Distributional weighting shows how benefit-cost analysis can be improved.
In one of his first actions after the inauguration, President Joseph R. Biden issued a memorandum instructing the Director of the Office of Management and Budget to propose recommendations for improving and modernizing regulatory review. The memorandum calls for proposals for “procedures that take into account the distributional consequences of regulations.” This memorandum could initiate an important shift toward equity in benefit-cost analysis.
The United States is afflicted by distributional inequities along racial, gender, socioeconomic, and other dimensions, and it is vitally important that regulatory impact analysis account for a proposed rule’s distributional impacts. Although Executive Order 12866, Executive Order 13563, and Circular A-4 do instruct agencies to consider distribution, regulatory analysis in practice does so only haphazardly.
Quantitative benefit-cost analysis (BCA) is a central component of the current regulatory review process in the United States. Discussions about how to incorporate distributional considerations into regulatory review will therefore need to grapple with the relation between BCA and distributional analysis.
BCA has been characterized as insensitive to distributional considerations, or even hostile to equity. Some commentaries on Biden’s memorandum take this view of BCA. The standard form of BCA is to sum up unweighted individual willingness-to-pay and willingness-to-accept amounts. Circular A-4 encourages agencies to engage in standard BCA, not as the overriding decision criterion, but as information for decision makers. Standard BCA is indeed indifferent to how a policy’s income costs are distributed among the population. But this feature of standard BCA is not the whole story of BCA and equity.
A fuller picture emerges when one unpacks the normative argument for BCA. Within welfare economics (where BCA originates), two, quite different arguments have been offered.
One argument in defense of BCA appeals to so-called Kaldor-Hicks efficiency. A policy is Kaldor-Hicks efficient—relative to the status quo—if those who benefit from the policy could hypothetically compensate those who are worse off via a costless, lump-sum transfer so that everyone is better off.
Standard BCA implements Kaldor-Hicks efficiency: If the sum of willingness-to-pay for a policy, on the part of those it benefits, is greater than the sum of willingness-to-accept, on the part of those made worse off, then the policy together with a costless transfer from the first group to the second would be universally beneficial.
According to the Kaldor-Hicks view of BCA, incorporating distributional considerations into BCA has no grounding. The Kaldor-Hicks approach offers no rationale for differential weighting of willingness-to-pay and willingness-to-accept amounts. Differential weighting flies in the face of the Kaldor-Hicks test because a policy that is not convertible into a universally beneficial policy via any costless, lump-sum transfer might still be chosen by weighted BCA. For example, imagine that one group is better off with a policy and has an aggregate willingness to pay of $10 million, while a second is worse off and has an aggregate willingness to accept of $15 million. If the benefits to the first group are weighted at twice the losses to the second, the policy passes a weighted CBA test. But there is no lump sum transfer from the first group to the second that would make the policy universally beneficial.
The Kaldor-Hicks defense of BCA is quite problematic. The deepest problem is that the Kaldor-Hicks criterion itself is purely hypothetical, and therefore lacks normative appeal. Consider a policy that passes the Kaldor-Hicks test—that is potentially universally beneficial if coupled with a certain hypothetical transfer fully compensating those harmed by the policy—but would not in fact benefit everyone, since no such transfer would in fact be adopted or is even possible given the actual administrative and incentive costs of taxation. The policy would in fact make some individuals worse off. Is this policy justified? The unrealized potential of universal benefit via a hypothetical lump-sum transfer is hardly a good justification.
In short, policymakers need to drop the problematic Kaldor-Hicks defense of BCA. Doing so will reveal how to refine standard BCA to take account of distribution.
I mentioned above that, within welfare economics, two quite distinct rationales for BCA have been offered. While the first rationale argues in favor of standard BCA, relying upon the problematic notion of Kaldor-Hicks efficiency, the second rationale argues in favor of weighted BCA that sums willingness-to-pay and -accept amounts multiplied by weighting factors that decrease with income.
This second rationale is based upon the notion of a social welfare function (SWF). The SWF was introduced into welfare economics in the 1930s and 1940s by Abram Bergson and Paul Samuelson and was developed by Amartya Sen. Now scholars widely use SWFs in theoretical welfare economics, the economic literature on optimal taxation, and scholarship on climate change.
The SWF uses a “utility” indicator, which measures individuals’ well-being, to model the status quo as a distribution of well-being among the population and a given policy as a change to this status quo distribution. Different functional forms for the SWF capture differing normative views about how to compare distributions of well-being. The SWF can—but need not—be utilitarian. The utilitarian SWF is the simple sum total of well-being. By contrast, “prioritarian” SWFs sum a concave function of well-being and thereby give greater weight to well-being changes affecting the worse off.
BCA with distributional weights can be used to approximate a utilitarian SWF, a prioritarian SWF, or any other type. Utilitarian distributional weights will decrease with income by virtue of “diminishing marginal utility”—an incremental dollar has a smaller well-being impact for those at higher income. Prioritarian distributional weights will decrease with income even more quickly than utilitarian weights, by prioritizing the worse off on top of diminishing marginal utility.
Distributional weights for BCA are not merely a theoretical idea. The Green Book—the authoritative BCA guidance for the United Kingdom—recommends using them and even provides specific values.
Naturally, specifying distributional weights is a value-laden enterprise. Revised regulatory review guidance could recommend that U.S. agencies undertake standard BCA alongside distributionally weighted BCA with some range of weights.
Which characteristics should be the basis for weighting, how the utility function should be constructed, and whether the weights are meant merely to reflect diminishing marginal utility or to incorporate other equity factors are all questions that implicate contested, normative issues that should be resolved at the policy level—not by unelected civil servants.
The theory of SWFs and distributionally weighted BCA offers a framework—itself contestable, to be sure—for incorporating distributional considerations into regulatory review. Clearing away the flawed Kaldor-Hicks story behind BCA shows how BCA can be improved to account for equity.