Enforcement of Contribution Norms in Public Good Games with Heterogeneous Populations∗

Ernesto Reuben IZA and Columbia University, e-mail: [email protected] Arno Riedl CESifo, IZA, and Maastricht University, e-mail: [email protected]

Abstract

We investigate the emergence and enforcement of contribution norms to public goods in homogeneous and heterogeneous groups. With survey data we demonstrate that uninvolved individuals hold well-defined yet conflicting normative ideas of fair contributions related to efficiency, equality, and equity. In the experiment, all groups converge towards free-riding in the absence of punishment. With punishment, strong and stable differences in contributions emerge across groups and individuals in different roles. These differences result from the enforcement of different relative contribution norms. Lastly, individuals in different roles largely agree on the enforced norm, even when it entails pronounced differences in earnings.

This version: January 2011

JEL Codes: H41, C92, D63 Keywords: public good, heterogeneous groups, punishment, cooperation, social norms, norm enforcement

∗Financial support from the Dutch Science Foundation (NWO) through the “Evolution & Behavior” grant 051-12-012 and from the EU-Marie Curie RTN ENABLE (MRTM-CT-2003-505223) is gratefully acknowledged. 1 Introduction

The need for cooperation among people with heterogeneous characteristics is an undeniable fact of social and economic life. At the work place, teams are composed of workers who may differ in their productivity, ability, and motivation (Hamilton et al. 2003). Irrigation systems are often jointly used and maintained by farmers with different plot sizes and water needs.1 People also can derive very different benefits from public goods. For example, the elevation of dams along the Mississippi River gives very different benefits to individuals who live close to the river compared to those who live further away. In the international political and economic arena, countries that greatly differ in size and wealth are often confronted with situations that require them to find joint agreements in order to overcome social dilemmas. Sandler and Hartley(2001) discuss this problem in the framework of international military alliances. Other prominent examples of international cooperation include the Kyoto Protocol, which aims to reduce greenhouse gas emissions, fishing quotas for European Union members to mitigate the over-fishing of open waters, and the Global Disease Detection Program spearheaded by the United States that seeks early detection of infectious diseases. As diverse as the above examples seem, they can all be viewed as special cases of a more general public goods problem where the enforcement of cooperation by third-parties is infeasible or very limited (e.g., due to the actions of others being unobservable or as the result of the lack of a supranational institution with coercive power). In such situations, cooperation has to be promoted through other mechanisms, such as informally enforced social norms (Elster 1989; Coleman 1990).2 For instance, Ostrom(1990) describes, among others, the case of fishermen in Alanya, Turkey, who overcame the commons problem through self-devised rules that are defended violently if necessary. The private lobster management in Maine provides another prominent case where it is reported that interlopers (free-riders) of the established self-regulatory system were “discouraged by surreptitious violence” (p. 92, Berkes et al. 1989). More recently, research on decentralized forest management has shown that effective community monitoring and sanctioning

1For instance, in the western states of the United States, family farms dependent on irrigation vary in annual farm sales from below $100,000 to above $500,000 (U.S.D.A. 2004). 2Social norms are a widespread empirical phenomenon (Becker 1996; Hechter and Opp 2001; Posner 2002). Numerous examples of the impact of norms on behavior have been meticulously documented (e.g., Roethlisberger and Dickson 1947; Whyte 1955; Hywel 1985; Sober and Wilson 1997; Gurven 2004). For examples of the role of norms in the use of common resources see Ostrom(1990).

2 is an important factor for institutional success (Ostrom and Nagendra 2006; Coleman and Steed 2009). The importance of social norms for sustaining cooperative behavior in public goods envi- ronments has also been suggested in a number of controlled laboratory experiments.3 However, this evidence is based on homogeneous-group environments and neglects the important fact that people differ. This is a potentially serious shortcoming because people who differ may also ad- here to different norms, which may lead to conflicts and inefficiencies. In this paper, we study the existence, emergence, and informal enforcement of contribution norms in homogeneous and heterogeneous groups. In their seminal paper, Fehr and G¨achter(2000) showed that in homogeneous groups high contributions to the public good are sustained because some people reliably sanction those who contribute less than they do. Such behavior is intuitively appealing and consistent with the enforcement of norms grounded in general fairness principles such as efficiency, equality, and, given that individuals are symmetric, also equity (Konow 2003).4 In heterogeneous groups it is a lot less obvious what contribution norm may emerge, if one emerges at all. Different fairness principles will often stipulate different actions in heterogeneous groups, which makes it less clear what the normatively correct behavior is. For example, even uninvolved individuals might find it hard to unambiguously answer questions such as: should high-income individuals contribute more to the public good even when they benefit equally from it? Such ambiguity in fairness principles is also well known in the public finance literature where it is discussed as the benefit-received versus the ability-to-pay principle (see, e.g. Musgrave 2008). Due to self-serving interpretations of fairness principles (Babcock and Loewenstein 1997) heterogeneity may make it difficult to agree on normatively correct behavior, even if individuals have clear ideas about it. For instance, if people have different tastes for the public good, equal contributions may be preferred by those who derive a lot of pleasure from it, whereas those who enjoy the public good less may prefer a norm with unequal contributions. In contrast to homogeneous groups, the experimental evidence regarding contributions to public goods in

3For recent reviews see Fehr and Fischbacher(2004) and G¨achter and Herrmann(2009). 4Efficiency, equality, and equity considerations are commonly called upon in normative research and have been extensively discussed by philosophers (e.g., Aristotle 1925; Rawls 1971; Corlett 2003). Equality is also commonly invoked in social choice theory as axioms of symmetry and anonymity (e.g., Moulin 1991; Gaertner 2006).

3 heterogeneous groups is much less conclusive,5 and evidence of the enforcement of contribution norms in heterogeneous groups is basically absent.6 In this paper we investigate the emergence and informal enforcement of different contribu- tion norms in a linear public good game when people differ in either their endowment or their preference for the public good. In total, we study three types of group heterogeneity. We look at groups with unequal endowments, where heterogeneity is introduced by providing one person (out of three) with an endowment that is twice as high as the endowment of the other group members. To isolate the effect of extending the contribution possibilities due to a larger en- dowment, in some groups, we restrict the contribution possibilities to be the same for all group members, whereas in others, we allow for contributions up to the entire endowment. In the third type of group heterogeneity all group members have the same endowment but one group member receives a 50 percent higher marginal benefit from the public good. In addition, we also explore homogeneous groups. We analyze data from two sources. First, we use a questionnaire study to examine whether the ideas of uninvolved individuals regarding normatively desirable behavior are related to the various fairness principles mentioned above and whether these ideas are affected by group heterogeneity. Second, we study directly the emergence and enforcement of contribution norms in a laboratory experiment. We implement eight treatments consisting of the four types of groups described above, each with and without punishment possibilities. Hence, our design allows us to isolate the effect of unequal endowments, unequal contribution possibilities, and unequal preferences for the public good on contribution behavior as well as their interaction with sanctioning possibilities within one experimental setting. We find that in both homogeneous and heterogeneous groups, the fairness principles of efficiency, equality, and equity strongly influence what is considered

5Experiments investigating endowment heterogeneity report mixed results. Ostrom et al.(1994), van Dijk et al. (2002), and Cherry et al.(2005) find that inequality leads to lower contributions, Chan et al.(1996) and Buckley and Croson(2006) report a positive effect, and Chan et al.(1999) and Sadrieh and Verbon(2006) no effect. With respect to heterogeneity in the marginal benefit from the public good, Fisher et al.(1995) find that individuals with a high marginal benefit contribute more than those with a low marginal benefit. 6To our knowledge, the only experiment that combines endowment heterogeneity and punishment possibilities is Visser and Burns(2006). They report that among South African fishermen punishment effectively promotes cooperation in both homogeneous and heterogeneous groups. Reuben and Riedl(2009) show that in privileged groups—that is, groups in which one player has a dominant strategy to contribute a positive amount—punishment does not promote contributions as effectively as in homogeneous groups. Tan(2008) finds a similar result for non- privileged heterogeneous groups and Noussair and Tan(2009) report that voting on punishment is not effectively increasing contributions in such groups.

4 normatively desirable behavior. However, unlike in homogeneous groups, uninvolved individuals in heterogeneous groups agree considerably less on which specific behavior is normatively correct. Interestingly, the fairness principle guiding the modal normative belief changes with the type of group heterogeneity. This suggests that normative behavioral rules, that could be the basis of a contribution norm, are not constant across different forms of heterogeneity. In the laboratory experiment, we find that without punishment possibilities, heterogeneity does not matter much. In all groups free-riding is relatively frequent and steadily increases over time. In other words, we do not find evidence for a contribution norm emerging. With punishment, the picture changes drastically. In both homogeneous and heterogeneous groups, contributions are much higher with punishment than without punishment and they do not de- crease over time. More importantly, in line with the observations from the questionnaire study, the contribution patterns differ strongly depending on the type of group heterogeneity. In groups with unequal endowments and unrestricted contribution possibilities, contributions are propor- tional to endowments. In contrast, in groups with unequal endowments but constrained contri- bution possibilities, group members with large endowments do not contribute more than other group members despite the fact that their endowment is twice as large. Likewise, in groups with unequal marginal benefits from the public good, contributions are similar irrespective of the marginal benefits. We show econometrically that contribution patterns do not differ accidently, but are the result of informal enforcement of different contribution norms in the different treat- ments. Interestingly, irrespective of differences in endowments, individuals within group types largely agree on which contribution norm to enforce—even when the norm implies that some individuals benefit relatively more.

2 Design and Procedures

The game used in both the questionnaire study and the experiment is a linear public good game with groups of three players. The game in its basic form consists of a contribution stage in which each player i receives an endowment of yi points. Players simultaneously decide how many points they want to contribute to the public good, ci ∈ [0, c¯i] wherec ¯i is i’s maximum contribution.

Every point contributed to the public good by any group member increases i’s earnings by αi points and every point not contributed by i increases i’s earnings by one point. If αi < 1 for P all i and i αi > 1, then each point contributed increases the sum of earnings in the group but decreases the earnings of the contributing player, which creates a tension between individual and

5 group interest. At the end of the contribution stage each player is informed of the contributions of the other group members and their earnings up to that point, which (for player i) are equal to X πi = yi − ci + αi cj. j We implement four types of groups. The first type is the homogeneous case where each group member i has the same endowment yi = 20 points and receives the same marginal benefit from the public good αi = 0.50. We refer to this group type as Equal. In the remaining group types we introduce heterogeneity. Specifically, in each group, one player receives either a higher endowment or a higher marginal benefit from the public good than the other two players. For convenience we refer to the former as the high player and to the two latter ones as low players.

In the second group type, the high player receives an endowment of yH = 40 points whereas low players get yL = 20 points. Importantly, in these groups contributions are restricted to a maximum of 20 points for all players (i.e.,c ¯L =c ¯H = 20 points). We refer to this group type as the unequal-restricted-endowment type or URE. In the third group type, the high player again receives yH = 40 points and low players yL = 20 points. However, in contrast to URE, the contributions of the high player is only restricted by its endowment (i.e.,c ¯L = 20 points and c¯H = 40 points). We refer to this group type as unequal-unrestricted-endowment or UUE. In the fourth group type, all players receive the same endowment of 20 points but the high player earns a marginal benefit from the public good equal to αH = 0.75 while low players earn αL = 0.50. Correspondingly, we refer to it as the unequal-marginal-benefit group type or UMB. The four types of groups are summarized in Table1. Equal and URE differ only in the higher endowment of one group member. Thus, comparing these groups allows us to isolate the effect of endowment heterogeneity. Moreover, because the contributions of high players are restricted in URE, we can be sure that any observed differences in behavior are due to high players possessing a higher endowment and not due to the capacity to contribute more to the public good. The effect of a higher capacity to contribute can be examined by comparing URE with UUE. Finally, comparing Equal with UMB allows us to investigate the effect of differences in the marginal benefits from the public good for given equal endowments.

6 Table 1: Group types

Group Player’s Parameters Respondents to the Subjects in treatments with

type role yi αi c¯i questionnaire no punishment punishment Equal low 20 points 0.50 20 points 39 21 33 low 20 points 0.50 20 points URE 60 21 33 high 40 points 0.50 20 points low 20 points 0.50 20 points UUE 64 18 33 high 40 points 0.50 40 points low 20 points 0.50 20 points UMB 62 21 30 high 20 points 0.75 20 points

The Questionnaire Study

In order to elicit the normative ideas of uninvolved individuals regarding desirable rules of behav- ior in the public goods game, we conducted an online questionnaire study. Specifically, we asked students from the subject pool of the University of Amsterdam’s CREED laboratory to take part in a 15-minute questionnaire. Importantly, the respondents had experience reading experimental instructions but had not participated in any of our experimental sessions (described below). To increase the response rate, students who participated in the questionnaire had a 2% chance of receiving e100 irrespective of their answers. Each respondent took part in one of four versions of the questionnaire. Each version cor- responds to one of the four group types (i.e., either Equal, URE, UUE, or UMB). At the beginning of the questionnaire, respondents were told that they will be answering normative questions concerning an experiment that had been run in the CREED laboratory. To ensure their understanding, respondents read the instructions seen by the subjects that participated in the experiment and answered a series of control questions. Respondents who did not answer the control questions correctly were not allowed to continue. In total 225 students completed the questionnaire. Table1 contains the number of respondents in each version of the questionnaire. The questionnaire contains two sets of questions. The first set consists of one question asking respondents to specify “what is the fair amount that each of the group members should contribute to the group project? [the public good]”. Respondents indicated a contribution for each group member and could choose any contribution between 0 andc ¯i. The second set corresponds to a series of questions of the form: “what is the fair amount that group member i and group

7 member j should contribute if group member k contributes x tokens to the group project? [the public good]”. Respondents indicated a contribution for group members i and j and could choose contributions between 0 and respectivelyc ¯i orc ¯j. In all questions, respondents are asked to put themselves in the position of a neutral uninvolved arbitrator. Moreover, in the heterogeneous treatments, respondents are reminded of the characteristics of each group member (i.e., their endowment, maximum contribution, and marginal benefit from the public good). The precise wording of the questions can be found in the online appendix.

The Laboratory Experiment

We conducted the laboratory experiment to study the emergence and enforcement of contribution norms when individuals actually interact with each other. Each subject took part in one of eight treatments, which vary along two dimensions: (i) the type of group they are in (either Equal, URE, UUE, or UMB), and (ii) whether or not they have the option to punish other group members. In all our treatments, subjects were matched with the same group of three subjects for ten consecutive periods. Moreover, in heterogeneous groups, subjects were randomly assigned to roles (high or low) at the beginning of the first period and kept the same role throughout the experiment. In treatments where subjects cannot punish each other, they simply play the linear public good game described above. Therefore, their earnings at the end of a period correspond to their earnings after the contribution stage. In the remaining treatments, subjects can punish each other as in Fehr and G¨achter(2002). In these treatments, the contribution stage is followed by a punishment stage in which each subject i simultaneously decides how many punishment points, pij ∈ [0, 10], to assign to each subject j 6= i in the group. Each punishment point costs the punisher one point and reduces the earnings of the punished subject by three points.7 After the punishment stage, subjects are informed of the total number of punishment points assigned to them. As in Fehr and G¨achter(2000, 2002), subjects do not receive specific information

7Subjects can identify other group members through a randomly assigned ID number that remained constant throughout the experiment. Moreover, the values of yi, αi,c ¯i of all group members is common knowledge. We impose an upper limit on the amount of punishment i can assign to each j (as Fehr and G¨achter(2002) and others). This restriction prevents subjects with higher earnings from having the capacity to punish more than subjects with lower earnings (as punishment is funded through their own earnings).

8 concerning who punished whom. In the treatments with punishment, at the end of a period, earnings of a subject i are given by8

X X X πi = yi − ci + αi cj − 3 pji − pij. j j6=i j6=i

The computerized experiment was conducted in the CREED laboratory using the typical procedures of anonymity, neutrally-worded instructions, and monetary incentives. In total, 210 subjects participated in the one-hour long experiment. About half of the subjects were female. Also, around half were students of economics (the other half came from other fields such as biology, engineering, political science, and law). Average earnings equaled e13.83 (≈US$17.50). After arrival in the lab’s reception room, each subject drew a card to be randomly assigned to a seat in the laboratory. Once everyone was seated, the instructions for the experiment were read aloud (a translation of the instructions, which are originally in Dutch, can be found in the online appendix). Thereafter, subjects answered a few questions to ensure their understanding of the instructions. When all subjects had correctly answered the questions, the computerized experiment (programmed in z-Tree, Fischbacher 2007) started. After the ten periods, subjects answered a short debriefing questionnaire and were confidentially paid their earnings in cash.

3 Focal and Conflicting Contribution Norms

If it is common knowledge that all subjects are rational and maximize solely their monetary earnings, all individuals in all treatments are predicted not to contribute to the public good. However, existing experimental evidence from homogeneous groups suggests that: (i) without punishment there is some initial cooperation that decreases to low levels over time (Ledyard 1995), and (ii) with punishment, sanctions are used to enforce high contribution levels that do not decline with repetition (Fehr and G¨achter 2000; G¨achter and Herrmann 2009). On the theoretical side, models assuming other-regarding preferences have been proposed to explain these behavioral patterns.9 Specifically, it has been shown that, with the appropriate assumptions on the strength

8As in Fehr and G¨achter(2002), in order to avoid excessive losses due to punishment by others, subject i in P P P fact earns: πi = max[0, yi − ci + αi j cj − 3 j6=i pji] − j6=i pij . This way, a subject cannot be punished below zero points but must always pay to punish others. 9These include, among others, Levine(1998), Fehr and Schmidt(1999), Bolton and Ockenfels(2000), Charness and Rabin(2002), Dufwenberg and Kirchsteiger(2004), Falk and Fischbacher(2006), and Cox et al.(2007). For an overview and discussion, see Sobel(2005).

9 of other-regarding preferences, social dilemma games are transformed into coordination games with multiple equilibria, most of which include positive contribution levels (see, e.g., Rabin 1993 and Propositions 4 and 5 in Fehr and Schmidt 1999).10 Our main interest is the possible emergence of social norms regarding contribution behavior, which we call contribution norms, in homogeneous groups and in groups with different types of heterogeneity. For that purpose we discuss here what we understand as a contribution norm in the public goods game. In the literature on (social) norms there is, by and large, agreement on the definition of conventions. For instance, Young(2008) refers to conventions as simple rules of behavior that are self-enforcing because they are part of an equilibrium of the underlying game. Similarly, Bicchieri(2006) refers to conventions as a special case of descriptive norms, which function purely as a coordination device. In other words, given the right expectations, everyone follows a convention because it is in each individual’s best material interest to do so. When it comes to the definition of a social norm, views are more divergent. In the tradition of Sudgen(1986) and Coleman(1990), Bicchieri(2006) makes a clear distinction between con- ventions and social norms by arguing that the function of the latter is not to solve a coordination problem but to enforce non-equilibrium behavior in situations where there is a tension between individual and collective material welfare. Although Young(2008, p. 647) agrees that next to “simple rules that are self-enforcing at a primary level” there are also “more complex rules that trigger sanctions against those who deviate”, he takes a different stance by arguing that it is not useful to make a strict distinction between conventions and norms. In his view, the term “norm” can only apply to games with multiple equilibria and, hence, cannot serve as an enforcement mechanism for non-equilibrium behavior. For the public good game, the definition of Bicchieri (2006) is most suitable when assuming narrow self-interest, implying a unique no-contributions equilibrium, whereas the definition of Young(2008) can be applied when assuming that subjects have other-regarding preferences, implying the existence of multiple equilibria. Although there is some disagreement on the precise definition of a social norm, there is largely agreement on the necessary conditions for a norm to exist and on the mechanisms by which a norm is held in place and enforced (Bicchieri 2006; Young 2008). Specifically, for a behavioral rule to be a social norm, the following must hold for sufficiently many people: first, it is known

10With the distribution of other-regarding parameters as assumed in Fehr and Schmidt(1999) their model predicts relatively low contribution levels in all our treatments without punishment. For the treatments with punishment a large number of equilibria, including some with high contribution levels are predicted.

10 that such a behavioral rule exists; second, the involved people are motivated to follow the rule under the condition that (a) it is believed that sufficiently many others also conform to the rule (empirical expectations), and either (b) it is believed that sufficiently many others expect oneself to follow the rule (normative expectations), or (b’) it is believed that sufficiently many others are willing to sanction deviations from the rule (normative expectations with sanctions).11 An important implication of the second part of this definition is that it allows a social norm to exist while not being followed and, hence, not being observed. Only if sufficiently many people have the appropriate expectations about others’ behavior and, if necessary, are able and ready to punish transgressions, an existing social norm will also be followed. In addition, it has to be noted that the existence of a social norm does not imply that all people care with the same strength about norm compliance.12 This implies that even if all involved people have the ‘right’ empirical or normative expectations, actual sanctioning may have to take place in order to make people with a weak inclination toward norm obedience follow the norm.

Hypotheses

We are now ready to formulate hypotheses on the basis of the developed framework. We hy- pothesize that contribution norms have two dimensions related to motivations for which there is mounting evidence indicating they are normatively and behaviorally important. The first di- mension is the maximization of collective welfare (for evidence see, Charness and Rabin 2002;

11This definition is based on the one proposed by Bicchieri(2006), which is in strong accordance with the view of Young(2008) on the necessary elements for the existence and enforcement of a norm. Young(2008) also assumes that people know that a behavioral rule exists because such a rule is an equilibrium strategy of the underlying game. In addition, he defines three mechanisms that are necessary for a norm to be held in place. First, some norms are “held in place by shared expectations” (p. 648), which parallels the above assumption of empirical expectations together with self-enforcement of an equilibrium. Second, norms are enforced “through (...) internalization” (p. 648), which parallels the above assumption of normative expectations (without sanctions). Third, to be held in place, some norms need “the threat of social disapproval or punishment for norm violations” (p. 648), which parallels the above assumption of normative expectations with sanctions. Elster(1989) also defines a social norm in a similar way when he writes that “[for] norms to be social, they must be (a) shared by other people and (b) partly sustained by their approval and disapproval” and “norms are social [in] that other people are important for enforcing them” (p. 99, emphasis in original). 12Ostrom(2000) observes that “social norms may lead individuals to behave differently in the same objective situation depending on how strongly they value conformance with (or deviance from) a norm” (p. 144) and Andreoni and Bernheim(2009) find that subjects in a dictator game experiment adhere with different intensities to the 50-50 division norm (see also, Krupka and Weber 2010).

11 Engelmann and Strobel 2004), which can be thought of as an absolute norm of efficiency that prescribes that one ought to contribute as much as possible to the public good.13 The second di- mension is reciprocity (see, Sobel 2005), which in public goods games translates into conditional cooperation (for evidence see, Keser and van Winden 2000; Fischbacher et al. 2001; Fischbacher and G¨achter 2010) or, in our context, a relative contribution norm, meaning that one should contribute a ‘fair amount’ in relation to what others contribute. What such a fair amount is may depend on the circumstances, which we discuss in detail below. Since collective welfare increases with contributions in all group types, we expect to find support for the absolute efficiency norm in homogeneous as well as heterogeneous groups. How- ever, since social norms are not absolute prescriptions of behavior, such as ‘always contribute everything to the public good’, but instead are to be followed only if sufficiently many others do so as well, we do not expect maximal contributions to be the (only) normatively desirable rule under all circumstances. In particular, in situations where maximum material efficiency is unattainable or when contributing maximally strongly violates conditional cooperation. We also expect support in all group types for a relative contribution norm. Given the sym- metry of homogeneous groups (Equal), we expect respondents to largely agree that the most attractive relative contribution norm is for everyone to contribute an equal amount. In hetero- geneous groups, it is less obvious what the most appealing relative contribution norm will be. Since, an important characteristic of social norms is that they are “local and context dependent” (Bicchieri 2008, p. 229), in heterogeneous groups, normative ideas about the relative contribu- tions of high and low players may depend on particularities that may be interpreted differently by different people. Yet, the literature on fair allocation rules provides two prominent fairness concepts that can be used to discuss the appeal of different relative contribution norms: equality and equity (Konow 2003; Konow et al. 2009). Equality is generally thought of as the equalization of outcomes with no necessary link to individual characteristics such as capacity. In contrast, eq- uity is mostly interpreted as the dependence of fair outcomes—in a proportional way—on effort or individual characteristics such as ability. In Table2, we summarize the relative contribution norms implied by the various interpretations of these two fairness concepts when applied to the group types we investigate. In the following paragraphs we discuss them in turn. If people apply the concept of equality to contributions, then it trivially follows that the

13Since, ex post, public good games have multiple Pareto efficient allocations, we refer here to efficiency from an ex ante perspective.

12 Table 2: Focal and conflicting relative contribution norms

Equality of Equality of Proportional to Proportional to Proportional to

contributions earnings endowments yi capacities c¯ benefits α

Equal ci = cj ci = cj ci = cj ci = cj ci = cj

URE cH = cL cH = 20, cL = 0 cH = 2cL cH = cL cH = cL

UUE cH = cL cH = 20 + cL cH = 2cL cH = 2cL cH = cL

UMB cH = cL cH = 2cL cH = cL cH = cL cH = 1.5cL equal-contributions norm will be the one that is viewed as normatively most attractive in both homogeneous and heterogeneous groups. If instead they apply equality to earnings (as argued by Dawes et al. 2007), then in both URE and UUE, high players should contribute 20 points more than low players, which in URE implies that low players do not contribute at all. In UMB equality in earnings means that high players contribute twice as much as low players. Alternatively, if the concept of equity is applied, then contributions ought to be proportional to some individual characteristic.14 In UUE, proportionality—irrespective of whether it is applied to endowments yi or capacitiesc ¯i—implies a relative contribution norm in which high players contribute twice as much as low players. In the other heterogeneous treatments the possibility of conflicting interpretations of proportionality arises. In URE, proportionality can be applied to endowments, which implies that high players should contribute twice as much as low players, or, consistent with Major and Deaux(1982), it can be applied to the capacity to contribute, which implies that all players should contribute the same. Similarly, in UMB, contributions proportional to marginal benefits αi entail a relative contribution norm in which high players contribute 50 percent more than low players, whereas proportionality with respect to the capacities translates into equal contributions for both roles. In summary, the application of these fairness concepts considerably narrows down the set of relative contribution norms that respondents might find normatively attractive. However, only in homogeneous groups do all concepts lead to one focal relative contribution norm. In heterogeneous groups, the discussed fairness concepts still allow for a variety of normatively appealing rules of behavior making it a priori difficult to predict which one will prevail.

14We do not discuss norms where earnings are the ones that ought to be proportional to endowments, capacities, or benefits. Although, doing this would be possible, it is inconsistent with modern theories of equity that invoke responsibility or accountability as a fairness principle (see Konow 1996).

13 The knowledge of one or more normatively appealing rules of behavior in public good games is only a necessary condition for a contribution norm to be observed in an experiment. In addition, a contribution norm has to be followed. As pointed out by Bicchieri(2006) and Young(2008), this may happen without sanctioning if the empirical and normative expectations are strong enough. However, given the existing evidence on public good games without punishment, we do not expect this to be the case. Even with similar expectations regarding the contribution norm that applies, individual differences regarding the willingness to comply with the norm together with the nonexistence of an effective tool to sanction norm violators, it is to be expected that low contribution levels will be observed. Since, we have no a priori reason to assume that the willingness to comply with norms varies with a groups’ type, we expect relatively low and decreasing contribution levels in all groups without punishment. In other words, without punishment we do not expect to observe contribution norms. If it is possible to punish others we expect to see—in concordance with evidence from homoge- neous groups public goods experiments—higher and stable contributions in all group types. Fur- thermore, we expect that (some) subjects use sanctions to (try to) enforce the absolute efficiency norm as well as a relative contribution norm. It is impossible to predict the precise contributions level because subjects are likely to differ in their willingness to comply with norms as well as their willingness to sanction norm violators. However, we can make some predictions concerning punishment patterns. Since higher contribution levels are more efficient in all group types, the existence of the absolute efficiency norm predicts that deviations from the maximum contribu- tion will be punished similarly in all group types. Furthermore, based on the above discussion of possible relative contribution norms, in homogeneous groups we expect that punishment will be used to (try to) make all group members contribute the same amount. In heterogeneous groups, we expect punishment to be in accordance with relative contribution norms based on equality or equity, but due to the multiplicity of attractive relative contribution norms, it is difficult to tell theoretically which specific norm will emerge, if a unique norm emerges at all. We can note, however, that in our experiment heterogeneous groups are composed of two low players and only one high player. Therefore, if individuals interpret fairness concepts in a self-serving manner (for evidence see, Babcock and Loewenstein 1997), then the higher joint punishment capacity of low players might make relative contribution norms that favor low players more likely.

14 4 Empirical results

This section consists of two parts. In the first part (Section 4.1), we analyze our questionnaire study to explore whether individuals uninvolved in the experiment have ideas of normative rules of behavior applicable in our public good games. In addition, we seek an answer to the following two questions. Are the elicited normative rules related to the fairness principles discussed in the previous section? And, do they coincide across the different group types? In the second part (Sections 4.2, 4.3, and 4.4), we study the behavior of people involved in the public good experi- ment. We first analyze the contributions to the public good in all treatments with and without punishment. We concentrate on the behavior of high and low players and on whether players in different roles display different contribution patterns in the different treatments. Thereafter, we investigate econometrically the enforcement of contribution norms through punishment. Lastly, we analyze the effects of enforcement on earnings.

4.1 Normative rules of behavior

A necessary condition for a contribution norm to exist is that such a behavioral rule is known (see Section3). To find out whether this is the case, we use the answers to the questionnaire study as they reflect the normative ideas of how one ought to behave in the various group types and roles. In particular, we are interested in knowing (a) whether and to what extent people allude to the absolute efficiency norm, (b) whether any of the relative contribution norms discussed in Section3 play a role in the respondents’ normative judgments, and (c) whether these contribution norms depend on the type of group heterogeneity. To investigate whether respondents adhere to the absolute efficiency norm, we analyze the first question of the questionnaire. In this question, respondents state what the fair contribution to the public good is for each of the three group members (see Section2). We find that in all group types the modal answer is for all group members to contribute as much as they can. Specifically, in Equal, 59 percent of the respondents say that contributing fully is the normatively fair rule. Interestingly, in the heterogeneous groups this percentage decreases to 50, 39, and 31 percent in URE, UUE, and UMB, respectively. A likelihood ratio χ2-test shows that the differences across group types are statistically significant (p = 0.022).15 In all group types, almost all deviations from efficiency are consistent with one of the relative

15Pair-wise comparisons reveal that, compared to Equal, the reported percentages are significantly smaller in UUE and UMB (p ≤ 0.049). This percentage is also smaller in UMB compared to URE (p = 0.029).

15 contribution norms described in Section3. In Equal, 38 percent of the choices are not efficient but are consistent with a norm of equality of contributions, which implies that only 3 percent of all choices are inconsistent with either the absolute efficiency norm or one of the discussed relative contribution norms. In heterogeneous groups, the percentage of choices inconsistent with any of the discussed contribution norms increases slightly but is still quite low: 8 percent in URE, 9 percent in UUE, and 15 percent in UMB. We also find that the percentage of choices consistent with each of the relative contribution norms varies across group types. Of all inef- ficient choices, between 12 percent (UMB) and 36 percent (UUE) are consistent with equality of contributions, between 23 percent (UMB) and 50 percent (URE) with proportionality with respect to endowments/benefits, and between 13 percent (UUE) and 44 percent (UMB) with equality of earnings. Hence, the data confirm that the absolute efficiency norm is an important normative rule of behavior. However, a substantial number of respondents perceive other contributions as normatively more appealing, and an overwhelming majority of these contributions is consistent with the relative contribution norms discussed in Section3. It is important to note that the absolute efficiency norm coincides with different relative contribution norms in the different group types, which makes it impossible to disentangle the weights given by respondents to the various relative contribution norms. To deal with this problem, we use the answers to the second set of questions, which were designed to exclude fully- efficient outcomes. As described in Section2, we asked respondents to indicate the normatively fair contributions of i and j given that k contributes ck < c¯k points to the public good. We varied k’s type (either high or low) and the amount ck so that the discussed relative contribution norms can be identified as clearly as possible in each group type (see the online appendix for the specific questions and answers used to identify each norm). Table3 presents for each group type the fraction of answers that coincides with the discussed relative contribution norms.16 For completeness, it also reports the percentage of answers con- sistent with the absolute efficiency norm (interpreted as choosing ci =c ¯i and cj =c ¯j irrespective of ck) as well as the percentage that is not consistent with any of the discussed norms. Lastly, in cases where various norms inevitably overlap (as they do in Equal), we assign the answers to the equality of contributions norm and leave the others blank. As can be seen in the table,

16Note that we do not differentiate relative contribution norms based on proportionality to capacities,c ¯, since they coincide with equality of contributions in Equal, URE, and UMB and with proportionality to endowments in UUE (see Table2).

16 Table 3: Normatively perceived contribution norms Note: Fraction of answers to the second set of questions in the questionnaire study that coincides with the contribution norms discussed in Section3. In group types where various norms inevitably overlap answers are assigned to the equality of contributions norm.

Group Equality of Proportional to Proportional to Equality of Efficiency Other type contributions endowments benefits earnings Equal 0.74 – – – 0.13 0.13 URE 0.32 0.24 – 0.14 0.03 0.27 UUE 0.12 0.36 – 0.26 0.02 0.24 UMB 0.16 – 0.24 0.29 0.00 0.31 when fully efficient outcomes are unattainable, the attractiveness of the absolute efficiency norm decreases strongly. In Equal only 13 percent of the respondents perceive the absolute efficiency norm as the most attractive rule of behavior. In heterogeneous groups this percentage drops to between 0 percent (UMB) and 3 percent (URE). A second noteworthy observation is that a large majority of respondents indicate contributions that are consistent with at least one of the discussed relative contribution norms: between 69 percent (UMB) and 74 percent (Equal). This is clear evidence that the relative contribution norms based on equality and equity are strong focal rules of behavior. As hypothesized in Section3, in homogeneous groups there is widespread agreement on the relevant relative contribution norm: 74 percent of the respondents think that equal contributions are normatively fair. In contrast, in heterogeneous groups we observe less agreement on the normatively correct way to behave: the most-commonly chosen norm accounts for 36 percent of all answers. As before, we also observe clear differences in the relative attractiveness of the focal rules of behavior across the different group types. While in URE more than 30 percent think that everybody should contribute equally, only 12 percent apply this rule in UUE. Conversely, the modal perception in UUE is that contributions ought to be proportional to the (unequal) endowments, whereas in URE only 24 percent subscribe to this view. Lastly, in UMB the reported normative ideas are most diverse. The modal relative contribution norm is for contributions that equalize earnings, implying that the high player contributes twice as much as the low player. However, a relatively large fraction of 31 percent reports contributions that do not fit into any of the discussed relative contribution norms. It seems that unequal benefits from the public good provide a less salient clue on which to base a normative rule of behavior than unequal

17 endowments do. A likelihood ratio χ2-test rejects the hypothesis that the distribution of relative contribution norms is the same across the three group types (p = 0.049). In summary, relative contribution norms based on equality and equity explain the majority of the normative rules of behavior favored by our respondents. However, only in homogeneous groups there is consensus on how one should behave. Moreover, the most favored normative rule varies with the type of group heterogeneity. Given this plurality of normatively attractive behavioral rules in heterogeneous groups, at the outset, it is not clear whether behavior consistent with any of the discussed contribution norms will be observed when people are not uninvolved but have stakes to gain or lose. This is explored in the next sections where we examine the contribution rates and punishment behavior of subjects in our experimental sessions.

4.2 Contribution rates

Without punishment, contributions in Equal show the commonly-observed decreasing pattern after initially positive contributions. The Spearman rank-order correlation between mean group contributions and periods is significantly negative (ρ = −0.584, p ≤ 0.001). In each of the heterogeneous group types, we observe a similar decreasing pattern for both low (ρ ≤ −0.373, p ≤ 0.003) and high players (ρ ≤ −0.315, p ≤ 0.008). Table4 reports the average contributions across all periods depending on the treatment and the subjects’ role. Any emerging contribution norm should be reflected by persistent differences in behavior. Therefore, we also report the averages for the second half of the game. Given that high players have twice the endowment of low players in URE and UUE, and a 50 percent higher marginal benefit from the public good in UMB, it is reasonable to expect that their contributions will be higher than those of low players. Surprisingly, the descriptive statistics for treatments without punishment (see first two rows labeled low and high in Table4) show only small differences in their average contributions. On average, high players contribute slightly more than low players, but as can be seen from the contributions in the last five periods, the difference decreases over time (in UUE it even reverses). This visual impression is corroborated by nonparametric statistical tests.17 Taking all periods into account, Wilcoxon signed-rank tests (henceforth WSR tests) do not detect a statistically significant difference in contributions between high and low players in URE and UUE (p > 0.128), and only a weakly significant difference in

17Throughout the paper, the units of observation used in nonparametric tests are group means (for the relevant subject type and periods).

18 Table 4: Descriptive statistics Note: Average contributions and punishment points given depending on the subjects’ role and treat- ment. Averages are calculated for all periods and for the last five periods. Standard deviations using group averages as the unit of observation are in parentheses.

All periods Last 5 periods Equal URE UUE UMB Equal URE UUE UMB without punishment 4.21 6.81 7.48 8.63 2.23 4.24 5.18 6.71 low (2.00) (2.97) (5.94) (4.96) (2.11) (2.52) (5.50) (5.08) Contributions – 9.41 9.05 9.87 – 5.63 4.10 7.77 high – (3.94) (7.42) (5.18) – (4.22) (4.29) (7.18) with punishment 16.22 15.68 15.39 12.21 16.87 15.58 16.44 12.24 low (2.88) (3.26) (4.63) (5.16) (3.62) (4.87) (4.78) (5.95) Contributions – 15.32 28.31 14.59 – 15.96 30.22 14.34 high – (5.31) (10.27) (5.61) – (5.62) (10.14) (6.47) 0.51 0.40 0.30 0.45 0.38 0.42 0.19 0.53 low→low (0.36) (0.50) (0.41) (0.37) (0.39) (0.72) (0.33) (0.47) – 0.88 0.66 0.69 – 0.86 0.42 0.71 low→high Punishment – (0.96) (0.63) (0.79) – (1.15) (0.63) (0.87) – 0.48 0.72 0.71 – 0.41 0.45 0.46 high→low – (0.55) (0.70) (0.60) – (0.64) (0.74) (0.39)

UMB (p = 0.051). In the last five periods, the contributions of high and low players are not only considerably lower but are also statistically indistinguishable from each other (WSR tests, p > 0.205). Table4 also reveals that mean contributions across group types are very similar. Kruskal-Wallis tests comparing the contributions of each player role across all treatments without punishment do not reject the hypothesis that contributions are drawn from the same distribution (p = 0.409 for low players and p = 0.797 for high players; in the last five periods the respective p-values are p = 0.374 and p = 0.711). Furthermore, in all group types contributions decrease over time towards zero,18 and as a consequence, by the last five periods, there are no statistically significant differences in con- tributions. In other words, despite the fact that the absolute efficiency norm is embraced by

18For example, in the last period, a supermajority of at least two-thirds of the subjects contributed nothing to the public good in all group types: 76.19% in Equal, 71.43% in URE, 88.89% in UUE, and 66.67% in UMB.

19 uninvolved individuals (Section 4.1), if there are no punishment opportunities we do not observe behavior consistent with this norm in either homogeneous or heterogeneous groups. Instead, (almost) full free-riding emerges as the prevalent form of behavior. When punishment is possible no significant decline in the contributions of either high or low players in either group type is observed (Spearman rank-order correlation coefficients for low players ρ ≥ 0.022 and high players ρ ≥ 0.035). Consequently, overall contributions tend to be higher than in the treatments without punishment. However, the size of this increase varies considerably across group types. For instance, the contributions of low players go up by 12.01 points in Equal but only by 3.58 points in UMB. Similarly, the contributions of high players increase by 19.26 points in UUE but only by 4.72 points in UMB. Using Fligner-Policello robust rank order tests (henceforth RRO tests), we find that the introduction of punishment leads to a significant increase in the contributions of high and low players in all group types (p ≤ 0.030) except for low players in UMB (p = 0.074). Introducing punishment opportunities has a strong differential effect on the contributions of high and low players, with interesting differences across group types. In URE, high and low players contribute almost the same amount: 15.32 vs. 15.68 points on average (WSR test, p = 0.789). This stands in stark contrast to UUE where the mean contribution of high players is almost twice as high as that of low players: 28.31 points vs. 15.39 points (WSR test, p = 0.003). In UMB, we observe that high players contribute a bit more than low players: 14.59 vs. 12.21 points (WSR test, p = 0.114). The differential effect of punishment is also reflected in a clear difference in the behavior of high players across group types. A Kruskal-Wallis test rejects the null hypothesis that the contributions of high players are drawn from the same distribution (p = 0.002). Pair-wise comparisons reveal that the contributions of high players in UUE are significantly different from those of high players in URE and UMB (RRO tests, p ≤ 0.001). In other words, punishment has the strongest effect on the behavior of high players in UUE. In this group type, high players contribute about six times more with punishment than without punishment, whereas in the other two group types there is ‘only’ a two- to threefold increase in contributions. In contrast, the contributions of low players are very similar across all group types (including Equal). For low players, a Kruskal-Wallis test does not reject the null hypothesis that contributions come from the same distribution (p = 0.241).19

19All the reported significant differences also hold if we concentrate only on the last five periods. The same is true for differences that are not statistically significant except that high players in UMB contribute significantly more than low players (WSR test, p = 0.047).

20 These results suggest that subjects are following different contribution norms in the different group types. Despite the multiplicity of possible contribution norms in heterogeneous groups and the variety of normative ideas found in the questionnaire there are clear contribution patterns emerging, when punishment is possible. First, the strongly increased contributions suggest a role for the absolute efficiency norm in all group types. Second, the distinctive differences in contributions between group types and player roles point toward the importance of different relative contribution norms. In URE, contributions are consistent with a norm of equality of contributions. In UUE, behavior is consistent with a norm of contributions proportional to endowments. Note that all these norms, if applied to the homogeneous case, imply that everyone should contribute the same amount. In UMB, the relative contributions of high and low players are somewhere in between with high players contributing slightly more (around 20%). Given that in treatments without punishment contributions are very similar across group types and roles, it is likely that the differences we observe in treatments with punishment are the result of differences in punishment behavior. In particular, subjects might be using punishment to enforce different contribution norms in the different group types. In the following section we explore precisely this conjecture.

4.3 Punishment and the enforcement of heterogeneous norms

In Table4 (bottom panel), we show the average number of punishment points assigned to each other subject depending on the role of the punishing and the punished subject. We do not observe large differences between group types or roles. Kruskal-Wallis tests do not reject the hypothesis that punishment points are drawn from the same distribution for all group types, irrespective of whether we look at overall punishment (p = 0.966), punishment from low players to low players (p = 0.319), low players to high players (p = 0.910), or high players to low players (p = 0.541). Similarly, we do not find significant differences within each group type in the amount of punishment given or received by high and low players (WSR tests, p > 0.140). The lack of significant differences in the amount of punishment across group types and roles indicates that the differences in contributions are not due to the quantity of punishment applied. It rather suggests that these differences are the result of different ways in which punishment is used. In order to analyze the way in which subjects punish, we build on our discussion in Section3 where we hypothesize that normative ideals in public good games are guided by a concern for collective material welfare (i.e., an absolute efficiency norm), and conditional cooperation (i.e., a relative contribution norm). Testing whether subjects punish deviations from an absolute

21 efficiency norm is simple since any contribution below the maximum contribution constitutes such a deviation. By contrast, evaluating whether subjects also punish deviations from a relative contribution norm is not as straightforward. In homogeneous groups, where there is consensus on the type of behavior that is normatively desirable, it seems reasonable to assume that individuals will punish deviations from equal contributions. In heterogeneous groups, where a variety of normative ideas regarding fair contributions prevail, this assumption would not be justified. In principle, one could assume a specific motivation for punishment (e.g., enforce contributions proportional to endowments) and then use it to make treatment comparisons. However, given the plurality of relative contribution norms, we opt for a more flexible empirical approach. Namely, we elicit the relative contribution norm that is most consistent with the observed punishment data, without imposing any a priori restriction on the potentially enforced norm.20 In order to elicit relative contribution norms, we assume that, ceteris paribus, subject i pun- ishes j depending on how much their contributions differ according to the following expression:

(1−µ)cj −µci, where the term µ ∈ [0, 1] captures the relative contribution norm used to compare one’s contribution to those of others. For example, if µ = 0.50 = 1 − µ then the above expression is negative if (and only if) cj < ci, which from i’s perspective implies a negative deviation from the norm by j. Alternatively, if µ = 0.75 and therefore 1 − µ = 0.25 then subject i considers that a negative deviation from the norm occurs when cj < 3ci (i.e., the norm prescribes that j should contribute three times as much as i). In the extremes, if µ = 0, the norm prescribes that i contributes everything and j contributes nothing, and vice versa if µ = 1. In Equal, as subjects are in symmetric positions, we estimate one value for µ. In the heterogeneous treat- ments, we distinguish between roles and estimate a value for µ in each of the following cases: high players punishing low players (µH→L), low players punishing high players (µL→H ), and low players punishing low players (µL→L).21 Specifically, we estimate the following model in each group type:

20Our approach is similar to that of Carpenter and Matthews(2008), who elicit norms in public good games with homogeneous groups. They find that the best description of the data is attained with a norm akin to our absolute efficiency norm. However, they do not consider, as we do, that subjects might be punishing due to both efficiency and reciprocal motivations. 21Since there is only one high player, there is no punishment of high players to other high players (µH→H ).

22 H→L H→L  H→L H→L  H→L  H→L H→L  pijtk = βpos max (1 − µ )cjt − µ cit, 0 + βneg max µ cit − (1 − µ )cjt, 0 H→L + λ(¯cj − cj) + γ + ηk + υi + ijt L→H L→H  L→H L→H  L→H  L→H L→H  pijtk = βpos max (1 − µ )cjt − µ cit, 0 + βneg max µ cit − (1 − µ )cjt, 0 L→H + λ(¯cj − cj) + γ + ηk + υi + ijt L→L L→L  L→L L→L  L→L  L→L L→L  pijtk = βpos max (1 − µ )cjt − µ cit, 0 + βneg max µ cit − (1 − µ )cjt, 0 L→L + λ(¯cj − cj) + γ + ηk + υi + ijt.

H→L The variable pijtk is the amount of punishment points assigned (not inflicted) by a subject L→H i in the high role to a subject j in the low role in period t and group k. The variables pijtk L→L and pijtk are analogously defined. The first two terms in each equation capture the effect of deviations from the relative contribution norm µH→L, µL→H , or µL→L. As can be seen, by estimating two coefficients for each norm, we allow for the possibility that positive and negative deviations from the norm are punished with different intensities. The third term in the equations,

(¯cj − cj), is simply the amount of points j did not contribute to the public good, which captures the effect of deviations from an absolute efficiency norm. Note that we estimate the same λ in all equations as an absolute efficiency norm ought to be applied equally by high and low players. H→L L→H L→L Finally, γ , γ , and γ , respectively, corresponds to the constant in each equation, ηk to group dummy variables, υi to unobserved individual characteristics, and ijt is the error term. Given that punishment is bounded by zero and ten, we use Tobit estimates. Furthermore, we treat the unobserved individual characteristics as random effects. In order to be consistent with our definition of norms, we assume that deviations from the norm have a positive effect on punishment (i.e., we restrict the values of all β’s as well as that of λ to be greater than or equal to zero). To find the combination of µ’s that best explains the data, we repeatedly estimate the model until—using the simplex method developed by Nelder and Mead(1965)—we find the values of µH→L, µL→H , and µL→L (rounded to two decimal points) that give the best fit.22 Note that we do not restrict the values of the different µ’s to be consistent with a mutually-shared contribution norm. In other words, we allow for cases where low players are punishing high players according to one norm, whereas high players are punishing low players according to another norm. In all

22We estimate the model using one regression and interaction variables to separate the coefficients that vary across the three equations. We use the log likelihood of this regression to measure the fit of a set of µ’s.

23 1.00 1.00

0.75 0.75

0.50 0.50

0.25 0.25 High to low Normalized Log Likelihood Normalized Log Likelihood Low to high Low to low Low to low 0.00 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 µ µ

(a) Equal (b) URE

1.00 1.00

0.75 0.75

0.50 0.50

0.25 0.25 High to low High to low Normalized Log Likelihood Low to high Normalized Log Likelihood Low to high Low to low Low to low 0.00 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 µ µ

(c) UUE (d) UMB

Figure 1: Goodness of fit for different values of µ Note: Log likelihood obtained using different values of µH→L, µL→H , and µL→L. The log likelihood is normalized such that 0 equals the log likelihood of the worst-fitting regression and 1 that of the best-fitting regression. group types, we find a unique combination of µ’s, µ∗H→L, µ∗L→H , and µ∗L→L, that globally maximizes the log likelihood function, which is visualized in Figure1. The figure shows the log likelihood of the estimated model as we vary one of the µ’s keeping the other two µ’s constant at their optimal value. For convenience and the sake of comparison, we normalize the log likelihood such that 0 equals the log likelihood of a regression without a relative contribution norm (i.e., one where all βneg’s and βpos’s are equal to zero), and 1 equals the log likelihood of the regression with the optimal µ’s. The precise values of µ∗H→L, µ∗L→H , and µ∗L→L are available in Table5. In Equal, one can see that the fit of the model has a clear maximum almost exactly at

24 Table 5: Values of µ that best describe the punishment data

Equal URE UUE UMB µL→L µH→L µL→H µL→L µH→L µL→H µL→L µH→L µL→H µL→L All 0.51 0.51 0.50 0.50 0.34 0.67 0.50 0.48 0.51 0.52 Uncooperative groups 0.51 0.51 0.50 0.52 0.34 0.67 0.50 0.44 0.65 0.47 Additional controls 0.51 0.51 0.54 0.52 0.33 0.68 0.50 0.48 0.51 0.51 Low punishers 0.52 0.52 0.50 0.52 0.33 0.67 0.50 0.48 0.51 0.52

µL→L = 0.50, and deviations from this value monotonically worsen the model’s performance. In other words, the best fit is obtained for the µ that implies that subjects should contribute the same amount. In URE we find values for µ∗H→L, µ∗L→H , and µ∗L→L that are all very close to 0.50. That is, low players enforce that high players contribute as much as they do and vice versa, which is consistent with an equality of contributions norm. In stark contrast, in UUE, both high and low players clearly enforce that high players contribute more than low players, and judging by the values µ∗H→L = 0.34 and µ∗L→H = 0.67, the expectation is for high players to contribute twice as much as low players (i.e., in proportion to their endowment). In UMB, we find once again µ∗’s around the 0.50 value, in accordance with an equal contributions norm. This evidence clearly points to the informal enforcement of relative contribution norms as the explanation for the observed differences in the contributions of high players in treatments with punishment. Importantly, the estimated optimal values µ∗H→L and µ∗L→H indicate that both high and low players agree on which relative contribution norm to enforce. Therefore, it is not simply a matter of players in one role using punishment to coerce others to contribute more. Of the possible relative contribution norms (see Table2), an equity-based norm where contributions are proportional to the capacity to contribute explains the data best. However, a reasonable concern with this interpretation of the punishment data may be that the observed values of µ∗H→L, µ∗L→H , and µ∗L→L are not the result of unobservable relative contribution norms but are due to other factors. Therefore, in the following paragraphs we present a series of robustness checks to verify the norm-based interpretation. An alternative explanation for the elicited relative contribution norms is that they are driven by behavior in highly cooperative groups. By design, if a group successfully enforces an absolute efficiency norm, it will exhibit equal contributions by high and low players (around 20 points) in all treatments but UUE, where high players would end up contributing twice as much as low players (40 vs. 20 points). Our punishment data are not entirely consistent with this explanation

25 as we find that deviations from both the absolute efficiency and the relative contribution norm have a significant effect on determining punishment.23 However, it might still be the case that highly cooperative groups are biasing our results. To explore this, we divide groups into cooper- ative groups (those that contribute more than the median group) and uncooperative groups (the rest) and examine the contribution rates and the contribution ratio of high to low players in these subsets of groups. Contributions in cooperative groups are indeed quite close to the maximum contribution (on average 93 percent in URE, 92 percent in UUE, and 86 percent in UMB). In contrast, contributions in uncooperative groups are well below the maximum (on average, 65 percent in URE, 59 percent in UUE, and 44 percent in UMB). Hence, in uncooperative groups high players are not artificially constrained and can in principle contribute substantially more than low players. As expected, in cooperative groups, the ratio of contributions of high to low players is ap- proximately equal to two (1.99) in UUE and is higher than in URE (1.06) and UMB (1.13) where it is close to one. Importantly, we see a similar pattern for uncooperative groups even though contributions in these groups are far from the maximum contribution. In URE, the ratio of contributions of high to low players is again close to one (0.87) and significantly lower than in UUE where it is 1.72 (RRO test, p ≤ 0.011). The average ratio of contributions in UMB is, with 1.49, in between that of URE and UUE, but it displays a larger variance that makes it statistically indistinguishable from either one (RRO tests, p > 0.429). Lastly, if we test, within each group type, whether the ratio of contributions is significantly different between cooperative and uncooperative groups, we find that this is not the case (RRO tests, p > 0.100 in URE, p > 0.278 in UUE, and p > 0.796 in UMB).24 The observed average relative contributions of high to low players in cooperative and unco- operative groups do not support the idea that the differences between group types are a result of highly cooperative groups. This observation is corroborated by the following analysis. If we look for the values of µ∗H→L, µ∗L→H , and µ∗L→L using only uncooperative groups (see Table5), we see that in both URE and UUE the µ∗’s remain practically identical. Interestingly, in UMB, we

23The regression coefficients are found in Table6. We discuss them in detail in subsequent paragraphs. 24The differences in the ratio of contributions of high to low players are stable over time. If we concentrate on the last five periods, the ratio of contributions within each group type is similar in cooperative groups (1.01 in URE, 2.00, in UUE, and 1.10 in UMB) and uncooperative groups (1.02 in URE, 1.70 in UUE, and 1.35 in UMB). Moreover, even among uncooperative groups, it is significantly lower in URE than in UUE, and the ratio in UMB is statistically indistinguishable from those in URE and UUE (RRO tests, p ≤ 0.022 and p > 0.405, respectively).

26 observe a shift in µ∗H→L and µ∗L→H . Among uncooperative groups in UMB, low players punish as if they expect high players to contribute about twice as much as they do, which is consistent with equalizing earnings, whereas high players punish as if they expect to contribute only 25 percent more than low players, which is midway of equal contributions and contributions in pro- portion to the benefit received from the public good. Hence, it appears that in UMB there is less consensus on what the ratio of contributions of high players to low players ought to be. Overall, the elicited relative contribution norms are consistent with the differences in contributions across group types also when only taking uncooperative groups into account. This indicates that the observed differences are not an artifact of the different contribution capabilities. In addition to group cooperativeness, we also checked whether the values of µ∗H→L, µ∗L→H , and µ∗L→L are robust to controlling for other motivations for punishment. Specifically, we include as additional variables in the regressions: the period number to capture strategic motivations such as punishing in early periods to elicit cooperation in latter periods, and a lagged variable for the punishment received in the previous period to capture punishment that might be motivated by revenge (Denant-Boemont et al. 2007; Nikiforakis 2008). As can be seen in Table5, these additional control variables have little effect on the elicited µ∗’s. Lastly, we also check whether our results are driven by the punishment behavior of only a few subjects. To do so, we elicit µ∗H→L, µ∗L→H , and µ∗L→L excluding the 4 subjects in each group type that punished the most. These subjects represent less than 15 percent of all subjects but account for more than a third of all punishment (39% in Equal, 46% in URE, 36% in UUE, and 36% in UMB). By excluding them we check whether other less belligerent subjects are enforcing the same behavior. Once again, we find very similar values for the µ∗’s (see Table5). 25 In addition to establishing which contribution norm is enforced, it is interesting to see how severely subjects punish deviations from the elicited norm. This can be observed in Table6, which reports the estimated coefficients of the regressions using the best-fitting µ’s and the simplest specification (i.e., for the first row in Table5). The regressions for the other specifications are available in the online appendix. To indicate the explanatory power of each regression, the table also shows each regression’s log likelihood and, as a baseline, the log likelihood obtained if we assume that none of the contribution norms is enforced (β’s = λ = 0). It is easy to

25By and large, the µ∗’s are also robust to using Logit estimates and treating punishment as a binary decision (either punish or not). This indicates that, for the purpose of identifying the norms, what matters most is not the amount of punishment but what behavior is or is not punished. The only case in which we see a substantial variation is in UMB where µ∗H→L = 0.42, which is close to the value elicited in that same group type for uncooperative groups. These regressions are available in the online appendix.

27 Table 6: Regressions for the best-fitting contribution norms Note: Coefficients of the best-fitting regressions (i.e., for the first set of µ∗’s in Table5). Tobit estimates with subject random effects and censoring at pij = 0. In addition to the shown coefficients, all regression have group dummies, a constant, and dummies indicating the role of i and j. Standard errors are in parentheses. The symbols ∗,∗∗ indicate statistical significance at the 5, and 1 percent level.

Coefficient Equal URE UUE UMB H→L ∗∗ ∗∗ βpos 0.50 0.12 0.73 (0.17) (0.14) (0.24) H→L ∗∗ ∗∗ ∗∗ βneg 0.56 0.64 0.73 (0.16) (0.16) (0.16) L→H βpos 0.09 0.28 0.06 (0.16) (0.20) (0.16) L→H ∗∗ ∗∗ ∗∗ βneg 0.47 0.43 1.01 (0.17) (0.17) (0.24) L→L ∗∗ βpos 0.27 0.15 0.49 0.40 (0.09) (0.20) (0.27) (0.22) L→L ∗∗ ∗∗ ∗∗ ∗∗ βneg 0.58 0.73 1.18 0.79 (0.13) (0.17) (0.24) (0.17) λ 0.17∗∗ 0.27∗∗ 0.20∗∗ 0.17∗∗ (0.06) (0.06) (0.05) (0.06) # obs. 660 660 660 600 log likelihood –501.86 –437.82 –445.10 –502.70 log likelihood (β’s = λ = 0) –578.02 –528.73 –512.66 –561.37 see that the contribution norms significantly improve the fit of all regressions.26 Moreover, the regressions reveal three important facts. First, the coefficients for negative deviations from the absolute efficiency norm (λ) and the elicited relative contribution norm (the βneg’s) are statistically significant in all regressions. Second, the value of the coefficients is such that in all regressions, free riding is not a profit-maximizing action.27 Third, negative deviations from

26If we use OLS estimates in order to obtain the easily-interpretable R2 statistic, we find that introducing the contribution norms improves the R2 from 0.07 to 0.37 in Equal, from 0.11 to 0.35 in URE, from 0.10 to 0.24 in UUE, and from 0.08 to 0.20 in UMB. 27For example, the linear estimates indicate that reducing one’s contribution by 1 point in Equal increases the punishment received from others by 0.91 points and therefore reduces one’s earnings by 2.72 points. In the heterogeneous groups, the same calculation yields a reduction that varies between 2.04 points (for high players in UUE) and 4.22 points (for low players also in UUE). If one separates the effect of each norm, in all cases the

28 the absolute efficiency as well as the estimated relative contribution norm seem to be punished similarly across treatments. In the case of the absolute efficiency norm, we cannot reject the hypothesis that the value of λ in Equal is equal to its value in the other group types (Wald tests, p ≥ 0.212). Similarly for the relative contribution norm, Wald tests do not reject that the L→L L→L value of βneg in Equal is equal to all of the other βneg’s (p ≥ 0.121) except for βneg in UUE (p = 0.028). This suggests that the motivation to punish negative deviations from norms is by and large independent of the type of group heterogeneity and the individuals’ roles.28 In summary, the absolute efficiency norm is similarly enforced in all group types. Therefore, the observed differences in the contributions of high players in the different group types can be attributed to the informal enforcement of different relative contribution norms. Both high and low players largely agree on the contribution norms that are to be enforced and spend similar amounts of effort punishing deviations from them. Of the possible relative contribution norms (see Table2), the one that is enforced depends on the type of heterogeneity in the group. In URE, both roles enforce a norm consistent with equal contributions, despite the fact that high players’ earnings are (almost) twice as high as low players’ earnings. In UUE, subjects enforce relative contributions proportional to endowments. This holds for highly cooperative as well as uncooperative groups. Finally, in UMB, the enforcement behavior in highly cooperative groups is consistent with an equal contributions norm. However, in uncooperative groups, low players enforce a contribution norm consistent with equal earnings, which is not matched by the enforcement behavior of high players. Hence, the differences in marginal benefits seem to be a weak guide as to which contribution norm ought to be followed.

4.4 Earnings

In the last part of our empirical analysis, we test whether the enforcement of contribution norms in heterogeneous groups increases material welfare. As we have seen, punishment possibilities lead to significantly higher contributions to the public good in all group types. This leads us to hypothesize that earnings are higher with rather than without punishment. For this to be true, absolute efficiency norm accounts for around 35% of the increase in punishment and the relative contribution norm for the remaining 65%. 28Unlike negative deviations, significant punishment of positive deviations from the relative contribution norm, the so-called antisocial punishment (see, Herrmann et al. 2008), is not very common. It occurs only in Equal and in the punishment of low players by high players in URE and UMB.

29 it must be the case that the increase in contributions is enough to compensate for the material loses caused by the costs of giving and receiving punishment. If we look at the average earnings in the last five periods of the game,29 we indeed find that earnings in homogeneous groups are significantly higher with punishment than without: 25.5 vs. 21.1 points (one-sided RRO test, p < 0.001). In heterogeneous groups, the effect of punishment is less clear. In all group types, average earnings are higher with punishment than without: 30.1 vs. 29.0 points in URE, 34.4 vs. 29.1 points in UUE, and 25.4 vs. 25.3 points in UMB. However, if we test for statistically significant differences we find that earnings are statistically higher in UUE (one-sided RRO test, p < 0.050), but not in URE and UMB (one-sided RRO tests, p > 0.380). Therefore, it looks like some heterogeneous groups perform less well in terms of delivering higher earnings. On closer inspection, one can see that this is due to a smaller decrease in the amount of punishment over time in URE and UMB compared to UUE (Spearman’s ρ between punishment points and periods are −0.130 and −0.148 for the former and −0.392 for the latter). This result could be due to subjects taking more periods to settle on one of the (conflicting) relative contribution norms. In this sense, it is telling that punishment increases earnings more in UUE, where there is only a conflict between equality and equity, compared to URE and UMB, where there is an additional conflict between different interpretations of equity.

5 Conclusions

We investigate the existence and informal enforcement of different contribution norms in public good games with homogeneous and heterogeneous groups. We define absolute efficiency and relative contribution norms, where the former prescribes to contribute as much as possible and the latter is defined relative to the contributions of others. According to scholars in social norm research (Bicchieri 2006; Young 2008) a norm is a rule of behavior that exists and can be observed if (a) people have knowledge of such a behavioral rule, and (b) sufficiently many people are following the rule, where the latter can come about through internalized beliefs or through (expected) sanctions in case of a norm violation. To investigate the knowledge of contribution norms we use data from a questionnaire study that elicits individuals’ normative ideas of how much one ought to contribute. In order to explore the actual existence and enforcement of

29As Fehr and G¨achter(2000), we concentrate on the last five periods because they are more representative of long-run earnings. The initial periods are characterized by lots of punishment as the norm is being established.

30 contribution norms we use data from a laboratory public good experiment with and without punishment opportunities. The questionnaire study reveals that uninvolved individuals indeed have clear ideas of what constitutes normatively desirable behavior. For homogeneous as well as heterogeneous groups we find support for both types of contribution norms. The absolute efficiency norm is favored for all group types, especially when full efficiency is feasible. In addition, we find that the prevailing ideas of relative contribution norms are those induced by the fairness concepts of equality and equity. For homogeneous groups, where ideas of equality and equity all lead to the relative contribution norm of equal contributions, we observe a consensus on this normative rule. For heterogeneous groups, while there is consensus that normatively desired contributions should be related to equality or equity, the various possible interpretations of equality and equity lead to considerably less agreement on the specific behavior that is considered normatively correct. In the laboratory experiment, we find that, in the absence of punishment possibilities, contri- butions steadily decline in all group types to the point where the prevalent behavior is (almost) full free-riding. In other words, in spite of there being the strong normative idea of absolute efficiency, we do not see this contribution norm emerging. The ubiquitous trend towards free- riding also dissipates any potential differences between the various forms of group heterogeneity or between individuals with different induced characteristics. In stark contrast, when punishment is possible, contributions are higher in all group types and also exhibit considerable differences in contributions across group types and between players with different roles. We show that the absolute efficiency norm is a guiding principle indepen- dent of group heterogeneity as deviations from full efficiency are similarly punished in all group types. In addition, we provide evidence that the observed differences in contributions of players in different roles and their sanctioning behavior are consistent with the enforcement of differ- ent relative contribution norms. Specifically, in groups with unequal endowments, we find that punishment behavior is consistent with the enforcement of a relative contribution norm that prescribes contributions that are proportional to the maximum feasible contribution. This pun- ishment behavior can be readily reconciled with the normative ideas elicited in the questionnaire. Indeed, despite the fact that there exists a plurality of normative ideas about the fair rule of behavior, the norm that is enforced coincides with the norm that is favored by the (relative) majority of questionnaire respondents. In groups with unequal marginal benefits from the public good, there is a less clear pattern regarding the enforced relative contribution norm. When looking at all groups we find support for

31 an emerging equal contributions norm. However, when looking only at uncooperative groups we find disagreement between high and low players on the relative contributions that are enforced. The latter points to an interesting avenue for future research on contribution norms. Namely, due to insufficient punishment data, we have to assume that players that share the same role within a type of group heterogeneity enforce the same relative contribution norm. However, it is conceivable that different players with the same characteristics will (try to) enforce a different norm. Such an investigation of norm enforcement at the individual group level could build on our work, but it calls for a different design where, for instance, there is considerably more punishment data at the group level. The main messages of our study are, first, that with heterogeneity there exists a plurality of normatively fair rules of behavior that are potential candidates for emerging contribution norms. In this respect, our paper contributes to the recent empirical literature on fairness ideals (e.g. Konow 2003; Konow et al. 2009). However, while the existing studies mainly examine two-person allocation tasks (Cappelen et al. 2007) or bargaining situations (G¨achter and Riedl 2006), we extend this research to the more complex decision problem of contributions to a public good. Second, in spite of the observed plurality of normative rules, those who are involved in the public good game are mostly able to coordinate on a unique relative contribution norm, provided that transgression of the norm can be sanctioned. Third, the enforced relative contribution norm is based on ideas of equality and equity and clearly related to salient features of the environment players are immersed in. In this sense behavior in public good games with heterogeneous groups is no less predictable than the behavior of homogeneous groups. Although, there is one caveat to be made that is suggested by both the larger variety of answers in our questionnaire study and the more ambiguous behavior of experimental groups with unequal benefits from the public good: when the features of the environment allow for too many different normatively-fair contribution rules then the emerging contribution norms of specific groups may be more difficult to predict. Recent theoretical and empirical studies underscore the importance of norms in diverse areas of the economy and society. On the empirical side, Kim et al.(2009) find that norms of depart- mental productivity strongly influences the individual productivity of academics, and Goette et al.(2006) report that group membership increases cooperation and the willingness to enforce cooperative norms in platoons of the Swiss Army. Norms have been found to influence behav- ior even after individuals have moved across societies. For example, Fisman and Miguel(2007) show that norms strongly influence illegal parking behavior of U.N. diplomats in New York, and Guiso et al.(2006) demonstrate how the level of trust exhibited by decedents of immigrants to

32 the United States correlates with the level of trust of the country from which their ancestors emigrated. On the theoretical side, Fischer and Huddart(2008) show that norms can put re- strictions on optimal organizational design. Our study confirms that important differences in behavior between groups can be attributed to the informal enforcement of different norms, and are not necessarily due to collectively different preferences of group members. Moreover, we add to this literature the insight that heterogeneity and salient variations in the environment can shift attention from one focal norm to another, resulting in considerably different outcomes.

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