# Small is Beautiful: Motivational Allocation in the Nonprofit Sector

Small is Beautiful: Motivational Allocation in the Nonprofit Sector Abstract We build an occupational-choice general-equilibrium model with for-profit firms, nonprofit organizations, and endogenous private warm-glow donations. Lack of monitoring on the use of funds implies that an increase of funds of the nonprofit sector (because of a higher income in the for-profit sector, a stronger preference for giving, or an inflow of foreign aid) worsens the motivational composition and performance of the nonprofit sector. We also analyze the conditions under which donors (through linking donations to the motivational composition of the nonprofit sector), nonprofits themselves (through peer monitoring), or the government (using a tax-financed public funding of nonprofits) can eliminate the low-effectiveness equilibrium. We present supporting case-study evidence from developing-country nongovernmental organization sector and humanitarian emergencies. 1. Introduction One major recent global economic phenomenon has been the rising importance of nonprofit and nongovernmental organizations as providers of public goods (Brainard and Chollet 2008). The massive increase in the number of international nongovernmental organizations (NGOs), from less than 5,000 in mid-1970s to more than 28,000 in 2013, attests to this (Union of International Associations 2014; Werker and Ahmed 2008). In developing countries, NGOs play a key role in the provision of public health and education services. They have also become fundamental actors in the empowerment of socially disadvantaged groups, such as women and ethnic/religious minorities (Brinkerhoff, Smith, and Teegen 2007). In addition, NGOs contribute actively to monitoring adherence by multinational firms to environmental and labor standards (Yaziji and Doh 2009). The expansion of nonprofit organizations as economic actors has not been restricted to the developing world. In the Organisation for Economic Co-operation and Development (OECD) countries, they also play a major role as public-good providers, especially in sectors such as health services, arts, education, and poverty relief (Bilodeau and Steinberg 2006). Quite remarkably, nonprofits represent a sizeable sector in terms of OECD countries’ employment share: on average, 7.5% of their economically active population is employed in the nonprofit sector. For some countries (Belgium, Netherlands, Canada, UK, and Ireland), this share exceeds 10% (Salamon 2010). One distinctive feature concerning the provision of public goods by NGOs is their financing structure. Although a part of these organizations’ operational costs is covered by government grants and by user fees, voluntary private donations also account for a major share of their budgets. Bilodeau and Steinberg (2006) report that for the 32 countries for which comparable data are available, on average, over 30% of nonprofits’ financing comes from voluntary private giving. Moreover, over 75% of this amount consists of small donations. Given the public-good nature of the services typically provided by nonprofits, this fact is particularly intriguing, because small donors could hardly expect their contributions to entail any meaningful effect on total public-good provision. A simple explanation of this phenomenon is that private contributions to nonprofits are partially motivated by impure altruism. Indeed, research in public and experimental economics has recurrently shown that rationalizing empirical regularities about altruism requires the explicit acknowledgment of private psychological benefits accruing to the donor from the act of giving.1 This is the so-called warm-glow motivation, first modeled by Andreoni (1989). Impure altruism by donors means, in turn, that the link between the motivation to give to nonprofit organizations and the ultimate provision of public goods by them may be very weak.2 In addition, the very nature of the goods and services provided by nonprofit organizations renders impossible to write contracts that condition their financing on their output, further weakening the link between donations and public-good provision.3 These two features, combined with the fact that individuals’ intrinsic motivation is private information, make the nonprofit sector particularly vulnerable to the misallocation of funds. In a context where the scope for funds diversion is quite extreme, the size and the structure of financing of the nonprofit sector may become major factors determining who enters this sector. This will in turn affect the level of intrinsic motivation of its managers, and consequently, the performance of the nonprofit sector. Analyzing this key issue requires a general-equilibrium framework. When the nonprofit sector is of non-negligible size, policies that influence the behavior of nonprofit managers will impact the returns in both the nonprofit and for-profit sectors. In such a setting, a partial-equilibrium model will miss out important sources of market interactions and may, therefore, lead to misguided policy recommendations (for instance, concerning the desirability of more extensive state financing to nonprofits or channeling foreign aid via NGOs). This paper proposes a tractable occupational-choice general-equilibrium model with for-profit firms, nonprofit organizations, and endogenous private donations. The model rests on five key assumptions. First, private donors give to nonprofits because of warm-glow motives (i.e., with a weak link to the expected public-good output generated with their own donations). Second, individuals self-select either into the for-profit or nonprofit sectors, whose returns are endogenous to the model, both because of aggregate occupational choices and endogenous donations. Third, there are decreasing returns at the level of single nonprofit organizations (because intrinsic motivation is an essential input in limited supply compared to money, and that mission deepening for nonprofits involves increasingly difficult tasks to accomplish). Fourth, monitoring the behavior and knowing the intrinsic motivation of the nonprofit managers is inherently difficult. Fifth (also resulting from the nonmeasurability of nonprofits’ output), private donations are shared among the existing nonprofits in a manner that is not strictly related to their performance. The main mechanism in our model relies on the notion that motivational self-selection into the nonprofit sector may be altered by the level of donations received by nonprofit firms. Imperfect monitoring of managers in the nonprofit sector, together with warm-glow motives by private donors, implies that the scope for misallocation of funds in this sector expands when private giving rises. Therefore, in a context of asymmetric information, warm-glow altruism and self-selection interact in nonmonotonic ways, possibly leading to equilibrium with severe misallocation of funds. Our model generates several important results concerning motivational allocation. First, selfish motives can crowd out altruistic motivation from the nonprofit sector. When this occurs, the nonprofit sector ends up being managed by selfish agents who exploit the lack of monitoring to divert funds for project dimensions that are misaligned with the interests of the beneficiaries. Moreover, because the scope for misallocation of funds rises with the level of donations received by each nonprofit firm, this problem is exacerbated in richer economies and in economies where private donors give more generously. Our model features thus a case where “small is beautiful”: motivational allocation in the nonprofit sector tends to be better when the overall financing of each nonprofit remains small. Second, foreign aid intermediation through the nonprofit sector in a developing country may entail perverse effects: it may cause the economy to switch from an equilibrium with a good allocation to one with a bad allocation of prosocial motivation. One further implication of this result is that total output of nonprofits can become nonmonotonic in the amount of foreign aid. At low levels of foreign aid, a small increase in aid leads to higher total NGO output, as the motivational composition of the nonprofit sector is unaltered. However, a large injection of foreign aid may lead to a motivational recomposition of the nonprofit sector, attracting self-interested agents into it, and thereby leading to a decline in total nonprofit output. Such nonmonotonic relation, in turn, can help explaining the micro–macro paradox observed by empirical studies of aid effectiveness (i.e., the absence of a positive effect of aid on output at the aggregate level, combined with numerous positive findings at the micro level). Third, we analyze a number of mechanisms that might prevent the emergence of the low-effectiveness equilibrium. From the donors’ side, if warm-glow motivation responds positively to the expected productivity of the nonprofit sector, the pure low-effectiveness equilibrium disappears. However, our model shows that, even in this case, when the amount of donations is sufficiently large, selfish agents still end up constituting an important share of the pool of nonprofit managers, thus hurting the aggregate provision of public goods. On the nonprofits’ side, peer-monitoring mechanisms can lead to multiple equilibria. In one equilibrium, the nonprofit sector is managed by motivated agents and the quality of peer monitoring is high. In the second equilibrium, the sector is instead managed by selfish individuals and no peer monitoring takes place. The reason for the multiplicity of equilibria is that the quality of monitoring is itself endogenous to the occupational choice of agents, and it improves with the average level of motivation in the nonprofit sector. Finally, we show that a properly designed public financing policy of the nonprofit sector may improve the motivational composition of the nonprofit sector. Besides the aforementioned papers by Andreoni (1989) and Benabou and Tirole (2006), our paper relates to several other key papers that study theoretically the implications of prosocial motivation for nonprofit organizations: Glaeser and Shleifer (2001), François (2003, 2007), Besley and Ghatak (2005), Lakdawalla and Philipson (2006), and Aldashev and Verdier (2010).4 We contribute to this line of research by endogenizing the returns of the different occupational choices available to individuals, and by exploring the general-equilibrium implications of the level of financing of the nonprofit sector. The second related strand of literature is the one focusing on the self-selection of individuals into the public sector and politics: for example, Caselli and Morelli (2004), Macchiavello (2008), Delfgaauw and Dur (2010), Bond and Glode (2014), and Jaimovich and Rud (2014). The insights from the theoretical research in this area, which mostly exploits occupational-choice models, have been confirmed by recent empirical studies. For instance, Georgellis, Iossa, and Tabvuma (2011) find, using the UK data, that individuals are attracted to the public sector by intrinsic rather than extrinsic incentives, and that (in the higher education and health sectors) higher extrinsic rewards reduce the propensity of intrinsically motivated agents to enter into the public sector. We extend this line of research by (i) analyzing how the selection mechanisms apply to the nonprofit/NGO sector within a context of endogenous voluntary donations, and (ii) studying the effectiveness of three mechanisms that potentially can improve the motivational selection into the nonprofit sector. Finally, there is growing literature that studies the effectiveness of different modes and levels of foreign aid (see the survey by Bourguignon and Platteau 2015). Among these studies, Svensson (2000) underlines how short-term increases in aid flows may trigger rent-seeking wars among competing elites. Another interesting contribution is Bourguignon and Platteau (2013), which concentrates on moral hazard problems (in particular, it studies the effect of domestic monitoring on the ultimate use of aid flows). Our model studies a separate and novel channel: that of motivational adverse selection into the sector that intermediates foreign aid flows between outside donors and beneficiaries. The rest of the paper is organized as follows: Section 2 builds our baseline model of occupational choice in the for-profit and nonprofit sectors; it also analyzes the effects of foreign aid and public financing on the motivational allocation in the nonprofit sector. Section 3 analyzes the functioning of three different oversight mechanisms: conditional warm glow of donors, peer-monitoring institutions by nonprofits, and tax-financed government grants to nonprofits. Section 4 discusses the main premises and modeling choices, as well as the generalizability of our results. Section 5 presents case-study evidence for the mechanisms of the model. Section 6 explores several avenues for future work, and concludes. The Appendix contains two extensions of the basic model, as well as some of the proofs of propositions. 2. Basic Model Consider an economy populated by a continuum of agents with unit mass. There exist two occupational choices: an agent may become either a private entrepreneur in the for-profit sector or a social entrepreneur by founding a firm in the nonprofit sector. Let us denote the choice of agent i with oi = private, social. We refer to the two types of firms as private and nonprofit firms, respectively. Let N denote the total mass of nonprofit entrepreneurs; thus, 1 − N is the mass of private entrepreneurs. All agents are identically skilled. They differ, however, in their level of prosocial motivation, mi, which indicates to which extent an individual is genuinely motivated to help others (the beneficiaries of her projects). There exist two levels of mi, which we refer to henceforth as types: mH (motivated) and mL (selfish) types, where mH = 1 and mL = 0. A selfish type can also set up projects whose declared aim is helping the beneficiaries, but where she cares only about the aspects of these projects that increase her own well-being (ego, perks, etc.). The type mi is private information. In what follows, we assume that the population is equally split between mH- and mL-types. The utility function of an agent has the following form: $$W_{i}=\mathbb {I}(o_{i})\left[ w_{i}^{1-m_{i}}g_{i}^{m_{i}}\frac{1}{m_{i}^{m_{i}}(1-m_{i})^{1-m_{i}}}\right] + ( 1-\mathbb {I}(o_{i})) \left[ c^{1-\delta }d^{\delta }\frac{1}{\delta \left( 1-\delta \right) ^{1-\delta }}\right] ,$$ (1) where $$\mathbb {I}(o_{i})$$ is the indicator function taking value 1 if oi = social. wi and c denote her consumption in the nonprofit and private sectors, respectively, whereas gi and d stand for her warm-glow prosocial contribution in the nonprofit and private sectors. Finally, δ ∈ (0, 1) is a parameter measuring the relative importance of giving as compared to private consumption. The details of this structure are explained in what follows. 2.1. For-Profit Sector We assume that each private entrepreneur produces an identical amount of output. There are decreasing returns in the private sector, thus while the aggregate output is increasing in the mass of private entrepreneurs, 1 − N, the output produced by each private entrepreneur is decreasing in 1 − N. More precisely, we assume that each private entrepreneur produces $$y=\dfrac{A}{\left( 1-N\right) ^{1-\alpha }}, \,\,\,\text{where }0<\alpha <1 \text{ and }A>0.$$ (2) Aggregate output is thus given by Y = A(1 − N)α.5 Private-sector entrepreneurs derive utility from their private consumption (c). In addition, they also enjoy warm-glow utility from donating to the nonprofit sector (d). The utility Wi of an entrepreneur in the private sector then reduces to6: $$W_{i}=V_{P}(c,d)=c^{1-\delta }d^{\delta }\frac{1}{\delta \left( 1-\delta \right) ^{1-\delta }}, \,\,\,\text{where }0<\delta <1.$$ (3) Private-sector entrepreneurs maximize (3) subject to (2). This yields c* = (1 − δ)y and d* = δy, which in turn implies that, at the optimum, their indirect utility is equal to the income they generate as private entrepreneurs: $$V_{P}^{\ast }=y.$$ (4) From the optimization problem of private-sector entrepreneurs, it follows that the total amount of entrepreneurial donations to the nonprofit sector is $$D=\delta \left( 1-N\right) ^{\alpha }A,$$ (5) which increases with the productivity of the private sector (A), the number of private firms (1 − N), and the propensity to donate out of income (δ). 2.2. Nonprofit Sector The nonprofit sector is composed of a continuum of nonprofit firms with total mass N. Each nonprofit firm is run by a social entrepreneur. We think of each single nonprofit firm as a mission-oriented organization, as in Besley and Ghatak (2005), with a narrow mission targeting one particular social problem (e.g., child malnutrition, air pollution, fighting malaria, etc.). Each nonprofit manager i collects an amount of donations σi from the aggregate pool of donations D. The collected donations σi can be allocated to two distinct dimensions of the project. One dimension, which absorbs a level of expenses equal to wi, does not serve the ultimate needs of the beneficiaries, but might increase the well-being of the nonprofit manager. Such self-serving dimensions may include his wages, in-kind perks such as a car with a driver, but can also be his pet projects or actions that might increase his ego utility. The second dimension uses the undistributed donations σi − wi as an input for the production of the service towards the organization’s mission and increases the well-being of beneficiaries. We measure the effectiveness/output of each specific nonprofit firm by gi, which is a function of the undistributed donations (σi − wi). We assume that the output generated by each specific nonprofit firm exhibits decreasing returns with respect to the funds invested into the project, namely: $$g_{i}=( {\sigma }_{i}-w_{i})^{\gamma }, \,\,\,\text{where }0<\gamma <1.$$ (6) An important feature of this specification is the fact that the curvature of the nonprofit sector technology is larger than that of the for-profit sector. As we will see, this assumption underlies the single-crossing result (Lemma 1), which, in turn, allows a simple characterization of the different types of equilibria that may arise. As we argue more precisely in our discussion in Section 4, this assumption seems reasonable in the context of the functioning of the nonprofit sector. A nonprofit manager derives utility from the two dimensions noted previously. The weight placed on each of the two components of utility is given by the nonprofit manager’s level of prosocial motivation mi. The utility Wi of a nonprofit manager with motivation mi reduces to $$W_{i}=U_{i}(w_{i},g_{i})=w_{i}^{1-m_{i}}g_{i}^{m_{i}}\frac{1}{m_{i}^{m_{i}}(1-m_{i})^{1-m_{i}}}, \,\,\,\text{where }m_{i}\in \lbrace m_{H},m_{L}\rbrace .$$ (7) We assume that the monitoring by donors of the nonprofit sector is weak, and donors cannot control how nonprofit managers split the donations between the two dimensions. For simplicity, we make the extreme assumption that nonprofit managers enjoy full discretion in deciding this allocation (subject to the feasibility constraint wi ≤ σi). In addition, we assume that the pool of total donations D is equally shared by all nonprofit firms.7 Therefore, donations collected by each nonprofit firm are given by \begin{equation*} {\sigma }_{i}=\dfrac{D}{N}=\dfrac{\delta A\left( 1-N\right) ^{\alpha }}{N}. \end{equation*} Notice that σi is decreasing in N through two distinct channels. Firstly, the level of aggregate donations D shrinks when the mass of private entrepreneurs (1 − N) gets smaller. Secondly, a rise in the mass of nonprofit firms N means that a given total pool of donations D must be split among a larger mass of nonprofit firms. Given that mH = 1, motivated nonprofit managers place all the weight in their utility function on the dimension that helps the beneficiaries g, and set accordingly $$w_{H}^{\ast }=0$$. As a result, choosing to become a nonprofit manager gives to a motivated agent the indirect utility equal to $$U_{H}^{\ast }=\left( \dfrac{D}{N}\right) ^{\gamma }=\left[ \delta A\dfrac{\left( 1-N\right) ^{\alpha }}{N}\right] ^{\gamma }.$$ (8) Analogously, given that mL = 0, selfish nonprofit managers disregard contributing to their organizations’ mission, and allocate all the donations to the self-serving (unproductive) dimension, $$w_{L}^{\ast }= {\sigma }_{i}$$. This implies that choosing to become a nonprofit manager gives to a selfish agent the level of utility $$U_{L}^{\ast }=\dfrac{D}{N}=\delta A\dfrac{\left( 1-N\right) ^{\alpha }}{N}.$$ (9) We can now state the following single-crossing result: Lemma 1. Let $$\widehat{N}$$ denote the level of N at which $$D(\widehat{N})=\widehat{N}$$. Then, \begin{equation*} U_{H}^{\ast }\gtreqless U_{L}^{\ast }\text{ if and only if }N\gtreqless \widehat{N}, \end{equation*} where (i) $$\delta A/(1+\delta A)<\widehat{N}<1$$, (ii) $$\widehat{N}$$ is strictly increasing in A and δ, and strictly decreasing in α, (iii) $$\underset{A\rightarrow \infty }{\lim }\widehat{N}=1$$, (iv) $$\underset{\alpha \rightarrow 0}{\lim}\widehat{N}=\delta A$$, and $$\underset{\alpha \rightarrow 1}{\lim }\widehat{N}=\delta A/(1+\delta A)$$. Lemma 1 states that a motivated individual obtains higher utility from becoming a nonprofit manager, as compared to a selfish individual making the same choice, only when donations per nonprofit are small enough, that is, D/N < 1. Both $$U_{H}^{\ast }$$ and $$U_{L}^{\ast }$$ are strictly increasing in donations per nonprofit, D/N. However, when the level of donations received by each nonprofit rises above a certain threshold (which here is equal to 1), $$U_{L}^{\ast }$$ surpasses $$U_{H}^{\ast }$$. The reason for this result essentially rests on the concavity of gi in (6), combined with the altruism displayed by motivated nonprofit managers in (7). These two features translate into a payoff function of motivated nonprofit managers, $$U_{H}^{\ast }$$, that is concave in D/N. Conversely, selfish nonprofit managers exhibit a payoff function, $$U_{L}^{\ast }$$, which is linear in D/N. This is because these agents only care about their perks or pet projects, and hence they exploit the lack of monitoring in the NGO sector in order to always set wi = D/N. 2.3. Equilibrium Occupational Choice Let NH and NL denote henceforth the mass of nonprofit managers of mH- and mL-type, respectively (the total mass of nonprofit managers is then N = NH + NL). In equilibrium, the following two conditions must be simultaneously satisfied: Given the values of NH and NL, each individual chooses the occupation that yields the higher level of utility, with some agents possibly indifferent between occupations. The allocation (NH, NL) must be feasible: (NH, NL) ∈ [0, 1/2] × [0, 1/2]. In this basic specification of the model, for a given parametric configuration, the equilibrium occupational choice will always be unique (except for one knife-edge case described in the next footnote). Nevertheless, the type of agents (in terms of their prosocial motivation) who self-select into the nonprofit sector will depend on the specific parametric configuration of the model. In what follows, we describe the main features of the two broad kinds of equilibria that may take place: an equilibrium where 0 = NH < NL = N (which we refer to as low effectiveness or L-equilibrium), and an equilibrium where 0 = NL < NH = N (which we denote as high effectiveness or H-equilibrium).8 L-equilibrium. In a “low-effectiveness equilibrium”, the nonprofit sector is populated exclusively by selfish individuals, and it arises when payoffs are such that: $$U_{H}^{\ast }(N)<V_{P}^{\ast }(N)\le U_{L}^{\ast }(N)$$, where $$V_{P}^{\ast }(N)$$ is given by (4), $$U_{H}^{\ast }(N)$$ by (8), $$U_{L}^{\ast }(N)$$ by (9), and N = NL ≤ 1/2. Lemma 1 implies that for $$U_{H}^{\ast }(N)<U_{L}^{\ast }(N)$$ to hold, the number of nonprofit firms should be sufficiently small (i.e., $$N<\widehat{N}$$), so that the donations received by each nonprofit firm turn out to be sufficiently large. In addition, the condition $$V_{P}^{\ast }(N)\le U_{L}^{\ast }(N)$$ leads to: $$N\le N_{0}\equiv \dfrac{\delta }{1+\delta }.$$ (10) From (10), we may observe that N0 < 1/2. As a result, in a low-effectiveness equilibrium it must necessarily be the case that N = NL = N0, so that the selfish agents turn out to be indifferent between the for-profit and nonprofit sectors. Indifference by mL-types leads a mass 1/2 − N0 of them to become private entrepreneurs, allowing thus “markets” to clear. Notice, finally, that $$U_{H}^{\ast }(N_{0})<V_{P}^{\ast }(N_{0})$$ needs to be satisfied; hence, the crucial parametric condition leading to an L-equilibrium boils down to $$N_{0}<\widehat{N}$$. H-equilibrium. This type of equilibrium takes place when all selfish individuals prefer to found private firms, whereas all motivated ones prefer (weakly) to be social entrepreneurs: $$U_{L}^{\ast }(N)<V_{P}^{\ast }(N)\le U_{H}^{\ast }(N)$$, where N = NH ≤ 1/2. Lemma 1 states that for $$U_{H}^{\ast }(N)>U_{L}^{\ast }(N)$$ to hold, the nonprofit sector should have a sufficiently large number of nonprofit firms: $$N>\widehat{N}$$. The condition $$U_{L}^{\ast }(N)<V_{P}^{\ast }(N)$$ requires that N > N0. Unlike the previous case, in the high-effectiveness equilibrium, we cannot rule out the possibility of full sectorial specialization of the two motivational types of agents (i.e., in principle, an H-equilibrium may feature NL = 0 and NH = 1/2). For future reference, we denote with N1 the value of N that makes mH-types indifferent between occupations. From (2) and (8), we can observe that N1 is implicitly defined by: $$\dfrac{(1-N_{1})^{\frac{1-\alpha (1-\gamma )}{\gamma }}}{N_{1}}\equiv \dfrac{A^{\frac{1-\gamma }{\gamma }}}{\delta }.$$ (11) Equilibrium Characterization. The following proposition characterizes the different kinds of equilibria that may arise, given the specific parametric configuration of the model. Proposition 1. Whenever A(1 + δ)1 − α ≠ 1, the equilibrium is unique. When A(1 + δ)1 − α > 1, the economy is in an L-equilibrium, whereas when A(1 + δ)1 − α < 1, the economy is in an H-equilibrium. More formally, Low-Effectiveness Equilibrium: if A(1 + δ)1 − α > 1, in equilibrium, there is a mass $$N^{\ast }=N_{L}^{\ast }=N_{0}$$ of nonprofit firms, all managed by mL-types. The mass of private entrepreneurs is equal to 1 − N0; among these, a mass 1/2 are mH-types and a mass 1/2 − N0 are mL-types. High-Effectiveness Equilibrium: if A(1 + δ)1 − α < 1, in equilibrium, there is a mass $$N^{\ast }=N_{H}^{\ast }=\min \left\lbrace N_{1},{1}/{2}\right\rbrace$$ of nonprofit firms, all managed by mH-types. The mass of private entrepreneurs is equal to max {1 − N1, 1/2}; among these, a mass 1/2 are mL-types and a mass max {0, 1/2 − N1} are mH-types. Proposition 1 characterizes the main types of equilibria that may arise in the model. These cases are depicted in Figure 1a–c. This figure portrays the indirect utilities of motivated and selfish agents in the nonprofit sector (UH and UL, respectively) and that of individuals in the private sector (y), all of them as functions of the size of the nonprofit sector, N. Figure 1. View largeDownload slide (a) Low-effectiveness equilibrium. (b) High-effectiveness equilibrium with incomplete sorting. (c) High-effectiveness equilibrium with full sorting. Figure 1. View largeDownload slide (a) Low-effectiveness equilibrium. (b) High-effectiveness equilibrium with incomplete sorting. (c) High-effectiveness equilibrium with full sorting. An implication of Proposition 1 is that more productive economies (i.e., those with a relatively large A) tend to exhibit a low-effectiveness equilibrium. This result rests on the fact that a larger A entails greater profits to private entrepreneurs. Hence, in equilibrium, a larger amount of donations to any nonprofit firm (σi) are needed in order to compensate for the higher opportunity cost of managing a nonprofit firm (i.e., the fact of not becoming a private entrepreneur). In turn, when σi is larger, the scope for rent seeking in the nonprofit sector is greater, which attracts more intensely selfish agents than motivated ones. A similar intuition applies to the effect of a higher warm-glow utility from giving; that is, a greater δ. This yields a larger amount of total donations, D, for a given mass of nonprofits N, making the nonprofit sector relatively more attractive to selfish agents than to motivated ones.9 2.4. Effect of Foreign Aid on the Equilibrium Allocation So far, all donations in our model were generated (endogenously) within the economy. However, in the context of developing economies, foreign aid represents also a major source of revenue for nonprofits organizations. In fact, an ever growing share of foreign aid is being channeled via NGOs. For instance, McCleary and Barro (2008) show that over 40% of US overseas development funds flows through NGOs. International aid agencies have been increasingly choosing NGOs over public-sector channels as well: for example, whereas between 1973 and 1988, only 6% of World Bank projects went through NGOs, by 1994 this share exceeded 50% (Hudock 1999).10 What would be the effect of a rise in foreign aid on the motivational composition and performance of the nonprofit sector of the recipient economy? In this section, we analyze this question by slightly modifying the above model to allow for an injection Δ > 0 of foreign aid into the economy. Foreign aid represents an exogenous increase in the total amount of donations available to the national nonprofit sector. Donations collected by a nonprofit firm now become: $$\dfrac{D}{N}=\dfrac{\delta A\left( 1-N\right) ^{\alpha }+\Delta }{N}.$$ (12) As done previously in Lemma 1, we first pin down the threshold $$\widehat{N}$$ such that for all $$N>\hat{N,}$$ the utility obtained by selfish nonprofit managers dominates that obtained by motivated nonprofit managers. Lemma 2. (i) Whenever 0 ≤ Δ ≤ 1, there exists a threshold $$\widehat{N}\le 1$$ such that $$U_{H}^{\ast }(N)\gtreqless U_{L}^{\ast }(N)$$ iff $$N\gtreqless \widehat{N}$$; the threshold $$\widehat{N}$$ is strictly increasing in Δ, and $$\lim _{\Delta \rightarrow 1}\widehat{N}=1$$. (ii) Whenever Δ > 1, $$U_{H}^{\ast }(N)<U_{L}^{\ast }(N)$$ for all 0 < N ≤ 1. The first result in Lemma 2 essentially says that the set of values of N for which the inequality $$U_{H}^{\ast }(N)<U_{L}^{\ast }(N)$$ holds—which is given by the interval $$(0,\widehat{N})$$—expands as the amount of foreign aid Δ increases. The second result states that when foreign aid is sufficiently large, $$U_{H}^{\ast }(N)<U_{L}^{\ast }(N)$$ becomes valid for any feasible value of N. The injection of foreign aid thus enlarges the set of parameters under which the economy features an equilibrium with selfish nonprofit managers (“L-equilibrium”). The proposition in what follows formalizes this perverse effect of foreign aid. For brevity, we restrict the analysis only to the more interesting case, in which A(1 + δ)1 − α < 1. For future reference, it proves useful to denote by $$\underline{N}$$ the level of N for which y(N) in (2) equals one; that is, $$\underline{N}\equiv 1-A^{\frac{1}{1-\alpha }}.$$ (13) In addition, in order to disregard situations in which $$\underline{N}\ge 0$$ fails to exist, we henceforth set the following upper bound on A: Assumption 1.  A ≤ 1. Note that if A > 1, then the condition A(1 + δ)1 − α < 1 for an “H-equilibrium” in Proposition 1 could never hold, and the model would always deliver—by construction—an “L-equilibrium”.11 Proposition 2. Consider an economy where 2 − (1 − α) < A < (1 + δ) − (1 − α). In these cases, the fraction of motivated nonprofit managers will depend nonmonotonically on the level of foreign aid. More precisely, by defining Δ0 ≡ 1 − A1/1 − α(1 + δ), where notice that Δ0 > 0, then: When 0 ≤ Δ < Δ0, all nonprofit firms are managed by mH-types. There exists a finite threshold ΔA > Δ0 such that, when Δ0 < Δ ≤ ΔA, all nonprofit firms are managed by mL-types. When Δ > ΔA, nonprofit firms are managed by a mix of types, with mL-type majority. In particular, there is a mass $$N_{L}^{\ast }={1}/{2}$$ of selfish nonprofit managers and a mass $$0<N_{H}^{\ast }<{1}/{2}$$ of motivated managers, where $$N_{H}^{\ast }$$ is strictly increasing in Δ. Proposition 2 describes the effects of changes in the amount of foreign aid Δ on the equilibrium allocation of an economy which, in the absence of any foreign donations, would display a high-effectiveness equilibrium. The proposition focuses on the case where A(1 + δ)1 − α < 1, but 21−αA > 1, which illustrates the nonmonotonic effect of foreign aid on motivational composition in the nonprofit sector in the cleanest possible way. However, in the Appendix C, we show that analogous results also arise for the case when 21−αA < 1 (see Proposition 2(bis) therein).12 According to Proposition 2, when foreign aid is not too large (Δ < Δ0), the nonprofit sector remains managed by motivated agents. However, when the level of donations surpasses the threshold Δ0, selfish agents start being attracted into the nonprofit sector due to the greater scope for rent extraction. Interestingly, for any Δ0 < Δ ≤ ΔA, the economy experiences a complete reversal in the equilibrium occupational choice: all mH-types choose the private sector, while the nonprofit sector becomes entirely managed by mL-types. Finally, when Δ > ΔA, foreign aid becomes so large that the nonprofit sector starts attracting back some of the mH-types in order to equalize the returns of motivated agents in the for-profit and nonprofit sectors. Notice, however, that when Δ > ΔA, the mass of nonprofits run by selfish agents is still larger than the mass of nonprofits managed by mH-types. Figure 2 depicts the above-mentioned results. The solid lines represent $$U_{H}^{\ast }(N)$$ and $$U_{L}^{\ast }(N)$$ when Δ = 0, the dashed lines shows nonprofit managers’ payoffs when Δ0 < Δ ≤ ΔA, and the dotted lines plots those payoffs when Δ > ΔA. A gradual injection of foreign aid from Δ = 0 to Δ = Δ0 initially has no effect on the motivational composition of the nonprofit sector. Beyond the amount of aid Δ = Δ0, the motivational composition of the nonprofit sector is completely reversed. Further increases in foreign aid have no effect on the nonprofit sector’s output, up to the point Δ = ΔA. There, all the unmotivated agents have moved into the nonprofit sector and thus its size equals 1/2. From then on, further injections of aid (beyond ΔA) start to attract back some motivated agents into the nonprofit sector, and the motivational composition of the sector therefore improves. Figure 2. View largeDownload slide Effect of foreign aid injection. Figure 2. View largeDownload slide Effect of foreign aid injection. A key corollary that stems from Proposition 2 refers to the total output of the nonprofit sector, G, at different values of Δ. Bearing in mind that only motivated nonprofit managers devote the donations collected to the dimension that produces the mission-oriented output gi (and, thus, contributes to the well-being of beneficiaries), an implication of Proposition 2 is that G(Δ) is nonmonotonic in Δ. In particular, nonprofit output grows initially with the amount of foreign aid, up to the level when Δ = Δ0 when it reaches $$G(\Delta _{0})=\underline{N}$$, which is the enhancing effect of foreign donations when the nonprofits are managed by motivated managers. However, for Δ0 < Δ ≤ ΔA, the motivation in the nonprofit sector gets completely “polluted” by the presence of selfish managers, and G(Δ) drops suddenly to zero. Finally, when foreign donations rise beyond ΔA, nonprofit output begins to grow again (starting off from G = 0), as some of the donations will end up in the hands of mH-types. This nonmonotonicity of the total output of the nonprofit sector is depicted by Figure 3. Figure 3. View largeDownload slide Foreign aid and nonprofit sector output. Figure 3. View largeDownload slide Foreign aid and nonprofit sector output. Note that our mechanism is quite different from the arguments previously raised concerning the perverse effects of foreign aid on the functioning of the public sector.13 In fact, our model shows that even when foreign aid is channeled through the NGO sector (hence, bypassing the public bureaucracy), perverse effects might still arise, because massive aid inflows may end up worsening the motivational composition of the NGO sector in the recipient country. Our results may also help shedding light on the so-called micro–macro paradox found in the empirical foreign aid literature; for example, Mosley (1986). On one hand, at the microeconomic level, there are numerous studies that find the positive effect of foreign-aid-financed projects on measures of welfare of beneficiaries. On the other hand, at the aggregate level most studies actually fail to find a significant positive effect. Our model rationalizes this paradox as follows: when aid inflows are small (or, alternatively, when you hold the motivational composition of the NGO sector constant), the general-equilibrium effect becomes negligible, and one may well find a positive effect of aid projects. However, when aid inflows are sufficiently large (e.g., when the well-functioning microlevel projects are scaled up), the general-equilibrium effects kick in, and the motivational adverse selection effect may neutralize the positive effect found at the micro level. 3. Eliminating Low-Effectiveness Equilibrium The analysis of the previous section raises a natural question: Can the low-effectiveness equilibrium be avoided? If so, through which channels? In this section, we explore three possible safeguard mechanisms that might prevent this equilibrium from emerging. The first focuses on the donors’ behavior and relaxes the assumption of donors being completely unaware of the motivational problems in the nonprofit sector. The second exploits the idea that managers in the nonprofit sector might have an informational advantage about the quality of the sector’s output, and thus there may be scope for creating nonprofit watchdog organizations. Finally, the third focuses on government policies, in particular on taxes and public financing of the nonprofit sector. 3.1. Donors’ Preferences: Conditional Warm Glow So far, we have assumed that entrepreneurs donate a fraction of their income simply because they enjoy the act of giving. Such disconnection between donations and their use may sound a bit too extreme. One may expect that motivated entrepreneurs will be unwilling to donate money when the nonprofit sector is entirely run by selfish types.14 In this section, we relax the assumption of fully naive warm glow giving by motivated entrepreneurs. In particular, we modify the basic model presented in Section 2 in two ways. First, we let the propensity to donate be type specific (δi) and increasing in mi. More precisely, assume that δi = δH ∈ (0, 1] when mi = mH, whereas δi = δL = 0 when mi = mL. Second, we let warm-glow weight rise with the fraction of motivated nonprofit managers, by postulating that mH-type private entrepreneurs have the following utility function: \begin{equation*} V_{H}(c,d)=\left[ \tilde{\delta }_{H}^{\tilde{\delta }_{H}}(1-\tilde{\delta }_{H})^{1-\tilde{\delta }_{H}}\right] ^{-1}c^{1-\tilde{\delta }_{H}}\,d^{\tilde{\delta }_{H}}, \end{equation*} $$\text{where} \quad \tilde{\delta }_{H}=f\, \delta _{H}\quad \text{ and }f\equiv \dfrac{N_{H}}{N_{H}+N_{L}}.$$ (14) The utility function (14) displays conditional warm-glow altruism, in the sense that the intensity of the warm-glow weight ($$\tilde{\delta }_{H}$$) is linked to the likelihood that the donation ends up in the hands of a motivated nonprofit manager. When prosocially motivated private entrepreneurs are characterized by (14), the level of donations obtained by a nonprofit firm will be given by: $$\dfrac{D}{N}=\dfrac{\delta _{H}\,A\left( \frac{1}{2}-N_{H}\right) N_{H}}{( 1-N_{H}-N_{L}) ^{1-\alpha }( N_{H}+N_{L}) ^{2}}.$$ (15) Proposition 3. Let the warm-glow weight be given by $$\tilde{\delta }_{i}=f\, \delta _{i}$$, where δH ∈ (0, 1], δL = 0 and f ≡ NH/(NH + NL). Then, defining Λ ≡ [(2 + δH)/(2 + 2δH)]1 − α: If A ≤ Λ, in equilibrium, $$N_{H}^{\ast }=\eta _{H}(A)$$ and $$N_{L}^{\ast }=0$$, where ∂ηH/∂A < 0. If Λ < A ≤ 1, in equilibrium, $$0<N_{H}^{\ast }<\tfrac{1}{2}$$ and $$0<N_{L}^{\ast }<\tfrac{1}{2}$$, with $$N_{H}^{\ast }+N_{L}^{\ast }=[ 1-A^{1/\left( 1-\alpha \right) }]$$. In particular, $$N_{H}^{\ast }=n_{H}(A)$$ and $$N_{L}^{\ast }=n_{L}(A)$$, where: \begin{align*} n_{H}(A) &=\dfrac{1}{4}-\sqrt{\dfrac{1}{16}-\dfrac{[ 1-A^{1/( 1-\alpha ) }] ^{2}}{\delta _{H}}}\text{,} \\ n_{L}(A) &=[ 1-A^{1/( 1-\alpha ) }] -n_{H}. \end{align*} Moreover, the fraction of motivated nonprofit managers decreases with A, ∂f/∂A < 0. Proposition 3 states that when warm glow weights depend on the fraction of motivated agents within the pool of nonprofit managers, the purely low-effectiveness equilibrium ceases to exist. The responsiveness of $$\tilde{\delta }_{H}$$ to f in (14) counterbalances the effect that a larger mass of mH-type entrepreneurs has on total donations, and thus neutralizes the source of interaction that leads to the rise of L-equilibrium. In other words, conditional warm-glow altruism removes the possibility that the nonprofit sector is managed fully by selfish agents, because in those cases motivated private entrepreneurs would refrain from donating any of their income. Nevertheless, conditional warm-glow altruism does not preclude the fact that the nonprofit sector may end up being partly managed by mL-types. This occurs when A is sufficiently large, which is in line again with the results of the baseline model in Proposition 1. Furthermore, Proposition 3 shows that the fraction of selfish nonprofit managers is monotonically increasing in A. 3.2. Nonprofits: Peer Monitoring by Watchdog Organizations Our benchmark model assumed that nonprofit managers are able to divert any amount of funds they receive away from the dimension that helps the ultimate beneficiaries. This extreme assumption intends to reflect the idea that monitoring the behavior of nonprofit managers (or knowing their intrinsic motivation) is an inherently difficult task for donors. In real life, cognizant of such pitfalls (and to ensure the credibility of the sector as a whole), nonprofits that care about the collective reputation of the sector often try to create peer-monitoring institutions, so as to discourage misbehavior within the sector. This is especially the case in developed economies, and examples of such institutions are the CFB quality label in the Netherlands and the Fundraising Standards Board in Britain (see Similon (2015) for a detailed description).15 In this section, we explore the consequences of peer monitoring in the nonprofit sector on the equilibrium occupational choices of motivated and selfish agents. To incorporate peer monitoring, we now assume that, after the decision by each nonprofit manager of how to split donations between the two dimensions (i.e., probeneficiary and perks), each nonprofit gets randomly matched together with another nonprofit. During this matching process, they may get to know each other’s accounts. In particular, with probability 0 < ρ < 1, a nonprofit observes the budget structure of its matching partner. We assume that only the motivated nonprofit managers care about the governance structure of their sector. Thus, if they realize that their matching partner has been diverting funds for perks or allocating the funds to projects useless for beneficiaries, they will make this information public. Publicizing this information leads to a penalty χ > 0 for the selfish agent (χ can reflect a reputation cost, disutility related to public shaming, or the cost of legal punishment meted out to the selfish nonprofit manager). With these assumptions, the expected utility of a selfish nonprofit manager becomes $$U_{L}^{\ast }(N,N_{H})=\dfrac{D}{N}-\frac{N_{H}}{N}\rho \chi =\delta A\dfrac{\left( 1-N\right) ^{\alpha }}{N}-\frac{N_{H}}{N}\rho \chi .$$ (16) The second term in (16) reflects the fact that, when a selfish nonprofit manager is matched with a motivated one (which occurs with probability NH/N), he suffers a loss equal to χ with probability ρ. Regarding motivated nonprofit managers, given that the matching process does not affect them, their indirect utility in the nonprofit sector remains as described by equation (8).16 This formulation intends to capture a number of relevant features of the monitoring aspect of the development nonprofit sector. First, on the motivational side, motivated agents clearly have an intrinsic motivation to also care about the public-good nature of having a well-functioning nonprofit sector. Relatedly, they may as well feel concerned about the general reputation of the sector.17 Second, in terms of information acquisition, because of contacts and information sharing between different NGOs on the ground (Meyer 1997), insiders are more likely to have access to information about the behavior of other members of the non–for-profit sector. The fact that the expected utility of selfish nonprofit managers in (16) is decreasing in the share of motivated managers opens up the possibility of multiple equilibria. Intuitively, a nonprofit sector that is mainly run by intrinsically motivated agents enjoys also high levels of monitoring and sanctioning of misbehavior in the sector. This, in turn, discourages selfish agents from entering the nonprofit sector as they expect a low probability of success in their intended diversion of funds. Conversely, when the nonprofit sector is relatively poor in terms of motivation, selfish agents feel more attracted to it, given the larger scope for successful rent extraction that poor monitoring allows. The next proposition fully characterizes the possible motivational equilibrium allocations in the nonprofit sector under the possibility of peer monitoring. Proposition 4. The equilibrium allocation of motivation in the nonprofit sector with peer monitoring nonprofits depends on the parametric configuration in the following way: If A(1 + δ)1 − α > 1, there exists a threshold value $$\bar{\Phi }>0$$ of the expected cost of monitoring ρχ such that: (a) If $$\rho \chi <\bar{\Phi }$$, only the ‘L-equilibrium’ prevails (with $$N^{\ast }=N_{0}=N_{L}^{\ast }<1/2$$). (b) If $$\rho \chi >\bar{\Phi }$$, the model exhibits multiple equilibria with three possible equilibrium outcomes: (i) an ‘L-equilibrium’ (with $$N^{\ast }=N_{0}=N_{L}^{\ast }<1/2$$), (ii) an ‘H-equilibrium’ (with $$N^{\ast }=N_{1}=N_{H}^{\ast }<1/2)$$, (iii) a ‘mixed-type equilibrium’ (with $$N^{\ast }=N_{1}=N_{H}^{\ast }+N_{L}^{\ast }<1/2$$ and $$N_{H}^{\ast }$$ and $$N_{L}^{\ast }>0$$). If A(1 + δ)1 − α < 1, only the ‘H-equilibrium’ prevails (with $$N^{\ast }=N_{H}^{\ast }=\min \lbrace N_{1},{1}/{2}\rbrace )$$. It is interesting to compare the above results to those in Proposition 1. When $$\rho \chi >\bar{\Phi }$$ (that is, when the expected punishment upon detection is high enough), peer monitoring by motivated agents in the nonprofit sector allows the possibility of a high-effectiveness equilibrium when A(1 + δ)1 − α > 1. These are parameter configurations that led to an “L-equilibrium” as a unique equilibrium in Proposition 1. However, peer monitoring by nonprofit managers does not ensure that such improved motivational allocation will necessarily emerge when A(1 + δ)1 − α > 1. In fact, multiple equilibria are possible in that range. The reason for this is that the quality of monitoring is itself endogenous to the occupational choice of agents. This negative externality from motivated nonprofit managers to selfish ones naturally creates a scope for expectation-driven multiple equilibria.18 3.3. Policies: Taxes and Public Financing of Nonprofit Sector In most economies, an important part of nonprofits’ revenues comes from public grants financed by taxes. This raises two main questions. First, what is the effect of partial public financing on the motivational composition and size of the nonprofit sector? Second, can public financing generate an improvement in the composition of the nonprofit sector, as compared to the decentralized equilibrium? In this section, we address these questions by adding a set of public policy variables into our basic model. We let the government impose a proportional tax on income in the for-profit sector and use its proceeds to distribute (unconditional) grants to nonprofit firms. Thus, the payoffs of individuals in the private sector now becomes $$V_{P}^{\ast }=\left( 1-t\right) y,$$ (17) where y is still given by (2). The level of donations collected by each nonprofit in this case are equal to $${\sigma }_{i}=\dfrac{D}{N}=\dfrac{\overset{\text{private donations}}{\overbrace{\delta \left( 1-t\right) (1-N)y}}+\overset{\text{public grant}}{\overbrace{t(1-N)y}}}{N}.$$ (18) Public financing via such a tax/grant system alters occupational choices of individuals via two distinct channels. First, we can see in (17) that taxation lowers returns in the private sector. Second, because the public sector distributes back all the taxes it collects, whereas the private sector only gives a fraction δ of its net income, σi in (18) increases with the tax rate t. Both channels, ceteris paribus, make the nonprofit sector more attractive to all individuals. However, within our general-equilibrium framework, the key issue is whether public financing increases the attractiveness of the nonprofit sector relatively more for motivated or for selfish individuals. To study the more interesting case, let us focus on a setting where our basic economy (without public financing) would give rise to a low-effectiveness equilibrium: A(1 + δ)1 − α > 1. Consider now an increase in taxes, with the transfer of all the proceeds to nonprofits as grants. For such policy to induce a motivational improvement in the nonprofit sector, it is crucial that, in the new equilibrium (after taxes), the selfish individuals who were initially managing the nonprofit sector switch occupations and move to the private sector. This will occur only if the policy attracts enough motivated agents from the private sector into the nonprofit sector, so that this entry sufficiently dilutes the amount of funds per nonprofit organization, even after taking into account the larger total funding of the nonprofit sector as a whole. The proposition in what follows formally proves that such a tax/grant policy exists. Proposition 5. For A(1 + δ)1 − α = 1 + ε, where $$0<\varepsilon <\bar{\varepsilon }$$, there exists a feasible range of tax rates $$[\underline {\mathit t},\bar{t}]$$, where $$\underline {\mathit t}>0$$ and $$\bar{t}\equiv (1-\delta )/(2-\delta )$$, such that when $$t\in [\underline {\mathit t},\bar{t}]$$ an ‘H-equilibrium’ arises. Figure 4 plots the equilibrium regions for different combinations of values of A and t (see Appendix C for the derivation of the equilibrium regions). There are four different regions. For combinations of relatively low values of A and t, the model features an “H-equilibrium” where the nonprofit sector is fully managed by motivated agents. On the other hand, given a certain level of t, for sufficiently high levels of A we have an “L-equilibrium”. Notice that when t = 0, the boundary between these two regions is given by A = 1/(1 + δ)1 − α, as previously stated in Proposition 1. In addition, with public financing, two new equilibrium regions arise: one with a mixed-type equilibrium with a fraction of motivated agents in the nonprofit sector larger than one-half (f > 0.5), and one with a mixed-type equilibrium with f < 0.5. These two types of equilibria occur when the tax rate is sufficiently large, while the former also requires that A is sufficiently small and the latter that A takes intermediate values. Figure 4. View largeDownload slide Public financing of nonprofit sector. Figure 4. View largeDownload slide Public financing of nonprofit sector. A crucial feature of Figure 4 is that the threshold level of A splitting the high- and low-effectiveness equilibrium regions is increasing in t (up to the point in which $$t=\bar{t}$$). As a consequence of this, there are situations in which introducing public funding of nonprofits via (higher) taxes on private incomes can make the economy switch from an “L-equilibrium” to an “H-equilibrium”. This is depicted in Figure 4 by the dashed line arrow. This result rests on a subtle general-equilibrium interaction. Consider an economy with no taxes that is on the low-effectiveness equilibrium region, located at point Z. At Z, all mH-types prefer the private sector, while mL-types are indifferent between both sectors.19 Because a higher tax rate makes the nonprofit sector more attractive, by sufficiently raising t we can make mH-types prefer nonprofit sector as well. However, when all motivated agents switch to the nonprofit sector, the value of N will rise, and the returns in this sector will accordingly decrease. When t lies within the interval $$[\underline {\mathit t},\bar{t}]$$, the new equilibrium allocation induced by the higher t leads to an increase in total funding of the nonprofit sector, while simultaneously reducing the value of per-organization funding (σi) enough so that only motivated agents are ultimately attracted to the nonprofit sector.20 In terms of actual implementation, our result implies that it may be advisable to give starting grants to new nonprofits. For instance, consider the recent proposals to do “philanthropy through privatization” (Salamon 2013), which consists in returning part of proceeds from the privatization of public-sector assets to foundations and charities. Our analysis suggests that this policy would work correctly only if the way these proceeds are used is such that they are scattered through a multitude of small organizations, rather than concentrating them on a few large nonprofits. In fact, while the latter risks worsening the motivational composition of the sector by attracting selfish agents, the former ensures that the returns in the nonprofit sector remain low enough to attract only motivated managers. 4. Discussion In this section, we proceed to discuss some of the key assumptions and modeling choices of our baseline framework. We also provide a discussion regarding the robustness of our results to relaxing these assumptions. 4.1. Decreasing Returns in the Nonprofit Sector One key assumption is the decreasing returns in the nonprofit sector (0 < γ < 1).21 This assumption underlies the single-crossing result (Lemma 1), which is, in turn, crucial for characterizing the different types of equilibria that may arise (Proposition 1). The nature of the functioning of the nonprofit sector makes this assumption seem appropriate in the context of our model. Two distinct reasons motivate our choice of decreasing returns at the level of single nonprofit organizations: (i) the fact that motivated agents may become a scarce input unable to grow at the same speed as donations; (ii) the fact that nonprofits tend to face increasingly difficult tasks to accomplish as their effort within their mission boundaries deepens. Nonprofit organizations are entities crucially defined by their missions (i.e., the specific social problems that these organizations aim to address). A fundamental scarce resource from the viewpoint of these organizations is then mission-oriented motivated labor, that is, individuals who are aligned with the mission of a particular nonprofit.22 The practitioners of the sector, in fact, underline that finding such people and expanding the staff of the organization is often extremely difficult, mainly because of the existing variety of missions and organizations.23 In this respect, a fundamental operational difference between nonprofit and for-profit firms is that, while (individually) the latter can easily purchase the required inputs in the market at a given market price, the former tends to face an often binding constraint on the amount of “mission-oriented motivation” it can acquire. Thus, as funding expands, if the nonprofit-motivated labor cannot grow at the same pace, some form of diminishing returns of those funds will eventually kick in. For instance, Robinson (1992, p. 38) notes about nonprofits working in rural areas that “ambitious attempts to expand or replicate successful projects can founder on the paucity of appropriately trained personnel who are experienced in community development”. Similarly, Hodson (1992) states that “Upgrading the management capability [of a development non-profit] usually implies new talent. Unfortunately, the story-book scenario under which the original team continues to develop its management capability at a rate sufficient to cope with rapid growth rarely comes true...” (p. 132) Concerning the second reason that motivates our assumption, the type of tasks that a nonprofit organization typically carries out tends to change along its expansion path. The first activities tend to concentrate on some form of emergency: saving individuals from imminent physical danger or starvation, helping to avoid some irreversible health problem, and so forth. In this sense, the marginal returns are extremely high at the beginning. However, the next activities of the nonprofit’s project involve usually tasks that are less emergency-driven and more oriented towards making the livelihoods of beneficiaries sustainable (e.g., putting children to school, providing economic activities so that beneficiaries can earn their living). Smillie (1995) argues that these types of tasks are much harder to accomplish successfully and involve a much longer period of time to realize. Such long-run perspective also implies that many organizations prefer to concentrate on the emergencies; however, the resulting competition among them for “saving lives” limits their expansion, as has been underlined by observers of large-scale humanitarian emergencies such as the 2004 tsunami (Mattei 2005). In our case, this implies that, for a given nonprofit organization, the slope of its production function is fairly steep at low levels of funding (when it first deals with emergency activities), whereas it becomes flatter at higher levels of funding (as the nonprofit moves its focus to sustainable development activities). 4.2. Informational Asymmetries and Lack of Contractibility Throughout the paper we have assumed that motives for giving are unrelated to the performance of nonprofit firms.24 This assumption would become untenable if motivated nonprofit managers could find a way to signal their motivation to donors. One possibility for such signaling would result from allowing nonprofit managers to “burn money”. In such case, a separating equilibrium where motivated types engage in “burning” enough money (so as to discourage self-interested types from joining the nonprofit sector) could arise. It is hard to envision, however, a practical way of carrying out these sort of actions. One possibility could be allowing for self-imposed restrictions on overheads. Yet, to be credible, such a scheme would require a third-party certification of such restrictions (for example, by the government), bringing up additional credibility issues to the model.25 More generally, our model has implicitly assumed that nonprofits’ output is completely unobservable or unverifiable. This assumption underlies the severe noncontractability of managers’ allocation decisions in the nonprofit sector. Noncontractability problems means that motivation serves as a substitute for contracts in our model, as it is exactly this problem that attracts selfish individuals into nonprofits when this sector is flooded with donations. Clearly, some degree of output measurability would ease the problem of adverse selection. However, it is exactly in those sectors where output is poorly measured that the role of nonprofits is greater, as has been argued by Glaeser and Shleifer (2001). In fact, in sectors where output can be measured relatively well, the production could be fully taken care of by for-profit firms. 4.3. Absence of Nonpecuniary Incentives Our model assumed away any form of nonpecuniary incentives, such as those that have been studied in the organizational economics literature (Besley and Ghatak 2008; Bradler et al. 2015). This seems quite relevant in our context, because nonpecuniary incentives could well be heterogeneously valued by agents with different levels of intrinsic motivation. If social prestige associated with working in the nonprofit sector is valued relatively more by motivated types (for example, because altruistic agents care more about the social signaling built around contributing to the production of public goods), this would enlarge the range of parameters displaying an H-equilibrium. However, it could be that social prestige is valued more strongly by self-interested agents (if there are large indirect pecuniary benefits that social prestige can deliver), and the range of parameters with an H-equilibrium would thus shrink. Lastly, there could also be nonpecuniary externalities associated to the presence of monetary rewards, as those in Benabou and Tirole (2006); when this is the case, large scope for earnings in the nonprofit sector may lead to the crowding out of prosocially motivated nonprofit managers who fear being (incorrectly) perceived as monetarily driven. 5. Case Studies In this section, we present two groups of case studies that illustrate the applications of our model to large-scale recent real-life phenomena in international development efforts. The first group presents the analysis of the NGO sector in developing countries (Uganda and Pakistan) and its governance problems, in particular related to the inflows of foreign aid. The second focuses on the international NGO humanitarian efforts and the dynamics of post-reconstruction by international NGOs, following the natural disasters (specifically, the December 2004 tsunami in the Indian Ocean and the January 2009 earthquake in Haiti). 5.1. The NGO Sector in Developing Countries 5.1.1. Uganda Substantial narrative evidence for several developing countries indicates that generous financing by foreign aid can lead to perverse effects by triggering opportunistic behavior and elite capture in these local NGO projects (see, e.g., Platteau 2004; Platteau and Gaspart 2003; the contributions in Bierschenk, Chauveau, and Sardan 2000; Gueneau and Leconte 1998). Here, we discuss one of the best documented analyses, that of the NGO sector in Uganda. This analysis was conducted by a team of development economists at Oxford University’s Center for Study of African Economies (see Barr, Fafchamps, and Owens 2004, 2005; Burger and Owens 2010, 2013; Fafchamps and Owens 2009). The analysis is based on a unique representative national survey of NGOs, collected by Abigail Barr, Marcel Fafchamps, and Trudy Owens in 2002, and financed by the World Bank and the Japanese government. The aim of the study was to collect information about Ugandan NGOs’ activities, their sources of funding, and their personnel. The surveys were conducted with about 300 NGOs (out of about 3500 registered ones), and the main descriptive findings were published as a CSAE report to the Government of Uganda in December 2003 (Barr et al. 2004). Several interesting facts emerge from this study. The bulk of funding of Ugandan NGOs comes from international NGOs. These latter often conduct their own monitoring, but despite this, the authors argue that it is difficult to exclude that there are “crooks” in the sector. The authors note: “It is possible that the fluidity of the NGO sector and the focus on non-material services (e.g., ‘talk’ and ‘advocacy’) enable unscrupulous individuals to take advantage of the system... There is indeed a suspicion among policy circles that not all Ugandan NGOs genuinely take public interest to heart. [Some] accounts speak of crooks and swindlers attracted to the sector by the prospect of securing grant money... In a context where most charity funding comes from international benefactors, new incentive problems emerge. One is that of opportunistic NGOs whereby talented Ugandans initiate a local NGO not so much because they care about public good but because they hope to attract external funding to pay themselves a wage” (Barr et al. 2004, p. 4–7). In a companion paper, Barr et al. (2005) write: “According to respondents, per diems to staff and beneficiaries account for less than 2% of the total expenditures for the sample as a whole (slightly more for small NGOs). However, we suspect these data are not fully accurate and that there may be additional per diems included in program and miscellaneous costs. Ugandan NGOs are well aware that they are scrutinized by members and donors for excessive salary and per diem payments. They may therefore be tempted to hide these payments in other costs, or to simply misreport them. Given the poor quality of financial accounts provided by surveyed NGOs, it is difficult to determine the extent to which NGO profits are redistributed to staff via the payment of per diems. What is clear, however, is that most surveyed NGOs do not have transparent accounts” (Barr et al. 2005, p. 667). If the Ugandan NGO sector is facing a serious problem of fraud, why is it unable to create institutions that screen or limit such behavior? The report provides some answers to this: “Developed countries all have instituted sophisticated legislation regulating charities. This is because unscrupulous individuals may solicit funds from the public without actually serving the public good they are supposed to serve. Hit-and-run crooks may take the money and disappear. More sophisticated crooks may set up an organization that partly serves its stated objective, but at the same time either divert funds directly to their pocket or spend part of the money on perks, allowances, and excess salaries. This kind of behavior is damaging to charitable organizations at large because it undermines the public’s trust in them and reduces funding. It is therefore in the interest of bona fide charities to regulate the industry so as to weed out crooks... Reporting requirements, however, impose an additional burden of work in charities. Moreover, they are useless unless they are combined with the Charities Commission’s capacity to investigate the veracity of the reports provided. Crooks smart enough to defraud granting agencies are also smart enough to produce a fake report for the Charities Commission” (Barr et al. 2004, p. 7). Would peer monitoring be a solution to this problem? The report indicates that certain Ugandan NGOs tried to create such institutions, but they do not seem to function: “While some NGO networks have actively sought to promote good governance among their member organizations, to our knowledge, none has sought to set up a formal certification system. Instead, networks and umbrella organizations have sought to be inclusive and have welcomed new members with little or no attempt at quality control” (Barr et al. 2005, p. 675). The only mechanism that limits the misbehavior of NGOs seems to be donors’ (imperfect) control. In fact, the international NGOs seem to concentrate most of their financing in a few Ugandan NGOs. The authors argue that “one possible explanation is that foreign donors cannot identify the most promising NGOs and therefore concentrate their activities on a small number of trusted NGOs. Another possibility is that many sampled NGOs are engaged in a ‘rent seeking’ process by which they seek self-employment by attracting grants. Donors may have correctly identified them as undeserving and denied them funding” (Barr et al. 2004, p. 27). 5.1.2. Pakistan Another interesting case study comes from Pakistan and is based on the analysis by Bano (2008). Motivated by the recent trend of aid policies aiming at strengthening the local civil society, this study focused on the effects of channeling development aid through local NGOs. The author conducted a comparative in-depth survey of 40 local Pakistani NGOs: 20 NGOs that rely on foreign aid for their financing and 20 that rely only on domestic financing. Although the sample is relatively small, the author tried to maximize the national coverage in selecting the organizations across all the regions of Pakistan and focusing strictly on the organizations providing public goods (i.e., excluding the organizations aimed at providing benefits only to their members). The main findings of the study are three. First, the NGOs that relied on foreign aid were much more likely to have no members. Interestingly, several authors (Henderson 2002; Tvedt 1998) previously had documented that the absence of members usually implies high salary of the NGO leader and poor overall performance of the organization. Thus, it is likely that these NGOs relying on foreign aid in many cases were just “empty shells”. Secondly, there were large motivational differences between the NGOs relying on foreign aid and those relying on domestic financing (see table 4 in Bano 2008). For instance, nearly all the aid-financed NGOs, the leader drew a salary above the governmental scale (while this happened in none of the domestic-financed ones). The offices of all the aid-financed NGOs located in luxury areas of the cities (none for domestic-financed ones), the majority of aid-financed NGOs had four-wheel drive cars (none for domestic-financed ones), and in all of aid-financed NGOs the project was designed first and beneficiaries chosen after (while the opposite was true for the domestic-financed NGOs. Finally, NGOs relying on foreign aid exhibited lower organizational performance, as measured by fluctuation in annuals budgets and the stability of the type of activities. The aid-financed NGOs showed dramatic fluctuations in their annual budgets, in response to aid flows, whereas the budgets of domestic-financed NGOs were quite stable. The activities of aid-financed NGOs kept changing in response to aid flows, whereas the focus of the domestic-financed organizations’ activities remained stable. Although the study relied on interviews and the causal identification of aid financing was not feasible quantitatively, on the basis of additional qualitative evidence Bano (2008) argues that foreign aid led to a modification of material aspirations among leaders of NGOs, which in turn resulted in lower performance. For instance, one of the interviewed NGO leaders noted that, as an organization starts to rely on foreign aid, “the people who are more interested in personal gains start getting attracted to the organization” (Bano 2008, p. 2303). Although our model assumes that the inflow of foreign aid is distributed equally among NGOs, the above findings can still be explained in the light of our model’s main mechanism, and can be interpreted as a transition stage when moving from the equilibrium without foreign aid to the one with foreign aid. Our model predicts that, starting with an honest equilibrium without foreign financing, an aid inflow would trigger entry into the NGO sector by selfish agents seeking rents. The 20 organizations in the study that rely on foreign aid can be thought of as such entrants. In the meanwhile, the NGOs without foreign aid financing still operate as under the “no foreign aid” regime. Over time, as selfish agents enter the NGO sector in even higher numbers, the motivated agents start to quit the sector. If our model is valid, we should observe over time that the number (and the share) of NGOs in Pakistan that do not rely on foreign aid financing with their leaders showing relatively low material aspirations should decrease. This is an interesting prediction that hopefully can be tested in the future work. 5.2. Humanitarian Emergencies and International NGOs 5.2.1. The 2004 Tsunami On December 26, 2004, a tsunami of unprecedented power, triggered by the Sumatra–Andaman undersea earthquake, hit the coastal areas of 14 countries in Asia and Africa (with Indonesia and Sri Lanka receiving the strongest impact). It was one of the deadliest natural disasters in recent history, killing close to 230,000 people and displacing over 1.75 million people. The scale of the disaster, coinciding with it happening right after Christmas and fed by a large-scale international media coverage, led to a massive humanitarian response, both through public and private channels. The amount of private donations to international NGOs was huge: for example, Save the Children USA received over 6 million USD in just 4 days, whereas Catholic Relief Services collected over 1 million USD in 3 days. In total, US-based charities raised about 1.6 billion USD for tsunami relief (Wallace and Wilhelm 2005), whereas total international response (both public and private) amounted to 17 billion USD (Jayasuriya and McCawley 2010). The evolution of the resulting humanitarian relief activity presents an interesting story. It started off with early successes: for instance, Fabrycky, Inderfurth and Cohen (2005) write: “The tsunami will be remembered as a model for effective global disaster response... Because of the speed and generosity of the response, its effectiveness compared to previous (and even subsequent) disasters, and its sustained focus on reconstruction and prevention, we give the overall aid effort a grade of ‘A’... ”. However, quite soon, numerous problems in relief activities started to emerge. These included inefficiencies in the distribution of funds, unsatisfactory plans for the rebuilding of houses, cost escalations, and coordination failures (Jayasuriya and McCawley 2010, p. 4). This is summarized by the Joint Evaluation Report of the Tsunami Evaluation Coalition: “Exceptional international funding provided the opportunity for an exceptional international response. However, the pressure to spend money quickly and visibly worked against making the best use of local and national capacities... Many efforts and capacities of locals and nationals were marginalized by an overwhelming flood of well-funded international agencies (as well as hundreds of private individuals and organizations), which controlled immense resources” (Telford, Cosgrave, and Houghton 2006, p. 18–19). The observers underline several mechanisms behind this failure. One of them was the pressure to rapidly disburse huge amount of donations, which weakened the control mechanisms on how the money was spent. Maxwell et al. (2012) note that: “During the response to the 2004 tsunami, many agencies reported intense pressure to speed up the rate at which donations were being expended, in part to ensure an ongoing flow of funds. Sometimes, however, the need to act swiftly may result from the situation on the ground, not just from donor or media pressure. While pressure to spend speedily does not, in itself, cause corruption, it may mean that standard checks and systems intended to prevent corruption are overridden or ignored” (Maxwell et al. 2012, p. 143). A related mechanism is the rush of too many NGOs to carry out highly visible activities in disaster-prone areas: “One of the striking features of the relief effort was the presence of a horde of small, often newly formed, foreign organizations with little if any experience in disaster relief but motivated by a strong humanitarian impulse that ‘something had to be done’. Throughout the tsunami affected areas small groups and individuals from a wide range of countries were active in all sorts of activities. For instance, a Slovakian organization was engaged in boatbuilding, while an Austrian NGO assisted in constructing houses. Neither had any previous experience of South Asia or disaster relief. Similarly individuals from Europe, North America and Asia whose only prior knowledge of Sri Lanka came from news bulletins arrived in the country and proceeded to do whatever they thought useful” (Stirrat 2006, p. 14) This dynamics fits well the main predictions of our model. A sudden natural disaster creates a sharp increase in the willingness to give of individual donors (an increase in δ) and/or a large increase in foreign aid (a big increase in Δ). This attracts a mass of agents to enter the nonprofit sector (here, founding new NGOs). However, given that many of these agents were mostly driven by ego utility obtained from high visibility, our model would predict that a large fraction of the donations will end up being spent in projects that do not necessarily help the beneficiaries (or possibly help them only in the short run, but prove to be useless in the medium run). An alternative explanation to the above patterns is the lack of experience and knowledge of certain NGOs that entered the donation market during natural disasters. As Willitts-King and Harvey (2005, Section 2.4) note, administrative inefficiency in humanitarian relief is different from corruption, although both are harmful for the performance of the humanitarian aid system. However, on the basis of an in-depth study and interviews with humanitarian relief professionals, conducted shortly after the massive inflow of humanitarian relief organizations into the tsunami-hit areas, they also provide a detailed list of major corruption risks at various levels of the humanitarian relief chain, including inflating overheads, setting up bogus NGOs, kickbacks from procurement, field staff collusion with diversion, listing phantom staff, and so forth. For instance, they write: “Once funds have been passed to an agency [NGO], there are many opportunities for individuals to make personal gain. This normally entails some collusion between agency staff internally, or between staff and outside suppliers or authorities. At field level, staff might be ‘paid off’ for turning a blind eye to the false registration of relatives on a distribution list, or theft from a warehouse. Staff might themselves extract payments directly to include people on beneficiary lists who do not fit vulnerability criteria. Procurement, storage and transport offer widespread opportunities for corruption. Staff might accept kickbacks or bribes to favor a particular supplier or agree an inflated quote, or relatives might be preferred even though the quality or price is uncompetitive... Other experiences included the use of agency vehicles to provide paid rides, taxi services, or in some cases public bus services” (Willitts-King and Harvey 2005, p. 21–22) Given this analysis, it is difficult to imagine that the main source of failure of the humanitarian aid system after the tsunami is driven only by the administrative inefficiency. More likely, it is the combination of entry of unscrupulous or visibility-seeking actors at various layers of the aid chain with administrative inefficiency and lack of coordination that generated the poor outcomes of the overall system.26 5.2.2. The 2010 Haiti Earthquake On January 12, 2010, a 7.0-magnitude earthquake hit Haiti, the poorest country of the Western hemisphere. This also was an extremely violent natural disaster, killing more than 200,000 people in a very short period of time, and destroying most of the administrative capacity of the state. Similar to the case of 2004 tsunami, the international humanitarian response to this disaster was massive. Between 2010 and 2012, the total amount over 8 billion USD (of which 3 billion came through international NGOs) was given by the international community for the post-earthquake reconstruction activities. One of the largest French NGOs, Medecins Sans Frontieres (MSF), noted that its Haiti intervention was the largest in the long history of this organization (Biquet 2013, p. 130). This rush in international humanitarian efforts fuelled by generous donations, made NGOs key players in the reconstruction efforts. The presence of NGOs, already considerable before the earthquake, became so massive as for Haiti being dubbed in international circles as “the Republic of NGOs” (Klarreich and Polman 2012). Similar to the post-tsunami reconstruction, early successes were followed by disappointing outcomes later on: the lack of coordination between NGOs and the complex overlapping system of aid actors that emerged became a problem rather than a solution. This was made most apparent during the cholera epidemics that hit Haiti in October 2010. Biquet (2013) reports that more than 80% of patients in the 3 months following the outbreak of the epidemics were taken care of by two actors (Cuban medical brigades and the MSF) acting outside the ‘Health Cluster’ that concentrated all the other NGOs with health-related activities (there were more than 600 international organizations in this cluster). One key explanation proposed for the failure of international humanitarian assistance in Haiti is the lack of accountability of organizations carrying out interventions, coupled with massive budgets. Klarreich and Polman (2012) argue that this resulted in a complete disconnection from the needs of the local population and exclusion of local civil society, more knowledgeable about the local conditions and needs, from the reconstruction effort: “From the very beginning, NGOs followed their own agendas and set their own priorities, largely excluding the Haitian government and civil society... The money that did reach Haiti has often failed to seed projects that truly respond to Haitians’ needs. The problem is not exactly that funds were wasted or even stolen, though that has sometimes been the case. Rather, much of the relief wasn’t spent on what was most needed... [As a result] the recovery effort has been so poorly managed as to leave the country even weaker than before.” (Klarreich and Polman 2012) As in the case of 2004 tsunami, the massive increase in the number of NGOs carrying out activities was driven by donors’ willingness to give, in the absence of any—even minimal—certification of NGOs. Haver and Foley (2011) state that “the response to the Haiti earthquake of 2010 [was one] in which thousands of NGOs, many of them unqualified ‘cowboy NGOs’, rushed in to help”. The authors argue that instituting a certification scheme would have curbed (at least in part) this drive; however, they also acknowledge that such a scheme would have been quite difficult to implement (for instance, it would have turned away many local or regional NGOs for whom the paperwork related to such certification would have been prohibitively complicated or costly). 6. Conclusion We built a tractable general-equilibrium model of private provision of public goods via endogenous voluntary contributions to the nonprofit sector. Our model shows that rent seeking or ego utility seeking motives may attract selfish individuals to the nonprofit sector, which in turn may end up crowding out intrinsically motivated agents from this sector. Selfish motives and the possibility of motivational crowding out become increasingly severe as economies get richer and give more generously to the nonprofit sector. The main applications of our theory belong to two domains. The first is foreign aid intermediation by NGOs. Aid is being increasingly channeled via NGOs. This is to a large extent the result of the growing disillusionment in government-to-government project aid, often considered to be politicized and easily corruptible (see, for instance, Alesina and Dollar (2000) and Kuziemko and Werker (2006)). The rise of NGO intermediation has meant an increasing emphasis of project ownership, decentralization, and participatory development. However, no theoretical analysis has been conducted so far concerning the general-equilibrium implications of such massive channeling of aid via NGOs.27 The application of our theory to foreign aid sheds light on these issues. In particular, a key implication of our results is that, as the NGO channel of aid expands, the investment into better accountability in the NGO sector becomes increasingly important, so as to curb self-interested motives. In other words, optimal aid delivery through NGOs requires harder controls accompanying the scaling-up of aid efforts. The second application pertains to the recent debates on the accountability and performance-based pay in the nonprofit sector in developed countries. The existing literature recognizes that firms in the nonprofit sector are often prone to agency problems, due to the inherent difficulty of measuring their performance. Understanding the conditions under which these problems are most salient is an open issue in the public economics literature. Our analysis contributes to this debate by indicating that the role of (endogenously determined) outside options of selfish and motivated individuals inside the nonprofit sector is crucial. In particular, what matters is whether it is motivated or selfish agents that exit more intensively the nonprofit sector when donations from the private sector decrease. If selfish agents exit more intensively, then recessions can have a cleansing effect regarding the motivational composition of the nonprofit sector. This is, in our view, an interesting hypothesis that could be tested empirically in future work. Two further promising avenues for future research are worth mentioning. The first is the role of specific public policy instruments towards the nonprofit sector. Several recent studies on the economics of charities and nonprofits have explored the effectiveness of direct versus matching grants (Andreoni and Payne (2003, 2011); Karlan, List, and Shafir (2011)). Our analysis indicates that matching grants might have an additional effect that operates through the motivational composition of the nonprofit sector: such financing induces nonprofits to engage more actively in fundraising (and thus to reduce their internal resources devoted to working on their projects), and this might induce the motivated individuals to quit the nonprofit sector. A more complete analysis of the effectiveness of matching grants as compared to direct ones, which takes into account these various effects, looks very promising. The second relates to the disconnection between who finances and who benefits from the activity of the nonprofit sector. The resulting monitoring problems create the need to coordinate the scaling up of financing with investment into improved monitoring. As suggested by Ruben (2012), evaluation of aid effectiveness may generate social benefits even when we can learn relatively little from the evaluation exercise. This is because the very fact of being evaluated makes the misallocation of aid resources more difficult and thus help improve the motivational composition in the nonprofit sector. Our framework may allow to study these indirect effects of evaluation of development projects. Appendix A: Endogenous Fundraising Effort Our benchmark model assumed that total donations are equally split (quite mechanically) between all nonprofit firms. It is well known, however, that nonprofits actively compete quite intensely for donations via fundraising activities.28 Here, we relax the assumption of fixed division of donations by incorporating the endogenous fundraising choice by nonprofits. In terms of the private sector, we keep the same structure described in Section 2.1. The main difference is that now nonprofit managers can influence the share of funds they obtain from the pool of total donations by exerting fundraising effort. We assume that each nonprofit manager i is endowed with one unit of time, which she may split between fundraising and working towards the mission of her nonprofit organization (project implementation). Fundraising effort allows the nonprofit manager to attract a larger share of donations (from the pool of aggregate donations) to her own nonprofit. Implementation effort is required in order to make those donations effective in addressing the nonprofit’s mission. We denote henceforth by ei ≥ 0, the effort exerted in fundraising and by ςi ≥ 0 the implementation effort. The time constraint means that ei + ςi = 1. As before, the nonprofit manager collects an amount of donations σi from the aggregate pool of donations D. One part of σi, equal to wi, is allocated for the perks, while σi − wi is used as input for the nonprofit’s production. In this section, in the sake of algebraic simplicity, we assume that the output of a nonprofit firm is linear in undistributed donations, namely: $$g_{i}=2( {\sigma }_{i}-w_{i})\varsigma _{i}.$$ (A.1) An important feature of gi in (A.1) is the fact that undistributed donations (σi − wi) and implementation effort (ςi) are complements in the production function of the nonprofit. We assume that aggregate fundraising effort does not alter the total pool of donations channeled to the nonprofit sector, D. However, the fundraising effort exerted by each specific nonprofit manager affects the division of D among the mass of nonprofit firms N. In other words, we model fundraising as a zero-sum game over the division of a given D. Formally, we assume that $${\sigma }_{i}=\dfrac{D}{N}\times \dfrac{e_{i}}{\bar{e}}=\dfrac{\delta A\left( 1-N\right) ^{\alpha }}{N}\times \dfrac{e_{i}}{\bar{e}},$$ (A.2) where $$\bar{e}$$ denotes the average fundraising effort in the nonprofit sector as a whole. Again, nonprofit managers derive utility from the two dimensions, with weights on each of two sources of utility determined by the agent’s level of prosocial motivation, mi. In addition, we assume the total effort exerted by nonprofit managers entails a level of disutility that depends on the agent’s intrinsic prosocial motivation: \begin{equation*} U_{i}(w_{i},g_{i})=\frac{w_{i}^{1-m_{i}}g_{i}^{m_{i}}}{m_{i}^{m_{i}}(1-m_{i})^{1-m_{i}}}- ( 1-m_{i}) ( e_{i}+\varsigma _{i}), \,\,\, \text{where }m_{i}\in \lbrace m_{H},m_{L}\rbrace . \end{equation*} Because mH = 1, in the optimum, motivated nonprofit managers will always set $$w_{H}^{\ast }=0$$ and $$e_{H}^{\ast }+\varsigma _{H}^{\ast }=1$$. The exact values of $$e_{H}^{\ast }$$ and $$\varsigma _{H}^{\ast }$$ are determined by the following optimization problem: \begin{equation*} e_{H}^{\ast }\equiv \underset{e_{i}\in \left[ 0,1\right] }{\arg \max }:g_{i}=2\dfrac{D}{N}\dfrac{e_{i}}{\bar{e}}( 1-e_{i}) , \end{equation*} with $$\varsigma _{H}^{\ast }=1-e_{H}^{\ast }$$. The above problem yields $$e_{H}^{\ast }=\varsigma _{H}^{\ast }=\dfrac{1}{2},$$ (A.3) which in turn implies that an mH-type nonprofit manager obtains a level of utility given by $$U_{H}^{\ast }=\dfrac{1}{2\bar{e}}\dfrac{D}{N}=\dfrac{1}{2\bar{e}}\dfrac{\delta A\left( 1-N\right) ^{\alpha }}{N}.$$ (A.4) With regard to selfish nonprofit managers, again, they will always set $$w_{L}^{\ast }= {\sigma }_{i}$$. In addition, because selfish agents care only about their private consumption, and ςi is only instrumental to producing nonprofit output, in the optimum, they will always set $$\varsigma _{i}^{\ast }=0$$. As a consequence, the level of $$e_{L}^{\ast }$$ will be determined by the solution of the following maximization problem: \begin{equation*} e_{L}^{\ast }\equiv \underset{e_{i}\in \left[ 0,1\right] }{\arg \max }:w_{i}=\dfrac{D}{N}\dfrac{e_{i}}{\bar{e}}-e_{i}, \end{equation*} which, given the linearity of both the benefit and the cost of effort, trivially yields $$e_{L}^{\ast }=\left\lbrace \begin{array}{c}0, \,\, \text{if }\bar{e}^{-1}D/N<1, \\ 1, \,\,\text{if }\bar{e}^{-1}D/N\ge 1.\end{array}\right.$$ (A.5) The utility that a selfish agent obtains from becoming a nonprofit manager is thus: $$U_{L}^{\ast }=\max \left\lbrace \dfrac{D}{N}\dfrac{1}{\bar{e}}-1,0\right\rbrace .$$ (A.6) Note that the indirect utility of the selfish agent decreases, as before, with the size of the nonprofit sector. However, it now reaches zero at an interior value, whereas in the basic model that occurred only when N = 1. The reason for this is that donations must now be obtained through exerting effort, which is costly to mH-types. For a sufficiently large size of the nonprofit sector, the level donations per nonprofit firm that can be obtained through fundraising effort is just too small to justify their effort cost. This means that a selfish agent will choose to stop competing for donations if the number of nonprofits firms N reaches a certain critical level (beyond such critical level of N selfish managers would optimally choose to exert no effort and collect zero donations, which accordingly yields $$U_{L}^{\ast }=0$$). H-equilibrium. In an H-equilibrium, all nonprofit managers are of mH-type and set $$e_{H}^{\ast }=0.5$$. This implies that each nonprofit manager ends up raising $$\sigma _{H}^{\ast }=\dfrac{\delta A\left( 1-N_{H}^{\ast }\right) ^{\alpha }}{N_{H}^{\ast }}.$$ (A.7) Recalling (4), (A.4), and (A.6), we can observe that an H-equilibrium exists if and only if $$\sigma _{H}^{\ast }\le 1$$. L-equilibrium. In an L-equilibrium, all nonprofit managers are of mL-type and set $$e_{L}^{\ast }=1$$. In this case, each nonprofit manager raises $$\sigma _{L}^{\ast }=\dfrac{\delta A\left( 1-N_{L}^{\ast }\right) ^{\alpha }}{N_{L}^{\ast }}.$$ (A.8) Using again (4), (A.4), and (A.6), it follows that an L-equilibrium exists if and only if $$\sigma _{L}^{\ast }>2$$. Mixed-Type Equilibrium. In a mixed-type equilibrium, all agents are indifferent across occupations and the nonprofit sector is managed by a mix of mH- and mL-types. That is, a mixed-type equilibrium is characterized by $$U_{H}^{\ast }(N^{\ast })=U_{L}^{\ast }(N^{\ast })=V_{P}^{\ast }(N^{\ast })$$, where $$N^{\ast }=N_{L}^{\ast }+N_{H}^{\ast }$$ and $$0<N_{L}^{\ast },N_{H}^{\ast }\le 1/2$$. Equality among (A.4) and (A.6) requires that average fundraising effort satisfies $$\bar{e}_{ {mixed}}=0.5\times \left( D/N\right)$$, which in turn means that $$U_{H}^{\ast }(N^{\ast })=U_{L}^{\ast }(N^{\ast })=1$$. The returns in the private sector must then also equal to one, which, using (4), implies that N* = 1 − A1/1−α. In addition, because $$e_{H}^{\ast }=0.5$$ and $$e_{L}^{\ast }=1$$, then $$\bar{e}_{ {mixed}}=0.5\times \left( D/N\right)$$, together with N* = 1 − A1/1−α, pin down the exact values of $$N_{L}^{\ast }$$ and $$N_{H}^{\ast }$$. Equilibrium Characterization with Fundraising Effort. We now fully characterize the type of equilibrium that arises in the model with fundraising effort. Proposition A.1. The equilibrium allocation that arises is always unique and depends on the specific parametric configuration of the model. If A ≤ 1/(1 + δ)1 − α, the economy exhibits an “H-equilibrium” with $$N^{\ast }=N_{H}^{\ast }=\delta /(1+\delta )$$. All nonprofit managers exert the same level of fundraising and project implementation effort: $$e_{H}^{\ast }=\varsigma _{H}^{\ast }=0.5$$. If A ≥ [2/(2 + δ)]1 − α, the economy exhibits an “L-equilibrium” with $$N^{\ast }=N_{L}^{\ast }$$, where $$\delta /(2+\delta )<N_{L}^{\ast }<\delta /(1+\delta )$$. All nonprofit managers exert the same level of fundraising and project implementation effort: $$e_{L}^{\ast }=1$$ and $$\varsigma _{L}^{\ast }=0$$. If 1/(1 + δ)1 − α < A < [2/(2 + δ)]1 − α, the economy exhibits a mixed-type equilibrium with a mass of nonprofit firms equal to $$N_{ {mixed}}^{\ast }=1-A^{{1}/{1-\alpha }}$$, where $$N_{H}^{\ast }=2[ 1-A^{\frac{1}{1-\alpha }}( 1+\delta /2) ]\, \text{ and }\,N_{L}^{\ast }=A^{\frac{1}{1-\alpha }}\left( 1+\delta \right) -1.$$ (A.9) Motivated nonprofit managers set $$e_{H}^{\ast }=\varsigma _{H}^{\ast }=0.5$$, whereas mL-types set $$e_{L}^{\ast }=1$$ and $$\varsigma _{L}^{\ast }=0$$. The result of an “H-equilibrium” when A ≤ 1/(1 + δ)1 − α is the analogous to that one previously obtained in the basic model. Similarly, when A ≥ [2/(2 + δ)]1 − α the model features a pure “L-equilibrium”. One novelty of this alternative setup is that for the intermediate range of A there exists a “mixed-type” equilibrium. Intuitively, the necessity of competition for donations reduces the utility of the unmotivated agents. As a consequence, this creates parameter configurations under which, in the absence of fundraising competition, the nonprofit sector would be populated only by selfish agents, whereas in the presence of competition a fraction of them moves into the private sector (and are in turn replaced by a fraction of motivated agents).29 Appendix B: Altruism-Dependent Private Donations The model presented in Section 2 assumes that all private entrepreneurs (regardless of their prosocial motivation) donate an identical fraction of their income to the nonprofit sector. However, if warm-glow giving is a driven by (impure) altruism, it is reasonable to expect the propensity to donate to be increasing in the degree of prosocial motivation of an individual. Here, we modify the utility function in (3) by letting the propensity to donate be type specific (δi) and increasing in mi. In particular, we now assume that δi = δH ∈ (0, 1] when mi = mH, whereas δi = δL = 0 when mi = mL.30 The key difference that arises when δi is an increasing function of mi is that, for a given value of 1 − N, the total level of donations will depend positively on the ratio (1 − NH)/(1 − N). Intuitively, the fraction of entrepreneurial income donated to the nonprofit sector will rise with the (average) level of warm-glow motivation displayed by the pool of private entrepreneurs. To keep the analysis simple, we abstract from fundraising effort, and assume that the mass of total donations is equally split between the mass of nonprofits. In addition, we let the payoff functions by motivated and selfish nonprofit entrepreneurs be given again by (8) and (9), respectively. Donations collected by a nonprofit are now given by $$\dfrac{D}{N}=\dfrac{\delta _{H}\,A\left( \frac{1}{2}-N_{H}\right) }{( 1-N_{H}-N_{L}) ^{1-\alpha }( N_{H}+N_{L}) }.$$ (B.1) When the total amount of donations to the nonprofit sector depends positively on the fraction of prosocially motivated private entrepreneurs, the model gives room to multiple equilibria. The main reason for equilibrium multiplicity is that, when δi is increasing in mi, the ratio between $$U_{H}^{\ast }$$ and $$U_{L}^{\ast }$$ does not depend only on the level of N, as it was the case with (8) and (9) in Section 2. Instead, observing (B.1), we see that it also depends on how N breaks down between NH and NL. Such dependence on the ratio NH/NL generates a positive interaction between the incentives by mL-types to self-select into the nonprofit sector and the self-selection of mH-types into the private sector. The next proposition deals with this issue in further detail. Proposition B.1 shows that for A sufficiently small the economy will exhibit a high-effectiveness equilibrium, whereas when A is sufficiently large the economy will fall into a low-effectiveness equilibrium. These two results are in line with those previously shown in Proposition 1. However, Proposition B.1 also shows that there exists an intermediate range, (1 − δH/2)1 − α < A < [1 − δH/(2 + 2δH)]1 − α, in which the economy displays multiple equilibria. For those intermediate values of A, the exact type of equilibrium that takes place will depend on the coordination of agents’ expectations. If agents expect a large mass of mH-types to choose the nonprofit sector (case a), then the total mass of private donations (for a given N) will be relatively small, stifling the incentives of mL-types to become nonprofit managers. Conversely, if individuals expect a large mass of mH-types to become private entrepreneurs (case b), the value of D (for a given N) will turn out to be large, which will enhance the incentives of mL-types to enter into the nonprofit sector more than it does so for mH-types. Notice that the range of productivity A for which multiple equilibria occur increases with the (relative) generosity of the motivated individuals, δH.32 Finally, Proposition B.1 also shows that, within the range of multiple equilibria, there is also the possibility of intermediate consistent expectations (case c). When this happens, both motivated and selfish agents are indifferent across occupations, and a mix of mL- and mH-types will end up populating the nonprofit sector. Appendix C: Proofs Proof of Proposition 1 Part (i). First of all, notice that by replacing N = N0 into (9), it follows that A(1 + δ)1 − α > 1 implies $$U_{L}^{\ast }(N_{0})>1$$. Hence, because $$U_{L}^{\ast }(\widehat{N})=1$$, it must necessarily be the case that $$N_{0}<\widehat{N}$$. Because of Lemma 1, this also means that $$U_{L}^{\ast }(N_{0})>U_{H}^{\ast }(N_{0})$$. Now, because $$U_{L}^{\ast }(N_{0})=y(N_{0})$$, then $$y(N)<U_{L}^{\ast }(N_{0})$$ for any N < N0, meaning that whenever N < N0, the mass of nonprofit managers must at least be equal to 0.5 (the total mass of mL-types). But this contradicts the fact that N0 < 0.5; hence an equilibrium with N < N0 cannot exist. Moreover, an equilibrium with N > N0 cannot exist either, because whenever N > N0 holds, $$y(N)>U_{H}^{\ast }(N)$$ and $$y(N)>U_{L}^{\ast }(N)$$, contradicting the fact that there is a mass of individuals equal to N > 0 choosing to become nonprofit managers. As a result, when A(1 + δ)1 − α > 1, an allocation with $$N^{\ast }=N_{L}^{\ast }=N_{0}$$ represents the unique equilibrium. Because $$U_{H}^{\ast }(N_{0})<U_{L}^{\ast }(N_{0})=y(N_{0})$$, in the equilibrium, all mH-type become private entrepreneurs, and a mass 0.5 − N0 of mL-type agents (who are indifferent between the two occupations) also become private entrepreneurs. Part (ii). Because A(1 + δ)1 − α < 1 implies $$U_{L}^{\ast }(N_{0})<1$$, when the former inequality holds, $$N_{0}>\widehat{N}$$. Moreover, notice that an equilibrium with N ≤ N0 cannot exist, as it would contradict the fact that N0 < 0.5. In turn, because the equilibrium must necessarily verify $$N>N_{0}>\widehat{N}$$, only motivated agents will become nonprofit managers, while all selfish agents will self-select into the for-profit sector. Now, by the definition of N1 in (11), it follows that if N1 ≤ 0.5, then $$N^{\ast }=N_{H}^{\ast }=N_{1}$$ represents the unique equilibrium allocation (notice that A(1 + δ)1 − α < 1 ensures N1 > N0). In this situation, the mH-types are indifferent across occupations (and there is a mass 0.5 − N1 of them in the private sector), while when N < N1 all motivated agents wish to become nonprofit managers contradicting N < 0.5, and when N > N1 nobody would actually choose the nonprofit sector, contradicting N > 0. With a similar reasoning, it is straightforward to prove that when N1 > 0.5, the unique equilibrium allocation is given by $$N^{\ast }=N_{H}^{\ast }=0.5$$, as in that case the condition $$U_{L}^{\ast }\left({1}/{2}\right) <y\left( {1}/{2}\right) <U_{H}^{\ast }\left( {1}/{2}\right)$$ holds, whereas for N < 0.5 all mH-types intend to become nonprofit managers, and when N > 0.5, there is either nobody or only a mass one-half of agents who wish to go the nonprofit sector. Proof of Proposition 2 Part (i). First of all, recalling (13), notice that 21−αA > 1 implies $$\underline{N}<{1}/{2}$$. Using the results in Proposition 1, it then follows that when A(1 + δ)1 − α < 1 < 21 − αA and Δ = 0, in equilibrium, $$N^{\ast }=N_{H}^{\ast }=N_{1}$$, where recall that N1 is implicitly defined by (11). Let now $$\mathcal {N}_{H}$$ be implicitly defined by the following condition: $$\mathcal {N}_{H}^{-\gamma }[ \delta A( 1-\mathcal {N}_{H}) ^{\alpha }+\Delta ] ^{\gamma }( 1-\mathcal {N}_{H}) ^{1-\alpha }\equiv A;$$ (C.1) in raw words, $$\mathcal {N}_{H}$$ denotes the level of N that equalizes (2) and the utility obtained by a motivated nonprofit manager when D/N is given by (12). From (C.1), it is easy to observe that when Δ = 0, $$\mathcal {N}_{H}=N_{1}$$. In addition, differentiating (C.1) with respect to $$\mathcal {N}_{H}$$ and Δ, we obtain that $$\partial \mathcal {N}_{H}/\partial \Delta >0$$. Let now $$\Delta _{0}\equiv 1-A^{\frac{1}{1-\alpha }}(1+\delta ),$$ (C.2) and, using (13), notice that $$[ \delta A( 1-\underline{N}) ^{\alpha }+\Delta _{0}] /\underline{N}=1$$; hence $$\mathcal {N}_{H}(\Delta _{0})=\underline{N}$$. As a consequence of all this, when A(1 + δ)1 − α < 1 < 21 − αA, for all 0 ≤ Δ < Δ0, in equilibrium, $$N^{\ast }=N_{H}^{\ast }=\mathcal {N}_{H}(\Delta )$$, where $$\partial \mathcal {N}_{H}/\partial \Delta >0$$, and $$\mathcal {N}_{H}( \Delta ) :[ 0,\Delta _{0}) \rightarrow [ N_{1},\underline{N})$$. Part (ii). Using again the fact that $$[ \delta A( 1-\underline{N}) ^{\alpha }+\Delta _{0}] /\underline{N}=1$$, from (12) it follows that, for all Δ > Δ0, the utility achieved as nonprofit managers by mL-types must be strictly larger than that obtained by mH-types. Let now $$\Delta _{A}\equiv 2^{-\alpha }A[( 2^{1-\alpha }A) ^{\frac{1-\gamma }{\gamma }}-\delta ] .$$ (C.3) Using (2) and (12), notice that when N = 1/2 and Δ = ΔA, the utility obtained by motivated nonprofit managers is equal to y(1/2). All this implies that, when A(1 + δ)1 − α < 1 < 21 − αA, for all Δ0 ≤ Δ < ΔA, in equilibrium, $$N^{\ast }=N_{L}^{\ast }=\mathcal {N}_{L}(\Delta )\le {1}/{2}$$, where $$\mathcal {N}_{L}(\Delta )$$ is nondecreasing in Δ. In particular, for all Δ0 ≤ Δ ≤ 2 − αA(1 − δ), the function $$\mathcal {N}_{L}(\Delta )$$ is implicitly defined by $$\left[ \dfrac{\delta A( 1-\mathcal {N}_{L}) ^{\alpha }+\Delta }{\mathcal {N}_{L}}\right] ( 1-\mathcal {N}_{L}) ^{1-\alpha }\equiv A,$$ (C.4) whereas for all 2 − αA(1 − δ) < Δ < ΔA, $$\mathcal {N}_{L}(\Delta )={1}/{2}$$. Lastly, when Δ = 2 − αA(1 − δ), the expression in (C.4) implies $$\mathcal {N}_{L}={1}/{2}$$, proving that $$\mathcal {N}_{L}(\Delta ):( \Delta _{0},\Delta _{A}] \rightarrow \left( \underline{N},{1}/{2}\right]$$ is continuous and weakly increasing. Part (iii). First, note that when Δ > ΔA, the expression in (C.1) delivers a value of $$\mathcal {N}_{H}>{1}/{2}$$. As a result, motivated agents must necessarily be indifferent in equilibrium between the two occupations, because some of them must choose to actually work as nonprofit managers to allow $$\mathcal {N}_{H}>{1}/{2}$$. In addition, because by definition of ΔA in (C.3), δA[(1 − N)α + ΔA]/N > y(N) when N = 1/2, all selfish agents must be choosing the nonprofit sector when Δ > ΔA. Let thus $$\mathcal {N}_{LH}$$ be implicitly defined by the following condition: $$\mathcal {N}_{LH}^{-\gamma }[ \delta A( 1-\mathcal {N}_{LH}) ^{\alpha }+\Delta ] ^{\gamma }( 1-\mathcal {N}_{LH}) ^{1-\alpha }\equiv A.$$ (C.5) Differentiating (C.5) with respect to $$\mathcal {N}_{LH}$$ and Δ, we can observe that $$\partial \mathcal {N}_{LH}/\partial \Delta >0$$. From (C.5), we can also observe that $$\lim _{\Delta \rightarrow \Delta _{A}}\mathcal {N}_{LH}={1}/{2}$$ and $$\lim _{\Delta \rightarrow \infty }\mathcal {N}_{LH}=1$$. As a result, we may write $$\mathcal {N}_{LH}(\Delta ):( \Delta _{A},\infty ) \rightarrow \left( \frac{1}{2},1\right)$$, with $$\partial \mathcal {N}_{LH}/\partial \Delta >0$$. Moreover, because $$N_{L}^{\ast }={1}/{2},\forall$$ Δ > ΔA, it must be the case that in equilibrium $$N_{H}^{\ast }=\mathcal {N}_{LH}(\Delta )-{1}/{2}$$. Proposition 2 (bis). If 21−αA < 1, there exists a threshold level ΔB ∈ (0, Δ0), such that: (i) when 0 ≤ Δ ≤ ΔB, all nonprofit firms are managed by mH-types; (ii) when ΔB < Δ ≤ Δ0, nonprofit firms are managed by a mix of types with mH-type majority; (iii) when Δ > Δ0, nonprofit firms are managed by a mix of types with mL-type majority. Proof. (i) Because of Proposition 1, when Δ = 0, in equilibrium, $$N_{H}^{\ast }\le {1}/{2}$$ and $$N_{L}^{\ast }=0$$. Next, let ΔB ≡ 2 − αA(1 − δ), and note that, $$2\left[ \delta A\left( \tfrac{1}{2}\right) ^{\alpha }+\Delta _{B}\right] =2^{1-\alpha }A,$$ (C.6) and note that the right-hand side of (C.6) equals y(1/2), whereas its left-hand side equals D/N when N = 1/2 and Δ = ΔB. Furthermore, notice that 2[δA(1/2)α + Δ] is strictly increasing in Δ. As a consequence, it follows that in equilibrium, $$N_{L}^{\ast }=0$$ for any 0 ≤ Δ ≤ ΔB. In addition, denoted by $$\mathfrak {N}_{H}\left( \Delta \right) =\min \lbrace {1}/{2},\chi \rbrace$$, where χ is the solution of [δA(1 − χ)α + Δ]/χ = A/(1 − χ)1 − α, the result, $$N_{H}^{\ast }=\mathfrak {N}_{H}\left( \Delta \right)$$ for any 0 ≤ Δ ≤ ΔB obtains. (ii) This part of the proof follows from the definition of Δ0 in (C.2), together with the fact that 2[δA(1/2)α + Δ] > 21 − αA, for all Δ > ΔB. As a result, we may implicitly define the function $$\mathfrak {N}_{HL}(\Delta )$$ by \begin{equation*} \left[ \dfrac{\delta A( 1-\mathfrak {N}_{HL}) ^{\alpha }+\Delta }{\mathfrak {N}_{HL}}\right] ( 1-\mathfrak {N}_{HL}) ^{1-\alpha }\equiv A, \end{equation*} and observe that $$\partial \mathfrak {N}_{HL}/\partial \Delta >0$$. Noting that, whenever $$N=\mathfrak {N}_{HL}(\Delta )$$, mL-types are indifferent across occupations completes the proof of this part. (iii) This part of the proof follows again from the definition of Δ0 in (C.2), which implies that for all Δ > Δ0, the expression in (12) yields D/N > 1 when $$N=\underline{N}$$. For this reason, whenever Δ > Δ0, the mH-types must be indifferent across occupations in equilibrium, whereas all mL-types will strictly prefer the nonprofit sector. We can then implicitly define the function $$\mathfrak {N}_{LH}(\Delta )$$ by \begin{equation*} \mathfrak {N}_{LH}^{-\gamma }[ \delta A( 1-\mathfrak {N}_{LH}) ^{\alpha }+\Delta ] ^{-\gamma }( 1-\mathfrak {N}_{LH}) ^{1-\alpha }\equiv A, \end{equation*} and observe that $$\partial \mathfrak {N}_{LH}/\partial \Delta >0$$ to complete the proof. □ Proof of Proposition 3 First of all, from (15), it is straightforward to observe that neither NH = 0.5, nor 0 = NH < NL can possibly hold in equilibrium, as both situations would imply D/N = 0, and no agent would thus choose the nonprofit sector. Second, set NL = 0 into (15), and take the limit of the resulting expression as NH approaches zero, to obtain \begin{equation*} \lim _{N_{H}\rightarrow 0}\left. \dfrac{D}{N}\right|_{N_{L}=0}=\dfrac{\delta _{H}\,A}{2}\dfrac{N_{H}}{( N_{H}) ^{2}}=\infty . \end{equation*} The above result in turn implies that 0 = NH = NL cannot hold in equilibrium either, as in that case the nonprofit would become infinitely appealing to mH-types. Third, suppose 0 < NH < NL = 1/2. Using (2) and (15), for this to be an equilibrium, it must necessarily be the case that $$\dfrac{\delta _{H}\,A\left( \frac{1}{2}-N_{H}\right) N_{H}}{\left( \frac{1}{2}-N_{H}\right) ^{1-\alpha }\left( \frac{1}{2}+N_{H}\right) ^{2}}\ge \dfrac{A}{\left( \frac{1}{2}-N_{H}\right) ^{1-\alpha }}.$$ (C.7) However, the condition (C.7) cannot possibly hold, because it would require δH (0.5 − NH)NH ≥ (0.5 + NH)2, which can never be true. Because of the previous three results, the only possible equilibrium combinations are as follows: (i) $$N_{L}^{\ast }=0$$ and $$0<N_{H}^{\ast }<0.5$$, (ii) $$0\le N_{L}^{\ast }\le 0.5$$ and $$0<N_{H}^{\ast }<0.5$$, with all types indifferent across occupations. Case i. For this case to hold in equilibrium, condition (C.23) must be verified, which following the same reasoning as before in the proof of Proposition 1 leads to the condition A < [(2 + δH)/(2 + 2δH)]1 − α. Case ii. For this case to hold in equilibrium, the following equalities must all simultaneously hold $$\dfrac{D}{N}=\dfrac{\delta _{H}\,A\left( \frac{1}{2}-N_{H}\right) N_{H}}{( 1-N_{H}-N_{L}) ^{1-\alpha }( N_{H}+N_{L}) ^{2}}=y(N)=\dfrac{A}{( 1-N_{H}-N_{L}) ^{1-\alpha }}=1.$$ (C.8) Taking into account the definition of $$\underline{N}$$ in (13), it follows that y(N) = 1 requires $$N_{H}+N_{L}=1-A^{\frac{1}{1-\alpha }}$$. As a result, (C.8) boils down to the following condition: $$\delta _{H}\left( \tfrac{1}{2}-N_{H}\right) N_{H}-\left( 1-A^{\frac{1}{1-\alpha }}\right) ^{2}=0.$$ (C.9) The expression in (C.9) yields real-valued roots if and only if $$A\ge \left( 1-\sqrt{\delta _{H}}/4\right) ^{1-\alpha }.$$ (C.10) When (C.10) is satisfied, the solution of (C.9) is given by $$N_{H}=\left\lbrace \begin{array}{c}\scriptstyle{r_{0}\equiv \dfrac{1}{4}-\sqrt{\dfrac{1}{16}-\dfrac{\left[ 1-A^{1/\left( 1-\alpha \right) }\right] ^{2}}{\delta _{H}}},} \\ \scriptstyle{r_{1}\equiv \dfrac{1}{4}+\sqrt{\dfrac{1}{16}-\dfrac{\left[ 1-A^{1/\left( 1-\alpha \right) }\right] ^{2}}{\delta _{H}}}.}\end{array}\right.$$ (C.11) Note now that the roots r0 and r1 are not necessarily the equilibrium solutions for NH. More precisely, because $$N_{L}=[1-A^{\frac{1}{1-\alpha }}]-N_{H}$$, then $$N_{L}\ge 0\Leftrightarrow N_{H}\le [1-A^{\frac{1}{1-\alpha }}]$$. As a consequence, for NH = r1 in (C.11) to actually be an equilibrium solution, it must then be the case that $$r_{1}\le 1-A^{\frac{1}{1-\alpha }}$$. But this inequality is true only in the specific case when $$A=( 1-\sqrt{\delta _{H}}/4) ^{1-\alpha }$$ and $$\sqrt{\delta _{H}}=1$$, which in turn also implies that r1 = r0 in (C.11). Without any loss of generality, we may thus fully disregard r1, and check under which conditions $$r_{0}\le 1-A^{\frac{1}{1-\alpha }}$$. Using (C.11), and letting $$x\equiv 1-A^{\frac{1}{1-\alpha }}$$, an equilibrium with NL ≥ 0 when NH = r0 requires the following condition to hold: $$\Psi (x)\equiv \dfrac{1}{4}-\sqrt{\dfrac{1}{16}-\dfrac{x^{2}}{\delta _{H}}}\le x.$$ (C.12) Now, notice that Ψ(x) = x when A = [(2 + δH)/(2 + 2δH)]1 − α. In addition, noting that Ψ΄(x) > 0 and Ψ″(x) > 0, it then follows that (i) Ψ(x) < x, for all A > [(2 + δH)/(2 + 2δH)]1 − α; whereas Ψ(x) > x, for all $$(1-\sqrt{\delta _{H}}/4)^{1-\alpha }<A<[ ( 2+\delta _{H}) /( 2+2\delta _{H}) ] ^{1-\alpha }$$. Consequently, when A ≥ [(2 + δH)/(2 + 2δH)]1 − α, there is an equilibrium with NH = r0 and $$N_{L}=[1-A^{\frac{1}{1-\alpha }}]-r_{0}$$. Lastly, to prove that ∂f/∂A < 0, note that f = Ψ(x)/x, hence \begin{equation*} \dfrac{\partial f}{\partial A}=\dfrac{1}{4x^{2}}\dfrac{\partial x}{\partial A}-\dfrac{1}{16x^{3}}\left( \dfrac{1}{16}-\dfrac{x^{2}}{\delta _{H}}\right) ^{-\frac{1}{2}}\dfrac{\partial x}{\partial A}, \end{equation*} from where ∂f/∂A < 0 stems from noting that ∂x/∂A < 0 and that \begin{equation*} 1-\dfrac{1}{4x}\left( \dfrac{1}{16}-\dfrac{x^{2}}{\delta _{H}}\right) ^{-\frac{1}{2}}>0, \end{equation*} because of (C.11). Proof of Proposition 4 The conditions for an “L-equilibrium”, “H-equilibrium”, and a “mixed-type equilibrium” are, respectively, as follows: \begin{gather} \left[ \delta A\dfrac{( 1-N_{L}) ^{\alpha }}{N_{L}}\right] ^{\gamma }<\dfrac{A}{( 1-N_{L}) ^{1-\alpha }}\le \delta A\dfrac{( 1-N_{L}) ^{\alpha }}{N_{L}}, \quad \text{with }N_{L}\le 1/2. \end{gather} (C.13) \begin{gather} \delta A\dfrac{( 1-N_{H}) ^{\alpha }}{N_{H}}-\rho \chi <\dfrac{A}{( 1-N_{H}) ^{1-\alpha }}\le \left[ \delta A\dfrac{( 1-N_{H}) ^{\alpha }}{N_{H}}\right] ^{\gamma }, \quad \text{with }N_{H}\le 1/2. \end{gather} (C.14) \begin{gather} \delta A\dfrac{( 1-N_{H}-N_{L}) ^{\alpha }}{N_{H}+N_{L}}-\dfrac{N_{H}}{N_{H}+N_{L}}\rho \chi =\dfrac{A}{( 1-N_{H}-N_{L}) ^{1-\alpha }}\\ =\left[ \delta A\dfrac{( 1-N_{H}-N_{L}) ^{\alpha }}{N_{H}+N_{L}}\right] ^{\gamma },\quad \text{with }N_{H}\le 1/2 \text{ and }N_{L}\le 1/2. \nonumber \end{gather} (C.15) First of all, note that the condition for a low-effectiveness equilibrium (C.13) is identical to that in Proposition 1, hence when A(1 + δ)1 − α > 1 there must still exist a low-effectiveness equilibrium in the model with peer monitoring. Notice also that the condition for existence of a high-effectiveness equilibrium without peer monitoring is identical to condition (C.14), except for the term −ρχ in the first argument of the condition. This implies that whenever the condition for existence of an “H-equilibrium” without peer monitoring is satisfied, then it must also be satisfied when there is peer monitoring. As a consequence, when A(1 + δ)1 − α < 1, there must still exist an “H-equilibrium” in the model with peer monitoring. Next, recalling the definition of N1 in (11), from (C.14) it follows that, even when A(1 + δ)1 − α > 1, an H-equilibrium will exist if the condition $$\frac{A( 1-N_{1}) ^{\alpha }}{N_{1}}\left[ \delta -\frac{N_{1}}{1-N_{1}}\right] <\rho \chi$$ (C.16) holds true. Given that, when A(1 + δ)1 − α > 1, N1 < N0, then condition (C.16) requires that ρχ is sufficiently large. Lastly, consider the specific case when A(1 + δ)1 − α > 1 and condition (C.16) holds true. In a mixed-type equilibrium, we must have that $$A\left( 1-N\right) ^{\alpha }\left[ \delta -\frac{N}{1-N}\right] =\rho \chi ( N-N_{L}) .$$ (C.17) Notice now that when condition (C.16) holds true, then there must necessarily exist some value 0 < NL < N < N0, with N > NL, satisfying condition (C.17). This implies that when A(1 + δ)1 − α > 1 and condition (C.16) holds true, there also exists a mixed-type equilibrium satisfying (C). Derivation of Equilibrium Regions in Figure 4 (i) H-equilibrium Region. This type of equilibrium arises when $$\sigma _{i}<1<V_{p}^{\ast }$$ for any 0 ≤ N ≤ 1/2, where $$V_{p}^{\ast }$$ is given by (17) and σi by (18). For $$\sigma _{i}<V_{p}^{\ast }$$ to hold for any 0 ≤ N ≤ 1/2, it suffices to pin down when it holds for N = 1/2, which in turn leads to $$t<\bar{t}\equiv \left( 1-\delta \right) /\left( 2-\delta \right) .$$ (C.18) Next, for $$\sigma _{i}<V_{p}^{\ast }$$, we need that $$N<\frac{\delta \left( 1-t\right) +t}{1+\delta \left( 1-t\right) }.$$ (C.19) Therefore, plugging the RHS of (C.19) into (18) leads to the condition that σi < 1 whenever $$A<\frac{1}{\left( 1-t\right) ^{\alpha }\left[ 1+\delta \left( 1-t\right) \right] ^{1-\alpha }}.$$ (C.20) As a result, the region bounded by (C.18) and (C.20) features a high-effectiveness equilibrium. (ii) L-equilibrium Region. This type of equilibrium needs, first, that condition (C.20) fails to hold. Second, it also needs that $$( \sigma _{i}) ^{\gamma }<V_{p}^{\ast }$$ holds, so that mH-types choose the private sector. For $$( \sigma _{i}) ^{\gamma }<V_{p}^{\ast }$$ to obtain, it must be that $$A>\frac{\left[ t+\delta \left( 1-t\right) \right] ^{\frac{\gamma }{1-\gamma }}}{2^{1-\alpha }\left( 1-t\right) ^{\frac{1}{1-\gamma }}}.$$ (C.21) Notice now that the RHS of (C.20) is equal to the RHS of (C.21) when $$t=\bar{t}$$, while the former lies above (below) the latter when $$t<\bar{t}$$ (when $$t>\bar{t}$$). As a consequence, the region exhibiting an “L-equilibrium” is given by A > (1 − t) − α[1 + δ(1 − t)]α − 1 whenever $$t\le \bar{t}$$ and by (C.21) whenever $$t>\bar{t}$$. (iii) Mixed-Type Equilibrium Region with f > 1/2. From the previous results, it follows that when (C.20) holds and $$t>\bar{t}$$, we must necessarily have an equilibrium in which all mH-types choose the nonprofit sector, whereas mL-types lie indifferent between the two sectors, and a fraction of them choose the nonprofit sector as well. (iv) Mixed-Type Equilibrium Region with f < 1/2. From the previous results it also follows that when both (C.20) and (C.21) fail to hold and $$t>\bar{t}$$, we must necessarily have an equilibrium in which mL-types choose the nonprofit sector, whereas mH-types lie indifferent between the two sectors, and a fraction of them choose the nonprofit sector as well. Proof of Proposition A.1. Part (i). First, recall that in an H-equilibrium $$\bar{e}={1}/{2}$$. Second, using (A.7) and (4) when $$N=N_{H}^{\ast }$$, we have that \begin{equation*} \dfrac{\delta A\left( 1-N_{H}^{\ast }\right) ^{\alpha }}{N_{H}^{\ast }}=\dfrac{A}{\left( 1-N_{H}^{\ast }\right) ^{1-\alpha }}\quad \Leftrightarrow \quad N_{H}^{\ast }=\dfrac{\delta }{1+\delta }<\dfrac{1}{2}. \end{equation*} Therefore, an H-equilibrium must necessarily feature $$N_{H}^{\ast }=\delta /\left( 1+\delta \right)$$, with mH types indifferent across the two occupations. In such an equilibrium, they obtain a level of utility equal to A(1 + δ)1 − α. Third, from (A.5) it follows that this solution is a Nash equilibrium, as the best response by mL-type nonprofit managers would be eL = 0 when 2A(1 + δ)1 − α < 1, while eL = 1 otherwise. In both cases, A(1 + δ)1 − α ≤ 1 implies that selfish agents should prefer the private sector to the nonprofit sector. Moreover, this must be the unique Nash equilibrium solution, because the incentives for an mL-type agent to start a nonprofit will decline with the average level of $$\bar{e}$$, which in equilibrium will never be below 0.5 as implied by (A.3). Part (ii). Preliminarily, let us first define $$\widetilde{N}\equiv \delta /(2+\delta )$$. Note then that, when $$\bar{e}=1$$, the payoff functions (A.4) and (4) are equalized when $$N=\widetilde{N}$$; namely, $$U_{H}^{\ast }(\widetilde{N})=V^{\ast }(\widetilde{N})$$. Next, notice that, for a given $$\bar{e}$$, both (A.4) and (A.6) are strictly decreasing in N, while they grow to infinity as N goes to zero. Hence, to prove that a low-effectiveness equilibrium exists, it suffices to show that the condition A ≥ [2/(2 + δ)]1 − α implies $$U_{H}^{\ast }(\widetilde{N})\le U_{L}^{\ast }(\widetilde{N})$$. To prove that the low-effectiveness equilibrium is unique, notice first that an H-equilibrium is incompatible with A ≥ [2/(2 + δ)]1 − α. Therefore, the only other alternative would be a mixed-type equilibrium with all agents indifferent between the private and nonprofit sector. Yet, for (A.4) and (A.6) to be equal, it must be that $$D/N=2\bar{e}$$. This equality, in turn, implies that all activities must yield a payoff equal to 1; however, when A ≥ [2/(2 + δ)]1 − α, this would be inconsistent with $$\bar{e}<1$$, therefore a mixed-type equilibrium cannot exist either. Part (iii). First of all, following the argument in the proof of part (i) of the proposition, notice that an H-equilibrium cannot exist, because when A(1 + δ)1 − α > 1 selfish agents would like to deviate to the nonprofit sector and set eL = 1. Secondly, notice that a necessary condition for an L-equilibrium to exist is that $$U_{H}^{\ast }>1$$ when $$N=\widetilde{N}$$ and $$\bar{e}=1$$, but replacing $$N=\widetilde{N}$$ and $$\bar{e}=1$$ into (A.4) yields a value strictly smaller than 1 when A < [2/(2 + δ)]1 − α. As a result, when A(1 + δ)1 − α < A < [2/(2 + δ)]1 − α the equilibrium must necessarily be of mixed type, with all agents indifferent across occupations. This requires that $$U_{H}^{\ast }(N^{\ast })=U_{L}^{\ast }(N^{\ast })=V_{P}^{\ast }(N^{\ast })=1$$. From (4), we obtain that $$V_{P}^{\ast }(N^{\ast })=1$$ implies $$N_{ {mixed}}^{\ast }=1-A^{\frac{1}{1-\alpha }}$$. In addition, $$U_{H}^{\ast }(N^{\ast })=U_{L}^{\ast }(N^{\ast })$$ requires that $$2\bar{e}_{ {mixed}}=D/N$$, which using $$N_{ {mixed}}^{\ast }=1-A^{{1}/{1-\alpha }}$$ leads to $$\bar{e}_{ {\mathit{mixed}}}=\frac{1}{2}\dfrac{\delta A^{\frac{1}{1-\alpha }}}{1-A^{\frac{1}{1-\alpha }}}.$$ (C.22) Therefore, using the facts that $$e_{H}^{\ast }=0.5$$ and $$e_{L}^{\ast }=1$$, the levels of $$N_{H}^{\ast }$$ and $$N_{L}^{\ast }$$ in (A.9) immediately obtain. Lastly, to prove that this equilibrium is unique, notice that $$e_{ {mixed}}^{\ast }$$ in (C.22) lies between 0.5 and 1, thus there must exist only one specific combination of $$N_{H}^{\ast }$$ and $$N_{L}^{\ast }$$ consistent with a mixed-type equilibrium. Proof of Proposition B.1 First of all, notice that NH = 0.5 cannot hold in equilibrium, as (B.1) implies that in that case D/N = 0, no agent would choose the nonprofit sector. We can then focus on three equilibrium cases: (i) $$N_{L}^{\ast }=0$$ and $$0<N_{H}^{\ast }<0.5$$, with mL-types strictly preferring the private sector, (ii) $$N_{L}^{\ast }\le 0.5$$ and $$N_{H}^{\ast }=0$$, with mH-types strictly preferring the private sector, and (iii) $$0\le N_{L}^{\ast }\le 0.5$$ and $$0\le N_{H}^{\ast }<0.5$$, will all types indifferent across occupations. Case (i). For this case to hold in equilibrium, the following condition must be verified: $$\underset{U_{L}^{\ast }(N_{H},0)}{\underbrace{\dfrac{\delta _{H}A\left( \frac{1}{2}-N_{H}\right) }{( 1-N_{H}) ^{1-\alpha }N_{H}}}}<\underset{y(N_{H},0)}{\underbrace{\dfrac{A}{( 1-N_{H}) ^{1-\alpha }}}}=\underset{U_{H}^{\ast }(N_{H},0)}{\underbrace{\left[ \dfrac{\delta _{H}A\left( \frac{1}{2}-N_{H}\right) }{( 1-N_{H}) ^{1-\alpha }N_{H}}\right] ^{\gamma }}}.$$ (C23) For $$U_{L}^{\ast }(N_{H},0)<y(N_{H},0)$$ in (C.23) to hold, NH > δH/(2 + 2δH) must be true. Next, because $$U_{L}^{\ast }(N_{H},0)<U_{H}^{\ast }(N_{H},0)\Leftrightarrow U_{L}^{\ast }(N_{H},0)<1$$, and y(NH, 0) is strictly increasing in NH while $$U_{H}^{\ast }(N_{H},0)$$ is strictly decreasing in it and $$U_{H}^{\ast }({1}/{2},0)=0$$, a sufficient condition for (C.23) to hold in equilibrium is that \begin{equation*} \dfrac{\delta _{H}A\left( \frac{1}{2}-N_{H}\right) }{( 1-N_{H}) ^{1-\alpha }N_{H}}<1 \text{ when }N_{H}=\dfrac{\delta _{H}}{2+2\delta _{H}}, \end{equation*} which in turn leads to the condition A < [(2 + δH)/(2 + 2δH)]1 − α. Case (ii). This case occurs when the following condition holds: $$\underset{U_{H}^{\ast }(0,N_{L})}{\underbrace{\left[ \dfrac{\frac{1}{2}\delta _{H}A}{( 1-N_{L}) ^{1-\alpha }N_{L}}\right] ^{\gamma }}}<\underset{y(0,N_{L})}{\underbrace{\dfrac{A}{( 1-N_{L}) ^{1-\alpha }}}}\le \underset{U_{L}^{\ast }(0,N_{L})}{\underbrace{\dfrac{\frac{1}{2}\delta _{H}A}{( 1-N_{L}) ^{1-\alpha }N_{L}}}}.$$ (C.24) Using the expressions in (C.24), notice that for $$U_{L}^{\ast }(0,N_{L})>y(0,N_{L})$$ to hold, NL < δH/2. But, because 0 < δH ≤ 1, NL < δH/2 and $$U_{L}^{\ast }(0,N_{L})>y(0,N_{L})$$ cannot possibly hold together. As a consequence, in equilibrium, $$U_{L}^{\ast }(0,N_{L})=y(0,N_{L})$$ must necessarily prevail, implying in turn that NL = δH/2. Next, because $$U_{L}^{\ast }(N_{H},0)>U_{H}^{\ast }(N_{H},0)\Leftrightarrow U_{L}^{\ast }(N_{H},0)>1$$, a sufficient condition for (C.24) to hold in equilibrium is that \begin{equation*} \dfrac{\frac{1}{2}\delta _{H}A}{( 1-N_{L}) ^{1-\alpha }N_{L}}>1 \text{ when }N_{L}=\dfrac{\delta _{H}}{2}, \end{equation*} which in turn leads to the condition A > (1 − δH/2)1 − α. Case (iii) Keeping in mind that $$U_{L}^{\ast }(N_{H},0)=U_{H}^{\ast }(N_{H},0)\Leftrightarrow U_{L}^{\ast }(N_{H},0)=1$$, this case will arise when the following equalities hold: $$\underset{y(N_{H},N_{L})}{\underbrace{\dfrac{A}{( 1-N_{H}-N_{L}) ^{1-\alpha }}}}=\underset{U_{L}^{\ast }(N_{H},N_{L})}{\underbrace{\dfrac{\delta _{H}A\left( \frac{1}{2}-N_{H}\right) }{( 1-N_{H}-N_{L}) ^{1-\alpha }( N_{L}+N_{H}) }}=1}.$$ (C.25) Recalling the definition of $$\underline{N}$$ in (13), $$U_{L}^{\ast }(N_{H},N_{L})=1$$ leads to [δH(0.5 − NH)]/[1 − A1/(1 − α)] = 1, from where we obtain: $$N_{H}=\dfrac{1}{2}-\dfrac{1-A^{\frac{1}{1-\alpha }}}{\delta _{H}}.$$ (C.26) Next, using again the definition of $$\underline{N}$$ in (13), we may obtain NL = [1 − A1/(1−α)] − NH, which using (C.26) yields: $$N_{L}=\left( 1-A^{\frac{1}{1-\alpha }}\right) \dfrac{1+\delta _{H}}{\delta _{H}}-\dfrac{1}{2}.$$ (C.27) Lastly, (C.26) implies that NH > 0⇔A > (1 − δH/2)1 − α, whereas (C.27) means that NL > 0⇔A < [(2 + δH)/(2 + 2δH)]1 − α, completing the proof. Acknowledgments We thank Nicola Gennaioli and Paola Giuliano (coeditors), four anonymous referees, François Bourguignon, Maitreesh Ghatak, Stephan Klasen, Cecilia Navarra, Susana Peralta, Jean-Philippe Platteau, Debraj Ray, Paul Seabright, Pedro Vicente, and participants at the N.G.O. workshop (London), OSE workshop (Paris), ThReD Conference (Barcelona), EUDN Conference (Oslo), as well as seminar participants at Collegio Carlo Alberto, Nova University of Lisbon, Tinbergen Institute, University of St Andrews, and University of Sussex for useful suggestions. Financial support from the Labex OSE and FNRS (FRFC grant 7106145 ”Altruism and NGO performance”) is gratefully acknowledged. Aldashev is a Research Fellow at ECARES. Verdier is a Research Fellow at CEPR. Notes The editors in charge of this paper were Nicola Gennaioli and Paola Giuliano. Footnotes 1 See, for example, Andreoni and Miller (2002), Ribar and Wilhelm (2002), Korenok, Millner, and Razzolini (2013), and Tonin and Vlassopoulos (2010). 2 In this paper, we mostly focus on the joy-of-giving (or warm-glow) motive for giving. However, an additional reason why people might be willing to donate is social signaling, as modeled by Benabou and Tirole (2006). Social signaling would complement and reinforce the joy-of-giving motive that we focus on in our model. One other reason that would also reinforce the act of giving, without any link to pure altruism, is tax incentives to giving. 3 See Chapter 12 of Hansmann (1996) and Bilodeau and Slivinski (1996) for detailed discussions on the issue of incomplete contracts in nonprofit organizations. 4 On the empirical side, Gregg et al. (2011) find that individuals in the nonprofit sector in the UK are significantly more likely to do unpaid overtime work as compared to their counterparts in the for-profit sector. Moreover, this differential willingness remains even when the former individuals move into the for-profit sector, strongly supporting theories based on self-selection (rather than sector-specific incentive structure). 5 Our assumption of decreasing marginal returns with respect to the aggregate mass of private entrepreneurs reflects the fact that, at a given point in time, there is a fixed factor in the economy (which we do not explicitly model) that enters the production of goods in the private sector. 6 In principle, it may seem more reasonable to assume that agents who exhibit a higher degree of prosocial motivation should also be more prone to donating for social causes, and therefore display a larger value of δ in (3). We stick to the simplest possible formulation in this basic model, to introduce in the stark way the idea that donations are endogenous, by shutting down additional effects. In Appendix B, we relax the assumption that warm-glow donations by private entrepreneurs are independent of their level of prosocial motivation by letting δ be type-specific (δi), with δL = 0 and 0 < δH ≤ 1. This introduces the additional complexity of making donations dependent on the degree of motivational heterogeneity in the for-profit sector, giving rise to the possibility of multiple equilibria. 7 Appendix A presents a model that relaxes the equal-sharing assumption by endogenizing fundraising effort. 8 These two cases exclude the set of parametric configurations for which $$\widehat{N}=N_{0}$$, where N0 is defined in what follows in (10). When $$\widehat{N}=N_{0}$$, all individuals in the economy will be indifferent in equilibrium across the two occupations. Consequently, there are multiple equilibria, with the set equilibria given by $$\lbrace N_{H}^{\ast }+N_{L}^{\ast }=N_{0} |0\le N_{H}^{\ast }\le {1}/{2},0\le N_{L}^{\ast }\le {1}/{2}\rbrace$$. Hereafter, for the sake of brevity, we skip this knife-edge case. 9 These results entail that, as the scale of the donations market increases, it may then become socially desirable to invest in certain types of changes in the organization of the NGO sector that help mitigating rent-seeking behavior, such as better accounting and monitoring mechanisms, tougher certification schemes, and so forth. 10 Kanbur (2006) argues that the rise of NGOs during the 1980s was one of the key changes in the functioning of the foreign aid sector. 11 Another way to avoid this problem would be to assume that the production function of private entrepreneurs is given by y(N), with y΄(N) > 0, y″(N) < 0, y(1) = ∞, and y(0) = 0. Note that all these properties are satisfied by (2), except for y(0) = 0. Intuitively, what is needed to give room for an “H-equilibrium” is that y(N) ≤ 1 for some N ≥ 0. Assumption 1 ensures this is always the case. 12 The only major qualitative difference is that when 21−αA < 1, the “L-equilibrium” where all nonprofit firms are managed by mL-types will no longer arise. Instead, when 21−αA < 1, while the economy still exhibits an “H-equilibrium” for levels of Δ that are sufficiently low, beyond a certain threshold of Δ, the economy switches directly to a mixed-type equilibrium. In that respect, the fraction of motivated nonprofit managers will still depend nonmonotonically on the level of foreign aid when 21−αA < 1. 13 For example, Svensson (2000) suggests that foreign aid channeled through the public sector may lead to higher bureaucratic corruption, break-up of accountability mechanisms of elected officials, and the ignition of ethnic-based rent-seeking behavior. 14 In a recent study, Metzger and Günther (2015) test, in a laboratory experiment, whether private donors seek information, before giving, about the impact of their donations to international NGOs. Interestingly, they find that only a small fraction of donors makes a well-informed donation decision and that demand for information mostly concerns the recipient type (and not the impact of donation). They also find that the information about the impact of donations does not change average donation size. 15 In some sense, the model developed in Section 2 could then be thought as more appropriate for underdeveloped and middle-income economies, where watchdog organizations are less present. 16 Motivated agents do not report anything in these matches, whereas selfish agents do not care about reporting. We disregard the unplausible case where selfish agents would make false reports concerning motivated agents, which seems rather far-fetched. 17 One could also rationalize these reputational concerns from a dynamic perspective as ensuring that the sector maintains its credibility vis-a-vis the donors. 18 Notice that the multiplicity of equilibria hinges crucially on the fact that selfish nonprofit managers do not care about reporting of misbehavior by their peers. One solution to this problem could then be (monetarily) rewarding whistleblowing, so as to induce also selfish nonprofit managers to report rent seeking. 19 Hence, at Z, one part of the mL-types choose the private sector and the other part choose nonprofit firms. 20 Notice that all this implies that, in the new equilibrium, the total mass of nonprofit firms must necessarily be larger than in Z, because from (18) it follows that σi will grow with t for a given level of N. In other words, after t is raised to a level within $$[\underline{ \mathit{t}},\bar{t}]$$, a mass $$N_{L}^{\ast }$$ of selfish nonprofit managers will be replaced by a mass $$N_{H}^{\ast }$$ of motivated nonprofit managers, where $$N_{H}^{\ast }>N_{L}^{\ast }$$. 21 This assumption is dispensed, though, in the model presented in the Appendix A, where we use a linear production function for each single nonprofit firm. 22 Although our model has treated prosocially motivated agents as identical (hence, without displaying heterogeneity in their type of prosocial motivation), the idea that each NGO manager operates a different nonprofit firm implicitly reflects the underlying notion that motivated agents also differ in the social mission they most strongly align with. 23 This has also been highlighted by the matching-to-mission model of Besley and Ghatak (2005). 24 Note, however, that Section 3.1 deals with the case where donations respond to the average motivation in the nonprofit sector, but the level of donations received by each nonprofit is still assumed to be proportional to aggregate donations. 25 Another form of signaling is possible if conditionally warm-glow donors differ in size, and large donors can obtain information (even if noisy) about the nonprofit managers’ types at some cost. The models by Vesterlund (2003) and Andreoni (2006), where obtaining a large leadership donation serves as a credible signal of quality, can serve as a microfoundation for this type of analysis. 26 Most of the existing discussions of the performance of humanitarian aid to the 2004 tsunami concern international or Northern NGOs. In the context of our model, given that these NGOs were founded in different countries, they could be facing different types of occupational equilibria. However, Willitts-King and Harvey (2005) show that the diversion of funds during humanitarian relief can occur both at the international organizations’ level and at the local level (and probably, both levels were subject to this problem). Therefore, our analytical framework still applies to this context. 27 In a partial-equilibrium framework, this issue has been studied in the contributions mentioned in the introduction and in a recent review by Mansuri and Rao (2013). 28 See, for example, De Waal (1997) and Hancock (1989) for some poignant recounts of the fundraising effort spent by nonprofit organizations by using the social media both in the developed and developing world. 29 It is interesting to compare these findings to those of Aldashev and Verdier (2010), where more intense competition for funds actually leads to higher diversion of donations by nonprofit managers. This occurs because when agents have to spend more time raising funds, then less time is left for working towards the nonprofit mission, and thus the opportunity cost of diverting money for private consumption falls. In that model, all agents are intrinsically identical, and thus the issue of more intense competition lies in aggravating a moral hazard problem. Here, instead, the existence of motivationally heterogeneous types implies that the main problem is one of adverse selection, and a more intense competition for funds mitigates the severity of this adverse selection problem. 30 Notice that, in the specific case in which δH = 1, the utility functions in the private sector and the nonprofit sector would display the same structure for both mH- and mL-types: for the former, all the utility weight is being placed on prosocial actions (either warm-glow giving or producing gi); for the latter, all the utility weight is being placed on private consumption. 31 In the specific cases, where A = (1 − δH/2)1 − α or A = [1 − δH/(2 + 2δH)]1 − α, the “mixed-type equilibrium” described in what follows disappears, whereas the other two equilibria remain. 32 The range of values of A subject to multiple equilibria vanishes as δH approaches zero. 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# Small is Beautiful: Motivational Allocation in the Nonprofit Sector

, Volume Advance Article (3) – Nov 14, 2017
51 pages

/lp/ou_press/small-is-beautiful-motivational-allocation-in-the-nonprofit-sector-joxQlf78dx
Publisher
Oxford University Press
ISSN
1542-4766
eISSN
1542-4774
D.O.I.
10.1093/jeea/jvx024
Publisher site
See Article on Publisher Site

### Abstract

Abstract We build an occupational-choice general-equilibrium model with for-profit firms, nonprofit organizations, and endogenous private warm-glow donations. Lack of monitoring on the use of funds implies that an increase of funds of the nonprofit sector (because of a higher income in the for-profit sector, a stronger preference for giving, or an inflow of foreign aid) worsens the motivational composition and performance of the nonprofit sector. We also analyze the conditions under which donors (through linking donations to the motivational composition of the nonprofit sector), nonprofits themselves (through peer monitoring), or the government (using a tax-financed public funding of nonprofits) can eliminate the low-effectiveness equilibrium. We present supporting case-study evidence from developing-country nongovernmental organization sector and humanitarian emergencies. 1. Introduction One major recent global economic phenomenon has been the rising importance of nonprofit and nongovernmental organizations as providers of public goods (Brainard and Chollet 2008). The massive increase in the number of international nongovernmental organizations (NGOs), from less than 5,000 in mid-1970s to more than 28,000 in 2013, attests to this (Union of International Associations 2014; Werker and Ahmed 2008). In developing countries, NGOs play a key role in the provision of public health and education services. They have also become fundamental actors in the empowerment of socially disadvantaged groups, such as women and ethnic/religious minorities (Brinkerhoff, Smith, and Teegen 2007). In addition, NGOs contribute actively to monitoring adherence by multinational firms to environmental and labor standards (Yaziji and Doh 2009). The expansion of nonprofit organizations as economic actors has not been restricted to the developing world. In the Organisation for Economic Co-operation and Development (OECD) countries, they also play a major role as public-good providers, especially in sectors such as health services, arts, education, and poverty relief (Bilodeau and Steinberg 2006). Quite remarkably, nonprofits represent a sizeable sector in terms of OECD countries’ employment share: on average, 7.5% of their economically active population is employed in the nonprofit sector. For some countries (Belgium, Netherlands, Canada, UK, and Ireland), this share exceeds 10% (Salamon 2010). One distinctive feature concerning the provision of public goods by NGOs is their financing structure. Although a part of these organizations’ operational costs is covered by government grants and by user fees, voluntary private donations also account for a major share of their budgets. Bilodeau and Steinberg (2006) report that for the 32 countries for which comparable data are available, on average, over 30% of nonprofits’ financing comes from voluntary private giving. Moreover, over 75% of this amount consists of small donations. Given the public-good nature of the services typically provided by nonprofits, this fact is particularly intriguing, because small donors could hardly expect their contributions to entail any meaningful effect on total public-good provision. A simple explanation of this phenomenon is that private contributions to nonprofits are partially motivated by impure altruism. Indeed, research in public and experimental economics has recurrently shown that rationalizing empirical regularities about altruism requires the explicit acknowledgment of private psychological benefits accruing to the donor from the act of giving.1 This is the so-called warm-glow motivation, first modeled by Andreoni (1989). Impure altruism by donors means, in turn, that the link between the motivation to give to nonprofit organizations and the ultimate provision of public goods by them may be very weak.2 In addition, the very nature of the goods and services provided by nonprofit organizations renders impossible to write contracts that condition their financing on their output, further weakening the link between donations and public-good provision.3 These two features, combined with the fact that individuals’ intrinsic motivation is private information, make the nonprofit sector particularly vulnerable to the misallocation of funds. In a context where the scope for funds diversion is quite extreme, the size and the structure of financing of the nonprofit sector may become major factors determining who enters this sector. This will in turn affect the level of intrinsic motivation of its managers, and consequently, the performance of the nonprofit sector. Analyzing this key issue requires a general-equilibrium framework. When the nonprofit sector is of non-negligible size, policies that influence the behavior of nonprofit managers will impact the returns in both the nonprofit and for-profit sectors. In such a setting, a partial-equilibrium model will miss out important sources of market interactions and may, therefore, lead to misguided policy recommendations (for instance, concerning the desirability of more extensive state financing to nonprofits or channeling foreign aid via NGOs). This paper proposes a tractable occupational-choice general-equilibrium model with for-profit firms, nonprofit organizations, and endogenous private donations. The model rests on five key assumptions. First, private donors give to nonprofits because of warm-glow motives (i.e., with a weak link to the expected public-good output generated with their own donations). Second, individuals self-select either into the for-profit or nonprofit sectors, whose returns are endogenous to the model, both because of aggregate occupational choices and endogenous donations. Third, there are decreasing returns at the level of single nonprofit organizations (because intrinsic motivation is an essential input in limited supply compared to money, and that mission deepening for nonprofits involves increasingly difficult tasks to accomplish). Fourth, monitoring the behavior and knowing the intrinsic motivation of the nonprofit managers is inherently difficult. Fifth (also resulting from the nonmeasurability of nonprofits’ output), private donations are shared among the existing nonprofits in a manner that is not strictly related to their performance. The main mechanism in our model relies on the notion that motivational self-selection into the nonprofit sector may be altered by the level of donations received by nonprofit firms. Imperfect monitoring of managers in the nonprofit sector, together with warm-glow motives by private donors, implies that the scope for misallocation of funds in this sector expands when private giving rises. Therefore, in a context of asymmetric information, warm-glow altruism and self-selection interact in nonmonotonic ways, possibly leading to equilibrium with severe misallocation of funds. Our model generates several important results concerning motivational allocation. First, selfish motives can crowd out altruistic motivation from the nonprofit sector. When this occurs, the nonprofit sector ends up being managed by selfish agents who exploit the lack of monitoring to divert funds for project dimensions that are misaligned with the interests of the beneficiaries. Moreover, because the scope for misallocation of funds rises with the level of donations received by each nonprofit firm, this problem is exacerbated in richer economies and in economies where private donors give more generously. Our model features thus a case where “small is beautiful”: motivational allocation in the nonprofit sector tends to be better when the overall financing of each nonprofit remains small. Second, foreign aid intermediation through the nonprofit sector in a developing country may entail perverse effects: it may cause the economy to switch from an equilibrium with a good allocation to one with a bad allocation of prosocial motivation. One further implication of this result is that total output of nonprofits can become nonmonotonic in the amount of foreign aid. At low levels of foreign aid, a small increase in aid leads to higher total NGO output, as the motivational composition of the nonprofit sector is unaltered. However, a large injection of foreign aid may lead to a motivational recomposition of the nonprofit sector, attracting self-interested agents into it, and thereby leading to a decline in total nonprofit output. Such nonmonotonic relation, in turn, can help explaining the micro–macro paradox observed by empirical studies of aid effectiveness (i.e., the absence of a positive effect of aid on output at the aggregate level, combined with numerous positive findings at the micro level). Third, we analyze a number of mechanisms that might prevent the emergence of the low-effectiveness equilibrium. From the donors’ side, if warm-glow motivation responds positively to the expected productivity of the nonprofit sector, the pure low-effectiveness equilibrium disappears. However, our model shows that, even in this case, when the amount of donations is sufficiently large, selfish agents still end up constituting an important share of the pool of nonprofit managers, thus hurting the aggregate provision of public goods. On the nonprofits’ side, peer-monitoring mechanisms can lead to multiple equilibria. In one equilibrium, the nonprofit sector is managed by motivated agents and the quality of peer monitoring is high. In the second equilibrium, the sector is instead managed by selfish individuals and no peer monitoring takes place. The reason for the multiplicity of equilibria is that the quality of monitoring is itself endogenous to the occupational choice of agents, and it improves with the average level of motivation in the nonprofit sector. Finally, we show that a properly designed public financing policy of the nonprofit sector may improve the motivational composition of the nonprofit sector. Besides the aforementioned papers by Andreoni (1989) and Benabou and Tirole (2006), our paper relates to several other key papers that study theoretically the implications of prosocial motivation for nonprofit organizations: Glaeser and Shleifer (2001), François (2003, 2007), Besley and Ghatak (2005), Lakdawalla and Philipson (2006), and Aldashev and Verdier (2010).4 We contribute to this line of research by endogenizing the returns of the different occupational choices available to individuals, and by exploring the general-equilibrium implications of the level of financing of the nonprofit sector. The second related strand of literature is the one focusing on the self-selection of individuals into the public sector and politics: for example, Caselli and Morelli (2004), Macchiavello (2008), Delfgaauw and Dur (2010), Bond and Glode (2014), and Jaimovich and Rud (2014). The insights from the theoretical research in this area, which mostly exploits occupational-choice models, have been confirmed by recent empirical studies. For instance, Georgellis, Iossa, and Tabvuma (2011) find, using the UK data, that individuals are attracted to the public sector by intrinsic rather than extrinsic incentives, and that (in the higher education and health sectors) higher extrinsic rewards reduce the propensity of intrinsically motivated agents to enter into the public sector. We extend this line of research by (i) analyzing how the selection mechanisms apply to the nonprofit/NGO sector within a context of endogenous voluntary donations, and (ii) studying the effectiveness of three mechanisms that potentially can improve the motivational selection into the nonprofit sector. Finally, there is growing literature that studies the effectiveness of different modes and levels of foreign aid (see the survey by Bourguignon and Platteau 2015). Among these studies, Svensson (2000) underlines how short-term increases in aid flows may trigger rent-seeking wars among competing elites. Another interesting contribution is Bourguignon and Platteau (2013), which concentrates on moral hazard problems (in particular, it studies the effect of domestic monitoring on the ultimate use of aid flows). Our model studies a separate and novel channel: that of motivational adverse selection into the sector that intermediates foreign aid flows between outside donors and beneficiaries. The rest of the paper is organized as follows: Section 2 builds our baseline model of occupational choice in the for-profit and nonprofit sectors; it also analyzes the effects of foreign aid and public financing on the motivational allocation in the nonprofit sector. Section 3 analyzes the functioning of three different oversight mechanisms: conditional warm glow of donors, peer-monitoring institutions by nonprofits, and tax-financed government grants to nonprofits. Section 4 discusses the main premises and modeling choices, as well as the generalizability of our results. Section 5 presents case-study evidence for the mechanisms of the model. Section 6 explores several avenues for future work, and concludes. The Appendix contains two extensions of the basic model, as well as some of the proofs of propositions. 2. Basic Model Consider an economy populated by a continuum of agents with unit mass. There exist two occupational choices: an agent may become either a private entrepreneur in the for-profit sector or a social entrepreneur by founding a firm in the nonprofit sector. Let us denote the choice of agent i with oi = private, social. We refer to the two types of firms as private and nonprofit firms, respectively. Let N denote the total mass of nonprofit entrepreneurs; thus, 1 − N is the mass of private entrepreneurs. All agents are identically skilled. They differ, however, in their level of prosocial motivation, mi, which indicates to which extent an individual is genuinely motivated to help others (the beneficiaries of her projects). There exist two levels of mi, which we refer to henceforth as types: mH (motivated) and mL (selfish) types, where mH = 1 and mL = 0. A selfish type can also set up projects whose declared aim is helping the beneficiaries, but where she cares only about the aspects of these projects that increase her own well-being (ego, perks, etc.). The type mi is private information. In what follows, we assume that the population is equally split between mH- and mL-types. The utility function of an agent has the following form: $$W_{i}=\mathbb {I}(o_{i})\left[ w_{i}^{1-m_{i}}g_{i}^{m_{i}}\frac{1}{m_{i}^{m_{i}}(1-m_{i})^{1-m_{i}}}\right] + ( 1-\mathbb {I}(o_{i})) \left[ c^{1-\delta }d^{\delta }\frac{1}{\delta \left( 1-\delta \right) ^{1-\delta }}\right] ,$$ (1) where $$\mathbb {I}(o_{i})$$ is the indicator function taking value 1 if oi = social. wi and c denote her consumption in the nonprofit and private sectors, respectively, whereas gi and d stand for her warm-glow prosocial contribution in the nonprofit and private sectors. Finally, δ ∈ (0, 1) is a parameter measuring the relative importance of giving as compared to private consumption. The details of this structure are explained in what follows. 2.1. For-Profit Sector We assume that each private entrepreneur produces an identical amount of output. There are decreasing returns in the private sector, thus while the aggregate output is increasing in the mass of private entrepreneurs, 1 − N, the output produced by each private entrepreneur is decreasing in 1 − N. More precisely, we assume that each private entrepreneur produces $$y=\dfrac{A}{\left( 1-N\right) ^{1-\alpha }}, \,\,\,\text{where }0<\alpha <1 \text{ and }A>0.$$ (2) Aggregate output is thus given by Y = A(1 − N)α.5 Private-sector entrepreneurs derive utility from their private consumption (c). In addition, they also enjoy warm-glow utility from donating to the nonprofit sector (d). The utility Wi of an entrepreneur in the private sector then reduces to6: $$W_{i}=V_{P}(c,d)=c^{1-\delta }d^{\delta }\frac{1}{\delta \left( 1-\delta \right) ^{1-\delta }}, \,\,\,\text{where }0<\delta <1.$$ (3) Private-sector entrepreneurs maximize (3) subject to (2). This yields c* = (1 − δ)y and d* = δy, which in turn implies that, at the optimum, their indirect utility is equal to the income they generate as private entrepreneurs: $$V_{P}^{\ast }=y.$$ (4) From the optimization problem of private-sector entrepreneurs, it follows that the total amount of entrepreneurial donations to the nonprofit sector is $$D=\delta \left( 1-N\right) ^{\alpha }A,$$ (5) which increases with the productivity of the private sector (A), the number of private firms (1 − N), and the propensity to donate out of income (δ). 2.2. Nonprofit Sector The nonprofit sector is composed of a continuum of nonprofit firms with total mass N. Each nonprofit firm is run by a social entrepreneur. We think of each single nonprofit firm as a mission-oriented organization, as in Besley and Ghatak (2005), with a narrow mission targeting one particular social problem (e.g., child malnutrition, air pollution, fighting malaria, etc.). Each nonprofit manager i collects an amount of donations σi from the aggregate pool of donations D. The collected donations σi can be allocated to two distinct dimensions of the project. One dimension, which absorbs a level of expenses equal to wi, does not serve the ultimate needs of the beneficiaries, but might increase the well-being of the nonprofit manager. Such self-serving dimensions may include his wages, in-kind perks such as a car with a driver, but can also be his pet projects or actions that might increase his ego utility. The second dimension uses the undistributed donations σi − wi as an input for the production of the service towards the organization’s mission and increases the well-being of beneficiaries. We measure the effectiveness/output of each specific nonprofit firm by gi, which is a function of the undistributed donations (σi − wi). We assume that the output generated by each specific nonprofit firm exhibits decreasing returns with respect to the funds invested into the project, namely: $$g_{i}=( {\sigma }_{i}-w_{i})^{\gamma }, \,\,\,\text{where }0<\gamma <1.$$ (6) An important feature of this specification is the fact that the curvature of the nonprofit sector technology is larger than that of the for-profit sector. As we will see, this assumption underlies the single-crossing result (Lemma 1), which, in turn, allows a simple characterization of the different types of equilibria that may arise. As we argue more precisely in our discussion in Section 4, this assumption seems reasonable in the context of the functioning of the nonprofit sector. A nonprofit manager derives utility from the two dimensions noted previously. The weight placed on each of the two components of utility is given by the nonprofit manager’s level of prosocial motivation mi. The utility Wi of a nonprofit manager with motivation mi reduces to $$W_{i}=U_{i}(w_{i},g_{i})=w_{i}^{1-m_{i}}g_{i}^{m_{i}}\frac{1}{m_{i}^{m_{i}}(1-m_{i})^{1-m_{i}}}, \,\,\,\text{where }m_{i}\in \lbrace m_{H},m_{L}\rbrace .$$ (7) We assume that the monitoring by donors of the nonprofit sector is weak, and donors cannot control how nonprofit managers split the donations between the two dimensions. For simplicity, we make the extreme assumption that nonprofit managers enjoy full discretion in deciding this allocation (subject to the feasibility constraint wi ≤ σi). In addition, we assume that the pool of total donations D is equally shared by all nonprofit firms.7 Therefore, donations collected by each nonprofit firm are given by \begin{equation*} {\sigma }_{i}=\dfrac{D}{N}=\dfrac{\delta A\left( 1-N\right) ^{\alpha }}{N}. \end{equation*} Notice that σi is decreasing in N through two distinct channels. Firstly, the level of aggregate donations D shrinks when the mass of private entrepreneurs (1 − N) gets smaller. Secondly, a rise in the mass of nonprofit firms N means that a given total pool of donations D must be split among a larger mass of nonprofit firms. Given that mH = 1, motivated nonprofit managers place all the weight in their utility function on the dimension that helps the beneficiaries g, and set accordingly $$w_{H}^{\ast }=0$$. As a result, choosing to become a nonprofit manager gives to a motivated agent the indirect utility equal to $$U_{H}^{\ast }=\left( \dfrac{D}{N}\right) ^{\gamma }=\left[ \delta A\dfrac{\left( 1-N\right) ^{\alpha }}{N}\right] ^{\gamma }.$$ (8) Analogously, given that mL = 0, selfish nonprofit managers disregard contributing to their organizations’ mission, and allocate all the donations to the self-serving (unproductive) dimension, $$w_{L}^{\ast }= {\sigma }_{i}$$. This implies that choosing to become a nonprofit manager gives to a selfish agent the level of utility $$U_{L}^{\ast }=\dfrac{D}{N}=\delta A\dfrac{\left( 1-N\right) ^{\alpha }}{N}.$$ (9) We can now state the following single-crossing result: Lemma 1. Let $$\widehat{N}$$ denote the level of N at which $$D(\widehat{N})=\widehat{N}$$. Then, \begin{equation*} U_{H}^{\ast }\gtreqless U_{L}^{\ast }\text{ if and only if }N\gtreqless \widehat{N}, \end{equation*} where (i) $$\delta A/(1+\delta A)<\widehat{N}<1$$, (ii) $$\widehat{N}$$ is strictly increasing in A and δ, and strictly decreasing in α, (iii) $$\underset{A\rightarrow \infty }{\lim }\widehat{N}=1$$, (iv) $$\underset{\alpha \rightarrow 0}{\lim}\widehat{N}=\delta A$$, and $$\underset{\alpha \rightarrow 1}{\lim }\widehat{N}=\delta A/(1+\delta A)$$. Lemma 1 states that a motivated individual obtains higher utility from becoming a nonprofit manager, as compared to a selfish individual making the same choice, only when donations per nonprofit are small enough, that is, D/N < 1. Both $$U_{H}^{\ast }$$ and $$U_{L}^{\ast }$$ are strictly increasing in donations per nonprofit, D/N. However, when the level of donations received by each nonprofit rises above a certain threshold (which here is equal to 1), $$U_{L}^{\ast }$$ surpasses $$U_{H}^{\ast }$$. The reason for this result essentially rests on the concavity of gi in (6), combined with the altruism displayed by motivated nonprofit managers in (7). These two features translate into a payoff function of motivated nonprofit managers, $$U_{H}^{\ast }$$, that is concave in D/N. Conversely, selfish nonprofit managers exhibit a payoff function, $$U_{L}^{\ast }$$, which is linear in D/N. This is because these agents only care about their perks or pet projects, and hence they exploit the lack of monitoring in the NGO sector in order to always set wi = D/N. 2.3. Equilibrium Occupational Choice Let NH and NL denote henceforth the mass of nonprofit managers of mH- and mL-type, respectively (the total mass of nonprofit managers is then N = NH + NL). In equilibrium, the following two conditions must be simultaneously satisfied: Given the values of NH and NL, each individual chooses the occupation that yields the higher level of utility, with some agents possibly indifferent between occupations. The allocation (NH, NL) must be feasible: (NH, NL) ∈ [0, 1/2] × [0, 1/2]. In this basic specification of the model, for a given parametric configuration, the equilibrium occupational choice will always be unique (except for one knife-edge case described in the next footnote). Nevertheless, the type of agents (in terms of their prosocial motivation) who self-select into the nonprofit sector will depend on the specific parametric configuration of the model. In what follows, we describe the main features of the two broad kinds of equilibria that may take place: an equilibrium where 0 = NH < NL = N (which we refer to as low effectiveness or L-equilibrium), and an equilibrium where 0 = NL < NH = N (which we denote as high effectiveness or H-equilibrium).8 L-equilibrium. In a “low-effectiveness equilibrium”, the nonprofit sector is populated exclusively by selfish individuals, and it arises when payoffs are such that: $$U_{H}^{\ast }(N)<V_{P}^{\ast }(N)\le U_{L}^{\ast }(N)$$, where $$V_{P}^{\ast }(N)$$ is given by (4), $$U_{H}^{\ast }(N)$$ by (8), $$U_{L}^{\ast }(N)$$ by (9), and N = NL ≤ 1/2. Lemma 1 implies that for $$U_{H}^{\ast }(N)<U_{L}^{\ast }(N)$$ to hold, the number of nonprofit firms should be sufficiently small (i.e., $$N<\widehat{N}$$), so that the donations received by each nonprofit firm turn out to be sufficiently large. In addition, the condition $$V_{P}^{\ast }(N)\le U_{L}^{\ast }(N)$$ leads to: $$N\le N_{0}\equiv \dfrac{\delta }{1+\delta }.$$ (10) From (10), we may observe that N0 < 1/2. As a result, in a low-effectiveness equilibrium it must necessarily be the case that N = NL = N0, so that the selfish agents turn out to be indifferent between the for-profit and nonprofit sectors. Indifference by mL-types leads a mass 1/2 − N0 of them to become private entrepreneurs, allowing thus “markets” to clear. Notice, finally, that $$U_{H}^{\ast }(N_{0})<V_{P}^{\ast }(N_{0})$$ needs to be satisfied; hence, the crucial parametric condition leading to an L-equilibrium boils down to $$N_{0}<\widehat{N}$$. H-equilibrium. This type of equilibrium takes place when all selfish individuals prefer to found private firms, whereas all motivated ones prefer (weakly) to be social entrepreneurs: $$U_{L}^{\ast }(N)<V_{P}^{\ast }(N)\le U_{H}^{\ast }(N)$$, where N = NH ≤ 1/2. Lemma 1 states that for $$U_{H}^{\ast }(N)>U_{L}^{\ast }(N)$$ to hold, the nonprofit sector should have a sufficiently large number of nonprofit firms: $$N>\widehat{N}$$. The condition $$U_{L}^{\ast }(N)<V_{P}^{\ast }(N)$$ requires that N > N0. Unlike the previous case, in the high-effectiveness equilibrium, we cannot rule out the possibility of full sectorial specialization of the two motivational types of agents (i.e., in principle, an H-equilibrium may feature NL = 0 and NH = 1/2). For future reference, we denote with N1 the value of N that makes mH-types indifferent between occupations. From (2) and (8), we can observe that N1 is implicitly defined by: $$\dfrac{(1-N_{1})^{\frac{1-\alpha (1-\gamma )}{\gamma }}}{N_{1}}\equiv \dfrac{A^{\frac{1-\gamma }{\gamma }}}{\delta }.$$ (11) Equilibrium Characterization. The following proposition characterizes the different kinds of equilibria that may arise, given the specific parametric configuration of the model. Proposition 1. Whenever A(1 + δ)1 − α ≠ 1, the equilibrium is unique. When A(1 + δ)1 − α > 1, the economy is in an L-equilibrium, whereas when A(1 + δ)1 − α < 1, the economy is in an H-equilibrium. More formally, Low-Effectiveness Equilibrium: if A(1 + δ)1 − α > 1, in equilibrium, there is a mass $$N^{\ast }=N_{L}^{\ast }=N_{0}$$ of nonprofit firms, all managed by mL-types. The mass of private entrepreneurs is equal to 1 − N0; among these, a mass 1/2 are mH-types and a mass 1/2 − N0 are mL-types. High-Effectiveness Equilibrium: if A(1 + δ)1 − α < 1, in equilibrium, there is a mass $$N^{\ast }=N_{H}^{\ast }=\min \left\lbrace N_{1},{1}/{2}\right\rbrace$$ of nonprofit firms, all managed by mH-types. The mass of private entrepreneurs is equal to max {1 − N1, 1/2}; among these, a mass 1/2 are mL-types and a mass max {0, 1/2 − N1} are mH-types. Proposition 1 characterizes the main types of equilibria that may arise in the model. These cases are depicted in Figure 1a–c. This figure portrays the indirect utilities of motivated and selfish agents in the nonprofit sector (UH and UL, respectively) and that of individuals in the private sector (y), all of them as functions of the size of the nonprofit sector, N. Figure 1. View largeDownload slide (a) Low-effectiveness equilibrium. (b) High-effectiveness equilibrium with incomplete sorting. (c) High-effectiveness equilibrium with full sorting. Figure 1. View largeDownload slide (a) Low-effectiveness equilibrium. (b) High-effectiveness equilibrium with incomplete sorting. (c) High-effectiveness equilibrium with full sorting. An implication of Proposition 1 is that more productive economies (i.e., those with a relatively large A) tend to exhibit a low-effectiveness equilibrium. This result rests on the fact that a larger A entails greater profits to private entrepreneurs. Hence, in equilibrium, a larger amount of donations to any nonprofit firm (σi) are needed in order to compensate for the higher opportunity cost of managing a nonprofit firm (i.e., the fact of not becoming a private entrepreneur). In turn, when σi is larger, the scope for rent seeking in the nonprofit sector is greater, which attracts more intensely selfish agents than motivated ones. A similar intuition applies to the effect of a higher warm-glow utility from giving; that is, a greater δ. This yields a larger amount of total donations, D, for a given mass of nonprofits N, making the nonprofit sector relatively more attractive to selfish agents than to motivated ones.9 2.4. Effect of Foreign Aid on the Equilibrium Allocation So far, all donations in our model were generated (endogenously) within the economy. However, in the context of developing economies, foreign aid represents also a major source of revenue for nonprofits organizations. In fact, an ever growing share of foreign aid is being channeled via NGOs. For instance, McCleary and Barro (2008) show that over 40% of US overseas development funds flows through NGOs. International aid agencies have been increasingly choosing NGOs over public-sector channels as well: for example, whereas between 1973 and 1988, only 6% of World Bank projects went through NGOs, by 1994 this share exceeded 50% (Hudock 1999).10 What would be the effect of a rise in foreign aid on the motivational composition and performance of the nonprofit sector of the recipient economy? In this section, we analyze this question by slightly modifying the above model to allow for an injection Δ > 0 of foreign aid into the economy. Foreign aid represents an exogenous increase in the total amount of donations available to the national nonprofit sector. Donations collected by a nonprofit firm now become: $$\dfrac{D}{N}=\dfrac{\delta A\left( 1-N\right) ^{\alpha }+\Delta }{N}.$$ (12) As done previously in Lemma 1, we first pin down the threshold $$\widehat{N}$$ such that for all $$N>\hat{N,}$$ the utility obtained by selfish nonprofit managers dominates that obtained by motivated nonprofit managers. Lemma 2. (i) Whenever 0 ≤ Δ ≤ 1, there exists a threshold $$\widehat{N}\le 1$$ such that $$U_{H}^{\ast }(N)\gtreqless U_{L}^{\ast }(N)$$ iff $$N\gtreqless \widehat{N}$$; the threshold $$\widehat{N}$$ is strictly increasing in Δ, and $$\lim _{\Delta \rightarrow 1}\widehat{N}=1$$. (ii) Whenever Δ > 1, $$U_{H}^{\ast }(N)<U_{L}^{\ast }(N)$$ for all 0 < N ≤ 1. The first result in Lemma 2 essentially says that the set of values of N for which the inequality $$U_{H}^{\ast }(N)<U_{L}^{\ast }(N)$$ holds—which is given by the interval $$(0,\widehat{N})$$—expands as the amount of foreign aid Δ increases. The second result states that when foreign aid is sufficiently large, $$U_{H}^{\ast }(N)<U_{L}^{\ast }(N)$$ becomes valid for any feasible value of N. The injection of foreign aid thus enlarges the set of parameters under which the economy features an equilibrium with selfish nonprofit managers (“L-equilibrium”). The proposition in what follows formalizes this perverse effect of foreign aid. For brevity, we restrict the analysis only to the more interesting case, in which A(1 + δ)1 − α < 1. For future reference, it proves useful to denote by $$\underline{N}$$ the level of N for which y(N) in (2) equals one; that is, $$\underline{N}\equiv 1-A^{\frac{1}{1-\alpha }}.$$ (13) In addition, in order to disregard situations in which $$\underline{N}\ge 0$$ fails to exist, we henceforth set the following upper bound on A: Assumption 1.  A ≤ 1. Note that if A > 1, then the condition A(1 + δ)1 − α < 1 for an “H-equilibrium” in Proposition 1 could never hold, and the model would always deliver—by construction—an “L-equilibrium”.11 Proposition 2. Consider an economy where 2 − (1 − α) < A < (1 + δ) − (1 − α). In these cases, the fraction of motivated nonprofit managers will depend nonmonotonically on the level of foreign aid. More precisely, by defining Δ0 ≡ 1 − A1/1 − α(1 + δ), where notice that Δ0 > 0, then: When 0 ≤ Δ < Δ0, all nonprofit firms are managed by mH-types. There exists a finite threshold ΔA > Δ0 such that, when Δ0 < Δ ≤ ΔA, all nonprofit firms are managed by mL-types. When Δ > ΔA, nonprofit firms are managed by a mix of types, with mL-type majority. In particular, there is a mass $$N_{L}^{\ast }={1}/{2}$$ of selfish nonprofit managers and a mass $$0<N_{H}^{\ast }<{1}/{2}$$ of motivated managers, where $$N_{H}^{\ast }$$ is strictly increasing in Δ. Proposition 2 describes the effects of changes in the amount of foreign aid Δ on the equilibrium allocation of an economy which, in the absence of any foreign donations, would display a high-effectiveness equilibrium. The proposition focuses on the case where A(1 + δ)1 − α < 1, but 21−αA > 1, which illustrates the nonmonotonic effect of foreign aid on motivational composition in the nonprofit sector in the cleanest possible way. However, in the Appendix C, we show that analogous results also arise for the case when 21−αA < 1 (see Proposition 2(bis) therein).12 According to Proposition 2, when foreign aid is not too large (Δ < Δ0), the nonprofit sector remains managed by motivated agents. However, when the level of donations surpasses the threshold Δ0, selfish agents start being attracted into the nonprofit sector due to the greater scope for rent extraction. Interestingly, for any Δ0 < Δ ≤ ΔA, the economy experiences a complete reversal in the equilibrium occupational choice: all mH-types choose the private sector, while the nonprofit sector becomes entirely managed by mL-types. Finally, when Δ > ΔA, foreign aid becomes so large that the nonprofit sector starts attracting back some of the mH-types in order to equalize the returns of motivated agents in the for-profit and nonprofit sectors. Notice, however, that when Δ > ΔA, the mass of nonprofits run by selfish agents is still larger than the mass of nonprofits managed by mH-types. Figure 2 depicts the above-mentioned results. The solid lines represent $$U_{H}^{\ast }(N)$$ and $$U_{L}^{\ast }(N)$$ when Δ = 0, the dashed lines shows nonprofit managers’ payoffs when Δ0 < Δ ≤ ΔA, and the dotted lines plots those payoffs when Δ > ΔA. A gradual injection of foreign aid from Δ = 0 to Δ = Δ0 initially has no effect on the motivational composition of the nonprofit sector. Beyond the amount of aid Δ = Δ0, the motivational composition of the nonprofit sector is completely reversed. Further increases in foreign aid have no effect on the nonprofit sector’s output, up to the point Δ = ΔA. There, all the unmotivated agents have moved into the nonprofit sector and thus its size equals 1/2. From then on, further injections of aid (beyond ΔA) start to attract back some motivated agents into the nonprofit sector, and the motivational composition of the sector therefore improves. Figure 2. View largeDownload slide Effect of foreign aid injection. Figure 2. View largeDownload slide Effect of foreign aid injection. A key corollary that stems from Proposition 2 refers to the total output of the nonprofit sector, G, at different values of Δ. Bearing in mind that only motivated nonprofit managers devote the donations collected to the dimension that produces the mission-oriented output gi (and, thus, contributes to the well-being of beneficiaries), an implication of Proposition 2 is that G(Δ) is nonmonotonic in Δ. In particular, nonprofit output grows initially with the amount of foreign aid, up to the level when Δ = Δ0 when it reaches $$G(\Delta _{0})=\underline{N}$$, which is the enhancing effect of foreign donations when the nonprofits are managed by motivated managers. However, for Δ0 < Δ ≤ ΔA, the motivation in the nonprofit sector gets completely “polluted” by the presence of selfish managers, and G(Δ) drops suddenly to zero. Finally, when foreign donations rise beyond ΔA, nonprofit output begins to grow again (starting off from G = 0), as some of the donations will end up in the hands of mH-types. This nonmonotonicity of the total output of the nonprofit sector is depicted by Figure 3. Figure 3. View largeDownload slide Foreign aid and nonprofit sector output. Figure 3. View largeDownload slide Foreign aid and nonprofit sector output. Note that our mechanism is quite different from the arguments previously raised concerning the perverse effects of foreign aid on the functioning of the public sector.13 In fact, our model shows that even when foreign aid is channeled through the NGO sector (hence, bypassing the public bureaucracy), perverse effects might still arise, because massive aid inflows may end up worsening the motivational composition of the NGO sector in the recipient country. Our results may also help shedding light on the so-called micro–macro paradox found in the empirical foreign aid literature; for example, Mosley (1986). On one hand, at the microeconomic level, there are numerous studies that find the positive effect of foreign-aid-financed projects on measures of welfare of beneficiaries. On the other hand, at the aggregate level most studies actually fail to find a significant positive effect. Our model rationalizes this paradox as follows: when aid inflows are small (or, alternatively, when you hold the motivational composition of the NGO sector constant), the general-equilibrium effect becomes negligible, and one may well find a positive effect of aid projects. However, when aid inflows are sufficiently large (e.g., when the well-functioning microlevel projects are scaled up), the general-equilibrium effects kick in, and the motivational adverse selection effect may neutralize the positive effect found at the micro level. 3. Eliminating Low-Effectiveness Equilibrium The analysis of the previous section raises a natural question: Can the low-effectiveness equilibrium be avoided? If so, through which channels? In this section, we explore three possible safeguard mechanisms that might prevent this equilibrium from emerging. The first focuses on the donors’ behavior and relaxes the assumption of donors being completely unaware of the motivational problems in the nonprofit sector. The second exploits the idea that managers in the nonprofit sector might have an informational advantage about the quality of the sector’s output, and thus there may be scope for creating nonprofit watchdog organizations. Finally, the third focuses on government policies, in particular on taxes and public financing of the nonprofit sector. 3.1. Donors’ Preferences: Conditional Warm Glow So far, we have assumed that entrepreneurs donate a fraction of their income simply because they enjoy the act of giving. Such disconnection between donations and their use may sound a bit too extreme. One may expect that motivated entrepreneurs will be unwilling to donate money when the nonprofit sector is entirely run by selfish types.14 In this section, we relax the assumption of fully naive warm glow giving by motivated entrepreneurs. In particular, we modify the basic model presented in Section 2 in two ways. First, we let the propensity to donate be type specific (δi) and increasing in mi. More precisely, assume that δi = δH ∈ (0, 1] when mi = mH, whereas δi = δL = 0 when mi = mL. Second, we let warm-glow weight rise with the fraction of motivated nonprofit managers, by postulating that mH-type private entrepreneurs have the following utility function: \begin{equation*} V_{H}(c,d)=\left[ \tilde{\delta }_{H}^{\tilde{\delta }_{H}}(1-\tilde{\delta }_{H})^{1-\tilde{\delta }_{H}}\right] ^{-1}c^{1-\tilde{\delta }_{H}}\,d^{\tilde{\delta }_{H}}, \end{equation*} $$\text{where} \quad \tilde{\delta }_{H}=f\, \delta _{H}\quad \text{ and }f\equiv \dfrac{N_{H}}{N_{H}+N_{L}}.$$ (14) The utility function (14) displays conditional warm-glow altruism, in the sense that the intensity of the warm-glow weight ($$\tilde{\delta }_{H}$$) is linked to the likelihood that the donation ends up in the hands of a motivated nonprofit manager. When prosocially motivated private entrepreneurs are characterized by (14), the level of donations obtained by a nonprofit firm will be given by: $$\dfrac{D}{N}=\dfrac{\delta _{H}\,A\left( \frac{1}{2}-N_{H}\right) N_{H}}{( 1-N_{H}-N_{L}) ^{1-\alpha }( N_{H}+N_{L}) ^{2}}.$$ (15) Proposition 3. Let the warm-glow weight be given by $$\tilde{\delta }_{i}=f\, \delta _{i}$$, where δH ∈ (0, 1], δL = 0 and f ≡ NH/(NH + NL). Then, defining Λ ≡ [(2 + δH)/(2 + 2δH)]1 − α: If A ≤ Λ, in equilibrium, $$N_{H}^{\ast }=\eta _{H}(A)$$ and $$N_{L}^{\ast }=0$$, where ∂ηH/∂A < 0. If Λ < A ≤ 1, in equilibrium, $$0<N_{H}^{\ast }<\tfrac{1}{2}$$ and $$0<N_{L}^{\ast }<\tfrac{1}{2}$$, with $$N_{H}^{\ast }+N_{L}^{\ast }=[ 1-A^{1/\left( 1-\alpha \right) }]$$. In particular, $$N_{H}^{\ast }=n_{H}(A)$$ and $$N_{L}^{\ast }=n_{L}(A)$$, where: \begin{align*} n_{H}(A) &=\dfrac{1}{4}-\sqrt{\dfrac{1}{16}-\dfrac{[ 1-A^{1/( 1-\alpha ) }] ^{2}}{\delta _{H}}}\text{,} \\ n_{L}(A) &=[ 1-A^{1/( 1-\alpha ) }] -n_{H}. \end{align*} Moreover, the fraction of motivated nonprofit managers decreases with A, ∂f/∂A < 0. Proposition 3 states that when warm glow weights depend on the fraction of motivated agents within the pool of nonprofit managers, the purely low-effectiveness equilibrium ceases to exist. The responsiveness of $$\tilde{\delta }_{H}$$ to f in (14) counterbalances the effect that a larger mass of mH-type entrepreneurs has on total donations, and thus neutralizes the source of interaction that leads to the rise of L-equilibrium. In other words, conditional warm-glow altruism removes the possibility that the nonprofit sector is managed fully by selfish agents, because in those cases motivated private entrepreneurs would refrain from donating any of their income. Nevertheless, conditional warm-glow altruism does not preclude the fact that the nonprofit sector may end up being partly managed by mL-types. This occurs when A is sufficiently large, which is in line again with the results of the baseline model in Proposition 1. Furthermore, Proposition 3 shows that the fraction of selfish nonprofit managers is monotonically increasing in A. 3.2. Nonprofits: Peer Monitoring by Watchdog Organizations Our benchmark model assumed that nonprofit managers are able to divert any amount of funds they receive away from the dimension that helps the ultimate beneficiaries. This extreme assumption intends to reflect the idea that monitoring the behavior of nonprofit managers (or knowing their intrinsic motivation) is an inherently difficult task for donors. In real life, cognizant of such pitfalls (and to ensure the credibility of the sector as a whole), nonprofits that care about the collective reputation of the sector often try to create peer-monitoring institutions, so as to discourage misbehavior within the sector. This is especially the case in developed economies, and examples of such institutions are the CFB quality label in the Netherlands and the Fundraising Standards Board in Britain (see Similon (2015) for a detailed description).15 In this section, we explore the consequences of peer monitoring in the nonprofit sector on the equilibrium occupational choices of motivated and selfish agents. To incorporate peer monitoring, we now assume that, after the decision by each nonprofit manager of how to split donations between the two dimensions (i.e., probeneficiary and perks), each nonprofit gets randomly matched together with another nonprofit. During this matching process, they may get to know each other’s accounts. In particular, with probability 0 < ρ < 1, a nonprofit observes the budget structure of its matching partner. We assume that only the motivated nonprofit managers care about the governance structure of their sector. Thus, if they realize that their matching partner has been diverting funds for perks or allocating the funds to projects useless for beneficiaries, they will make this information public. Publicizing this information leads to a penalty χ > 0 for the selfish agent (χ can reflect a reputation cost, disutility related to public shaming, or the cost of legal punishment meted out to the selfish nonprofit manager). With these assumptions, the expected utility of a selfish nonprofit manager becomes $$U_{L}^{\ast }(N,N_{H})=\dfrac{D}{N}-\frac{N_{H}}{N}\rho \chi =\delta A\dfrac{\left( 1-N\right) ^{\alpha }}{N}-\frac{N_{H}}{N}\rho \chi .$$ (16) The second term in (16) reflects the fact that, when a selfish nonprofit manager is matched with a motivated one (which occurs with probability NH/N), he suffers a loss equal to χ with probability ρ. Regarding motivated nonprofit managers, given that the matching process does not affect them, their indirect utility in the nonprofit sector remains as described by equation (8).16 This formulation intends to capture a number of relevant features of the monitoring aspect of the development nonprofit sector. First, on the motivational side, motivated agents clearly have an intrinsic motivation to also care about the public-good nature of having a well-functioning nonprofit sector. Relatedly, they may as well feel concerned about the general reputation of the sector.17 Second, in terms of information acquisition, because of contacts and information sharing between different NGOs on the ground (Meyer 1997), insiders are more likely to have access to information about the behavior of other members of the non–for-profit sector. The fact that the expected utility of selfish nonprofit managers in (16) is decreasing in the share of motivated managers opens up the possibility of multiple equilibria. Intuitively, a nonprofit sector that is mainly run by intrinsically motivated agents enjoys also high levels of monitoring and sanctioning of misbehavior in the sector. This, in turn, discourages selfish agents from entering the nonprofit sector as they expect a low probability of success in their intended diversion of funds. Conversely, when the nonprofit sector is relatively poor in terms of motivation, selfish agents feel more attracted to it, given the larger scope for successful rent extraction that poor monitoring allows. The next proposition fully characterizes the possible motivational equilibrium allocations in the nonprofit sector under the possibility of peer monitoring. Proposition 4. The equilibrium allocation of motivation in the nonprofit sector with peer monitoring nonprofits depends on the parametric configuration in the following way: If A(1 + δ)1 − α > 1, there exists a threshold value $$\bar{\Phi }>0$$ of the expected cost of monitoring ρχ such that: (a) If $$\rho \chi <\bar{\Phi }$$, only the ‘L-equilibrium’ prevails (with $$N^{\ast }=N_{0}=N_{L}^{\ast }<1/2$$). (b) If $$\rho \chi >\bar{\Phi }$$, the model exhibits multiple equilibria with three possible equilibrium outcomes: (i) an ‘L-equilibrium’ (with $$N^{\ast }=N_{0}=N_{L}^{\ast }<1/2$$), (ii) an ‘H-equilibrium’ (with $$N^{\ast }=N_{1}=N_{H}^{\ast }<1/2)$$, (iii) a ‘mixed-type equilibrium’ (with $$N^{\ast }=N_{1}=N_{H}^{\ast }+N_{L}^{\ast }<1/2$$ and $$N_{H}^{\ast }$$ and $$N_{L}^{\ast }>0$$). If A(1 + δ)1 − α < 1, only the ‘H-equilibrium’ prevails (with $$N^{\ast }=N_{H}^{\ast }=\min \lbrace N_{1},{1}/{2}\rbrace )$$. It is interesting to compare the above results to those in Proposition 1. When $$\rho \chi >\bar{\Phi }$$ (that is, when the expected punishment upon detection is high enough), peer monitoring by motivated agents in the nonprofit sector allows the possibility of a high-effectiveness equilibrium when A(1 + δ)1 − α > 1. These are parameter configurations that led to an “L-equilibrium” as a unique equilibrium in Proposition 1. However, peer monitoring by nonprofit managers does not ensure that such improved motivational allocation will necessarily emerge when A(1 + δ)1 − α > 1. In fact, multiple equilibria are possible in that range. The reason for this is that the quality of monitoring is itself endogenous to the occupational choice of agents. This negative externality from motivated nonprofit managers to selfish ones naturally creates a scope for expectation-driven multiple equilibria.18 3.3. Policies: Taxes and Public Financing of Nonprofit Sector In most economies, an important part of nonprofits’ revenues comes from public grants financed by taxes. This raises two main questions. First, what is the effect of partial public financing on the motivational composition and size of the nonprofit sector? Second, can public financing generate an improvement in the composition of the nonprofit sector, as compared to the decentralized equilibrium? In this section, we address these questions by adding a set of public policy variables into our basic model. We let the government impose a proportional tax on income in the for-profit sector and use its proceeds to distribute (unconditional) grants to nonprofit firms. Thus, the payoffs of individuals in the private sector now becomes $$V_{P}^{\ast }=\left( 1-t\right) y,$$ (17) where y is still given by (2). The level of donations collected by each nonprofit in this case are equal to $${\sigma }_{i}=\dfrac{D}{N}=\dfrac{\overset{\text{private donations}}{\overbrace{\delta \left( 1-t\right) (1-N)y}}+\overset{\text{public grant}}{\overbrace{t(1-N)y}}}{N}.$$ (18) Public financing via such a tax/grant system alters occupational choices of individuals via two distinct channels. First, we can see in (17) that taxation lowers returns in the private sector. Second, because the public sector distributes back all the taxes it collects, whereas the private sector only gives a fraction δ of its net income, σi in (18) increases with the tax rate t. Both channels, ceteris paribus, make the nonprofit sector more attractive to all individuals. However, within our general-equilibrium framework, the key issue is whether public financing increases the attractiveness of the nonprofit sector relatively more for motivated or for selfish individuals. To study the more interesting case, let us focus on a setting where our basic economy (without public financing) would give rise to a low-effectiveness equilibrium: A(1 + δ)1 − α > 1. Consider now an increase in taxes, with the transfer of all the proceeds to nonprofits as grants. For such policy to induce a motivational improvement in the nonprofit sector, it is crucial that, in the new equilibrium (after taxes), the selfish individuals who were initially managing the nonprofit sector switch occupations and move to the private sector. This will occur only if the policy attracts enough motivated agents from the private sector into the nonprofit sector, so that this entry sufficiently dilutes the amount of funds per nonprofit organization, even after taking into account the larger total funding of the nonprofit sector as a whole. The proposition in what follows formally proves that such a tax/grant policy exists. Proposition 5. For A(1 + δ)1 − α = 1 + ε, where $$0<\varepsilon <\bar{\varepsilon }$$, there exists a feasible range of tax rates $$[\underline {\mathit t},\bar{t}]$$, where $$\underline {\mathit t}>0$$ and $$\bar{t}\equiv (1-\delta )/(2-\delta )$$, such that when $$t\in [\underline {\mathit t},\bar{t}]$$ an ‘H-equilibrium’ arises. Figure 4 plots the equilibrium regions for different combinations of values of A and t (see Appendix C for the derivation of the equilibrium regions). There are four different regions. For combinations of relatively low values of A and t, the model features an “H-equilibrium” where the nonprofit sector is fully managed by motivated agents. On the other hand, given a certain level of t, for sufficiently high levels of A we have an “L-equilibrium”. Notice that when t = 0, the boundary between these two regions is given by A = 1/(1 + δ)1 − α, as previously stated in Proposition 1. In addition, with public financing, two new equilibrium regions arise: one with a mixed-type equilibrium with a fraction of motivated agents in the nonprofit sector larger than one-half (f > 0.5), and one with a mixed-type equilibrium with f < 0.5. These two types of equilibria occur when the tax rate is sufficiently large, while the former also requires that A is sufficiently small and the latter that A takes intermediate values. Figure 4. View largeDownload slide Public financing of nonprofit sector. Figure 4. View largeDownload slide Public financing of nonprofit sector. A crucial feature of Figure 4 is that the threshold level of A splitting the high- and low-effectiveness equilibrium regions is increasing in t (up to the point in which $$t=\bar{t}$$). As a consequence of this, there are situations in which introducing public funding of nonprofits via (higher) taxes on private incomes can make the economy switch from an “L-equilibrium” to an “H-equilibrium”. This is depicted in Figure 4 by the dashed line arrow. This result rests on a subtle general-equilibrium interaction. Consider an economy with no taxes that is on the low-effectiveness equilibrium region, located at point Z. At Z, all mH-types prefer the private sector, while mL-types are indifferent between both sectors.19 Because a higher tax rate makes the nonprofit sector more attractive, by sufficiently raising t we can make mH-types prefer nonprofit sector as well. However, when all motivated agents switch to the nonprofit sector, the value of N will rise, and the returns in this sector will accordingly decrease. When t lies within the interval $$[\underline {\mathit t},\bar{t}]$$, the new equilibrium allocation induced by the higher t leads to an increase in total funding of the nonprofit sector, while simultaneously reducing the value of per-organization funding (σi) enough so that only motivated agents are ultimately attracted to the nonprofit sector.20 In terms of actual implementation, our result implies that it may be advisable to give starting grants to new nonprofits. For instance, consider the recent proposals to do “philanthropy through privatization” (Salamon 2013), which consists in returning part of proceeds from the privatization of public-sector assets to foundations and charities. Our analysis suggests that this policy would work correctly only if the way these proceeds are used is such that they are scattered through a multitude of small organizations, rather than concentrating them on a few large nonprofits. In fact, while the latter risks worsening the motivational composition of the sector by attracting selfish agents, the former ensures that the returns in the nonprofit sector remain low enough to attract only motivated managers. 4. Discussion In this section, we proceed to discuss some of the key assumptions and modeling choices of our baseline framework. We also provide a discussion regarding the robustness of our results to relaxing these assumptions. 4.1. Decreasing Returns in the Nonprofit Sector One key assumption is the decreasing returns in the nonprofit sector (0 < γ < 1).21 This assumption underlies the single-crossing result (Lemma 1), which is, in turn, crucial for characterizing the different types of equilibria that may arise (Proposition 1). The nature of the functioning of the nonprofit sector makes this assumption seem appropriate in the context of our model. Two distinct reasons motivate our choice of decreasing returns at the level of single nonprofit organizations: (i) the fact that motivated agents may become a scarce input unable to grow at the same speed as donations; (ii) the fact that nonprofits tend to face increasingly difficult tasks to accomplish as their effort within their mission boundaries deepens. Nonprofit organizations are entities crucially defined by their missions (i.e., the specific social problems that these organizations aim to address). A fundamental scarce resource from the viewpoint of these organizations is then mission-oriented motivated labor, that is, individuals who are aligned with the mission of a particular nonprofit.22 The practitioners of the sector, in fact, underline that finding such people and expanding the staff of the organization is often extremely difficult, mainly because of the existing variety of missions and organizations.23 In this respect, a fundamental operational difference between nonprofit and for-profit firms is that, while (individually) the latter can easily purchase the required inputs in the market at a given market price, the former tends to face an often binding constraint on the amount of “mission-oriented motivation” it can acquire. Thus, as funding expands, if the nonprofit-motivated labor cannot grow at the same pace, some form of diminishing returns of those funds will eventually kick in. For instance, Robinson (1992, p. 38) notes about nonprofits working in rural areas that “ambitious attempts to expand or replicate successful projects can founder on the paucity of appropriately trained personnel who are experienced in community development”. Similarly, Hodson (1992) states that “Upgrading the management capability [of a development non-profit] usually implies new talent. Unfortunately, the story-book scenario under which the original team continues to develop its management capability at a rate sufficient to cope with rapid growth rarely comes true...” (p. 132) Concerning the second reason that motivates our assumption, the type of tasks that a nonprofit organization typically carries out tends to change along its expansion path. The first activities tend to concentrate on some form of emergency: saving individuals from imminent physical danger or starvation, helping to avoid some irreversible health problem, and so forth. In this sense, the marginal returns are extremely high at the beginning. However, the next activities of the nonprofit’s project involve usually tasks that are less emergency-driven and more oriented towards making the livelihoods of beneficiaries sustainable (e.g., putting children to school, providing economic activities so that beneficiaries can earn their living). Smillie (1995) argues that these types of tasks are much harder to accomplish successfully and involve a much longer period of time to realize. Such long-run perspective also implies that many organizations prefer to concentrate on the emergencies; however, the resulting competition among them for “saving lives” limits their expansion, as has been underlined by observers of large-scale humanitarian emergencies such as the 2004 tsunami (Mattei 2005). In our case, this implies that, for a given nonprofit organization, the slope of its production function is fairly steep at low levels of funding (when it first deals with emergency activities), whereas it becomes flatter at higher levels of funding (as the nonprofit moves its focus to sustainable development activities). 4.2. Informational Asymmetries and Lack of Contractibility Throughout the paper we have assumed that motives for giving are unrelated to the performance of nonprofit firms.24 This assumption would become untenable if motivated nonprofit managers could find a way to signal their motivation to donors. One possibility for such signaling would result from allowing nonprofit managers to “burn money”. In such case, a separating equilibrium where motivated types engage in “burning” enough money (so as to discourage self-interested types from joining the nonprofit sector) could arise. It is hard to envision, however, a practical way of carrying out these sort of actions. One possibility could be allowing for self-imposed restrictions on overheads. Yet, to be credible, such a scheme would require a third-party certification of such restrictions (for example, by the government), bringing up additional credibility issues to the model.25 More generally, our model has implicitly assumed that nonprofits’ output is completely unobservable or unverifiable. This assumption underlies the severe noncontractability of managers’ allocation decisions in the nonprofit sector. Noncontractability problems means that motivation serves as a substitute for contracts in our model, as it is exactly this problem that attracts selfish individuals into nonprofits when this sector is flooded with donations. Clearly, some degree of output measurability would ease the problem of adverse selection. However, it is exactly in those sectors where output is poorly measured that the role of nonprofits is greater, as has been argued by Glaeser and Shleifer (2001). In fact, in sectors where output can be measured relatively well, the production could be fully taken care of by for-profit firms. 4.3. Absence of Nonpecuniary Incentives Our model assumed away any form of nonpecuniary incentives, such as those that have been studied in the organizational economics literature (Besley and Ghatak 2008; Bradler et al. 2015). This seems quite relevant in our context, because nonpecuniary incentives could well be heterogeneously valued by agents with different levels of intrinsic motivation. If social prestige associated with working in the nonprofit sector is valued relatively more by motivated types (for example, because altruistic agents care more about the social signaling built around contributing to the production of public goods), this would enlarge the range of parameters displaying an H-equilibrium. However, it could be that social prestige is valued more strongly by self-interested agents (if there are large indirect pecuniary benefits that social prestige can deliver), and the range of parameters with an H-equilibrium would thus shrink. Lastly, there could also be nonpecuniary externalities associated to the presence of monetary rewards, as those in Benabou and Tirole (2006); when this is the case, large scope for earnings in the nonprofit sector may lead to the crowding out of prosocially motivated nonprofit managers who fear being (incorrectly) perceived as monetarily driven. 5. Case Studies In this section, we present two groups of case studies that illustrate the applications of our model to large-scale recent real-life phenomena in international development efforts. The first group presents the analysis of the NGO sector in developing countries (Uganda and Pakistan) and its governance problems, in particular related to the inflows of foreign aid. The second focuses on the international NGO humanitarian efforts and the dynamics of post-reconstruction by international NGOs, following the natural disasters (specifically, the December 2004 tsunami in the Indian Ocean and the January 2009 earthquake in Haiti). 5.1. The NGO Sector in Developing Countries 5.1.1. Uganda Substantial narrative evidence for several developing countries indicates that generous financing by foreign aid can lead to perverse effects by triggering opportunistic behavior and elite capture in these local NGO projects (see, e.g., Platteau 2004; Platteau and Gaspart 2003; the contributions in Bierschenk, Chauveau, and Sardan 2000; Gueneau and Leconte 1998). Here, we discuss one of the best documented analyses, that of the NGO sector in Uganda. This analysis was conducted by a team of development economists at Oxford University’s Center for Study of African Economies (see Barr, Fafchamps, and Owens 2004, 2005; Burger and Owens 2010, 2013; Fafchamps and Owens 2009). The analysis is based on a unique representative national survey of NGOs, collected by Abigail Barr, Marcel Fafchamps, and Trudy Owens in 2002, and financed by the World Bank and the Japanese government. The aim of the study was to collect information about Ugandan NGOs’ activities, their sources of funding, and their personnel. The surveys were conducted with about 300 NGOs (out of about 3500 registered ones), and the main descriptive findings were published as a CSAE report to the Government of Uganda in December 2003 (Barr et al. 2004). Several interesting facts emerge from this study. The bulk of funding of Ugandan NGOs comes from international NGOs. These latter often conduct their own monitoring, but despite this, the authors argue that it is difficult to exclude that there are “crooks” in the sector. The authors note: “It is possible that the fluidity of the NGO sector and the focus on non-material services (e.g., ‘talk’ and ‘advocacy’) enable unscrupulous individuals to take advantage of the system... There is indeed a suspicion among policy circles that not all Ugandan NGOs genuinely take public interest to heart. [Some] accounts speak of crooks and swindlers attracted to the sector by the prospect of securing grant money... In a context where most charity funding comes from international benefactors, new incentive problems emerge. One is that of opportunistic NGOs whereby talented Ugandans initiate a local NGO not so much because they care about public good but because they hope to attract external funding to pay themselves a wage” (Barr et al. 2004, p. 4–7). In a companion paper, Barr et al. (2005) write: “According to respondents, per diems to staff and beneficiaries account for less than 2% of the total expenditures for the sample as a whole (slightly more for small NGOs). However, we suspect these data are not fully accurate and that there may be additional per diems included in program and miscellaneous costs. Ugandan NGOs are well aware that they are scrutinized by members and donors for excessive salary and per diem payments. They may therefore be tempted to hide these payments in other costs, or to simply misreport them. Given the poor quality of financial accounts provided by surveyed NGOs, it is difficult to determine the extent to which NGO profits are redistributed to staff via the payment of per diems. What is clear, however, is that most surveyed NGOs do not have transparent accounts” (Barr et al. 2005, p. 667). If the Ugandan NGO sector is facing a serious problem of fraud, why is it unable to create institutions that screen or limit such behavior? The report provides some answers to this: “Developed countries all have instituted sophisticated legislation regulating charities. This is because unscrupulous individuals may solicit funds from the public without actually serving the public good they are supposed to serve. Hit-and-run crooks may take the money and disappear. More sophisticated crooks may set up an organization that partly serves its stated objective, but at the same time either divert funds directly to their pocket or spend part of the money on perks, allowances, and excess salaries. This kind of behavior is damaging to charitable organizations at large because it undermines the public’s trust in them and reduces funding. It is therefore in the interest of bona fide charities to regulate the industry so as to weed out crooks... Reporting requirements, however, impose an additional burden of work in charities. Moreover, they are useless unless they are combined with the Charities Commission’s capacity to investigate the veracity of the reports provided. Crooks smart enough to defraud granting agencies are also smart enough to produce a fake report for the Charities Commission” (Barr et al. 2004, p. 7). Would peer monitoring be a solution to this problem? The report indicates that certain Ugandan NGOs tried to create such institutions, but they do not seem to function: “While some NGO networks have actively sought to promote good governance among their member organizations, to our knowledge, none has sought to set up a formal certification system. Instead, networks and umbrella organizations have sought to be inclusive and have welcomed new members with little or no attempt at quality control” (Barr et al. 2005, p. 675). The only mechanism that limits the misbehavior of NGOs seems to be donors’ (imperfect) control. In fact, the international NGOs seem to concentrate most of their financing in a few Ugandan NGOs. The authors argue that “one possible explanation is that foreign donors cannot identify the most promising NGOs and therefore concentrate their activities on a small number of trusted NGOs. Another possibility is that many sampled NGOs are engaged in a ‘rent seeking’ process by which they seek self-employment by attracting grants. Donors may have correctly identified them as undeserving and denied them funding” (Barr et al. 2004, p. 27). 5.1.2. Pakistan Another interesting case study comes from Pakistan and is based on the analysis by Bano (2008). Motivated by the recent trend of aid policies aiming at strengthening the local civil society, this study focused on the effects of channeling development aid through local NGOs. The author conducted a comparative in-depth survey of 40 local Pakistani NGOs: 20 NGOs that rely on foreign aid for their financing and 20 that rely only on domestic financing. Although the sample is relatively small, the author tried to maximize the national coverage in selecting the organizations across all the regions of Pakistan and focusing strictly on the organizations providing public goods (i.e., excluding the organizations aimed at providing benefits only to their members). The main findings of the study are three. First, the NGOs that relied on foreign aid were much more likely to have no members. Interestingly, several authors (Henderson 2002; Tvedt 1998) previously had documented that the absence of members usually implies high salary of the NGO leader and poor overall performance of the organization. Thus, it is likely that these NGOs relying on foreign aid in many cases were just “empty shells”. Secondly, there were large motivational differences between the NGOs relying on foreign aid and those relying on domestic financing (see table 4 in Bano 2008). For instance, nearly all the aid-financed NGOs, the leader drew a salary above the governmental scale (while this happened in none of the domestic-financed ones). The offices of all the aid-financed NGOs located in luxury areas of the cities (none for domestic-financed ones), the majority of aid-financed NGOs had four-wheel drive cars (none for domestic-financed ones), and in all of aid-financed NGOs the project was designed first and beneficiaries chosen after (while the opposite was true for the domestic-financed NGOs. Finally, NGOs relying on foreign aid exhibited lower organizational performance, as measured by fluctuation in annuals budgets and the stability of the type of activities. The aid-financed NGOs showed dramatic fluctuations in their annual budgets, in response to aid flows, whereas the budgets of domestic-financed NGOs were quite stable. The activities of aid-financed NGOs kept changing in response to aid flows, whereas the focus of the domestic-financed organizations’ activities remained stable. Although the study relied on interviews and the causal identification of aid financing was not feasible quantitatively, on the basis of additional qualitative evidence Bano (2008) argues that foreign aid led to a modification of material aspirations among leaders of NGOs, which in turn resulted in lower performance. For instance, one of the interviewed NGO leaders noted that, as an organization starts to rely on foreign aid, “the people who are more interested in personal gains start getting attracted to the organization” (Bano 2008, p. 2303). Although our model assumes that the inflow of foreign aid is distributed equally among NGOs, the above findings can still be explained in the light of our model’s main mechanism, and can be interpreted as a transition stage when moving from the equilibrium without foreign aid to the one with foreign aid. Our model predicts that, starting with an honest equilibrium without foreign financing, an aid inflow would trigger entry into the NGO sector by selfish agents seeking rents. The 20 organizations in the study that rely on foreign aid can be thought of as such entrants. In the meanwhile, the NGOs without foreign aid financing still operate as under the “no foreign aid” regime. Over time, as selfish agents enter the NGO sector in even higher numbers, the motivated agents start to quit the sector. If our model is valid, we should observe over time that the number (and the share) of NGOs in Pakistan that do not rely on foreign aid financing with their leaders showing relatively low material aspirations should decrease. This is an interesting prediction that hopefully can be tested in the future work. 5.2. Humanitarian Emergencies and International NGOs 5.2.1. The 2004 Tsunami On December 26, 2004, a tsunami of unprecedented power, triggered by the Sumatra–Andaman undersea earthquake, hit the coastal areas of 14 countries in Asia and Africa (with Indonesia and Sri Lanka receiving the strongest impact). It was one of the deadliest natural disasters in recent history, killing close to 230,000 people and displacing over 1.75 million people. The scale of the disaster, coinciding with it happening right after Christmas and fed by a large-scale international media coverage, led to a massive humanitarian response, both through public and private channels. The amount of private donations to international NGOs was huge: for example, Save the Children USA received over 6 million USD in just 4 days, whereas Catholic Relief Services collected over 1 million USD in 3 days. In total, US-based charities raised about 1.6 billion USD for tsunami relief (Wallace and Wilhelm 2005), whereas total international response (both public and private) amounted to 17 billion USD (Jayasuriya and McCawley 2010). The evolution of the resulting humanitarian relief activity presents an interesting story. It started off with early successes: for instance, Fabrycky, Inderfurth and Cohen (2005) write: “The tsunami will be remembered as a model for effective global disaster response... Because of the speed and generosity of the response, its effectiveness compared to previous (and even subsequent) disasters, and its sustained focus on reconstruction and prevention, we give the overall aid effort a grade of ‘A’... ”. However, quite soon, numerous problems in relief activities started to emerge. These included inefficiencies in the distribution of funds, unsatisfactory plans for the rebuilding of houses, cost escalations, and coordination failures (Jayasuriya and McCawley 2010, p. 4). This is summarized by the Joint Evaluation Report of the Tsunami Evaluation Coalition: “Exceptional international funding provided the opportunity for an exceptional international response. However, the pressure to spend money quickly and visibly worked against making the best use of local and national capacities... Many efforts and capacities of locals and nationals were marginalized by an overwhelming flood of well-funded international agencies (as well as hundreds of private individuals and organizations), which controlled immense resources” (Telford, Cosgrave, and Houghton 2006, p. 18–19). The observers underline several mechanisms behind this failure. One of them was the pressure to rapidly disburse huge amount of donations, which weakened the control mechanisms on how the money was spent. Maxwell et al. (2012) note that: “During the response to the 2004 tsunami, many agencies reported intense pressure to speed up the rate at which donations were being expended, in part to ensure an ongoing flow of funds. Sometimes, however, the need to act swiftly may result from the situation on the ground, not just from donor or media pressure. While pressure to spend speedily does not, in itself, cause corruption, it may mean that standard checks and systems intended to prevent corruption are overridden or ignored” (Maxwell et al. 2012, p. 143). A related mechanism is the rush of too many NGOs to carry out highly visible activities in disaster-prone areas: “One of the striking features of the relief effort was the presence of a horde of small, often newly formed, foreign organizations with little if any experience in disaster relief but motivated by a strong humanitarian impulse that ‘something had to be done’. Throughout the tsunami affected areas small groups and individuals from a wide range of countries were active in all sorts of activities. For instance, a Slovakian organization was engaged in boatbuilding, while an Austrian NGO assisted in constructing houses. Neither had any previous experience of South Asia or disaster relief. Similarly individuals from Europe, North America and Asia whose only prior knowledge of Sri Lanka came from news bulletins arrived in the country and proceeded to do whatever they thought useful” (Stirrat 2006, p. 14) This dynamics fits well the main predictions of our model. A sudden natural disaster creates a sharp increase in the willingness to give of individual donors (an increase in δ) and/or a large increase in foreign aid (a big increase in Δ). This attracts a mass of agents to enter the nonprofit sector (here, founding new NGOs). However, given that many of these agents were mostly driven by ego utility obtained from high visibility, our model would predict that a large fraction of the donations will end up being spent in projects that do not necessarily help the beneficiaries (or possibly help them only in the short run, but prove to be useless in the medium run). An alternative explanation to the above patterns is the lack of experience and knowledge of certain NGOs that entered the donation market during natural disasters. As Willitts-King and Harvey (2005, Section 2.4) note, administrative inefficiency in humanitarian relief is different from corruption, although both are harmful for the performance of the humanitarian aid system. However, on the basis of an in-depth study and interviews with humanitarian relief professionals, conducted shortly after the massive inflow of humanitarian relief organizations into the tsunami-hit areas, they also provide a detailed list of major corruption risks at various levels of the humanitarian relief chain, including inflating overheads, setting up bogus NGOs, kickbacks from procurement, field staff collusion with diversion, listing phantom staff, and so forth. For instance, they write: “Once funds have been passed to an agency [NGO], there are many opportunities for individuals to make personal gain. This normally entails some collusion between agency staff internally, or between staff and outside suppliers or authorities. At field level, staff might be ‘paid off’ for turning a blind eye to the false registration of relatives on a distribution list, or theft from a warehouse. Staff might themselves extract payments directly to include people on beneficiary lists who do not fit vulnerability criteria. Procurement, storage and transport offer widespread opportunities for corruption. Staff might accept kickbacks or bribes to favor a particular supplier or agree an inflated quote, or relatives might be preferred even though the quality or price is uncompetitive... Other experiences included the use of agency vehicles to provide paid rides, taxi services, or in some cases public bus services” (Willitts-King and Harvey 2005, p. 21–22) Given this analysis, it is difficult to imagine that the main source of failure of the humanitarian aid system after the tsunami is driven only by the administrative inefficiency. More likely, it is the combination of entry of unscrupulous or visibility-seeking actors at various layers of the aid chain with administrative inefficiency and lack of coordination that generated the poor outcomes of the overall system.26 5.2.2. The 2010 Haiti Earthquake On January 12, 2010, a 7.0-magnitude earthquake hit Haiti, the poorest country of the Western hemisphere. This also was an extremely violent natural disaster, killing more than 200,000 people in a very short period of time, and destroying most of the administrative capacity of the state. Similar to the case of 2004 tsunami, the international humanitarian response to this disaster was massive. Between 2010 and 2012, the total amount over 8 billion USD (of which 3 billion came through international NGOs) was given by the international community for the post-earthquake reconstruction activities. One of the largest French NGOs, Medecins Sans Frontieres (MSF), noted that its Haiti intervention was the largest in the long history of this organization (Biquet 2013, p. 130). This rush in international humanitarian efforts fuelled by generous donations, made NGOs key players in the reconstruction efforts. The presence of NGOs, already considerable before the earthquake, became so massive as for Haiti being dubbed in international circles as “the Republic of NGOs” (Klarreich and Polman 2012). Similar to the post-tsunami reconstruction, early successes were followed by disappointing outcomes later on: the lack of coordination between NGOs and the complex overlapping system of aid actors that emerged became a problem rather than a solution. This was made most apparent during the cholera epidemics that hit Haiti in October 2010. Biquet (2013) reports that more than 80% of patients in the 3 months following the outbreak of the epidemics were taken care of by two actors (Cuban medical brigades and the MSF) acting outside the ‘Health Cluster’ that concentrated all the other NGOs with health-related activities (there were more than 600 international organizations in this cluster). One key explanation proposed for the failure of international humanitarian assistance in Haiti is the lack of accountability of organizations carrying out interventions, coupled with massive budgets. Klarreich and Polman (2012) argue that this resulted in a complete disconnection from the needs of the local population and exclusion of local civil society, more knowledgeable about the local conditions and needs, from the reconstruction effort: “From the very beginning, NGOs followed their own agendas and set their own priorities, largely excluding the Haitian government and civil society... The money that did reach Haiti has often failed to seed projects that truly respond to Haitians’ needs. The problem is not exactly that funds were wasted or even stolen, though that has sometimes been the case. Rather, much of the relief wasn’t spent on what was most needed... [As a result] the recovery effort has been so poorly managed as to leave the country even weaker than before.” (Klarreich and Polman 2012) As in the case of 2004 tsunami, the massive increase in the number of NGOs carrying out activities was driven by donors’ willingness to give, in the absence of any—even minimal—certification of NGOs. Haver and Foley (2011) state that “the response to the Haiti earthquake of 2010 [was one] in which thousands of NGOs, many of them unqualified ‘cowboy NGOs’, rushed in to help”. The authors argue that instituting a certification scheme would have curbed (at least in part) this drive; however, they also acknowledge that such a scheme would have been quite difficult to implement (for instance, it would have turned away many local or regional NGOs for whom the paperwork related to such certification would have been prohibitively complicated or costly). 6. Conclusion We built a tractable general-equilibrium model of private provision of public goods via endogenous voluntary contributions to the nonprofit sector. Our model shows that rent seeking or ego utility seeking motives may attract selfish individuals to the nonprofit sector, which in turn may end up crowding out intrinsically motivated agents from this sector. Selfish motives and the possibility of motivational crowding out become increasingly severe as economies get richer and give more generously to the nonprofit sector. The main applications of our theory belong to two domains. The first is foreign aid intermediation by NGOs. Aid is being increasingly channeled via NGOs. This is to a large extent the result of the growing disillusionment in government-to-government project aid, often considered to be politicized and easily corruptible (see, for instance, Alesina and Dollar (2000) and Kuziemko and Werker (2006)). The rise of NGO intermediation has meant an increasing emphasis of project ownership, decentralization, and participatory development. However, no theoretical analysis has been conducted so far concerning the general-equilibrium implications of such massive channeling of aid via NGOs.27 The application of our theory to foreign aid sheds light on these issues. In particular, a key implication of our results is that, as the NGO channel of aid expands, the investment into better accountability in the NGO sector becomes increasingly important, so as to curb self-interested motives. In other words, optimal aid delivery through NGOs requires harder controls accompanying the scaling-up of aid efforts. The second application pertains to the recent debates on the accountability and performance-based pay in the nonprofit sector in developed countries. The existing literature recognizes that firms in the nonprofit sector are often prone to agency problems, due to the inherent difficulty of measuring their performance. Understanding the conditions under which these problems are most salient is an open issue in the public economics literature. Our analysis contributes to this debate by indicating that the role of (endogenously determined) outside options of selfish and motivated individuals inside the nonprofit sector is crucial. In particular, what matters is whether it is motivated or selfish agents that exit more intensively the nonprofit sector when donations from the private sector decrease. If selfish agents exit more intensively, then recessions can have a cleansing effect regarding the motivational composition of the nonprofit sector. This is, in our view, an interesting hypothesis that could be tested empirically in future work. Two further promising avenues for future research are worth mentioning. The first is the role of specific public policy instruments towards the nonprofit sector. Several recent studies on the economics of charities and nonprofits have explored the effectiveness of direct versus matching grants (Andreoni and Payne (2003, 2011); Karlan, List, and Shafir (2011)). Our analysis indicates that matching grants might have an additional effect that operates through the motivational composition of the nonprofit sector: such financing induces nonprofits to engage more actively in fundraising (and thus to reduce their internal resources devoted to working on their projects), and this might induce the motivated individuals to quit the nonprofit sector. A more complete analysis of the effectiveness of matching grants as compared to direct ones, which takes into account these various effects, looks very promising. The second relates to the disconnection between who finances and who benefits from the activity of the nonprofit sector. The resulting monitoring problems create the need to coordinate the scaling up of financing with investment into improved monitoring. As suggested by Ruben (2012), evaluation of aid effectiveness may generate social benefits even when we can learn relatively little from the evaluation exercise. This is because the very fact of being evaluated makes the misallocation of aid resources more difficult and thus help improve the motivational composition in the nonprofit sector. Our framework may allow to study these indirect effects of evaluation of development projects. Appendix A: Endogenous Fundraising Effort Our benchmark model assumed that total donations are equally split (quite mechanically) between all nonprofit firms. It is well known, however, that nonprofits actively compete quite intensely for donations via fundraising activities.28 Here, we relax the assumption of fixed division of donations by incorporating the endogenous fundraising choice by nonprofits. In terms of the private sector, we keep the same structure described in Section 2.1. The main difference is that now nonprofit managers can influence the share of funds they obtain from the pool of total donations by exerting fundraising effort. We assume that each nonprofit manager i is endowed with one unit of time, which she may split between fundraising and working towards the mission of her nonprofit organization (project implementation). Fundraising effort allows the nonprofit manager to attract a larger share of donations (from the pool of aggregate donations) to her own nonprofit. Implementation effort is required in order to make those donations effective in addressing the nonprofit’s mission. We denote henceforth by ei ≥ 0, the effort exerted in fundraising and by ςi ≥ 0 the implementation effort. The time constraint means that ei + ςi = 1. As before, the nonprofit manager collects an amount of donations σi from the aggregate pool of donations D. One part of σi, equal to wi, is allocated for the perks, while σi − wi is used as input for the nonprofit’s production. In this section, in the sake of algebraic simplicity, we assume that the output of a nonprofit firm is linear in undistributed donations, namely: $$g_{i}=2( {\sigma }_{i}-w_{i})\varsigma _{i}.$$ (A.1) An important feature of gi in (A.1) is the fact that undistributed donations (σi − wi) and implementation effort (ςi) are complements in the production function of the nonprofit. We assume that aggregate fundraising effort does not alter the total pool of donations channeled to the nonprofit sector, D. However, the fundraising effort exerted by each specific nonprofit manager affects the division of D among the mass of nonprofit firms N. In other words, we model fundraising as a zero-sum game over the division of a given D. Formally, we assume that $${\sigma }_{i}=\dfrac{D}{N}\times \dfrac{e_{i}}{\bar{e}}=\dfrac{\delta A\left( 1-N\right) ^{\alpha }}{N}\times \dfrac{e_{i}}{\bar{e}},$$ (A.2) where $$\bar{e}$$ denotes the average fundraising effort in the nonprofit sector as a whole. Again, nonprofit managers derive utility from the two dimensions, with weights on each of two sources of utility determined by the agent’s level of prosocial motivation, mi. In addition, we assume the total effort exerted by nonprofit managers entails a level of disutility that depends on the agent’s intrinsic prosocial motivation: \begin{equation*} U_{i}(w_{i},g_{i})=\frac{w_{i}^{1-m_{i}}g_{i}^{m_{i}}}{m_{i}^{m_{i}}(1-m_{i})^{1-m_{i}}}- ( 1-m_{i}) ( e_{i}+\varsigma _{i}), \,\,\, \text{where }m_{i}\in \lbrace m_{H},m_{L}\rbrace . \end{equation*} Because mH = 1, in the optimum, motivated nonprofit managers will always set $$w_{H}^{\ast }=0$$ and $$e_{H}^{\ast }+\varsigma _{H}^{\ast }=1$$. The exact values of $$e_{H}^{\ast }$$ and $$\varsigma _{H}^{\ast }$$ are determined by the following optimization problem: \begin{equation*} e_{H}^{\ast }\equiv \underset{e_{i}\in \left[ 0,1\right] }{\arg \max }:g_{i}=2\dfrac{D}{N}\dfrac{e_{i}}{\bar{e}}( 1-e_{i}) , \end{equation*} with $$\varsigma _{H}^{\ast }=1-e_{H}^{\ast }$$. The above problem yields $$e_{H}^{\ast }=\varsigma _{H}^{\ast }=\dfrac{1}{2},$$ (A.3) which in turn implies that an mH-type nonprofit manager obtains a level of utility given by $$U_{H}^{\ast }=\dfrac{1}{2\bar{e}}\dfrac{D}{N}=\dfrac{1}{2\bar{e}}\dfrac{\delta A\left( 1-N\right) ^{\alpha }}{N}.$$ (A.4) With regard to selfish nonprofit managers, again, they will always set $$w_{L}^{\ast }= {\sigma }_{i}$$. In addition, because selfish agents care only about their private consumption, and ςi is only instrumental to producing nonprofit output, in the optimum, they will always set $$\varsigma _{i}^{\ast }=0$$. As a consequence, the level of $$e_{L}^{\ast }$$ will be determined by the solution of the following maximization problem: \begin{equation*} e_{L}^{\ast }\equiv \underset{e_{i}\in \left[ 0,1\right] }{\arg \max }:w_{i}=\dfrac{D}{N}\dfrac{e_{i}}{\bar{e}}-e_{i}, \end{equation*} which, given the linearity of both the benefit and the cost of effort, trivially yields $$e_{L}^{\ast }=\left\lbrace \begin{array}{c}0, \,\, \text{if }\bar{e}^{-1}D/N<1, \\ 1, \,\,\text{if }\bar{e}^{-1}D/N\ge 1.\end{array}\right.$$ (A.5) The utility that a selfish agent obtains from becoming a nonprofit manager is thus: $$U_{L}^{\ast }=\max \left\lbrace \dfrac{D}{N}\dfrac{1}{\bar{e}}-1,0\right\rbrace .$$ (A.6) Note that the indirect utility of the selfish agent decreases, as before, with the size of the nonprofit sector. However, it now reaches zero at an interior value, whereas in the basic model that occurred only when N = 1. The reason for this is that donations must now be obtained through exerting effort, which is costly to mH-types. For a sufficiently large size of the nonprofit sector, the level donations per nonprofit firm that can be obtained through fundraising effort is just too small to justify their effort cost. This means that a selfish agent will choose to stop competing for donations if the number of nonprofits firms N reaches a certain critical level (beyond such critical level of N selfish managers would optimally choose to exert no effort and collect zero donations, which accordingly yields $$U_{L}^{\ast }=0$$). H-equilibrium. In an H-equilibrium, all nonprofit managers are of mH-type and set $$e_{H}^{\ast }=0.5$$. This implies that each nonprofit manager ends up raising $$\sigma _{H}^{\ast }=\dfrac{\delta A\left( 1-N_{H}^{\ast }\right) ^{\alpha }}{N_{H}^{\ast }}.$$ (A.7) Recalling (4), (A.4), and (A.6), we can observe that an H-equilibrium exists if and only if $$\sigma _{H}^{\ast }\le 1$$. L-equilibrium. In an L-equilibrium, all nonprofit managers are of mL-type and set $$e_{L}^{\ast }=1$$. In this case, each nonprofit manager raises $$\sigma _{L}^{\ast }=\dfrac{\delta A\left( 1-N_{L}^{\ast }\right) ^{\alpha }}{N_{L}^{\ast }}.$$ (A.8) Using again (4), (A.4), and (A.6), it follows that an L-equilibrium exists if and only if $$\sigma _{L}^{\ast }>2$$. Mixed-Type Equilibrium. In a mixed-type equilibrium, all agents are indifferent across occupations and the nonprofit sector is managed by a mix of mH- and mL-types. That is, a mixed-type equilibrium is characterized by $$U_{H}^{\ast }(N^{\ast })=U_{L}^{\ast }(N^{\ast })=V_{P}^{\ast }(N^{\ast })$$, where $$N^{\ast }=N_{L}^{\ast }+N_{H}^{\ast }$$ and $$0<N_{L}^{\ast },N_{H}^{\ast }\le 1/2$$. Equality among (A.4) and (A.6) requires that average fundraising effort satisfies $$\bar{e}_{ {mixed}}=0.5\times \left( D/N\right)$$, which in turn means that $$U_{H}^{\ast }(N^{\ast })=U_{L}^{\ast }(N^{\ast })=1$$. The returns in the private sector must then also equal to one, which, using (4), implies that N* = 1 − A1/1−α. In addition, because $$e_{H}^{\ast }=0.5$$ and $$e_{L}^{\ast }=1$$, then $$\bar{e}_{ {mixed}}=0.5\times \left( D/N\right)$$, together with N* = 1 − A1/1−α, pin down the exact values of $$N_{L}^{\ast }$$ and $$N_{H}^{\ast }$$. Equilibrium Characterization with Fundraising Effort. We now fully characterize the type of equilibrium that arises in the model with fundraising effort. Proposition A.1. The equilibrium allocation that arises is always unique and depends on the specific parametric configuration of the model. If A ≤ 1/(1 + δ)1 − α, the economy exhibits an “H-equilibrium” with $$N^{\ast }=N_{H}^{\ast }=\delta /(1+\delta )$$. All nonprofit managers exert the same level of fundraising and project implementation effort: $$e_{H}^{\ast }=\varsigma _{H}^{\ast }=0.5$$. If A ≥ [2/(2 + δ)]1 − α, the economy exhibits an “L-equilibrium” with $$N^{\ast }=N_{L}^{\ast }$$, where $$\delta /(2+\delta )<N_{L}^{\ast }<\delta /(1+\delta )$$. All nonprofit managers exert the same level of fundraising and project implementation effort: $$e_{L}^{\ast }=1$$ and $$\varsigma _{L}^{\ast }=0$$. If 1/(1 + δ)1 − α < A < [2/(2 + δ)]1 − α, the economy exhibits a mixed-type equilibrium with a mass of nonprofit firms equal to $$N_{ {mixed}}^{\ast }=1-A^{{1}/{1-\alpha }}$$, where $$N_{H}^{\ast }=2[ 1-A^{\frac{1}{1-\alpha }}( 1+\delta /2) ]\, \text{ and }\,N_{L}^{\ast }=A^{\frac{1}{1-\alpha }}\left( 1+\delta \right) -1.$$ (A.9) Motivated nonprofit managers set $$e_{H}^{\ast }=\varsigma _{H}^{\ast }=0.5$$, whereas mL-types set $$e_{L}^{\ast }=1$$ and $$\varsigma _{L}^{\ast }=0$$. The result of an “H-equilibrium” when A ≤ 1/(1 + δ)1 − α is the analogous to that one previously obtained in the basic model. Similarly, when A ≥ [2/(2 + δ)]1 − α the model features a pure “L-equilibrium”. One novelty of this alternative setup is that for the intermediate range of A there exists a “mixed-type” equilibrium. Intuitively, the necessity of competition for donations reduces the utility of the unmotivated agents. As a consequence, this creates parameter configurations under which, in the absence of fundraising competition, the nonprofit sector would be populated only by selfish agents, whereas in the presence of competition a fraction of them moves into the private sector (and are in turn replaced by a fraction of motivated agents).29 Appendix B: Altruism-Dependent Private Donations The model presented in Section 2 assumes that all private entrepreneurs (regardless of their prosocial motivation) donate an identical fraction of their income to the nonprofit sector. However, if warm-glow giving is a driven by (impure) altruism, it is reasonable to expect the propensity to donate to be increasing in the degree of prosocial motivation of an individual. Here, we modify the utility function in (3) by letting the propensity to donate be type specific (δi) and increasing in mi. In particular, we now assume that δi = δH ∈ (0, 1] when mi = mH, whereas δi = δL = 0 when mi = mL.30 The key difference that arises when δi is an increasing function of mi is that, for a given value of 1 − N, the total level of donations will depend positively on the ratio (1 − NH)/(1 − N). Intuitively, the fraction of entrepreneurial income donated to the nonprofit sector will rise with the (average) level of warm-glow motivation displayed by the pool of private entrepreneurs. To keep the analysis simple, we abstract from fundraising effort, and assume that the mass of total donations is equally split between the mass of nonprofits. In addition, we let the payoff functions by motivated and selfish nonprofit entrepreneurs be given again by (8) and (9), respectively. Donations collected by a nonprofit are now given by $$\dfrac{D}{N}=\dfrac{\delta _{H}\,A\left( \frac{1}{2}-N_{H}\right) }{( 1-N_{H}-N_{L}) ^{1-\alpha }( N_{H}+N_{L}) }.$$ (B.1) When the total amount of donations to the nonprofit sector depends positively on the fraction of prosocially motivated private entrepreneurs, the model gives room to multiple equilibria. The main reason for equilibrium multiplicity is that, when δi is increasing in mi, the ratio between $$U_{H}^{\ast }$$ and $$U_{L}^{\ast }$$ does not depend only on the level of N, as it was the case with (8) and (9) in Section 2. Instead, observing (B.1), we see that it also depends on how N breaks down between NH and NL. Such dependence on the ratio NH/NL generates a positive interaction between the incentives by mL-types to self-select into the nonprofit sector and the self-selection of mH-types into the private sector. The next proposition deals with this issue in further detail. Proposition B.1 shows that for A sufficiently small the economy will exhibit a high-effectiveness equilibrium, whereas when A is sufficiently large the economy will fall into a low-effectiveness equilibrium. These two results are in line with those previously shown in Proposition 1. However, Proposition B.1 also shows that there exists an intermediate range, (1 − δH/2)1 − α < A < [1 − δH/(2 + 2δH)]1 − α, in which the economy displays multiple equilibria. For those intermediate values of A, the exact type of equilibrium that takes place will depend on the coordination of agents’ expectations. If agents expect a large mass of mH-types to choose the nonprofit sector (case a), then the total mass of private donations (for a given N) will be relatively small, stifling the incentives of mL-types to become nonprofit managers. Conversely, if individuals expect a large mass of mH-types to become private entrepreneurs (case b), the value of D (for a given N) will turn out to be large, which will enhance the incentives of mL-types to enter into the nonprofit sector more than it does so for mH-types. Notice that the range of productivity A for which multiple equilibria occur increases with the (relative) generosity of the motivated individuals, δH.32 Finally, Proposition B.1 also shows that, within the range of multiple equilibria, there is also the possibility of intermediate consistent expectations (case c). When this happens, both motivated and selfish agents are indifferent across occupations, and a mix of mL- and mH-types will end up populating the nonprofit sector. Appendix C: Proofs Proof of Proposition 1 Part (i). First of all, notice that by replacing N = N0 into (9), it follows that A(1 + δ)1 − α > 1 implies $$U_{L}^{\ast }(N_{0})>1$$. Hence, because $$U_{L}^{\ast }(\widehat{N})=1$$, it must necessarily be the case that $$N_{0}<\widehat{N}$$. Because of Lemma 1, this also means that $$U_{L}^{\ast }(N_{0})>U_{H}^{\ast }(N_{0})$$. Now, because $$U_{L}^{\ast }(N_{0})=y(N_{0})$$, then $$y(N)<U_{L}^{\ast }(N_{0})$$ for any N < N0, meaning that whenever N < N0, the mass of nonprofit managers must at least be equal to 0.5 (the total mass of mL-types). But this contradicts the fact that N0 < 0.5; hence an equilibrium with N < N0 cannot exist. Moreover, an equilibrium with N > N0 cannot exist either, because whenever N > N0 holds, $$y(N)>U_{H}^{\ast }(N)$$ and $$y(N)>U_{L}^{\ast }(N)$$, contradicting the fact that there is a mass of individuals equal to N > 0 choosing to become nonprofit managers. As a result, when A(1 + δ)1 − α > 1, an allocation with $$N^{\ast }=N_{L}^{\ast }=N_{0}$$ represents the unique equilibrium. Because $$U_{H}^{\ast }(N_{0})<U_{L}^{\ast }(N_{0})=y(N_{0})$$, in the equilibrium, all mH-type become private entrepreneurs, and a mass 0.5 − N0 of mL-type agents (who are indifferent between the two occupations) also become private entrepreneurs. Part (ii). Because A(1 + δ)1 − α < 1 implies $$U_{L}^{\ast }(N_{0})<1$$, when the former inequality holds, $$N_{0}>\widehat{N}$$. Moreover, notice that an equilibrium with N ≤ N0 cannot exist, as it would contradict the fact that N0 < 0.5. In turn, because the equilibrium must necessarily verify $$N>N_{0}>\widehat{N}$$, only motivated agents will become nonprofit managers, while all selfish agents will self-select into the for-profit sector. Now, by the definition of N1 in (11), it follows that if N1 ≤ 0.5, then $$N^{\ast }=N_{H}^{\ast }=N_{1}$$ represents the unique equilibrium allocation (notice that A(1 + δ)1 − α < 1 ensures N1 > N0). In this situation, the mH-types are indifferent across occupations (and there is a mass 0.5 − N1 of them in the private sector), while when N < N1 all motivated agents wish to become nonprofit managers contradicting N < 0.5, and when N > N1 nobody would actually choose the nonprofit sector, contradicting N > 0. With a similar reasoning, it is straightforward to prove that when N1 > 0.5, the unique equilibrium allocation is given by $$N^{\ast }=N_{H}^{\ast }=0.5$$, as in that case the condition $$U_{L}^{\ast }\left({1}/{2}\right) <y\left( {1}/{2}\right) <U_{H}^{\ast }\left( {1}/{2}\right)$$ holds, whereas for N < 0.5 all mH-types intend to become nonprofit managers, and when N > 0.5, there is either nobody or only a mass one-half of agents who wish to go the nonprofit sector. Proof of Proposition 2 Part (i). First of all, recalling (13), notice that 21−αA > 1 implies $$\underline{N}<{1}/{2}$$. Using the results in Proposition 1, it then follows that when A(1 + δ)1 − α < 1 < 21 − αA and Δ = 0, in equilibrium, $$N^{\ast }=N_{H}^{\ast }=N_{1}$$, where recall that N1 is implicitly defined by (11). Let now $$\mathcal {N}_{H}$$ be implicitly defined by the following condition: $$\mathcal {N}_{H}^{-\gamma }[ \delta A( 1-\mathcal {N}_{H}) ^{\alpha }+\Delta ] ^{\gamma }( 1-\mathcal {N}_{H}) ^{1-\alpha }\equiv A;$$ (C.1) in raw words, $$\mathcal {N}_{H}$$ denotes the level of N that equalizes (2) and the utility obtained by a motivated nonprofit manager when D/N is given by (12). From (C.1), it is easy to observe that when Δ = 0, $$\mathcal {N}_{H}=N_{1}$$. In addition, differentiating (C.1) with respect to $$\mathcal {N}_{H}$$ and Δ, we obtain that $$\partial \mathcal {N}_{H}/\partial \Delta >0$$. Let now $$\Delta _{0}\equiv 1-A^{\frac{1}{1-\alpha }}(1+\delta ),$$ (C.2) and, using (13), notice that $$[ \delta A( 1-\underline{N}) ^{\alpha }+\Delta _{0}] /\underline{N}=1$$; hence $$\mathcal {N}_{H}(\Delta _{0})=\underline{N}$$. As a consequence of all this, when A(1 + δ)1 − α < 1 < 21 − αA, for all 0 ≤ Δ < Δ0, in equilibrium, $$N^{\ast }=N_{H}^{\ast }=\mathcal {N}_{H}(\Delta )$$, where $$\partial \mathcal {N}_{H}/\partial \Delta >0$$, and $$\mathcal {N}_{H}( \Delta ) :[ 0,\Delta _{0}) \rightarrow [ N_{1},\underline{N})$$. Part (ii). Using again the fact that $$[ \delta A( 1-\underline{N}) ^{\alpha }+\Delta _{0}] /\underline{N}=1$$, from (12) it follows that, for all Δ > Δ0, the utility achieved as nonprofit managers by mL-types must be strictly larger than that obtained by mH-types. Let now $$\Delta _{A}\equiv 2^{-\alpha }A[( 2^{1-\alpha }A) ^{\frac{1-\gamma }{\gamma }}-\delta ] .$$ (C.3) Using (2) and (12), notice that when N = 1/2 and Δ = ΔA, the utility obtained by motivated nonprofit managers is equal to y(1/2). All this implies that, when A(1 + δ)1 − α < 1 < 21 − αA, for all Δ0 ≤ Δ < ΔA, in equilibrium, $$N^{\ast }=N_{L}^{\ast }=\mathcal {N}_{L}(\Delta )\le {1}/{2}$$, where $$\mathcal {N}_{L}(\Delta )$$ is nondecreasing in Δ. In particular, for all Δ0 ≤ Δ ≤ 2 − αA(1 − δ), the function $$\mathcal {N}_{L}(\Delta )$$ is implicitly defined by $$\left[ \dfrac{\delta A( 1-\mathcal {N}_{L}) ^{\alpha }+\Delta }{\mathcal {N}_{L}}\right] ( 1-\mathcal {N}_{L}) ^{1-\alpha }\equiv A,$$ (C.4) whereas for all 2 − αA(1 − δ) < Δ < ΔA, $$\mathcal {N}_{L}(\Delta )={1}/{2}$$. Lastly, when Δ = 2 − αA(1 − δ), the expression in (C.4) implies $$\mathcal {N}_{L}={1}/{2}$$, proving that $$\mathcal {N}_{L}(\Delta ):( \Delta _{0},\Delta _{A}] \rightarrow \left( \underline{N},{1}/{2}\right]$$ is continuous and weakly increasing. Part (iii). First, note that when Δ > ΔA, the expression in (C.1) delivers a value of $$\mathcal {N}_{H}>{1}/{2}$$. As a result, motivated agents must necessarily be indifferent in equilibrium between the two occupations, because some of them must choose to actually work as nonprofit managers to allow $$\mathcal {N}_{H}>{1}/{2}$$. In addition, because by definition of ΔA in (C.3), δA[(1 − N)α + ΔA]/N > y(N) when N = 1/2, all selfish agents must be choosing the nonprofit sector when Δ > ΔA. Let thus $$\mathcal {N}_{LH}$$ be implicitly defined by the following condition: $$\mathcal {N}_{LH}^{-\gamma }[ \delta A( 1-\mathcal {N}_{LH}) ^{\alpha }+\Delta ] ^{\gamma }( 1-\mathcal {N}_{LH}) ^{1-\alpha }\equiv A.$$ (C.5) Differentiating (C.5) with respect to $$\mathcal {N}_{LH}$$ and Δ, we can observe that $$\partial \mathcal {N}_{LH}/\partial \Delta >0$$. From (C.5), we can also observe that $$\lim _{\Delta \rightarrow \Delta _{A}}\mathcal {N}_{LH}={1}/{2}$$ and $$\lim _{\Delta \rightarrow \infty }\mathcal {N}_{LH}=1$$. As a result, we may write $$\mathcal {N}_{LH}(\Delta ):( \Delta _{A},\infty ) \rightarrow \left( \frac{1}{2},1\right)$$, with $$\partial \mathcal {N}_{LH}/\partial \Delta >0$$. Moreover, because $$N_{L}^{\ast }={1}/{2},\forall$$ Δ > ΔA, it must be the case that in equilibrium $$N_{H}^{\ast }=\mathcal {N}_{LH}(\Delta )-{1}/{2}$$. Proposition 2 (bis). If 21−αA < 1, there exists a threshold level ΔB ∈ (0, Δ0), such that: (i) when 0 ≤ Δ ≤ ΔB, all nonprofit firms are managed by mH-types; (ii) when ΔB < Δ ≤ Δ0, nonprofit firms are managed by a mix of types with mH-type majority; (iii) when Δ > Δ0, nonprofit firms are managed by a mix of types with mL-type majority. Proof. (i) Because of Proposition 1, when Δ = 0, in equilibrium, $$N_{H}^{\ast }\le {1}/{2}$$ and $$N_{L}^{\ast }=0$$. Next, let ΔB ≡ 2 − αA(1 − δ), and note that, $$2\left[ \delta A\left( \tfrac{1}{2}\right) ^{\alpha }+\Delta _{B}\right] =2^{1-\alpha }A,$$ (C.6) and note that the right-hand side of (C.6) equals y(1/2), whereas its left-hand side equals D/N when N = 1/2 and Δ = ΔB. Furthermore, notice that 2[δA(1/2)α + Δ] is strictly increasing in Δ. As a consequence, it follows that in equilibrium, $$N_{L}^{\ast }=0$$ for any 0 ≤ Δ ≤ ΔB. In addition, denoted by $$\mathfrak {N}_{H}\left( \Delta \right) =\min \lbrace {1}/{2},\chi \rbrace$$, where χ is the solution of [δA(1 − χ)α + Δ]/χ = A/(1 − χ)1 − α, the result, $$N_{H}^{\ast }=\mathfrak {N}_{H}\left( \Delta \right)$$ for any 0 ≤ Δ ≤ ΔB obtains. (ii) This part of the proof follows from the definition of Δ0 in (C.2), together with the fact that 2[δA(1/2)α + Δ] > 21 − αA, for all Δ > ΔB. As a result, we may implicitly define the function $$\mathfrak {N}_{HL}(\Delta )$$ by \begin{equation*} \left[ \dfrac{\delta A( 1-\mathfrak {N}_{HL}) ^{\alpha }+\Delta }{\mathfrak {N}_{HL}}\right] ( 1-\mathfrak {N}_{HL}) ^{1-\alpha }\equiv A, \end{equation*} and observe that $$\partial \mathfrak {N}_{HL}/\partial \Delta >0$$. Noting that, whenever $$N=\mathfrak {N}_{HL}(\Delta )$$, mL-types are indifferent across occupations completes the proof of this part. (iii) This part of the proof follows again from the definition of Δ0 in (C.2), which implies that for all Δ > Δ0, the expression in (12) yields D/N > 1 when $$N=\underline{N}$$. For this reason, whenever Δ > Δ0, the mH-types must be indifferent across occupations in equilibrium, whereas all mL-types will strictly prefer the nonprofit sector. We can then implicitly define the function $$\mathfrak {N}_{LH}(\Delta )$$ by \begin{equation*} \mathfrak {N}_{LH}^{-\gamma }[ \delta A( 1-\mathfrak {N}_{LH}) ^{\alpha }+\Delta ] ^{-\gamma }( 1-\mathfrak {N}_{LH}) ^{1-\alpha }\equiv A, \end{equation*} and observe that $$\partial \mathfrak {N}_{LH}/\partial \Delta >0$$ to complete the proof. □ Proof of Proposition 3 First of all, from (15), it is straightforward to observe that neither NH = 0.5, nor 0 = NH < NL can possibly hold in equilibrium, as both situations would imply D/N = 0, and no agent would thus choose the nonprofit sector. Second, set NL = 0 into (15), and take the limit of the resulting expression as NH approaches zero, to obtain \begin{equation*} \lim _{N_{H}\rightarrow 0}\left. \dfrac{D}{N}\right|_{N_{L}=0}=\dfrac{\delta _{H}\,A}{2}\dfrac{N_{H}}{( N_{H}) ^{2}}=\infty . \end{equation*} The above result in turn implies that 0 = NH = NL cannot hold in equilibrium either, as in that case the nonprofit would become infinitely appealing to mH-types. Third, suppose 0 < NH < NL = 1/2. Using (2) and (15), for this to be an equilibrium, it must necessarily be the case that $$\dfrac{\delta _{H}\,A\left( \frac{1}{2}-N_{H}\right) N_{H}}{\left( \frac{1}{2}-N_{H}\right) ^{1-\alpha }\left( \frac{1}{2}+N_{H}\right) ^{2}}\ge \dfrac{A}{\left( \frac{1}{2}-N_{H}\right) ^{1-\alpha }}.$$ (C.7) However, the condition (C.7) cannot possibly hold, because it would require δH (0.5 − NH)NH ≥ (0.5 + NH)2, which can never be true. Because of the previous three results, the only possible equilibrium combinations are as follows: (i) $$N_{L}^{\ast }=0$$ and $$0<N_{H}^{\ast }<0.5$$, (ii) $$0\le N_{L}^{\ast }\le 0.5$$ and $$0<N_{H}^{\ast }<0.5$$, with all types indifferent across occupations. Case i. For this case to hold in equilibrium, condition (C.23) must be verified, which following the same reasoning as before in the proof of Proposition 1 leads to the condition A < [(2 + δH)/(2 + 2δH)]1 − α. Case ii. For this case to hold in equilibrium, the following equalities must all simultaneously hold $$\dfrac{D}{N}=\dfrac{\delta _{H}\,A\left( \frac{1}{2}-N_{H}\right) N_{H}}{( 1-N_{H}-N_{L}) ^{1-\alpha }( N_{H}+N_{L}) ^{2}}=y(N)=\dfrac{A}{( 1-N_{H}-N_{L}) ^{1-\alpha }}=1.$$ (C.8) Taking into account the definition of $$\underline{N}$$ in (13), it follows that y(N) = 1 requires $$N_{H}+N_{L}=1-A^{\frac{1}{1-\alpha }}$$. As a result, (C.8) boils down to the following condition: $$\delta _{H}\left( \tfrac{1}{2}-N_{H}\right) N_{H}-\left( 1-A^{\frac{1}{1-\alpha }}\right) ^{2}=0.$$ (C.9) The expression in (C.9) yields real-valued roots if and only if $$A\ge \left( 1-\sqrt{\delta _{H}}/4\right) ^{1-\alpha }.$$ (C.10) When (C.10) is satisfied, the solution of (C.9) is given by $$N_{H}=\left\lbrace \begin{array}{c}\scriptstyle{r_{0}\equiv \dfrac{1}{4}-\sqrt{\dfrac{1}{16}-\dfrac{\left[ 1-A^{1/\left( 1-\alpha \right) }\right] ^{2}}{\delta _{H}}},} \\ \scriptstyle{r_{1}\equiv \dfrac{1}{4}+\sqrt{\dfrac{1}{16}-\dfrac{\left[ 1-A^{1/\left( 1-\alpha \right) }\right] ^{2}}{\delta _{H}}}.}\end{array}\right.$$ (C.11) Note now that the roots r0 and r1 are not necessarily the equilibrium solutions for NH. More precisely, because $$N_{L}=[1-A^{\frac{1}{1-\alpha }}]-N_{H}$$, then $$N_{L}\ge 0\Leftrightarrow N_{H}\le [1-A^{\frac{1}{1-\alpha }}]$$. As a consequence, for NH = r1 in (C.11) to actually be an equilibrium solution, it must then be the case that $$r_{1}\le 1-A^{\frac{1}{1-\alpha }}$$. But this inequality is true only in the specific case when $$A=( 1-\sqrt{\delta _{H}}/4) ^{1-\alpha }$$ and $$\sqrt{\delta _{H}}=1$$, which in turn also implies that r1 = r0 in (C.11). Without any loss of generality, we may thus fully disregard r1, and check under which conditions $$r_{0}\le 1-A^{\frac{1}{1-\alpha }}$$. Using (C.11), and letting $$x\equiv 1-A^{\frac{1}{1-\alpha }}$$, an equilibrium with NL ≥ 0 when NH = r0 requires the following condition to hold: $$\Psi (x)\equiv \dfrac{1}{4}-\sqrt{\dfrac{1}{16}-\dfrac{x^{2}}{\delta _{H}}}\le x.$$ (C.12) Now, notice that Ψ(x) = x when A = [(2 + δH)/(2 + 2δH)]1 − α. In addition, noting that Ψ΄(x) > 0 and Ψ″(x) > 0, it then follows that (i) Ψ(x) < x, for all A > [(2 + δH)/(2 + 2δH)]1 − α; whereas Ψ(x) > x, for all $$(1-\sqrt{\delta _{H}}/4)^{1-\alpha }<A<[ ( 2+\delta _{H}) /( 2+2\delta _{H}) ] ^{1-\alpha }$$. Consequently, when A ≥ [(2 + δH)/(2 + 2δH)]1 − α, there is an equilibrium with NH = r0 and $$N_{L}=[1-A^{\frac{1}{1-\alpha }}]-r_{0}$$. Lastly, to prove that ∂f/∂A < 0, note that f = Ψ(x)/x, hence \begin{equation*} \dfrac{\partial f}{\partial A}=\dfrac{1}{4x^{2}}\dfrac{\partial x}{\partial A}-\dfrac{1}{16x^{3}}\left( \dfrac{1}{16}-\dfrac{x^{2}}{\delta _{H}}\right) ^{-\frac{1}{2}}\dfrac{\partial x}{\partial A}, \end{equation*} from where ∂f/∂A < 0 stems from noting that ∂x/∂A < 0 and that \begin{equation*} 1-\dfrac{1}{4x}\left( \dfrac{1}{16}-\dfrac{x^{2}}{\delta _{H}}\right) ^{-\frac{1}{2}}>0, \end{equation*} because of (C.11). Proof of Proposition 4 The conditions for an “L-equilibrium”, “H-equilibrium”, and a “mixed-type equilibrium” are, respectively, as follows: \begin{gather} \left[ \delta A\dfrac{( 1-N_{L}) ^{\alpha }}{N_{L}}\right] ^{\gamma }<\dfrac{A}{( 1-N_{L}) ^{1-\alpha }}\le \delta A\dfrac{( 1-N_{L}) ^{\alpha }}{N_{L}}, \quad \text{with }N_{L}\le 1/2. \end{gather} (C.13) \begin{gather} \delta A\dfrac{( 1-N_{H}) ^{\alpha }}{N_{H}}-\rho \chi <\dfrac{A}{( 1-N_{H}) ^{1-\alpha }}\le \left[ \delta A\dfrac{( 1-N_{H}) ^{\alpha }}{N_{H}}\right] ^{\gamma }, \quad \text{with }N_{H}\le 1/2. \end{gather} (C.14) \begin{gather} \delta A\dfrac{( 1-N_{H}-N_{L}) ^{\alpha }}{N_{H}+N_{L}}-\dfrac{N_{H}}{N_{H}+N_{L}}\rho \chi =\dfrac{A}{( 1-N_{H}-N_{L}) ^{1-\alpha }}\\ =\left[ \delta A\dfrac{( 1-N_{H}-N_{L}) ^{\alpha }}{N_{H}+N_{L}}\right] ^{\gamma },\quad \text{with }N_{H}\le 1/2 \text{ and }N_{L}\le 1/2. \nonumber \end{gather} (C.15) First of all, note that the condition for a low-effectiveness equilibrium (C.13) is identical to that in Proposition 1, hence when A(1 + δ)1 − α > 1 there must still exist a low-effectiveness equilibrium in the model with peer monitoring. Notice also that the condition for existence of a high-effectiveness equilibrium without peer monitoring is identical to condition (C.14), except for the term −ρχ in the first argument of the condition. This implies that whenever the condition for existence of an “H-equilibrium” without peer monitoring is satisfied, then it must also be satisfied when there is peer monitoring. As a consequence, when A(1 + δ)1 − α < 1, there must still exist an “H-equilibrium” in the model with peer monitoring. Next, recalling the definition of N1 in (11), from (C.14) it follows that, even when A(1 + δ)1 − α > 1, an H-equilibrium will exist if the condition $$\frac{A( 1-N_{1}) ^{\alpha }}{N_{1}}\left[ \delta -\frac{N_{1}}{1-N_{1}}\right] <\rho \chi$$ (C.16) holds true. Given that, when A(1 + δ)1 − α > 1, N1 < N0, then condition (C.16) requires that ρχ is sufficiently large. Lastly, consider the specific case when A(1 + δ)1 − α > 1 and condition (C.16) holds true. In a mixed-type equilibrium, we must have that $$A\left( 1-N\right) ^{\alpha }\left[ \delta -\frac{N}{1-N}\right] =\rho \chi ( N-N_{L}) .$$ (C.17) Notice now that when condition (C.16) holds true, then there must necessarily exist some value 0 < NL < N < N0, with N > NL, satisfying condition (C.17). This implies that when A(1 + δ)1 − α > 1 and condition (C.16) holds true, there also exists a mixed-type equilibrium satisfying (C). Derivation of Equilibrium Regions in Figure 4 (i) H-equilibrium Region. This type of equilibrium arises when $$\sigma _{i}<1<V_{p}^{\ast }$$ for any 0 ≤ N ≤ 1/2, where $$V_{p}^{\ast }$$ is given by (17) and σi by (18). For $$\sigma _{i}<V_{p}^{\ast }$$ to hold for any 0 ≤ N ≤ 1/2, it suffices to pin down when it holds for N = 1/2, which in turn leads to $$t<\bar{t}\equiv \left( 1-\delta \right) /\left( 2-\delta \right) .$$ (C.18) Next, for $$\sigma _{i}<V_{p}^{\ast }$$, we need that $$N<\frac{\delta \left( 1-t\right) +t}{1+\delta \left( 1-t\right) }.$$ (C.19) Therefore, plugging the RHS of (C.19) into (18) leads to the condition that σi < 1 whenever $$A<\frac{1}{\left( 1-t\right) ^{\alpha }\left[ 1+\delta \left( 1-t\right) \right] ^{1-\alpha }}.$$ (C.20) As a result, the region bounded by (C.18) and (C.20) features a high-effectiveness equilibrium. (ii) L-equilibrium Region. This type of equilibrium needs, first, that condition (C.20) fails to hold. Second, it also needs that $$( \sigma _{i}) ^{\gamma }<V_{p}^{\ast }$$ holds, so that mH-types choose the private sector. For $$( \sigma _{i}) ^{\gamma }<V_{p}^{\ast }$$ to obtain, it must be that $$A>\frac{\left[ t+\delta \left( 1-t\right) \right] ^{\frac{\gamma }{1-\gamma }}}{2^{1-\alpha }\left( 1-t\right) ^{\frac{1}{1-\gamma }}}.$$ (C.21) Notice now that the RHS of (C.20) is equal to the RHS of (C.21) when $$t=\bar{t}$$, while the former lies above (below) the latter when $$t<\bar{t}$$ (when $$t>\bar{t}$$). As a consequence, the region exhibiting an “L-equilibrium” is given by A > (1 − t) − α[1 + δ(1 − t)]α − 1 whenever $$t\le \bar{t}$$ and by (C.21) whenever $$t>\bar{t}$$. (iii) Mixed-Type Equilibrium Region with f > 1/2. From the previous results, it follows that when (C.20) holds and $$t>\bar{t}$$, we must necessarily have an equilibrium in which all mH-types choose the nonprofit sector, whereas mL-types lie indifferent between the two sectors, and a fraction of them choose the nonprofit sector as well. (iv) Mixed-Type Equilibrium Region with f < 1/2. From the previous results it also follows that when both (C.20) and (C.21) fail to hold and $$t>\bar{t}$$, we must necessarily have an equilibrium in which mL-types choose the nonprofit sector, whereas mH-types lie indifferent between the two sectors, and a fraction of them choose the nonprofit sector as well. Proof of Proposition A.1. Part (i). First, recall that in an H-equilibrium $$\bar{e}={1}/{2}$$. Second, using (A.7) and (4) when $$N=N_{H}^{\ast }$$, we have that \begin{equation*} \dfrac{\delta A\left( 1-N_{H}^{\ast }\right) ^{\alpha }}{N_{H}^{\ast }}=\dfrac{A}{\left( 1-N_{H}^{\ast }\right) ^{1-\alpha }}\quad \Leftrightarrow \quad N_{H}^{\ast }=\dfrac{\delta }{1+\delta }<\dfrac{1}{2}. \end{equation*} Therefore, an H-equilibrium must necessarily feature $$N_{H}^{\ast }=\delta /\left( 1+\delta \right)$$, with mH types indifferent across the two occupations. In such an equilibrium, they obtain a level of utility equal to A(1 + δ)1 − α. Third, from (A.5) it follows that this solution is a Nash equilibrium, as the best response by mL-type nonprofit managers would be eL = 0 when 2A(1 + δ)1 − α < 1, while eL = 1 otherwise. In both cases, A(1 + δ)1 − α ≤ 1 implies that selfish agents should prefer the private sector to the nonprofit sector. Moreover, this must be the unique Nash equilibrium solution, because the incentives for an mL-type agent to start a nonprofit will decline with the average level of $$\bar{e}$$, which in equilibrium will never be below 0.5 as implied by (A.3). Part (ii). Preliminarily, let us first define $$\widetilde{N}\equiv \delta /(2+\delta )$$. Note then that, when $$\bar{e}=1$$, the payoff functions (A.4) and (4) are equalized when $$N=\widetilde{N}$$; namely, $$U_{H}^{\ast }(\widetilde{N})=V^{\ast }(\widetilde{N})$$. Next, notice that, for a given $$\bar{e}$$, both (A.4) and (A.6) are strictly decreasing in N, while they grow to infinity as N goes to zero. Hence, to prove that a low-effectiveness equilibrium exists, it suffices to show that the condition A ≥ [2/(2 + δ)]1 − α implies $$U_{H}^{\ast }(\widetilde{N})\le U_{L}^{\ast }(\widetilde{N})$$. To prove that the low-effectiveness equilibrium is unique, notice first that an H-equilibrium is incompatible with A ≥ [2/(2 + δ)]1 − α. Therefore, the only other alternative would be a mixed-type equilibrium with all agents indifferent between the private and nonprofit sector. Yet, for (A.4) and (A.6) to be equal, it must be that $$D/N=2\bar{e}$$. This equality, in turn, implies that all activities must yield a payoff equal to 1; however, when A ≥ [2/(2 + δ)]1 − α, this would be inconsistent with $$\bar{e}<1$$, therefore a mixed-type equilibrium cannot exist either. Part (iii). First of all, following the argument in the proof of part (i) of the proposition, notice that an H-equilibrium cannot exist, because when A(1 + δ)1 − α > 1 selfish agents would like to deviate to the nonprofit sector and set eL = 1. Secondly, notice that a necessary condition for an L-equilibrium to exist is that $$U_{H}^{\ast }>1$$ when $$N=\widetilde{N}$$ and $$\bar{e}=1$$, but replacing $$N=\widetilde{N}$$ and $$\bar{e}=1$$ into (A.4) yields a value strictly smaller than 1 when A < [2/(2 + δ)]1 − α. As a result, when A(1 + δ)1 − α < A < [2/(2 + δ)]1 − α the equilibrium must necessarily be of mixed type, with all agents indifferent across occupations. This requires that $$U_{H}^{\ast }(N^{\ast })=U_{L}^{\ast }(N^{\ast })=V_{P}^{\ast }(N^{\ast })=1$$. From (4), we obtain that $$V_{P}^{\ast }(N^{\ast })=1$$ implies $$N_{ {mixed}}^{\ast }=1-A^{\frac{1}{1-\alpha }}$$. In addition, $$U_{H}^{\ast }(N^{\ast })=U_{L}^{\ast }(N^{\ast })$$ requires that $$2\bar{e}_{ {mixed}}=D/N$$, which using $$N_{ {mixed}}^{\ast }=1-A^{{1}/{1-\alpha }}$$ leads to $$\bar{e}_{ {\mathit{mixed}}}=\frac{1}{2}\dfrac{\delta A^{\frac{1}{1-\alpha }}}{1-A^{\frac{1}{1-\alpha }}}.$$ (C.22) Therefore, using the facts that $$e_{H}^{\ast }=0.5$$ and $$e_{L}^{\ast }=1$$, the levels of $$N_{H}^{\ast }$$ and $$N_{L}^{\ast }$$ in (A.9) immediately obtain. Lastly, to prove that this equilibrium is unique, notice that $$e_{ {mixed}}^{\ast }$$ in (C.22) lies between 0.5 and 1, thus there must exist only one specific combination of $$N_{H}^{\ast }$$ and $$N_{L}^{\ast }$$ consistent with a mixed-type equilibrium. Proof of Proposition B.1 First of all, notice that NH = 0.5 cannot hold in equilibrium, as (B.1) implies that in that case D/N = 0, no agent would choose the nonprofit sector. We can then focus on three equilibrium cases: (i) $$N_{L}^{\ast }=0$$ and $$0<N_{H}^{\ast }<0.5$$, with mL-types strictly preferring the private sector, (ii) $$N_{L}^{\ast }\le 0.5$$ and $$N_{H}^{\ast }=0$$, with mH-types strictly preferring the private sector, and (iii) $$0\le N_{L}^{\ast }\le 0.5$$ and $$0\le N_{H}^{\ast }<0.5$$, will all types indifferent across occupations. Case (i). For this case to hold in equilibrium, the following condition must be verified: $$\underset{U_{L}^{\ast }(N_{H},0)}{\underbrace{\dfrac{\delta _{H}A\left( \frac{1}{2}-N_{H}\right) }{( 1-N_{H}) ^{1-\alpha }N_{H}}}}<\underset{y(N_{H},0)}{\underbrace{\dfrac{A}{( 1-N_{H}) ^{1-\alpha }}}}=\underset{U_{H}^{\ast }(N_{H},0)}{\underbrace{\left[ \dfrac{\delta _{H}A\left( \frac{1}{2}-N_{H}\right) }{( 1-N_{H}) ^{1-\alpha }N_{H}}\right] ^{\gamma }}}.$$ (C23) For $$U_{L}^{\ast }(N_{H},0)<y(N_{H},0)$$ in (C.23) to hold, NH > δH/(2 + 2δH) must be true. Next, because $$U_{L}^{\ast }(N_{H},0)<U_{H}^{\ast }(N_{H},0)\Leftrightarrow U_{L}^{\ast }(N_{H},0)<1$$, and y(NH, 0) is strictly increasing in NH while $$U_{H}^{\ast }(N_{H},0)$$ is strictly decreasing in it and $$U_{H}^{\ast }({1}/{2},0)=0$$, a sufficient condition for (C.23) to hold in equilibrium is that \begin{equation*} \dfrac{\delta _{H}A\left( \frac{1}{2}-N_{H}\right) }{( 1-N_{H}) ^{1-\alpha }N_{H}}<1 \text{ when }N_{H}=\dfrac{\delta _{H}}{2+2\delta _{H}}, \end{equation*} which in turn leads to the condition A < [(2 + δH)/(2 + 2δH)]1 − α. Case (ii). This case occurs when the following condition holds: $$\underset{U_{H}^{\ast }(0,N_{L})}{\underbrace{\left[ \dfrac{\frac{1}{2}\delta _{H}A}{( 1-N_{L}) ^{1-\alpha }N_{L}}\right] ^{\gamma }}}<\underset{y(0,N_{L})}{\underbrace{\dfrac{A}{( 1-N_{L}) ^{1-\alpha }}}}\le \underset{U_{L}^{\ast }(0,N_{L})}{\underbrace{\dfrac{\frac{1}{2}\delta _{H}A}{( 1-N_{L}) ^{1-\alpha }N_{L}}}}.$$ (C.24) Using the expressions in (C.24), notice that for $$U_{L}^{\ast }(0,N_{L})>y(0,N_{L})$$ to hold, NL < δH/2. But, because 0 < δH ≤ 1, NL < δH/2 and $$U_{L}^{\ast }(0,N_{L})>y(0,N_{L})$$ cannot possibly hold together. As a consequence, in equilibrium, $$U_{L}^{\ast }(0,N_{L})=y(0,N_{L})$$ must necessarily prevail, implying in turn that NL = δH/2. Next, because $$U_{L}^{\ast }(N_{H},0)>U_{H}^{\ast }(N_{H},0)\Leftrightarrow U_{L}^{\ast }(N_{H},0)>1$$, a sufficient condition for (C.24) to hold in equilibrium is that \begin{equation*} \dfrac{\frac{1}{2}\delta _{H}A}{( 1-N_{L}) ^{1-\alpha }N_{L}}>1 \text{ when }N_{L}=\dfrac{\delta _{H}}{2}, \end{equation*} which in turn leads to the condition A > (1 − δH/2)1 − α. Case (iii) Keeping in mind that $$U_{L}^{\ast }(N_{H},0)=U_{H}^{\ast }(N_{H},0)\Leftrightarrow U_{L}^{\ast }(N_{H},0)=1$$, this case will arise when the following equalities hold: $$\underset{y(N_{H},N_{L})}{\underbrace{\dfrac{A}{( 1-N_{H}-N_{L}) ^{1-\alpha }}}}=\underset{U_{L}^{\ast }(N_{H},N_{L})}{\underbrace{\dfrac{\delta _{H}A\left( \frac{1}{2}-N_{H}\right) }{( 1-N_{H}-N_{L}) ^{1-\alpha }( N_{L}+N_{H}) }}=1}.$$ (C.25) Recalling the definition of $$\underline{N}$$ in (13), $$U_{L}^{\ast }(N_{H},N_{L})=1$$ leads to [δH(0.5 − NH)]/[1 − A1/(1 − α)] = 1, from where we obtain: $$N_{H}=\dfrac{1}{2}-\dfrac{1-A^{\frac{1}{1-\alpha }}}{\delta _{H}}.$$ (C.26) Next, using again the definition of $$\underline{N}$$ in (13), we may obtain NL = [1 − A1/(1−α)] − NH, which using (C.26) yields: $$N_{L}=\left( 1-A^{\frac{1}{1-\alpha }}\right) \dfrac{1+\delta _{H}}{\delta _{H}}-\dfrac{1}{2}.$$ (C.27) Lastly, (C.26) implies that NH > 0⇔A > (1 − δH/2)1 − α, whereas (C.27) means that NL > 0⇔A < [(2 + δH)/(2 + 2δH)]1 − α, completing the proof. Acknowledgments We thank Nicola Gennaioli and Paola Giuliano (coeditors), four anonymous referees, François Bourguignon, Maitreesh Ghatak, Stephan Klasen, Cecilia Navarra, Susana Peralta, Jean-Philippe Platteau, Debraj Ray, Paul Seabright, Pedro Vicente, and participants at the N.G.O. workshop (London), OSE workshop (Paris), ThReD Conference (Barcelona), EUDN Conference (Oslo), as well as seminar participants at Collegio Carlo Alberto, Nova University of Lisbon, Tinbergen Institute, University of St Andrews, and University of Sussex for useful suggestions. Financial support from the Labex OSE and FNRS (FRFC grant 7106145 ”Altruism and NGO performance”) is gratefully acknowledged. Aldashev is a Research Fellow at ECARES. Verdier is a Research Fellow at CEPR. Notes The editors in charge of this paper were Nicola Gennaioli and Paola Giuliano. Footnotes 1 See, for example, Andreoni and Miller (2002), Ribar and Wilhelm (2002), Korenok, Millner, and Razzolini (2013), and Tonin and Vlassopoulos (2010). 2 In this paper, we mostly focus on the joy-of-giving (or warm-glow) motive for giving. However, an additional reason why people might be willing to donate is social signaling, as modeled by Benabou and Tirole (2006). Social signaling would complement and reinforce the joy-of-giving motive that we focus on in our model. One other reason that would also reinforce the act of giving, without any link to pure altruism, is tax incentives to giving. 3 See Chapter 12 of Hansmann (1996) and Bilodeau and Slivinski (1996) for detailed discussions on the issue of incomplete contracts in nonprofit organizations. 4 On the empirical side, Gregg et al. (2011) find that individuals in the nonprofit sector in the UK are significantly more likely to do unpaid overtime work as compared to their counterparts in the for-profit sector. Moreover, this differential willingness remains even when the former individuals move into the for-profit sector, strongly supporting theories based on self-selection (rather than sector-specific incentive structure). 5 Our assumption of decreasing marginal returns with respect to the aggregate mass of private entrepreneurs reflects the fact that, at a given point in time, there is a fixed factor in the economy (which we do not explicitly model) that enters the production of goods in the private sector. 6 In principle, it may seem more reasonable to assume that agents who exhibit a higher degree of prosocial motivation should also be more prone to donating for social causes, and therefore display a larger value of δ in (3). We stick to the simplest possible formulation in this basic model, to introduce in the stark way the idea that donations are endogenous, by shutting down additional effects. In Appendix B, we relax the assumption that warm-glow donations by private entrepreneurs are independent of their level of prosocial motivation by letting δ be type-specific (δi), with δL = 0 and 0 < δH ≤ 1. This introduces the additional complexity of making donations dependent on the degree of motivational heterogeneity in the for-profit sector, giving rise to the possibility of multiple equilibria. 7 Appendix A presents a model that relaxes the equal-sharing assumption by endogenizing fundraising effort. 8 These two cases exclude the set of parametric configurations for which $$\widehat{N}=N_{0}$$, where N0 is defined in what follows in (10). When $$\widehat{N}=N_{0}$$, all individuals in the economy will be indifferent in equilibrium across the two occupations. Consequently, there are multiple equilibria, with the set equilibria given by $$\lbrace N_{H}^{\ast }+N_{L}^{\ast }=N_{0} |0\le N_{H}^{\ast }\le {1}/{2},0\le N_{L}^{\ast }\le {1}/{2}\rbrace$$. Hereafter, for the sake of brevity, we skip this knife-edge case. 9 These results entail that, as the scale of the donations market increases, it may then become socially desirable to invest in certain types of changes in the organization of the NGO sector that help mitigating rent-seeking behavior, such as better accounting and monitoring mechanisms, tougher certification schemes, and so forth. 10 Kanbur (2006) argues that the rise of NGOs during the 1980s was one of the key changes in the functioning of the foreign aid sector. 11 Another way to avoid this problem would be to assume that the production function of private entrepreneurs is given by y(N), with y΄(N) > 0, y″(N) < 0, y(1) = ∞, and y(0) = 0. Note that all these properties are satisfied by (2), except for y(0) = 0. Intuitively, what is needed to give room for an “H-equilibrium” is that y(N) ≤ 1 for some N ≥ 0. Assumption 1 ensures this is always the case. 12 The only major qualitative difference is that when 21−αA < 1, the “L-equilibrium” where all nonprofit firms are managed by mL-types will no longer arise. Instead, when 21−αA < 1, while the economy still exhibits an “H-equilibrium” for levels of Δ that are sufficiently low, beyond a certain threshold of Δ, the economy switches directly to a mixed-type equilibrium. In that respect, the fraction of motivated nonprofit managers will still depend nonmonotonically on the level of foreign aid when 21−αA < 1. 13 For example, Svensson (2000) suggests that foreign aid channeled through the public sector may lead to higher bureaucratic corruption, break-up of accountability mechanisms of elected officials, and the ignition of ethnic-based rent-seeking behavior. 14 In a recent study, Metzger and Günther (2015) test, in a laboratory experiment, whether private donors seek information, before giving, about the impact of their donations to international NGOs. Interestingly, they find that only a small fraction of donors makes a well-informed donation decision and that demand for information mostly concerns the recipient type (and not the impact of donation). They also find that the information about the impact of donations does not change average donation size. 15 In some sense, the model developed in Section 2 could then be thought as more appropriate for underdeveloped and middle-income economies, where watchdog organizations are less present. 16 Motivated agents do not report anything in these matches, whereas selfish agents do not care about reporting. We disregard the unplausible case where selfish agents would make false reports concerning motivated agents, which seems rather far-fetched. 17 One could also rationalize these reputational concerns from a dynamic perspective as ensuring that the sector maintains its credibility vis-a-vis the donors. 18 Notice that the multiplicity of equilibria hinges crucially on the fact that selfish nonprofit managers do not care about reporting of misbehavior by their peers. One solution to this problem could then be (monetarily) rewarding whistleblowing, so as to induce also selfish nonprofit managers to report rent seeking. 19 Hence, at Z, one part of the mL-types choose the private sector and the other part choose nonprofit firms. 20 Notice that all this implies that, in the new equilibrium, the total mass of nonprofit firms must necessarily be larger than in Z, because from (18) it follows that σi will grow with t for a given level of N. In other words, after t is raised to a level within $$[\underline{ \mathit{t}},\bar{t}]$$, a mass $$N_{L}^{\ast }$$ of selfish nonprofit managers will be replaced by a mass $$N_{H}^{\ast }$$ of motivated nonprofit managers, where $$N_{H}^{\ast }>N_{L}^{\ast }$$. 21 This assumption is dispensed, though, in the model presented in the Appendix A, where we use a linear production function for each single nonprofit firm. 22 Although our model has treated prosocially motivated agents as identical (hence, without displaying heterogeneity in their type of prosocial motivation), the idea that each NGO manager operates a different nonprofit firm implicitly reflects the underlying notion that motivated agents also differ in the social mission they most strongly align with. 23 This has also been highlighted by the matching-to-mission model of Besley and Ghatak (2005). 24 Note, however, that Section 3.1 deals with the case where donations respond to the average motivation in the nonprofit sector, but the level of donations received by each nonprofit is still assumed to be proportional to aggregate donations. 25 Another form of signaling is possible if conditionally warm-glow donors differ in size, and large donors can obtain information (even if noisy) about the nonprofit managers’ types at some cost. The models by Vesterlund (2003) and Andreoni (2006), where obtaining a large leadership donation serves as a credible signal of quality, can serve as a microfoundation for this type of analysis. 26 Most of the existing discussions of the performance of humanitarian aid to the 2004 tsunami concern international or Northern NGOs. In the context of our model, given that these NGOs were founded in different countries, they could be facing different types of occupational equilibria. However, Willitts-King and Harvey (2005) show that the diversion of funds during humanitarian relief can occur both at the international organizations’ level and at the local level (and probably, both levels were subject to this problem). Therefore, our analytical framework still applies to this context. 27 In a partial-equilibrium framework, this issue has been studied in the contributions mentioned in the introduction and in a recent review by Mansuri and Rao (2013). 28 See, for example, De Waal (1997) and Hancock (1989) for some poignant recounts of the fundraising effort spent by nonprofit organizations by using the social media both in the developed and developing world. 29 It is interesting to compare these findings to those of Aldashev and Verdier (2010), where more intense competition for funds actually leads to higher diversion of donations by nonprofit managers. This occurs because when agents have to spend more time raising funds, then less time is left for working towards the nonprofit mission, and thus the opportunity cost of diverting money for private consumption falls. In that model, all agents are intrinsically identical, and thus the issue of more intense competition lies in aggravating a moral hazard problem. Here, instead, the existence of motivationally heterogeneous types implies that the main problem is one of adverse selection, and a more intense competition for funds mitigates the severity of this adverse selection problem. 30 Notice that, in the specific case in which δH = 1, the utility functions in the private sector and the nonprofit sector would display the same structure for both mH- and mL-types: for the former, all the utility weight is being placed on prosocial actions (either warm-glow giving or producing gi); for the latter, all the utility weight is being placed on private consumption. 31 In the specific cases, where A = (1 − δH/2)1 − α or A = [1 − δH/(2 + 2δH)]1 − α, the “mixed-type equilibrium” described in what follows disappears, whereas the other two equilibria remain. 32 The range of values of A subject to multiple equilibria vanishes as δH approaches zero. 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Published: Nov 14, 2017

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