Social preferences can make imperfect sanctions work: Evidence from a public good experiment

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Social preferences can make imperfect sanctions work: Evidence from a public good experiment Christoph Engel ∗ Max Planck Institute for Research on Collective Goods, Kurt-Schumacher-Straße 10, D 53113 Bonn, Germany

a r t i c l e

i n f o

Article history: Received 21 April 2013 Received in revised form 2 January 2014 Accepted 14 February 2014 Available online xxx

JEL classification: C33 C91 D03 H41 K13 K14

a b s t r a c t Sanctions are often so weak that a money maximizing individual would not be deterred. In this paper I test the hypothesis that imperfect sanctions may nonetheless serve a forward looking purpose if sufficiently many individuals are averse against advantageous inequity. Using a linear public good with centralized punishment, I find that participants increase contributions even if severity had been insufficient to deter a profit-maximizing individual. The more an individual is averse against exploiting others, the less it matters whether punishment was deterrent. © 2014 Published by Elsevier B.V.

Keywords: Imperfect sanctions Punishment Inequity aversion Social value orientation

1. Introduction Elinor Ostrom compressed decades of fieldwork into just five principles. If these principles are respected, chances are that the commons can be preserved. Her final two principles are vigilance and graduated sanctions. Communities who have tried to do away with sanctions entirely have usually not been successful. But many successful communities have frequently had recourse to mild sanctions (Ostrom, 1990). In other areas of social life, sanctions are also frequently imperfect. Crime often goes unnoticed. For instance in most parts of the US, prostitution is a crime. Yet the risk for a prostitute to be arrested has been estimated to be as low as 1:450 (Levitt and Venkatesh, 2007). The police do often not have enough resources to investigate petty crime. Criminal sanctions are rarely so severe that the expected value of committing crime becomes negative. Likewise, as a rule tort only entitles the victim to compensation. If there is only a small risk that the victim will not sue, or will not win in court,1 the expected loss from being sued is below the expected gain from tortious behavior. In this paper I model and experimentally test one reason why imperfect sanctions might not be pointless: a sufficient fraction of

∗ Tel.: +49 228 9141610; fax: +49 228 9141611. E-mail address: [email protected] 1 And if the perpetrator’s gain is a mirror image of the victim’s loss. http://dx.doi.org/10.1016/j.jebo.2014.02.015 0167-2681/© 2014 Published by Elsevier B.V.

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the addressees might hold social preferences. Sanctions might help stabilize the willingness of inequity-averse individuals to do what is in society’s best interest. This is of course not the only reason why imperfect sanctions may help govern behavior. Individuals may not simply compare the gain from deviation with the expected loss from a sanction. They may expect additional social sanctions, like scorn from their peers. They may have moral compunctions. They may consider the socially undesirable act as detrimental to self-esteem. They may be risk averse and therefore weigh the prospect of the sanction more heavily than its expected value. In repeated interaction, initially mild sanctions may serve an educational purpose, and they may signal to loyal members of the community that society cares. I do not mean to say that such alternative explanations are immaterial. All I want to show is that social preferences provide one consistent explanation for the governance effect of imperfect sanction. Sanctions that would be too weak to deter individuals who straightforwardly maximize their utility from non-social preferences may suffice to deter individuals holding social preferences, even if their disutility from outperforming others is small. Imperfect sanctions extend the domain of cooperation to individuals who do not care strongly about others, but who are also not immune to the detriment they inflict on others. For such individuals, even imperfect sanctions deter. I proceed in two steps. I develop a simple model, derived from the canonical formalization of social preferences in Fehr and Schmidt (1999). This model demonstrates that, under ideal circumstances, sanctions are not a precondition for cooperation. Yet this presupposes that all individuals involved are strongly averse against exploiting others, and know all others are. In that case, all they need to end up in the efficient equilibrium is a coordination device. Yet often conditions are not that ideal. At least some members of the group in question may not hold social preferences that are sufficiently pronounced, or preferences of other group members may be uncertain. In that case, society need not shift to the opposite extreme and deter everybody, including selfish individuals. It may suffice to back up weak social preferences by imperfect sanctions. To test whether social preferences make imperfect sanctions instrumental, I use one experimental standard design that has been at the origin of this theoretical model, the linear public good. I entrust an additional anonymous participant with the right to punish the four active members of the current group. With considerable frequency my experimental authorities indeed mete out imperfect sanctions. I also administer a standard test of social preferences (Liebrand and McClintock, 1988). Using this information, I find that the more participants have disutility from advantageous inequity the less it matters for their reactions to punishment whether punishment had been deterrent. The remainder of the paper is organized as follows. Section 2 explains how I contribute to the literature. Section 3 develops the hypothesis. Section 4 presents the design of the experiment. Section 5 reports results. Section 6 concludes with discussion. 2. Existing knowledge This paper aims at bridging two literatures: the relatively small experimental literature on the effectiveness of imperfect sanctions, and the considerably richer theoretical literature on social preferences. There is, of course, an extensive literature on the effects of a punishment option on contributions in a linear public good (for recent summaries see Balliet et al., 2011; Chaudhuri, 2011). This literature shows that contributions are sensitive to manipulations of the severity (Ambrus and Greiner, 2011; Casari, 2005; Egas and Riedl, 2008; Nikiforakis and Normann, 2008) and of the certainty of punishment (Grechenig et al., 2010; Sousa, 2010). Punishers react to the opportunity cost of punishment (Carpenter, 2007). Yet only few papers have explicitly investigated the beneficial effect of sanctions that are too weak to deter a participant determined to maximize payoff. Tyran and Feld (2006) manipulate the expected value of sanctions in a public good. They impose a norm of full contribution. In their exogenous treatments, this norm is either not sanctioned at all, it is enforced by a deterrent sanction, or by a mild sanction that would not deter a money maximizing agent. In their endogenous mild treatment, group members can vote for mild sanctions. In their endogenous severe treatment, they can vote for severe sanctions. They do not find a significant effect of exogenously imposed mild sanctions, while mild sanctions chosen by majority vote have a beneficial effect. They explain the difference by a commitment effect, which translates into a higher willingness of conditional cooperators to make substantial contributions. Putterman et al. (2011) give participants in a linear public good the opportunity to vote for imperfect sanctions. But most of their groups quickly move toward perfect deterrence. The focus of Markussen et al. (2013) is on preferences for central vs. decentral punishment. But they allow both forms of punishment also to be non-deterrent. If non-deterrent sanctions are imposed exogenously, they are less effective than if group members have introduced them at free will. But they are not pointless. Most publications on public good experiments do not derive their hypotheses about the effect of punishment from formal behavioral theory. In principle, a case could be made for punishment reacting to perceived intentions (for models of intentions see Dufwenberg and Kirchsteiger, 2004; Falk and Fischbacher, 2006; Rabin, 1993; from an evolutionary perspective see Carpenter et al., 2004), to violations of exogenous norms (Andreoni and Bernheim, 2009; Dufwenberg et al., 2011), or to violations of efficiency (Charness and Rabin, 2002; Engelmann and Strobel, 2004). Yet to the extent the effects of punishment have been modeled, all papers have assumed that punishees are motivated by inequity aversion (Bolton and Ockenfels, 2000; Fehr and Schmidt, 1999). Markussen et al. (2013) conjecture that the effect of imperfect sanctions might result from some participants holding social preferences. Thöni (2011) uses inequity aversion to explain antisocial punishment. Gürerk et al. (2010) hypothesize Please cite this article in press as: Engel, C., Social preferences can make imperfect sanctions work: Evidence from a public good experiment. J. Econ. Behav. Organ. (2014), http://dx.doi.org/10.1016/j.jebo.2014.02.015

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that punishment may not explain a cooperative equilibrium if players are inequity averse and the setting is such that the current ability to contribute to the public good is a fraction of total earnings from the game. Kosfeld et al. (2009) use inequity aversion to explain under which conditions players will endogenously introduce a punishment option (also see Masclet and Villeval, 2008). The theoretical paper that has started the literature (Fehr and Schmidt, 1999) shows that, if sufficiently many group members are sufficiently averse against inequity and if there is a punishment option, there may exist equilibria where the strongly inequity averse players contribute positive amounts while the remaining players contribute nothing. Yet they are interested in explaining how the second order public good (Heckathorn, 1989; Yamagishi, 1986) is overcome: if inequity averse individuals suffer enough disutility from being exploited, they gain by punishing freeriders. By contrast I am interested in understanding how an imperfect threat with sanctions serves a purpose. This paper makes the following contribution to the literature. From a simple model, I derive the hypothesis that nondeterrent sanctions are effective for inequity averse individuals. The hypothesis is supported in a public good experiment with centralized punishment.

3. Model and hypothesis The prime purpose of sanctions is to overcome a conflict between individual and social rationality. The canonical situation that calls for sanctions thus is a dilemma. The conflict is most pronounced if the resulting game does not have an interior solution and socially desirable behavior is dominated. The classic illustration is a linear public good as in (1). N 

i = e − ci + 

cn

(1)

n=1

In this standard model, i is each group member’s payoff.  is the marginal per capita rate, and determines the profitability of contributions. If N > 1, all players contributing their entire endowment is efficient. Yet if  < 1, keeping the endowment is the best response for a player who holds standard preferences. Now assume all active players hold Fehr–Schmidt preferences (Fehr and Schmidt, 1999), with defined and identical parameters ˛ and ˇ, and all of this is common knowledge. Then utility is given by (2). ui = i −

  1 1 max{j − i , 0} − max{i − j , 0} ˛ ˇ N−1 N−1 j= / i

(2)

j= / i

Provided ˇ > 1 − , this game has multiple equilibria. Group members can coordinate on any level of contributions, including the efficient level ci = e. In the online Appendix I show under which conditions cooperation can even be sustained if preferences are known to be heterogeneous, or if there is preference uncertainty. Now introduce a credible threat with sanctions of severity s for deviations from target contribution level cˆi . This changes (1) to (3). N 

i = e − ci + 

cn − s max{ˆci − ci , 0}

(3)

n=1

Provided s > 1 − , the threat deters. Profit maximizing individuals contribute cˆi . Provided target level cˆi = e is chosen, contributions are efficient. This leads to the essential point: plugging (3) into (2), the critical degree of aversion against advantageous inequity softens. In the presence of imperfect sanctions, a small degree of inequity aversion may suffice to sustain cooperation. In a society with known, identical preferences, the critical condition changes to ˇ > 1 − (/(1 − s)). Sanctions that are too weak to induce profit maximizing individuals to overcome the dilemma suffice to back up positive, but insufficiently strong aversion against exploiting others. Sanctions that would be pointless in a society of selfish individuals are instrumental if they can build on weak aversion against advantageous inequity. In the online appendix I show that, by analogous argument, non-deterrent sanctions also make it easier to sustain cooperation in a society with heterogeneous preferences, or with preference uncertainty. This leads to the hypothesis:

Individuals who are averse to exploiting others are sensitive to sanctions that are too weak to deter an individual determined to maximize profit. Please cite this article in press as: Engel, C., Social preferences can make imperfect sanctions work: Evidence from a public good experiment. J. Econ. Behav. Organ. (2014), http://dx.doi.org/10.1016/j.jebo.2014.02.015

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4. Design Since my hypothesis is derived from a formal model, the straightforward test is an experimental game with an opportunity structure as in (3), i.e. a linear public good with punishment. I use the parameters that are standard in the literature, i.e. e = 20,  = 0.4, N = 4. I prefer centralized over decentral punishment to exclude a confound with positive utility another active group member might derive from sanctioning a free-rider, like revenge (cf. Crosetto et al., 2012; Masclet et al., 2003). I prefer sanctions meted out by an experimental participant over automatic sanctions executed by the computer. Thereby the source of uncertainty is the behavior of another human agent, not a deterministic machine. This is closer to the source of uncertainty in the field. To that end, I randomly assign a fifth player to each group. In every round, this player earns a fixed amount of 1 D . She receives 20 tokens that she may use for punishing any of the active players. If assigned, each token destroys three Taler of the active player’s income. Any token the authority does not use is credited with 0.01 D . If the authority does not use any tokens, she thus earns 1.20 D , the equivalent of 30 Taler. Consequently, I implement a fine to fee ratio of 1:12.2 Interaction is anonymous. After the end of the first round, active group members are informed about the contributions of all other active members, and of punishment points assigned to each of them. They also learn their period income as well as their current total income from the experiment. After the end of the first round, there is a surprise restart with another 10 rounds of the same game. The separate one shot experiment is meant as a manipulation check. If social preferences explain cooperation in this first round of the experiment, I can be sure that results are not driven by the prospect of gains in future rounds. Yet I need panel data to infer the motivating effect of a (perfect or imperfect) threat with punishment from observed behavior. With panel data I can use the experience of having been punished in the previous period as a proxy for the motive I am interested in. To that end, in the second phase of the experiment, participants learn that they will be rematched every round, but that roles are kept constant. I choose a stranger design for reasons of internal and external validity. In terms of internal validity, the stranger design excludes that cooperation is driven by reputation effects. Moreover in the legal applications that motivate this research, judges are unlikely to regularly meet the same defendants. Following the procedure that is standard in the experimental literature (see e.g. Charness, 2000; Montero et al., 2008), participants are assigned to matching groups of 10, but do only learn that they will be re-matched every period, not that matching groups have limited size. This procedure is meant to guarantee independent observations, without inducing participants to try to second guess group composition. Each period, one authority and four active players are randomly matched. While I need variance in punishment policies, it would not be good for my explanatory variable if punishment was chaotic. In the interest of inducing an exogenous norm, at the end of the instructions I therefore inform participants about mean contributions in a structurally similar experiment of myself with a co-author in the same lab (Engel and Irlenbusch, 2010). I communicate this information in the form of a graph.3 My hypothesis expects the sensitivity to non-deterrent punishment to be driven by social preferences. I therefore need a reliable measure of individuals’ social preferences. To that end, I use a standard tool from social psychology, the social value ring measure (Liebrand and McClintock, 1988).4 This test has participants define a series of allocations between themselves and another anonymous participant. Each choice is incentivized. Aggregating these choices I learn participants’ willingness to pay for either not exploiting or, to the contrary, for exploiting others.5 While this design provides a direct test of the hypothesis, I do not implement treatments. I could of course have exogenously fixed or capped the severity of punishment. But that would have meant a different test. Instead of learning whether non-deterrent sanctions are instrumental for participants averse against advantageous inequity, I would have tested whether imperfect sanctions even work if perfect sanctions are technically excluded. More importantly, I am interested in a process hypothesis. I want to test whether social preferences explain the governance effect of imperfect punishment. While I might have randomly assigned participants to different sanctioning regimes, I could not randomly assign social value orientation scores. Social preferences are a personality trait that can only be measured, not assigned. Therefore an econometric approach can anyhow not be avoided. The experiment was conducted in the Cologne Laboratory for Economic Research in 2012. The experiment is programmed in zTree (Fischbacher, 2007). Participants were invited using the software ORSEE (Greiner, 2004). 90 participants, most of them students of various majors, had mean age 25.39. 44.44% were female. Participants on average earned 15.11 D (19.82 $ on the days of the experiment), 14.80 D for active players, and 16.38 D for authorities. I had 3 sessions of 30 participants.

2

Assigning 1 token costs 1 Cent. The active player loses 3 Taler. 1 Taler is worth 4 Cent. For details see the transcription of the instructions in the Appendix. This way, I also follow the lead of Tyran and Feld (2006), who also exogenously induced a contribution norm. 4 For a similar empirical strategy (but a different research question) see Johnson et al. (2009). See the results sections for the precise mapping of social value orientation to inequity aversion. 5 Since my results might also be explained by the individual specific degree of risk aversion, I also administer the standard test by Holt and Laury (2002). Since this variable turns out uninformative, I do not report tests using it. 3

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effect of social value orientation on contributions

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0

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contribution not deterrent

deterrent

zero punishment not included

Fig. 2. Punishment. Markersize indicates frequency.

5. Results 5.1. Manipulation checks Since I do not have treatments, I must first make sure that my experiment has generated data that allows me to test my hypothesis. The left panel of Fig. 1 collects social value orientation scores of active participants. Selfish participants have a score of 0. A score of 45 results if a participant equalizes payoffs to the maximum extent possible. In the Fehr/Schmidt model, this corresponds to ˇ = 1. Participants with a negative score are willing to give up money to increase the distance between themselves and other participants.6 In the model, cooperation is a best response for ˇ ≥ 0.6. This translates into a social value score of 27. In the experiment, 87.5% of all active players had a score below this most optimistic benchmark. I thus have enough variance of social value orientation to use the social value score as an explanatory variable, and enough scores to make imperfect sanctions meaningful. The right panel of Fig. 1 demonstrates the effect of social value orientation on contributions in the public good in the first round. As one sees, the effect is pronounced, and in the expected direction. The visual impression is supported by statistical analysis (OLS, cons 10.093 (0.778), social value score 0.142 (0.037), N = 72, p model 0.0003). I can thus exclude that the effect requires repeated interaction, and thus a shadow of the future. Fig. 2 shows that punishment authorities that have punished at all have sometimes meted out fairly harsh sanctions. Yet in almost half of the cases where there was punishment, it was imperfect (102 vs. 152 cases).7 If I include cases where authorities have not punished an active participant at all, deterrent sanctions are only inflicted in less than 20% of all cases (152 of 792). I thus also have enough variation of punishment and, most importantly, enough non-deterrent sanctions.

6 The ring measure is more encompassing than the Fehr/Schmidt model. The ring measure allows for scores above 45. They imply that a player has a willingness to pay for making an anonymous partner better off even if this means a smaller payoff for herself than for the other player. 7 Punishment deters a selfish participant if s > 12 − 0.6 * contr.

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received punishment

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6

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social value orientation score deterrent

not deterrent

zero punishment not included

Fig. 3. Distribution of punishment by social value orientation. Bubble size indicates frequency. Table 1 Deterrent effect of imperfect sanctions. Model 1 Lagged punishment Punishment was deterrent lpun * ldeterr lpun * svo ldeterr * svo lpun * ldeterr * svo Period Lagged certainty Cons N Individuals Clusters R2 between R2 within R2 overall

***

0.230

Model 2 (0.038)

−0.598*** (0.110) 720 72 9 0.001 0.14 0.101

**

Model 3 *

Model 4 *

0.366 (0.106) 1.094 (1.084) −0.191 (0.124)

0.442 (0.135) 2.559+ (1.217) −0.377* (0.144) −0.015 (0.009) −0.070* (0.026) 0.020+ (0.009)

0.445 (0.133) 2.567+ (1.221) −0.387* (0.141) −0.015 (0.009) −0.071* (0.025) 0.020* (0.009) −0.064 (0.039)

−0.761** (0.173) 720 72 9 0.002 0.149 0.104

−0.751** (0.159) 720 72 9 0 0.171 0.123

−0.330 (0.270) 720 72 9 0 0.174 0.127

Model 5 0.457* (0.138) 1.893+ (1.104) −0.401* (0.148) −0.015 (0.009) −0.069* (0.024) 0.021* (0.009) 2.593 (1.508) −1.225* (0.382) 720 72 9 0.002 0.180 0.105

Standard errors in parenthesis. Linear with individual fixed effects, se clustered for 9 matching groups. lpun: lagged amount of punishment; ldeterr: dummy that is 1 if punishment was deterrent; svo: ring measure score; lagged certainty: # of having received deterrent punishment in the past/# of past periods. *** p < 0.001. ** p < 0.01. * p < 0.05. + p < 0.1.

Punishment can only work as a deterrent if it is sensitive to the degree by which an active participant deviates from the social optimum of contributing her entire endowment. This is indeed the case. Any additional Taler contributed reduces (received) punishment by 0.418 (0.071) Taler. If I only consider participants who have actually been punished, the reduction is 0.608 (0.101) Taler.8 Finally, the effect would be spurious if participants with high social value scores always had been the targets of deterrent punishment. As Fig. 3 shows, this is not the case. 5.2. Effect of imperfect sanctions I now turn to my research question, the nexus between imperfect sanctions and social preferences. As explained in the design section, I use reactions to experienced punishment as a proxy for the motivating effect of the threat of punishment. If my hypothesis is supported by the data, I must be able to show three things: [1] in reaction to punishment participants increase their contributions; [2] the beneficial effect of punishment is also present if punishment was not severe enough to deter a profit maximizing individual; [3] the beneficial effect of non-deterrent punishment is the more pronounced the more the participant is averse against exploiting others.

8 Linear random effects, with standard errors clustered for matching groups. I estimate fixed effects models since the Hausman test turns out significant. Dependent variable is the size of the subtraction from period income. Independent variable is the number of Taler contributed. Standard errors in parenthesis.

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social value orientation score deterrent=0

deterrent=1

Fig. 4. Marginal Effects from Model 3 of Table 1 for Critical Range of Social Value Orientation Scores.

This is exactly what models 1–3 of Table 1 demonstrate.9 The dependent variable is first differences of contributions. The explanatory variables capture experiences the participant has made in the previous period. The model thus measures reactions to experiences. The significant negative constant in Model 1 shows that, on average, participants who have not been punished in the previous period slightly reduce their contributions. By contrast, those who have been punished increase their contributions, the more so the more severe the intervention. This follows from the significant positive coefficient of lagged received punishment. By the design of the experiment the minimum loss from punishment is 3 Taler, so that the negative constant is overcompensated whenever there is punishment. This supports statement [1]. Model 2 controls for the fact that punishment was strong enough to deter a profit maximizing individual.10 In this specification, the additional control variable, and its interaction with the amount of profit lost through punishment, are insignificant. By contrast, the main effect of experienced punishment remains significant and becomes even stronger. Due to the additional controls, this main effect now measures the pure effect of non-deterrent punishment. Non-deterrent punishment induces participants to increase their contributions in the subsequent period, the more so the more it is severe. This supports statement [2]. Model 3 further interacts all variables with the participant’s social value orientation score.11 The effect of experienced punishment remains significant and becomes even stronger. With the additional controls, there is a plausible weakly significant positive effect of punishment being deterrent. Deterrent punishment is even more effective than non-deterrent punishment. Yet this does not hold for Draconian punishment. The main effect of punishment being deterrent is reversed by the interaction effect if the individual has lost more than 7 Taler through punishment.12 Figs. 2 and 3 show that this is not an infrequent event. Most importantly though, for my hypothesis, the interaction between punishment being deterrent and social value orientation is significantly negative. The more a participant is averse against exploiting others, the less it matters for the beneficial effect of punishment whether punishment was strong enough to even deter a profit maximizing individual. Statement [3], and hence my process hypothesis, is supported by the data. In Model 3, the three-way interaction is only weakly significant, but has opposite sign. The negative effect from the two-way interaction is neutralized if punishment was more severe than 3.5 Taler.13 If deterrent punishment is sufficiently severe, participants become more sensitive to it, despite the fact that they are averse against exploiting others. The most appropriate way of interpreting econometric models with interaction effects is analyzing marginal effects. Fig. 4 does so for the critical region of social value orientation scores: the score is positive, but not strong enough to support cooperation irrespective of the threat with punishment.14 The figure collects marginal effects of a one unit increase in punishment on the change of contributions in the subsequent period, split up by the degree of aversion against advantageous inequity. If punishment was deterrent, it has a significant effect on behavior if only social value orientation is positive.

9 In all models, standard errors are clustered at the level of matching groups, taking the possibility into account that observations might be contaminated by earlier experiences, despite the fact that groups are rematched every period. 10 By the design of the experiment, this is the case if the individual loses more than 12 − 0.6 * contribution. If this is the case, the dummy variable has expression 1. For descriptives, please refer to Fig. 2. 11 Given the Hausman test turns out significant, I must estimate fixed effects models. Through mean differencing, the main effect of the social value orientation score drops out since it does not vary over time. Yet all interactions with social value orientation are nonetheless identified. These interaction terms are all I need for testing my hypothesis. 12 2.599/0.377 = 6.894. 13 0.070/0.020 = 3.5. 14 Recall that a social value orientation score of 27 corresponds to ˇ = 0.6 in the Fehr/Schmidt model.

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The more social value orientation is pronounced, the more intensely a participant reacts to an increase in the severity of punishment. If punishment is deterrent, severity and social value orientation are complements. Interestingly, they are substitutes if punishment is not deterrent. The model even predicts a decrease in contributions if punishment increases and the target had pronounced aversion against advantageous inequity, yet with high social value orientation the marginal effect is not significantly different from zero. Actually the marginal effect swaps sign almost precisely when the social value orientation score is so strong that punishment is no longer needed to sustain cooperation. There is, however, a significant marginal effect of imperfect sanctions if social value orientation is positive, but not strong. Imperfect sanctions thus precisely work for that group of participants where theory expected them to matter: participants whose aversion against advantageous inequity is too weak to sustain cooperation without punishment.15 5.3. Robustness checks In the final step, I check the robustness of this result. The significant effect of lagged punishment, plus the interaction terms, could just pick up the time trend. Model 4 of Table 1 shows that this is not the case. If I control for time, results are almost the same. The coefficient of time is insignificant. In criminological jargon, the proxy for sensitivity to punishment is experienced severity. Participants might not take such experiences seriously if they have rarely been punished in the past. Certainty could thus moderate the effect. Model 5 of Table 1 shows that this is not a concern. Results again look very similar if I control for the total number of times that this participant has been punished in the past, divided by the number of past periods, as a proxy for certainty. For an economic and for a statistical reason, one might be skeptical about Model 3 of Table 1. Eventually, the economic reason is not strong given the dependent variable in that model is first differences, and given I estimate a fixed effects model. For both reasons, individual specific differences in the willingness to contribute are anyhow taken into consideration. Yet estimating contribution levels, and controlling for lagged contributions, is another way of checking whether results are sensitive to specification. The statistical concern is more relevant. Strictly speaking, one cannot exclude that controlling for the question whether punishment in the previous period was deterrent creates a dynamic panel. For in deciding whether punishment is deterrent, one must take last period’s contribution into account. As is well known, dynamic panels create the risk of inconsistency. To be on the safe side, model 1 of Table 2 therefore also presents a dynamic panel, with all potentially endogenous explanatory variables properly instrumented. Since this is not a fixed effects model, I can now also estimate the main effect of social value orientation. Model 3 of Table 1 and Model 1 of Table 2 look very similar indeed. Lagged contributions have the expected strong and significant positive effect. Participants are quite likely not to change how much they contribute at all, and if they make a change, the new amount is close to the previous amount. But conditional on this conservative element, all coefficients from Model 3 of Table 1 go through, have the same sign and similar size, and are at least as highly significant. Moreover I find a weakly significant small additional main effect of social value orientation, on top of the idiosyncrasy captured by the lagged dependent variable. The dynamic panel enables a further robustness check. The fact that participants are sensitive to punishment might result from pointing them to the fact that they have themselves been freeriding. A natural definition of freeriding is a contribution below the average of the current group. Model 2 of Table 2 shows that this is indeed an important motive. Participants who have contributed less than the average of their previous group contribute significantly more in the subsequent period. Nonetheless all regressors from Model 3 of Table 1 still go through, and have about the same size. The final robustness check in Model 3 of Table 2 is the structural model corresponding to Model 1 of the same table. In the spirit of the Arellano Bond model, the potentially endogenous variable lagged contribution is instrumented by lagged first differences.16 In this structural model, there is no need to also instrument the fact that punishment was deterrent. The only possible reason for inconsistency originates in lagged contributions, which is part of the structural model and properly instrumented itself. One again sees the same picture. In particular the critical interaction of the fact that punishment was deterrent with social value orientation is highly significant, has the same negative sign and about the same size. Note that in this model social value orientation has a direct and indirect effect on contributions. The indirect effect stems from its importance for lagged contributions.17

15 I find similar results if I replace the dummy variable for punishment being deterrent by an ordinal variable that captures whether punishment was not deterrent at all, very mild, mild, such that a selfish individual would ex post be indifferent, harsh or draconian. With harsh and draconian punishment, the marginal effect of a one unit increase in lagged punishment increases in social value orientation, with all other degrees of punishment it decreases. This additional analysis is available from the author upon request. 16 Through this instrument one loses one period, which explains the smaller N. 17 The structural model may also be used for a further robustness check. Given I implement a stranger design, one might wonder whether punishment has a lasting effect. In a structural model, I can explain current contributions by contributions last round, punishment last round and punishment two rounds ago; contributions last round by punishment two rounds ago, contributions two rounds ago and the difference between contributions 4 and 3 rounds ago (the instrument); contributions two rounds ago by the difference between contributions 4 and 3 rounds ago (the instrument again), and can allow for correlation between all error terms for contributions (to capture potential endogeneity in the dynamic panel). I find a significant direct positive effect of punishment 2 periods ago on contributions 1 period ago, and a significant positive indirect effect of punishment 2 periods ago on contributions now, through contributions 1 period ago. The effect of punishment is thus not only momentary.

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Table 2 Dynamic panel estimation and structural model.

dv: contribution Lagged punishment Punishment was deterrent lpun * ldeterr svo lpun * svo ldeterr * svo lpun * ldeterr * svo Lagged contribution Lagged contribution below average cons

Model 1

Model 2

Model 3

0.396** (0.122) 2.597** (0.849) −0.386** (0.124) 0.013 (0.011) −0.009 (0.007) −0.072*** (0.021) 0.015* (0.007) 0.962*** (0.023)

0.302* (0.119) 1.776* (0.744) −0.282* (0.117) 0.013 (0.011) −0.014* (0.007) −0.058** (0.018) 0.019** (0.006) 1.018*** (0.022) 1.827*** (0.368) −1.660*** (0.501)

0.208*** (0.059) 2.141** (0.710) −0.212* (0.084) 0.039* (0.019) −0.015+ (0.008) −0.064*** (0.015) 0.020* (0.008) 0.712*** (0.059)

−0.294 (0.240)

dv: punishment was deterrent Lagged contribution Lagged punishment cons dv: lagged contribution svo Contribution (t−1) − Contribution (t−2) cons N Individuals Clusters Wald Chi Log Pseudolikelihood

2.859*** (0.674) 0.010*** (0.003) 0.049*** (0.008) −0.094* (0.044)

720 72 9 91002.02

720 72 9 33436.19

0.096** (0.036) 0.621*** (0.041) 11.865*** (1.755) 648 72 9 −5770.069

Models 1–2: Arellano Bond systems (GMM) estimator. Instrumenting lagged contribution, lagged contribution below average, fact that punishment was deterrent, and all interactions with this variable. Data from periods 2–11 only (since lagged explanatory variables are included). Model 3: Linear Structural Model. cov(error[contr] * error[lcontr]) estimated. All models: standard errors clustered for matching groups. lpun: lagged amount of punishment, ldeterr: dummy that is 1 if punishment was deterrent, svo: ring measure score. *** p < 0.001. ** p < 0.01. * p < 0.05. + p < 0.1.

6. Conclusion As a matter of fact, sanctions are often imperfect. The expected value of the sanction, i.e. the probability of enforcement multiplied by the severity of the sanction, is often smaller than the expected benefit from socially detrimental behavior. Sometimes the legal order cannot avail itself of a sufficiently severe sanction. Take the person who ignores the rules for access to donor organs and does so to save her own life. Even if the legal order does not bar capital punishment in the first place, buying a donor organ will likely not qualify. In other instances, society cannot afford perfect sanctions. Many crimes go undetected because the police have not enough personnel to investigate them. Finally, the legal order may dislike deterrent sanctions for other normative reasons. It for instance is afraid that sending first offenders to jail will introduce them to a criminal career. From a rational choice perspective, deterrent sanctions are appealing. If only there is a credible threat with a sufficiently severe sanction, rational would-be criminals desist from crime. By the very fact that crime no longer pays, the actual enforcement of the sanction becomes an action off the equilibrium path. The mere threat is enough. From this perspective, imperfect sanctions are not only pointless, they are even counter-productive. Rational perpetrators realize that breaking the rules of social conduct is profitable business. If society does not want to entirely give up on its normative expectations, a lot of costly enforcement becomes necessary precisely because the sanction is not perfect. This paper tries to rebut this argument on its own turf, i.e. with an argument from rational choice theory. I introduce sanctions into a standard model of social preferences. With the help of this very simple model I show that imperfect sanctions do serve a socially desirable purpose if only a sufficient fraction of the population is not completely selfish but also cares about the negative effects of their own actions on the well-being of others. The theoretical argument even goes through if the population is known to be heterogeneous, with some selfish individuals. The theoretical argument is also robust to the introduction of mild uncertainty about the willingness of others to forego additional benefit for themselves at the expense of others. I use a standard experimental design, the linear public good with punishment, to test the prediction: if participants hold social preferences, imperfect sanctions help them sustain cooperation. The prediction is supported by the data. Actually, the stranger design puts this prediction to a particularly strong test. Participants neither know which peers, nor which authority they will meet in the next round. As in a one-shot game, their social preferences can only be of an abstract nature, directed toward anyone like them. And punishment in the previous period only gives them a signal about a possible reaction of next Please cite this article in press as: Engel, C., Social preferences can make imperfect sanctions work: Evidence from a public good experiment. J. Econ. Behav. Organ. (2014), http://dx.doi.org/10.1016/j.jebo.2014.02.015

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period’s authority. This is less than knowing the authority’s precise reaction function, as they would if there was an explicit penal code. Lab experiments are not meant to map reality. Exploiting other anonymous group members in a public good game is not crime. There is not even an explicit normative expectation (although informing participants about results from an earlier experiment with a very similar setup was meant to induce an implicit normative expectation). On purpose economic experiments are unframed. The naked opportunity structure does not trigger moral compunctions the same way as those real life situations that trigger criminal investigations or tort liability. Since there is no frame, would-be perpetrators are also derived of the possibility to construct the situation such that the victim falls outside their reference groups (“the anonymous department store is not a person who deserves my empathy”). In the lab, no more than a few cents are at stake, whereas the effects of crime or tort on victims tend to be much more severe. Gains from misbehavior are also much more contained in the lab than they tend to be in the field. Therefore socially desirable behavior might be cheaper in the lab. I am happy to acknowledge all these limitations inherent in my empirical approach. In the light of these limitations, one certainly should be hesitant to directly extrapolate from these findings to policy choices. All I hope to contribute to the policy discourse is one argument. If it is reasonable to expect heterogeneous preferences, then imperfect sanctions may serve a useful purpose. They deter those who are somewhat inclined to care about harm on others, but not strongly enough. The prospect of mild sanctions may suffice to tilt the balance in favor of socially desirable behavior. 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