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cost-benefit analysis, CBA, distributional weights, inequality, value of statistical life, VSL, utilitarianism, social welfare function


Standard cost-benefit analysis (CBA) is insensitive to distributional concerns. A policy that improves the lives of the rich, and makes the poor yet worse off, will be approved by CBA as long as the policy’s aggregate monetized benefits are positive. Distributional weights offer an apparent solution to this troubling feature of the CBA methodology: adjust costs and benefits with weighting factors that are inversely proportional to the well-being levels (as determined by income and also perhaps non-income attributes such as health) of the affected individuals.

Indeed, an academic literature dating from the 1950s discusses how to specify distributional weights. And the current official guidance document for governmental CBA in the U.K. recommends their use. However, CBA scholarship in the U.S. has usually ignored the possibility of distributional weights. The prevailing wisdom, in the U.S., seems to be that the specification of weights is hopelessly “value laden” and that distributional concerns are best handled through the tax system. There is no history of distributional weighting in the U.S. government. Although CBA is now entrenched in the federal regulatory bureaucracy, via OIRA review, distributional considerations — let alone the specific device of weights — are barely mentioned in OIRA guidance.

This paper provides a systematic overview of the specification of distributional weights. It shows, in detail, how to “put structure” on the problem. Two kinds of weights are described: utilitarian weights, which correct for the diminishing marginal utility of money; and isoelastic/Atkinson weights, which embody an aversion to inequality in the distribution of well-being itself. Both kinds of weights can be captured in simple and quite implementable formulas. Although the choice to adjust CBA with weights does involve a contestable ethical/moral judgment, that is equally true of the decision to use CBA in the first place — which remains intensely controversial outside the community of economists.

The paper illustrates the effect of weights by applying them to the “value of statistical life” (VSL), capturing individuals’ willingness to pay for fatality risk reduction. Richer individuals have higher VSL values, and this creates a policy dilemma: CBA with income-differentiated VSL can benefit the rich at the expense of the poor; but CBA with undifferentiated, population-average, VSL may require the poor to pay more than they can afford for risk reduction. I show how the use of distributionally weighted VSL values can greatly mitigate this dilemma.

The paper also dissects the “tax system” objection to the use of weights. Although distributional weights would be unnecessary in an idealized economy with a lump-sum tax system, real-world taxation is beset by imperfections (administrative costs, incomplete governmental information, divided government) that create a space for weights. To be sure, in using distributional weights to assess non-tax policies, governmental decisionmakers should consider the possibility of tax-code changes that might produce yet greater weighted benefits. In other words, tax code changes (if feasible) should be on the “menu” of policy choices that are evaluated by means of distributionally weighted CBA. But this nuanced approach is quite different than the problematic view of the tax system as a distributional cure-all which rationalizes the practice of unweighted CBA.

The main part of the paper is meant to be systematic and rigorously grounded but accessible. A lengthy formal appendix provides back-up.

Library of Congress Subject Headings

Social service, Cost effectiveness, Quality of life, Equality, Utilitarianism, Life--Valuation