Benefit–Cost Analysis and Distributional Weights: An Overview

264 Benefit–Cost Analysis and Distributional Weights: An Overview Matthew D. Adler* Introduction Benefit–cost analysis (BCA)1 evaluates governmental policies by summing individuals’ monetary equivalents, and is insensitive to distributional concerns. BCA does not take into account whether those made better off by a policy have higher or lower incomes, or higher or lower levels of nonincome welfare-relevant attributes (e.g., health), than those made worse off. Arguably, distributional considerations should be incorporated into BCA via “distributional weights.” A scholarly literature dating from the 1950s endorses distributional weights and analyzes how to specify them (Meade 1955, chap. 2; Weisbrod 1968; Dasgupta and Pearce 1972; Dasgupta, Sen, and Marglin 1972; Little and Mirrlees 1974; Squire and van der Tak 1975; Boadway and Bruce 1984, pp. 271–81; Brent 1984; Ray 1984; Drèze and Stern 1987; Drèze 1998; Cowell and Gardiner 1999; Yitzhaki 2003; Johansson-Stenman 2005; Creedy 2006; Liu 2006; Fleurbaey et al. 2013; Boadway 2016). Distributional weights were adopted, for a time, at the World Bank (Little and Mirrlees 1994). They are currently recommended by the UK’s official BCA guidance document (HM Treasury 2003, pp. 91–94). However, it appears that distributional weights have rarely if ever been used by BCA practitioners in the U.S. government, and the parallel U.S. guidance document does not mention them (Office of Management and Budget 2003). This article, which is part of a symposium on Distributional Considerations in Benefit–Cost Analysis, provides an introduction to distributional weights.2 The fulcrum for my discussion will be the concept of the social welfare function (SWF). The SWF is a fundamental construct in many areas of welfare economics, including optimal tax theory, growth theory, and analysis of climate change. BCA with distributional weights, in turn, is a practicable method for implementing an SWF. This is the view of BCA running through the literature on distributional weights, and is presented here. This account of BCA is quite different from the familiar view that sees BCA as a tool for implementing the criterion of Kaldor–Hicks efficiency (potential Pareto superiority). The * Richard A. Horvitz Professor of Law and Professor of Economics, Philosophy, and Public Policy, Duke University. Many thanks to Marc Fleurbaey, James Hammitt, Alex Pfaff, and Nicolas Treich for their comments. 1 Some prefer the term cost–benefit analysis (CBA). In conformity with this journal’s style, I use BCA here. 2 The other articles in the symposium are Fleurbaey and Rafeh (2016), which uses insights from welfare economics to examine how distributional weights can be introduced into benefit–cost analysis, and Robinson, Hammitt, and Zeckhauser (2016), which focuses specifically on the role of distributional considerations in U.S. regulatory analyses. Review of Environmental Economics and Policy, volume 10, issue 2, Summer 2016, pp. 264–285 doi:10.1093/reep/rew005 ß The Author 2016. Published by Oxford University Press on behalf of the Association of Environmental and Resource Economists. All rights reserved. For Permissions, please email: Benefit–Cost Analysis and Distributional Weights 265 Kaldor–Hicks criterion has the advantage of avoiding interpersonal comparability, but has various flaws, described in a literature beginning with Scitovsky (1941; see also Gorman 1955; Chipman and Moore 1978; Sen 1979; Boadway and Bruce 1984; Boadway 2016).3 The article is not a comprehensive survey of the literature on distributional weights. Rather, it aims to explain the key ideas. I first describe the SWF concept, with a particular focus on two specific SWFs: the utilitarian and isoelastic/Atkinson SWFs. The article then discusses the functional form of weights matching these two SWFs. Next, it provides a concrete example, involving risk-reduction policies and the “value of statistical life.” The article concludes by considering two objections to weights. One concerns the possibility of interpersonal comparisons given heterogeneous preferences. The second is that distributional considerations are better handled via the combination of the tax system and unweighted BCA. The discussion aims to be accessible. The fundamentals of distributional weighting are illustrated with a simple, one-period model. Space constraints preclude a treatment of certain additional issues that arise in the intertemporal context, in particular the relation between distributional weights and discounting. Key mathematical formulas are provided in a Technical Appendix. A more rigorous, mathematical analysis of many of the topics discussed in the main text is provided in the online supplementary materials. The reader should consult these materials, along with cited references, as backup for the discussion. Social Welfare Functions: An Overview The concept of the SWF originated with work by Bergson and Samuelson. It was reenergized by Sen, in response to Arrow’s impossibility theorem, and was the basis for Mirrlees’ groundbreaking scholarship on optimal tax theory. It now permeates many subdisciplines within economics (although less so governmental practice).4 Key Elements of the SWF Framework The SWF framework has two key elements: an interpersonally comparable utility function, which transforms any given outcome (a possible consequence of policy choice) into a list or “vector” of utility numbers, one for each person in the population; and some rule for ranking these vectors. To illustrate, imagine that there are three people in the population and two outcomes are being compared. Jim has a particular bundle of attributes in outcome x and a different bundle in outcome y. The same is true of Sue. Laura has the same attributes in both outcomes, and thus is unaffected by the choice between them (her well-being does not change). “Attributes,” here, means the characteristics that determine an individual’s well-being, such as income, health, leisure, the quality of the environment, and so forth.5 3 The debate about the Kaldor–Hicks criterion is well known and will not be recapitulated here. See Adler (2012, pp. 79-88), for a summary of scholarly development of the SWF concept. 5 It is, of course, infeasible for a decision maker and the policy analyst advising her to consider how policies affect the totality of individuals’ attributes. Rather, policy analysis will focus on a subset of attributes: for example, income and leisure; income, health, and leisure; etc. 4 M. D. Adler 266 Our utility function assigns Jim’s bundles of attributes in x and y the utility values 10 and 11, respectively; it assigns Sue’s bundles the values 30 and 25, respectively; and it assigns 40 to Laura’s bundle. Thus outcome x is mapped onto the utility vector (10, 30, 40) and y is mapped onto the vector (11, 25, 40)—with the first entry the utility number for Jim, the second for Sue, and the third for Laura (see table 1). (...truncated)