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Incentives and Prosocial Behavior
by Roland Bénabou and Jean Tirole 1 This Version: July 14, 2005
Abstract We develop a theory of prosocial behavior that combines heterogeneity in individual altruism and greed with concerns for social reputation or self-respect. Rewards or punishments (whether material or image- related) create doubt about the true motive for which good deeds are performed and this “overjustification effect” can induce a partial or even net crowding out of prosocial behavior by extrinsic incentives. We also identify settings that are conducive to multiple social norms and those where disclosing one’s generosity may backfire. Finally, we analyze the choice by public and private sponsors of incentive levels, their degree of confidentiality and the publicity given to agents’ behavior. Sponsor competition is shown to potentially reduce social welfare.
Keywords: altruism, rewards, motivation, esteem, crowding out, overjustification effect, identity, social norms, morals, greed, psychology
JEL Classification: D64, D82, H41, Z13. (^1) Bénabou: Department of Economics and Woodrow Wilson School, Princeton University, Princeton, NJ 08544, CEPR, IZA and NBER. Tirole: Institut d’Economie Industrielle, 21 Allées de Brienne, 31000 Toulouse, France, GREMAQ, CERAS and MIT. We thank for useful comments George Akerlof, Roland Fryer, Timur Kuran, Bentley MacLeod, Tom Romer, Armin Falk, participants at various seminars and con- ferences and three anonymous referees. We are especially indebted to Ian Jewitt for valuable sugges- tions. Bénabou gratefully acknowledges support from the John Simon Guggenheim Memorial Founda- tion in 2004 and from the National Science Foundation.
People commonly engage in activities that are costly to themselves and mostly benefit others. They volunteer, help strangers, vote, give to political or charitable organizations, donate blood, join rescue squads and sometimes sacrifice their life for strangers. Many experiments and field studies confirm that a significant fraction of people engage in altruistic or reciprocal behaviors. A number of important phenomena and puzzles, however, cannot be explained by the sole presence of individuals with other-regarding preferences. First, providing rewards and punishments to foster prosocial behavior sometimes has a perverse effect, reducing the total contribution provided by agents. Such a crowding-out of “intrinsic motivation” by extrinsic incentives has been observed in a broad variety of social interactions (see Bruno S. Frey (1997) and Frey and Reto Jegen (2001) for surveys). Studying schoolchildren collecting donations for a charitable organization, Uri Gneezy and Aldo Rustichini (2000b) thus found that they collected less money when given performance incentives (see also Frey and Lorenz Götte (1999) on volunteer work supply). These findings are in line with the ideas in Richard Titmuss (1970), who argued that paying blood donors could actually reduce supply. On the punishment side, George A. Akerlof and William T. Dickens (1982), suggested that imposing stiffer penalties could sometimes undermine individuals’ “internal justification” for obeying the law. Frey (1997) provided some evidence to that effect with respect to tax compliance and Gneezy and Rustichini (2000a) found that fining parents for picking up their children late from day-care centers resulted in more late arrivals. In experiments on labor contracting, subjects provided less effort when the contract specified fines for inadequate performance than when it did not (Fehr et al. (2001) and Fehr and Gächter (2002)) and they behaved much less generously when the principal had simply removed from their choice set the most selfish options (Armin Falk and Michael Kosfeld (2004)). These findings extend a large literature in psychology documenting how explicit incentives can lead to decreased motivation and unchanged or reduced task performance (see, e.g. Edward Deci (1975), Deci and Richard Ryan (1985)). In studying this class of phenomena, however, one cannot simply assume that rewards and punishments systematically crowd out spontaneous contributions. Indeed, there is also much evidence to support the basic premise of economics that incentives are generally effective, for instance in workplace contexts (e.g., Robert Gibbons (1997), Canice Prendergast (1999) and Edward P. Lazear (2000a,b)). A more discriminating analysis is thus required. A second set of issues relates to the fact that people commonly perform good deeds and refrain from selfish ones because of social pressure and norms that attach honor to the former and shame to the latter
Kuang, and Roberto Weber (2003) thus reveals that when people are given the opportunity to remain ignorant of how their choices affect others, or of their precise role in the outcome (as with firing squads, which always have one blank bullet), many “altruists” choose not to know and revert to selfish choices.^5 To examine this broad array of issues, we develop a theory of prosocial behavior that combines hetero- geneity in individuals’ degrees of altruism and greed with a concern for social reputation or self-respect. The key property of the model is that agents’ pro- or anti-social behavior reflects an endogenous and unobservable mix of three motivations: intrinsic, extrinsic, and reputational, which must be inferred from their choices and the context. We obtain four main sets of results.
— Rewards and punishments. The presence of extrinsic incentives spoils the reputational value of good deeds, creating doubt about the extent to which they were performed for the incentives rather than for themselves. This is in line with what psychologists term the “overjustification effect” (e.g., Mark R. Lepper et al. (1973)), to which we give here a formal content in terms of a signal-extraction problem.^6 Rewards act like an increase in the noise-to-signal ratio, or even reverse the sign of the signal, and the resulting crowding out of the reputational (or self-image) motivation to contribute can make aggregate supply downward-sloping over a wide range, with possibly a sharp drop at zero.
— Publicity and disclosure. The prominence and memorability of contributions strengthen the signaling motive and thus generally encourage prosocial behavior. When individuals are heterogeneous in their image concerns, however, a greater prominence also acts like an increase in the noise-to signal-ratio: good actions become suspected of being motivated by appearances, which limits the effectiveness of policies based on “image rewards” such as praise and shame. The same concern can lead individuals to refrain from overtly disclosing their good deeds and from turning down any rewards that are offered. Sponsors may respond to contributors’ desire to appear intrinsically rather than extrinsically motivated by publicly announcing low rewards, but then find it profitable to offer higher ones in private, creating a commitment problem.
about the true preferences of their neighbors or average compatriots, they give dramatically reversed rankings. Interviews with car dealers show intermediate results. (^5) In a related vein, J. Keith Murnighan et al. (2001) find that the fairness of offers in dictator games is significantly decreased when the precision with which offerers can split the cake is decreased, allowing them to construe the outcomes as largely outside their control. 6 It is also consistent with the informal explanation provided by Frey and Jegen (2001), namely that “An intrinsically motivated person is deprived of the chance of displaying his or her own interest and involvement in an activity when someone else offers a reward, or orders him/her to do it”.
— Spillovers and social norms. The inferences that can be drawn from a person’s actions depend on what others choose to do, creating powerful spillovers that allow multiple norms of behavior to emerge as equilibria. More generally, individuals’ decisions will be strategic complements or substitutes, depending on whether their reputational concerns are (endogenously) dominated by the avoidance of stigma or the pursuit of distinction. The first case occurs when there are relatively few types with low intrinsic altruism and when valid excuses for not contributing are more rare than events that make participation inevitable, or unusually easy. The second case applies in the reverse circumstances.
— Welfare and competition. When setting rewards and publicizing contributions, sponsors will exploit these complementarities or substitutabilities, which respectively increase or decrease the elasticity of the supply curve. Because they do not internalize the reputational spillovers that fall on non-participants or on those who contribute through other sponsors, however, their policies will generally be inefficient. Thus, even a monopoly sponsor may offer rewards and “perks” (preferred seating, meetings with famous performers, valuable social networking opportunities, naming rights to a building, stadium or professorial chair, etc.) that are too generous from the point of view of social welfare, and sponsor competition may further aggravate this inefficiency. The socially optimal incentive scheme, by contrast, subtracts from the standard Pigouvian subsidy for public goods provision a “tax” on reputation-seeking, which, per se, is socially wasteful. In the market for prosocial contributions, finally, a form of holier-than-thou competition can also lead sponsors to offer agents opportunities for reputationally motivated sacrifices that will again reduce social welfare, without any increase in the supply of public goods.. While a number of related themes have been examined in the literature, none of the existing models provides a unified account of this broad range of phenomena. Standard models of public goods provision or altruistic behavior, whether based on a concern for others’ welfare, a pure joy of giving, or reciprocity, are not consistent with a (locally) downward-sloping response of prosocial behavior to incentives, nor with people choosing not to know how their actions will affect others and reverting to selfish behavior when such ignorance is feasible. Models of giving as a signal of wealth explain monetary donations but not in-kind prosocial acts such as volunteering, helping, giving blood, etc. (these should instead be avoided, as they signal a low opportunity cost of time), the greater admiration reserved for anonymous contributions, or people’s choosing to be modest about their good deeds. Models that postulate a reduced-form crowding out
The paper is organized as follows. Section I presents the model and an intuitive illustration of the image- spoiling effect of rewards. Section II formally demonstrates the crowding-out phenomenon, as well as a related form of the overjustification effect. Section III deals with social norms and more generally identifies the features of the market that make individual decisions strategic complements or substitutes. Section IV explores issues of confidentiality and disclosure with respect to rewards or actions. Section V examines the setting of incentives by public or private sponsors and the effects of competition on social welfare. Section VI concludes with possible directions for further research. All proofs are gathered in the Appendix.
I. The Model
A. Preferences and information
We study the behavior of agents who choose the extent of their participation in some prosocial activity: contributing to a public good or worthy cause, engaging in a friendly action, refraining from imposing negative externalities on others, etc. Each selects a participation level a from some choice set A ⊂ R that can be discrete (voting, blood donation) or continuous (time or money volunteered, fuel efficiency of car purchased). Choosing a entails a utility cost C(a) and yields a monetary or other material reward ya. The incentive rate y ≷ 0 may reflect a proportional subsidy or tax faced by agents in this economy, or the fact that participation requires a monetary contribution. It is set by a principal or “sponsor” and, for now, individuals take it as given. Denoting by va and vy an agent’s intrinsic valuations for contributing to the social good and for money (consumption of market goods), participation at level a yields a direct benefit
(1) (va + vyy) a − C(a).
Each individual’s preference type or “identity” v ≡ (va, vy ) ∈ R^2 is drawn independently from a continuous distribution with density f (v) , marginal densities g (va) and h (vy) and mean (¯va, ¯vy ). Its realization is private information, known to the agent when he acts but not observable by others. Social signaling. In addition to these direct payoffs, decisions carry reputational costs and benefits,
Our work is also technically related to a recent literature on signals that convey diverging news about different underlying characteristics (Aloisio Pessoa de Araújo et al. (2004), Philipp Sadowski (2004), David Austen-Smith and Roland G. Fryer (2005)).
reflecting the judgements and reactions of others —family, friends, colleagues, employers. The value of reputation can be instrumental (making the agent a more attractive match, as in Denrell (1998), Herbert Gintis et al. (2001) or Seabright (2002)) or purely hedonic (social esteem as a consumption good). For simplicity, we assume that it depends linearly on observers’ posterior expectations of the agent’s type v, so that the reputational payoff from choosing a, given an incentive rate y is
(2) R(a, y) ≡ x £γaE (va|a, y) − γy E (vy |a, y)¤^ , with γa ≥ 0 and γy ≥ 0.^8
The signs of γa and γy reflect the idea that people would like to appear as prosocial (public-spirited) and disinterested (not greedy), while the factor x > 0 measures the visibility or salience of their actions: probability that it will be observed by others, number of people who will hear about it, length of time during which the record will be kept, etc. Defining μa ≡ xγa and μy ≡ xγy , an agent with preferences v ≡ (va, vy) and reputational concerns μ ≡ ¡μa, μy^ ¢^ thus solves
(3) max a∈A^ ©(va + vy y) a − C(a) + μaE (va|a, y) − μy E (vy |a, y)ª^.
In the basic version of the model, μ is taken to be common to all agents and thus public knowledge. In the full version we also allow for unobserved heterogeneity in image-consciousness, with μ distributed independently of v according to a density m(μ). Note, finally, that while we shall generally cast the analysis in terms of effortful or time-consuming prosocial actions such as volunteering, voting, etc., it is equally applicable to purely monetary (e.g., charitable) donations. 9
Self-signaling and identity. The model admits an important reinterpretation in terms of self-image. Suppose that, at the time he makes his decision, the individual engages in a self-assessment or receives
(^8) This payoff is defined net of the constant (1 − x) ¡γa v¯a − γy ¯vy^ ¢, which corresponds to the case where aover the agent’s type (such as its expectation) avoids building into his preferences either information-aversion remains unobserved. Note that a value of reputation that is a linear functional of the posterior distribution (concave functional) or information-loving (convex functional). The more restrictive assumption, which we make for tractability, is that the coe 9 fficients in (2) are independent of the agent’s type v. Let a now be the number of dollars contributed by an individual with a known, concave utility over income, represented by the term −C(a). Each dollar generates one unit of public good and entitles the contributor to y units of perks and privileges (meeting with performers, gala events, networking, etc.), a “currency” for which he has utility vy. This alternative interpretation of (3) is fully consistent with the analysis in Section II. One can also capture the case where instead of perks, the sponsor offers a matching rate y : let vy ≡ 1 and C(a) = ca, where c is the cost of providing a unit of public good, so the net cost to the contributor is only c−y. This corresponds to the specification of (3) used in most of Sections III-V.
in the intrinsic propensity to contribute or reciprocate, va, no matter its source, and that agents value being perceived, or perceiving themselves, as having a high va. This (self) esteem benefit, μaE (va|a, y) , is perhaps what corresponds best to the idea of a “warm glow” of giving: gaining social approval, feeling good about oneself, etc. Finally, note that the action a chosen by agents and giving rise to reputation could be their reaction to someone else’s behavior, such as cooperation or defection. The model is thus applicable to reciprocity as well as to unconditional prosocial behavior. We now turn to the terms in (3) relating to material compensation. That in vy y requires no explanation, except to note that if the individual believes that his receiving y reduces the resources available to the sponsor for supporting other activities he cares about, it will be attenuated by an “eviction effect”.^13 Consider next the potential negative reputation attached to “greed” or money-orientation, −μy E (vy |a, y). Note first that all the paper’s results but one (Proposition 3) obtain with μy ≡ 0 as well. It is nonetheless natural to allow for such an effect —“greedy” is no compliment. Someone who has a high valuation for money relative to effort and / or public goods is not a very attractive partner in friendship, marriage, hiring to a position of responsibility, electing to office and other situations where it is difficult to always monitor behavior or write complete contracts. Demonstrating a low marginal utility for money vy can also be valuable because it signals high wealth, a motive that figures prominently in the literatures on charitable contributions and on conspicuous consumptions (e.g., Glazer and Conrad (1996), Bagwell and Bernheim (1996)).
B. The image-spoiling effect of rewards: basic insights
We begin with an intuitive presentation of some key mechanisms. Consider the first-order condition for an agent’s choice of a, assuming a well-behaved decision problem over a continuous choice set. By (3), an individual with type (v, μ) who faces a price y equates (4) C^0 (a) = va + vy y + r(a, y; μ),
(^13) In experiments on charitable giving (e.g., Gneezy and Rustichini (2000b)), it is typically emphasized to subjects that any rewards will come from an entirely separate research budget and therefore not reduce the amount actually donated. In the real world, the presence and magnitude of an eviction effect will depend on individuals’ beliefs about the level at which the budget constraint binds and how they value the alternative uses of funds. Suppose, for instance, that a charity has a fixed budget and will use any funds left over to hire “professionals” who produce τ units of a per dollar, or some other public good of equivalent value. An individuals’ valuation of a reward y for his contribution will now be (vy −τ wa/nα)y. This simply amounts to a redefinition of vy , in a way that contributes to making it negatively correlated with va.
no-reward condition ( y^ =^0 )
reward condition adjusted reputation ( y >0 ,) benefit
rewardcondition unadjusted^ (^ y^ >0 ,) reputation benefit
A^ B
C v a
vy
v^ ** a^ ≡ C '( ) a − r a y ( , )
slope -1/y C '( ) a − r a ( ,0) ≡ v^ * a Figure 1: the effects of rewards on the pool of participants
where the last term is his (marginal) reputational return from contributing at level a :
(5) r(a, y; μ) ≡ μa^ ∂E^ (v ∂aa| a, y)− μy^ ∂E^ (v ∂ay^ | a, y).
Three important points are apparent from (4). First, observing someone’s choice of a reveals the sum of his three motivations to contribute (at the margin): intrinsic, extrinsic, and reputational. In general all three vary across people, so that learning about va or vy corresponds to a signal-extraction problem. Second, a higher incentive rate y will reduce the informativeness of actions about va, and the converse for vy. Third, heterogeneity in agents’ image concerns μ represents an additional source of noise that makes inferences about both va and vy less reliable, and that is amplified when actions become more visible (higher x). To gain further insight into the impact of incentives on inferences and behavior, let us now focus on the benchmark case where va and vy are independent random variables, while μa and μy are fixed and omitted from the notation. Figure 1 then shows, for any a > 0 , how the set of agents who contribute at least a varies with the reward y. This group, which we shall term “high contributors”, comprises all agents with
(6) va + vy y ≥ C^0 (a) − r(a, y),
so its boundary is a straight line corresponding to (4), along which agents choose exactly a. The same condition applies when the participation decision is discrete, a ∈ { 0 , 1 }, as will be the case in the second half of the paper, provided we denote C^0 (1) ≡ C(1) − C(0) and r(1, y) ≡ R(1, y) − R(0, y). Along the boundary, agents are now indifferent between participating and abstaining. When no reward is offered, y = 0, the separating locus is vertical: an agent’s contribution reveals nothing
total supply actually declines when a reward y > 0 is introduced, starting from a no-reward situation.
II. The overjustification effect and crowding out
We now turn to the formal analysis, establishing three main results. First, we show how the “overjustifi- cation effect” discussed by psychologists can be understood as a signal-extraction problem in which rewards amplify the noise, leading observers (or a retrospecting individual) to attribute less of role to intrinsic moti- vation in explaining variations in behavior. We then identify the conditions under which monetary incentives crowd out reputational motivation, resulting in a supply curve that is downward-sloping over a potentially wide range, or exhibits a sharp drop at zero. Finally, we assess the effectiveness of non-material rewards such as praise and shame, showing in particular that it is also limited by a form of overjustification effect. We use here a specification of the model that builds on the familiar normal-learning setup. Let actions vary continuously over A = R, with cost C(a) = ka^2 / 2.^15 ⎛ ⎜⎝^ va vy
⎟⎠ ∼ N
⎜⎝v^ ¯a v ¯y
⎢⎣^ σ^2 a^ σay σay σ^2 y
(7) ⎟⎠ , ¯va ≷ 0 , ¯vy > 0 ,
and at first we continue to focus on the case where everyone has the same reputational concerns, μ ≡ (¯μa, ¯μy ). We then extend the analysis to the case where μ is also normally distributed across individuals.^16
A. Material rewards
With fixed μ’s, the reputational return (5) is constant across agents and equal to (8) r ¯(a, y) ≡ μ¯a^ ∂E^ (v ∂aa| a, y)− μ¯y^ ∂E^ (v ∂ay^ | a, y). Thus, by (4), an agent’s choice of a reveals his va + yvy , equal to C^0 (a) − r¯(a, y). Standard results for normal random variables then yield
(^15) The case of a general convex function C(a) is treated in Bénabou and Tirole (2004b). Both here and there, 16 we focus attention on equilibria in which the reputation vector, E^ (v|a, y)^ ,^ is differentiable in^ a.^. As is often the case, normality yields great tractability at the cost of allowing certain variables to take implausible negative values. By choosing the relevant means large enough, however, one can make the probability of such realizations arbitrarily small; but (7) and (17) below should really be interpreted as local approximations, consistent with the linearity of preferences assumed throughout the paper.
(9) E (va|a, y) = ¯va + ρ(y) · (ka − ¯va − ¯vy y − ¯r(a, y)) (10) E (vy |a, y) = ¯vy + χ(y) · (ka − ¯va − ¯vy y − ¯r(a, y)) , where (11) ρ(y) ≡ (^) σ (^2) a + 2σ^2 ayσ^ +^ ayyσ +ay y (^2) σ (^2) y and yχ(y) ≡ 1 − ρ(y). Intuitively, the posterior assessment of an agent’s intrinsic motivation, E (va|a, y) , is a weighted average of the prior v¯a and of the marginal cost of his observed contribution, net of the average extrinsic and reputational incentives to contribute at that level. Finally, substituting (8) into (9)-(10) shows that an equilibrium corresponds to a pair of functions E (va|a, y) and E (vy |a, y) that solve a system of two linear differential equations. Proposition 1 Let all agents have the same image concern (¯μa, μ¯y ). There is a unique (differentiable- reputation) equilibrium, in which an agent with preferences (va, vy) contributes at the level (12) a = va^ +k^ v y^ y+ ¯μaρ(y) − ¯μy χ(y), where ρ(y) and χ(y) are defined by ( 11 ). The reputational returns are ∂E(vy |a, y)/∂a = ρ(y)k and ∂E(vy |a, y) /∂a = χ(y)k, resulting in a net value r¯(y) = k ¡μ¯aρ(y) − μ¯y χ(y)¢^. The effects of extrinsic incentives on inferences and behaviors can now be analyzed. While a higher y increases agents’ direct payoff from contributing, va + vy y, it also tends to reduce the associated signaling value along both dimensions. In the benchmark case of no correlation (σay = 0), for instance, (13) ρ(y) = (^) 1 + y (^21) σ (^2) y /σ (^2) a and χ(y) ≡ (^) 1 +yσ y^2 y 2 /σσ (^2) y 2 a/σ (^2) a , so a higher y acts much like an increase in the noise-to-signal ratio θ ≡ σy/σa, leading observers who parse out the agent’s motives to decrease the weight attributed to social orientation, ρ(y), and increase its counterpart for greediness, χ(y).^17 When σay 6 = 0, a positive correlation tends to amplify the decline in ρ(y), a negative one works to weaken it.^18 Indeed, the more va and vy tend to move together, the less observing
(^1718) More precisely, yχ(y) = 1 − ρ(y) rises with y everywhere, but the same is true of χ(y) only for |y| ≤ 1 /θ. For instance, as the correlation between va and vy rises from − 1 to 0 to 1 , the function ρ(y) pivots downwards over the range 0 < y < 1 /θ , from 1 /(1−θy) to 1 /(1+θ^2 y^2 ) and then to 1 /(1+θy). The effect of σay on the slope χ^0 (y) is more complex, as it depends on σ^2 ay ; the formula is provided in the Appendix.
-2.5 0 2.5 5 7.5 10 12.5 15
50
25
-2.5 -1.25 0 1.25 2.
6 4 2 0 Figure 2a: varying (with 0). The straight line corresponds to (^) a 0 (no reputation concern).^ a^ y
μ μ μ
= =^ y^ a
Figure 2b: varying / (with 0). The lower straight line corresponds toto 0 (standard one-dimensional signaling model). (^) y 0 (no reputation concern), the upper one^ a
μ μ
θ σ σ θ
= = = =
Incentive y Incentive y
Supply a y ( ) Supply a y ( )
situations where time has an opportunity cost, they will actually correspond to substantial values of y.
Proposition 3 (small net incentives and signal-reversal). (1) Small rewards or punishments are counterproductive, ¯a^0 (0) < 0 , whenever
¯vy k <^ μ¯a
μ (^) σay σ^2 a
à (^) σ 2 y −^2 σ^2 ay /σ^2 a σ^2 a
(2) Let μ¯y > 0 and assume that va and vy are uncorrelated, or more generally not too correlated. Then, as σa/σy becomes small, the slope of the supply function at y = 0 tends to −∞. (3) Suppose that participation entails a unit opportunity cost with monetary value y.ˆ Then ¯a^0 (ˆy) < 0 and ¯a^0 (ˆy) → −∞ under the conditions stated in (1) and (2) respectively.
The first term on the right-hand side of (16) reflects the intuition given earlier about the role of correlation in generating crowding out -or in. Most important is the second term, whose dependence on the noise-to- signal ratio is illustrated in Figure 2b: letting σay = 0, for instance, shows that ¯a^0 (0) = ¯vy /k − ¯μy(σy /σa)^2. Thus, when individuals’ desire for money becomes much more uncertain (to observers) than their motivation for the specific task at hand, and even if they have only a minimal concern about appearing greedy (μ¯y is small), the supply response becomes discontinuous (downward) at zero. The intuition for why “zero is special” is that, at that point, participation switches from being an “unprofitable” to a “profitable” activity and thus comes to be interpreted as a signal of greed rather than disinterestedness. This signal reversal effect, operating specifically around a zero net reward, creates an additional source of crowding out on top
of the general signal-jamming effect (decrease in ρ(y) ) that was shown to operate at all levels of y.^20 If the empirical validity of this signal reversal was restricted to very small prizes and fines, it would be of somewhat limited interest. The third result, shows, however, that the relevant “tipping point” is not really zero (except in laboratory experiments, where subjects, once there, have no profitable alternative uses of their time) but agents’ monetary value of time, which can be quite substantial.
B. Image rewards
Public authorities and private sponsors aiming to foster prosocial behavior make heavy use of both public displays and private mementos conveying honor or shame. Nations award medals and honorific titles, char- itable organizations send donors pictures of “their” sponsored child, non-profits give bumper stickers and T-shirts with logos, universities award honorary “degrees” to scholars, etc. Conversely, the ancient practice of the pillory has been updated in the form of televised arrests and publishing the names of parents who are delinquent on child support, or the licence plate numbers of cars photographed in areas known for drug trafficking or prostitution. Peer groups also play an important role by creating a rehearsal mechanism: if acquaintances all contribute to a cause, one is constantly reminded of one’s generosity, or lack thereof.^21 Formally, greater publicity or prominence corresponds to a homothetic increase in (μa, μy ). Our model then confirms the above intuitions, but also delivers important caveats. In particular, when agents are heterogeneous in their reputational concerns, giving greater scrutiny to their behavior may not work that well, as good actions come to be suspected of being image-motivated. To analyze these issues we now allow agents’ image concerns, like their valuations, to be normally distributed: ⎛ ⎜⎝^ μa μy
⎟⎠ ∼ N
⎜⎝μ^ ¯a μ ¯y
⎢⎣^ ω^2 a^ ωay ωay ω^2 y
(17) ⎟⎠ , μ¯a ≥ 0 , ¯μy ≥ 0 ,
with v and μ independent. In the first-order condition (4), the reputational return r(a, y; μ) is now also normal and independent of v (conditionally on a), with mean r¯(a, y) given by (8) and variance
(^20) When the two effects are combined it is easy to get supply curves that have a sharp local minimum 21 at y^ = 0,^ so that neither offering rewards (up to a point) nor requiring sacrifices raises supply. People indeed volunteer more help in response to a request to do so, especially when it comes from a friend, a colleague or family (Freeman 1997), whose opinion of them they naturally care about more than that of strangers.
factor, x; the material incentive y remains constant. Aggregate supply is now (22) ¯a(y, x) = ¯va^ +^ ky ·^ ¯vy+ x ¡¯μaρ(y, x) − μ¯y χ(y, x)¢^ , where the dependence on x indicates that all the covariance terms ¡ω^2 a, ωay , ω^2 y^ ¢^ in the original equation (20), corresponding to x = 1, are now multiplied by x^2. A greater visibility of actions (and of any rewards attached to them) thus has two offsetting effects on the reputational incentive to contribute: a) a direct amplifying effect, the sign of which is that of μaρ(y, x) − μyχ(y, x) for an individual and μ ¯aρ(y, x) − ¯μyχ(y, x) on average. For people who are mostly concerned about appearing socially-minded (μa À μy ) this increases the incentive to act in a prosocial manner, whereas for those most concerned about not appearing greedy (μy À μa) it has the reverse effect.^23 b) a dampening effect, as reputation becomes less sensitive to the individual’s behavior, which observers increasingly ascribe to image concerns. Formally, the “effective noise” Ω(y, x) increases with x (in any stable equilibrium) and ρ(y, x) and χ(y, x) consequently tend to decrease with it. This tradeoff implies that giving increased publicity to pro- or anti-social behavior may be of somewhat limited effectiveness, even when it is relatively cheap to do. Consider for instance the case where μy is known (ωy = 0), possibly equal to zero. As x becomes large (more generally, xkω^2 a >> 1), equation (20) yields ρ(y, x) ≈
μ (^) σ (^2) a + yσay k^2 ω^2 a
(23) x−^2 /^3. The aggregate social benefit from publicity ¯μaxρ(y, x) thus grows only as x^1 /^3 , implying that it is optimal to provide only a finite level of x even when it has a constant marginal cost, or even a marginal cost that declines slower than x−^2 /^3.^24 Policies by parents, teachers, governments and other principals that rely on the “currency ” of praise and shame are thus effective up to a point, but eventually self-limiting.
III. Honor, stigma, and social norms
The second main issue we explore is that of social and personal norms. We first show how multiple
(^23) We are focussing this discussion, for simplicity, on the “natural” case where ρ and χ are both positive, 24 which occurs as long as σay^ is not too negative; see (19). On the other hand there cannot be full crowding out, namely xρ(y, x) actually decreasing with x : otherwise, by (19) and (20) ρ(y, x) would be increasing in x, a contradiction.
standards of “acceptable” behavior can arise from the interplay of honor and shame, then examine what characteristics of the “market”, such as the distribution of social preferences, the availability of excuses or the observability of action and inaction, facilitate or impede their emergence. For the remainder of the paper we focus on the case of a binary participation decision, A = { 0 , 1 }, in which the notions of honor and stigma are most sharply apparent. Unless otherwise specified (Sections IV.B and IV.C) we also assume that all agents share the same reputational concern μ ≡ (μa, μy ) and the same valuation for money, which we normalize to vy ≡ 1. Their prosocial orientation va, by contrast, is distributed on some interval [v− a , v+ a ].^25 Indeed, whereas two-dimensional uncertainty is essential to the overjustification and backfiring-incentives effects analyzed earlier, it is not needed for most of the other results. This simplification also removes any potential incentive for agents to “burn money” in order to signal a low vy. We again denote r(y) ≡ R(1, y) − R(0, y) and let c ≡ C(1) − C(0). Thus, an agent now participates if va ≥ c − y − r(y) ≡ v a∗(y). To determine the equilibrium threshold of altruism let us define, for any candidate cutoff va, the conditional means in the upper and lower tails: (24) M−^ (va) ≡ E (˜va |v˜a ≤ va) , (25) M+^ (va) ≡ E (˜va |v˜a ≥ va). The first expression governs the “honor” conferred by participation, which is the difference between M+^ (va) and the unconditional mean v¯a. The second one governs the “stigma” from abstention, which is ¯va − M (va). Since both are nondecreasing functions, the net reputational gain M+^ (va) − M−^ (va) and the marginal agent’s total non-monetary return to contributing, (26) Ψ(va) ≡ va + μa^ £M+^ (va) − M−^ (va)¤^ ≡ va + ∆ (va) , may increase or decrease with overall participation, [va, v+ a ]. The slopes of these two functions will play central roles in what follows.^26
(^25) The results generalize to the case where va and vy are independently distributed and reputation bears only 26 on the former (μy^ = 0). Recall also that, in the discussion of Figure 1, it was argued that the reputation for prosociality of contributors may worsen either more or less than that of non-contributors when the separating locus pivots to the left due to the presence of a reward y > 0. Indeed, for any given value of vy (over which one then
