Incentives to cheat under loss aversion
Celia Blanco,1 Lara Ezquerra,2 Ismael Rodriguez-Lara2
1 Department
of Economics, Royal Holloway University of London
2 Department
of Economics, Middlesex University
June 2015
Abstract
We present an experiment designed to measure the effect of three different incentive schemes on cheating behaviour. Participants receive a
dice, which they roll privately. In the baseline treatment subjects receive a fix amount for rolling the dice. We can assume that there is no
incentive to lie in this treatment. In the second treatment, they receive
a payoff that will depend on the reported number. In the third treatment, subjects receive an initial endowment before rolling the dice.
The outcome of the die will determine if subjects lose part of their
endowment or keep the whole initial capital that they we allocated.
Since their payoff in the second and third treatments depend on the
reported roll of the die, the subjects have an incentive to be dishonest and report higher numbers to get a higher payoff. This design
has two advantages. First, cheating cannot be detected on the individual level. Second, the underlying true distribution of the outcome
under full honesty is known, and hence it is possible to test different
theoretical predictions. Theoretically, Prospect Theory predicts lying
behaviour to be higher on a loss domain; however, our findings show
that the individuals do lie less when they face a loss possibility.
1
1
Introduction
Economists believe in monetary incentives. They argue that people react
to them by affecting their behavior. Although individuals do not always
respond in the expected direction (Gneezy and Rustichini 2000a, 2000b),
economists stand by the idea that monetary incentives can be used to induce
the desired behavior (e.g., more effort). Thus, if appropriate, incentives
may serve to overcome any crowding-out effect in the intrinsic motivation of
individuals (Gneezy et al. 2011). Therefore understanding how incentives
work is of first order importance to induce better outcomes.
Probably, one of the most relevant ideas is the use of loss aversion in incentives. The recent work of Fryer et al. (2012) is an important contribution
along these lines. The authors use different payment schemes to incentivize
teachers and observes that students performance increases more when their
teachers are paid in advance and have to give that money back if their students do not succeed (loss dominion). They highlight that individuals may
be risk averse in the gain, as suggested by prospect theory (Kahneman and
Tversky, 1979). Although loss aversion has served to improve performance.
Arguably, there may be a concern regarding dishonest behavior.
Honest behavior has been shown to be relevant in a variety of contexts
such as accounting, auditing, insurance claims, job interviews, labor negotiations, regulatory hearings, and tax compliance. Honest behavior is
important because the lack of it could induce losses in the economy. The
well known Enron fraud can be an example of this. The American energy
company declared benefits while they had loses. When this fraud was discovered at the end of 2001, the fall of the firm had a huge impact on the
American economy as it was one of the biggest firms of the country. In addition, its shareholders and workers also suffered the consequences of their
savings and work being lost in a matter of days. A more recent case would
be the one affecting Volkswagen. They invented a scheme to manipulate
the measurement tests of their diesel emissions. It had a big impact on
the perception and value of this firm and the credibility of the sector and
2
institutions regulating emissions.
Researchers have studied that individuals are prone to cheating (Vanberg, 2015; Gneezy, 2005). In addition, other studies claim that there is a
fraction of subjects that do not lie even when is pareto optimal to do so
(Lopez-Perez and Spiegelman, 2013). This means that dishonest behaviour
has a cost for individuals. More studies have study cheating on different
contexts to see how supervision (Pascual-Ezama, 2013; Gino et al., 2012),
bonuses (Fryer, 2012), context (Erat and Gneezy, 2012; Cappelen et al.2013)
and information (Clots-Figueras et al., 2015) can affect the likelihood of being dishonest. The extent to which people react to loss, however, has not
been studied yet. The aim of this paper is to see if different payment schemes
have different effect on dishonesty.
We design an experiment in which individuals have incentives to lie. To
avoid any effect of incentives on effort, we use the task in Fischbacher and
Follmi- Heusi (2013) where individuals have to roll a dice and report the
obtained number.
Economists have always been interested in incentives and dishonesty.
Both affect the behavior of the relevant agents, who determine the final
economic outcomes. We want to test if subjects lie under different scenarios,
that differ in the form of different incentives schemes.
We modify the experimental design proposed by Fischbacher and FollmiHeusi (2013) to analyze the lying patterns of subjects under a gain domain
and a loss domain, to test if the prospect theory’s prediction works in an
scenario that is different from a lottery: a game in which lying leads to
higher profits or smaller loses.
The remainder of this paper is organized as follows. In Section 2 we
present our experimental design and the procedure. Section 3 presents the
main hypothesis. In Section 4 we explain our main results. Section 5 will
summarize the conclusions of the paper.
3
2
Experimental design
We run a one-shot decision making experiment at the Laboratory for Research in Experimental Economics (LINEEX) at the University of Valencia.
We recruited a total of 144 subjects, all of them undergraduate students.
This is a short experiment therefore, we used the procedures in Fischbacher
and Follmi- Heusi (2013) and added this experiment at the end of a previous
one.
1
At the beginning of the experiment, subjects received a ten-sided dice
and a copy of the experimental instructions.2 Their task consisted in rolling
the dice and reporting the number they obtained in the first roll. Subjects
were allowed to roll the dice as many times as they wanted, but it was
common information that only the first throw was relevant to their payment.
Is important to remark that we could not detect individual cheating and it
was known by subjects. Still, as each of the numbers should appear on on
tenth of the cases, there is evidence of cheating when the distribution is very
far from the theoretical one.
It is a between subjects design on which subjects only participate on one
treatment. Their payoffs then depended on the treatment assigned, as we
show in Table 1.
Table 1: Summary of the treatment conditions
1
2
3
4
5
6
7
8
9
0
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
Gain
1
1.5
2
2.5
3
3.5
4
4.5
5
0
Loss
-4
- 3.5
-3
- 2.5
-2
- 1.5
-1
- 0.5
-0
-5
Baseline
1
We made sure that the previous experiment was the same in all our treatments,
therefore all subjects have the same history. In addition, subjects did not receive any
feedback about the previous experiment when they were asked to participate in this one.
They were told that both experiments were independent and could earn some additional
money. All subjects decided to participate in this experiment.
2
A translated version of the instructions can be found in Appendix A
4
All treatments consisted of 48 subjects. In the Baseline treatment, subjects received e2.5 regardless of the reported number. This will be our control treatment where subjects do not have any incentives to lie. In the Gain
treatment, subjects received different payoffs depending on the reported
number. They obtained e1 if they reported a 1, e1.50 if they reported a
2,... e5 if they reported a 9, and nothing in the case of reporting a 0. As
for the loss treatment, subjects received e5 at the beginning of the session.
They were asked to keep this amount during the previous experiment, which
lasted around 100 minutes. The reported number in the Loss treatment determined the amount that subjects needed to return. Thus, if the reported
a 1 they had to return e4, if they report a 2 they return e3.50,...., they
return e5 with a 9 and they keep thee5 when they report a 0.
These payoffs were received at the end of the session in a sealed envelope,
except for the Loss treatment. In that treatment, subjects had an envelope
on their table. They were asked to put the money they had to return inside
the envelope and sealed it before leaving the room. The experiment lasted
around 10 minutes and the average payoffs of our subjects were e3.05.
3
Hypothesis
This research attempts to study how incentives affect lying behavior. In this
setting subjects gain more by reporting a number x* that is different from
the obtained one x.
We consider that the utility coming from reporting a number different
from the obtained one (x* > x) is a function of that difference: v(x*−x).
As we mentioned in the introduction, lying has a cost for subjects. In
this case, the material cost of cheating will be: c(x*−x) when c(x*− x ) >
0 if x*6=x.
There is evidence that subjects lie when there are incentives to do so
(Fischbacher and Follmi-Heusi, 2013). We then expect that subjects report
higher numbers in the Gain than in the Baseline treatment. According to
prospect theory Kahneman and Tversky, (1979), individuals perceive gains
5
and loses in a different way. This means that they assign a different weight
to the same amount of money depending on it being a loss or a gain, being
the loses weighted more than the gains.
If we assume that the cost of cheating c(.) is equal across treatments,
according to prospect theory we expect subjects to get more utility from
cheating in the loss than in the gain treatment vLoss(x*−x) ≥ vGain(x*−x),
therefore xLoss ≥ xGain.
The hypothesis that we want to test is then as follows:
Hypothesis 1: The reported numbers are the same in the Baseline, the
Loss and the Gain treatments.
4
Results
Figure 1 displays the cumulative distribution of the reported numbers for
each of the three treatments. Table 2 below the figure gives an overview of
our data by presenting the mean, the standard deviation and the number
of subjects who reported a low (0-5) and high (6-9) number in each of the
treatments.
6
Figure 1: Cumulative distribution per treatment
Table 2: Descriptive statistics
Obs.
Mean
Std. Dev.
Low
High
Baseline
48
5.06
2.85
23 (48%)
25 (52%)
Gain
48
6.44
2.46
14 (29%)
34 (71%)
Loss
48
5.06
3.12
24 (50%)
24 (50%)
The Kruskal-Wallis test suggest that the treatments follow different distributions (p= 0.02). The previous result can be seen graphically in Figure
1. It shows that the cumulative distribution of the reported number for
subjects who have been exposed to the Baseline and the Loss treatments
first-order stochastically dominates that for subjects exposed to the Gain.
We observe that roughly half of the sample reports low numbers in the
7
Baseline and Gain treatments. The frequency of low numbers on the Gain
treatment is however, smaller (29%). If we focus on high numbers, around
half of the subjects report these type of numbers in the Baseline and Loss
treatments while a much higher amount of subjects report these numbers in
the Loss treatment (71%).
As the die’s roll product follows a uniform distribution, the average obtained by our participants should be around 4.5. We find that the reported
means for Baseline and Loss are identical and equal to 5.06 (a two sample
t-test confirms that these means are not statistically different). The mean
for the Gain treatment is higher and equal to 6.43 (a two sample t-test rejects the equality of means between Baseline and Gain and between Gain
and Loss).
The descriptive statistics of Baseline and Loss are very close hinting that
they may follow very similar distributions. Meanwhile, Gain is very different
from Baseline and Loss, meaning that it is very unlikely that it follows a
distribution that is close to any of the other treatments.
We use A Mann-Whitney test to see if the observations of two treatments
come from the same population. We find that the samples in the Baseline
and Loss come from the same population (p = 0.781) while Gain comes from
a different population than the Baseline (p = 0.01) and Loss (p = 0.03)
treatments. We also run a Kolmogorov-Smirnov equality of distributions
test. It results in Baseline and Loss coming from a similar distribution
(p=0.609) while Gain follows a different distribution that Baseline (p=0.068)
and Loss (p=0.068).
This proves that subjects follow a very similar behaviour when they do
not have incentives to lie and when they can lie to avoid losing money. On
the contrary, individuals lie in order to earn money.
In Table 3 we report a Tobit model, where the dependent variable is the
reported number. We want to test if the results are consistent when we do
a parametric analysis. This model will include Gain and Loss treatments as
well as for two covariates: gender and the result of a three question cognitive
reflection test (CRT) filled by each subject at the end of the experiment.
8
Table 3: Tobit estimation
Coefficients
Gain
1.769***
Loss
0.164
Gender
0.012
CRT
-0.297
Constant
5.255
Table 3 shows that the only significant coefficient (at a 1% level) is the
one associated to the gain treatment. Its value is also positive (1.769). With
respect to the Baseline treatment we predict higher numbers in the Gain
treatment. Meanwhile, the coefficient linked to the loss treatment, gender
and CRT test are not significant. A test on the coefficients associated to
Gain and Loss resolves that they are statistically different (p=0.03).
Thus, we reject Hypothesis 1, as reported numbers are not the same in
all the treatments. These result is new to our knowledge, and one possible
explanation is that subjects feel fairly treated when they are given the money
in advance. Thus the cost of being dishonest is higher in the Loss treatment
than in the Gain treatment, as subjects feel more guilty when they lie to
someone who trusted them on the first place. In this context, being paid in
advance can be translated in being honest.
5
Conclusions
People are lying averse, but they are dishonest when this entails earning
more money. According to Prospect Theory, subjects weight more equivalent
amounts of loses than gains. Nonetheless, even though this is translated into
a risk seeking behaviour in the loss domain when a lottery is played, subjects
do not lie more in order to avoid losing money in a certain scenario. This
contradicts the postulates of Prospect Theory.
9
Secondly, our paper is related to the lying aversion literature. In many
important economic settings, people engage in dishonest behavior in order
to increase their expected material gain. According to the classic economic
theory, rational individuals should maximize their payoffs whenever it is
possible, not caring about non pecuniary motives such as honesty. However,
experimental literature shows that people tell the truth in cases where this is
detrimental of their material payoffs. One possible explanation is that people
bear an utility cost when they tell a lie (pure lying aversion, e.g., Ellingsen
and Johannesson, 2004; Kartik, 2009). Furthemore, people sometimes reject
a lie even when this could improve both their and someone else’s payoffs
(Erat and Gneezy, 2012).
One potential issue with our design is the way on which we pay in the
loss treatment. The fact that in this treatment subjects manipulate money,
may affect the cost of lying as in Baseline and Gain they do not manipulate
money until the end of the session. This could affect our assumption of all
the costs being equal. This should be investigated in future research.
Finally, incentives can affect cheating behavior, but no evidence of cheating behavior is observed in the loss domain. This could have serious implications that should be studied by future research. It would be interesting to
analyse if we should change bonus schemes and the way in which we declare
taxes in order to avoid dishonest behavior.
6
References
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lie?. Journal of Economic Behavior and Organization, 93, 258-265.
Clots-Figueras, I., Hernan-Gonzales, R., and Kujal, P. (2015). Information asymmetry and deception. Frontier in Behavioural Neuroscience.
Ellingsen, T., and Johannesson, M. (2004). Promises, Threats and Fairness. Economic Journal, 114(495), 397-420.
Erat, S., and Gneezy, U. (2012). White lies. Management Science, 58(4),
723-733.
10
Fryer, R. G. (2013). Teacher incentives and student achievement: Evidence from New York City public schools. Journal of Labor Economics,
31(2), 373-427.
Fryer R. G., Levitt, S. D., List, J., and Sadoff, S. (2012). Enhancing the
efficacy of teacher incentives through loss aversion: A field experiment (No.
w18237). National Bureau of Economic Research.
Fischbacher, U., and Follmi-Heusi, F. (2013). Lies in disguisean experimental study on cheating. Journal of the European Economic Association,
11(3), 525-547.
Gino, F., Krupka, E. L., and Weber, R. A. (2013). License to cheat:
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Economic Review, 384-394.
Gneezy, U., Meier, S., and Rey-Biel, P. (2011). When and why incentives
(don’t) work to modify behavior. Journal of Economic Perspectives, 25(4),
191-209.
Gneezy, U., Rustichini, A. (2000a). Pay enough or don?t pay at all.
Quarterly Journal of Economics, 115(3), 791?810.
Gneezy, U., Rustichini, A. (2000b). A Fine is a Price. Journal of Legal
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of decision under risk. Econometrica: Journal of the Econometric Society,
263-291.
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Lopez-Perez, R., and Spiegelman, E. (2013). Why do people tell the
truth? Experimental evidence for pure lie aversion. Experimental Economics, 16(3), 233-247.
Pascual-Ezama, D., Prelec, D., and Dunfield, D. (2013). Motivation,
money, prestige and cheats. Journal of Economic Behavior and Organization, 93, 367-373.
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Vanberg, C. (2015). Who never tells a lie?. Work in progress.
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Appendix A: Instructions
The aim of this experiment is to study how individuals make decisions. We
are only interested in what average individuals do. Do not think that certain
behaviour is expected. However, take into account that your decisions along
the experiment may affect your earnings. You can ask questions in any
moment by raising your hand and waiting to be answered. Any type of
communication among you is forbidden and subject to immediate expulsion
from the experiment.
Baseline:
Your task consists on throwing the 10 sided dice that you received memorizing the number that you obtain in the first throw. This number will
determine your earnings as is shown in the table below.
Baseline
1
2
3
4
5
6
7
8
9
0
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
This means that you will earn 2.50 with any number that you obtain
rolling the dice.
First, we ask you to roll the dice and memorize the number you obtain
in the first throw. Then, introduce this number in the computer screen.
You can throw the dice as many times as you want to test that it works
properly, still your payment depends only on number obtained on the first
throw.
At the end of the experiment, you will receive your earnings (in an anonymous way) in a sealed envelope.
Gain:
Your task consists on throwing the 10 sided dice that you received memorizing the number that you obtain in the first throw. This number will
12
determine your earnings as is shown in the table below.
Gain
1
2
3
4
5
6
7
8
9
0
1
1.5
2
2.5
3
3.5
4
4.5
5
0
This means that you will obtain 1 if on your first throw you get the
number 1, 1.50 if you obtain a 2, 2 if on your first roll you get a 3, and so
on, obtaining an amount of 0 if the number you obtain is 10. First, we ask
you to roll the dice and memorize the number you obtain in the first throw.
Then, introduce this number in the computer screen.
You can throw the dice as many times as you want to test that it works
properly, still your payment depends only on number obtained on the first
throw.
At the end of the experiment, you will receive your earnings (in an anonymous way) in a sealed envelope.
Loss:
Before starting the experiment you received 5.
Your task consists on throwing the 10 sided dice that you received memorizing the number that you obtain in the first throw. This number will
determine your earnings as is shown in the table below.
Loss
1
2
3
4
5
6
7
8
9
0
-4
- 3.5
-3
- 2.5
-2
- 1.5
-1
- 0.5
-0
-5
This means that you will return 4 if you obtain the number 1 on your
first throw, you will return 3.50 if you get a 2, you will return 3 if you
obtain a 3, and so on, returning 5 if you get a 10 the first time you roll the
dice.
First, we ask you to roll the dice and memorize the number you obtain in
the first throw. Then, introduce this number in the computer screen. Place
13
the amount that you need to return in the envelope and sealed it.
You can throw the dice as many times as you want to test that it works
properly, still your payment depends only on number obtained on the first
throw.
At the end of the experiment, the instructor will pick up the envelopes.
Your earnings will be anonymous.
14