Elsevier

Omega

Volume 100, April 2021, 102227
Omega

Optimal dynamic management of a charity under imperfect altruism☆,☆☆

https://doi.org/10.1016/j.omega.2020.102227Get rights and content

Highlights

  • •

    We propose a dynamic optimization model for allocating donations to a charity.

  • •

    Donations serve to finance projects, advertising and managers benefits.

  • •

    We characterize the optimal policies and discuss their implications.

  • •

    We determine the conditions under which the manager behaves ethically, or not.

Abstract

Nonprofit organizations play an important role in providing goods and services in all countries. The objective of this paper is to determine optimal policies for a charity when its managers are imperfectly altruistic. The starting point of our analysis is that the donations a charity receives are a function of its reputation, which is an asset that can be built up over time, not overnight. To account for this important aspect, we propose a dynamic model where the charity can allocate its revenues to three main activities, namely, the program expenditures (charitable projects), information (promotion of its causes, website, etc.) and unproductive consumption benefiting its managers. We compute optimal policies and discuss their implications. We notably find conditions under which imperfectly altruistic managers nevertheless behave ethically. In addition, we show that where they behave non-ethically, advertising and unproductive consumption always move in opposite directions.

Introduction

The objective of this paper is to determine the optimal management of a nonprofit organization or charity by a manager who is imperfectly altruistic. By this we mean that, while the manager cares about the social programs offered by the organization, she also cares about the advantages obtained through unproductive expenditures, which are largely her decision.

Anecdotal evidence as well as some empirical studies suggest that imperfectly altruistic managers do exist. In her empirical study, Feigenbaum [16] obtains that, at least for the medical research industry, “increases in market concentration lead to reduced funding for research projects and greater discretionary expenditures.” In the same vein, Glaeser [7] shows that wealthy nonprofit organizations tend to conform to objectives of elite workers rather than donors, and Malani and Choi [18] establish that nonprofit compensation structures in hospitals promote similar goals. Glazer [17] provides vivid examples of profit-maximizing nonprofits.

There is a small emerging literature that studies the causes and consequences of the diversion of funds by nonprofits. Castaneda et al. [15] assess the effect of an increase in the number of competing nonprofits on the amount of diverted funds and on fundraising expenses. They show that an increase in competition reduces diversion and increases fundraising. Aldashev and Verdier [1] study how nongovernmental organizations (NGOs) choose between fundraising and working on their projects when they can divert part of the donations for private use. They find that the ease of entry determines the level of diversion, and that multiple equilibria (with high and low diversion of funds) can occur. When fundraising competition is weak, NGOs devote most of their time to their projects and there is little diversion, and the reverse is true when fundraising competition is strong. While the literature has focused on the impact of competition on resource diversion, here we overlook this aspect and concentrate rather on the dynamic choices made by an imperfectly altruistic manager.1

The rationale for adopting a dynamic approach is as follows: while managers can divert some resources, there are limits to such behavior because it is generally considered unacceptable by the donors. More specifically, resource diversion is likely to negatively impact the charity’s reputation (an asset that can be built over time, not overnight) and, consequently, donations as well. As a result, there are potentially fewer funds that can be diverted. However, reputation can be boosted through costly advertising, which is an instrument controlled by the manager. Accounting for these features can only be achieved through a dynamic approach. In fact, Feng and Shanthikumar [5] stated that:

“... nonprofit organizations should take a dynamic view of their operations. There is a delicate balance in how much resources to allocate in the current period to generate potential current and future funds while not hurting the efficiency measured in the current period to reduce the funders’ giving incentive.”

Our objective is to answer the following research questions:

  • 1.

    How should advertising and unproductive consumption be combined over time? Are they complementary, meaning that advertising compensates for the loss of reputation caused by unproductive consumption?

  • 2.

    Are there instances where the charity’s environment is such that frugality is the optimal solution?

  • 3.

    Can it be optimal not to advertise?

Our study can be of interest to the following organizations: (i) foundations, which often contribute to charities; (ii) united charities (like Centraide in Canada, or the United Way in the US) which audit and monitor the programs run by more specialized charities; (iii) charity rating agencies, which notably use various ratios to assess the efficiency of nonprofits. We believe our study gives insights about a charity’s future actions. Computing financial ratios is necessary, but it does not necessarily yield decisive information about a manager’s future decisions or about the future value of the charity’s programs. By contrast, a dynamic analysis helps thinking about possible future scenarios and can inform the decisions stakeholders have to make now.

The rest of the paper is organized as follows: In Section 2, we introduce the model. In Section 3, we state the general constrained optimization problem. Sections 4 and 5 present the optimal solutions with non-ethical and ethical behavior, respectively. In Section 6, we interpret the sufficient conditions for optimality and in Section 7, we present the impact of varying the administrative cost norm on the results. Section 7 briefly concludes.

Section snippets

Model

We consider a charity managing its operations over an infinite planning horizon. Denote time by t∈[0,∞) and let G(t) be a positive variable that measures the charity’s goodwill with the public at time t. In the language of dynamic optimization, G(t) is a state variable, that is, a stock or an asset, whose evolution over time depends on some other variables, which will be defined below.

The revenues or donations received by the charity depend on its goodwill (reputation or brand equity) and are

A general constrained problem

To solve the dynamic constrained-optimization problem, we introduce the HamiltonianH(a(t),c(t),e(t),λ0,λ(t),ψ(t),s(t),x(t),y(t))=λ0(φc(t)−c2(t)2+e(t))+λ(t)(a(t)−γ(c(t)−c¯)−δG(t))+ψ(t)(θ1G(t)−G2(t)2−c(t)−e(t)−ω1a(t)−a2(t)2)+s(t)a(t)+x(t)c(t)+y(t)e(t),where: λ(t) is the adjoint variable appended to the dynamics in (1); ψ(t) is the Lagrange multiplier appended to the budget constraint in (2); s(t), x(t) and y(t) are Lagrange multipliers corresponding to the non-negativity constraints a(t) ≥ 0, c(t

Non-ethical behavior

In many realistic instances, resources diversion by the charity manager is unavoidable. We have two subcases: (i) the charity invests in advertising to inform the public about its projects and also to control the potentially negative effect of resources diversion; and (ii) the charity does not wish to allocate any budget to advertising. In both solutions, we have e(t) > 0; otherwise, the charity looses its raison d’être. The first case is the interior solution where all control variables assume

Ethical behavior

Even if the charity’s manager is imperfectly altruistic, she may behave ethically, that is, there will be no resources diverted (c(t)=0, for all t). The charity environment, by which we mean the public sensitivity to unacceptable behavior, efficiency of fundraising, efficiency of advertising campaigns, the taste for indirect compensation, etc., can indeed be such that frugality is an optimal solution. We shall consider in turn two subcases: in the first one, we have a(t) positive for all t, and

Interpretation of the sufficient conditions

In Proposition 1, Proposition 3, Proposition 4 and 5, we studied the optimal solution in four scenarios, namely, N, N0, E and E0. The sufficient conditions stated in these propositions are very complex. The reason is that each condition is stated, as it should be, to hold for all instants of time. In particular, they ensure that the program expenses, which are obtained from the charity budget constraint, are always positive. To interpret the sufficient conditions it is useful to consider them

The impact of the social spending norm

In this section, we do two things. First, we assess the impact of varying the norm c¯ on the results at the steady state. Second, we derive conditions under which the steady-state unproductive consumption is below this norm in the two cases where the manager’s behavior is unethical. The importance of c¯ stems from the fact that donors want to see their contributions being dedicated to financing the causes in which they believe, not being diverted for the sole benefit of the charity’s manager.

Concluding remarks

A starting point of this research is that the revenues (donations) collected by a charity, and more generally by any nonprofit organization (NGO), depend on its reputation (or goodwill) in the public. As reputation is an asset that takes time and effort to build, we adopted a dynamic approach to optimally determine the charity’s program, advertising and consumption expenditures. A second anchor point is that the public, which is the target market for donations, is sensitive to how charities are

Author statement

All authors collaborated and contributed equally to all aspects of the paper.

References (18)

There are more references available in the full text version of this article.

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We would like to thank two reviewers for their very helpful comments.

☆☆

This manuscript was processed by Area Editor Oleg Prokopyev.

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