2. Determining optimal programs

The academic literature proceeds as if an enlightened social planner is choosing and evaluating projects. In truth, individual agencies often initiate and evaluate projects and face different budgeting constraints determined by legislatures or higher administrative units. Taxation and revenue raising are often determined by distinct agencies from those determining expenditure. The perspective of a social planner may well differ from that of an agency administrator with a fixed budget to spend on a collection of projects. Criteria useful for bureaucrats may differ sharply from those needed to evaluate social optimality.

Converting utils into dollar equivalents, as is common in the literature, the NSB of the project $ j $ is:

(1) $$ {\mathrm{NSB}}_j\hskip0.35em =\hskip0.35em {B}_j-\Omega \left({D}_j\right). $$

$ {\mathrm{NSB}}_j $ is a measure of the net expansion or contraction of the social possibility frontier. Projects may vary in scale and content. A project $ j $ at one scale when implemented at another scale may produce benefits and costs, nonproportional to the expansion of scale of costs and benefits, a feature captured by (1) but rarely addressed in computations of the BCR or MVPF.

García et al. (Reference García, Heckman, Leaf and Prados2020, Reference García, Bennhoff, Heckman and Leaf2021) are examples of studies that properly define and estimate $ {\mathrm{NSB}}_j $ . Both studies quantify the long-term benefits and costs of productivity-enhancing early childhood education programs, which increase labor income, reduce criminal activity, and promote behaviors that improve the long-term health of their participants. Their estimate of $ {\mathrm{NSB}}_j $ includes the reduction in welfare costs due to lower costs of the criminal justice system (e.g., costs of imprisonment). It also includes private gains due to better health (e.g., better quality of life) and reductions in welfare costs of taxation due to lower costs for the public health system. Enhanced tax revenue due to, for example, reduced participation in safety-net programs because of higher earned (gross) income induced by the programs, should not be part of $ {B}_j $ – it is a transfer between two parties (the government and the public), if these parties are assumed equally weighted. However, any welfare-cost changes generated by such tax enhancement should be counted as part of $ \Omega \left({D}_j\right) $ . García et al. (Reference García, Heckman, Leaf and Prados2020, Reference García, Bennhoff, Heckman and Leaf2021) quantify these changes in excess burden costs.

Provided inclusive costs and benefits are properly accounted for, from a social planner’s point of view, all projects $ j\in \left\{1,\dots, J\right\} $ that satisfy $ {\mathrm{NSB}}_j>0 $ are worth undertaking. Note further that arbitrary decisions of what goes into costs and benefits are irrelevant for computing NSBs using (1), provided double counting is avoided. Projects with the highest NSBs should be selected in rank order. Note that benefits include welfare evaluations of the project for the larger society, but, in practice, these are rarely measured and dollar values for direct benefits are used on pragmatic grounds. The set of possible projects considered should recognize mutual exclusivity across some projects. Let $ {J}^{\ast } $ be the set of all possible projects. Note that there may be additional political constraints such as restrictions on direct costs $ \left({\sum}_{j\in {J}^{\ast }}{D}_j\hskip0.35em \le \hskip0.35em \overline{D}\right) $ or restrictions on net revenue $ \left({\sum}_{j\in {J}^{\ast }}\left({D}_j-{R}_j\right)\le \hskip0.35em \overline{R}\right) $ that limit the set of politically attainable projects.

3. Benefit-cost ratio

The BCR is widely used. It counts the full social benefits $ {B}_j $ (which of course include expansions of the potential tax base). The full expansion of the social possibility frontier $ {B}_j $ is the appropriate total benefit. The BCR is

$$ {\mathrm{BCR}}_j\hskip0.35em =\hskip0.35em \frac{B_j}{\Omega \left({D}_j\right)}. $$

If $ {\mathrm{NSB}}_j\hskip0.35em =\hskip0.35em {B}_j-\Omega \left({D}_j\right)>0 $ , $ {\mathrm{BCR}}_j>1 $ .

The rule $ {\mathrm{BCR}}_j>1 $ is not a sufficient guide to the optimality of choosing $ j $ over some alternative $ {j}^{\prime } $ . Evidence that $ {\mathrm{BCR}}_j>1 $ is only evidence that program $ j $ pays for itself in the sense of a Kaldor criterion including the utility of equally weighted altruistic agents, but does not necessarily indicate optimality. $ {\mathrm{BCR}}_j $ ignores the scale of net benefits. This is a general property of any ratio measure, including BCR and MVPF. However, rarely do economists value alternative projects by using NSB to establish optimality and this limits the validity of many current criteria. Hendren and Sprung-Keyser (Reference Hendren and Sprung-Keyser2020) is a recent example. They use, instead, the following ratio criterion.

4. Marginal value of public funds

The MVPF focuses attention on one component of the total benefits: namely, the revenues of the government raised by the program. As previously noted, such revenues depend on institutional details regarding taxation. These revenues are transfers unless the government is more efficient than the public in using funds. MVPF adopts a peculiar posture of evaluating the social benefits of projects assuming a predetermined social cost of public revenue collected or, alternatively, ignoring it. The criterion might be defended from the standpoint of an administrative agency or set of such agencies with a total fixed pool of funds, determined by the legislature that gets to keep (and spend) any revenue benefits $ {R}_j $ of its programs and which are free to disregard the welfare costs of taxation.Footnote ³ The MVPF criterion is

$$ {\mathrm{MVPF}}_j\hskip0.35em =\hskip0.35em \frac{B_j}{D_j-{R}_j}. $$

If the agency or collection of agencies providing the program capture the generated “revenue” $ {R}_j $ and can spend against it, MVPF selects projects with the highest “bang for the buck” from available funds so determined. However, there is, in general, no logical necessity for determining the funds available to an agency in this manner. MVPF assumes that the opportunity cost of $ j $ , $ {D}_j $ , is the amount spent by the agency, which might have gone to another agency or returned to the public, and ignores the excess burden of taxes. Notice that

$$ {\displaystyle \begin{array}{l}{\mathrm{MVPF}}_j>1\Rightarrow {B}_j>{D}_j-{R}_j\\ {}\hskip7.5em \Rightarrow {B}_j+{R}_j-{D}_j>0.\end{array}} $$

This expression ignores the social cost of raising revenue. In application, one should not include $ {R}_j $ in $ {B}_j $ or $ \Omega \left({D}_j\right) $ because revenue transfers are not a social benefit or offset to social cost.

Any application of MVPF consistent with basic economics requires that any new choice of a project takes into account any expansion of total expenditure induced by it, by accounting for the social costs of raising those funds. This is not done by Hendren and Sprung-Keyser (Reference Hendren and Sprung-Keyser2020), who compare projects with vastly different scales and budgetary requirements, and, hence, social costs of funds.

For an administrative agency with a prespecified budget or with access to a pool of funds somehow determined, MVPF characterizes a certain type of efficiency in spending its budgeted funds. Ignoring the social costs of raising the funds allocated, it violates guidelines for the evaluation of federal programs that recognize such costs and require that evaluations quantify them.Footnote ⁴ If the social cost of funds is unaffected by a particular policy, it can safely be ignored.

MVPF shares with BCR the property that it ignores the scale of programs evaluated. It further ignores the welfare costs of taxation. A large MVPF could justify expenditure on programs generating low benefits (NSB) at a high direct cost as long as $ {D}_j\to {R}_j $ . It favors programs that operate in institutional tax and expenditure environments that produce government revenue that might or might not be used to offset direct costs and not necessarily programs with the greatest social benefits, including the social opportunity costs of public funds.