ANAL. 801 (2005);
151. Tammy O. Tengs et al., Federal Policy Mandating Safer Cigarettes: A Hypothetical Simulation of the Anticipated Population Health Gains or Losses, 23 J. POL'Y ANAL. & MGMT. 857 (2004) and sources cited therein.
152. On cancer policy, see David Fone et al., Systematic Review of the Use and Value of Computer Simulation Modelling in Population Health and Health Care Delivery, 25 J. PUB. HEALTH MED. 325, 332 (2003).
153. Tengs et al., supra note 94, at 860.
154. See, e.g., Tony Blakely & Nick Wilson, Shifting Dollars, Saving Lives: What Might Happen to Mortality Rates, and Socio-Economic Inequalities in Mortality Rates, if Income Was Redistibuted?, 62 SOC. SCI. MED. 2024, 2024-25 (2006);
155. Braveman, supra note 19, at 169-70, 172;
156. Ulf-G. Gerdtham & Magnus Johannesson, Income-Related Inequality in Life-Years and Quality-Adjusted Life-Years, 19 J. HEALTH ECON. 1007, 1007-08 (2000).
157. See also Angus Deaton, Health, Inequality, and Economic Development, 41 J. ECON. LIT. 113, 113-14 (2003) (discussing literature concerning connection between income inequality and health).
158. For example, the Tobacco Policy Model described above uses gender as one predictor of annual transitions. See Tengs et al., supra note 94, at 860.
159. See, e.g., Braveman, supra note 19, at 170-72;
160. Peter Franks et al., The Burden of Disease Associated with Being African-American in the United States and the Contribution of Socio-Economic Status, 62 SOC. SCI. & MED. 2469, 2469-70 (2006).
161. See Adler, supra note 78, at 1965-68;
162. Adler, supra note 48, at 53-57, 55 n.184.
163. See generally Adler, supra note 78.
164. See Adler, supra note 48, at 19-20, 47;
165. Aki Tsuchiya & Paul Dolan, The QALY Model and Individual Preferences for Health States and Health Profiles over Time: A Systematic Review of the Literature, 25 MED. DECISION MAKING 460 (2005).
166. To be sure, surveys to elicit respondents' preferences regarding longevity-health-income histories must be designed to be feasible, given respondents' cognitive limitations. Respondents cannot be asked to evaluate every possible history. On this score, it should be noted that the proposal of some health scholars to use a survey format which would value health histories - the "healthy year equivalent" or "HYE" format - has been criticized as infeasible. See id. at 465-67.
167. However, it is not clear why using surveys to assign values to temporally extended histories is qualitatively less feasible than using surveys to value momentary states, which is what the QALY format does. Just as it is impossible for a cognitively limited respondent to consider all possible histories, so it is impossible for her to consider all possible momentary states. QALY survey designers circumvent this difficulty in various ways. For example, they may use standardized "health state classification systems" to describe health states as a combination of locations on a discrete number of dimensions, and ask each respondent to value a sample of the total set of possible states, so as to estimate a function that maps each combination of locations along the dimensions to a QALY value. See, e.g., Adler, supra note 48, at 48-50. It is not clear why similar devices could not be used to elicit valuations of temporally extended histories.
168. See, e.g., Adler, supra note 48, at 40-41 n.133 (citing surveys of health-related contingent valuation studies).
169. In particular, Harsanyi's account of interpersonal comparisons, which reduces judgments of overall well-being to preferences over lotteries of possible life histories, provides a theoretical basis for the lifetime standard gamble. See Adler, supra note 48, at 17-24 (presenting Harsanyi's account).
170. See Ann M. Holmes, A Method to Elicit Utilities for Interpersonal Comparisons, 17 MED. DECISION MAKING 10 (1997).
171. See James K. Hammitt, How Much is a QALY Worth? Admissible Utility Functions for Health and Wealth 2 (May 2002) (unpublished manuscript, on file with the Harvard Environmental Law Review).
172. k, but to avoid unwieldy symbols I have omitted the "k" subscript.
173. See Han Bleichrodt & John Quiggin, Life-Cycle Preferences over Consumption and Health: When Is Cost-Effectiveness Analysis Equivalent to Cost-Benefit Analysis?, 18 J. HEALTH ECON. 681, 683-90 (1999).
174. i,k).
175. Cf. William N. Evans & W. Mp Viscusi, Estimation of State-Dependent Utility Functions using Survey Data, 73 REV. ECON. & STAT. 94 (1991) (using contingent-valuation surveys to estimate the structure of utility as a function of health and income);
176. W. Kip Viscusi & William N. Evans, Utility Functions that Depend on Health Status: Estimates and Economic Implications, 80 AM. ECON. REV. 353 (1990) (same);
177. Beatrice Rey & Jean-Charles Rochet, Health and Wealth: How Do They Affect Individual Preferences?, 29 GENEVA PAPERS ON RISK & INS. THEORY 43 (2004) (discussing possible test to discriminate between different health-and-wealth utility functions).
178. See, e.g., Paul Dolan et al., The Time Trade-Off Method: Results from a General Population Survey, 5 HEALTH ECON. 141, 150 (1996).
179. See, e.g., Adler, supra note 48, at 21-22;
180. ADLER & POSNER, supra note 1, at 49-50, 161-62, 161 n.28;
181. Matthew D. Adler, Incommensurability and Cost-Benefit Analysis, 146 U. PA. L. REV. 1371, 1401-08 (1998).
182. See, e.g., TUOMALA, supra note 76, at 47;
183. Olof Johansson-Stenman, On the Value of Life in Rich and Poor Countries and Distributional Weights Beyond Utilitarianism, 17 ENVTL. & RESOURCE ECON. 299, 302-03 (2000);
184. CHRISTIAN GOLLIER, THE ECONOMICS OF RISK AND TIME 27 (2001).
185. See David J. Evans, The Elasticity of Marginal Utility of Consumption: Estimates for 20 OECD Countries, 26 FISCAL STUDIES 197, 200 (2005).
186. See Frank A. Cowell & Karen Gardiner, Welfare Weights 25-29 (STICERD, London School of Economics, 1999);
187. Evans, supra note 113;
188. David Pearce & David Ulph, A Social Discount Rate for the United Kingdom 9-15 (CSERGE Working Paper GEC 95-01, 1995).
189. See also Louis Kaplow, The Value of a Statistical Life and the Coefficient of Relative Risk Aversion, 31 J. RISK & UNCERTAINTY 23 (2005) (discussing high values of e estimated in literature on "equity premium," and the inconsistency between those values and existing estimates of the income elasticity of the value of statistical life);
190. Louis R. Eeckhoudt & James K. Hammitt, Background Risks and the Value of a Statistical Life, 23 J. RISK AND UNCERTAINTY 261, 276-77 (2001) (discussing relation between income elasticity of VSL and coefficient of relative risk aversion).
191. For an interesting recent study that uses a Harsanyi-style veil of ignorance format to estimate e, see Olof Johansson-Stenman et al., Measuring Future Grandparents' Preferences for Equality and Relative Standing, 112 ECON. J. 362 (2002).
192. Pearce & Ulph, supra note 114, at 14-16. These authors focus on the range of e appropriate for policymaking in the United Kingdom.
193. Cowell & Gardiner, supra note 114, at 33.
194. See also Johansson-Stenman et al., supra note 114, at 363 (noting that "values in the interval 0.5-2 [for relative risk aversion] are often referred to").
195. See Viscusi & Evans, supra note 109, at 363-67.
196. See also Frank A. Sloan et al., Alternative Approaches to Valuing Intangible Health Losses: The Evidence for Multiple Sclerosis, 17 J. HEALTH ECON. 475, 478, 489-90 (1998).
197. As already mentioned, Ann Holmes has conducted surveys where respondents are asked to value hypothetical lives described both in terms of health and in terms of other characteristics. The additional characteristics include gender. See Holmes, supra note 104.
198. See TUOMALA, supra note 76, at 28-29;
199. Johansson-Stenman, supra note 112, at 302-03;
200. Samuel Fankhauser et al., The Aggregation of Climate Change Damages: A Welfare Theoretic Approach, 10 EVNTL. & RESOURCE ECON. 249, 257 (1997).
201. In some of this literature, the social welfare function is an Atkinsonian function that takes individual incomes rather than utilities as its arguments. See Parry et al., supra note 57, at 26-28;
202. Louis Kaplow, Concavity of Utility, Concavity of Welfare, and Redistribution of Income 2 (Harvard L. Sch. Discussion Paper No. 437, 2003).
203. Atkinsonian SWFs are also used in the health economics literature that discusses applying SWFs to QALYs. See sources cited supra note 51.
204. See, e.g., BOJER, supra note 38, at 110.
205. The formula for the Atkinsonian SWF is sometimes multiplied by 1 /N, where N is the population size. Where N is the same in all outcomes - as assumed throughout this Article, See supra text accompanying note 84 - that formula is equivalent to the one given in the text, both in its ranking of utility vectors and in its ranking of policies. In the case where γ = 1, the formula for the Atkinsonian SWF is sometimes given as the product of individuals' utilities rather than the sum of the logarithms of utilities. These formulations are increasing transformations of each other (see, e.g., Fankhauser, supra note 119, at 257-58) and therefore order utility vectors (but not necessarily policies) the same way.
206. See infra note 121.
207. N)), where g is what's known as an "increasing" or "monotonically increasing" function, which means that the graph of g always slopes up). Because W* is an increasing transformation of W, W* and W order utility vectors the same way. However, W* and W applied in an ex post fashion to policies (probability distributions over utility vectors) may not order these policies the same way. This raises the difficult question, which I cannot address here, about how one identifies the appropriate transformation to use in PPPA, once one has specified γ. That identification involves determining the degree to which policy-makers should be risk averse in social welfare. As an initial matter, I suggest, PPPA should assume risk-neutrality in social welfare, i.e., simply use the Atkinsonian SWF itself rather than some nonlinear transformation. But the issue certainly deserves more exploration.
208. See LAMBERT, supra note 38, at 94-102;
209. Anthony Atkinson, On the Measurement of Inequality, 2 J. ECON. THEORY 244, 244-45, 249-52 (1970).
210. 1-γ/(1-γ) is either undefined or, if defined, is either decreasing or strictly convex. Therefore, the SWF will not satisfy both the Pareto principle and the Pigou-Dalton principle. Identifying an appropriate SWF that can allow for negative utilities is a difficult task that I will not attempt to resolve here. See Campbell Brown, Matters of Priority 192-197 (Mar. 2005) (unpublished Ph.D. thesis, The Australian National University) (on file with the Harvard Environmental Law Review) (proving that no SWF has the prioritarian form of summing an increasing, strictly concave function of individual utilities and has an unrestricted domain and is invariant to a ratio transformation);
211. Amartya Sen, Social Choice Theory, in 3 HANDBOOK OF MATHEMATICAL ECONOMICS 1073, 1127 & n.74 (Kenneth J. Arrow & Michael D. Intriligator eds., 1986). As for utility vectors that include zeros, the Atkinsonian SWF will be defined only for γ < 1.
212. See Adler & Sanchirico, supra note 43, at 300-02.
213. Harsanyi-style utility numbers, the expectations of which represent well-informed individuals' convergent preferences over lotteries of life histories, will be unique up to an affine transformation. It is a well-known feature of such "von-Neumann/Morgenstem" utilities, meant to represent decisions under risk or uncertainty, that they are unique up to an affine transformation. In other words, given a utility function U which maps life histories onto utilities, such that the expected utility numbers calculated using these utilities accurately represent a well-informed individual's preferences over lotteries of those histories, we can multiply U by a positive constant c and add a constant d. Expectations with respect to these new utilities will produce the very same ordering of lotteries as expectations with respect to the original utilities. By taking a morally significant zero point - for example, a life no better than nonexistence - and giving it a utility of zero, we can narrow down the set of admissible utility functions. Consider a function U* that represents the well-informed individual's ordering of lotteries and assigns a value of zero to the zero point. Any admissible function will have to be produced by taking U* and multiplying it by a positive constant. However, that transformation remains admissible. Any new function produced by multiplying U* by a positive constant will still assign zero to the zero point, and expectations formed with respect to this new function will still order lotteries of life histories correctly. To preclude multiplying utilities assigned to life histories by a positive constant, we would need to have morally significant information beyond (1) well-informed individuals' (convergent) ordering of life histories and lotteries of life histories, and (2) their (convergent) identification of the zero point. It is hard to see what that information would be.
214. See, e.g., LAMBERT, supra note 38, at 99-102;
215. Kristof Bosmans, Extreme Inequality Aversion Without Separability, 32 ECON. THEORY 589, 592 (2007).
216. See Fankhauser et al., supra note 119, at 257-59.
217. Many studies use a smaller range of values of γ, often in the context of an SWF that takes incomes rather than utilities as its arguments. See LAMBERT, supra note 38, at 129;
218. Parry, supra note 57, at 28.
219. +, is lower the greater the value of γ. Also, for a given pair of individuals at utility levels High and Low, the ratio between the marginal social value of Low's utility and High's utility increases with γ.
220. See Yoram Amiel et al., Measuring Attitudes Towards Inequality, 101 SCANDINAVIAN J. ECON. 83, 86-88 (1999) (discussing Atkinson's proposal).
221. See, e.g., Cowell & Gardiner, supra note 114, at 15-16;
222. Pearce & Ulph, supra note 114, at 14-15;
223. Stern, supra note 76, at 47-48.
224. A closely related kind of question asks about the choice between benefiting some individual by a certain amount and a better-off individual by a greater amount. See Dolan, supra note 51, at 51-52.
225. Other variants could specify the two individuals' health, income and longevity positions and ask about leaky transfers of health, income or longevity. Given a utility function from longevity-health-income histories to utility, answers to these sorts of question will also fix or help fix a γ.
226. See, e.g., Lindholm & Rosén, supra note 51;
227. Williams, supra note 51.
228. It should be stressed that leaky-bucket and equalization thought experiments are only two particularly straightforward forms of normative reflection about the value of γ. Any analysis of the implications of a given γ for some principle that the analyst endorses, or some scenario about which the analyst has intuitions, could be helpful in specifying γ. See, e.g., Fankhauser et al., supra note 119, at 259-62 (identifying values of γ consistent with use of uniform per-unit global warming damages).
229. On the distinction between policy surveys and welfare polls, see Adler, supra note 78.
230. See, e.g., Paul Dolan et al., QALY Maximisation and People's Preferences: A Methodological Review of the Literature, 14 HEALTH ECON. 197 (2005).
231. See Amiel et al., supra note 128, at 86;
232. Lindholm & Rosén, supra note 51.
233. For related survey work, see Ignacio Abasolo & Aki Tsuchiya, Exploring Social Welfare Functions and Violation of Monotonicily: An Example from Inequalities in Health, 23 J. HEALTH ECON. 313 (2004);
234. Louis Gevers et al., Professed Inequality Aversion and its Error Component, 81 SCANDINAVIAN J. ECON. 238 (1979);
235. Herbert Glejser et al., An Econometric Study of the Variables Determining Inequality Aversion Among Students, 10 EUR. ECON. REV. 173 (1977);
236. Magnus Johannesson & Ulf-G. Gerdtham, A Note on the Estimation of the Equity-Efficiency Trade-off for QALYs, 15 J. HEALTH ECON. 359 (1996);
237. Magnus Johannesson & Ulf-G. Gerdtham, A Pilot Test of Using the Veil of Ignorance Approach to Estimate a Social Welfare Function for Income, 2 APPLIED ECON. LETT. 400 (1995).
238. See LAMBERT, supra note 38, at 129;
239. Cowell & Gardiner, supra note 114, at 24-25.
240. See Adler & Sanchirco, supra note 43, at 296-302.
241. See Adler & Sanchirico, supra note 43, at 302.
242. Actually, there are many different variations on the simple rank-weighted SWF described in the text. Consider any SWF which ranks utilities from lowest to highest, multiplies each by a positive weight which is a decreasing function of rank, and sums the weighted utilities. Any such SWF will be ratio-rescaling-invariant, satisfy the Pareto principle, and satisfy the Pigou-Dalton principle. So an equity analyst who is conducting a particularly full PPPA analysis might want to consider evaluating policies using different rank-weighted SWFs within this general family. See generally BLACKORBY ET AL., supra note 84, at 75-82, 99-100 (discussing rank-weighted family of SWFs).
243. See supra text accompanying notes 80-81.
244. Although it is possible to have "non-Paretian" SWFs - SWFs that sometimes fail to prefer a Pareto-superior outcome - the case for the Pareto principle is powerful, and it is certainly possible for SWFs to both satisfy the Pigou-Dalton principle and be Paretian. In particular, Atkinsonian SWFs and the rank-weighted SWF have both characteristics See Adler & Sanchirico, supra note 43, at 291-304;
245. BLACKORBY ET AL., supra note 84, at 69-82.
246. W, outcomes with greater total utility are preferred.
247. See ADLER & POSNER, supra note 1.
248. See, e.g., LAMBERT, supra note 38, at 94-102;
249. SEN, supra note 38, at 38-39;
250. BOJER, supra note 38, at 108-11;
251. Cowell, supra note 39, at 113-15.
252. See ADLER & POSNER, supra note 1.