Status Incentives. By TIMOTHY BESLEY AND MAITREESH GHATAK

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1 Status Inentives By TIMOTHY BESLEY AND MAITREESH GHATAK When eonomists study inentives in organizations, the main fous has been on using monetary payments in exhange for performane on spei measurable dimensions. But organizations use a wide variety of means to motivate their workers. One suh method whih has not been studied muh to date, is the expliit reation of status rewards attahed to good performane. Under suh shemes, an agent is given a positional good suh as a job title or a medal whose value omes from its sarity. Some organizations, suh as the military, make extensive use of medals as status rewards rather making ash payments. Aademia too is awash with job titles, fellowships and prizes whose value is mostly symboli but whih onvey status on their reipients. In this paper, we onsider the role of suh status awards as an inentive devie. We allow a prinipal to reward an agent for good performane in onventional terms (i.e. with money) and/or by giving him a positional good. We suppose that the latter has a zero marginal ost. (We have in mind rewards like employee of the month or full professor or vie president.) To the extent that the positional good is valued, the organization is exploiting a preferene for status to motivate agents. However, the extent of the status onveyed depends on how sare the reward is and requires a well-dened rule whih rewards only the deserving. The paper studies a model with moral hazard and limited liability whih limits the ability of an organization to ahieve its desired effort level using monetary inentives. Beside the standard problems that stem from this, we also add the possibility that desired output is hard to measure. Speially, even if the - nal output is observable, we assume that it is not veriable. The prinipal needs to ondition rewards on Besley LSE, Houghton Street, London WC2A 2AE, UK, t.besley@lse.a.uk. Ghatak LSE, Houghton Street, London WC2A 2AE, UK, m.ghatak@lse.a.uk. We thank our disussant, Bob Gibbons, as well as partiipants in the session for omments. The authors are grateful to the Mirosoft Corporation for support. For an exeption, see Benny Moldovanu et al [2007]. an imperfet, but ontratible, signal of ahievement. Even if the prinipal an observe the true output, it will not be ex post inentive ompatible for him to pay a reward to an agent who has produed it. 2 The fat that status inentives are ostless means that they are ex post inentive ompatible in suh irumstanes. By the same token, status inentives also inrease effort while reduing the optimal level of monetary inentives. The eonomi impliations of the idea that human beings have a raving for status has been widely studied (see, for example, Robert H. Frank (985)). A key omponent of the quest for status omes from the fat that humans make soial omparisons when assessing the value of what they reeive, something whih has reently been found in brain ativity (see K. Fleissbah et al (2007)) and in studies of subjetive happiness (see Rihard Layard (2005)). This paper is also linked to the literature on how onerns about fairness and inequality affet wage strutures within rms. Reent empirial evidene by Gordon D.A. Brown et al (2007) suggests that an individual's rank in the wage distribution affets job satisfation even when monetary wage differentials are ontrolled for. Our paper is also related to the work of Ernst Fehr and Klaus M. Shmidt (999) who emphasize the role of relative rewards within organizations due to pereptions of fairness and their impliations for the design of inentives. This paper is part of a wider projet whih onsiders how organizations foster effort using means other than by the promise of money (or, private goods). The use of status is a way of reating motivated agents in the sense of Timothy Besley and Maitreesh Ghatak (2005). It is also related to reent work by George Akerlof and Rahel Kranton (2005) who disuss the importane of reating identities to improve organizational performane. 2 This learly depends on the fat that we have a stati model. For example, we do not onsider the use of relational inentive ontrats along the lines of George P. Baker, Robert Gibbons and Kevin J. Murphy (2002).

2 2 PAPERS AND PROCEEDINGS MAY 2008 I. The Benhmark Model A prinipal employs a ontinuum of agents of size one, eah of whom works independently on a projet whose suess depends on effort and is unorrelated aross the agents. The projet yields an output 0 in all states of the world. In addition, it generates > 0 for the prinipal if is suessful. The agent's effort e determines the probability of suess. We assume e 2 [0; ] and the ost of effort is 2 e2. The agent has an outside option of u whih we set at zero. 3 We assume also that the agent has no wealth, i.e. there is limited liability. Following Baker (992), we assume that the stohasti part of the prinipal's payoff is observable but not veriable. However, there is a ontratible signal 2 f0; g on whih ontrats an be onditioned. It is important to note that, even though the prinipal's payoff may be observable, the fat that it is not veriable means that there is no ex post inentive ompatible means of rewarding the agent when he produes This is beause the prinipal would always have an inentive to lie after is realized in the event that D 0 and the output is. This weakens the ability of the prinipal to reate inentives for the agent to overome the moral hazard problem. Let. / denote the probability that the projet is suessful onditional on the signal being and assume that the signal is (weakly) informative in the sense that./.0/. If./ D and.0/ D 0, then output is perfetly observed. All agents are idential so we an study the determination of inentives for a representative agent. As a benhmark onsider the rst best where effort is hosen to maximize the joint surplus of the prinipal and agent. This yields effort level n e D arg max e e 2 e2o D We assume < to fous on interior solutions. A ontrat is a pair fb. /g 2f0;g. It is straightforward to solve for the optimal inentive sheme. Let D./.0/. First, observe that the optimal 3 It would be straightforward, although taxanomi, to extend the model to the ase where the partiipation onstraint binds. effort level of the agent is Oe D arg maxfe [b./ b.0/] C e h.0/ [b./ b.0/] C b.0/ D [b./ b.0/] 2 e2i g Plugging this into the prinipal's payoff funtion, she hooses the ontrat to maximize This yields [b./ b.0/] [ [b./ b.0/]].0/ b./..0// b.0/ PROPOSITION The optimal ontrat sets b.0/ D 0 and b./ D max 0; The orresponding effort level is.0/ 2 2 e D max 0; b./ This result is intuitive. It is optimal to redue b.0/ down to the minimum possible level (given limited liability), i.e., 0; as extra effort an be eliited while reduing the prinipal's ost. The interesting issue is whether it is worthwhile to offer a bonus when the veriable signal D is observed. Here, Proposition says that, if the output is sufiently wellmeasured, then there is positive inentive pay to eliit effort. Speially, this will be the ase if.0/ whih will always hold when./ is lose enough to one and/or.0/ is lose enough to zero. If this ondition does not hold, it is not worthwhile for the prinipal to use any inentive pay at all. This is basially the main nding of Baker (992) applied to this framework. II. Introduing Status Inentives We now allow the prinipal to introdue a purely nominal reward a pure positional good to the agent

3 VOL. 98 NO. 2 STATUS INCENTIVES 3 in the event that he produes high output for the prinipal. As disussed above, this ould be a job title hange (promotion from Assoiate to Full Professor), granting some agents interior ofes rather than openplan desks or alling some employees employee of the week. We fous on the ase where this good is ompletely free from the prinipal's point of view. We denote the award of a disrete positional good by 2 f0; g and suppose that this good generates utility of h Oe where Oe is the fration of workers in the organization who are awarded the positional good. Assume that h 0 Oe < 0 and h Oe D 0 for Oe e where e This says that there is a rowding effet if everyone gets the positional good then its value goes to zero. 4 We assume that granting the honour is part of an impliit ontrat and ould, in priniple, be onditioned on rather than just. However, it has to be inentive ompatible for the prinipal to award the positional good to everyone who produes after output is realized. This is where the fat that the positional good has a zero marginal ost plays a key role and differs from monetary inentives. The prinipal is atually indifferent about awarding the positional good to anyone so it is weakly optimal for him to ommit to a rule./ D and./ D 0; i.e. status is onferred only on those who produe high output. This is an important feature of purely nominal rewards whih we reord as PROPOSITION 2 Even though the prinipal's payoff is not veriable, it is inentive ompatible for the prinipal to award the positional good to every agent who produes high output. Of ourse, the ase where the positional good is ostless is the extreme ase, but there is a differene between rewards whih exploit status from those that require money (as in a dynami model along the lines 4 It is possible to provide more expliit mirofoundations for this preferene. Consider for example a simple areer onerns setting. Suppose that there are high ability types in the population who always produe high output and a fration of the agents is of that kind. Status (and possibly future rewards) ome from being this type. Then with ommon effort level Oe among the low ability agents, the probability that the agent is good onditional on having reeived the award is C. / Oe whih is dereasing in Oe. of Baker, Gibbons and Murphy (994)) sine it will generally require less stringent reputational enforement in a dynami setting. We now onsider how awarding positional goods to all agents who produe affets the hoie of monetary inentives. To get a simple losed form solution suppose that h Oe Oe if Oe = D 0 otherwise. Thus, Ne D = is the fration of agents produing high effort above whih the value of status goes to zero. 5 In this ase organizational effort (in a Nash equilibrium) will be Oe D C [b./ b.0/] C whih we assume is less than =. Repeating the logi that lead to Proposition, we now have PROPOSITION 3 The optimal ontrat sets b.0/ D 0 and b./ D max 0; The orresponding effort level is e D. /.0/. C / 2 2 C b./ C It is lear upon inspetion that b./ is lower and e is higher ompared to the previous ase. This result gives a lear idea of how adding status inentives has an impat on the hoie of monetary ompensation. They relax monetary inentives in two distint ways. First, there is a diret effet due to the fat that status inentives reate motivated agents in the sense of Besley and Ghatak (2005). Seond, there is an indiret effet due to rowding whereby inreasing monetary rewards redue the value of status and hene redue the prinipal's use of monetary inentives. We will now see a bonus being offered if D if 5 One possible interpretation of this formulation is as follows. Suppose that D Then. Oe/ is the perentage of workers who do not sueed and hene the size of group to whom the suesful group feels superior.

4 4 PAPERS AND PROCEEDINGS MAY 2008 and only if C.0/ The ondition for the use of inentive pay to be optimal for the prinipal is more stringent than in the absene of status inentives. Intuitively, inentive pay is ostly while status is ostless from the prinipal's point of view. What is the inentive of the rm to use status inentives? We show that rms that use status inentives will have higher payoffs, other things being equal. The expeted payoff of the prinipal from a single agent, in the ase of an interior solution, is 5 D 0 C e eb./.0/b./ As b./ D.C/e this an be viewed as a funtion of e. Sine the prinipal an be viewed as "hoosing" e via b./ by the envelope theorem, only the diret effet of needs to be onsidered. This turns out to D e C.0/ > 0 That is, the prinipal always benets from having a status-motivated agent and sine reating status inentives is ostless in our framework, will always do so. The intuition is simple anything that raises effort for "free" will raise expeted prots. III. Impliations Our model has impliations for the balane of monetary and status inentives that we are likely to see an organization using. Even though an organization faes no variable ost in reating status inentives, suppose that it bears a xed ost in setting up suh a system of rewards. We are interested in understanding whih rms will make use of suh inentives. Differentiating () 2 D 2. C / > 0 Hene rms with higher returns from high output will tend to benet most from introduing status inentives. To see this, observe that how muh expeted prots go up when inreases depends on e whih is inreasing in The model also predits that the ase for status inentives is higher, the more severe is the problem of measuring To see this most learly, we normalize./ C.0/ D and let q.0/ D./ The higher is q; the less informative is as a measure of high output. Now it is straightforward to show 2 D 2. 2q/ 2 > 0 To understand this, note that an inrease in raises expeted prots via two hannels. First, it raises effort for a given bonus level. Seond, it enables the rm to redue the bonus. Bonuses are a ostly and inefient instrument to eliit effort when the signal of output is noisy. As a result, if q goes up, even though the rst soure of the gain is smaller, the seond soure of the gain is large and the net effet is to raise the marginal gain from having motivated workers. We reord these fats as PROPOSITION 4 All rms gain from using status inentives but the gains are higher for rms where output is harder to verify and the return to higher output is greater. The nding that status inentives are inentive ompatible hinges on there being no possibility of agents bribing the prinipal to reeive a status reward. Sine suh rewards an be reated for free and they are valuable to agents, there is the possibility of orruption within in the organization whih would undermine the suess of these rewards sine in the limit they will sold by the prinipal to a point where h.e/ D 0. This explains why in pratie organizations that use status inentives may go to pains to point out that they are given out only to the deserving and that there is no market in suh rewards. 6 Status inentives work by reating soial divisions. So far, we have assumed that they raise the utility of the winner while having no impat on the utility of those who are not awarded them. But this need not be the ase. It ould even be true that the disutility from the shame that arues from not reeiving a positional good outweighs the utility from the honor 6 The reation of honor from a status reward also omes from a general pereption that those who reeive have produed high output. This would be the ase we have assumed where is observable, but not veriable. However, it would be interesting to explore the role of status rewards where whether an agent has produed is not observed by everyone in the organization.

5 VOL. 98 NO. 2 STATUS INCENTIVES 5 among those who reeive it. 7 This reates a potential ost to the prinipal of introduing status inentives. However, in the urrent setting where the agent gets a rent from working for the prinipal, this ost is not internalized by the prinipal. 8 So status inentives ould be introdued even in situations where the welfare of agents goes down. To illustrate this formally, for simpliity suppose that./ D and.0/ D 0 and D 0. Suppose that status yields utility N and failure to ahieve status yields. Now Oe D C NC 2 and b./ D NC 2 9 It is straightforward to show that introduing a status reward raises agent utility if and only if 8 C N C > This an never hold if N D D, i.e. when the disutility of low status exatly offsets the utility of gaining status. 0 The intuition is simple. Suppose we set N D 0 and onsider a small inrease in starting from 0. By the envelope theorem, the effet via e an be ignored. However, the bonus will go down and in addition, there is a rst-order negative effet on the agent's utility onditional on failure. As a result, he is worse off. In ontrast, if N goes up from 0 by a similar logi, the bonus will go down, but this will be dominated by the rst-order effet of the utility onditional of suess. Naturally, the higher is the more likely the agent is worse off. IV. Conluding Comments This paper has studied the role of status inentives by rms to inrease effort. In future work it would be interesting to look at broader aspets of status inentives, espeially the ontrast between those reated within rms with those reating outside rms (suh as 7 Of ourse the same ould be true of regular inentive pay too. However, for positional goods as opposed to money, this effet seems more plausible. 8 This would be not be the ase if the outside option onstraint was binding. 9 Assuming that > N C 0 To see this, observe that this ondition redues to C 2 > whih onntradits the requirement that Oe D C2 2 < national honors systems, as well as professional honors). REFERENCES Akerlof, George and Rahel Kranton, [2005], Identity and the Eonomis of Organizations, Journal of Eonomi Perspetives, 9(), Baker, George P., [992], Inentive Contrats and Performane Measurement, Journal of Politial Eonomy, 00(3), Baker, George P., Robert Gibbons, and Kevin J. Murphy, [2002], Relational Contrats and the Theory of the Firm, Quarterly Journal of Eonomis, 09(4), Baker, George P., Robert Gibbons, and Kevin J. Murphy, [994], Subjetive Performane Measures in Optimal Inentive Contrat, Quarterly Journal of Eonomis, 7(), Besley, Timothy and Maitreesh Ghatak [2005], Competition and Inentives with Motivated Agents, Amerian Eonomi Review, 95(3), Brown, Gordon D.A., Jonathan Gardner, Andrew Oswald and Jing Qian, [2007], Does Wage Rank Affet Employees Well-being? Industrial Relations, forthoming. Fehr, Ernst and Klaus M. Shmidt, [999], A Theory of Fairness, Competition, and Cooperation, Quarterly Journal of Eonomis, 4(3), Fleissbah, K., B. Weber, P. Trautner, T. Dohmen, U. Sunde, C.E. Elger and A. Falk, [2007], Soial Comparisons Affets Reward-Related Brain Ativity in the Human Ventral Stratum, Siene, November 2007, volume 38, Frank, Robert, [985], Choosing the Right Pond Human Behavior and the Quest for Status, New York Oxford University Press. Layard, Rihard, [2005], Happiness Lessons from a New Siene, London Penguin. Moldovanu, Benny, Aner Sela and Xianwen Shi, [2007], Contests for Status, Journal of Politial Eonomy, 5,

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