Feedback, Self-Esteem, and Performance in...

MANAGEMENT SCIENCEVol. 58, No. 1, January 2012, pp. 94–113ISSN 0025-1909 (print) � ISSN 1526-5501 (online) http://dx.doi.org/10.1287/mnsc.1110.1379

© 2012 INFORMS

Feedback, Self-Esteem, andPerformance in Organizations

Camelia M. KuhnenDepartment of Finance, Kellogg School of Management, Northwestern University, Evanston, Illinois 60208,

[email protected]

Agnieszka TymulaCenter for Neural Science, New York University, New York, New York 10003, [email protected]

We examine whether private feedback about relative performance can mitigate moral hazard in competitiveenvironments by modifying the agents’ self-esteem. In our experimental setting, people work harder and

expect to rank better when told that they may learn their ranking, relative to cases when feedback will notbe provided. Individuals who ranked better than expected decrease output but expect a better rank in thefuture, whereas those who ranked worse than expected increase output but lower their future rank expectations.Feedback helps create a ratcheting effect in productivity, mainly because of the fight for dominance at the topof the rank hierarchy. Our findings suggest that organizations can improve employee productivity by changingthe likelihood of feedback, the reference group used to calculate relative performance, and the informativenessof the feedback message.

Key words : organizational studies; personnel; motivation-incentives; productivityHistory : Received July 9, 2010; accepted April 19, 2011, by Brad Barber, Teck Ho, and Terrance Odean,

special issue editors. Published online in Articles in Advance August 12, 2011.

1. IntroductionPerformance appraisals, such as the 360-degree feed-back process, have become common features of theworkplace over the last two decades (Prewitt 2007).Although the goal of these appraisals is to encour-age employee development and improve perfor-mance, empirical evidence suggests that providingfeedback does not always lead to better outcomesin organizations, because it can negatively impactthe employees’ self-esteem (Kluger and DeNisi 1996,Smither et al. 2005). Recently, companies such as GE,Yahoo, and Whirpool have changed aspects of theappraisal process such as the frequency of feedback,the labels provided for particular performance lev-els (e.g., “successful” versus “middle 50%”), and thebenchmarks used to define performance (e.g., abso-lute criteria versus relative rankings), indicating thatit is still unclear what constitutes effective feedback(see Business Week 2006, White 2006). To shed light onthis issue, in this paper we examine theoretically andempirically how feedback and self-esteem considera-tions interact and influence employee performance.

Self-esteem has long been thought of in the psy-chology literature as a strong motivator of humanbehavior (Maslow 1943, McClelland et al. 1953). Peo-ple derive utility from thinking of themselves as good,productive, or valuable according to social criteria,

and their actions are shaped by the desire to main-tain high levels of self-esteem. Recently, this con-cept has been introduced in theoretical models ofeconomic choice in noncompetitive settings as “egoutility” (Benabou and Tirole 2002, Koszegi 2006).However, ego utility may also affect strategic interac-tions, where self-esteem is determined by an individ-ual’s perception of his relative standing among peers,and not necessarily by beliefs about absolute mea-sures of his ability. In such settings, as in the work-place, the existence of relative performance feedbackimplies that ego utility is influenced not only by anindividual’s own actions, but also by those of otherplayers. Although these strategic considerations aresimilar to those studied in the tournaments literature,existing theory models do not capture the behaviorof agents in settings where the benefit of being themost productive player is simply ego utility, or self-esteem. Moreover, there are no empirical or experi-mental accounts of behavior in such settings. We seekto address these gaps in the literature.

Specifically, our goal is to understand the impactof ego utility on productivity in competitive settingswhere participants receive private feedback abouttheir relative standing. The theoretical framework wedevelop and the experimental results imply that pri-vate feedback about relative ranking has ex ante andex post effects on the productivity of workers and on

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Kuhnen and Tymula: Feedback, Self-Esteem, and Performance in OrganizationsManagement Science 58(1), pp. 94–113, © 2012 INFORMS 95

the dynamics of social hierarchies. As predicted bythe model, in our experimental setting, agents workharder and expect to rank better when they are toldthey may learn their ranking, relative to cases whenthey are told feedback will not be provided. Afterreceiving feedback, individuals who learn that theyhave ranked better than expected decrease their out-put but expect an even better rank in the future,whereas those who were told they ranked worse thanexpected increase their output and at the same timelower their rank expectations going forward. Theseeffects are stronger in earlier rounds of the task, whilesubjects learn how they compare to their peers interms of output produced. This rank hierarchy isestablished early on, and it remains relatively stablelater in the task. Private information regarding rela-tive standing helps create a ratcheting effect in thegroup’s average output. This increase in output overtime is mainly because of the fight for dominance atthe top of the hierarchy. Moreover, increasing the het-erogeneity in the ability of peers leads to lower outputfrom low ability individuals, but has no impact on theoutput of high-ability workers.

In the model and the experimental setting we iso-late the ego utility effect from other reasons why feed-back about rank may change behavior. For instance,feedback may influence productivity if compensa-tion is performance based, because people may caremore about their relative, rather then objective, levelof wealth (Clark and Oswald 1996, Easterlin 1995,Luttmer 2005). Feedback may also change behav-ior if it provides information about the nature ofthe project (Seta 1982, Bandura 1986). Moreover, iffeedback is public, and thus the relative ranking iscommon knowledge among participants, peer mon-itoring or concerns for social status and reputationmay influence the behavior of participants (Kandeland Lazear 1992, Falk and Ichino 2006, Mas andMoretti 2009). Therefore, to minimize the influenceof these other channels through which relative rankinformation may impact actions, we use a settingwhere participants receive a flat wage, the task thatthey work on does not involve changes in strategy,and feedback is private and anonymous.

Our premise that people’s self-esteem depends ontheir relative standing among peers is supported by alarge body of evidence. Research from social psychol-ogy shows that when effort is unobservable, peoplework harder when they are provided with a socialcomparison criterion, for example, with the aver-age productivity of past participants (Szymanski andHarkins 1987, White et al. 1995), suggesting that peo-ple dislike falling behind the average. Moreover, Falket al. (2006) show that low-productivity subjects aremore likely than high-productivity ones to choose not

to learn their rank in the group at the end of an exper-imental task, whereas Burks et al. (2010) find thatindividuals who are confident that they have highability are interested in learning information abouttheir relative performance. This evidence is consis-tent with the idea that utility is influenced by learn-ing about one’s relative ranking. Furthermore, recentneuroeconomics evidence shows that the mere fact ofoutperforming other workers generates activation inthe brain’s reward centers, and therefore is a pleasantexperience (Dohmen et al. 2011).

This paper contributes to the two strands of eco-nomics literature focused on ego utility, and, respec-tively, on feedback provision. Benabou and Tirole(2002) argue that self-confidence is valuable becauseit enhances the motivation to act, and they investigatea variety of strategies that people may use to enhancetheir self-image. They show that people may handi-cap their performance by exerting low effort and useself-deception through selective memory to maintainhigh self-perception about their ability. This keepsthem motivated to undertake profitable endeavors inthe future. Weinberg (1999) and Bandiera et al. (2009)treat self-esteem as a consumption good by assum-ing that an individual’s utility is increasing with hisperception of his own ability. Koszegi (2006) alsoincorporates perceptions about one’s ability in theutility function and shows how ego-motivated indi-viduals manage their self-image and how this laterinfluences their effort choice. Ertac (2005) and Ederer(2010) study optimal feedback provision in settingswhere information about relative performance is usedto learn about one’s own ability, but has no effect onthe utility function. In these two papers there are noself-esteem considerations, and behavior changes onlywhen new information about output becomes avail-able. As a result, such settings preclude the existenceof the ex ante feedback effects that we study in ourmodel and also document empirically.

Because prior models of ego utility do not accountfor the possibility that in settings such as the work-place one’s self-esteem is not shaped in isolationbut is also influenced by the actions of others, theyhave ambiguous implications for the effect of rela-tive rank information on behavior. When feedbackis likely to be provided, ex ante concerns for self-image may increase effort, because agents seek tolearn that they rank high, as in Weinberg (1999). How-ever, the prospect of receiving feedback may also leadto lower ex ante effort, because agents with posi-tive beliefs about themselves will avoid competing,to preserve their self-esteem, as in Koszegi (2006).1

1 Contrary to this prediction, the evidence in Burks et al. (2010)indicates that people with positive beliefs about their own abilityactually seek to learn information about their relative performance,

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Kuhnen and Tymula: Feedback, Self-Esteem, and Performance in Organizations96 Management Science 58(1), pp. 94–113, © 2012 INFORMS

Ex post effects of feedback are also difficult to predictbased on existent theories. For instance, after receiv-ing bad feedback about relative performance, peoplewith self-image concerns could use deception strate-gies, as in Benabou and Tirole (2002), to discard thisinformation or interpret it to their advantage. Theymay give up competing if the perceived chances ofwinning in the future are low, or may engage inthe task again because it is the only way to regainself-confidence, as in Koszegi (2006). Complementingthese prior models, our theoretical framework appliesto multiagent settings and makes clear predictionsabout the ex ante and ex post effects of feedback.

In our model we focus on the consumption valueof self-esteem and assume that the agents’ utilityis increasing in the level of their own output anddecreasing in the output of their peers, to capture thefact that self-esteem is often determined by relativeperformance comparisons (Szymanski and Harkins1987). Unlike in models where ego utility is deter-mined by absolute performance or ability, in oursetting we can account for the possibility that thesame individual may behave differently dependingon whether he is surrounded by less or more pro-ductive peers. We also allow agents to endogenouslyset the reference standard against which they com-pare themselves, to account for the possibility thatgoals are chosen by each agent as a function of theirbeliefs and environment (White et al. 1995). In themodel we show that goals (or the importance thatpeople place on relative comparisons) indeed dependendogenously on the beliefs about one’s relative abil-ity in the reference group, and this dependence hasimplications for the agent’s choice of effort. We arealso able to characterize the optimal feedback fre-quency and show that it depends on the agent’s rela-tive standing in the peer group. Therefore, the noveltyof the model is that it captures the effect of feedbackon purely ego-motivated individuals in a competi-tive setting. Furthermore, the theoretical frameworkwe develop—although quite stylized for tractabilityreasons—is helpful in understanding the experimen-tal results that we document in the paper.

Related to the work on self-esteem is a large lit-erature on status and peer effects. People care aboutsocial status as defined by their relative income(Frank 1984, 1985), they value public recognition inde-pendently of any monetary consequence (Delfgaauwet al. 2009) and are willing to trade off material gainsto obtain it (Huberman et al. 2004). The quest forstatus has labor market implications, for instance,

suggesting that relative performance, and not the level of abilityper se, enters the utility function. Our model and experimental datapoint in the same direction, that relative performance matters forthe agents’ utility.

regarding incentives and promotion schemes, or jobsearch and sorting (Cowen and Glazer 2007, Clarket al. 2010, Neckermann and Frey 2008). Peer moni-toring has also been proposed as an effective incen-tive mechanism (Major et al. 1991, Kandel and Lazear1992), even when output does not have an impacton monetary payoffs (Falk and Ichino 2006, Mas andMoretti 2009).

In contrast to the streams of work on status-seekingand peer-monitoring effects, our focus is on the inter-nal drive of individuals to rank well relative to others,and not on people’s need for public recognition orreputation among peers. In line with prior evidence,we assume that people enjoy performing well rela-tive to others even in situations when performance isprivate information, or when there are no future con-sequences via reputation or career concerns channels.A related driver of behavior to the one studied here isintrinsic motivation: people enjoy effortful endeavors,even in the absence of incentive pay, because com-pleting such endeavors generates a sense of personalgrowth and fulfillment (e.g., Deci 1975). Benabou andTirole (2003) formalize the concepts of intrinsic andextrinsic motivation and show under which condi-tions the latter will “crowd out” or “crowd in” theformer. There is extensive empirical evidence thatexternal intervention (for example, output-based payor monitoring) crowds out intrinsic motivation andundermines productivity (Frey 1997, Deci et al. 1999,Frey and Jegen 2001). For instance, Gneezy and Rus-tichini (2000) show that piece rates lead to increasedperformance only if they are substantial, and evenpiece rates as high as 10% may lead to a decrease inoutput as compared to a situation where no incentivepay is used. Because extrinsic motivators often turnout to have detrimental effects, finding the optimallevel of incentive pay that would improve rather thanimpair productivity is not trivial. We are thereforeconsidering an alternative incentive device—privateinformation about one’s relative performance in thegroup—that can potentially reinforce intrinsic moti-vation in ego-driven individuals.

An important question left for future work iswhether in environments where monetary incentivesare strong enough to actually motivate people towork hard, they may crowd out the effects of feed-back driven by self-esteem that we demonstrate herein a flat-wage environment. The evidence so far ismixed. On one hand, Eriksson et al. (2009) find in anexperimental setting that releasing information aboutrelative performance does not significantly influencethe subjects’ average effort when they face piece-rate or tournament pay. On the other hand, Blanesi Vidal and Nossol (2011) and Azmat and Iriberri(2010) find that when piece-rates incentives are used

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to induce effort, providing individuals with relativeperformance feedback increases productivity.

Our results suggest that in settings where mone-tary incentives are weak or nonexistent, moral haz-ard can be mitigated by optimally providing feedbackto agents regarding their relative performance. Egoutility, or self-esteem, can be used as a motivator forproductivity. In light of these findings, it is possiblethat by changing the reference peer group, the timingand the recipients of feedback, organizations can ben-efit from the dynamics of social hierarchy effects onproductivity.

2. Theoretical Framework andImplications

In our model two agents, i and j , work on similartasks. For agent i (and similarly for j), output is givenby yi = ai + ei + �i, where ai represents the agent’sinnate ability level, ei is the agent’s effort, and �i ∼

N401�25 is an exogenous shock independently andidentically distributed across agents. The agent doesnot know his own ability, nor the ability of the otherworker.

Each agent’s utility is increasing in his own out-put and decreasing in the output of the opponent,because people enjoy performing better relative toothers (Szymanski and Harkins 1987). Agents workfor a fixed wage. Similar to Falk and Knell (2004),we assume that agents can choose how much to careabout the feedback about the opponent’s output, andtherefore about their relative rank. This choice is cap-tured by the variable si ≥ 0, which we call the agent’sstandard.2

At the end of the working period each agent knowshow much he produced, and he may also learn howmuch the other agent produced. In the beginning ofthe period each agent is told the probability withwhich he will get information about the output ofhis opponent. We will denote this probability as p foragent i, and q for agent j . Agent i knows p but notq, and the opposite is true for agent j . It is commonknowledge that random variables p and q are inde-pendent and have a probability distribution functionf such that, unconditionally, E4p5= E4q5= 1

2 .We assume that the agent’s utility after he observes

only his own output is equal to the level of his out-put yi. If he also observes the output of his oppo-nent, his utility is equal to yi − yj ln4k/4k− si55, wherek > si is a parameter. Because expression ln4k/4k− si55is increasing in si, this means that all else equal,

2 This variable can be interpreted as a measure of how much theindividual would be hurt by an increase in the output of the otherplayer, how frequently he decides to compare himself to the other,or how ambitious and motivated he is. The higher si is, the moreambitious is the agent’s goal.

the higher a standard si the agent sets, the more heneeds to produce to achieve a given level of utilityfrom comparing his output to that of the competi-tor. If the standard si played no further role in ourmodel, it would be optimal for the agent to alwayschoose the lowest standard possible. In the psychol-ogy literature, such behavior is attributed to a “self-enhancement” motive: To feel good about themselves,people compare themselves downward, i.e., to thosewho are less productive. At the same time, peoplewho set high standards have been shown to performbetter. We capture this “self-improvement” motive byusing a cost-of-effort function that is decreasing inthe standard si, which implies that a given level ofeffort is less costly when one works on ambitious anddemanding tasks. Concretely, we assume that agent iexperiences the following cost of effort while work-ing: ci4ai1 ei5 = � − �ai ln4� − ei + psi5, where �1�> 0and 0 < � < 1 are parameters. These assumptionsensure that effort is less costly if agents set a higherstandard si for themselves. Further, because � > 0,effort is less costly for a more able worker, that is,being better skilled to do a task makes the job moreenjoyable or less stressful.3

Therefore, an agent who does not know his ownor his opponent’s ability and expects to get feedbackabout the opponent with probability p must chooseeffort and standard levels to maximize the followingexpected utility function:

Ei4ui5 = 41 − p5Ei4yi5+ p

(

Ei4yi5−Ei4yj5 ln(

k

k− si

))

−�+�Ei4ai5 ln4�− ei + psi50

In Appendix A, we solve for the general equilibriumof the model and prove several propositions, whichare shown below:

Proposition 1. If the agent believes that his ability isrelatively high (low) compared to the ability of the com-petitor, then he will produce more (less) output and expectbetter (worse) relative performance when the likelihood offeedback increases.

Proposition 2. After receiving good (bad) feedbackabout one’s own ability, i.e., after the agent learns that heis better (less) skilled than he expected, the agent’s outputwill decrease (increase) if p < 4≥53�/241 −�5 (sufficientcondition is that � > 4≤5 2

5 ).

3 The dependence of the cost function on p is purely technical. Itensures that when p = 0, the standard si does not change the costfunction, because then the agent can not compare himself with thecompetitor.

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Proposition 3. If the agent learns that his competitoris better (less) skilled than he expected, he will decrease(increase) his future output.4

Proposition 4. When the agent’s beliefs about relativeperformance are revised upward (downward), he expectsbetter (worse) relative performance in the future.

Proposition 5. When the agent’s beliefs about relativeability are revised upward (downward), he will choose ahigher (lower) standard.

Proposition 6. If abilities ai and aj and feedback prob-abilities p and q are common knowledge, then for a givenq if agent i is good enough relative to agent j (that is, ifai ≥ 1/q4aj − 44k−�541 − q55/41 −�55), it is optimal forthe principal to increase the frequency of feedback for thehigh-ability worker i.

Therefore, the model predicts that the feedbackpolicy can influence productivity and beliefs beforeand after rank information is revealed to the agents.Agents with different likelihoods of receiving infor-mation about their opponents’ output will (all elseequal) expect to rank differently and will producedifferent levels of output. Agents who initially donot know their relative position in the group adjusteffort and beliefs about future rank as they changetheir perceptions of relative ability. Different patternsin behavior and beliefs will occur after good andbad feedback, that is, after the subject learns that heranked better or worse than he expected. We use thesetheoretical implications to guide our interpretation ofthe patterns observed in the experimental data.

3. Experimental DesignWe use a simple task to understand the role of pri-vate feedback regarding relative rank on productiv-ity and to examine whether self-esteem considerationsare important. In the experiment we ask subjects tosolve multiplication problems (i.e., to multiply one-digit numbers by two-digit numbers) during severalidentically structured rounds. We use this task forseveral reasons. First, no previous task knowledge isrequired, and it is easy to explain. Second, task learn-ing effects, which we would like to avoid, should beminimal. In other words, we expect that participantsknow how to solve multiplication problems beforethey come to the lab, and their ability to solve theseproblems does not change much during the duration

4 Propositions 2 and 3 imply that an agent will change his out-put based on feedback about his own or his opponent’s ability. Anagent who learned that his own ability is higher or the ability ofhis opponent is lower will increase his output if p ≥ 3�/241 −�5.For p < 3�/241 −�5, the direction of change in the output dependson the strength of the effect of own ability relative to that of thecompetitor’s ability.

of the task. Third, the score on this task depends onthe subjects’ ability as well as on their effort choice.Therefore, different subjects will end up with differentscores, which will lead to dispersed rankings. Fourth,the subjects’ ranks depend not only on their own(possibly unknown to them) abilities, but also on theunknown skills and effort decisions of other partic-ipants. As a result, we are likely to find situationswhere the subjects’ expectations are not confirmed bythe received feedback. This allows us to study howthis mismatch between expectations and reality affectsfuture expectations and productivity.

In the task it is necessary to control for the difficultylevel of the multiplication problems. We therefore fol-low Cromer (1974) and generate 206 multiplicationproblems of the same difficulty level (for example,89 · 4, 76 · 9, or 73 · 8). Problems are presented to eachsubject on a computer screen. Each time the subjectsolves the multiplication correctly, one point is addedto his score and the next problem is presented. If thesubject provides a wrong answer, the score remainsunchanged and he is asked to solve the same problemagain until it is answered correctly. By not allowingsubjects to move on to the next question unless theprevious one is solved, we avoid a situation whereparticipants may strategically skip difficult problemslooking for easy ones.

The experiment consists of 18 identically structuredrounds. In each round and for each subject, three feed-back conditions are possible. The conditions differwith respect to the probability with which the subjectreceives feedback about his relative rank at the endof the round. This probability is either 0, 005, or 1. Werefer to these as the “No,” “Maybe,” or “Sure” treat-ments, respectively. The feedback condition is deter-mined randomly and independently for each subjectat the beginning of every round. Therefore, in thesame round different subjects face different feedbackconditions. Importantly, each subject knows only hisown feedback probability.

Figure 1 shows the sequence of events in eachround. First, subjects are told which feedback condi-tion they are in. This allows us to study the ex anteeffect of feedback probability on rank, expectedrank, and output. Then subjects are asked to reporttheir expected rank in that round.5 Following this,

5 We do not pay subjects if their rank expectations turn out to becorrect at the end of the round, because doing so would distortbehavior: all subjects would declare that they rank last, solve zeroproblems, and achieve the last rank indeed. We understand theimportance of incentive compatibility, and in other tasks wherefinal compensation depends on output—and is not a flat wage likein the current experiment—paying people if they make the correctrank guess would certainly be desirable. However, as explainedearlier, to understand how ego utility (i.e., liking to believe thatwe rank higher that others) changes behavior, we are confined to aflat-wage environment.

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Figure 1 Sequence of Events in a Round

Your id is: 2 Your id is: 2

Your id is: 2

Your id is: 2Your id is: 2

Your id is: 2

1 out of 18

Period 1

You MAY see the ranking in this period

You are about to start a multiplication task

Please state your expected rank in the group by entering anumber from 1 (the best) to 9 (the worst)

Out of 9 participants I expect to rank as number

Submit

Submit

Period Period

PeriodPeriod

GET READY Question 6: 29*9

Your last answer was: CorrectCorrect answers: 5

1 out of 18

1 out of 18

1 out of 181 out of 18

1 out of 18

The multiplication task will start soon!

Period PeriodRemaining time [sec]: 15

Remaining time [sec]: 40

Remaining time [sec]: 0Remaining time [sec]: 11

This period is over!

OK

How much effort did you put into the task?

no effort at all a lot of effort

Ranking in this period

Rank123444789

13--

------

You1210999864

Name Score

participants have 90 seconds to work on multiplica-tion problems. For each subject, their score is dis-played on the screen throughout the round and isupdated after every correct answer (the score is resetto zero at the beginning of every round). Therefore,subjects are always informed about their own output,independent of their feedback condition. After the 90seconds pass, subjects are asked to asses how mucheffort they have put into the task in the current round.

Answers are provided using a six-point scale rangingfrom “no effort at all” to “a lot of effort.”6

6 As a caveat, it is possible that the self-declared effort is not a per-fect measure of the true effort the subject put into solving problemsthat round, because participants may strategically choose whatlevel of effort to report. Because the predictions of Propositions 1–4are about output, not effort levels, we test them by using the outputmeasure, which is the actual number of problems solved. We onlyuse the self-reported effort variable for one robustness check at the

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In the final stage of each round, which lasts for15 seconds, each subject either sees the performanceranking or not, depending on the feedback conditionthey have been assigned to in that round. The rankingis determined by the current period scores of all sub-jects in the group. The subject who solves the highestnumber of problems ranks as number one, the personwho solves the second-highest number of problemsranks as number two, and so forth. Participants whosolve the same number of problems in a round receivethe same rank. Each subject can see the scores andranks of all the participants, but he can identify onlyhis rank and score. Therefore, each subject knows thatnobody else can associate his identity to his rank andscore.

Given our design, the baseline condition in theexperiment refers to trials where subjects know thatthe feedback probability is zero. An alternative base-line condition could have been one where subjectsparticipate in the same problem-multiplication task asin our experiment but are never told that it is pos-sible to learn their relative productivity and neverreceive relative rank feedback. We chose to design theexperiment as described above to match the theoret-ical setting, where agents are always informed aboutthe value of the feedback probability, and also to cap-ture the fact that in most corporate settings employeesknow that feedback is possible.

The experiment was programmed using the z-Treesoftware (Fischbacher 2007). Subjects were given awritten copy of the instructions (see Appendix B). Thetask was also described verbally by the experimenter.Subjects then practiced the task for one period, butfeedback about relative rank was not provided duringthat time. This practice period therefore served a dualpurpose: it helped subjects understand how to use thesoftware, and it also provided them individually withnoisy information about their own ability on the mul-tiplication task, because each person observed howmany problems they solved in those 90 seconds. Nocommunication or external aids (calculators, scratchpaper, etc.) were allowed during the experiment. Sub-jects were recruited from Northwestern Universityusing standard procedures. We conducted eight ses-sions, but one of them had to be excluded becauseof technical problems. We therefore present data fromthe 54 subjects (24 men and 30 women) participatingin the remaining seven sessions. Each subject groupconsisted of six to nine people. Subjects received afixed fee of $23 for their participation, independent ofperformance.

end of the empirical analysis. Also, because the correlation coeffi-cient between self-reported effort and actual outcome produced is0.34 (p < 00001), this indicates that the effort variable is related tohow hard people work.

Figure 2 Feedback Likelihood, Output, and Expected Rank

4.0

4.5

5.0

Exp

ecte

d ra

nk9101112

Out

put

0 0.5 1.0

Feedback likelihood

Average outputAverage expected rank

4. Experimental Results4.1. Ex Ante Effects of FeedbackAs predicted by Proposition 1, ex ante informationabout the likelihood of receiving feedback at the endof the period about one’s rank has a significant impacton the subjects’ expected relative performance, as wellas on their actual output, measured as the numberof multiplication problems solved correctly.7 Theseeffects are illustrated in Figure 2.

Output is 12.20% higher (11.31 versus 10.08 solvedproblems per round, p < 00001 in a one-sided meancomparison test), and the expected rank is better (3.98vs. 4.80, p < 00001 in a one-sided mean comparisontest) for participants who are in the “Maybe” feed-back condition, than for those in the “No” feedbackcondition. In the “Sure” condition the average out-put is also significantly higher (10.78 versus 10.08, p <0004 in a one-sided mean comparison test) and theexpected rank better (4.12 versus 4.80, p < 00001 ina one-sided mean comparison test) than in the “No”feedback condition. There is no significant differencebetween the output or expected rank of subjects inthe “Maybe” feedback condition versus “Sure” feed-back condition. These effects characterize most sub-jects, because 61% of participants produce a higheroutput on average in trials when the feedback proba-bility is 0.5 compared to when it is 0. Similarly, 69% ofsubjects produce, on average, higher output when thefeedback probability is 1, compared to when it is 0.

7 Although Proposition 1 has implications for beliefs about relativeoutput (Ei6yi7−Ei6yj 7), it is difficult to elicit these beliefs in a settingwith more than two participants. We could have asked subjects inthe beginning of each round to state how many more problemsthey expected to solve relative to, say, the median participant inthe room. Nonetheless, given the heterogeneity in the number ofpeople across all sessions of the experiment, the answers of partic-ipants in different sessions would have been difficult to compare.Hence, we instead proxied for these beliefs about relative outputby eliciting the subjects’ beliefs about their relative rank (e.g., “Thisround I expect to rank first”).

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Figure 3 Feedback Likelihood, Output, and Expected Rank, by Gender

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Figure 3 reveals significant gender effects on out-put and rank expectations in each of the three feed-back likelihood conditions. Men solve significantlymore problems than women. Across all treatments,the average number of problems solved is 13.13 formen, and 8.80 for women (p < 00001 in a one-sidedmean comparison test), in line with the prior literatureon gender and competitiveness (e.g., Gneezy et al.2003). Also, men expect to rank better than womendo (i.e., men report lower values for ExpectedRankt).Across all conditions, men expect to receive a rank of3.40, whereas women expect to receive a rank of 5.01.The difference is statistically significant (p < 00001).This is consistent with prior findings. For instance,Huberman et al. (2004) observe that males seek statusmore than women, and Falk and Knell (2004) find thatwomen have significantly lower aspiration levels thanmen regarding college education accomplishments.

Although these results suggest an unconditionaleffect of the feedback likelihood on output and rankexpectations, Proposition 1 specifically implies thatonly subjects who believe they have high relativeability will increase their output, and expect a betterrank, when they are told that they are in a condi-tion in which relative performance feedback is morelikely to be received. The evidence shown in Figure 4is consistent with its prediction. We document thatsubjects who have better than median rank expec-tations in the prior round (and hence believe thatthey have high relative ability) are those individualswho respond more to the ex ante feedback conditionin the current round. If told that feedback is possi-ble (that is, when they are in the “Sure” or “Maybe”feedback conditions), these individuals increase out-put and expect a better rank relative to situationswhen they are told rank feedback will not be pro-vided. Specifically, output increases from an averageof 11.88 in the “No” feedback condition to 12.91 in the“Sure” and “Maybe” conditions. Similarly, expectedrank decreases (i.e., people expect to do better) from

Figure 4 The Effect of Increasing the Likelihood of Relative RankFeedback on Output and Expected Rank as a Function ofthe Subjects’ Beliefs About Their Relative Ability

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3.72 in the “No” feedback condition to 3.02 in the“Sure” and “Maybe” conditions. Both effects are sig-nificant at p < 0001. Compared to these individualswho think they have high relative ability, those sub-jects with poor rank expectations in the prior rounddo not react as much, in terms of output and futurerank beliefs, to information about the feedback condi-tion they face. For these subjects, output does not dif-fer significantly depending on whether rank feedbackis possible or not, and rank expectations only improveby 0.36 if feedback is possible, an effect half the sizeof that observed among participants who think theyare relatively more able than their peers. These resultssupport the predictions of Proposition 1 regarding therole of the ex ante feedback condition on the agents’output and beliefs.

Additionally, we find that the subjects’ rank expec-tation and their actual rank are positively corre-lated, and this relationship becomes stronger in laterperiods. The Spearman rank correlation betweenExpectedRankt and Rankt is 0.62 in the first six periods,

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0.81 in periods 7–12, and 0.82 in periods 13–18 (p <00001 in all cases). The difference between the rankcorrelation measured in the first six periods and thatmeasured in the last 6 or 12 rounds is significant atp < 00001. Therefore, as the task progresses, people getbetter at guessing their actual rank in the hierarchy.

4.2. Ex Post Effects of FeedbackPropositions 2–4 imply that the feedback receivedregarding one’s relative standing in the group haseffects on the expectations of future rank and on theactual output produced in future rounds. We find evi-dence consistent with these predictions.

At the end of each round, subjects can receiveone of three types of feedback regarding their rela-tive ranking, depending on the relationship betweentheir actual rank and the rank they expected toget. If Rankt > ExpectedRankt , feedback is negative,because subjects did worse than they expected. IfRankt < ExpectedRankt , feedback is positive, and ifRankt = ExpectedRankt , it is neutral. We use threeindicator variables, BadFeedbackt , GoodFeedbackt , andNeutralFeedbackt to capture these three types of events.

The regression models in Table 1 show the role ofreceived feedback on future output, expectations ofrank, and actual rank. The reported effects are mea-sured relative to getting neutral feedback (but similareffects are obtained if measured relative to not gettingany feedback at all). Relative to getting neutral feed-back, doing better than expected in round t − 1 (i.e.,GoodFeedbackt−1 = 1) leads the subjects to expect a rankbetter by 0.50 in round t. Doing worse than expected(i.e., BadFeedbackt−1 = 1) has the opposite effect, lead-ing subjects to declare a worse expected rank, that is,a value higher by 0.54 for the variable ExpectedRankt .

As predicted by Propositions 2–4, subjects whoreceived good feedback believe they will rank evenbetter in the future (compared to their initial expec-tations) but end up ranking worse, whereas thosewho received bad feedback think they will rank worse(compared to their initial expectations), but in factwill rank better. After receiving negative feedback,people solve 0.74 more problems and achieve a rankbetter by 0.38. After receiving positive feedback, out-put is lower by 0.76 problems and the actual rankworsens by 0.63. In all regression models we includegroup fixed effects because unknown common factorsmay drive the effort and beliefs of all subjects in thesame experimental session, and also cluster standarderrors by subject. In unreported robustness checks,we cluster them by session, and the results remainstatistically significant. We also control for the roundnumber to account for possible time trends in out-put production or beliefs, and find that on averagesubjects solve 0.05 more problems in each additionalround, but there is no significant effect of round on

Table 1 The Ex Post Impact of Feedback on Expected Rank, ActualRank, and Output

Output t ExpectedRank t Rank t

Coef./t Coef./t Coef./t

GoodFeedback t−1 −0076 −0050 00634−20555∗∗ 4−40565∗∗∗ 430545∗∗∗

BadFeedback t−1 0074 0054 −0038420195∗∗ 440175∗∗∗ 4−20265∗∗

ExPostFeedback t−1 −0012 0023 −00074−00365 410495 4−00445

FeedbackLikely t 0056 −0055 −0031410525 4−20815∗∗∗ 4−10795∗

Output t−1 00754130435∗∗∗

ExpectedRank t−1 00794130525∗∗∗

Rank t−1 00664100155∗∗∗

Male 1035 −0039 −0069430335∗∗∗ 4−20195∗∗ 4−20635∗∗

Round t 0005 −0001 −0000430795∗∗∗ 4−10495 4−00205

Adj. R2 00664 00701 00540No. of obs. 918 918 918

Notes. Output t is the number of multiplication problems solved correctly bythe subject in round t . ExpectedRank t is the rank that the subject expectsto get in round t , as declared in the beginning of the round. Rank t is theactual rank achieved by the subject in round t . Low values for ExpectedRankand Rank indicate better rank expectations, and actual rank, respectively(e.g., the top-performing subject has Rank = 1). ExPostFeedback t is an indi-cator variable equal to 1 if the subject received relative ranking feedbackat the end of round t . GoodFeedback t is an indicator variable equal to 1if the subject received positive feedback at the end of round t , i.e., whenRank t < ExpectedRank t . BadFeedback t is an indicator variable equal to 1if the subject received negative feedback at the end of round t , i.e., whenRank t > ExpectedRank t . FeedbackLikely t is an indicator variable equal to1 if the probability the subject will receive feedback on relative ranking is0.5 or 1 (i.e., if the subject is in the “Maybe” or “Sure” feedback treatment).Male is an indicator variable equal to 1 if the subject is male. Round t isthe round number. The reference category is given by observations wheresubjects received neutral rank information at the end of the prior round(NeutralFeedback t−1 = 1). The t-statistics are in parentheses. Robust stan-dard errors are clustered by subject. Session fixed effects, constant termincluded.

∗p < 0010; ∗∗p < 0005; ∗∗∗p < 0001.

average rank expectations. We return to this outputincrease effect in the next section and examine itspotential causes.

An important concern is that the effect of good orbad rank feedback on output may simply be drivenby a mechanical mean-reversion process and there-fore may not be caused by self-esteem considerations.For instance, after performing very well in round tby solving many problems, a subject is likely to getgood feedback, that is, to learn he ranked better thanexpected, but in the next round his performance willdecrease because of mean reversion (perhaps becausepeople get tired after working particularly hard inthat round). We would then mistakenly attribute the

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lower subsequent output to the fact that the per-son was informed that they exceeded their own rankexpectations in the prior round (i.e., we would thinkof this as a feedback/self-esteem driven effect). To iso-late the relative rank feedback effect from a potentialmechanical mean reversion effect, in the regressionmodels in Table 1 we control for the prior values ofoutput produced by the subject. Therefore, the esti-mated coefficient on the GoodFeedbackt−1 variable inthe first column in Table 1, for instance, tells us thedifference in output produced in period t by two indi-viduals who solved the same number of problemsin period t − 1, but differ in that one received nofeedback about his relative rank at the end of roundt − 1, whereas the other was informed he exceededhis rank expectations. If there exists mean reversionin output, it should influence both these individu-als equally, because they solved the same number ofproblems during period t−1 (and each person knowsperfectly their output), and should not depend onwhether they were told how many problems otherparticipants solved that period. In other words, mean-reversion effects are orthogonal to the effects of theGoodFeedbackt−1 variable once we control for prior out-put. The same argument applies for the interpretationof the effect of the BadFeedbackt−1 variable. Similarly,when predicting expected rank and rank in the cur-rent period (see Table 1) we control for the values ofthese variables in the prior period to account for themechanical effect that people who are top ranked canonly stay put or move lower in the rankings, whereaspeople who are already at the bottom of the hierarchycannot rank any lower.

To further examine whether mean reversion is atplay, we conduct the following analysis: For par-ticipants who do not receive rank feedback in aparticular round, we sort them into those whose(unreported) rank was better than estimated (i.e.,those who would have received positive feedback had

Table 2 Mean Reversion or Feedback Effect?

Did not receive relative rank Received relative rankfeedback at end of round t − 1 feedback at end of round t − 1

Got better rank than expected Output in round t = 10044 Output in round t = 10024in round t − 1 Rank = 4036 Rank = 4032

Observations = 170 Observations = 146

Got worse rank than expected Output in round t = 10060 Output in round t = 11041in round t − 1 Rank = 4044 Rank = 4007

Observations = 281 Observations = 321

Diff. in output = 0016 (p = 004) Diff. in output = 1017∗∗∗ (p = 0001)Diff. in rank = 0008 (p = 004) Diff. in rank = −0025∗ (p = 001)

Notes. For participants who do not receive rank feedback in a particular round, we sort them into those whose (unre-ported) rank was better than estimated (i.e., those who would have received positive feedback had they receivedfeedback) and those whose (unreported) rank was worse than estimated (i.e., those who would have received neg-ative feedback had they received feedback). We then calculate for each group the number of problems solved inthe next round and the average rank. We do the same calculations for participants who receive feedback.

they received feedback) and those whose (unreported)rank was worse than estimated (i.e., those who wouldhave received negative feedback had they receivedfeedback). We then calculate for each group the num-ber of problems solved in the next round and theaverage rank. We do the same calculations for partic-ipants who receive feedback.

As you can see from the results in Table 2, forindividuals who did not receive feedback at the endof round t − 1, whether or not in that round theyranked better than expected has no significant impacton how much output they produce in round t, oron their rank in round t, indicating that we do notobserve mean reversion in productivity. For the sam-ple of people who received feedback at the end ofround t − 1, output (as well as the rank) in round tis dependent on whether these people were told thatin round t− 1 they did better or worse than they hadexpected. Specifically, for this subsample of peoplewho got rank feedback, output in round t is on aver-age 11.41 problems if the feedback in the prior roundwas negative, and 10.24 if the feedback was positive.This difference in output of 1.17 problems is signifi-cant statistically (p = 0001) and economically, becauseit represents about 9% of the average output producedper round in this task. The evidence in the table there-fore indicates that the difference in output producedby those who did better or worse than expected inthe prior round is not driven by mechanical meanreversion, but it depends critically on whether peo-ple actually received feedback regarding their rank inthat prior round.

The regression models in Table 1 also indicate thatthe likelihood of receiving feedback in the currentround and the gender of the subject have similareffects on output and expected rank as shown earlierin the univariate analysis, and illustrated in Figures 2and 3. If feedback is likely to be received—that is,the probability of seeing the ranking at the end of

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the period is not zero, as captured by the indica-tor variable FeedbackLikelyt—then subjects expect andachieve better ranks, and the output is larger (how-ever, the last effect is no longer statistically signif-icant). Males expect better ranks than females, andsolve more problems.

We also find evidence suggesting that the ex antedifference in expected ability influences the agents’beliefs about relative rank and their actual output,in the direction predicted by the model. Proposi-tions 3 and 4 imply that the better agent i believeshis competitor j is, the worse is the rank expectedby i, and the lower is the output produced by i. Inour experiment, the number of men in the group isan exogenous manipulation of the beliefs of womenparticipants regarding their relative ability at solvingthe task. This argument is suggested by the resultsin Gneezy et al. (2003) and Niederle and Vesterlund(2007), who show that women are less effective thanmen in competitive environments, and this effect isstronger in settings where women compete againstmen than in single-sex competitive environments.Stereotypes about men being better at solving mathe-matical problems can also contribute to women com-petitors being more pessimistic about their relativeability when more of the session participants aremale. Hence, we measure the difference in the agents’expected ability by the gender composition of oursubject groups. As shown by the results in Table 3, wefind that the number of men in the group matters forthe productivity of women, but not for that of men.Women’s expected and actual ranks are worse, and

Table 3 Heterogeneity in Subjects’ Competitive Abilities, Output, and Expectations

Panel A: Women only Panel B: Men only

Output t ExpectedRank t Rank t Output t ExpectedRank t Rank t

Coef./t Coef./t Coef./t Coef./t Coef./t Coef./t

MenInGroup t −1010 0037 0060 0025 −0020 −00104−20595∗∗ 410695∗ 420685∗∗ 400325 4−00505 4−00255

GroupSize t 0042 0029 0019 −1033 0066 0063400975 410255 400865 4−10135 410205 410185

Round t 0011 0001 0001 0022 −0002 0000440575∗∗∗ 400725 400885 450535∗∗∗ 4−10005 400175

Constant 7085 1047 1056 20075 −0092 −1033420975∗∗∗ 410065 410105 420465∗∗ 4−00325 4−00475

Adj. R2 00157 00192 00240 00096 00067 00064No. of obs. 540 540 540 432 432 432

Notes. Heterogeneity in the ability to compete is proxied by the gender mix in each subject group. The sample issplit by the subjects’ gender (panel A: women; panel B: men). MenInGroup t and GroupSize t are the number of malesubjects and the total number of subjects in the group, respectively. Round t is the round number. Output t is thenumber of multiplication problems solved correctly by the subject in round t . ExpectedRank t is the rank that thesubject expects to get in round t , as declared in the beginning of the round. Rank t is the actual rank achieved bythe subject in round t . Low values for ExpectedRank and Rank indicate better rank expectations and actual rank,respectively (e.g., the top-performing subject has Rank = 1). The t-statistics are in parentheses. Robust standarderrors are clustered by subject.

∗p < 0010; ∗∗p < 0005; ∗∗∗p < 0001.

their output is lower, the more men there are in thegroup, as predicted by Propositions 3 and 4.

4.3. Hierarchies and the Fight for DominanceThe experimental evidence so far indicates that feed-back about rank can impact the dynamics of rankings.However, these effects should be less important oncethe performance hierarchy is established. Indeed,as shown in Table 4, when we estimate the sameregression models as in Table 1 for rounds 1–9 and10–18 separately, we find that GoodFeedbackt−1 andBadFeedbackt−1 strongly influence the subjects’ rankexpectations in the early rounds, but these effects areno longer statistically significant during later rounds.In other words, feedback about relative performancein a particular round does not influence a subject’sexpectations about where he will stand in the hierar-chy in the future, once the hierarchy is determined.

In light of this suggestive evidence, we examine fur-ther whether stable hierarchies do get formed, andwhether this influences output and beliefs. First, thedata indicate that output grows over time: the aver-age number of problems solved in rounds 1 and 18are 9.48 and 12.5, respectively, and the difference isstatistically significant (p < 0001). This could in part bebecause of learning effects (i.e., participants find bet-ter ways to do multiplications), and in part becauseof a competition or ratcheting effect that is caused bypeople’s desire not to lose their status in the hierar-chy. We revisit these two effects at the end of thissection. Moreover, we find that the standard devia-tion of output increases over time, from 3.31 problems

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Table 4 Diminishing Effects of Feedback over Time

Panel A: Rounds 1–9 Panel B: Rounds 10–18

Output t ExpectedRank t Rank t Output t ExpectedRank t Rank t

Coef./t Coef./t Coef./t Coef./t Coef./t Coef./t

GoodFeedback t−1 0008 −0073 0025 −1070 −0022 1003400195 4−40195∗∗∗ 400945 4−30825∗∗∗ 4−10125 440265∗∗∗

BadFeedback t−1 1020 0089 −0048 0040 0024 −0032420715∗∗∗ 440985∗∗∗ 4−10845∗ 400795 410235 4−10365

ExPostFeedback t−1 −0039 0009 0005 0017 0031 −00184−10085 400705 400245 400345 410395 4−00765

FeedbackLikely t 0041 −0031 −0026 0075 −0075 −0037410395 4−10825∗ 4−10525 410435 4−30105∗∗∗ 4−10615

Output t−1 0081 00704160605∗∗∗ 4100425∗∗∗

ExpectedRank t−1 0082 00774160745∗∗∗ 4100645∗∗∗

Rank t−1 0069 00634100355∗∗∗ 480645∗∗∗

Male 0085 −0035 −0059 1080 −0042 −0079420205∗∗ 4−20635∗∗ 4−20075∗∗ 430735∗∗∗ 4−10885∗ 4−20915∗∗∗

Round t 0008 −0001 −0002 0006 0000 0000410665 4−00735 4−00945 410785∗ 400045 400155

Adj. R2 00665 00717 00526 00657 00697 00547No. of obs. 432 432 432 486 486 486

Notes. This table illustrates the ex post impact of feedback on estimated rank, actual rank, and effort for rounds1–9 (panel A) and rounds 10–18 (panel B). Output t is the number of multiplication problems solved correctly bythe subject in round t . ExpectedRank t is the rank that the subject expects to get in round t , as declared in thebeginning of the round. Rank t is the actual rank achieved by the subject in round t . Low values for ExpectedRankand Rank indicate better rank expectations, and actual rank, respectively (e.g., the top-performing subject hasRank = 1). ExPostFeedback t is an indicator variable equal to 1 if the subject received relative ranking feedbackat the end of round t . GoodFeedback t is an indicator variable equal to 1 if the subject received positive feedbackat the end of round t , i.e., when Rank t < ExpectedRank t . BadFeedback t is an indicator variable equal to 1 if thesubject received negative feedback at the end of round t , i.e., when Rank t > ExpectedRank t . FeedbackLikely t is anindicator variable equal to 1 if the probability the subject will receive feedback on relative ranking is 0.5 or 1 (i.e., ifthe subject is in the “Maybe” or “Sure” feedback treatment). Male is an indicator variable equal to 1 if the subject ismale. Round t is the round number. Robust standard errors are clustered by subject. Session fixed effects, constantterm included.

∗p < 0010; ∗∗p < 0005; ∗∗∗p < 0001.

in round 1 to 5.32 problems in round 18, consistentwith subjects expending the appropriate effort levelsneeded to maintain their rank (i.e., high effort for top-ranked individuals, and low effort for bottom-rankedones). The standard deviation of expected rank alsoincreases in later rounds, from 1.87 in round 1 to2.31 in round 18, suggesting that people’s expecta-tions “fan out” as they learn about their relative per-formance. Early on, subjects have similar priors abouttheir relative ability, but as they get feedback regard-ing their output level, posterior beliefs about rankbecame more heterogeneous, in accordance with thegroup’s diversity in abilities.

Another way to illustrate that hierarchies formearly on and remain relatively stable is to see whetherpeople who were at the bottom of the ranking in theearly rounds of the task tend to stay at the bottomin later rounds, whereas people who started by beingat the top of the ranking will stay at the top. Foreach participant we calculate their average rank in

the first six, middle six, and last six rounds of thetask. We will refer to these as the early, middle, andlate stages of the task. For each of theses three stages,we assign subjects to one of three rank performancebins: low, middle, and high, depending on their aver-age rank during the six rounds that comprised thestage. Thus, subjects in the low-rank performance binin a particular stage are those in the bottom third ofthe performance distribution, as determined by howtheir average rank compares to the average rank ofthe others in their peer group. Subjects in the high-rank performance bin are those in the top third of theperformance distribution as measured by their aver-age rank during that stage.

Figures 5 and 6 show how people transition acrossrank performance bins as the task progresses. Four-teen of the 17 (82%) of the individuals who are in thebottom third of the rank hierarchy during rounds 1–6end up in the same low-rank performance bin duringrounds 7–12, and also during rounds 13–18. Of the

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Figure 5 Transitions Across Ranks: Rounds 1–6 to Rounds 7–12

Low7–12 Medium7–12 High7–12

Low1–6 13/17 4/17 0/17

Medium1–6 4/18 12/18 2/18

High1–6 0/19 2/19 17/19

21 subjects who are in the top third of the rank hier-archy during the first six rounds, 18 (86%) are still topperformers during rounds 7–12, and 15 (71%) remainat the top during rounds 13–18. Thus, although thereare instances where subjects move up and down thehierarchy, most people stay in the same rank perfor-mance bin they are in during the first six rounds ofthe task. This indicates that by the end of the first sixrounds the hierarchy is already established.

Whereas people’s ranks do not change much oncethe hierarchy is formed, the average output of thegroup increases over time, as shown above and inthe results in Table 1. Does this increase come fromtop performers working harder to maintain their toprank, or by people in the middle or low end ofthe hierarchy who want to get better rankings? Theanswer to this question is relevant for optimal teamformation and dynamics. If the increase in outputcomes from people at the top of the ranking fightingfor dominance, and not from people at the bottomtrying to get a better rank, then it may be efficient toreshuffle peer groups by assigning bottom perform-ers to new teams. There, they have a chance to behigher up in the ranking, and will expend effort topreserve their newly acquired position, thus increas-ing the total output produced. The evidence we findis consistent with this hypothesis.

Figure 7 shows that the ratcheting effect observedin average output comes mainly from subjects whowere at the top or in the middle of the hierarchy inthe first six rounds. Individuals who ranked in thebottom third of the hierarchy early on have a slowerrate of productivity increase relative to the other par-ticipants. Therefore, the increase in output over timecomes mainly from high-productivity subjects whofight to maintain or improve their rank.

An alternative interpretation of the increase in out-put over time seen in Figure 7 is that people sim-ply get better at solving multiplication problems asthe task progresses, and those that had better perfor-mance earlier on learn faster. This interpretation is

Figure 6 Transitions Across Ranks: Rounds 1–6 to Rounds 13–18

Low13–18 Medium13–18 High13–18

Low1–6 13/17 4/17 0/17

Medium1–6 4/18 11/18 3/18

High1–6 0/19 3/19 16/19

Figure 7 The Average Output Produced Each Round by Subjects WhoWere at the Top, in the Middle, or at the Bottom of the RankHierarchy During the First Six Rounds

5

10

15

20

Out

put

0 3 6 9 12 15 18Round

Bottom of hierarchy in rounds 1–6Middle of hierarchy in rounds 1–6Top of hierarchy in rounds 1–6

unrelated to ego utility or to the ratcheting effect (thatis, strategically choosing to work harder to obtain agood rank). To investigate this alternative explana-tion, we obtain a measure of how difficult it is forsubjects to solve multiplication problems. We calcu-late the cost of effort (CostOfEffortt) per multiplica-tion problem as the ratio of declared effort to outputproduced by each subject in each round. We aver-age this quantity across the three performance cat-egories (early top, middle and bottom performers).For learning to explain the patterns in Figure 7, itshould be the case that the rate of change in outputand the rate of change in the cost of effort over timeare negatively related. In other words, early top per-formers will increase their output at a faster pace rel-ative to bottom performers because their cost of effortdecreases at a faster pace over time. As the data inTable 5 show, we do not find this to be the case.

The output of early top performers increases attwice the rate over time as that of early bottom per-formers (ãOutput/ãRound is 0.21 and 0.11 for these

Table 5 Ratcheting Effect or Learning?

ãOutputãRound

ãCostOfEffortãRound

Average Average Averagedeclared output cost of

Ranking in effort per effortrounds 1–6 per round round per round

Top of hierarchy 4040 14090 0030 0021 −00004Middle of hierarchy 4038 10017 0044 0016 −0001Bottom of hierarchy 4002 6065 0061 0011 −0001

Notes. Subjects are divided into three categories (top, middle and bottom performers)depending on their rank in the hierarchy during the first six rounds of the task, as in Fig-ure 7. Effort t is an input provided by each subject at the end of each round, before theranking information is shown. Outputt is the number of multiplication problems solvedcorrectly by each subject in each round. CostOfEffortt is calculated as Effort t/Output t .The average rate of change in output and in the cost of effort over time are capturedby variables ãOutput/ãRound and ãCostOfEffort/ãRound , respectively, and are esti-mated by regressing Output t and CostOfEffort t on Round t for subjects in each of thethree early performance categories. The reported estimates are significantly differentfrom zero at conventional levels (p < 0005).

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two categories, respectively). The cost of effort, how-ever, decreases faster over time for bottom performers(ãCostOfEffort/ãRound is −0.01 for bottom perform-ers and −0.004 for top performers). These averagerates of change in output and in the cost of effortover time are estimated by regressing Outputt andCostOfEffortt on Roundt , for participants in each ofthe three early performance categories, and are sta-tistically significant at conventional levels (p < 0005).Therefore, learning effects (i.e., the task getting eas-ier over time) cannot be the sole explanation for theincrease in output of those ranking well early on,because the task seems to get easier faster for earlybottom performers. Hence, ego utility—as shown byour model and previous empirical results—can be adriver of output and lead to ratcheting at the top ofthe hierarchy, a pattern illustrated by the data in Fig-ure 7 and Table 5. Consistent with the fight for domi-nance interpretation, we observe that throughout thetask early top performers declare higher effort levelsrelative to early bottom performers (4.40 versus 4.02,on a scale from 1 to 6) and produce higher output(14.90 versus 6.65 multiplication problems per round)They also have a lower average cost of effort (0.30versus 0.61). All of these differences are statisticallysignificant (p < 0001).

Because the above results come with the caveat thatself-reported effort may not represent the true effortspent by participants, we use an additional approachfor testing the learning-based alternative hypothesis.We invited 26 new participants, ages 18–24 (8 men

Figure 8 Output Produced Each Round by Top, Middle, and Low Early Performers, Classified Based on Their Output During the First Six Rounds

0

5

10

15

20

0 3 6 9 12 15 18

High-performance rounds 1–6 Mid-performance rounds 1–6

Low-performance rounds 1–6 Fitted values high group

Fitted values mid group Fitted values low goup

Out

put

Round

Note. Lines of best fit from the regression of output on round, using data from rounds 7–18, are also shown, for observations belonging to high, medium, orlow initial performers.

and 18 women), all students at Northwestern Univer-sity to take part in a “no rank feedback” version ofthe experiment. In this version, each participant knewhis or her absolute performance, namely, the num-ber of problems solved correctly during each round.However, the possibility of seeing one’s relative per-formance was never mentioned, and relative rankinformation was never provided. There were between6 and 7 participants in each of four experimentalgroups, working concurrently on solving the samemultiplication problems as in the main experiment,for the same fixed pay of $23. Using this sample,we wanted to understand whether better initial per-formers improve faster than poor initial performerswhen no feedback about relative rank was provided.If that happened in the data, it would have sheddoubt on our assertion that the increase over timein the output of the top performers in the feedbackexperiment was due to fighting for the top ranks, andit would have suggested that our “ratcheting effect”could have been simply driven by faster learning byinitial top performers, and not by competition.

We present the data from the “no rank feedback”experiment in Figure 8. We assign each participantto one of three early performance groups—high,medium, and low performers—based on the outputproduced in the first 6 rounds of the experiment. Inthe figure, we show the output produced by eachof the 26 participants in each of the 18 rounds. Wealso plot a regression line for each of the three earlyperformance groups, indicating the rate of growth of

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output after the rounds during which initial perfor-mance is measured (i.e., rounds 7–18). In other words,we regress output on round numbers, for each of thethree subsamples of high, medium, and low perform-ers, and plot the line of best fit. The figure showsthat those labeled as high performers early on do notimprove faster than those who are medium or lowearly performers. Specifically, looking at the improve-ment in output during rounds 7–18, the slope of out-put with respect to round is 0.08 for the high group,0.20 for the middle group, and 0.23 for the low ini-tial performance group. Therefore, the data from the“no rank feedback” experiment indicate that althoughpeople tend to improve with time during our experi-ment, it is not the case that those who did well in thebeginning will increase their output faster than theother participants. This suggests that learning effectsare not the driver of the result we documented in themain experiment (where relative rank feedback waspossible) that high initial performers improved fasterthan the low performers. Therefore, this supports ourinterpretation that in the main experiment the ratch-eting of output observed among the best participantswas related to their ego utility and interest in main-taining a top rank.

5. Implications for CorporateFeedback Policies

In light of our findings, it is natural to ask whatare the characteristics of optimal feedback policies.It is important to know whether organizations canincrease their total output through optimal feedbackprovision, perhaps by changing the timing and con-tent of information released to workers or by reveal-ing information to certain individuals only. Eventhough the current experimental setup does not allowus to compare such complex feedback policies, ourresults have several implications for improving pro-ductivity that match the observed actions undertakenby firms to improve their performance appraisals(e.g., changes in frequency, benchmarks, or perfor-mance labels).

For instance, firms could take advantage of theex ante effect of feedback likelihood on effort pro-vision. Proposition 1 suggests that an organizationcould produce more if it tailored the feedback prob-ability to the agent’s expected or true relative ability.In particular, by providing more-frequent feedbackto agents who believe that they have relatively highability, managers can take advantage of the positiveex ante effect that the likelihood of feedback has onoutput. This result, as shown by Proposition 6, con-tinues to hold in well-established teams where work-ers’ abilities and feedback probabilities are commonknowledge. A manager of a well-established team can

increase the overall output simply by providing feed-back more frequently to workers who posses rela-tively high ability.

Note, however, that the firm needs to commit to afeedback policy ex ante. The model does not allowfor the strategic choice of when to reveal to workerstheir rank. That is, the likelihood of receiving feed-back in the model is not conditional on the employeehaving achieved a bad or good rank. Thus, Proposi-tion 2, which states that those who get bad feedbackwill increase output in the future relative to its level inthe absence of feedback, does not imply that provid-ing only bad feedback (i.e., telling people their rankonly when the underperform compared to others) isan optimal policy. This is because the equilibriumderived in the model assumes that the firm commitsto a probability of rank feedback provision that isindependent of the agents’ actual output.

The principal could also manipulate the beliefs ofthe agents to use both the ex ante and ex post effectsof feedback. Proposition 3 suggests that if competi-tors appear to be too tough, agents will decrease theiroutput. Moreover, Proposition 1 implies that the pos-sibility of receiving rank feedback only has motiva-tional effects for agents who believe they are betterskilled than their competitors. Therefore, if the firmcan improve workers’ beliefs about their relative abil-ity, these optimistic beliefs will have a positive impacton productivity.

As shown in Table 4, however, the ex post effects offeedback wear off as time goes by and people learntheir true standing among their peers. To prolong theeffectiveness of relative rank information, organiza-tions could provide noisy feedback to slow down thelearning of one’s rank in the hierarchy, or reshufflework groups once the hierarchy is established.

Lastly, our empirical results show that outputincreases over time, and that this effect is possiblydue to the competition for top ranks among the best-performing individuals (as suggested by Figure 7).The data thus indicate that agents in heterogeneousgroups will split into top performers who keep fight-ing for high ranks, and bottom performers who com-pete much less. Similarly, we also observe that womenproduce significantly less output when there are moremen in the group (as shown in Table 3). Making teamsmore homogeneous may therefore provide otherwiselow-rank workers with an opportunity to climb thehierarchy, and as a result, may restore their incentivesto generate more output.

6. ConclusionWe propose that individuals’ utility is influenced byprivate information regarding their relative perfor-mance. This hypothesis implies that feedback about

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rank has effects on both productivity and on thedynamics of the rank hierarchy in groups of workersdoing similar tasks. These predictions are supportedby experimental evidence. To separate our hypothesisfrom alternative explanations as to why rank infor-mation may change behavior, we employ an experi-mental setting where subjects receive a flat wage forworking on a simple problem-solving task, and wherethere cannot exist reputation, strategy learning, orpeer monitoring effects.

We find that agents who believe they have rela-tively high ability will increase output, and expect torank better, if told feedback is likely. After receivingfeedback, those who got better ranks than expectedwill decrease output, but expect even better ranks inthe future, whereas the opposite is true of people whoranked lower than expected. The productivity hierar-chy is established early on in the task, and there isa ratcheting effect in output. People at the top of thehierarchy early on work harder over time, whereaspeople at the bottom do not improve their productiv-ity as much.

These results suggest that in competitive settingsproductivity and beliefs are influenced by privatelyobserved information about relative rank. The effectsof private rank feedback on output are comparable tothose of peer-monitoring mechanisms documented inprior work. For example, Mas and Moretti (2009) findthat a 10% increase in average coworker productivityis associated with a 1.7% increase in a worker’s effort.By optimally arranging the mix of workers in eachshift, the firm in their sample could improve produc-tivity by 0.2%. Similarly, Falk and Ichino (2006) findthat a 10% increase in a peer’s output results in a1.4% increase in a given individual’s effort. We findthat giving people an opportunity to privately com-pare themselves to others raises individual output onaverage by 12.20%, an effect comparable to that ofpeer monitoring.

Our results suggest that relative rank feedbackcan be strategically used to improve employeeperformance in organizations. Firms can vary thefrequency and content of information released toworkers, they can provide feedback to subsets ofemployees, depending on their actual abilities or per-ceptions of their standing among their peers, or canreshuffle teams to encourage all workers to work hardto achieve a good rank. Therefore, the value that indi-viduals assign to learning that they compare well totheir peers makes relative rank feedback a useful toolfor increasing firm productivity.

AcknowledgmentsFor valuable comments and discussion, the authors thankTerrance Odean (special issue coeditor); an anonymousreferee; Pierpaolo Battigalli; Stefano DellaVigna; Shimon

Kogan; David Myatt; Jonathan Parker; Imran Rasul; PaolaSapienza; Nora Szech; participants at the 2008 ESA Euro-pean Meeting, the 2008 La Pietra-Mondragone TheoryWorkshop, the 2008 International ESA Conference, the 2008NBER Behavioral Finance Meeting, and the 2009 IZA Work-shop on Genes, Brains and Labor Markets; and seminarparticipants at New York University, Northwestern Univer-sity, and University of California, Berkeley. This paper waspreviously circulated as “Rank Expectations, Feedback andSocial Hierarchies.” C. M. Kuhnen gratefully acknowledgesfinancial support from the Zell Center for Risk Research.

Appendix A. ModelAs indicated in the main text, an agent who does not knowhis own or his opponent’s ability and expects to get feed-back about the opponent with probability p has the follow-ing expected utility function:

Ei4ui5 = 41 − p5Ei4yi5+ p

(

Ei4yi5−Ei4yj5 ln(

k

k− si

))

−�+�Ei4ai5 ln4�− ei + psi50 (A1)

Agent i, therefore, faces the following problem:

maxei1 si

Ei4ai5+ ei − pEi4yj54ln k− ln4k− si55

−�+�Ei4ai5 ln4�− ei + psi5 (A2)

and the resulting first-order conditions yield

e∗

i = �−�Ei4ai5+ p4k−Ei4y∗

j 551 (A3)

s∗

i = k−Ei4y∗

j 50 (A4)

Equation (A3) shows that effort is decreasing in expec-tations of one’s own ability. This effect comes from thefact that the marginal cost of effort is increasing in Ei4ai5.Because the cost function we use is decreasing in the abil-ity level; being more able makes performing the task lessunpleasant. This cost specification means that the benefits(coming from the cost function) of being of high ability arehighest for low levels of effort and decrease as the effortlevel increases. This assumption captures the idea that thereare limits to human effort, and as we continue to workharder or longer, the ability-driven advantages wear off,and at some level of effort everybody is equally exhausted.Also, the equilibrium level of effort increases in the levelof the chosen standard. Being more motivated for the taskmakes a given level of effort seem less costly and allows theagent to take on extra work. Furthermore, the more agenti expects agent j to produce, the lower a standard he setsand the lower a level of effort he puts into his task.

We now proceed to the general equilibrium solution ofthe model. For simplicity, to avoid infinite hierarchies ofbeliefs, we restrict attention to the first-order beliefs, thatis, to beliefs about one’s own ability (Ei4ai5 and Ej4aj5) andbeliefs about ability of the other player (Ei4aj5 and Ej4ai5).Second-order beliefs—that is, beliefs of player i about thebeliefs of player j—are such that Ei4Ej4aj55 = Ei4aj5 andEi4Ej4ai55= Ei4ai5.

Also, Ei4Ej4p55 = Ej4p5 = Ej4Ei4q55 = Ei4q5 = 12 . Therefore,

agent i expects agent j to produce the following:

Ei4y∗

j 5= Ei4aj5+�−�Ei4aj5+k

2−

12Eiai −

12Ei4Ej4e

∗

i 550 (A5)

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Let e∗i ≡ Ei4Ej4e

∗i 55 =

∫ 10 e∗

i 4p5f 4p5dp. Then, combiningEquations (A5) and (A3) we get that

e∗

i =�+pk

2−p�+

(

p

2−�

)

Ei4ai5−p41−�5Ei4aj5+p12e∗

i 0 (A6)

After taking expectations with respect to probability p inEquation (A6) we obtain

e∗

i =13 42�+ k+ 41 − 4�5Ei4ai5− 241 −�5Ei4aj550 (A7)

Combining Equations (A7) and (A6), we obtain the for-mula for the equilibrium level of effort of agent i, who hasbeliefs Ei4ai5 and Ei4aj5:

e∗

i =2p41−�5−3�

3Ei4ai5−

4p41−�5

3Ei4aj5+�−

2�p3

+2kp3

0

(A8)

Using Equations (A4) and (A8), we obtain the equilibriumlevel of standard:

s∗

i =241 −�5

3Ei4ai5−

441 −�5

3Ei4aj5+

234k−�50 (A9)

In equilibrium, agent i produces the following amount ofoutput:

y∗

i = ai +2p41 −�5− 3�

3Ei4ai5−

4p41 −�5

3Ei4aj5

+�−2�p

3+

2kp3

+ �i (A10)

and ex ante expects to produce the following:

Ei4y∗

i 5 =42p+ 3541 −�5

3Ei4ai5−

4p41 −�5

3Ei4aj5

+�−2�p

3+

2kp3

0 (A11)

We use Equations (A8)–(A11) to derive the main propo-sitions in the paper.

Our model predicts that the feedback policy can influenceboth productivity and beliefs even before any rank infor-mation is revealed to the agents. In particular, agents withdifferent likelihoods of receiving information about theiropponent’s output will (all else equal) expect to rank differ-ently and will produce different levels of output.

Proposition 1. If the agent believes that his ability is rela-tively high (low) compared to the ability of the competitor, then hewill produce more (less) output and expect better (worse) relativeperformance when the likelihood of feedback increases.

Proof. Using Equation (A10), we get that dy∗i /dp =

23 441 − �54Ei4ai5 − 2Ei4aj55 + k − �5. Because � < 1, dy∗

i /dp >0 ⇔ Ei4ai5 > 2Ei4aj5 − 4k−�5/41 −�5 and dy∗

i /dp ≤ 0 ⇔

Ei4ai5≤ 2Ei4aj5− 4k−�5/41 −�5.We measure expected relative performance using the dif-

ference in agents’ expected outputs, Ei4y∗i 5−Ei4y

∗j 5, and say

that agent expects better relative performance when this dif-ference increases. The probabilities with which the agentsreceive feedback are not correlated, and thus we get thefollowing:

d4Ei4y∗i 5−Ei4y

∗j 55

dp=

dEi4y∗i 5

dp

=23441 −�54Ei4ai5− 2Ei4aj55+ k−�50

Because � < 1, 4d4Ei4y∗i 5−Ei4y

∗j 555/dp > 0 ⇔ Ei4ai5 >

2Ei4aj5 − 4k−�5/41 −�5 and 4d4Ei4y∗i 5−Ei4y

∗j 555/dp ≤ 0 ⇔

Ei4ai5≤ 2Ei4aj5− 4k−�5/41 −�5. �This proposition implies that giving subjects the opportu-

nity to compare themselves to others makes the sufficientlyself-confident ones (i.e., individuals for whom Ei4ai5 is suf-ficiently high relative to Ei4aj5) more productive and moreoptimistic about their relative position in the group, whichis highly desirable for the principal.

Comparative statics allow us to predict how agents whoinitially do not know their relative position in the groupadjust effort and beliefs about future rank as they changetheir perceptions of relative ability (but note that we donot explicitly model the belief updating process). Differentpatterns in behavior and beliefs will occur after good andbad feedback, that is, after the subject learns that he rankedbetter or worse than he expected.

Proposition 2. After receiving good (bad) feedback aboutone’s own ability, i.e., after the agent learns that he is better (less)skilled than he expected, the agent’s output will decrease (increase)if p < 4≥53�/241 −�5 (sufficient condition is that � > 4≤5 2

5 ).

Proof. From Equation (A10) we get the following:

dy∗i

dEi4ai5=

2p41 −�5− 3�3

and

dy∗i

dEi4ai5< 0 ⇔ p <

3�241 −�5

and

dy∗i

dEi4ai5≥ 0 ⇔ p ≥

3�241 −�5

0

Note that because p ≤ 1, if � > 25 , then dy∗

i /dEi4ai5 < 0. �There are two channels through which changes in

expected own ability exert influence on output. First, foran agent who believes to be better skilled than initiallythought, the same level of effort, other things equal, isless costly because the cost-of-effort function is assumed todecrease in ability. Nonetheless, because the marginal costof effort increases in ability, whereas the marginal bene-fit is constant (and equal to 1), in equilibrium the agentwhose beliefs about own ability have improved will choosea lower effort level. Second, he increases the level of stan-dard, which in turn leads to higher effort level. This iscaused by the fact that the cross-partial derivative of thecost of effort with respect to standard and ability is nega-tive, which means that the more skilled agent i is, the morehe enjoys difficult tasks. For high � or low feedback prob-ability p the overall effect of increased own ability expecta-tions on future output is negative. This happens because ahigh value of � implies that the marginal cost of effort isincreasing in ability at a faster pace, and a low probabilityof feedback p weakens the positive motivational effect ofhigh standard on effort.

Proposition 3. If the agent learns that his competitor is bet-ter (less) skilled than he expected, he will decrease (increase) hisfuture output.

Proof. From Equation (A10) we get dy∗i /dEi4aj5 =

−4p41 −�5/3 < 0. �

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If Ei4aj5 increases, agent i expects to be more hurt by therelative comparison with his peer, and to protect himself hesets a lower standard (which makes the relative compari-son less important in the utility function) and, as a result,works less.

From Propositions 2 and 3 we learn that an agent willchange his future output when the feedback he receivesabout his own and/or his opponent’s ability is not in accor-dance with his current beliefs. For example, an agent wholearned that he is higher in the talent hierarchy (i.e., hisown ability is higher and the ability of his opponent islower) will increase his future output if p ≥ 3�/241 −�5. Forp < 3�/241 −�t5, the direction of change in the output willdepend on the strength of the effect of own ability relativeto that of the competitor’s ability.

The next proposition establishes formally how agent’sbeliefs change after he receives feedback about his relativeposition in the group.

Proposition 4. When the agent’s beliefs about relative per-formance are revised upward (downward), he expects better(worse) relative performance in the future.

Proof. As in Proposition 1, we measure relativeperformance using the difference in agents’ outputs,Ei4y

∗i 5 − Ei4y

∗j 5, and say that agent expects better relative

performance when this difference increases:

d4Ei4y∗i 5−Ei4y

∗j 55

dEi4ai5=

dEi4y∗i 5

dEi4ai5−

dEi4y∗j 5

dEi4ai51

Ei4y∗

j 5=4341 −�5Ei4aj5−

2341 −�5Ei4ai5+

2�+ k

3

⇒d4Ei4y

∗i 5−Ei4y

∗j 55

dEi4ai5=

42p+ 3541 −�5

3−

241 −�5

31

=42p+ 1541 −�5

3> 01

d4Ei4y∗i 5−Ei4y

∗j 55

dEi4a∗j 5

= −4p41 −�5

3−

441 −�5

3

= −441 −�541 + p5

3< 00 �

Furthermore, feedback also influences the agents’ moti-vation. An individual who receives good feedback willbecome more ambitious in the future, in the sense thathe will set more demanding goals for himself. This resultcomes through two separate channels. First, when agent ilearns that agent j is less skilled, he expects to do better infuture relative comparisons, and as a result it is optimal forhim to put greater importance (that is, choose a higher si) onsuch comparisons. Second, learning that agent i’s own abil-ity is higher translates to higher benefits of choosing a highstandard, since the effort cost function decreases in the stan-dard si. This is summarized in the following proposition:

Proposition 5. When the agent’s beliefs about relative abilityare revised upward (downward), he will choose a higher (lower)standard.

Proof. Using Equation (A9) we obtain the following:

ds∗i

dEi4ai5=

2 41 −�5

3> 0 and

ds∗i

dEi4aj5= −

4 41 −�5

3< 00 �

The previous propositions indicate that feedback aboutrelative rank has ex ante and ex post effects on beliefs andproductivity in the setting where agents still learn wherethey stand in the rank hierarchy. It is therefore natural toask what would be the effect of feedback in well-establishedteams, that is, in settings where workers’ abilities and feed-back policies are common knowledge. We address this ques-tion below. Recall Equation (A3) and assume that there iscommon knowledge of abilities and feedback probability.We then get that in equilibrium:

e∗

i =�41 − p5+ pk41 − q5+ p�aj + pqai − paj −�ai

41 − pq51 (A12)

y∗

i =�41 − p5+ pk41 − q5+ 41 −�54ai − paj5

41 − pq5+ �i0 (A13)

Therefore, the principal who hires a pair of workers 4i1 j5and provides worker i with feedback with probability p andworker j with probability q expects the following level oftotal output:

Y ∗4i1 j5 = y∗

i + y∗

j =�42 − p− q5+ qk41 − p5+ pk41 − q5

1 − pq

+41 −�5

41 − pq54ai41 − q5+ aj41 − p550 (A14)

Proposition 6. For a given q, if agent i is good enough rela-tive to agent j (that is, if ai ≥ 1/q4aj − 44k−�541 − q55/41 −�55)it is optimal for the principal to increase the frequency of feedbackfor worker i.

Proof. dY ∗/dp = 441 − q5/41 − pq52544k − �541 − q5 +

41 − �54aiq − aj550 dY ∗/dp ≥ 0 ⇔ ai ≥ 1/q4aj −

4k−�541 − q5/41 −�55. �This proposition implies that a principal can extract more

output from agents if he provides more frequent feedbackto high-ability workers. Feedback about relative rank isa cheap way to motivate the high types to work harder,since they enjoy learning that they did better than thecompetition.

A few comments regarding the modeling choice are inorder: (1) An alternative specification would be to makethe utility dependent on relative ability, not output. Theproblem with having a model where agents learn abouttheir ability (a constant trait) is that this learning shouldtake place relatively quickly. In the absence of other output-based rewards, there is no incentive to continue produc-tion after ability is known and therefore such model couldnot explain the increase in output over time observed inthe data from our experiment. (2) In the economic liter-ature standards or goals against which agents comparethemselves have been traditionally assumed to be exoge-nous variables. Nonetheless, findings from social psychol-ogy (e.g., Wood and Taylor 1991, White et al. 1995) aswell as economics (Falk and Knell 2004) suggest that goalsare to some extent chosen by individuals. Therefore, wemodel the standard si as a choice variable. An exogenouscomponent of goal setting could easily be incorporated in

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our framework without changing the predictions of themodel. However, because in the experimental setup wedid not manipulate goals exogenously, we focus the modelon the endogenously chosen standard. (3) As suggestedby a reviewer, it is plausible that even in the absence offeedback people may still enjoy believing that they prob-ably performed well in relative terms. In such a case, thelikelihood of feedback should not affect effort decisions,contrary to Proposition 1 and our empirical findings. Therelationship between effort and the likelihood of feedbackcould be restored by assuming a different utility func-tion of the form u1 = y1 + v4y1 − y25, with appropriateassumptions on the function v. (4) In many real life situ-ations, as well is in our experimental setup, people com-pare themselves with a larger number of peers, and themodel can be easily extended to allow for more than twoagents. In such a setting where agent i receives feedbackabout the output of multiple opponents, his utility equalsyi −

∑

j 6=i yj/4n− 15 ln4k/4k− si55, where n is the number ofagents performing the task. All propositions, with onlyminor modifications, continue to hold for this specification.For tractability and ease of exposition, we restrict our atten-tion to the two-agent setting. (5) Note also that in a two-agent setting where each agent receives perfect feedbackabout their competitor’s output, and where agents have theopportunity to interact after the task, social status concernsare likely to arise (i.e., people want to look good in front ofthe other person by having produced high output). How-ever, our experiment was designed to eliminate social statusconcerns or peer pressure, because the large number of par-ticipants in the room made it impossible for a subject toattribute a particular level of output to specific individualsaround them. Because each person’s performance was onlyknown to themselves, we believe concerns for social statusare minimal. Given this feature of the experimental setup,and the model’s aim to facilitate the interpretation of thedata, we choose not to incorporate the social status aspectin the theoretical framework.

Appendix B. Experiment InstructionsWelcome to our experiment on economic decision making!The study will last about 60 minutes, during which youwill participate in a 45-minute experiment and will fill outsome questionnaires. Your task during the experiment is tosolve multiplication problems. Each time you provide a cor-rect answer, one point is added to your score. Your scoreis refreshed in each period, and you are going to play for18 periods. In each of the periods:

(1) You will be told what information you will receive at theend of the period regarding your rank in the group. Your rankis based on the number of correct answers provided by youand the other participants. You will see one of the follow-ing three statements on the screen, selected at random foreach one of the participants in each period: “You WILL seethe ranking this period.” In this case, you will see the rankinformation at the end of the period. “You MAY see the rank-ing this period.” In this case, there is an equal chance thatyou will or will not see the rank information at the end ofthe period. You WILL NOT see the ranking this period.” In this

case, you will not see the rank information at the end of theperiod.

(2) You will be asked to estimate your rank in the group beforeseeing any of the multiplication problems. Your rank is deter-mined by your score in the current period. If you have thehighest score (i.e., nobody solved more multiplication prob-lems than you did), you will rank as number 1. If thereis only one person who solved more problems, you willrank as number 2, and so on. Therefore, if you expect thatx people will have higher score than yours, please type ina number equal to x + 1 as your expected rank and pressthe “Submit” button. Example: You expect that 5 people will dobetter than you. Type in 6 and press “Submit”.

(3) You will be presented with multiplication problems tosolve. In each period you will have 90 seconds during whichyou can work on the multiplication problems. To providean answer, type it in the box and press “Submit”. If youranswer is correct, a point will be added to your score andyou will see another multiplication problem. If your answeris incorrect, your score will remain unchanged and you willsee the message “Incorrect. Please try again.” You will beasked to solve the same problem again. Only after you pro-vide the correct answer will the program move on to thenext multiplication problem.

(4) You will be asked to report the level of effort you have putinto doing the task during that period. Check the appropriatefield that reflects how much effort you have put into doingthe task, ranging from “no effort at all” to “a lot of effort,”then press “Submit”.

(5) You may see how you have ranked relative to others duringthe period, depending on what you were told in the beginningof the period (see (1)). If the ranking information is providedto you this round, you will have 15 seconds to see it. Theranking is presented in such a way that every participantcan identify only his/her own score. In other words, yourexact ranking for that period will be known to you only.No other participant can see how you ranked that period.Example: There are 10 participants. You solved 3 problems andfive people did better than you. The screen that you will see maylook like this:

This period is over!Ranking in this period:

Rank Name Score

1 . 101 . 103 . 94 . 85 You 35 . 35 . 35 . 39 . 19 . 1

In case you do not see the ranking, you will be asked towait for 15 seconds for the experiment to continue. Then,the experiment moves on to the next period and all thestages are repeated. In the end of the experiment we willask you to fill in a short questionnaire.

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Payment. You will receive a total of $23 in cash for yourparticipation in our study.

Practice periods. You will have a chance to practice thistask for one period. We encourage you to type in at leastone correct and one incorrect answer so that you know howto behave in both cases. You will not see any ranking infor-mation in the practice period.

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