1 Introduction

“Pecunia non olet” (money doesn’t stink), as the Roman emperor Vespasian said to alleviate concerns that a presumably impure source of money would lower its value. One such impure source is dishonestly earned money. While some people are incorruptible and will suffer from lying, others follow Vespasian’s adage and will cheat for personal gain without hesitation. This trait allows them to extract additional rents, and may make professions that allow for misreporting opportunities particularly attractive to them. Indeed, survey evidence indicates large differences in trust in different professions. Typically, those professions with cheating opportunities, such as insurance agents, advertising executives but also politicians are the least trusted ones. In contrast, professions with little potential for manipulation, such as firefighters or teachers, are among the most trustworthy professions globally.Footnote ¹ These opposites in the trustworthiness of different professions involve a deeper problem of causality. On the one hand, it is conceivable that the mere existence of a cheating opportunity in a certain profession might induce dishonesty. On the other hand, it is also conceivable that individuals self-select deliberately ex ante into different professions with different degrees of cheating opportunities. Such a self-selection could occur according to an individual’s attitude toward honesty because money might stink for some, but not for others.

These considerations lead to empirical questions. Are individuals willing to pay to earn in an honest fashion? How badly do they suffer as a side effect of dishonest earnings? How is this lying cost related to their choice between an honest earning opportunity and one that allows them to make more money, but only if they are prepared to cheat? Finally, is dishonest behavior the outcome of the misreporting opportunity per se, or is it rather the outcome of deliberate self-selection into such opportunities? In other words, do certain professions attract dishonest people, or is it the cheating opportunity that makes people dishonest? We provide causal evidence of a self-selection effect, and rule out that the mere likelihood of facing the cheating opportunity induces dishonest behavior. Moreover, we show that the individual’s lying costs determine the self-selection. Hence, abstracting from self-selection may lead to an underestimation of actual cheating behavior.

We generate these insights from a theory-guided experiment in the laboratory in which individuals choose between two binary lotteries in two different choice conditions. One lottery, let us call it the ‘Bad Lottery,’ has a zero outcome with high probability and a win outcome with a low probability. The other lottery yields the zero outcome with a low probability and the win outcome with a high probability. Let us refer to it as the ‘Good Lottery.’ The Bad Lottery is costless. To obtain the Good Lottery instead, individuals have to pay a price. We elicit individuals’ willingness to pay (WTP) for the Good Lottery which has higher odds of having an opportunity to earn honestly instead of earning money through a misreporting opportunity. This WTP can reflect how badly different individuals suffer from making dishonest earnings. Therefore, this WTP can be seen as a subtle way to measure the heterogeneity in lying costs. Their lottery choice is recorded for two different conditions. One condition is truthful by design, and the lottery outcome is identical to the individual’s final payout. Here, an individual’s attitude toward truth-telling is irrelevant. The other condition allows for misreporting. In particular, the individual may claim the win outcome even if the true lottery outcome is zero. Observing individuals’ actual reporting behavior when the misreporting opportunity emerges allows us to study how the WTP and the reporting behavior are related to each other. These findings give a good indication of whether individuals self-select into honest or dishonest earnings based on their lying costs.

Our results indicate that some, but not all individuals have a smaller WTP for the Good Lottery in the condition with the misreporting opportunity. Some individuals are not willing to spend money to obtain the Good Lottery. They also tend to misreport whenever the opportunity arises. Other individuals expend considerable resources to obtain the Good Lottery. These individuals with a higher WTP are also less likely to misreport if the misreporting opportunity emerges. Importantly, the finding does not depend on whether they are assigned to the preferred Good Lottery or whether they are exogenously assigned to the Bad Lottery instead. Their consistently honest behavior clearly indicates that (dis)honesty is determined by self-selection and not by the probability of facing the cheating opportunity.

Our work is related to the literature on cheating in general (as recently surveyed by Abeler et al. Reference Abeler, Nosenzo and Raymond2019 and Gerlach et al. Reference Gerlach, Teodorescu and Hertwig2019), and to two strands of this literature in particular. One literature strand touches on the issue of the self-selection of dishonest subjects into, or out of, lying opportunities. Several field experiments analyze the relationship between the occupational choice to work in corrupt sectors and the individual propensity to cheat. Departing from high corruption in the public sector of India, Banerjee et al. (Reference Banerjee, Baul and Rosenblat2015) show that aspirants for public sector jobs engage in more corruptive behavior compared to aspirants for the private sector. Similarly, Hanna and Wang (Reference Hanna and Wang2017) find a positive correlation between dishonest behavior in the laboratory and fraudulent behavior in the field for government nurses. A further dimension is the role of cheating opportunities for self-selection into competitive settings as documented by Faravelli et al. (Reference Faravelli, Friesen and Gangadharan2015) and Gino et al. (Reference Gino, Krupka and Weber2015). However, clean and theory-guided evidence on whether subjects deliberately self-select into cheating opportunities based on their lying costs is limited so far. In Shalvi et al. (Reference Shalvi, Handgraaf and De Dreu2011) the individuals are offered a fixed payoff as an exit option over participating in the dice-rolling game. In their framework the take-up of the exit option is not much affected by the possibility to lie, and lying behavior seems to be almost unrelated to the value of the exit option. We advance this literature since our design allows us to show that it is self-selection rather than the mere existence of a cheating opportunity which drives dishonest behavior. Additionally, by relating the WTP for honest earnings to reporting behavior, we identify an individual’s lying costs as the determinant of self-selection. A potential implication is that screening procedures for applicants might be particularly promising for fighting dishonest behavior in certain professions.

Second, we contribute to the literature on the role of monetary incentives for lying and the measurement of lying costs. One approach is to vary the incentive size between treatments/experiments. Fischbacher and Föllmi-Heusi (Reference Fischbacher and Föllmi-Heusi2013) do not find a significant increase in lying when monetary incentives are tripled. Kajackaite and Gneezy (Reference Kajackaite and Gneezy2017) come to a similar conclusion and show that the lying rate is largely insensitive to the multiplication of stakes. In meta-studies, Abeler et al. (Reference Abeler, Nosenzo and Raymond2019) and Gerlach et al. (Reference Gerlach, Teodorescu and Hertwig2019) confirm this pattern and document only little variation in dishonest behavior with respect to the reward size. Hilbig and Thielmann (Reference Hilbig and Thielmann2017) use an alternative approach and vary the incentive size within-subjects for repeated cheating opportunities. They find evidence of ‘brazen liars’ and ‘incorruptible subjects,’ but also of subjects whose reporting decision is dependent on the stake size. However, the repeated setting might have an effect on cheating in itself. Finally, Gibson et al. (Reference Gibson, Tanner and Wagner2013) and Vranceanu and Dubart (Reference Vranceanu and Dubart2019) elicit subjects’ reservation price to engage in fraudulent reporting and deceptive communication. Both find considerable heterogeneity in reservation prices, which suggests that misreporting is sensitive to monetary incentives. In contrast to most of the literature on dishonest decision-making, this approach implies that cheating is not a binary decision but rather there is a price for being dishonest by design. We propose a more subtle procedure to measure lying costs at the individual level. Our setting allows us to pin down a subject’s lying costs in a two-step procedure, but avoids implying that there is a price for misreporting by design. Hence, we complement the findings of the previous literature, and resolve some of the conflicting results on the heterogeneity of lying costs.

We proceed as follows. First, we sketch the backbones of the decision-theoretic framework which is closely mapped in our experimental design. We then derive predictions and provide a benchmark for the interpretation of the behavior in our laboratory experiment. We describe and discuss our experimental results before we finally conclude.

2 The decision-theoretic framework

Consider an individual that maximizes its expected monetary payoff. The individual chooses between two binary lotteries (labeled ‘Good Lottery’ and ‘Bad Lottery’). Each lottery yields either a high payout $x_H$ (denoted as ‘win outcome’) or a low payout $x_L$ (denoted as ‘zero outcome’), with $x_H>x_L$ . The Bad Lottery B yields the high outcome $x_H$ with probability $p_B$ and the zero outcome $x_L$ with probability $1-p_B$ . The Good Lottery G yields $x_H$ with probability $p_G$ and $x_L$ with probability $1-p_G$ . Lottery G is the better lottery because $p_G>p_B$ .

2.1 The Honest Condition: choosing in the absence of a misreporting opportunity

An individual can choose the Bad Lottery B for a zero price. For a price $z\ge 0$ she can choose the Good Lottery G instead. We denote the two choice alternatives by (B, 0) and (G, z). Once this choice is made, the individual learns the lottery outcome and is rewarded with this true outcome as her payoff. The expected payoffs from (B, 0) and (G, z) are ${\pi }_B=p_B{x}_H+(1-p_B)x_L$ and ${\pi }_G=p_G{x}_H+(1-p_G)x_L-z$ . The indifference price

(1) $\begin{array}{c}{z}^{\ast }=(p_G-p_B)(x_H-x_L)\end{array}$

gives the individual the same expected payoff from (B, 0) and from $(G,z^{\ast })$ . For a price $z\le z^{\ast }$ the purchase of the Good Lottery G leads to an equal or higher expected payoff. Hence, the expected payoff-maximizing individual chooses (G, z) for $z\le z^{\ast }$ and (B, 0) for $z>z^{\ast }$ . The fraction of individuals who choose (G, z) as a function of z is depicted as a function ${\gamma }_T\left(z\right)$ in Fig. 1: ${\gamma }_T\left(z\right)=1$ for $z\le (p_G-p_B)(x_H-x_L)$ and ${\gamma }_T\left(z\right)=0$ for any higher price.

Fig. 1 Predicted fraction of individuals purchasing the Good Lottery G as a function of its price z

2.2 The Untruthful Reporting Condition: choosing with a misreporting opportunity

Let us change one assumption in the setup. As before, the individual chooses between (B, 0) and (G, z) and then learns the true lottery outcome. But then the individual is asked to report the lottery outcome. This report does not need to be truthful, i.e., the individual can choose any report $\xi \in \{x_H,x_L\}$ . She receives exactly this reported value $\xi$ as her payoff.

Suppose that the individual has a (behavioral) cost of reporting untruthfully. Let this cost be equal to $\theta \ge 0$ and a draw from a random variable with cumulative distribution function $F\left(\theta \right)$ with support $[0,\infty )$ .Footnote ² This $\theta$ might be interpreted as the sum of internal lying costs, including (self-) image concerns and the costs of violating (self-imposed) social norms, as modeled explicitly e.g., in Gneezy et al. (Reference Gneezy, Kajackaite and Sobel2018) or Abeler et al. (Reference Abeler, Nosenzo and Raymond2019). For brevity, we refer to $\theta$ as the individual’s lying costs.

Based on these primitives the optimal reporting behavior of an individual with lying costs $\theta$ is the following. A win outcome $x_H$ is always reported honestly, $\xi \left(x_H\right)=x_H$ . In contrast, whether the individual reports truthfully if the lottery outcome is $x_L$ depends on $\theta$ : $\xi \left(x_L\right)=x_L$ if $\theta \ge (x_H-x_L)$ and $\xi \left(x_L\right)=x_H$ if $\theta <(x_H-x_L)$ . The individual misreports on $x_L$ if and only if her lying costs $\theta$ fall short of the monetary benefits of misreporting. Taking this reporting behavior into account, the expected payoffs for the choices (B, 0) and (G, z) are

(2) ${\pi }_B\left(\theta \right)=\left(\begin{array}{c}{x}_H-(1-p_B)\theta \text{if}\theta <x_H-x_L\\ p_B{x}_H+(1-p_B)x_L\text{if}\theta \ge x_H-x_L\end{array}\right)$

and

(3) ${\pi }_G\left(\theta \right)=\left(\begin{array}{c}{x}_H-(1-p_G)\theta -z\text{if}\theta <x_H-x_L\\ p_G{x}_H+(1-p_G)x_L-z\text{if}\theta \ge x_H-x_L\end{array}\right)\text{.}$

This makes the lottery choice straightforward: an individual pays z and chooses (G, z) if ${\pi }_G\left(\theta \right)-{\pi }_B\left(\theta \right)\ge 0$ , and goes for (B, 0) if ${\pi }_G\left(\theta \right)-{\pi }_B\left(\theta \right)<0$ , where

(4) ${\pi }_G\left(\theta \right)-{\pi }_B\left(\theta \right)=\left(\begin{array}{c}(p_G-p_B)\theta -z\text{if}\theta <x_H-x_L\\ (p_G-p_B)(x_H-x_L)-z\text{if}\theta \ge x_H-x_L\end{array}\right)\text{.}$

For the case of indifference, we assume that the individual chooses (G, z). The fraction of individuals who purchase (G, z) as a function of z is depicted as ${\gamma }_M\left(z\right)$ in Fig. 1.

For a price $z>z^{\ast }=(p_G-p_B)(x_H-x_L)$ the individual will never purchase (G, z). This behavior is independent of the individual’s $\theta$ : for $\theta \ge x_H-x_L$ the individual reports truthfully, but we have ${\pi }_G\left(\theta \right)-{\pi }_B\left(\theta \right)=(p_G-p_B)(x_H-x_L)-z<0$ . For $\theta <x_H-x_L$ the individual reports $\xi =x_H$ for any true lottery outcome, and we have ${\pi }_G\left(\theta \right)-{\pi }_B\left(\theta \right)=(p_G-p_B)\theta -z<$ $(p_G-p_B)(x_H-x_L)-z<0$ . Hence, ${\gamma }_M\left(z\right)={\gamma }_T\left(z\right)=0$ for all $z>z^{\ast }.$

For z $\le z^{\ast }$ , individuals with $\theta \ge x_H-x_L$ report truthfully and choose (G, z), as purchasing (G, z) gives them a higher expected payoff than (B, 0). In contrast, individuals with $\theta <x_H-x_L$ report $\xi =x_H$ for any true lottery outcome. For these individuals, ${\pi }_G\left(\theta \right)-{\pi }_B\left(\theta \right)$ is weakly increasing in $\theta$ : the higher the individual’s lying costs, the worse the zero outcome is compared to the win outcome, and the higher the individual’s WTP for the Good Lottery. An individual is just indifferent between (B, 0) and (G, z) for $(p_G-p_B)\theta -z=0$ , or $\theta =z/(p_G-p_B)$ .Footnote ³ Individuals with a lying cost higher than (or equal to) $z/(p_G-p_B)$ purchase (G, z), while individuals with smaller lying costs choose (B, 0). Accordingly, for a given z the fraction of individuals who choose (G, z) is equal to the probability that $\theta \ge z/(p_G-p_B)$ , or,

(5) $\begin{array}{c}{\gamma }_M\left(z\right)=1-F\left(\frac{z}{p_G-p_B}\right)\text{for}z\le z^{\ast }\text{.}\end{array}$

3 Experimental analysis

5 Robustness discussion

In this section, we discuss several features of our experimental design. A main point is the observability of lying at the individual level in our data. It allows for a one-to-one analysis of the relationship between reporting behavior and individual characteristics, and for a direct comparison of dishonest behavior between the three lottery allocations.Footnote ²⁴ The computerized implementation of the URC also minimizes differences in the implementation of the HC. However, the observability may have consequences for subjects’ reporting behavior. On the one hand, it may increase subjects’ lying costs, for example, through more pronounced social image concerns. In turn, subjects may lie less as compared to unobservable settings, leading to a lower bound for dishonesty. On the other hand, subjects may anticipate the purpose of the experiment due to the observability of true outcomes, or even consider lying as an implicit rule. This raises concerns about an experimenter demand effect, which may imply a larger propensity to cheat. Moreover, subjects’ behavior may reverse outside the laboratory, which could challenge the external validity of our findings. In the following, we discuss these concerns, and provide robustness analyses with our post-experimental control questions. We also address how lying under passive observability in the data is different from active audits or being caught with probability one.

The literature on dishonesty has used paradigms with different degrees of observability, ranging from lying in one’s mind (Jiang Reference Jiang2013) over lying on an unobservable dice roll (Fischbacher and Föllmi-Heusi Reference Fischbacher and Föllmi-Heusi2013) to computerized settings such as ours (e.g., Kocher et al. Reference Kocher, Schudy and Spantig2018). Differences in the lying behavior between these paradigms indicate that changes to the observability of outcomes may have an impact on a subject’s lying cost. For example, in Jiang’s mind game (Reference Jiang2013) subjects tend to cheat more as compared to other settings (Kajackaite and Gneezy Reference Kajackaite and Gneezy2017). Some contributions address the role of observability directly, for example, van de Ven and Villeval (Reference van de Ven and Villeval2015) show that lying behavior is largely insensitive to privacy interventions, while Mol et al. (Reference Mol, van der Heijden and Potters2020) conclude that only active as opposed to passive observation deters cheating behavior. An underlying question is whether dishonesty under observability is lying at all, and how it affects the structure of lying costs. Social norms may give insights to the first part of the question. Simon (Reference Simon2020) finds that misreporting on a computerized lottery outcome is regarded as dishonest behavior by the majority of subjects. Finally, there are typically lower levels of dishonesty as well as no partial lying in observable as compared to ‘unobservable’ settings, but lying behavior is still substantial (Gneezy et al. Reference Gneezy, Kajackaite and Sobel2018; Abeler et al. Reference Abeler, Nosenzo and Raymond2019). Importantly, none of the mentioned paradigms completely rule out feelings of being observed. At least subjects themselves, and depending on their religious attitudes a metaphysical third party, observe their dishonesty. Therefore, considerations about who is able to observe one’s lie are present in all settings, and the fear of being regarded as a liar is an essential component for the trade-off on whether to be dishonest or not. Observability becomes a matter of how much, rather than whether or not. The observability in the data may increase the weight of this component, but does not change the qualitative nature of the lying problem.Footnote ²⁵

Complementary to this discussion, we assess the effect of observability empirically. One of our post-experimental control questions asked whether subjects felt observed at any point in time (please also refer to Appendix A.3 in the Supplementary Information). Overall, a large group of 78 percent of subjects stated not having felt observed. Only a small group of 22 percent of subjects were concerned about being observed.Footnote ²⁶ This indicates that the computerized setting may have had only a limited impact on the reporting behavior. More importantly, the behavioral differences between the two groups are in line with our quantitative interpretation of higher lying costs under passive observability. Subjects who felt observed are marginally less likely to lie than their counterparts (35 percent vs. 53 percent, ${\chi }^2$ -test: $p=0.10$ ) and have larger estimated empirical lying costs (EUR 10.29 vs. EUR 7.16, Wilcoxon-Mann-Whitney test: $p=0.02$ ). This fits well into our theoretic framework. The subjects who felt observed may be more concerned about their social image and have higher lying costs. In contrast, an experimenter demand effect would predict that these subjects are more likely to lie and would have smaller estimated empirical lying costs. In a second step, we repeat our analysis in section 4 for both subgroups separately. Due to the small sample of subjects who felt observed as well as due to the theoretical reasoning of larger lying costs, results are stronger in the group of subjects who did not feel observed but we confirm our results in both subgroups. Figure 8 in the Appendix A.3 in the Supplementary Information illustrates the WTP for the Good Lottery in the HC and the URC (compare to Fig. 2). The gap in the WTP the HC and URC is larger for subjects who did not feel observed, but subjects who felt observed also exhibit a difference in the WTP between both conditions. In summary, these results dampen concerns of an experimenter demand effect. Both from a theoretical and empirical perspective, it rather seems that the observability increased subjects’ lying costs.

As a further robustness analysis, we compare the reporting behavior of experienced to unexperienced subjects. Unexperienced subjects might be less prone to consider cheating as part of the game. We calculate an experience score based on self-reported previous knowledge of our post-tests. Even though unexperienced subjects are less likely to lie (34 percent vs. 67 percent, ${\chi }^2$ -test: $p<0.01$ ) and have higher estimated lying costs (EUR 9.72 vs. EUR 5.73, Wilcoxon-Mann-Whitney test: $p<0.01$ ), we confirm our findings in a subsample analysis for unexperienced subjects.Footnote ²⁷

Finally, in light of the initial example of self-selection into different occupations, the question of the external validity of our results arises. There is convincing evidence of a positive correlation between cheating in the lab and dishonest behavior in the field (e.g., Hanna and Wang Reference Hanna and Wang2017 for skipping work, Potters and Stoop Reference Potters and Stoop2016 for the return of overpayment, Dai et al. Reference Dai, Galeotti and Villeval2018 for fare dodging in public transport, Cohn and Maréchal Reference Cohn and Maréchal2018 for school misconduct, and Cingl and Korbel Reference Cingl and Korbel2020 for adolescent delinquents). This also applies to the related setting of tax compliance experiments (Alm et al. Reference Alm, Bloomquist and McKee2015). A corresponding field experiment is beyond the scope of this paper. However, the findings on the external validity of other forms of cheating behavior suggest that our results may allow for conclusions on the behavior outside the laboratory.