Explaining cheating in schools with Situational Action Theory: Within-estimations using a German school panel

Wikström's Situational Action Theory (SAT) explains rule-breaking by reference to the cognitive perception-choice process, which indicates how a person's propensity to break rules interacts with the setting's criminogeneity. SAT's situational model claims that the interaction between personal morality and the moral norms of the setting, the so-called moral filter, is critical in the explanation of rule-breaking, and that the influence of self-control is subordinate to this process. Self-control becomes relevant when individuals whose personal morality discourages rule-breaking are exposed to settings in which the moral norms encourage rule-breaking, that is, if the moral filter is conflicted. Whereas most previous studies have equated the moral filter with personal morality, we consider the moral norms of the setting as well. This allows for a more rigorous test of the moral filter, and thus the conditionality of self-control. Here, we investigate student cheating, using data from two waves of a large-scale German school panel study, and we conceptualise the setting's moral norms by reference to the descriptive norm: other students’ cheating behaviour. This ensures the spatio-linkage between the setting's criminogeneity and rule-breaking, which is necessary for investigating SAT. Additionally, our estimation strategy – person and school fixed-effect models – controls for alternative explanations by the selection of people into settings with different levels of criminogeneity. Moreover, it controls for heterogeneity across persons and schools. The findings are in line with SAT's predictions. In cases of a correspondence between personal morality and the moral norms of a setting, students with rule-abiding morality are least likely to cheat, whereas students with a rule-breaking morality are the most likely to cheat. Also, in line with SAT, self-control only matters for students with rule-abiding morality when they are exposed to moral norms that encourage rule-breaking.


Introduction
Crime is increasingly explained by reference to the interplay between person and environment (Barnum and Solomon, 2019;Beier, 2016;Berg et al., 2012;Ernst and Lenkewitz, 2020;Simons et al., 2014;Zimmerman, 2010). In this vein of research, Situational Action Theory (SAT; Wikström, 2006Wikström, , 2014Wikström et al., 2012) provides a particularly comprehensive and detailed framework that explicitly integrates person and environmental approaches, and puts their interplay at the centre of the explanation of crime.
SAT states that people first have to perceive rule-breaking as an action alternative, and then either act habitually or choose deliberatively between action alternatives. The perception of rule-breaking action alternatives is constituted by a person's morality and the moral norms of the setting, the so-called moral filter, which 'sets the boundaries for the choice process' (Wikström et al., 2012: 17). If personal morality and the moral norms are in accordance, people follow their morality unconditionally (principle of moral correspondence). This is independent of their internal controls (self-control) and the external controls (deterrence). But if personal morality and the moral norms of the setting conflict, people deliberate. Only in this condition do self-control (as an internal control) and deterrence (as an external control) matter (principle of the conditional relevance of controls).
It follows that for an appropriate investigation of the principle of the conditional relevance of controls, it is necessary to address the configuration of the moral filter. However, quite surprisingly, research on the principle of moral correspondence is rare, and only a few studies have considered the interplay of personal morality and the moral norms of the setting when studying the principle of conditional relevance of controls (for exceptions, see Brauer and Tittle, 2017;Pauwels, 2018;Schepers and Reinecke, 2018). We add to this research on the principle of moral correspondence and the conditional relevance of self-control by explaining student cheating using data from a large-scale panel study in five German cities ('Friendship and Violence in Adolescence'). We focus on self-control because it matters whenever people deliberate about rule breaking; this is when their own morality and the moral norms conflict. First, self-control matters when persons with rule-abiding morality are exposed to the moral norms of a setting that encourage rule breaking. In this case, their ability to exercise self-control determines whether they will stick to their own morality (Wikström et al., 2012: 26). Second, when people with rule-breaking morality are in settings that discourage cheating, SAT proposes that deterrence (as an external control) becomes relevant. Nonetheless, also in this condition self-controls matters by conditioning the effect of deterrence (Hirtenlehner and Meško, 2019).
Our aim is to provide a methodologically more rigorous test by using schools as a strategic research site. Contrary to most of the existing SAT tests, we do not have to rely on measures of the moral norms of the setting that are not linked to the setting in which rules are broken, such as participants' self-reports about friends' deviant behaviour. Instead, we use the cheating of classmates to explain cheating in school. This brings us closer to a situational convergence, which is crucial in SAT (see Hardie, 2020). As cheating by definitiontakes place within the school setting, we can ensure that the observed behaviour is taking place at the moment that students are exposed to the influence of the moral norms of the setting. Additionally, by employing person as well as school fixed-effects models, we can control for selection into settings with different levels of criminogeneity, as well as unobserved heterogeneity across adolescents and schools. This allows us to attribute with greater certainty our findings to the proposed actiongenerating mechanism.

Situational action theory
SAT explains the breaking of moral rules as the outcome of a situational person-environment interaction (Wikström et al., 2012: 11-12). Situational causes lie in the interplay between persons' propensity for rule-breaking and the criminogeneity of the setting in which they take part. A person's propensity for rule-breaking (P) is determined by their morality (i.e. their personal moral rules and their moral emotions, guilt and shame) as well as by their ability to stick to those moral rules when externally pressured to break them (i.e. their ability to exercise self-control). A setting is defined as the environment (E) an actor perceives at a particular moment in time (Oberwittler and Wikström, 2009: 36), and is characterised by its criminogeneity. The setting's criminogeneity depends on the moral context, that is the moral norms it conveys, and the ability to enforce these norms in a specific situation, deterrence. The strength of a moral norm that applies to a setting 'is the degree to which it is shared by those taking part in the setting' (Wikström, 2010: 222). This criminogenic interaction (P x E) initiates a cognitive perception-choice process (Wikström et al., 2012: 17-22), which is depicted in Figure 1.
The starting point of this perception-choice process is the presence of a motivation, such as temptation or provocation (otherwise path a). First and foremost, the perception is guided by the so-called moral filter, which is constituted by personal morality and the moral norms of the setting. The moral filter determines whether a person perceives rule-breaking as an action alternative in response to a motivation.
According to the principle of moral correspondence, under conditions of correspondence between personal morality and the moral norms of the setting, people are most likely to perceive only those action alternatives that are in line with their morality. If people perceive only this one action alternative, they will habitually follow their morality without active consideration (Wikström et al., 2012: 19). If people with rule-abiding morality are exposed to moral norms of a setting that discourage rule-breaking, it is unlikely that they will perceive rule-breaking as a viable action alternative and, thus, it is unlikely that rules will be broken (path b). Therefore, we hypothesise that when students with a rule-abiding morality are in classrooms with moral norms that discourage cheating, they will be unlikely to cheat (Hypothesis 1.1).
In cases in which people's morality and the moral norms of the setting encourage rule-breaking, people will habitually break the rules when a motivation to do so is present (path c). It follows that when students with a rule-breaking morality are in classrooms with moral norms that encourage cheating, they will be likely to cheat (Hypothesis 1.2).
Only if people's own morality conflicts with the moral norms of the setting does a deliberative choice process determine whether people will break a rule (Wikström et al., 2012: 26). According to the principle of conditional relevance of controls, it is only in situations where persons with rule-abiding morality are exposed to moral norms that encourage rule-breaking that self-control matters independently of a setting's deterrence (Wikström et al., 2012: 26). People with high self-control will be able to withstand the external pressure and not break the rules (path d), while people with low selfcontrol, who cannot withstand the external pressure, will break the rules (path e). Hence, when students with a rule-abiding morality are in classrooms with moral norms that encourage cheating, their likelihood of cheating depends on their ability to exercise selfcontrol (Hypothesis 2).

Literature review
Empirical evidence relating to our hypotheses is limited. While a wide range of factors has been identified as being associated with student cheating, such as attitudes and beliefs regarding cheating (e.g. Eisenberg, 2004;Teixeira and Rocha, 2008), self-control (e.g. Cochran et al., 1998;Muraven et al., 2006;Williams and Williams, 2012), moral norms (e.g. Eisenberg, 2004;Teixeira and Rocha, 2008) and peer influence (e.g.  , 1992;McCabe and Trevino, 1997), only a few studies speak to SAT's principle of moral correspondence and the conditional relevance of self-control.

McCabe
We review the limited empirical evidence on cheating in the next section. Given the small amount of research on cheating relating to our research interest, we also review the SAT literature that addresses the principle of moral correspondence and the conditional relevance of self-control on rule-breaking acts other than cheating.

Studies on cheating
Studies that take both morality and moral norms into consideration usually assume independent effects of both (e.g. Eisenberg, 2004;Jordan, 2001;Salter et al., 2001;Schuhmann et al., 2013;Teixeira and Rocha, 2008). The few studies that test an interactive influence of morality and the moral norms of the setting, which speaks to the principle of moral correspondence, find mixed results. Studying the influence of students' morality on their cheating, Malinowski and Smith (1985) found that students with a rule-breaking morality cheated more. At the same time, they found that those with a rule-abiding morality cheated when they felt more tempted to cheat. By contrast, when studying the interplay of morality and moral norms among college students, O'Rourke et al. (2010) found that those who considered cheating unacceptable (i.e. those with a rule-abiding morality) were little affected by direct knowledge about someone else's cheating. For those with a rule-breaking morality who considered cheating more acceptable, knowing that someone else cheated increased their likelihood of cheating.
Regarding the conditional relevance of self-control, we did not find a single study testing SAT's proposed three-way interaction between morality, moral norms, and selfcontrol in relation to cheating. Even studies taking into consideration the influence of all three factors independently are rare, and only provide mixed results. For example, Bolin (2004) found no direct relationship either of the moral norms of the setting or of selfcontrol with cheating in a sample of university students in the US. However, he found that both moral norms and self-control had an indirect effect on cheating via morality. On the other hand, Tibbetts and Myers (1999) found that friends' cheating, and morality, each influenced the cheating intention of university students independently, but that the strong association of self-control with cheating propensity was accounted for by the effects of other variables, most notably shame (which taps into the morality conceptualisation of SAT). Freiburger et al. (2017) found that self-control and cheating morality had a direct effect on cheating in a sample of US university students, but the influence of friends' cheating was entirely mediated by the perceived likelihood of getting caught.

SAT tests on other outcomes than cheating
Turning to studies testing SAT's principle of moral correspondence and the conditional relevance of self-control for outcomes other than cheating, the evidence is also scarce and inconclusive.
Regarding the principle of moral correspondence, a vignette study with Bangladeshi adults found independent effects of rule-abiding morality and exposure to the moral norms of the setting on the intention to engage in violent offending (Brauer and Tittle, 2017). However, there was no evidence for the interaction between personal morality and the moral norms as predicted by SAT's moral filter. In this study, the moral norms of the setting were captured by participants' perceptions of friends' and families' moral assessment of the use of violence, as well as participants' perceived use of violence in their neighbourhood. By contrast, a vignette study among Belgian secondary education and university students found support for the principle of moral correspondence (Pauwels, 2018). In line with SAT's predictions, the most substantial share of the respondents contemplated violence in the condition of moral correspondence when both their personal morality and the moral norms of the setting encouraged rule-breaking; the smallest share to do so was found when personal morality and the moral norms of the setting discouraged rule-breaking.
Both studies tested the conditional relevance of self-control as well. Again, evidence on this is inconclusive. 2 Pauwels (2018) found that self-control influences the reporting of the use of violence irrespective of the configuration of the moral filter. Thus, contrary to SAT's predictions, self-control influences the contemplation of violence not only in the condition of conflict between personal morality and the moral norms but also in the scenario of moral correspondence. Whereas SAT predicts that only people with a rule-abiding morality who are exposed to rule-breaking moral norms of the setting should be influenced by self-control, Brauer and Tittle (2017) found that self-control (operationalised as impulsivity) only increases the likelihood of perceiving and contemplating violence as a realistic possibility for participants with a rule-breaking morality.
Schepers and Reinecke (2018) compared the influence of self-control (operationalised as risk-seeking) across subgroups based on the level of morality and the level of the moral norms of the setting (operationalised as participants' reports about their friends' delinquent behaviour) in two cohorts of German middle school students. While they found that the effect of self-control is conditional on the specific combination of personal morality and the setting's moral norms, they also found that self-control has an influence in subgroups of moral correspondence.

Limitations of existing studies
The fact that these studies provide mixed evidence about the principle of moral correspondence and the conditional relevance of self-control could be due to methodological shortcomings that result in two challenges.
The first challenge is the mismatch between the theoretical presupposed convergence and the actual measurement of actors exposure to a behavioural setting and rule-breaking. For testing SAT's situational model, it is crucial that we spatially link the exposure to the observed act of rule-breaking (Wikström et al., 2012; for a detailed discussion Hardie, 2020). Studies using observational data often rely on indirect measures of criminogenic exposure and could only assume that an actor is exposed to a behavioural setting in the moment of crime occurrence (besides studies using space-time budget data, see Gerth, 2020;Wikström et al., 2018). These indirect measures of exposure, such as the rule-breaking of friends (Freiburger et al., 2017;Schepers and Reinecke, 2018;Tibbetts and Myers, 1999), do not provide information about whether a specific act of rule-breaking happened when those friends were present.
Additionally, the selection mechanism challenges the investigation of the actiongenerating mechanism (on this point, see also Ernst and Lenkewitz, 2020). Explaining and testing the action-generating mechanism presupposes the convergence between actors and their exposure to behavioural settings. The selection mechanism precedes SAT's situational model by explaining how the convergence comes about. Although SAT recognises both mechanisms theoretically, studies on observational data, that do not inform about the circumstances under which rule-breaking emerged, cannot disentangle whether the observed outcome is due to selecting different kinds of people into different kinds of places or SAT's situational model 3 . This aspect is significant as people systematically select themselves, and are selected into, settings with different levels of criminogeneity Wikström and Treiber, 2016).

Present Study
We aim to provide a stricter test of the principle of moral correspondence and the conditional relevance of self-control than previous studies have done by focussing on the initial condition of the perception-choice process, the interplay between personal morality and the moral norms of the setting, and by addressing the outlined methodological challenges. Hereto, we investigate school cheating and make strategic use of the school setting.
Addressing the challenge of spatio-linkage, we make use of the fact that school cheating is committed within the school, and we operationalise the moral norms of the setting by a measure capturing the cheating of the other students in the class (the descriptive norm). Thus, the link between the moral norms of the setting and rule-breaking is ensured. Moreover, the descriptive norm corresponds to SAT's twofold argument about the moral norms of the setting, which addresses the definition of the moral norms and their perception. On the one hand, the perception links an actor to the behavioural setting (Wikström, 2006). Thus, it is not an objective rule that guides the actor, but rather their subjective perception of that rule at that moment. Even though cheating, by its very nature, is committed secretly and may not be seen, we assume that students of the same class will discuss it, and, thus, it becomes perceivable to the actor. On the other hand, moral norms are an attribute of the behavioural setting actors are exposed to (Oberwittler and Wikström, 2009;Wikström, 2006). The descriptive norm corresponds to SAT's consideration that the strength of the moral rule reflects 'the degree to which it is shared by those taking part in the setting' (Wikström, 2010, 222). Evidence shows that people act by reference to the behaviour of others in the behavioural setting they are exposed to, and thus are oriented towards the descriptive norm (Cialdini et al., 1991;Paternoster et al., 2013).
Additionally, we aim to ensure that our analytical strategy addresses the proposed action-generating mechanism and thus control the selection mechanism. In combination with within-estimators, the school setting is particularly suitable for testing action-theories, such as SAT, as schooling is compulsory and exposure to the school setting varies on fewer dimensions than other comparisons of exposure. As the within-estimators only compare students with themselves, by using person fixed-effect estimators, and students of the same school with each other, by using school fixed-effects estimators, far-reaching aspects of the selection mechanism, namely the school track choice and school choice, are controlled for (for the use of fixed-effects estimation, see Allison, 2009;Andreß et al., 2013). Additionally, the use of person fixed-effects eliminates time-invariant person characteristics, and the use of school fixed-effects eliminates constant school attributes.

Data and measures
This study is based on data from the German large-scale school panel study 'Friendship and Violence in Adolescents' (Kroneberg et al., 2016), conducted in five cities in the metropolitan Ruhr area. Because data on cheating were collected only in wave 3 and wave 4, we limit our analysis to these waves. Data collection took place between September and December of 2015 (wave 3; 9th grade) and 2016 (wave 4; 10th grade). Apart from special needs schools, all schools with the respective grades were asked to participate with their entire grades. 4 In wave 3, a total of 46 of 55 of all requested schools (wave 4: 45 of 52), and 3793 of 4400 (wave 4: 3809 of 4320) students participated, which yields a student participation rate of 86% (wave 4: 88%). Most participants attend a comprehensive school (34%) or an intermediate secondary school (32%; upper secondary school: 22%; lower secondary school: 12%). Our analysis sample comprises 3038 observations (52 percent boys; median age in wave 3: 15 years).
The study used an Audio-Computer Assisted Self-Interview (Audio-CASI); all questions were presented in text and audible via headphones, to increase confidence and improve comprehension of survey questions (Beier and Schulz, 2015). Participants used netbooks provided by the research team.

Cheating
The dependent variable, cheating, captures students' cheating incidence in the last 12 months. 'How often have you cheated in the last 12 months (i.e. since October 2015)? If you don't know exactly, then please guess as best you can.'. (For a descriptive overview  of all measures, see table 3

Moral norms of the setting
We use the same question for creating a measure reflecting the moral norms of the setting, that is the descriptive norm. For each participant, we estimate the share of their classmates who reported at least one cheating incident in the 12 months preceding data collection. We estimate scores for each participant individually and exclude participants' own cheating score, in order to create a context measure that is not confounded with participants' own cheating. As we argued above, our operationalization rests on the assumption that students perceive their classmates' cheating.

Morality
For the sake of comparability with previous SAT tests, we use measures comparable to the personal morality scale used in PADS+ (Wikström et al., 2012: 132). For 18 different acts of rule-breakingsuch as 'hitting a classmate so that he or she bleeds', or 'smashing a streetlight for fun'participants were asked how bad they think these acts are.
Response options ranged from 1 'not bad at all' to 4 'very bad' (see Appendix B for a list of all items). We averaged the answers to all 18 items to build our measure of personal morality. The scale was transformed so that low values represent a rule-abiding morality and high values a rule-breaking morality. Although these measures do not refer to specific situations, we follow the interpretation that these generalised measures are related to adolescents' personal morality in specific situations (Wikström et al., 2012: 132).

Self-control
Self-control was only measured in wave 3. In line with previous studies on SAT, we use an adaptation of PADS+ measure of self-control (Wikström et al., 2012: 136) which is based on the Grasmick scale (Grasmick et al., 1993), with items such as 'I lose my temper pretty easily' and 'I sometimes find it exciting to do things that may be dangerous' (see Appendix B for a list of all items). Response options ranged from 1 'strongly agree' to 5 'strongly disagree'. Responses were averaged. High values represent low self-control.

Analytical Strategy
To test our hypotheses derived from SAT's principal of moral correspondence and conditional relevance of controls, we employ within-estimators in the form of person and school fixed-effects.
As can be seen from equation (1), differences in cheating behaviour, y ist , for student i in school s at time t are regressed on differences from the specific means in the independent variables, student i's morality at time t, m it , and the descriptive norm student i is exposed to at time t, dN it .
The effects of person time-invariant heterogeneity, α i , and heterogeneity between schools, λ s are cancelled out. However, this advantage comes with less efficient estimates as the standard errors of within-estimates are relatively large as all betweenness variation is cancelled out (Allison, 2009: 17).
To test our hypotheses, we specify interaction effects. For the principle of moral correspondence (hypotheses 1.1 and 1.2), we test the interaction effect of personal morality and the moral norms of the setting. For the test of the conditional relevance of self-control (hypothesis 2), we divide the sample into three different groups based on their morality. For each group, we estimate the interaction of self-control with the moral norms of the setting separately. As morality is highly skewed (Kroneberg and Schulz, 2018), with only a few participants judging the various rule-breaking acts as 'not bad at all' or 'not bad', we classify students who have an average of .5 on the morality scale as having a rule-breaking morality. Students with an average between .2 and .5 are classified as having a medium morality, and students with an average below .2 are classified as having a rule-abiding morality.
In our models, we include all constitutive terms alongside the interaction and, therefore, we interpret the coefficients of the constitutive terms as conditional effects (as advised by Brambor et al., 2006). To ease the interpretation of the interaction effects, we standardise both independent variables to the interval between 0 and 1 (Braumoeller, 2004).
The interaction effects are also presented in marginal effect plots, alongside histograms (see Hainmueller et al., 2019;Xu et al., 2017). The histogram shows areas of common support between the moderator and predictor and allows us to see whether the prediction of the marginal effects is covered by the data. If the data would not support the prediction, the effect would be extrapolated to combinations of the moderator and predictor that do not exist.

Results
We present our results, starting with our findings on the principle of moral correspondence (hypotheses 1.1 and 1.2) and then turning to the conditional relevance of self-control (hypothesis 2). Table 1 shows the results for our investigation of the principle of moral correspondence. Models 1 and 2 give the person fixed-effect estimators. Models 3 and 4 also controlin addition to the time-constant person heterogeneityfor school heterogeneity in the form of school fixed-effect estimators. Models 1 and 3 show the independent effects of morality and the descriptive norm on cheating. In general, a rule-breaking morality increases on average students' cheating (Model 1: 3.15; Model 3: 3.13), as does an increase in the rule-breaking descriptive norms (Model 1: 2.22; Model 3: 2.22). As we turn to models 2 and 4, which include the interaction effects, the significant interaction terms Notes: † p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001. Standard errors in parentheses.

Principle of moral correspondence
M*dN indicate that the association between personal morality and cheating depends on the moral norm of the setting. To test hypotheses 1.1 and 1.2, we compare a given level of personal morality under changes in the descriptive norm, and then we compare a given level of the descriptive norm under changes in personal morality, for each hypothesis. From hypothesis 1.1, it follows that students with a rule-abiding morality cheat less when they are exposed to moral norms that discourage cheating than when they are exposed to moral norms that encourage cheating. However, the results show that students with a rule-abiding morality, on average, do not change their cheating behaviour following the descriptive norm (Model 2: -.09; Model 4: .02) but have a low likelihood of cheating in general. Moreover, it follows from hypothesis 1.1 that students with a rule-abiding morality cheat less than students with a rule-breaking morality if both are exposed to moral norms that discourage cheating. Our results show that, on average, personal morality makes no substantial difference in cheating if students are exposed to moral norms of the setting which discourage cheating (Model 2: -.57; Model 4: -.45). Thus, our results on hypothesis 1.1 are inconclusive. On the one hand, the comparison between different levels of morality being exposed to moral norms that discourage cheating, and the comparison of students with a law-abiding morality being exposed to different levels of the descriptive norm, do not show significant differences. On the other hand, students with a rule-abiding morality that are exposed to moral norms that discourage cheating are unlikely to cheat, as predicted by SAT.
Analogous implications result from hypothesis 1.2. In line with our expectations, we find that students with a rule-breaking morality cheat, on average, more if they are exposed to moral norms that encourage cheating than if they are exposed to moral norms that discourage cheating (Model 2: -.09 + 6.85; Model 4: .02 + 6.40). Moreover, we find that, as we would expect from hypothesis 1.2, students with a rule-breaking morality cheat, on average, more than students with a rule-abiding morality when they are exposed to moral norms that encourage cheating (Model 2: -.57 + 6.85; Model 4: -.45 + 6.40). Figure 2 illustrates the findings of Model 2. The figure shows the marginal effects of the descriptive norm on cheating behaviour, on the y-axis, given different levels of personal morality, x-axis. The grey area represents confidence intervals. We see that students with the highest level of rule-abiding morality are not influenced in their cheating by exposure to different levels of the descriptive norm. For this group, the confidence interval includes zero. As consent to rule-breaking morality increases, exposure to different levels of the descriptive norms affects cheating substantially.

Principle of conditional relevance of controls
Now we turn to the results on the principle of the conditional relevance of self-control, and thus our sub-group analysis. Models 5 to 10 in table 2 give school fixed-effect estimators on data of wave 3. We find that in all morality subgroups, with a decrease in selfcontrol, cheating becomes more likely (Model 5: 1.94; Model 7: 2.82; Model 9: 3.06). Likewise, all groups are affected by an increase in the descriptive norm. As the share of classmates who cheat increases, students are more likely to cheat themselves (Model 5: 1.09; Model 7: 1.86; Model 9: 2.28).
The findings on the interaction between self-control and the descriptive norm supports SAT's principle of the conditional relevance of self-control. Following this principle, we hypothesised that self-control only influences the choice process when students with a  rule-abiding morality are exposed to moral norms of the setting that encourage cheating. In line with that hypothesis, we find that neither in the medium-morality group (see Model 8: n.s.), nor in the rule-breaking morality group (see Model 10: n.s.), does the association of self-control with cheating depend on levels of the descriptive norm. On the contrary, and following our expectations, we see that the association between self-control and cheating depends on the level of the descriptive norm in the rule-abiding morality group (see Model 6: 9.75). Figure 3 illustrates this relation and shows the marginal effects of self-control for different levels of the descriptive norm for students with a rule-abiding morality. In line with our expectations, self-control only has a significant effect on cheating when the number of students who cheat is high, and thus the moral norms of the setting encourage cheating. In this case, a decrease in self-control increases cheating.

Discussion
This study provides a strict test of SAT's principles of moral correspondence and the conditional relevance of self-control. By combining within-estimators with data from the German school study 'Friendship and Violence in Adolescence', we study student cheating in the setting of its occurrencethe classroombringing us closer to the spatio-linkage that Figure 3. The dark line and grey 95% confidence interval band depicts the conditional marginal effects of the school fixed-effect estimation, model 6. The graph reports the marginal effects of self-control on the incidence of cheating for different levels of the descriptive norm for the group of students with a rule-abiding morality.
is crucial in testing SAT (Hardie, 2020). This comes with the advantage of a stricter control for selection into settings with a certain level of criminogeneity and the accompanying unobserved heterogeneity. Moreover, we explicitly address the interplay between personal morality and the moral norms of the setting when testing the conditional relevance of selfcontrol. By investigating cheating, this study also joins the growing body of literature that applies SAT in the context of rule-breaking, which is not restricted to types of behaviour covered by laws (Beier, 2018;Cochran, 2015;Gerth, 2020).
In line with SAT's principle of moral correspondence, we find that in classes where students' morality is in correspondence with the class moral norms, they are likely to follow their own morality. Students with a rule-abiding morality in classes where cheating is uncommon do not cheat often. On the other hand, students with a rule-breaking morality in classes with a high share of cheating classmates cheat more often than when they are in classrooms that discourage cheating.
In line with the principle of the conditional relevance of self-control, the ability to exercise self-control has an impact on cheating only when students' morality and the moral norms are in conflict. When exposed to norms that encourage cheating, students with a rule-abiding morality and high self-control can stick to their morality and cheat less, whereas students with a rule-abiding morality and low self-control cheat more often.
However, we also find that under moral norms that discourage cheating, personal morality does not influence cheating. Following SAT, this may imply a lack of motivation to cheat, so that the perception-choice process is not stimulated, or that students perceive an extreme level of deterrence, so that even students that might be likely to cheat distance themselves from cheating as an action alternative. Therefore, we cannot ignore the possibility that the descriptive norm reflects, in addition to the moral norms of the setting, a setting's deterrence ability.
Our work has some limitations. Data restrictions force us to rely on a very general measurement of morality that does not include cheating-specific morality. Therefore, we can only assume that the general level of morality corresponds to the specific cheating morality. Given that research explicitly addressing this issue in the context of SAT is rare, this would be an interesting area for future investigation. Moreover, in a close reading of SAT, personal morality is not only comprised of a person's law-relevant moral rules but also of their moral emotions, guilt and shame (Wikström et al., 2012). This issue did not receive much attention in SAT tests in general (for an exception, see e.g. Trivedi-Bateman, 2019) and should be examined in the future. Another issue that needs further investigation is the empirical existence of the habitual pathway which is usually only assumed (for an exception see Beier, 2016).
Even if we could approach the spatio-linkage between exposure and rule-breaking behaviour, we still could not address the temporal dimension (for this point, see Hardie, 2020). Although students are familiar with the behaviour of their classmates, cheating might result from a motivation to cheat in a specific subject or even a specific exam. Additionally, cheating may vary by students' perceptions of the deterrence abilities of teachers, or moral norms might differ when students are taught in different classes for different subjects. While our study shares this limitation with all studies that use regular observational data, we would encourage research looking more closely at the situational level, such as vignette studies or space-time budgets.
Notwithstanding these limitations, our study contributes to discussing the relation between morality and self-control (Kroneberg and Schulz, 2018). Previous findings show (Kroneberg and Schulz, 2018;Svensson et al., 2010;Wikström and Svensson, 2010) that the relation between self-control and morality could be either readin line with SATas the conditionality of self-control on morality, orcontrary to SATas the conditionality of morality on self-control. However, these findings are based on studies equating morality with the moral filter, not recognising the moral norms of the setting. Thus, they do not test the moral filter, which is crucial for investigating and discussing the relation between morality and self-control within SAT.
While recognising the moral filter, we find that self-control only matters when students with a law-abiding morality are exposed to rule-breaking encouraging moral norms of the setting. With this, we show that recognising exposure to the moral norms of the setting matters for investigating the moral filter and thus the principle of moral correspondence and the principle of the conditional relevance of controls. However, our findings do not address the question of symmetry between morality and self-control. Investigating the relation between personal morality, moral norms of the setting, and self-control is an essential issue for future research.
Comparing students within different classes in the same school allows to draw a very practical conclusion from our findings. Students with rule-breaking morality may cheat when exposed to many others who cheat, but not when exposed to fewer others who cheat. This suggests that moving students with rule-breaking morality into classes with cheating discouraging moral norms would be an effective way of reducing individual cheating behaviour. Moreover, this supports the creation of moral norms in schools in which deviance is deemed unacceptable.