Received: 22 May 2021 DOI: 10.1111/ecin.13094 ORIGINAL ARTICLE - Accepted: 26 April 2022 Financing public education when agents have retirement concerns Daniel Montolio1,3 | Amedeo Piolatto2,3 | Luca Salvadori2,3,4 1 Department of Economics, University of Barcelona (UB), Barcelona, Spain 2 UFAE ‐ Department of Economics and Economic History, Autonomous University of Barcelona (UAB), Bellaterra, Spain 3 Barcelona Institute of Economics (IEB), Barcelona, Spain 4 Tax Administration Research Centre (TARC), Exeter, UK Correspondence Amedeo Piolatto, UFAE ‐ Department of Abstract Economics and Economic History, We study, theoretically and empirically, the link between voters' support for Autonomous University of Barcelona public education and pensions. We show that the (inter‐generational) redis- (UAB), Bellaterra, Spain. Email: amedeo.piolatto@uab.es tributive component of the retirement system creates a link between current spending on education and future pensions. Specifically, investments in edu- Funding information cation increase the young's productivity and, hence, future tax proceeds that Ministerio de Ciencia, Innovación y Universidades, Grant/Award Numbers: will finance the current workers' pension. Consequently, the support for PGC2018‐094348, RTI2018‐095983‐B‐I00, publicly financed education grows together with the generosity and degree of RYC‐2016‐19371; Agència de Gestió d'Ajuts Universitaris i de Recerca, Grant/ redistribution of the retirement system. The empirical analysis uses repeated Award Number: 2017SGR796; Economic cross‐country surveys to confirm the model predictions. and Social Research Council, Grant/ Award Number: ES/S00713X/1 KEYWORDS inter‐generational redistribution, majority voting, pension system, private education, public [Correction added on 26 May, 2022, after education, public spending, retirement, taxes first online publication: ORCID has been added to the author Daniel Montolio in JEL CLASSIFICATION this version.] D7, H31, H42, H44, H52, H55, I22 1 | INTRODUCTION Education and pensions are used for inter‐ and intra‐generational redistribution. They constitute major components of the annual budget. The incessant need to free additional resources out of tightened budgets may explain why most western governments are contemplating reforms to both the education and the pension systems. However, voter preferences cannot be ignored by career‐concerned politicians: both pensions and education come under very close scrutiny, which limits the policy space of politicians with re‐election concerns. Abbreviation: OECD, Organisation for Economic Co‐operation and Development. Managing Editor: Stefano Barbieri - This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2022 The Authors. Economic Inquiry published by Wiley Periodicals LLC on behalf of Western Economic Association International. Economic Inquiry. 2022;1–22. wileyonlinelibrary.com/journal/ecin 1 2 - MONTOLIO ET AL. F I G U R E 1 Public spending on education (% of GDP) in OECD countries with above‐average spending on pensions versus: [left] Bismarck factor and [right] spending on pensions (% of GDP). Authors' calculations based on World Bank, OECD and Krieger and Traub's (2011, 2013) data. [left] Correlation Education‐Bismark ≈ − 0.33; [right] Correlation Education‐Pensions ≈ 0.52. See Appendix B for more details Public spending on education correlates (Figure 1) negatively with the Bismarkian factor (the contributory component of the pension) and positively with the total spending on pensions. Our paper contributes to the literature on the political economy of publicly provided goods, by combining voters' concerns for the provision of public education and pensions. In particular, we investigate the interconnection between public spending on education and pensions, when citizens are also offered a private‐education alternative. We are specifically interested in looking at how the voters' support for publicly‐funded education may vary depending on the characteristics and generosity of the retirement scheme. Education provides private benefits to students and public education may help to level the playing field for new generations. Together with parents' altruism toward their own children, this may explain some support for a publicly funded system. However, the political equilibrium may depend on the presence of a private alternative (Epple & Romano, 1996a,b; Cohen‐Zada & Justman, 2003) and, possibly, also on how private school is financed (Akyol, 2016; Chen & West, 2000; Epple et al., 2018; Epple & Romano, 1998; Gradstein & Justman, 2005; Piolatto, 2010). Beyond that, education produces positive externalities, for example, it helps to reduce social conflicts (Brutti & Montolio, 2021; Gradstein, 2000). More importantly, education affects employment, economic growth, income and productivity (Altindag et al., 2022; Barro, 2013; Baum & Lake, 2003; Gradstein & Justman, 1997; Romer, 1986; Sanchez‐Losada, 2000). Investing in education becomes a way to increase the productivity of the future labor force. Our model shows that citizens can reappropriate part of the spending on education through the pension system as long as it includes a ‘pay‐as‐ you‐go’ (inter‐generation redistributive) component.1 When this is the case, citizens start to care about the quality of education of all the young, not just of their offspring, because a larger investment in education today affects the state ability to finance pensions tomorrow. This mechanism affects positively the support for publicly funded education also among households who opted for a private‐education school. The importance of such a redistribution channel depends on the magnitude of the retirement system. Consequently, the generalized support for publicly funded education hinges on the combination of the Bismark (contributory) component of pensions and of the size of the pension scheme. Our empirical analysis tests and confirms the model's predictions. In our two‐period stylized model, adults choose the type of education for their offspring (private or public) and vote over the income tax rate that finances current public education. Agents are concerned by their current and future consumption, where the latter depends on pensions. We take the tax rate that finances pensions as exogenous (Section 2.1 discusses this assumption), yet agents can influence their future pensions by investing in the education of young agents, as this increases future average income and, therefore, the level of inter‐generational redistribution. We investigate the extent to which incentives to invest in education are affected by the pension system and, more particularly, by the importance of its contributory and redistributive components. We conclude that the agents' support for publicly funded education is i) decreasing in the Bismarck (contributory) component of pensions and ii) increasing in the magnitude/generosity of the pension system. Hence, the lower the degree of intergenerational redistribution characterizing the pension system, the less willing agents are to invest in public education. Furthermore, agents care more about public education as the stake in their pensions increases. MONTOLIO ET AL. - 3 We combine micro‐level and country‐level data, to provide a formal test for these theoretical predictions. We exploit four waves of a survey on public opinion about public policies run between 1985 and 2006 in 13 countries among a nationally representative sample of individuals including, on aggregate, more than 30,000 respondents. We provide strong validation of the theoretical predictions by employing several different specifications and a progressively less parsimonious set of control variables. Namely, our results confirm that the support for publicly financed education is decreasing in the Bismarckian factor (estimated by Krieger & Traub, 2013) while it is increasing in the generosity of the pension system measured as the public expenditure (% of GDP) on old‐age pensions. Lancia and Russo (2016) consider a setting similar to ours. Their dynamic theoretical model focuses on the generational conflict between workers and pensioners over the allocation of budget. Current pensioners are not interested in education spending, while workers are only interested in future pensions. They study the conditions under which the implementation of public education and social security survive voting in a small open economy. What crucially distinguishes our work from theirs is the fact that we allow parents to choose between public and private education, that we explicitly model the degree of redistribution of the pension system (through the Bismark factor) and that we test our predictions using individual‐level data. Our work is also related to Bishnu and Wang (2017), who study how investments in education and pensions have general equilibrium effects. Their focus is specifically on the welfare consequences of it. We are also close in spirit with Bellettini and Ceroni (1999) who, in the words of the authors, ‘show that redistributive and growth‐oriented policies, although competing for scarce tax revenues, might go hand in hand and bring about fast economic growth. In particular, the aim of [their] paper is not to provide a positive theory for the existence of social security systems, but rather to show how to design a social security system which may foster public investment and economic growth.’ The idea that education, affecting growth, allows increasing the tax proceeds that will finance future pensions is not new. Kaganovich and Zilcha (1999) focus on the optimal allocation of fixed tax proceeds between education and social security. Bellettini and Ceroni (2000); Pecchenino and Pollard (2002) and Zhang and Zhang (2004) study the impact of social security and education on growth; Soares (2003) studies the preference of agents for public investment in edu- cation and how they allocate their time between education and work. Boldrin and Montes (2005, 2009) undertake normative studies of education and pensions and the optimal intergenerational transfer scheme. Poterba (1998); Echevarría (2004); Sanz and Velázquez (2007); Cattaneo and Wolter (2009); Rattsø and Sørensen (2010) and Gonzalez‐ Eiras and Niepelt (2012) look at how a change in the composition of society (age distribution, life expectancy, etc.) affects the provision of pensions and education, given a fixed budget. Those authors disregard the political feasibility of policies aimed at financing public education. Instead, we focus on how forward‐looking adults change their behavior and invest in young's education, to guarantee a sustainable pension system in the future. The paper is structured as follows. Section 2 presents the model. In Section 3 we bring the model predictions to the data. Section 4 concludes. Proofs are in Appendix A. 2 | THE MODEL This work aims to study the interaction between the willingness to invest in education and the pension system. We propose a stylized model that, as customary, requires some assumptions. In Section 2.1 we motivate some of the (possibly controversial) assumptions and discuss possible limitations of the model. We consider a two‐period model that could be easily interpreted as a reduced form of an OLG model.2 For the sake of parsimony, we assume no population growth and no discount of the future.3 In period 0 each adult works and votes over the tax to finance public schools. They allocate income between their own consumption (current and future) and their child's education. In period 1, adults retire and enjoy their pension. Young agents attend school in 0, while in 1 they work and pay the tax to finance pensions. In our model, all the decisions are taken in 0 by adults, while young agents play no active role. Compulsory education is both publicly and privately provided: the two are mutually exclusive. The quality of ed- ucation, measured as per‐student expenditure, is denoted by XP for the public sector and XR for the private. X is the average quality of education, measured as the average spending on instruction. Our interest lies in adults' willingness to pay both for the education of their own offspring and to finance public education. We only need to focus on education in period 0, hence we do not need a time index for X. Public education is financed through a universal and proportional tax (t) on income (ω) and access to it is free. We assume the quality of education to be homogeneous among all public schools. Private schools are costly and adults choose the level of quality they wish to buy for their offspring.4 4 - MONTOLIO ET AL. Adults vote on the tax rate for financing public education and how much to spend for their own child's education (in the case of public schooling, the expenditure is simply 0). The residual income is used to consume the numeraire good b. Adults (in 0) are concerned by their child's education X and their current and future consumption of the numeraire good (respectively b0 and b1), as in the models of ‘intergenerational altruism’. Their lifetime utility function is U ðb0 ; b1 ; X Þ ¼ b0 þ b1 þ λωβ0 ln X: ð1Þ In Equation (1), λ defines the weight of education relative to the consumption of the numeraire good while β ≥ 0 determines how income and willingness to pay for education are related. With β = 0, all agents care equally about education, while if β > 0, the utility of education is increasing in income. The quasi‐linear specification comes naturally: in this setting, consumption (b) is the numeraire, which should shift the indifference curves outward as consumption of it increases, without changing their slope. Consistently with that, the quasi‐linear specification guarantees that the marginal rate of substitution only depends on the consumption of education (X ). Adults' income in period 0 (ω0) is exogenous and uniformly distributed among a unit mass of agents: ω0 ∼ U[0, 1]. Investing in education affects young agents' productivity and, therefore, their income (received in period 1). To incorporate this feature in the model, we use a reduced form where young agents' income (ωy) is increasing and concave in the education they received in 0 (hence, the marginal product of education is diminishing). In particular, we assume young's income in 1 to be ωy ¼ ω0 þ X ϕ ; ð2Þ with ϕ < 1. The average income of young agents in 1 is ωy . Pensions are adults' sole source of income in period 1 and are not taxed. Following Casamatta et al. (2000), the pension system comprises a contributory and a redistributive component. We denote by α ∈ ½0; 1� the Bismarckian (or contributory) component, that is, the share of a pension that depends on the agent's previous contributions. The remaining (1 − α) of the pension, the redistributive component, depends on the average contribution of the current workers. Using s to indicate the income tax that finances pensions, in period 0 each adult pays sω0 to the pension system, of which (1 − α)sω0 is used to pay current pensions, while αsω0 is paid back to the worker in period 1 as a pension. Therefore, an adult in period 1 receives a pension s αω0 þ ð1 − αÞωy Þ. We assume both α and s to be exogenous. Then, adults' disposable income in period 0 is ð1 − t − sÞω0 , from which follows that their numeraire consumption in the first period is b0 ¼ ð1 − t − sÞω0 − XR , where XR = 0 if a child attends public school. Let n denote the share of students attending public school. The quality of public school XP (corresponding to the per‐ student expenditure) follows directly from the public school budget constraint nXP ≤ tω0 , and is: tω0 XP ¼ ; ð3Þ n 2.1 | Discussion of the model design Some of the modeling choices that we made deserve some comments: we regrouped them here. We will begin dis- cussing Equation (1) and, in particular, the role of β. Then we will spend some words about the marginal product of education and Equation (2). Next, we will discuss the choice of keeping the choice of s exogenous. Finally, we will briefly speculate on why fertility may matter. Role of β Looking at Equation (1), the marginal utility of education depends on an agent (ω0). Implicitly, this is based on the idea of a positive correlation between wealth and willingness to invest in the own child's education. This is consistent with the literature (see, e.g., Dur et al., 2004; Griliches & Mason, 1972) and can be intended as a consequence of the preference of wealthy (and possibly well‐educated) parents to invest in human capital and to enhance their offspring future productivity. However, by assuming β ≥ 0 we are allowing income to impact the marginal utility of education either linearly (β = 0) or increasingly (β > 0). This assumption, again, is consistent with the literature: indeed, Tolley and Olson (1971) estimates that a 1% increase in non‐human wealth leads to an increase in education expenditure of 1.65%. MONTOLIO ET AL. - 5 Marginal product of education The assumption on the distribution of the initial income ω0 is made to be able to compute the first moment and analytically solve the model in a closed‐form. The main results are robust to modifi- cations in the distribution of income. Furthermore, the functional form of Equation (2) is only relevant to the extent that it ensures a strictly positive relationship between current investment in education and future income. The specific functional form of Equation (2), especially when combined with Equation (1), can indeed be considered a reduced form that accounts for the fact that earnings are positively correlated with education and that we observe a high intergenerational persistence of income. The idea that income is positively correlated with education is widely supported in the literature (see Tolley and Olson, 1971; Card, 2001; Lemieux, 2006, and the references therein). High persistence of income is found, among others, by Lee and Solon (2009) for the US. Mazumder (2005) estimates the US Intergenerational Income Elasticity (IIE) to be 0.61. Lefgren et al. (2012) estimates for Sweden are slightly lower (between 0.29 and 0.4). The reduced form that we use, combined with the fact that low‐income agents tend to prefer public education, would suggest a non‐linear persistence of income, with a tendency to converge for low incomes. This is precisely reported by Bratsberg et al. (2007) for Denmark, Finland and Norway. Voting on pensions: We assume the tax rate that finances pensions to be exogenous. Interested readers may refer to Casamatta et al. (2000) for a model on retirements with vote on s. Our setting fits with the idea that a change in the pension system requires more time and a larger consensus than, for example, the expenditure decision for education.5 Proposition 2 studies the impact of a variation in s on our equilibrium (comparative statics). Our decision to keep the pension tax fixed follows two rationales. First, within our stylized setting with selfish agents and no commitment, a decision upon tax s simply leads to a generational clash: each generation would like to extract surplus from the subsequent one and to leave nothing to the previous one. A corner solution is inevitable unless imposing some (arbitrary) inter‐generational agreement or assuming that the decision is the outcome of some coop- erative bargaining.6 Shall we do that, results would follow directly from the imposed assumptions (i.e., results would be assumption‐driven) and would bring no additional insights. Second, when decisions are taken by majority voting, choosing over a two‐dimensional policy is methodologically problematic.7 The existence of a unique equilibrium de- pends on the specific voting design. In particular, which policy is voted first may matter (Cremer et al., 2004). Results may still be qualitatively robust, but the set of assumptions required to solve the model would be at least as arbitrary as the choice of keeping the variable exogenous. Given the purpose of our analysis, we believe that keeping s exogenous is both reasonable and convenient. Fertility: In their work, Croix and Doepke (2009) show that households opting for a private education reduce their fertility to partially compensate for the additional source of expenditure that education represents. Therefore, the endogenous educational choice has an impact on the share of young attending public school. While we agree that fertility could be intrinsically related to education, none of the attempts to endogenize the fertility decision in a tractable way within our setting provides novel insights. Still, based on what we learn from Croix and Doepke (2009), we can speculate that our model underestimates the share of students attending public schools. Since households opting for public education are also keener to support it through taxes, this also means that we expect a (weakly) positive cor- relation between fertility and the voters' support for expanding the public investment in education. Our empirical analysis (Table 2) shows that this is indeed the case. 2.2 | Adults' utility maximizing behavior In our model, the only active citizens are adults in period 0. In period 0, young agents are not allowed to vote and their consumption of education is decided by adults. Adults retire in period 1 and enjoy consumption, based on the decisions taken in period 0. We compute here the optimal adults' behavior. Adults first vote over the tax rate to finance public education, then they decide between public and private edu- cation, and finally they choose the share of budget to devote to consumption and to private education (where a zero share implicitly means choosing public education). It stands to reason that an agent prefers public to private education if and only if the utility derived is higher. This means that people attend a private school if and only if U(b0, b1, XR) ≥ U (b0, b1, XP). Solving the model backward, we consider separately the optimal behavior of an agent depending on which path is taken (i.e., public vs. private education), starting with the choice for households that opt for public education. Once computed the preferred tax rate for both types of agent, we compute the conditions under which an agent prefers public 6 - MONTOLIO ET AL. to private education, given the tax rate. Finally, we study how total expenditure on education depends on the tax rate and derive some properties of the preferred tax by an agent. Conditional on opting for public education, adults' consumption directly depends on the tax rate and, hence, on disposable income: we immediately obtain that b0 = (1 − t − s)ω0, and b1 ¼ s αω0 þ ð1 − αÞωy Þ. At the first stage of the decision process, the preferred tax rate t to finance public education is the one that solves the following maximization problem: β max U ðb0 ; b1 ; XP Þ ¼ b0 þ b1 þ λω0 ln XP t s:t: b0 ¼ ð1 − t − sÞω0 � ð4Þ b1 ¼ s αω0 þ ð1 − αÞωy tω0 XP ¼ n The first order condition is: � � ∂ωy β 1 1 ∂n ð1 − αÞs þ λω0 − ¼ ω0 : ð5Þ ∂t t n ∂t Equation (5) implicitly defines the preferred tax tP to finance public education for an adult opting for the public school system. The right hand side represents the cost of an increase in tax rate t (i.e., the reduction in disposable income). On the left hand side, the first term accounts for how the agent's own future income is affected by a change in the average current consumption of education, via the redistributive component of pensions. The second term accounts for the direct utility change following a change in the quality of public education. More specifically, following an in- crease in t, the first term within the parentheses accounts for the increase in resources invested in public education, while the second one considers the variation of XP due to the change in the number of students in public schools.8 Conditional on opting for private education, the maximization problem of an adult consists instead in choosing the share of budget to devote to education, and the tax rate that would be optimal: max U ðb0 ; b1 ; XR Þ ¼ b0 þ b1 þ λωβ0 ln XR t;XR s:t: b0 ¼ ð1 − t − sÞω0 − XR ð6Þ b1 ¼ s αω0 þ ð1 − αÞωy Þ The first order conditions are: β XR ¼ λω0 ð7Þ ∂ωy ω0 ¼ ð8Þ ∂t ð1 − αÞs Equation (7) defines the preferred consumption of private education XR, while Equation (8) defines the preferred tax ∂ω ∂2 ω rate tR of an adult opting for private education.9 For an internal solution we need ∂ty > 0 and ∂t2 y < 0, which occurs if an increase in public expenditure in education induces a concave increase in total expenditure in education. Knowing the preferred expenditure in private education, we can now study the condition under which an agent prefers private to public education, given a generic tax rate t. Agents choose private school if and only if U(b0, b1, XR) ≥ U(b0, b1, XP), that is, if −XR þ λωβ0 ln XR ≥ λωβ0 ln tωn0 . Then, we denote by ω~ the income for which an adult is indifferent to the two types of schooling: � �1=β � � etω0 et 1=β ~ ¼ ω ¼ ; ð9Þ λn 2λn MONTOLIO ET AL. - 7 where e is the Napier's constant (or Euler number). By construction, R the number of agents attending public school (n) corresponds to all agents with income below ω ~ . Hence, n ¼ 0ω~dω0 and we obtain that �1 � et βþ1 ~ ¼n¼ ω ; ð10Þ 2λ � �βþ1 1 λtβ XP ¼ : ð11Þ e2β Lemma 1. The average income in period 1 of those who were young in period 0 is � e �1−ϕ � �� �βϕþ1 1 λϕ βþ1 eϕ t βþ1 ωy ¼ þ þ 1− ð12Þ 2 βϕ þ 1 λ βϕ þ 1 2 Proposition 1. An increase in the tax t always improves the quality of public school. This attracts more students to the public sector, which mitigates the increase in per capita expenditure, but nevertheless the total impact is positive. However, the total per capita expenditure in private and public education may fall, and this would have a negative impact on the average income in the subsequent period. Corollary. The tax rate preferred by an adult is always higher when opting for the public education system. Furthermore, for adults opting for private education, the preferred tax rate is decreasing and convex in income. Proposition 1 has important policy implications: it says that an increase in the total expenditure for public education may be offset by a decrease in private expenditure. Hence, increasing the tax rate t may induce a reduction in future total wealth. This is because an increase in the tax to finance public education makes the individual's budget constraint more stringent and, at the same time, public school becomes more attractive. Therefore, fewer people attend a private school (~ω increases). Given that, in equilibrium, the per pupil expenditure in private school is higher than that in the public sector, a shift from the private to the public sector may imply an overall fall in investment in education. This implies that the average income in the subsequent period also falls. ϕ The condition β > e ϕ−1 guarantees that an increase in the tax rate induces a higher aggregate expenditure on edu- cation. It requires that ϕ is sufficiently small compared to β. This means either that we need the desire for high quality education to be increasing rapidly in income, or that the returns on education are sufficiently small. Actually, the above‐ mentioned condition, together with ϕ ≤ 1, is both necessary and sufficient for the maximization problem of adults preferring private education to be well behaved and, therefore, we assume it to hold. As discussed in Section 2.1, these assumptions seem consistent with results in Tolley and Olson (1971). As a first step toward our analysis of the impact of the pension system on the choice to invest in public education, the following proposition studies the sign of the change in the preferred tax rate following a change in the parameters of the pension system (α and s). ϕ Proposition 2. Under the maintained assumption that β > e ϕ−1, the equilibrium tax rate t, decided by the majority vote of all adults, is decreasing in the Bismarckian factor α (the contributory component of the pension system) while it is increasing in the tax rate s that finances pensions. According to Proposition 2, both s and α impact all agents in a same way, regardless of their choice about the type of schooling. This means that all agents, including the decisive voter (regardless of his identity) will behave in a pre- dictable way. The intuition behind Proposition 2 is that voters care about their future consumption, which depends on the two components of the pension (the Bismarckian factor α and the redistributive component). The redistributive component of pensions depends on the population average income, which in turn depends on the average investment in education. Hence, agents are willing to invest in public education in order to raise the average level of education and, hence, their own future pension. The smaller α is (hence, the greater the degree of redistribution provided by the pension system is), 8 - MONTOLIO ET AL. the stronger this channel is. Consequently, lower levels of α coincide with a more vigorous support for the public investment in education. By contrast, the share of others' private‐returns‐on‐education that an agent can appropriate through pensions decreases when α increases, hence, voters are less willing to sacrifice their own current consumption (by paying a higher tax on their income). The magnitude of this effect depends on size of the pension scheme (s). In particular, the channel is stronger when s is larger. To better understand this, it is helpful to distinguish between the two components of the pension scheme (Bismarkian/contributory and redistributive). Concerning the Bismarckian component of the pension scheme, a change in s corresponds to an intertemporal shift of consumption within the same agent and, as such, it does not affect the voters' willingness to pay for public education. Nevertheless, for any α < 1, the size of s is relevant through the redistributive component, because an increase of s implies an increase in the amount of the wealth that is redistributed across generations. Public education can be seen as an investment leading to an increase in the future average income, with s(1 − α) being the share of the returns on the investment that agents are able to appropriate. Hence, s magnifies the importance of the redistributive component and induces adults to vote for a higher tax rate t. ϕ Proposition 2 depends crucially on the condition that β > e ϕ−1. Intuitively, this condition ensures that the equilib- rium total expenditure in education (hence, including private education) is increasing when public investment in education increases. Investments in private education are substantial: if an increase in the quality of public education were to attract too many households and divert too much money away from the educational system, the mechanism behind the model would backfire. 2.3 | The voting equilibrium The previous results are independent of the voting process and the identity of the decisive voter. We now analyze the voting equilibrium, focusing on the possible types of coalitions that might form when voting on the tax t. Although the richness of the model limits our possibilities of studying the voting equilibrium and of having a closed‐ form solutions, Proposition 3 does indicate the type of voting equilibrium that the model might generate. Proposition 3. When adults vote on t, two types of equilibrium may prevail: � i) the median income voter ω ¼ 12 is decisive; all agents poorer than the median would prefer a higher tax rate, while the others would prefer a lower tax rate. This equilibrium occurs� if and only if the median voter's preferred tax is larger than the one preferred by the agent with income ω ~ , that is, t∗P 12 ≥ t∗P ðω ~ Þ. ii) Otherwise, in the prevailing equilibrium the two opposing coalitions include: a) the richest agents in the population, together with agents in the neighborhood of the median income voter (seeking for a reduction in the tax rate), opposed to b) the poorest agents in the population, together with agents in a neighborhood of ω ~ (all in favor of a rise of the tax rate). In our model, agents with income below ω ~ attend a (tuition‐free) public school, while agents with income ω > ω ~ opt for a (costly) private education and invest more in education than the per pupil expenditure in the public sector. To understand the intuition behind the voters' behavior, we must consider that two mechanisms are operating simultaneously: on the one hand, publicly financed education generates redistribution from the wealthier to the poorer agents in society via two channels (public schools and the redistributive component of pensions); on the other hand, richer agents care more for their children's education, and so are more willing to substitute consumption of the numeraire good for education than are other agents. The redistribution channel means poorer agents ask for higher taxes, while the other channel means the middle classes (the richest agents attending public schools) ask for higher taxes. If we combine the two effects, the tax preferred by an agent attending public school may either be decreasing in income over all its support, or it may be decreasing up to some income ω, and then increase for ω� ∈ ½ω; ω~ �. When t∗P 12 > t∗P ðω ~ Þ (see Figure A1 in the appendix), the redistribution effect is so strong that the first half of the population always favors a sufficiently high tax rate, so that we have the very standard result whereby the median voter is pivotal (although preferences are not unimodal). Poor agents are in favor of high taxation, since they profit from wealth redistribution and enjoy public� education services, and wealthier agents prefer a lower taxation.10 For the alternative case, when t∗P 12 < t∗P ðω ~ Þ (see Figure A2 in the appendix), a number of agents in public school are neither sufficiently poor to enjoy significant gains from redistribution, nor rich enough to be sufficiently willing to pay for private education. These agents have an ‘intermediate’ income, that is, their income is in a neighborhood of the MONTOLIO ET AL. - 9 median income; hence, they are neither the poorest nor the richest in the public school system. This group forms a coalition with the richest agents in the economy, with the aim of lowering the tax rate. This coalition opposes a coalition of the poorest adults (who gain from redistribution) and the middle classes with income in the neighborhood of ω ~ .11 3 | EMPIRICAL ANALYSIS The theoretical framework presents interesting and novel insights about the link between voters' support for publicly provided education and the retirement system. According to the model predictions, the share of public resources (voted and) devoted to finance public education is decreasing in the contributory component of the pension system, the Bismarckian factor, while it is increasing in the pension system's generosity, that is, the share of public resources used to finance public pensions (Proposition 2). Such prediction is robust to voters' income or schooling choice. Next, we present the methodology and data employed to test these findings, discuss our identification strategy, and finally present and comment the main results. The data that support the findings of this study are openly available (Montolio et al., 2022a). 3.1 | Identification strategy and data Following the theoretical discussion, we test the predictions of Proposition 2 by employing micro data on individual preferences and attitudes toward the financing of publicly provided education. In particular, we rely on data extracted from repeated waves (1985, 1990, 1996, 2006) of the survey ‘ISSP Role of Government’ conducted and released by GESIS – Leibniz Institute for the Social Sciences. This repeated cross‐section survey reports information on subjective pref- erences and attitudes toward government responsibilities and government spending, state intervention in the economy, civil liberties, political interest, trust and efficacy across several countries.12 The relevant question used to define our dependent variable is: Listed below are various areas of government spending [including Education]. Please show whether you would like to see more or less government spending in each area. Remember that if you say ‘much more’, it might require a tax increase to pay for it. The set of possible answers included: ‘spend much more’; ‘spend more’; ‘spend the same as now’; ‘spend less’; ‘spend much less’. This question has remained unchanged over the 1985–2006 period. For any respondent i, in country j, in period p, we code the answer to this question into the variable tijp, which we have re‐scaled from ‘spend much less’ (1) to ‘spend much more’ (5) according to the answer. Thus, by defining tijp as an ordinal dependent variable measuring individual i's unobservable actual desired share of public resources to devote to public education ðt∗ijp Þ, we can design an ordered response model: t∗ijp ¼ β1 αjp þ β2 sjp þ Yijp β3 þ Xjp β4 þ θj þ τ p þ εijp ð13Þ 8 > > 1 if t∗ijp ≤ w1 > > > < 2 if > w1 < t∗ijp ≤ w2 tijp ¼ 3 if w2 < t∗ijp ≤ w3 ð14Þ > > > > > 4 if w3 < t∗ijp≤ w4 > : 5 if t∗ijp > w4 We estimate the coefficients in Equation (13) as well as the cut‐points in Equation (14) through ordered logit models by means of maximum likelihood techniques. In order to measure the contributory component of the pension system (the Bismarckian factor), we use Krieger and Traub (2013) estimates,13 which are computed using microdata (at the household level) taken from the Luxembourg Income Study (2008). Pensions are decomposed into two parts: the redistributive (flat) component, and the contributory (earnings‐related) component. The Bismarckian factor, denoted as α, is the share of the pension which is contributory, while 1 − α is the redistributive share of the pension.14 Thus, in 10 - MONTOLIO ET AL. Equation (13) the term αjp is the Bismarkian factor of country j in period p which we expect to negatively impact t∗ijp (Proposition 2). We measure the generosity of the pension system sjp in country j and period p as the public expenditure on (old age) pensions expressed as a share of GDP and collected from the OECD statistics database. According to Proposition 2 we expect a positive sign of coefficient β2. We control for several individual‐level variables including demographic characteristics, labor market characteristics, political and religious attitudes that are likely to influence the individual support for expansions in the financing of public education. These variables, collected from the survey data, are included in vector Yijp with the purpose of filtering/polishing the effect of our two main explanatory variables on the dependent variable and thus providing more precise estimate of β1 and β2. Additional information on contextual country‐level controls is collected in vector Xjp including GDP, Population (both collected from OECD statistics database) and Public Spending on Public Education (World Bank database). Table 1 presents a summary statistics of these variables. Finally θj and τp are respectively country‐level fixed effects and time fixed effects, while ɛijp is the error term. In order to ensure perfect coherence with the theoretical model, for our empirical analysis we restrict the sample of respondents to the surveys to include only people belonging to the labor force, that is, by excluding students and retirees. Next section presents the results of the empirical analysis. 3.2 | Results T2 Table 2 presents the results of our empirical analysis. Models 1‐4 estimate alternative specifications of Equations (13) and (14) that include progressively less parsimonious set of control variables. More precisely, our baseline model in column (1) includes basic demographic controls, (2) adds further individual‐level variables related to education and labor market status, (3) enriches the set of individual characteristics including political and religious attitudes while (4) adds country‐level covariates. Finally, as a robustness check, (5) presents the results of the logit model obtained redefining the dependent variable in a dichotomous way and also includes all the covariates included in (4). TABLE 1 Summary statistics Observations Mean SD Min. Max. Pref. Public spending education 36,130 3.92 0.82 1.00 5.00 Bismarckian factor 36,130 0.32 0.23 −0.09 0.73 Pension system's generosity 36,130 6.20 2.02 2.97 10.54 Gender 36,063 1.51 0.50 1.00 2.00 Age 35,886 41.62 13.08 16.00 96.00 Age, squared 35,886 1902.81 1175.54 256.00 9216.00 Marital status 34,165 2.14 1.68 1.00 5.00 Household composition 32,009 3.01 1.45 1.00 18.00 Children 36,130 0.26 0.44 0.00 1.00 Highest education level 35,830 2.73 1.41 0.00 5.00 Current employment status 35,376 2.38 2.50 1.00 9.00 Employed in private sector 36,130 0.42 0.49 0.00 1.00 Self‐employed 36,130 0.08 0.27 0.00 1.00 Supervise other employee 36,130 0.32 0.46 0.00 1.00 Political attitudes 28,904 3.62 1.78 1.00 7.00 Attendance to religious services 32,267 6.00 2.11 1.00 8.00 GDP 36,130 2343.28 3573.83 41.28 16,047.56 Population 36,130 59.07 76.37 1.99 298.38 Government spending in public education 28,876 81.72 154.00 2.02 791.31 MONTOLIO ET AL. - 11 T A B L E 2 Impact of Bismarckian factor and pension system's generosity on voters' support for increasing spending in public education (1985–2006) Model Ordered logit Logit (1) (2) (3) (4) (5) Bismarckian factor (α) −1.026*** −1.176*** −1.659*** −1.255** −1.446** (0.316) (0.319) (0.358) (0.514) (0.619) Generosity pension system (s) 0.064*** 0.075*** 0.064** 0.473*** 0.230** (0.025) (0.025) (0.028) (0.089) (0.114) Age 0.015*** 0.011** −0.000 −0.008 −0.003 (0.005) (0.005) (0.006) (0.007) (0.008) Age, squared −0.000*** −0.000*** −0.000 0.000 −0.000 (0.000) (0.000) (0.000) (0.000) (0.000) Household size 0.028*** 0.035*** 0.042*** 0.056*** 0.057*** (0.009) (0.009) (0.011) (0.013) (0.016) Children 0.116*** 0.116*** 0.133*** 0.123*** 0.102** (0.029) (0.029) (0.033) (0.037) (0.046) Highest education level 0.097*** 0.105*** 0.096*** 0.116*** (0.009) (0.010) (0.011) (0.013) GDP 0.004*** 0.004*** (0.001) (0.001) Population −0.180*** −0.169*** (0.051) (0.063) Public education spending −0.072*** −0.076*** (current level) (0.008) (0.010) Observations 31,727 31,218 24,666 19,528 19,952 Log‐likelihood −36250.97 −35555.13 −28272.05 −21878.59 −11644.80 Wald chi2 (all variables) 3200.62 3285.09 2279.94 2136.47 1656.77 p‐value 0.000 0.000 0.000 0.000 0.000 R2M&Z 0.10 0.11 0.10 0.12 0.13 R2Count 0.47 0.47 0.46 0.47 0.69 AIC 72,561.95 71,184.27 56,642.10 43,861.19 23,387.60 BIC 72,812.90 71,493.17 57,039.65 44,270.93 23,774.75 Labor market controls NO YES YES YES YES Political and religious attitudes NO NO YES YES YES Note: Each model includes both Time and Country Fixed Effects and controls for gender and marital status (through indicator variables for: widowed; divorced; separated, but married; single; never married). Labor Market controls include dummies for employment status (employed‐part time, unemployed, other), employed in the private sector, self‐employed, supervisor of other employees. Political and Religious Attitudes controls for respondent's position in the political spectrum (through indicator variables for: far left; left, center left; center, liberal; right, conservative; far right; other, no specific) and frequency of attendance at religious services (once a week; 2 or 3 times a month; once a month; several times a year; once a year; less frequently; never). R2M&Z is McKelvey and Zavoina's R2; R2Count is the proportion of correct predictions. Abbreviations: AIC, Akaike's information criterion; BIC, Bayesian information criterion; Robust standard errors in parentheses. *p < 0.10, **p < 0.05, ***p < 0.01. 12 - MONTOLIO ET AL. All specifications include both country and year fixed effects. The different number of observations is due to coverage of the surveys for the relevant questions, we use all the available observations in every regression. Table 2 also includes several indexes of goodness to fit (i.e., the log‐likelihood; the McKelvey and Zavoina's R2; the R2Count measuring the proportion of correct predictions; the Akaike's information criterion – AIC and the Bayesian information criterion – BIC) in order to guide model selection. These suggest that the fully fledged model in (4) outperforms any other ordered logit specifications, thus it is our preferred estimate of Equations (13) and (14).15 Using the interpretation we have given to the latent variable, it is possible to interpret the estimated coefficients in terms of the marginal effects of the regressors on the latent actual desired share of public resources to devote to public education ðt∗ijp Þ. In every model both the Bismarckian factor and the proxy for the pension system's generosity are highly significant and their signs confirm the predictions of Proposition 2. In other words, the support for expansion of public spending in public education is lower the higher the contributory component of the pension system (the Bismarckian factor) and it is increasing in the generosity of the pension system. As explained in Section 3.1, the control variables have been included as part of our identification strategy and filtering process in order to obtain better estimates of the main independent variables of interest. Thus, the interpre- tation of their impact on the dependent variable is not key for the purpose of this paper. Nevertheless, it is interesting to stress some results. Regarding individual characteristics, we find that support for an increase in public expenditure for education is stronger among members of large households and respondents with children. This result is consistent with the discussion about fertility in Section 2.1. The non‐linear explanatory power of age appears in specifications (1) and (2), however, the effect is absorbed once political controls are introduced. Not surprisingly, more educated individuals are in favor of more spending in public education. Political attitudes also matter and estimates presents the expected signs: left‐leaning voters are more favorable to expansions of public education than the right‐leaning ones.16 Concerning macro‐level control variables, we find that the existing level of public spending in education has a negative effect on support for further increases and so does the size of population, while GDP is positively associated with an increase in support for expansion of public expenditure in education. These additional results on the de- terminants of the support for publicly financed education tend to corroborate and in some cases extend previous ev- idence (e.g., Busemeyer & Iversen, 2014). As a further robustness check, a multilevel version of both the ordered logit and logit models is also performed, which confirms and reinforces the results of the main analysis. These results are reported in Appendix C. 4 | CONCLUSIONS Adults voluntarily use part of their income to finance the education of the young in an act which might be interpreted as intergenerational altruism. However, voters may want something in return. We have extended the standard model in which adults vote on the tax to finance public education by adding a second time period during which adults retire and when, if their pensions are redistributive, they might obtain some monetary benefits from the new generation being better educated. We show that rational voters can increase their future consumption by investing in the education of the young, as the redistributive component of pensions depends on the young's future income. This induces all voters, including those opting for private education, to favor a positive tax to finance public education. Furthermore, by increasing the social returns on education, the preferred tax rate by any agent increases (compared to the case with no retirement concerns). We conclude (Proposition 2) that, regardless of the identity of the pivotal voter, when retirement concerns are intro- duced, the preferred tax rate for financing public education increases. This effect would be even greater if we assumed imperfect financial markets or should the population grow faster than the intertemporal discount rate. We can expect an analogous effect to appear as long as education produces other positive externalities on society (i.e., less social conflict, or more technological and scientific progress, possibly leading to better infrastructures, medical treatment and services for the elderly). The effect of pensions on preferences in education depends on the degree of redistribution provided by the pension system and on its absolute size. This effect disappears in a purely Bismarckian (i.e., purely contributory) pension system, as there is no link between the education of the young and the agents' own future pensions. However, under a redis- tributive pension system, any investment in current education results in an increase in future pensions. The larger the redistributive component of the pension system is, the greater this effect becomes. Hence, we show that voters agree on larger tax rates to finance education when the redistributive component is larger. Moreover, this effect is amplified when MONTOLIO ET AL. - 13 pensions represent a larger proportion of total life income. The motivating evidence in the introduction casually con- firms these results at the macro‐level, showing that over the last 3 decades, countries with a larger Bismarckian factor invested less in education and that there is a positive correlation between expenditure in public pensions and public education. Our empirical analysis goes further by formally testing the theoretical predictions of the model and by providing strong evidence of these relationships using micro‐level data. More precisely, by exploiting four waves of surveys on public opinion about public policies repeated for 20 years across 13 countries and national representative samples of individuals including on aggregate more than 30,000 respondents over the waves, we document that the support for expansions in the public financing of public education is decreasing in the Bismarckian factor and it is increasing in the generosity of the pension system. These results are robust to different specifications and a progressively less parsimonious set of control variables providing a strong validation of the theoretical predictions of Proposition 2. The theoretical model provides additional predictions about the type of equilibrium that should emerge (Proposi- tion 3). Depending on the value of the parameters, we may expect the voting equilibrium to result either in a standard class conflict ‐ with poor voters in favor of more public education than the rich ones ‐ or we may observe that part of the lower‐middle class joins the richest in their attempt not to increase public education spending. The latter equilibrium is the result of two opposing forces: redistribution through education (decreasing in income) and the interest for a high‐ quality public school (increasing in income among public school consumers only). Some intermediate‐income agents may not be rich enough to care for a high‐quality public education system, but not poor enough to enjoy significant benefits from redistribution. These agents may form a coalition with agents opting for private education and ask for lower tax rates, while the upper‐middle class, together with the poorest agents in society, asks for more public education. Note that changing the size of the redistributive component of pensions s(1 − α) has a clear effect on welfare. Investing in education has positive returns, but the amount of current income devoted to education tends to be sub‐ optimal since adults do not benefit from the increase in wealth that education will produce among the young. With pensions, part of the returns on the investment is enjoyed by adults, which makes them more willing to reduce their current consumption. Still, the share of the return that they enjoy is proportional to s(1 − α). Therefore, the benefit becomes more internalized the larger the redistributive part of the pension becomes. We conclude that aggregate welfare should increase when the redistributive part of the pension is larger. Finally, the recent contribution by Andersen et al. (2021) studies the retirement system (in particular under pay‐as‐ you‐go) and the consequences of having agents with reference‐dependent preferences and a pattern of time inconsis- tency. Our hope is that future research will combine their approach with our and investigate how the investment in education can move the reference point of agents and induce a different pattern of consumption and saving. ACKN O WLE DG EM EN T S For their helpful comments, we are grateful to co‐editor S. Barbieri, the anonymous referees and many colleagues. A special thank goes to H. Cremer, Ph. De Donder, D. Epple, M. Gilli, G. Glomm, M. Justman, P. Natale, R. Romano. We are also thankful to Collegio Carlo Alberto and NYU‐Stern (Piolatto), and the Max Planck Institute for Tax Law and Public Finance (Salvadori) for the hospitality provided and for the enriching conversations from which this project has benefitted. Montolio gratefully acknowledges support from the Catalan Government (2017SGR796). Piolatto gratefully acknowledges support from the Spanish (RYC‐2016‐19,371 and PGC2018‐094348) government. Salvadori gratefully acknowledges support from the Economic and Social Research Council (ES/S00713X/1) and the MCIU/AEI/FEDER‐ UE (RTI2018‐095983‐B‐I00). DA TA AVA I L A BI LI T Y ST A T E M E NT The data that support the findings of this study are openly available in openICPSR at https://doi.org/10.3886/ E169521V1, reference number openicpsr‐169521. ORC ID Daniel Montolio https://orcid.org/0000-0002-6751-6701 Amedeo Piolatto https://orcid.org/0000-0002-3571-8069 Luca Salvadori https://orcid.org/0000-0001-7610-439X ENDN OTE S 1 In most OECD countries, pension systems include a pay‐as‐you‐go component, albeit with varying degrees of redistribution. Kritzer and Jankowski (2010) provide an overview of the salient characteristics of all European countries' pension systems. 14 - MONTOLIO ET AL. 2 Focusing on a two‐period model allows to simplify the setting and the notation in a convenient way. 3 Both assumptions have no qualitative impact on the results. 4 Since public education is free, by revealed preferences, agents willing to attend a costly private school must perceive it to be of higher quality than public schools. 5 For example, this occurs when a generation of adults chooses the pension tax rate that will apply for a sufficiently long period. 6 The latter would be similar, in spirit, to what occurs, for example, in Lancia and Russo (2016). 7 Lancia and Russo (2016); Bishnu and Wang (2017) avoid the issue by choosing a probabilistic voting design. 8 The proof of Proposition 3 will show that the preferred tax rate is convex in income. Notice that this is needed to derive the properties of the voting equilibrium, however, Propositions 1 and 2 only rely on the properties of the preferred tax by an individual, regardless of the type of voting equilibrium. 9 Notice that Equation (7) disregards any possible effect of a change in XR on average income ωy . One could then argue that the term − ∂b1/ ∂XR on the left hand side of the equation is missing. However, this term represents the change in the population average income due to a variation in the expenditure of a single agent. With atomistic agents (i.e., with a sufficiently large population), this effect tends to zero rapidly and this effect is negligible. 10 This type of equilibrium appears, among others, in Epple and Romano (1996b) and Cohen‐Zada and Justman (2003). 11 Coalitions that are non‐linear in income are not new in the education literature. In Epple and Romano (1996a); Piolatto (2010), an ‘Ends Against the Middle’ equilibrium occurs under the assumption of single crossing denoted slope rising in income (SRI). 12 We included in our analysis the 13 countries for which all relevant measures of interest are available for the whole considered period. Namely, we encompass Australia, Czech Republic, France, Germany, Hungary, Israel, Norway, Slovenia, Spain, Sweden, Switzerland, United Kingdom and United States. 13 Whenever necessary, data were complemented using Krieger and Traub (2011). 14 See Appendix B for additional information. 15 The logit model presented in column (5) tends to outperform the ordered‐logit specifications in terms of indexes of goodness to fit, but the two approaches aren't directly comparable: the logit model, where the dependent variable is re‐coded to be binary, is merely considered as a robustness check. 16 For the full table, including the estimates for all the controls, see Montolio et al. 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Available from: https://doi.org/10.1111/ecin.13094 APP EN DI X A | P ro of s Proof of Lemma 1 Using Equation (2), Z 1 � ωy ¼ ω þ X ϕ dω ðA1Þ 0 Z 1 1 βϕ ~ X ϕp þ λϕ ωy ¼ þ ω ω0 dω ðA2Þ 2 ω~ � e �1−ϕ � �� �βϕþ1 1 λϕ βþ1 eϕ t βþ1 ωy ¼ þ þ 1− ðA3Þ 2 βϕ þ 1 λ βϕ þ 1 2 Proof of Proposition 1 If we derive the previous Equations (10)–(12) with respect to t, we obtain the variation of the number of public school students, of the quality of public school and of the average income in the second period, when the equilibrium tax varies. MONTOLIO ET AL. - 17 ∂n 1 � e �βþ1 1 −β n ¼ tβþ1 ¼ >0 ðA4aÞ ∂t β þ 1 2λ ðβ þ 1Þt � �βþ1 1 ∂XP β λ −1 ¼ tβþ1 > 0 ðA4bÞ ∂t β þ 1 e2β 1−ϕ � � βϕþ1 ∂ωy βϕ þ 1 − eϕ � e �βþ1 1 βþ1 −βð1−ϕÞ ¼ t βþ1 ðA4cÞ ∂t βþ1 λ 2 ϕ The first two equations are both positive. The sign of Equation (A4c) is positive if β > e ϕ−1. ϕ To prove the corollary, notice that if β < e ϕ−1 or ϕ > 1, we have a corner solution for the problem of adults ϕ opting for private education and their preferred tax is t = 0. If β > e ϕ−1 and ϕ ≤ 1, then both types of agent are in favor of a positive taxation, but then comparing Equations (5) and (8) we can see that in the former we have an � � ∂2 ωy extra term λωβ0 X1P ∂X ∂t , which is always positive by Equation (A4b). It is sufficient to notice that ∂t2 < 0, to P conclude that for a same income ω0, the value of t that solves Equation (8) must be lower than that for Equa- tion (5). By the same reasoning, if we compare two adults opting for private education, a decrease in ω0 implies ∂ω ∂2 ω that the optimal value for ∂ty is also lower, hence (from ∂t2 y ) it must be that the preferred tax is lower for a wealthier agent. To show that t∗R is decreasing and convex in income, it is sufficient to derive Equation (A6) to see that the first derivative is negative and the second is positive. Proof of Proposition 2 The proof consists of three steps. The first one consists in rewriting the first order conditions in a convenient way. The second step defines the derivatives that we want to compute. The last one shows that the sign of the derivative is unambiguous. 1. We can first rewrite the first order conditions of both types of agent. For agents opting for public education, Equation (5) is rewritten using Equations (A4a) and (A4c) � � ∂ωy 1 1 ∂n ð1 − αÞs þ λωβ0 − − ω0 ¼ 0 ðA5aÞ ∂t t n ∂t 1−ϕ � �� �βϕþ1 ! βϕ þ 1 � e �βþ1 eϕ 1 βþ1 −βð1−ϕÞ λωβ0 β ð1 − αÞs 1− t βþ1 þ − ω0 ¼ 0 ðA5bÞ βþ1 λ βϕ þ 1 2 t βþ1 � e �1−ϕ � �βϕþ1 � t βþ1 þ βλωβ0 − ðβ þ 1Þω0 t ¼ 0 βþ1 ϕ ð1 − αÞs βϕ þ 1 − e ðA5cÞ λ 2 Differentiating Equation (A5b) with respect to t, we can see that if a solution to Equation (5) exists, then the second derivative is always negative; hence, the stationary point solving Equation (5) is a maximum of the problem. For agents preferring private education, Equation (8) can be rewritten in closed form as � � 1−ϕ � �− βþ1 − βþ1 βϕþ1 λ βð1−ϕÞ βþ1 βð1−ϕÞ t¼ ω0 βð1−ϕÞ ð2Þβð1−ϕÞ ϕ : ðA6Þ e ð1 − αÞsðβϕ þ 1 − e Þ 2. Define Equations (8) and (A5c) respectively as Γ(tP) = 0 and Ω(tR) = 0. From these equations, we can describe the change in the agent's optimal tax, when the pension system changes: ∂ΓðtP Þ ∂tP ∂α ¼− ∂Γ ðA7aÞ ∂α ∂tP 18 - MONTOLIO ET AL. ∂ΩðtR Þ ∂tR ∂α ¼− ∂Ω ðA7bÞ ∂α ∂tP ∂ΓðtP Þ ∂tP ∂s ¼− ∂Γ ðA8aÞ ∂s ∂tP ∂ΩðtR Þ ∂tR ∂s ¼− ∂Ω ðA8bÞ ∂s ∂tP Equations (A7a) and (A7b) describe the change in the preferred tax resulting from a change in the Bismarckian factor α, while Equations (A8a) and (A8b) consider a change in the tax rate s in order to finance pensions. In both cases, equation (a) refers to the optimal tax of an adult opting for public education, while (b) is for the case of private education. 3. We are interested in the sign of the previous equations and we know that all the denominators are negative, therefore, we have that: � � � � � � ∂tP ∂ΓðtP Þ ∂ωy sign ¼ sign ¼ sign − s <0 ðA9aÞ ∂α ∂α ∂t � � � � � � ∂tR ∂ΩðtR Þ ∂ωy sign ¼ sign ¼ sign − s <0 ðA9bÞ ∂α ∂α ∂t � � � � � � ∂tP ∂ΓðtP Þ ∂ωy sign ¼ sign ¼ sign ð1 − αÞ >0 ðA10aÞ ∂s ∂s ∂t � � � � � � ∂tR ∂ΩðtR Þ ∂ωy sign ¼ sign ¼ sign ð1 − αÞ >0 ðA10bÞ ∂s ∂s ∂t From Equations (A9a), (A9b), (A10a) and (A10b) it can be noted that for all voters the sign of the variation of the preferred tax due to a change in either α or s does not depend on income or on the schooling choice. Therefore, we do not need to identify the pivotal voter at the election in order to confirm that the preferred tax rate of the pivotal voter is decreasing in α and increasing in s. ∗ 1 � ∗ Proof of Proposition 3 Proposition 3 characterizes the voting equilibrium for the two cases of t P ~ Þ and ≥ t P ðω ∗ 1 � ∗ 2 ~ Þ. The proof is organized as follow: in part A., we derive the optimal tax rate for adults having opted for t P 2 < t P ðω � public education, and show that it is convex, with a minimum at ω ¼ ω. In part B., we show that for t∗P 12 ≥ t∗P ðω ~ Þ, the only possible equilibrium is that the median voter is decisive, with all agents poorer than the median being in favor of a larger tax rate, opposing � the remaining agents, who are in favor of a lower tax rate. In part C., we analyze the voting ∗ 1 ∗ ~ equilibrium when tP 2 < tP ðωÞ, showing that the median voter cannot be decisive, and we show the characteristics of the equilibrium. � A. We rewrite Equation (A5c) as Γ t∗P ¼ 0. We can describe the change in the agent's optimal tax, when the income changes as: ∂Γðt∗P Þ ∂t∗P ∂ω0 ¼− ∂Γ ðA11Þ ∂ω0 ∂t∗P ∂Γ We know, from the second order condition, that ∂t∗P < 0, hence � � � �� ∂t∗P ∂Γ t∗P sign ¼ sign : ðA12Þ ∂ω0 ∂ω0 MONTOLIO ET AL. - 19 � �β−1 1 ∂t∗ ð1þβÞt Therefore, ∂ωP0 > 0 if and only if ω0 > β2 λ ≡ ω. Under the conditions of existence of the model, β > 1, therefore ω is a minimum and is convex in ω0. t∗P B. From the corollary of Proposition 1, we know that for ω ~ (as for any level of income), t∗P ðω~ Þ > t∗R ðω ~ Þ, furthermore, the ∗ 1 � � ∗ ∗ ~ tR is decreasing in income. If tP 2 ≥ tP ðωÞ, then there can be no income ω b ∈ ½ω ∗ ~ ; 1� such that tR ð ωb Þ ≥ t∗P 12 . Finally, if � � � � t∗P 12 ≥ t∗P ðω ~ Þ, then ω > 12 and for all ω00 ∈ 12; ω ~ , it must be that t∗P 12 ≥ t∗P ω00 , as represented in Figure A1. Since the preferred tax is decreasing in income for ω0 < ω, the preferred one for agents with income ω0 < 12 (who represent half of the population) is larger than that of the median voter. Meanwhile, for all agents with income above the median the preferred � tax is smaller than that of the median voter. We conclude that � the median �← � voter is decisive. C. If t∗P 12 < t∗P ðω ~ Þ, then, by continuity, there will be some neighborhood around 12 ω ∈ ω; 12 in Figure A2) and around � ~ (ω ∈ ð! ω ω;ω ~ � in Figure A2) where the preferred tax rate is larger than t∗P 12 . � � ← � � � Define ! ω ≡ ω : t∗P 12 ¼ t∗P ! ← ω , and ω ≡ ω : t∗P ðω ~ Þ ¼ t∗P ω . By the convexity of t and t∗P 12 < t∗P ðω ~ Þ, it must be that h← i ← ω < 12, while ! ← ω ∈ ω; ω ~ can be larger or smaller than 12. Since ω < 12, the group of poorest agents with the highest ← preferred tax rate (i.e., ω < ω) is not large enough to form a winning coalition. We must include some more agents, in order to have a coalition of that half of the population with the highest preferred tax rate. Hence, the coalition is ← formed by all agents with income ω < ω, together with some agents with income 8 � � ← 1 1 > > < ω ∈ ω; and ω > ! ω if ! ω> 2 2 ðA13Þ > > h � 1 1 ← ! :ω ∈ ω ; ω and ω > if ! ω≤ 2 2 so that the coalition's size is 12.17 □ 1 � FIGURE A1 t∗P 2 ≥ t∗P ðω ~Þ 1 � FIGURE A2 t∗P 2 < t∗P ðω ~Þ 20 - MONTOLIO ET AL. B | S ourc es u s e d f o r th e mo ti v a ting e v iden ce Figure 1 is constructed using as sources of information: the Bismarckian factor estimated by Krieger and Traub (2013) and public expenditure, as a share of GDP, on education and on (old‐age) pensions. The data used for the Bismarckian factor are reproduced in Table A1. The distribution of the Bismarckian factor across countries and years shows a bimodal distribution with one mode around the value 0.15 and the other mode around 0.42 (the Bismarckian factor has a minimum of −0.086 and a maximum of 0.737). This information has been used to determine the cut‐off point that defines above‐ and below‐average countries with respect to the redistributive part of the pensions system. Data on public expenditure on education (as a share of GDP) come from the World Development Indicators (WDI) of the World Bank (http://data.worldbank.org/). Data on public expenditure on pensions (old age) as a share of GDP come from OECD (http://data.worldbank.org/). Table A2 reports them for the selection of OECD countries used in Figure 1. C | S en s i ti v it y a n a ly s es : M ulti le ve l m o d el s Table A3 presents the results of the multilevel analysis (see Goldstein, 2011)18 corresponding to both the ordered logit and logit models in Table 2. More precisely, given that individuals responding to the surveys are nested within countries, we perform two‐level models. The results of the main analysis still hold for any specification of the multilevel models corroborating and reinforcing the analysis presented in the main text. This analysis is performed to better account for within‐groups correlation of the error term at country level although in the main analysis we are already indirectly taking into account this issue and controlling for most of the within‐country correlation of the error term by including country‐level fixed effect. This is confirmed also by the results of the likelihood‐ratio (LR) test reported in Table A3, which indicate that the multilevel version of both the ordered logit and logit models presented here do not represent a significant improvement in fit relative to standard ordered logit and logit models with fixed effects presented in Table 2. T A B L E A1 Bismarckian factor Country 1979–1983 1983–1987 1988–1992 1993–1997 1998–2002 2003–2008 Australia 0.014 −0.086 0.046 0.113 0.010 0.029 Austria 0.501 0.525 Belgium 0.417 0.463 0.488 0.430 Canada 0.035 0.046 0.066 0.270 0.307 0.277 Denmark 0.181 0.173 0.056 0.024 −0.004 Finland 0.019 0.594 0.416 0.364 France 0.710 0.701 0.711 0.730 0.737 0.715 Germany 0.579 0.583 0.539 0.564 0.589 0.562 Greece 0.694 0.639 0.638 Ireland 0.121 0.234 0.347 0.327 0.348 Italy 0.379 0.375 0.54 0.549 0.595 Luxemburg 0.445 0.367 0.315 0.351 0.508 Mexico 0.506 0.506 0.522 0.689 0.709 Netherlands 0.156 0.253 0.353 0.289 0.278 Norway 0.301 0.194 0.226 0.434 Spain 0.528 0.432 0.470 0.554 Sweden 0.422 0.476 0.571 0.421 0.432 0.214 Swiss 0.190 0.169 0.147 0.123 0.099 0.052 UK 0.198 0.157 0.141 0.168 0.088 0.095 USA 0.342 0.532 0.533 0.545 0.462 0.445 MONTOLIO ET AL. - 21 T A B L E A2 Public spending as a share of GDP for Public education and Pensions Public education Old‐age pensions Country 1980 1985 1990 1995 2000 2005 1980 1985 1990 1995 2000 2005 Australia 5.1 5.1 ‐ 4.9 4.7 4.7 3.0 2.9 2.7 3.4 3.2 3.1 Austria 5.3 5.6 ‐ 6.2 5.8 5.5 8.4 9.0 7.3 8.0 8.1 8.8 Belgium 5.7 5.7 ‐ ‐ ‐ 5.9 5.5 6.0 6.0 6.7 6.5 6.7 Canada 6.8 6.5 ‐ 5.6 5.6 4.9 2.8 3.4 3.8 4.2 3.9 3.7 Denmark 6.4 6.6 ‐ 8.3 8.3 8.3 4.6 4.1 4.4 5.4 4.6 5.1 Finland 5.1 ‐ ‐ ‐ 5.9 6.3 4.6 ‐ 6.2 7.0 6.1 6.8 France 4.9 5.4 ‐ 5.8 5.7 5.7 7.4 8.3 8.6 10.0 10.0 10.2 Germany ‐ ‐ ‐ 4.6 ‐ 4.4 9.0 8.8 8.5 7.0 7.7 8.4 Greece 1.9 2.3 ‐ 3.1 3.4 4.0 4.4 6.8 6.5 6.6 7.2 7.9 Ireland 5.8 5.4 ‐ 4.4 4.3 4.8 3.5 3.6 3.0 2.4 1.6 1.8 Italy 4.3 4.9 ‐ 4.6 4.5 4.4 7.2 8.9 7.8 8.7 10.6 11.1 Luxembourg 5.6 2.6 ‐ ‐ 3.7 ‐ 5.7 5.4 7.2 8.0 6.9 3.8 Mexico ‐ 3.7 ‐ 4.2 4.9 5.0 ‐ 0.1 0.3 0.5 0.5 0.9 Netherlands 7.0 6.0 ‐ 4.9 5.0 5.5 5.6 5.4 5.7 5.0 4.6 4.6 Norway 6.3 5.8 ‐ 7.5 6.6 7.0 4.0 4.3 5.2 5.1 4.4 4.4 Spain 2.1 3.1 ‐ 4.4 4.3 4.2 4.6 5.7 6.4 7.5 5.9 5.4 Sweden 8.5 7.4 ‐ 7.6 7.2 6.9 6.1 6.8 6.9 7.3 6.6 6.8 Swiss 4.9 4.8 ‐ 5.3 5.2 5.7 5.3 5.4 5.2 6.2 6.2 6.3 UK 5.3 5.1 ‐ 4.9 4.5 5.4 3.7 4.0 4.0 4.1 4.0 4.1 USA 6.5 6.4 ‐ 5.0 5.8 5.3 5.0 5.2 5.1 5.3 5.0 5.2 T A B L E A3 Impact of Bismarckian factor and pension system's generosity on voters' support for increasing spending in public education (1985–2006) ‐ Multilevel models (ML) Model ML ordered logit ML logit (1) (2) (3) (4) (5) Bismarckian factor (α) −1.026*** (0.331) −1.176*** (0.335) −1.659*** (0.373) −1.255** (0.541) −1.446** (0.642) Generosity pension system (s) 0.064*** (0.025) 0.075*** (0.025) 0.064** (0.028) 0.473*** (0.088) 0.230** (0.110) var (_cons[Country]) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) Observations 31,727 31,218 24,666 19,528 19,952 Log‐likelihood −36250.97 −35555.13 −28272.05 −21878.59 −11644.80 Wald chi2 (all variables) 3216.38 3326.06 2234.87 2126.18 1647.41 p‐value 0.000 0.000 0.000 0.000 0.000 AIC 72,561.95 71,184.27 56,644.10 43,863.19 23,387.59 BIC 72,812.90 71,493.17 57,049.76 44,280.80 23,774.75 LR test (chi2) 0.000 0.000 0.000 0.000 0.000 LR test (p‐value) 1.000 1.000 1.000 1.000 1.000 (Continues) 22 - MONTOLIO ET AL. T A B L E A3 (Continued) Model ML ordered logit ML logit (1) (2) (3) (4) (5) Basic demographic controls YES YES YES YES YES Labor market controls NO YES YES YES YES Political and religious attitudes NO NO YES YES YES Country‐level controls NO NO NO YES YES Note: Each model includes both Time and Country Fixed Effects. AIC is the Akaike's information criterion; BIC is the Bayesian information criterion. Control variables are described in Section 3.1. Robust standard errors in parentheses. *p < 0.10, **p < 0.05, ***p < 0.01.