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BY 4.0 license Open Access Published by De Gruyter May 29, 2023

Bridging the Gap: The Role of the Charity in Voluntary Public Good Provision

  • Stephanie Karol EMAIL logo


This paper investigates how donors to food assistance charities respond to exogenous changes in recipients’ unmet needs. When food insecurity rises by one percentage point, the average food assistance charity increases fundraising by 0.9 %. Without this response, private contributions would have fallen by at least 0.2 %. These results are consistent with a model in which economic inequality simultaneously raises the donor’s marginal benefit of giving and reduces their awareness of the recipient’s circumstances. Charitable fundraising plays a key role in maintaining the charity’s revenues at a time when they are most needed.

1 Introduction

Standard models of voluntary public good provision – alternatively called charity – follow Samuelson (1954). A representative donor derives utility from a public good, which can be funded using contributions from the government, private actors, or a combination of the two. These standard models therefore describe the behavior of a charitable donor who simultaneously consumes the charitable good to which they donate. It is easy to imagine a real-world example of a charity where the same individual might appear as both a donor and a client: this arrangement neatly describes many museums, schools, and hospitals. These organizations satisfy the legal definition of charity set out by Section 501(c) of the United States Internal Revenue Code. However, they do not always satisfy the more colloquial definition of a charity: an organization set up to provide for those in need (Cambridge University Press 2022). This definition describes food banks, shelters for the unhoused, foster care service providers, and many others. These organizations are also considered charities under Section 501(c). Unlike a museum or a theater, it would be highly unusual for these charities’ donors to consume the services produced by these organizations. The standard models of voluntary public good provision are therefore not designed to describe donation behavior at the charities set up to serve the most vulnerable members of society.

This paper fills that gap in the literature by developing a model of the interactions between donors, recipients, and charities, in a context where donors and recipients are drawn from different subpopulations within the economy. As many motivating examples are organizations which use funds raised from the well-to-do to support those less fortunate, the distinction between donors and recipients in this model arises from differences in their resources. The distinction between donors and recipients will therefore be exacerbated by income inequality and social stratification.

The purpose of this model is to ask how donors would respond to recipients’ unmet needs, when donors may have low awareness of recipients’ social and economic conditions. This response is related to traditional notions of crowd-out, which is the main focus of both the theoretical and empirical literature that follows from Samuelson (1954). These models (for example, Warr 1983; Bergstrom, Blume, and Varian 1986; Andreoni 1990) are primarily concerned with private donors’ supply responses to changes in others’ supply of the public good, but would require substantial modification in order to predict how supply of this public good changes with demand by non-donors.

In the model, donors derive warm-glow utility from making charitable contributions to charities which serve the poor. This warm glow increases in inequality between donors and recipients – when this inequality is made salient to donors. By fundraising, the charity can raise this salience. The model makes a surprising prediction about donors’ responsiveness to changes in recipients’ unmet needs. When recipients’ circumstances worsen, donors are less likely to give to charities which support them. This perverse tendency can be overcome if the charity steps up its fundraising efforts, reminding donors of their moral commitments.

This paper proceeds to verify the predictions of this model in the context of the food assistance industry. Unmet need for food assistance is measured by food insecurity. This charitable cause is of particular interest for two reasons. First, nutrition is a basic physiological need. Previous research shows that food insecurity is associated with a vast array of negative outcomes for both mental and physical health (Gundersen et al. 2011). For adults and the elderly, the negative effect of food insecurity on nutritional outcomes operates independently of the correlation between food insecurity and poverty (Bhattacharya, Currie, and Haider 2004). Second, food insecurity is a pervasive and persistent problem in the United States. In 2020, an estimated 10.5 % of the American population experienced food insecurity at some point of the year (Coleman-Jensen et al. 2021). The pandemic has brought a great deal of much-deserved awareness to the ongoing crisis of food insecurity in the United States, but this issue does not typically command attention in the news cycle. The mundane nature of this national emergency implies that at baseline, its salience to the donor class is often low. Charitable organizations looking to raise funds to help the food-insecure may therefore have great scope to raise donors’ awareness of the problem.

The empirical analysis begins by identifying the set of charitable providers of food assistance. These charities are identified using Guidestar’s Philanthropy Classification System, which yields a set of 1389 unique charities, observed between the years 2013 and 2018. On average, these organizations increase fundraising by 0.9 % when food insecurity rises by one percentage point. By contrast, private contributions to these organizations do not appear responsive to the prevalence of food insecurity in the charity’s state. While the point estimate characterizing the overall response of private giving to food insecurity is positive, it falls below zero after controlling for changes in the charity’s fundraising expenses. The effect of food insecurity on donors’ private contributions is not statistically distinguishable from zero, regardless of whether it is expressed as gross or net of fundraising. This indicates that in the most optimistic scenario, donors appear insensitive to food insecurity, unless the charity’s additional fundraising prompts them to give more. Further results illustrate that rising food insecurity generates more charitable fundraising, and therefore more private contributions, in states where income inequality is rising as well.

When compared to the predictions of the model, these empirical estimates imply that the “warm glow” donors derive from making charitable contributions does increase in inequality. This would seem to suggest that donors’ generosity will always increase in recipients’ unmet need. However, the estimates demonstrate that this additional generosity should not be taken for granted. In the context of the American food assistance industry, donors’ generosity will increase only if the charity also steps up its fundraising. This is because hunger is not very visible to those who do not experience it, and so its salience to the donor class will be low, in the absence of some informational intervention.

The paper proceeds as follows. Section 2 outlines the contribution to the literature. Section 3 develops a model of the interaction between donors, recipients, and charities in the voluntary provision of goods and services in demand by low-income people. Section 4 describes the empirical strategy used to estimate several key relationships which arise from the model, using data sources described in Section 5. Section 6 presents and interprets the empirical results. Section 7 concludes.

2 Contribution to the Literature

Standard models of voluntary public good provision follow Samuelson (1954), Warr (1983), Bergstrom, Blume, and Varian (1986), and Andreoni (1990). These models demonstrate that if donors’ income remains unchanged, then so will voluntary provision of the public good. In each of these models, so long as donors receive some altruistic utility from total public good provision and believe that their own gift is large enough to affect the overall level of provision, then each donor’s choice of gift depends on the gifts – and therefore the income – of all other donors. Previous work has used this fact to argue that changes to the income distribution can affect charitable contributions.[1] However, while these workhorse models successfully show that donors’ gifts can depend on changes to the distribution of income among donors, these models predict that donors’ gifts will be invariant to changes to the income distribution which affect only non-donors.[2]

This case may be particularly important in an environment of rising income segregation. If donors to, and recipients of, charitable provision come from different parts of the income distribution, then these previous models imply that a shock to recipients’ incomes, but not donors’ incomes, should result in a level of public good provision which is unchanged or greater than before. If recipients’ unmet needs fall in their incomes, then this is equivalent to suggesting that donors’ contributions to the public good should not fall, and may rise, in recipients’ unmet needs. The present work addresses this question.

This work builds upon the model of Duquette and Hargaden (2021). In that model, the authors impose the assumption that donors believe their contributions are small relative to the public good. However, donors do derive a private benefit, or “warm glow”, from their own charitable gift. This warm glow depends upon the entire income distribution, not only the segment of the income distribution from which donors are drawn. The present work innovates upon this framework by noting that donors may have trouble observing the shape of the income distribution, or the needs of those who derive income from a different part of that distribution, without an informational intervention by the charity. Whereas Duquette and Hargaden find that charitable contributions fall in income inequality, this paper comes to a different, though complementary, conclusion. The donor derives a greater marginal benefit of giving when they perceive the recipient’s needs are greater. An increase in income inequality, coming from changes in the recipient’s portion of the income distribution, will simultaneously increase the recipient’s unmet needs and reduce the donor’s ability to perceive those needs.

This result is particularly consequential in light of recent work, which shows that donors’ altruism relies in part on the donor’s attitudes towards inequality, as well as their sense of social connectedness, affinity, or empathy for the recipients of their gifts (Buckley and Croson 2006; Derin-Güre and Uler 2010; Duquette and Hargaden 2021; Mastromatteo and Russo 2017; Payne and Smith 2015; Uler 2011; Small and Simonsohn 2008). The bulk of this literature comes to the theoretical conclusion that charitable giving should rise in inequality, though empirical results are mixed. In an environment characterized by increasing income segregation (Reardon et al. 2018), high-income and low-income households may both become isolated from the mainstream of American society (Krivo et al. 2013). One natural consequence of this growing social isolation is that potential donors may become less aware of, or less concerned with, recipients’ needs. This paper contributes to the growing literature on the relationship between inequality and charity by estimating the extent to which local measures of inequality may affect the generosity of the relatively high-income towards the relatively low-income, when demand for charitable nutritional aid increases among the latter group. In doing so, it rationalizes the disconnect between papers which predict that inequality should raise donors’ generosity, and those which find that this result is not always discernible in empirical work. Economic inequality will simultaneously increase recipients’ unmet needs, and reduce donors’ ability to perceive these needs.

Depending on the type of charitable good or service, donors may not always have trouble understanding the needs of recipients. Previous research on the response to changes in demand for specific types of charitable services has thus far focused mainly on disaster relief (Deryugina and Marx 2021; Eckel, Grossman, and Milano 2007; Evangelidis and Van den Bergh 2013; Lilley and Slonim 2016; Simon 1997; Smith, Scharf, and Ottoni-Wilhelm 2018), which is made highly salient to donors via news coverage. These studies find that private donations exhibit a large and positive response to natural disasters, which is exacerbated by news coverage of these events. Smith, Scharf, and Ottoni-Wilhelm (2018) find that the death toll of a natural disaster is more strongly related to donations for its victims than the count of people affected by the disaster, suggesting that even when donors are well aware of the conditions which create demand for charitable services, their donative behavior is not closely related to the magnitude of the demand for charity. However, this means that innovations to demand for services which are too mundane for the news cycle – such as nutritional assistance – may not be made salient to donors at all.

In the food assistance context, private charity is regarded as an imperfect substitute for public assistance by end users. Despite the fact that food insecurity is associated with a plethora of negative health outcomes (Gundersen et al. 2011), takeup of charitable food assistance is quite limited. Pruitt et al. (2016) find that only 21.7 % of adults living in food-insecure households received charity food. While stigma plays a role in reducing take-up of these services (Byrne 2021; Edin et al. 2013; Fong, Wright, and Wimer 2016), food banks[3] represent an important supplement to public nutrition assistance.[4] Si (2018) finds that households become 19.9 % more likely to use food bank services in response to a negative income shock, and that living in close proximity to a source of charity food increases take-up. This result clearly implies that changes in unmet need will noticeably alter the size and composition of an anti-hunger charity’s clientele. If these changes are significant from the perspective of the charity providing this assistance, this charity may be more likely to communicate this news to its donors, in the hope of keeping or increasing their contributions.

3 Donors, Charities, and Clients in the Market for Charitable Funds

This paper contributes to the literature on charitable giving by modeling the behavior of charities, their donors, and their clients as these organizations seek to use donors’ funds to provide social services to their clients. This model departs from previous work by imposing the restriction that charitable donors and recipients hail from two distinct portions of the income distribution. Owing to the differences in their material circumstances, they also maximize different objective functions.[5] This section first describes the recipient’s problem, followed by the donor’s problem and the charity’s problem. Finally, it derives comparative statics, which describe donors’ responses to changes in demand for social services they fund, but do not consume.

3.1 The Recipient’s Problem

A mass of R identical recipients each solve the following constrained optimization problem:

(1) max { max x R , c u R ( x R , c ) s  s.t.  y R = p c c + x R ; u ( y R , 0 ) }

The stigma costs, s, are distributed according to cumulative distribution function H(s), defined on the domain [0, ∞). The price of the charitable good, p c , represents the monetary value of the individual-specific time, transportation, or effort costs involved in procuring charitable good c. If the value of the first argument exceeds the value of the second argument, the recipient takes up the charitable good with probability t. The charitable good, c, is assumed inferior, and takeup is assumed to decline in income y R as well.[6] For individuals who take up the charitable good, the ideal consumption of charity (c*) is given by:

(2) u R 1 p c = u R 2

As each recipient’s first-order condition (2) is identical, each will want to consume the same c*. However, the actual amount of the charitable good available to recipients is given by GF. This is the sum of donors’ charitable contributions, G, net of the fundraising expenses the charity incurs to raise this amount, F. The charity provides an equal amount of its good to all recipients who wish to take it up. This realized level of consumption is given by c ̄ = G F R t . Unmet need is defined by the difference c * c ̄ , shown below (Figure 1) as a function of net charitable contributions, GF:

Figure 1: 
Unmet need.
Figure 1:

Unmet need.

For any GF < Rtc*, the recipient’s desired consumption of the charitable good will exceed their actual consumption, and there will be unmet need. When y R falls, c* and t both rise; the increase in takeup raises the denominator of c ̄ . Unless GF rises, there will be even less of the charitable good to go around, and unmet need will increase.

3.2 The Donor’s Problem

Assume a mass of D identical donors. For a given donor, preferences can be expressed as follows:

(3) u ( x D ) + v ( g D , σ ( F , y D y R ) ( R t c * G + F ) )

These donors receive utility from private consumption, u D , as well as a warm-glow utility from their own charitable gift, g D .[7] Following Duquette and Hargaden (2021), the warm glow depends on the broader social and economic context. In particular, the donor’s gift can generate more warm-glow utility when the charitable recipient’s unmet needs rise – provided, of course, that the donor is aware of these needs. This awareness is captured by the salience function, σ(F, y D y R ), defined on the unit interval. The greater the income inequality between the donor and recipient class (y D y R ), the less salient recipients’ needs are likely to be to donors.[8] Through its fundraising expenses, the charity can increase the donor’s awareness of the recipient’s unmet need.

The donor maximizes (3) subject to the budget constraint y D = x D + p g g D , where p g represents the tax-inclusive price of charitable giving. The first-order condition of the donor’s problem is given by:

(4) u ( y D p g g D ) p g + v 1 ( g D , σ ( F , y D y R ) ( R t c * G + F ) ) = 0

By appealing to the implicit function theorem, and noting that total gifts to the charity are given by G = Dg D , expression (4) yields the following relationship between total charitable contributions and the charity’s fundraising, shown in Equation (5). The arguments of the warm-glow and salience functions are suppressed for notational convenience.

(5) G ( F ) = D v 12 ( σ 1 ( R t c * G + F ) + σ ) u ( y D p g g D ) p g 2 + v 11

The denominator of this expression will be negative, so long as the donor’s flow utility function u(x D ) is concave in private consumption, and their warm-glow function is concave in charitable giving. In the numerator, Rtc* − G + F > 0 if unmet need exists among recipients. If charitable fundraising has any power to raise the salience of this unmet need, then σ 1 > 0. The salience function is assumed weakly positive. Finally, for charitable fundraising to be productive (G′(F) > 0), it must be the case that v 12 > 0: the marginal warm glow a donor receives from giving to charity must increase in unmet need.

Expression (4) can also reveal how charitable contributions will respond to changes in recipients’ resources, absent a change in charitable fundraising:

(6) G y R = D v 12 σ 2 y D ( R t c * G + F ) + σ R t c * y R u ( y D p g g D ) p g 2 + v 11

If fundraising is held constant, then the change in giving is proportional to:

σ 2 y D ( R t c * G + F ) + σ R t c * y R

The second summand is negative, as takeup of the charitable good falls as recipients’ incomes rise. The first summand will be positive, as salience falls in social distance. Then the sign of G y R is theoretically ambiguous. As recipients’ incomes fall, donors will become less generous if the loss in salience, weighted by the volume of unmet need, exceeds the salience-weighted increase in takeup.

Note that if salience falls in social distance, then G y R will be most negative when social distance is small, and least negative when social distance is large. In other words, donors should be most responsive to changes in recipients’ unmet needs when inequality is low, and least responsive when it is high.

These results illustrate that while donors are well-intentioned, it is by no means certain that they would increase their generosity when recipients need it most, without the intervention of a charity. If fundraising is allowed to vary with recipients’ resources, then the total change in charitable giving can be expressed as:

(7) d G d y R = G F F y R + G y R

The overall change in resources available to provide social services to the recipient class therefore depends on how the charity responds to changes in recipients’ incomes.

3.3 The Charity’s Problem

The charity chooses its fundraising expenses to solve the following problem:

(8) max F ( R t c * G ( F ) + F ) ψ ( F , y D y R )  s.t.  G ( F ) F

The charity derives disutility from unmet need among the recipient class. The second summand, ψ(F, y D y R ), represents the charity’s distaste for fundraising. It is increasing in its first argument, F. If the charity finds fundraising less distasteful in an environment of greater inequality, then the cross-partial ψ 12 will be negative.

Letting λ represent the Lagrange multiplier for the charity’s budget constraint, the charity’s first-order condition is given by:

(9) G ( F ) ( 1 + λ ) ψ 1 ( F , y D y R ) = 0

This in turn implies:

(10) F y R = G ( F ) y R + ψ 12 ( F , y D y R ) G ( F ) ( 1 + λ ) ψ 11 ( F , y D y R )

The denominator will be negative so long as the second-order condition holds.[9] The numerator includes two summands. The first term will be negative if fundraising is less successful when recipients are better-off financially. As mentioned above, the second term will be negative if the charity is less hesitant to fundraise when society is more unequal. Then charities should fundraise less as recipients’ incomes rise and unmet need falls.

This model provides a framework for decomposing and interpreting the effects of exogenous changes in recipients’ unmet need on donors’ contributions and charities’ fundraising expenses.[10] The following section outlines the empirical strategy for estimating these objects.

4 Empirical Strategy

The previous section illustrated the mechanisms through which recipients’ unmet need may affect provision of charitable goods and services. This section develops an empirical framework for estimating these mechanisms.

4.1 Cumulative Effects of Food Insecurity on Contributions and Fundraising

Consider the two outcomes of interest discussed above: fundraising expenses and private contributions. Each outcome y ist can be represented as follows:

(11) y ist = exp ( β H H ist + β X X ist + u ist )

Due to the frequency with which zeroes may appear in the fundraising variable, Equation (11) is estimated using a Poisson pseudo-maximum likelihood estimator. The Poisson specifications are estimated using the ppmlhdfe command (Correia, Guimarães, and Zylkin 2020), a quasi-maximum likelihood estimator. When the likelihood function belongs to the linear exponential family, quasi-maximum likelihood estimators consistently estimate the parameters of the conditional mean function; while the conditional mean must be correctly specified, this estimation method is robust to other forms of distributional misspecification (Gourieroux et al. 1984; Imbens and Wooldridge 2009; Wooldridge 2014).

Unmet need is measured as the food insecurity rate in the state where charity i is headquartered, H ist . As charities’ expenditures during period t cannot alter food insecurity rates at the beginning of that period, state-level food insecurity rates are taken as exogenous from the perspective of charity i.

Specification (11) includes a vector of state- and organization-level controls, X ist . This vector includes organization and year fixed effects, as well as a measure of local income. Organizations may fundraise more, and receive more private contributions, in higher-income states. At the same time, income is negatively correlated with food insecurity. It is clearly necessary to control for some measure of local income. Measures of income among non-poor households are most appropriate in this context, as it is more relevant for the relationships between food insecurity and fundraising, private contributions, and government budgets. Measures of income that are too closely correlated with either the food insecurity rate or the poverty rate may result in inappropriately large standard errors. Therefore, the local measure of income included in these specifications is the log of average income among households above 500 % of the poverty line.

Finally, many specifications include a measure of state-level income inequality, as well as its interactions with unmet need.

4.2 Decomposing the Private Charitable Response to Hunger

While Equation (11) can be used to produce estimates of the overall effect of food insecurity on fundraising and private contributions, Equation (7) illustrates that the latter effect is a function of the former. A decomposition of the overall effect of food insecurity on private contributions into its component parts will reveal the extent of the charity’s role in stimulating donors’ response to food insecurity. This decomposition is accomplished by estimating the following system of equations:

(12) y ist = exp ( β f ln ( f ist ) + β H H ist + β X X ist + u ist )

(13) f ist = exp ( γ Z Z ist + γ H H ist + γ X X ist + ν ist )

where y ist represents private contributions, f ist represents fundraising, and Z ist is an explanatory variable appearing in Equation (13) and not Equation (12). Note that Equation (13) is equivalent to:

(14) ln ( f ist ) = γ Z Z ist + γ H H ist + γ X X ist + ν ist

Therefore the first-stage equation can be written such that the disturbance term is additively separable from the explanatory variables. Since this is the case, it is possible to estimate this system using a control-function approach (Blundell and Powell 2003; Wooldridge 2014, 2015). This requires the following set of assumptions:

(15) ( u ist , ν ist ) ( H ist , X ist , Z ist )

(16) E ( u ist | H ist , X ist , Z ist ) = 0

(17) E ( ν ist | H ist , X ist , Z ist ) = 0

(18) γ Z 0

These assumptions will be satisfied if the excluded instrument, Z ist , has a strong relationship to f ist , and affects y ist only through f ist . Andreoni and Payne (2011) argues that the occupancy costs faced by a charity fit this description – all else equal, charities which face higher rent have an incentive to fundraise more – but unfortunately, this choice of instrument proved relatively weak in this sample. However, the charity’s office expenses prove to be a stronger instrument. Office expenses include payments for office supplies, telephone services, equipment rental, bank fees, and costs related to postage and printing. The argument supporting the relevance of this instrument is identical to the argument made by Andreoni and Payne (2011) in favor of occupancy costs. Furthermore, office expenses should prove exogenous so long as they are not correlated with unobservable determinants of charitable contributions. It is possible that growth in an organization’s assets may simultaneously bring about growth in both its office expenses and the contributions it receives. This would constitute a violation of the exclusion restriction. To address this problem, these specifications include a control for charities’ assets, measured at the beginning of the charity’s fiscal year.

The control function approach proceeds in two steps. The first step consists of estimation of Specification (13) via Poisson fixed-effects regression. The second step is to calculate ν ̂ ist , the estimated residuals of Specification (13). This variable is normalized[11] and included in (H ist , X ist ), the vector of controls in Specification (12), and can be understood as a sufficient statistic for the endogenous components of f ist . Finally, standard errors are calculated via the bootstrap.

The system of Equations (12) and (13) imperfectly divides the overall effect of food insecurity on private contributions into two mechanisms: a direct mechanism which operates independently of the charity’s fundraising activities, and an indirect mechanism, capturing the extent to which food insecurity affects private contributions through fundraising. This division is imperfect because, even in the absence of measurement error, not all fundraising effort costs money. As illustrated in Figure 2, anti-hunger charities may change the content of their donor communications to incorporate current information about unmet need. These efforts would not be reflected in the dollar amount of fundraising expenses reported on the Form 990. If these non-financial aspects of fundraising play an important role in raising donors’ awareness of food insecurity, the coefficient β H will reflect the “direct” mechanism but also capture some of the “indirect” mechanism. Furthermore, since the variable f ist is measured with error, and this variable is now included on the right-hand side of Equation (12), it follows that the resulting estimates will suffer from attenuation bias.

Figure 2: 
Communication with donors via fundraising appeal. Source: Food Gatherers (2021).
Figure 2:

Communication with donors via fundraising appeal. Source: Food Gatherers (2021).

4.3 Measurement Error

Charities may exercise some discretion in reporting each line item on the Form 990. This discretion is assumed to be limited to the way expenses may be allocated between fundraising, program spending, and other activities, as the other outcomes of interest are much more easily verifiable. Some activities may contain both a fundraising component and a program service component, and as a result, even an organization that is subject to a moderate degree of scrutiny could reasonably reallocate reported spending between categories. At the same time, charity watchdog groups incentivize organizations to underreport fundraising expenses. Mayo (2022) finds that organizations classified as Food charities by Charity Navigator relabel non-program service expenses as program service expenses in order to achieve an extra star under the Charity Navigator rating system. Not all organizations are eligible to be rated by Charity Navigator – in some cases, because the fundraising budget does not exceed 1 % of total spending – but these charities may still face weaker versions of the same incentive.

The fundraising measure is therefore considered to contain some multiplicative measurement error, such that fundraising expenses appear artificially low. This measurement error will tend to inflate the variance of the estimates, but will not affect the consistency of the estimates so long as it is uncorrelated with other covariates (Cameron and Trivedi 1998). As all specifications contain charity-level fixed effects, this assumption will hold so long as any deviations in the measurement error from its charity-specific mean are uncorrelated with within-state deviations in food insecurity or donors’ income, or deviations in charities’ assets from their charity-specific means.

5 Data

This section describes the data compiled to estimate the specifications described in the previous section. First, charities dedicated to fighting food insecurity are identified using GuideStar’s Philanthropy Classification System. Next, these organizations are matched to the financial data reported on their federal information returns. Finally, these charities are matched to state-level measures of hunger, income, and inequality.

5.1 Candid

This project uses data collected from Candid, a non-profit organization created by the 2019 merger of GuideStar and the Foundation Center (Candid 2021a, 2021b; McCambridge 2019). GuideStar is a directory of non-profit organizations. Its listings include all organizations exempt from taxation under Section 501(c) of the Internal Revenue Code, based on their appearance in the IRS’ Business Master File of tax-exempt organizations and Publication 78, which lists all organizations eligible to receive tax-deductible charitable contributions. Newly exempt organizations may enter the database with a lag of up to six months. Organizations which are not required to apply for tax exemption, such as religious organizations, are only listed on GuideStar upon the organization’s request.

Food aid organizations are identified using Candid’s Philanthropy Classification System (PCS). This is a multi-dimensional taxonomy, which assigns organizations to at least one cause category. Recipient organizations can be matched to as many as five distinct cause categories. All GuideStar-listed organizations are classified according to the PCS at the point of their inclusion in the database, though some are classified as “Unknown or not classified”. The set of charities listed as “food aid organizations” by GuideStar therefore includes all organizations for which provision of charitable food assistance constitutes one of its top five functions.[12] The geographic distribution of these charities is depicted in Figure 3.

Figure 3: 
Distribution of food aid organizations 2015.
Figure 3:

Distribution of food aid organizations 2015.

5.2 IRS Form 990

Organizations which claim tax exemption under Section 501(c)(3) of the Internal Revenue Code are required to file an annual information return, known as the Form 990. Organizations which hold over $500,000 in total assets at the end of the tax year, and which normally take in at least $50,000 in gross receipts, are required to file the full Form 990, the most detailed of these information returns (Internal Revenue Service 2021a). Until 2013, the IRS and the National Center for Charitable Statistics (NCCS) had digitized only a subset of fields from relatively small samples of Form 990 filings. These data limitations were effectively lifted for electronically filed forms beginning in 2013, when the IRS made the universe of Form 990 e-filings available to the public. This e-filing data contains many additional fields relative to the extracts previously published by the IRS or the NCCS, including a breakdown of organizations’ contributions by source (Internal Revenue Service 2021b). In order to exploit this degree of detail, this analysis focuses on charities which file Form 990 in electronic format (Lecy 2021).

Figure 4: 
Share of food aid organizations represented in sample.
Figure 4:

Share of food aid organizations represented in sample.

This sample restriction is not representative of the universe of 501(c)3 organizations, for two reasons. The first is that electronic filing has become more common since 2011, the first fiscal year for which data are available. The IRS will require Form 990 to be filed electronically for all fiscal years ending after July 31, 2020. As such, organizations which are observed for all seven years of the sample may be considered early adopters of a technology which eventually becomes compulsory. Secondly, the sample omits Form 990-EZ filers, due to differences in information reported between the two forms. Marx (2018) presents evidence that the relative complexity of Form 990 compared to Form 990-EZ induces charities to bunch at reporting thresholds. This paper finds that these charities manipulate their receipts by as much as $1000 in order to avoid filing Form 990, but that the manipulation is concentrated among organizations which face filing the more complex form for the first time. Taken together, these data are clearly missing nonrandomly: the sample reflects larger, more technologically savvy organizations, and the smaller organizations represented in the sample have chosen to file a more onerous and costly form.

The IRS’ Annual Extract of Tax-Exempt Organization Financial Data includes an indicator variable for electronic filing, which enables comparison between electronic and paper filers along several relevant dimensions. This comparison can be found in Appendix A. Electronic filers appear larger than paper filers in every way, although the selection attenuates in 2019, as the deadline for all organizations to convert to e-filing approaches. The lack of symmetry between electronic filers and paper filers confirms that the sample is nonrandomly selected. This selection may create some negative bias in the results if smaller charities are more responsive to food insecurity than larger charities, where “small” refers to the charity’s level of assets, contributions, and/or expenses.

The resulting sample accounts for roughly 30 % of all food aid organizations identified using the Candid’s Philanthropy Classification System. However, since the organizations in this sample are, by definition, large compared to 990-N filers and 990-EZ filers, the sample used in the below analysis represents approximately 88 % of gross revenue received by all food aid organizations (Figure 4).[13]

The Form 990 contributes data for a variety of charity-level outcome variables and covariates, for the years 2013 through 2018. These outcomes include fundraising expenses and private contributions.[14] Fundraising expenses include all expenses incurred to solicit both cash and in-kind contributions from public and private sources, including overhead expenses associated with fundraising.[15] Total private contributions are defined as total contributions less government grants and membership dues.[16] Importantly for food aid charities, these contributions must reflect the value of both cash and non-cash contributions, such as donated food. Private contributions may come from any source other than the government, including individual donors, foundations, or businesses. Other variables sourced from the IRS Form 990 include total charitable assets at the beginning of the fiscal year[17] and total office expenses.[18]

5.3 Food Insecurity

Unmet need for charitable nutrition assistance is measured using the food insecurity rate. Food insecurity is defined as “limited or uncertain availability of nutritionally adequate and safe foods or limited or uncertain ability to acquire acceptable foods in socially acceptable ways” (Anderson 1990). The Current Population Survey Food Security Supplement (CPS-FSS), administered by the Census each December, asks an 18-question battery of all respondents in order to capture the degree of food security experienced at the household level (Bickel et al. 2000). Households with children are considered to be experiencing food insecurity if they answer more than 3 of these questions in the affirmative, and experiencing very low food security if they answer at least 8 of these questions positively. For households without children, the relevant thresholds are 3 or 6 questions, respectively. As is standard practice in the charity literature, these data are matched to the Form 990 by the state in which the organization is headquartered. However, it is clear that charities’ service area may be a subset of its overall state. Since the only estimates of food insecurity available below the state level are model-based imputations (Gundersen et al. 2015), the relevant measure of food insecurity for a particular charity is assumed to be the state-level rate for the states in which it operates. These data are retrieved from the University of Kentucky Center for Poverty Research (2020).

Reliance on state-level measures of food insecurity will create a bias against finding a charitable response to hunger. To see why, note that in many cases, charities’ service areas do not coincide with state borders. Anti-hunger charities may serve a particular metropolitan area, a particular county, or a particular region; all of these levels of geography may occur at the sub-state level. If, for example, a charity in the sample serves an urban population, but changes in the food insecurity rate are driven by that state’s rural population, the charity may appear insensitive to these innovations in the food insecurity rate. This apparent null effect would obtain not because charities are actually insensitive to hunger, but rather because the measure of hunger employed is insufficiently relevant. However, while Form 990 data on anti-hunger charities provides information as to the set of states where a charity operates (National Council of Nonprofits 2018), it does not provide much insight into where this charity operates within a state. While the Form 990 can identify the county or metro area where a charity is headquartered, assuming that a charity only operates in this geographic area will result in estimates biased away from zero in the event that this assumption is wrong. As Si (2018) points out that proximity to a food bank is an important determinant of take-up, anti-hunger charities are assumed to operate only within the state’s borders.

Food insecurity rates are measured as of the beginning of period t. This is accomplished by using a one-period lag of the food insecurity rate, noting that measures for period t − 1 reflect food insecurity as of December of year t − 1, and assuming that any difference between the food insecurity rate at the beginning of December and the food insecurity rate at the beginning of January is negligible. Figure 5 depicts food insecurity rates measured at the beginning of December 2015, assumed to bear negligible differences to the food insecurity rates as they stand at the beginning of January 2016.

Figure 5: 
Food insecurity rates by State, 2015. Source: Flood et al. (2020).
Figure 5:

Food insecurity rates by State, 2015. Source: Flood et al. (2020).

5.4 Additional Covariates

As higher-income states have a greater capacity for generosity, it is useful to control for the income of the donor class in each state. Due to the high correlation between food insecurity rates and income among the poor, this measure will reflect the average income among the non-poor, defined as the households living above 500 % of the federal poverty line. This variable is constructed based on data from the American Community Survey’s one-year public use microdata sample. It is calculated by taking a weighted sum of household income by state and year, for the subset of respondents with an income-to-poverty ratio above 500 %, and then dividing by the sum of the weights for this group. Tables produced using an alternative measure of income – personal income per capita – are presented in Appendix C.

Per the model, inequalities between the donor and recipient classes will affect donors’ generosity, as it may change the warm glow a donor derives from their gift. This dynamic is captured by including a control for state-level inequality: the Gini index. This variable, measured at the state-year level, is constructed using data from IPUMS-CPS. Summary statistics are presented in Table 1.

Table 1:

Summary statistics.

Mean St. dev. Min. Median Max.
Organization-level variables
Fundraising expenses 0.27 1.43 0.00 0.01 41.23
Private contributions 8.04 68.88 0.00 0.57 2621.02
Total assets 6.89 74.24 0.00 0.91 2713.57
Office expenses 0.10 0.76 0.00 0.01 25.07
State-level variables
Food insecurity rate (%) 14.11 3.07 6.36 13.74 25.22
Avg. income > 500 % of poverty line 0.16 0.01 0.13 0.16 0.20
Personal income per capita (thousands) 0.05 0.01 0.03 0.05 0.08
Gini index 0.48 0.04 0.39 0.48 0.61
  1. The data includes 6583 observations of 1389 unique charities, observed between the years 2013 and 2018, inclusive. All financial variables measured in millions of constant 2015 dollars, unless otherwise specified.

6 Results

This section begins by presenting estimates of Equation (11). Next, it proceeds to decompose the private charitable response to food insecurity into two channels. The first, an “indirect” mechanism, reflects the extent to which this private charitable response is moderated by the charity’s fundraising response to hunger. The second, a “direct” mechanism, reveals how donors would respond to changes in food insecurity if the charity had held fundraising constant. Finally, these results are interpreted in the context of the model presented in Section 3. Comparing the theoretical objects derived in Section 3 to the estimates presented in Section 6 yields some insight into the relationship between donors’ generosity and local income inequality.

6.1 Food Insecurity Increases Charitable Fundraising

The results of this analysis begin in Table 2, which examines the mean effect of food insecurity on charities’ outcomes. The first three columns take fundraising as the outcome variable, whereas the specifications which take private contributions as the outcome variable are presented in the second three columns.[19] When food insecurity rises by one percentage point, fundraising rises by 0.9 %, on average. This estimate appears in Column 1 of Table 2. The estimates presented in Column 2 reveal that this relationship is robust to the inclusion of a control for state-level income inequality. Since fundraising increases in unmet need, Equation (10) implies that at least one of two conditions hold. It must be the case that either charitable fundraising is more effective when the charity’s recipients are less well off, or that fundraising is less unattractive to the charity when their clients are in greater need. Per Column 3, rising income inequality appears to amplify charities’ fundraising response to food insecurity. This indicates that the charity is indeed less hesitant to fundraise when society grows more unequal. While the estimates in Column 3 lack some precision, this may be due to the measurement error in the outcome variable, which will inflate the standard errors in a Poisson model.

Table 2:

Average effect of food insecurity on charity outcomes.

Fundraising Private contributions
(1) (2) (3) (4) (5) (6)
Food insecurity 0.009* 0.009* −0.032 0.002 0.002 −0.062*
(0.005) (0.005) (0.034) (0.007) (0.007) (0.037)
Gini 0.218 −0.964 −0.364 −2.278*
(0.424) (1.006) (0.748) (1.288)
Food insecurity × Gini 0.081 0.128*
(0.071) (0.075)
Log avg. inc. of non-poor 2.448* 2.485* 2.490* 2.939** 2.892** 2.906**
(1.368) (1.397) (1.397) (1.143) (1.200) (1.196)
Pseudo-R 2 0.663 0.663 0.663 0.948 0.948 0.948
No. obs 5029 5029 5029 6583 6583 6583
No. charities 1071 1071 1071 1389 1389 1389
  1. *p < 0.1; **p < 0.05; ***p < 0.01. Standard errors clustered at the organization level. All specifications include organization and year fixed effects. All financial variables measured in millions of constant 2015 dollars.

On average, private contributions appear invariant to the food insecurity rate. The point estimates presented in both Columns 4 and 5 of Table 2 are positive, but quite close to zero and imprecisely estimated. While it may appear disheartening to observe that charitable contributions do not rise in food insecurity, neither do they fall. This is an average response. Column 6 reveals that private donations fall in food insecurity, but that the loss in private charity attenuates as income inequality grows.

These results shed new light on the relationship between income inequality and donors’ generosity towards charities serving a low-income population. Previous work has explored similar questions in experimental contexts, with mixed results. In particular, both Sheremeta and Uler (2021) and Duquette and Hargaden (2021) conduct experiments in which subjects are asked how much they would like to give to some external charity, given a degree of inequality in subjects’ endowments. As such, both of these papers ask how inequality within the donor class affects willingness to give to a charity which likely serves a separate class of recipients. By contrast, the present work asks how inequality between the donor and recipient classes affect generosity towards a charity which serves a separate class of recipients. A more closely related paper is Payne and Smith (2015). The authors use data on individual-level charitable giving in Canada to examine the relationship between local income inequality and individuals’ gifts to charity. They find that changes in income inequality increase charitable giving, but cannot say which types of charities benefit. Since the present work measures the relationship between income inequality and giving to one particular type of redistributive charity, it is not necessarily inconsistent with Payne and Smith’s results. Even if their results can be attributed to increased giving to redistributive charities, or food banks in particular, it remains possible that the relationship between income inequality and charitable giving depends on the institutional context.

The estimates in Columns 3–6 of Table 2 capture the total derivative of private contributions to food insecurity. Equation (7) models this total derivative as the sum of two channels. Food insecurity may affect private contributions either directly or indirectly, where the indirect channel operates through charitable fundraising. Since fundraising rises in food insecurity, and fundraising must generate private contributions in order to be a productive activity, it follows that the indirect effect of food insecurity on private giving should be positive. For the total effect of food insecurity on private giving to be so close to zero, it may be the case that private giving would fall in food insecurity, were it not for the fundraising response. It follows that charities may spend more on fundraising in order to maintain their level of contributions, as unmet need rises. The next section verifies this prediction by decomposing the relationship between food insecurity and private giving into its two component channels.

6.2 Fundraising Rises to Maintain Charitable Contributions

Table 2 clearly demonstrates that charities actively fundraise more when their clients’ unmet needs rise. But what would happen to charitable contributions if these anti-hunger charities did not change their fundraising behavior? Per Equation (7), after partialling out the effect of fundraising on private contributions, private contributions may fall in food insecurity. Estimates of coefficients in the system formed by Equations (12) and (13), presented in Table 4, seek to verify this prediction.

The estimates for the first stage of this system (Equation (13)) are presented in Table 3. The inverse hyperbolic sine of office expenses is used as an instrument for charitable fundraising. This instrument exhibits a strong relationship to the endogenous regressor.[20] Several variations on the first-stage specification are presented in Table 3, some of which include the state-level Gini coefficient and its interaction with the food insecurity rate. However, comparison of these three specifications reveals that the first stage regression with the best fit to the data is found in Column 1. Therefore, this is the first-stage equation used to estimate Equation (12).

Table 3:

First stage specifications.

(1) (2) (3)
Food insecurity 0.008* 0.008* −0.021
(0.005) (0.004) (0.028)
Gini 0.236 −0.606
(0.459) (0.888)
Food insecurity × Gini 0.058
IHS(office expenses) 0.235*** 0.235*** 0.234***
(0.090) (0.091) (0.089)
Log avg. inc. of non-poor 1.922* 1.962* 1.969*
(1.075) (1.103) (1.105)
Log total assets 0.188*** 0.187*** 0.187***
(0.051) (0.051) (0.050)
Pseudo-R 2 0.663 0.663 0.663
No. obs 5025 5025 5025
No. charities 1071 1071 1071
χ 2 IHS(Office expenses) 6.793 6.706 6.886
p > χ 2 0.009 0.010 0.009
AIC 3260.769 3262.758 3264.717
BIC 3286.858 3295.369 3303.850
  1. * p < 0.1; ** p < 0.05; *** p < 0.01. Standard errors clustered at the organizational level. All specifications include organization and year fixed effects. All financial variables measured in millions of constant 2015 dollars.

The estimates of Equation (12) are presented in Table 4, which reports bias-corrected point estimates and confidence intervals.[21] These estimates reveal that, after controlling for fundraising expenses, charities which operate in states where food insecurity rises do not receive more private donations. In each column of Table 4, the point estimates of the direct effect of food insecurity on private contributions appear negative and very close to zero. While it is not possible to reject a one-sided null hypothesis that β H ≥ 0, the negative values predicted by the model and implied by the other estimates remain a possibility.

Table 4:

Direct and indirect effects of food insecurity on contributions.

(1) (2) (3) (4) (5) (6)
Log fundraising 0.149 0.149 0.099 0.122 0.116 0.094
[0.055, 0.459] [0.054, 0.464] [−0.001, 0.320] [−0.005, 0.430] [−0.007, 0.411] [−0.032, 0.349]
Food insecurity −0.002 −0.002 −0.002 −0.002 −0.032 −0.026
[−0.019, 0.008] [−0.020, 0.008] [−0.018, 0.009] [−0.019, 0.009] [−0.096, 0.038] [−0.092, 0.042]
Gini −0.436 −0.448 −1.324 −1.132
[−2.032, 0.582] [−1.999, 0.693] [−4.083, 0.849] [−4.190, 0.844]
Log fundraising × food insecurity 0.003 0.003
[−0.005, 0.008] [−0.005, 0.008]
Log fundraising × Gini 0.051 0.059 0.012
[−0.189, 0.484] [−0.179, 0.464] [−0.212, 0.441]
Food insecurity × Gini 0.060 0.048
[−0.089, 0.191] [−0.099, 0.181]
Log avg. Inc. of non-poor 2.720 2.670 2.640 2.667 2.685 2.596
[1.195, 5.153] [1.046, 5.023] [1.200, 5.155] [1.055, 5.045] [1.077, 5.019] [1.086, 5.163]
Log total assets 0.075 0.075 0.071 0.074 0.074 0.070
[−0.096, 0.175] [−0.097, 0.173] [−0.104, 0.170] [−0.097, 0.173] [−0.102, 0.175] [−0.110, 0.175]
ν ̂ −0.001 −0.001 −0.001 −0.001 −0.001 −0.001
[−0.020, −0.002] [−0.020, −0.002] [−0.020, −0.002] [−0.020, −0.002] [−0.020, −0.002] [−0.020, −0.002]
No. obs 4397 4397 4397 4397 4397 4397
No. charities 990 990 990 990 990 990
  1. * p < 0.1; ** p < 0.05; *** p < 0.01. Bias-corrected point estimates and 95 % confidence intervals (reported in brackets) are produced using 500 bootstrap replications. Bootstrap standard errors clustered at the organizational level. All specifications include organization and year fixed effects. All financial variables reported in millions of constant 2015 dollars. ν ̂ represents the standardized, generalized residual of the first-stage specification, which is included in estimation of the structural equation as part of the control function approach. For further details, see Wooldridge (2015).

In interpreting these results, it is important to recall that the fundraising variable reflects only financial aspects of fundraising. Non-financial aspects of fundraising – such as unobservable changes to fundraising effort, or the content of donor appeals – are not captured by this variable. If increases in local food insecurity affect both unmeasured and measured dimensions of fundraising in the same direction, then this will create a positive bias in the estimates of β H , the coefficient on food insecurity. As discussed in Section 4.2, this follows because food insecurity may affect private contributions through both a direct and an indirect channel. Measurement error in the fundraising variable, which mediates some of the effect of food insecurity on private contributions, will cause some portion of the “indirect” effect to be attributed to the “direct” channel instead. This implies that the coefficients on food insecurity in Table 4 are upper bounds for the true effect. This provides additional support for the interpretation that the true “direct effect” of food insecurity on private contributions is negative, and therefore consistent with the model presented in Section 3.

By comparing these estimates with the model in Section 3, it is possible to gain some insight into donors’ motivations. Recall that, per Equation (5), the marginal return to an additional dollar of fundraising expenses will be positive if two conditions hold.

The first condition states that the marginal warm glow donors derive from their charitable giving grows stronger as perceived inequality rises. The second condition requires that either charitable fundraising must increase the salience of recipients’ unmet need to donors, or donors must have some positive level of awareness of recipients’ unmet need to begin with.

As the estimates of the elasticity of charitable giving to fundraising shown in Table 4 are consistently positive, both of these conditions appear to hold. The crucial condition to verify is the first condition, which is mathematically equivalent to v 12 > 0. Note that if v 12 = 0, and the marginal warm glow is unrelated to perceived inequality, then it would follow that G F = 0 ; this is not the case. If, instead, v 12 < 0, and the marginal warm glow diminishes with perceived inequality, the observed estimates could only obtain if charitable fundraising were to reduce donors’ awareness of recipients’ unmet needs. While it is possible that donors ignore information provided by the charity, as in Figure 2, it is implausible to suggest that these communications actually make donors less knowledgeable of recipients’ circumstances. Therefore, while it is not possible to firmly conclude that salience increases in fundraising expenses, these estimates are consistent with the interpretation that donors derive greater warm-glow utility from giving in an environment of greater economic inequality.[22]

If this is the case, then why would donors’ gifts fall in food insecurity, if fundraising were held constant? In Equation (6), the model predicts that donors’ gifts will rise in recipients’ resources if:

(19) σ 2 y D ( R t c * G + F ) > σ R t c * y R

If an exogenous increase in food insecurity follows from a reduction in recipients’ incomes, it will be accompanied by an increase in inequality. Under the assumptions of the model, the salience of recipients’ unmet needs should fall as inequality rises; this is captured by the term on the left-hand side.[23] As recipients’ incomes fall, takeup of food assistance should rise; this is captured by the term on the right-hand side. Per Table 4, donors’ gifts fall in food insecurity, after holding fundraising constant. If these exogenous changes in food insecurity come from changes in recipients’ resources, and if donors’ incomes are held constant, then the model predicts that donors give less when recipients experience greater hardships. Under the model assumptions, this counterintuitive result must obtain because the loss in salience generated by rising income inequality, weighted by the volume of unmet need, exceeds the salience-weighted increase in takeup of the charitable good. The same changes which exacerbate recipients’ needs make it harder for donors to observe those needs, in the absence of an informational intervention from the charity.

7 Conclusions

When hunger rises, charities respond by increasing their fundraising. For each percentage point increase in the food insecurity rate, anti-hunger charities spend an additional 0.9 % on fundraising. This pattern is consistent with a model in which charities are more willing to fundraise when their recipients’ unmet needs rise. If charities were to hold fundraising constant in such a situation, donors to these organizations would not increase their generosity. On the contrary, estimates suggest that, after controlling for fundraising, a one-percentage-point increase in the food insecurity rate will reduce private contributions by at least 0.2 %. This upper bound is statistically indistinguishable from zero, suggesting that in the most optimistic case, donors are completely unresponsive to changes in the food insecurity rate.

At first glance, this reaction to increased hunger among recipients seems quite ungenerous. However, these findings are consistent with the model presented in this paper. This model, which draws on Duquette and Hargaden (2021), rationalizes a disconnect in the emerging literature on the relationship between inequality and charity. The estimates imply that the marginal utility donors derive from giving is actually enhanced by social inequality. Unfortunately, this same rise in inequality makes donors less aware of changes to recipients’ unmet need. Without this awareness, donors derive less of a warm glow from supporting charities which provide their clients with essential social services, and therefore face less of an incentive to donate to these groups when their contributions are needed most.

These results underscore the importance of communication in forging links between donors and recipients. This link is crucial: if donors are not aware of changes in recipients’ circumstances, then the private provision of charitable goods can become unreliable. This link is trivially present in previous models of voluntary public good provision, which assume that all donors to the charity also consume the goods and services this organization produces. In those models, exogenous reductions in the resources of non-contributors to the public good – which would bring about exogenous increases in unmet need – cannot affect the amount of voluntary public good provision. Only changes to contributors’ resources, or the composition of the set of donors, can do that. This paper demonstrates empirically that when non-contributors’ unmet need rises, contributors’ gifts are affected, in an adverse way. Through fundraising – a form of communication – charities can mitigate this tendency, and thereby maintain their level of service provision.

Unfortunately, this communication can be costly for charities. So long as fundraising expenses are penalized by the key performance indicators used to evaluate nonprofits, charities which spend money to advocate to donors on their clients’ behalf will appear less effective than organizations which do no such advocacy. As some causes generate more media attention than others, it may be the case that charities addressing some types of unmet need will find it necessary to spend money on advocacy more frequently than charities operating in other cause areas. Organizations which draw both donors and recipients from the same segment of the population are also less likely to face these challenges. When evaluating the performance of charitable providers of basic social services, overreliance on performance indicators which penalize fundraising may therefore cause donors to undervalue the benefit that these charities confer on their clients. Were it not for their additional fundraising, these organizations would have lost contributions, and each member of their growing clientele would receive a smaller slice of a shrinking pie.

Corresponding author: Stephanie Karol, University of Michigan, Ann Arbor, USA, E-mail:


I am grateful for advice from Ash Craig, Jim Hines, and Joel Slemrod, as well as for comments from Luke Shaefer, Nic Duquette, David Agrawal, Shanthi Ramnath, Anasuya Raj, Thomas Helgerman, several anonymous referees, and conference participants at the University of Michigan, the Michigan Tax Invitational, and the National Tax Association Annual Conference 2021.

Appendix A: Selection into Electronic Filing

Figure 6: 
Comparison of E-filers to paper filers, 2011–2019.
Figure 6:

Comparison of E-filers to paper filers, 2011–2019.

Appendix B: Income Redistributions May Reduce Voluntary Public Good Provision

Bergstrom, Blume, and Varian (1986) proves an assertion that changes in the income distribution, which do not affect the aggregate income received by donors, will not reduce total provision of the public good. This assertion is found in Theorem 4. However, this prediction relies on several important modeling assumptions, which may not be well-suited to a setting in which charitable donors and recipients are drawn from disjoint parts of the income distribution. As previously mentioned, these results rely on two key assumptions: first, that all donors to the public good derive some utility from its provision, and second, that each donor believes their own gift will strictly increase total public good provision. Without these assumptions, the prediction that donors’ contributions weakly increase in recipients’ unmet needs will not obtain.

To see this, note that Bergstrom, Blume, and Varian (1986) specifies each agent’s utility maximization problem as follows:

max x i , g i u ( x i , G )  s.t.  x i + g i = y i g i 0 G = i g i

Bergstrom, Blume, and Varian (1986) notes that donors who give g i > 0 belong to a contributor set, C, whereas donors who give g i = 0 are non-contributors. If donors in the contributor set derive no utility from G, then optimally they will allocate all income to private consumption, x i . This implies that no donor belongs to the contributor set. This extreme outcome can be relaxed by allowing donors to derive warm-glow utility from their own donation, re-specifying the utility function as u(x i , g i ). In this case, per Andreoni (1990), the donor’s optimal gift can be expressed as g i = f i (y i ) and the utility functions of agents in both the contributor and non-contributor sets will no longer be interdependent. In Theorem 4 of Bergstrom, Blume, and Varian (1986), the authors assert that any redistribution of income which leave the incomes of the contributor set unchanged will weakly increase public good provision. This assertion does not go through in the case of perfectly egoistic utility. To see this, note that:

g i = f i ( y i ) i C ϕ i ( g i ) = y i i C

where ϕ i (g i ) represents the inverse function of f i (y i ), and C denotes the contributor set. Suppose there are two contributors in the contributor set, contributing g 1 and g 2 respectively, such that total public good provision is given by G = g 1 + g 2. Does there exist some redistribution of their income such that G = g 1 + g 2 > G ?

First, note that:

G = g 1 + g 2 = f 1 y 1 + f 2 y 2 G = g 1 + g 2 = f 1 ( y 1 ) + f 2 ( y 2 )

and suppose that this redistribution of income among the contributor set can be represented by taking Δy 2 > 0 from contributor 2 and giving it to contributor 1. Then y 1 = y 1 + Δ y 2 and y 2 = y 2 Δ y 2 . Then:

G < G f 1 y 1 + f 2 y 2 < f 1 ( y 1 ) + f 2 ( y 2 ) f 1 ( y 1 + Δ y 2 ) + f 2 ( y 2 Δ y 2 ) < f 1 ( y 1 ) + f 2 ( y 2 ) f 1 ( y 1 + Δ y 2 ) f 1 ( y 1 ) Δ y 2 < f 2 ( y 2 ) f 2 ( y 2 Δ y 2 ) Δ y 2 lim Δ y 2 0 f 1 ( y 1 + Δ y 2 ) f 1 ( y 1 ) Δ y 2 < lim Δ y 2 0 f 2 ( y 2 ) f 2 ( y 2 Δ y 2 ) Δ y 2 f 1 ( y 1 ) < f 2 ( y 2 )

where the final inequality follows if both functions are differentiable. Then, if donors have purely egoistic preferences, a redistribution of income among this two-person contributor set can reduce total public good provision, if two conditions hold. First, both individuals’ contributions must be increasing in their own income. Second, the contributor who loses income due to redistribution must have a greater marginal propensity to give to charity than the contributor who benefits from the redistribution. This can be accomplished easily, by setting f 1(y 1) = 0.5 ln(y 1) and f 2(y 2) = ln(y 2). Then the results of Theorem 4 do not obtain for donors who derive no altruistic utility from the total level of public good provision.

If these same donors did derive altruistic utility from total G, but did not internalize the effect of their own gift on total public good provision ( G g i = 0 ) , then this altruistic term will simply fall out of the donor’s first-order condition if G is either additively or multiplicatively separable from the rest of the donor’s utility function. The remainder of the proof is unaffected, and G may fall following a redistribution of income, such that the total wealth of the contributor set remains unchanged.

This paper is concerned with one particular type of change in the income distribution, in which Δy 2 = 0, but where at least some agents who lie outside the contributor set experience y i < 0. In this case, are the assumptions which underlie Theorem 4 of Bergstrom, Blume, and Varian (1986) appropriate? If so, then voluntary public good provision should weakly increase; if not, then voluntary public good provision may fall.

The first assumption is reasonable under one of two cases. In the first case, all private agents in the economy actively consume the same public good, regardless of whether these agents are donors or not. In the second case, this public good may generate an atmospheric externality which affects all private agents. For some types of charity, it may be appropriate to think of all agents as consuming the same public good; for example, anyone may visit an art museum, regardless of whether or not that person is a donor. However, there exists a whole suite of charitably provided goods and services which are unlikely to be consumed by the donors who fund these services. As an example, a donor to a homeless shelter is unlikely to spend the night in that establishment.

But what if these goods and services can be thought of as generating an atmospheric externality? By conceptualizing the public good in this way, previous models may appear appropriate ways of characterizing voluntary public good provision. However, unless the second assumption holds, and donors believe their gifts strictly increase total public good provision, then the prediction of the model will not go through. This assumption is not trivial, and it is not always employed by other models which include atmospheric externalities. These other works, e.g. Sandmo (1975), typically assume the agent does not internalize the effect of their own behavior, or equivalently, that the agent believes they are small. This approach has been implemented in more recent models of public good provision, such as Duquette and Hargaden (2021), to which the model in the present work is closely related.

Appendix C: Results with Alternative Definitions of Income

This section presents results estimated using an alternative definition of income to the one employed in the main text. These tables use the log of personal income per capita at the state level. As this measure reflects income per capita which accrues to charitable recipients as well as donors, it is more closely correlated with food insecurity than the measure of income employed in the main text.[24] Consequently, the coefficients on the food insecurity variables displayed in Tables 5 7 are measured with less precision than those presented in Tables 2 4. However, the coefficients are qualitatively similar to those presented in the main text.

Table 5:

Average effect of food insecurity on charity outcomes.

Fundraising Private contributions
(1) (2) (3) (4) (5) (6)
Food insecurity 0.006 0.006 0.002 0.001 0.001 −0.040
(0.004) (0.004) (0.027) (0.006) (0.006) (0.043)
Gini 0.137 0.030 −0.535 −1.766
(0.476) (0.983) (0.740) (1.693)
Food insecurity × Gini 0.007 0.082
(0.054) (0.088)
Log personal income per capita 2.288** 2.295** 2.291** 1.527** 1.503* 1.461*
(1.064) (1.078) (1.086) (0.773) (0.791) (0.806)
Pseudo-R 2 0.663 0.663 0.663 0.948 0.948 0.948
No. obs 5029 5029 5029 6583 6583 6583
No. charities 1071 1071 1071 1389 1389 1389
  1. * p < 0.1; ** p < 0.05; *** p < 0.01. Standard errors clustered at the organization level. All specifications include organization and year fixed effects. All financial variables measured in millions of constant 2015 dollars.

Table 6:

First stage specifications.

(1) (2) (3)
Food insecurity 0.006 0.005 0.005
(0.004) (0.004) (0.028)
Gini 0.150 0.135
(0.479) (0.999)
Food insecurity × Gini 0.001
IHS(office expenses) 0.187*** 0.188*** 0.188***
(0.053) (0.054) (0.054)
Log personal income per capita 1.800** 1.807** 1.806**
(0.814) (0.824) (0.836)
Log total assets 0.177*** 0.176*** 0.176***
(0.043) (0.043) (0.043)
Pseudo-R 2 0.663 0.663 0.663
No. obs 5025 5025 5025
No. charities 1071 1071 1071
χ 2 IHS(office expenses) 12.373 12.243 12.273
p > χ 2 0.000 0.000 0.000
AIC 3259.523 3261.519 3263.519
BIC 3285.612 3294.130 3302.652
  1. * p < 0.1; ** p < 0.05; *** p < 0.01. Standard errors clustered at the organizational level. All specifications include organization and year fixed effects. All financial variables measured in millions of constant 2015 dollars.

Table 7:

Direct and indirect effects of food insecurity on contributions.

(1) (2) (3) (4) (5) (6)
Log fundraising 0.160 0.160 0.118 0.170 0.169 0.146
[0.079, 0.421] [0.078, 0.421] [0.005, 0.282] [0.010, 0.337] [0.015, 0.354] [0.003, 0.322]
Food insecurity −0.003 −0.003 −0.003 −0.003 −0.003 0.002
[-0.017, 0.009] [-0.017, 0.009] [-0.017, 0.010] [-0.016, 0.009] [-0.082, 0.077] [−0.069, 0.083]
Gini −0.594 −0.613 −0.626 −0.446
[−2.032, 0.738] [−2.005, 0.849] [−3.574, 2.575] [−3.441, 2.460]
Log fundraising × food insecurity 0.003 0.003
[−0.005, 0.009] [−0.005, 0.009]
Log fundraising × Gini −0.021 −0.021 −0.063
[−0.182, 0.482] [−0.197, 0.477] [−0.242, 0.433]
Food insecurity × Gini 0.001 −0.010
[−0.163, 0.153] [−0.165, 0.143]
Log personal income per capita 1.319 1.300 1.268 1.293 1.296 1.256
[−0.077, 2.668] [−0.103, 2.715] [−0.023, 2.749] [−0.109, 2.759] [−0.107, 2.785] [−0.180, 2.766]
Log total assets 0.068 0.069 0.064 0.068 0.068 0.064
[−0.045, 0.188] [−0.045, 0.191] [−0.047, 0.193] [−0.045, 0.190] [−0.040, 0.192] [−0.048, 0.194]
ν ̂ −0.002 −0.002 −0.002 −0.002 −0.002 −0.002
[−0.015, −0.001] [−0.015, −0.001] [−0.014, −0.001] [−0.017, −0.001] [−0.017, −0.001] [−0.016, −0.001]
No. obs 4397 4397 4397 4397 4397 4397
No. charities 990 990 990 990 990 990
  1. * p < 0.1; ** p < 0.05; *** p < 0.01. Bias-corrected point estimates and 95 % confidence intervals (reported in brackets) are produced using 500 bootstrap replications. Bootstrap standard errors clustered at the organizational level. All specifications include organization and year fixed effects. All financial variables reported in millions of constant 2015 dollars. ν ̂ represents the standardized, generalized residual of the first-stage specification, which is included in estimation of the structural equation as part of the control function approach. For further details, see Wooldridge (2015).


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Received: 2023-02-07
Accepted: 2023-05-03
Published Online: 2023-05-29

© 2023 the author(s), published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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