Fines as enforcers’ rewards or as a transfer to society at large? Evidence on deterrence and enforcement implications

We analyze experimental data to assess whether the deterrent effect of expected fines depends on who receives the fines’ proceeds. We compare behavior in treatments when the revenue is a reward for enforcement agents to the alternative when fines are transferred to society at large. Most important, with a fixed detection probability, potential offenders’ material incentives are held constant across treatments. Our evidence suggests that the deterrent effect of expected fines is greater when enforcement agents obtain the fine revenue. Our results also document that the characteristics of enforcers who are willing to incur private costs to create a positive detection probability seem to depend on whether fines reward enforcers or are transferred to society at large.


Introduction
The use of financial rewards to incentivize individual law enforcement agents was once a common practice in the United States but was largely eliminated by the late nineteenth century over concerns that such incentives distort enforcement effort (e.g., Parrillo, 2013).
In some arenas, such as asset forfeiture laws, financial incentives remain commonplace in the United States and increasingly are the subject of scrutiny (e.g., Carpenter et al., 2015;Miceli & Johnson, 2016). Discussion regarding enforcement agents' financial incentives concentrates on both the level and allocation of enforcement resources. The relevant literature relates to the issue of deterrence only insofar as the induced change in enforcement effort lowers or increases expected sanctions. However, the possibility that financial rewards for law enforcement agents may affect deterrence even when the expected sanction remains the same has been neglected in the discussion thus far. The discussion's focus may be attributable to data availability. With field data, it is impossible to disentangle the deterrence implications of financial rewards resulting solely from the remuneration scheme (that is, with fixed enforcement effort) and the effects resulting from varied enforcement efforts (i.e., variation in the expected sanction).
This paper contributes to filling the gap by analyzing data from a laboratory experiment with varying enforcement agent remuneration schemes. By comparing offender choices at predetermined levels of enforcement effort, we can measure the deterrence effects resulting exclusively from the remuneration scheme while holding the expected sanction constant. The experimental methodology enables us to conduct a clean ceteris paribus comparison between compliance choices in a treatment in which fine revenue benefits society at large and enforcers receive a lump sum payment (where, in the lab, a charity serves as a proxy for society) and decisions in a treatment in which enforcers receive fines as rewards for effort.
In our experiment, we consider a taking game with three players. First, enforcers decide whether to incur a cost creating a positive detection probability or not. Next, potential offenders learn the level of the detection probability (either 0% or 50%) and then choose whether to take points from the potential victim. That sequence enables us to compare potential offenders' taking decisions across treatments, holding both the detection probability and the level of the sanction constant (thus only varying who receives the fine revenue). 1 By comparing offenders' decisions for a given level of enforcement effort (i.e., for a given expected sanction), we provide a clean test of whether potential offenders' compliance with the law depends directly on the enforcement agents' remuneration scheme. Three treatments are considered: in treatment FLAT, the potential fine revenue is allocated to society at large, and enforcers receive a lump sum payment; in treatment REWARD, the fine is transferred to the enforcer responsible for the offender's detection. We also consider a third treatment entitled CORRUPTION, in which the fine is intended to benefit society but can be diverted by the enforcer for a private gain (which may be interpreted as embezzlement). In treatment CORRUPTION, potential offenders condition their taking choice on the enforcer's decisions regarding both enforcement and possible fine diversion. That treatment allows us to shed light on the implications of receivers of the fine when the allocation is determined endogenously by the enforcer. As a theoretical basis for our experiment, we augment a standard model of law enforcement with risk-neutral potential offenders by accounting for offenders' inequity aversion or the possibility that the enforcers' decision conveys information about social norms to potential offenders.
Our paper tests a central assumption of the standard model of optimal law enforcement, according to which a fine is considered to be a costless transfer from the offender to society, and the precise allocation of fine revenue is assumed to be irrelevant to potential offenders' compliance choices (see, e.g., Becker, 1968;Polinsky & Shavell, 2007). That irrelevance assumption also is adopted in very recent contributions that focus on the choice of enforcers' remuneration. For example, in the political economy model of Yahagi (2021), a democratic government determines the extent to which fine revenue is used in order to incentivize enforcement agents to invest in higher detection probabilities. In that paper, offender behavior is guided exclusively by the expected sanction. Likewise, Adamson and Rentschler (2021) discuss the allocation of enforcement resources to patrolling (higher detection probability) and investigating (lower probability of false convictions), assuming that potential offenders' decisions are guided by expected sanctions alone. Our analysis is inspired by Becker and Stigler (1974) who provide the first economic analysis of a remuneration regime in which enforcers are compensated from fines the detected offenders paid. They discussed, inter alia, the possible effects of the remuneration scheme on law enforcement effort but also that deterrence might be affected by non-effort factors like the potential effect of financial incentives on enforcers' honesty. At the time, Becker and Stigler's recommendation contrasted starkly with the common practice of paying public enforcement agents a flat salary. Those two scenarios, fines as enforcer rewards and fines as a transfer to society while enforcers receive a flat payment, represent our main experimental treatments.
Our analysis suggests that potential offenders are influenced by who receives fine revenue, a mechanism that is not taken into consideration in the standard model of optimal law enforcement. In our data, the enforcer's creation of a positive detection probability generates a weakly greater deterrent effect when enforcers benefit from fine revenue than when society benefits from fines. In terms of mechanisms, our finding is consistent with inequity aversion on behalf of potential offenders (e.g., Fehr & Schmidt, 1999). In contrast, the idea that enforcers who invest in detection probabilities without explicit financial motives signal to potential offenders strong social norms regarding the unacceptability of taking and, thereby, influence deterrence, is not supported by our evidence. Although our conclusions are based only on a laboratory experiment and we cannot identify a specific mechanism to account for our results, we believe that the findings are very relevant and promising for the study of optimal law enforcement.
In addition to our interest in enforcement's deterrent effect, we explore how the different regimes influence enforcement effort. Specifically, we study the frequency of costly law enforcement and the types of individuals engaging in it. 2 With respect to enforcement effort, our evidence shows that financial incentives induce more enforcers to invest into positive detection probabilities, corresponding to economic intuition. Moreover, the characteristics of enforcement agents who invest in the detection probability seem to depend on who receives fine revenue. More specifically, we find that the increase in the enforcement probability in response to financial incentives is most pronounced for individuals with low morality scores. 3 That result sheds light on how financial incentives influence the selection of law enforcement actors.
The rest of the paper is organized as follows. Section 2 discusses the related literature. Section 3 introduces the experimental design, and Sect. 4 presents behavioral predictions. In Sect. 5, we present our empirical results. We offer some concluding remarks in Sect. 6.

Related literature
Our paper explores whether allocating fines to either reward enforcers or redistribute them to society at large influences law enforcement's deterrent effect and the frequency of enforcement. We thereby touch on contributions from both the experimental economics literature as well as the law and economics literature on private law enforcement.
Our experiment was stimulated by the mostly theoretical discussion of private law enforcement initiated by Becker and Stigler (1974) and Landes and Posner (1975). That literature asked, inter alia, whether enforcers should receive fine revenue, which is a prominent feature of private law enforcement (but could be applied in public law enforcement as well). Contributions to the strand of relevant research dealt extensively with topics such as the level of expected enforcement under private and public regimes (implying asymmetric detection probabilities). While Becker and Stigler (1974) argue that private enforcement can lead to the same enforcement level as public enforcement's theoretical optimum, Landes and Posner (1975) anticipate overenforcement under private legal arrangements. Later contributions include Polinsky (1980) and Garoupa (1997), who provide theoretical studies of the distortions likely to occur under private enforcement (e.g., over-or underenforcement) and their social implications. For example, Polinsky (1980) argues that public enforcement yields higher welfare than private enforcement in many circumstances. In all previous contributions, deterrence is determined solely by the level of the expected sanction. As such, our empirical work 4 explores whether the deterrent effect of a fixed expected sanction depends on the enforcer's remuneration, as would be consistent with inequity aversion or the possibility that the enforcer's decision conveys information about social norms to potential offenders. Our design allows us to isolate the effect of the enforcer's material incentives on potential offenders' behavior, ceteris paribus. To our knowledge, that possibility has not been considered in the relevant literature so far.
There is by now a rich empirical literature presenting evidence that incentives to raise revenue influence policing (e.g., Benson & Rasmussen, 1995;Garret & Wagner, 2009;Mast et al., 2000). For instance, Stratmann (2009, 2011) find that traffic citations increase when the municipality has pressing budgetary needs, thereby improving traffic safety. Makowsky et al. (2019) consider the joint effect of local budget deficits and possibilities for revenue retention from civil asset forfeitures on policing. The authors hint, for example, at the racial implications of a revenue motivation. From an analysis of forfeiture laws, Baicker and Jacobsen (2007) deduce that police behavior reacts to the incentives thereby created and that local governments reduce their transfers to the police by the amount collected through seizures. Along those same lines, the 2015 US Department of Justice report "Investigation of the Ferguson Police Department" comes to the conclusion that "Ferguson's law enforcement practices are shaped by the City's focus on revenue rather than by public safety needs" (US Department of Justice, 2015, p. 2). We are interested herein whether the use of fine revenue itself has implications for deterrence and thus compare violation rates across treatments for the same level of enforcement effort.
The paper closest to ours in terms of research question and methodology is Xiao (2013). She considers third-party enforcers in a sender-receiver game who may have profit motives. In her game, third-party enforcers' payoffs increase unconditionally by punishing others. Therefore, enforcers with a profit motive may punish senders for dishonesty, independent of whether a violation actually occurred. In that specific context, Xiao (2013) finds a substantial degradation of punishment's ability to influence potential offenders' behavior. It is crucial that, in contrast to our setting, Xiao (2013) allows third-party enforcers to extort payments from compliant subjects. While we do not question the empirical relevance of that concern, we purposefully designed a setup without such framing incentives so as to provide clean evidence about the effect of enforcer incentives alone. Our evidence suggests that when the possibility of wrongful punishment is excluded, having fines that benefit enforcers can lead to a greater deterrent effect of enforcement.
Our paper also is related to other studies from the experimental literature on third-party punishment. For example, Leibbrandt and Lopez-Perez (2012) and Fehr and Fischbacher (2004) present evidence that third-party punishment often is motivated by inequity aversion. We focus on the behavior of potential offenders and find results that are consistent with inequity aversion as well.
Our research interest, the deterrence implications of enforcer remuneration schemes that go beyond their direct effects on enforcement effort, is related to the more general public choice literature on law enforcement. In that realm, Yahagi (2021) investigates how a democratic government chooses enforcers' remuneration. The work extends contributions that investigate law enforcement with self-interested principals, as in Garoupa and Klerman (2002) or Langlais and Obidzinski (2017). Regarding financial incentives, Friehe and Mungan (2021) employ a median-voter setup to show that the equilibrium enforcer liability for wrongful suspect stops likely will be suboptimal, that is, unable to curtail excessive policing. On a different note, Wickelgren (2003) explores the hypothesis that more costly forms of punishment are adopted to prevent policymakers from excessively punishing those agents with little political influence.

Experiment design, treatments, and procedures
Our computerized experiment consisted of six parts. Subjects first received a general introduction beforehand and then separate instructions for Parts 1-6. While subjects knew from the start that the experiment comprised several parts, the content of later parts was not revealed to participants until the appropriate time. We first summarize the experiment.
In Part 1, participants earn a fixed endowment in a real-effort task. Afterward, subjects learn their role in the experiment, either potential offender, potential victim, or enforcer. 5 In Parts 2-5, which constitute the core of our experiment, subjects participate in 1 3 treatment-specific taking games with random matching in each part. In each taking game, enforcers first decide whether to create a positive detection probability at a private cost before potential offenders observe the enforcer's decision and decide about taking points from their potential victim. In Part 2, participants play one treatment in a direct-response format. In Part 3, participants play the same treatment, and potential offenders choose according to a strategy-method format.
In the strategy-method format, subjects make contingent decisions for all nodes at which they may have to play (e.g., Brandts & Charness, 2011). In our setting, potential offenders decide whether and how much to take from the potential victim conditional on all possible choices by the enforcer. 6 Part 4 (5) mirrors Part 2 (3) for a different treatment. Potential victims remain passive throughout Parts 2-5. In Part 6, we collect information about our subjects' morality and their attitudes towards both justice and risk.
For each subject, one part out of Parts 2 to 5 was chosen randomly as payoff relevant. In addition, subjects received payoffs for the tasks in Part 6 (one of the questions was selected randomly to determine the payoff). Finally, a showup fee of 7 euros was paid to all participants. Throughout the experiment, payoffs are described as points; the exchange rate was 100 points = 1 euro. Subjects were informed of their earnings at the end of the experiment.

The key component: the taking game
Our taking game follows the experimental literature on the economics of crime (Rizzolli & Stanca, 2012;Schildberg-Hörisch & Strassmair, 2012). We depart from that literature by introducing a detection probability that depends on the enforcer's investment in effort.
At the beginning of the taking game, all participants in a group have 500 points in their accounts from Part 1's real-effort task.
First, the enforcer chooses whether to invest 50 points to create a detection probability amounting to 50%. Without investment, the detection probability is equal to zero.
Next, the potential offender learns the enforcer's choice and chooses how many points x to take from the potential victim's account, where x ∈ [0, 500] . The offender receives half of the points taken. 7 The symmetric endowments, the fact that the endowment was earned in a real-effort task, and the drastic inefficiency resulting from theft make not taking a social norm.
Finally, the offender's detection chance is determined. A detection can occur only if the enforcer created the 50% positive detection probability and the offender took points from the victim (our design does not allow for wrongful convictions, in contrast to Xiao, 2013). Detected offenders pay a fine amounting to 250 points but keep their criminal gains (as in, e.g., Rizzolli & Stanca, 2012). For simplicity, the fine is independent of the number of points taken; the fine amounting to 250 points applies when the offender has taken any positive number of points from the victim (as in, e.g., Schildberg-Hörisch & Strassmair, 2012).

3
Before subjects choose their actions, potential offenders (enforcers) state their beliefs about enforcer (potential offender) conduct. Potential victims state their beliefs about both potential offenders' and enforcers' behavior. Players earn an additional 100 points if their stated beliefs roughly match either the share of people enforcing/taking or the average amount taken. 8 Before we proceed, we want to provide a motivation for our specific design of the taking game. Our research focuses on the implications of enforcer compensation on deterrence when the expected sanction is fixed across conditions. We thus seek to compare taking choices in circumstances in which the enforcer's compensation differs, but the enforcement effort and monetary fine are the same. To fulfill the requirement of a fixed expected sanction, we can compare only cases with exactly the same enforcer investment and sanction. The restriction to only two investment levels for enforcement effort allows us to collect enough observations for each circumstance. In addition, note that taking is a dominant strategy for potential offenders solely concerned about monetary payoffs. In other terms, we rely fully on the relevance of non-monetary aspects motivating behavior to create heterogeneity in terms of the taking choice. 9

Treatments
We study three treatments denoted FLAT, REWARD, and CORRUPTION (see Table 1 for an overview).
In treatment FLAT, fines benefit society at large. It was common knowledge that we proxy society at large with the charity Les Resto du Coeur. 10 The enforcer's final payoff from the taking game is equal to the endowment minus any enforcement cost.
In treatment REWARD, fines benefit enforcers, meaning that the enforcer's expected remuneration depends on whether an offense is detected. The enforcer's final payoff from the taking game is equal to the endowment minus any enforcement cost plus the fine in case of detection.
Treatments FLAT and REWARD differ only regarding who benefits from fine revenues. The comparison between those two treatments is central in addressing our main research question concerning how the use of fine revenue influences law enforcement's deterrent effect.
In treatment CORRUPTION, fines are meant to benefit society at large; however, the enforcer can divert any collected fine. Accordingly, the enforcer makes two decisions, whether to enforce and, conditional on enforcement, whether to divert the fine should the offender be detected. In our design, no sanction is applied for enforcers' diverting of the fine's proceeds. At the time of deciding whether to take, the potential offender is informed about both of the enforcer's decisions.
Treatment CORRUPTION differs from FLAT and REWARD in that the enforcer makes decisions not only about investing but also about diverting the fine meant to benefit society. Accordingly, in this treatment, the enforcer's receipt of the fine results from the enforcer's choice, where diverting presumably is a norm infraction. Clearly, it may matter for the potential offenders' choice whether the regime is designed such that enforcers always receive the fine revenue (as in treatment REWARD) or whether enforcers can profit only from their own misconduct (as in treatment CORRUPTION). Table 1 provides an overview of our treatments. To sum up, the game proceeds as follows: • Part 1: a real-effort task is completed; • Parts 2-5: subjects participate in taking games; subjects play one treatment in Parts 2-3 and another treatment in Parts 4-5 with, first, a direct-response format and, second, a strategy-method format; • Part 6: information about participants is collected.

Part 1: The real-effort task
We include the real-effort task, in which participants work for their endowment of 500 points, to create a notion of entitlement (e.g., Faillo et al., 2019;Falk & Fischbacher, 2002;Oxoby & Spraggon, 2008). We selected a threshold task to create symmetric endowments (e.g., Duersch & Müller, 2015). The task consists of correctly counting the number of zeros in tables consisting of 100 randomly ordered zeros and ones. Each participant must report the correct number in at least two tables within 10 minutes. Failing to do so leads to the subject's exclusion from the experiment. As Abeler et al. (2011) emphasize, that boring task does not require any prior knowledge, performance is easily measurable, comes at a positive cost of effort, and there is little learning possibility. Circumstantially, all participants were successful in the task.

Part 6: Subject characteristics
In Part 6, participants make choices in incentivized tasks without strategic payoff interdependence and provide us information about their attitudes on different aspects related to their decisions in the taking game. Specifically, we inquire about their morality (using the items from Traxler & Winter, 2012) and justice attitudes (using the different points of view conceptualized by Schmitt et al., 2010). Regarding morality, we present eight different norm violations taken from Traxler and Winter (2012) to our participants (drunk driving, hazardous waste disposal, speeding, steeling newspapers, absenteeism from work, evading TV fees, fare dodging, and tax evasion), and ask for their evaluation of the behaviors on a scale from 1 (very severe) to 10 (not severe). In our empirical analysis, we rely on the inverted sum of the eight responses as our morality measure (with 80 as the possible maximum). With regard to justice sensitivity, we follow Schmitt et al (2010), and ask for participants' assessment of eight situations that are framed to entail some level of unfairness. Participants should rate their agreement with statements such as "It makes me angry when others are undeservingly better off than me" and "I feel guilty when I am better off than others for no reason" using a six-point rating scale ranging from 0 (not at all) to 5 (exactly). We rely on the eight-item sum as our justice sensitivity measure (with 40 as the possible maximum).
In addition, we incentivize responses to a social value orientation (SVO) test (Murphy et al., 2011) and a risk elicitation task (Eckel & Grossman, 2008). Finally, we collected observations on subjects' demographics. Summary statistics on the subjects' characteristics are shown in Tables A.1 and A.2. in Appendix A.

Procedures
We conducted the experiment in the laboratory of the University Panthéon-Sorbonne, Paris, between May and October 2019. 11 Participants were administered and recruited via ORSEE (Greiner, 2015) from the laboratory's subject pool. We collected data from 447 participants in 26 sessions, 298 of which were active participants (i.e., either potential offenders or enforcers). Subjects' mean age was about 35 years. Our participants (about 60% female) primarily were students from various fields of study but also included a few retirees. Table 2 presents the number of groups and subjects per treatment sequence. Overall, we had 115 groups for FLAT, 103 groups for REWARD, and 80 groups for CORRUP-TION (with each group going through two treatments).
A typical session lasted around 80 minutes (including payment). During the experiment, subjects earned points that were converted to euros at a conversion rate of one euro cent per point. Participants were paid in cash at the end of each session, the average earning being around 11.75 euro. The experimenter made the charity donation after the relevant sessions were concluded, and participants were informed at the beginning of each session that the charity donation would be made in accordance with the result of the experiment.

Hypotheses
We now briefly formulate hypotheses for our design. We start with the benchmark of "standard" agents before we introduce behavioral aspects that might lead to different conjectures regarding how the deterrent effect depends on who receives fine revenues. We generally assume that risk-neutral agents' payoffs depend on expected income and moral disutility.

Hypotheses relying on standard assumptions
For our standard agents, moral concerns stem only from the agent's own behavior. Potential offenders incur moral disutility if they take points from the victim. Following Fees et al.  Using backward induction, we first consider the potential offender's decision for the two cases in which the enforcer did or did not invest in establishing a positive detection probability. If the detection probability is positive, the potential offender takes the amount b from the victim if where y is initial income, p the detection probability, and F the fine in the event of detection. 12 Taking occurs if moral disutility is less than the expected monetary gain (m O j < b − pF) , which results in a taking rate equal to G(b − pF) . If the detection probability is zero, the potential offender takes from the victim if which results in a taking rate equal to G(b) . The deterrent effect from the enforcer's investment is given by the difference in taking rates and equal to In other words, enforcement reduces the probability that a potential offender has a moral disutility level small enough to make taking preferable by the difference in relation (3). The difference is independent of how the fine's proceeds are allocated. We summarize: Hypothesis 1 (Standard theory): (a) Enforcement's deterrent effect on the potential violators' taking choice is the same in treatments FLAT and REWARD. (b) Enforcement's deterrent effect on the potential violators' taking choice is independent of whether the enforcer diverts the fine in treatment CORRUPTION.
Next, we examine the enforcer's choice in Stage 1. That choice depends on who receives fine's revenue, and we concentrate on treatments FLAT and REWARD. If fine revenue benefits society at large (treatment FLAT), the enforcer creates a positive detection probability if where c denotes the enforcer's investment cost. The enforcer invests if the monetary cost falls short of moral disutility from non-enforcement ( c < m E i ) , and the share of enforcers investing in a positive detection probability amounts to 1 − H(c) . In contrast, if enforcers receive fine revenues (treatment REWARD), enforcement takes place if where q is the enforcers' belief about the taking rate. 13 Accordingly, enforcers invest if the moral disutility from non-enforcement exceeds the expected net enforcement cost, m E i > c − qpF . That critical level implies that the share of investing enforcers amounts to 1 − H(c − qpF) . Comparing the two regimes, we find that the probability that a potential enforcer has a moral disutility level large enough to trigger the investment rises if financial incentives are provided. The difference amounts to In addition, we note that the lower critical level for moral disutility in treatment REWARD implies that, conditional on investing in the detection probability, the enforcers' average moral concern is lesser.
We summarize:

Hypothesis 2 (Enforcer behavior): (a) More enforcers invest in a positive detection proba-
bility in treatment REWARD than in treatment FLAT. (b) Among the enforcers who invest in a positive detection probability, morality scores are lower in treatment REWARD than in treatment FLAT.

Taking behavioral effects into account
For "standard" potential offenders, we find that deterrence is unaffected by the identity of fine recipients. Below, we outline how the consideration of two behavioral ideas can fuel the expectation that enforcement's deterrent effect should be affected by the recipients' identity even when the expected sanction remains the same. First, we consider the possibility that potential offenders respond to different normative meanings of enforcement in the two remuneration regimes. 14 Second, we allow for the possibility that potential offenders suffer disutility from unfavorable income comparisons along the lines of Fehr and Schmidt (1999) and Bolton and Ockenfels (2000).
Regarding the normative meaning of enforcers' investment decisions, note that people are willing to forfeit resources to prevent or punish non-compliance with norms about which they care (e.g., Fehr & Fischbacher, 2004). Against that background, enforcers who invest in treatment FLAT signal that they perceive "not taking" to be a strong social norm because creating a positive detection probability is costly and not associated with any personal material benefits. In contrast, subjects who enforce in treatment REWARD may be driven by a profit-seeking motive and thus are, on average, less concerned about social norms than subjects who enforce in treatment FLAT. The 13 With rational expectations and perfect information, we have q = G(b − pF). 14 Related contributions in the realm of normative meaning are varied and include work by Bénabou and Tirole (2016) on the relationship between beliefs and action; Adriani & Sondereggger (2018), in which parents' behavior signals the normative content of human action to their children; and the stream of literature on leading-by-example (on leaders influencing the normative meaning of behavior, see, e.g., Dannenberg 2015). potential offender may consider the enforcer's belief about the strength of the norm to be informative about social conventions more generally. The receiver of fine revenue then will affect the normative information that can be deduced from enforcement and thereby enforcement's deterrent effect. If the potential offender cares about aligning own choices with strong social norms (as seems to be true in many circumstances; see, e.g., Kimbrough & Vostroknutov, 2016), then taking after enforcers invest in detection imposes larger norm non-compliance costs in treatment FLAT, which should result in a stronger deterrent effect.
To be specific, assume that the offender's moral costs, m O j , are augmented by an amount s according to the normative signal obtained from the enforcer's investment decision. Consequently, given enforcement, the offender takes from the victim if This ranking implies a taking rate amounting to G(b − pF − s) . If the normative meaning of enforcement is higher in FLAT than in REWARD (i.e., if s FLAT > s REWARD ), as argued above, we obtain that the deterrent effect of the enforcer's enforcement on the potential violators' taking choice is greater in FLAT than in REWARD: In treatment CORRUPTION, the enforcer decides whether to divert the fine, thereby providing a strong signal about the normative meaning of enforcement. Once again, if potential offenders care about how the enforcer perceives the norm, the deterrent effect of enforcement will be affected. In summary, the foregoing considerations suggest:

Hypothesis 3 (Normative meaning of enforcement): (a) Enforcement's deterrent effect
on the potential violators' taking choice is greater in treatment FLAT than in treatment REWARD. (b) In treatment CORRUPTION, enforcement's deterrent effect on the potential violators' taking choice is greater when the enforcer does not divert the fine.
Next, consider the possibility that potential offenders experience disutility from unfavorable income comparisons. In that case, we expect enforcement's deterrent effect to be greater in treatment REWARD than in FLAT. The intuition runs as follows: consider an offender who takes the maximum possible amount such that F = b > c , and the victim's loss is equal to 2b in our experiment. Taking creates advantageous inequity for the offender vis-à-vis the victim and, in the case of no detection, vis-à-vis the enforcer in both treatments. In contrast, in the event of detection, the offender enjoys a higher income vis-à-vis the enforcer only in treatment FLAT (enforcer income: −c ; offender income:y + b − F = y ) but not in treatment REWARD (enforcer income: y − c + F ; offender income:y ). Denoting with the measure of how an unfavorable income comparison translates into disutility, we find that the offender takes with a positive detection probability in treatment REWARD if where y + b − pF is expected income from taking and (F − c) represents the weighted difference in enforcer and offender payoffs in the case of detection which occurs with probability p . Inequality (9) results in a taking rate equal to G(b − pF − p (F − c)) , which compares to a taking rate of G(b − pF) in treatment FLAT. The deterrent effect of a positive detection probability is stronger in treatment REWARD than in treatment FLAT according to A similar logic applies to the treatment CORRUPTION when the enforcer decides to divert the fine after detecting a crime.

Hypothesis 4 (Inequity aversion): (a) Enforcement's deterrent effect on the potential
violators' taking choice is greater in treatment REWARD than in treatment FLAT. (b) In treatment CORRUPTION, enforcement's deterrent effect on the potential violators' taking choice is greater when the enforcer diverts the fine.
Thus, inequity aversion leads to predictions that are opposite to those stemming from a theory building on a normative meaning of enforcement and a desire to comply with norms. The mechanisms are quite different as well. The normative meaning of enforcement implies that potential violators behave differently in treatments REWARD and FLAT because the enforcer's decision to create the positive detection probability conveys a stronger signal about the norm in FLAT than in REWARD. In contrast, the theory of inequity aversion assumes that agents anticipate and seek to avoid disadvantageous payoff comparisons. In our setup, enforcement can induce disadvantageous inequity for the offender only in treatment REWARD, such that enforcement would create more deterrence in REWARD than FLAT.
In summary, we note that the standard framework in Sect. 4.1 predicts a null result for the effect of the enforcer's remuneration on offenders' taking for a given detection probability. With the incorporation of selected behavioral aspects, it is possible to obtain different effect signs. All in all, the direct link between enforcement's deterrent effect and the enforcers' remuneration is unclear, making an empirical analysis particularly valuable.

Results
In our analysis, we focus on observations from Parts 2 and 4, that is, the parts adopting the direct response method. 15 Below, we enter a dummy variable that indicates whether the observation is collected from Part 2 or 4, whose coefficient is not significant in any empirical model.

A glance at the data
Figures 1 and 2 summarize offenders' taking behavior in our experiment. As is clear from Fig. 1, which shows the amounts taken by treatment across different choices by the enforcer, a very large share of subjects takes the maximum amount (i.e., 500  15 We emphasize the strategy method parts of our experiment because we initially were concerned about data that were too unbalanced, a concern that proved to be unwarranted. Building on Brandts and Charness (2011), differences between the direct-response method and the strategy method can be expected because emotions are involved, subjects make only a few conditional choices in the real world, and the game's structure is one-shot. However, we find no significant differences between direct response and strategy methods in our experiment for the potential violators. See Parts A and D in our Supplementary Material for a thorough analysis. points) from the victim, and another large share chooses not to take at all. On average, only about 34% choose some amount of taking between those extremes across treatments, whereas 24.5% choose not to take at all and 41.28% take the maximum amount. Figure 2 reports amounts taken conditional on taking and enforcers' choice, confirming that the majority of violators opt for the maximum taking amount. Indeed, boxplots show that the median taking always is 500 except in treatment REWARD when the enforcer does not invest in enforcement (where the median is 475 points). From those distributions, we deduce that a dummy variable that is equal to one if the offender takes and zero otherwise is not associated with a substantial loss of information because the choice seems to reduce to not taking or taking the maximum amount for most individuals. Thus, when we analyze offenders' taking below, we will focus on results from probit regressions.
In Fig. 3, we illustrate the distribution of enforcers' choices. As expected, monetary incentives increase the likelihood of enforcement. In treatment CORRUPTION, enforcers had to decide about enforcement and, conditional on enforcement, whether to divert the fine into their own pockets. In our experiment, 65% of enforcers who invested in detection chose to divert the fine to their own benefit. Table A.3 in our Supplementary Material provides detailed statistics about the offenders' taking and the enforcers' choices in our experiment.

Deterrent effect of enforcement
We now test Hypotheses 1, 3, and 4 on individual choice data and subjects' characteristics elicited in Part 6 of the experiment. Our experimental design and the distribution of amounts taken (see, e.g., Fig. 1) suggest using a random-effects probit model because the observation of a given subject across several decision points creates a panel dataset.
Entering Taking it as a dummy variable equal to one if subject i decided to take points from the victim in period t , we specify with Taking * it as the latent variable and Z i as a vector containing subject-specific characteristics such as SVO angle, Morality, Justice Sensitivity, Risk Attitude, Age, and Sex. Remember that a higher SVO angle indicates greater prosociality (Murphy et al., 2011) and that the individual's risk attitude was elicited using the lottery selection task by Eckel (11) Table 3 Coefficients and AMEs from random-effects probit regressions for taking for FLAT & REWARD treatments Coefficients and AMEs from random-effects probit regressions. The dependent variable is equal to one (zero) if (no) taking occurred. REWARD is a dummy variable equal to one if the observation is from treatment REWARD. Enforcement is a dummy variable equal to one if the enforcer created a positive detection probability; *, **, *** indicate significance at the 10%, 5%, and 1% levels. Cluster robust standard errors are shown in parentheses and Grossman (2008) where a larger number represents greater risk tolerance. For each potential violator i , Treatment it varies across periods, and Enforcement it may vary as well.
To control for order effects, Order it is entered as a dummy variable that is equal to one if the potential offender's decision stems from Part 4 of the experiment (instead of Part 2). The equation contains two error terms, the conventional error term it and the individualspecific unobservable effect u i . The relationship between the latent variable Taking * it and the observed binary variable Taking it is: First, we compare treatments FLAT and REWARD. In Table 3, we report the estimated coefficients and average marginal effects (AMEs) of our variables of interest. The latter describes the average difference in the expected probability of taking associated with a one-unit change in the variable of interest, averaged over the distribution of the other variables in the dataset. We find that enforcement reduces the taking probability while the enforcers' remuneration scheme has no significant direct effect. However, our research question concerns whether the deterrent effect of enforcement depends on enforcer remuneration. Column (3) in Table 3 reports a significant and negative coefficient for the interaction between enforcement and the REWARD treatment.
However, according to Norton et al. (2004), the statistical significance of the interaction effect cannot be tested with a simple t-test on the coefficient of the interaction term in non-linear models. For that purpose, Williams (2012) suggests visual display and analysis of differences between treatments. Along those lines, Fig. 4  adjusted probabilities for both treatments by enforcer's choice and SVO angle with 95% confidence intervals. Except at very small SVO angles, the confidence intervals are not overlapping in treatment REWARD, whereas they do so in treatment FLAT. As another piece of evidence, we report a significant interaction between Enforcement and REWARD from random-effects linear probability models in our Supplementary Material (Table B.1). Thus, we conclude that enforcement reduces the probability of taking in treatment REWARD but not in treatment FLAT. The interaction described above is evident at the extensive margin but is insignificant at the intensive margin. That conclusion follows from regressions that enter the amounts taken as the dependent variable (for details, see Table B.2 in our Supplementary Material). Moreover, the effect seems to be weaker in our strategy-method experiment such that the interaction effect is insignificant (see Table A.4 in our Supplementary Material), which seems consistent with differences in outcomes reported for other experimental settings (e.g., Brandts & Charness, 2011).
We summarize: Result 1: Enforcement's deterrent effect is (weakly) larger in treatment REWARD than in treatment FLAT.
A larger deterrent effect of enforcement in REWARD is inconsistent with Hypotheses 1 and 3, which consider the standard agent and the possibility that norm enforcement conveys normative meaning to the potential offender. However, Result 1 is consistent with Hypothesis 4, according to which potential offenders are inequity averse. Our finding is consistent with the idea that agents respond to income comparisons and that they behave in order to avoid situations perceived as personally disadvantageous. To the extent that treatment REWARD ultimately can result in an unfavorable income comparison from the potential offender's perspective, the deterrent effect of enforcement is stronger than in treatment FLAT.
Regarding personal characteristics, we find that the SVO angle is relevant for explaining variation in the binary taking variable in our empirical model, whereas the coefficients for Justice Sensitivity, Risk Attitude, and Morality are insignificant. The finding that Morality does not contribute to explaining taking behavior is surprising (but we will show that the Morality score is relevant for the enforcement decision). We admit that the finding may result from our imprecise measure of the complex construct "morality".
Next, we address treatment CORRUPTION. As that treatment differs structurally from treatments FLAT and REWARD, we restrict our analysis to treatment CORRUP-TION and focus on gauging how enforcement's deterrent effect depends on the enforcer's diversion choice (i.e., the endogenous remuneration change).
The  16 To test our hypotheses, we evaluate the AME associated with the enforcer's behavior. Enforcers' fine diversions raise enforcement's deterrent effect significantly: we report a significant AME for Enforcement & Fine Diversion in Columns (2) and (4) (which is the difference in the deterrence effect versus Enforcement & No Fine Diversion). Results from linear probability models reported in our Supplementary Material corroborate that finding. That finding is inconsistent with Hypotheses 1 and 3 (i.e., the assumption of a standard agent or the conveyance of normative meaning by enforcement) but consistent with Hypothesis 4 (i.e., potential offenders' inequity aversion).

Enforcers' investment
Next, we consider enforcer behavior and test Hypothesis 2. In treatments FLAT and REWARD, enforcers choose between no investment and investment in different periods. In our analysis of enforcement choices, we are particularly interested in which types of individuals willingly incur private costs to enforce the norm. To classify individuals, we rely on our Morality score since it informs us about subjects' perceptions regarding  (Traxler & Winter, 2012). For our analysis, we consider a random-effects probit model of the following form: with Enforcement * it as the latent variable and Z i as a vector containing subject-specific characteristics.
The results reported in Table 5 are set against treatment FLAT as the base category. Table 5 confirms the intuition that enforcement is more likely in treatments that provide personal financial motives. In Columns (3) and (4), we also find that a higher Morality score significantly reduces the probability of enforcement. We aim at resolving that puzzle in Column (5), where we show that the negative effect stems from the treatments with financial incentives.
To interpret the interaction between the treatment and Morality score, we plot the adjusted probabilities of enforcement by Morality score with 95% confidence intervals (Fig. 5). Whereas the enforcement probability is significantly higher in the treatments with financial incentives at low and intermediate morality scores, that no longer is true at high morality scores.

Result 3: (a) More enforcers invest in the detection probability in treatments REWARD and CORRUPTION than in treatment FLAT. (b) The morality scores of enforcers who invest in the detection probability in treatments offering financial rewards (REWARD and CORRUPTION) is less than that of enforcers in treatment FLAT.
Result 3 (a) is confirmed in random-effects linear probability models reported in our Supplementary Material and consistent with our Hypothesis 2. The higher enforcement effort in treatments with financial enforcement incentives accords with previous evidence (e.g., Harvey, 2020). Moreover, as Result 3 (b) suggests, the remuneration scheme influences the characteristics of active enforcers (we focus on the enforcer's Morality score). Figure 6 confirms Result 3 (b). That figure shows the boxplots of enforcers' morality scores by treatment and enforcement choice. The boxplots indicate that subjects with low morality scores are more prevalent among enforcers who chose to invest in a positive detection probability in the treatments with financial incentives (REWARD and CORRUPTION) than in treatment FLAT. Those observations align with our regression results in Table 5 and are consistent with the positive selfselection results presented in Friebel et al. (2019) for police applicants in Germany, where no monetary rewards for enforcement successes are granted.

Discussion and concluding remarks
This paper relies on experimental data to explore whether enforcement's deterrent effect depends on the enforcer remuneration regime even when the expected sanction is constant across regimes. The previous literature focused on the implications of varying enforcers' financial incentives on the level of enforcement effort and the allocation of enforcement resources. We compare enforcement's deterrent effect for a given expected sanction when the enforcer receives the fine to the case in which the fine is transferred to society at large while the enforcer receives a lump sum payment.

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Enforcement * it = + 1 Treatment it + 2 Treatment it * Morality i + 3 Order it + Z i + u i + it Our paper presents some evidence that questions the standard assumption in the theory of law enforcement that the identity of the recipient of fine revenue is irrelevant for compliance choices if the levels of the detection probability and the fine are held constant. The deterrent effect of enforcement seems to be stronger if enforcers receive fine revenue. With respect to possible mechanisms, our results seem consistent with potential offenders' inequity aversion. In addition, we confirm that regimes offering financial incentives to enforcers lead to more enforcement effort but also a different mix of subjects choosing to engage in enforcement. With financial incentives, subjects with low morality scores are more likely to invest in enforcement.
Our experiment identifies the consequences of the enforcer remuneration choice in a laboratory experiment. Clearly, we must be careful when deriving implications for the real world from our findings. Enforcement's deterrent effect seems to be greater in treatment REWARD, but we do not view that result as a basis for recommending financial incentives for enforcers. In fact, some evidence exists that subjects are more likely to take in REWARD in the absence of enforcement effort. More important, our design allows only two possible levels for the detection probability (zero or 50%), so that we do not know how the differential effects reported herein will bear out at other levels of the detection probability. In reality, potential offenders may not be informed about actual enforcement choices and likely will expect more vigorous enforcement in the presence of personal financial incentives, an effect that we purposefully exclude from our design. It is also important to acknowledge that our design highlights a possible selection effect at the stage where individuals consider becoming a law enforcer. One could fear that by implementing financial incentives, agents with lower moral values would be selected as law enforcers. We also must be careful in extrapolating our results because of possible issues of external validity that often arise in laboratory experiments also apply here (such as greater scrutiny; see, e.g., Levitt & List, 2007).
Moreover, in order to concentrate on the pure remuneration effect, we omitted the possibility that enforcers extort compliant agents on purpose. In reality, such concerns may arise. The theoretical literature and the findings of Xiao (2013) make clear that the possibility of Type II legal errors (i.e., being fined despite compliance) weakens deterrence. Therefore, incentivizing law enforcers financially might entail a series of consequences that our experiment can capture only partially. We believe that it may be interesting for future work to investigate the implications of such additional issues in isolation.

Supplementary Information
The online version contains supplementary material available at https:// doi. org/ 10. 1007/ s11127-022-01000-5. permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.