The Performance Measurement Trap - Berkeley Haasfaculty.haas.berkeley.edu/villas/performancemeasurement...The Performance Measurement Trap Dmitri Kuksov, a J. Miguel Villas-Boas b

MARKETING SCIENCEVol. 38, No. 1, January–February 2019, pp. 68–87

http://pubsonline.informs.org/journal/mksc/ ISSN 0732-2399 (print), ISSN 1526-548X (online)

The Performance Measurement TrapDmitri Kuksov,a J. Miguel Villas-Boasb

aNaveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080; bHaas School of Business, University ofCalifornia, Berkeley, Berkeley, California 94720Contact: [email protected], http://orcid.org/0000-0002-3157-5013 (DK); [email protected],

http://orcid.org/0000-0003-1299-4324 (JMV-B)

Received: June 29, 2017Revised: March 19, 2018; June 12, 2018Accepted: June 22, 2018Published Online in Articles in Advance:January 30, 2019

https://doi.org/10.1287/mksc.2018.1122

Copyright: © 2019 INFORMS

Abstract. This paper investigates the effect of performance measurement on the optimaleffort allocation by salespeople when firms are concerned about retention of salespeoplewith higher abilities. It shows that introducing a salesperson performance measurementmay result in productivity, profit, and welfare losses when all market participants opti-mally respond to the expected information provided by the measurement and the (ex post)optimal retention efforts of the firm cannot be (ex ante) contractually prohibited. In otherwords, the dynamic inconsistency of the management problems of inducing the desiredeffort allocation by the salespeople and the subsequent firm objective to retain high-abilitysalespeople may result in performance measurement yielding an inferior outcome.

History: Yuxin Chen served as the senior editor and Anthony Dukes served as associate editor for thisarticle.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/mksc.2018.1122.

Keywords: game theory • contract design • principal-agent problem • sales force compensation

Theworker is not the problem. The problem is at the top!Management!

—W. Edwards Deming,The Complete Deming Library Collection Discussion Guide,

W. Edwards Deming Institute, p. 409.

1. IntroductionMeasurement of salesperson performance is one of thekey tasks ofmany sales organizations. It is a complicatedtask, because what a firm can measure is often not verywell aligned with what it is trying to achieve in the longrun. As Likierman (2009) argues, what is measuredmaypotentially provide little insight into a firm’s perfor-mance, and may potentially hurt the firm. In particular,firms may use what can be more easily measured, orwhat is more popular, and not activities that are difficulttomeasure, immeasurable, or less popular. For example,Likierman (2009) points out that the Net Promoter Score(Reichheld 2003), which measures the likelihood thatcustomers will recommend a product, may be a usefulindicator only when recommendations play a crucialrole in the consumers’ decisions, but the importance ofcustomer recommendations may vary from industry toindustry. As another example, the number of telephonecalls of a salesperson may be easy to document, al-though the content and preparation for those telephonecalls may not be as easy to measure but potentially bea more important component of the selling effort.

It iswell known that putting toomuchweight onvisiblemeasures not perfectly aligned with the organization’s

objectives may lead to a detrimental distortion of theemployee’s effort allocation. As a recent example frombusiness practice, Wells Fargo’s incentives for employeesto cross-sell accounts to customers led to adverse behaviorby employees, and in the fall of 2016, Wells Fargo endedup considerably hurt by both customer backlash andregulatory actions (see Corkery 2016). These incentivesalso involve future employee promotions, which affect theemployees that decide to continue with the bank and theemployees that decide to move on. Likewise, if a productmanager is evaluated on the proportion of successfulproduct introductions (which is easier to measure thanthe contribution of themanager to the overall profitabilityof a manufacturer), the manager may distort work to-ward pushing products that are likely to fail (Simesterand Zhang 2010). Because these evaluations may affectthe careers of the managers at the company, they alsoendogenously affect which mangers decide to stay withthe company versus taking positions in other companies.Retention of good employees is an important man-

agement goal. Therefore, even in the absence of explicitincentives, expected future retention efforts and othercareer concerns introduce implicit incentives (Dewatripontet al. 1999). For an example related to the marketing ofacademic ideas,1 consider an assistant professor in a ten-ure track position at a university. The university wants toretain scholars whomake and disseminate advancementsin their fields (e.g., teaching and research). But the uni-versity imperfectly observes the assistant professor’sability. Good assistant professors may receive offers

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from other universities, which may induce strong scholarsto be productive in their rookie positions. In addition, theuniversity might try to measure some of the assistantprofessor’s output directly, but imperfectly. For instance,the university may simply count publications and teach-ing ratings. This could be detrimental to the university’smission because the scholars could distort their efforts infavor of the measured variables, in contrast to making anddisseminating advancements in their field more generally.

Retention of top salespeople is always seen as a topconcern for companies (e.g., Sager 1990, Forbes CoachesCouncil 2018). According to Rocco (2017), the level ofturnover of salespeople is between 25% and 30% peryear, and identifying and retaining talent is a challengefor companies, with a reported average cost perturnover of $97,690. As noted by Zoltners et al. (2008,figure 3, p. 120), “in a successful sales system,” themanagement team has to work at “retaining goodpeople.”

Broadly speaking, one can categorize an organiza-tion’s objectives when creating an incentive structureinto objectives linked to inducing the desired perfor-mance (effort level and effort allocation across variousproductive tasks) and objectives linked to hiring and/or retaining the most productive salespeople. In amultiperiod employmentmarket where relatively short-lived contracts are renewedperiodically (e.g., each year),the effort, effort allocation inducement, and salespeopleretention problems are intertemporarily linked. Per-formance measurement in one period is used for cur-rent compensation according to the current incentivecontract, but it also affects the future contract(s) offeredto the salesperson because of the management’s (fu-ture) inference of the salesperson’s ability from the past(at the time of the inference) performance measure-ments. This, in turn, means that when deciding on theeffort and its allocation, a salesperson needs to takeinto account not only the current contract’s incentives,but the expected effect of his effort and its allocationon the value he expects from the future contracts. Inother words, the full incentives will always have animplicit component coming from the value of thefuture contracts.

Furthermore, management decides not only how touse the available information (performance measure-ments) about the salespeople, but it also decideswhetherand how to implement performance measurement (i.e.,which kind of information about salespeople to obtain).The number of measures, or the amount of monitoring,is a frequently considered decision (Likierman 2009).The obvious tradeoff is between the costs of measure-ment (e.g., the salespeople’s compliance costs) and theassumed benefit of the more extensive measurement,which could lead, supposedly, to a better-designed in-centive structure. It is well known that there could bea tendency to put too much weight on visible measures.

One may hope that a rational manager would be able tooptimally weigh each metric so that the above problemis resolved, andmoremeasurementwould end up beingbeneficial to management. In other words, if manage-ment is fully rational, it seems intuitive that it should beable to design a better contractwhenmoremeasurementsare available. After all, it is within the power of man-agement to not reward any of themetrics (see, e.g., theflatcompensation result in Holmstrom and Milgrom 1991).However, the implicit nature of incentives discussed

above implies that management is unable to commit toappropriately weighing metrics over the long haul.Contract renewal introduces a dynamic inconsistencyproblem of the current objective of incentivizing effortand its allocation and the future objective of retain-ing salespeople whose records suggest better abilities.2

Because salespeople are forward looking and can ex-pect this inconsistency, introduction of a new metricresults not only in an enlargement of the set of theavailable instruments for the management, but also ina change of the salespeople’s environment. Althoughthe larger set of instruments could help to achieve themanagement’s objectives and increase social welfare,the dynamic inconsistency could be detrimental. Thenet effect is not immediately clear, and as we show, itcan be negative both on the profits and on overall pro-ductivity and social welfare. In the assistant professor ex-ample we used previously, the assistant professor allocatesmore effort to the number of publications and teachingratings than what could potentially be optimal for theobjective of making and disseminating advancements inthe field. If measurement exists, removing the retentionor career concerns through, for example, the tenure systemis a potential solution. For example, removing the potentialdetriment of implicit incentives has been noted as themainargument for the lifetime appointment of judges (seehttps://judiciallearningcenter.org/judicial-independence/).A better solution could be not having the measurements(observations) thatmay introduce the implicit incentivesto start with.One may be inclined to ascribe negative outcomes

of measurements or incentives to boundedly rationalbehavior or the coordination issues within an organi-zation’s management. But what we show in this paperis that under some conditions, even fully rationalagents designing and responding to the optimal in-centive contracts cannot avoid being hurt by the veryfact of the measurement’s existence. Specifically, weshow that the net effect of an additional dimensionbeing measured can decrease productivity, profits, andwelfare, even when the management fully accounts forthe current and future effects when designing the op-timal compensation structure. We formalize the fol-lowing intuition: Suppose that the total effort that aparticular salesperson would exert is essentially fixed(i.e., not easily changed by incentives), and that in the

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absence of additional performance measurement(s),salespeople are incentivized to allocate effort acrosstwo components in an efficient way. For example, inthe absence of the number of telephone calls being mea-sured, the salesperson allocates effort efficiently betweenthe number of telephone calls made and the prepara-tion for those calls. However, suppose the existing in-centive to allocate effort efficiently (using the existingmeasurements) is not particularly strong so that a sales-person would distort his effort allocation if a new,nonnegligible incentive to do so is introduced.

For example, management may be able to observeand enforce the time spent at work, and any allocationof time across activities may not impose a disutility onthe salespeople so far as they have to spend that time atwork. In this case, a slight weight on overall output ofthe organization, even if this output is only weaklycorrelated with the effort allocation of a given sales-person, is sufficient to induce the salesperson’s optimaleffort allocation. As a result, the system is workingnearly perfectly. Different salespeople contribute dif-ferently to the total output because of their differentabilities, but each does what he can (providing theeffort he is capable of and efficiently allocating it acrossthe effort components), and nothing can be done aboutthe abilities themselves.

To simplify the presentation, we will identify thetotal effort the salesperson is capable of with the sales-person’s ability. Now suppose that because of a ran-dom value of the outside option (e.g., because of thechanging preferences for living close to the currentemployment area), each salesperson may leave thecompany at the beginning of each period, but thisdecision may, at least for some salespeople, be affectedby the compensation that he is offered. Then, to en-courage the better salespeople not to leave the orga-nization through an appropriate retention policy, thatis, by offering a better next period contract to the bettersalespeople, management is interested in evaluating itssalespeople’s abilities.

Suppose further that the feasiblemeasurement underconsideration is the measurement of one, but not all, ofthe effort components. Note that without this addi-tional performance measurement, given the optimaleffort allocation, the salesperson’s ability (total effort) isperfectly correlated with each of the effort components.Then a salesperson’s ability could be perfectly judgedfrom either component. This seems to providea compelling argument for introduction of the per-formance measurement, even though it measures onlyone of the effort/performance components.3 However,knowing that management will offer better contracts inthe next period to those salespeople who performedbetter on the measured component, if managementstarts measuring one of the dimensions of effort, andeven if no weight is placed on it in the current

compensation schedule, salespeople will distort effortallocation toward that dimension in hopes of secur-ing better contract offers in the next period. If thisdistortion is not costly for the salespeople, all effortmay be allocated to only one component, thus possiblyhaving a negative effect on the total output. In thesalesperson example above, the salesperson would pre-pare the telephone calls minimally, and would justmaximize the number of telephone calls made.But would not management then be able to adjust

the current compensation package to eliminate thisdistortion, perhaps through a negative weight in thecurrent contract on the performance component mea-sured? The answer is, generally, no. The reason, again,is salesperson heterogeneity. Generally, one mightexpect that salespeople will have some independentand private estimate of their likelihood of staying withthe organization in the next period. Therefore, the bestmanagement can hope to achieve with the optimallydesigned “reverse incentives” contract is that somesalespeople, knowing that they are more likely thanaverage to leave, will be incentivized by the reverseincentive to distort the effort toward the other compo-nent,whereasmost of the remaining salespeople, havinga higher likelihood of staying than management esti-mates, will still distort their effort toward the measuredcomponent. The outcome is that, although any aggre-gate mix of effort allocations can be achieved, almost allsalespeople may end up allocating effort inefficiently.Note that perfect information, if costlessly available to

management, should be welfare enhancing. However,imperfect measurement, insofar as it measures some,but not all, of the components of productive output, islikely to distort effort allocation. Although this mea-surement can be used for better retention and a bettertotal effort incentive policy, these improvements are atthe expense of the efficiency of the effort allocation.Furthermore, inability to commit to future contractsmeans that this asymmetric measurement problem maynot be fully solvable.4 Therefore, when deciding onwhether to introduce a partial (or imperfect) measure-ment (i.e., a measurement that weighs some of theeffort/output components more heavily than others),the firm needs to decide whether the problems of effortenforcement and salesperson retention are more im-portant than the problem of effort allocation. Thus, thecommonpractice of collecting the datafirst and decidingwhat to do with them later could be a treacherous patheven if the management is fully rational and benevolent.We present this paper in the context of incentives for

salespeople, but the ideas presented here could equallyapply to incentives for product managers for newproduct development (e.g., Simester and Zhang 2010).More generally, the results here would apply to em-ployees in an organization whose compensation de-pends on incentives.

Kuksov and Villas-Boas: Performance Measurement Trap70 Marketing Science, 2019, vol. 38, no. 1, pp. 68–87, © 2019 INFORMS

The remainder of this paper is organized as follows.The next section discusses the related literature. Section 3presents the model, and Section 4 considers the caseswhen measurement is not possible and when mea-surement is available on the first-period effort level.Section 5 presents the effects of different measurementtechnologies, and Section 6 concludes. The proofs arecollected in the appendix (and the online appendix).

2. Related LiteratureThis paper builds on the extensive literature on theprincipal-agent and sales force compensation problems.5

This literature, in particular, explores the optimal weightsthe principal needs to place on measurements to ac-count for effort distortion across multiple tasks (e.g.,Holmstrom and Milgrom 1991, Hauser et al. 1994, BondandGomes 2009).6 For example,HolmstromandMilgrom(1991) show that when the effort distortion betweentasks is sufficiently severe, flat pay (i.e., contracts ig-noring performance measurement) may be optimal, andthey discuss how it applies to the ongoing teachercompensation debate. Hauser et al. (1994) explore mak-ing the incentive scheme based on customer satisfactionmeasures as a way for employees to put effort on di-mensions that have longer-term implications. Bond andGomes (2009) explore the ability of the principal to affecta multitasking agent’s efforts. The literature has alsodiscussed what happens in a dynamic setting with thequestion of desirability of long-term contracts (e.g.,Malcomson and Spinnewyn 1988) and renegotiation-proofness. One usual assertion is that the principal andwelfare are not hurt bymore information (measurement),but this is due to the assumed ability of the principal toput a sufficiently low weight on what is being measured.Alternatively, we consider the problem of the principal’spossible inability to commit to the future contracts andshow that the optimal contract in the presence of moreinformation (more performance measures) may lead todecreased profitability and social welfare.

More generally, this paper can be seen in the contextof more information potentially leading to worse out-comes in strategic situations (e.g., Akerlof 1970). Thepolitical economy literature also has some resultsshowing that transparency about actions can havenegative effects (e.g., Prat 2005). In contracting, withshort-term contracts, we can also have the ratchet effectof agents trying not to reveal their private information inearlier periods (e.g., Laffont and Tirole 1988).7 Mostrelated to this paper, Crémer (1995) considers a dynamicconsistency problem of the principal’s commitment toincentivize effort by the threat of firing the agent in thepresence of exogenous shocks to output. Assuming thatthe agent values job renewal, Crémer (1995) shows thatin some cases, the principal would like to commit to notobserving the agent’s ability (or the exogenous reasonfor failure) to increase the agent’s incentive to perform.

By not observing the reason for failure and thereforeeffectively committing to fire the agent if output is notup to a standard, the principal is able to circumvent thepositive-pay restriction and increase the incentive for theagent to perform well without increasing the expectedpay. In contrast to Crémer (1995), we examine the op-posite problem: when the principal would like to pro-vide fewer incentives to distort effort (Crémer 1995considers only one component of effort, and thereforethe problem of effort allocation does not arise).Dynamic (in)consistency issues have been studied in

various other contexts, such as a durable-goods mo-nopoly setting prices over time (e.g., Coase 1972, Desaiand Purohit 1998) and central bank policies on moneysupply (e.g., Kydland and Prescott 1977). In this paper,we essentially consider the implications of the dynamicinconsistency issue in a principal-agent framework.

3. The ModelIn the next subsection, we formulate the model setupwith only a limited justification for the assumptions andthen, in the following subsection, discuss some assump-tions, their consequences, and potential variations.

3.1. Model SetupConsider a principal-agent model with agents havingdifferent abilities and interacting with the firm (prin-cipal) during two periods, indexed by t � 1, 2. In thecontext of this paper, the agent is a salesperson. Becausewe abstract away from any effects of one salesperson’sbehavior on other salespeople or the incentives theprincipal has in treating other salespeople, we consider,without loss of generality, a single agent whose type isuncertain to the principal. The principal’s (manage-ment’s) objective is to maximize the total expectedpayoff (profit) net of the compensation paid to the sales-person across the two periods by choosing a contract(compensation conditional on observables) to offer thesalesperson at the beginning of each period. Let πtdenote the profit gross of the expenditure on salespeoplecompensation in period t, and let Ct be the compen-sation paid to the salesperson in period t. Table 1 presentsthe full notation. To simplify the presentation, assumeno discounting. Then the firm’s problem is

maxC1,2≥0

∑2t�1

E(πt − Ct). (1)

The salesperson compensation (contract) could dependon everything the principal observes prior to the offer orat the time of payment, beause we assume the paymentis done after the relevant period is over. However, thecontract is restricted to provide nonnegative pay to thesalesperson for any outcome (limited liability). This couldbe justified, for example, because obtaining money froma salesperson who received no income in the currentperiod may not be possible.


Period t’s profit is uncertain and depends on thesalesperson’s choice of the effort allocation e ≡ (x, y) ∈R+2,where x and y are the two dimensions of effort. Forexample, x could represent the number of telephonecalls, and y could represent the time spent preparing forthose calls. To be clear, we will call the vector e ≡ (x, y)the effort allocation and the sum of effort componentse ≡ x + y the total effort. Assume that the salespersonhas a per-period budget constraint on his total effortxit + yit ≤ ei; where ei depends on the salesperson’s type,which can be high, h, or low, ℓ, that is, i∈ {ℓ, h}.Assumethat besides the budget constraint on effort, the sales-person has no intrinsic disutility of effort.

To simplify the potential contract structures, we modelprofit as possibly attaining one of just two possible values,one of which is normalized to 1 and the other of which isdenoted by −B, with B> 0, and model the effect of thesalesperson’s effort allocation as affecting the probability ofachieving the high profit level. Assume that the probabilityof high profit increases in the salesperson’s productivity,defined as α(x, y) � x · y. Let us call the maximal pro-ductivity of a salesperson his ability a. Maximizing α(x, y)subject to x + y≤ ei, we have ai � (ei/2)2. Thus, the sales-person’s ability is a characteristic of the salesperson,whereas his productivity is his choice variable constrainedby his ability. To be specific, we assume the following

gross profit specification as a function of the salesperson’sproductivity:

πt(αit) � 1, with probability (b + αit)/(b + 1);−B, with probability (1 − αit)/(b + 1),

{(2)

where αit � xityit is the salesperson’s choice of pro-ductivity in period t, and b> 0 is a parameter thatdetermines how much the profit is (in expectation)informative about the salesperson’s ability.To satisfy the constraint that the probabilities of the two

profit outcomes are positive, we need 0≤ eℓ < eh ≤ 2. (Ifeh�2, the efficient allocation x � y � 1 leads to ah � 1.) Tosimplify derivations, assume eℓ � 0 and eh � 2 so thataℓ � 0 and ah � 1. To avoid considerations of the boundaryconditions on the wage of the low-type salesperson, as-sume b≥B (so that the expected profit from the low-typeworker given no wage is nonnegative).To introduce a nontrivial employee retention problem,

assume that the salesperson has an outside option z in thesecond period, where z is uniformly distributed on [0, 1]and independent of salesperson’s type. The outside op-tion is zero in the first period, so the salesperson ac-cepts any nonnegative offer in the first period.8 Thesecond-period outside option is known to the salespersonbefore his decision of whether to accept the second-periodoffer but may or may not be known to him before hischoice of the effort allocation e1 in the first period.We firstassume that the salesperson does not know z beforethe effort allocation stage of the first period; he learnsit just before he needs to decide whether to accept thesecond-period offer. We then consider a variation ofthe model to see how the results change if the sales-person can condition his effort allocation e1 on thesecond-period outside option z, or if he has some (butnot full) information about it.In addition to choosing the contract to offer, the

principal needs to decide whether to introduce mea-surement m(x) of the x component of the salesperson’seffort.9 In the example above, this would be mea-surement of the number of telephone calls made by thesalesperson. We assume that the measurement of they component, beyond its inference from the profit re-alization and any available measurement of x, is notfeasible. In the example above, it is not possible tomeasure the time spent by the salesperson in prepa-ration for the telephone calls, or in a typical sales funnel(e.g., Zoltners et al. 2008), after leads are generated, it isnot possible to measure the lead qualification effort. Toreduce the complexity of the compensation structure,assume that m(x) may take only one of two values, callthem 0 and 1, but the probability of the highmeasurement

Table 1. Notation

Variable Description

t Period, either period 1 or period 2πt Profit in period t gross of payment to salespersonCt Payment to salesperson in period tx Dimension of effort that can be potentially measured

(xt means x in period t)y Dimension of effort that cannot be measurede Vector (x, y) of effort choicesei Total effort that can be exerted by a salesperson of

type i, ei � xi + yi assuming eh � 2 and eℓ � 0α “Productivity” of salesperson, affecting probability of

high outcome, α � xyai Ability of salesperson of type imaximal “productivity,”

ai � (ei/2)2b Parameter that indexes informativeness of profit

realizationb+α1+b Probability of high outcome (whose payoff is set to “1”)−B Low profit outcome, with B> 0z Outside option of salesperson in the second period,

distributed uniformly on [0, 1]m(x) Measurement of effort dimension x; 1 with probability

x/eh and 0 with probability 1 − x/ehPh Posterior probability of the high-type salesperson given

the observables in the first periodc1 Base compensationc2, c2, c2 Payment to salesperson if high outcome and/or high

measurement


realization (1) increases in x.10 For analytical tractabilityassuming linearity and that the high type can ensurem(x) � 1 by allocating all effort toward x, we use thefollowing measurement specification:

m(x) � 1, with probability x/eh � x/2;0, with probability 1 − x/eh � 1 − x/2.

{(3)

If measurement is introduced, the compensation ineach period is a function of the current and past profitsand measures of x. If measurement is not introduced,the compensation can be a function of only currentand past profits. There are three conceptually differentpossibilities of the timing when m(x) is introduced:(1) after the salesperson decided on his effort allo-cation e1 in the first period, (2) before the salespersondecided on his effort allocation e1 in the first period butafter the first-period compensation rule was set (and itwas done without having the possibility of measure-ment inmind), and (3) before the salesperson decided onhis effort allocation e1 in the first period and the first-period compensation rule was determined with thepossibility of the measurement in mind. We considereach of these cases. We first analyze the case in whichthe measurement of the component x is possible only inthe first-period effort (Section 4). In Section 5.2, weconsider the case in which the measurement of com-ponent x is possible in both the first and second periods.

3.2. Discussion of the Model AssumptionsIn the model setup, we have made some specific as-sumptions about the functional forms of the sales-person’s productivity α(x, y), the profit function π(α),the effort component measurement function m(x), theoutside option z, and some parameter values either tobe specific or to simplify the analysis. We now discussthese assumptions in turn.

First, we have assumed a multiplicative productionfunction α(x, y) � xy. In the running example of thesalesperson allocating effort between preparing forcalls and making calls, this specification captures theidea that salesperson telephone calls without prepa-ration have limited effect, and preparing telephonecalls without actually making them has also zero effecton sales. The probability of high profits in this speci-fication is maximized at x � y � ei/2; that is, the effi-cient effort allocation, which is also the most desired bythe firm, is for the salesperson to equally split the totaleffort between the two effort components. This exactfunctional form of α(x, y) is not important, but what weneed is that there is some optimal split of effort acrosstwo (or more) components, so that directing all efforttoward one of the components reduces profits. Forexample, we have checked that our main results alsohold if α(x, y) � ��

x√ + ��

y√

.

Let us next consider the functional form of the profitfunction. The informativeness of the profit realization(whether it is 1 or −B) about the salesperson’s actionsdepends on b and tends to zero when b tends to infin-ity. For clearer presentation, we will focus the analysison the case of large b and B but discuss, when ap-propriate, what happens when these parameters arenot too large. The case of large b and B can be seen asa case in which the positive output is highly likely (sothat even the low-ability salespeople can easily sell),but the loss is important when the positive output doesnot occur. For example, in some types of work, a mis-take (selling a dangerous item, causing an injury whiledemonstrating a product, making an inappropriatecomment, etc.) may lead to a lawsuit or a viral consumerbacklash. In terms of the model, a large b means that theoutput obtained is not very informative of the sales-person’s ability, which is realistic, for example, when anindividual salesperson is a part of a large group (i.e., theprofit of a large retailer is not very informative about thecontribution of each individual employee). A special caseb � B of the above profit specification has a specialmeaning: in this case, the expected profit is equal to αit.Therefore, considering this case allows one to considerhow the results depend on the informativeness of profitrealization (driven by b) keeping constant the importanceof the salesperson’s ability to the firm.Note that, given aℓ � 0, the allocation decision of the

low type (allocating zero across the two components)is immaterial, which considerably simplifies theanalysis. When aℓ � 0, the probability of the profitbeing high (being 1) is b/(b + 1), and the probability ofthe profit being low (being −B) is 1/(b + 1).When ah � 1and the salesperson chooses the efficient effort allo-cation, the firm gets the high profit with probabilityone. If the salesperson is choosing the efficient effortallocation, a low profit implies that the salespersonhas low ability for sure (this part also considerably sim-plifies the analysis), but a high profit does not neces-sarily imply that the salesperson has the high ability.Turning to the technology of measurement (the

specification ofm(x)), it is important for our results thatonly one component could possibly be measured, butthe exact specification is not essential. Allowingm(x) toprobabilistically take one of the two outcomes sim-plifies the analysis because it implies that the com-pensation is not a function of a continuous variable butof a binary one. At the same time, it could be realisticthat the measurement is noisy and more discrete thanthe effort component value. For example, a managercould measure the number of a salesperson’s calls byobserving whether the salesperson is on the phone ata particular one time. We model performance mea-surement as a (noisy) measure of effort component.Although various aspects of performance (e.g., currentsales, profit, or customer satisfaction rating) are distinct


from various components of effort (e.g., number ofsales calls or the time spent doing research or preparingfor teaching), sometimes they can be linked becausea specific type of effort (input) is most productive fora specific type of performance (output). For example,learning students’ names may be useful for increasingteaching evaluations but may not be so effective foractual student learning (for which the time spent pre-paring teaching materials could be more useful).

Note that with the measurement technology as de-fined, and given the assumptions eℓ � 0 and eh � 2,a measurement of 1 indicates that the salesperson hashigh ability (which simplifies the analysis), whereasa measurement of 0 does not necessarily indicate thatthe salesperson has low ability as long as the high-ability salesperson is not expected to shift all his efforttoward component x. We have also analyzed (seeSection 5.1) the possibility that x can be measuredprecisely, and although that analysis is more compli-cated (in particular, because it requires the consider-ation of aℓ > 0), our main results continue to hold. Thisshows some robustness to the assumptions on themeasurement technology.

Finally, we have assumed that the salesperson has anoutside option z in the second period. It is important forour results, because it introduces the retention problemin the firm’s objective function, which leads to thesecond-period compensation being correlated with thefirm’s expectation of the salesperson’s ability. Thisoutside option could come from the utility of workingelsewhere or staying at home (e.g., given familychanges), the changing cost of traveling to work due tothe potential salesperson’smove for family reasons, etc.For simplicity, we assume that z does not depend onthe salesperson’s type i. This could potentially bejustified by idiosyncratic preferences of the salespeopleor other employers that are not related to how pro-ductive the salesperson is in the present firm. For ex-ample, the cost of traveling to work could affect theoutside option of a salesperson without affecting theproductivity of the salesperson once employed, or thesalesperson’s desire to stay at home to raise a babymaynot be dependent on the salesperson’s skill at work. Onthe other hand, outside work offers may be positivelycorrelated with the salesperson’s ability. If we con-sidered z to be positively correlated with ability, wewould have that the probability of retention of low-ability salespeople would be increased, and this couldincrease the incentives to discriminate between thehigh- and low-ability salespeople and, therefore, po-tentially further increase distortions.

4. Model AnalysisTo understand the effect of measurement, we need tocompare the outcomes when measurement is notpossible, which we will call the benchmark case, with

the outcomes whenmeasurement is introduced and theagents (the salesperson and the manager) optimallyreact to the new information. For the latter, the out-comes could be different depending on when themeasurement is introduced and, if it is not intro-duced at the start, whether the introduction is ex-pected by the salesperson. We therefore consider whathappens under different timings of the measurementintroduction.We first derive the optimal compensation schedule in

the benchmark case when the measurement of x is nota possibility (Section 4.1). We then consider how thesecond-period compensation and outcomes are affectedif themeasurement of the first-period component x of theeffort is unexpectedly introduced in period 1 after thesalesperson already committed to his first-period effortallocation (Section 4.2). Next, we consider how theoutcomes change if the salesperson optimally respondsto the presence of the measurement of the first-periodeffort, but assuming that the first period’s compensationrule is unchanged after themeasurement is unexpectedlyintroduced (Section 4.3). Conceptually, the last consid-eration is when the measurement introduction wasunexpected by the firm, whereas the earlier one is whenit was unexpected by the salesperson. Finally, we con-sider optimal compensation contracts in both periodsgiven that the measurement of the first period’s xcomponent is present, or is expected to be introduced(Section 4.4). Comparing the outcomes under the lastscenario with the previous ones, we show that the in-troduction of measurement could be detrimental to theprincipal and to social welfare. We discuss what onewould expect in equilibrium where the introduction ofthe measurement is a manager’s decision variable inSection 4.5. The case of measurement of the x componentin both periods is presented in Section 5.2.

4.1. Benchmark Case: Optimal ContractWithout Measurement

Given that the salesperson’s outside option is zero inthe first period and that he does not have an intrinsicpreference as to how to allocate the maximum effort eiat his disposal, compensation C1�ε1π1�1 with ε> 0achieves efficient allocation (so far as the salespersondoes not expect the second-period contract to provideperverse incentives for the salesperson to lower thefirm’s expectation of his abilities).11 Thus, in equilib-rium,we have efficient effort allocation andC1 � 0, thatis, the first best for the principal (because contracts arenot allowed to have negative pay) with the expectedfirst-period profit of 1

2 + 12b−Bb+1.

In the second period, the problem is slightly morecomplicated. Let Ph be the posterior probability of thesalesperson having high ability given the observablesafter the first period, that is, the first-period profitin this case. Then one can derive that the optimal


second-period contract C2 � c1+c21π2�1 has (see theappendix for details)

c1 � 0 and c2 � Ph(1 + b)2 + (1 − Ph)(b − B)b2(b2 + Ph + 2Phb) . (4)

If Ph � 1, then the firm is indifferent between any c1 > 0and c2 > 0 as long as their sum is the same; this isbecause π2 � 1 for sure for the high type. But if Ph < 1,the above solution is uniquely optimal. By Bayes’ rule,

Pr(h |π1 � 1) � 1 + b1 + 2b

, and Pr(h |π1 � −B) � 0. (5)

Substituting these into (4), we obtain the second-periodpayment C2 to the salesperson as a function of the first-and second-period profits:

C2 � b − B2b

+ c21π1�1( )

· 1π2�1, where

c2 ≡ (1 + b)3B2(1 + 2b)(1 + b + b2)b . (6)

The expected net-of-compensation profit is 1 − 12B+1b+1 in

the first period (it is equal to 1 if the salesperson is ofhigh ability and b−B

b+1 if he is of low ability), and

E(π2 − C2) � ((1 + b)3 + (b − B)b2)28(1 + b)3(1 + 2b)(1 + b + b2) +

(b − B)28(b + 1)3

(7)

in the second period. This follows from substituting theoptimal contract, (6), into the expected profit, (A.1),and taking into account that the probability of π1 � 1is 2+b

2(1+b).For example, for b � B � 0, we haveC2 � 1/2 · 1π1�π2�1,

E(π2 − C2) � 1/8, and the expected total net profitof 5/8.12 For b � B � 10, we have C2 � 0.29 · 1π1�π2�1,E(π2 − C2) � 0.07, and the expected total net profit of 0.57.As b � B→∞, we have C2 → 1/4, E(π2 − C2)→ 1/16,and the expected total net profit converging to 9/16.

Intuitively, the second-period profit and the total netprofit decline with b � B because the first-period profitbecomes less informative of the salesperson’s abilitywhen b � B increases, and the resulting less efficientretention is detrimental to both the firm and, on average(across salesperson types), the salesperson. In particular,as b � B increases from zero to infinity, the high-typesalesperson’s expected surplus (over the outside option z)from the second-period compensation decreases from1/8 to 1/32, whereas the low-type salesperson’s surplusincreases from zero to 1/32, resulting in the averagesalesperson’s surplus decreasing from 1/16 to 1/32.Note that the average compensation remains the same,but the expected value of it decreases because the value of

C2 to the salesperson is Pr(C2 > z) ·E(C2 − z | C2 > z) �E(C2

2)/2, that is, convex in C2.Note also that the analysis and all the results of the

benchmark case apply whether the salesperson knowshis second-period outside option at the beginning ofthe game or only just before his decision on whetherto accept the second-period offer. This is because, inequilibrium, the salesperson allocates the effort effi-ciently in the first period regardless of whether heplans to leave or stay with the firm in the secondperiod.By differentiating c2 in (4) with respect to Ph, one can

see that the optimal offer increases in the principal’sbelief about the salesperson’s ability:

d c2d Ph

� (1 + b)2Bb2(b2 + Ph + 2Phb)2 > 0. (8)

This means that if there is some way for the sales-person to demonstrate high ability without incurringa significant cost, he would strictly prefer to do so.This is the key to the result that a performance mea-surement of one effort component would be used bythe high-type salesperson to convince the firm that heis of the high type at a cost to the first-period profit.Of course, if profit is itself very informative or if theweight on the first-period profit is sufficiently high,then this first-period possible distortion by the sales-person may not happen. Also note that the aboveinequality means that, effectively, the expectation ofthe second-period contract puts an implicit positiveweight on the first-period profit (because, all elsebeing equal, π1 � 1 implies a higher probability of thehigh type than π1 � −B does), which gives the sales-person a strictly positive incentive to allocate the firstperiod’s effort correctly; that is, even though the first-period equilibrium contract leaves the salespersonindifferent as to how to allocate his effort if the sales-person is myopic, the equilibrium is actually strictbecause of the expected-by-the-salesperson second-period contract’s positive dependence on the firstperiod’s profit realization.

4.2. Unexpected Measurement Introduced After theFirst Period’s Effort Allocation

Now consider a situation in which the measurement isunexpectedly introduced after the first period’s effortallocation. This is an off-equilibrium case because weassume that the salesperson expects to be in the situationof the benchmark case; that is, he does not expect per-formancemeasurement, but the firm then introduces theperformance measurement. Thus, the results of this caseare going to be used to understand the driving forcesand incentives to introduce the performance measure-ment, and not as predictions in and of themselves. Thiscase is also useful for understanding and predicting


what the salespeople should expect if the firm is unableto commit to whether it would, or would not, introducea performance measurement midgame.

In this case, the first-period contract, effort allocation,and profits are the same as in the previous case becausethe firm can do no better and the salespeople do notexpect any measurement to occur. But the second-period contract can now be conditioned not only onπt (t � 1, 2) but also on the measurement realizationm(x1).13 Given the efficient effort allocation in the firstperiod, which we have because the salesperson (sales-people) did not expect the performance measurement,Bayes’ rule now gives the following probabilities of thesalesperson being of the high type conditional on therealizations of π1 and m(x1):

Pr(h |π1 � 1 andm(x1) � 1) � 1;

Pr(h |π1 � 1 andm(x1) � 0) � 1 + b1 + 3b

;

Pr(h |π1 � −B andm(x1) � 1) � 1;

Pr(h |π1 � −B andm(x1) � 0) � 0.

(9)

Note that the event {π1 � −B andm(x1) � 1} does notoccur if effort is allocated efficiently, so Bayes’ rule does notapply in that case. Therefore, Pr(h |π1 � −B andm(x1) �1) could take any value. We set this value at 1 becausea low-type salesperson could never get m(x1) � 1,whereas a high-type salesperson could get π1�−B andm(x1) � 1 by not choosing an efficient effort allocation. Inother words, this belief assignment is required for anequilibrium to be sequential. However, the results belowwill also hold if any other value (between 0 and 1) isassumed.

Because, in the second period, the only new observ-able is π2, (4) continues to hold with Ph now dependingon both the first period’s profit and the first period’smeasurement of x according to (9). Thus, the optimalsecond-period contract offer is c21π2�1, where c2 � 1/2when m(x1) � 1 or π1�−B andm(x1) � 1, c2 � (b − B)/(2b) when π1�−B andm(x1) � 0, and

c2 � c2 ≡ (1 + b)3 + 2(b − B)b22[2b3 + (1 + b)3] when

π1 � 1 andm(x1) � 0.(10)

Although the first-period decisions and, hence profit,are the same as in the benchmark case, the optimalcontract above leads to the expected second-period netprofit of

E(π2 − C2) � 18(1 + 2b)(1 + b + b2)

2b3 + (1 + b)3

+ (b − B) 2(b + 1)2b2 + (2b + 1)(b2 + 1)(b − B) − b8(b + 1)2(2b3 + (1 + b)3) , (11)

which is higher than the second-period net profit in thebenchmark case by 1

8b4B2

(b2+b+1)(1+2b)(1+3b+3b2+3b3). As b � Bincreases from zero to infinity, the above profit de-creases from 1/8 to 1/12. Given that the firm now hasbetter information about the salesperson’s ability inthe current case relative to the benchmark, as onewould expect, the high-type salesperson retentionis higher, the low-type salesperson retention is lower,and the profit and average salesperson surplus areincreased.

4.3. Measurement Introduced Before the FirstPeriod’s Effort Allocation

Consider now that themeasurement is introducedwhenthe first-period compensation is set to zero, as in thebenchmark case (Section 4.1), but before the salespersondecides on his effort allocation. Then the salespersonknows that the manager will observe the measurem(x1)at the end of the first period. Then it is a dominant strategyfor the high-type salesperson to fully distort hisfirst-periodeffort allocation toward the x component. This is becausedemonstrating a high type increases the expected payoffin the second period in some instances but in no instancedecreases it.Therefore, the expected first-period profit is reduced

to (b − B)/(b + 1); that is, it is as if all salespeoplewere ofthe low type. The expected second-period profit in-creases to (1 − 1/2) · 1/2 � 1/4 if the salesperson is ofthe high type, which is the net profit from a retainedhigh-type salesperson multiplied by the probability ofretention of a high-type salesperson given the optimalcontract. (A high-type salesperson is identified for surethrough m(x) � 1 in this case.) Likewise, it increases tob−Bb+1 − 1

2b−Bb · b

b+1( )

12b−Bb · b

b+1( )

� 14

b−Bb+1

( )2 if the salesperson

is of the low type (which is also identified for surethrough m(x) � 0). The total net second-period profit is

thus 18 1 + (b−B)2

(b+1)2( )

. Note that, relative to the benchmark

case, the expected second-period net profit increasesbecause of the better identification and the better re-tention of the high-type salesperson, but the first-period profit suffers.The negative impact of the measurement on the first-

period effort allocation due to the expected second-period contract adjustment leads to the idea that thefirst period’s incentive to distort effort allocationshould be countered in the first-period compensationpackage. We consider this strategy in the followingsubsection. But first, to illustrate the difficulty ofcountering the first-period distortion, let us derive thehigh-type salesperson’s benefit of the maximal dis-tortion in the first period relative to no distortion, as-suming that the firm does not expect a distortion.14

The salesperson’s benefit of distortion comes fromthe possibility of the {π1 � 1 andm1 � 0} outcome in


the first period. In this case, which has probability 1/2from the high-type salesperson’s point of view, theexpected second-period offer is c2 � c2, defined in (10).The salesperson will accept it with probability c2,achieving an average surplus, over the outside optionand given acceptance, of c2/2. Thus, the expected secondperiod’s surplus contribution of this event (π1 � 1 andm(x1) � 0) to the salesperson’s expected utility is c 2/4.If the high-type salesperson converts this outcome tom(x1) � 1, the surplus is calculated similarly but withc2 replaced by 1/2, which results in the expected sur-plus of 1/16. For example, for b � B � 10, the benefit is0.0525, which can be seen as quite substantial whencompared with the expected second-period net profitof 0.07 derived in Section 4.1. This example illustratesthat convincing salespeople not to distort the first-period effort allocation is going to be quite costly tothe firm relative to its expected second-period netprofit. On the other hand, as we have seen above, notcountering the maximal distortion is quite detrimentalto the first-period profit.

The above analysis was performed under the as-sumption that the salesperson does not know the second-period outside option’s value z before allocating effortin the first period. Let us now consider what happens ifthe salesperson knows z before allocating effort in thefirst period. As presented above, we need to consideronly the high-type salesperson’s effort allocation de-cisions because the low-type salesperson can exert onlyzero effort. In this case, if z≥ 1/2, the high-type sales-person, in equilibrium, does not value the possiblesecond-period offers and thus will, in equilibrium,efficiently allocate his effort in the first period. Ifz< 1/2, the high-type salesperson strictly prefers toshow that he is of the high type to receive the second-period offer with c2 � 1/2. Therefore, he will distort hiseffort maximally. Thus, the high-type salesperson dis-torts his effort with a probability of one-half, and if hedistorts it, he does so maximally. Therefore, the first-period profit contribution coming from high-typesalespeople decreases to 1

2 ·12 � 1

4. Because all sales-people who can potentially stay distort their effortmaximally in the first period, the second-period netprofit is the same as that in the case where salespeopledid not know their outside offer, and the first-periodprofit reduces to 1

4 + 34b−Bb+1.

15 Thus, the total profit is stillreduced relative to the one in the benchmark case.Note that in this case, the benefit of distortion is notthe same for all salespeople who distort their effortallocation: those with z close to 1/2 are almost in-different between distorting and not distorting theireffort allocation, whereas those with z below c2 offeredin the {π1 � 1 andm(x1) � 0} outcome have the highestincentive to distort.

4.4. Measurement Introduced Before the First-Period Contract

We now turn to the main case of the contract designwhen all the parties know at the beginning of the gamethat the measurement was introduced. Because dis-torting x upward from the efficient allocation in the firstperiod reduces the first period’s expected profits be-cause of the increased x1, the principal may try, at leastpartially, to counteract this first-period distortion in thefirst-period contract by a combination of (a) paying forπ1 � 1 when m(x1) � 1, (b) paying for π1 � 1 whenm(x1) � 0, or (c) paying for m(x1) � 0 when π1 � −B.Option (c) is clearly worse than (b) because it allocatesmore spending toward low-type salespeople andprovides less incentive to efficiently allocate effort toincrease profit. The relative optimality of the first twoinstruments is less straightforward. Still, for b> 4, anincrease in the weight on outcome in (a) is counter-productive. (Increasing x increases the probability ofthis outcome when b≥ 4.16) Therefore, for large b, theoptimal contract will involve a positive pay only on theoutcome in (b). This is intuitive because such a contractgives salespeople the incentive to move x down towardthe efficient amount both through conditioning on π1being high (profit sharing incentivizes an efficient al-location) and through conditioning on m(x1) being low(an incentive to reduce x from whatever level it wouldotherwise be set to).Consider now the conditions underwhich a high-type

salesperson prefers no distortion to the maximal dis-tortion given the first-period incentive C1 � c1π1�1,m(x1)�0and assuming that the firm expects no distortion. (Theappendix also shows that partial distortion is neveroptimal.) Note that the maximal distortion redistributesthe event {π1 � 1 andm(x1) � 0}, which for a high-typesalespersonwith no distortion has probability 1/2, to theevent {π1 � 1 andm(x1) � 1}with (total additional) prob-ability b−1

2(1+b) and to the event {π1 � −B andm(x1) � 1}with (total additional) probability 1

1+b. Each of thesecases leads to an increase in the second-period offerfrom c2 � c2 derived in Subsection 4.2 to 1/2 and re-sults in a loss of the first-period incentive c. Note that thebenefit of increased pay in the second period needs to becounted net of foregoing the outside option and takinginto account the probability of staying with the firm. Inother words, the expected benefit of a contract with theexpected pay of w is ∫ w0 (w − z) dz � w2/2. Thus, to pre-vent a high-type salesperson deviation to the full dis-tortion of x, we need

c≥ c ≡ (1/2)2/2 − c 22 /2 ≡ 18− c22

2. (12)

Consider now whether it is beneficial for the principalto incentivize no distortion in the first period. (As we


established above, this needs to be compared with themaximal distortion.) Given no effort distortion in thefirst period, the low-type salesperson will get c withprobability b

1+b, and the high-type salesperson will get cwith probability 1/2. The expected cost for the principalof incentivizing no distortion in the first period istherefore 1+3b

4(1+b) c. The expected gross benefit of in-centivizing no distortion (relative to full distortion) inthe first period is 1

2B+1b+1.

The salesperson’s effort allocation distortion in thefirst periodwould help the profit in the secondperiod byallowing a superior second period’s contract (because ofthe salesperson’s ability being fully revealed). Subtractingthe second-period net profit given no first-period dis-tortion (derived in Section 4.2) from the second-period netprofit under maximal first-period distortion (derived inSection 4.3), we obtain that the second-period value of thedistortion to the firm is

18

b3

2b3 + (1 + b)3+ (b − B) b − 2(b + 1)2b2 + (1 + b)(b − B)b

8(b + 1)2(2b3 + (1 + b)3) . (13)

We can then obtain that the benefit of countering themaximal distortion is higher than the total cost of doingso. Given that the principal counters the distortion, thefirst-period profit (net of the cost of preventing the

distortion) becomes 12 1 + b−B

b+1( )

− 1+3b4(1+b) c, the second-

period profit is as in (14), and therefore, the total netprofit is smaller than it would be in the benchmark case.For example, for b � B→∞, the net profit converges to1/2, which is smaller than the net profit when themeasurement is not possible (which tends to 9/16) butgreater than the net profit would be if the firm didnot counter the first-period distortion (0 + 1/8 � 1/8).Summarizing the results of this subsection, we obtainthe following proposition (in the above, we needed b> 4to rule out strategy (a); see the appendix for the proofthat the statements hold also for other values of b).

Proposition 1. Suppose salespeople do not know their second-period outside option z before allocating their first-period effort.Then, if the measurement of one of the effort components isimplemented at the start of the game, we have the following:

(1) The firm chooses to incentivize salespeople not todistort their first-period effort allocation. This results in a lossin the first period’s profit but with no change in efficiency.

(2) The firm uses the first period’s measurement for a betterretention of high-type salespeople in the second period. This is(on average) beneficial to the high-type salespeople and det-rimental to the low-type salespeople, and results in increasedsecond-period profits.

(3) The net result of the two effects above is that the total netprofit decreases, whereas the salespeople, on average, are better off.

(4) Social welfare increases.

The proposition states that there is no loss of efficiencyin the first period and that the total social welfare in-creases. Let us now discuss the generality of these tworesults when productive salespeople are heterogeneousin the first period. As we show below, the incentive todistort may be too large, and the firm may then choosenot to counter it. This can then lead to the possibility ofwelfare losses due to lower productivity. In fact, if theproductive salespeople are heterogeneous in the firstperiod, there could be no way to design an incentive tonot distort effort. To show this within this model, let usget back to the possibility that the salespeople have someinformation about their second-period outside optionbefore they choose their first-period effort allocation.17

In contrast to the previousmodel analysis, nowassumethat at the beginning of the first period, the salespeopleknow z precisely. In this case, if measurement is in-troduced, salespeople who know that they are going toleave for sure, for example, those with z> 1/2, do nothave an incentive to distort x1 unless the first-periodcontract provides themwith an incentive to distort effort.Therefore, because potentially half of the productive

salespeople will leave, when designing the incentivestructure to induce no (or less) distortion by the othersalespeople, the firm needs to make sure that the in-centive is not strong enough to fully distort the effortallocation of the salespeople who will leave. The firmcan use a combination of a positive weight on the first-period profit π1 to incentivize no distortion of thoseplanning to leave and an additional incentive througha positive weight on m(x1) � 0.The optimal compensation for π1 cannot be higher

than 2 because that is the maximum possible output overtwo periods of a high-ability salesperson. Therefore,the maximal incentive that it provides tends to zero as btends to infinity. This implies that if any weight is put onm(x1) � 0 in thefirst-period contract, as b tends to infinity,the salespeople that are expecting to leave the firm forsure (i.e., those with z> 1/2) will distort their effort al-location maximally toward the lowest x1 (i.e., towardx1 � 0). Because the firm benefits from identifying thetype of the salespeople who are staying with the orga-nization for better retention efficiency in the second pe-riod, it prefers those salespeople who will stay to distorttheir effort allocation, as opposed to the salespeople whowill leave. Therefore, to not have the salespeoplewhowillleave distort their effort allocation fully, the optimalweight on m(x1) � 0 must tend to zero as b tends to in-finity; that is, as b tends to infinity, thefirst-period contractapproaches the form p1π1�1 (for some nonnegative p).Again, because the optimal p is bounded from above

(as it is by 2), the incentive it provides to not distortthe effort allocation tends to zero as b tends to infinity.Therefore, as b tends to infinity, almost all salespeoplewho will stay distort their effort allocation maximally.(Only those with z close to 1/2 do not care much about


the second-period offer and therefore do not distort theireffort given a small incentive.) In turn, because p has littleeffect on salesperson behavior for large b, the optimal ptends to zero as b→∞. It then follows that for large b,the first-period profit approximately equals 1/4 + 3/4 ·(b − B)/(b + 1), and the second-period profit approxi-

mately equals 18 1 + (b−B)2

(b+1)2( )

, and we have the following

proposition. (See the appendix for a formal proof.)

Proposition 2. Suppose the high-type salespeople knowtheir second-period outside option z before allocating effort inthe first period. Then, if measurement is introduced, forsufficiently large b, we have the following results:

(1) Half of the high-type salespeople maximally distorttheir first-period x1 upward and stay in the second period(accept the second-period offer).

(2) Half of the high-type salespeople do not distort theirfirst-period effort and leave (do not accept the second-periodoffer).

(3) The total net profit and the total social welfare arelower than if the measurement were not introduced.

Note that in a more complete model, which wouldaccount for the origins of the outside option and thebenefit to other firms of salespeople leaving this firm,one can argue that any information asymmetry betweenfirms and salespeople is welfare reducing because itresults in inefficient allocation of salespeople acrossfirms. (Essentially, compensation packages may be onlyreallocating surplus from firms to salespeople, but un-equal compensations, due to different information thatdifferent firms have about the salesperson, means thatthe salesperson may stay at a less preferable firm.) Suchconsideration of the social desirability of retention ef-forts is beyond the scope of this paper.

Proposition 2 shows how some heterogeneity amonghigh-type salespeople (namely, their knowledge of dif-ferent outside option values in the second period) re-sults in the inability of the firm to prevent salespersoneffort distortion in the first period by up to one-half ofthe salespeople. The only reason most salespeople donot distort effort is that half of the salespeople areessentially homogenous: the effort allocation of thosewho know they will be leaving for sure is not affected

by the exact value of the outside option. With moreheterogeneity in salesperson beliefs about the proba-bility of leaving, one could obtain that, although inaggregate the firm may incentivize any proportion ofx and y efforts, it may be that nearly all salespeoplemaximallydistort their effort. Theonlineappendixpro-vides an example of such a model variation.Although in all the different setups above we have

that measurement, on average, benefits the high-typesalespeople, one can now see that introducing a first-period outside option or competition between organi-zations so that the salespeople may share the expectedwelfare surplus from employment through the first-period offer could lead to the introduction of mea-surement decreasing the payoffs of the salespeople andthe organization alike.

4.5. Equilibrium Measurement DecisionSo far, we have considered the effects of measurementwithout an explicit consideration of the equilibrium de-cision of whether to introduce it. Table 2 summarizes theresults of the previous subsections with respect to theeffects of measurement on productivity and profitsdepending on the expectations andwhen it is introduced.If a measurement can be introduced at a moment’s notice(i.e., if we add measurement introduction stages aftereach decision possibility of the original game), then, giventhe assumed time line of decisions, the analysis of Sec-tion 4.2 implies that the measurement will be introduced.The salesperson will rationally expect it, and the equi-librium outcome will be as if measurement were actuallyintroduced at the beginning of the game. According toProposition 1, this leads to lower profits. In other words,the manager would like to commit to not introducing themeasurement. If such a commitment is possible at the be-ginning of the game, again as is clear from Proposition 1,the equilibrium outcome will be the manager’s com-mitment to not measure, and we will have outcomes asin the benchmark case.In reality, measurement technology may not allow

instant introduction. Consider, for instance, our exampleofmeasuring the number (or duration) of a salesperson’scalls. If the salesperson has an office without all-glass

Table 2. Effects of Measurement

TimingOutcome

Productivity in period 1 Productivity in period 2 Total net profits

After effort allocation No change Increase IncreaseBefore effort allocation Decrease Increase DecreaseBefore contract choice No change Increase Decrease

Notes. All changes are relative to the corresponding outcomes without measurement. Timing is relativeto the first-period decisions. Productivity changes are due to the effort allocation changes in period 1 andchanged retention in period 2.


walls and the phone bill does not itemize calls, intro-ducing the measurement (requiring a call log or open-office environment) could happen simultaneously withthe salesperson adjusting his effort allocation. In thiscase, the measurement technology is as if the intro-duction is possible only before the salesperson’s choiceof effort, and the equilibrium outcome (given the restof our model) will be that measurement will not beintroduced.

For an example from an academic setting, considerevaluating teaching effectiveness at universities throughstudents’ evaluations. Because it practically takes monthsto adopt or change the survey, teachers can adjust theirteaching (e.g., making classes more entertaining insteadof providing knowledge that students cannot immedi-ately verify) concurrently with when the administrationstarts collecting the evaluations. In this case, in equilib-rium, we have the benchmark case if measurement is notintroduced. For another example, consider the manage-ment decision of whether to provide per-diem reim-bursement of travel expenses (a set amount per day, noreceipts required) versus reimbursing all reasonablynecessary expenses (but requiring receipts). The latter canbe viewed as measurement of allocation of expenses.Clearly, if the salesperson was not told to keep mealreceipts, it would be hard to collect them later.

The above examples illustrate how, depending onthe measurement technology, management may beable to commit to not measuring in some situations,and, in those cases, employees may know that there isno measurement. On the other hand, in some situa-tions, if past records or surveys about the past can beused for measurement, it could be that even thoughmeasurement is detrimental for the organization’s ob-jectives, it will occur in equilibrium because of the in-ability of management to commit to not measuring.

5. Model Variations5.1. Precise MeasurementIn the main model, we assumed that the x componentof effort can be measured only probabilistically. In thissection, we show that the main results that an in-troduction of measurement could decrease profits andsocial welfare also hold if the measurement is precise,that is, if after introduction of the measurement, x can bedirectly observed. Formally, instead of m(x) definedby (3), assume m(x) � x. When aℓ � 0, if x can be ob-served, then the type is revealed as far as high-typesalespeople choose a positive x. Therefore, measurementintroduction may lead to effectively full informationabout types and no distortion. In this case, the first-periodprofit is the same as in the benchmark model, and thesecond-period net profit increases because of the betteridentification and retention of high-type salespeople. Wetherefore consider a more general case of aℓ ∈ [0, 1) andshow that the main results hold for sufficiently high aℓ.

If aℓ > 1/4, the efficient choice x � 1 of high-typesalespeople may not identify them as the high typebecause the low-type salespeople can mimic x up to2

��aℓ

√. If no incentive is provided in the first-period

contract, in equilibrium, high-type salespeople willchoose x> 2

��aℓ

√to credibly signal to the firm that they

are of the high type. Thus, with an infinitesimallypositive weight on π1 in the first-period contract, theunique equilibrium salesperson strategy is for the lowtype to choose efficient x � ��

aℓ√

and for the high type tochoose x � 2

��aℓ

√. Clearly, for aℓ only slightly above 1/4,

this results in a higher total net profit because thedetriment of a slight effort distortion by the high-typesalespeople in the first period is more than offset bya higher profit in the second period. However, for aℓclose to ah � 1, the tradeoff is reversed: the benefit ofidentifying a salesperson’s type tends to 0 as aℓ tendsto 1, but the effort distortion and, therefore, its detri-ment to the firm increase. The firm is then interested inpreventing the effort distortion of the high types.The two possibilities of reducing effort distortion of

the high-type salespeople are (1) to provide a sufficientincentive for the high-type salespeople not to separatefrom the low-type ones, that is, to offer compensationfor a choice of x< 2

��aℓ

√(perhaps contingent on the

value of π1) sufficient for the high types not to bewilling to separate by choosing x above 2

��aℓ

√, and

(2) offer an incentive for lower x designed to make thelow-type salespeople unwilling to mimic the hightype’s choice. The first possibility would result ina pooling equilibrium. It turns out (see the online ap-pendix) that it is always suboptimal (i.e., it results intotal net profits lower than those without either mea-surement or the second strategy listed above). Thesecond possibility would result in the separatingequilibrium because a high-type salesperson valuesmore being recognized as such. (An increase in thesecond-period contract’s weight on π2 � 1 is valued moreby the high-type salesperson because he is more likely toachieve π2 � 1.) The firm would benefit in the secondperiod, but at the cost of the incentive paid to the low-typesalespeople in thefirst period. It turns out that the net effectis always negative (see the online appendix for details).Let us now consider the possibility that the salespeople

know their second-period outside option z before de-ciding on their first-period profit allocation. As in thecorresponding consideration in the main model, if no (ornegligible) incentive is given in the first-period contract,half of the high-type salespeople (those with z< 1/2) willthen distort their effort allocation to separate from the lowtype. Alternatively, if the incentive is given for the lowtype to not try to mimic the high type, then half of thehigh-type salespeople (the ones with z> 1/2) will take onthe offer and distort their x1 down. Therefore, the in-creased social welfare in the second period will come ata cost of the decreased one in thefirst period.Unlike in the


main model, neither upward nor downward distortionsare maximal. The upward distortion in the absence ofa nonnegligible incentive in the first-period contract is tochoose x1 � 2

��aℓ

√, whereas the downward distortion is

under the control of the firm. Which will be preferable tothe firm depends on the relative magnitudes of thesedistortions. The online appendix presents a formalanalysis and establishes the following proposition.

Proposition 3. Introduction of a precise measurement ofone of the components of effort decreases profits when thedifference in salespeople’s abilities is not very high. Fur-thermore, introduction of the precise performance mea-surement may decrease the total welfare.

5.2. Measurement of Effort in Both PeriodsIn this section, we investigate what happens when themeasurement of component x can be done in bothperiods. In other words, we consider the analysis ofthe previous section with the added possibility ofm(x2) also being available. As we will see, this bringsadditional complexity into the analysis without af-fecting the main messages of the previous section. Foranalytical tractability, we perform this analysis fo-cusing on large b.

5.2.1. Unexpected Measurement Introduced After theFirst Period’s Effort Allocation. Consider first the casein which there is an unexpected introduction of themeasurement after the first period’s effort allocation. Justas in the analysis of Section 4.2, in the second period,uncertainty about the salesperson’s type remains onlyif m(x1) � 0.

In this case, if m(x2) is also observable, and absentconcerns about the second-period effort allocation, theprincipalmaywant to put a positiveweight on the second-period measurement for a better retention of the high-type salespeople. This is so when m(x2) is informativeof the salesperson’s ability on top of the informationderived from the first-period observables (π1 and m(x1))and the second-period profit realization π2. If effort isefficiently allocated in the first period, this would bewhen π1 � 1 and m(x1) � 0 (otherwise, first-period ob-servations reveal the type). Thus, one can expect astrictly positive weight on 1m(x2)�1 in the second-periodcontract when (and only when) m(x1) � 0.18 The onlyreason that this weight may not be positive is if it couldlead to a second-period effort allocation distortion andthe manager finds this suboptimal. The outcome ofthis tradeoff depends on the probability of the sales-person being of a high type: if this probability is lower,the benefit of identifying the high type (and not spend-ing on the low type) is higher.

Similarly to the proof of Proposition 2, for anypositive incentive on m(x2), as b→∞, a high-type

salesperson will distort the effort allocation in thesecond period maximally. Because maximal distortionleads to zero productivity, for large b, the weight onm(x2) must be small, and, therefore, most of the paycomes from theweight onπ2. (Clearly, aweight onπ2 isbetter than a constant component, so the constant willnot be used.) Thus, asymptotically, the second-periodoutcomes are as if the measurement did not exist in thesecond period; that is, the results of Section 4.2 applyhere asymptotically for large b.For an illustration, consider the objective function of

a high-type salesperson who has a contract c21π2�1(1 +w2m(x2)) for some c2 > 0 and w2 > 0. If the salespersonchooses effort allocation x2, his expected compensa-tion is

w2e � (b + x2(2 − x2))(1 + w2x22

)c2

1 + b. (14)

The first-order condition with respect to x2 implies thatthe optimal x2 is

x2 � min 2,2w2 − 2 + ��(2w2 + 1)2 + 3(1 + w2

2b)√

3w2

{ }.

(15)

Note that for larger and larger b, if w2 is small, theoptimal x2 approaches 1 + 1+b

4 w2. Using the decisionrule given by (15), we can now write the first-orderconditions with respect to c2 and w2 on the second-period profit in the case {π1 � 1 andm(x2) � 0} using theprobability of the high type given in (9). The analysisis presented in the online appendix. For b � 10, wecan obtain c2 � 0.20 andw2 � 0.02, resulting in x2 � 1.05.

5.2.2. Unexpected Measurement Introduced After theFirst-Period Contract but Before the First-Period EffortAllocation. In this case, exactly as in the case of Sec-tion 4.3, all salespeople maximally distort their effortallocation in the first period. The first period’s measure-ment m(x1) is then fully informative about the sales-person’s type, and, thus, exactly the same outcomesfollow. Note that in the first period, salespeople mayexpect the second-period offer following m(x1) � 0 tohave some positive weight on m(x2), but because anysignificant weight on m(x2) will result in the maximaldistortion (for sufficiently large b) and, therefore, zeroexpected profits, the second-period offer that thesalespeople may expect following m(x1) � 0 is strictlyworse than the second-period offer that they expectfollowing m(x1) � 1, which is 1/2 · 1π2�1. Therefore, themaximal effort distortion in thefirst period guaranteeingm(x1) � 1 is strictly optimal for the salespeople. Again,note that the first-period profit loss due to this distortionin the first period is 1/2.


5.2.3. Measurement Introduced Before the First-PeriodContract. In this case, it follows from the results in theprevious section that the firm will want to preventmaximal distortion. As the second-period offer givenno distortion is asymptotically the same as if the mea-surement in the second period did not exist, the resultsof Section 4.4 hold here asymptotically. We thus con-firm all the results of Propositions 1 and 2, except thatthe firm uses the second-period measurement for re-tention in a small amount.

6. DiscussionOne may find it curious to reflect on the Finnish ed-ucation achievement puzzle from the point of viewoffered by the above model. As demonstrated byeventual student abilities, Finland was able to im-prove performance by largely eliminating both theteacher and student performance measurements (seeDarling-Hammond 2010).

A tenure system may also be considered as a com-mitment to limit the use ofmeasurements. For example,a standard justification for lifetime appointments ofjustices is that otherwise they could be swayed byunscrupulous decision makers. Our research puts it ina different light: even if the supervisors are fully be-nevolent (they have only the objective of maximizingpublic welfare) and are fully rational, they may not beable to not interfere and not distort the socially efficientdecisions of the salespeople.

The considerations illustrated by the model easilyapply to not-for-profit organizations. In such organi-zations, the productivity/output (α) in fact may not beobservable at all in the absence of measurement, yet theorganization cares about it by definition. Note that anymeasurement of efforts or productivity componentsmight have the property of not being completely un-biased between the different components of output,that is, almost always under- or overweigh one type ofthe input efforts. Furthermore, both the employees andthe management of such organizations may have pridein their work, which leads to the employees preferringto optimize α absent other incentives (in the model,because of a small weight on the total output of thefirm). The management, although by definition inter-ested in the “good deeds” α brought to the society, alsoprides itself in the amount of work done by its par-ticular organization, and therefore values the retentionof the productive (i.e., high-a) employees.

Note further that retention by itself is not necessarilysocially desirable. In the model we formulated, it isefficient (socially desirable) to retain a salesperson ifand only if the salesperson’s outside option z is lessthan the productive output a he can generate. There-fore, it is efficient to offer better contracts (higher basepay) to those salespeople who are expected to be moreproductive. As we have shown, the firm may be worse

off, although the salespeople and the social welfare arebetter off, in our model when the principal is willingand able to incentivize salespeople not to distort theireffort allocations in the first period (although socialwelfare is lower in the model variation where sales-people observe their second-period outside offers be-fore the first period). However, another interpretationis that z comes from the idiosyncratic salespersonpreferences for outside attributes such as job locationplus a job offer from an organization with exactly thesame production function. In this case, given equal pay(contracts), salespeoplewould produce the same a’s butrealize the best possible location choices; that is, thelocation-inconvenience costwouldbeminimized. Sales-person retention then makes utility generated by lo-cations inefficiently distributed while only shifting a’sbetween organizations. Then the management’s work(introducing measurements and fine-tuning contracts)could make both the organization and, on average, thesalespeople worse off (although some salespeople maybe better off). The model can then be most strikinglycharacterized as exploring the tug of war between thesalespeople’s pride in their work being a force towardan efficient society and the managerial pride in theirwork being a force against efficiency and toward adistortion of both the salespeople’s effort allocation andsalesperson locations.Practitioners use various metrics of performance

measurement (for an overview, see, e.g., Anderson andOliver 1987). Some of them are output based (e.g., sales,growth, customer satisfaction, and evaluation by col-leagues or supervisors), whereas others measure effortcomponents (behavior or the process; e.g., productknowledge, services performed, number of active ac-counts, calls made, amount of correspondence, or daysworked). Most directly, this paper relates to the pitfallsof the latter measurements, although some outputmeasures can also be more or less directly linked witha component of effort.Of course, in many other situations, the problem of

effort inducement and salesperson retention is themainproblem an organization faces, and the problem of op-timal effort allocation between unobserved (not well-measured) components is not as essential. In thosecases, performance measurements could benefit theorganization and an average salesperson. The point ofthis paper is not that performance measurement isalways or even usually counterproductive, but that itcould be, and hence one should consider the implica-tions of measurement before its introduction. In otherwords, one should have an idea of how to use the databefore collecting them.This paper assumes that one effort dimension can be

measured costlessly, whereas the other effort di-mension cannot be measured, which can also beinterpreted as it being infinitely costly to measure or


too noisy to provide any useful information. Morebroadly, one could consider the problem of the firm ofwhich effort dimensions to try to measure given theirdifferent measurement costs and different levels ofinformativeness of the noisy measure. In this setting,one may expect that the firm may prefer to measureeffort dimensions that are measured more precisely orare measured at a lower cost. The investigation of thisgeneral problem is left for future research.

AcknowledgmentsComments by Navin Kartik and Michael Raith are gratefullyappreciated.

AppendixSecond-Period Contract and Profit in theBenchmark CaseBecause the outside option in the second period is pos-itive and uniformly distributed on [0, 1], the salesperson hasa positive chance of leaving and a positive chance of stayinggiven any reasonable offer. (Because profit is either one ornegative, the optimal contract cannot provide expected utilityto the salesperson that exceeds the outside option withprobability one.) Consider now the second period’s contractC2 � c1 + c21π2�1, where c1 ≥ 0 and c2 ≥ 0 are the firm’s de-cision variables and are functions of the observables after thefirst period (i.e., functions of π1). Thus, in this benchmarkcase, c1 and c2 may be functions of the first period’s profitrealization and are nonnegative to ensure a nonnegativecompensation in any possible outcome.19

Given this contract, the expected pay of the salespersonwith ability ai is c1+c2(b + ai)/(1 + b) if the salespersonchooses the efficient effort allocation, which is assured byc2 > 0. Because the outside option is uniformly distributed on[0, 1], this expected pay is also the probability that thesalesperson stays. The expected gross second-period profitfrom the type i salesperson who is staying and allocatinghis effort optimally for the firm is 1 − (B + 1)(1 − ai)/(b + 1),which leads to the expected net second-period profit of 1 −c1 − c2 − (B + 1 − c2)(1 − ai)/(b + 1). Letting the probabilitythat the salesperson is of the high type be Ph, one can thencompute that the expected net second-period profit as afunction of Ph is

E(π2 − C2) � (1 − c1 − c2)(c1+c2)Ph

− c1 + B − b + bc21 + b

( )c1 + c2

b1 + b

( )(1 − Ph).

(A.1)

Maximizing the above expected profit with respect to c1 andc2 under the constraint that c1 ≥ 0, we find that the constraintc1 ≥ 0 is binding (first-order condition without the constraintleads to negative c1), and given c1 � 0, the optimal c2 is as inEquation (4).

Suboptimality of Partial First-Period DistortionConsider the high-type agent’s first-period effort allocationdecision x1 given the first-period contract c1π1�1andm(x1)�0 and

the expected second-period offer 121m(x1)�1 + c21π1�1andm(x1)�0 +

b−B2b 1π1�−Bandm(x1)�0. The salesperson’s value of increasing xabove x � 1 is coming from the increased probability ofm(x1) � 1 and the associated second-period equilibrium payincrease from c2 to 1/2:

Benefit� x2− 12

( ) (1/2)22

− c 222

( ). (A.2)

This benefit comes at a cost of lower expected first-period pay,

Costfirst period � 12− b + α

1 + b1 − x

2

( )( )c, where α � x(2 − x),

(A.3)

and of the possibility that the compensation is reduced fromc2 to b−B

2b (event {π1 � −B andm(x1) � 0} becomes possible),which decreases salesperson’s expected utility by

Costsecond period � 1 − α

1 + b1 − x

2

( ) c 2

2− (b − B)2

8b2

( ). (A.4)

Subtracting the two costs from the benefit, we obtain thesalesperson’s objective function as

f (x, c) � 116

(x − 1)(1 + b + 4(x2 − 3x − b + 1)( c 22 + 2c

))+ (2 − x)(x − 1)2(1 − B/b)2

1 + b. (A.5)

This yields f (x, c) � 0 at x � 1. At c � c ≡ 18 − c 2

22 , it simplifies to

f (x, c ) � −(x − 1)2(2 − x)(1 − B/b)B/b16(1 + b) , (A.6)

which clearly achieves the maximum (of 0) at x � 1 and x � 2.Thus, the incentive that is just enough to prevent the sales-person from preferring no distortion to maximal distortionmakes the salesperson strictly prefer no distortion to anyintermediate distortion. Furthermore,

∂f (x, c)∂c

< 0 and∂2f (x, c)∂c ∂x

< 0 for x∈ (1, 2]. (A.7)

In other words, f (x, c) decreases in c, and the speed (by ab-solute value) of this decrease increases in x. This implies thatif for some x1 < x2, we have f (x1, c1) ≤ f (x2, c1), then for anyc< c1, we have f (x1, c)< f (x2, c). Applying this to c1 � c andx2 � 2, we obtain that for any smaller incentive than c (i.e., forc< c ), we have that the effort allocation x � 2 is preferable toany effort allocation x ∈ [1, 2). Conversely, any incentivelarger than c results in x< 1.

Proof of Proposition 1. We have already established that itis always optimal for the firm to incentivize no first-period ef-fort allocation distortion through a positive weight on π1 � 1and m(x1) � 0 instead of allowing effort distortion. This im-plies that it will be optimal to do so if other contract structuresare allowed. (Recall that we have not considered allowinga contract with a positive weight on π1 � 1 and m(x1) � 1 whenb≤ 4.) This immediately implies that social welfare increasesif measurement is introduced.

Let us now compare incentivizing less upward distortionof x1 with a positive weight on π1 � 1 andm(x1) � 0 versus a


positive weight on π1 � 1 andm(x1) � 1. The first strategy(per unit of the weight) provides a higher incentive to reducex1 from any value above the optimal x1 � 1, but the secondstrategy is cheaper for the firm as it results in no payments tothe low-type salespeople (because they can never achievem(x) � 1). Therefore, although the second strategy is poten-tially optimal (only for low b, because it is counterproductivefor b> 4), allocating all the weight toward the first strategywould be optimal if the firmwas able to avoid payment to thelow-type salespeople.

Let us then establish an upper bound on the firm’s profitswith measurement by using this lower bound on the cost ofthe first strategy above; that is, assume that the total ex-penditure on the wages coming from the weight c on π1 � 1and m(x1) � 0 in the first period will be not 1+3b

4(1+b) c butc4. In

this case, as we have argued above, it will be optimal not touse any weight on π1 � 1 andm(x1) � 1 in the first-periodcontract. The firm will still use the minimal c required toincentivize no distortion, that is, c � c. The first-period profitwith measurement will be c

4 lower than that without mea-surement (because of the cost of wages), and the second-period profit will be higher than the one in the benchmarkcase by b4B2/[8(b2 + b + 1)(2b + 1)(b3 + (b + 1)3)], which issmaller than c

4 for all b>B. Therefore, measurement alwaysdecreases profits, and the proposition is proven.

Proof of Proposition 2. If measurement is introduced andthe firm provides minimal incentives not to distort effortallocation in the first period, all high-type salespeople withz< 1/2 will distort their x1 maximally upward to guaranteethemselves the second-period offer 1/2 · 1π2�1, and the restwill choose an efficient effort allocation and leave. Thissalesperson strategy will result in the firm having full in-formation about the types of salespeople who might stay butat the cost of inefficiently low profit in the first period.

Let us estimate howmuch the firmmay be willing to spendon preventing the high-type first-period effort distortion and,consequently, how many salespeople may be, in equilibrium,prevented from themaximal distortion of their effort allocationin the first period. For this purpose, we will ignore the second-period benefit of the first-period effort allocation distortion(without the distortion, some high-type employees end upwith π1 � 1 and m(x1) � 0 and are pooled with the low-typesalespeople), thereby deriving an upper bound on the firm’swillingness to prevent effort allocation distortion and, there-fore, a lower bound on the mass of high-type employees withz< 1/2 who distort their x1 maximally upward.

To discourage upward distortion of x1, the firm may puta positive weight on π1 � 1 and, additionally, possibly anegative weight on m(x) � 1. We therefore consider the first-period contract of the form p1π1�1(1 − wm(x1)). Given thiscontract, the expected first-period pay of a high-type sales-person for x1 � x is (b + (2 − x)x)(1 − wx/2)p/(b + 1). Check-ing when the derivative of this with respect to x is negative onx ∈ [0, 2] when b> 4, we observe that the optimal choice ofa high-type salesperson who is sure to leave is x � 0 ifw≥ 4/b.

Facing the maximal effort distortion of the high-typesalespeople with z> 1/2, the firm would prefer to insteadhave salespeople with z> 1/2 not distort their effort allocationfrom the optimal one (x1 � 1) at all, while having the rest ofthe salespeople distort the effort allocation maximally upward

(i.e., choose x1 � 2). Because the latter outcome is achievedwith the (near) zero-pay contract, a contract with w≥ 4/bcannot be optimal. Thus, the optimal contract must havew< 4/b. Furthermore, because of the benefit to the firm ofa high-type salesperson’s not distorting effort in thefirst periodis at most 1− b−B

b+1 � B+1b+1, and only half of high-type salespeople

will distortwith the (near) zero-pay contract (which is a quarterof all salespeople), the firm will not be willing to pay morethan 1

4B+1b+1 in the total first-period’s wages to all salespeople.

On the other hand, the above contract will result in the totalexpected expenditure on the first-period wages higher than12

bb+1 p + 1

2b

b+1 (1 − 4b )p � b−2

b+1 p. Therefore, in the optimal con-tract, p< B+1

4(b−2).Now, fix arbitrary x∗1 ∈ [0, 2), and consider a high-type

salesperson with the second-period outside option z∗ ≤ 1/2.If m(x1) � 1, the second-period contract provides this sales-person the expected second-period pay of 1/2. On the otherhand, in either event {m(x1) � 0 andπ1 � −B} or {m(x1) � 0andπ1 � 1}, the firm has to believe that the probability thatthe salesperson’s type is high is at most 1/2/(1/2 + b/2/(b + 1)) � (b + 1)/ (2b + 1). Substituting this upper bound onthe probability of high type into Equation (7), we obtain thatthe salesperson’s second-period wage increases by at leastb2B/[2(2b + 1) (b2 + b + 1)] if m(x1) increases from 0 to 1.Therefore, increasing x1 from x∗1 to 2 increases the expectedpay (conditional on the salesperson accepting the offer) inthe second period by at least b2B/[2(2b + 1)(b2 + b + 1)] withprobability (1 − x∗1/2) and never decreases it. (Once x1 � 2, theexpected pay is 1/2 for sure.) The salesperson values thisexpected increase in the second-period offer by at least

1 − x∗12

( )min

12− z∗, b2B

2(2b + 1)(b2 + b + 1){ }

. (A.8)

Let us now consider an upper bound on the salesperson’s first-period cost of such adjustment of x1 due to its effect on thefirst-periodpay for b> 4. Given the upper bounds established aboveon p and w, when the salesperson chooses x1 � 2 instead ofx1 � x∗1, his expected first-period income decreases by

b + x(2 − x)b + 1

p 1 − wx2

( )− b(1 − w)

b + 1� (2 − x)wb + 2x − wx2

2(b + 1) p≤

(2 − x∗1)4(b − 2)(b + 1)b p≤ (2 − x∗1)

B + 1(b + 1)b, for b≥ 8,

(A.9)

where the first inequality follows frommaximizingwb + 2x −wx2 over x∈ [0, 2] and w for b≥ 8 and w≤ 4/b. Let b∗ be suchthat

b2B4(2b + 1)(b2 + b + 1)>

B + 1(b + 1)b, for b> b∗. (A.10)

Such b∗ exists because the left-hand side is of the order B/band the right-hand side is of the order B/b2 as b→∞.Comparing the benefit and the cost of full distortion to thehigh-type salesperson with z< 1/2, we then obtain that forb> b∗, the benefit outweighs the cost if 1/2 − z> 8(b−2)p

(b+1)b . Thus,high-type salespeople with z ∈

[0, 1/2 − 8(b−2)p

(b+1)b)will be maxi-

mally distorting their x1 upward.


Let us now revisit the upper bound on the optimal pestablished at the beginning of the proof of this proposition.We have used an estimate of the potential benefit of p> 0coming from preventing the distortion of high-type sales-people with z< 1/2. However, for b> b∗, as we have shownabove, the maximal distortion may be possibly preventedonly for salespeople with z∈ [1/2 − 8(b−2)p

(b+1)b , 1/2]. The ratio ofthe mass of these high-type employees to all employees is4(b−2)p(b+1)b . We thus have that for b> b∗, the upper bound of thebenefit (to the firm, relative to the minimal incentives in thefirst period) is 4(b−2)p

(b+1)bB+1b+1 instead of 1

4B+1b+1. Comparing this to

the lower bound on the first-period wage costs establishedabove (b−2b+1 p), one obtains that for b(b + 1)> 4(B + 1) (which isalways true for b> 4), the lower bound on the cost outweighsthe potential benefit. Therefore, minimal incentive in the firstperiod is optimal for b> b∗ defined above. As we have alreadynoted, minimal incentives result in all high-type employeeswith z≥ 1/2 allocating effort efficiently, and all high-typeemployees with z< 1/2 maximally distorting their x1 up-ward. This establishes the first two parts of the proposition.

We now turn to the calculation of the effect of measure-ment on the profits and the social welfare for large b, spe-cifically, for b> b∗ defined above. The net profit withoutmeasurement is derived in the main text (see Equation (7) andthe sentence that precedes it). If b> b∗, the total expected netprofit with measurement equals

12+ 12·b − Bb + 1

+ 1212� 34+ b − B2(b + 1) (A.11)

in the case of a high-type salesperson, and equals

b − Bb + 1

+ b − Bb + 1

− pay( )

· pay (A.12)

in the case of a low-type salesperson, where “pay” is the ex-pected payment in the second period, which is b

b+1b−B2b � b−B

2(b+1).Averaging the above two expressions, we obtain the profitwith measurement. Subtracting it from the profit withoutmeasurement, we obtain that measurement reduces profit by

Δπ �4b3B − B2b2 + 4b3 − B2b + 6b2+ 6b2B + 6b + 6Bb + 2B + 28(b + 1)(1 + 2b)(1 + b + b2) + o(1/b)

� B + 14(b + 1) −

bB2

8(2b + 1)(b2 + b + 1) + o(1/b), (A.13)

which is positive for large b (as far as b>B).The social welfare without measurement can be calculated

as the average welfare of the low-type and high-type sales-person scenarios. If the salesperson is of the low type, thewelfare is

WLNoM � b − Bb + 1

+ bb + 1

b − Bb + 1

· c21L + 1 − c221L2

[ ]+ 1b + 1

b − Bb + 1

· c20L + 1 − c220L2

[ ], (A.14)

where c21L is the expected pay of the low-type salesperson inthe second period if π1 � 1, c20L is his expected second-periodpay if π1�−B, andNoM stands for nomeasurement. We havec2iL� b

b+1 c2i, where c2i is the equilibrium wage conditional on

the first-period profit given by Equation (6). The aboveequation represents the expected first-period profit plus theprobability of π1 � 1 times [the expected second-period profitgross of wages times the probability of acceptance (which isthe event z< c21L) plus the surplus coming from the outsideoption in case of rejection] plus the similar term representingthe event of π1 � 0. If the salesperson is of the high type, thesocial welfare is

WHNoM � 1 + 1 · c21 + 1 − c2212

[ ]+ 0 � (1 + c21)(3 − c21)

2.

(A.15)

This is derived in the same way as the previous equation, butit is much simpler because Prob(π1 � 1 | high type) � 1, andthe expected second-period pay of the high type given wagec · 1π2�1 is c.

If the measurement is introduced (and b> b∗), the sales-people with z< 1/2 fully distort their effort allocation in thefirst period, and those with z> 1/2 allocate effort efficientlyand leave in the second period. Furthermore, the high-typesalespeople with z< 1/2 are then recognized as the hightypes, receive a second-period wage offer of 1/2, and stay.Therefore, if the salesperson is of high type, the expectedwelfare is

WHm � 1 ·12+ 12·b − Bb + 1

+ 1 − (1/2)22

+ 12� 11

8+ 12b − Bb + 1

,

(A.16)

where the first two terms represent the expected profits in thefirst period (coming from those with z> 1/2 and z< 1/2,respectively), and the last two terms represent the expectedsocial welfare in the second period (coming from those withz> 1/2 and z< 1/2, respectively). The low-type salespeopleare identified by the measurement precisely and, therefore,receive the second-period wage offer of b−B

2b 1π2�1, which theyvalue at c2L � b−B

2(b+1). Therefore, the social welfare conditionalon low type is

WLm � b − Bb + 1

+ b − Bb + 1

c2L + 1 − c22L2

[ ]� (3b − B + 2)(5b − 3B + 2)

8(b + 1)2 . (A.17)

Averaging the two social welfare equations above, we obtain

Wm � 316

+ 316

(3b − B + 2)2(b + 1)2 . (A.18)

Subtracting the above from the social welfare without mea-surement, we obtain that the welfare without measurement isgreater by

ΔW �8b3B − 3B2b2 + 8b3 − 3B2b + 12b2B

+ 12b2 + 12Bb + 12b + 4B + 416(b2 + b + 1)(2b + 1)(b + 1)

� B + 14(b + 1) −

3B2

16(b2 + b + 1)(2b + 1)> 0, for b>B,

(A.19)

which concludes the proof of the proposition.


Endnotes1We thank the associate editor for the suggestion of this example.2Even if long-term contracts are possible, unless management cancommit to not giving out bonuses (which are not fully spelled out inthe contract), the implicit nature of incentives remains present.3Thismeasurement of one of the components can potentially bemadewith noise.4Management can offer long-term contracts, but the problem is thatonce management sees evidence of high ability, and given theprobability that salespeople will quit, it will then offer retentionbonuses to some salespeople; that is to say, a commitment to neveruse the measurement is not renegotiation-proof. One could alsoenvision “slavery contracts” that commit salespeople towork forever.Although such contracts would solve the issue of commitment (be-cause retention is no longer an issue), theywould result in inefficiencybecause, due to the random outside options (if they are not perfectlypredictable by the salespeople), sometimes it is efficient fora salesperson to leave. From a profitability standpoint, such contractswould come at the expense of offering higher base salaries up front.Thus, the negative value of measurement would persist even ifslavery contracts were allowed.5 See, for example, Basu et al. (1985), Rao (1990), and Raju and Srinivasan(1996). See alsoGodes (2003) on how touse different types of salespeople.6 Some measurement can also be obtained on the market conditionsby allowing lobbying by salespeople on the incentive scheme (e.g.,Simester and Zhang 2014).7 For a discussion of this literature, please see Bolton andDewatripont(2005, chapters 9 and 10).8To avoid potential incentives for salespeople to signal high abilitythrough refusing a first-period offer to gain a higher compensation inthe second period, assume that the firm does not engage in hiring atall in the second period. From the equilibrium that we derive, suchsignaling will also not be optimal in this setting.9Another possibility to explore, not considered here, is cheap talk reportsby the salesperson about his ability (see, e.g., Ambrus et al. 2013; in theadvertising setting, see, e.g., Gardete 2013 and Gardete and Bart 2018).10This measurement structure simplifies the analysis. In Section 5.1,we also consider the case of precise measurement, m(x) � x, whichyields similar results.11The term 1condition is the indicator function; it takes the value 1 if the“condition” is true and takes the value 0 otherwise.12Note that the assumption of a relatively low retention rate (rela-tively high outside option) forces the profit to be low in the secondperiod, because of both the low retention probability and the extraexpenditure on salesperson compensation. However, reducing theupper bound on the outside option would complicate the analysis,as it would require considering the boundary case of the retentionprobability equal to one under a potentially optimal contract. One pos-sibility to bring the first- and second-period profits closer—withoutchanging the effects presented—would be to consider z to be amixture ofzero and the uniform component (i.e., amass point at zero and the rest ofthe distribution still uniform on [0, 1]).13The case when the second-period contract can also be conditionedon the second period’s measurement realization m(x2) is consideredin Section 5.2.14The benefit will be even higher if the firm expects a distortiontoward x> 1, because in that case the high-type salesperson is betteridentified, and, therefore, the second-period contract offer followingm(x1) � 0 will be even lower, whereas the offer following m(x1) � 1will be the same and equal to c2 � 1/2.15Note that not everything is the same in the second period: Given thesalesperson strategy, the firm optimally updates its belief about theoutside option of the salespeople based on the profit and performance

measurement realization. Effectively, m(x1) � 0 signals that the sales-person expects a high outside option or is of low ability. But if the firmthen decides to increase the second-period offer in this case to 1/2 · 1π2�1or greater, the total profit becomes less than if the firm just committed tohaving the second-period wage 1/2 · 1π2�1 regardless of π1, whichobviously results in a total profit lower than in the benchmark case.16For a high-type salesperson, the probability of the outcome {π1 � 1 andm(x1) � 1} is x1

2b+x1(2−x1)

1+b , which is increasing in x1 ∈ [0, 2] when b≥ 4.17Another possibility is due to different incentives needed for em-ployees with different ability levels. This results in equilibriumdistortion when aℓ > 0. However, the analytical expressions are muchmore complex when aℓ > 0, and, numerically, we were unable to findparameter values that led to lower equilibrium social welfare due tothe measurement introduction.18Note that this could look like a special treatment for apparent(i.e., as measured) substandard salespeople to “encourage im-provement.” This is not exactly the case because achievingm1(x1) � 1does not lead to lower expected compensation in the second periodfor retention reasons.19Although c2 < 0 is technically allowed as long as c1 + c2 ≥ 0, it isstraightforward to check that it cannot be a part of an optimalcontract—it would give an incentive to inefficiently allocate effortwithout the benefit of higher retention of high-type salespeople.

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