Does philanthropy reduce inequality

J Econ Inequal (2011) 9:1–21 DOI 10.1007/s10888-009-9123-6 Does philanthropy reduce inequality? Indraneel Dasgupta · Ravi Kanbur Received: 6 August 2008 / Accepted: 28 October 2009 / Published online: 19 November 2009 © Springer Science + Business Media, LLC 2009 Abstract Wealthy individuals often voluntarily provide public goods that the poor also consume. We show that, rather than reducing it, such philanthropy may ag- gravate absolute inequality in welfare achievement, while leaving the change in relative inequality ambiguous. Additionally, philanthropic preferences may increase the effectiveness of policies to redistribute income, instead of weakening them. Our results thus suggest that philanthropy and direct redistribution may often be better viewed as complements, rather than substitutes, in the context of inequality reduction. In so doing, they also bring into question the general normative case for large tax deductions for charitable contributions. Keywords Community · Public goods · Inequality · Distribution · Philanthropy 1 Introduction Rich individuals often voluntarily contribute large amounts towards the provision of public goods that are intrinsically important for the well-being of poor individuals, but have limited impact on their incomes. Examples of such public goods that routinely acquire rich patrons include places of worship, ethnic festivals, literary We thank two anonymous referees for many useful comments. We have also benefited from helpful discussions with Richard Cornes, Amrita Dhillon, Prasanta Pattanaik and seminar audiences at Brunel, Delhi School of Economics, Indian Statistical Institute and Jadavpur University. Financial support from The Pew Charitable Trusts is gratefully acknowledged. I. Dasgupta (B) Department of Economics, Durham University, 23-26 Old Elvet, Durham DH1 3HY, UK e-mail: indraneel.dasgupta@durham.ac.uk R. Kanbur Cornell University, Ithaca, NY, USA e-mail: sk145@cornell.edu 2 I. Dasgupta, R. Kanbur and cultural activities, sports clubs, civic/neighborhood amenities (including parks, museums, theatres, community halls, libraries), facilities for scientific research, etc. Poor individuals often benefit from these public goods without having to incur any major expenditure, while rich donors claim large tax deductions on grounds of their contribution. These tax deductions however reduce the resources available for direct redistribution. Standard measurement of inequality concentrates on the distribution of consump- tion expenditure. If the rich spend part of their income on public goods that are also consumed by the poor, would standard inequality measures overstate inequality in the distribution of welfare? Second, would the direct income gain the poor make from a given redistribution be largely negated by the consequent reduction in public good provision by the rich; so that the observed reduction in standard measures of income inequality comes to overstate the fall in welfare inequality? The purpose of this paper is to examine these two questions. The thrust of the literature on voluntary provision of public goods has been on investigating how (income) inequality affects provision.1 Our focus is on addressing the exact opposite question: how voluntary provision affects (welfare) inequality, and measures to reduce it. The concrete policy context in which we pose our questions involves a tax deduction for charitable contributions to public goods. The standard, Pigouvian, case for such a deduction is based on the idea that a balanced-budget tax-subsidy intervention can provide a corrective to the inefficiently low level of voluntary provision. The tax deduction on public contributions (in essence a subsidy) is to be funded by a lump-sum tax or a higher tax on income, wealth or private consumption. Consequently, the tax deduction will have no income effect, only a pure substitution effect. This substitution effect will increase private provision of public goods, making everybody better off.2 In reality, tax deductions for public contributions typically make the tax burden lighter for rich philanthropists, since identically wealthy selfish and philanthropic individuals face identical tax rates on income or private consumption. It is thus the income effect of tax deductions for public contributions that we are concerned with, in contrast to the standard focus on the substitution effect. We consider a game of voluntary contributions to a public good, among agents with identical preferences, who vary in terms of their personal income. In the Nash equilibrium, all rich agents contribute to the public good, while all non-rich individu- als completely free-ride. As in standard measurement of inequality, we wish to focus on a money-metric measure of welfare achievement. However, since individuals 1See Cornes and Sandler [12] for an overview. Voluntary contribution to local, or community- specific, ‘club’ goods is also likely to have important implications for distributive conflicts among economic classes and identity groups, as well as for organizing measures to combat poverty. These themes are addressed by Dasgupta [16] and Dasgupta and Kanbur [17–19]. 2Diamond [20] shows that subsidizing donations may also mitigate the incentive problems associated with income taxation, thereby allowing the government to achieve higher redistribution. Our formal focus on lump-sum redistribution of exogenously given wealth will abstract from this issue. Intuitively, our analysis thus relates to a status quo where the incentive-compatibility constraint is not binding for the wealthy, unlike in Diamond [20]. While the optimal taxation literature has done much to clarify the theoretical limits to redistribution, it seems unlikely that any country at present is actually taxing at those limits. Blumkin and Sadka [4, 5] have offered arguments against the substitution-effect case. Does philanthropy reduce inequality? 3 can freely access the public good contributions of others, their personal earnings can no longer provide such a measure. Instead, we utilize the standard notion of equivalent variation to develop a money-metric measure of welfare achievement that incorporates the benefits from the public good. Inequality in welfare achievement is then measured in terms of pair-wise gaps in such ‘real’, or ‘equivalent’ income, instead of differences in personal income. Aggregation of absolute gaps leads to absolute measures of inequality, while aggregation of the gaps normalized by the average or the maximum of the income distribution leads to relative measures of inequality. We show that, under standard restrictions on preferences, the following must be true. The mediation of philanthropy makes the absolute difference in real income (or welfare achievement) between two non-rich individuals larger than that in their nominal incomes. Thus, philanthropy magnifies the welfare consequences of income inequality among the non-rich. If the non-rich are sufficiently poorer than the rich, or if the rich are sufficiently numerous, this is true of the gap between rich and non- rich individuals as well. Hence, according to absolute measures of inequality, the community may in fact be made more unequal, rather than less, by philanthropy. The result with relative inequality measures is ambiguous—even here, there can be no guarantee that philanthropy reduces inequality. Our conclusion is driven essentially by the fact that any given amount of the public good is worth less to the poorer individual. Thus, while each rich individual benefits every non-rich individual through her spending on the public good, she also benefits more than the latter from the spending by other rich individuals on the public good. These two effects contradict one another in terms of their impact on welfare inequality. When the second effect dominates, absolute welfare inequality between the rich and others exceeds the corresponding nominal inequality. We proceed to address the issue of effectiveness of nominal redistribution in reducing welfare inequality. We show that a given (lump-sum) redistribution of monetary income may reduce absolute inequality in real incomes (i.e. welfare achievements) more, rather than less, when the rich contribute to the public good. The same may also hold for relative inequality. As before, two contradictory effects turn out to be at play. A nominal redistribution reduces the supply of the public good from the rich. However, the presence of the public good also makes a dollar of private income more valuable to poorer individuals, compared to a private consumption society. Real inequality would fall by a greater magnitude than nominal inequality when the second effect dominates. Using a standard, strictly concave, social welfare function, we further show that the social welfare-maximizing lump-sum redistributive tax on the rich may be higher, rather than lower, with philanthropic contributions, compared to the case where all consumption is private. Thus, the income effect of a tax deduction for charitable contributions, by reducing the extent of direct redistribution, may reduce social welfare. Our results therefore suggest that philanthropy and direct redistribution may often be better viewed as complements, rather than substitutes, in the context of inequality reduction. In so doing, they also bring into question the general normative case for large tax deductions for charitable contributions. An important strand of political thought seeks to legitimize large inequalities in income or wealth by emphasizing public functions performed by private wealth. At ethical, programmatic and propagandist levels, political formations on the right 4 I. Dasgupta, R. Kanbur often counter-pose ‘duty’ to ‘justice’, or private charity to large-scale redistribution.3 In recent years, this policy thrust has also become prominent in many developing countries. The earlier emphasis on state-organized redistribution of income and wealth has largely been supplanted by attempts to encourage the rich to voluntarily contribute to local public goods. The explosive proliferation of charity intermedi- ation professionals in developing countries is in part a reflection of this process. Our results may be interpreted as contesting the logic of such a policy thrust. They suggest a rejection of the claim that philanthropy is necessarily equality enhancing. Nor do they admit the presumption that philanthropy reduces the efficacy of direct income redistribution. Equality-enhancing claims of specific acts of philanthropy need to be individually established—our results appear to contest any indiscriminate presumption in their favor. What appears to be of critical importance in assessing such claims is the magnitude of their direct impact on the private asset base of poorer individuals, i.e., on their private consumption. Philanthropic contributions to basic health, education, housing and sanitation facilities, medical research into diseases that disproportionately affect the poor, and to technologies that improve demand for low-skilled labor, seem to generally fall in this category. Such contributions reach the non-rich, directly or indirectly, largely in the form of a significant increment in private consumption, and can hence be reasonably perceived as a substitute for direct redistribution of private income. Our analysis suggests that, in contrast, philanthropic provision of public goods that are intrinsically valuable, but have negligible income-augmenting effects on the non-rich, may often be reasonably viewed as complementary to a policy of redistribution. The poor do benefit from such provision, but the rich benefit more. Thus, from an egalitarian perspective, the case for exempting donations to, say, churches, temples, museums, art galleries, opera houses, sports clubs, community centers, public parks, universities, elite private schools, private hospitals etc., from taxation appears questionable.4 Our analysis points to the need for further empirical evaluation of this issue in specific policy contexts. Section 2 lays out the basic model. Section 3 presents our results regarding the relationship between inequality in personal incomes and inequality in welfare 3Benjamin Disraeli, the leading Conservative ideologue of nineteenth century Britain, argued that “the tenure of property should be the fulfilment of duty” (Scruton [26]; p. 109). Thus, Disraeli’s position, which echoed a core ethical principle of feudalism, justified wealth inequality provided the rich performed social functions, i.e., generated public goods in a broad sense, but not otherwise. A similar idea underlies the Gandhian view of property-ownership as trusteeship, as well as much of Catholic and Islamic social thought. Traditional political hierarchies in many countries base much of their ideological appeal on such notions of public function. 4For example, the publicized priorities of the Gates–Buffet project, or those of George Soros, would appear to be broadly in accord when considered globally, but not self-evidently so when considered in the restricted context of American society. Few Americans are likely to experience a significant rise in their private consumption from improvements in malaria medicines. Federal and State governments in the USA have long encouraged the wealthy to donate art to reduce tax liability as a matter of policy [14]. Our results suggest such a policy stance is not self-evidently beyond reproach, when equality is considered an objective of social policy. The Obama administration has sought to reduce itemized tax deductions for charitable contributions for those earning more than $250,000 a year. The administration proposes to use the additional revenue for direct redistribution, in the form of extended health coverage and subsidized premiums for the poor [21]. Our analysis can be read to clarify some arguments that may perhaps be adduced in support. Does philanthropy reduce inequality? 5 outcomes. We discuss the effects of nominal redistribution on welfare inequality in Section 4. We also show how philanthropy might increase, rather than reduce, the social welfare maximizing lump-sum redistributive tax. Section 5 discusses some extensions. Section 6 concludes. Proofs are relegated to the “Appendix.” 2 The model We begin by setting up our benchmark model of philanthropy. The model presented in this section very closely resembles that of Dasgupta and Kanbur [19]. However, while they use this model to investigate the connections between philanthropy and individual attitudes towards redistribution, the present paper uses it to clarify the connections between philanthropy and welfare inequality. The substantive questions that we address in Sections 3–5 below are thus completely different. Let a community consist of n ≥ 3 individuals. The set of individuals is N = {1, ..., n}. Each individual consumes a private good and a public good. For any i ∈ N, xi is the amount of the private good consumed, yi is the amount of the public good provided by i herself, whereas y−i is the amount of the public good provided by all other agents. Preferences are given by a strictly quasi-concave and twice continuously differentiable utility function u (xi, Bi), where Bi ≡ yi + θy−i, θ ∈ (0, 1]. Thus, agents may be concerned only with the total amount of the public good. This possibility, the so-called ‘pure’ public good (e.g. [3, 12, 13, 17, 18]) case, implies θ = 1. The public good may also be ‘impure’—agents may derive greater utility from an additional unit of the public good if they themselves provide it (e.g. [1, 11, 19]) due at least partly to a ‘warm glow’ (i.e., psychic satisfaction) from giving. In this case 0 < θ < 1. The lower the value of θ , the stronger the marginal benefit from giving.5 We assume agents have identical preferences. 5Preferences can also be equivalently represented by U(xi, yi, y), where y is the total amount of the public good, and ∂U ∂yi / ∂U ∂y is some non-negative constant, this term being 0 for the pure public good case. Lower values of θ evidently correspond to higher values of ∂U ∂yi / ∂U ∂y . We thus identify the degree of impurity in the public good with the extent of substitutability between own contribution and others’ contribution. ‘Warm glow’, i.e. private psychic satisfaction from the act of giving per se, is the intuitively obvious reason for agents being better off if a unit of others’ contribution is replaced by a unit of own contribution, private consumption remaining constant. Such satisfaction can intrinsically arise from giving; it can also reflect private non-pecuniary gains due to joint production of some otherwise non-purchasable good, along with own contribution to the public good (e.g. status gain or credits in the afterlife). An alternative way of interpreting impurity is in terms of the extent to which consumption involves rivalry. This can be captured by the simple formulation Bi = ynγ , γ ∈ [0, 1], the parameter γ capturing the degree of rivalry in consumption. When γ = 1 we have perfect rivalry, whereas γ = 0 captures perfect non-rivalry. In the general formulation which incorporates both notions of impurity, the utility function can be written as: U˜ ( xi, 1θnγ (yi + θy−i) ) , where 0 < θ ≡ 1 (τnγ +1) ≤ 1; the parameter τ ≥ 0 captures the degree of impurity in the first (private psychic satisfaction) sense, while the parameter γ captures that in the second (consumption rivalry) sense. Under the separability assumption [ U˜ ( xi, 1θnγ (yi + θy−i) ) = Uˆ(u(xi, yi + θyi), 1θnγ )] , preferences reduce to our parsimonious representation u(xi, yi + θyi). Thus, the parameter θ incorporates both possible sources of impurity. Notice that ‘no warm glow’ (τ = 0) is both necessary and sufficient for the public good to be pure (θ = 1). We will accordingly identify impurity of the public good with the presence of warm glow. Given positive warm glow, however, the exact degree of impurity also depends on the extent of consumption rivalry. 6 I. Dasgupta, R. Kanbur Agent i ∈ N has own money (or nominal) income, Ii ∈ (0,IC]. Thus, the highest income in the community is IC ∈ �++. Let C = {i ∈ N|Ii = IC}, n > |C| = nC. Thus, C is the set of rich members of the community, who all earn IC; the community con- tains nC such individuals. The community also contains some non-rich individuals, who earn less than IC. Define P = [N\C], and let I¯P = max{Ii|i ∈ P}. Thus, P is the set of non-rich individuals, i.e., all individuals who earn less than IC; I¯P is the second- highest income level in the community. Agents simultaneously choose the allocation of their expenditure between the two goods.6 For notational simplicity, we shall assume that all prices are unity. Thus, incomes in our analysis are all implicitly price-deflated. A community member’s maximization problem then is the following. Max xi,Bi u (xi, Bi) subject to: xi + Bi = Ii + θy−i, (2.1) Bi ≥ θy−i. (2.2) The solution to the maximization problem, subject to the budget constraint (Eq. 2.1) alone, yields, in the standard way, the unrestricted demand functions: [Bi = g(Ii + θy−i)], and [xi = h(Ii + θy−i)]. Our main assumptions regarding preferences are the following. A1. g′, h′ > 0. A2. Lim [Ii+θy−i]→∞ h(Ii + θy−i) = ∞. A3. Lim xi→0 u(xi, Bi) = Lim xi→0 u(xi, 0). A1 is the assumption that all goods are normal. By A1, there must exist a unique and symmetric Nash equilibrium in the voluntary contributions game.7 In any Nash equilibrium, it must be the case that: Bi = max [ θy−i, g (Ii + θy−i) ] for all i ∈ N. (2.3) A2 implies that demand function for the private good is unbounded from above, i.e., one can generate any arbitrary level of demand for the private good by suitably choosing the nominal income level.8 A3 is the assumption that the public good is worthless when one has no private consumption.9 6Indiv