Nonprofit and Voluntary Sector Quarterly http://nvs.sagepub.com/ Should Donors Care About Overhead Costs? Do They Care? Woods Bowman Nonprofit and Voluntary Sector Quarterly 2006 35: 288 DOI: 10.1177/0899764006287219 The online version of this article can be found at: http://nvs.sagepub.com/content/35/2/288 Published by: http://www.sagepublications.com On behalf of: Association for Research on Nonprofit Organizations and Voluntary Action Additional services and information for Nonprofit and Voluntary Sector Quarterly can be found at: Email Alerts: http://nvs.sagepub.com/cgi/alerts Subscriptions: http://nvs.sagepub.com/subscriptions Reprints: http://www.sagepub.com/journalsReprints.nav Permissions: http://www.sagepub.com/journalsPermissions.nav Citations: http://nvs.sagepub.com/content/35/2/288.refs.html >> Version of Record - May 1, 2006 What is This? Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 288 Should Donors Care About Overhead Costs? Do They Care? Woods Bowman DePaul University This article reports on a theory-based experiment to determine whether there is an observable relationship between changes in charitable giving to an organization and changes in the proportion of revenue it spends on administration and fund-raising (“overhead ratio”). This article argues that overhead ratios are meaningless for comparing organizations, but changes in overhead ratios communicate useful, though incomplete, information to donors. Empirical studies have used organization-level data with mixed results. This research improves on past work by using donor-level information on federal employees in the Chicago area who donate through the Combined Federal Campaign with ready access to information on the overhead ratios of all participating charities. Donations are aggregated by charity and compared over time. Statistical tests give evidence of an inverse relationship between changes in overhead ratios and changes in giving that are robust with respect to model specification; however, collectively other factors are much more important. Keywords: overhead; administrative costs; fund-raising costs Between 1994 and 1998, U.S. charities allocated 87% of their spending to programs, with the balance going to general management and fund-raising (General Accounting Office [GAO], 2002, p. 8).1 This figure, which is based on self-reported information, may not be accurate because most charities, large and small, assign a low priority to measuring functional expenses and allocate costs among categories in a variety of ways (Wing & Hager, 2004). In any case, it is an average; some charities spend a trivial amount on programs. Two examples: Note: I am grateful to Ms. Jan Stinson, executive director of the Chicago Federal Executive Board, and Mr. Tony Padgett, then of the United Way of Chicago, for their assistance in providing data used in this study, also to Dolores Kalayta for programming assistance, and Rich Steinberg, Mark Hager, Wes Lindahl, Dan Tinkelman, and an anonymous referee for reading an earlier draft and making helpful observations. I alone am responsible for remaining errors of omission and commission. Nonprofit and Voluntary Sector Quarterly, vol. 35, no. 2, June 2006 288-310 DOI: 10.1177/0899764006287219 © 2006 Association for Research on Nonprofit Organizations and Voluntary Action 288 Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 289 Donors and Overhead Costs 289 The James Beard Foundation, a prestigious culinary charity named after the renowned chef whose bequest established it, had U.S. $4.7 million in revenue in 2003 but spent only $29,000 on scholarships, “one of the primary aspects of its mission.” In addition, thousands of dollars were unaccounted for. Donors, believing that most of their money financed scholarships, were shocked to learn that the foundation’s scholarship program was virtually nonexistent (Moskin, 2004). Commercial solicitors working in Illinois for Telemarketing Associates told prospects that a “significant amount of each dollar donated would be paid over to VietNow,” a charitable veterans assistance organization. In fact, the contract provided for paying only 15% to VietNow, which spent only 3% of its $1.1 million share on charitable programs (Madigan v. Telemarketing Associates, Inc., 2003).2 These extreme situations prompt a question: Why would anyone give to organizations with such high overhead ratios, that is, high general administration and fund-raising expenses divided by total revenue?3 Keating, Parsons, and Roberts (2003) proposed that such donors are either ill informed or so moved by an organization’s mission that they do not care about its overhead ratio. A very different possibility is that overhead ratios are meaningless (Steinberg, 1986b, 1994), and rational donors should not care about them. The first section of this article surveys current theory on the question of whether donors should care. The second section offers a new view of how overhead ratios are relevant to donors. The third section briefly surveys the literature on the question of whether donors, in fact, care about overhead ratios and discusses a hypothesis based on the theory presented in the previous section and two exploratory hypotheses. The fourth section discusses how the Combined Federal Campaign (CFC) works, explains how data were collected, and describes their limitations. The fifth section presents and discusses the results. The experiment reported here improves on past work by using multiperiod donor-level information on a group of federal employees who donate at work through the CFC, which informs them of the overhead ratios of all participating charities. A final section draws conclusions. SHOULD DONORS CARE? EXISTING THEORY Different organizational characteristics and circumstances imply different costs for one component of overhead—fund-raising (Hall 1996, pp. 35-36). The New York Attorney General speculates that fund-raising expense as a proportion of total expenses could differ among organizations because [1] Identifying new donors may be more time consuming and thus more expensive than contacting previous contributors. [2] An organization may conduct a telemarketing campaign simply to test-market new fundraising ideas without any certainty that its campaign will Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 290 290 Bowman prove efficient and productive. [3] An organization may also achieve goals other than raising funds—such as public education or recruitments of volunteers—at the same time that it is conducting a fundraising campaign. Those other benefits will not be reflected in the revenue received by the charity. [4] A newly created charity or one advocating new programs or new ideas may experience greater fundraising costs without any certainty that its campaign will prove cost effective. (Spitzer 2001, para. 11; numbers in brackets added) No one has written more often or more forcefully arguing the irrelevance of fund-raising ratios than Steinberg (1983, 1986a, 1986b, 1988-89, 1990, 1991, 1992, 1994). He pointed out that optimizing donated funds requires balancing costs and returns at the margin, whereas a fund-raising ratio (fund-raising expense divided by total expenses) is an average that provides donors with no useful information about marginal costs and returns. He (1994) illustrated with the following example of alternative solicitation budgets: The first budget of $10,000 will produce $50,000 in donations and provide a 500 percent ratio return ($40,000 actual net return). The second budget of $100,000 will produce $200,000, a 200 percent ratio return ($100,000 actual net return). If a charity wished to maximize the rate of return on its fund-raising investment, it would choose the first budget; if it cared about maximizing its resources for providing charitable services, it would choose the second. . . . Except by an incredible coincidence, the level of solicitation that best supports service provision is different from the level that maximizes the ratio of return or the level that minimizes the fundraising cost ratio. (p. 14) Steinberg (1986b) also argued that when the marginal contribution is very small relative to total contributions, 100% of a marginal dollar will be spent on programs, independently of the overhead ratio. Finally, as a technical matter, large gifts and bequests cause volatility in aggregate contributions and, hence, in overhead ratios. Coupled with a significant time lag between fund-raising activity and receipt of a large gift, researchers should expect difficulty in detecting a relationship between fund-raising expenses and giving (Lindahl, 1994). Practitioners and scholars also caution against judging efficiency from administrative expenses. The Maryland Association of Nonprofits asserted that larger nonprofits often benefit from an economy of scale on management and fundraising expenses and can direct a larger percentage of money raised to program. However, a smaller organization may deal with an issue we are passionate about, may be located in our neighborhood, and may have helped a family member or us.” (Maryland Standards for Excellence, n.d., para. 12) Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 291 Donors and Overhead Costs 291 Rooney, Hager, and Pollak (2003) gave evidence that (a) administrative costs are inversely related to organizational size; (b) as organizations grow older, their administrative expenses rise relative to total expenses; and (c) increasing dependence on government grants as a source of revenue similarly increases administrative expenses relative to total expenses. SHOULD DONORS CARE? ANOTHER VIEW The overhead ratio affects the price of buying a dollar of charitable output, that is, price of giving (Callen, 1994; Okten & Weisbrod, 2000; Posnett & Sandler, 1989; Tinkelman, 1999, 2004; Weisbrod & Dominguez, 1986). The price of giving is typically defined as price of giving = (1 – MTR)/(1 – OR), where MTR is the donor’s marginal tax rate and OR is the overhead ratio for the receiving charity, namely the sum of its fund-raising and general administrative expenses divided by its total revenue.4 However, comparing prices of anything—whether commodities or giving to charity—is frustrating and pointless. Debate over the overhead ratio recalls the classic question from the early days of economics: Why are useless diamonds so expensive while necessary water is so cheap? As with this example, there are many good reasons why the price of one commodity might differ from another (e.g., diamonds are scarce, water is plentiful); however, at the margin the quantity demanded of any normal product or service always falls when its price rises, and vice versa, other things being equal. It should be the same with charity. Assume rational prospective donors consider the balance (trade-off) between overhead ratio and absolute yield when they choose between two charities. In equilibrium, for idiosyncratic reasons, some donors give to one charity and some to the other. Now assume the two charities increase their fund-raising budgets by the same amount. Their overhead ratios will change relative to each other, except in the unlikely event that both raise money in exactly the same proportion as before. Donors who find the trade-off in the new equilibrium acceptable will continue to donate as before. Other donors—marginal donors who just barely accepted the trade-off between rate of return and absolute yield before the change—will switch to a less “expensive” charity with a similar mission. Researchers should be very cautious interpreting the results of crosssectional studies comparing donations to various charities with their overhead ratios. Such comparisons are like comparing the prices of different goods such as diamonds and water. Because administrative costs are inversely related to organizational size (Rooney et al., 2003), an observed inverse relationship between overhead ratios of various charities and their total donations may simply be the result of scale economies in producing charitable services. Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 292 292 Bowman On the other hand, a person who knows nothing of a charity’s finances except its overhead ratio can draw inferences relevant for her decision to donate by observing it increase or decrease relative to the overhead ratios of other charities. The argument depends on several economic assumptions. 1. Prospective donors are rational and risk averse. This is the standard model of an economic decision maker. 2. Donors, in the aggregate, have more information about any given charity than a single individual, and their knowledge can be inferred from their collective behavior. This assumption is borrowed from the rational expectations model of securities pricing. 3. Charities solicit donations from various prospect pools in descending order of their likely productivity. This is equivalent to assuming diminishing returns to fund-raising expenses. 4. For any given level of programming there exists a unique optimal level of administration. The assumption of an optimal level of administrative cost is novel and requires explanation. There are two views of administrative costs. One view is that they are wasteful—featuring excessive salaries, numerous perquisites, and unnecessary staff. Thirty-six percent of the public strongly agrees or mostly agrees with the statement that charities are wasteful.5 Another view holds that administration enhances organizational capacity, which is a good thing. Chang and Tuckman (1991) argued that robust administrative expenses enhance the viability of organizations by giving them a cushion in case of fiscal adversity. There is evidence that, on average, charities do not increase marginal spending on programs when resources increase; however, when resources decrease, charities cut programs (Roberts, Smith, & Taranto, 2005). This is consistent with charities operating with a suboptimal level of administrative capacity. These opposing views of administrative overhead imply the existence of an optimal level of spending on administration relative to programs between the extremes—a level that likely differs from organization to organization. Below the optimal level of spending on administration, increased spending causes increasing returns in organizational effectiveness, whereas above the optimal level, increased spending is accompanied by diminishing returns in organizational effectiveness. It is reasonable to suppose that changes in effectiveness would be observable. Whenever a charity increases spending on overhead (fund-raising plus administrative expenditures) relative to programming, there are three possibilities: 1. In Situation #1, donations fall, causing the charity’s overhead ratio to increase sharply. Its marginal fund-raising and/or administration are counterproductive. The fund-raising message it is communicating to Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 293 Donors and Overhead Costs 293 prospects dissuades existing donors from contributing. Alternatively, additional administration degrades organizational effectiveness, which shows up in less service or lower quality, and drives donors away. A rational donor should withhold support in this situation. 2. In Situation #2, donations grow proportionally or more slowly than overhead expenditures. The charity’s overhead ratio either remains constant or increases more slowly than in Situation #1. This is an ambiguous situation. Observationally, without additional information, Situation #2 is indistinguishable from Situation #1. A rational, risk-averse prospective donor without other current knowledge about a charity should play it safe and withhold support while seeking more information. 3. In Situation #3, donations grow more rapidly than expenditures. Now, the charity’s overhead ratio decreases. Because the assumption of diminishing returns excludes the possibility that the charity is reaching previously untapped high-productivity prospect pools, it is reasonable to conclude that the message the charity is communicating to new prospects is more powerful than past messages. Marginal donors may be receiving information our hypothetical rational donor missed. Alternatively, additional administrative expenditures are improving organizational effectiveness, which is noted by others who increase their support. A rational prospective donor should feel comfortable contributing too. In each situation, an increase in the overhead ratio causes a person who is rational and risk averse to withhold support, whereas a decrease encourages support. It is easy to recast these situations in terms of decreases in overhead spending with the same results. DO DONORS CARE? SOME HYPOTHESES When asked what proportion of spending by charities should go to programs, 78% of Americans say 70% or higher (Princeton Survey Research Associates, 2001, p. 5). This is consistent with earlier surveys by Roper and the Hudson Institute (Silvergleid, 2003). On the other hand, just because persons have an opinion on the proper proportion does not mean they care very much when it comes to their own giving. Only one third of Americans actually seek information on organizational finances (Princeton Survey Research Associates, 2001, p. 20). Administrative efficiency is not a major concern in Australia either (Berman & Davidson, 2003). Numerous studies have attempted to detect a relationship between actual giving and overhead ratios, with inconclusive results. Steinberg (1983, 1986a, 1986b), using a first-difference specification to control for omitted variables that are constant over time, reported no statistical association between fundraising overhead and donations. Callen (1994), Okten and Weisbrod (2000), Posnett and Sandler (1989), Tinkelman (1999, 2004), and Weisbrod and Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 294 294 Bowman Dominguez (1986) analyzed cross-sectional data using models with different log-linear specifications and found an inverse relationship between donations and the price of giving.6 Frumkin and Kim (2001), using organizationlevel, pooled cross-sectional and time series data, found no statistically significant negative correlations between overhead and contributions for nonprofit organizations; however, in five of six subcategories of nonprofit organizations, fund-raising expenditures exerted a significant positive effect.7 Results have been sensitive to model specification. Furthermore, all studies have used organization-level data from IRS Form 990, which implicitly assumes that donors know the overhead ratios of the charities to which they give, and the overhead ratios of competing charities. Given the results of the Princeton survey (Princeton Survey Research Associates, 2001), it strains credulity that a preponderance of donors would do the necessary research on a charity’s cost structure before writing a check, although the information for many charities is readily available online through GuideStar. Most persons probably trust their instincts because they know the organization, or have heard about its work. Nevertheless, several charity “watchdogs” have adopted standards for program spending.8 Silvergleid (2003) used multiple regression to analyze the relationship between lagged donations to a charity and its rating by the American Institute of Philanthropy. After controlling for size, year, subsector, and organizational characteristics, he found that neither rating nor a change in rating had a statistically significant effect on donations. He found some evidence that giving to regionally focused charities in Minnesota responded to whether they met the standards of the local Charities Review Council (CRC); however, his Minnesota sample consisted of only 125 charities, of which 86% received perfect evaluations across all 4 years in his study, so it is a suspect result. Based on theory presented in the second section, we have Hypothesis 1: Assuming donors have information concerning the overhead ratios of all alternative charities, the number of contributions to any given charity should decrease when its overhead ratio rises relative to the others, and increases when its overhead ratio falls, other things being equal. This hypothesis is couched in terms of first differences, similar to Steinberg’s tests (1983, 1986a, 1986b). As he noted, this method controls for omitted variables that remain roughly constant throughout 24-month intervals. This is a stringent test because he is one of the few researchers who found no relationship between overhead ratios and contributions. In preparation for this test, assume a zero marginal tax rate for individuals and convert each overhead ratio to a price of giving according to the conventional formula given above. A dummy variable indicating that a charity operates only within the local area is included as a control variable in tests of this hypothesis. Its coefficient Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 295 Donors and Overhead Costs 295 will capture the differential drift in favor of local charities. In other words, when the total number of dollars contributed increases, as it does in each of the years studied, a positive coefficient on the local dummy indicates local charities are capturing more of the additional dollars on average, and a negative coefficient indicates they are capturing fewer. Intuitively, large donors should be more careful and more responsive to changes in overhead ratios because they have more money at risk. Tinkelman (1998) found this to be true for corporate and foundation philanthropy. On the other hand, individuals may act differently from corporate entities. People who give a lot of money to a particular organization may be strong boosters, uninterested in overhead ratios. A new study, based on focus group research, by Public Agenda (Arumi, Wooden, & Johnson, 2005), concluded that “most small donors appear to base their giving on a gut-level interest in a cause and a faith in the people involved. Very few of those interviewed carefully researched their giving decisions” (p. 5). Donor interest in overhead ratios was not specifically plumbed; however, it would seem that small donors especially rely on trust and instinct rather than objective metrics. Without theory as a guide, it is an empirical question. The exploratory hypothesis is stated in the positive; the null hypothesis is that there is no relationship. Exploratory Hypothesis 2: Responsiveness to changes in overhead ratios increase with size of contribution. The same equations can be used to test this hypothesis as to test Hypothesis 1, but with the universe restricted to large donors. If they are more responsive, the absolute value of the coefficient on the price of giving in these regression equations will be larger than corresponding coefficients in the full sample. Unfortunately, with the CFC data, it is impossible to control for donor’s income and marginal tax rate, so small differences may be masked by the error term. Furthermore, the amount that nearly all donors give is very small. It is possible that at very low levels of giving people care little about organizational financial details such as overhead ratios. This experiment will use a threshold for large donors of $500 (the 97th percentile). Another question that these data might shed light on is whether local charities have any special advantage because of their proximity to donors. To participate in the CFC, local charities must document a substantial presence in the local campaign area, whereas national and/or international charities need have active programs in only 15 states, which may not include Illinois, the site of the current experiment. During the study period, the number of local charities participating in the Chicago CFC fluctuated between a high of 530 and a low of 383, whereas the number of national and/or international charities remained fairly close to 1,300. There are two possible proximity effects. On the one hand, “[d]onors may have alternative means of monitoring local organizations, as their service efforts may be more visible” (Tinkelman, 1999, Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 296 296 Bowman p. 140), which should make them more sensitive to changes in the price of giving of local charities. In this case, the coefficient on the price of giving when the sample is restricted to local charities should be larger in absolute value than the coefficient on price of giving when it is restricted to national and/or international charities. On the other hand, commitment to a local charity might be stronger a priori because the donor may know the founder or executive director, or because it is the only organization with a narrowly defined mission that the donor cares about deeply. In other words, a donor may be in a better position to monitor but may not have the inclination, and so would be less responsive to changes in the price of giving local charities. Again, theory provides no guidance, so this research resorts to the exploratory hypothesis that there is a positive effect. Exploratory Hypothesis 3: Donors are more responsive to changes in the overhead ratio of local charities. If this is true, the coefficient on the price of giving in a sample of local charities should be less in absolute value than the coefficient on the price of giving in a sample of national/international charities. The null hypothesis is no difference. Finally, by drawing on other data sources, it is possible to explore the question of whether other characteristics of a charity influence giving. Theory is meager; however, Weisbrod (1988) proposed that total donations are a metric for the output of public goods.9 People might feel more inclined to donate to organizations that produce public goods because they are more likely to experience some benefit. On the other hand, the free-rider effect might be stronger, which would imply that they would be more likely to withhold support. People might have a preference for large organizations because they feel safety in numbers, or they might prefer small organizations because their donation will have greater impact. Because theory does not favor any particular option, the exploratory hypothesis is that organizational characteristics exert a positive effect. This is difficult to test because major variables such as mission, total donations, and size change over long periods, but very little from one year to the next. The best the current research can do is to examine whether average changes in donations vary by organizational characteristic, holding changes in the price of giving constant. THE EXPERIMENT The CFC is a coordinated group of local workplace giving campaigns conducted in 376 federal administrative regions under the aegis of Local Federal Coordinating Committees (LFCCs), which bring together top local officials— military, civil service, and postal service leaders in each region (Bowman, 2003).10 These committees implement the law and regulations promulgated by the Office of Personnel Management (OPM). The Office of Personnel Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 297 Donors and Overhead Costs 297 Management determines which national and international charities are eligible to participate, whereas each LFCC determines eligibility of local charities. To participate, an organization must be a 501(c)(3), must formally apply, submit audited financial statements, and provide proof that not more than 80% of its funding comes from government sources. In theory, only charities with overhead that is less that 25% of revenue are eligible. During an annual campaign, each employee receives a Donor Guide (the Guide), which provides important information on every participating charity: its name, a campaign identification number, telephone number, Web address, federal Employer Identification Number, a 25-word description of its mission, its overhead ratio,11 and whether it is local, national, or international. Donors do not have the option of ignoring the Guide. Each donor must consult it to find the campaign identification number of the charity, which she must then write on a form authorizing a payroll deduction. The Guide flags charities whose overhead ratios exceed the 25% ceiling with an asterisk keyed to the following footnote: “This organization has administrative and fundraising expenses above 25%, and is taking the steps necessary to bring these expenses below the 25% level.” In the years studied, 1999 to 2001, between 6% and 7% of participating charities exceeded the nominal 25% ceiling, with the highest above 40%. At the other extreme, only 2% to 3% of charities reported suspiciously low overhead ratios of less than 1% in any year. Researchers who use organization-level data from IRS Form 990 are forced to assume that donors seek out the relevant information; the current study makes the far weaker assumption that donors use information they are given. The source of the overhead ratio information is the IRS 990 form, which was also used in previous research. Whatever the limitations of IRS data, it would be natural for federal employees to assume that the CFC has vetted the overhead ratios it publishes in the Donor Guide—especially because it makes a point of announcing that 25% is the maximum allowable overhead ratio for participating charities. On balance, it is unlikely donors in other experiments have actual knowledge of overhead ratios, whereas CFC donors are likely to see the published overhead ratios, and to regard them as reliable. The data for the current study come from the 1999, 2000, and 2001 Chicago Area CFC. Prior to 1999, the Chicago Area CFC covered a much smaller area and fewer employees, and after 2001 a new third-party administrator conducted the campaign. The years 1999 to 2001 covered by the current study are the only ones with the same campaign boundaries and same third-party administrator. A short time period is actually advantageous because it minimizes the effects of changes in popularity over time. In CFC parlance, donations are called designations and charities receiving donations are called designated charities. Employees may designate up to five charities through a single payroll deduction. They also have the option of making a lump-sum contribution by writing a personal check. Initially, information for the current study resided in two files: (a) a donor file and (b) a charity file, which were combined into a merged file for analysis. Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 298 298 Bowman DONOR FILE In 1999, there were 38,845 designations, 37,333 in the following year, and 35,824 in 2001. Because employees may make multiple designations, the number of designations in any year exceeds the number of donors by 10,000 to 15,000 (see Table 1). Each record contains (a) an encoded donor identification number to preserve anonymity while providing consistency over time, (b) year of designation, (c) a code indicating lump-sum or payroll deduction, (d) an account number for the designated charity, (e) the name of the designated charity, (f) a location code, and (g) the amount of the designation. Unfortunately, the file has no demographic data about donors. According to Table 1, in 1999 the average designation was $113, in 2000 it was $120, and in 2001, it was $129. There are major outliers, including several designations exceeding $1,000 with one as high as $4,000. Many designations cluster around $2. Because the smallest payroll deduction is one dollar per pay period, the smallest designations were either lump-sum payments or partialyear payments from newly hired or departing employees. Account numbers associated with each charity were used to consolidate the donor file, resulting in an almost unduplicated count of 2,095 designated charities during 3 years. It is “almost” unduplicated because 31 charities had multiple account numbers, such as the American Cancer Society, which had four; multiple accounts were consolidated for analysis. If a charity participated in the campaign but received no contributions (i.e., it was not designated) in a given year, it was absent from the donor file for that year but may have participated in subsequent campaigns. CHARITY FILE There is no information in the donor file about overhead ratios, so a second file was created on all participating charities by manually keying from the Donor Guides for 1999 to 2001 (a) the year, (b) the charity’s name, (c) its overhead ratio for that year, and (d) a code indicating whether it was local, national, or international. This file contains a duplicated count of 5,467 participating charities, identified by name and the year in which they took part. Using charity identification numbers as a means of keeping track of how often each charity participated, and manually adjusting for multiple account numbers, it appears that 1,259 charities participated in all three years, another 550 participated at least twice, and 590 participated only once. Comparing the number of designated charities with the number participating for each of the 3 years (Table 1) shows that the number of undesignated charities (those receiving no money) ranged from a low of 222 in 1999 to a high of 291 in 2000. Notice that the overhead ratios of designated charities are, on average, lower than those of participating charities generally. It is striking that many charities received no designations, and many others received only one. In the Year 2001, these groups together made up Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 299 Donors and Overhead Costs Table 1. 299 Summary Data for the Chicago Area Combined Federal Campaign (CACFC), 1999-2000 Employeesa Donorsa Designations Dollars, pledgeda Dollars, collected Dollars per designationc Localc Otherc Donors designating $500 or more Participating charities, totala Local Other Participating charities, overhead averagea Not designated Designated charities, total Locald Otherd With unmatched account numbers Overhead ratio, designated charity averagea,d Designations per charityc Dollars per designated charityc % Change 1999-2000 2000-2001 1999 2000 2001 61,407 23,493 38,845 $4,446,801 $4,370,715 $112.52 $118.10 $110.91 409 61,606 27,380 37,333 $4,621,240 $4,494,992 $120.40 $125.76 $117.98 447 60,177b 20,613 35,824 $4,735,780 $4,615,793 $128.85 $134.74 $127.85 462 0.3 16.5 –3.9 3.9 2.8 7.0 6.5 6.4 –2.3 –24.7 –4.0 2.5 2.7 7.0 7.1 8.4 1,812 499 1,313 14.1% 1,911 530 1,381 14.0% 1,745 383 1,362 13.9% 5.5 6.2 5.2 –0.7 –8.7 –27.7 –1.4 –0.7 222 1,590 291 1,620 224 1,521 31.1 1.9 –23.0 –6.1 419 1,045 126 437 1,092 91 317 1,121 83 4.3 4.5 –27.8 –27.5 2.7 –8.8 14.0% 13.6% 13.6% –2.9 — 24.4 $2,748 23.1 $2,774 23.6 $3,034 –5.3 0.9 2.2 9.4 Source: Unless otherwise noted, data are derived from donor records supplied to the author. a. Data for 1999 and 2000 from CACFC donors guides. b. Interpolated from 2000 and 2002 data; 2002 data from CACFC. c. Calculated from data in this table. d. Excludes unmatched account numbers. 29% of the participating charities. The most popular charity that year was the United Negro College Fund, which received 2,020 designations. Second was the American Red Cross with 1,344 designations. Notably, 847 designations were not for any particular charity, which were the third most-popular option. In all, $102,691 (2.2%) of collections were undesignated (CFC, 2002). Undesignated amounts are distributed to charities in proportion to the designations of all other employees. By not designating the charity to receive their money, donors are in effect allowing their coworkers to vote on how their gift should be allocated. However, because campaign costs are paid out of gross receipts before allocations are made to designated charities, gifts not designated to a particular charity merely help underwrite the campaign’s Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 300 300 Bowman cost, which is approximately 13% of collections (Chicago Area Combined Federal Campaign, 2001, p. 7). MERGED FILE Each record in the merged file contains the name of the participating charity, and in each of 3 years its overhead ratio, its number of designations, and the total amount designated.12 As many matches as possible were made electronically; however, hundreds of charities remained unmatched and the account numbers had to be supplied manually by comparing the unmatched names with charities that had account numbers. This laborious process resolved more than one half of the unknown accounts. Still, it was impossible to uniquely identify account numbers for 587 participating charities in the donor file, even after close inspection described above. An unknown, but large, number was undesignated and, hence, received no money. Gaps in the data cause the N in various statistical tests involving the merged file to be less than the number of designated charities in the charity file alone. Chicago is the third largest campaign in the continental U.S. outside of greater Washington, D.C., area.13 Table 1 gives summary data on the 1999, 2000, and 2001 Chicago Area CFC campaigns. Although the number of employees solicited declined between 1999 and 2001,14 the size of an average designation climbed steadily from $113 to $129, which pushed up total collections. Yearover-year differences between mean overhead ratios for participating charities and designated charities are not significant at the p = .05 level. The charity file contained no information on the National Taxonomy of Exempt Entities (NTEE) categories, so I drew a 25% sample and manually added to each record an NTEE code and data from GuideStar on total expenditures and donations. Table 2 shows the codes of those charities that make up at least 2% of designated charities. Advocacy and legal organizations, which are 11% of designated charities, have the highest average overhead ratios (15%). The most popular designated charities are either disease-related or human services, comprising 30% of designated charities, 36% of the designations, and 35% of the dollars contributed. There is no relationship between the overhead ratio and popularity, as measured by the number of designations. Ranking the NTEE categories on these variables gives a Spearman rank order coefficient that is statistically indistinguishable from zero (t = .32), which is consistent with the proposition that the level of the overhead ratio (as opposed to changes in the ratio) is not a critical factor in a typical decision to give. RESULTS AND DISCUSSION The first analysis (Tables 3a and 3b) counts the cases in each cell of a 3 x 3 matrix where the rows indicate whether the number of designations to a charity increased, stayed the same, or decreased, and the columns indicate Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 301 Donors and Overhead Costs 301 Table 2. Distribution of Charities, Designations, Dollars, and Overhead by National Taxonomy of Exempt Entities (NTEE) Category, 2001 (based on a 25% sample) % of Designated Charities % of Designationsa % of Dollars Mean Overhead in %a Diseases Human services Animal related International relief Advocacy Education Environment Medical research Youth development Legal related Health Religion Crisis intervention 16.3 14.5 8.4 6.8 6.8 5.0 4.7 4.7 4.2 3.9 3.7 3.2 2.6 19.5 17.1 8.4 3.2 1.8 2.5 2.3 9.4 3.1 2.0 3.5 1.5 0.7 19.0 16.1 7.1 4.7 1.7 2.3 2.0 8.5 3.4 1.9 3.6 1.8 0.7 14.7 12.1 13.4 9.1 15.3 9.9 13.4 12.4 12.3 15.4 12.6 11.1 11.5 Total 85.0 75.1 72.8 NTEE Purpose G P D Q R B C H O I E X F a. Spearman rank order correlation coefficient is .10, t = .32; insignificant at p = .10. whether the charity’s overhead rate went down, stayed the same, or went up. Rows and columns are arranged so that a negative relationship between the corresponding variables is displayed by a preponderance of cases arranged along the principal diagonal (northwest to southeast). Fortunately for hypothesis testing, there is considerable year-to-year variation in overhead ratios. The correlation between changes in overhead ratios for the years 1999 to 2000 and for 2000 to 2001 is –.341, which is significant at the p = .01 level (two-tailed test). In other words, if a charity’s overhead ratio went up in a given year, it was likely to go down the next year, which is an expected outcome. Otherwise, overhead ratios would tend to be bimodally distributed. If overhead rates were the only thing that mattered to donors, and theorybased Hypothesis 1 is true, cells on the principal diagonal would be the only ones populated; however, because the total number of designations declined in both periods, there will be a bias toward the top row of the tables. If the overall reduction in designations is concentrated in just a few charities, the bias will be slight. Although only 44% of the cases in Table 3a and 50% in Table 3b behave according to theory, the principal diagonals in both tables are strong enough to produce negative correlations significant at the p = .01 level (−.12 in Table 3a and −.22 in Table 3b). There appears to be a bias toward the top row in Table 3a, but not in Table 3b. Next in importance to the principal diagonals are the central column and row on each table. The central column shows all cases in which the overhead ratio was constant. Nevertheless, about 8% of the charities experienced changes in the number of designations without apparent stimulus. The center Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 302 302 Bowman Table 3a. Number of Designations Versus Overhead Ratio, 1999 to 2000 (cells contain count of cases) Change in Overhead Ratio Decrease in designations No change Increase in designations Total Increase None Decrease Total 298 77 150 525 57 9 34 100 257 100 218 575 612 186 402 1,200 Pearson χ2 = 20.0** Spearman correlation = −.115** **p = .01 (two-tailed). Table 3b. Number of Designations Versus Overhead Ratio, 2000 to 2001 (cells contain count of cases) Change in Overhead Ratio Decrease in designations No change Increase in designations Total Increase None Decrease Total 288 72 192 552 50 11 48 109 148 64 279 491 486 147 519 1,152 Pearson χ2 = 59.0** Spearman Correlation = −.224** **p = .01 (two-tailed). row displays counts of charities receiving a constant number of designations year-to-year, regardless of changes in the overhead ratio. Fifteen percent of charities in Table 3a and 12% of charities in Table 3b showed no change in the number of designations in response to either a decrease or increase in their overhead ratios. Clearly, overhead ratios are only one of many influences responsible for the changes in number of designations. This effect is brand loyalty, consumer ignorance, the result of offsetting changes in omitted variables, or a statistical anomaly. In the first pair of regressions (Table 4a), the dependent variable is the first difference in the number of donors to a charity, and the independent variable is the first difference in the price of giving. It is included in the analysis to test robustness with respect to the logarithmic transformation used in the second pair of equations. In the second pair of regressions (Table 4b), the dependent variable is the first difference of the natural logarithm of the number of donors to a charity, and the independent variable is the first difference in the natural Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 303 Donors and Overhead Costs 303 Table 4a. Ordinary Least Squares (OLS) Linear First Difference Model: Change in Number of Designations 1999-2000 SE Coefficient Constant Change in price of giving Proximity (local = 1) Adjusted R2 F statistic Total df 2000-2001 –0.14 –1.54 –0.09 .020 11.46 1,021 .0** .3** .1 Coefficient SE 0.11 –2.08 –0.33 .059 37.12** 1,151 .0** .3** .1** **p = .01 level (two-tailed). Table 4b. Ordinary Least Squares (OLS) Log-Linear First Difference Model: Change in Natural Log of Number (LN) of Designations 1999-2000 Constant Change in LN price of giving Proximity (local = 1) Adjusted R2 F statistic Total df 2000-2001 Coefficient SE −0.10 −1.58 −0.04 .030 17.01** 1,021 .0** .3** .0 Coefficient SE 0.09 −1.86 −0.17 .049 30.53** 1,151 .0** .3** .0** **p = .01 level (two-tailed.) logarithm of the price of giving. Both specifications include a dummy variable, which equals 1 for local charities. Double log is the preferred specification because data span two orders of magnitude, and cumulative distributions of gift size and number of designations per charity are normally distributed between the 15th and 85th percentiles. At the high end, there are more donors than a normal distribution implies, and fewer at the low end. Sparseness at the low end is probably the result of a minimum size payroll deduction ($1 dollar per pay period), and partial year contributions by new or departing employees. The results are robust with respect to specification: In all regression equations the price of giving coefficient is negative, larger than 1 in absolute value, and significant at the p = .01 level, which supports the theory as expressed by Hypothesis 1. The adjusted R2 is quite small—less than .05—although the F statistic is significant at the p = .01 level (two-tailed). These results may mean that donors do care about changes in the overhead ratio; however, other Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 304 304 Bowman factors that influence their giving decisions are much more important in the aggregate. Signs on the dummy variable for local charities, used as a control variable, tend to be negative; however, only one half are significant. Tables 5a and 5b show estimates of the demand for charitable giving, as measured by the total number of dollars designated to a charity, in each of the two time periods. First differences in total dollars designated and the price of giving are in Table 5a, whereas in Table 5b the first differences are between the natural logs of total dollars designated and the price of giving. Again, the preferred specification involves logarithmically transformed variables. In all four equations, the price of giving coefficient is negative and significant at the p = .01 level, offering further support for the theory as expressed by Hypothesis 1. The price of giving coefficient in the transformed equations is the elasticity of demand for charitable giving. In all cases, demand is highly elastic, meaning that a change of 1% in the price of giving causes total designated dollars to change in the opposite direction by more than 2%. This effect is caused, in part, by incumbent donors changing the level of their giving, but also by marginal donors switching to “lower priced” providers of similar charitable services. Signs on the dummy control variable for local charities are negative only in the double log specification, one of which is significant.15 Because the corresponding price of giving coefficients on Tables 4b and 5b are dimensionless, they can be compared without having to adjust for different scales. The average designation changed 70% between the years 1999 and 2000 in response to change in the price of giving.16 This is a large effect. Because donors who give above-average amounts would have the most impact, an effect of this size hints that above-average donors might be more sensitive to changes in the price of giving than other donors, per Exploratory Hypothesis 2. Unfortunately, this is not a direct test of Exploratory Hypothesis 2 and must be regarded as inconclusive. A direct test of Exploratory Hypothesis 2 uses a truncated donor file restricted to “large donors”—that is, donors in the 97th percentile who gave $500 or more to any single charity, namely about $40 per monthly paycheck or $20 per biweekly paycheck. There were 409 large donors in 1999, 447 in 2000, and 462 in 2001. The maximum number of large donors that any charity claimed was 89 in 1999, 64 in 2000, and 82 in 2001. The average number of large donors per charity was between two and three for all years (excluding those with 0) with standard deviations near 5. Again, the dependent variable was the difference in the natural log of number of designations, and the independent variable was the difference in the natural log of the price of giving. The price of giving coefficient was –.69 for the period 1999 to 2000 and insignificant (t = 1.10), and .04 for the period 2000 to 2001 and insignificant (t = .05). Adjusted R2 were negative in both cases. Perhaps large donors have strong personal reasons and are unaffected by information about overhead ratios, or perhaps their incomes are sufficiently high that $500 is of little consequence, or maybe the sample size is too small and the error term is too large. In any case, a direct test does not support Exploratory Hypothesis 2, so the regression results are not tabulated. Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 305 Donors and Overhead Costs 305 Table 5a. Ordinary Least Squares (OLS) Linear First Difference Model: Change in Dollars Designated 1999-2000 Constant Change in price of giving Proximity (local = 1) Adjusted R2 F statistic Total df 2000-2001 Coefficient SE Coefficient 36.85 −2,717.0 6.25 .007 4.70 1,021 85.8 888.3** 183.0 453.35 −2,565.0 356.17 .003 2.53 1,151 SE 137.7** 1,347.3* 289.7 *p = .05 level (two-tailed). **p = .01 level (two-tailed). Table 5b. Ordinary Least Squares (OLS) Log-Linear First Difference Model: Change in Log of Dollars Designated 1999-2000 Constant Change in natural log of number (LN) price of giving Proximity (local = 1) Adjusted R2 F statistic Total df 2000-2001 Coefficient SE Coefficient SE −0.042 .034 0.210 .033** −2.241 −0.013 .022 12.43 1,017 .045** .073 −2.544 −0.227 .037 23.13 1,146 .420** .071** **p = .01 level (two-tailed). To test Exploratory Hypothesis 3, the sample is split into local and national and/or international and estimated the price of giving coefficient in a double-log, first-difference specification (without the local dummy, of course). In 1999 to 2000, the price of giving coefficient was –2.427 (SE = .687) for local charities and –2.179 (SE = .549) for national and/or international charities. Given their standard errors, there is no significant difference. In 2000 to 2001, the price of giving coefficient was –1.650 (SE = .799) for local charities and –2.734 (SE = .486) for national and/or international charities. This difference is not significant either. These results do not support Exploratory Hypothesis 3, and are therefore not tabulated. To see if other organizational factors might cause shifts in demand for giving, I used a 25% sample with additional data on NTEE category, total donations, and total expenses extracted from GuideStar and added manually to estimate a demand equation with the first difference in the natural logs of the dollars designated as the dependent variable and the first difference of Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 306 306 Bowman the natural logs of price of giving as the dependent variable with control variables for size of organization and donations as a percentage of total revenue. Total expenditures and donations were entered as a series of dummy variables indicating the quartile to which a charity belonged (omitting the lowest quartile) to detect possible nonlinearities. When parameter estimates were calculated stepwise, only the price of giving coefficient entered in the period 1999 to 2000 and the price of giving coefficient and local dummy entered in 2000 to 2001. The adjusted R2 did not materially improve. Consequently, the results are not tabulated. CONCLUSIONS Donors should care about changes in overhead ratios. A change in a charity’s overhead ratio correlates positively with a change in the price of giving, which, like any price, contains useful information for consumers. And, yes, donors do care about changes in overhead ratios, but only as one of many things, and collectively other factors are much more important. Adjusted R2 are very low, which suggests that the importance of overhead ratios in the larger context of public policy is easily exaggerated. There is emphatically no objective basis for saying that a particular ratio is too high. Although, the Beard Foundation, VietNow, and their ilk raise disturbing questions, the important issue in these and all such cases is whether fund-raising materials and solicitors misled donors. Deception in any form is intolerable. One hopes that courts will take a hard look at representations made by solicitors (see endnote 2). This experiment reveals that the demand for charitable giving (measured by total dollars designated) changes by a greater percentage than the price of giving changes, and in the opposite direction. The ratio of these two quantities (the price elasticity of giving) is stable over time and robust with respect to model specification. Evidence on whether large donors are more sensitive to changes in the price of giving than other donors is inconclusive at best. Evidence on the sensitivity of donors to changes in the price of giving among local charities is mixed. The negligible adjusted R2 demand attention. Some unexplained variance is because of the assumption that marginal tax rates were constant for all donors; however, this cannot be the whole story. In market transactions, price is a major consideration for consumers, but apparently not so in this experiment. This could be because of the fact that most donors are contributing small amounts and may not care about price of giving (i.e., overhead ratios). Although this database contained some large donors, the average payroll deduction was small. Further experiments with a greater range of variation in gift size are needed to determine if donors are less sensitive to information about charities when they have very little money at stake. This experiment uncovered two tantalizing observations that invite further inquiry. First, for many charities, the number of designations did not change when the overhead Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 307 Donors and Overhead Costs 307 ratio changed. This could be brand loyalty, consumer ignorance, the result of offsetting effects of omitted variables, or just a statistical anomaly. Second, the popularity of the “not-designated” option hints that people give just to be giving, not necessarily to support a particular mission. Perhaps, as Andreoni’s (1990) “warm glow” theory suggests, the act of giving itself increases a donor’s utility, independent of the use to which his or her gift is put. Alternatively, social pressure may be responsible.17 More research is clearly needed. Organization characteristics, like size and reliance on donations, appear to be largely irrelevant. However, what is relevant? Do donors use information on overhead ratios they are given? If not, why? Did these donors have prior association with the charities they designated to receive their gifts?18 If so, what kind? Were they influenced by marketing campaigns that targeted federal employees during the CFC campaign? If so, what techniques were particularly successful? Why? More research is needed on these questions. We have probably gone as far as possible with data in the public domain. Further progress in our understanding of these issues requires custom tailored experiments that probe how donors form their perceptions of charities, what information is most relevant to giving decisions, under what circumstances donors explicitly seek information, where they search, and how far in advance of making a gift they begin their search. Notes 1. GAO is now termed the Government Accountability Office. 2. When state courts dismissed the case on First Amendment grounds, Attorney General Madigan appealed to the U.S. Supreme Court, which remanded the case to the trial court for a hearing on its merits, ruling that the First Amendment does not protect willful misrepresentations of fact. The outcome hinges on the actual representations that Telemarketing Associates made to prospective donors and its intent. In earlier charitable solicitation cases, the U.S. Supreme Court decided in Schaumberg v. Citizens for a Better Environment (1980), and in Secretary of State of Md. v. Joseph H. Munsen Co., (1984) that capping fund-raising costs violated the First Amendment. It also held in Riley v. National Federation of the Blind of N.C., Inc. (1988) that requiring solicitors to announce the percentage of donations going to fund programs also violated the First Amendment. 3. There are various ways to calculate an overhead ratio. Using expenses in the denominator would produce a ratio that is less volatile because large gifts and bequests occasionally boost revenues. However, the available dataset dictated the choice to use revenue here. 4. To see how the formula works, imagine overhead expenses are 0. Then all gifts are spent entirely on programs, and the price of buying $1 of charitable output is $1. As overhead expenses become an increasingly large fraction of total expenses, gifts are increasingly spent on overhead and less on programs, causing the price of giving to approach infinity. Weisbrod and Dominguez (1986) divided the sum of administrative and fund-raising cost by donations, whereas the CFC divides by total revenue. 5. Calculated by author from the Independent Sector’s 1996 Giving and Volunteering survey data. 6. In this article, the marginal tax rate for each donor is unavailable. I assume it is constant for all donors in the Chicago CFC, and by inference that all variation in price of giving is due to variation in overhead ratios. 7. More precisely, they used a logarithmic transform of total contributions as the dependent variable in a generalized least squares model, and for independent variables they used lagged Downloaded from nvs.sagepub.com at Stanford University Libraries on November 19, 2014 NVSQ287219.qxd 4/7/2006 12:58 PM Page 308 308 Bowman logarithmic transform of fund-raising expenditures and the lagged ratio of administrative costs to total costs. 8. Charity “watchdogs” (e.g., American Institute of Philanthropy, Wise Giving Alliance, Charity Navigator, Maryland Association of Nonprofits) do not agree on a method of calculation. See Bowman and Bies (2005, p. 43). 9. A pure public good is one that is nonrival and nonexcludable. Nonrival means that more than one person can consume the good without interfering with anyone else’s enjoyment of the same good at the same time. Nonexcludabilty means that a person cannot be excluded from consuming the good if they do not pay. 10. In 28 large cities that have Federal Executive Boards, it wears the mantle of the Local Federal Coordinating Committees (LFCC). Chicago is one of these cities. 11. The organizations themselves develop this information subject to LFCC verification using IRS 990 informational returns. Although eligible charities are required to submit audits, these documents are not used in verification. 12. Account codes in the donor file were not the same as charities’ identification numbers published in the Donor Guide, which complicated the process of merging them. An attempt was made to merge based on charities’ names; however, it was not effective because of multiple account codes (see Donor File above), and minor differences (e.g., and in one file, & in another). Furthermore, the donor file contained only the first 40 characters of a name, and different charities might have the same first 40 characters; this was a frequent source of confusion between national/international charities and their local chapters. 13. The greater Washington, D.C., area consists of the Capital Area Campaign plus campaigns in eastern Virginia and central Maryland. Other campaigns larger than Chicago’s are San Diego and San Antonio. 14. The number given for 2001 in the Detail Location: Combined Federal Campaign (CFC) Results (Combined Federal Campaign, 2002) is incorrect according to Jan Stinson, executive director of the Chicago Area Federal Executive Director, who recommended averaging the 2 years adjacent years (personal communication with author, February 24, 2006). 15. Experiments measuring demand should hold the conditions of supply constant; however, if we are willing to assume that the Chicago CFC contributes only a small portion of the income of all participating charities, then receiving charities can expand their output at nearly zero marginal cost, which is equivalent to holding conditions of supply constant. Under these conditions, the estimated price of giving parameter measures only demand effects, and is not distorted with supply effects. 16. Let total dollars designated to a charity be D = NG, where N is the number of designations and G is the average size of designation. If we let ∆ indicate a change in a variable, then ∆D/D = ∆N/N + ∆G/G. Dividing this equation through by ∆P/P, gives the price of giving coefficient on Table 5b ([∆D/D]/[∆P/P]) on the left and, on the right, the price of giving coefficient from Table 4a ([∆N/N]/[∆P/P]) plus (∆G/G)/(∆P/P). Thus, (∆G/G)/(∆P/P) = 1.54 – 2.24 = –.70. The percentage change is found by multiplying the decimal fractions by 100. 17. “Warm glow” is simply a name Andreoni (1990) gave to a mental state to explain why donors might gain utility without reference to the impact their gifts are likely to have on the beneficiaries. In mathematical terms, social pressure serves the same function as warm glow. 18. Brown and Lankford (1992) showed that donations of money and time are complementary, which implies that, other things being equal, volunteers are more likely to give than nonvolunteers. References Andreoni, J. (1990). Impure altruism and donations to pubic goods: A warm-glow theory of giving. 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