Government consumption in the DINA framework: allocation methods and consequences for post-tax income inequality

Riedel, Lukas; Stichnoth, Holger Article — Published Version Government consumption in the DINA framework: allocation methods and consequences for post-tax income inequality International Tax and Public Finance Provided in Cooperation with: Springer Nature Suggested Citation: Riedel, Lukas; Stichnoth, Holger (2024) : Government consumption in the DINA framework: allocation methods and consequences for post-tax income inequality, International Tax and Public Finance, ISSN 1573-6970, Springer US, New York, NY, Vol. 31, Iss. 3, pp. 736-779, https://doi.org/10.1007/s10797-024-09832-1 This Version is available at: https://hdl.handle.net/10419/315307 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Vol:.(1234567890) International Tax and Public Finance (2024) 31:736–779 https://doi.org/10.1007/s10797-024-09832-1 1 3 Government consumption intheDINA framework: allocation methods andconsequences forpost‑tax income inequality LukasRiedel1· HolgerStichnoth1,2,3,4 Accepted: 8 February 2024 / Published online: 1 May 2024 © The Author(s) 2024 Abstract About half of government expenditure in the United States takes the form of government consumption (e.g., education, defense, infrastructure). In many studies of post-tax inequality based on the Dina framework (including the influential study by Piketty etal. (Q J Econ 133(2):553–609, 2018), government consumption is allocated either proportionally to post-tax disposable income or on a per-capita basis, and the level of inequality is fairly sensitive to this choice. This paper provides direct evidence on how public education spending (a substantial part of government consumption) is actually distributed. An allocation proportional to post-tax disposable income is clearly rejected, while a lump-sum allocation is found to provide a good approximation. Keywords Inequality· Redistribution· Education· In-kind transfers JEL Classification D31· H41· H52· I24 We thankthe editor David Agrawal,two anonymous referees, Christina Gathmann, Valentina Melentyeva, Sebastian Siegloch, Michaela Slotwinski, and David Splinter as well as seminar participants at Mannheim, Strasbourg, and ZEW, and conference participants at ECINEQ, IIPF, and Verein für Socialpolitik for valuable comments and suggestions. Hanne Albig and Lena Göhringer provided excellent research assistance. * Holger Stichnoth [email protected] 1 ZEW Mannheim, Mannheim, Germany 2 University ofStrasbourg, Strasbourg, France 3 IZA Bonn, Bonn, Germany 4 Research Group Inequality andPublic Policy, ZEW Mannheim, L7,1, 68161Mannheim, Germany 737 1 3 Government consumption intheDINA framework: allocation… 1 Introduction The United States and many other countries have seen an increase in income inequality in recent decades that has received attention from academic researchers and the general public alike. However, while there is a broad consensus about the increase, there is a debate about its extent, in particular for post-tax income, i.e., income after taxes, transfers, and government expenditure (Auten & Splinter, 2024; Bricker etal., 2016; Larrimore etal., 2021a; Piketty etal., 2018; Saez & Zucman, 2020; Splinter, 2020). The present paper contributes to this debate by showing that the level of post-tax inequality is fairly sensitive to assumptions regarding the allocation of government expenditure, and by providing evidence on the actual distribution of public education spending, an important part of government expenditure. The measurement of income inequality has traditionally relied on micro-data from surveys or administrative tax records. These data, however, capture only about 60% of macro totals from national accounts, so a substantial share of national income has been missing from the debate about inequality. In an important contribution, Piketty etal. (2018) propose a method for constructing distributional national accounts ( Dina ) that measure how the entire national income is distributed among individuals. When computing post-tax income, this approach requires the allocation of the entirety of government expenditure to individuals. In recent years, about half of government expenditure in the United States has taken the form of government consumption (e.g., education, defense, infrastructure); depending on the year, this represents between 16% and 20% of national income.1 In their main specification, Piketty, Saez, and Zucman assume that government consumption is distributed proportionally to post-tax disposable income, which corresponds to pre-tax income minus all taxes plus all individualized monetary transfers, but excluding in-kind transfers. This means that, by construction, an important part of national income is assumed to be distributionally neutral. The Dina Guidelines (Alvaredo et al., 2020) explicitly recognize the difficulty surrounding the allocation of government consumption, calling it “approximate and exploratory.” As shown by Blanchet etal. (2022), Bozio etal. (2022), and Bruil etal. (2022), the level of post-tax inequality is fairly sensitive to this assumption. We confirm this for the US study by Piketty, Saez, and Zucman. When we replace their proportionality assumption with a lump-sum allocation, the Top 10% share of national income decreases by about 5 percentage points, while the share of the Bottom 50% increases by roughly the same amount.2 1 See Appendix1 for the definition and measurement of government consumption. 2 Piketty et al. (2018) themselves present a robustness check along these lines. However, they only allocate education spending on a different basis, not the remaining parts of government consumption. Moreover, they assign public education spending based on the number of children in the tax unit. This means that spending on tertiary education is typically allocated to the parents who claim their children as exemptions. As a result, the allocation is more regressive than when allocating the expenditure to tax units of the students themselves, as we do in the present paper. Both approaches have their merits. However, we believe that allocating public education expenditure to the parents is a departure from the rest of their paper, in which they allocate all items of national income to tax units without taking economic links between these units into account. We will return to this point below. Finally, their robustness check does not take differences in per-capita expenditure between the different education levels into account. 738 L.Riedel, H.Stichnoth 1 3 As a result, the gap between the income shares of the Top 10% and the Bottom 50% is reduced by half, from about 20–10 percentage points in the most recent years.3 In light of this sensitivity, the contribution of the present paper is to provide direct evidence on how an important fraction of government consumption is actually distributed in the United States. We focus on public spending on education, which makes up about 30% of government consumption and 5% of national income in most OECD countries, and is much easier to assign individually than defense or infrastructure expenditure. Our paper is part of a series of recent studies on the allocation of in-kind transfers in the Dina framework (Insee 2021 for France, Bruil etal. 2022 for the Netherlands, Chatterjee etal. 2023 for South Africa, and De Rosa etal. 2022 for Latin America). Our data for the United States are from the 2017 wave of the American Community Survey (ACS). In addition to the large sample size (about 3.2M individuals in 1.4M households), the ACS has the advantage that participants are legally obligated to answer the survey questions. The ACS has information on whether household members are currently in education, and, importantly for our purpose, distinguishes between public and private institutions. Finally, the ACS includes individuals in group quarters, which is key for measuring public expenditure that goes to college students who no longer live with their parents. Annual public expenditure per student (net of tuition fees) at different levels of education is taken from the OECD. We find that, for education at least, public expenditure is not proportional to income. On the contrary, average public education spending is highest in the poorest income decile and lowest in the richest decile. The Bottom50% of the pre-tax income distribution receive an average of $4.9K per year in terms of public education spending, followed by the Middle40% with $4.7K, and, as noted, the Top10% with $4.3K. The differences are not great, however, so a lump-sum allocation provides a good approximation, at least when income is measured using the equal-split assumption of the Dina framework (i.e., household income is divided by the number of adults aged20 and above).4 When equivalised household income is used instead, the negative income gradient is steeper (i.e., the distribution is more progressive) and the approximation is less accurate. These results are strongly driven by age effects. The most striking case are college students who no longer live with their parents. They receive substantial public 3 Our calculations are documented in Sect.A of theAppendix. 4 Two caveats apply. First, the American Community Survey does not provide the comprehensive income measure that is the raison d’être of the Dina approach. While imputed rents tend to be concentrated at the bottom and middle of the income distribution and thus have an inequality-reducing effect, undistributed profits are concentrated among the higher deciles. The second caveat is that the ACS provides pre-tax income, while Piketty etal. (2018) assume that government consumption expenditure is proportional to post-tax income. However, when we simulate post-tax income based on the ACS pre-tax measure and the NBER’s TAXSIM model (Feenberg & Coutts, 1993), we still clearly reject the proportionality assumption. 739 1 3 Government consumption intheDINA framework: allocation… expenditure while having low current income.5 But public spending at other levels (pre-primary, primary, secondary) also has an age component, as parents with kindergartenor school-age children are typically still below the peak of their ageincome profiles. Note that our analysis uses average expenditure per student at the national level and, in a robustness check, at the state level. While for primary and secondary education differences in average per-student expenditure between school districts are not large and U-shaped (with the richest and poorest districts spending the most, cf. De Brey etal. 2021), we cannot rule out that unobserved spending differences for tertiary education or, at all levels, within-district variation leads us to overestimate the progressivity of public education spending. However, we find such a strong departure from proportionality that these effects would have to be very large in order to justify the proportionality assumption. In our second contribution, we examine two justifications for an allocation of government consumption proportionally to income that have been proposed in the Dina literature. Piketty etal. (2017) argue for a proportional allocation by pointing to the positive correlation between public education spending and lifetime earnings. Using the American Community Survey and proxying for lifetime earnings using earnings at age 40–45 (where the rank correlation with lifetime earnings is maximal), we quantify this argument by showing that the 10% of individuals with the highest earnings have received average public education spending of $335K, about 1.4 times the amount that the bottom 50% received ($234K). The allocation is still not proportional to earnings, however; proportionality would require a factor of about 14. More importantly, adjusting for age effects in public education spending, but not in earnings, capital income, or certain cash transfers, would be inconsistent with the Dina framework, which so far has adopted a strictly cross-sectional perspective. The Dina Guidelines (Alvaredo et al., 2020) argue that a lump-sum allocation would overestimate the extent of redistribution because of the unequal access to education observed in most countries. While the American Community Survey does not allow us to address this point, we use the Panel Study of Income Dynamics (PSID) to show that more public education spending indeed goes to children of more educated parents. On average, individuals with the most educated parents received about 30% more public education spending than individuals with the least educated parents. However, while these intergenerational patterns are arguably more important than the cross-sectional results for the distributional debate, they again do not provide the right empirical basis for an allocation of government expenditure in the cross section. 5 This result would be mitigated by assigning the spending on tertiary education to the parents even in cases in which the students no longer live at home. The data from the ACS do not allow us to do this, but even by shifting all spending on tertiary education from the first to the tenth decile (unlikely given that we consider only public education while private enrollment plays a large role in the top decile), the resulting distribution of public education spending would still be nowhere near a distribution that is proportional to post-tax disposable income. 740 L.Riedel, H.Stichnoth 1 3 Related literature Following the paper by Piketty et al. (2018) for the United States, the Dina approach has been applied to other countries. Garbinti etal. (2018) study pre-tax income inequality in France using a Dina approach, and Bozio etal. (2022) extend this to post-tax income and compare France with the United States. Using a simplified approach, Blanchet et al. (2022) create distributional national accounts for the member countries of the European Union. Other applications of the Dina framework are for Austria (Jestl & List, 2020), China (Piketty etal., 2019), Germany (Bach et al., 2021), the Netherlands (Bruil et al., 2022), and Sweden (Hammar etal., 2020). In a related effort, the OECD and Eurostat set up an expert group to disaggregate the household sector in the system of national accounts; see Zwijnenburg (2019) for a comparison with the Dina approach. Our paper contributes to the discussion about methodological issues in the measurement of income inequality in the Dina framework and beyond. Note that we focus exclusively on the effect of government (in-kind) consumption and remain silent on the debate about issues in the measurement of pre-tax income, such as the allocation of business profits or untaxed pension income (Auten & Splinter, 2024; Saez & Zucman, 2020).6 There is a literature on the distribution of (in-kind) expenditure which precedes the Dina approach, dating back to Gillespie (1965). While a number of papers focuses on single countries—typically the US or the UK (Gillespie, 1965; Reynolds & Smolensky, 1977; Ruggles & O’Higgins, 1981; O’Higgins & Ruggles, 1981; Smeeding, 1977; Musgrave etal., 1974; Wilson etal., 2006; Horton & Reed, 2010; O’Dea & Preston, 2012; Higgins et al., 2016)—-it is also common to compare several countries. Such comparisons are either made among selected high-income countries (Callan etal., 2008; Garfinkel etal., 2006; Smeeding etal., 1993) or across larger sets of OECD countries (Marical etal., 2006; Verbist etal., 2012; Zwijnenburg etal., 2017). Education and health are by far the most common expenditure categories studied, followed by housing. The results of the studies that include education are, across the different countries, consistent with our results. In particular, none of the studies find that the allocation of public education spending is proportional to cash income. We contribute to this literature by using a much larger dataset that distinguishes between public and private education as well as different levels of education (pre-primary, primary, secondary, tertiary) and that includes students in group quarters, which is important for the allocation of public spending on tertiary education.7 We also contribute by linking our findings to the Dina literature. In 6 There is also a debate about measurement issues regarding wealth inequality, see Saez and Zucman (2016), Smith etal. (2019) and Saez and Zucman (2020). 7 In their study of Brazil and the United States, Higgins etal. (2016) also use a large dataset, the Current Population Survey (CPS). However, the CPS allows no distinction between enrollment in private and public institutions. The authors therefore rely on the American Community Survey (ACS), but unlike us only in a supplementary role, i.e., they predict private vs. public enrollment based on the ACS and then merge this information into the CPS. Moreover, they do this only for primary and secondary education, although private enrollment also plays an important role in tertiary education. They also do not capture individuals living in group quarters such as college dormitories. Our in-depth look at education in the United States therefore complements their broader focus on several types of social spending in two countries. 741 1 3 Government consumption intheDINA framework: allocation… particular, we break down education spending by individualized income for adults age20 and above, using the “equal-split” approach of Piketty etal. (2018). Most nonDina studies use equivalised household income instead, which we include as a robustness check. In independent work, Bruil etal. (2022) also study the distribution of education and other in-kind transfers using both the equal-split approach and the approach based on equivalised household incomes. Finally, while existing studies examine public spending in the cross section, we additionally distinguish by lifetime earnings and by the socioeconomic status of the parents. This earlier literature has raised the important question of whether government in-kind expenditure should be measured at cost or should rather measure the increase in individual welfare that results from the expenditure (see O’Dea & Preston, 2012, on this and other methodological issues). With an assignment based on cost, inefficiencies in the provision of public services show up as income, and there is no accounting for different needs of individuals. However, attempts to measure welfare instead of income or to account for different needs by adjusting equivalence scales (Paulus etal., 2010; Aaberge etal., 2010, 2013, 2019) depart from the Dina framework, which—following the practice in national accounts—measures government expenditure on a cost basis. Moreover, we see the issue of valuation as orthogonal to the question of correctly determining who receives the public expenditure in the first place. The remainder of this paper is organized as follows. Section2 describes the data and methods we use in our empirical study of how public education spending in the United States is actually allocated across the income distribution. Section3 presents our results. We focus on the distribution in the cross section, which is the perspective that has been adopted in the Dina literature, but also report the distribution by lifetime earnings (proxied for by earnings at age 40–45). Finally, in a supplementary analysis based on PSID data, we study how public education expenditure varies by parents’ educational attainment. Section4 concludes. 2 Methods anddata 2.1 Overview Given that the level of post-tax income inequality is sensitive to the assumption about how government consumption is allocated, we provide direct evidence on how an important part of this expenditure is actually distributed. We focus on public spending on education, which makes up about 5% of national income in the US and in most OECD countries and is much easier to assign individually than defense or infrastructure expenditure. Our method for allocating public education expenditure is straightforward. We use a micro-dataset—the American Community Survey 2017—that allows us to observe the income of the household and that has information on who in the household currently attends a public educational institution, distinguishing pre-primary, primary, secondary, and tertiary education. We then multiply the number of students per household with the average public expenditure for students of the respective 742 L.Riedel, H.Stichnoth 1 3 education level, which we take from the OECD’s “Education at a Glance” database. In a robustness check, we use state-level expenditure data from the National Center for Education Statistics (De Brey etal., 2021), which has only small effects on our results. Following the Dina framework, our main analysis is cross-sectional, i.e., we study the distribution of public education expenditure by current income. In addition, we analyze public education expenditure by lifetime earnings, proxied for by earnings at age 40–45. However, based on another dataset—the Panel Study of Income Dynamics, PSID (Survey Research Center, 2022)—we also adopt an intergenerational perspective and document how the expenditure differs by parents’ education and occupational prestige. 2.2 American Community Survey Our main source of individual-level microdata is the American Community Survey (ACS). The ACS is conducted by the United States Census Bureau to collect information similar to the decennial census. Our data for the year 2017 is from the public use file of the ACS provided by IPUMS USA (Ruggles et al., 2020). It provides information on around 3.2M individuals in 1.4M households. In addition to the large sample size, the ACS has the advantage that—unlike in other datasets such as the Current Population Survey—respondents are legally obligated to answer the survey questions. Enrollment The ACS has information on whether household members are currently enrolled in an educational institution, and, importantly for our purpose, distinguishes between public and private institutions.8 Moreover, the ACS includes individuals in group quarters including college dormitories, which is key for measuring public expenditure that goes to college students who no longer live with their parents. The ACS provides a very accurate picture of the number of individuals enrolled in the education system (Fig.11 inthe Appendix). For public institutions at the preprimary, primary, and secondary levels in 2017, our own calculations based on the ACS result in 51.4M students. The OECD (OECD Statistics, 2020) and the National Center for Education Statistics (De Brey etal., 2021) report values of 50.6M and 50.7M, respectively. At the tertiary level, our ACS number is 16.8M, which is a little higher than the value of 14.6M reported by the OECD and the NCES.9 For completeness, Fig.11 also shows the number of students in private education, although we do not include these students when allocating public education expenditure. Private education is empirically relevant only at the pre-primary level (kindergarten) 8 The ACS has no information on the field of study for students who are currently enrolled in higher education (the information is only available for completed degrees), which means that we cannot take into account differences in per-capita spending between students in science, technical or vocational tracks relative to humanities programs. 9 In a robustness check, we scale down the ACS numbers accordingly. 743 1 3 Government consumption intheDINA framework: allocation… and then again at the tertiary level. Our ACS numbers are again close to the OECD values, while the numbers reported by the NCES are slightly lower. Income concept Income is measured in the ACS as the aggregate of personal income from different sources over all household members above the age of 15. For individuals in group quarters, such as students in college dormitories, the concept of household income does not apply and only personal income is reported. Income in the ACS is pre-tax and post-cash-transfer.10 The period of reference for the income measurement are the previous twelve months. Note that, as the ACS is administered throughout the year, this means that the income in most cases does not correspond to a calendar year. Also, despite the legal obligation to answer the survey, some of the individual income components are actually imputed by the data provider. In a robustness check, we drop all households in which more than half of household income is based on an imputation. Regarding the comparison with the Dina approach, two additional caveats are in order. First, while the American Community Survey provides a fairly comprehensive measure of income, it falls short of the Dina approach, in which pre-tax income sums up to the whole of national income. While imputed rents tend to be concentrated at the bottom and middle of the income distribution and thus have an inequality-reducing effect, undistributed profits are concentrated among the higher deciles. The second caveat is that the ACS provides pre-tax, post-cash-transfer income, while Piketty etal. (2018) assume that government consumption is proportional to post-tax disposable income, i.e., post-tax, post-cash-transfer income. However, when we simulate post-tax income using the NBER TAXSIM model, we still clearly reject the proportionality assumption.11 Unit of measurement In our main specification, we follow Piketty etal. (2018) and the other Dina studies and measure income and transfers at the level of adult individuals aged 20 and above. For couples, we apply an equal-split rule, i.e., each adult gets 10 “Personal income, or ‘money income,’ as per the Census Bureau, is the income received on a regular basis (exclusive of certain money receipts such as capital gains and lump-sum payments) before payments for personal income taxes, Social Security and Medicare taxes, union dues, etc. It includes income received from wages, salary, commissions, bonuses, and tips; self-employment income from own nonfarm or farm businesses, including proprietorships and partnerships; interest, dividends, net rental income, royalty income, or income from estates and trusts; Social Security or Railroad Retirement income; Supplemental Security Income (SSI); any cash public assistance or welfare payments from the state or local welfare office; retirement, survivor, or disability benefits; and any other sources of income received regularly such as Veterans’ (VA) payments, unemployment and/or worker’s compensation, child support, and alimony.” (https:// www. pewre search. org/ socialtrends/ 2018/ 07/ 12/ metho dology15/). The income components such as wage or business income are top-coded at the 99.5th percentile of the respective federal state. Higher values are coded as the state-specific average of all values above the threshold. 11 TAXSIM (Feenberg & Coutts, 1993) simulates the tax liability for federal, state, and payroll taxes. We use TAXSIM version 32 (https:// users. nber. org/ ~taxsim/ taxsi m32/). The simulations are for tax units, which we identify in our ACS household sample following the procedure outlined by Samwick (2013). We assume that all married couples file jointly. 750 L.Riedel, H.Stichnoth 1 3 excess number of full-time equivalents is independent of income—and as a bounds analysis in which we assume that the excess mass is concentrated in either the bottom or the top half of the income distribution. 3 Results 3.1 Distribution ofpublic education spending Allocation based on actual enrollment Figure1 shows how public education spending (net of tuition fees20) in the United States in 2017 is distributed among the deciles of the income distribution.21 Following Piketty etal. (2018), the distribution is for adults age20 and above; in households with more than one adult, income is split equally. Income is pre-tax income as reported in the American Community Survey; below, we report results when we use simulated post-tax income instead, as a first step toward the more comprehensive measure of post-tax disposable income used by Piketty, Saez, and Zucman. Public education spending is highest in the first decile—with an average of $6.0K per adult—and lowest in the tenth decile of the pre-tax income distribution, where the average is $4.3K. In deciles 2–9, the means of per-capita spending are fairly close together, at between $4.5K and $4.8K. The overall average is $4.8K. The Bottom50% of the pre-tax income distribution receive an average of $4.9K per year in terms of public education spending, followed by the Middle40% with $4.7K, and, as noted, the Top10% with $4.3K. Turning to the different levels of education, we see little differences by income for pre-primary and primary education. Per-capita expenditure on secondary education tends to grow with income, with an average of $1.4K allocated to each adult in decile1 and about $1.9K in deciles 9 and 10. Public spending on tertiary education shows the opposite pattern. It is the driver behind the progressivity of public education spending, being concentrated in the bottom decile of the income distribution, where average annual spending is $3.3K, more than three times the average in the top decile ($1.0K).22 The high average in the poorest decile is mostly explained by college students who no longer live with their parents. By contrast, the public expenditure on students who are still in the parental household is spread out much more evenly across the income distribution. 20 There is a literature that studies the distribution of (higher-)education spending net not only of tuition fees, but of taxes as well (e.g., Hansen & Weisbrod, 1969; Johnson, 2006). We refrain from doing so as we see our analysis as a building block in the Dina framework, which provides a much more comprehensive measure of the tax burden than these earlier studies, although similar caveats regarding tax incidence apply. Regarding the related question of how income inequality affects tuition fees and college attendance, see the recent article by Cai and Heathcote (2022). 21 The numerical values are reported in Table4 inthe Appendix. 22 Figure12 inthe Appendix expresses public education spending as a share of income, which makes the progressivity (i.e., expenditure representing a higher share of income for lower-income groups) directly visible. 751 1 3 Government consumption intheDINA framework: allocation… Comparison with proportional and lump-sum allocations Figure2 contrasts the actual distribution based on the American Community Survey with the proportional allocation used by Piketty etal. (2018). For public spending on education (about 30% of government consumption in the United States), a proportional allocation is clearly not a good assumption. It implies annual per-capita spending of $0.6K in the poorest decile, only a tenth of the value that we find based on actual enrollment data from the American Community Survey. At the top of the income distribution, the proportionality assumption allocates $18.4K to each adult in the richest decile, more than four times the value based on the ACS. Furthermore, as pointed out in Sect. A in the Appendix, given the unequal distribution of pre-tax income even within the top decile, a proportional allocation implies implausibly high per-capita values among individuals in, say, the Top1% or Top0.1% of the distribution. As microdata on enrollment in education is easily available for the United States and other countries, we believe that the precision of the Dina approach can be improved at little cost by replacing the proportionality assumption with an allocation based on actual enrollment. An even easier fix consists in replacing the allocation proportional to post-tax disposable income—which the Dina Guidelines recommends as the benchmark—by a lump-sum allocation. As Fig.2 shows, assigning the mean of $4783 to each adult is a good approximation to the distribution based on actual enrollment. Figure2 also includes the distribution that arises from allocating public education spending as a lump-sum transfer per child below the age of 20, as in the robustness check in the paper by Piketty etal. (2018). This assumption performs much better than the proportional allocation. The differences with respect to our baseline results arise from the fact that this shortcut method does not take into account the differences in per-capita expenditure by level of education (tertiary education is much more expensive than the rest, at least in the United States), and especially that it does not capture public spending that goes to college students age20 and above. Progressivity driven by age effects The progressivity of public education spending in the cross section is strongly driven by age effects (Fig.3). Individuals aged 20–24 receive a lot of education spending on average, mostly for their own (tertiary) education. At the same time, they have by far the lowest current income of all age groups. Pre-primary and primary education does not play a large role in this age group, as the share of parents is still low. Spending on secondary education is a bit higher because some individuals are still in secondary education themselves. In the age group 25–29, average public education spending is much lower. (Own) tertiary education is still significant, but less so than for individuals in their early 20s. Secondary education also drops in importance, while public expenditure on pre-primary and primary education starts building up as individuals in this group have more (and older) children than in the age group just below. In the older age groups, the share of parents and the age of their children continue to rise, as reflected in the increasing public expenditure at the pre-primary, primary, and secondary levels. While the first two peak in the age group 35–39, spending on secondary and tertiary education continues into age groups 40–44 and 45–49, respectively. At later ages, expenditure falls for them as well as children leave the parental household. The maximum of total public education spending is reached in 752 L.Riedel, H.Stichnoth 1 3 the age group 40–44. Pre-tax income, by contrast, peaks at age 45–49, and is still fairly high thereafter, while public education spending declines steeply for individuals in their late 40s and in their 50s. Together with the high level of tertiary education spending for the poorest age group 20–24, this drives the progressivity of public education spending in the cross section. 3.2 Robustness checks Post-tax cash income So far, our results have been for pre-tax income, which is directly observable in the American Community Survey. However, Piketty et al. (2018) assume that education and other items of government consumption are allocated proportionally to post-tax disposable income. We therefore run a robustness check in which we use our measure of post-tax disposable income—simulated using TAXSIM—to divide adults into deciles (Fig.13 and Table4 inthe Appendix). As for pre-tax income, the proportionality assumption is rejected, while a lump-sum Fig. 1 Public education spending by pre-tax income, allocated based on actual enrollment. Notes: The figure shows how public education spending in the United States in 2017 is distributed among the deciles of the pre-tax income distribution. For each decile, the bars show the average values of annual public education spending (in 2017 US Dollars) at the pre-primary, primary, secondary, and tertiary levels of education. Source: Enrollment in public educational institutions is taken from the American Community Survey 2017. Each pupil or student is assigned the per-capita value of public education spending taken from the OECD (see Table2). Public education expenditure is summed up at the household level, and the resulting sum is split equally among adults aged20 and above in the household. Household income is likewise split equally among all adults 753 1 3 Government consumption intheDINA framework: allocation… allocation is a reasonable approximation except for the bottom and the top of the income distribution.23 Household equivalence income As noted in Sect.1, there are also several nonDina studies that augment the standard survey measures of disposable (money) income by different components of public in-kind spending, often with a crosscountry focus. These studies measure income at the household level and attempt to Fig. 2 Public education spending by pre-tax income: comparison of allocation methods. Notes: The figure compares the actual distribution of public education spending (in black, this is the same distribution as in Fig.1) with the distributions that result from an allocation that is proportional to pre-tax income as in the paper by Piketty etal. (2018) (“PSZ”, dark gray) and from a lump-sum transfer (light gray) to all children below age20, irrespective of actual enrollment and disregarding the differences in per-capita spending between pre-primary, primary, secondary, and tertiary education. The figure also shows the value of $4783 that would result from a lump-sum allocation to all adults. Source: Enrollment in public educational institutions is taken from the American Community Survey 2017. Each pupil or student is assigned the per-capita value of public education spending taken from the OECD (see Table2). Public education expenditure is summed up at the household level, and the resulting sum is split equally among adults aged20 and above in the household. Pre-tax household income is likewise split equally among all adults 23 Figure14 in the Appendix expresses public education spending as a share of post-tax income to visualize its progressivity. 754 L.Riedel, H.Stichnoth 1 3 make households of different size and age composition comparable through equivalence scales. As Fig.15 inthe Appendix shows, public education spending remains progressive when adopting such a household perspective.24 The average amount of public education spending received is now higher as the transfers are measured at the household level and not divided equally among adults. When the deciles are defined based on pre-tax income, average spending declines throughout the distribution. For a distribution based on post-tax disposable income, a lump-sum allocation is a decent approximation for the bottom three or four deciles, but the upper half of the distribution is again characterized by a negative relationship between public education spending and household income. The finding that public education spending declines with household income is in line with the study by Zwijnenburg etal. (2017) who report the percentage of total education spending by quintiles of household disposable income for the United States and several other countries. In the United States in 2012, 25.4% of public education spending goes to households in the bottom quintile, compared with 15.3% in the top quintile. In our data for 2017, the shares are similar, but the progressivity is even more pronounced: 26.3% of public spending goes to the 20% of households with the lowest post-tax disposable income, while the richest 20% receive 11.1% of the total. Other checks We also ran a number of other, more technical robustness checks. As noted above, despite the legal obligation to answer the survey, some of the Fig. 3 Public education spending and pre-tax income by age. Notes: The left panel of the figure shows how the average value of public education spending (allocated based on actual enrollment) differs by age. The right panel depicts average pre-tax income for the same age categories. Source: Enrollment in public educational institutions is taken from the American Community Survey 2017. Each pupil or student is assigned the per-capita value of public education spending taken from the OECD (see Table2). Public education expenditure is summed up at the household level, and the resulting sum is split equally among adults aged20 and above in the household. Pre-tax household income is likewise split equally among all adults 24 The numerical values are reported in Table4 in theAppendix. 755 1 3 Government consumption intheDINA framework: allocation… individual income components are actually imputed by the data provider. When we drop all households in which more than half of household income is based on an imputation (slightly less than 20% of our sample), the results are virtually unchanged (Table5). The same holds when we drop all households with negative income or all households with income below the 1st percentile. When the threshold is increased to the 2.5th percentile, average public education spending in the first decile is reduced from $6.0 to $5.4K, but is still higher than in all other deciles. Dropping all households whose income is above the 99.5th percentile likewise has no effect on the results. As seen in Fig.11, the ACS slightly overestimates the enrollment in educational institutions by comparison with the numbers reported by the OECD and the NCES. When we scale down our ACS enrollment numbers to meet the NCES numbers, average public education spending goes down in all deciles, but the negative relationship with income is preserved. In our main specification, we use a single value for per-student expenditure at the different levels of education, as the OECD does not provide information on within-country variation. When we use state-specific values from the NCES instead, the difference between the first and the tenth deciles is slightly reduced, but the poorest decile still receives substantially more public education spending. A lump-sum allocation is again a good approximation for the deciles in between. The OECD calculates expenditure per student on the basis of full-time equivalents; students in part-time education—relevant only at the pre-primary and the tertiary level—are assumed to represent one-third of a full-time equivalent. In the ACS, there is no information on whether individuals are enrolled only part-time, and we assign the expenditure per full-time equivalent to all students in our main specification. As a robustness check, we randomly assign part-time status based on the share of part-time students reported by the OECD. This brings down the average expenditure by decile, but leaves the negative income gradient intact. The OECD only reports a single number for annual per-student expenditure at the tertiary level, which is an average over 2-Year and 4-Year colleges. In a robustness check, we assign all graduate students to 4-Year colleges, and randomly assign undergraduates to either 2-Year or 4-Year colleges, based on the relative importance of the two types as reported by the NCES. Average expenditure is higher than in the main specification, but the relationship between income and expenditure remains the same. In our main specification, public expenditure per student includes both current expenditure (a large share of which are salaries and wages) and capital outlays, but excludes R &D—which is relevant only at the tertiary level—as well expenditure for ancillary services. Alternatively, we have used a narrower (only current expenditure) and a broader (all expenditure types plus R &D and ancillary services) definition of public education spending. This changes the level of expenditure, but has little impact on the income gradient. 756 L.Riedel, H.Stichnoth 1 3 3.3 Beyond thecrosssection The Dina literature invokes two arguments for assigning public education spending proportionally to post-tax disposable income: the unequal access to education by parental income—e.g., Alvaredo etal. (2020,p.65) or Saez and Zucman (2020,p.33)—and “a lifetime perspective where everybody benefits from education, and where higher earners attend better schools and for longer” (Piketty etal. 2017,p.27/28). In the following, we show that individuals with higher lifetime earnings (proxied for by earnings at age 40–45) have indeed received substantially more public education spending in the past. We also show—based on PSID data—that more public education spending goes to children whose parents have a higher socioeconomic status (proxied for by educational attainment). In both cases, we depart from the cross-sectional perspective we have adopted so far. In particular, we do not consider the public education spending received in a single year, but the sum of spending received in the education system. We classify individuals by their highest degree and assume that a given degree implies that the individual has passed through all the stages below, and that everyone needed the same number of years to complete each stage.25 This is admittedly a simplification. For instance, not every child attends kindergarten, and some students repeat a year in school or take longer to finish a bachelor’s or master’s degree, and this variation is likely correlated with both lifetime earnings and parents’ socioeconomic status. However, with our data there is little we can do about this, and the differences that we find are so large that they are robust to different assumptions. A potentially more important qualification is that we do not observe whether individuals completed their education abroad. We have no information about this in our data, and assume that the entire schooling was obtained in the United States. Another shortcut that we take is to use the 2017 per-student values for public education expenditure (Table2) although the cohort of individuals that we consider—40–45-year-olds in 2017, i.e., people born in the early and mid-1970s—obtained their education in the past. Given that we consider a cohort of only six years and that our interest is in the gradient and not the level of spending, this assumption should be fairly innocuous as well. Finally, moving beyond the cross section—i.e., current educational enrollment—means that we cannot distinguish between public and private institutions anymore. We assume that all individuals obtained their degrees in the public education system. This means that we overestimate the level of expenditure and, more importantly, the income gradient, as graduating from a private college is positively correlated with both own lifetime earnings and parents’ socioeconomic status. Differences by lifetime earnings We proxy for lifetime earnings using current earnings of individuals aged 40–45. At this age, the rank correlation between current earnings and lifetime earnings reaches its maximum (e.g., Haider & Solon 2006; Bönke etal. 2015). As we now consider earnings and not income, we do not 25 The details of our mapping between the highest degree observed in the ACS and the number of years spent at the different ISCED levels are presented in Table6 inthe Appendix. 757 1 3 Government consumption intheDINA framework: allocation… use the equal-split assumption that we adopt in the cross section, but directly use the personal earnings information available in the ACS. Figure4 shows how the highest degree and public education spending received vary with earnings. As expected, the highest degree is positively correlated with earnings (Panel a). While in the bottom half of the earnings distribution most individuals have at most a high school diploma or attended college without obtaining a degree, the share of people with a bachelor’s, master’s, or professional and doctor’s degree increases in the upper half of the earnings distribution. When translating these differences in degrees into differences in public education spending received, there is—unlike in the cross section—a positive income (or, more precisely, earnings) gradient. The 10% of individuals with the highest earnings have received average public education spending of $335K, about 1.4 times the amount of the bottom 50% ($234K). The allocation is still not proportional to earnings, however; proportionality would require a factor of about 14 ($196K vs. $14K). Intergenerational perspective The second argument invoked in the Dina literature for assigning public education spending proportionally to post-tax disposable income is the unequal access to education by parents’ income or, more generally, socioeconomic status (SES). Studies documenting this inequality are legion. Children from a more advantaged socioeconomic background tend to go to better schools and are more likely to attend college. We show that these differences indeed produce a positive relationship between parents’ SES and the public education expenditure that their children receive. Unfortunately, we do not observe parents’ SES in the American Community Survey. We therefore make use of the Panel Study of Income Dynamics (PSID) instead, which we again combine with information from the OECD on current public expenditure per student.26 Like in the analysis based on lifetime earnings, we restrict the sample to individuals aged 40–45 in 2017. As we do not observe individual trajectories, we again assume that individuals followed a stylized path to their highest degree (no grade retentions etc.). Figure5 shows that individuals whose parents attended college received substantially more public education spending than children of parents with a high school degree or no degree at all. As almost all individuals attended school at least until grade 8, differences start to arise for upper secondary education (ISCED level 3). Individuals whose mother (father) did not complete high school received around $50K ($46K) in public spending for upper secondary education. If a parent attended college, public spending at the upper secondary level was higher by around $7.5K (mothers) and $11.5K (fathers). The differences at the tertiary level (ISCED levels 5–8) are more pronounced. Among individuals whose parents have no high school degree, only around 13% completed college (the share is about the same both for maternal and paternal education). This group therefore has a low (unconditional) average of public education spending at the tertiary level of $32K (mothers) and $37K (fathers). By contrast, individuals 26 The data are described in Sect.B inthe Appendix. 758 L.Riedel, H.Stichnoth 1 3 where one or both parents attended college received an average of around $90K in terms of public spending on tertiary education. Total public spending on education was on average $267 K for the cohort considered here. The difference between individuals from the most and the least privileged background with respect to parents’ education is $66K on the father’s side and $68K on the mother’s side. This implies that going from the least to the most privileged parental background relates to around 30% additional education spending. DINA as a cross-sectional approach That children from already more privileged backgrounds receive almost $70K more in public education expenditure is more important for the distributional debate than the progressive pattern of public expenditure found in any given year, which, as seen above, is strongly driven by age effects. However, the positive association between public expenditure and parental SES or own lifetime earnings does not provide a justification for allocating public education expenditure proportionally to income in the Dina approach. So far, the approach has been exclusively cross-sectional, and departing from this cross-sectional perspective only for public education spending seems ad hoc. After all, age effects are also present in earnings or capital income, but are not adjusted for when measuring pre-tax income. Likewise, many cash transfers such as family benefits or in-kind transfers such as Medicare are also age-dependent Fig. 4 Highest degree and public education spending by current earnings, individuals aged 40–45. Notes: The figure shows the highest degree (left panel) and public education spending by current earnings (right panel) for individuals aged 40–45. Source: Own calculations based on the American Community Survey 2017. When calculating public education spending, we assume that a given degree implies that the individual has passed through all the stages below, and that everyone needed the same number of years to complete each stage (see Table6 inthe Appendix for details). We also assume that all individuals have attended only public educational institutions. Each year in the education system is multiplied with the per-capita value of public education spending taken from the OECD (see Table2). We use the 2017 values of per-capita spending although the individuals who were 40–45 years old in 2017 obtained their education in earlier years 759 1 3 Government consumption intheDINA framework: allocation… (e.g., Auerbach etal., 2023), but are assigned to current recipients in the Dina approach. 4 Conclusion In the distributional national accounts ( Dina ) created by Piketty etal. (2018) and others, government consumption (e.g., education, defense, infrastructure) is typically allocated proportionally to post-tax disposable income, which renders half of government expenditure distributionally neutral and implies large differences in the per-capita value of government consumption. The level of post-tax inequality is fairly sensitive to this assumption. When the expenditure is allocated on a lump-sum basis instead—an assumption that the recent version of the Dina Guidelines (Alvaredo etal., 2020) suggests as an alternative to the proportional allocation—the gap in post-tax income shares between the Top10% and Bottom 50% is reduced by half. The trend in US post-tax income shares is hardly affected by the assumptions, however. Note, however, that this parallel shift is to some extent mechanical. The true question is whether the empirical relevance of the two approaches has changed over time. In the context of public education spending, changes in fiscal equalization (Hoxby, 2001) or income-specific changes in Fig. 5 Public education spending by parents’ education. Individuals aged 40–45. Notes: The figure depicts average public education spending by parents’ education for individuals aged 40–45. The left panel distinguishes by the education of the father, the right panel by the education of the mother. Source: Own calculations using the Panel Study of Income Dynamics (PSID) 2017. When calculating public education spending, we assume that a given degree implies that the individual has passed through all the stages below, and that everyone needed the same number of years to complete each stage. We also assume that all individuals have attended only public educational institutions. Each year in the education system is multiplied with the per-capita value of public education spending taken from the OECD (see Table2). We use the 2017 values of per-capita spending although the individuals who were 40–45 years old in 2017 obtained their education in earlier years 766 L.Riedel, H.Stichnoth 1 3 highlighted enough in the Dina literature29 and motivates our analysis of how this expenditure (or parts thereof) is actually distributed. However, the key finding of Piketty, Saez, and Zucman, namely the sharp increase not only in pre-tax, but also post-tax inequality over the past four decades or so, also holds with a lump-sum allocation of government consumption. As Fig.10 shows, replacing the proportional allocation with a lump-sum allocation leads to a parallel shift in the series for the national income shares of the Bottom 50% and the Top 10%. With the lump-sum allocation, the series intersect both in the mid-1960s and the mid-1980s. However, given that the population shares of the two groups differ, an identical share of national income means that the average post-tax income of the Top 10% is five times larger than for the Bottom 50%. In 2014, the ratio of average incomes is 10.1 with a proportional allocation and 6.9 with a lump-sum allocation (Fig.17). There are two reasons for the parallel shift. First, the share of government consumption in national income has been fairly stable between 15 and 20% over the period considered here. Second, while the income shares based on a proportional allocation merely reflect the trends observed for post-tax disposable income, the series for the lump-sum allocation is based on population shares that are time-constant by construction (Top 10%, Middle 40%, Bottom 50%) and thus cannot capture any real movements in the allocation of government consumption either. The finding of a parallel shift is therefore somewhat mechanical, while the true question is whether the empirical relevance of the two approaches has changed over time. In the context of public education spending, changes in fiscal equalization (Hoxby, 2001) or income-specific changes in enrollment (e.g., Cai & Heathcote, 2022) could mean that an allocation proportional to income may work better or worse for different years. Likewise, there may have been changes in the income-specific use of public transportation or other items of government consumption over time. Supplementary analyses: PSID data linking parents andchildren For some of the supplementary analyses, we draw on additional data from the Panel Study of Income Dynamics (PSID), a well-established panel study that began to survey 5000 families in 1968 (McGonagle etal., 2012). As with the ACS, we use the 2017 wave. The PSID is much smaller than the ACS, but tracks individuals after 29 Piketty etal. (2018) do run a robustness check in which they assign public education spending not proportionally to post-tax income, but as a function of the number of children in the tax unit. This check does not take into account the differences in per-capita expenditure by level of education (tertiary education is much more expensive per capita than primary and secondary education, at least in the USA) and, importantly, it allocates tertiary education spending to the tax units of the parents and not to the students themselves, thus making the allocation more regressive. In our view, this choice makes sense when studying educational inequality, but constitutes a departure from the purely cross-sectional, separate tax-unit approach that is adopted elsewhere in their paper. Finally, the robustness check only reports the consequences for the average income of the Bottom 50% and not the change in the income shares of all three groups. 767 1 3 Government consumption intheDINA framework: allocation… they leave their original household, which allows us to link parents’ and children’s educational attainment in many cases. The PSID provides information on the highest grade or year of school someone has completed and, if applicable, on the type of college degree (associate’s, bachelor’s, master’s, PhD). Like the ACS, the PSID does not record complete educational Fig. 10 Effect of the assumptions on post-tax income shares, 1962–2014. Notes: The figure shows how the assumption regarding the allocation of government consumption affects the distribution of post-tax income in the USA over the years 1962–2014. Each panel shows the share of the Bottom 50% and the Top 10%. The left panel is for the assumption adopted by Piketty et al. (2018), i.e., an allocation of government consumption that is proportional to post-tax disposable income. The right panel shows the income shares that result from assuming a lump-sum allocation. Source: Own calculations based on Piketty etal. (2018), Appendix Tables I-SA11, II-C1b, II-C2, II-C3b Table 3 Summary statistics: comparison of ACS and PSID, individuals aged 40–45 The table compares means (and standard errors in parentheses) of some key variables for individuals aged 40–45 across the ACS and the PSID data. The ACS data are used in Fig.4, the PSID data are used in Fig.5. The difference in the number of weighted observations is due to missing values for parental education in the PSID. Without conditioning on education information for at least one parent being present, the PSID has 1770 observations and 23.858M weighted observations, very close to the ACS number ACS PSID Age 42.5 (0.004) 42.5 (0.059) Share female (%) 50.9 (0.001) 48.1 (0.016) Annual labor income ($) 51,143 (143) 51,007 (1889) High school education (%) 23.8 (0.001) 26.5 (0.015) Associate’s degree (%) 9.3 (0.001) 9.7 (0.010) Bsc. degree (%) 21.4 (0.001) 20.5 (0.013) Msc. degree (%) 10.5 (0.001) 10.3 (0.010) Total education transfers ($) 261,440 (172) 269,224 (2055) N216,278 925 N, weighted 23.787M 11.962M 768 L.Riedel, H.Stichnoth 1 3 histories. We therefore assume that a given degree implies that the individual has passed through all the stages below, that everyone needed the same number of years to complete each stage (see Table6 inthe Appendix for details), and that all education was received in the USA. We use the PSID only for the intergenerational analysis in Sect.3.2, where we focus on individuals aged 40–45 in 2017. As a check on the data, we compare summary statistics between the PSID and individuals from the same age group in the ACS (Table3). The check is important because we can link information on education between parents and children for only about half of individuals in our age group. Reassuringly, the table shows that summary statistics for both samples are very close, which suggests that selection is not a major issue. Additional tables andfigures See Figs.11, 12 and 13 and Tables4, 5 and 6 Fig. 11 Enrollment in educational institutions, USA 2017. Notes: The figure compares our ACS-based numbers for the enrollment in educational institutions in the USA in 2017 with statistics published by the OECD and the National Center for Education Statistics (NCES). The left panel shows the number of students enrolled in pre-primary, primary, or secondary education, the right panel is for tertiary education. A distinction is made between public and private institutions. Source: Own calculations based on the American Community Survey 2017. OECD: Education at a Glance 2020 (OECD Statistics, 2020), Table: Enrollment data adjusted to the financial year. Sum of students in full-time and part-time education. Parttime is only non-zero at the pre-primary and the tertiary levels. Students in post-secondary non-tertiary education not included (110K are enrolled in public institutions, 273K in private institutions). NCES: National Center for Education Statistics, Digest of Education Statistics 2019 (De Brey et al., 2021), Table105.30: Enrollment in elementary, secondary, and degree-granting post-secondary institutions, by level and control of institution: Selected years, 1869-70 through fall 2029 769 1 3 Government consumption intheDINA framework: allocation… Fig. 12 Public education spending as share of pre-tax income by deciles of pre-tax income. Notes: The figure shows how public education spending in the USA in 2017 is distributed among the deciles of the pre-tax income distribution. For each decile, the bars show the average of annual public education spending expressed as shares of average pre-tax income for the pre-primary, primary, secondary, and tertiary levels of education. Source: Enrollment in public educational institutions is taken from the American Community Survey 2017. Each pupil or student is assigned the per-capita value of public education spending taken from the OECD (see Table2). Public education expenditure is summed up at the household level, and the resulting sum is split equally among adults aged20 and above in the household. Household income is likewise split equally among all adults. Observations with income below the 2.5th percentile are dropped 770 L.Riedel, H.Stichnoth 1 3 Fig. 13 Public education spending by post-tax cash income, allocated based on actual enrollment. Notes: The figure shows how public education spending in the USA in 2017 is distributed among the deciles of the post-tax disposable income distribution. For each decile, the bars show the average values of annual public education spending (in 2017 US Dollars) at the pre-primary, primary, secondary, and tertiary levels of education. Source: Enrollment in public educational institutions is taken from the American Community Survey 2017. Each pupil or student is assigned the per-capita value of public education spending taken from the OECD (see Table2). Public education expenditure is summed up at the household level, and the resulting sum is split equally among adults aged20 and above in the household. Household posttax disposable income is simulated using TAXSIMv32, and is likewise split equally among all adults 771 1 3 Government consumption intheDINA framework: allocation… Table 4 Public education spending by income: detailed results The table shows how public education spending in the USA in 2017 is distributed among the deciles of the income distribution. All values in 2017 US Dollars. For the sake of presentation and given the large sample size, standard errors are omitted. The deciles are based on pre-tax income (panel A), post-tax disposable income (panel B), and equivalised pre-tax household income (panel C). The same information is presented in graphical form in Fig.1 in the main text and Figs.13 and 15 inthe Appendix. Source: Enrollment in public educational institutions is taken from the American Community Survey 2017. Each pupil or student is assigned the per-capita value of public education spending taken from the OECD (see Table 2). Public education expenditure is summed up at the household level. In panels A and B, the resulting sum is split equally among adults aged20 and above in the household, and household income is likewise split equally among all adults. Panel C reports public education spending at the household level instead, and deciles are based on equivalised pre-tax household income, using the modified OECD equivalence scale, which assigns a value of 1 to the first adult in the household, of 0.5 to each additional household member aged 14 and above, and of 0.3 to each child below the age of 14. Pre-tax income is directly taken from the American Community Survey, while post-tax disposable income is simulated using TAXSIMv32 Income decile 1 2 3 45678910 A. Pre-tax income (adults) Pre-primary 179 165 169 153 146 141 144 152 136 114 Primary 1209 1214 1230 1144 1098 1118 1165 1218 1245 1237 Secondary 1386 1447 1514 1505 1504 1542 1635 1758 1920 1913 Tertiary 3253 1927 1852 1821 1817 1812 1716 1534 1379 992 Total 6027 4752 4765 4623 4564 4613 4660 4661 4680 4256 B. Post-tax Cash Income (Adults) Pre-primary 138 141 162 174 164 157 153 163 138 110 Primary 935 978 1189 1277 1217 1231 1254 1294 1293 1209 Secondary 1102 1248 1430 1604 1591 1678 1709 1877 1953 1926 Tertiary 3402 2046 1889 1834 1798 1742 1652 1468 1312 976 Total 5577 4413 4670 4888 4769 4808 4768 4802 4696 4221 C. Equivalised Pre-tax Income (Households) Pre-primary 379 409 378 333 306 271 241 189 154 124 Primary 2701 3074 2874 2627 2222 2176 1923 1716 1481 1290 Secondary 3254 3890 3890 3495 3275 3152 2691 2428 2049 1723 Tertiary 6771 3447 3476 3524 3455 3462 3147 2953 2566 1686 Total 13,106 10,820 10,618 9978 9258 9061 8002 7286 6250 4822 772 L.Riedel, H.Stichnoth 1 3 Table 5 Robustness checks Notes: The table summarizes the results of our robustness checks. For comparison, results for the main specification are shown in the first row as well. The amounts reported in the table are annual public education transfers in thousand US Dollars. Source: In the main specification, enrollment in public educational institutions is taken from the American Community Survey 2017. Each pupil or student is assigned the per-capita value of public education spending taken from the OECD (see Table2). Public education expenditure is summed up at the household level, and the resulting sum is split equally among adults aged20 and above in the household. Household income is likewise split equally among all adults. The robustness checks modify the measurement of enrollment, of per-capita expenditure, or of the household income that enters the computation of the deciles. For details, see Sect.3.2 Decile of pre-tax income 12345678910 Main specification 6.0 4.8 4.8 4.6 4.6 4.6 4.7 4.7 4.7 4.3 Drop if > 50% of income imputed 5.9 4.7 4.8 4.6 4.5 4.6 4.7 4.7 4.6 4.2 Drop if income negative 6.0 4.7 4.8 4.6 4.6 4.6 4.7 4.7 4.7 4.3 Drop if income < 1% 6.0 4.7 4.8 4.6 4.6 4.6 4.7 4.7 4.7 4.3 Drop if income < 2.5% 5.4 4.7 4.8 4.6 4.6 4.6 4.7 4.7 4.7 4.3 Drop if income > 99.5% 6.0 4.8 4.8 4.6 4.6 4.6 4.6 4.7 4.7 4.3 Enrollment as in NCES 5.5 4.4 4.4 4.3 4.2 4.3 4.3 4.4 4.4 4.0 Variation across states 5.6 4.4 4.5 4.4 4.3 4.3 4.4 4.5 4.6 4.4 Full-time equivalents 4.6 3.8 3.8 3.7 3.7 3.7 3.8 3.8 3.9 3.6 2/4-year college 6.8 5.2 5.2 5.1 5.0 5.1 5.1 5.1 5.1 4.6 Current expenditure 5.5 4.3 4.3 4.2 4.1 4.2 4.2 4.2 4.2 3.9 All expenditure 7.2 5.5 5.5 5.4 5.3 5.3 5.4 5.3 5.3 4.8 773 1 3 Government consumption intheDINA framework: allocation… Table 6 Construction of educational trajectories The table documents how we map the information on the highest degree in the American Community Survey (ACS) 2017 into educational trajectories. The rows correspond to the values of the variable “Highest degree” (educd) in the ACS. The question reads: “What is the highest degree or level of school this person has completed?”. As our method is retrospective and we do not have information on grade repetition or, more generally, the individual pathways to a given degree, we assign the same number of years to all individuals with the same degree. For instance, individuals with a regular high school diploma are assumed to have spent 2 years at ISCED level 0, 6 years at ISCED level 1, 3 years at ISCED level 2, and 4 years at ISCED level 2. Individuals with a bachelor’s degree are assigned the same trajectory plus 4 years at ISCED level 6, and a master’s degree would add two years at ISCED level 7. The last column of the table gives the total number of years thus obtained. The number is meant as a summary measure only. When computing the public expenditure for each degree, we multiply the number of years at each ISCED level with the corresponding OECD per-student expenditure from Table2 Highest degree (ACS) Years spent at ISCED level Total 012345678 No schooling completed 0 0 0 0 0 0 0 0 0 0 ISCED 0 Nursery school, preschool 2 0 0 0 0 0 0 0 0 2 ISCED 1 Kindergarten 2 1 0 0 0 0 0 0 0 3 Grade 1 2200000004 Grade 2 2300000005 Grade 3 2400000006 Grade 4 2500000007 Grade 5 2600000008 ISCED 2 Grade 6 2610000009 Grade 7 2 6 2 0 0 0 0 0 0 10 Grade 8 2 6 3 0 0 0 0 0 0 11 ISCED 3 Grade 9 2 6 3 1 0 0 0 0 0 12 Grade 10 2 6 3 2 0 0 0 0 0 13 Grade 11 2 6 3 3 0 0 0 0 0 14 12th grade, no diploma 2 6 3 3 0 0 0 0 0 14 Regular high school diploma 2 6 3 4 0 0 0 0 0 15 GED or alternative credential 2 6 3 4 0 0 0 0 0 15 Some college, but less than 1 year 2 6 3 5 0 0 0 0 0 16 ISCED 4 Associate’s degree, type not specified 2 6 3 4 2 0 0 0 0 17 ISCED 5 1 or more years of college credit, no degree 2 6 3 4 0 2 0 0 0 17 ISCED 6 Bachelor’s degree 2 6 3 4 0 0 4 0 0 19 ISCED 7 Master’s degree 2 6 3 4 0 0 4 2 0 21 Professional degree beyond a bachelor’s degree 2 6 3 4 0 0 4 2 0 21 ISCED 8 Doctoral degree 2 6 3 4 0 0 4 2 4 25 774 L.Riedel, H.Stichnoth 1 3 See Figs.14, 15, 16 and 17 Fig. 14 Public education spending as share of post-tax income by deciles of post-tax income. Notes: The figure shows how public education spending in the USA in 2017 is distributed among the deciles of the post-tax income distribution. For each decile, the bars show the average of annual public education spending expressed as shares of average post-tax income for the pre-primary, primary, secondary, and tertiary levels of education. Source: Enrollment in public educational institutions is taken from the American Community Survey 2017. Each pupil or student is assigned the per-capita value of public education spending taken from the OECD (see Table2). Public education expenditure is summed up at the household level, and the resulting sum is split equally among adults aged20 and above in the household. Household income is likewise split equally among all adults. Household post-tax disposable income is simulated using TAXSIMv32, and is likewise split equally among all adults. Observations with post-tax income below the 2.5th percentile are dropped 775 1 3 Government consumption intheDINA framework: allocation… Fig. 15 Public education spending by equivalised household income, allocated based on actual enrollment. Notes: The figure shows how public education spending in the USA in 2017 is distributed among households over deciles of the equivalised household income distribution. Left panel: deciles based on pre-tax income. Right panel: deciles based on post-tax disposable income simulated using TAXSIMv32. For each decile, the bars show the average values of annual public education spending (in 2017 US Dollars) at the pre-primary, primary, secondary, and tertiary levels of education. Source: Enrollment in public educational institutions is taken from the American Community Survey 2017. Each pupil or student is assigned the per-capita value of public education spending taken from the OECD (see Table2). Public education expenditure is then summed up at the household level. Household income is equivalised using the modified OECD equivalence scale, which assigns a value of 1 to the first adult in the household, of 0.5 to each additional household member aged 14 and above, and of 0.3 to each child below the age of 14 Fig. 16 Effects of the assumptions on the distribution of post-tax income. Notes: The figure shows how the assumption regarding the allocation of government consumption affects the distribution of post-tax income. When government consumption is allocated based on post-tax disposable income as in Piketty etal. (2018), the Bottom 50% receive 19.3% of national post-tax income, while the Middle 40% receive 41.6%, and the Top 10% receive 39.1% (left panel). Under the alternative assumption in which each adult receives the same amount of government consumption, the shares are 24.6%, 41.4%, and 33.9% instead (right panel). Source: Own calculations for the USA in 2014 based on Piketty etal. (2018), Appendix Tables I-SA11, II-C1b, II-C2, II-C3b