Charity, impure altruism, and marginal redistributions of income.

Pure altruists receive utility from how much the poor consume, whereas warm glow is utility from the size of one's own contribution. Andreoni (1989, 1990) showed that if households receive warm-glow utility, then government giving to a public good does not crowd--out private giving dollar-for-dollar. More recently, however, Diamond (2006) argued that warm-glow utility should be ignored for normative tax analysis because warm glow amounts to a preference over how a good is produced. The goal of this research is to identify how warm-glow utility alters the costs and benefits of a marginal redistribution of income funded by a higher labor tax rate on the rich. Andreoni's (1989, 1990) analytical framework is used to derive expressions for the change in utility arising from higher taxes on rich households that are used to fund cash transfers to the poor. The general conclusion is that if households receive warm-glow utility, then it is more likely that a marginal redistribution of income fails the Pareto or cost-benefit test.

Absent warm glow, a redistribution of income increases the utility of rich, altruistic households if they value the increased consumption of the poor more than the additional costs imposed on them from a higher tax rate. However, rich households value increased consumption of the poor less, at the margin, when they also receive warm-glow utility. To see this, remember that a rich household gives to charity until the marginal benefit equals the marginal cost. The marginal cost of tax-deductible giving is simply one minus the marginal tax rate. The marginal benefit of giving another dollar is the increase in utility from the increased consumption of the poor (willingness to pay (WTP) for altruism) plus the additional warm-glow utility (WTP for warm glow). If, for example, the marginal tax rate is 30 percent and the WTP for warm glow is twenty cents, then the marginal WTP for altruism is fifty cents. That is, a one dollar increase in the consumption of the poor increases the utility of the rich fifty cents. If households do not receive warm glow then the WTP for altruism equals seventy cents, and the redistribution is more likely to pass either the cost-benefit or Pareto tests.

There is a large literature that attempts to measure the costs of raising additional tax revenue. This literature typically assumes that households are non-altruistic and receive no warm glow, so that giving to the poor has no direct effect on the utility of the rich. The current model is able to yield comparable cost numbers when using data and elasticities similar to those found in the literature. However, the results suggest that the utility gains of rich households are smaller if leisure and charitable giving are substitutes and if one's charitable giving is negatively related to the giving of others. This result largely reflects that these behavioral responses lead to less crowding-in or more crowding-out of private charity. There are no empirical estimates of the WTP for altruism or warm glow. The numerical calculations show that, in general, households must value altruism more than warm glow, at the margin, for reforms to pass the Pareto test.

INTRODUCTION

Corneo and Gruner (2002) find that the demand for government redistribution is not motivated solely by consideration of a personal monetary gain. Such results bring renewed relevance to the work of Hochman and Rogers (1969, 1974) who argue that interdependent preferences imply that some redistributions of income make everyone better off. However, Wart (1982) shows that incremental fiscal redistribution is not necessarily Pareto improving because government redistribution crowds-out private charity dollar-for-dollar. If the rich view the consumption of the poor as a public good, public redistribution of income is only a Pareto improvement once private giving has been driven to zero. Andreoni (1989, 1990) shows that if households receive utility from the size of the public good and they receive a "warm glow" from the size of their own contribution, public redistribution does not crowd-out private charity dollar-for-dollar. Although Andreoni demonstrates that subsidies for private giving are preferred to direct government contributions, little is known about how warm glow alters the welfare effects of marginal redistributions of income, such as in Allgood and Snow (1998) and Dahlby (1998). (1)

In this paper, the efficiency of a marginal redistribution of income is considered, given that rich households are impure altruists that make tax deductible gifts to private charities. Impure altruists receive utility from the amount consumed by the poor and from their own contribution to the consumption of the poor. One might expect that if households receive utility from giving to the poor, then marginal redistributions of income are more likely to pass the Pareto or cost-benefit test. However, there are two reasons why this may not be the case. First, government giving to the poor may crowd-out private giving, and this will generate utility losses because of lost warm glow. Of course, crowding-in of private charity has the opposite normative implications.

The second reason is best understood by thinking in terms of the marginal costs and benefits of giving to charity. A household gives to charity until the marginal benefit of contributing equals the marginal cost. The marginal cost of giving is one minus the marginal tax rate (MTR). For an impure altruist, the marginal benefit is the gain in utility from the increased consumption of the poor, the willingness to pay (WTP) for altruism, plus the gain in utility from an increase in one's own contribution to the poor, the WTP for warm glow. The household does not receive warm glow if a dollar increase in the consumption of the poor is because of a government transfer (or giving by other households). In this case, the increase in utility equals the WTP for altruism, which is marginal cost minus the WTP for warm glow. On the other hand, if a rich household is a pure altruist, then the increase in utility due to a one dollar increase in the consumption of the poor is just one minus the MTR. (2)

Diamond (2006) acknowledges that warm glow may improve our description of how individuals and households behave. However, he argues for ignoring the effects of warm-glow utility on social welfare when considering optimal tax structures because warm glow amounts to preferences over how the public good is produced. (3) Diamond compares the social welfare implication of models with and without warm glow by inserting a parameter that is set to zero when the social planner wants to ignore changes in utility arising from warm glow.

Diamond's (2006) analysis highlights an important modeling decision that must be made for normative tax evaluation. Should households be treated as impure altruists, pure altruists, or even non-altruists? Even if households receive warm-glow utility, one may choose to not incorporate this element of preferences into the model. This paper identifies and quantifies the implications of these different assumptions about preferences for marginal redistributions of income.

The interpretation of the analytical model builds on the work of Andreoni (1989, 1990) and Diamond (2006), and the analytical model provides a general guide for how impure altruism alters the efficiency of marginal reforms. However, there is also a large literature that attempts to quantify the welfare costs of increasing the tax rate on labor income to fund a marginal redistribution of income. This literature mainly focuses on the marginal efficiency costs caused by reductions in labor supply. (4) The general conclusion of this literature is that redistributing income does not pass the cost-benefit test because such reforms generate a positive welfare cost as higher tax rates shrink the tax base. Warm glow and charitable giving introduce elasticities not used in past analysis, in addition to the welfare effects just discussed. The numerical evaluation of the model illustrates how sensitive calculations of marginal welfare cost are to the introduction of these elasticities and the importance of the WTP for altruism to the overall welfare effects of reforms.

The paper proceeds as follows. First, the model is developed and equations for evaluating marginal reforms to tax and spending policy are derived. Then a numerical example is provided. The final section provides concluding comments.

THE MODEL

Basics of the Model

Consider a model with two types of households, the rich (indexed by r) and the poor (indexed by p). For simplicity, there is only one poor household and the number of (identical) rich households is n > 1. Rich households are assumed to have greater labor market productivity [[delta].sub.r] > [[delta].sub.p] and larger endowed income [M.sub.r] > [M.sub.p] = 0. If W is the market wage rate, then an hour of labor earns a rich household [[delta].sub.r]W and a poor household earns [[delta].sub.r]W. Households sell their labor supply h in the market at these prices. Output for the economy is produced by a linear production function that is a function of a fixed supply of capital and aggregate effective labor supply [H.sup.a] = [[delta].sub.p][h.sub.p] + n[[delta].sub.r][h.sub.r].

Government collects taxes via a graduated tax structure on labor earnings with two MTRs. The two tax brackets are defined by the income level y. It is assumed that the labor income of the rich exceeds y, and the income of the poor does not. The tax rate for the rich, [m.sub.r], includes all taxes on labor income such as payroll taxes. Poor households pay payroll taxes, but it is assumed that the poor face a zero federal income rate on earned income (Rosen, 2005). As a result, the poor household does not explicitly pay taxes on other income sources, such as transfers received from private charities.

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