{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"longbench-v2","formal_name":"LongBench v2","introduction":"長い資料の深い理解と推論を、多肢選択問題で評価するベンチマークです。公式紹介では503問を収録し、単一・複数文書の質問応答やコードリポジトリ理解などを扱います。\n\nLongBench v2 evaluates deep understanding and reasoning over long contexts through multiple-choice questions. Its official description lists 503 questions spanning tasks such as single-document and multi-document QA and code-repository understanding.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/zai-org/LongBench-v2","indexing_mode":"noindex"},"task_id":"1ad6c59b-5732-599a-bd97-b5a8cee7390d","task_key":"train--66f950acbb02136c067c5021","task_revision_id":"1","upstream_id":"66f950acbb02136c067c5021","short_description":"In the context of the MVPF (Marginal Value of Public Funds) framework, which of…","config":"","split":"train","body":"{\"choice_A\":\"The policy increases the recipients' willingness to pay due to consumption-smoothing benefits provided by the in-kind transfers, thereby enhancing their welfare more than the cost to the government.\",\"choice_B\":\"The policy generates substantial positive fiscal externalities, such as increased long-term tax revenues from individuals whose earnings were boosted by the in-kind transfers.\",\"choice_C\":\"The MVPF calculation reflects a situation where the marginal cost of the in-kind transfers is underestimated, leading to artificially high welfare estimates due to incomplete cost-benefit accounting.\",\"choice_D\":\"The marginal excess burden of taxation used to fund the policy is higher than the policy’s actual implementation cost, which leads to an inflated MVPF value.\",\"context\":\"THE\\nQUARTERLY JOURNAL\\nOF ECONOMICS\\nVol. 135\\n2020\\nIssue 3\\nA UNIFIED WELFARE ANALYSIS OF GOVERNMENT\\nPOLICIES∗\\nNATHANIEL HENDREN AND BEN SPRUNG-KEYSER\\nWe conduct a comparative welfare analysis of 133 historical policy changes\\nover the past half-century in the United States, focusing on policies in social in-\\nsurance, education and job training, taxes and cash transfers, and in-kind trans-\\nfers. For each policy, we use existing causal estimates to calculate the benefit\\nthat each policy provides its recipients (measured as their willingness to pay)\\nand the policy’s net cost, inclusive of long-term effects on the government’s bud-\\nget. We divide the willingness to pay by the net cost to the government to form\\neach policy’s Marginal Value of Public Funds, or its “MVPF”. Comparing MVPFs\\nacross policies provides a unified method of assessing their effect on social welfare.\\nOur results suggest that direct investments in low-income children’s health and\\n∗We first and foremost thank the several hundred researchers whose em-\\npirical results form the foundation of our estimates. We are deeply indebted to\\na wonderful team of research assistants: Caroline Dockes, Harris Eppsteiner,\\nAdriano Fernandes, Jack Hoyle, Omeed Maghzian, Kate Musen, Nicolaj Thor, and\\nthe rest of the exceptional team of Pre-Doctoral Fellows at Opportunity Insights.\\nWe are also grateful to Raj Chetty, David Deming, Winnie van Dijk, Amy Finkel-\\nstein, John Friedman, Andrew Goodman-Bacon, Jeff Grogger, Hilary Hoynes, John\\nEric Humphries, Larry Katz, Sarah Miller, Evan Soltas, Larry Summers, Michael\\nStepner, and Laura Wherry for helpful comments and suggestions, along with sem-\\ninar participants at the University of Chicago, Georgetown, IFS, the University\\nof Kentucky, LSE, Michigan, Minnesota, and Texas A&M, along with confer-\\nence participants at the NBER and the National Tax Association meetings. This\\nresearch was funded by the National Science Foundation (#CAREER1653686\\n(Hendren) and #DGE1745303 (Sprung-Keyser)), the Sloan Foundation (Hendren),\\nthe Bill & Melinda Gates Foundation (Hendren), and the Chan Zuckerberg Ini-\\ntiative (Hendren). Any opinions, findings, and conclusions or recommendations\\nexpressed in this material are those of the author(s) and do not necessarily reflect\\nthe views of the National Science Foundation.\\nC\\n⃝The Author(s) 2020. Published by Oxford University Press on behalf of President and\\nFellows of Harvard College. This is an Open Access article distributed under the terms\\nof the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/),\\nwhich permits unrestricted reuse, distribution, and reproduction in any medium, provided the\\noriginal work is properly cited.\\nThe Quarterly Journal of Economics (2020), 1209–1318. doi:10.1093/qje/qjaa006.\\nAdvance Access publication on March 5, 2020.\\n1209\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1210\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\neducation have historically had the highest MVPFs, on average exceeding 5. Many\\nsuch policies have paid for themselves as the government recouped the cost of their\\ninitial expenditures through additional taxes collected and reduced transfers. We\\nfind large MVPFs for education and health policies among children of all ages,\\nrather than observing diminishing marginal returns throughout childhood. We\\nfind smaller MVPFs for policies targeting adults, generally between 0.5 and 2. Ex-\\npenditures on adults have exceeded this MVPF range in particular if they induced\\nlarge spillovers on children. We relate our estimates to existing theories of optimal\\ngovernment policy, and we discuss how the MVPF provides lessons for the design\\nof future research. JEL Codes: H00, I00, J24.\\nI. INTRODUCTION\\nWhat government expenditures are most effective at improv-\\ning social well-being? Are in-kind transfers preferable to cash\\ntransfers? Does government-provided social insurance efficiently\\naddress market failures? Should we invest more in low-income\\nchildren? If so, at what age? Should they be direct investments\\nor subsidies to parents?\\nA large empirical literature estimates the causal effects of\\nhistorical government policies. These papers frequently conclude\\nwith a brief welfare analysis. The method of that analysis, how-\\never, often differs from paper to paper. When reporting the ef-\\nfects of health insurance expansions, it is common to report cost\\nper life saved (e.g., Currie and Gruber 1996). Studies of tax pol-\\nicy changes often report the implied marginal excess burden or\\nthe marginal cost of funds (e.g., summarized in Saez, Slemrod,\\nand Giertz 2012). Higher education analyses often report the cost\\nper enrollment (e.g., Kane 1994; Dynarski 2000). The early child-\\nhood education literature often reports a social benefit-cost ra-\\ntio (e.g., Heckman et al. 2010). These varying welfare measures\\nmake it difficult to compare policies, especially if one wishes to\\ntake a bird’s-eye view and perform welfare analysis across policy\\ncategories.\\nThis article conducts a comparative welfare analysis of\\n133 historical tax and expenditure policies implemented in the\\nUnited States over the past half-century. We focus on policies in\\nfour domains: social insurance (e.g., health, unemployment, and\\ndisability insurance), education (e.g., preschool, K–12, college, job\\nand vocational training), taxes and cash transfers (e.g., top tax\\nrates, Earned Income Tax Credit (EITC), Aid to Families with\\nDependent Children (AFDC)), and in-kind transfers (e.g., housing\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1211\\nvouchers, food stamps). We draw on existing analyses of the\\nimpacts of these policies to construct the benefit that each policy\\nprovides to its recipients and the policy’s net cost to the govern-\\nment. Benefits are captured by the willingness to pay of policy\\nrecipients. The net cost combines both initial program spending\\nand the long-run effect of the policy on the government’s budget\\n(i.e., fiscal externalities). We then take the ratio of the benefits to\\nnet government costs to generate each policy’s marginal value of\\npublic funds (MVPF).1 Putting these components together allows\\nus to measure each policy’s “bang for the buck.”2\\nThe MVPF is useful because it measures the amount of wel-\\nfare that can be delivered to policy beneficiaries per dollar of gov-\\nernment spending on the policy. Equivalently, the MVPF mea-\\nsures the shadow price of raising revenue from the beneficiaries\\nof the policy by reducing spending on the policy. For point of refer-\\nence, a simple nondistortionary transfer from the government to\\nan individual would have an MVPF of 1. The cost to the govern-\\nment would be exactly equal to the individual beneficiary’s willing-\\nness to pay. The MVPF can differ from this benchmark value of 1 if\\nindividuals value an expenditure at more or less than its resource\\ncost. For instance, if the government provides insurance, willing-\\nness to pay may be greater than the resource costs of provision\\nto individuals if the insurance provides consumption-smoothing\\nbenefits. By contrast, willingness to pay may fall below resource\\ncosts if individuals distort their behavior to receive higher trans-\\nfers.3 The MVPF may also deviate from the benchmark value of 1\\nif the policy induces fiscal externalities. For example, if spending\\na dollar on a government policy caused individuals to work less,\\ngovernment tax revenue might fall slightly and then the net cost\\nof the policy would rise above $1. By contrast, if spending that dol-\\nlar caused them to get more schooling and consequently increased\\n1. See Mayshar (1990), Slemrod and Yitzhaki (1996, 2001), and Kleven and\\nKreiner (2006) for original definitions, and Hendren (2016) for a comparison of the\\nMVPF to alternative measures of welfare.\\n2. In several cases where authors constructed their own MVPFs, we incor-\\nporate those estimates directly. Where applicable, we adjust these estimates to\\nharmonize assumptions (e.g., discount rates). In cases where previous literature\\nhas conducted comprehensive cost-benefit analyses of a policy, we draw on the\\ncomponents of those analyses to reformulate them into their implied MVPF.\\n3. The intuition here comes from the envelope theorem. Willingness to pay\\nfor a government transfer is determined by the “mechanical cost” of that transfer.\\nAdditional costs due to behavioral responses are not valued dollar for dollar.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1212\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\ntheir income, government revenue would rise and the net cost of\\nthe policy would fall below $1. In some cases, positive fiscal exter-\\nnalities may be large enough to fully offset the initial cost of the\\npolicy. In that instance, the policy has an infinite MVPF, and conse-\\nquently, spending on the policy results in a Pareto improvement.4\\nMore generally, comparisons of MVPFs correspond to precise\\nstatements about social welfare using the intuition of Okun’s\\nleaky bucket experiment (Okun 1975). Given two policies, A and\\nB, suppose MVPFA = 2 and MVPFB = 1. Then one prefers more\\nspending on policy A financed by less spending on policy B if and\\nonly if one prefers giving $2 to policy A beneficiaries over giving\\n$1 to policy B beneficiaries. Whether this is desirable ultimately\\ndepends on one’s social preferences for the beneficiaries of\\npolicies A and B. MVPFs measure the feasible trade-offs to the\\ngovernment—in Okun’s metaphor, the “leaks” in the bucket. By\\nmeasuring these shadow prices of raising revenue from different\\ngroups, the MVPF provides a unified method of welfare analysis\\nthat can be applied both across and within diverse policy domains.\\nWe outline the construction of the MVPF for six represen-\\ntative examples in Section III. At a high level, our construction\\nof willingness to pay often relies on intuition provided by the\\nenvelope theorem. Our construction of net government costs\\ninvolves calculating changes in taxes paid and transfers received,\\nalong with savings or additional costs from crowding out of other\\ngovernment spending. In Online Appendices A–F we also provide\\na detailed explanation of how each MVPF in our sample is\\ncalculated. As is common with any welfare analysis, the creation\\nof our MVPFs requires various judgment calls. We conduct an\\nextensive set of robustness analyses, examining our assumptions\\nabout interest rates, tax rates, and forecasting methods.5 In\\n4. To align with terminology in existing literature, we use various terms inter-\\nchangeably to refer to the same phenomenon. Any policy with a positive willing-\\nness to pay and negative net costs we define to have an infinite MVPF. Given the\\nnegative net costs, we also say that these policies “pay for themselves” or “recoup\\ntheir initial costs.” In the taxation literature, this is also known as a Laffer effect.\\nWe often note that spending on policies with infinite MVPFs results in a Pareto\\nimprovement. This is because the expenditure is valued by beneficiaries and has\\nno net cost on the government. This final claim regarding Pareto improvement\\nformally assumes that all beneficiaries have positive willingness to pay, which is\\nnatural in many of our contexts in which the policies expanded the choice sets of\\nall beneficiaries.\\n5. We also provide a Stata do-file for each program that is available on GitHub\\n(https://github.com/Opportunitylab/welfare analysis).\\nThese\\nprograms\\nallow\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1213\\naddition, many MVPF estimates for individual policies contain\\nconsiderable sampling uncertainty. We address this by construct-\\ning category averages that pool across multiple policies and help\\nimprove the precision of our conclusions. We also test and correct\\nfor publication bias using the methods of Andrews and Kasy\\n(2019). Given these potential sources of uncertainty, we also focus\\nour results on broad patterns in the data, rather than conclusions\\nabout individual policies.\\nOur analysis is inevitably constrained by the scope of existing\\nliterature. Not all policies have been studied with the same degree\\nof completeness. For each policy, we incorporate all effects that\\ncan reliably be translated into the MVPF, but an omitted impact\\ncould affect our welfare analysis. We therefore assess the robust-\\nness of our broad patterns to sample restrictions focused on more\\ncomprehensively studied policies. In addition, we discuss how the\\nMVPF of each particular policy may vary with the addition (or\\nremoval) of certain effects.6 For example, we find that our MVPF\\nestimates are most sensitive to changes in the estimated earnings\\nof beneficiaries—specifically dynamic effects within or across\\ngenerations. In the results we discuss below, we focus our primary\\nconclusions on the broad lessons that are robust to variations in\\nthe availability of estimates on underlying causal estimates.\\nI.A. Main Results\\nOur estimates reveal a stark pattern: MVPFs vary sub-\\nstantially based on the age of each policy’s beneficiaries. We\\nfind the highest MVPFs for direct investments in the health\\nand education of low-income children. This includes Medicaid\\nexpansions, childhood education spending, and expenditures on\\ncollege. In many cases, these policies actually pay for themselves\\nin the long run. Children pay back the initial cost as adults\\nthrough additional tax revenue and reduced transfer payments.\\nFor example, we examine four major health insurance expansions\\nto children over the past 50 years. We calculate an average across\\nthose policies and find that for each $1 of initial expenditure they\\nrepaid $1.78 back to the government in the long run. In particular,\\nwe find that three of four policies fully repaid their initial costs.\\nresearchers to easily modify the set of input assumptions into each MVPF\\nbeyond the robustness we readily provide in the article and the Online Appendix.\\n6. We provide an extended discussion of these in the Online Appendix.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1214\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nWe find high MVPFs for policies targeting children through-\\nout childhood. We do find high MVPFs for early childhood\\neducation programs, including an MVPF of roughly 44 for Perry\\nPreschool and 12 for Abecedarian.7 In addition, we find large\\nMVPFs for policies targeting older children, such as historical\\nequalizations in K–12 school financing (studied in Jackson,\\nPersico, and Johnson 2016) and policies increasing college\\nattainment. Our broad patterns contrast with the notion that\\nopportunities for high-return investment in children decline\\nrapidly with age (Heckman 2006).\\nOur results show lower MVPFs for policies targeted to adults.\\nMost of these MVPFs lie between 0.5 and 2. For example, we find\\nMVPFs ranging from 0.40–1.63 for health insurance expansions\\nto adults, 0.65–1.04 for in-kind transfers such as housing vouchers\\nand food stamps, and from negative values to 1.20 for tax credits\\nand cash welfare programs to low-income households. These lower\\nMVPFs reflect the fact that spending on many of these policies\\nreduced labor earnings. This stands in contrast to our finding that\\nmany policies spending on children increased later-life earnings.\\nIt is important to note that these differences in returns by age\\nrepresent general patterns but do not hold uniformly. There are a\\nnumber of exceptions. For child policies, we find large variation in\\nMVPFs across policies, with some estimates relatively close to 1.\\nIn particular, we find lower MVPFs for job training programs and\\nfor college subsidies that do not lead to increases in attainment.\\nWe also find lower MVPFs for transfers to disabled children\\nand their families. This latter case illustrates that policies with\\nlower MVPFs are not necessarily “undesirable”—they can be\\nwelfare enhancing depending on one’s social preferences. Unlike\\nexpenditures with infinite MVPFs, policies with low MVPFs\\ninvolve a budgetary trade-off that should be weighed against\\none’s preference for redistribution.\\nAmong expenditures on adults, we find relatively large\\nMVPFs for reductions in top marginal tax rates, with estimates\\n7. In our baseline specifications that harmonize government revenue compo-\\nnents across policies, we estimate that the government recoups 92% of the up-front\\ncost of Perry Preschool and 78% of the cost of Abecedarian. Because the cost of\\ncrime impacts are often difficult to quantify, they are not included in our base-\\nline analyses (when crime estimates are available, we we incorporate them in\\nalternative specifications discussed in the Online Appendix for each policy). In\\nthis case, if one includes additional estimated effects such as the cost of crime, we\\nestimate that Perry Preschool does pay for itself and Abecedarian pays for 92% of\\nthe up-front cost.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1215\\nfrom 1.16 to infinity. There is, however, substantial sampling\\nuncertainty in these estimates.8 We also find high MVPFs for\\nspending on adults that generates spillover effects on children.\\nFor example, providing vouchers with counseling services to\\nfamilies residing in high-poverty public housing (as part of the\\nMoving to Opportunity Experiment) helped these families move\\nto lower-poverty neighborhoods. This led to large increases in\\nchildren’s earnings in adulthood that generated sufficient tax rev-\\nenue to pay for the program cost. Our results highlight the value\\nof further work to uncover when such spillovers are likely to occur.\\nI.B. Relation to Previous Theories\\nThe ratio of MVPFs measures the extent to which the govern-\\nment can transfer welfare across individuals in society. For this\\nreason, it relates to the literature on optimal government policy\\nand redistribution (e.g., Mirrlees 1971, 1976). After presenting\\nour results, we interpret them in light of this theory. For example,\\nwe tend to find tax cuts to top earners have higher MVPFs than\\ncuts targeted to low-income households, a result consistent with\\nthe behavior of a progressive planner setting the tax rate in a\\nMirrleesian optimal tax model (Mirrlees 1971, 1976). We also\\ncompare the MVPFs of cash transfers to those of in-kind trans-\\nfers, testing the applicability of the Atkinson-Stiglitz theorem\\n(Atkinson and Stiglitz 1976; Hylland and Zeckhauser 1981).\\nI.C. Implications for Future Research\\nWe conclude by providing three lessons for future research.\\nFirst, we show how the MVPF framework allows us to quantify\\nthe value of such research. Because the MVPF is a shadow price,\\none can use a standard decision-theoretic framework to quantify\\nthe value of reducing uncertainty in our MVPF estimates. Just\\nas a consumer would be willing to pay to learn the true value of\\nthe products he or she buys, a welfare-maximizing government\\nshould be willing to pay to reduce uncertainty in the cost of\\nredistribution. Using this approach, we show that a welfare-\\nmaximizing government deciding whether to raise taxes to spend\\nan additional $1 on the Supplemental Nutrition Assistance\\nProgram (SNAP) would be willing to pay $0.24 to make this\\ndecision using a more precise causal estimate of the long-run\\n8. For example, we estimate an infinite MVPF for the 1981 reduction in the\\ntop marginal income tax rate from 70% to 50%. Our confidence interval, however,\\nincludes both 1 and infinity.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1216\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nimpact of SNAP using administrative data (as in Bailey et al.\\n2019) as opposed to survey data (as in Hoynes, Schanzenbach,\\nand Almond 2016). This highlights the value of expanding the\\naccess to, and use of, large administrative linked datasets for the\\nstudy of long-run policy impacts on children.\\nSecond, we show the added insights that come using the\\nMVPF framework as opposed to traditional cost-benefit analy-\\nsis.9 It turns out that our general findings would be very similar\\nin a traditional cost-benefit framework, but the MVPF leads to\\ndifferent conclusions in certain key instances. This is because the\\nMVPF and traditional benefit-cost analysis rely on similar inputs,\\nbut the MVPF is unique in incorporating all fiscal externalities in\\nits denominator.10 For example, when taxes are at the top of the\\nLaffer curve, the social benefit of reducing taxes by $1 is $2,11 but\\nthe MVPF of that policy is infinite because the benefits to the in-\\ndividual are $1 and the net cost of the policy is $0. More generally,\\nour results suggest there is value in calculating the MVPF in other\\nsettings, such as crime policy or tax enforcement, where the causal\\neffects of the policy have clear effects on the government’s budget.\\nLast, we discuss the implications of the MVPF framework\\nfor future empirical designs. In particular, we highlight the im-\\nportance of determining whether willingness to pay is positive or\\nnegative. In this article, we sought to analyze state-level welfare\\nreforms from the 1980s and 1990s. There were 27 large-scale\\nstate-level randomized controlled trials (RCTs) analyzing welfare\\nreform. These studies increased our understanding of the employ-\\nment and revenue impacts of welfare policy. They demonstrated\\nthat these welfare reforms had low net costs. That said, while the\\ntreated participants in these studies often received additional\\nservices such as job search assistance, these policies also cut ben-\\nefits for those who did not comply with program requirements. As\\n9. The edited volume from Weimer (2009) provides a discussion of cost-benefit\\nanalyses from different researchers in a range of different domains. The Washing-\\nton State Institute for Public Policy (WSIPP 2019) conducts ongoing cost-benefit\\nanalyses to assess policies relevant to state legislatures. See also Rea and Burton\\n(2020) for an application of the WSIPP data to comparative welfare analysis.\\n10. Traditional cost-benefit approaches include fiscal externalities in the nu-\\nmerator (see Greenberg, Deitch, and Hamilton 2010).\\n11. The individual is willing to pay $1 for the tax cut and the government\\nreceives a $1 benefit from increased tax revenue from the behavioral response to\\nthe tax. In traditional cost-benefit analysis, increases in government tax revenue\\nare included in the numerator of the expression.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1217\\na result, it is unclear whether willingness to pay for these reforms\\nwas positive or negative. Despite randomizing more than 100,000\\nfamilies into 27 large-scale RCTs, we are unable to reach any reli-\\nable estimates of the MVPFs of these policies. The evaluations of\\nwelfare reform may have led to more valuable information if the\\nRCT designs had been created with a social welfare framework\\nin mind.\\nI.D. Relationship to Existing Literature\\nIn constructing our MVPFs and presenting evidence for\\nhigh returns to investment in low-income children, we build\\non a substantial line of existing research making the argument\\nfor investment in children.12 Our work is also related to recent\\nresearch on the long-run effect of safety net protections for\\nchildren reviewed by Hoynes and Schanzenbach (2018). In light\\nof the evidence, they conclude that “reallocation of investments\\nover the life course to earlier periods can be efficiency-enhancing,”\\nwhich aligns with our conclusions.\\nThere are also analyses—many of which we draw on in\\nthis article—in which researchers have previously argued that\\nsome government expenditures largely pay for themselves.\\nThis argument is particularly prominent in discussion of early\\neducation (e.g., Heckman et al. 2010; Garc´\\nıa et al. 2017) and child\\nhealth care expenditures (e.g., Brown, Kowalski, and Lurie 2015;\\nWherry et al. 2018).13 The argument also appears in the tax\\nliterature, where some have argued that reducing top marginal\\ntax rates produces a “Laffer effect,” raising total revenue.14 Our\\nanalysis builds on that work by evaluating policies at scale and\\nsearching for the presence of high-return policies across a wide\\nrange of policy domains. We find the most robust evidence for\\nLaffer effects for policies investing directly in children.\\n12. For example, foreshadowing many of our conclusions, Currie (1994) writes,\\n“Although the evidence is incomplete, it suggests that in-kind programs have\\nstronger effects on children than cash transfers, and that programs that target\\nspecific benefits directly to children have the largest positive effects.”\\n13. Outside the scope of this article, some suggest certain macroeconomic\\npolicies can pay for themselves, such as fiscal expansions during deep recessions\\n(DeLong et al. 2012). More generally, we omit many potentially relevant categories\\nof policies, such as macroeconomic stabilization, infrastructure investment, and\\nenvironmental policies.\\n14. In this sense, testing whether the MVPF of a policy change is infinite is a\\ngeneralization of Werning (2007)’s proposed test for identifying local Laffer effects\\nin the income tax schedule.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1218\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nI.E. Roadmap\\nThe rest of this article proceeds as follows. Section II\\npresents the general social welfare framework that motivates the\\nconstruction of the MVPF. Section III discusses the sample and\\npresents six example constructions of the MVPF. Section IV\\ndiscusses our main results and the distinction between MVPFs\\nof policies targeting children versus adults. Section V places the\\nMVPF estimates in the context of existing theories of optimal\\ngovernment policy. Section VI presents lessons for future work.\\nSection VII concludes. As noted already, Online Appendices A–F\\nprovide step-by-step details for constructing each MVPF, and all\\nStata do-files for the construction of each MVPF are available on\\nGitHub.\\nII. MVPF FRAMEWORK\\nThis section presents a general framework to measure the\\nwelfare impact of changes in government policies. The frame-\\nwork illustrates how the marginal value of public funds provides\\nnatural guidance on the social welfare impact of economic policies.\\nConsider a government seeking to measure the welfare im-\\npact of a government policy change under consideration. We define\\nsocial welfare, W, by the weighted sum of individual utilities,\\nW =\\n\\u0002\\ni\\nψiUi,\\nwhere Ui is individual i’s utility function and ψi is their social\\nwelfare weight. The latter measures how much a 1-unit increase\\nin utility corresponds to an impact on social welfare, W.15 The\\nutility function, Ui, measures both current and future well-being\\nof the individual. For example, if utility were additive over time,\\none could nest uncertainty about future outcomes within this\\nframework, letting Ui = E[\\u0003\\nt ⩾0βtuit] where uit is the individual’s\\nutility t periods from today.\\nBecause the utility function is allowed to vary arbitrarily\\nacross individuals, it will be helpful to normalize units across\\nindividuals. To that aim, let λi denote individual i’s marginal\\nutility of income at the time the policy is under consideration.\\n15. For now, we do not place any assumption on these weights, and therefore\\nthey can result from any particular social welfare function. We also assume the\\nweights do not change in response to the policy, but this is without loss of generality\\nbecause we focus on small policy changes below.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1219\\nThis is equal to the effect on individual utility of providing $1\\nto that individual. Let ηi = ψiλi denote the individual’s social\\nmarginal utility of income at the time of the policy. The value of\\nηi measures the impact on social welfare, W, of an additional $1\\nplaced in individual i’s budget today.\\nThe government is considering a set of policy changes indexed\\nby j = 1, ..., J that change the economic environment (e.g., prices,\\npublic goods) by a small amount. We parameterize the up-front\\ninitial spending on policy j by dpj (which can either be an increase\\nor decrease). The net impact on social welfare of the policy is\\n(1)\\ndW\\ndpj\\n=\\n\\u0002\\ni\\nψi\\ndUi\\ndpj\\n=\\n\\u0002\\ni\\nηiWTP j\\ni = ¯\\nη j\\n\\u0002\\ni\\nWTP j\\ni ,\\nwhere \\u0003\\ni WTP j\\ni is the sum of individuals’ willingness to pay for\\npolicy j out of their own income, WTP j\\ni = dUi\\ndpj\\n1\\nλi , and ¯\\nη j is the\\naverage social marginal utility of the beneficiaries of the policy,\\n¯\\nη j =\\n\\u0002\\ni\\nηi\\nWTP j\\ni\\n\\u0003\\ni WTP j\\ni\\nwith weights given by the economic incidence of the policy,\\nWTP j\\ni\\n\\u0003\\ni WTP j\\ni .\\nThe values ¯\\nη j measure how much social welfare increases if one\\nwere to provide an average of $1 to the beneficiaries of policy\\nj. Each individual is willing to pay WTP j\\ni for the expansion by\\ndpj of policy j.16 Therefore, multiplying ¯\\nη j by \\u0003\\ni WTP j\\ni measures\\nthe impact on social welfare of an expansion of the policy by\\ndpj. This means that the welfare effect depends on the effect of\\nproviding $1 to a policy’s beneficiaries, ¯\\nη j, and the beneficiaries’\\nwillingnesses to pay for the policy relative to cash, \\u0003\\ni WTP j\\ni .\\nIn accounting for costs, we let R denote the present discounted\\nvalue of the government budget, and let Gj = dR\\ndpj denote the net\\nimpact of the policy on the government budget.17 This net cost is\\n16. In the derivation of the MVPF, we remain fully general about each individ-\\nual’s utility function. We abstract from any behavioral biases in the utility function\\nthat might cause willingness to pay to be incongruent with choices that maximize\\nwell-being. Moreover, in practice, our approaches to inferring willingness to pay\\noften require assumptions of rationality in individual utility that do not account\\nfor the potential presence of behavioral biases.\\n17. In practice, the dpj variations that are identified in an empiricist’s re-\\ngressions will not, in general, correspond to budget-neutral policies. Traditional\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1220\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\ninclusive both of the initial cost of the program and all other effects\\nof behavioral responses on the government budget. For example, if\\nspending $1 on preschool increases wages in the future, Gj should\\nincorporate the effect of those increases in future tax receipts.\\nCrucially, both the willingness to pay measures, WTP j\\ni , and the\\nnet cost, Gj, should include effects on both parents and children.\\nPolicies that directly affect children should include willingness\\nto pay by parents and the impacts of their behavioral responses\\non the cost of the policy. Conversely, policies that directly affect\\nparents should include any spillovers onto children.18\\nThe MVPF of policy j is given by the aggregate willingness\\nto pay, WTP j = \\u0003\\ni WTP j\\ni , for the policy divided by the net cost to\\nthe government, Gj:\\n(2)\\nMVPF j =\\n\\u0003\\ni WTP j\\ni\\nGj\\n=\\nWTP j\\nNet Cost.\\nThe MVPF is previously defined in Mayshar (1990), where it is\\nreferred to as the marginal excess burden (MEB); in Slemrod and\\nYitzhaki (1996), where it is referred to as both the marginal cost\\nof funds and the marginal benefit of projects, depending on the\\npolicy in question; and in Kleven and Kreiner (2006), where it is\\nreferred to as the marginal cost of funds (MCPF). However, the\\nMVPF formally differs from both the traditional definition of the\\nmarginal excess burden in Auerbach (1985), Auerbach and Hines\\n(2002), and the marginal cost of funds in Stiglitz and Dasgupta\\n(1971), Atkinson and Stern (1974). Because of this, Hendren\\n(2016) defines this quantity as the MVPF to contrast it with the\\nMEB and MCPF.\\napproaches would attempt to account for government spending by modifying\\nthe observed policy into a different policy that raised revenues via lump-sum\\ntaxation. This would then require the researcher to observe not the causal effect of\\nthe policy, but the “compensated effect” of the policy to identify the welfare effect.\\nIn contrast, our approach hypothetically closes the budget constraint by comparing\\ntwo MVPFs: one that involves an increase in spending and another that involves\\na reduction in spending or increase in revenue. Hence, welfare analysis can be\\ndone with two sets of causal effects (one for the two policies under consideration)\\nas opposed to attempting to measure the compensated effect of a policy.\\n18. We sum the benefits accruing to both parents and children, but we do not\\ninclude any willingness to pay that arises because of parental altruism toward\\ntheir children (or children’s altruism toward their parents). This means that a\\nchild’s willingness to pay for a policy is only counted once. Including willingness\\nto pay from parental altruism would only reinforce our central results. Similarly,\\nwe do not incorporate individual willingness to pay for redistribution to others.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1221\\nCombining equations (1) and (2), the effect on social welfare\\nper dollar of government expenditure on policy j is\\ndWt\\ndpj\\ndR\\ndpj\\n= ¯\\nη jMVPF j.\\nGiven the MVPF for any two policy changes, one can construct hy-\\npothetical budget-neutral policy changes. For example, consider\\nincreasing spending on policy 1 by a net amount G1, financed by\\nreducing spending (or increasing revenue) from policy 2 by the\\nsame amount. Pursuing this combined policy, dp, increases social\\nwelfare if and only if\\n(3)\\n¯\\nη1MVPF1 > ¯\\nη2MVPF2.\\nWelfare increases if and only if the welfare gains from increasing\\nspending on policy 1, ¯\\nη1MVPF1, exceed the welfare loss from\\nreducing spending on policy 2, ¯\\nη2MVPF2. The MVPFs of the\\ntwo policies characterize the cost of moving welfare between the\\ntwo groups of beneficiaries. One prefers the policy if and only if\\n¯\\nη1\\n¯\\nη2 > MVPF2\\nMVPF1 . If MVPF1 = 1 and MVPF2 = 2, then an individual\\nprefers spending on policy 1 financed by policy 2 if and only\\nif providing $1 to beneficiaries of policy 1 is valued more than\\nproviding $2 to beneficiaries of policy 2.\\nAs this example illustrates, welfare statements that com-\\npare policies generally require comparisons of their MVPFs. The\\nMVPFs allows the researcher to form hypothetical budget-neutral\\npolicies and assess their welfare implications using equation (3).\\nTo reduce the role of social preferences in driving conclusions, one\\ncan compare policies with the same beneficiary group. In this case,\\none would expect that ¯\\nη1 ≈¯\\nη2 so that comparisons of the MVPFs\\ncorrespond to statements about social welfare. For example,\\nHendren (2017a) suggests comparing the MVPF of a particular\\npolicy to the MVPF of a tax cut with similar distributional inci-\\ndence. More generally, one can compare different redistributive\\npolicies, such as food stamps and housing vouchers, among each\\nother to evaluate the most effective method of redistribution.\\nIn some cases, one does not need to compare an MVPF to\\nanother policy to reach a welfare conclusion. This occurs when\\nthe MVPF is infinite. Mathematically, this happens when a\\npolicy has positive willingness to pay by its beneficiaries and the\\nbehavioral response to the policy generates fiscal externalities\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1222\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nthat are sufficient to cover the cost of the program, Gj < 0. The\\ntextbook example of such a case is lowering taxes when they are\\nbeyond the peak of the Laffer curve. In this case, lowering taxes\\nincreases government revenue, and so these policies represent a\\nPareto improvement for any positive welfare weights assigned to\\nthe recipients.19 More generally, the MVPF framework facilitates\\na search for other cases where policies have positive willingness\\nto pay and negative net costs, such as investment in kids.\\nThe definition of the MVPF is theoretically motivated using\\nsmall (marginal) changes in government expenditures. Although\\nsome empirical variation we use has marginal effects on individ-\\nuals’ budget constraints, one can also continue to construct the\\nMVPF as the ratio of willingness to pay to net government cost\\nfor nonmarginal policy changes. This approach uses the actual\\nempirical variation in existing literature to estimate the return\\non the observed nonmarginal expenditure. Future work could\\nexplore how the MVPF for a given policy change varies within a\\nprogram’s size of spending. This would facilitate improved welfare\\ncomparison for policies that were evaluated at different scales.20\\nII.A. Comparison to Social Cost-Benefit Analysis\\nThe MVPF approach builds on a large literature on social\\ncost-benefit analysis (see the edited volume Weimer and Vining\\n2009 and Boardman et al. 2017, and the cost-benefit estimates\\nprovided by WSIPP 2019). The MVPF uses many of the same un-\\nderlying estimates used to create benefit-cost ratios, but combines\\nthem in a different way. A comparison with cost-benefit analysis\\nfrom Heckman et al. (2010) helps illustrate the importance of\\n19. In practice an expenditure policy may have been combined with a sep-\\narate tax policy to raise revenue at the time the policy is implemented. In this\\ncase, the combined expenditure and tax policy would not deliver a Pareto improve-\\nment, as some current taxpayers would be made worse off. However, the infinite\\nMVPF corresponds to a case where the government need not raise revenue to im-\\nplement a policy that does not cost money in the long-run. The government could\\nhave borrowed against the future returns on the policy and generated a Pareto\\nimprovement.\\n20. Consider the case where policy 1 was a $1M government expenditure and\\npolicy 2 was a $2M government expenditure. Comparing policy 1 and policy 2 would\\nrequire the MVPF for a version of Policy 1 that is scaled up to cost $2M. This same\\nlogic would also apply if considering a large-scale expenditure on a policy that\\nhad previously been analyzed with a narrower RCT—one would have to make the\\nadditional assumption that the average treatment effect of this expanded policy is\\ngiven by the effect identified in the RCT.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1223\\nthese differences. Heckman et al. (2010) compare the net social\\nbenefits of the policy, inclusive of benefits that accrue back to\\nthe government, against the up-front budgetary spending on the\\npolicy, Cj. They use the following formula:\\n(4)\\nBCRj = Social Benefits\\nSocial Costs\\n= WTP j + FEj\\n(1 + φ) C j\\n,\\nwhere FEj = Gj −Cj are the benefits accruing to the government\\nbudget from the behavioral responses to the policy. The initial\\nprogram outlays in the denominator are often multiplied by 1 +\\nφ, where φ is the marginal deadweight loss of raising government\\nrevenue. This is thought to translate the up-front costs into social\\ncosts by accounting for the welfare impact of an implicit tax\\npolicy that raises the needed funds. Often, φ is taken to be 0.3 or\\n0.5 (Heckman et al. 2010). Policies are then deemed to pass the\\ncost-benefit test if the BCR exceeds 1.\\nIn contrast to the BCR, the MVPF is given by MVPF j =\\nWTP j\\nC j+FEj . It differs in two primary ways. First, the impact of be-\\nhavioral responses on the government budget is counted in the\\ndenominator, not the numerator. For example, consider a tax cut\\nof $1 for which the behavioral response increases tax revenue by\\n$1. In this case, the policy perfectly pays for itself, and so the\\nMVPF is infinite. Expenditures on the policy represent a Pareto\\nimprovement. In a BCR framework, however, that $1 in increased\\ntax revenue is considered social benefit and counted in the numer-\\nator. That leaves a BCR estimate of (\\n2\\n1 + φ ). This illustrates why\\nthe BCR may be a particularly misleading guide to optimal policy\\nwhen policies have strong impacts on the government budget. We\\nfound a policy with a BCR of (\\n2\\n1 + φ ) that was a Pareto improvement,\\nbut we could find a different policy with a BCR above 2 that does\\nnot deliver a Pareto improvement. For example, if we compare\\nthis hypothetical tax cut to government-provided insurance with\\nwillingness to pay of $2 for each $1 of insurance, the traditional\\ncost-benefit framework cannot distinguish between these policies.\\nSecond, the MVPF approach does not require the government\\nto close the budget constraint through an increase in taxation.\\nTherefore, one does not adjust for the “deadweight cost of tax-\\nation” based on this particular assumed method of government\\nfinance. Rather, the MVPF directly measures the amount of\\nwelfare delivered to beneficiaries per dollar of government\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1224\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nexpenditure. One closes the budget constraint by comparing the\\nMVPF of a given policy to the MVPF of other policies. This allows\\nthe researcher to think through the library of feasible levers\\navailable to the government. In contrast to the cost-benefit frame-\\nwork, this approach reinforces the idea that incidence matters: a\\npolicy that provides benefits to the poor cannot be readily\\ncompared to the raising of revenue on the rich without thinking\\nabout Okun’s bucket and the social welfare weights placed on the\\nbeneficiaries (i.e., the values of ¯\\nη j for the policies).\\nDespite our advocacy for the value of the MVPF over a tradi-\\ntional cost-benefit analysis, it is perhaps reassuring to note that,\\nin most cases, these two approaches generate similar conclusions.\\nSo although we argue that the MVPF is more appropriate for\\nmeasuring welfare, and consequently more informative in cases\\nwhere these two welfare measures diverge, the broad pattern of\\nour results remain the same under either framework.\\nIII. CALCULATING MVPFS: EXAMPLES\\nWe estimate the MVPF for 133 policies spanning social\\ninsurance (e.g., health, unemployment, and disability insurance),\\neducation (e.g., preschool, K–12, college, job and vocational train-\\ning), taxes and cash transfers (e.g., top tax rates, EITC, AFDC),\\nand in-kind transfers (e.g., housing vouchers, food stamps). Our\\nfocus here is on policies, rather than papers. In many cases\\nwe combine estimates from multiple different papers, putting\\ntogether the puzzle pieces to build the full picture.21\\nWe form a sample of policies in each domain by drawing on\\nsurvey and summary articles from each field. We supplement this\\ninitial set of estimates with recent work in each area not captured\\nin the survey or summary articles. We restrict our attention to\\npolicies in which there is an experimental or quasi-experimental\\nidentification strategy used to estimate the policy’s impact.22\\nFormally, such papers identify causal effects using variations dpj\\nin the economic environment. We form our baseline sample with\\n21. If multiple papers analyze the same causal effect, we generally focus on\\nthe most recent published estimates unless otherwise noted. We provide a detailed\\ndiscussion of the alternative specifications in the Online Appendix.\\n22. We exclude purely cross-sectional identification using controls for ob-\\nservables in our baseline sample. Within the set of experimental and quasi-\\nexperimental studies, we do not impose our own filter on the quality or validity of\\nthese empirical designs.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1225\\npolicies where one observes effects of the policy that are sufficient\\nto form a reasonably comprehensive view of both the WTP and\\nnet cost of the policy. We discuss in Online Appendices A–F the\\nstandard for policy inclusion in our categories and the set of\\ncausal effects used in each case. Because this process involves\\njudgment calls, we also assess robustness of our conclusions to\\nan expanded sample (e.g., that expands the set of identification\\nand forecasting methods) and a more restricted sample (e.g., that\\nrequires direct observation of causal effects on income).\\nTable I lists the set of policies studied, along with the\\nempirical papers used to form each policy’s MVPF. Column (9)\\ndenotes the set of papers used to construct the MVPF. In many\\ncases, we draw from multiple papers to form a single MVPF. For\\nexample, some publications might estimate the impact of the\\npolicy on adults, while other papers focus on longer-run effects on\\nchildren.\\nIn this section, we illustrate the construction of these esti-\\nmates using six examples spanning the domains we consider. We\\nattempt here to provide a diverse set of examples to demonstrate\\nthe range of approaches used to create our estimates. Online\\nAppendices A–F provides a detailed step-by-step discussion of the\\nconstruction of each MVPF. In Section IV.C, we assess robustness\\nof our primary conclusions to alternative assumptions (e.g.,\\ndifferent interest rates and tax rate imputations) and alternative\\nsamples.\\nIII.A. Admission to Florida International University\\nWe begin by constructing the MVPF of admitting an addi-\\ntional student into Florida International University (FIU). This\\nexample illustrates the construction of the MVPF for a policy\\ntargeting youth with effects on later-life earnings. We use similar\\nmethods for other child policies.\\nWe draw on the work of Zimmerman (2014). He uses an RD\\ndesign at the school’s academic performance cutoff for applicants\\nto measure the effect of FIU admission on state university system\\nenrollment and medium-term earnings outcomes. We translate\\nhis estimates into an MVPF, incorporating the net cost of the\\npolicy and the beneficiaries’ willingness to pay. Throughout,\\nwe construct confidence intervals for our estimates using a\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1226\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I\\nDETAILS OF ALL PROGRAMS STUDIED\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nPanel A: Education and job training\\nChild education\\nCarolina Abecedarian\\nAbecedarian\\n1975\\n3\\nx\\nx\\nx\\nBarnett and Masse (2007)\\nStudy\\nCampbell et al. (2012)\\nHelburn (1995)\\nMasse and Barnett (2002)\\nMasse (2003)\\nChicago Child-Parent\\nCPC Extended\\n1985\\n6\\nx\\nReynolds et al. (2002)\\nCenters, Extended\\nReynolds et al. (2011)\\nProgram\\nChicago Child-Parent\\nCPC\\n1983\\n4\\nx\\nReynolds et al. (2002)\\nCenters, Preschool\\nPreschool\\nReynolds et al. (2011)\\nProgram\\nChicago Child-Parent\\nCPC\\n1986\\n8\\nx\\nReynolds et al. (2002)\\nCenters, School\\nSchool\\nReynolds et al. (2011)\\nAge Program\\n(Table 1 is continued at the end of Section VII, before the Appendix.)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1227\\nsemiparametric bootstrap procedure discussed in detail in Online\\nAppendix H.23\\n1. Costs.\\nFigure I, Panel A shows how we calculate the net\\ncost of FIU admission. We start with initial costs of $11,403, which\\nrepresents the state university system’s educational expenditures\\non each marginal admit to FIU.24 Students pay some fraction\\nof those educational expenses, so we subtract $3,184 to account\\nfor private student contributions. Next we account for the fact\\nthat some new admits would have attended a state community\\ncollege if they had not enrolled in FIU. We subtract $5,601,\\nZimmerman’s estimate of the amount the government would\\nhave paid to support their education at those community colleges.\\nTaken together, that leaves us with an up-front government cost\\nof $2,617 per admitted student.\\nThe remaining cost considerations all stem from earnings\\nchanges caused by FIU admission.25 Zimmerman (2014) calcu-\\nlates that in the first seven years after admission, earnings fall\\nby $10,942.26 We use estimates from the Congressional Budget\\nOffice to estimate that the tax and transfer rate on these earnings\\nis 18.6%. This suggests the earnings change reduces government\\nrevenue by $2,035.27 Next, Zimmerman (2014) estimates that FIU\\n23. In particular, we conservatively account for correlations across estimates\\nin a given policy, and we develop a method to adjust for the uncertainty in the\\ndenominator (with many thanks to conversations with Isaiah Andrews). We pro-\\nvide the intuition for the approach and Monte Carlo simulations with appropriate\\ncoverage. In fact, the coverage is sometimes overly conservative, especially when\\ncosts approach 0.\\n24. Zimmerman (2014) calculates costs and student contributions using the\\ndata on educational expenditures from the Delta Cost Project (American Institutes\\nfor Research 2017). We adopt this approach for other college policies analyzed in\\nour sample. Online Appendix B explains the details of our approach.\\n25. Zimmerman (2014) does not include any information on attendance of\\nfederally supported graduate schools among marginal FIU enrollees. If that infor-\\nmation were available, it could be incorporated as an additional fiscal cost.\\n26. All earnings changes are discounted back to the time of the initial expen-\\nditure using a 3% discount rate. We toggle these discount rates in our robustness\\ndiscussion in Section IV.C. We also use CPI-U-RS when we need to deflate from\\nnominal dollar values to real ones.\\n27. To be conservative, we exclude payroll taxes because individuals may ben-\\nefit from a portion of these contributions. More detail on our calculations can be\\nfound in Online Appendix G. The tax and transfer rate includes federal and state\\nincome taxes along with food stamps, but excludes housing vouchers and other\\nwelfare programs. We use the income-specific rate from the 2016 CBO estimates,\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1228\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nFIGURE I\\nWTP and Cost Components for Admission to Florida International University\\nThis figure illustrates the cost and willingness to pay components for admission\\nto Florida International University as studied in Zimmerman (2014). Panel\\nA breaks the total cost down into its various components, including increased\\nstudent payments on tuition, reduced government spending on community\\ncolleges, and the changes in tax revenue from earnings. Panel B shows the\\ncumulative discounted cost of the policy over the lifetime of the beneficiary.\\nThe solid line represents cumulative costs for ages up until 33, the oldest age\\nat which incomes are observed in Zimmerman (2014). The dotted lines provide\\nthe 95% bootstrap (pointwise) confidence intervals with adjustments discussed\\nin Online Appendix H. The dashed line shows total costs inclusive of projected\\ncosts at subsequent ages. The projection method is detailed in Section III and in\\nOnline Appendix I. Panel C reports the components of our WTP calculations. The\\npoint estimate measures WTP as the change in incomes after taxes and expenses\\non tuition. All numbers are in 2005 dollars deflated using the CPI-U-RS and\\ndiscounted using a 3% real interest rate.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1229\\nadmission causes earnings to rise by $36,369 in years 8–14. Once\\nagain, we apply a tax and transfer rate and determine that the\\ngovernment’s revenue rises by $7,274. At this point our net costs\\nare −$2,622, as shown in Figure I, Panel B. This suggests the\\nexpenditure has paid for itself within 14 years of the initial outlay.\\nFinally, Zimmerman’s earnings data extend 14 years, but we\\ncan extrapolate from the observed effects to estimate earnings\\nchanges over the full life cycle. Online Appendix I describes this\\nprocedure in detail, and Appendix Figure I provides a graphi-\\ncal illustration of the approach. We use ACS data to estimate\\nlife cycle earnings trajectories and then map the control group in\\nZimmerman (2014) onto those trajectories. In particular, we ob-\\nserve an average earnings for the control group of $28,964, which\\nwe estimate to be 113% of mean earnings for this cohort in the\\nACS. In contrast, the treated group earns $6,372 more during\\nthese ages, or 22% more than the control group. We assume that\\nthe control group earnings remain constant as a fraction of av-\\nerage ACS earnings throughout the life cycle. We also assume\\nthat the percentage earnings increase for the treatment group\\nalso remains constant throughout the life cycle. These assump-\\ntions mean that we assume the trajectories for the treatment and\\ncontrol groups differ by a constant percentage throughout the life\\ncycle.28 This yields an estimated discounted earnings increase of\\n$117,330 through age 65. We subsequently calculate that the as-\\nsociated fiscal externality reduces government costs by $21,823.\\nWhen combined with our previous cost components, we find that\\neach marginal FIU admission has a net cost of −$24,445. The\\nexpenditure pays for itself.\\nand we apply this rate uniformly across years for simplicity. With more reliable\\nhistorical information on marginal tax and transfer rates across the income distri-\\nbution, one could perform the analysis separately by year. We are not aware of any\\ncomprehensive historical source on the distribution of those rates. For this reason,\\nwe take the simpler approach of using a consistent 2016 tax and transfer rate\\nand then assessing the robustness of all our results to alternative rate assump-\\ntions. We present robustness to alternative tax and transfer rate assumptions in\\nSection IV.C.\\n28. Although this is a strong assumption, we show in the robustness analysis\\nthat our results are actually not very sensitive to the method we use to construct\\nthese forecasts. For example, we conduct a conservative forecast that assumes\\nzero income growth over the life cycle. This yields similar results (see Figure VI,\\nPanel B).\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1230\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\n2. Willingness to Pay.\\nHaving established that the initial\\ncosts of increasing admission at FIU leads to long-run net savings\\nto the government, the policy has an infinite MVPF as long as\\nWTP > 0. That said, constructing a measure of willingness to pay\\nremains useful in making our confidence intervals and evaluating\\nalternate specifications. The components of our baseline estimate\\nof WTP are illustrated in Figure I, Panel C.\\nThroughout, our approaches to estimating WTP rely heavily\\non the logic of the envelope theorem and revealed preference. For\\nthe baseline estimate, we assume that increases in income among\\nthe college educated stem from returns to human capital, not from\\nhigher levels of effort.29 In this case, the envelope theorem implies\\nthat we can form an estimate of WTP using the policy’s impact\\non net income after taxes and other expenses (and ignore the\\ncomposition of individuals’ spending).30 We begin by noting that\\nthose who are admitted to FIU have an increase in private costs\\nassociated with additional tuition and fee payments at the four-\\nyear school. This leads to a negative WTP component of $2,851.\\nNext, the earnings fall in the first seven years after admission\\nleads to a further negative WTP of $8,907. The earnings gains in\\nyears 8–14 yield a positive WTP of $29,095. Projecting through\\nthe rest of the life cycle yields an additional WTP of $95,507.\\nCombined, this yields a total willingness to pay of $112,844.31\\n29. We refrain from incorporating general equilibrium effects in our willing-\\nness to pay due to a lack of evidence on this point. If higher educational attainment\\nproduced positive spillovers on others, aggregate willingness to pay would rise. If\\nthe college earnings premium were driven by signaling effects, then we would\\nexpect other individuals to have a negative willingness to pay.\\n30. To see this, consider the decision problem of choosing a vector of consump-\\ntion goods x to maximize u(x; p) subject to q · x ⩽y(p) where q is the price of goods\\nand y(p) is after-tax income. In principle, the government’s policy choices, p, can\\ndirectly affect utility and the budget constraint. For the baseline WTP measure\\nfor FIU, we assume admission to FIU only affects y(p) so that ∂u\\n∂p = 0, which means\\nwillingness to pay is given by dy\\ndp (the impact on the vector x can be ignored by\\nthe envelope theorem). However, if effects on income of admission to FIU is the\\nresult of higher levels of effort, that would require an adjustment for the disutility\\nof labor and our baseline approach would overstate WTP; conversely, if individ-\\nuals derive additional utility from attending college that is not captured in their\\nearnings, the baseline approach would understate willingness to pay.\\n31. We also form a “conservative WTP” of $1 that relies on the logic of revealed\\npreference that individuals are willing to pay a nonnegative amount for admission\\ninto FIU.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1231\\nIII.B. Medicaid Expansion to Pregnant Women and Infants\\nNow, we consider a Medicaid expansion to pregnant women\\nand children in the United States that occurred across states\\nbetween 1979–1992. This example illustrates a case where we\\nconstruct the MVPF using examples from several papers using the\\nsame identification strategy but focusing on different outcomes.\\nWe construct our MVPF using several different analyses of\\nthese reforms, each of which use the differential timing of the re-\\nforms across states to measure their impacts.32 Currie and Gruber\\n(1996) document a significant increase in health insurance cover-\\nage for pregnant women, along with a corresponding reduction in\\ninfant mortality and low birth weight. Cutler and Gruber (1996)\\nfind significant crowd-out of private insurance policies. Dave\\net al. (2015) find reductions in labor supply of eligible women.\\nMiller and Wherry (2019) find positive effects on children’s future\\nearnings and health for those whose parents obtained Medicaid\\neligibility. We translate these estimates into their implied MVPF,\\nbeginning with costs and then turning to willingness to pay.\\n1. Costs.\\nThe bar chart in Figure II, Panel A illustrates\\nthe translation of estimates from the literature into their\\nimplied costs to the government. Currie and Gruber (1996)\\nestimate that the cost of insuring an additional pregnant woman\\nthrough the Medicaid expansion was $3,473.33 In addition to\\nthe direct Medicaid costs, Dave et al. (2015) estimate that\\nMedicaid eligibility leads to a 21.9% reduction in female labor\\nforce participation, which corresponds to an earnings impact\\nof roughly $2,834. We estimate that these individuals face a\\ntax-and-transfer rate of 18.9% from the CBO using our procedure\\ndiscussed in Online Appendix G. This means that the earnings\\neffect implies an additional cost to the government of $564 per\\neligible child. As a result, a short-run analysis of the policy would\\nconclude that the causal effects of the policy lead to an increase\\nin costs.\\n32. Our analysis also explores other policies that expanded Medicaid to chil-\\ndren, such as the national expansion of Medicaid to those born after September 30,\\n1983. These policy changes correspond to separate MVPF constructions because\\nthey arise from different sources of policy variation.\\n33. For consistency across papers analyzing the reform, we deflate all numbers\\nto 2012 US$ using the CPI-U-RS; as a result, they differ slightly from reported\\nfigures in each paper.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1232\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nFIGURE II\\nWTP and Cost Components for Medicaid Expansions to Pregnant Women and\\nInfants\\nThis figure illustrates the cost to the government of providing Medicaid to\\npregnant women and infants. The evidence comes from state Medicaid expansions\\nbetween 1979 and 1992. Panel A breaks the total cost down into its various\\ncomponents. The savings on uncompensated care come from Currie and Gruber\\n(1996), who estimate rates of uninsurance, and Gold and Kenney (1985) who\\nestimate the quantity of uncompensated care for the uninsured. The savings\\non future health costs come from Miller and Wherry (2019). The increase in\\ngovernment revenue combines an effective tax rate with the estimates of earnings\\ngains from Miller and Wherry (2019). Panel B reports the components of our WTP\\ncalculations. The point estimate includes the willingness to pay for reductions\\nin infant mortality, combined with the change in income for children over their\\nlife cycle after taxes and educational expenses. All numbers are in 2011 dollars\\ndeflated using the CPI-U-RS and discounted using a 3% real interest rate.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1233\\nTurning to the effects on children, Miller and Wherry (2019)\\nestimate that a 1 percentage point increase in parental eligibility\\nleads to a reduction in future hospitalizations of 0.237% when\\nchildren are 19 to 32 years old. With a 3% discount rate, this im-\\nplies government savings on Medicaid and uncompensated care\\nof $868 over the 14-year period from ages 19 to 32.34 Miller and\\nWherry (2019) also find a 3.5% increase in college attendance and\\nan 11.6% increase in earnings for children made eligible. On the\\none hand, to the extent to which the government subsidizes col-\\nlege expenses, increased enrollment raises government costs. We\\nestimate that effect to be $371. On the other hand, the increase in\\nearnings when children are 23–36 years old leads to an increase in\\ngovernment revenue of $3,909. By the time children are 36 years\\nold, the estimates suggest that the policy has paid for itself.\\nAs with the example in Section III.A, we forecast these\\nearnings gains to age 65 by assuming that the percentage impact\\non earnings remains constant throughout the life cycle. This\\nsuggests that the government recoups an additional $6,114 in\\ntax revenue over this period, for a total of $10,024. The up-front\\ncost of $3,473 led to a long-run net government surplus of $7,014\\n(95% CI of [1,178, 12,971]).\\nBefore moving on to discussing the details of willingness to\\npay, it is worth noting that the MVPF of this expenditure has al-\\nready been determined. For a policy to have an infinite MVPF, net\\ncosts must be negative and willingness to pay must be any positive\\nvalue. The policy evaluated here expanded health care opportu-\\nnities to parents and children, so it is safe to assume willingness\\nto pay is positive. In fact, if the policy did not make anyone worse\\noff, then these expenditures resulted in a Pareto improvement.\\n2. WTP.\\nWhile the baseline MVPF estimate is infinite, we\\ncalculate willingness to pay for use in constructing confidence\\nintervals and evaluating alternate specifications where costs are\\npositive. We briefly summarize this construction, which consists\\nof three components. (Step-by-step details of this calculation can\\nbe found in Online Appendix D.)\\nFirst, Cutler and Gruber (1996) document that half of the\\nincrease in Medicaid actually crowded out private coverage. As-\\nsuming that the public and private costs of insurance were roughly\\n34. We forecast to age 65 by assuming a constant dollar saving and discounting\\nby 3%, which implies $530 of total savings, as shown in Figure II.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1234\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nsimilar, this finding implies that beneficiaries no longer had to pay\\nroughly $1,737 in health insurance costs. This means that WTP\\nis at least $1,737. Second, Currie and Gruber (1996) estimate a\\ncausal effect of the Medicaid expansion on infant mortality. We\\nassume parents have a willingness to pay out of their own income\\nof $1M to avoid an infant death (and assess robustness to alterna-\\ntive specifications).35 Third, we consider the WTP by the children\\nfor improved labor market prospects in adulthood. To do so, we\\nassume that the increase in earnings documented by Miller and\\nWherry (2019) reflects an expansion of labor market opportunities\\nand not an increase in costly labor effort. This means that the chil-\\ndren should be willing to pay the increase in their net income after\\nprivate expenses that results from increased educational attain-\\nment. The increase in after-tax income is $16,775 for the observed\\n14-year age range (23–36) in Miller and Wherry (2019) and an\\nadditional $26,236 in the subsequent years. Subtracting the cost\\nof college expenses reduces this by $111 for a net WTP of $47,400.\\nWe also provide a conservative WTP estimate using solely\\nthe transfer value of the insurance of $1,737. This would be\\nvalid if the increase in after-tax earnings came at the expense\\nof increased effort as opposed to increased opportunities. To\\nbe sure, the difference between the conservative and baseline\\nWTP estimate is quite large. As we discuss below, our primary\\nconclusions remain valid under either approach.\\nIII.C. Introduction of Food Stamps\\nThird, we construct an MVPF for the impact of the intro-\\nduction of the Food Stamp Program, today known as the Supple-\\nmental Nutritional Assistance Program (SNAP). This example\\nillustrates how we incorporate potential spillovers of adult-\\ntargeted policies onto children.\\nThe Food Stamp Program provides in-kind transfers to\\nlow-income families that can be used on food. Its introduction in\\nthe 1970s was staggered across counties in the United States.36\\n35. Note we should think of this as a “private” not a “social” willingness to pay.\\nIt assumes that parents are willing to pay $10,000 out of their own pocket to have\\na 1% reduction in infant mortality. It is important to note that society may well be\\nwilling to pay more than $1M. In the language of the social welfare function, this\\nsuggests that the population has a high social marginal utility of income, ηj.\\n36. This variation was initially studied by Currie and Moretti (2006) in Cal-\\nifornia and extended nationally by Almond, Hoynes, and Schanzenbach (2011),\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1235\\nHoynes and Schanzenbach (2012) exploit this variation to analyze\\nits impact on labor income and welfare participation of adult\\nbeneficiaries; Almond, Hoynes, and Schanzenbach (2011) study\\nits effect on birth outcomes. Bailey et al. (2019) use the same\\nvariation to study its impacts on the adult earnings of children\\nwhose parents received food stamps.\\n1. Costs.\\nThe first component of our total costs is the average\\nyearly benefit from food stamp enrollment, equal to $2,904. To\\nthis, we add the fiscal externality resulting from the effects on\\nboth adults and children. For adults, Hoynes and Schanzenbach\\n(2012) document large yet imprecise reductions in earnings of\\n$3,650 that imply a fiscal externality of $471 from reductions\\nin tax revenue—roughly $0.16 per $1 of food stamps provided.\\nFor children, Bailey et al. (2019) find increases in earnings in\\nadulthood corresponding to 7.1% for six full years of childhood\\nexposure to food stamps between the ages of zero and five. In\\nOnline Appendix E, we show that this corresponds to an estimated\\nincrease in tax revenue of $0.24 per $1 of food stamps for every\\nfamily with a child aged 0–5. We then multiply this by 0.35, the\\nfraction of SNAP benefits received by households with children\\nage 0–5. We subsequently multiply by 1.32, the average number\\nof children in these households. This suggests that for each $1\\nin food stamp spending, the resulting effects on children increase\\ngovernment revenue by $0.11.37 Taken together, these estimates\\nimply that every $1 of spending on food stamps costs $1.05.38\\n2. WTP. We provide a willingness to pay from three compo-\\nnents. First, the envelope theorem suggests that individuals are\\nHoynes and Schanzenbach (2012), Hoynes, Schanzenbach, and Almond (2016),\\nand Bailey et al. (2019).\\n37. We assume no impact on children at older ages, but clearly such effects\\ncould alter the MVPF. In Section V, we discuss the implications for a policy targeted\\nto families with children aged 0–5; this leads to a larger MVPF.\\n38. Our costs estimates here are constrained by the set of observed outcomes\\nthat we can reliably translate into effects on the government budget. For example,\\nHoynes, Schanzenbach, and Almond (2016) report that the introduction of food\\nstamps was associated with a reduction in adult metabolic syndromes. Although\\nour earnings estimates likely capture the effect of those health changes on labor\\nsupply, we lack a reliable way to measure the impact of those health changes on\\nhealth care utilization. Future work documenting long-run health impacts that\\nreduce (increase) government spending on medical care could lead to a higher\\n(lower) MVPF than we estimate here.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1236\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nwilling to pay for the mechanical cost of SNAP benefits, which\\nwe estimate to be $1,809. We arrive at this number by taking\\nthe $3,650 increase in earnings and noting that SNAP benefits\\ndecline with earnings at a 30% phaseout rate. This means that\\n$1,095 of the food stamp cost is the result of a cost increase from\\nbehavioral responses. Consequently, our point estimate suggests\\nindividuals value $0.62 for each $1 spent by the government on\\nfood stamps.39 Second, we incorporate the WTP for reductions in\\ninfant mortality and increases in longevity among their children.\\nAs in the case of Medicaid in Section III.D, we assume this is\\ngiven by the reduction in child mortality multiplied by a value of\\na statistical life (VSL) of $1M (2012US$). We add to that value\\nthe number of years of increased longevity multiplied by a quality\\nof adjusted life-year (QALY) of $20k (2012US$). This leads to\\nan additional WTP of $0.02. Last, we incorporate an additional\\nwillingness to pay because of increases in after-tax income among\\nthose who received food stamps as children. These estimates of\\nafter-tax income are based on the earnings gains we calculate\\nabove. Combining costs with willingness to pay creates an MVPF\\nof 1.04 (95% CI of [−0.97, ∞]).40\\nIt is important to note in this case that statistical uncertainty\\nin these estimates is quite high. The combination of substantial\\nearnings reductions among parents and large earnings gains\\namong children mean that we cannot reject MVPFs of 0 or ∞. We\\nreturn to this uncertainty in more detail in Section VI.A when\\nwe discuss the value of additional research or data access in\\nreducing sampling uncertainty.\\nIII.D. Paycheck Plus in New York City\\nFourth, we measure the MVPF of the Paycheck Plus program.\\nThis construction illustrates how we create the MVPF from RCTs.\\n39. It is also worth noting that this willingness to pay is nearly identical to the\\nvalue we would receive if we did not apply the envelope theorem in this context, but\\nrather used estimates from Whitmore (2002) suggesting that food stamps have a\\ntrade value of at least 65%. For our “conservative” willingness to pay specification,\\nwe make both the envelope theorem and trade value modifications and find that\\nthe MVPF falls to 0.39.\\n40. In Online Appendix E, we also explore several alternate specifications\\nand find that these produce only small changes to the MVPF. For example, we\\nassume a higher VSL of $9M and a QALY of $180k and find an MVPF of 1.22.\\nWe incorporate the impact of reduced incarceration based on effects estimated in\\nBailey et al. (2019) and costs of incarceration from Heckman et al. (2010). We find\\nthat the MVPF rises from 1.04 to 1.07.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1237\\nIt also provides guidance on the ideal set of measures future\\nresearchers could construct to more directly estimate the MVPF\\nassociated with RCTs.\\nThe Paycheck Plus program is modeled after the Earned\\nIncome Tax Credit (EITC). The EITC provides income subsidies to\\nlow-income workers that are intended to encourage employment.\\nIf workers face high marginal tax rates due to the benefit schedule\\nfor means-tested transfers such as food stamps, the EITC may\\noffset those high rates. While the EITC generally targets adults\\nwith children, the Paycheck Plus program in New York City\\nconducted an RCT to evaluate the provision of EITC-like benefits\\nto single adults without dependents—a group not traditionally\\neligible for significant EITC benefits. The credit is worth up to\\n$2,000 a year and is available over three years (2014–2016 fiscal\\ntax years with bonuses paying out in 2015–2017).\\nMiller et al. (2017) estimate the effect of the policy on income,\\nemployment, and after-tax income for the first two years of the\\npolicy, which we translate here into their implied MVPF.41 We\\nbegin with costs.\\n1. Cost.\\nThe cost of the policy is the observed causal effect of\\nthe policy on the government budget.42 To measure the costs, let Tj\\ndenote the tax schedule faced by the control (j = 0) and treatment\\n(j = 1) groups. Let y j\\ni denote individual i′s earnings if they face\\nthe j = 0, 1 tax/transfer schedule. The cost is then given by:\\n(5)\\nCost = E\\n\\u0004\\nT 0 \\u0005\\ny0\\ni\\n\\u0006\\u0007\\n−E\\n\\u0004\\nT 1 \\u0005\\ny1\\ni\\n\\u0006\\u0007\\n.\\n41. As discussed in Online Appendix D, the current set of results from the third\\nyear do not include sufficient information to form the MVPF in as precise a manner\\nas we do here; but we note how imposing a reasonable additional assumption\\nsuggests that the third-year effects lead to a very similar MVPF also near 1.\\n42. In the context of an RCT, our approach measures the welfare impact of\\nrandomly assigning additional people to the treatment as opposed to the control\\ngroup. As a result, one can use the reduced-form results to form our welfare\\nanalysis (i.e., one need not separately isolate a LATE/TOT). The denominator\\nis the causal effect of this assignment on the budget and the numerator is the\\naggregate WTP by members of the control group to be in the treatment group. As\\na result, whether our welfare analysis can be externally generalized to a different\\npolicy with different take-up of benefits would depend on how its treatment effects\\nvary across the population.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1238\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nBecause Paycheck Plus is an RCT, we compute equation (5)\\nusing the difference in tax and transfer revenue obtained by the\\ngovernment. In 2014, the causal impact on government costs was\\n$621; in 2015, this cost was $453. Combining these values, the\\ncost is $1,074.\\n2. WTP. We use the envelope theorem to estimate the WTP\\nfor Paycheck Plus. In 2014, the average bonus paid is $1,399\\namong those who take it up, and 45.9% of people do so. The en-\\nvelope theorem suggests that participants do not value the full\\n$1,399 subsidy dollar for dollar. This is because part of this cost\\nreflects the impact of behavioral responses. To the first order, those\\nwho entered the labor force to obtain the transfer are indifferent\\nbetween working and not working. Miller et al. (2017) find a causal\\neffect of the program on the extensive margin labor supply of 0.9%.\\nAbsent behavioral responses, this implies that 45% of the sample,\\nas opposed to 45.9%, would have received the transfer had they not\\nchanged their behavior. Consequently, 98% of the transfer ( 45\\n45.9)\\nis valued by the beneficiaries, which implies a WTP of $630 for\\nthe transfers in 2014.43 Repeating this calculation using the data\\nfrom 2015 yields a WTP of $441. This suggests a two-year WTP of\\n$1,070. The estimated WTP of $1,070 combined with the net cost\\nof $1,074 implies an MVPF of 0.996 (which rounds to 1 in Table II).\\nOne can also construct an MVPF separately using the 2014 or\\n2015 transfers and responses. This yields similar MVPFs of 1.014\\nand 0.973. This dynamic similarity will be a recurring theme\\namong transfer programs to adults. It means that a static model\\nof the labor market distortions provides a reasonable approxi-\\nmation to measuring the MVPF for these policies. Every $1 the\\ngovernment spends in transfers leads to a benefit of roughly $1.44\\n43. This calculation assumes no intensive-margin responses. If one observed\\nthe microdata from the RCT, one could allow for intensive-margin responses.\\nTo the first order, the WTP is the mechanical change in the tax schedule (i.e.,\\nreplacing T0 with T1) holding behavior fixed for each individual at y0\\ni :\\n(6)\\nWTP = E\\n\\u0004\\nT 0 \\u0005\\ny0\\ni\\n\\u0006\\n−T 1 \\u0005\\ny0\\ni\\n\\u0006\\u0007\\n.\\nThis means the ideal method of calculating WTP is to feed the distribution of\\ncontrol group earnings into both the control and treatment group tax schedule.\\nIn practice, this number is rarely reported, but future work conducting welfare\\nanalyses of RCTs can directly construct this measure.\\n44. If the provision of work subsidies today leads to an increase in labor\\nearnings and thus tax revenue after the earnings subsidies have ended, then\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1239\\nTABLE II\\nMVPF, WTP, AND COST ESTIMATES WITH CONFIDENCE INTERVALS, ALL PROGRAMS\\nProgram\\nMVPF\\nMVPF CI\\nWTP\\nWTP CI\\nCost\\nCost CI\\nBaseline\\nChild education\\n∞\\n[17.83, ∞]\\n4.82\\n[3.38, 6.28]\\n−0.21\\n[−0.59, 0.19]\\nAbecedarian\\n11.89\\n[−0.18, ∞]\\n2.62\\n[−0.24, 5.63]\\n0.22\\n[−0.76, 1.15]\\nx\\nCPC Extended\\n∞\\n[−∞, ∞]\\n4.15\\n[−21.80, 27.36]\\n−1.22\\n[−6.13, 4.36]\\nCPC Preschool\\n∞\\n[∞, ∞]\\n2.23\\n[0.24, 4.21]\\n−0.35\\n[−0.62, −0.10]\\nCPC School\\n1.32\\n[−∞, ∞]\\n−0.18\\n[−1.23, 0.83]\\n−0.14\\n[−1.27, 0.98]\\nHead Start\\n∞\\n[10.58, ∞]\\n4.42\\n[2.90, 6.08]\\n−0.11\\n[−0.52, 0.27]\\nx\\nHead Start RD\\n0.72\\n[−0.02, ∞]\\n0.72\\n[−12.90, 11.46]\\n0.99\\n[−0.03, 1.78]\\nHead Start RCT\\n2.41\\n[1.90, 3.15]\\n1.29\\n[1.10, 1.50]\\n0.54\\n[0.49, 0.59]\\nK12 Spend\\n∞\\n[∞, ∞]\\n8.78\\n[4.58, 13.03]\\n−1.03\\n[−2.02, −0.06]\\nx\\nK12 Spend Mich.\\n0.65\\n[0.05, 2.19]\\n0.62\\n[−0.01, 1.58]\\n0.95\\n[0.79, 1.08]\\nPerry Preschool\\n43.61\\n[1.83, ∞]\\n3.45\\n[1.19, 5.70]\\n0.08\\n[−0.52, 0.68]\\nx\\nCollege adult\\n−5.59\\n[−∞, ∞]\\n−2.68\\n[−143.04, 61.16]\\n0.48\\n[−7.74, 18.61]\\nAOTC (IS)\\n6.75\\n[−1.61, ∞]*\\n2.45\\n[−6.52, 13.42]*\\n0.36\\n[−6.64, 6.47]*\\nx\\nAOTC (JE)\\n−1.77\\n[−17.06, ∞]*\\n−7.63\\n[−68.99, 40.12]*\\n4.31\\n[−11.54, 24.28]*\\nx\\nAOTC (JS)\\n∞\\n[−5.96, ∞]*\\n9.96\\n[−44.67, 76.39]*\\n−1.37\\n[−16.83, 12.68]*\\nx\\nAOTC (SI)\\n10.05\\n[−18.36, ∞]\\n5.36\\n[−89.06, 104.44]\\n0.53\\n[−12.93, 13.61]\\nx\\nAOTC (SE)\\n−0.02\\n[−2.25, ∞]*\\n−0.02\\n[−7.28, 5.59]*\\n1.12\\n[−6.30, 8.17]*\\nx\\nAOTC (SS)\\n∞\\n[−8.00, ∞]*\\n23.39\\n[−112.96, 191.48]*\\n−1.61\\n[−26.75, 19.56]*\\nx\\nHOPE Cred.\\n12.58\\n[−24.72, ∞]\\n5.27\\n[−745.41, 518.28]\\n0.42\\n[−61.22, 131.34]\\nx\\nHTC (IS)\\n18.86\\n[−2.87, ∞]*\\n5.91\\n[−24.65, 43.39]*\\n0.31\\n[−11.81, 11.68]*\\nx\\nHTC (JE)\\n2.37\\n[−2.22, ∞]*\\n8.21\\n[−35.77, 61.73]*\\n3.47\\n[−21.81, 28.40]*\\nx\\nHTC (JS)\\n∞\\n[−3.51, ∞]*\\n18.41\\n[−87.39, 148.22]*\\n−3.15\\n[−69.14, 53.90]*\\nx\\nHTC (SE)\\n11.83\\n[−4.48, ∞]*\\n4.59\\n[−17.25, 31.56]*\\n0.39\\n[−4.19, 4.15]*\\nx\\nHTC (SS)\\n−1.64\\n[−13.38, ∞]*\\n−1.91\\n[−22.71, 14.11]*\\n1.16\\n[−3.87, 6.67]*\\nx\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1240\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE II (CONTINUED)\\nProgram\\nMVPF\\nMVPF CI\\nWTP\\nWTP CI\\nCost\\nCost CI\\nBaseline\\nHOPE/LLC\\n−8.81\\n[−∞, ∞]\\n−42.82\\n[−266.09, 9.92]\\n4.86\\n[−7.59, 31.13]\\nx\\nAdult Pell\\n2.18\\n[0.71, 6.11]\\n3.42\\n[1.02, 6.25]\\n1.57\\n[1.03, 2.31]\\nx\\nTuition deduc (JE)\\n0.77\\n[−1.92, 38.88]\\n1.00\\n[−4.88, 6.49]\\n1.29\\n[0.17, 2.51]\\nx\\nTuition deduc (JS)\\n−0.02\\n[−2.50, 5.62]\\n−0.03\\n[−5.59, 4.43]\\n1.38\\n[0.55, 2.49]\\nx\\nTuition deduc (SE)\\n∞\\n[−∞, ∞]\\n1.00\\n[−7.76, 8.53]\\n−1.13\\n[−2.04, −0.26]\\nx\\nTuition deduc (SS)\\n∞\\n[−∞, ∞]\\n5.38\\n[−1.58, 14.00]\\n−5.10\\n[−6.36, −3.41]\\nx\\nCollege child\\n∞\\n[4.18, ∞]\\n8.79\\n[3.05, 15.65]\\n−0.36\\n[−1.76, 0.73]\\nCal Grant GPA\\n∞\\n[10.72, ∞]\\n9.41\\n[3.43, 16.44]\\n−0.57\\n[−1.63, 0.32]\\nx\\nCal Grant Inc\\n−0.69\\n[−2.36, 7.41]\\n−1.04\\n[−5.37, 4.29]\\n1.51\\n[0.63, 2.21]\\nx\\nCUNY Pell\\n1.39\\n[−2.95, 12.88]\\n1.42\\n[−3.42, 7.15]\\n1.02\\n[0.48, 1.56]\\nx\\nCC Mich\\n29.46\\n[−2.33, ∞]\\n7.80\\n[−9.29, 29.19]\\n0.26\\n[−3.39, 2.72]\\nx\\nCC Texas\\n349.51\\n[1.61, ∞]\\n10.69\\n[1.73, 20.89]\\n0.03\\n[−2.08, 2.10]\\nx\\nDC Grant\\n22.98\\n7.62\\n0.33\\nx\\nFIU GPA\\n∞\\n[∞, ∞]\\n13.73\\n[1.40, 62.13]\\n−2.97\\n[−15.62, −0.02]\\nx\\nFlorida Grant\\n7.42\\n[1.09, ∞]\\n7.40\\n[1.24, 15.61]\\n1.00\\n[−0.32, 2.42]\\nx\\nFree FAFSA (dep)\\n4.03\\n[0.65, 10.75]\\n33.67\\n[3.04, 95.17]\\n8.35\\n[2.00, 20.03]\\nFree FAFSA (indep)\\n2.12\\n[−0.06, 9.71]\\n5.32\\n[−0.89, 15.05]\\n2.51\\n[0.77, 4.91]\\nGeorgia HOPE\\n4.00\\n[0.37, 20.63]\\n3.60\\n[0.73, 6.48]\\n0.90\\n[0.28, 1.57]\\nx\\nHAIL Aid\\n1.30\\n[0.24, 3.65]\\n0.97\\n[0.14, 1.78]\\n0.75\\n[0.54, 0.95]\\nKalamazoo\\n1.93\\n[0.97, 5.61]\\n1.93\\n[0.93, 3.71]\\n1.00\\n[0.77, 1.24]\\nx\\nMA scholarship\\n0.72\\n[−0.92, 3.05]\\n1.21\\n[−1.81, 4.00]\\n1.68\\n[1.25, 2.23]\\nx\\nOhio Pell\\n2.49\\n[0.80, 5.40]\\n2.88\\n[1.29, 4.40]\\n1.16\\n[0.80, 1.56]\\nx\\nTN Pell\\n0.84\\n[−1.59, 3.57]\\n0.78\\n[−1.64, 2.84]\\n0.93\\n[0.62, 1.24]\\nx\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1241\\nTABLE II (CONTINUED)\\nProgram\\nMVPF\\nMVPF CI\\nWTP\\nWTP CI\\nCost\\nCost CI\\nBaseline\\nTexas Pell\\n∞\\n[∞, ∞]\\n85.74\\n[0.77, 173.60]\\n−17.38\\n[−33.15, −1.92]\\nx\\nSoc Sec College\\n4.86\\n[0.98, 52.39]\\n5.03\\n[0.82, 10.92]\\n1.03\\n[0.32, 1.95]\\nx\\nCollege spend\\n4.00\\n[1.25, 20.44]\\n3.17\\n[1.26, 5.48]\\n0.79\\n[0.36, 1.21]\\nx\\nTN Hope\\n1.86\\n[0.92, 5.08]\\n1.94\\n[0.94, 3.51]\\n1.05\\n[0.81, 1.36]\\nx\\nCollege tuition\\n1.02\\n[−1.06, 5.47]\\n1.02\\n[−1.47, 3.58]\\n1.00\\n[0.68, 1.32]\\nx\\nWI scholarship\\n1.43\\n[1.00, 2.32]\\n1.46\\n[1.04, 2.08]\\n1.02\\n[0.93, 1.13]\\nx\\nJob training\\n0.44\\n[−19.57, 0.91]\\n0.36\\n[−0.82, 1.51]\\n0.83\\n[−0.09, 1.75]\\nJob Corps\\n0.15\\n[−0.23, 0.58]\\n0.15\\n[−0.23, 0.55]\\n0.98\\n[0.93, 1.03]\\nx\\nJTPA adult\\n1.38\\n[−0.21, 2.13]*\\n1.17\\n[−0.17, 2.64]*\\n0.85\\n[0.08, 1.65]*\\nx\\nJTPA youth\\n−0.23\\n[−3.43, 1.27]*\\n−0.21\\n[−1.70, 1.29]*\\n0.91\\n[0.15, 1.66]*\\nx\\nJobStart\\n0.20\\n[0.04, 0.42]\\n0.20\\n[0.06, 0.34]\\n1.02\\n[0.80, 1.24]\\nx\\nNSW Women\\n1.48\\n[−∞, ∞]\\n0.57\\n[−0.50, 1.64]\\n0.39\\n[−0.09, 0.86]\\nx\\nNSW Ex-Addict\\n0.44\\n0.35\\n0.79\\nx\\nNSW Ex-Offender\\n0.64\\n0.53\\n0.82\\nx\\nNSW Youth\\n0.60\\n[−∞, ∞]\\n0.47\\n[−4.23, 5.15]\\n0.78\\n[−3.32, 4.87]\\nx\\nWork Advance\\n0.78\\n[0.26, 1.34]*\\n0.64\\n[0.21, 1.11]*\\n0.83\\n[0.83, 0.83]*\\nx\\nYear Up\\n0.43\\n[0.37, 0.48]\\n0.41\\n[0.36, 0.45]\\n0.96\\n[0.95, 0.97]\\nx\\nDisability ins.\\n0.85\\n[0.82, 0.88]\\n1.00\\n[1.00, 1.00]\\n1.18\\n[1.14, 1.22]\\nDI generosity\\n0.96\\n[0.95, 0.97]\\n1.00\\n1.04\\n[1.03, 1.05]\\nx\\nDI judge\\n0.78\\n[0.72, 0.85]\\n1.00\\n1.28\\n[1.18, 1.39]\\nx\\nDI examiner\\n0.74\\n[0.71, 0.78]\\n1.00\\n1.34\\n[1.28, 1.41]\\nx\\nDI veterans\\n0.95\\n[0.92, 0.98]\\n1.00\\n1.05\\n[1.02, 1.08]\\nx\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1242\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE II (CONTINUED)\\nProgram\\nMVPF\\nMVPF CI\\nWTP\\nWTP CI\\nCost\\nCost CI\\nBaseline\\nHealth adult\\n0.89\\n[0.56, 1.57]\\n1.49\\n[1.00, 1.99]\\n1.67\\n[1.01, 2.39]\\nMass HI (150%FPL)\\n0.80\\n1.00\\n1.25\\nx\\nMass HI (200%FPL)\\n0.85\\n1.00\\n1.18\\nx\\nMass HI (250%FPL)\\n1.09\\n1.00\\n0.92\\nx\\nMedicare intro\\n1.63\\n[0.52, 3.83]\\n2.00\\n[0.58, 3.44]\\n1.23\\n[0.48, 1.78]\\nx\\nOregon Health\\n1.16\\n[1.08, 1.25]\\n1.46\\n[1.19, 1.83]\\n1.26\\n[1.04, 1.57]\\nx\\nMedigap tax\\n0.40\\n[0.22, 1.54]\\n1.00\\n2.53\\n[0.64, 4.44]\\nx\\nHealth child\\n∞\\n[24.82, ∞]\\n6.10\\n[3.05, 13.17]\\n−0.78\\n[−2.52, 0.17]\\nMC child 83+\\n∞\\n[0.26, ∞]\\n0.86\\n[0.66, 1.44]\\n−0.20\\n[−0.47, 1.82]\\nx\\nMC pregnant & infants\\n∞\\n[∞, ∞]\\n13.65\\n[5.92, 40.80]\\n−2.02\\n[−7.85, −0.27]\\nx\\nMC child (state exp)\\n∞\\n[−0.37, ∞]\\n8.13\\n[−0.24, 14.00]\\n−1.08\\n[−2.25, 0.57]\\nx\\nMC intro\\n10.24\\n[0.93, ∞]\\n1.78\\n0.17\\n[−1.60, 1.93]\\nx\\nSupp. Sec. Inc.\\n0.75\\n[0.64, 0.85]\\n1.00\\n[1.00, 1.00]\\n1.33\\n[1.17, 1.56]\\nSSI review\\n0.76\\n[0.56, 1.00]\\n1.00\\n1.32\\n[1.00, 1.78]\\nx\\nSSI judge\\n0.74\\n[0.72, 0.77]\\n1.00\\n1.34\\n[1.30, 1.39]\\nx\\nUnemp. ins.\\n0.61\\n[0.53, 0.74]\\n1.20\\n[1.15, 1.24]\\n1.95\\n[1.63, 2.26]\\nUI ben (state max)\\n0.68\\n[0.48, 1.13]\\n1.17\\n[1.11, 1.22]\\n1.71\\n[0.99, 2.41]\\nx\\nUI ben (DD)\\n0.43\\n[0.28, 0.78]\\n1.17\\n[1.11, 1.22]\\n2.74\\n[1.51, 4.17]\\nx\\nUI ben (DD w UR)\\n0.48\\n[0.30, 1.69]\\n1.17\\n[1.11, 1.22]\\n2.43\\n[0.79, 3.90]\\nx\\nUI ben (GA)\\n1.03\\n[0.97, 1.09]\\n1.17\\n[1.11, 1.22]\\n1.14\\n[1.09, 1.18]\\nx\\nUI ben (MO Exp.)\\n0.74\\n[0.67, 0.81]\\n1.17\\n[1.11, 1.22]\\n1.59\\n[1.46, 1.73]\\nx\\nUI ben (MO Rec.)\\n0.44\\n[0.39, 0.50]\\n1.17\\n[1.11, 1.22]\\n2.68\\n[2.36, 3.01]\\nx\\nUI ben (NY)\\n0.89\\n[0.82, 0.97]\\n1.17\\n[1.11, 1.22]\\n1.31\\n[1.21, 1.41]\\nx\\nUI ben (RK)\\n0.84\\n[0.76, 0.92]\\n1.17\\n[1.11, 1.22]\\n1.40\\n[1.28, 1.52]\\nx\\nUI dur (DD)\\n0.45\\n[0.25, 2.12]\\n1.30\\n[1.24, 1.36]\\n2.89\\n[0.61, 5.19]\\nx\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1243\\nTABLE II (CONTINUED)\\nProgram\\nMVPF\\nMVPF CI\\nWTP\\nWTP CI\\nCost\\nCost CI\\nBaseline\\nUI dur (MO)\\n0.83\\n[0.76, 0.90]\\n1.30\\n[1.24, 1.36]\\n1.57\\n[1.46, 1.69]\\nx\\nHousing vouchers\\n0.77\\n[0.74, 0.81]\\n0.91\\n[0.91, 0.91]\\n1.19\\n[1.13, 1.24]\\nHCV RCT to welfare\\n0.91\\n[0.86, 0.96]\\n1.00\\n1.10\\n[1.04, 1.17]\\nx\\nHCV Chicago lottery\\n0.65\\n[0.61, 0.70]\\n0.83\\n1.27\\n[1.18, 1.37]\\nx\\nJobs+\\n1.42\\n[0.45, 2.83]∗\\n1.14\\n[0.41, 1.91]∗\\n0.81\\n[0.67, 0.93]∗\\nMTO\\nMTO\\n∞\\n[−2.80, ∞]\\n18.40\\n[−15.46, 51.85]\\n−2.44\\n[−11.35, 6.81]\\nx\\nNutrition\\nWIC\\n1.38\\n[1.10, 1.66]\\n1.28\\n[1.08, 1.47]\\n0.93\\n[0.88, 0.98]\\nSNAP assist\\n0.92\\n[0.91, 0.96]∗\\n0.92\\n[0.91, 0.96]∗\\n1.00\\nx\\nSNAP info\\n0.89\\n[0.89, 0.89]∗\\n0.89\\n[0.89, 0.89]∗\\n1.00\\nx\\nSNAP intro\\n1.04\\n[−0.97, ∞]\\n1.09\\n[−2.45, 4.55]\\n1.05\\n[−0.38, 2.51]\\nx\\nCash transfers\\n0.74\\n[0.36, 1.47]\\n0.86\\n[0.50, 1.37]\\n1.16\\n[0.89, 1.34]\\nEITC 1986\\n1.20\\n[1.05, 1.38]\\n1.00\\n0.84\\n[0.73, 0.95]\\nx\\nEITC 1993\\n1.12\\n[0.82, 1.21]\\n1.00\\n0.89\\n[0.67, 1.06]\\nx\\nAFDC generosity\\n0.91\\n[0.83, 1.00]\\n1.04\\n[0.96, 1.11]\\n1.14\\n[1.10, 1.18]\\nx\\nAFDC term limits\\n0.81\\n[0.73, 0.90]\\n1.00\\n1.23\\n[1.11, 1.38]\\nx\\nAlaska UBI\\n0.92\\n[0.89, 0.96]\\n1.00\\n1.09\\n[1.05, 1.12]\\nx\\nPaycheck+\\n1.00\\n[0.87, 1.19]\\n1.00\\n1.00\\n[0.85, 1.15]\\nx\\nNeg. inc. tax\\n−0.01\\n[−0.82, 9.83]\\n−0.02\\n[−2.50, 3.53]\\n1.96\\n[0.18, 3.20]\\nx\\nTop taxes\\n3.03\\n[1.35, ∞]\\n1.00\\n[1.00, 1.00]\\n0.33\\n[−0.09, 0.74]\\nTop tax 2013\\n1.16\\n[0.87, 1.92]\\n1.00\\n0.86\\n[0.54, 1.16]\\nx\\nTop tax 1993\\n1.85\\n[1.19, 4.07]\\n1.00\\n0.54\\n[0.25, 0.84]\\nx\\nTop tax 1986\\n44.27\\n[2.37, ∞]\\n1.00\\n0.02\\n[−0.37, 0.42]\\nx\\nTop tax 2001\\n1.37\\n[0.92, 2.86]\\n1.00\\n0.73\\n[0.36, 1.09]\\nx\\nTop tax 1981\\n∞\\n[0.94, ∞]\\n1.00\\n−0.51\\n[−2.13, 1.06]\\nx\\nNotes. This table presents our baseline estimates for each program in our extended sample, along with the category averages reported in the bold header rows in each category.\\nWe exclude the welfare-to-work policies discussed in Section VI.C. For each policy, we report its MVPF, cost per dollar of programmatic spending, and willingness to pay per\\ndollar of programmatic spending. We also report bootstrapped 95% confidence intervals with adjustments discussed in Online Appendix H. The final column indicates whether the\\nprogram is included in the baseline estimates (and thus included in the category averages). Confidence intervals are marked with an asterisk in cases where we infer p-values\\nusing reported interval ranges. Programs in which the confidence interval is either inferred from p-values or missing are excluded from category averages.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1244\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nIII.E. Job Corps\\nNext we construct the MVPF for an RCT of Job Corps,\\none of the largest vocational education programs in the United\\nStates. This example illustrates how not all attempts to increase\\nchildren’s human capital and earnings have high MVPFs.\\nEstablished in 1964, Job Corps is administered by the U.S.\\nDepartment of Labor and provides job training and other services\\nto at-risk youth between the ages of 16 and 24 via a network\\nof centers run by local public and private agencies (Schochet,\\nBurghardt, and McConnell 2008). Between 1994 and 1996, the\\nNational Job Corps study randomized 80,000 eligible applicants\\ninto the program. We form an MVPF for this RCT using the\\nrecent work of Schochet (2018), who links the original RCT to tax\\ndata; we supplement this analysis with the earlier cost-benefit\\nanalysis of Schochet et al. (2006).\\n1. Cost. Schochet et al. (2006) estimates that the up-front\\nprogrammatic cost per recipient is $16,158. Schochet (2018) then\\nestimates the earnings impact of the program over the course of\\n20 years and finds minimal effects. In particular, they find that\\nthe program increases the present discounted value of participant\\nearnings by $121 using a 3% discount rate. We estimate that this\\ncorresponds to an increase in tax and transfer revenue of $52.45\\nTo these, we add the value of the products produced by the Job\\nCorps participants, which Schochet, Burghardt, and McConnell\\n(2008) estimates to be $220. Summing, this implies a net cost\\nof the program over 20 years of $15,886. Given the small effects\\non earnings, we use this 20-year observed period as our baseline\\nestimate. In Online Appendix C, we show that if one extrapolates\\nthe MVPF would be higher. We discuss these forecasts and their implied MVPFs\\nin Online Appendix F. To ensure our conclusions are not biased by including\\npolicies for adults that do not have long-run follow-ups, in Section IV.C we conduct\\nrobustness of all our analysis to policies where long-run follow-ups have been\\nmeasured.\\n45. As discussed in Online Appendix C, we form this estimate by summing\\nthe observed increase in tax revenue for years 6–20 in administrative data from\\nSchochet (2018) combined with an application of the CBO tax rate to the earnings\\neffects for the first five years. We note that a fiscal externality of $52 in this case\\ncorresponds to a high implicit marginal tax rate. This is driven by a low tax rate\\non initial earnings declines and a comparatively higher tax rate on subsequently\\nsmall earnings gains.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1245\\nthese earnings effects to age 65, the net cost of the program would\\nfall to $15,832 due to a small subsequent earnings gain.\\n2. WTP.\\nFollowing our approach for other policies that have\\nthe potential to increase human capital, our baseline measure of\\nwillingness to pay consists of the impact of the policy on after-tax\\nincome.46 This is given by the $69 increase in after-tax earned\\nincome plus the $2,314 component of the programmatic cost that\\nis a transfer to participants to pay for food and clothing while\\nparticipating in the program. Summing, this yields a WTP of\\n$2,383. Dividing by the government cost of $15,886 yields an\\nMVPF of 0.15. If one extrapolates the earnings affects to age 65,\\nthe resulting MVPF is 0.18.47\\nIII.F. Top Marginal Tax Rates\\nFinally we turn to the MVPF of top marginal tax rate\\nchanges. This example illustrates how we can utilize estimates\\nfrom existing literature that attempts to provide empirical\\nguidance on optimal government policy (e.g., optimal top tax\\nrates, optimal unemployment insurance benefits). Whereas those\\nliteratures often consider the policies in isolation (e.g., optimal UI\\npolicy), we can translate the estimates into their implied MVPF\\nto facilitate comparisons across policy domains.\\n46. A pure revealed-preference approach in this context could rely on the as-\\nsumption that job training is accessible in the private market at its programmatic\\ncost. One could then set willingness to pay equal to (or perhaps below) the up-front\\ncost of program enrollment. In contrast, setting willingness to pay equal to after-\\ntax earnings does not require the assumption that potential Job Corps enrollees\\nhave perfect information about the returns to job training at the time of initial\\nenrollment. However, it does require that after-tax income is sufficient to capture\\nwillingness to pay. This means we do not incorporate any welfare costs from opti-\\nmization errors in consumption decisions that stem from program participation.\\n47. Our analysis here focuses on the MVPF of the entire treatment group.\\nHowever, it is worth noting that Schochet (2018) finds larger effects for the sub-\\nsample of age 20–24 participants, including a 2.4 percentage point reduction in\\ndisability insurance receipt and a roughly $500 a year increase in earnings. To see\\nhow this could lead to a different MVPF, we can first take a back-of-the-envelope\\ncalculation of a PDV of lifetime disability insurance receipt of roughly $200k con-\\nsistent with Von Wachter, Song, and Manchester (2011). This implies a cost saving\\nof $4,800. Second, we note that the $500 a year impact on earnings corresponds\\nto a PDV increase in earnings of $12.8k. Applying an approximate 20% tax and\\ntransfer rate implies an increase in WTP by $10.2k and an increase in tax revenue\\nof $2.6k. This implies a net cost of roughly $8,600, which implies an MVPF of 1.18.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1246\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nThere is a large theoretical and empirical literature dis-\\ncussing the optimal top marginal income tax rate, summarized\\nin Saez, Slemrod, and Giertz (2012). This literature notes that\\na tax cut providing $1 in additional after-tax income is valued\\nat $1 by mechanical beneficiaries. In other words, the tax cut is\\nvalued at cost by those who would receive it in the absence of any\\nbehavioral response to the change in the tax code. As a result,\\nmeasuring WTP is straightforward. The cost to the government of\\nthe tax policy is more difficult. The cost of a tax cut that provides\\n$1 of benefits in the absence of a behavioral response is given by\\n1 + FE, where FE is the impact of the behavioral response to the\\ntax cut on government revenue.\\nFor top marginal tax rate reductions, Saez, Slemrod, and\\nGiertz (2012) and Diamond and Saez (2011) show that this FE\\ncan be expressed as −\\nτ\\n1 −τ αϵETI, where α is the Pareto parameter\\nof the income distribution48 and ϵETI = 1 −τ\\nE[y]\\ndE[y]\\nd(1 −τ) is the elasticity\\nof taxable income for top earners with respect to the top marginal\\n“keep” rate of 1 −τ.49\\nThe elasticity ϵETI has been estimated using various tax\\nreforms including the 1981 and 1986 tax decreases and 1993\\nincreases in the top marginal income tax rate. We compute\\nthe MVPF of the historical tax policy changes that allowed\\nresearchers to identify ϵETI. The MVPF for each tax reform is the\\nratio of WTP to cost,\\n1\\n1+FE:\\n(7)\\nMVPF =\\n1\\n1 −\\nτ\\n1 −τ αϵETI .\\nWe translate estimates of ϵETI estimated from five major tax\\nreforms in 1981, 1986, 1993, 2001, and 2013, which are outlined\\nin Online Appendix F.\\nTo take one example, consider the 1981 tax cut that reduced\\nthe top marginal income tax rate from 70% to 50%. Saez (2003)\\nfinds an estimate of ϵ = 0.311. We estimate α = 2.299 from Atkin-\\nson, Piketty, and Saez (2011). We plug these into equation (7).\\nWe use marginal tax rates of τ = 75% and τ = 55% before and\\nafter the reform, which include a 5% state tax adjustment.\\n48. Mathematically, α =\\nE[yi|yi⩾¯\\ny]\\nE[yi−¯\\ny|yi⩾¯\\ny] where ¯\\ny is the threshold over which the\\ntop marginal income tax rate applies.\\n49. Online Appendix F provides a derivation.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1247\\nCombining, and averaging FE obtained using the prereform\\nand postreform tax rates, we obtain FE =\\nτ\\n1 −τ αϵETI = 1.51. This\\nmeans that the 70% marginal tax rate appears to have been on\\nthe “wrong side of the Laffer curve,” so reducing tax rates may\\nhave increased revenue. In other words, the MVPF is infinite and\\nthe tax cut “pays for itself.” However, it is important to note the\\nstatistical uncertainty in this estimate: we cannot reject an MVPF\\nof 1 or ∞.\\nIn contrast, for later reforms we find lower MVPFs. For\\nexample for the 1993 tax increase from 31% to 39.6% we find\\nan MVPF of 1.85 (95% CI of [1.19, 4.07]). This distinction is not\\nbecause of differences in ϵ, but results from the fact that τ was\\nmuch lower in 1993 than it was in 1981.\\nComparison to the “Optimal” Top Tax Rate.\\nTo compare\\nour results to the literature on the “optimal” top tax rates, it is\\nhelpful to consider the case studied in Diamond and Saez (2011)\\nwhere society is assumed to place no weight on the additional\\nconsumption of the rich. If the social welfare weights, ηi, are\\nequal to 0 for top earners, then the optimal tax is set to maximize\\ngovernment revenue: τ is chosen to be at the peak of the Laffer\\ncurve. This occurs when taxes are set so that the net cost to the\\ngovernment of providing a tax cut is 0, or FE = −1.\\nThis approach then makes the additional assumption that\\nthe elasticity, ϵETI, and α do not change when the tax rate changes.\\nSolving for the optimal tax rate then implies τ ∗=\\n1\\n1 + αϵETI .\\nFor α = 2.299 and ϵETI = 0.311, this implies τ ∗= 58%\\ninclusive of state and federal tax rates. The fact that this number\\nis slightly below 70% is consistent with our finding of an infinite\\nMVPF for the 1981 reform, in which tax rates were around\\n70%. In contrast to this optimal tax approach, the MVPF does\\nnot impose an assumption that society places no weight on the\\nconsumption of the rich.\\nIV. MAIN RESULTS: TARGETING KIDS VERSUS ADULTS\\nWe construct the MVPF for each policy in our sample. Here,\\nwe present all our baseline MVPF estimates and outline our\\nmain results. As noted, details on our MVPF constructions are\\nprovided in Online Appendices A–F.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1248\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nFIGURE III\\nMVPF Estimates by Age of Policy Beneficiary\\nThis figure presents MVPF estimates for all policies in our baseline sample. For\\neach MVPF, we plot them as a function of the average age of the policy’s beneficia-\\nries. In cases where both parents and children potentially benefit, we assign the\\nage of the individuals with the highest willingness to pay. Where policies within\\na category have the same age, we stagger these ages around this common value\\nfor visual clarity. On the vertical axis, we report the MVPF estimates, capping\\nthese estimates at 5. We separately report cases where the MVPF is infinite on\\nthe uppermost line in green (shown in color in the online version only).\\nIV.A. Kids\\nWe begin our discussion with the MVPFs of policies targeting\\nchildren. Figure III presents the MVPF for each policy on the\\nvertical axis plotted by the average age of the beneficiaries of the\\npolicy on the horizontal axis.50 Each dot represents the MVPF of\\na particular policy, with labels provided in Table I.\\n50. In cases where both parents and children are beneficiaries of the policy, we\\nassign the age of the “economic” beneficiary based on who has the highest WTP.\\nFor example, when analyzing the Movement to Opportunity (MTO) experiment,\\nwhich provided housing vouchers and counseling to parents with children, the age\\nshown is the average age of the children in the household. This is because the\\npolicy induced higher earnings among the children, leading them to have a higher\\nWTP for the policy than their parents.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1249\\nThe figure reveals our primary result: direct investments in\\nchildren have historically had the highest MVPFs, often paying\\nfor themselves. In addition to the evidence on the Medicaid expan-\\nsions and admission to FIU, we also find high MVPFs for other ed-\\nucation and child health policies. For example, Wherry et al. (2018)\\ndocument that the discontinuous Medicaid coverage eligibility for\\nchildren born after September 30, 1983 led to reduced medical\\ncosts and chronic conditions in adulthood. In Online Appendix D,\\nwe calculate that the up-front costs are fully repaid in the long run\\nfrom reduced Medicaid and uncompensated care costs, leading to\\nan infinite MVPF. More generally, all four major health insurance\\nexpansions to children studied in the past 50 years have MVPFs\\nin excess of 10, with three of them paying for themselves.51\\nIn addition to health policies, we find large MVPFs for edu-\\ncation policies. The widely studied Perry Preschool program has\\nan MVPF of 43.61; the more expensive Abecedarian model has an\\nMVPF of 11.89 (neither of these estimates are statistically distin-\\nguishable from ∞).52 In contrast with the idea that the returns to\\nhuman capital investment diminish rapidly with age (Heckman\\n2006), we find there is potential for high MVPFs investments\\nthroughout childhood. We find an infinite MVPF for increased\\nK–12 spending due to school finance equalization as studied\\nin Jackson, Persico, and Johnson (2016).53 We also find infinite\\nMVPFs for several college policies, such as admissions to FIU and\\n51. The only policy that does not have an infinite MVPF is the introduc-\\ntion of Medicaid. For this policy, we directly incorporate MVPF estimates from\\nGoodman-Bacon (2017). This working paper includes estimated impacts through\\nage 55; our back-of-the-envelope calculations suggest that it is likely that forecast-\\ning these effects through 65 would lead the policy to pay for itself as well.\\n52. To harmonize these estimates with other programs, we do not include the\\nbenefits to the government from reduced crime. This is both because these costs are\\ndifficult to quantify and most papers do not estimate impacts on crime outcomes.\\nIf we include a forecast of reduced government spending on the criminal justice\\nsystem and policing, our point estimates suggest that Perry Preschool paid for\\nitself. However, the standard errors of these estimates also significantly increase.\\nIncluding these costs for Abecedarian also increases its MVPF, but the policy does\\nnot appear to pay for itself.\\n53. It is important to note that we only analyze one paper on K–12 education\\nspending because of limitations in existing evidence on long-term outcomes. While\\nthere is a large literature looking at the effect of school spending on test scores, we\\nlack a reliable method to translate these effects into long-run impacts. Jackson,\\nPersico, and Johnson (2016) demonstrate the potential for high returns to K–12\\neducation, but future work is needed to robustly establish the presence of high\\nreturns to K–12 investment.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1250\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nthe provision of CalGrants to low-income students.54 A key insight\\nof our results is that many policies targeting children do not face\\nthe classic budgetary trade-off. Instead, those expenditures pay\\nfor themselves in the long run.\\nBefore drawing too many conclusions about each data point\\nin Figure III, it is important to note there is sampling uncertainty\\ninherent in our estimates. Figure IV, Panel A plots each MVPF\\nalong with its 95% confidence interval. In some cases, our\\nestimates are relatively precise. For example, both the Medicaid\\nexpansion to pregnant women and infants and admissions to FIU\\nhave confidence intervals that reject any finite MVPF. We can\\nrule out any positive net cost to the government. In many other\\ninstances, however, the conclusions at the individual policy level\\nare less clear due to the sampling variation in the underlying\\nestimates. For example, the 1990 health care expansion to\\nchildren born after September 30, 1983 has a confidence interval\\nranging from 0.26 to infinity. In other words, we cannot with 95%\\nconfidence reject the hypothesis that the policy paid for itself, nor\\ncan we reject the hypothesis that the policy provides much less\\nthan $1 of benefits per dollar of government spending.\\nTo reach more precise conclusions at a broader level, we pool\\nacross policies using category averages. We imagine a new policy\\nthat spends $1 of initial program cost on each policy j in category\\nJ containing NJ policies. We then construct the MVPF of this\\ncategory-average policy as:\\n(8)\\nMVPFJ =\\n1\\nNJ\\n\\u0003\\nj∈J\\nWTP j\\nC j\\n1\\nNJ\\n\\u0003\\nj∈J\\n\\u0005\\n1 + FEj\\nC j\\n\\u0006,\\nwhere the numerator is the average willingness to pay per dollar\\nof program cost and the denominator is the average net cost to\\nthe government of the category-average policy.55\\nFigure IV, Panel B presents the category-average MVPFs.\\nOn average, spending on child education, child health insurance,\\n54. It is important to be clear that although our estimates suggest high returns\\nto policies investing in older youth, the policies in our sample affect a range of\\nsubpopulations. As a result, further work is needed to assess how the rate of\\nreturn on investment varies for a given child over the life cycle.\\n55. We construct this average measure, as opposed to a precision-weighted\\naverage or other measure, because it corresponds to a feasible policy at the time\\nof initial implementation. It is straightforward for the government to construct a\\npolicy that spends an equal amount on each of these programs.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1251\\nFIGURE IV\\nMVPF Estimates and Category Averages with Confidence Intervals\\nPanel A presents the MVPFs and 95% confidence intervals for each policy in our\\nbaseline sample, plotted as a function of the average age of the policy’s beneficia-\\nries. Panel B presents $1 spend domain averages and 95% confidence intervals\\nacross categories of programs, plotted as a function of the average age of each pol-\\nicy’s beneficiaries within a category. Individual policy MVPFs are shown in smaller\\ndots, color-coded to align with their respective categories. In both panels, we report\\nthe MVPF estimates on the vertical axis, capping these estimates at 5 and sepa-\\nrately reporting cases where the MVPF is infinite on the uppermost line in green\\n(shown in color in the online version only). All confidence intervals are 95% boot-\\nstrapped confidence intervals with adjustments discussed in Online Appendix H.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1252\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nFIGURE V\\nNet Government Costs per Dollar of Programmatic Spending\\nThis figure presents estimates of costs normalized by initial programmatic for\\neach category-average group of policies in our baseline sample. We plot these\\nestimates as a function of the average age of each policy’s beneficiaries within\\ncategory. Bootstrapped 95% confidence intervals with adjustments discussed in\\nOnline Appendix H are shown for the category averages. The normalized costs\\nof individual policies are shown in smaller dots, color-coded to align with their\\nrespective categories (shown in color in the online version only).\\nand college policies have historically had high or infinite MVPFs.\\nOne dollar of spending across each of the policies in each of these\\ncategories has an MVPF of ∞in child education (95% CI of [17.8,\\n∞]), ∞in child health (95% CI of [24.8, ∞]), and ∞in college\\npolicies (95% CI of [4.2, ∞]).\\nWe can dig deeper into these category averages by focusing on\\nthe net costs to the government of these policies (the denominator\\nin our formula in equation (8)). Figure V computes the average\\nnet cost to the government per $1 of programmatic expenditure\\nspent evenly across the policies in each category. This allows us\\nto explore the extent to which different types of policies have\\npaid for themselves. For example, $1 invested in the four major\\nMedicaid expansions to children has paid back an estimated\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1253\\n$1.78. In other words, the spending actually generated $0.78 of\\nsurplus to the government in the long run.56\\nHaving established this primary result, it is important to\\nqualify that these patterns do not hold uniformly across policies.\\nThere is considerable variation in MVPFs from policy to policy.\\nFor example, we find lower MVPFs ranging from −0.23 to 1.48 for\\njob-training policies, such as an estimate of 0.15 for Job Corps—\\na program targeted toward at-risk youth.57 We also analyze 14\\nexamples of college policies where the MVPFs fall below 2.58\\nIn most cases, this is because those policies represent trans-\\nfers to existing students, rather than expenditures that increase\\nattainment.59 In some cases, expenditures may even negatively\\naffect student attainment. For example, Cohodes and Goodman\\n(2014) analyze the impact of the Adams Scholarship in Mas-\\nsachusetts. They find that this merit aid program does not induce\\nmore students to go to or complete college. Rather, it induces indi-\\nviduals to change colleges to attend in-state schools where they are\\n56. Analogously, Appendix Figure II presents willingness to pay per dollar of\\nprogrammatic spending. For our baseline WTP measures, we find very similar pat-\\nterns: much higher estimates of\\n1\\nNJ\\n\\u0003\\nj∈J\\nWTP j\\nC j\\nfor child policies than for policies\\ntargeting adults.\\n57. The one potential exception to this is the recent Year Up RCT, analyzed in\\nFein and Hamadyk (2018), who document large increases in earnings in the two\\nyears after initial implementation. As we discuss in Online Appendix C, if these\\nearnings gains persist for an additional 5 years, the MVPF would be 2.78, and if\\nthey persist for 21 years, the MVPF would be infinite. In addition, in estimates\\noutside of our sampling frame, the nine-year follow-up results from the sectoral\\ntraining program Project Quest suggest an MVPF of 1.52, which increases to an\\ninfinite MVPF if projected to age 65. This suggests a high value to future work\\nestimating the continued persistence of these more promising sectoral training\\nprograms.\\n58. Our analysis also demonstrates the limitations of the traditional way that\\nresearch papers report the impact of college expenditures. It is very common for\\npapers to note the percentage point increase in enrollment associated with $1,000\\nin expenditures. The difficulty with that approach is that it doesn’t account for the\\nnumber of inframarginal students receiving the benefit. Providing $1,000 to 10% of\\nthe school-age population to achieve a 3.6 percentage point increase in enrollment\\nmay be a very efficient investment, while providing $1,000 to 80% of the school-\\nage population to achieve a 3.6 percentage point increase is mostly a transfer to\\nexisting students. For this reason, there are cases where we find substantially\\ndifferent MVPFs for policies that had similar percentage point enrollment effects.\\n59. In Section IV.C we discuss how our results on college expenditures vary\\nwith the method of our MVPF calculation. Although we find persistently high\\nMVPFs when long-run earnings outcomes are observed, we find lower MVPFs\\nwhen we project earnings gains from attainment outcomes.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1254\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\neligible to use the scholarship. The change in schooling actually\\nresults in a fall in graduation rates arguably due to switching from\\nmore selective schools with higher graduation rates. Incorporat-\\ning these schooling declines, we calculate that the program has an\\nMVPF of 0.72. Job training or education polices like this one do not\\nsubstantially increase human capital and so they do not recoup\\nmeaningful portions of their initial costs via higher tax revenue.\\nWe also find lower MVPFs for transfers to disabled children,\\nsuch as an MVPF of 0.76 for expanded eligibility for Supplemental\\nSecurity Income (SSI) at age 18 analyzed in Deshpande (2016). It\\nis important to note that spending on these policies may increase\\nsocial welfare, even though they have lower MVPFs. Decisions\\nabout optimal policy are determined by the welfare weights the\\ngovernment places on policy beneficiaries. If the government\\nmakes it a priority to provide support for disabled children, these\\nSSI expansions may be welfare enhancing.\\nIV.B. Adults\\nIn contrast to policies targeting children, we generally find\\nlower MVPFs (e.g., 0.5–2) for policies targeting adults. For\\nexample, in contrast to the nearly infinite MVPFs for child health\\ninsurance expenditures, we find MVPFs ranging from 0.40 to\\n1.63 for the six health insurance policies in our baseline sample\\ntargeted to adults.60 Along the same lines, we find MVPFs ranging\\nfrom 0.43 to 1.03 for unemployment insurance policies, 0.74–0.96\\nfor disability insurance expansions, and 1.12–1.20 for earned\\nincome tax credits. We find MVPFs of housing vouchers ranging\\nfrom 0.65 using assignment of vouchers in Chicago via lottery\\n(Jacob and Ludwig 2012) to 0.91 using an RCT of the provision of\\nhousing vouchers to families on cash welfare (Mills et al. 2006).\\nThe lower MVPFs reflect the fact that many of these expen-\\nditures have been shown to reduce labor earnings through labor\\nmarket distortions. As depicted in Figure V, the average cost per\\n$1 of government spending on these adult policies is generally\\n60. Those adult health insurance estimates include expenditures such as the\\nsubsidies in the Massachusetts health insurance exchange prior to the Affordable\\nCare Act. In that case, Finkelstein, Hendren, and Shepard (2019) exploit discon-\\ntinuities in the subsidy schedule to estimate both individuals’ willingness to pay\\nfor insurance and the cost those individuals impose on the government. Translat-\\ning these estimates into an MVPF suggests values ranging from 0.800 to 1.09 for\\ndifferent subsidy eligibility levels.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1255\\nslightly above $1. This result contrasts with our findings on expen-\\nditures directed toward children, for whom labor market earnings\\ntended to rise, leading to a decline in net costs. There are a limited\\nnumber of cases, such as the Job Training Partnership Act and Na-\\ntional Supported Work Experiment, where investment in adults\\nsought to increase earnings by increasing human capital. Those\\npolicies, however, did not produce persistent earnings gains, so\\nthey still yield relatively low MVPFs.61 The MVPFs of job-training\\nprograms for adults over the age of 23 range from 0.44 to 1.48.62\\nAs with our main results for policies targeting children, these\\nfindings represent general patterns. They do not hold uniformly\\nacross all policies targeting adults. In particular, there are two\\ntypes of adult policies that tend to result in higher MVPFs:\\nreductions of high marginal tax rates for top incomes and policies\\nwith indirect spillovers onto children.\\n1. Top Tax Rates.\\nWe find high MVPF point estimates for his-\\ntorical reductions in the top marginal tax rate when the initial tax\\nrate lay at 50% or higher. In the case of the 1981 reform, the tax bill\\nreduced the top federal marginal tax rate on income from 70% to\\n50%. Using estimates of the elasticity of taxable income from Saez\\n(2003), we calculate that the MVPF is ∞(95% CI of [0.94, ∞]).\\nThis implies that marginal tax rates were beyond the top of the\\nLaffer curve prior to 1981. Our confidence interval, however, sug-\\ngests this estimate contains considerable sampling uncertainty.63\\n61. For this reason, we calculate the MVPFs of job-training programs based\\non the number of years of earnings effects observed, rather than projecting the\\neffects out to age 65. In Online Appendix C we discuss the sensitivity of our results\\nto that assumption.\\n62. The presence of high MVPFs for spending on children and low MVPFs for\\nspending on adults does not necessarily indicate that families are failing to opti-\\nmize their investment decisions. Even if families are fully informed of available\\ninvestment decisions, a simple model of parental investment could produce these\\noutcomes if parents are credit constrained. A higher MVPF for investment in chil-\\ndren could occur if low-income parents expect intergenerational regression to the\\nmean such that their children will earn more than them. That would produce lower\\nmarginal utilities of income for those children, and therefore increase the return\\non spending. In addition, this logic also suggests that when parents are given cash\\ntransfers, they would rationally not spend all of it on their children despite high\\nreturns—this is because their marginal utility of their own consumption is also\\nhigh.\\n63. As we discuss in Online Appendix F, these estimates appear to have consid-\\nerable uncertainty not just from sampling uncertainty but also model uncertainty:\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1256\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nAlong the same lines, we analyzed the 1986 reform and found an\\nMVPF of 44.27, with a confidence interval ranging from 2.37 to ∞.\\nAlthough this may be considered by some to be suggestive\\nevidence for Laffer effects in tax policy, it is important to ap-\\nproach that conclusion with considerable caution. In the case\\nof the 1981 reform our confidence intervals suggest we cannot\\nrule out an MVPF close to 1. In other words, we cannot rule\\nout the conclusion that the policy produced no positive fiscal\\nexternality. Moreover, estimates of the impacts of recent reforms\\nhave produced substantially smaller MVPFs (e.g., 1.16 for the\\n2013 top tax rate increase). Compared with these findings on\\ntaxes, our results suggest stronger evidence for the presence of\\nLaffer effects when investing in young children.\\n2. Spillovers onto Children.\\nWe also find that spending on\\nadults may have high MVPFs if those policies have spillover ef-\\nfects on children. For example, Chetty, Hendren, and Katz (2016)\\nstudy the long-run impact of the MTO experiment, which gave\\nfamilies residing in public housing projects a voucher and coun-\\nseling to assist them in moving to lower-poverty neighborhoods.64\\nChetty, Hendren, and Katz (2016) document that the program\\nsignificantly increased later-life earnings for young children, but\\nthey find null or even slightly negative effects on earnings for\\nchildren who were teenagers at the time their parents obtained\\nthe vouchers. Combining these effects across all subgroups\\nsuggests the effects on the young children outweigh the adverse\\neffects on the older children, leading to an infinite MVPF.65 This\\nusing different taxable income estimates from existing literature studying these\\nreforms can generate wide variation in the MVPFs of these tax reforms, preventing\\nprecise conclusions about their MVPFs.\\n64. Because the program was targeted to families already in public housing\\nand because the cost of public housing is similar to the cost of a voucher, the\\nprimary marginal cost of the program was the cost of the counseling (roughly\\n$3,783 per family).\\n65. Not all policies providing benefits to parents generate such large spillover\\neffects onto children. For example, Price and Song (2018) find that the Nega-\\ntive Income Tax experiment led to a reduction in children’s earnings in adult-\\nhood, which partially explains its low MVPF of −0.01. In other cases, such as\\nthe provision of housing vouchers in Chicago, and the provision of housing vouch-\\ners to families on AFDC and the expansion of AFDC benefits, there is sugges-\\ntive evidence that positive spillovers on children are small. In those cases, re-\\nsearchers have documented that the policies have limited effects on outcomes such\\nas test scores, college attendance, and birthweight. Appendix Figure III, Panel A\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1257\\nhigh MVPF is driven solely by child outcomes, as the policy has\\nno significant effect on economic outcomes for adult beneficiaries.\\nOne policy with a substantial degree of uncertainty about\\npotential\\nspillovers\\nonto\\nchildren\\nis\\nthe\\nEITC.\\nAppendix\\nFigure III, Panel C shows how our MVPF estimates would change\\nif one attempted to impute effects on children using different\\nestimates from previous literature. In particular, we take the\\nMVPF for the 1993 OBRA tax reform and supplement that\\nestimate with spillover effects of the EITC estimated in other\\ncontexts. Projecting earnings effects based on child test scores\\nproduces MVPFs that range from 3.48 to ∞, while incorporating\\neffects on college attendance produces MVPFs from 0.84 to 1.12.66\\nIncorporating the work of Bastian and Michelmore (2018) on\\nlong-term earnings would result in an infinite MVPF, suggesting\\nthat the policy pays for itself.67\\nThis uncertainty highlights the importance of understanding\\nthe potential spillovers onto children. It also reinforces our\\nconclusion that policies raising children’s human capital often\\nhave the highest MVPFs. We return to this issue in Section VI.A,\\nwhere we use the MVPF framework to quantify the value to\\ngovernments of more precise estimates for potential long-run\\neffects of policies on children.\\nIV.C. Robustness\\nCreating these MVPF estimates inevitably requires that we\\nmake a number of judgment calls regarding the set of causal\\neffects included and the methodology used to translate those\\neffects into an MVPF. Here, we provide a short summary of the\\nrobustness of our main conclusions to those assumptions.68\\npresents results for policies in our baseline sample where child effects are observed.\\nPanels B and C show how the MVPFs change when effects on children are incor-\\nporated or removed from the MVPF calculation.\\n66. The college effects are restricted to a small subset of recipients, so it is\\nunsurprising that the MVPFs remain small.\\n67. We exclude these results from the baseline estimates because Bastian and\\nMichelmore (2018) do not estimate the effect of a particular EITC expansion, but\\nrather pool across many state and federal policy changes. In Online Appendix F,\\nwe note the impact of incorporating their estimates. The fact that these impacts\\nmatter is consistent with our broader conclusions that potential spillovers onto\\nchildren can generate high MVPFs for adult-targeted policies.\\n68. Online Appendix J details an extensive set of robustness analyses.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1258\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nConstructing the MVPF for policies with dynamic effects\\nrequires the choice of a discount rate. Although our baseline\\napproach assumes 3%, Appendix Figure IV shows that higher dis-\\ncount rates do not substantively change our conclusions. Discount\\nrates of 7% or 10% produce slightly lower MVPFs for child-\\ntargeted policies (more so for young children), but we still find\\nthose policies have higher MVPFs than policies targeting adults.\\nOur baseline approach uses the cross-sectional life cycle\\nearnings profile to forecast lifetime effects from observed earnings\\nchanges. Our results are robust to alternative methods of fore-\\ncasting earnings, such as assuming no income growth over the life\\ncycle. The baseline sample also includes some policies targeting\\nchildren for which effects on income are not directly measured.\\nMost notably, we include college policies where researchers have\\nobserved a measure of attainment such as initial enrollment,\\ncollege credits, or degree receipt. In those cases we forecast\\nincome impacts using estimates from Zimmerman (2014) on the\\nreturns to college. Online Appendix J provides a discussion of\\nhow our estimates vary depending on the use of intermediate\\noutcomes to construct long-run forecasts. In particular, Appendix\\nFigure III shows the effects of restricting our analysis to policies\\nwhere earnings are directly observed. We continue to find high,\\noften infinite MVPFs for these child-targeted policies.\\nIn many cases, our MVPFs for policies targeting adults rely\\nupon estimates of short-run earnings impacts. Consequently,\\none might be worried that our low MVPFs for adult policies are\\ndriven by policies for which we do not observe long-run impacts.\\nIn order to assess this, Appendix Figure VII, Panel B restricts\\nthe analysis to the subset of policies for which we observe at least\\nfive years of income estimates. We continue to find higher MVPFs\\nfor policies targeting children.69\\nOur baseline willingness to pay approach often relies on\\nmeasures of a policy’s impact on after-tax income. Appendix\\nFigure VI, Panel A reports our MVPFs using our conservative\\n69. Related to this, the pattern of higher MVPFs for children could be driven by\\nlonger payoff periods for children relative to adults, as children have their entire\\nlives to experience higher earnings. However, the length of the payoff period is\\nnot what is driving our results—even restricting child benefits to accrue only up\\nto age 45 or 55, we find similar high returns for child-targeted policies. Rather,\\nthe patterns are generally driven by a higher positive impact on per-year future\\nearnings for policies targeting children.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1259\\nmeasure of willingness to pay. Although the willingness to pay\\nmeasures are much lower, we continue to find high MVPFs for\\npolicies targeting children, generally exceeding 5 on average. This\\nis to be expected as many policies analyzed have very low net costs,\\nleading to large MVPFs even when willingness to pay is small.\\nOne might also be concerned that the causal effects incor-\\nporated in our MVPFs may vary in quality due to variation\\nin the underlying techniques used to produce those estimates.\\nAppendix Figure VII, Panel C shows our results remain the same\\nwhen restricting our sample to policies evaluated via randomized\\ncontrolled trial, lottery, or a regression discontinuity design. The\\nresults are also robust to restricting our sample to peer-reviewed\\npublications. In all these robustness analyses, direct childhood\\ninvestments continue to have the highest MVPFs.\\nFinally, one might worry that MVPFs for child policies were\\nhigh in previous decades but have declined over time—perhaps\\nas the government takes advantage of high-return investments.\\nAppendix Figure IX assesses this by plotting the child- and adult-\\naverage MVPFs separately by decade. We find no evidence for\\nthat pattern of decline. Instead, we find high MVPFs for policies\\ntargeting children throughout the past 50 years.70 The robustness\\nof high MVPFs for direct investments in children over time may\\nsuggest the presence of fundamental political constraints to\\nenacting policies in which the benefits have a long time horizon.71\\nIV.D. Publication Bias\\nAll of the robustness analyses above take the estimates from\\nexisting literature as given. However, one might be concerned that\\nthe research and publication process suffers from the problem\\n70. The one exception to this pattern is the low average MVPF among child\\npolicies implemented in the 1970s. The child policies in that decade primarily\\nconsisted of job-training programs that did not have significant effects on children’s\\nearnings.\\n71. There are a range of forms that these political constraints might take.\\nFor example, it could be that governments (and politicians) apply a much higher\\ndiscount rate, requiring projects to pay off over short horizons. Alternatively, un-\\nderinvestment might occur because these policies require spending by state and\\nlocal governments, but much of the benefits accrue to the federal tax system.\\nHence, local incentives may not be sufficient to make efficient investments. It\\nmay also be that the high MVPF policies are undersupported because low-income\\nchildren have little political power. We leave a formal analysis of these potential\\nmechanisms for future work.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1260\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE III\\nPUBLICATION BIAS ESTIMATION\\nChildren estimates\\nAdult estimates\\n(1)\\n(2)\\n(3)\\n(4)\\n(5)\\n(6)\\nZ > 1.64\\n3.72\\n–\\n2.52\\n–\\n(2.46)\\n(1.32)\\nZ < −1.64\\n1.15\\n–\\n7.90\\n–\\n(0.44)\\n(1.48)\\nZ ∈[1.64, 1.96]\\n3.65\\n1.36\\n(3.46)\\n(1.14)\\nZ ∈[−1.96, −1.64]\\n1.02\\n4.19\\n(0.57)\\n(0.81)\\nZ > 1.96\\n–\\n3.09\\n3.78\\n–\\n3.27\\n3.59\\n(1.09)\\n(2.17)\\n(1.50)\\n(1.21)\\nZ < −1.96\\n–\\n1.21\\n1.24\\n–\\n10.39\\n11.52\\n(0.50)\\n(0.62)\\n(2.53)\\n(2.43)\\nN\\n237\\n237\\n237\\n150\\n150\\n150\\nNotes. The numbers shown are the estimated likelihood ratio of publication relative to an insignificant\\nresult. Standard errors are in parentheses.\\nof publication bias, where studies are published only if they find\\nclear positive (or negative) effects. In particular, one might worry\\nthat research on children is more likely to be published if it finds\\nstatistically significant positive effects on children in adulthood.\\nConversely, one could imagine that research on adults is more\\nlikely to be published if it finds statistically significant evidence\\nof distortionary or negative effects on adult outcomes.\\nTo address this, we implement the approach developed in\\nAndrews and Kasy (2019).72 They provide a method to test\\nand correct for the effect of publication bias on the observed\\nset of estimates. Online Appendix K discusses the details of\\nour implementation of their approach. Table III documents the\\nevidence of publication bias in our estimates.\\nThe results suggest the presence of a moderate degree of\\npublication bias. In the baseline sample, we find studies of child\\noutcomes are 3.7 times more likely to be published if they find\\npositive effects on children with p < .10 relative to a finding of\\nno statistically significant effect. In contrast, we find that studies\\n72. We thank Isaiah Andrews and Max Kasy for their invaluable guidance in\\nimplementing these procedures.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1261\\non adult policies are 11 times more likely to be published if they\\nfind significant distortionary effects on outcomes.\\nDespite evidence of publication bias in our samples, Appendix\\nFigure VIII, Panel A shows that correcting for the observed degree\\nof publication bias in this manner does not affect our conclusion\\nof higher MVPFs for policies targeting children. Although we find\\na slight decrease in the MVPFs for child education policies, such\\nas preschool programs, the general patterns are quite similar\\nto our baseline results. Moreover, Appendix Figure VIII, Panel\\nB shows that even if we assumed that statistically significant\\nestimates of positive effects on children are 35 times73 more likely\\nto be published, our primary conclusions still hold.\\nV. MAPPING THE MVPFS TO THEORY\\nThe MVPF provides an empirical method for evaluating the\\neffectiveness of different policies for improving social welfare.\\nHaving established the key patterns of the data, it is natural\\nto place our empirical results into the context of theoretical\\nliterature on optimal government policy. In this section, we\\noutline how our results speak to that theory.\\n1. Optimal Taxation.\\nTo begin, the MVPF measures the\\nprice of redistributing to different policy beneficiaries. In this\\nsense, the approach is related to a large body of theoretical and\\nempirical optimal tax literature in the spirit of Mirrlees (1971)\\nand Saez (2001).\\nAs previously explained using the Okun’s bucket logic, the\\nratio of MVPFs across two different tax changes measures the\\nprice of moving money between the respective beneficiaries. In\\ngeneral, optimal tax theory suggests that a progressive planner\\nshould be willing to incur efficiency losses to move resources from\\nthe affluent toward the lower regions of the income distribution.\\nThe MVPF provides an empirical means of testing that basic\\nprediction: the MVPF of tax changes should increase with the\\nincome of the beneficiaries.\\nFigure VI, Panel A explores the relationship between the\\nMVPF of each tax policy change we analyze and the income levels\\nof the associated beneficiaries. Consistent with this prediction,\\n73. A publication bias of 35x is the degree of publication bias documented in\\nAndrews and Kasy (2019) for small-sample experimental economics studies.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1262\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nFIGURE VI\\nMVPF by Income of Beneficiaries\\nPanel A shows MVPFs for tax and transfer policies in our baseline sample\\nagainst the income of their economic beneficiaries. Panel B adds in-kind transfers\\nto parents and direct expenditures on children (child education, health, job train-\\ning, and college policies). See Figure III for an explanation of the color scheme. The\\nincome measures should be considered approximations, as not all papers report\\nconsistent measures of incomes of their samples. We include all papers for which\\nwe are able to obtain a measure of income of the beneficiaries, and we attempt\\nto normalize these measures to correspond to a notion of individual income per\\nadult in the household at age 30. All confidence intervals are 95% bootstrapped\\nconfidence intervals with adjustments discussed in Online Appendix H.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1263\\nwe observe an upward slope. For example, the 1993 tax reform\\n(OBRA93) simultaneously raised top marginal tax rates and\\nexpanded the EITC. The MVPF of the increased top tax rates led\\nto an MVPF of 1.85 (95% CI of [1.19, 4.07]), and the expansion\\nof the EITC led to an MVPF of 1.12 (95% CI of [0.82, 1.21]).\\nThis suggests the tax schedule created under the 1993 reform\\nis optimal if one is indifferent to providing $1.85 to top earners\\nversus $1.12 to those on the EITC. To the extent one’s social\\npreferences strictly prefer $1.12 to low earners (or strictly prefer\\n$1.85 to top earners), our results suggest that more progressive\\n(regressive) taxation than the 1993 schedule would be optimal.74\\nAlthough our MVPF estimates for tax changes are loosely\\nconsistent with the preferences of a progressive planner, this is\\nno longer the case when we consider policies targeting children.\\nAs shown in Figure VI, Panel B, there is no clear relationship\\nin our sample between MVPFs and the incomes of beneficiaries\\nwhen including direct investments in children. This means that,\\nhistorically, investments in the next generation have been more\\nefficient than transfers within generations.75\\n2. In-Kind versus Cash Transfers.\\nThe low MVPFs for\\npolicies targeting very low-income households raises the question\\nof whether other methods of redistribution—perhaps through\\nin-kind transfers—can be more effective than cash.76 Figure VII\\n74. Our estimate for the MVPF of the 1993 EITC is based on evidence from\\nMeyer and Rosenbaum (2001) on the fiscal externality associated with the labor\\nsupply responses of single women. It is worth noting, however, that there is con-\\nsiderable debate over the fiscal externalities associated with the EITC. On the\\none hand, several recent papers have argued that reductions in transfers have\\noffset a substantial portion of the cost of historical EITC expansions (Hoynes and\\nPatel 2018; Bastian and Jones 2019). These large fiscal externalities can produce\\ninfinite MVPFs (Bastian and Jones 2019). On the other hand, recent debates have\\nargued that the effects are overstated in the current literature because the impact\\nof the EITC expansions cannot be disentangled from the effects of contemporane-\\nous welfare reforms (Kleven 2019). These conflicting estimates suggest there is a\\nhigh value to future work that reconciles these findings.\\n75. We develop this argument formally in Online Appendix L, where we relate\\nthis logic to the nonexistence of a social welfare function that can rationalize our\\nresults of high MVPFs for low-income children but low MVPFs for low-income\\nadults.\\n76. There is a large theoretical debate on this question, which largely centers\\naround the applicability of the Atkinson-Stiglitz theorem (Atkinson and Stiglitz\\n1976; Hylland and Zeckhauser 1981). When utility satisfies a “weak separability”\\nassumption, one would expect that the MVPF for an in-kind transfer would fall\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1264\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nFIGURE VII\\nMVPF by Income of Beneficiaries: Cash versus In-Kind Transfers\\nThis Figure presents MVPFs as a function of the average income of beneficiaries\\nfor tax and transfer policies (shown in Figure IX, Panel A) combined with our\\nestimates for in-kind transfer policies. The income measures should be considered\\napproximations, as not all papers report consistent measures of incomes of their\\nsamples. We include all papers for which we are able to obtain a measure of\\nincome of the beneficiaries, and we attempt to normalize these measures to\\ncorrespond to a notion of individual income per adult in the household at age\\n30. All confidence intervals are 95% bootstrapped confidence intervals with\\nadjustments discussed in Online Appendix H.\\nadds the MVPF estimates for housing and food subsidies to the\\nestimates provided in Figure VI, Panel A for cash transfers and\\ntax credits. Broadly, we find a pattern consistent with our general\\nresult: in-kind transfers are most effective when they induce\\nspillover effects onto children.\\nFor example, the housing vouchers in Chicago (Jacob and\\nLudwig 2012; Jacob, Ludwig, and Kapustin 2014) and the\\nprovision of Welfare to Work housing vouchers (Mills et al. 2006)\\nfind minimal spillover effects on children. This means that the\\nbelow the MVPF of a cash transfer or tax credit targeted to beneficiaries at the\\nsame income level.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1265\\ndistortionary impact on adults’ earnings leads them to have\\nMVPFs below that of distributionally equivalent tax cuts. In\\ncontrast, the MTO experiment explained previously increased\\nearnings of young children by a sufficient amount to pay for the\\ncost of the in-kind policy (the policy had an infinite MVPF with\\na 95% confidence interval of [−2.80, ∞]). Similarly, the spillover\\neffects onto children for the introduction of food stamps policy\\nleads to an MVPF of 1.04. Both point estimates suggest these\\nin-kind transfers are as efficient or more efficient than cash\\ntransfers as a result of the spillovers onto children.77\\n3. Tagging.\\nThere is a large literature in optimal policy\\ndesign focused on improving efficiency by targeting the right\\nsubset of individuals. In general, this work focuses on the use of\\n“tags”—characteristics of program eligibility that are generally\\nnot manipulable (Akerlof 1978).78 With that in mind, previous\\nliterature has identified recipient age as a potentially valuable\\ntag for optimal government policy. Consistent with that work, we\\nobserve that the MVPFs of certain policies differ substantially\\nbased on the age of the recipients.\\nFor example, our analysis of the MTO experiment finds an\\ninfinite MVPF with a confidence interval of [−2.80, ∞]. That said,\\nthe result masks substantial heterogeneity in the program’s ef-\\nfects. In families with children younger than 12, the MVPF is in-\\nfinite with a confidence interval contained at infinity. In families\\nwith children older than 12, the MVPF is negative, as their point\\nestimates imply a reduction in earnings. Along the same lines, our\\nanalysis of the introduction of food stamps produces an MVPF of\\n1.04. This MVPF is partly buoyed by large positive effects on chil-\\ndren ages 0–5 (Bailey et al. 2019). If we excluded any effects on\\nchildren, the MVPF would fall from 1.04 to 0.54. By contrast, if\\nwe restricted our analysis to families with young children and\\nassumed that causal effects of food stamp introduction remained\\nthe same for that targeted policy, we would find an MVPF of 2.28.\\n77. In relation to the Atkinson-Stiglitz theorem, the violation of the weak\\nseparability assumption for these policies comes not from a short-term change in\\nearnings but from the long-run indirect impact on children.\\n78. If the tag were manipulable, then individuals not intended as beneficiaries\\nof the policy could distort their behavior to obtain the benefit. To the first order,\\nthey would not value the transfer by the envelope theorem, consequently lowering\\nthe MVPF of the policy.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1266\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nDespite this substantial variation in MVPFs by the age\\nof policy recipients, we do not report subgroup-specific MVPFs\\nin our main tables. This is a deliberate choice to restrict our\\nanalysis to policy changes defined by explicit identification\\nconditions established in existing work. Reporting MVPFs for\\nsubgroups requires the additional assumption that the observed\\nbehavioral response to the policy among the relevant subgroup\\nis not impacted by the provision of the policy to other subgroups.\\nAlthough this may be plausible in certain cases, we have no\\ndisciplined way of adjudicating its plausibility across all possible\\npermutations of subgroup analysis. Instead, we highlight the\\npotential for age-specific tagging but refrain from more definitive\\nstatements regarding subgroup-specific welfare impacts.\\nVI. LESSONS FOR FUTURE WORK\\nIn this section, we discuss three implications for future\\neconomic research. First, we show how the MVPF framework\\nfacilitates a straightforward method to quantify the value of\\nfuture work that reduces the statistical uncertainty in our esti-\\nmates. Second, we show the value-added provided by measuring\\nthe MVPF relative to what is provided by a more traditional\\ncost-benefit analysis. Third, we discuss how the intuitions of the\\nMVPF framework might influence future empirical designs. The\\nkey is to design experiments in a way that facilitates measuring\\nwillingness to pay. In particular, we discuss how 27 different\\nwelfare reform programs in the 1980s–90s randomized upwards\\nof 100,000 participants into RCTs, but the nature of the research\\ndesigns makes it infeasible to conduct reliable welfare analysis.\\nVI.A. Value of Information in Evidence-Based Policy Making\\nOur MVPF estimates measure the welfare impact of a\\nrange of government policies. Although it is our hope that these\\nestimates can be useful for a policy maker seeking to conduct\\n“evidence-based” policy, it is quite clear from Figure IV, Panel A\\nthat many of our individual policy estimates contain considerable\\nsampling uncertainty. Here, we show how one can use the MVPF\\nframework to understand the value of future research that\\nreduces the uncertainty in our estimates. The MVPF framework\\nprovides a measure of the value of information because it\\nis a price: it measures the price faced by the government to\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1267\\nredistribute across beneficiaries of different types of policies.\\nA welfare-maximizing government should be willing to pay to\\nreduce the uncertainty in these prices, just as consumers would\\nbe willing to pay to learn the true value of the products they buy.\\nThere are many ways one could conceptualize reducing\\nthe various sources of modeling and sampling uncertainty in\\nour estimates. In this section, we develop a simple approach\\nto measure the value of reducing sampling uncertainty. We\\ndefer an exhaustive treatment to future work. We use this\\nexample to illustrate the value of future research that increases\\nestimate precision, perhaps through improved access to larger\\nadministrative longitudinal data sets.79\\nOur conceptual experiment is organized as follows: suppose\\na policy maker is considering whether to raise revenue to spend\\nan additional $1 on policy j. The policy has a net cost to the\\ngovernment of Gj and a willingness to pay of WTPj per dollar\\nof programmatic cost. The policy maker does not know the true\\nvalues of WTPj and Gj. Instead, we assume she only observes\\nthe estimates,\\nˆ\\nWTP j and ˆ\\nGj, and their sampling distributions.80\\nWe assume the policy maker has an uninformed prior about the\\nimpact of the policy so that the estimated sampling distribution\\nreflects her belief about the policy’s effects.\\nFor simplicity, we assume the policy is financed with a tax\\nchange that targets the same beneficiaries and has an MVPF of\\n1. A budget-neutral policy that increases taxes to spend on policy\\nj has a welfare gain of\\nU\\n\\b\\nWTP j, Gj\\n\\t\\n= WTP j −Gj.\\nIdeally, the policy maker would wish to pursue this policy if and\\nonly if U(WTPj,Gj) > 0 (i.e., the policy increases welfare). In\\npractice, the policy maker only observes estimates and sampling\\ndistributions of these values. We assume these estimates are\\nunbiased but noisy estimates of the truth (e.g., E[ ˆ\\nGj|Gj] = Gj).\\nUtility is linear in WTPj and Gj, so the policy maker will choose\\nthe policy if and only if\\nˆ\\nWTP j > ˆ\\nGj. The expected utility of this\\n79. The focus here is on reducing uncertainty among the observed outcomes of\\neach program. Uncertainty regarding unobserved causal effects remains beyond\\nthe scope of this exercise.\\n80. For simplicity, we assume programmatic costs are known and equal to\\ntheir point estimates.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1268\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nstrategy given the point estimates (\\nˆ\\nWTP j, ˆ\\nGj) is\\nEU Uninf ormed \\u0005\\nˆ\\nWTP j, ˆ\\nGj\\n\\u0006\\n= E\\n\\u0004\\nU\\n\\b\\nWTP j, Gj\\n\\t\\n∗1\\n\\nU\\n\\u0005\\nˆ\\nWTP j, ˆ\\nGj\\n\\u0006\\n> 0\\n\\u000b\\n|W ˆ\\nTPj, ˆ\\nGj\\n\\u0007\\n=\\n\\u0005\\nˆ\\nWTP j −ˆ\\nGj\\n\\u0006\\n∗1\\n\\nˆ\\nWTP j > ˆ\\nGj\\n\\u000b\\n.\\nNow suppose that instead of spending $1 on the policy, the\\npolicy maker can invest a fraction of this dollar, vj, into learning\\nmore about the WTPj and Gj of the policy before making this\\ndecision. We begin by considering a case where spending vj allows\\nthe policy maker to perfectly learn WTPj and Gj before deciding\\nwhether to invest in the policy. Once informed, the government\\nchooses to pursue the policy if and only if U(WTPj, Gj) > 0. Now it\\ncan decide to pursue the policy if and only if the true WTP exceeds\\nthe true costs. In that case, the net utility to the government is\\nU inf ormed \\b\\nWTP j, Gj, v j\\n\\t\\n=\\n\\b\\n1 −v j\\n\\t \\b\\nWTP j −Gj\\n\\t\\n∗1\\n\\f\\nWTP j > Gj\\n\\n−v j,\\nwhere the first term is the surplus from investing the remaining\\nfraction 1 −vj in the policy and the second term is the cost of\\npaying for the information.\\nThe value to the government of learning the true willingness\\nto pay and cost for policy j is the value of vinf o\\nj\\nwhich solves the\\nfollowing equation:\\nE\\n\\u0004\\nU inf ormed \\u0005\\nWTP j, Gj, vinf o\\nj\\n\\u0006\\n|\\nˆ\\nWTP j, ˆ\\nGj\\n\\u0007\\n= EU uninf ormed \\u0005\\nˆ\\nWTP j, ˆ\\nGj\\n\\u0006\\n.\\n(9)\\nHere, vinf o\\nj\\nequates the government’s expected utility in the case\\nwhere it spends vinf o\\nj\\nto receive additional information and the\\ncase where it remains uninformed. The expectation in the left side\\nof equation (9) is taken with respect to the distribution of the true\\nparameters, (WTPj, Gj), given the estimates, (\\nˆ\\nWTP j, ˆ\\nGj). Since\\nwe assume uninformed priors, this distribution is parameterized\\nby the sampling distribution of the estimates. This implicitly\\ndefines vinf o\\nj\\nas the value that makes one indifferent to remaining\\nuninformed versus paying for the information and making a\\ndecision based on it.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1269\\nFIGURE VIII\\nValue of Information\\nThis figure presents the value of information, vinfo, discussed in Section VI.A,\\nfor each policy in our sample as a function of the average age of the policy\\nbeneficiaries. See Figure III for an explanation of the color scheme.\\n1. Results.\\nWe estimate the value of info in equation (9) both\\nfor each individual policy and for our category averages. Figure\\nVIII presents the results of vinf o\\nj\\nfor each policy, j, plotted relative\\nto the age of the policy’s beneficiaries. Broadly, we find the highest\\nvalues of future research for policies with uncertain long-run\\neffects on children. For example, we estimate vinf o\\nFS = $0.50 for\\nthe introduction of food stamps. Moreover, we also find large\\nvalues of information for policies with potential indirect effects on\\nchildren and uncertain effects on adults. We also find large values\\nof information for college subsidies to parents (shown in green;\\ncolor version available online). This reflects the fact that these\\npolicies have highly uncertain effects on college attainment, and\\nsmall increases in attainment can translate into large gains. In\\ncontrast, we find smaller values of information for policies where\\nthe effects have been already precisely estimated. For example,\\nwe find the evidence-based policy maker would be willing to\\npay little to remove the statistical uncertainty in the estimated\\nimpact of disability insurance on labor earnings (e.g., we estimate\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1270\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nthe policy maker is willing to pay $0 to learn the precise impact\\nof assignment to a more lenient disability insurance judge). This\\nlower value of information reflects the relatively high precision\\nof existing estimates in those studies.\\n2. Administrative verus Survey Data: Long-Run Impacts of\\nFood Stamps.\\nOur estimates in Figure VIII report the value\\nof learning the true effect of the policy. In practice, the true\\neffect is never observable. That said, improved access to larger\\nadministrative data sets can help obtain more precise effects\\nof government policies. For example, a policy maker can decide\\nwhether a researcher should use a survey data set for the analysis\\nor obtain access to linked administrative data on the population.\\nTo illustrate this decision, we consider the case of the intro-\\nduction of food stamps discussed in Section III.C. Earlier work\\nby Hoynes and Schanzenbach (2009) used the Panel Study of\\nIncome Dynamics (PSID) survey data set to identify the long-run\\neffect of food stamps on children’s outcomes. More recently, Bailey\\net al. (2019) used linked census data to estimate those effects\\nmore precisely. Here, we imagine that a policy maker is deciding\\nwhether to introduce food stamps based on the existing evidence.\\nConsider the hypothetical example that they know the PSID\\nestimates from Hoynes and Schanzenbach (2009),\\nˆ\\nWTP\\nPSID and\\nˆ\\nFE\\nPSID. Suppose that they can instead invest vCensus to learn the\\nestimates with the same statistical precision as those found in\\nBailey et al. (2019) based on census data. Instead of learning the\\ntrue value of WTP and FE, the policy maker learns\\nˆ\\nWTP\\nCensus\\nand\\nˆ\\nFE\\nCensus. The policy maker will expect these estimates to\\nbe drawn from the PSID sampling distribution but contain the\\nstandard errors found in the census data estimates. The value of\\nlearning the census estimates, vCensus, then solves\\nE\\n\\u0004 \\u0005\\n1 −vCensus\\u0006\\nU\\n\\u0005\\nˆ\\nWTP\\nCensus, ˆ\\nFE\\nCensus\\u0006\\n× 1\\n\\nˆ\\nWTP\\nCensus > 1 −\\nˆ\\nFE\\nCensus\\u000b\\n−vCensus |\\nˆ\\nWTP\\nPSID, ˆ\\nFE\\nPSID\\u0007\\n= U\\n\\u0005\\nˆ\\nWTP\\nPSID, ˆ\\nFE\\nPSID\\u0006\\n1\\n\\nˆ\\nWTP\\nPSID > 1 −\\nˆ\\nFE\\nPSID\\u000b\\n(10)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1271\\nThe left side of equation (10) is the expected value of investing\\nin administrative data at a price vCensus. The right side is the\\nexpected value of the policy if she makes her decision using the\\ninformation in the PSID.\\nWe reconstruct the estimates of the WTP and FE for the\\nintroduction of food stamps using the estimates from Hoynes and\\nSchanzenbach (2009) in place of those in Bailey et al. (2019), nor-\\nmalizing by the mechanical program cost. This yields an infinite\\npoint estimate for our MVPF, and we find a willingness to pay\\nestimate of 6.06 (95% CI of [−12.07, 23.78]) and cost of −0.19 (95%\\nCI of [−5.19, 4.92]). These estimates are notably less precise than\\nthose using the results from Bailey et al. (2019) that use census\\ndata, which generate a WTP of 1.09 (95% CI of [−2.45, 4.55]).\\nPlugging these estimates into equation (10) suggests the\\npolicy maker would be willing to invest $0.24 per dollar of\\ninvestment in the food stamp program to learn the long-run\\nestimates from census data instead of PSID data. This exercise\\nillustrates that if the policy maker only knew the PSID estimates,\\nthere would be a large value in learning additional information\\nbefore making this investment decision.\\nThis is, of course, a stylized exercise. We are imagining a\\npolicy maker that sees the ex post evaluation of a policy prior\\nto making her decision—something that is clearly not feasible.\\nThe goal here is merely to illustrate potential value of expanding\\naccess to administrative data sets that can generate more precise\\nestimates of long-run policy effects.\\nVI.B. Comparison to Benefit-Cost Ratios\\nWhile we focus on computing the MVPF for each policy, the\\nmost common form of welfare analysis in previous literature is\\nbenefit-cost analysis, as in equation (4). With that in mind, we\\ncompare our results to the benefit-cost ratios for the same policies.\\nFigure IX, Panel A plots the benefit-cost ratio for a deadweight\\nloss of φ = 50% as in Heckman et al. (2010) as a function of the\\nage of the beneficiary of the policy. Our general conclusion about\\nthe high returns to investment in children would remain true\\neven if one used a benefit-cost ratio instead of the MVPF. The\\naverage benefit-cost ratio is 4.13 for child education, 5.30 for child\\nhealth, and 6.78 for college policies. In contrast, we find smaller\\nbenefit-cost ratios for adult policies—often less than 1.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1272\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nFIGURE IX\\nComparison to CBA\\nThis figure presents estimates of benefit-cost ratios for all policies evaluated\\nin the article and shows their relationship to the MVPF. The method for calcu-\\nlating these benefit-cost ratios is outlined in Section II. We assume a marginal\\ndeadweight loss of φ = 50% for these calculations. Panel A plots the benefit-cost\\nratio of each policy as a function of the age of the beneficiaries, along with cat-\\negory average estimates and their confidence intervals. The capped lines show\\nthe 95% bootstrapped confidence intervals with adjustments discussed in Online\\nAppendix H. Panel B plots the benefit-cost ratio of each policy as a function of the\\nMVPF estimate for the policy. See Figure III for an explanation of the color scheme.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1273\\nTo directly compare the two methods of welfare analysis,\\nFigure IX, Panel B plots the benefit-cost ratio on the vertical\\naxis (again for φ = 50%) against the MVPF on the horizontal\\naxis. In general, we find a fairly monotonic relationship—policies\\nwith high benefit-cost ratios also have high MVPFs. There are,\\nhowever, some notable distinctions. For example, the Medicaid\\nexpansion to children born after September 30, 1983, has an infi-\\nnite MVPF but a BCR of just 1.37. Similarly, the 1981 top tax rate\\nreduction has an infinite MVPF but a benefit-cost ratio of 1.67. By\\nthe standards of benefit-cost ratios, these policies may not appear\\nall that desirable, even though the MVPF point estimates imply\\nthat they pay for themselves and provide a Pareto improvement.\\nThe difference between the MVPF and benefit-cost ratio in\\nthese cases reflects the fact that the benefit-cost ratio places all\\ncausal effects of the program in the numerator while the MVPF\\nincorporates effects based on their incidence. In particular, the\\nnumerator of the MVPF captures the effects on beneficiaries while\\nthe denominator captures all effects on the government budget.\\nIn measuring the welfare effects of the 1983 Medicaid expansion\\nand the 1981 tax cut, MVPF places all fiscal externalities in\\nthe denominator. The results show us that these policies have\\nsubstantial benefits and limited or no net government cost. In\\nthe benefit-cost ratio framework these reforms would have been\\ninterpreted as high-cost policies with substantial benefits.\\nThe second crucial distinction between the MVPF and benefit-\\ncost ratio is how the two approaches conceptually close the budget\\nconstraint. While the MVPF closes the budget constraint by com-\\nparing MVPFs of different policies (and aggregating using Okun’s\\nbucket as in equation (3)), the same consistency does not exist\\nin the benefit-cost ratio approach. In many cases, benefit-cost\\nanalysis includes no discussion of closing the budget constraint.\\nIn cases where the concept is addressed, it is customary to close\\nthe budget constraint in the same manner regardless of the policy\\ncontext. For example, BCRs in Heckman et al. (2010) and Garc´\\nıa\\net al. (2016) imagine that the policy was funded by an increase\\nin the marginal tax rate that led to a distortion in tax revenue\\nand a deadweight loss of φ. Consequently, the deadweight loss\\nparameter φ in equation (4) is not context dependent.\\nTo see how this matters, consider the 1993 tax reform\\nthat simultaneously raised top marginal income tax rates and\\nexpanded the EITC. One could, in principle, use a benefit-cost\\nratio to evaluate whether the EITC expansion was desirable. As\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1274\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nshown in Figure IX, Panel A, the benefit-cost ratio for the 1993\\nEITC expansion is 0.74 after adjusting for a 50% deadweight\\nloss. The costs exceed the benefits and so, if the government were\\napplying a strict benefit-cost test, we would not expect this policy\\nto be implemented. This is because the hypothetical 50% cost of\\nraising the funds is too large to justify the expenditure.\\nThat said, the goal of the EITC expansion was to provide\\nredistributive benefits to low-income workers. Its MVPF is 1.12,\\nnear the highest among policies targeting adults. Rather than\\nruling this out as a means of redistribution, we can compare\\nthe MVPF of the EITC to the MVPF of a tax increase used to\\nfund this policy. Comparisons of MVPFs correspond to precise\\nstatements of social welfare using Okun’s bucket. As noted, the\\nMVPF point estimate for the 1993 top tax rate change is 1.85. If\\nsociety prefers giving $1.12 to a low-income worker on EITC to\\ngiving $1.85 to a high-income individual facing the top marginal\\nincome tax rate, then the policy is welfare enhancing despite its\\nrelatively low benefit-cost ratio.\\nVI.C. Welfare Reform: Lessons for Future RCTs\\nWe end with a lesson of how an MVPF perspective can help\\ninform the design of RCTs. Throughout, we aimed to include all\\npossible MVPFs in the categories we considered. We included any\\npolicy where we thought we could provide reasonable measures\\nof both costs and WTP. One set of notable omissions are the state-\\nlevel welfare reforms made by states that sought to increase fam-\\nily self-sufficiency. Throughout the 1980s and early 1990s, states\\nexperimented with a range of reforms to cash welfare programs\\nthat imposed term limits, provided job training and other educa-\\ntional services, and provided job search and placement assistance.\\nThe omission of these reforms is not because they were not\\nanalyzed. Many states rigorously evaluated the effect of these\\nreforms. Upward of 100,000 participants were enrolled into 27\\nRCTs nationwide (Greenberg, Deitch, and Hamilton 2010). These\\nRCTs measured and provided a clear estimate of the net cost\\nof each reform. However, the design of the policies enacted in\\neach state makes it difficult to understand their welfare effects.\\nGenerally, programs contained both a carrot and a stick.81 As\\n81. Welfare reform experiments were expected to place no additional costs on\\nthe federal government and so it is natural that states bundled increases in some\\ntypes of financial support with potential decreases in others.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1275\\na result, we cannot even accurately sign the WTP. As noted by\\nManpower Demonstration Research Corporation (MDRC) who\\nimplemented the evaluations of these policies,82 “all [programs]\\ncontained a core quid pro quo arrangement in which the gov-\\nernment would offer education, training, job search assistance,\\nand support services to people receiving cash welfare, while\\nmost recipients—the majority of them single parents—would be\\nrequired to participate in such services in order to qualify for\\nbenefits.” Although we can evaluate whether the government\\nsaved money, we do not know if the people in these programs\\nbenefited from their participation. It may be that government\\nrevenue gains were the result of expanded job opportunities due\\nto program participation. In that case, willingness to pay would\\nbe positive. By contrast, it may be that the government revenue\\ngains were the result of stricter attendance requirements that\\ndrove individuals off welfare. In that case, willingness to pay\\nwould be negative.83\\nThis highlights the value of isolating the carrot and the stick\\ninto separate RCTs.84 It also demonstrates the value of designing\\nexperiments to estimate individual WTP for nonmarket goods\\nsuch as job training, job search assistance, or other educational\\npolicies. In Appendix Figure X, we conduct a range of bounding ex-\\nercises that attempt to construct lower and upper bounds on WTP\\nfor these welfare reform programs. Unfortunately, the bounds\\nare very wide. In many cases, the policies are Pareto dominated,\\nMVPF < 0, under one set of assumptions and represent a Pareto\\nimprovement, MVPF = ∞, under another set of assumptions.85\\nDespite substantial expenditures on the evaluation of these re-\\nforms, the designs of these reforms in each state make it difficult\\n82. See https://www.mdrc.org/project/evaluations-state-welfare-work-\\nprograms#design-site-data-sources (accessed on July 7, 2019).\\n83. Previous work (Greenberg, Deitch, and Hamilton 2010) has conducted a\\ncost-benefit analysis of these reforms by assuming willingness to pay is given by\\nafter-tax earnings. However, if the term limit is what causes individuals to choose\\nto move off of welfare and into the labor market (thus increasing earnings), the\\nenvelope theorem would suggest the WTP is negative, even if after-tax earnings\\nincrease.\\n84. Welfare reform RCTs have been criticized for not experimentally varying\\neach of the components of welfare reform (see Grogger and Karoly 2005). The\\nMVPF framework suggests bundling carrots and sticks into a single treatment is\\nparticularly problematic for conducting welfare analysis, because it is difficult to\\nknow even whether willingness to pay is positive or negative.\\n85. In fact, we find policies that follow this pattern in each subcategory of\\nwelfare reform programs. These subcategories include job search assistance.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1276\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nto know whether this massive shift in providing welfare benefits\\nto low-income families led to an increase or decrease in welfare.\\nVII. CONCLUSION\\nIn this article, we examine the MVPF of 133 different histori-\\ncal policies over the past half-century in the United States. We find\\na clear and persistent pattern that direct investments in children\\nhave yielded the largest MVPFs. There is a large “bang for the\\nbuck” associated with a range of expenditures on children from\\nearly education to child health insurance to college expenditures.\\nWe also demonstrate that in a meaningful number of cases,\\nthese policies pay for themselves. In particular, when government\\nexpenditures boost human capital, the resulting increase in\\nnet government revenue can offset the policy’s up-front costs.\\nFrom a taxpayer perspective, these expenditures on children are\\ninvestments, rather than just transfers.\\nWe find that opportunities for high-return investments in\\nchildren have persisted across policy categories for many decades.\\nThis is, however, no guarantee that all future investment in these\\ncategories will produce high MVPFs. Indeed, we find that MVPFs\\nvary substantially within policy categories. Low-return policies\\nexist even in high-return categories. This highlights the value of\\nfurther understanding the mechanisms behind the high MVPFs\\nof successful historical investments.\\nEven in cases where there is existing research, much remains\\nunknown about the welfare consequences of government policy. To\\nthat aim, we quantify the value of future work that uses new data\\nto reduce estimate uncertainty. We show that in many cases, an\\nevidence-based policy maker seeking to maximize social welfare\\nshould be willing to make substantial budgetary expenditures to\\nlearn more about policy effectiveness. In particular, our results\\nhighlight the value of expanded use of administrative data for\\npolicy analysis.\\nThe 133 policies included in this article are just a small subset\\nof those that could be analyzed using the MVPF. We do not discuss\\nthe MVPF of crime policies, environmental policies, macroeco-\\nnomic stabilization policies, or infrastructure policies, among\\nmany others. With careful tracking of willingness to pay and net\\ncosts, the MVPF can be used in any of these contexts and can guide\\ncost-benefit analyses. We leave that analysis for future work.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1277\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nHead Start Introduction\\nHead Start\\n1965\\n4\\nx\\nx\\nx\\nJohnson and Jackson (2019)\\nHead Start Regression\\nHead\\n1970\\n4\\nx\\nLudwig and Miller (2007)\\nDiscontinuity\\nStart RD\\nHead Start\\nHead\\n2002\\n3\\nx\\nx\\nKline and Walters (2016)\\nImpact Study\\nStart RCT\\nK–12 School\\nK12\\n1991\\n11\\nx\\nx\\nx\\nHyman (2017)\\nFinance Reform\\nSpend\\nK–12 School\\nK12 Spend\\n1994\\n11\\nx\\nHeckman et al. (2010)\\nSpending in Michigan\\nMich.\\nPerry Preschool Program Perry Preschool\\n1962\\n4\\nx\\nx\\nx\\nHeckman et al. (2011)\\nCollege adult\\nAmerican Opportunity\\nAOTC (IS)\\n2011\\n25\\nx\\nx\\nBulman and Hoxby (2015)\\nTax Credit,\\nIndependent Single\\nFilers at Phase Start\\nAmerican Opportunity\\nAOTC (JE)\\n2011\\n55\\nx\\nx\\nBulman and Hoxby (2015)\\nTax Credit, Joint Filers\\nat Phase End\\nAmerican Opportunity\\nAOTC (JS)\\n2011\\n20\\nx\\nx\\nBulman and Hoxby (2015)\\nTax Credit,\\nJoint Filers at\\nPhase Start\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1278\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nAmerican Opportunity\\nAOTC (SI)\\n2009\\n20\\nx\\nx\\nBulman and Hoxby (2015)\\nTax Credit,\\nSimulated Instrument\\nAmerican Opportunity\\nAOTC (SE)\\n2011\\n55\\nx\\nx\\nBulman and Hoxby (2015)\\nTax Credit,\\nSingle Filers at\\nPhase End\\nAmerican Opportunity\\nAOTC (SS)\\n2011\\n20\\nx\\nx\\nBulman and Hoxby (2015)\\nTax Credit,\\nSingle Filers at\\nPhase Start\\nHope Tax Credit\\nHOPE Cred.\\n1999\\n20\\nx\\nx\\nTurner (2011)\\nHope Tax Credit,\\nHTC (IS)\\n2007\\n25\\nx\\nx\\nBulman and Hoxby (2015)\\nIndependent Single\\nFilers at Phase Start\\nHope Tax Credit,\\nHTC (JE)\\n2007\\n20\\nx\\nx\\nBulman and Hoxby (2015)\\nJoint Filers at Phase End\\nHope Tax Credit,\\nHTC (JS)\\n2007\\n20\\nx\\nx\\nBulman and Hoxby (2015)\\nJoint Filers at\\nPhase Start\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1279\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nHope Tax Credit,\\nHTC (SE)\\n2007\\n20\\nx\\nx\\nBulman and Hoxby (2015)\\nSingle Filers at\\nPhase End\\nHope Tax Credit, Single\\nHTC\\n2007\\n55\\nx\\nx\\nBulman and Hoxby (2015)\\nFilers at Phase Start\\n(SS)\\nHope and Lifetime\\nHOPE/LLC\\n1998\\n55\\nx\\nx\\nLong (2004)\\nLearners Tax Credits\\nPell Grants\\nAdult\\n1973\\n28\\nx\\nx\\nSeftor and Turner (2002)\\nIntroduction to Adults\\nPell\\nTax Deduction for Postsecondary\\nTuition\\n2006\\n55\\nx\\nx\\nHoxby and Bulman (2016)\\nTuition, Joint Filers at Phase End\\nDeduc (JE)\\nLaLumia (2012)\\nTax Deduction for Postsecondary\\nTuition\\n2006\\n55\\nx\\nx\\nHoxby and Bulman (2016)\\nTuition, Joint Filers at Phase Start\\nDeduc (JS)\\nLaLumia (2012)\\nTax Deduction for Postsecondary\\nTuition\\n2006\\n55\\nx\\nx\\nHoxby and Bulman (2016)\\nTuition, Single Filers at Phase End\\nDeduc (SE)\\nLaLumia (2012)\\nTax Deduction for Postsecondary\\nTuition\\n2006\\n20\\nx\\nx\\nHoxby and Bulman (2016)\\nTuition, Single Filers at Phase Start Deduc (SS)\\nLaLumia (2012)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1280\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nCollege child\\nCal Grant, GPA Threshold\\nCal Grant GPA\\n1998\\n20\\nx\\nx\\nx\\nBettinger et al. (2019)\\nCal Grant, Income Threshold\\nCal Grant Inc\\n1998\\n20\\nx\\nx\\nx\\nBettinger et al. (2019)\\nCity University of New York\\nCUNY\\n2009\\n20\\nx\\nx\\nMarx and Turner (2018)\\nPell Grants\\nPell\\nCommunity College Tuition\\nCC Mich\\n2005\\n20\\nx\\nx\\nActon (2018)\\nChanges, Michigan\\nCommunity College Tuition\\nCC\\n2005\\n20\\nx\\nx\\nDenning (2017)\\nChanges, Texas\\nTexas\\nDistrict of Columbia Tuition\\nDC\\n1999\\n20\\nx\\nx\\nAbraham and Clark (2006)\\nAssistance Grant Program\\nGrant\\nFlorida International University\\nAdmissions at GPA Threshold\\nFIU GPA\\n1999\\n20\\nx\\nx\\nx\\nZimmerman (2014)\\nFlorida Student Access Grant\\nFlorida Grant\\n2001\\n20\\nx\\nx\\nCastleman and Long (2016)\\nFree Application for Federal\\nFree FAFSA\\n2008\\n20\\nx\\nU.S. Department of Education\\n(Dep)\\nOffice of Postsecondary\\nStudent Aid, Dependent Year\\nImpact\\nEducation (2010)\\nBettinger et al. (2012)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1281\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended\\nEstimates\\nUtilized\\nMVPF\\nFree Application\\nFree FAFSA\\n2008\\n20\\nx\\nU.S. Department\\nfor Federal Student Aid,\\n(Indep)\\nof Education Office\\nIndependent Year\\nof Postsecondary\\nImpact\\nEducation (2010)\\nBettinger et al. (2012)\\nGeorgia HOPE Scholarship\\nGeorgia HOPE\\n1995\\n20\\nx\\nx\\nCornwell et al. (2003)\\nCornwell et al. (2006)\\nHAIL Michigan Aid\\nAwareness Letter\\nHAIL Aid\\n2016\\n20\\nx\\nDynarski et al. (2018)\\nHoekstra (2009)\\nKalamazoo Promise\\nScholarship\\nKalamazoo\\n2006\\n20\\nx\\nx\\nBartik et al. (2016)\\nBartik et al. (forthcoming)\\nMassachussetts Adams\\nScholarship\\nMA Scholarship\\n2005\\n20\\nx\\nx\\nCohodes and Goodman (2014)\\nGoodman (2008)\\nPell Grants in Ohio\\nOhio Pell\\n2000\\n19\\nx\\nx\\nBettinger (2004)\\nPell Grants\\nTN Pell\\n2008\\n20\\nx\\nx\\nU.S. Department of Education\\nin Tennessee\\nOffice of Postsecondary\\nEducation (2010)\\nCarruthers and Welch (2019)\\nPell Grants in Texas\\nTexas Pell\\n2008\\n20\\nx\\nx\\nx\\nDenning et al. (2019)\\nSocial Security Student\\nBenefit Program\\nSoc Sec College\\n1982\\n20\\nx\\nx\\nDynarski (2003)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1282\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented\\nBeneficiaries\\nBaseline\\nRestricted\\nExtended\\nEstimates\\nUtilized\\nMVPF\\nSpending at Colleges from State\\nAppropriations\\nCollege Spend\\n2001\\n20\\nx\\nx\\nDeming and Walters (2017)\\nTennessee HOPE Scholarships\\nTN Hope\\n2008\\n20\\nx\\nx\\nBruce and Carruthers (2014)\\nTuition Cuts at Colleges from\\nState Appropriations\\nCollege Tuition\\n2001\\n20\\nx\\nx\\nDeming and Walters (2017)\\nWisconsin Scholar Grant to\\nLow-Income College Students\\nWI Scholarship\\n2009\\n20\\nx\\nx\\nGoldrick-Rab et al. (2016)\\nJob training\\nJob Corps\\nJob Corps\\n1995\\n19\\nx\\nx\\nx\\nSchochet et al. (2006, 2008)\\nSchochet (2018)\\nJob Training Partnership Act,\\nAdults\\nJTPA Adult\\n1988\\n34\\nx\\nx\\nx\\nBloom et al. (1997)\\nJob Training Partnership Act,\\nYouth\\nJTPA Youth\\n1988\\n19\\nx\\nx\\nx\\nBloom et al. (1997)\\nJobStart\\nJobStart\\n1986\\n19\\nx\\nx\\nx\\nCave et al. (1993)\\nNational Supported Work\\nDemonstration, Adult Women\\nNSW Women\\n1976\\n34\\nx\\nx\\nx\\nHollister, Kemper, and Maynard (1984)\\nCouch (1992)\\nNational Supported Work\\nDemonstration, Ex-Addicts\\nNSW Ex-Addict\\n1976\\n33\\nx\\nx\\nx\\nHollister, Kemper, and Maynard (1984)\\nNational Supported Work\\nDemonstration, Ex-Offenders\\nNSW Ex-Offender\\n1976\\n33\\nx\\nx\\nx\\nHollister, Kemper, and Maynard (1984)\\nNational Supported Work\\nDemonstration, Youth\\nNSW Youth\\n1976\\n18\\nx\\nx\\nx\\nHollister, Kemper, and Maynard (1984)\\nCouch (1992)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1283\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented\\nBeneficiaries\\nBaseline\\nRestricted\\nExtended\\nEstimates\\nUtilized\\nMVPF\\nWork Advance\\nWork Advance\\n2012\\n34\\nx\\nx\\nx\\nSchaberg (2017)\\nHendra et al. (2016)\\nYear Up\\nYear Up\\n2013\\n21\\nx\\nx\\nx\\nFein and Hamadyk (2018)\\nPanel B: Social insurance\\nDisability ins.\\nDisability Insurance\\nChanges in Benefit\\nGenerosity\\nDI Generosity\\n2004\\n50\\nx\\nx\\nx\\nGelber, Moore, and Strand (2017)\\nDisability Insurance\\nJudge Leniency\\nDI Judge\\n2005\\n47\\nx\\nx\\nx\\nMaestas, Mullen, and Strand (2013)\\nGelber, Moore, and Strand (2017)\\nDisability Insurance\\nDI Examiner\\n1995\\n48\\nx\\nx\\nx\\nGelber, Moore, and Strand (2017)\\nMedical Examiner\\nFrench and Song (2014)\\nLeniency\\nDisability Insurance to\\nVeterans\\nDI Veterans\\n2001\\n53\\nx\\nx\\nx\\nAutor et al. (2016)\\nHealth adult\\nHealth Insurance\\nMass HI\\n2011\\n44\\nx\\nx\\nx\\nHendren (2017c)\\nSubsidies in\\n(150%FPL)\\nFinkelstein, Hendren, and\\nMassachusetts to Indi-\\nShepard (2019)\\nviduals at 150% of the\\nFederal Poverty Line\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1284\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nHealth Insurance\\nMass HI (200%FPL)\\n2011\\n44\\nx\\nx\\nx\\nHendren (2017c)\\nSubsidies in\\nFinkelstein, Hendren, and\\nMassachusetts to\\nShepard (2019)\\nIndividuals at 200% of the\\nFederal Poverty Line\\nHealth Insurance Subsidies Mass HI (250%FPL)\\n2011\\n44\\nx\\nx\\nx\\nHendren (2017c)\\nin Massachusetts to\\nFinkelstein, Hendren, and\\nIndividuals at 250% of the\\nShepard (2019)\\nFederal Poverty Line\\nMedicare Introduction\\nMedicare\\n1965\\n78\\nx\\nx\\nx\\nU.S. Census Bureau (1966)\\nin 1965\\nIntro\\nFinkelstein and McKnight (2008)\\nOregon Health Insurance\\nOregon\\n2008\\n42\\nx\\nx\\nx\\nFinkelstein et al. (2012)\\nExperiment (Provided to\\nHealth\\nFinkelstein, Hendren, and\\nSingle Adults)\\nLuttmer (2019)\\nTaxation of Medigap\\nPolicies\\nMedigap Tax\\n2002\\n75\\nx\\nx\\nx\\nCabral and Mahoney (2019)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1285\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended\\nEstimates\\nUtilized\\nMVPF\\nHealth child\\nMedicaid Expansion to\\nMC\\n1990\\n11\\nx\\nx\\nx\\nLo Sasso and Seamster (2007)\\nChildren Born after\\nChild 83+\\nWherry and Meyer (2016)\\nSeptember 30, 1983\\nWherry et al. (2018)\\nMedicaid Expansions to\\nMC Pregnant &\\n1986\\n0\\nx\\nx\\nx\\nDave et al. (2015)\\nPregnant Women &\\nInfants\\nCurrie and Gruber (1996)\\nInfants\\nMiller and Wherry (2019)\\nMedicaid Expansions to\\nMC Child\\n1986\\n9\\nx\\nx\\nx\\nBoudreaux, Golberstein, and McAlpine (2016)\\nYoung Children\\n(State Exp)\\nBrown, Kowalski, and Lurie (2017)\\nMedicaid Introduction to\\nMC\\n1968\\n9\\nx\\nx\\nx\\nx\\nGoodman-Bacon (2017)\\nAFDC-eligible Families\\nIntro\\nSupplemental Security\\nIncome\\nSupplemental Security\\nIncome Age 18\\nSSI\\nReview\\n1996\\n18\\nx\\nx\\nx\\nx\\nDeshpande (2016)\\nMedical Review\\nSupplemental Security\\nSSI\\n2005\\n48\\nx\\nx\\nx\\nDeshpande (2016)\\nIncome Medical\\nJudge\\nFrench and Song (2014)\\nExaminer Leniency\\nGelber, Moore, and Strand (2017)\\nU.S. Social Security Administration (2014)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1286\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended\\nEstimates\\nUtilized\\nMVPF\\nUnemployment insurance\\nUnemployment Insurance\\nBenefit Changes (Diff in\\nDiff Across States in\\nChetty 2008)\\nUI Ben\\n(State Max)\\n1992\\n37\\nx\\nx\\nx\\nChetty (2008)\\nGruber (1997)\\nHendren (2017b)\\nSchmieder and Von Wachter\\n(2016)\\nUnemployment Insurance\\nBenefit Changes (Diff in\\nDiff Across States in Katz\\nand Meyer 1990)\\nUI Ben\\n(DD)\\n1980\\n33\\nx\\nx\\nx\\nGruber (1997)\\nHendren (2017b)\\nKatz and Meyer (1990)\\nSchmieder and Von Wachter\\n(2016)\\nUnemployment Insurance\\nUI Ben\\n1992\\n37\\nx\\nx\\nx\\nGruber (1997)\\nBenefit Changes (Diff in\\n(DD w UR)\\nHendren (2017b)\\nDiff Across States in Kroft)\\nKroft and Notowidigdo (2016)\\nand Notowidigdo 2016)\\nSchmieder and Von Wachter\\n(2016)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1287\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended\\nEstimates\\nUtilized\\nMVPF\\nUnemployment Insurance\\nBenefit Changes in Georgia\\nUI Ben\\n1979\\n42\\nx\\nx\\nx\\nGruber (1997)\\n(GA)\\nHendren (2017b)\\nSchmieder and Von Wachter\\n(2016)\\nSolon (1985)\\nUnemployment Insurance\\nBenefit Changes in Missouri\\n(Expansion Estimates)\\nUI Ben\\n2005\\n42\\nx\\nx\\nx\\nCard et al. (2015)\\n(MO Exp)\\nGruber (1997)\\nHendren (2017b)\\nSchmieder and Von Wachter\\n(2016)\\nUnemployment Insurance\\nUI Ben\\n2010\\n42\\nx\\nx\\nx\\nCard et al. (2015)\\nBenefit Changes in Missouri\\n(MO Rec)\\nGruber (1997)\\n(Recession Estimates)\\nHendren (2017b)\\nSchmieder and Von Wachter\\n(2016)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1288\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nUnemployment Insurance\\nBenefit Changes in\\nNew York\\nUI Ben\\n(NY)\\n1989\\n42\\nx\\nx\\nx\\nGruber (1997)\\nHendren (2017b)\\nMeyer and Mok (2007)\\nSchmieder and Von Wachter (2016)\\nUnemployment Insurance\\nBenefit Changes via\\nRegression Kink in\\nBenefit Schedule\\nUI Ben\\n1980\\n34\\nx\\nx\\nx\\nGruber (1997)\\n(RK)\\nHendren (2017b)\\nLandais (2015)\\nSchmieder and Von Wachter (2016)\\nUnemployment Insurance\\nDuration Extensions (Diff\\nin Diff Across States in\\nKatz and Meyer 1990)\\nUI Dur\\n1980\\n33\\nx\\nx\\nx\\nGanong and Noel (2019)\\n(DD)\\nGruber (1997)\\nHendren (2017b)\\nKatz and Meyer (1990)\\nSchmieder and Von Wachter (2016)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1289\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended\\nEstimates\\nUtilized\\nMVPF\\nUnemployment Insurance\\nDuration Extensions in\\nMissouri\\nUI Dur\\n2011\\n42\\nx\\nx\\nx\\nGanong and Noel (2019)\\n(MO)\\nGruber (1997)\\nHendren (2017b)\\nJohnston and Mas (2018)\\nSchmieder and Von Wachter (2016)\\nPanel C: In-kind transfers\\nHousing vouchers\\nEffects of Housing Vouchers\\nHCV RCT\\n2000\\n31\\nx\\nx\\nJacob and Ludwig (2012)\\non AFDC Families Experiment\\nto Welfare\\nMills et al. (2006)\\nWood, Turnham, and Mills (2008)\\nHousing Vouchers\\nHCV\\n1997\\n31\\nx\\nx\\nJacob and Ludwig (2012)\\nin Chicago\\nChicago Lottery\\nJacob, Ludwig, and Kapustin (2014)\\nJobs Plus\\nJobs+\\n1998\\n35\\nx\\nBloom, Riccio, and Verma (2005)\\nRiccio (2006)\\nMTO\\nMoving to Opportunity\\nExperiment Providing\\nVouchers and Counseling\\nMTO\\n1996\\n10\\nx\\nx\\nx\\nChetty, Hendren, and Katz (2016)\\nGoering et al. (1999)\\nSanbonmatsu et al. (2011)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1290\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended\\nEstimates\\nUtilized\\nMVPF\\nNutrition\\nSpecial Supplemental\\nWIC\\n1975\\n26\\nx\\nBlack, Devereux, and Salvanes (2007)\\nNutrition Program for\\nHoynes, Page, and Stevens (2011)\\nWomen, Infants, and\\nWhitmore (2002)\\nChildren\\nSupplemental Nutrition\\nAssistance Program\\nApplication Assistance\\nSNAP Assist\\n2016\\n69\\nx\\nx\\nx\\nx\\nFinkelstein and Notowidigdo (2019)\\nSupplemental Nutrition\\nAssistance Program\\nApplication\\nInformation\\nSNAP Info\\n2016\\n69\\nx\\nx\\nx\\nx\\nFinkelstein and Notowidigdo (2019)\\nSupplemental Nutrition\\nAssistance Program\\nIntroduction\\nSNAP Intro\\n1968\\n32\\nx\\nx\\nx\\nHoynes, Schanzenbach, and Almond (2016)\\nAlmond, Hoynes, and Schanzenbach (2011)\\nBailey et al. (2019)\\nHoynes, Page, and Stevens (2011)\\nHoynes and Schanzenbach (2012)\\nEast (2018)\\nFinkelstein and Notowidigdo (2019)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1291\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nPanel D: Taxes and cash transfers\\n1986 Earned Income\\nEITC 1986\\n1986\\n28\\nx\\nx\\nx\\nAckerman, Holtzblatt, and Masken (2009)\\nTax Credit Expansion\\nTax Policy Center (2016)\\nBlank and Ruggles (1996)\\nHotz and Scholz (2003)\\nMeyer and Rosenbaum (2001)\\nMoffitt (2002)\\nScholz (1993)\\nCrouse and Waters (2014)\\nEissa and Hoynes (2004)\\nEissa and Liebman (1996)\\n1993 Earned Income\\nEITC 1993\\n1993\\n29\\nx\\nx\\nx\\nTax Policy Center (2016)\\nTax Credit Expansion\\nHotz and Scholz (2003)\\nDahl and Lochner (2012)\\nMeyer and Rosenbaum (2001)\\nBastian and Michelmore (2018)\\nChetty, Friedman, and Rockoff (2011)\\nCrouse and Waters (2014)\\nEissa and Hoynes (2004)\\nHoynes and Patel (2018)\\nManoli and Turner (2018)\\nMaxfield (2018)\\nMichelmore (2013)\\nMeyer and Rosenbaum (2001)\\nAckerman, Holtzblatt, and Masken (2009)\\nCurrie and Cole (1993)\\nMoffitt (2003)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1292\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nAid to Families with\\nAFDC Term Limits\\n1996\\n27\\nx\\nx\\nx\\nGrogger (2003)\\nDependent Children (Term\\nLimit Modifications)\\nPavetti (1995)\\nAlaska Permanent Fund\\nAlaska UBI\\n1998\\n34\\nx\\nx\\nx\\nAckerman, Holtzblatt, and Masken (2009)\\nDividend\\nBhargava and Manoli (2015)\\nBlank and Ruggles (1996)\\nHotz and Scholz (2003)\\nJones and Marinescu (2018)\\nMeyer and Rosenbaum (2001)\\nMoffitt (2002)\\nPaycheck Plus Experiment\\nProviding EITC-benefits to\\nAdults without Dependents\\nPaycheck+\\n2013\\n35\\nx\\nx\\nx\\nMiller et al. (2017)\\nSeattle-Denver Income\\nNeg Inc Tax\\n1971\\n35\\nx\\nx\\nx\\nPrice and Song (2018)\\nMaintenance Experiment\\nU.S. Social Security Administration (2018)\\nTax Foundation (2013)\\nU.S. Department of Health\\nHuman Services (1983)\\nVon Wachter, Song, and Manchester (2011)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1293\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended\\nEstimates\\nUtilized\\nMVPF\\nTop taxes\\nTop Tax 2013 Increases\\nfrom Affordable Care Act\\nTop Tax 2013\\n2013\\n49\\nx\\nx\\nx\\nKawano, Weber, and\\nWhitten (2016)\\nHendren (2017a)\\nTop Tax Rate Increase in\\nTop Tax 1993\\n1993\\n49\\nx\\nx\\nx\\nAtkinson, Piketty, and Saez (2011)\\nOmnibus Budget\\nReconciliation Act 1993\\nCarroll (1998)\\nTop Tax Rate Reductions\\nTop Tax 1986\\n1986\\n49\\nx\\nx\\nx\\nAtkinson, Piketty, and Saez (2011)\\nin Tax Reform Act of 1986\\nAuten and Caroll (1999)\\nTop Taxes, Economic\\nTop Tax 2001\\n2001\\n49\\nx\\nx\\nx\\nAtkinson, Piketty, and Saez (2011)\\nGrowth and Tax Relief\\nReconciliation Act 2001\\nHeim (2009)\\nTop Taxes, Economic\\nTop Tax 1981\\n1981\\n49\\nx\\nx\\nx\\nAtkinson, Piketty, and Saez (2011)\\nRecovery Tax Act 1981\\nSaez (2003)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1294\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nPanel E: Welfare reform\\nWelfare to Work Alameda\\nGAIN Alm.\\n1988\\n31\\nx\\nFreedman et al. (1996)\\nMandatory Mixed-\\nInitial-Activity Programs\\nGreenberg, Deitch, and Hamilton (2010)\\nWelfare to Work Atlanta\\nHCD NEWWS Atl.\\n1992\\n33\\nx\\nGreenberg, Deitch, and Hamilton (2010)\\nMandatory Education-\\nFirst Programs\\nHamilton et al. (2001)\\nWelfare to Work Atlanta\\nLFA NEWWS Atl.\\n1992\\n33\\nx\\nHamilton et al. (2001)\\nMandatory Job-Search-\\nFirst Programs\\nGreenberg, Deitch, and Hamilton (2010)\\nWelfare to Work Butte\\nMandatory Mixed-Initial-\\nActivity Programs\\nGAIN Butte\\n1987\\n31\\nx\\nHamilton et al. (2001)\\nFreedman et al. (1996)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1295\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended\\nEstimates\\nUtilized\\nMVPF\\nWelfare to Work Columbus\\nIntegrated Mandatory\\nNEWWS Col. Int.\\n1992\\n32\\nx\\nGreenberg, Deitch, and\\nHamilton (2010)\\nEducation-First Programs\\nHamilton et al. (2001)\\nWelfare to Work Columbus\\nTraditional Mandatory\\nEducation-First Programs\\nNEWWS Col. Trad.\\n1992\\n32\\nx\\nGreenberg, Deitch, and\\nHamilton (2010)\\nHamilton et al. (2001)\\nWelfare to Work Connecticut\\nJobs First\\n1996\\n31\\nx\\nBloom et al. (2002)\\nTime-Limit-Mix Programs\\nGreenberg, Deitch, and\\nHamilton (2010)\\nWelfare to Work Cook County\\nMandatory Work\\nExperience Program\\nWIN Demo.\\n1985\\n32\\nx\\nGreenberg, Deitch, and\\nHamilton (2010)\\nBrock, Butler, and Long (1993)\\nWelfare to Work Detroit\\nMandatory Education-First\\nNEWWS Det.\\n1992\\n30\\nx\\nGreenberg, Deitch, and\\nHamilton (2010)\\nPrograms\\nHamilton et al. (2001)\\nWelfare to Work Florida\\nMandatory Mixed-Initial-\\nProj. Ind. FL\\n1990\\n32\\nx\\nGreenberg, Deitch, and\\nHamilton (2010)\\nActivity Programs\\nKemple, Friedlander and\\nFellerath (1995)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1296\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nWelfare to Work Florida\\nTime-Limit-Mix Programs\\nFTP\\n1994\\n29\\nx\\nBloom et al. (2000)\\nGreenberg, Deitch, and\\nHamilton (2010)\\nWelfare to Work Grand\\nRapids Mandatory\\nEducation-First Programs\\nHCD NEWWS Gr. Rap.\\n1991\\n28\\nx\\nGreenberg, Deitch, and\\nHamilton (2010)\\nHamilton et al. (2001)\\nWelfare to Work Grand\\nRapids Mandatory Job-\\nSearch-First Programs\\nLFA NEWWS Gr. Rap.\\n1991\\n28\\nx\\nHamilton et al. (2001)\\nGreenberg, Deitch, and\\nHamilton (2010)\\nWelfare to Work Los Angeles\\nMandatory Job-Search-\\nFirst Programs\\nGAIN LA jobs\\n1996\\n34\\nx\\nFreedman et al. (2000)\\nGreenberg, Deitch, and\\nHamilton (2010)\\nWelfare to Work Los Angeles\\nMandatory Mixed-Initial-\\nActivity Programs\\nGAIN LA\\n1988\\n31\\nx\\nGreenberg, Deitch, and\\nHamilton (2010)\\nFreedman et al. (1996)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1297\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplemented Beneficiaries Baseline Restricted Extended Estimates\\nUtilized\\nMVPF\\nWelfare to Work Minnesota\\nEarnings Supplement\\nPrograms\\nMFIP\\n1994\\n29\\nx\\nGreenberg, Deitch, and\\nHamilton (2010)\\nMiller et al. (2000)\\nWelfare to Work Portland\\nMandatory Mixed-Initial-\\nActivity Programs\\nNEWWS Port.\\n1993\\n30\\nx\\nGreenberg, Deitch, and\\nHamilton (2010)\\nHamilton et al. (2001)\\nWelfare to Work Riverside\\nMandatory Education-First\\nPrograms\\nHCD NEWWS Riv.\\n1991\\n32\\nx\\nHamilton et al. (2001)\\nGreenberg, Deitch, and\\nHamilton (2010)\\nWelfare to Work Riverside\\nMandatory Job-Search-First\\nPrograms\\nLFA NEWWS Riv.\\n1991\\n32\\nx\\nHamilton et al. (2001)\\nGreenberg, Deitch, and\\nHamilton (2010)\\nWelfare to Work Riverside\\nMandatory Mixed-Initial-\\nActivity Programs\\nGAIN Riv.\\n1987\\n31\\nx\\nFreedman et al. (1996)\\nGreenberg, Deitch, and\\nHamilton (2010)\\nWelfare to Work San Diego\\nMandatory Job-Search-First\\nPrograms\\nSWIM\\n1985\\n31\\nx\\nGreenberg, Deitch, and\\nHamilton (2010)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1298\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nTABLE I (CONTINUED)\\nSample\\nProgram\\nLabel\\nYear\\nAge of\\nPaper\\nPapers\\nImplementedBeneficiariesBaselineRestrictedExtended Estimates\\nUtilized\\nMVPF\\nWelfare to Work San Diego\\nMandatory Mixed-\\nInitial-Activity Programs\\nGAIN SD\\n1987\\n31\\nx\\nGreenberg, Deitch, and Hamilton\\n(2010)\\nFreedman et al. (1996)\\nWelfare to Work San Diego\\nMandatory Work\\nExperience Program\\nWork Exp. SD\\n1982\\n32\\nx\\nGreenberg, Deitch, and Hamilton\\n(2010)\\nBrock, Butler, and Long (1993)\\nWelfare to Work Tulane\\nMandatory Mixed-Initial-\\nActivity Programs\\nGAIN Tul.\\n1988\\n31\\nx\\nGreenberg, Deitch, and Hamilton\\n(2010)\\nFreedman et al. (1996)\\nWelfare to Work Vermont\\nEarnings Supplement\\nPrograms\\nWRP Earn Supp.\\n1994\\n31\\nx\\nGreenberg, Deitch, and Hamilton\\n(2010)\\nScrivener et al. (2002)\\nWelfare to Work Vermont\\nTime-Limit-Mix Programs\\nWRP Time lim.\\n1994\\n31\\nx\\nScrivener et al. (2002)\\nGreenberg, Deitch, and Hamilton\\n(2010)\\nWelfare to Work West\\nVirginia Mandatory Work\\nExperience Program\\nCWEP\\n1983\\n33\\nx\\nBrock, Butler, and Long (1993)\\nGreenberg, Deitch, and Hamilton\\n(2010)\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1299\\nAPPENDIX\\nAPPENDIX FIGURE I\\nIncome Projections Using the ACS\\nPanels A and B present a decomposition of the elements that make up our\\nincome projection process for the examples in Section III.A. The “Pop Avg” series\\nis constructed in each case from the 2015 ACS and using a 0.5% wage growth\\nassumption. At each age “Pop Avg” gives the mean wage level that would prevail\\nin the population for individuals of that age, when individuals in the treatment\\ngroup for the relevant policy were that age. This number is constructed by\\nassuming that the mean wage level at each age will rise (and has previously\\nrisen) by 0.5% in each year. The “Control Forecast” series is constructed by taking\\nan estimate of earnings for a relevant control group at a particular age or range of\\nages, then calculating the implied proportion of the “Pop Avg” series at those ages,\\nthen projecting the series forwards (and backwards) as this constant fraction\\nof “Pop Avg.” The “Treatment” series is constructed by summing the observed\\ntreatment effects in dollar terms and the “Control Forecast” series. To construct\\nthe “Predicted” series we take the final value of the “Treatment” series, then\\ncalculate the ratio of this value to the value of the “Pop Avg” series at that same\\nage, before applying this ratio to the “Pop Avg” series up to age 65. See Online\\nAppendix I for further details of this methodology.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1300\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nAPPENDIX FIGURE II\\nWillingness to Pay per Dollar of Programmatic Spending\\nThis figure presents estimates of WTP normalized by initial programmatic\\nspending for each category-average group of policies in our baseline sample. We\\nplot these estimates as a function of the average age of each policy’s beneficiaries\\nwithin category. Bootstrapped 95% confidence intervals with adjustments\\n(discussed in Online Appendix H) are shown for the category averages. The\\nnormalized willingness to pay of individual policies are shown in smaller dots,\\ncolor-coded to align with their respective categories.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1301\\nAPPENDIX FIGURE III\\nRobustness to Child Effects\\nThis figure assesses the impact of observing child effects on our estimates as\\na function of the average age of the economic beneficiaries of the policy. Panel\\nA restricts our sample to the subset of policies for which we observe estimates\\nof the impact of the policy on children. In addition, Panel B shows projected\\nMVPFs for additional policies that do not observe earnings impacts but do observe\\nanother intermediate outcome such as birthweight (AFDC), college attendance\\n(housing vouchers to AFDC recipients), and test scores (housing vouchers in\\nChicago). Panel C reports the MVPF for the EITC under alternative methods of\\nincorporating indirect effects on children through test scores, college attendance,\\nand income of EITC more broadly.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1302\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nAPPENDIX FIGURE IV\\nRobustness to Alternative Interest Rates\\nThis figure presents our MVPF estimates as in Figure III and the category av-\\nerages as in Figure IV, Panel B under alternative real interest rate assumptions,\\nas opposed to our baseline specification of 3%. Panel B differs slightly from our\\nbaseline specification because we restrict to the subset of policies for which we are\\nable to vary the discount rate (e.g., we exclude papers where we directly import\\nan MVPF that relied on a particular discount rate). We omit confidence intervals\\nfor ease of viewing, but caution the reader that the estimate for the college adult\\ncategory has a CI that includes 0 and infinity.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1303\\nAPPENDIX FIGURE V\\nRobustness to Alternative Tax Rates\\nThis figure presents our MVPF estimates as in Figure III and the category\\naverages as in Figure IV, Panel B under alternative tax rate assumptions. Panel\\nA replicates our baseline specification using the CBO estimates of the tax rates.\\nPanels B–D adjust the tax rate to 10%, 20%, and 30%.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1304\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nAPPENDIX FIGURE VI\\nSpecification Robustness\\nThis figure presents the category-average MVPFs from Figure III using a range\\nof different alternative specifications that are more conservative than our baseline\\nspecifications. Panel A replaces our point estimate WTP measures with our\\nconservative measures of WTP. We report bootstrapped 95% confidence intervals\\nwith adjustments (discussed in Online Appendix H) for each category average.\\nPanel B replaces our baseline income projection procedure with a procedure that\\nassumes zero income growth over the lifecycle. We use our restricted sample of\\npolicies for this specification. See Online Appendix I for further details.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1305\\nAPPENDIX FIGURE VII\\nSample Restrictions\\nThis figure presents the category-average MVPFs from Figure III using a range\\nof alternative sample restrictions. Panel A considers our restricted sample that\\ndrops estimates for which we are forecasting earnings effects based on a policy’s\\nimpact on college attendance. Panel B restricts the sample to only policies for\\nwhich earnings outcomes are estimated for at least five years of follow-up after\\nthe policy. For this panel we show group averages even for groups with a single\\npolicy. Panel C restricts the sample to policies whose identification strategy is a\\nrandomized control trial, lottery, or regression discontinuity. Panel D restricts to\\npolicies whose primary analyses have been published in a peer-reviewed journal.\\nWe report bootstrapped 95% confidence intervals with adjustments (discussed in\\nOnline Appendix H) for each category average.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1306\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nAPPENDIX FIGURE VIII\\nPublication Bias\\nThis figure presents the MVPF estimates from Figure III and category averages\\nin Figure IV, Panel B using estimates corrected for publication bias from the\\nmethod of Andrews and Kasy (2019). Panel A reports estimates using the\\ncorrections using the publication likelihood estimated from our model that\\nimposes jumps at p = .05 and p = .10, as shown in Table III, columns (3) and\\n(6). In Panel B we report corrected estimates under an assumption that child\\npolicies are 35 times more likely to be published if they find a positive effect on\\nchildren’s outcomes (and we assume no publication bias for adult policies or for\\nchild policies that find negative effects on children). This 35 times corresponds to\\nthe estimated publication bias implied by a large-scale replication of experimental\\neconomics papers by Camerer et al. (2016) (Table 1 of Andrews and Kasy 2019\\nreports that insignificant results are 0.029 times as likely to be published). We\\ndo not report confidence intervals for these estimates (to our knowledge there is\\nno well-accepted method of constructing such intervals); but we refer readers to\\nFigure IV, Panel B to note that some of these category averages are imprecise.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1307\\nAPPENDIX FIGURE IX\\nMVPFs by Decade\\nThis figure presents MVPFs for all policies evaluated in the article based on\\nthe year in which the policy was implemented. Policies are divided into categories\\nbased on their decade of implementation and the average age of their economic\\nbeneficiaries. For policies implemented in each decade there are two categories—\\npolicies with beneficiaries over age 23 and policies with beneficiaries aged 23 or\\nyounger. Within each decade by age category we construct the MVPF for a hypo-\\nthetical policy that allocates $1 of programmatic spending equally among all the\\npolicies in the category. This is the same approach used to create MVPF estimates\\nfor policy domains in previous figures. The capped lines show the 95% bootstrapped\\nconfidence intervals with adjustments discussed in Online Appendix H.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\n1308\\nTHE QUARTERLY JOURNAL OF ECONOMICS\\nAPPENDIX FIGURE X\\nWelfare Reform\\nThis figure presents estimates of the MVPF of 27 welfare reform policies\\ndiscussed in Section VI.C. We report MVPF estimates using three potential\\nmeasures of WTP: (i) cost, the mechanical cost of the program incurred by the\\ngovernment, excluding any fiscal externalities from behavior change. Estimates\\nfrom this specification are denoted by circles. (ii) Change in transfer payments\\n(welfare, food stamps, and Medicaid). Estimates from this specification are\\ndenoted by Xs. (iii) Change in post-tax income, which includes the change in\\nparticipants’ incomes due to changes in employment and the change in their\\ntransfer payments. Estimates from this specification are denoted by triangles.\\nDownloaded from https://academic.oup.com/qje/article/135/3/1209/5781614 by guest on 29 September 2024\\n\\n\\nUNIFIED WELFARE ANALYSIS OF GOVERNMENT POLICIES 1309\\nHARVARD UNIVERSITY\\nHARVARD UNIVERSITY\\nSUPPLEMENTARY MATERIAL\\nAn Online Appendix for this article can be found at The\\nQuarterly Journal of Economics online. Data and code replicating\\ntables and figures in this article can be found in Hendren and\\nSprung-Keyser\\n(2020),\\nin\\nthe\\nHarvard\\nDataverse,\\ndoi:\\n10.7910/DVN/ZHOSGC.\\nREFERENCES\\nAbraham, Katharine G., and Melissa A. 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