NGO mission design

Accepted Manuscript Title: NGO Mission Design Author: Anthony Heyes Steve Martin PII: DOI: Reference:

S0167-2681(15)00223-1 http://dx.doi.org/doi:10.1016/j.jebo.2015.08.007 JEBO 3646

To appear in:

Journal

Received date: Revised date: Accepted date:

9-12-2014 13-8-2015 15-8-2015

of

Economic

Behavior

&

Organization

Please cite this article as: Anthony Heyes, Steve Martin, NGO Mission Design, Journal of Economic Behavior and Organization (2015), http://dx.doi.org/10.1016/j.jebo.2015.08.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

*Highlights (for review)

• We model the mission statement design of non-governmental organizations (NGOs) and how it affects donations and project quality. • We contrast mission-width and donor-width as alternative concepts of NGO scope—in equilibrium they do not coincide.

the impactfulness of the sector.

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• There is excess entry into the quasi-market for impact.

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• Competing NGOs choose missions that are too narrow and overlap, reducing

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Title Page (with Full Author Details)

NGO Mission Design∗ Steve Martin Department of Economics University of Ottawa 120 University Private Canada K1N 6N5

Abstract

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Anthony Heyes Department of Economics University of Ottawa 120 University Private Canada K1N 6N5

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NGOs compete in mission statements. Opportunities for impact vary across issues—NGOs with broader missions expect to execute higher-impact projects but provide less precision to donors as to the sorts of projects that will be funded. This matters if donors have preferences among issues. The mission-design problem faced by an impact-motivated NGO is analyzed. Interestingly, expected donations are non-monotonic in mission-width. A monopoly NGO engages in “donorstretching,”choosing a mission statement that includes issues not preferred by any of its donors, but still narrower than socially desirable. Under free entry, issue-widths are strategic complements among NGOs. In equilibrium there are too many NGOs, each with too narrow a mission. The issue-space is exactly donor-covered (all donors will have an NGO they wish to give to) but issue over-covered (mission statements overlap). Expected NGO impact is higher at issues at the periphery of any particular NGO’s issue-domain, which is socially inefficient. Keywords: NGOs, donations, mission statement design. JEL Classification: D4, H8, L12

∗ Heyes is corresponding author ([email protected]). We are grateful to colleagues at the LSE, UCL, McGill University, WCERE (Istanbul 2014), the Public Choice Society Annual Conference (Charleston 2014) and two referees and an editor of this journal for constructive advice. We acknowledge the generous financial support of SSHRC under its Insight Program (Grant Number 435-2012-472) and the Canada Research Chairs Program in the execution of this research. Errors are ours.

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*Manuscript

NGO Mission Design∗ Steve Martin

Department of Economics

Department of Economics

University of Ottawa

University of Ottawa

120 University Private

120 University Private

Canada K1N 6N5

Canada K1N 6N5

an

Abstract

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Anthony Heyes

NGOs compete in mission statements. Opportunities for impact vary across issues—NGOs with broader missions expect to execute higher-impact projects but provide less precision to donors as to the sorts of projects that

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will be funded. This matters if donors have preferences among issues. The mission-design problem faced by an impact-motivated NGO is analyzed. Interestingly, expected donations are non-monotonic in mission-width. A

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monopoly NGO engages in “donor-stretching,”choosing a mission statement

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that includes issues not preferred by any of its donors, but still narrower than socially desirable. Under free entry, issue-widths are strategic complements among NGOs. In equilibrium there are too many NGOs, each with

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too narrow a mission. The issue-space is exactly donor-covered (all donors will have an NGO they wish to give to) but issue over-covered (mission statements overlap). Expected NGO impact is higher at issues at the periphery of any particular NGO’s issue-domain, which is socially inefficient. Keywords: NGOs, donations, mission statement design. JEL Classification: D4, H8, L12

∗

Heyes is corresponding author ([email protected]). We are grateful to colleagues at the LSE, UCL, McGill University, WCERE (Istanbul 2014), the Public Choice Society Annual Conference (Charleston 2014) and two referees and an editor of this journal for constructive advice. We acknowledge the generous financial support of SSHRC under its Insight Program (Grant Number 435-2012-472) and the Canada Research Chairs Program in the execution of this research. Errors are ours.

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Introduction A refresher: What’s the first rule of nonprofits? That’s right: MISSION, MISSION, and more MISSION. If you are a donor you are drawn by what? The same thing that attracts the staff and volunteers: The

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mission - what the organization does. (Brinckerhoff, 2009, p. 195)

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Non-governmental Organizations (NGOs) play vital roles in society, from combating animal cruelty in North American farming to fighting climate change to protecting historic buildings in war zones.1 Yet the “industrial organization” of

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the sector has been subject to comparatively little formal analysis. In particular there has been no analysis of economies of scope in the sector, and the resulting

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implications for understanding organizational width. Our focus is on NGO mission design. An NGO is defined by its mission statement; its “turf.”2 Here we treat mission design as a key strategic institution-design decision that affects both volume of donations and quality of impact-opportunities. This is consistent with the advice that “if mission is your most important resource

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(and it is), you need to get the most from this resource in every way, every day.” (Brinckerhoff, 2009, p. 39). Under plausible assumptions, mission design can be expected to affect both

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the type and quality (in a sense to be defined) of projects that the NGO ends up executing, and so how attractive it is to prospective donors of varying tastes. We model the design of mission statement—in particular its width—and develop a series of new positive and normative results. How does an NGO decide what set of issues to include in its mission statement? How is that choice affected

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by competition? What are the welfare properties of the choices made? NGOs are set-up by social entrepreneurs who are impact-motivated in the spirit of Duncan (2004), Scharf (2014) and others. Donors have spatially-adjusted warm 1

There is not a universally accepted definition of an NGO. For our purpose an NGO is an entity funded by donations and doing “good deeds” on a not-for-profit basis. For more discussion of definitions, see Salamon and Anheier (1992), Willetts (2002), and Yaziji and Doh (2009). 2 NGOs choose how wide a mission statement to adopt. Compare for example Save the Whales (issue-narrow) with the WWF (issue-wide). The model here has quite a few “moving parts” and the equilibria that we characterize are symmetric—not allow for coexistence of narrow and broad missions—but permits us to characterize the strategic considerations that go into mission design. We point to extensions of the model that generate heterogeneity.

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glow preferences—they prefer their dollars be directed to high impact projects, but also have varying preferences among issues (Baron, 2010). We envisage a simple three-step process. At the start an NGO is defined—publishes a mission statement. This is the institution-design stage. On the basis of that mission statement it receives donations. Impact opportunities of varying “quality” then arise as a result of stochastic external events and the NGO directs funds to opportunities that arise

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within the set of issues contained in its mission statement such as to maximize impact. In this horizontal setting an NGO effectively offers the prospective donor

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a lottery over how his donation will be used. The mission statement constrains the NGO in the projects it might execute (Save the Tiger cannot devote funds to saving dolphins) and so the support and terms of the lottery that donors are

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offered. We first consider a monopoly NGO, examining mission-design by a single social

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entrepreneur in isolation. As well as a natural measure of scale (total funds raised, which equals total expenditure on projects) our analysis points to two distinct notions of NGO scope. First, issue-domain—the set of activities/issues that are

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included in its mission. Second, donor-domain—the set of donor types that choose to support it. These do not coincide in equilibrium in either a single-NGO or the

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quasi-market setting that is the focus of the second part of the paper. This paper adds to the small existing set of model that feature horizontallydifferentiated charities or NGOs. Rose-Ackerman (1982) models a fixed number of nonprofits, varying in a dimension called ideology, deciding what portion of donor revenues to devote to fund-raising effort. Fund-raising effort is mutually-

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offsetting so non-cooperative choices lead to socially excessive fund-raising in the sector. Most of the subsequent literature focuses on this sort of inefficiency in fund-raising/advertising effort. Aldashev and Verdier (2010) develop a model in which prospective donors care about issues but do not know of the existence of an NGO and so need to be “awakened” (e.g. by leaflet, television advertising), corresponding to the notion of charities’ “power to ask” (Andreoni and Payne, 2013). We consciously exclude fund-raising effort from the model altogether (while acknowledging its significance) to ensure none of the results here are driven by the fund-raising externalities that have been the focus of the prior research. In Pestieau and Sato (2006), charities—all focused on the same issue—attract donations by 3

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virtue of ideological proximity with free entry of leading to a excessive entry. Morales-Belpaire (2012) considers the design of a mission for a single NGO, without competitors, as coverage of a target population. In all of these contributions a charity is single-issue—there is no concept of mission width. Economides and Rose-Ackerman (1993), Bilodeau and Slivinski (1997), and Sandford and Scharf (2012) also model the decentralized provision

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of local public goods but in quite different ways and addressing quite different questions. These papers complement a much larger literature on charitable giving

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and public goods games that take place in a single-issue setting (see Bilodeau and Steinberg (2006) or Andreoni and Payne (2013) for review). Our analysis departs from existing contributions in a number of important

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ways. An NGO has mission “width” in a continuous issue-space. Further, by recognizing that NGO impact-opportunities are likely to vary across the issue-

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space according to external events we are able to make explicit and endogenous the issue-location of projects that NGOs execute and the impact per dollar disbursed.3 Mission statement design, donations and impact-outputs are codependent in subtle

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ways. The remainder of the paper proceeds as follows. Section 2 presents the core of

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the model. The key elements that we build into the model are as follows:

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• Social entrepreneurs are impact-motivated such that the NGOs that they establish are analogous to warm glow charities (Scharf, 2014) or impact philanthropists (Duncan, 2004).

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• The mission statement is a key institution-design feature. Impact opportunities vary across issues in a stochastic way according to external events with realizations apparent only after the mission statement has been written.

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In their pioneering model, Bilodeau and Slivinski (1997) allow nonprofits to contribute to two different public goods in varying proportions. Our model is quite different. In particular, the “doing” stage and the conception/role of mission are unique to us. We introduce the plausible assumption that an NGO will face varying impact opportunities after it has defined a mission (everything in Bilodeau and Slivinski is deterministic) such that an NGO offers a donor a lottery over how his dollar will be spent. Most importantly their paper does not touch on missiondefinition as a strategic instrument in sourcing both donations and impact-opportunities, our central focus here. Identical comments apply to the paper on NGO fragmentation by Sandford and Scharf (2012).

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• Mission statements have “width”—they are not simply points in issue-space— and can be used by an NGO as a strategic instrument in the pursuit of both donations and impact opportunities.

Model

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Section 3 considers competition among NGOs, section 4 concludes. All proofs are in the Appendix.

Setting

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There is a set of social, environmental or other issues, the solution to which an NGO might contribute. More concretely there exists an issue-space that can be represented by the circumference of a unit circle, L. The circle has been widely-

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used in economics as a space within which to model diversity. Salop (1979), for example, uses a product-characteristic circle to analyze the incentives for product

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differentiation in oligopoly. It has been applied to models of charitable giving by Pestieau and Sato (2006), Aldashev and Verdier (2010) and self-regulation by Baron (2010). The issue-space circle is illustrated in Figure 1 where issue x1 is

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threat of elephant extinction and issue x2 is threat of rhinoceros extinction. To be consistent with a more straight-forward geographical interpretation of the issue-

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space, we could alternatively label x1 and x2 as “environmental damage in Peru” and “environmental damage in Mozambique”. The analysis that follows could equally be conducted on a line of infinite length.

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After an NGO is defined opportunities for impact arise according to external events. Elephants may be particularly threatened this season because of a particular weather event, or socioeconomic events that influence pressure from poachers. More generally—and plausibly—the impact generated by a dollar of NGO effort will vary across issues in a way that is not known (or known fully) at the moment the NGO is constituted.4 To formalize this notion, define a function b : L → R+ ; b(x) that describes the marginal (= average) impact or benefit of 4

We use the terms impact and benefit interchangeably as a location-neutral term to describe the productivity of NGO expenditure at a point in L. How that impact is valued by any particular prospective donor will also depend on the donor’s preferences among locations.

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x2 = threat of rhinoceros extinction

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x1 = threat of elephant extinction

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Figure 1: Issue-space.

the expenditure of a dollar of resources at each location x.5 Those beneficiaries

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reside outside the circle (they are the elephants saved or environmental damage thwarted) but prospective donors derive a warm glow type satisfaction from contributing to them (Andreoni, 1990). No restriction is placed on b(x) except that

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it is everywhere non-negative. Importantly the NGO manager knows b(x) at the moment he is deciding how to allocate funds between projects, but it is not re-

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alized at the time the NGO is designed (the mission statement determined). For illustration, one possible function b is sketched in Figure 2 for a portion of L. Our model is the first formal analysis of NGOs to recognize that the productivity of resources spent will vary across locations in the issue-space, and it is crucial to our results. It is also the first model to apply the notion of scope to NGOs, and

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the two elements are connected. In particular, the incentive for an NGO to want to widen its scope will be driven by the recognition that a wider mandate gives it more flexibility to seek out high-impact opportunities. We develop this argument more fully once we specify what an NGO is. 5

Characterizing the technology of producing social benefit as constant returns to scale may be inappropriate if multiple NGOs channel funds towards an issue. Two points recommend making such an assumption however: i) it seems reasonable when funds are small relative to social impact, and ii) it takes no stances on economies of scope with provision by multiple NGOs. In any case, this assumption is without loss of generality given the particular issue space. It is also worth pointing out that each NGO has the same technology of producing social benefit. Introducing heterogeneity in technology could produce NGOs with differing scopes, although this line of inquiry will not be pursued.

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b(xj )

Figure 2: Impact opportunities vary across issues.

An NGO

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xj

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An NGO in this model is defined by its mission statement. We treat this as an institution-design choice to which the NGO commits. There are number of ways to motivate such an assumption (e.g., building of reputation) but in passing we

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note the legal significance of mission statements:

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The mission statement is not only the reason you donate to or volunteer for an organization but it also has important legal implications for staff

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and board. If you do not perform your mission, in the United States, the IRS can take away your tax-exempt status under section 501(c) of the Internal Revenue Code. The same holds true in other countries

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around the world. (Brinckerhoff, 2009, p. 39) We operationalize the notion of a mission statement as follows:

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Definition 1 (Issue-domain) The “issue-domain” I ⊂ L of an NGO contains the set of issues to which the NGO may direct funds. It is assumed to be compact   and convex, such that for NGO i, Ii = ℓi − w2i , ℓi + w2i where it has location ℓi ∈ L and issue-width wi .

In the example in Figure 3, NGO i has a mission statement that describes Ii . It may devote funds it raises to issue xj ∈ Ii , but not to issue xk which lies outside its issue-domain. Save the Tigers cannot devote funds to saving dolphins. Of course this is a simplification. In a repeated setting NGOs may from time to time choose to redefine themselves by updating their missions, but we abstract 7

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Ii xj w 2

ℓi +

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Figure 3: Issue-domain of NGO i.

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xk

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from that here. Equally we acknowledge that on occasion a new NGO may form

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specifically in response to an impact-opportunity—such as a particular environmental or humanitarian crisis—but this is a different setting to ours. Here mission

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is treated as an institutional-design characteristic that is set in advance. The notion of issue-domain allows us to differentiate between narrow and wide NGOs in a way that has not been done before, and indeed would not have made any sense in the sorts of settings in which formal modeling of NGOs has previously been conducted.

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Social entrepreneurs do not have location preferences, but rather seek to maximize the expected impact that their NGO generates. In other words, the social entrepreneur wants to “do good,”but does not mind where in the issue-space he

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does it (following, for example, Scharf (2014)). This is clearly one of a number of alternative assumptions that we could have made here and is consistent with, for example, the theory of impact philanthropy (Duncan, 2004). Examples of NGO founders consistent with such an assumption can be found in A&S Perspectives (2009).

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Keeping with the notion of impact philanthropy, NGOs are assumed to care only about the social output they produce. While a strong assumption, it is fairly standard in the literature on competing NGOs (e.g., Aldashev and Verdier (2010)) and helps to keep the model focused on competition. Scharf (2014, p. 50) further motivates this assumption. To the extent that charities (or the non-profit entrepreneurs who run them) are prosocially motivated, they care about what they provide. However, they also typically favour their own output relative to that of 8

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other providers—which is why, for example, they compete with charities similar to themselves for available funds. In establishing an NGO the social entrepreneur defines an issue-domain (that is writes down a mission statement). The realization of b(x) is not known at that

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time but the process that generates it is understood (we will formalize this below). Once established, we conceptualize an NGO working in the following way: (a) It collects donations (we will discuss the donation decision shortly), (b) the social

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the NGO directs the funds it collects to xmax (Ii ) where

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entrepreneur observes b(x) for all x ∈ I (learns the opportunities for impact within his domain) and, (c) directs the funds to have maximum impact. Formally, then,

xmax (Ii ) = arg max{b(x)|x ∈ Ii }.

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The NGO channels all of its resources towards the single location where it will produce the largest marginal (= average) benefit.6 Note that ex-ante there is an equal likelihood of funds going to any particular location in the NGO’s issue-

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domain. The assumption that the NGO allocates money in this way is consistent with the observation that modern NGOs increasingly use cost-benefit analysis to

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choose between candidate projects (see for discussion Bond (2012), Copper (2012)). It is useful to define β(w) as the expected marginal (= average) impact of funds spent by an NGO of issue-width w. As should be obvious, β ′ (w) > 0—a wider NGO expects to be able to pick a higher impact project because it has a wider set of candidate issues amongst which to choose. It is intuitive to suppose that

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β ′′ (w) < 0 —as an NGO becomes wider, the expected value of the best project that it finds is increasing, but at a decreasing marginal rate.7 6

Our assumption that b(x) is both marginal and average benefit at location x—there is not, for example, diminishing marginal productivity to expenditure at the project level—removes outcomes in which funds are spread across more than one project in the domain. 7 It is straight-forward to provide micro-foundations for such an assumption. Consider for example w as analogous to the sample size n of a random variable X distributed uniformly over the support [0, 1]. Define M (n) as the expected maximum value of X for a given sample size (given n draws) and consider how M varies with n. Taking some arbitrary value x, the probability that this realization is the maximum from n random draws from the sample is nxn−1 . Integrating over all realizations of X gives M (n) = n/(n + 1) such that M ′ (n) = 1/(n + 1)2 > 0 and M ′′ (n) = −2/(n + 1)3 < 0. If we imagine starting with a value α, then the maximum expected value will be M (n) = α + n/(n + 1).

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The β function describes a feature of the underlying stochastic process which generates impact-opportunities and our analysis does not require that we adopt a particular functional form for it. However when we later note a condition that it is useful for β to satisfy we will demonstrate that it holds for the functional form w 1+w

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β(w) = α +

(where α is some positive constant) which is what comes out of the intuitive micro-

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foundation in footnote 7. The results in the paper do not rest on this functional form—they are more general.

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The NGO’s issue-domain is fixed at the start—an institution-design variable established when the NGO is set up. In this paper we consider only a single round of donations and operations. It would, however, be natural to think of

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repetition of the donation/operation cycle. With realizations of b(x) varying period to period, an NGO that is defined by an issue-domain that is fixed through time by constitution would collect donations each period and direct those donations to

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wherever within its issue-domain the benefits are greatest at that time.8 Next we turn to the question of how NGOs attract donations. Once we have

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described donor preferences, we characterize how the amount of funds available to an NGO is sensitive to its issue-domain in a non-obvious way.

We assume there is a set of risk neutral donor types Θ = L, with a mass of donors uniformly distributed on Θ,9 with the following characteristics:

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1. Donors care about the impact of their donation; other things being equal, a donor prefers their funds going to issue x over x′ if b(x) > b(x′ ).

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Extra complexity would be introduced if the NGO were also permitted to move resource between periods, by saving or borrowing. If realized values of b(x) for all x ∈ I happened to be low in a particular period, for example, an NGO interested in the maximizing the net present value of benefits, might choose to save some of that period’s donations for future periods when the impact of its activities are greater. 9 Having a non-uniform distribution of donors may generate NGOs with asymmetric missions. Such an approach, however, introduces considerable difficulties and will not be pursued here.

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2. Donors also have preferences among issues. In particular, consider a donor of type θ ∈ Θ and define d(θ, x) = |θ − x|. Donors then care about the distance between where funds are used and their own preferred location; other things equal, a donor prefers funds going to location x over x′ if d(θ, x) < d(θ, x′ ).

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There are a variety of objective functions that have been attributed to donors in the philanthropy and charitable giving literature. We adopt a spatially-adjusted

variant on the warm glow preferences popularized by Andreoni (1990) and others. Point 2 implies that warm glow of doing good is limited (in the sense of Baron

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(2010)) in that the donor has preferences over impacts at different locations. Some people prefer, ceteris paribus, that their dollars go to help elephants, others prefer they go to help butterflies.

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We operationalize this by defining the utility a donor of type θ derives from donating one unit of money to a project executed at x as u(x; θ) = b(x)e−d(θ,x) .

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This is similar in spirit to that adopted by Baron (2010) in his model of empathetic

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distance and self-regulation. The donor values the impact of his donation (which is described by b(x)) but discounts impacts generated at locations away from his preferred issue.10 The warm glow specification has the helpful implication of al-

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lowing us to abstract from strategic considerations among donors, though we note that the analysis remains the same if we consider a mixed public/private good with standard (non warm glow) preferences. The donor understands the setting and recognizes that there is ex ante an equal likelihood of funds going to any issue in the NGO’s issue-domain. So the

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donor’s expected utility from a one unit donation to an NGO at location ℓ with issue-width w is Z w β(w) ℓ+ 2 −d(θ,x) e dx. E[u(ℓ, w; θ)] = w ℓ− w 2 10

There is an appealing analogy between temporal and spatial discounting, with distance in issue-space replacing dislocation in time. Smith (1975) provides an axiomatic treatment of spatial discounting.

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While spatial discounting with an exponential discount function has intuitive appeal given the familiarity with temporal discounting, to aid with the analysis we approximate felicity in a neighborhood of θ = ℓ so that β(w) E[u(ℓ, w; θ)] = w

Z

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[1 − d(θ, x)] dx.

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It should be clear that this approximation embodies the essential components of a spatial discount function: it is decreasing in distance and between zero and one. Each donor has one unit of money that she can either donate or apply to some

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outside private good to receive utility u¯ > 0. This corresponds to the unit demand assumption common in product differentiation models. Donors maximize their expected utility, so if more than one NGO exists, they donate to the NGO that

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delivers the largest expected utility (provided that exceeds the outside option u¯). To avoid being sidetracked by participation constraints we restrict attention to

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cases in which β(0) > u¯ (a donor will always donate to an NGO that chooses ℓ = θ and w = 0) and u¯ > 43 β(1) (an NGO can become so wide as to repel all donors).

Timing

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The following summarizes the time-line:

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1. The social entrepreneur writes down a mission statement (i.e., fixes the NGO’s issue-domain I). The set of impact opportunities (i.e., the realized values of b(x)) are not known at this stage but the process that generates them and therefore β(w) is common knowledge.

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2. Observing I donors make donation decisions. Total donations to an NGO are denoted by m.

3. Values of b(x) are realized and observed ∀x ∈ I by the NGO. The NGO directs the funds at its disposal to xmax (I), generating impact m(w)xmax (I) at issue location xmax (I).

4. (The cycle of donations, realization of b(x) and NGO operations—stages 2 and 3—could readily be repeated indefinitely with the analysis characterizing 12

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a steady-state mission though to save notation here we restrict attention to a single cycle). The assumptions we make about timing are stark and it is useful to reflect on

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the motivations. Central is that an NGO fixes its mission before impact opportunities are realized and before donors make donation decisions. While it is true that in some cases an NGO is set-up in response to a specific impact opportunity, there are two reasons for not wanting to sequence things in that way. Most importantly, this is a model of the strategic use of missions by

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NGOs. Having an NGO act first and design its mission captures the notion that mission is important in attracting donors—consistent with much of the practitioner literature and summarized well in the quotation at the start of the introduction. A more demand-driven approach in which donors decide initially to which issue they want their money devoted, and an NGO then emerged to execute that, seems

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to us less interesting. If donors care about mission and NGOs want to exploit that strategically—as surely they do—it makes little sense to construct a model in which mission is chosen after donors have formed donation intentions.11 The analysis here reflects the idea that “[m]ission statements are intentionally vague, as too much specificity risks alienating selected groups of stakeholders.”(Powell

te

d

and Steinberg, 2006, p. 133). Even in those cases where impact opportunity is thought to come first, it is sensible to think that in order to sustain the NGO will have to recast its mission— in effect redesign itself—once the initial impact opportunity has waned or been solved. Oxfam is often given as an example of an organization born out of a specific

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crisis. According to its website it was set-up in 1942 as the Oxford Committee for Famine Relief to help women and children in south and eastern Europe who were suffering famine as result of the allied forces’ blockade of key transport routes during the war. That impact opportunity clearly disappeared with the end of the war. The Oxfam that we know today was effectively “designed” in 1947 to have a much wider missions both in terms of the geographical spread and content of its activities (to include not just famine response but education, health and other 11

There are instances where an NGO emerges to satisfy demand on the part of donors for social enterprise. The NGO, however, must still design a mission before it can attract funds.

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sorts of programs). Its remit has changed little since. In effect the trade-offs that might have informed that 1947 decision are what are modeled in a highly-stylized way in this paper. Uncertainty over social outcomes is motivated by the idea that at any moment there is only less-than-perfect knowledge of what the impact of particular projects in the future will turn out to be. If there were no uncertainty over the impact of

ip t

projects, there would be no strategic value to keeping a mission vague. If we donate a dollar to a children’s charity such as Barnardos, we do not know specifically which

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child will benefit from my dollar, or what precise maltreatment that child will be suffering. But by virtue of Barnardo’s mission we do know in more general terms how it will be spent—it will go to help a child in need. Equating here a child with

us

a project, that NGO’s operational staff will decide later, in response to evolving evidence gathered in-the-field or from tip-offs, exactly which project (child) turns

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out to be the best one to which to apply our dollar. In this way, the timing captures long-run considerations; an NGO must design its mission to give itself sufficient flexibility and develop a donor base. It is reasonable to think there is

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likely to be substantial “stickiness” in adjusting mission. There could be various sources to this, from having to go back through the approval process for charitable

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tax-status to the need to develop “brand” and name awareness. Second, implicit in our timeline is that the NGO commits credibly to the mission that it announces. We think this a natural assumption. As noted, in the United States and many other places there are legal considerations keeping NGOs to mission. Having collected donations on the basis of a wildlife mission

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WWF would not be allowed to use those funds to support orphanages in Mexico. But more generally, in a repeated variant of this game we would expect an NGO to have strong incentive to build a reputation for sticking to mission. Donors have preferences among impact-activities and under our assumptions would not find appealing an organization that did not commit credibly—at least within a range—to the sorts of projects to which donations would be applied.

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3

Design of a Monopoly NGO

Consider first the problem facing a single social entrepreneur who faces no competition for donations from other NGOs. Since donors are uniformly distributed in terms of issue preferences, the social entrepreneur is indifferent regarding location

ip t

ℓ. The choice of issue-width—the breadth of NGO interests—is more complex, and to understand the mechanics of the model we need to characterize how donor incentives vary with the NGO’s issue-domain.

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Proposition 1 For a given w, the expected utility derived by a donor of type θ from giving a dollar to NGO {ℓ, w} is decreasing in d(θ, ℓ). It is strictly concave   for all θ ∈ ℓ − w2 , ℓ + w2 , affine elsewhere. In the case of a single NGO, a donor-type θ will donate to the NGO if and only

if

an

E[u(ℓ, w; θ)] ≥ u¯.

Definition 2 The “donor-domain” D ⊂ L of an NGO contains the set of donor

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types that donate to that NGO. That is θ ∈ D if and only if E[u(ℓ, w; θ)] ≥ u¯. The donor-domain is compact, convex and its width is the NGO’s “donor-width”.12

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In Figure 4, it is simple to identify the donor-domain Di by adding the horizontal line u¯. Donors with issue preferences associated with locations outside Di

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derive less than reservation utility from the activities of the NGO so do not donate. Importantly we can now address the following question: What is the effect of a marginal widening of the NGO’s issue-domain on the expected utility from donation to donors at different types?

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Lemma 1 A marginal increase in w increases the expected utility from donating for donor types who’s preferred issue lies outside the NGO’s issue-domain, or inside but within a neighborhood of the periphery. It will decrease the expected utility for donor types who’s preferred issue lies sufficiently close to the centre of the NGO’s issue-domain. 12

The donor domain is the upper contour set of expected utility with respect to θ. Since expected utility is quasi-concave in θ, all upper contour sets are convex. Since expected utility is continuous in θ, all upper contour sets are closed. Since Θ is compact, the upper contour set is a closed subset of a compact set and is thus compact.

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E[u(ℓ, w; θ)]

w 2

ℓ

ℓ+

θ

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D

w 2

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ℓ−

ip t

u¯

Figure 4: Donor domain, single NGO case.

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Some intuition for this point can be derived from Figure 5. Suppose that issuedomain widens from I to I ′ . There are two effects: (i) the NGO will now be expected to find a higher-impact project, but (ii) expectations over the location of

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that winning project will also be updated. All donors benefit from the fact that the extra width means the NGO expects

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to finds a higher-impact use for donations (since β ′ (w) > 0). But the widening of the NGO’s issue-domain also relocates where (probabilistically) the donor expects his money to be used—it could now be anywhere across a now wider domain I ′ . For a donor located at θj internal to the NGO’s issuedomain candidate projects are added at either margin serving to take the expected

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location of the NGO’s chosen impacts away from θj . So in terms of project location j unambiguously dislikes the widening of scope. The perspective of a donor at θk outside I is quite different. The widening adds candidate projects closer to those he prefers (the right-hand margin on the diagram) but others at the left-hand margin that he likes even less than the original possibilities. However, the increasing marginal disutility of distance means that in expected utility terms he values the gain at the near margin more highly than the loss at the more distant one. Combining the two effects, the overall impact on expected utility of a widening is positive only for donors outside or close to the periphery of I.

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I′ I

θk

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θj

Figure 5: Widening of issue-domain.

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cr

Importantly, from the point of view of thinking about the solution to the social entrepreneur’s problem, we can now derive the relationship between an NGO’s donor-width—and therefore the funds it will have available for projects—and its issue-width.

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Proposition 2 (Donations non-monotonic in issue-width) Total donations to the NGO are increasing in issue-width up to some critical value, decreasing thereafter (i.e. m(w) is quasi-concave in w with a single peak).

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On a technical note, to ensure m is strictly concave the function β, in addition to being increasing and concave, will be such that

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d

w2 w − 4 β(w)

is convex in w. The economic interpretation of this condition is not evident, but we can demonstrate that it holds—for example—for the micro-founded specification presented in footnote 7. (The paper could sensibly be presented based on the micro-foundation in footnote 7 and the resulting particular specification for

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β(w). Our analysis points to the results being robust to a wider set of underlying stochastic processes.) 2

w Remark 1 The set of increasing, concave function β such that w4 − β(w) is convex w is non-empty. In particular, β(w) = α + 1+w satisfies this condition.

The non-monotonicity plays an important role in the results in this paper as it places limits on an NGO’s desire to expand horizontally. Getting issue-wider then has two effects, both of which influence donor appeal. First, a broader NGO 17

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can expect to find a better project, one with a larger “bang for its buck.”This is captured by β ′ (w) > 0. All donors like this. Second, however, the widening alters (probabilistically) how near or far a particular donor expects that project to be in relation to his or her own preferred issue. All issues in the “old” issue-domain are realized with a smaller probability. As we saw from lemma 1, the net effect of this second impact for a donor depends upon her location: for those close enough to ℓ

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it is utility reducing, for those further out it is utility enhancing. Proposition 2 says that up to some critical point donor-width (and therefore

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aggregate donations) is increasing in issue-width. But beyond some point, an NGO with wider interests narrows the range of θ-types that find it attractive to donate. While a very broad NGO may be able to find a very high-impact project,

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prospective donors are turned-off by their anticipation that the issue to which their donation ends up being directed (the location of xmax ) is likely to be a long way

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from the issues that really interest them. The social entrepreneur’s problem in designing an NGO is to choose w to maximize total expected impact. Denoting this by a function B and recognizing

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that in the single NGO case the uniform distribution of donor types around the circle mean that location, ℓ, does not matter, we can write ex-ante total impact as B(w), where

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B(w) = m(w)β(w).

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The associated first-order condition is as follows, where w ∗ is the solution to the social entrepreneurs problem,

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B ′ (w ∗ ) = m(w ∗ )β ′ (w ∗) + m′ (w ∗ )β(w ∗ ) = 0.

(1)

If funds were fixed, the social entrepreneur would want to set w as large as possible since his interest is in finding the project for those funds with the highest possible impact. That is captured by the composite term m(w)β ′ (w) which is always positive. He is restricted, however, by the need to attract donations; he has to cater to prospective donors and, as described in Proposition 2, beyond some point additional issue-width discourages donations. This is captured by the

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m′ (w)β(w) term which is in general ambiguous in sign. Rearranging (1) gives m′ (w ∗) = −m(w ∗ )

β ′ (w ∗ ) < 0, β(w ∗ )

which leads directly to the following.

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Proposition 3 (Foregone donations) The social entrepreneur will design an NGO that has within its mission statement a wider set of issues than would be consistent with maximizing total donations. That is m′ (w ∗ ) < 0 such that donations

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to the NGO would be increased by a marginal reduction in issue-width.

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It is also instructive to formalize the relationship between the issue-domain I that the social entrepreneur will choose, and the associated donor-domain D.

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Corollary 1 (Donor-stretching) In equilibrium D ⊂ I. In equilibrium, the NGO will have within its mission statement a set of issues that are not the preferred issue of any of its donors.

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In particular, there will be a set of issues contained in I but not in D, at each

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periphery of the NGO’s issue-domain. This implies directly that with positive probability the NGO will allocate the funds it collects to an issue that is not the preferred issue of any of its donors.

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We refer to this as a donor-stretching result because the NGO is constituted in such a way that the set of projects to which funds may be assigned stretches beyond the bounds preferred by donors. Donors understand this, and donate in this knowledge.

3.1

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Welfare with a Monopoly NGO

Before leaving the single NGO context to consider NGO competition and the quasi-market for NGOs we develop a simple normative result. There has been some debate in the literature as to how to treat warm-glow benefits in the evaluation of social welfare. We follow Diamond and Hausman (1994), Andreoni (2006) and Diamond (2006) in assuming that warm glow benefits should be ignored in normative analysis. Bernheim and Rangel (2012, p. 82) offer the following summary and assessment: 19

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Diamond (2006) argues that, given the limited state of knowledge concerning processes, measures of social welfare should exclude the apparent benefits from the warm glow. He advocates using the warm glow

ip t

model for positive purposes (that is, to describe behavior), but favors the standard model for evaluating welfare. Andreoni (2004) expresses a similar view.

(2)

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B(w) − m(w)u = m(w) (β(w) − u) .

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Excluding such benefits in our framework implies that the expected contribution of the NGO on welfare can be written

This is the sum of the impacts or benefits generated by the NGO project minus

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the foregone outside option for donors (in the absence of an NGO, each prospective donor would simply hold onto there one monetary unit and use it to derive outside option of value u.). Given this we can state the following:

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Proposition 4 (Mission statement too narrow) The single social entrepreneur will design an NGO with an issue-width less than that which maximizes expected

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social welfare.

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To see this differentiate (2) with respect to w. The welfare maximizing issuewidth w welfare is then implicitly defined by B ′ (w welfare) = m′ (w welfare)u < 0,

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whilst the social entrepreneur chooses w = w ∗ such that B ′ (w ∗ ) = 0,

together implying that w ∗ < w welfare. Intuitively, the NGO attaches no weight to the outside option (opportunity cost) of a donor’s dollar, whereas the social planner does. Conventional normative analysis in this sort of circumstance would involve invoking the envelope theorem to conclude that if a marginal individual chooses to donate rather than take an outside option, then that individual (and therefore 20

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society) can be no worse off as a result of that decision. While it is true that the individual remains no worse off from the donation, however, the welfare inference is different here because when aggregating the planner disregards the altruistic

4

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component of individual utility. Note that if u = 0—the donated money has no opportunity cost—then the NGO and planner incentives are exactly aligned.

NGO Competition

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The single NGO setting considered in the previous section gave us significant insight into the trade-offs implicit in NGO design. In reality, however, we observe

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many NGOs defined by different issue-domains—that is to say with different mission statements—coexisting but competing for donations. In defining their mission

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statements, social entrepreneurs use width strategically. In this section we hypothesize and model a quasi-market for NGOs with free entry onto the circle. Free entry is an assumption seen in existing models of NGO

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differentiation (e.g., Rose-Ackerman (1982) and Aldashev and Verdier (2010)). Thornton (2006) argues that legal and financial barriers for the formation of a non-profit are low. Weisbrod (2000) offers local advocacy groups as an example of

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a type of NGO subject to low barriers to entry stemming from low start-up costs. In sum, “[low barriers to entry are] an incentive for founders to create a new

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organization rather than examining ways in which their goals might be achieved through existing organizations,” Eagan (2011). Before characterizing the free entry equilibrium, we will present some more

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partial results assuming that the number of NGOs in existence is fixed exogenously at n, and that those NGOs are placed at an equal distances apart around the issuespace circle L. If two NGOs are far enough apart, in particular if the distance between them is no less than 12 m(w ∗ ), then their decisions are not interdependent in a meaningful way. Each can act as if it were “in isolation” in the manner specified in the previous section, without being impacted by the activities of the other. Given that the issue-space circle has circumference of one, this implies the following. Lemma 2 If n < 1/2m(w ∗), then the circle is donor-uncovered. That is there will 21

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I1 D1 ℓ1 ˜θ

˜θ

˜θ

I2

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ℓ2 D2

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ip t

˜θ

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Figure 6: Equilibrium with a fixed number of NGOs and no encroachment; illustrated for n = 2.

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be a subset of donor types that will not donate to any NGO. If n = 1/2m(w ∗), then

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the circle is exactly-donor-covered.

The uncovered case is illustrated for n = 2 in Figure 6. Each NGO acts ignoring the existence of other NGOs (chooses issue-width w ∗ ). Gaps remain between the resulting donor-domains. Meaningful strategic interdependence between NGOs requires that they be less dispersed on the circle. In particular, this requires

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encroachment.

Definition 3 (Encroachment) NGOs i and j encroach if the preferred donordomain of NGO i (the donor-domain that would result if it acted as if were the only NGO) intersects with the preferred donor-domain of NGO j. Encroachment is equal if the length of the intersection of NGO i’s preferred donor-domain with that of its two neighbors is equal.

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In the case of NGOs equally-spaced around the circle, it follows that equal encroachment will result if n > 1/2m(w ∗ ). With encroachment, NGOs are close enough that they are competing for donations with their neighbors. Preferred donor-domains overlap. Of course, given the set-up in which each donor on the circle has only one unit of money to donate and donates it to his preferred NGO, realized donor-domains cannot intersect. It is straight-forward to establish what

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happens in that case.

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Lemma 3 If two NGOs encroach, the marginal donor type between the NGOs will be located at the midpoint of the intersection of their preferred donor-domains.

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Shortly we will turn to location choices but, for the moment, continue to consider the case of n NGOs exogenously placed at equal intervals around the circumference of the issue-space circle. Lemma 4 With equal encroachment, each NGO j will wish to reduce wj below w∗.

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In effect, when preferred donor-domains overlap, each NGO finds it beneficial

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to narrow its issue-domain, to shrink itself in at each margin. By reducing its width below w ∗ the NGO can, other things equal, attract more donors—recall that w ∗ lies beyond the peak of m(w). Such a mechanism is seen in the NGO sector, where

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competition leads NGOs to compromise on or alter mission to attract donors (e.g., Fruttero and Gauri (2005); Bose (2014)): “Another way to increase funds from private givers [in the presence of competition], and ensure continued funds from changing governments, is to compromise on policy positions. . . ” (Glennie, 2012). Though the fixed-n case is not our focus in this paper, it is worthwhile noting

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that each NGO will still choose an issue-width such that m′ (w) < 0 (i.e., beyond the level that would maximize donations). Sargeant and Jay (2002) find evidence to this point; non-profit mergers that increase the scope of an NGO can reduce donations received by the new NGO. The next proposition follows directly from NGO symmetry. Proposition 5 If NGOs are placed exogenously at equal distances around the issue-space circle L with equal encroachment and social entrepreneurs simulta23

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neously choose issue-widths, then there is some w ∈ (0, w ∗) which is a symmetric Nash equilibrium.

4.1

Equilibrium with NGO entry

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We have seen that with an exogenously fixed number n of NGOs there are three possible types of equilibrium. For n small, the donor-space is uncovered and

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individual NGOs are far enough apart that they act as if in isolation. For some critical value of n there is exact coverage. For n beyond that value, there is encroachment (in the sense defined) and NGOs will wish to reduce their issue-

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widths below w ∗ . We are now in a position to close the model by considering the free entry

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outcome. We conceive of NGOs that compete in mission statements; that is, in establishing an NGO the social entrepreneur makes a strategic choice of issuedomain I. There are a large number of potential social entrepreneurs ready to

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enter if a sufficiently opportunity arises. The strategic interdependence in w’s is summarized by the following Remark 2 (Mission statement widths are strategic complements) Consider two neighboring NGOs i and j with encroachment. In the neighborhood of a

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Nash equilibrium, wi and wj are strategic complements.

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The width of the mission statement of one NGO both influences—and is influenced by—the choice of mission statements of other NGOs. Other things being equal, if one NGO widens its mission statement to include more issues, neigh-

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boring NGOs will respond by increasing theirs. Put another way, if an NGO can increase its impact by reducing width to steal donors from a neighboring NGO, the neighboring NGO also has an incentive to shrink to steal donors. This strategic interdependence is embodied in entry equilibrium below. Formally, the entry decisions of NGOs are taken simultaneously, but as usual we can have in mind NGOs making entry decisions sequentially and without commitment, with existing NGOs having the opportunity to reset their w’s when another enters. In what follows we assume NGOs face an opportunity cost13 13

Aldashev and Verdier (2010) treat the presence of an opportunity cost against which NGOentrepeneurs weight the “psychological” benefit of their operation as a stylized fact.

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I1 D1

˜θ41 = ˜θ 14

D4 ℓ4

ℓ1

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I4

ℓ3

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˜θ12

˜θ

ℓ2

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D2

˜θ

D3

I2

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I3

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Figure 7: Equilibrium under free entry; illustrated for case n = 4.

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¯b ∈ (0, m(w ∗ )β(w ∗ )) of entering so that an NGO will only enter if the impact they create is greater than ¯b. The bounds placed on ¯b are worth explaining; the

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lower bound implies that an NGO’s next best alternative is not so poor that the NGO would always wish to enter. The upper bound implies that an NGO cannot do better elsewhere than if they were the only NGO.

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Proposition 6 (Free-entry equilibrium) The Nash equilibrium is characterized by the entry of nentry NGOs; NGO issue-domains will overlap; each NGO will choose an issue-domain narrower than if they were the only NGO; realized donor-domains will not overlap and will be collectively exhaustive. This is summarized in Figure 7, illustrated for a case in which nentry = 4. The NGO centred at ℓ1 (for example) attracts donations from types between ˜θ14 and ˜θ12 (the arc between those two cut-off types is D1 ). Note that ˜θ14 = ˜θ41 , in other words donor-domains of neighboring NGO’s abut.

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Corollary 2 (Donor coverage) In free entry equilibrium the circle will be exactlydonor-covered. Intuitively, if there are gaps in donor coverage, an prospective NGO can enter,

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filling a gap to produce a payoff greater than its reservation value.

The issue-domain of NGO 1 is the arc from ℓ1 − w2 to ℓ1 + w2 and donorstretching by all NGOs continues to be a feature in this equilibrium, Di ⊂ Ii . This,

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combined with abutting donor-domains implies that the I’s of neighboring NGO’s will overlap.

Corollary 3 (Issue over-coverage) In the free entry equilibrium, the circle is

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issue over-covered. Issue-domains of neighboring NGOs overlap; if i and j are neighboring NGOs then Ii ∩ Ij 6= ∅. Expected NGO activity is higher at issues

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in the intersection of neighboring NGOs, issues at the periphery of any particular NGOs issue-domain. This is an interesting result. Even though donor-domains will exactly abut,

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competition for turf amongst social entrepreneurs will lead to issue-domains or mission statements that overlap in equilibrium. This result is consistent with evidence found in Koch et al. (2009).

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What are the implications of this for the distribution of NGO activity across different issues? Recall that ex-ante an NGO is equally likely to choose any point

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within I for the project it executes; the probability that xmax (I) = x is uniformly distributed across I. One interesting implication of the overlapping issue-domains is that expected impact generated by NGO activities on a subset of issues—in

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particular those that lie within the intersection of two NGOs issue-domains—will be greater (twice as great) as other issues. As observed in the corollary, those “favored” issues will be at the periphery, not the core, of any individual NGO’s issue-domain.

4.2

Welfare with NGO entry

What about welfare in the quasi-market equilibrium in which entry onto the circle is a free-for-all? Taking aggregate donations as given, it is apparent that a welfaremaximizing planner would prefer that the aggregate sum be allocated to a single 26

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NGO with an issue-domain covering the whole circle, I = L. We use as our welfare benchmark, however, the second-best that takes the need to induce donations as a constraint. The planner can hypothetically mandate the set of NGOs in existence and their issue-domains, but cannot force individual donations. On this basis we can state the following

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Proposition 7 In the free entry equilibrium each NGO will choose a mission statement (issue-domain) that is narrower than socially-optimal. The number of

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NGOs in the free entry equilibrium will be larger than is socially-optimal.

In contrast to the single NGO case, there are now two effects causing w to

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be too small. First, in comparison to a welfare-benchmark each NGO fails to account for the reservation utility of donors (the opportunity cost of funds that

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they collect). Second, in choosing to enter each NGO creates a negative externality on all other NGOs by causing them to have, in equilibrium, narrower mission statements. NGOs do not take either of these effects into account and so face the

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wrong incentives for both entry and determination of issue-domain.14 If we view NGO mergers as a way of increasing issue-domain, the following quote effectively captures the normative results of the model.

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The reality is that mergers among nonprofits are necessary. In many

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parts of the country today, there are simply too many nonprofits. This situation is caused by many factors, including the best of intentions, but the plain fact is that having an excessive number of nonprofit organizations actually weakens the collective power of the entire field. (McLaughlin, 2010, p. xvi)

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The idea that there are too many NGOs with too narrow a mission can also be seen in Werker and Ahmed (2008); Nursey-Bray (2012) discusses some criticisms that NGOs have too narrow a focus. The free entry equilibrium characterized in this Section is described by too many NGOs, each too niche in its remit. From the point of view of the efficacy of 14

Comparing with Aldashev and Verdier (2010), issue width has a similar effect to fundraising, where impact across NGOs is decreasing with entry and free entry delivers too many NGOs. The mechanisms from which these outcomes are realized, however, are distinct.

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the NGO sector as a whole, the implication is that while such focus is individually rational given the competition for funds, the narrowness of the I’s in equilibrium mean that those funds end up being allocated to poor quality (low impact) projects.

Conclusions

ip t

5

The paper offers the first formal economic analysis of NGO competition in issue-

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domain. We will not repeat the key elements of the model or results here. The final insight—that NGOs will choose missions statements (issue-domains) that are too narrow or too niche in nature—has a number of implications. Little formal

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analysis has been directed to trying to understand how policy towards the NGO sector should be designed, but the biases we have identified point to intervention

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to encourage issue-width in NGOs. That intervention could come in a variety of forms—tax advantages on the basis of issue-width, practices aimed at facilitating merger between neighboring NGOs, regulating NGO entry and so on. We leave

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development of policy to future work. While other commentators have pointed to the possible over-supply of NGOs, their analyses have been driven by concern for diversion of funds from impact

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activities to mutually-offsetting fund-raising activities (Rose-Ackerman (1982) and the models that have followed her). We have no fund-raising effort or expenditure

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variable in our model and our result is driven by a more fundamental consideration of the impact-activities in which NGOs are engaged. Save the Tiger cannot devote resources to saving dolphins however rich the set of high-impact dolphin-saving

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projects may turn out to be, and regardless of the paucity of good tiger-saving projects this period. NGOs with wider remits—more generic mission statements— have a wider set of issues to which to direct efforts and can therefore be expected to find better projects to fund.

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Proof of Proposition 7 Since nentry > n∗ , total impact is not maximized under free entry. We now consider the planner’s problem of choosing both n and w to maximize total impact less the opportunity cost of donating, n[m(w)(β(w) − u¯) − ¯b]. We claim that n∗∗ NGOs, where n∗∗ is the smallest number of NGOs that can cover the issue space with w ∗∗ ,

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with w ∗∗ will maximize welfare. If the issue-space is covered, then the planner will choose n∗∗ as any other n will produce the same total impact with a greater

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opportunity cost for social entrepreneurs. As with the single NGO case, the planner can choose w ∗∗ to maximize impact for an NGO. Now suppose there is one fewer NGO. Welfare will then decrease as this NGO produced a positive contribution to

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welfare (from the single NGO case) and welfare cannot be increased by changing w for the other NGOs. Proceeding with this logic establishes the result.

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We now wish to show that n∗∗ < nentry . Suppose not so that n∗∗ ≥ nentry . Then nentry cannot cover the issue space for w ∗∗ . Since w entry < w ∗ < w ∗∗ , nentry cannot cover the issue space with w entry , a contradiction.

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