Managing Members,Donors,and Member-Donors for Effective Nonprofit Fundraising

Abstract

Nonprofit organizations (NPOs) play a central role in many economies in the form of private entities serving a public purpose. Strengthening the fundraising capabilities of NPOs can have a large impact on their survival and effective functioning. NPOs typically elicit financial contributions through multiple forms of giving, such as donation and membership. These options enable individuals to express their altruism by giving in one or multiple forms. The authors develop a utility-based multiple discrete-continuous model that provides insights into potentially large differences in individuals’ giving behaviors. Through Bayesian Gaussian processes, the model also incorporates changes in givers’ preferences for forms of giving. The authors apply their model to five years of individual giving data. They find that the effects of lifetime, recency, seasonality, and appeals on donation and membership options change nonmonotonically over time and in distinctive ways. The authors demonstrate that the model estimates help predict who will give in more than one form in the future as well as build appeal targeting strategies. The model also shows that fundraising attempts should emphasize participation rather than amount, and that long-lapsed members are still worth pursuing for renewal, whereas long-lapsed donors are less productive for repeat giving.

Keywords

Bayesian estimation charitable giving choice models fundraising capabilities Gaussian process nonprofit

In 2019, U.S. households donated $309.7 billion, nearly 2% of their annual income, to nonprofit organizations (NPOs) (Giving USA 2020). Yet many NPOs are under considerable financial pressure to close the gap between their resources and the social missions they serve. In the midst of the COVID-19 pandemic of 2020, charitable giving in the United States increased during the first half of the year relative to the previous year; however, fears remained that the sluggish economy would depress long-term giving (Stiffman 2020). A major challenge that many NPOs face is the volatility of individual giving: the literature reports that approximately half of newly acquired donors churn after they give once (Khodakarami, Petersen, and Venkatesan 2015; Sargeant and Woodliffe 2007). In response to such instability, NPOs strive to increase repeat giving by individuals as well as to identify and retain givers who are more committed. The purpose of this article is to help NPOs to succeed in their endeavor by developing a model that provides insights into givers’ preferences, differences between givers, and the dynamics of giving behavior.

How does our research contribute to better marketing for a better world? In this article, we view nonprofits broadly as belonging to the “third sector” of the political economy, in addition to the for-profit business and government sectors, which are well-defined (Kallman and Clark 2016). The nonprofit sector includes a broad array of private organizations serving public purposes. While a literature has debated alternative theories about the economic role of NPOs (Malani, Philipson, and David 2003), there is little doubt that, in practice, NPOs play a substantial role in sectors such as religion, health care, education, arts and culture, and the environment.

Individual charitable giving is a key source of funding for many NPOs, especially for small and midsize organizations in the United States (National Council of Nonprofits 2019). Not surprisingly, therefore, the average ratio of fundraising cost to donation is quite high, at about 12% (Andreoni and Payne 2011; List 2011). To improve the effectiveness and efficiency of fundraising from individuals, our research develops and applies marketing science tools, thereby strengthening the ability of NPOs to fulfill their social missions.

We propose a framework of individual giving behavior that incorporates three important factors that have previously remained understudied in the literature. First, NPOs’ revenue depends on both the decision to give (i.e., choice to participate) and how much to give (i.e., the dollar amount).¹ Previous studies often do not differentiate between givers’ participation and amount decisions (Dickert, Sagara, and Slovic 2011; Fajardo, Townsend, and Bolander 2018). Distinguishing between the two decisions enables the NPO to learn whether its marketing efforts should focus on encouraging more participation, larger donation amounts, or both. This allows the NPO to set priorities to maximize return on its efforts.

Second, many NPOs structure fundraising programs for individuals around two major forms of giving: donation and membership. For instance, the list of the 100 largest nonprofits in the United States based on 2019 revenues includes eight organizations that focus on the environment and animals (Hrywna 2019), which is the domain of operation of the focal NPO in our empirical application. Of those eight, five nonprofits allow individuals to give through both donation and membership programs. Donors support an NPO’s mission financially without any expectation of reciprocal tangible benefits. Instead, donors receive a “warm glow” that makes their own financial contributions to the NPO more valuable to them than the contributions of others (Andreoni 1989). Furthermore, the U.S. government incentivizes donations by providing tax deductions (Auten, Sieg, and Clotfelter 2002). Membership, in contrast, confers a defined set of membership benefits that expand with the level of contribution in addition to the warm glow and tax deductions. Membership programs can thus be viewed as “commercial” activities in the sense that NPOs exchange mission-related goods or services for membership fees (Weisbrod 1998). For instance, members of an art museum may receive benefits such as invitations to exclusive tours.

Multiple forms of giving allow individuals to choose to be pure donors, pure members, or member-donors. Pure donors and pure members give exclusively through donation programs and membership programs, respectively, whereas member-donors support an NPO through both donation and membership programs. These choices are expressions of individual motivations. The literature in charitable giving has categorized these motivations into two kinds: intrinsic and extrinsic (e.g., Bénabou and Tirole 2006; Ariely, Bracha, and Meier 2009). Intrinsic motivation is the value of giving per se, represented by preference for helping others, while extrinsic motivation is the desire to receive tangible benefits associated with giving. Donors’ choice of donation as the form of giving reveals their greater intrinsic motivation since there is no tangible benefit received in return. By contrast, members’ choice of membership reveals greater extrinsic motivation (than donors) because members choose to receive membership benefits. Membership is also intended to induce a sense of belonging and identity that increases the likelihood of repeat giving, and thereby reduces the volatility of NPOs’ cash inflows (Bhattacharya, Rao, and Glynn 1995; Bhattacharya 1998). Although multiple forms of giving allow greater choices for individuals, they involve additional administrative costs for the NPO. Therefore, from the NPOs’ perspective, managing two streams of giving makes sense when the incremental revenue from multiple forms of giving is expected to outweigh the incremental costs.

Third, recognizing that repeat giving is highly desired by NPOs, we focus on the dynamics of individual giving behavior. By contrast, extant research has primarily focused on single observations of individual giving (i.e., cross-sectional data). We expect that previous giving decisions are likely to influence subsequent decisions to give (Leliveld and Risselada 2017; White, Habib, and Dahl 2020). This is evident with membership that remains valid for a specific duration; an individual having paid an annual membership fee may not consider giving until the membership is about to expire, 12 months later. Donations, unlike membership, have no such associated term, making it less obvious how the probability of repeat giving should change over time. We conjecture that an individual may not actively consider giving for some time after donating due to a “licensing effect” (Khan and Dhar 2006). This effect postulates that the choice probability of a more hedonic option increases after a prior, virtuous, license-generating decision. Khan and Dhar (2006) found that subjects in the license condition exhibited less altruism and reduced intention to donate. In our context, this implies that recent donors may feel justified not giving for some time, after which the desire to donate may reemerge and grow. Conversely, if an individual has not donated or renewed membership for a long time, this might be a sign of churn. Therefore, it is important for NPOs to understand how to think about and act on individuals who vary in the time since their last giving occasion.

In addition to repeat giving, member-donors’ decision to give in the two forms typically evolves over time with some individuals who start out as pure members or pure donors subsequently adding a second form of giving. We conceptualize this to be the result of two phenomena. First, the individual’s intrinsic desire to give may change as the relationship with the NPO deepens. Second, the individual experiences diminishing marginal utility (Andreoni 1990; DellaVigna, List, and Malmendier 2012; Morgan 2000) from giving larger amounts in a single form. For instance, some members may not value the additional benefits conferred by a higher tier of membership and instead add a donation to their giving portfolio. Similarly, some donors seek a sense of belonging and tangible benefits in addition to the warm glow from larger donations and thus add membership to their giving portfolio. Importantly, the availability of multiple forms of giving allows individuals to express their idiosyncratic giving preferences to start their relationship with the NPO and to modify it over time.

To model giving behavior, we propose a utility-based multiple discrete-continuous model with Gaussian process (GP) priors. We apply the model to the five-year giving behavior of a cohort of 2,171 individuals who began their relationship with an NPO in 2011 to investigate three research questions: (1) What factors influence the choices of multiple forms of giving and amount, and how do their effects change over time?, (2) How can our framework be used to increase participation rates and contribution amounts?, and (3) Can our model identify contributors who are more committed to the NPO?

Our empirical analyses yield several insights that we summarize briefly here. First, the propensity to donate increases over the lifetime of the relationship, whereas we do not see such a positive trend for membership. Instead, propensity to participate in membership remains cyclical, peaking every 12 months, even as the lifetime grows. This finding is consistent with membership being more reciprocal in nature, in the sense of being more extrinsically motivated.

Second, we find evidence that the propensity to give again remains low for seven months following a donation, providing support for a licensing effect. The propensity peaks at 11 and 24 months after giving, making those opportune times to ask for a new donation. Thereafter, however, there is no remaining positive predisposition, implying that these donors are likely to be similar to new prospects. By contrast, lapsed members remain positively predisposed for a duration longer than 24 months and may be worth continuing to pursue. Therefore, our research supports previous findings that providing tangible benefits increases giving, possibly by encouraging feelings of reciprocity or gratitude.

Third, the effects of donation appeals for our focal NPO were inconsistent, indicating room for improvement through targeting. However, membership appeals were effective at encouraging renewals, perhaps because they were naturally targeted to reach individuals just before their membership was about to expire.

Fourth, not surprisingly, we find substantial heterogeneity in the giving preferences of individuals; the heterogeneity is partially explained by observable characteristics such as demographics, but a significant part is not.

Finally, we find that our models can help the NPO predictively identify member-donors, who are more committed contributors in terms of both amount and frequency of giving, and also develop targeting strategies for more effective appeal campaigns. In the “Discussion and Conclusions” section, we use these findings to present a list of recommendations for NPOs.

Related Literature

The literature on charitable giving is vast. We provide a brief review, with the goal of highlighting differences between our proposed framework and the extant literature. With regard to the separation of givers’ decisions to participate versus the amount given, as noted, this distinction has typically not been made in the literature. Fajardo, Townsend, and Bolander (2018, p. 142) emphasize that “previous studies consider only one decision, leaving readers to assume, implicitly, that results apply to both (choice and amount) or to consider the two dimensions interchangeably.” However, Dickert, Sagara, and Slovic (2011) demonstrate that different mechanisms govern the two decisions. For instance, they find that mood management (i.e., how one feels about oneself) primarily governs the participation decision, while empathetic feelings (i.e., how one feels about the victim) predicate the amount decision. By separating the two decisions, we are able to not only obtain insights into givers’ behavior but also derive implications for more effective fundraising.

Previous research has recognized that benefits provided by charitable organizations can encourage feelings of reciprocity or gratitude that may lead to increased giving (Falk 2007; Bartlett and DeSteno 2006). However, benefits can have the undesirable effect of “crowding out” altruistic motives by diluting intrinsic motivation or the signaling value of prosocial behavior (Bénabou and Tirole 2006; Ariely, Bracha, and Meier 2009). Moreover, external benefits may shift one’s mindset from an altruistic to a more monetary perspective (Gneezy and Rustichini 2000) and potentially decrease the amount of charitable giving (Newman and Shen 2012). Previous research thus makes ambiguous predictions regarding the effects of tangible benefits on giving, some studies reporting positive effects, others negative effects.

Despite the prevalence of multiple forms of giving in practice, and the recognition that benefits can have an effect on subsequent giving, previous marketing studies typically treat giving via membership and donation as a composite (Netzer, Lattin, and Srinivasan 2008; Van Diepen, Donkers, and Franses 2009; Khodakarami, Petersen, and Venkatesan 2015; Kumar et al. 2015). Such aggregation across forms of giving masks potentially large differences in individuals’ motivations and giving behaviors. By contrast, in our framework we recognize the different options facing givers. Consequently, we are able to offer prescriptions about how an NPO should manage available forms of giving to strengthen revenues. As we have noted, while multiple forms of giving may increase the top line, they also typically involve separate administrative structures and thus additional costs for the NPO. Finally, by studying individuals’ choices in the presence of giving options with and without external benefits—namely, membership and donation—we are able to shed some light on the opposing viewpoints in the literature about the effects of external benefits.

Although there is a large body of research on charitable giving and its drivers, much of it is based on cross-sectional analysis and “no research has investigated the longitudinal dynamics of individual donation decisions” (Leliveld and Risselada 2017, p. 1). More recently, White, Habib, and Dahl (2020, p. 11) note that there are relatively few studies on repeated prosocial actions over time and propose that future research should examine the factors that lead to increases or decreases in repeated donations. We refer the reader to excellent review papers available in the literature (Andreoni and Payne 2013; Sargeant and Woodliffe 2007; White, Habib, and Dahl 2020) and provide selected examples that use cross-sectional designs here. Gneezy and Rustichini (2000) find that subjects who were given performance incentives performed more poorly than those who were offered no compensation in a door-to-door fundraising context. Ariely, Bracha, and Meier (2009) confirm that the effects of extrinsic incentives on prosocial behavior crucially depend on visibility; monetary rewards facilitate private, rather than public, prosocial activity. That is, people want to be seen by others as generous; therefore, receiving visible extrinsic incentives dilutes the signals of their prosocial acts. DellaVigna, List, and Malmendier (2012) find evidence that both warm glow and social pressure affect charitable giving. They argue that high social pressure solicitation leads to decreased welfare of the givers.

Related to the management of charitable donations is the literature on crowdfunding. This literature has identified three forms—investment-based, reward-based, and donation-based crowdfunding—the latter two bearing similarities to fundraising by NPOs (Belleflamme, Omrani, and Peitz 2015). Kuppuswamy and Bayus (2018) provide examples of reward-based crowdfunding, in which individuals receive tangible but not monetary benefits from their donations to the project. This type is most similar to the benefits one would receive in the membership model of NPOs. Furthermore, Gerber and Hui (2013) offer examples showing that the reward itself is important for the participant to fund.

As we have discussed, our research builds on the previous literature to deepen understanding of individual giving behavior by focusing on three important but understudied aspects: (1) separating choice to participate from amount of giving, (2) giving in multiple forms, and (3) the dynamics of individual giving. The remainder of the article is organized as follows. In the next section, we describe our data. We then discuss the modeling framework and estimation approach and report our results. A discussion of managerial implications follows, and we conclude with a summary of findings and suggestions for future research.

Data

We collaborated with a large nonprofit scientific research center (SRC; the organization has asked to remain anonymous) that studies an animal species. The mission of the SRC is to promote environmental and natural causes, which it does by conducting scientific research and by a large public outreach initiative. An important source of funding for the SRC is financial gifts from over 100,000 individuals via donation and membership programs.

We consider the cohort of all 2,542 individuals in the United States who made their first financial gift to the SRC during 2011, and we follow them until February 2016. The giving data of this cohort was obtained in late 2016. Individuals who gave more than $10,000 in any year are excluded from the cohort we study because they are managed by a designated fundraiser via a separate and different process. To be able to estimate the dynamics of giving, we retain the subset of 2,171 individuals who gave at least twice during our time window.² For each individual in the cohort, we have monthly data on giving: the amount given, when given, and to which giving options. We also obtained data on the following demographic: age, gender, physical distance of residence from the SRC, and estimated annual income (all assumed to be time invariant).

Our data also include marketing activities of the SRC, namely, the number and kinds of appeals sent to each individual. The SRC conducts two major appeal campaigns for donations: at the end of the calendar year, for which appeals are sent in November, and in the spring in the United States; it also conducts several minor campaigns throughout the year. For membership, the SRC sends annual renewal appeals to current members just before their membership term is about to expire. The organization did not conduct any individually targeted marketing activities during the period of our data. Although we do not have access to the content of appeals, the SRC told us that for each kind of appeal (i.e., donation or membership) and campaign, messages were identical across individuals.

To test whether appeals were targeted to givers who were more generous or more responsive to appeals, leading to an endogenous relationship between giving and appeals, we conducted an endogeneity test motivated by Manchanda, Rossi, and Chintagunta (2004). Separately for donation and membership, we estimated a system of two equations. In the first equation, the number of giving occasions of a giver in a year is modeled as a random coefficient Poisson regression whose rate parameter is a function of the number of appeals and year fixed effects. In the second equation, the number of appeals sent to a giver in a year is modeled as a Poisson regression whose rate parameter is a function of the appeals coefficient and intercept of the previous random coefficient Poisson regression, and year fixed effects. We find that in the estimated second equation the 95% credible intervals of coefficients of both the intercept and the appeals coefficient include zero; this holds for both donation and membership. Therefore, we conclude that appeals are not endogenous in our data, corroborating what the SRC told us: namely, that givers who give more often and/or are more appeal-responsive do not receive more appeals.

Table 1 presents summary statistics of the data. We classify the 2,171 individuals in our sample into three giving groups. “Pure donors” are the 232 individuals who gave only donations during the five-year period, “pure members” are the 720 individuals who gave only through the membership program, and “member-donors” are the 1,219 individuals who gave through both the donation and membership options. We identified members of each group on the basis of the full five-year observation period. Table 1 highlights that giving behaviors are considerably different across the three giving groups. On average, member-donors give 1.3 times and $80 per year, while non-member-donors give .8 times and $42 per year. Member-donors’ giving frequency is thus larger by a factor of 1.6 times, and dollar amount by a factor of 1.9 times, than that of non-member-donors. Relative to pure donors or pure members, member-donors receive a larger number of appeals overall but receive similar numbers of appeals of each kind. This further supports the SRC’s assertion that appeals are not targeted at the individual level.³

Table 1.

Characteristics of Three Groups of Individuals in the Sample Data.

	Pure Donors	Pure Members	Member-Donors	All Givers
Number of individuals (#)	232	720	1,219	2,171
Annual mean gift amount (US$)	45.8 (85.6)	40.6 (55.6)	80.2 (141.7)	63.4 (115.9)
Annual mean gift frequency (#)	.7 (.8)	.8 (.5)	1.3 (.9)	1.1 (.8)
Annual mean appeals (#)	3.8 (2.4)	6.1 (3.5)	6.5 (3.8)	6.1 (3.6)
Annual mean donation appeals (#)	3.1 (2.1)	2.8 (1.8)	3.6 (2.0)	3.3 (2.0)
Annual mean membership appeals (#)	.7 (.9)	3.3 (2.6)	2.9 (2.6)	2.8 (2.6)
Mean age (years)	57.2 (11.5)	59.9 (11.8)	61.9 (11.0)	60.7 (11.4)
Female (%)	71.6	53.3	61.6	60.0
Mean distance from SRC (miles)	881.1 (769.3)	853.7 (817.8)	876.5 (833.8)	869.4 (821.6)
Monthly median income (US$)	5,458 (89,038)	5,467 (39,599)	6,250 (14,014)	5,935 (38,411)

Notes: Figures in parentheses are standard deviations. The three groups shown are mutually exclusive, and an individual’s membership in a group is determined based on the entire window of five years of data.

Members pay an annual fee in one of nine tiers. However, the SRC adjusts membership fees as well as the number of tiers in most years. Moreover, the SRC encourages members to make an additional contribution by giving more than the minimum membership fee. These two phenomena are apparent in the histogram in Web Appendix A, which shows the membership fees paid in the five most popular tiers. These constitute 98% of all membership payment transactions. Because there are many more than five payment amounts in the data, we prefer to model individual membership decisions not as the selection of a tier, but as a continuous amount decision.

All members receive quarterly magazines related to the SRC’s research, as well as token gifts such as a mug, blanket, and so on after joining and after each renewal. Moreover, members in higher tiers are invited to attend exclusive scientific tours. Under U.S. tax laws, membership fees are tax deductible to the extent of the fee amount less $20, which is considered to be the annual private value of the free quarterly magazines.

Figure 1 shows the mean giving amount and frequency by group over time. We see declines in giving amount and frequency for pure donor and pure member groups, whereas the member-donor group displays an increase in the amount and frequency of giving over the five years. As a consequence, the SRC’s management especially values member-donors. Therefore, predictively identifying potential member-donors in the early stage of the contributor–NPO relationship and nurturing them will be beneficial for the SRC as well as for contributors who find the SRC to be a good match for their philanthropic goals.

Figure 1.

Mean annual giving amount and frequency by group.

Figure 2 shows the number of appeals sent by the SRC during the five-year period. As we have discussed, there is conspicuous seasonality in donation appeals, but less so in membership appeals. This is because the SRC sends donation appeals mostly in the spring in the United States, which is a migratory season for the animal species (and thus interest is high), and it is during “tax season.” By contrast, the SRC sends membership renewal appeals throughout the year to individuals one or two months ahead of their membership expiration date.

Figure 2.

Number of appeals sent by month for donation (left) and membership (right).

A Model of Individual Giving Behavior

Overview

The previous data description sheds light on the differences in giving patterns across the three groups. However, we would like to quantify the role of factors that influence givers’ decisions over time. For this, we require a model that accounts for the roles of both observed factors, such as appeals, demographics, givers’ lifetime, and time since the last giving occasion, and unobserved factors, such as individual differences. Moreover, a model can be used to predict the effectiveness of future marketing actions, such as targeted appeals by the NPO.

As we have noted, a model of individual giving behavior needs to have separate mechanisms to deal with discrete (i.e., participation) and continuous (i.e., amount) decisions. Single discrete-continuous models have been widely used in the marketing literature due to their flexibility and utility theory–based primitives (Arora, Allenby, and Ginter 1998; Chiang 1991; Chintagunta 1993; Hanemann 1984; Mehta, Chen, and Narasimhan 2010; Nair, Dubé, and Chintagunta 2005). However, this framework assumes that individuals choose only one option at a time, which is not the case in many real-life situations. To overcome this limitation, Kim, Allenby, and Rossi (2002) proposed a multiple discrete-continuous utility maximizing model. However, Bhat (2005, 2008) points out that Kim, Allenby, and Rossi’s model is difficult to estimate due to its computational complexity. Instead, he proposes a tractable, closed-form utility maximizing model that allows individuals to also choose multiple alternatives simultaneously. This model is appropriate for our data, wherein 14% of givers gave in multiple forms and amounts in the same month at least once. Our model of giving behavior, which is further described in the “Givers’ Decision Making” subsection, is in line with this stream of literature.

Accommodating parameter evolution is important in our context, and in many marketing contexts in which consumers’ preferences and responsiveness to marketing activities change over time. In addition, as previously discussed, we expect that an individual’s probability of giving will change with the passage of time since the last giving occasion, due to the fact that membership has an expiration date and the licensing effect (Khan and Dhar 2006). Moreover, Figure 1 also suggests that individuals’ intrinsic preferences and responsiveness to solicitation appeals for giving options are likely to change over the lifetime of their relationship with the NPO (Netzer, Lattin, and Srinivasan 2008). The considerable seasonality in giving observed in our data is yet another dynamic factor. To accommodate these dynamics, we extend Bhat (2008)’s multiple discrete-continuous (extreme value) choice model by allowing the structural parameters to change over time through GP priors (Dew and Ansari 2018; Rasmussen and Williams 2005). We model these dynamics through three different GP components: lifetime, recency, and calendar time (Dew and Ansari 2018). We explain details of these dynamics in the “Capturing Time-Varying Parameters in the Giving Decision” subsection.

Previous literature has found that individuals are very heterogeneous in their giving behavior; some are more altruistic than others (Simpson and Willer 2008). Further, women (Winterich, Mittal, and Ross 2009), individuals who have less real or perceived distance to the NPO (Touré-Tillery and Fishbach 2017), and older individuals (Midlarsky and Hannah 1989) have been found to be more generous. Thus, including individual differences in the model is useful for targeting. Controlling for individual heterogeneity also ensures we are not biasing the dynamic components of the model by introducing spurious state dependence (Heckman 1981). Therefore, we incorporate observed individual heterogeneity via demographics and unobserved heterogeneity via a random effects specification (Allenby and Rossi 1998).

Givers’ Decision Making

We model an individual’s decision to give to an NPO that allows multiple giving options (e.g., donation and membership). We consider the individual’s choices among the giving options and the amount of money given to each option as utility-maximizing behavior. Individual $i$ $(i = 1, \dots, I)$ is assumed to maximize latent utility $U_{i t}$ by choosing the amounts of money allocated to the outside good $q_{i 0 t}$ , and to giving option $j$ after tax deduction, $q_{i j t}$ $(j = 1, \dots, J)$ , at time $t$ $(t = 1, \dots T)$ :

U_{i t} = ψ_{i 0 t} \times ln q_{i 0 t} + \sum_{j = 1}^{J} γ_{i j t} \times ψ_{i j t} \times ln (\frac{q_{i j t}}{γ_{i j t} p_{i j t}} + 1),

s . t \sum_{j = 0}^{J} q_{i j t} = Q_{i t}, q_{i 0 t} > 0, q_{i j t} \geq 0.

The utility in Equation 1 is quasiconcave, continuously differentiable, and an increasing function of expenditure $q_{i j t}$ .⁴ To be a valid utility function, we need restrictions on Equation 1 such that $ψ_{i 0 t},$ $ψ_{i j t} > 0$ , and $γ_{i j t} > 0$ . The expenditure on the outside good $q_{i 0 t}$ is defined as a numeraire that includes the aggregate expenditure on all outside goods (e.g., rent, grocery, gas), but excludes charitable giving to the focal NPO. Individuals consume outside goods in each time period, and the price of the outside good is normalized to unity ( $p_{i 0 t} = 1$ ). The “price” of giving to option $j$ , $p_{i j t}$ , is related to an individual’s marginal tax rate. Austin (2016) reports that in two-thirds of countries, including the United States, taxpayers can claim charitable giving as a deduction from taxable income. If the marginal tax rate is $0 < d_{i j t} < 1$ , as determined by an individual’s income and the characteristics of giving option $j$ , we define $p_{i j t} = (1 - d_{i j t})$ .⁵ When an individual gives $g_{i j t}$ to option $j$ , the net expenditure on the gift is $q_{i j t} = p_{i j t} \times g_{i j t}$ because of the tax deduction associated with giving. We assume that the tax exemption (i.e., $d_{i j t} \times g_{i j t}$ ) is spent on the outside option and for simplification ignore the gap in time between the giving occasion and when the tax deduction is received. The sum of all expenditures $Q_{i t}$ , which includes both spending on the outside good and giving to $J$ options, is the income of individual $i$ in time $t$ .

$ψ_{i j t}$ is the baseline marginal utility associated with option $j$ at the point of zero giving for individual $i$ in period $t$ . This can be seen by calculating the marginal utility of spending with respect to option $j$ (i.e., $\frac{\partial U_{i t}}{\partial g_{i j t}} |_{g_{i j t = 0}} = ψ_{i j t}$ ). For two choices $k$ and $l$ with the same prices, if the baseline marginal utility of choosing charitable option $k$ is higher than for option $l$ $(k \neq l)$ , then an individual will choose option $k$ at the point of no giving to all options. Therefore, $ψ_{i j t}$ determines the set of options $(j = 1, \dots, J)$ which the individual chooses. In the subsequent discussion, we refer to $ψ_{i j t}$ as the “baseline utility parameter,” which we interpret as the individual’s preference to choose option $j$ . Similarly, $ψ_{i 0 t}$ captures the baseline utility of the outside option.

Parameter $γ_{i j t}$ serves to capture satiation effects in that it determines the change in marginal utility for inside option $j$ as the amount given to option $j$ by individual $i$ increases. This point is illustrated in Web Appendix B. In general, it can be shown that the higher the value of $γ_{i j t}$ , the lower the satiation due to expenditure on option $j$ . Therefore, $γ_{i j t}$ influences the amount given to option $j$ and allows multiple options to be chosen together (e.g., nonzero giving to both membership and donation options) through its impact on satiation (Bhat 2008). We refer to $γ_{i j t}$ as the “satiation parameter” and interpret all parameters related to $γ_{i j t}$ as affecting the levels of satiation.

Capturing Time-Varying Parameters in the Giving Decision

The GP prior is a flexible and parsimonious way of representing time-varying parameters. It is flexible in that it can accommodate various data patterns such as periodicity and short-term and long-term effects via different covariance function specifications and the additive property of the GP (for details, see Dew and Ansari [2018]). It is parsimonious because a GP structure is determined by a small number of hyperparameters.

When compared with another common dynamic model—the hidden Markov model (HMM)—GPs require neither an assumption of discrete hidden states nor the Markov assumption. To illustrate the substantive importance of this feature, consider recent research which has shown that reciprocal motives to give can decay over time (Chuan, Kessler, and Milkman 2018). Potential dynamic patterns of decay could be a gradual decline, a sudden drop, or all variations between these two extremes. A small number of discrete states would be able to capture the sudden drop pattern, while a larger number of discrete states would be needed to capture the gradual decline. Rather than making ad hoc assumptions, a good model should be able to detect the number of discrete states based on the data. Unlike HMMs, GPs do not assume a discrete, fixed number of hidden Markov states. Instead, they estimate a continuous state and automatically infer the type of decay from the data.

Furthermore, because the duration over which reciprocity can decay is unknown, the Markov assumption of an HMM requires the modeler to also conduct model selection on the correct number of time periods, which adds additional complexity to the model specification process. Again, the GP overcomes this problem by estimating the relevant duration as a feature of the model, based on the data.

Here, we briefly introduce the concept of GP. Readers are referred to Rasmussen and Williams (2005) for a comprehensive review, and Dew and Ansari (2018) and Dew, Ansari, and Li (2020) for other GP applications in the marketing literature. GP is defined by a mean function and a covariance function, just as a multivariate Gaussian distribution is characterized by a mean vector and a covariance matrix. We denote this using notation $f (x) \sim G P [μ (x), K (x, x')]$ , where $μ (x) = E [f (x)]$ is the mean function and $K (x, x') = c o v [f (x), f (x')]$ is a covariance function. In the GP literature, the mean function is commonly set to be a constant, reflecting the lack of prior knowledge about the trends of the function (Rasmussen and Williams 2005; Roberts et al. 2013). In contrast, a covariance function, also termed a kernel, plays a major role in determining the structure of a GP by governing its smoothness, amplitude, and differentiability.

As mentioned, we want to incorporate dynamic effects of lifetime, recency, and seasonality into our model. For this, we use lifetime ( $l_{i}$ ), defined as the time (in months) elapsed since individual $i$ gave for the first time; recency ( $r_{i j}$ ), defined as the time elapsed since $i$ ‘s last giving occasion to option $j$ ; and calendar time ( $t$ ) as GP inputs. Among various available options of covariance functional forms (Rasmussen and Williams 2005; Roberts et al. 2013), we use the squared exponential (SE) covariance function to model dynamic lifetime, recency, and appeal effects,⁶ and adopt periodic covariance function (Per) to model the option specific seasonality. Details of covariance function specifications are available in Web Appendix C.

Baseline Utility and Satiation

We incorporate factors such as lifetime, recency, seasonality, appeals, and individual heterogeneity into the model by parameterizing the baseline marginal utility ( $ψ_{i 0 t}, ψ_{i j t} > 0$ ) as follows:

ψ_{i 0 t} = e x p (ε_{i 0 t}),

ψ_{i j t} = e x p β_{L_{j}} (l_{i}) + β_{R_{j}} (r_{i j}) + β_{S_{j}} (t) + [β_{A_{j}} (l_{i}) + β_{A_{i j}}] \times a p p e a l_{i j t} + (β_{D_{j}} \times d e m o_{i} + β_{0_{i j}}) + ε_{i j t},

As the relationship between the giver and the NPO evolves, individuals’ intrinsic preferences for giving option $j$ and responsiveness to appeals can change over time. Moreover, we expect recency effects on baseline utility to be nonmonotonic. To capture such effects, we define $β_{L_{j}} (l_{i})$ , $β_{R_{j}} (r_{i j})$ , $β_{S_{j}} (t)$ to represent time-varying influences of lifetime, recency, and seasonality for giving option $j$ , with input values in parentheses, respectively. The dynamic appeal effects for giving option $j$ are captured by $β_{A_{j}} (l_{i})$ where $a p p e a l_{i j t}$ represents the number of option-specific appeals that individual $i$ receives at time $t - 1$ .⁷ Note that we use lifetime as a GP input that varies along with the individual-level time scales at any point in calendar time, thereby effectively capturing heterogeneity in the appeal effects. We model such dynamics in baseline utility via GP priors that are common across individuals as follows:

β_{L_{j}} (l_{i}) \sim G P [μ_{β_{L_{j}}}, K_{S E} (l, l'; η_{β_{L_{j}}}, ρ_{β_{L_{j}}})],

β_{R_{j}} (r_{i j}) \sim G P [0, K_{S E} (r, r'; η_{β_{R_{j}}}, ρ_{β_{R_{j}}})],

β_{S_{j}} (t) \sim G P [0, K_{P e r} (t, t'; η_{β_{S_{j}}}, ρ_{β_{S_{j}}}, ω = 12)],

β_{A_{j}} (l_{i}) \sim G P [μ_{β_{A_{j}}}, K_{S E} (l, l'; η_{β_{A_{j}}}, ρ_{β_{A_{j}}})] .

We incorporate observed individual heterogeneity by including demographics and incorporate unobserved heterogeneity via a random effects specification (Allenby and Rossi 1998). $d e m o_{i}$ is a vector that includes age, gender, and distance of residence from the focal NPO, and $β_{D_{j}}$ is the vector of corresponding parameters. $β_{0_{i j}}$ and $β_{A_{i j}}$ account for unobserved heterogeneity in intrinsic preference and responsiveness to appeals for option $j$ , respectively.

The error term $ε_{i j t}$ represents unobserved factors that affect the attractiveness of option $j$ , and $ε_{i 0 t}$ represents unobserved factors associated with the outside option. Following Bhat (2008), we assume that both $ε_{i 0 t}$ and $ε_{i j t}$ follow i.i.d. type I extreme-value distributions.

To incorporate the factors that affect the level of satiation in giving, we parameterize $γ_{i j t}$ similar to $ψ_{i j t}$ as follows:

γ_{i j t} = e x p δ_{L_{j}} (l_{i}) + δ_{R_{j}} (r_{i j}) + δ_{S_{j}} (t) + [δ_{A_{j}} (l_{i}) + δ_{A_{i j}}] \times a p p e a l_{i j t} + (δ_{D_{j}} \times d e m o_{i} + δ_{0_{i j}}) .

$δ_{L_{j}} (l_{i})$ represents time-varying average satiation level for option $j$ over time since the first giving occasion, and $δ_{R_{j}} (r_{i j})$ is the dynamic effect of time elapsed since the last giving occasion on satiation. $δ_{S_{j}} (t)$ and $δ_{A_{j}} (l_{i})$ respectively represent the seasonality and time-varying effects of appeals on satiation for option $j$ . Similar to modeling dynamics in baseline utility, we incorporate dynamics in satiation via GP priors that are common across individuals (i.e., the specification is the same as Equation 3 except that we change $β$ to $δ$ ). $δ_{D_{j}}$ is the effect of observed individual characteristics on satiation, and $δ_{0_{i j}}$ and $δ_{A_{i j}}$ account for unobserved heterogeneity in satiation that are associated with the intrinsic preferences and responsiveness to appeals, respectively.

The Probability of Giving

The utility-maximizing allocations of the giver’s budget across $J$ options (including the outside option) can be derived by solving the Kuhn–Tucker conditions. (For a detailed derivation, see Bhat [2005]). From the Kuhn–Tucker conditions and i.i.d. type I extreme value distribution assumption on error terms, we obtain the following closed-form expression for the probability of optimal expenditure allocation on chosen $M$ giving options:

P (q_{i 0 t}, q_{i 1 t}, \dots, q_{i M t},0, \dots,0) =

(M!) (\prod_{m = 0}^{M} \frac{1}{q_{i m t} + γ_{i m t} p_{i m t}}) (\sum_{m = 0}^{M} q_{i m t} + γ_{i m t} p_{i m t}) [\frac{\prod_{m = 0}^{M} e x p (V_{i m t})}{{(\sum_{j = 0}^{J} e x p (V_{i j t}))}^{M + 1}}],

where $V_{i 0 t}$ and $V_{i j t}$ $(j = 1, \dots, J)$ are defined as

V_{i 0 t} = - ln (q_{i 0 t}),

V_{i j t} = β_{L_{j}} (l_{i}) + β_{R_{j}} (r_{i j}) + β_{S_{j}} (t) + [β_{A_{j}} (l_{i}) + β_{A_{i j}}] \times a p p e a l_{i j t} + (β_{D_{j}} \times d e m o_{i} + β_{0_{i j}}) -

ln (\frac{q_{i j t}}{γ_{i j t} p_{i j t}} + 1) - ln (p_{i j t}) .

Model Identification and Estimation

Bhat (2008) discusses empirical identification issues of the general multiple discrete-continuous choice model and discusses the specification termed the “gamma-profile,” which we adopt here. A unique feature of our model is its incorporation of dynamics over time using GP priors in the multiple discrete-continuous choice model. We need restrictions on GP priors due to the additive structure of baseline utility and satiation specifications. Specifically, sums of two latent functions, such as $β_{L_{j}} (l_{i}) + β_{R_{j}} (r_{i j})$ , are equivalent to $β_{L_{j}}^{*} (l_{i}) + β_{R_{j}}^{*} (r_{i j})$ , where $β_{L_{j}}^{*} (l_{i}) = β_{L_{j}} (l_{i}) + c$ and $β_{R_{j}}^{*} (r_{i j}) = β_{R_{j}} (r_{i j}) - c$ for any $c \in ℝ$ , as both sums imply the same probability of giving. We address this problem by following Dew and Ansari’s (2018) identification strategy, which is to set the initial function values of recency and seasonality to zero in both baseline and satiation, but we impose no restriction on lifetime terms. With these restrictions, $β_{L_{j}} (l_{i})$ and $δ_{L_{j}} (l_{i})$ capture the average baseline utility and satiation level trends over time since the first giving occasion, respectively, and $β_{R_{j}} (r_{i j})$ , $β_{S_{j}} (t)$ , $δ_{R_{j}} (r_{i j})$ , and $δ_{S_{j}} (t)$ capture deviations from these mean trends. We discuss prior specifications and estimation procedures in Web Appendices D and E, respectively.

Results

Overview

We compare the full model estimated using Equation 5, which incorporates both random effects (unobserved heterogeneity) and GP (dynamics), which we denote by M1, with more restrictive benchmark models, M2–M5. As we have discussed, a distinctive feature of our framework is that we allow for multiple forms of giving, whereas previous research combines different forms of financial giving as a composite amount (Khodakarami, Petersen, and Venkatesan 2015; Kumar et al. 2015; Netzer, Lattin, and Srinivasan 2008; Van Diepen, Donkers, and Franses 2009). We investigate the effect of not distinguishing between forms of giving by estimating a “single giving option” model (M2), which shares all features of M1 (such as GP and random effects), but the parameters are restricted to be common across the two giving options. We discuss the results of M2 subsequently. To assess the importance of controlling for individual heterogeneity and time varying preferences, we estimate three restricted model specifications, M3–M5. M3 includes random effects, but omits the GP component. M4 incorporates dynamics, but omits random effects. M5 omits both random effects and GP components.

We find that accounting for multiple forms of giving and controlling for unobserved heterogeneity and dynamics in parameters significantly improves the predictive accuracy of the model. M1 exhibits the best model fit, significantly better than the second-best-fitting model, M2. This implies that aggregation across forms of giving indeed disguises differences in individual giving behavior, thus explicit modeling of both forms is necessary. The superiority of M1 over M3 indicates that including dynamics is desirable, while the superiority of M1 over M4 suggests that including unobserved heterogeneity is desirable. Hereinafter, we focus on the results of the full model (M1) because it shows the best performance (model comparison results are available in Web Appendix F).

Figures 3 through 6 plot the evolution of time-varying parameters estimated using the GP priors. In all figures, the solid lines represent posterior means and the gray areas are 95% credible intervals. Subscripts 1 and 2 stand for donation and membership, respectively.

Figure 3.

Lifetime effects on baseline utility ( $β_{L_{1}} (l_{i})$ , $β_{L_{2}} (l_{i})$ ).

Table 2 shows posterior means and standard deviations related to the GP and the $\hat{R}$ statistic. As explained in Web Appendix C, these parameter estimates summarize the characteristics of the GP structures. Table 3 provides observed and unobserved heterogeneity parameter estimates and the $\hat{R}$ statistic. The $\hat{R}$ statistic is a measure of convergence of the model (Gelman and Rubin 1992). $\hat{R}$ values less than 1.1 indicate successful convergence. Next, we discuss the estimated parameters with an emphasis on their implications for the SRC.

Table 2.

Covariates of Baseline Utility and Satiation Parameters.

Baseline Utility					Satiation
Component	Parameter	Mean	SD	$\hat{R}$	Component	Parameter	Mean	SD	$\hat{R}$
Lifetime	$μ_{β_{L_{1}}}$	−14.36	(.23)	1.01	Lifetime	$μ_{δ_{L_{1}}}$	3.89	(.16)	1.01
	$ρ_{β_{L_{1}}}^{2}$	1.09	(.09)	1.00		$ρ_{δ_{L_{1}}}^{2}$	2.35	(2.02)	1.00
	$η_{β_{L_{1}}}^{2}$	.05	(.02)	1.00		$η_{δ_{L_{1}}}^{2}$	.02	(.01)	1.00
	$μ_{β_{L_{2}}}$	−15.66	(.25)	1.01		$μ_{δ_{L_{2}}}$	4.11	(.13)	1.05
	$ρ_{β_{L_{2}}}^{2}$	1.59	(.52)	1.01		$ρ_{δ_{L_{2}}}^{2}$	1.96	(1.99)	1.01
	$η_{β_{L_{2}}}^{2}$	.26	(.09)	1.00		$η_{δ_{L_{2}}}^{2}$	.01	(.00)	1.00
Recency	$ρ_{β_{R_{1}}}^{2}$	2.28	(1.18)	1.01	Recency	$ρ_{δ_{R_{1}}}^{2}$	1.26	(.73)	1.00
	$η_{β_{R_{1}}}^{2}$	.13	(.06)	1.00		$η_{δ_{R_{1}}}^{2}$	.00	(.00)	1.01
	$ρ_{β_{R_{2}}}^{2}$	11.37	(4.28)	1.01		$ρ_{δ_{R_{2}}}^{2}$	1.55	(.52)	1.01
	$η_{β_{R_{2}}}^{2}$	2.35	(.49)	1.00		$η_{δ_{R_{2}}}^{2}$	.01	(.01)	1.01
Seasonality	$ρ_{β_{S_{1}}}^{2}$	.41	(.08)	1.00	Seasonality	$ρ_{δ_{S_{1}}}^{2}$	1.35	(.74)	1.00
	$η_{β_{S_{1}}}^{2}$	1.14	(.49)	1.00		$η_{δ_{S_{1}}}^{2}$	.13	(.18)	1.00
	$ρ_{β_{S_{2}}}^{2}$	.43	(.11)	1.00		$ρ_{δ_{S_{2}}}^{2}$	1.37	(.84)	1.00
	$η_{β_{S_{2}}}^{2}$	.33	(.30)	1.00		$η_{δ_{S_{2}}}^{2}$	.01	(.02)	1.00
Appeals	$μ_{β_{A_{1}}}$	.48	(.09)	1.00	Appeals	$μ_{δ_{A_{1}}}$	-.06	(.05)	1.00
	$ρ_{β_{A_{1}}}^{2}$	.71	(.20)	1.00		$ρ_{δ_{A_{1}}}^{2}$	1.30	(.75)	1.00
	$η_{β_{A_{1}}}^{2}$	.14	(.05)	1.00		$η_{δ_{A_{1}}}^{2}$	.00	(.00)	1.01
	$μ_{β_{A_{2}}}$	.84	(.10)	1.00		$μ_{δ_{A_{2}}}$	−.20	(.04)	1.02
	$ρ_{β_{A_{2}}}^{2}$	1.20	(.45)	1.01		$ρ_{δ_{A_{2}}}^{2}$	1.55	(1.22)	1.01
	$η_{β_{A_{2}}}^{2}$	.15	(.05)	1.00		$η_{δ_{A_{2}}}^{2}$	.00	(.00)	1.00

Notes: Subscripts 1 and 2 represent donation and membership, respectively. Mean and SD refer to posterior means and posterior standard deviations, respectively. The $\hat{R}$ statistic, called potential scale reduction factor, measures Hamiltonian Monte Carlo model convergence. $\hat{R}$ values less than 1.1 indicate successful convergence.

Table 3.

Observed and Unobserved Heterogeneity in Baseline Utility and Satiation Parameters.

Baseline Utility				Satiation
Parameter	Mean	SD	$\hat{R}$	Parameter	Mean	SD	$\hat{R}$
$β_{f e m a l e_{1}}$	.36	(.07)	1.00	$δ_{f e m a l e_{1}}$	−.01	(.05)	1.00
$β_{f e m a l e_{2}}$	−.09	(.06)	1.00	$δ_{f e m a l e_{2}}$	−.02	(.04)	1.00
$β_{a g e_{1}}$	.01	(.00)	1.01	$δ_{a g e_{1}}$	−.01	(.00)	1.01
$β_{a g e_{2}}$	.01	(.00)	1.01	$δ_{a g e_{2}}$	−.00	(.00)	1.03
$β_{d i s t a n c e_{1}}$	−.07	(.04)	1.00	$δ_{d i s t a n c e_{1}}$	.06	(.03)	1.00
$β_{d i s t a n c e_{2}}$	−.03	(.03)	1.01	$δ_{d i s t a n c e_{2}}$	−.00	(.02)	1.00
$σ_{β_{0_{1}}}$	1.28	(.04)	1.00	$σ_{δ_{0_{1}}}$	.05	(.03)	1.00
$σ_{β_{0_{2}}}$	1.05	(.04)	1.01	$σ_{δ_{0_{2}}}$	.02	(.01)	1.00
$σ_{β_{A_{1}}}$	.27	(.06)	1.03	$σ_{δ_{A_{1}}}$	.03	(.02)	1.00
$σ_{β_{A_{2}}}$	.15	(.05)	1.01	$σ_{δ_{A_{2}}}$	.02	(.01)	1.00

Notes: Subscripts 1 and 2 represent donation and membership options, respectively. Mean and SD refer to posterior means and posterior standard deviations, respectively. Values in bold are estimates whose 95% credible intervals do not include zero. The $\hat{R}$ statistic is a measure of convergence of the model. $\hat{R}$ values less than 1.1 indicate successful convergence.

Parameter Estimates and Their Implications

Managing givers over the long term: lifetime effects

In Figure 3, we show how the baseline utility of donation ( $β_{L_{1}} (l_{i})$ ) and membership ( $β_{L_{2}} (l_{i})$ ) evolves with lifetime, which is defined as the time in months since an individual’s first giving occasion. All the individuals in our cohort first gave in 2011, but at different dates, as a result their lifetimes are different from calendar times. The time-varying baseline utilities reflect changes in the propensity to donate or to renew a membership as the length of an individual’s relationship with the SRC grows.

In the left panel of Figure 3, we find that the propensity to donate increases with lifetime, implying that individuals tend to add donation to their giving portfolio, or donate repeatedly over their lifetime, even in the presence of a membership option that provides tangible benefits. The increasing pattern is consistent with previous findings that prosocial behaviors can become habitual over time (Gęsiarz and Crockett 2015; White, Habib, and Dahl 2020).

The propensity to participate in membership (right panel of Figure 3) is cyclical, exhibiting peaks every 12 months. We note that the cyclicality pertains not to the utility derived from consuming membership benefits, which our data cannot identify, but to the utility from the act of renewing membership. Further, unlike donation, the utility from membership does not increase over the five-year period. Bhattacharya (1998) reported that members with longer lifetimes have lower hazards of lapsing. However, we do not find evidence consistent with this finding, perhaps because of the availability of donation as an option in our setting.

We show how satiation levels for donation ( $δ_{L_{1}} (l_{i})$ ) and membership ( $δ_{L_{2}} (l_{i})$ ) vary with lifetime in Web Appendix G. We see that both $δ_{L_{1}} (l_{i})$ and $δ_{L_{2}} (l_{i})$ tend to increase over time, which means givers feel less satiated with their giving as lifetime increases. In other words, the amount they give increases as their relationship with the SRC continues.

Will an individual give again?: recency effects

Individuals may not actively consider giving every month, due to the aforementioned licensing effect of donation and the duration of a valid membership. The estimated recency effects help us think about how people’s giving preferences change with the passage of time since the last giving occasion.

In Figure 4, we show the estimated changes in the baseline utility of donation ( $β_{R_{1}} (r_{i j})$ ) with recency. The utility is low immediately after giving for about seven months, which is consistent with a licensing effect because a recent donation gives the donor “license” to not give for some time (Khan and Dhar 2006). However, the 95% credible interval of $β_{R_{1}} (r_{i j})$ contains zero for most of the seven-month period. This finding is in line with a recent meta-analysis that reported relatively small licensing effects in the literature (Blanken, Van de Ven, and Zeelenberg 2015). The estimated $β_{R_{1}} (r_{i j})$ in each of the first two years is cyclical, with peaks at 11 and 24 months, which can be interpreted as an intrinsic cyclicality of donating since we have controlled for the effects of appeals and seasonality in the model. After 24 months, the 95% credible interval contains zero throughout. This suggests that the SRC can reasonably assume that if more than 24 months have elapsed since the last donation, an individual is likely to have churned.

Figure 4.

Recency effects on baseline utility ( $β_{R_{1}} (r_{i j})$ , $β_{R_{2}} (r_{i j})$ ).

Estimated changes in baseline utility of membership ( $β_{R_{2}} (r_{i j})$ ) with recency are shown in the right panel of Figure 4, and they exhibit a different pattern. The utility decreases for a brief period, then peaks at about 12 months, and then declines slowly till around month 56. As expected, the initial drop and 12-month peak capture the annual membership renewals. The subsequent trend indicates that even if an individual does not renew membership after one year, there is a reasonable possibility of renewal in future years.

The contrast in the effect of recency on baseline utilities of donation versus membership is informative. The longer-lasting positive effect in the case of membership suggests that the twin rewards of tangible benefits (e.g., mugs, T-shirts) and intangible benefits (e.g., sense of affiliation, and warm glow) play a role, and therefore renewal efforts should be continued. To some extent, our finding is consistent with the reported positive effects of extrinsic benefits on prosocial behavior (Bartlett and DeSteno 2006; Bhattacharya 1998; Falk 2007).

Unlike baseline parameter estimates, the effects of recency on satiation for both options are small, and the 95% credible intervals contain zero except for a limited time for membership. The results are available in Web Appendix G.

Variability in giving due to seasonality

As discussed previously, there is considerable seasonality in giving to the SRC. Figure 5 displays option-specific seasonal changes in baseline utility over calendar time ( $β_{S_{j}} (t)$ ). Seasonality is salient for donations and peaks every spring and calendar year-end; spring is the migration season of the animal species that the SRC studies, and year-end increases are due to the tax-year definition. GP priors with periodic kernel capture this pattern well. The seasonality of membership shows only a calendar year-end peak. This is because more members have joined, and consequently renewed, at the end of the calendar year, presumably to capitalize on tax benefits. Again, seasonal effects on satiation are smaller in magnitude compared with those on baseline utility (see Web Appendix G).

Figure 5.

Seasonal effects on baseline utility of donation ( $β_{S_{1}} (t)$ , $β_{S_{2}} (t)$ ).

How effective are donation and membership appeals?

In Figure 6, we show effects of appeals on baseline utility over time. Both pure donors and pure members received both kinds of appeals: pure donors received 3,686 donation appeals and 827 membership appeals, while pure members received 10,331 donation appeals and 12,035 membership appeals. Moreover, on approximately 20% of occasions, members did not receive renewal notices when their membership was about to expire.⁸ These variations in the data make it possible to estimate the effectiveness of each type of appeal separately from inherent unobserved differences between donors and members.

Figure 6.

Appeal effects on baseline utility ( $β_{A_{1}} (l_{i})$ , $β_{A_{2}} (l_{i})$ ).

Time-varying appeal effects on baseline utility differ between the giving options. In the left panel of Figure 6, the effects of donation appeals on baseline utility ( $β_{A_{1}} (l_{i})$ ) over givers’ lifetime exhibit a notable decrease in the early stages followed by a gradual increase over time. Although donation appeals generally have positive effects on donation participation, their effectiveness is not consistent; the 95% posterior intervals contain zero in many periods. This implies that some donors would have given regardless of receiving donation appeals, while others do not give despite receiving appeals. We conjecture that this is partly because the SRC sends standardized appeals to all potential donors rather than targeted and personalized donation appeals. This suggests room for improvement in the efficiency and effectiveness of donation appeals by targeting. One interesting anomaly is that the effectiveness of donation appeals shows a conspicuous peak around month 48. This is because in 2015 the SRC celebrated a special event based on the time since its founding (we do not provide details to protect the anonymity of the SRC). To encourage participation in the celebration, the SRC sent more appeals at the year-end of 2015 (see Figure 2) perhaps with a special message of celebration. Therefore, individuals were especially responsive to donation appeals at that time.

Membership appeals ( $β_{A_{2}} (l_{i})$ ) have a consistent positive effect on membership renewal, although these appeals are more effective in the first three years and substantially less so later. We conjecture that membership appeals are effective because membership programs provide a natural structure for sending targeted renewal notices to individuals whose membership is about to expire. Interestingly, compared with lifetime effects, the membership appeal effect exhibits a delay relative to the 12-month cycle: it peaks around month 15, month 31, and month 43. This is related to the fact that many members do not renew their membership in exactly 12 months. Among individuals who renewed at least three times, the mean interrenewal time is about 15 months between the first two renewals, and about 14 months between the second and third renewals. This delayed renewal behavior leads to loss of revenue for the SRC because an annual membership renewed in month 15 instead of month 12 next expires in month 27, instead of month 24. Thus, in a five-year span, three renewals each delayed by three months lead to a loss of nine months of membership fee.

Web Appendix G shows the time-varying effects of appeals on satiation for each option. We see that the 95% credible intervals of donation appeals ( $δ_{A_{1}} (l_{i})$ ) contain zero in all periods. By contrast, the average effect of membership appeals on satiation ( $δ_{A_{2}} (l_{i})$ ) is consistently negative, suggesting that members may feel satiated with the large number of membership appeals. Previous literature has found mixed effects of solicitation appeals on the amount decision; Meer and Rosen (2011) reported that solicitation appeals are effective for encouraging participation in donations, but have no effect on the amount given, whereas Van Diepen, Donkers, and Franses (2009) found that too many appeals cause annoyance and reduce giving. We find evidence in support of the former result for the donation option and the latter result for the membership option.

We notice that appeal effects on baseline show greater variability over time than appeal effects on satiation. To compute the magnitude of the effect of an incremental appeal on the probability of participation separately from the amount given, we proceed as follows, separately for donation and membership appeals. For each individual we add one hypothetical appeal at a random point in time during the five-year period and use the estimated model to compute the percentage change in the participation probability and expected amount given, relative to the baseline number of appeals in the observed data. We choose the random point in time at which the additional appeal is inserted 500 times and repeat the exercise, thereby obtaining the average percentage changes. For donations, we find that on average the additional appeal increases the probability of participation by 1.21% (95% credible interval = [1.18, 1.24]), but the additional appeal does not change the expected amount given (conditional on participation). Similarly, for membership, we find an increase in participation probability of 1.5% (95% credible interval = [1.35, 1.66]) but no change in the expected amount given. Therefore, we conclude that individuals are more responsive in the likelihood to participate than in the amount given. The detailed analysis procedure is described in Web Appendix H.

Differences between givers: individual heterogeneity

The upper part of Table 3 shows the estimated effects of demographic characteristics and their convergence diagnostic $\hat{R}$ . Our results add nuance to previous studies that have found that women give more frequently than men (Sargeant and Woodliffe 2007). We find that women have higher baseline utility for the more intrinsically motivated option, donation, whereas men have higher intrinsic preference for the more extrinsically motivated option, membership. Older individuals have higher baseline utility than younger individuals for both options, which corresponds to Midlarsky and Hannah (1989)’s findings. We also find that individuals who live closer to the SRC exhibit a lower satiation level with the donation option and make larger donations. This corresponds to Touré-Tillery and Fishbach’s (2017) finding that donations increase as real or perceived distance to the recipient decreases. The SRC could use this finding to guide its future targeting efforts.

The lower part of Table 3 presents posterior estimates of the standard deviations of the random intercept and the appeal effect. We can judge the statistical significance of an estimated standard deviation by whether the posterior mean is no less than twice the posterior standard deviation. This is because we have restricted all standard deviation estimates to be positive, and therefore the posterior distributions of these parameters do not contain zero. Using this criterion, the standard deviations of baseline utility parameters are all greater than zero, whereas the standard deviations of satiation parameters are in all cases not different from zero.

Based on the baseline utility, we show individuals whose 95% credible intervals of intrinsic preferences for the two giving options do not contain zero in Web Appendix I. There are 165, 130, and 83 individuals whose estimated intrinsic preferences for donation only, membership only, and both, respectively, meet the criteria (i.e., the 95% credible intervals do not contain zero). We use these results to identify potential member-donors in the “Managerial Applications” section.

What happens if donation and membership are not considered distinct options?

One of the key contributions of this article is to shed light on factors that drive different forms of giving. As discussed previously, the effects of lifetime, recency, seasonality, appeals, and individual heterogeneity on donation and membership are distinctive. To further assess the importance of allowing multiple forms of giving in the individual model, we estimate a “single giving option” model (see M2).

We found that the “single giving option” model blurs the dynamic effects of lifetime, recency, seasonality, and appeals on baseline utility. Moreover, it misses key insights about appeal effects on satiation. Therefore, in the absence of insights about differences in giving behavior, the SRC can mistakenly focus its marketing efforts on one option, when a focus on the other option would be more productive. The results and discussion are available in Web Appendix J.

Managerial Applications

While the primary purpose of the proposed model is to describe how specific factors drive individual giving behavior, the model estimates can also usefully inform decision making aimed at augmenting the SRC’s revenues. We discuss here two applications of our model for fundraising by the SRC. The first application demonstrates how our model can help the SRC to predictively identify potential member-donors, the second explores how the SRC can increase revenue from each giving option by using targeted appeals.

To enable these predictions, we have derived the conditions in our model for a giving option to be chosen by a utility-maximizing individual, as well as the optimal expenditure on the chosen option (see Web Appendix K). The condition for option $l$ to be chosen can be written as follows:

λ_{i t} < \frac{ψ_{i l t}}{p_{i l t}},

where $λ_{i t}$ is a parameter stemming from the giver’s budget constraint, expressed mathematically in Web Appendix K. The optimal expenditure on the chosen option $l$ is

q_{i l t} = γ_{i l t} (\frac{ψ_{i l t}}{λ_{i t}} - p_{i l t}) .

Because $ψ_{i 0 t}$ and $ψ_{i j t}$ are functions of error terms, we draw 3,000 random samples of $ε_{i 0 t}$ and $ε_{i j t}$ from the type I extreme value distribution. We use the conditions in Equations 7 and 8 in the following analyses.

Predicting Potential Member-Donors

Member-donors are particularly valuable to the SRC compared with pure donors and pure members because they give more frequently, they give larger amounts, and their donation amounts increase over time (see Figure 1). It is thus important to predict which pure donors and pure members are likely to become member-donors in the future, prioritize these individuals, and nurture relationships with them.

Here, we show how our model estimates can be used to predictively identify member-donors. For this exercise, we divide the 62 months of our data into the first 42 months (January 2011 to June 2014) as an estimation sample, and the remaining 20 months (July 2014 to February 2016) as a holdout sample. In the estimation sample, the cohort of 2,171 individuals includes 284 “pure donors” and 963 “pure members”; these are individuals who give only through donation programs or membership programs, respectively, during the estimation sample period. In the holdout sample, 52 of the 284 pure donors (18.3%) and 243 of the 963 pure members (25.2%) became member-donors.

We use the model estimates based on the estimation sample to calculate an ordinal metric of the potential to become a member-donor in the future, which we term the “donor susceptibility to membership” for pure donors, and “member susceptibility to donations” for pure members. The exercise is conducted separately for pure members and pure donors. We describe first the exercise for pure donors. For each individual and each month in the estimation sample, we calculate the expected probability of choosing membership (i.e., the option not chosen by a pure donor) by using Equation 7.⁹ The expected probability depends on lifetime, recency, seasonality, and individual heterogeneity, because the numerator of the right-hand side of Equation 7—the baseline utility $ψ_{i l t}$ —is a function of these factors. Because the expected probability of choosing membership is time-varying, we compute the average probability of membership across months for each pure donor. We then rank the 284 pure donors in decreasing order of this average probability, the donor susceptibility to membership. For example, if pure donor A has a higher donor susceptibility to membership than another pure donor B, we expect that A has a higher probability of becoming a member-donor in the future than B. An analogous exercise is conducted for pure members, whereby we rank-order them based on a similar ordinal metric, the member susceptibility to donations. To compare the predictive accuracy of our model, we conducted the same analyses with the aforementioned benchmark models M2–M5.

Figure 7 plots the gains charts computed in the holdout sample based on the exercises described previously. The gains chart on the left depicts on the horizontal axis pure donors arranged in decreasing order of the expected probability of membership computed in the estimation sample. The vertical axis depicts the percentage of the 52 member-donors in the holdout sample who are “captured.” The dotted (black) 45-degree line indicates baseline performance, which is random targeting without a model. In the left panel, for example, randomly choosing 50% of 284 pure donors in the estimation period would yield half of 52 (i.e., 26) member-donors in the holdout sample period. The solid (red) line indicates the % captured using the proposed model. For instance, our model helps to identify 90% of the member-donors (i.e., 47 of 52 member-donors) if we choose 50% of pure donors. Similarly, in the right panel, if we randomly choose 50% of 963 pure members in the estimation period, we would expect to identify 122 of the 243 member-donors in the holdout sample, whereas using our model the SRC can identify 75% of member-donors (i.e., 183 of 243 member-donors).

Figure 7.

Gains charts for targeting member-donors in holdout sample.

Comparison of the left and right panels of Figure 7 shows that model M1 does better in predicting which pure donors will become member-donors than in predicting which pure members will become member-donors. One reason for this difference is that at least 25.2% (243 out of 963) of pure members need to be targeted to reach 100% of those who converted, while the corresponding number is only 18.3% (52 out of 284) for pure donors. This is indicated by the solid black lines labeled “maximum” in the left and right panels. Thus, there is less opportunity for any model in the case on the right. A second reason is indicated by an analysis of the estimated probabilities of membership (data underlying left panel) and donation (data underlying right panel). The coefficient of variation (i.e., standard deviation/mean) of the probabilities of membership estimated via model M1 is .52, and of the estimated probabilities of donation is .39. We conjecture that the lower variability in the estimated probabilities across pure members translates into a lower ability of the model to bring to the top of the data those who became member-donors.

The other dashed lines indicate the gains from using the benchmark models (M2–M5). Gains from the proposed model are greater than those from the benchmark models at all levels of cutoffs (i.e., 50% and other levels) in both pure donor and pure member cases. The proposed model thus provides a useful predictive tool that enables the SRC to identify pure donors and pure members who will become member-donors.

Targeting Appeals to Individuals and Times

Here, we illustrate the impact of targeting appeals on the basis of the revenue gains for each giving option, thereby improving the effectiveness of appeals. Specifically, we consider a counterfactual situation in which the SRC reallocates 1% of appeals sent during the sample period, holding constant the total number of appeals sent. To achieve this, we simulate two cases: counterfactual and baseline. In the baseline case, appeals sent to individuals in the data are left unchanged. In the counterfactual case, 1% of appeals sent are randomly chosen and reassigned according to the targeting strategies explained next.

As Web Appendix I shows, we can identify individuals with a high intrinsic preference for each giving option. We have further found that (a) recency effects show that repeat giving is more likely when recency is between 11 and 13 months for both options, (b) lifetime effects on baseline utility are high every 12 months for membership, and (c) both options exhibit considerable seasonality. These findings suggest that the SRC may benefit by sending appeals in months when the likelihood of giving is high. Using these results, we consider three targeting strategies for the SRC: (1) one that targets individuals with higher intrinsic preference for a specific giving option (i.e., individuals who are identified in Web Appendix I) but does not target timing; (2) one that targets timing when the likelihood of repeat giving is high due to lifetime, recency, and seasonal effects on baseline utility (i.e., conditions a, b, and c explained previously) but does not target individuals; and (3) one that targets both individuals and timing.¹⁰ In each strategy, we compare outcomes with the baseline case, in which the SRC does not reallocate appeals. To obtain the expected revenues in both counterfactual and baseline cases, we calculate the optimal expenditure using Equation 8. To compute the standard error of the revenue increase in each counterfactual scenario, we randomly draw 500 posterior samples of every parameter estimate and repeat the calculations.

In Figure 8, we show the “appeal elasticity of expected revenue” across different targeting strategies. We define appeal elasticity as the percentage gain in revenues relative to baseline for each strategy. The left panel indicates that from the “individual,” “timing,” and “both” strategies, the SRC can expect, on average, 1.12%, 1.37%, and 1.53% increases in the donation revenue, respectively. Targeting “when” is slightly more effective than targeting “who” in our empirical context. Further, as we expected, the gains from targeting both individuals and timing are the largest. Currently, the SRC conducts two untargeted appeal campaigns for donation in the spring and at the year-end, and our result indicates that the SRC has a lot of room for improving. The right panel indicates that individual targeting (i.e., strategy 1) results in a .32% decline in membership revenue. This is unsurprising because, currently, the SRC sends an appeal to individuals when their memberships are about to expire. Reallocating appeals to individuals who have high preference for membership is suboptimal because targeted timing is critical. However, we do find that sending membership renewal appeals at the right time, or targeting both the right individuals and the right time, can increase membership revenue by 1.30% and 1.94%, respectively.¹¹ Again, targeting “both” is significantly more effective than targeting “when” for the membership case as well. These analyses show that the SRC can be better off in terms of revenue with more targeted marketing efforts based on the model.

Figure 8.

Appeal elasticity of expected revenue across different targeting strategies.

Discussion and Conclusions

Nonprofit organizations play a central role in many economies in the form of private entities discharging a public purpose. Because individual philanthropy is the primary funding source for many such organizations, strengthening their fundraising capabilities can have a large impact on their survival, growth, and effectiveness. Our article is motivated by this goal. We propose an empirical model of giving behavior to an NPO that offers multiple giving options. To our knowledge, extant research does not consider this case. Our utility-based framework accounts for separate mechanisms that determine baseline utility and satiation for each giving option by modeling factors that affect individual giving decisions. A unique feature of our multiple discrete-continuous choice model is that it allows the structural parameters to dynamically change over time via Bayesian GPs. Incorporating the dynamics of structural parameters is important in modeling giving behavior because we expect the effects of lifetime, recency, seasonality, and responsiveness to appeals on baseline utility and satiation to change over time as the relationship between the giver and the NPO evolves. With our proposed model, managers of NPOs can manage more effectively.

Insights for Managing Giving

Our analysis of the five-year giving data of the SRC leads to several insights about how to better manage fundraising activities of NPOs. We summarize these insights next.

Multiple options to give are a pathway for committed givers

Some nonprofit organizations have questioned the need for maintaining two ways of individual giving (i.e., donation and membership), because they involve separate cost structures. These costs include administrative and managerial overheads, ongoing fundraising campaigns for donations, and costs of benefits provided to members. Our data indicate that a strategy of having multiple giving programs has two benefits. First, it allows differently motivated individuals to choose a form of giving that is best for them. Second, it creates a path for more committed givers to broaden and deepen their engagement over time by contributing in multiple forms (see Figures 1, 3, and 4). Further, data on individual characteristics and past giving that are easily available to the NPO can be helpful to identify those givers who are likely to adopt a second giving option in the future and thus enable the organization to focus its resources on cultivating such individuals (see Figure 7).

Emphasize participation, not amount

Our results show that givers exhibit greater responsiveness with respect to participation in a giving program than with the amount of donation or the membership tier (see the “How Effective Are Donation and Membership Appeals?” subsection). Although our data do not reveal the reasons for this, there is a clear implication for NPOs, which is to focus their efforts on encouraging repeat donations, membership renewals, and adding on a second form of giving. In our case, it is less useful to emphasize giving larger amounts or upselling to higher membership tiers.

Treat long-lapsed donors as new prospects

Given the low rates of repeat giving experienced by many NPOs, an important question facing the SRC and most NPOs in general is how to manage individuals who have not given for some time. In the case of donors, we learned that after two years since the last giving occasion, there is little positive predisposition to give again (see Figure 4). Therefore, the SRC should pursue donors for two years after their first giving occasion as potential repeat givers. Subsequently, these individuals may need the same level of effort as new prospects to be cultivated all over again.

Don’t give up on lapsed members too soon

In contrast to lapsed donors, members who have not renewed for several years are still positively predisposed to return to the NPO (see Figure 4). Thus, renewal efforts should be continued and may yield greater success than pursuing a new “cold” prospect for membership. Our recommendation is similar to one that follows from the “recency trap” in the context of customer relationship management (Neslin et al. 2013); because customers with higher recency (i.e., bought a long time ago) tend to have lower purchase likelihood now, the firm ignores them in its marketing, thereby making them even less likely to buy in the current and subsequent periods. Moreover, relative to new prospects, the NPO knows more about lapsed members’ interests and motivations given data on their past usage of the NPO’s products and services, thereby allowing customized marketing.

Optimize the timing of appeals

In the case of the SRC, appeals for donations have been inconsistently effective in the data (see Figure 6). This suggests room to improve, perhaps through reassignment of appeals via targeting. Our analysis indicates directions to guide such targeting, in particular, that targeting “when” an appeal is sent is likely to be more fruitful than “to whom” an appeal is sent (see Figure 8). Of course, there may also be room to improve through personalization of the content of appeals, but our data are unable to speak to this question. By contrast, membership appeals, whose timing is already targeted, are effective, with one caveat. The SRC may be sending too many renewal appeals (the average “pure member” currently gets 3.3 appeals each year), creating a negative effect (see Web Appendix G). Understanding this issue better may require focus groups or surveys of current members.

To what extent do our findings based on the organization we studied extend to the context of nonprofits more broadly? Interested givers are very diverse in terms of their level of engagement with the inherent subject (i.e., the animal species), the utility they derive from the content, and their capacity to give. In this respect, our SRC is likely to be similar to many NPOs that are engaged with arts, culture and entertainment (e.g., theaters, galleries, museums, historic preservation societies), and the environment (e.g., botanical gardens, parks, conservation societies), and we expect that many of our findings about giving behaviors may readily translate. For instance, in these settings, it is possible to construct multitiered membership programs with well-defined benefit packages that are tied to the central mission of the NPO. By contrast, our findings are likely to be less applicable to NPOs that are engaged in contexts such as religion (churches), health care (hospitals), or education (universities), because the concept of membership is less natural in these settings.

Fundraising for a Better World

As noted in the introduction, nonprofit organizations often play key roles in domains such as health, education, the arts, and conservation of the environment and animals. Successful fundraising is critical to the survival and health of most nonprofits; however, fundraising is costly, resulting in a dilution of their full potential impact on the world. An important reason for the high cost of fundraising is the inordinate focus on acquiring new givers because of low repeat giving rates. Our research highlights the need and the opportunity to use data and marketing science tools to understand how individuals’ motivations for giving evolve over time and thereby develop strategies to increase giving rates and amounts. In particular, we examine the strategy of using multiple forms of giving that provides a path for committed givers to grow their giving over time. The net effect of employing these tools should be that a larger percentage of funds raised can be deployed in the service of the mission of the nonprofit.

Limitations and Future Research

Our study has the following limitations and leaves open several directions for future research. First, we did not model nonfinancial contributions such as volunteering or donations in kind, although these are important aspects of giving. In future research, it will be important to accommodate the value of nonfinancial contributions within the model.

Second, our model and data account for only one focal NPO. In reality, individuals often give to more than one organization and NPOs compete with one another for philanthropic dollars. The NPO we study is involved in a very specific scientific research area (an animal species), and therefore does not face much direct competition. However, in other contexts, competition can be intense between NPOs or between NPOs and for-profits. Therefore, modeling competitive interactions in giving can be a fruitful avenue for future studies.

Finally, the sparsity of our data (e.g., annual frequency of giving is 1.1) hinders modeling the evolution of parameters at the individual level; thus, we only allow for population-level evolution of parameters. In other applications, disaggregating the population-level evolution of parameters to the individual level may reveal additional layers of important insights.

In summary, our work examines the who, when, and why of individual-level giving to an NPO. We hope that our framework enables NPOs’ fundraising strategies to be more effective, thereby empowering them to contribute more to a better world.

Supplemental Material

Supplemental Material, sj-lyx-1-jmx-10.1177_0022242921994587 - Managing Members, Donors, and Member-Donors for Effective Nonprofit Fundraising

Supplemental Material, sj-lyx-1-jmx-10.1177_0022242921994587 for Managing Members, Donors, and Member-Donors for Effective Nonprofit Fundraising by Sungjin Kim, Sachin Gupta and Clarence Lee in Journal of Marketing

Supplemental Material

Supplemental Material, sj-pdf-1-jmx-10.1177_0022242921994587 - Managing Members, Donors, and Member-Donors for Effective Nonprofit Fundraising

Supplemental Material, sj-pdf-1-jmx-10.1177_0022242921994587 for Managing Members, Donors, and Member-Donors for Effective Nonprofit Fundraising by Sungjin Kim, Sachin Gupta and Clarence Lee in Journal of Marketing

Footnotes

Acknowledgments

This paper is based on the first author’s doctoral dissertation at Cornell University. The authors are grateful to the management and staff of the anonymous scientific research center, who were very generous with their time, wisdom, and data. This article truly benefited from the constructive feedback of the JM review team. The authors also appreciate feedback from seminar participants at Cornell University, McGill University, the University of Texas at Dallas, and the Marketing Dynamics Conference 2018.

Associate Editor

Scott Neslin

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Sungjin Kim

Sachin Gupta

Clarence Lee

Online supplement:

Notes

References

Allenby

Greg M.

Rossi

Peter E.

(1998), “Marketing Models of Consumer Heterogeneity,” Journal of Econometrics, 89 (1/2), 57–78.

Andreoni

James

(1989), “Giving with Impure Altruism: Applications to Charity and Ricardian Equivalence,” Journal of Political Economy, 97 (6), 1447–58.

Andreoni

James

(1990), “Impure Altruism and Donations to Public Goods: A Theory of Warm-Glow Giving,” Economic Journal, 100 (401), 464–77.

Andreoni

James

Payne

A. Abigail

(2011), “Is Crowding Out Due Entirely to Fundraising? Evidence from a Panel of Charities,” Journal of Public Economics, 95 (5/6), 334–43.

Andreoni

James

Payne

A. Abigail

(2013), “Charitable Giving,” Handbook of Public Economics, 5, 1–50.

Ariely

Dan

Bracha

Anat

Meier

Stephan

(2009), “Doing Good or Doing Well? Image Motivation and Monetary Incentives in Behaving Prosocially,” American Economic Review, 99 (1), 544–55.

Arora

Neeraj

Allenby

Greg M.

Ginter

James L.

(1998), “A Hierarchical Bayes Model of Primary and Secondary Demand,” Marketing Science, 17 (1), 29–44.

Austin

Amy

(2016), “Two Thirds of Countries Offer Individual Tax Incentives on Charity Donations,” Accountancy Daily (May 17), https://www.accountancydaily.co/two-thirds-countries-offer-individual-tax-incentives-charity-donations.

Auten

Gerald E.

Sieg

Holger

Clotfelter

Charles T.

(2002), “Charitable Giving, Income, and Taxes: An Analysis of Panel Data,” American Economic Review, 92 (1), 371–82.

10.

Bartlett

Monica Y.

DeSteno

David

(2006), “Gratitude and Prosocial Behavior: Helping When It Costs You,” Psychological Science, 17 (4), 319–25.

11.

Belleflamme

Paul

Omrani

Nessrine

Peitz

Martin

(2015), “The Economics of Crowdfunding Platforms,” Information Economics and Policy, 33, 11–28.

12.

Bénabou

Roland

Tirole

Jean

(2006), “Incentives and Prosocial Behavior,” American Economic Review, 96 (5), 1652–78.

13.

Bhat

Chandra R.

(2005), “A Multiple Discrete-Continuous Extreme Value Model: Formulation and Application to Discretionary Time-Use Decisions,” Transportation Research Part B: Methodological, 39 (8), 679–707.

14.

Bhat

Chandra R.

(2008), “The Multiple Discrete-Continuous Extreme Value (MDCEV) Model: Role of Utility Function Parameters, Identification Considerations, and Model Extensions,” Transportation Research Part B: Methodological, 42 (3), 274–303.

15.

Bhattacharya

C.B.

(1998), “When Customers Are Members: Customer Retention in Paid Membership Contexts,” Journal of the Academy of Marketing Science, 26 (1), 31–44.

16.

Bhattacharya

C.B.

Rao

Hayagreeva

Glynn

Mary Ann

(1995), “Understanding the Bond of Identification: An Investigation of Its Correlates Among Art Museum Members,” Journal of Marketing, 59 (4), 46–57.

17.

Blanken

Irene

van de Ven

Niels

Zeelenberg

Marcus

(2015), “A Meta-Analytic Review of Moral Licensing,” Personality and Social Psychology Bulletin, 41 (4), 540–58.

18.

Chiang

Jeongwen

(1991), “A Simultaneous Approach to the Whether, What and How Much to Buy Questions,” Marketing Science, 10 (4), 297–315.

19.

Chintagunta

Pradeep K.

(1993), “Investigating Purchase Incidence, Brand Choice and Purchase Quantity Decisions of Households,” Marketing Science, 12 (2), 184–208.

20.

Chuan

Amanda

Kessler

Judd B.

Milkman

Katherine L.

(2018), “Field Study of Charitable Giving Reveals That Reciprocity Decays over Time,” Proceedings of the National Academy of Sciences, 115 (8), 1766–71.

21.

DellaVigna

Stefano

List

John A.

Malmendier

Ulrike

(2012), “Testing for Altruism and Social Pressure in Charitable Giving,” Quarterly Journal of Economics, 127 (1), 1–56.

22.

Dew

Ryan

Ansari

Asim

(2018), “Bayesian Nonparametric Customer Base Analysis with Model-Based Visualizations,” Marketing Science, 37 (2), 216–35.

23.

Dew

Ryan

Ansari

Asim

Yang

(2020), “Modeling Dynamic Heterogeneity Using Gaussian Processes,” Journal of Marketing Research, 57 (1), 55–77.

24.

Dickert

Stephan

Sagara

Namika

Slovic

Paul

(2011), “Affective Motivations to Help Others: A Two-Stage Model of Donation Decisions,” Journal of Behavioral Decision Making, 24 (4), 361–76.

25.

Fajardo

Tatiana M.

Townsend

Claudia

Bolander

Willy

(2018), “Toward an Optimal Donation Solicitation: Evidence from the Field of the Differential Influence of Donor-Related and Organization-Related Information on Donation Choice and Amount,” Journal of Marketing, 82 (2), 142–52.

26.

Falk

Armin

(2007), “Gift Exchange in the Field,” Econometrica, 75 (5), 1501–11.

27.

Gelman

Andrew

Rubin

Donald B.

(1992), “Inference from Iterative Simulation Using Multiple Sequences,” Statistical Science, 7 (4), 457–72.

28.

Gerber

Elizabeth M.

Hui

Julie.

(2013), “Crowdfunding: Motivations and Deterrents for Participation,” ACM Transactions on Computer-Human Interaction, 20 (6), 1–32.

29.

Gęsiarz

Filip

Crockett

Molly J.

(2015), “Goal-Directed, Habitual and Pavlovian Prosocial Behavior,” Frontiers in Behavioral Neuroscience, 9, 135.

30.

Giving USA (2020), “Giving USA 2020: The Annual Report on Philanthropy for the Year 2019,” technical report.

31.

Gneezy

Uri

Rustichini

Aldo

(2000), “Pay Enough or Don’t Pay at All,” Quarterly Journal of Economics, 115 (3), 791–810.

32.

Hanemann

W. Michael

(1984), “Discrete/Continuous Models of Consumer Demand,” Econometrica, 52 (3), 541–61.

33.

Heckman

James J.

(1981), “Heterogeneity and State Dependence,” in Studies in Labor Markets, Rosen

Sherwin

, ed. Chicago: University of Chicago Press, 91–140.

34.

Hrywna

Mark

(2019), “NPT Top 100 (2019): An In-Depth Study of America’s Largest Nonprofits,” The Nonprofit Times (November 4), https://www.thenonprofittimes.com/report/npt-top-100-2019-an-in-depth-study-of-americas-largest-nonprofits/.

35.

Kallman

Megan E.

Clark

Terry N.

(2016), The Third Sector: Community Organizations, NGOs, and Nonprofits. Champaign: University of Illinois Press.

36.

Khan

Uzma

Dhar

Ravi

(2006), “Licensing Effect in Consumer Choice,” Journal of Marketing Research, 43 (2), 259–66.

37.

Khodakarami

Farnoosh

Petersen

J. Andrew

Venkatesan

Rajkumar

(2015), “Developing Donor Relationships: The Role of the Breadth of Giving,” Journal of Marketing, 79 (4), 77–93.

38.

Kim

Jaewhan

Allenby

Greg M.

Rossi

Peter E.

(2002), “Modeling Consumer Demand for Variety,” Marketing Science, 21 (3), 229–50.

39.

Kumar

Sharma

Amalesh

Donthu

Naveen

Rountree

Carey

(2015), “Practice Prize Paper—Implementing Integrated Marketing Science Modeling at a Non-Profit Organization: Balancing Multiple Business Objectives at Georgia Aquarium,” Marketing Science, 34 (6), 804–14.

40.

Kuppuswamy

Venkat

Bayus

Barry L.

(2018), “A Review of Crowdfunding Research and Findings,” in Handbook of Research on New Product Development, Golder

Peter N.

Mitra

Debanjan

, eds. Cheltenham, UK: Edward Elgar Publishing Section, 361–73.

41.

Leliveld

Marijke C.

Risselada

Hans

(2017), “Dynamics in Charity Donation Decisions: Insights from a Large Longitudinal Data Set,” Science Advances, 3 (9), e1700077.

42.

List

John A.

(2011), “The Market for Charitable Giving,” Journal of Economic Perspectives, 25 (2), 157–80.

43.

Malani

Anup

Philipson

Tomas

David

Guy

(2003), “Theories of Firm Behavior in the Nonprofit Sector. A Synthesis and Empirical Evaluation,” in NBER Chapters. Cambridge, UK: National Bureau of Economic Research, Inc, 181–216.

44.

Manchanda

Puneet

Rossi

Peter E.

Chintagunta

Pradeep K.

(2004), “Response Modeling with Nonrandom Marketing-Mix Variables,” Journal of Marketing Research, 41 (4), 467–78.

45.

Meer

Jonathan

Rosen

Harvey S.

(2011), “The ABCs of Charitable Solicitation,” Journal of Public Economics, 95 (5), 363–71.

46.

Mehta

Nitin

Chen

Xinlei J.

Narasimhan

(2010), “Examining Demand Elasticities in Hanemann’s Framework: A Theoretical and Empirical Analysis,” Marketing Science, 29 (3), 422–37.

47.

Midlarsky

Hannah

M. E.

(1989), “The Generous Elderly: Naturalistic Studies of Donations Across the Life Span,” Psychology and Aging, 4 (3), 346–51.

48.

Morgan

John

(2000), “Financing Public Goods by Means of Lotteries,” Review of Economic Studies, 67 (4), 761–84.

49.

Nair

Harikesh

Dubé

Jean-Pierre

Chintagunta

Pradeep

(2005), “Accounting for Primary and Secondary Demand Effects with Aggregate Data,” Marketing Science, 24 (3), 444–60.

50.

National Council of Nonprofits (2019), “Nonprofit Impact Matters: How America’s Charitable Nonprofits Strengthen Communities and Improve Lives,” technical report (accessed February 24, 2021), https://www.nonprofitimpactmatters.org/site/assets/files/1/nonprofit-impact-matters-sept-2019-1.pdf.

51.

Neslin

Scott A.

Taylor

Gail A.

Grantham

Kimberly D.

McNeil

Kimberly R.

(2013), “Overcoming the ‘Recency Trap’ in Customer Relationship Management,” Journal of the Academy of Marketing Science, 41 (3), 320–37.

52.

Netzer

Oded

Lattin

James M.

Srinivasan

(2008), “A Hidden Markov Model of Customer Relationship Dynamics,” Marketing Science, 27 (2), 185–204.

53.

Newman

George E.

Shen

Y. Jeremy

(2012), “The Counterintuitive Effects of Thank-You Gifts on Charitable Giving,” Journal of Economic Psychology, 33 (5), 973–83.

54.

Rasmussen

Carl E.

Williams

Christopher K.I.

(2005), Gaussian Processes for Machine Learning. Cambridge, MA: MIT Press.

55.

Roberts

Osborne

Ebden

Reece

Gibson

Aigrain

(2013), “Gaussian Processes for Time-Series Modelling,” Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 371 (1984), 1–25.

56.

Sargeant

Adrian

Woodliffe

Lucy

(2007), “Gift Giving: an Interdisciplinary Review,” International Journal of Nonprofit & Voluntary Sector Marketing, 12 (4), 275–307.

57.

Satomura

Takuya

Kim

Jaewhan

Allenby

Greg M.

(2011), “Multiple-Constraint Choice Models with Corner and Interior Solutions,” Marketing Science, 30 (3), 481–90.

58.

Sethuraman

Raj

Tellis

Gerard J.

Briesch

Richard A.

(2011), “How Well Does Advertising Work? Generalizations from Meta-Analysis of Brand Advertising Elasticities,” Journal of Marketing Research, 48 (3), 457–71.

59.

Simpson

Brent

Willer

Robb

(2008), “Altruism and Indirect Reciprocity: The Interaction of Person and Situation in Prosocial Behavior,” Social Psychology Quarterly, 71 (1), 37–52.

60.

Stiffman

Eden

(2020), “Giving was up 7.5% in the First Half of 2020,” The Chronicle of Philanthropy (October 6), https://www.philanthropy.com/article/giving-was-up-7-5-in-the-first-half-of-2020-new-report-says.

61.

Touré-Tillery

Maferima

Fishbach

Ayelet

(2017), “Too Far to Help: The Effect of Perceived Distance on the Expected Impact and Likelihood of Charitable Action,” Journal of Personality and Social Psychology, 112 (6), 860–76.

62.

Tuchman

Anna E.

Nair

Harikesh S.

Gardete

Pedro M.

(2018), “Television Ad-Skipping, Consumption Complementarities and the Consumer Demand for Advertising,” Quantitative Marketing and Economics, 16 (2), 111–74.

63.

Van Diepen

Merel

Donkers

Bas

Franses

Philip H.

(2009), “Dynamic and Competitive Effects of Direct Mailings: A Charitable Giving Application,” Journal of Marketing Research, 46 (1), 120–33.

64.

Weisbrod

Burton A.

(1998), To Profit or Not to Profit: The Commercial Transformation of the Nonprofit Sector. Cambridge, UK: Cambridge University Press.

65.

White

Katherine

Habib

Rishad

Dahl

Darren W.

(2020), “A Review and Framework for Thinking about the Drivers of Prosocial Consumer Behavior,” Journal of the Association for Consumer Research, 5 (1), 2–18.

66.

Winterich

Karen

Mittal

Vikas

Ross

William T.

Jr (2009), “Donation Behavior Toward In-Groups and Out-Groups: The Role of Gender and Moral Identity,” Journal of Consumer Research, 36 (2), 199–214.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.05 MB

0.81 MB