Do Convex Incentive Schemes Attract Overconfident Employees? Experimental Evidence*
Ian Larkin, Harvard Business School
Stephen Leider, Ross School of Business, University of Michigan
PRELIMINARY DRAFT – DO NOT CITE
Abstract
Convex incentive schemes, which pay employees an increasing percentage of output as their output increases, are commonly used by companies, especially in sales environments. Research has demonstrated these schemes carry large costs as employees “game” them, yet they are still persistently used. Using a set of experiments where subjects have the choice of incentive scheme, we examine whether a convex incentive scheme attracts overconfident subjects compared to a linear scheme. We find that subjects who are overconfident, measured both by the degree of bias in performance expectation on the task and by a general personality test, are much more likely to choose the convex scheme over the linear one. Furthermore, these subjects are 45 percentage points more likely to mistakenly select the convex scheme. These mistakes cost subjects 15% of their potential earnings. More strikingly, these mistakes persist throughout the experiment, despite receiving clear feedback about their performance and their predictions between each period. Furthermore, the rate of persistent wrong choice of scheme is not affected by a comparative feedback condition, where subjects are clearly shown how much they would have earned under each scheme. These results may suggest that convex incentive schemes attract overconfident employees, who persist in staying in jobs with this pay scheme despite not meeting their own performance expectations.
* We thank Matthew Chao for excellent research assistance, and participants at the ESA 2009 conference and seminars at the University of Michigan and Harvard Business School for useful feedback.
Introduction
The use of non‐linear, performance‐based incentive contracts is extremely common in many
business environments. The most well‐known example is salesperson compensation, where surveys
indicate nearly 90% of salespeople are compensated via a non‐linear system (Dartnell, 1997)1. In
addition, many other types of performance‐based pay, including stock options, bonus systems based on
defined metrics, and pay based on subjective performance, often exhibit non‐linear characteristics.
Despite the prevalence of non‐linear pay schemes, their benefits are not well understood by
academics. Research has demonstrated that non‐linear incentives are highly distortionary, as
employees manipulate their work in order to maximize their pay. Roy (1952) provides the seminal
discussion of this behavior with a detailed study of gaming behavior by machine shop employees in
response to a highly non‐linear piece rate system, resulting in employee shirking an estimated 50% of
the time. Larkin (2007) estimates that “timing gaming” by salespeople, where salespeople artificially
accelerate or delay the closing of deals in order to advantage of non‐linearities in their pay package, cost
a leading enterprise software vendor 4‐7% of revenue, since salespeople cut price in order to influence
customers to purchase on the salesperson’s timeline.
These results have led some scholars to opine that companies should desist from using non‐
linear incentives. Michael Jensen, for example, argues that “all kinks, discontinuities and non‐linearities
[should be taken] out of the pay‐for‐performance profile of each employee and manager” due to the
“huge costs [they] impose on organizations” (Jensen, 2004). Other scholars feel that the widespread use
of non‐linear incentive schemes suggests “there must be some benefit of these contracts that outweighs
1 Non‐linear commission schemes in sales environments take many forms. The most typical is a quota system, where salespeople receive no commission on sales until their “quota” is filled, after which they receive a commission on incremental sales. Bonus pay for reaching a discrete sales target is another common example of a non‐linear sales incentive system.
these apparent costs” (Lazear and Oyer, 2008). However, little research has been done in economics
which investigates possible benefits to non‐linear schemes.
In this paper, we explore the role that overconfidence, a behavioral bias affecting some
employees, may play in explaining the prevalence of non‐linear incentive schemes. In particular, we
study convex or “kinked” incentive schemes commonly seen in sales environments2. In these schemes,
a salesperson’s commission on a successful sale rises the more sales she makes in a financial period. For
example, Larkin (2007) reports that at the software vendor investigated in the paper, the commission on
a sale could range from 2% to 25%, depending on the total sales the salesperson had made in that
quarter. Larkin reports that these “kinked” systems are common not only in enterprise software, but
also in hardware, telecom equipment, aerospace and other industries.
Overconfidence potentially interacts with convex incentive schemes in several ways. First and
foremost, a convex scheme is arguably attractive to potential employees who are overconfident, in that
they overestimate the likelihood of receiving a commission rate from the steep portions of the curve. If
confidence is an important skill for employees to have – which is a common argument in the sales force
management literature (Zoltners et al, 2006) – then a convex incentive scheme could help attract and
retain desirable employees. Second, without convex schemes it may be difficult for a firm with unbiased
expectations of employee performance to agree on a linear compensation schedule with an employee
with biased expectations. A convex scheme neatly allows this agreement to take place. Finally, and
most speculatively, firms may reduce their sales commission wage bill by proposing convex schemes to
biased employees, similar to the argument that gyms and other services take advantage of biases of
their customer groups when setting contracts (DellaVigna and Malmendier, 2006).
2 The industry term for these pay schemes is an “accelerating” commission system. This is because the commission increases at each “kink” in the commission curve is communicated as an “accelerator” from the base commission rate.
In our study, we allowed experimental subjects facing a standard multiplication task to choose
how they wanted to be compensated: via a typical, linear piece rate, or via a convex payout schedule
that paid them more per correct answer as their productivity increased. The choice continued over nine
rounds. We tracked the choices of the subjects, whether their choice of scheme was correct (in that it
maximized their pay), and their level of confidence, measured in a number of different ways. We used
initial “practice rounds” to gauge subject skill at multiplication, and to set payoff functions so that
subjects expecting to perform at a similar level as the “practice round” should rationally have a slight
preference for the linear pay scheme.
Our results are striking. Subjects who are highly overconfident, measured both by their
performance expectations on the task and by a general personality test, are 45 percentage points more
likely to incorrectly choose the convex scheme. These mistakes cost the subjects 15% of their payoff in
these rounds. Interestingly, this propensity to wrongly sort into the convex pay scheme does not go
down with experience; overconfident subjects are just as likely to wrongly pick the convex scheme in
round 9 as they are in early rounds. We reported performance at the end of each round, and it was
therefore clear to subjects whether they chose the right scheme. However, in one treatment we gave
even clearer comparative feedback to subjects after the third choice period, indicating how much they
would have earned under each scheme given their performance and told them exactly how much
money they lost by choosing the wrong scheme. This comparative feedback made no statistical
difference to the level of overconfidence, nor to the propensity of overconfident subjects to mistakenly
choose the convex scheme.
Finally, and interestingly, we gave subjects a second task, asking them to respond to trivia
questions. We measured overconfidence on this task by asking subjects how many questions they
expected to get right, and how sure they were of each of their answers. Overconfidence on the trivia
task overall was not predictive of choosing (correctly or incorrectly) the convex scheme in the
multiplication task; however individuals who were highly confident about many incorrect answers in the
trivia task were more likely to mistakenly choose convex in the multiplication task. This is partially
corroborative with recent work in the psychology literature (Moore, 2007), which suggests that
overconfidence is not a general bias held by a certain type of people, but rather is specific to the task at
hand.
Previous Literature
Overconfidence has been closely defined and scrutinized by multiple streams of literature. The
literature defines overconfidence in one of three ways: overstimation of actual performance,
overplacement of performance relative to others, and overprecision in beliefs about the accuracy of
one’s knowledge. However, overconfidence is often confounded by imperfect information about the
performance of oneself and the performance of others (Healy and Moore 2007). Similarly,
overconfidence can be skewed by having excess information. Stuart Oskamp demonstrated that
psychologists overweighted additional but largely non‐useful information given to them concerning a
case study, and became overconfident about the accuracy of their diagnoses (1965). Additionally,
Klayman et al (1999) find that overconfidence varies systematically with the task or domain, and is not
necessarily generalized across all domains. People who are overconfident in one domain often do not
exhibit overconfidence in other environments..
Overconfidence has been linked to several personality traits, which may also influence sorting
behavior. Using overprecision as the measure, extraversion has been linked to overconfidence, though
none of the other five factor traits have been linked (Schaefer et al 2004). Additionally, optimism, self‐
efficacy, and need for cognition have been positively tied to overconfidence, while negative affectivity
has been negatively associated with overconfidence (Wolfe and Grosch 1990).
To our knowledge, the only studies linking confidence to pay scheme choice are experimental
papers by Niederle and Vesterlund (2007) and Dohmen and Falk (2006)3. Niederle and Vesterlund
demonstrate that men are much more likely to select to be compensated via a tournament than
women, who prefer to be paid via a piece rate. Using a task‐specific measure of confidence, the paper
demonstrates that men tend to be more overconfident than women, which helps explain their
preference for the tournament. Dohmen and Falk allow individuals to choose between receiving a fixed
payoff, or sorting into either an individual linear piece rate, a tournament, or a group revenue‐sharing
scheme. They find that overestimating one’s productivity predicts sorting into the tournament, but not
sorting into an individual piece‐rate or a group revenue sharing scheme. Our paper builds on these
results in three ways: it investigates convex piece rates, a commonly‐used incentive scheme, instead of
a tournament4; it adds a number of different confidence measures, and it examinines the interaction of
overconfidence across tasks.
Though no other studies have examined overconfidence and pay scheme choice directly,
research has linked overconfidence to other types of decisions. Barber and Odean (2001) demonstrates
that based on account data for over 35,000 households, men trade stocks 45 percent more than
women, reducing men’s net returns by 2.65 percent a year as compared to 1.72 percent for women.
Combined with theoretical models predicting that overconfident investors trade excessively, and that
men are more overconfident than women, these results suggest that overconfidence in men influences
decisions in a manner that negatively impacts their returns. Though not directly related to incentive
scheme choice, this is one example of the possible effects of overconfidence on decisions involving
financial incentives.
3 Cadsby et al. (2007) also examine experimentally sorting between fixed pay and performance pay schemes, but do not measure overconfidence. 4 Although promotion decisions can be usefully thought of as a tournament, there are very few actual incentive systems in companies that base pay on explicit tournaments (Lazear and Oyer, 2008).
One other relevant paper is Camerer and Lovallo’s (1999) study on excess entry into markets. In
an experimental setting, Camerer and Lovallo asked participants to decide whether to opt into a pay‐
scheme that diminishes in pay as more participants enter, but will also pay by rank of performance on
the task at hand (trivia). Camerer and Lovallo demonstrate that when given the option to opt in, net
profit per subject decreases significantly, and more so for those who are most overconfident, even when
controlling for imperfect information about the performance of others. The authors conclude that
overconfidence is perhaps one of the reasons for the high rate of failed new entrants in a market. It is
important to note that the authors deliberately avoided providing participants with feedback on their
performance, so as to simulate firms that “do not learn much about their competitive advantage until
after they incur substantial nonsalvageable fixed costs.” The lack of feedback is a key difference
between a new business entrant and an employee who has selected a convex payscheme, as the
employee can receive constant feedback on his or her performance against that payscheme.
Experimental Design
Our experiment consisted of nine periods of solving multiplication problems, one period of
answering trivia questions, a risk aversion measure, and a concluding questionnaire that included
several psychological measures. Subjects were paid for their earnings in two randomly selected
math/trivia periods, one randomly selected risk decision, as well as a $10 show‐up fee. Screen shots of
the experiment, including instructions, are available at <URL>.
Multiplication Task
In each 150 second period, subjects solved as many randomly generated two digit by one digit
multiplication problems as they could. Their score on the task was the number of correct answers minus
half the number of incorrect answers. In the first two periods a subject’s payoff was based on a linear
piece rate equal to $0.30*score. We then calculated the subject’s baseline ability (B) as the maximum
score in the first two periods. We used each subject’s baseline ability to calibrate a subject‐specific
convex piece rate (that remained fixed throughout the rest of the experiment). We used a subject‐
specific rather than a universal convex payoff function because there is substantial variance between
subjects in ability, and we want to avoid low‐ and high‐ability subjects having a trivial choice over pay
schemes5. The convex piece rate was set as follows, where each cell shows the total piece rate6:
Score (B‐3) or less (B‐2.5) to (B+1) (B+1.5) to (B+5) (B+5.5) or more
Basic Convex $0.20 $0.25 $0.35 $0.50
Escalated Convex $0.20 $0.25 $0.35 $0.75
Therefore, the linear scheme yields a higher payoff for scores equal to (B+1) or less, while the convex
scheme yields a higher payoff for scores of (B+1.5) or higher. In the third period all subjects were paid
under the basic convex piece rate.
In periods four through nine the pay scheme used varies between treatments. In the control No
Choice treatment, each subject was randomly assigned to either the linear or basic convex scheme in
each period. In the Choice treatment subjects chose each period whether they would like their pay to
be calculated using the linear or basic convex scheme. In the Escalation treatment, subjects chose
between the linear and basic convex pay schemes for period four through six, and between the linear
and escalated convex pay schemes in periods seven through nine.
In each period we also elicited two measures of subjects’ beliefs about their performance.
Before the multiplication task (but after the payment scheme is determined) subjects predicted what
score they would achieve. An additional 50 cents was added to their round earnings if they were
correct, or an additional 25 cents if their guess was within one point. After the task, subjects were asked
5 Having individual‐specific payment schemes is also realistic. Many firms have individualized performance hurdles and bonus points. For example, sales quotas are usually set based on a salesperson’s individual performance in previous years. 6 In an early pilot we tried using a payoff function with varying marginal piece rates (e.g. $0.20 per point for the first 10 points, then $0.25 per point for the next 5 points…) to avoid discontinuities in the payoff function and more closely match typical convex commission schemes. However, subjects found this pay scheme too confusing. Additionally, by applying one piece rate to the total score it is very easy for subjects to identify the minimum score needed to make the convex scheme optimal. While convex schemes with varying marginal piece rates are more common than schemes with varying absolute piece rates, the incentive effects of the two schemes are always in the same direction.
to guess which quartile their score fell in for that period compared to the other experimental subjects in
the room, earning an additional 50 cents for the period if they were correct. We used these two beliefs
to create measures of both absolute and relative overconfidence in each period.
After each Multiplication Task, subjects were informed of their score on the task, their payoff
given the pay scheme, whether their guesses were correct, and the actual quartile of their score.
Trivia Task
In order to get a measure of overconfidence in an entirely separate domain, we had subjects
answer trivia questions. Subjects had two and a half minutes to answer 10 multiple choice trivia
questions drawn from Nelson and Narens (1980). Subjects earned $0.75 for each question they
answered correctly. As in the multiplication task, subjects predicted their score before the task and
guessed their relative ranking after the task. We also asked subjects to state a subjective confidence in
their answer for each question.
Risk Measure
Because differences in risk aversion can also explain the choice of either the linear or convex
piece rate, we assessed subject risk tolerance using the risk elicitation mechanism from Dohmen and
Falk (2006). Subjects made fifteen choices between a lottery and a fixed payment. In each case the
lottery was a 50‐50 lottery between $4 and $0, while the fixed payment increased in $0.25 increments.
Subjects were paid for one randomly selected decision.
Psychological and Demographic Questionnaire
At the end of the experiment subjects filled out a questionnaire that asked for basic
demographic information, took one version of the Big 5 personality test7, and answered a number of
questions regarding optimism and overconfidence. Specifically, subjects were asked to rate the
likelihood of a variety of events happening to them over the course of their life compared to other
7 Questions were taken from Gosling et al. (2003), Rammstedt and John (2007) and Saucier (1994).
people they know of the same age and sex. Half the events were things that are largely out of one’s
control (e.g. being selected randomly for an audit), while the subject could potentially influence the
likelihood of the other events (e.g. getting a job in the next 5 years that pays more than $75,000/year).
Subjects were also asked, in the same format as the Big 5 questions, to rate the accuracy of several
statements reflecting overconfidence (e.g. “I am a better driver than most people”) or optimism (e.g. “In
uncertain times, I usually expect the best”).
Results
Sessions were run at the Harvard Business School CLER lab using the standard subject pool. A
total of 179 subjects participated, with 41 in the No Choice control, 68 in the Choice treatment and 70 in
the Escalation treatment. The average subject earnings were $28.78.
Figure 1 reports average subject performance in the Multiplication Task in each treatment.
Subjects earned a score of approximately 16 in the first period, increasing to roughly 21 in period 4, and
to 24 in period 9. The treatments do not substantially differ.
Figure 1: Multiplication Task Performance
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9
No Choice No Escalate Escalate
Overconfidence
We will now examine the amount of overconfidence exhibited by the subjects. Figure 2 displays
the percent of subjects who are overconfident (i.e. who predict a higher score than they achieve) in each
period. The three treatments show a very similar pattern: only 20 to 25% of subjects are overconfident
in the first two periods, while in periods 3 through 9 between 30 and 45% of subjects are overconfident.
Averaging across treatments and periods, subjects are slightly underconfident: the mean difference
between prediction and performance is ‐1.36. However, many subjects did make large errors: 21% of
subject‐rounds involved an overestimate of the subject’s their score by at least 10 percent, and 12% of
subject‐rounds involved an overestimate of at least 20 percent.
Of particular note, a substantial fraction of subjects continue to be overconfident even after a
number of periods. Moreover, the number of overconfident subjects does not decrease over time, even
though subjects received feedback on their prediction and actual performance after every period.
Similarly, if we look at absolute prediction errors, the mean error in each treatment is between 2 and 4.5
in periods 4 through 9 with no significant time trend in any treatment. Taken together, these results
suggest that at least some overconfident subjects did not update their belief of their ability over the
course of the experiment.
Figure 2: Frequency of Overconfident Subjects
We can also show that specific individuals were more prone to being overconfident in any given
period. To do this, we first build a measure of “initial overconfidence,” defined as the average
difference between predicted and actual score for the first three periods. We then compare the
average difference between predicted and actual score for the group of subjects who were initially
overconfident and the group of subjects that were not initially overconfident. The mean difference
between for the former group was 0.40, suggesting the average subject in this group remained
overconfident. Conversely, the mean overconfidence of the latter group was ‐1.12. This difference is
statistically significantly (using a nonparametric permutation test p < 0.01). Similarly, initially
overconfident subjects were overconfident an average of 2.80 times in the last six periods, while the
other subjects were overconfident 2.16 times, and this difference is also statistically significant (p =
0.02).
More formally, we regress the difference between predicted and actual score on initial
overconfidence, as well the corresponding overconfidence measure from the Trivia task, and the
0%
10%
20%
30%
40%
50%
1 2 3 4 5 6 7 8 9
No Choice No Escalate Escalate
psychological measure of overconfidence from the concluding questionnaire89. The results of a random
effects regression are presented in Table 1.
Table 1: Overconfidence MeasuresVARIABLES (1) (2) (3) (4)
Mean Overconfidence (Pds 1‐3) 0.111*** (0.0237)
Trivia Overconfidence (Total) ‐0.0156 (0.0627)
Trivia Overconfidence (Question Rating) 0.998** (0.423)
Psychological Overconfidence 0.517*** (0.181)
Choice Treatment 0.0714 ‐0.157 ‐1.027 ‐0.164 (0.476) (0.514) (0.872) (0.443)
Escalation Treatment 0.0342 ‐0.193 ‐1.010 ‐0.160 (0.452) (0.492) (0.854) (0.444)
Period 0.0203 0.0203 0.293*** ‐0.0106 (0.0709) (0.0710) (0.0774) (0.0741)
Constant ‐0.765 ‐0.844 ‐2.565*** ‐0.623 (0.625) (0.650) (0.924) (0.636)
Observations 1074 1074 1611 984 Number of Subjects 179 179 179 164
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
Subjects who were more overconfident in the first three periods are significantly more
overconfident in the last six periods. Similarly, subjects who rated themselves as more overconfident
according to the psychological measure are more likely to be overconfident in their predictions.
Therefore the observed overconfidence is coming disproportionately from a specific set of subjects,
rather than simply being random errors. Subjects who were overconfident on the Trivia Task as
measured by the difference between their guess and their score, however, were not more likely to be
overconfident on the Multiplication Task. However, subjects who gave more incorrect answers that
8 We use the z‐score of the answers to the overconfidence questions from the questionnaire. Subjects were excluded whose answers on the questionnaire were nonresponsive. 9 We also examined the psychological measures of optimism, however none of the measures were significant.
they rated subjectively as being very confident in were more overconfident on the Multiplication Task.
Also, note again that there are no significant differences between treatments, and no time trend. After
an initial learning period there is a stable persistent level of overconfidence that is the same across
treatments.
We also look at the other demographic predictors of overconfidence. We regress
overconfidence in periods 4 through 9 on gender, predicted salary in 5 and 20 years, predicting a
prestigious future job or company type (e.g. doctor, engineer, lawyer, finance, etc.) as well as the Big 5
personality traits. The estimates of the random effects regression are presented in Table 2. We find,
corroborative of the existing literature, that men are marginally significantly more overconfident than
women, and that extraverted subjects are also marginally more overconfident. Predictions about their
future career path do not appear to be indicative of overconfidence10.
Table 2: Overconfidence Demographics
VARIABLES Coeff. Std. Err.
Male 0.618* (0.369)
Salary in 5 years ($1,000s) 0.00140 (0.00133)
Salary in 20 years ($1,000s) ‐4.37e‐05 (0.000186)
Prestige future job 0.0918 (0.429)
Prestige future company 0.0375 (0.404)
Extraversion 0.315* (0.170)
Agreeableness ‐0.0112 (0.198)
Conscientiousness ‐0.115 (0.192)
Emotional Stability ‐0.0994 (0.195)
Openness 0.263 (0.225)
Choice ‐0.0467 (0.484)
Escalation ‐0.112 (0.500)
Period 0.00324 (0.0757)
Constant ‐1.281 (0.835)
Observations 948
Number of Subjects 158
Robust standard errors in parentheses 10 Although not presented here, students predicting a future career in finance are statistically significantly more likely to be overconfident.
*** p<0.01, ** p<0.05, * p<0.1
Pay Scheme Choices
We now examine subjects’ choices over the linear and convex pay schemes. Figure 3 reports
the fraction of subjects who chose the convex scheme in each period (pooling between the Choice and
Escalation treatments), as well as the fraction of subjects who made a mistake in choosing linear and
convex. In the first choice period 52% of subjects choose convex, increasing to 72% by period 9. This
increase in the choice of convex is not surprising, given the increase in subject scores seen in Figure 1. In
each period between 10 and 20 percent of subjects mistakenly choose convex when they would have
earned more under the linear scheme, and similarly between 10 and 20 percent choose the linear
scheme when they would have earned more under convex. Combined mistakes were between 20 and
30 percent. While subjects are certainly doing better than random choice it is notable that even after
several periods (including clear feedback after each period) a substantial number of subjects continue to
make mistakes in choosing their compensation scheme. While there is a slight downward trend, 23% of
subjects are still making a mistake in period 9.
Figure 3: Pay Scheme Choices
0%
10%
20%
30%
40%
50%
60%
70%
80%
4 5 6 7 8 9
% Convex % Mistake Convex % Mistake Linear
Additionally, subjects who are overconfident are much more likely to mistakenly choose the
convex scheme, while subjects who are underconfident are more likely to mistakenly choose the linear
scheme. Figure 4 shows the frequency of mistakes for each decile of overconfidence. Almost all of the
convex mistakes come from very overconfident subjects. Less than 10% of subjects in the 8th decile and
below mistakenly choose convex, while almost 70% of subjects in the 10th decile make this mistake.
Conversely, subjects in the 1st through 5th deciles mistakenly choose linear at least 20% of the time,
while subjects in the 6th and above make this mistake less than 10% of the time.
Figure 4: Mistakes by Overconfidence Decile
To further analyze the role of overconfidence in sorting between the piece rate options, we
regress payment scheme choices on overconfidence, a dummy for the escalated convex piece rate in the
last three periods of the Escalation treatment, an interaction term, as well as the certainty equivalent
from the lottery choices.11 Results of the random effects regressions are presented in Table 3. Column
1 uses pay scheme choice as the dependent variable, column 2 uses an indicator for mistakenly choosing
11 Two subjects were excluded because they did not have a unique switching point between the lottery and the certain payoff. Quantitatively similar results for overconfidence obtain if we run the regressions for all subjects excluding the risk measure.
0%
10%
20%
30%
40%
50%
60%
70%
80%
1 2 3 4 5 6 7 8 9 10Mistake Linear Mistake Convex
the convex scheme, column 3 uses the amount (in percentage terms) of the foregone payoff from this
mistake, and columns 4 and 5 have the corresponding variables for mistakenly choosing linear.
Table 3: Pay Scheme Choices (1) (2) (3) (4) (5)
VARIABLES Chose Convex
Mistakenly Chose Convex
% Lost Pay From Convex
Mistake
Mistakenly Chose Linear
% Lost Pay From Linear Mistake
Overconfidence 0.0182*** 0.0362*** 0.0124*** ‐0.0266*** ‐0.0109*** (0.00327) (0.00383) (0.00161) (0.00328) (0.00174)
Escalated Convex Available 0.0387 0.0207 0.000317 ‐0.0218 ‐0.00612 (0.0338) (0.0314) (0.00967) (0.0279) (0.0128)
Escalated x Overconfidence ‐0.00671 0.0113 0.000984 0.00761 0.000154 (0.00528) (0.00787) (0.00289) (0.00557) (0.00497)
Lottery Certainty Equivalent 0.283*** 0.131*** 0.0348** ‐0.164*** ‐0.0412** (0.106) (0.0460) (0.0142) (0.0535) (0.0195)
Period 0.0308*** ‐0.0161** ‐0.00446* ‐0.0136* ‐0.00124 (0.00787) (0.00778) (0.00235) (0.00769) (0.00280)
Constant 0.160 0.147** 0.0448** 0.381*** 0.0872*** (0.119) (0.0641) (0.0208) (0.0731) (0.0259)
Observations 816 816 816 816 816 Number of Subjects 136 136 136 136 136
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 From the first specification we can again see that overconfidence strongly predicts choosing the
convex pay scheme. For example, subjects in the 90th percentile of overconfidence are 23 percentage
points more likely to choose convex than subjects in the 10th percentile. For comparison, this is roughly
the same magnitude as the effect of risk aversion: subjects in the 90th percentile of risk attitudes (most
risk loving) are 21 percentage points more likely to choose the convex scheme than subjects in the 10th
percentile. As we showed previously, subjects are 15 percentage points more likely to choose convex in
period 9 than in period 4.
Highly overconfident subjects are also 45 percentage points more likely to mistakenly choose
the convex scheme than subjects who are not highly overconfident, with the mistake costing them 15%
of their payoff. Risk‐loving subjects are similarly more likely to mistakenly choose the convex scheme.
The frequency of these mistakes decreases by 8 percentage points between period 4 and period 9.
Conversely, underconfident subjects are more likely to mistakenly choose the linear scheme. Subjects at
the 10th percentile of overconfidence are 33 percentage points more likely to mistakenly choose the
linear scheme than subjects at the 90th percentile, with these mistakes costing them 14% of their payoff.
Risk averse subjects are similarly more likely to make this mistake: subjects at the 10th percentile of
certainty equivalent are 12 percentage points more likely to make this mistake than subjects at the 90th
percentile. The frequency of mistakenly choosing the linear scheme decreases by 7 percentage points
between period 4 and period 9.
The effect of overconfidence on choice mistakes is persistent throughout the experiment.
Running the same regression specification for only the last three periods results in essentially the same
estimates. For example, the estimated coefficient on overconfidence for mistakenly choosing convex is
β = .0386 (s.e. = .00579, p < 0.001). Similarly, the estimated coefficient on overconfidence for
mistakenly choosing linear is β = ‐.0251 (s.e. = .00549, p < 0.001). Therefore even though the overall
frequency of the mistakes decreases slightly over time, overconfidence still causes the mistakes to occur
even at the end of the experiment.
Several other measures of overconfidence are also informative. As a robustness check, Table 4
reports the results of regressing mistakenly choosing convex on the same explanatory variables as
Column 2 in Table 3, however we use a different measure of overconfidence in each specification. In
column 1 we use the difference between the subject’s prediction for their score and the subject’s
baseline ability (their maximum score in the first two periods), while in column 2 we use the average
overconfidence in the first three periods. In column 3 we use a dummy variable that equals one if the
subject guessed that their score was in a higher quartile than it actually was. Columns 4 and 5 use the
two measures from the Trivia Task (guess minus actual score, and number of incorrect answers rated as
very confident). Column 6 uses the z‐score from the psychological survey. All of the alternate measures
are at least marginally significant, except for overconfidence on the Trivia task. This suggests that a
quite broad notion of overconfidence underlies the propensity of overconfident subjects to (mistakenly)
prefer the convex piece rate; however, it also suggests that overconfidence on one specific task does not
necessarily correlate with overconfidence on another specific task.
Table 4: Alternate Measures of Overconfidence
VARIABLES (1) (2) (3) (4) (5) (6)
Guess ‐ Baseline Ability 0.00948**
(0.00434)
Escalated x (Guess ‐ Baseline) 0.00398
(0.00553)
Mean Overconfidence (Pds 1‐3) 0.00687*
(0.00358)
Escalated x Overconfidence (Pds 1‐3) ‐0.00650
(0.00498)
Relative Overconfidence 0.215***
(0.0427)
Escalated x Relative Overconfidence 0.0304
(0.0817)
Trivia Overconfidence (Total) 0.00252
(0.00441)
Escalated x Trivia (Total) ‐0.00369
(0.0122) Trivia Overconfidence (Question Rating) 0.0305*
(0.0185)
Escalated x Trivia (Question) ‐0.0220
(0.0300)
Psychological Overconfidence 0.0374**
(0.0162)
Escalated x Psych. Overconfidence ‐0.0566**
(0.0268)
Escalated Convex Available 0.0260 0.0160 0.0319 0.0379 0.0472 0.0379
(0.0338) (0.0385) (0.0324) (0.0363) (0.0383) (0.0353)
Lottery Certainty Equivalent 0.0739 0.0812* 0.0747 0.0751 0.0874* 0.0858
(0.0497) (0.0483) (0.0502) (0.0492) (0.0490) (0.0581)
Period ‐0.0261*** ‐0.0206** ‐0.0201** ‐0.0207** ‐0.0206** ‐0.0222**
(0.00933) (0.00883) (0.00855) (0.00884) (0.00885) (0.00891)
Constant 0.213*** 0.209*** 0.146** 0.195*** 0.166** 0.189**
(0.0744) (0.0724) (0.0729) (0.0728) (0.0730) (0.0758)
Observations 816 816 816 816 816 738
Number of Subjects 136 136 136 136 136 123
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Incentive Effects
We now want to consider whether the convex piece rate has a different incentive effect
compared to the linear piece rate. Table 5 reports the results of the random effects regression of
subject score in periods 4 through 9 on baseline ability, treatment dummies, and choice dummies
representing whether the convex piece rate was selected by choice or was randomly assignment. In the
No Choice control the convex piece rate appears to have no differential incentive effect compared to
the linear piece rate: subjects in this condition who were randomly assigned the convex piece rate do
not perform any better than subjects randomly assigned the linear piece rate. In the two choice
treatments, however, subjects who opt into the linear piece rate perform significantly worse than
subjects with the linear piece rate in the control (a difference of approximately 8% for a subject with
average baseline ability). There is no significant difference, however, between subjects who choose a
convex piece rate and those who were randomly assigned. Additionally, there is no significant
difference between the basic and escalated convex piece rate (p = 0.11). Thus while it appears that a
linear piece rate does not have a deleterious incentive effect in general, when subjects are free to sort
into the linear scheme it induces less effort.
Table 5: Incentive Effects
VARIABLES Coeff. Std. Err.
Choice Treatment ‐1.412** (0.678)
Escalation Treatment ‐1.521** (0.637)
Random Convex 0.166 (0.439)
Chosen Convex (Basic) 1.476*** (0.378)
Chosen Convex (Escalated) 0.840* (0.442)
Baseline Ability 0.896*** (0.0358)
Period 0.534*** (0.0660)
Constant 2.149** (0.942)
Observations 1074
Number of Subjects 179
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1 Subject Payoffs
How costly are these mistakes to subjects, and how much would a firm save in wage payments?
Table 6 reports the average total earnings for the six choice periods in Multiplication Task for each
treatment12, as well as the minimum earnings subjects would earn if they were always placed in the
lower payoff scheme and the maximum earnings subjects could earn if they were always placed in the
higher payoff scheme. In the No Choice condition subjects earnings are, not surprisingly, roughly
halfway between their worst possible earnings and their best possible earnings. Subjects in the Choice
treatment certainly do better than random choice, but they make mistakes one third of the time, costing
them on average $3.64 over the six periods, or 31% of their potential improvement in payoffs from
choosing correctly. In the Escalated condition subjects make mistakes one fourth of the time, losing out
on $2.49, or 18% of their potential payoff improvement. Moreover, subjects in the choice treatments
who were overconfident in the first three periods earned on average $41.40, and only improved their
payoffs by 53% relative to the worst possible decisions ‐ comparable to the randomly assigned subjects.
Despite getting clear feedback on their performance every period, subjects who can select their pay
scheme still leave money on the table, earning less than they ought to.
Table 6: Subject Payoffs
Treatment Actual Payoff Min Payoff
Max Payoff
Payoff Improvement
Mistake Pct
No Choice $47.62 $39.60 $55.55 50% 52%
Choice $50.66 $39.04 $54.30 69% 34%
Escalate $55.47 $37.75 $57.96 82% 25%
Experiment 2: Direct Comparative Feedback
12 Recall, however, that we only paid subjects for two periods from the nine Multiplication Task periods and the one Trivia Task period.
In order to further examine the persistence of these kinds of mistakes, we ran an additional
Comparative Feedback treatment. This treatment was the same as the Choice treatment; however, in
addition to the feedback subjects receive on their score, guess and payoff after each period they
received an additional screen of feedback after period 6 (the third choice period) comparing what their
payoff would have been under each pay scheme given their performance in period 6. This makes it even
easier for subjects to see what the optimal pay scheme choice would have been, and makes the exact
cost of their mistake completely clear.
Results
An additional 76 subjects participated in these sessions. Average earnings were $25.63. Figure
5 shows the frequency of convex choices, as well as mistake choices, in each period.
Figure 5: Comparative Feedback Treatment
As in our first experiment subjects increasingly choose the convex piece rate over the course of
the experiment, however they continue to mistakenly choose linear and convex between 10 and 20
percent of the time each. Additionally, there does not appear to be a decrease in the frequency of these
mistakes in the last three periods despite having received the comparative feedback.
0%
20%
40%
60%
80%
4 5 6 7 8 9% Convex % Mistake Convex % Mistake Linear
Table 7 reports the results of random effects regressions with either mistakenly choosing convex
or mistakenly choosing linear as the dependent variables13. In Columns 1 and 3 we include a dummy
variable for the periods after the comparative feedback was given (i.e. periods 7 to 9), while in Columns
2 and 4 we have a dummy for the last three periods for the subjects who had made a mistake during the
comparative feedback period. Providing comparative feedback does not significantly decrease the
frequency of mistakes, nor does it affect the relationship between overconfidence and mistakes, even
for the subjects who were shown that they were making a mistake by the comparative feedback. Thus it
seems that the propensity for overconfidence and underconfidence to lead individuals to choose the
wrong pay scheme is robust even to very clear feedback showing which pay scheme was better given
their performance.
Table 7: Comparative Feedback Treatment
(1) (2) (3) (4)
VARIABLES Mistakenly Chose Convex Mistakenly Chose Linear
Overconfidence 0.0308*** 0.0315*** ‐0.0387*** ‐0.0431***
(0.00588) (0.00519) (0.00665) (0.00593)
After Feedback Given ‐0.0293 ‐0.0154
(0.0320) (0.0281)
After Feedback x Overconfidence 0.00431 ‐0.00309
(0.00835) (0.00939)
After Feedback & Mistake at Feedback 0.00363 ‐0.0194
(0.0566) (0.0430)
Feedback Mistake x Overconfidence 0.00242 0.0164
(0.0110) (0.0104)
Lottery Certainty Equivalent 0.0350 0.0351 ‐0.0869 ‐0.0928
(0.0779) (0.0726) (0.0635) (0.0610)
Constant 0.147* 0.131* 0.255*** 0.260***
(0.0851) (0.0781) (0.0702) (0.0667)
Observations 450 450 450 450
Number of Subjects 75 75 75 75
13 One subject is excluded because he did not have a unique switching point in the risk measure. The same results obtain if we run the specifications without the risk measure and include this subject.
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1 Summary and next steps
Taken together, our results suggest that overconfidence – the upwardly biased assessment of
future performance – helps explain the prevalence of convex incentive schemes in corporate
environments. Overconfident employees facing a choice between a linear system and a convex one are,
extrapolating from our results with experimental subjects, 23 percentage points more likely to choose a
job setting with convex pay. The fact that these subjects appear less likely to learn they are making a
mistake may help explain why convex schemes have lasted so long in corporate environments.
This sorting has several plausible benefits to firms. The first is that overconfidence is likely
beneficial for certain job functions. For example, a typical salesperson is rejected “hundreds if not
thousands of times before he hears ‘yes’” (Zoltners et al, 2006), and successful salespeople must
therefore be highly confident of their abilities in the face of persistent negative feedback.
Second, a convex incentive system allows firms and biased employees to agree ex‐ante on a pay
scheme despite having different beliefs about likely productivity. This is similar to arguments made in
the entrepreneurship literature on the role of non‐linear “payout” functions in the venture capital
industry. It is likely that employers and employees would be unable to enter into an ex‐ante agreement
if the contract was limited to a linear function.
Finally, a convex incentive system may allow firms to lower their wage bill, by taking advantage
of overconfident employees’ systematic and persistent bias. Indeed, subjects in our experiment lost
approximately 15% of their potential payment because they made mistakes in their choice of incentive
scheme. Of course, the role these three explanations actually play in explaining convex schemes is a
subject for future research. Having established that convex schemes can attract overconfident workers,
natural follow up experiments could directly examine tasks where overconfidence is beneficial to
productivity or include wage bargaining where overconfidence could lead to impasse in the absence of
convex pay schemes.
Finally, our study confirms recent findings in the psychology literature that overconfidence is not
an individual trait as much as it is a trait around a specific task. This may explain why firms do not
typically give tests of confidence to employees before hiring them: general tests will be unreliable at
uncovering overconfidence for a specific task. In our experiment, even when other measures of
overconfidence were correlated with subject behavior, they had much less predictive power than the
task‐specific measures of overconfidence. Under this argument, the incentive system itself takes the
role of personality test, and sorts appropriate employees to the firm.
References
Barber, Brad and Terrance Odean (2001). “Boys Will be Boys: Gender, Overconfidence, and Common
Stock Investment.” The Quarterly Journal of Economics, 116 (1), 261‐292.
Cadsby, C. Bram, Fei Song and Francis Tapon (2007). “Sorting and Incentive Effects of Pay‐for‐
Performance: An Experimental Investigation.” Academy of Management Journal, 50(2), 387‐405.
Camerer, Colin and Dan Lovallo (1999). “Overconfidence and Excess Entry: An Experimental Approach.”
The American Economic Review, 89 (1), 306‐318.
DellaVigna, Stefano and Ulrike Malmendier (2006). “Paying Not to Go to the Gym.” The American
Economic Review, 96(3), 694‐719.
Dohmen, Thomas and Armin Falk (2006). “Performance Pay and Multidimensional Sorting: Productivity,
Preferences and Gender.” IZA Discussion Paper No. 2001.
Gosling, Samuel D., Peter J. Rentfrow and William B. Swann Jr. (2003). “A Very Brief Measure of the Big
Five Personality Domains.” Journal of Research in Personality, Vol. 37(6), p. 504‐528.
Healy, Paul and Done Moore (2007). “Bayesian Overconfidence.” Working paper. Available at
http://cess.nyu.edu/exp_seminar/fall_08_papers/Healy_Moore‐Overconfidence.pdf. Retrieved on
July 30, 2009.
Jensen, Michael (2003). “Paying People to Lie: The Truth About the Budgeting Process.” European
Financial Management, 9, 379‐406.
Klayman, Joshua, Jack Soll, Claudia Gonzalez‐Vallejo and Sema Barlas (1999). “Overconfidence: It
Depends on How, What, and Whom You Ask.” Organizational Behavior and Human Decision
Processes, 79(3), 216‐247.
Larkin, Ian. (2007). “The Cost of High‐Powered Incentives: Employee Gaming in Enterprise Software
Sales.” Working paper, Harvard Business School.
Lazear, Edward P., and Paul Oyer (2008). “Personnel Economics.” Forthcoming chapter in Handbook of
Organizational Economics, Robert Gibbons and John Roberts, editors. Princeton University Press.
Nelson, Thomas O., and Louis Narens (1980). “Norms of 300 general‐information questions: Accuracy of
recall, latency of recall, and feeling‐of‐knowing ratings.” Journal of Verbal Learning and Verbal
Behavior, Vol. 19, p. 338‐368.
Niederle, Muriel and Lise Vesterlund (2007). “Do Women Shy Away from Competition? Do Men
Compete Too Much?” The Quarterly Journal of Economics, 122(3), 1067‐1101.
Oskamp, Stuart (1965). “Overconfidence in Case‐Study Judgments.” Journal of Consulting Psychology,
29(3), 261‐265.
Oyer, Paul. (1998). “Fiscal Year Ends and Nonlinear Incentive Contracts: The Effect on Business
Seasonality,” Quarterly Journal of Economics, 113(1): 149‐185.
Rammstedt, Beatrice and Oliver P. John (2007). “Measuring Personality in One Minute or Less: A 10
Item Short Version of the Big Five Inventory in English and German.” Journal of Research in
Personality, Vol. 41(1), p. 203‐212.
Roy, Donald (1952). “Quota Restriction and Goldbricking in a Machine Shop.” The American Journal of
Sociology, 57(5), 427‐442.
Saucier, Gerard (1994). “Mini‐Markers: A Brief Version of Goldberg’s Unipolar Big‐Five Markers.”
Journal of Personality Assessment, Vol. 63(3), p. 506‐516.
Schaefer, Peter S., Cristina C. Williams, Adam S. Goodie, and W. Keith Campbell (2004). “Overconfidence
and the Big Five.” Journal of Research in Personality, 38, 473‐480.
Wolfe, R.N., and J.W. Grosch (1990). “Personality Correlates of Confidence in One’s Decisions.” Journal
of Personality, 58, 515‐534.
Zoltners, Andris A., Prabhakant Sinha, and Sally E. Lorimer (2006). The Complete Guide to Sales Force
Incentive Compensation: How to Design and Implement Plans That Work. AMACOM, USA.