Subjectivity in Tournaments: Implicit Rewards and ... Files/18-070_2173c99a-dc1b...anonymous...

Subjectivity in Tournaments: Implicit Rewards and Penalties and Subsequent Performance

Wei Cai Susanna Gallani

Working Paper 18-070

Working Paper 18-070

Copyright © 2018 by Wei Cai and Susanna Gallani

Working papers are in draft form. This working paper is distributed for purposes of comment and discussion only. It may not be reproduced without permission of the copyright holder. Copies of working papers are available from the author.


Wei Cai Harvard Business School

Susanna Gallani Harvard Business School


Wei Cai Harvard Business School

Morgan Hall 15 Harvard Way, Boston MA 02163

Ph: 617-496-2758 Fax: 617-496-7363

[email protected]

Susanna Gallani* Harvard Business School

Morgan Hall 15 Harvard Way, Boston MA 02163

Ph: 617-496-8613 Fax: 617-496-7363 [email protected]

Acknowledgements: We are sincerely thankful to the research site for providing the data for this project. We gratefully acknowledge John Beshears, Brian Hall, Paul Healy, Matthias Mahlendorf, Asís Martinez-Jerez, Greg Sabin, Jee Eun Shin, the HBS Research Coaching Brownbag series participants, and the anonymous reviewer for the 2018 AAA Management Accounting Section Meeting for their insightful comments and useful suggestions. We are appreciative of Harvard Business School for the financial support during the development of this study. All errors are our own. *Corresponding Author

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Abstract: This study extends the literature on the tradeoffs associated with subjectivity in tournament incentive systems by describing the effects of implicit penalties (rewards), whereby workers ranked at the top (bottom) of objective performance rankings fail to receive the reward (penalty) due to management’s subjective performance evaluations. Using data from a field setting where incentive contracts are structured as repeated tournaments, we find that workers respond differently to subjective versus objective awards of rewards and penalties. Additionally, workers subject to implicit rewards (penalties) exhibit performance reactions that counterbalance those of workers receiving subjective penalties (rewards), with net effects indistinguishable from zero. However, while the effects of subjective rewards and penalties reverse in the subsequent period, the performance effects of implicit rewards and penalties persist. Our study documents consequences of subjectivity that might alter the effectiveness of tournament incentives, and is relevant for the practice of incentive design. Keywords: Tournaments, Subjectivity, Relative Performance Evaluation, Implicit Rewards and Penalties, Reciprocity JEL Codes: M12, M41, M52 Data availability: The data used in this project is subject to a confidentiality agreement and cannot be shared without express consent of the organization’s legal representatives. Funding: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sector.

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I. INTRODUCTION

Tournament-based incentive systems reward employees based on performance rankings within a

reference group. While in most cases, tournaments are used to determine allocations of favorable

outcomes, such as promotions, recognition, or monetary rewards, tournament-based incentive

systems involving both rewards and penalties are often observed in practice. For example, General

Electric’s “vitality curve” made the employees ranked in the top 20% of the performance

distribution eligible for pay raises, bonuses, or promotion, while those in the bottom 10% would

likely be demoted, reassigned to less prestigious roles, or at risk of losing their jobs.1 Other

examples include “up or out” systems, common in the military and in many service industries (i.e.

investment banking, consulting, public accounting, academia, etc.) by which employees that do

not meet the standards for promotion are asked to leave the organization (Anand, Gardner, and

Morris [2007], Lazear [1991]). While these performance evaluation systems are heavily based on

objective performance measures, they often include important elements of subjectivity.

Significant literature on incentive systems has addressed the benefits and costs of

subjectivity in compensation contracting and performance evaluation (Baker, Gibbons, and

Murphy [1994], Baker, Jensen, and Murphy [1988], Bol [2007], Prendergast [1999], Prendergast

and Topel [1993]). Prior studies show that the use of subjectivity, while useful to curb some of the

shortcomings of objective performance measurement systems (Baiman and Rajan [1995], Baker

et al. [1994], Gibbs, Merchant, Van der Stede, and Vargus [2004]), is often confounded with bias

(Gibbs et al. [2004], Prendergast and Topel [1993]), and can generate perceptions of unfairness

1 Source: “Microsoft, GE, and the Futility of Ranking Employees”, Fortune blog Nov 18, 2013: http://fortune.com/2013/11/18/microsoft-ge-and-the-futility-of-ranking-employees/

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and procedural injustice (Baker et al. [1988], Ittner, Larcker, and Meyer [2003], Moers [2005],

Prendergast [1999]). Accordingly, if the allocation of rewards and penalties critically hinges on

subjective performance evaluations, tournament-based incentives may introduce unintended

motivation effects.

Prior research on tournament incentives has primarily focused on single period

tournaments, where the incentive effect operates ex-ante – that is, the prospect of receiving a

reward or penalty influences individual effort choices relative to the period in which the

tournament takes place (Campbell [2008], Hannan, Hoffman, and Moser [2005], Lazear and Rosen

[1981], Libby and Lipe [1992]). In practice, however, tournaments often span across multiple

periods of performance measurement (Casas-Arce and Martinez-Jerez [2009], Ederer [2010],

Hannan, Krishnan, and Newman [2008]), or repeat multiple times over consecutive periods

(Berger, Klassen, Libby, and Webb [2013]). In these cases, the choice of effort in any given period

might be influenced by prior outcomes. While prior literature provides evidence of dysfunctional

behaviors, such as complacency and giving-up, associated with interim feedback effects (Casas-

Arce and Martinez-Jerez [2009]) or prior tournament results (Berger et al. [2013]), the effects of

subjectivity on subsequent choices of effort are largely unexplored.

Using subjectivity to determine tournament rewards and penalties often results in an ex-

post override of rankings compiled on the basis of objective performance measures (hereafter:

objective rankings).2 That is, workers may receive a reward despite not being ranked at the top of

the objective ranking (subjective reward), or a penalty despite not being ranked at the bottom

(subjective penalty). We posit that, due to the ‘zero-sum game’ structure of tournament incentive

systems, whereby the number of winners and losers is pre-determined and bounded, subjective

2 Subjectivity could also be introduced in the relative weights assigned to different performance measures (Bol [2007], Campbell [2008]).

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overrides of objective rankings also give rise to implicit rewards (i.e. avoiding a penalty while

ranked at the bottom of the objective ranking) and implicit penalties (i.e. missing out on a reward

while being ranked at the top). In this study, we explore the influence of subjective and implicit

rewards and penalties on workers’ subsequent effort choices and performance.

We use field data from a Chinese manufacturing firm that operates a tournament-based

incentive system linked to departmental performance. In each month of production, members of

the department with highest performance receive a monetary bonus, while members of the worst

performing department are penalized with deductions from their pay. The reward/penalty decision

is made by top executives of the firm and is based on both objective and subjective assessments.

At the end of each month, the firm discloses to all members of the organization both the objective

performance rankings and the ultimate awardees of the reward and penalty, but there is no

disclosure of the subjective criteria informing the decision or of the weights assigned respectively

to objective and subjective elements of performance.3 Therefore, employees can detect and

measure the extent to which subjective assessments override the objective rankings to award

rewards and penalties, but do not receive explicit information about the determinants of the

override. This setting allows us to empirically observe how workers react to subjective overrides

of objective performance rankings, and to examine the effect of implicit rewards and penalties on

subsequent workers performance.

We find that assigning rewards and penalties subjectively elicits different workers reactions

with respect to subsequent effort and performance compared to the determination of rewards and

penalties based on objective rankings alone. That is, workers react not only to receiving a reward

3 Interviews with members of the management team indicated that subjective evaluations take into consideration the attitude, morale, and the influence of uncontrollable factors that might have impacted objective performance. These considerations are not disclosed with the employees. We provide more details in Section III.

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or a penalty, but also to the procedure by which rewards and penalties were assigned. In particular,

while rewards awarded based on objective rankings are associated with a subsequent performance

decline, subjective rewards drive an increase in subsequent performance. With respect to penalties,

instead, we find no significant reaction to penalties assigned based on objective performance, while

subjective penalties are associated with a subsequent performance decline. This combination of

results is consistent with the predictions of equity theory and reciprocity (Akerlof [1984], Falk and

Fischbacher [2006], Fehr and Schmidt [1995]).

Next, we study the effects of implicit rewards and penalties. That is – we examine the

reactions of workers that, due to subjective overrides of objective performance, miss out on (are

spared from) the reward (penalty) they would have received in absence of subjectivity. Our results

document that implicit rewards (penalties) induced by subjective performance evaluations are

significantly associated with subsequent performance improvements (declines). Even if the

economic effect of implicit rewards and penalties is only defined in terms of opportunity costs (i.e.

there are no actual cash inflows or outflows because workers do not receive a bonus or a pay cut

in this case), workers appear to experience implicit rewards or penalties in similar fashion as they

do explicit subjective ones, in line with the predictions of reference-dependent preferences

(Koszegi and Rabin [2006]). This result suggests that tournament-based incentives may have wide-

ranging incentive effects spanning beyond the ultimate awardees of rewards and penalties.

Finally, we analyze the net performance effects of subjectivity. Because of the mechanical

relation described above, positive performance effects associated with subjective rewards might

be diminished by negative effects associated with corresponding implicit penalties. Similarly,

negative effects generated by subjective penalties might be counterbalanced by positive effects

associated with implicit rewards. We in fact find that the net performance effect between paired

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explicit and implicit rewards and penalties is non-distinguishable from zero. Taken together, our

results indicate that, in tournament settings, effects arising from subjective rewards (penalties)

might be muted by effects of opposite sign associated with implicit penalties (rewards).

Our study offers several contributions to the literature and to the practice of incentive

design. First, our study is the first to document the existence of implicit rewards and penalties in

tournament settings where performance evaluations involve elements of subjectivity. Prior

literature has primarily focused on the incentive effects related to members of the organization that

were directly affected by subjective performance evaluations. We extend the knowledge on the

use of subjectivity in incentive contracting by exploring its consequences relative to members of

the organization that are indirectly impacted by the subjective decision via implicit rewards and

penalties.

Second, we contribute to the scant literature on repeated and dynamic tournaments by

providing field-based empirical evidence on the role of subjectivity in performance evaluations

and its effect on subsequent effort choices. Additionally, our paper focuses on rank-and-file

workers, which have received insufficient attention in the literature on tournament incentives.

Third, we extend the empirical literature on penalties. Extant research has addressed

subjectivity predominantly from a bonus-allocation standpoint, limiting the consideration of

subjective penalties to a minimum (McLeod [2003], Rajan and Reichelstein [2009]). Important

research stemming from the seminal work of Kahneman and Tverski [1979] and Thaler [1980] has

provided evidence that individuals do not experience rewards and penalties as symmetrical

changes in utility (Franciosi, Kujal, Michelitsch, Smith, and Deng [1996], Kahneman, Knetsch,

and Thaler [1990], Luft [1994]). Therefore, the effects of subjective rewards on effort allocation

documented by the literature may not be directly extended to the case of subjective penalties. Our

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study provides insights into the interplay between the effects of subjective rewards and subjective

penalties on subsequent performance.

Finally, our findings are relevant to the practice of incentive contracting because, despite

individual preferences for incentive systems framed in positive terms over systems associated with

penalties (Christ, Sedatole, and Towry [2012], Kahneman and Tverski [1979], Lazear [1991], Luft

[1994]), tournament systems including both reward and penalty mechanisms continue to be

observed and to include important elements of subjective evaluation. Our study sheds light on

potential pitfalls, and documents the existence of counterbalancing effects that might reduce the

overall effectiveness of these types of incentives.

The remainder of this paper proceeds as follows. In Section II, we provide an account of

relevant theories and prior empirical work related to the purpose of our study. Next, we describe

the field settings (Section III) and the research design (Section IV). Section V presents the results

of our main statistical tests and our inferences. We report the results of supplemental and

robustness tests in Section VI. The last section concludes.

II. RELEVANT LITERATURE AND HYPOTHESES

A large portion of the literature on tournament incentive schemes focuses on single-period

tournaments (Baker et al. [1988]), where ex-ante effort choices of the workers impact the

probability of receiving a reward or a penalty. However, some studies in accounting posit that the

incentive effects of a tournament scheme do not necessarily exhaust their influence once the prizes

are awarded. For example, Campbell [2008] finds that certain performance improvements

achieved in hope of winning the tournament persist in the aftermath even for employees that did

not win the prize; Casas-Arce and Martinez-Jerez [2009] study the effect of interim feedback in

multi-period contests, where the performance of each period contributes to the final ranking and

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the awarding of prizes; Berger et al. [2013] study the effect of winning and losing on subsequent

performance in a series of independent repeated tournaments. Repeated tournaments appear to be

pervasive in practice (Berger et al. [2013]).

Extensive research in accounting and economics has addressed many aspects of tournament

incentives, including the size of the delta between winning and losing prizes (Becker and Huselid

[1992], Lazear and Rosen [1981], Nalebuff and Stiglitz [1983]), the number of contestants

(Nalebuff and Stiglitz [1983]), the provision and form of interim feedback (Casas-Arce and

Martinez-Jerez [2009], Ederer [2010], Hannan et al. [2008]). Little attention, however, has been

devoted to the fact that the determination of winners and losers in a tournament is often impacted

by subjective elements of performance evaluation (Campbell [2008]).

The general consensus of prior literature addressing subjectivity in incentive contracting is

that a system of performance evaluation that includes both objective metrics and some elements

of subjectivity is superior to systems based on objective measures alone (Baker et al. [1994], Gibbs

et al. [2004]). Objective performance metrics, albeit informative of workers’ effort and therefore

useful for incentive contracting (Holmstrom [1979]), are imperfect to the extent that they lack

sensitivity or precision (Banker and Datar [1989], Feltham and Xie [1994]), that they allow for

gaming (Baker et al. [1994], Hopwood [1972]), and that they provide distorted incentives often

focused excessively on the short term (Baker et al. [1994], Bol [2007], Kaplan and Norton [1992]).

One view is that integrating subjective performance evaluation components yields Pareto

improvements over incentive contracting based on objective performance metrics alone (Baiman

and Rajan [1995]).

Subjective performance evaluations can correct many of the shortcomings of objective

metrics. For example, subjectivity improves incentive contracting by allowing inclusion of

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information that could not be foreseen ex-ante, thereby saving the cost of renegotiating the

contract, and, at the same time, reducing the risk for the manager, thus lowering the cost of the

incentive contract (Baker et al. [1988], Bol [2007]). Additionally, subjectivity can be used to foster

a long term view among employees, and subjective evaluations can help supervisors deal with

interdependencies among subordinates’ performance (Gibbs et al. [2004]). Nonetheless, because

subjectivity is subject to bias, it carries the risk of distorting the incentive system and reducing its

effectiveness altogether (Gibbs et al. [2004], Moers [2005]).

Perceived bias removes or weakens the connection between effort and payoffs, thereby

increasing the risk and reducing the expected value of subordinates’ investment of time and effort

(Aryee, Chen, and Budhwar [2004], Ittner et al. [2003]). Employees may, therefore, become less

motivated and offer lower levels of effort in the future (Moers [2005]).4 Claims of biased

performance evaluation procedures or unfair treatment are more likely when the result of

subjective performance evaluation yields unfavorable outcomes (Cropanzano and Folger [1989],

Matsumura and Shin [2006]).

Our first research question explores whether subjective tournament outcomes (i.e. rewards

and penalties) yield subsequent performance effects that are different from those associated with

objective rankings. In other words, we explore whether workers react to the methodology by which

a tournament outcome is determined in addition to the outcome itself. If workers are motivated

simply by tournament outcomes (i.e. receiving a reward or a penalty), then we should observe

similar reactions, independently from the methodology by which rewards and penalties were

assigned. On the other hand, if workers react also to the procedure by which those outcomes are

4 Prior research also posits that social norms such as reputation and desirability bias of the supervisor limit the deliberate application of favoritism and discrimination, especially in repeated interactions, where the subordinate’s reactions to the subjective assessment might influence performance in multiple future periods (Bol [2007], Prendergast [1999]).

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assigned, then we might observe different ex-post effort choices relative to subjective and

objective allocations of rewards and penalties. To address our first research question we test the

following hypothesis, expressed in null form:

H1: Subjective rewards (penalties) have no incremental effects on performance in the subsequent period compared to rewards (penalties) corresponding to objective performance rankings alone.

We do not formalize a directional expectation for H1 for the following reasons. If

integrating subjective evaluations yields improvements in the effectiveness of an incentive contract

based on objective evaluations (Baiman and Rajan [1995]), then we should observe superior

subsequent performance associated with subjective tournament outcomes compared to outcomes

determined uniquely on the basis of objective performance evaluations. On the other hand, if

subjective allocations of rewards and penalties are perceived to be biased, workers might reduce

effort in an attempt to reduce costs in presence of increased risk (Gibbs et al. [2004], McLeod

[2003], Prendergast and Topel [1993]). In this case, performance subsequent to receiving a reward

or penalty assigned subjectively should be lower, all else equal, than performance subsequent to

objectively determined awards. Additionally, because individuals do not experience gains and

losses as symmetric changes in utility (Kahneman and Tverski [1979], Thaler [1980]), reactions

to tournament outcomes might also differ with respect to the type of outcome – that is, reactions

to rewards might differ from reactions to penalties.

Prior research has explored the influence of wins and losses on effort choices in tournament

settings, albeit without finding a consensus. Muller and Schotter [2009] find that high ability

workers ranking in leading positions work even harder for fear of not winning the reward, while

low ability workers give up and exert little to no effort. Casas-Arce and Martinez-Jerez [2009],

instead, find that contestants that receive interim feedback signaling their leading position in a

multi-period tournament tend to become complacent and reduce their subsequent effort, while

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contestants ranked at the bottom of the interim rankings give up, but only if the gap between their

position and the winning levels of performance becomes too large. Berger et al. [2013] analyze

repeated tournaments and find that winners’ complacency is observed immediately after the prize

is awarded, while employees that did not receive the reward tend to give up in the medium term

and only after having attempted a change in strategy. In addition to reaching different conclusions

with respect to the reactions of winners and losers, none of the aforementioned studies take into

consideration the effect of subjectivity, or account for the effect of penalties (i.e. in those studies

contestants ranked at the bottom do not receive any reward, but are also not inflicted any penalty).

Our study begins to fill this gap.

Recipients of subjective rewards (penalties) might interpret them as favorable

(unfavorable) treatment. Economists and social psychologists have theorized and shown

empirically that reciprocal behavior plays a role in many important economic domains

(Malmendier, te Velde, and Weber [2014]), including labor exchanges (Akerlof [1982], Akerlof

[1984]). Reciprocity theory predicts that workers receiving favorable treatment will respond with

greater effort than contractually required, while those subject to unfavorable treatment will exhibit

undesired behaviors, ranging from lower than expected effort to retaliatory actions that may

damage the profitability of the firm (Falk and Fischbacher [2006], Fehr and Schmidt [1995],

Krueger and Mas [2009]). If subjectivity is perceived as bias and workers experience subjective

rewards as a “gift” and subjective penalties as “injustice”, then we will observe positive reactions

(i.e. increases in subsequent effort and performance) to the former and negative ones to the latter,

as workers attempt to rebalance the economic exchange with their organization (Akerlof [1984],

Falk and Fischbacher [2006]).

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In addition to workers reactions to receiving a subjective reward or penalty, we are also

interested in studying potential spillover effects that might impact other workers participating in

the tournament. While prior research has highlighted the general effects of subjectivity in

performance evaluations (Bol [2007], Campbell [2008], Gibbs et al. [2004], Moers [2005]), we

focus our attention on workers for whom the application of subjectivity has the most impact. That

is, in addition to workers that did receive subjective rewards and penalties, we study the reactions

of workers that would have received the reward or penalty in absence of subjective overrides of

objective rankings.

Tournaments restrict the number of rewards available and, in case of incentive contracts

including both rewards and penalties, force to identify a number of contestants that will suffer a

penalty. The combination of the forced rankings and the predetermination of prizes and penalties

(Prendergast [1999]) gives rise to a peculiar feature of tournament-based incentives. Subjective

performance evaluations assign explicit rewards (penalties) to workers that are not ranked at the

top (bottom) of objective rankings. Consequently, other employees receive an implicit penalty

(reward) by being ranked at the top (bottom) of the objective rankings but failing to receive (suffer)

the reward (penalty) due to the subjective override. Explicit subjective rewards (penalties)

correspond to bonuses (pay-cuts) actually assigned based on subjective evaluations, whereas

implicit rewards (penalties) are only defined in terms of opportunity cost (missing out on a reward

or avoiding a penalty).5 Figure 1 summarizes the framework and the definitions.

----- Insert Figure 1 about here -----

Koszegi and Rabin [2006] posit that individuals measure gains and losses as favorable or

unfavorable deviations from a reference point, which corresponds to their rational expectations

5 In the remainder of the paper we refer to explicit subjective rewards and penalties as subjective rewards and penalties.

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held in recent past about outcomes and the utility associated with such outcomes. That is, when a

person is rationally expecting to experience a positive (negative) event, if that event does not

materialize it might feel like a loss (gain). On the one hand, objective rankings can give rise to

rational expectations of receiving rewards or penalties. On the other hand, workers could embed

in their rational expectations the uncertainty related to management subjective considerations in

deciding the ultimate awardees of rewards and penalties, thereby assigning little to no weight to

the objective rankings. Whether tournament contestants experience implicit rewards and penalties

as gains and losses, which then exert influence on subsequent effort and performance, is an open

empirical question. If they do, we expect to observe similar performance effects associated with

both subjective and implicit rewards and penalties. If, instead, workers form rational expectations

accounting for both objective and subjective management considerations, it is possible that implicit

rewards and penalties have no material influence on subsequent effort choices. To resolve this

tension, we formulate the following hypothesis in null form:

H2: Implicit rewards (penalties) have no effect on subsequent performance.

Finally, conditional on finding evidence that implicit reward and penalties influence

subsequent choices of effort and performance, we study the relative magnitude of these effects.

Understanding the net effect of explicit and implicit rewards and penalties will provide important

insights into the overall effects of subjectivity in tournament incentive systems. For every

subjective reward (penalty), we can identify subjects experiencing a corresponding implicit

penalty (reward). While subjective rewards and penalties correspond to actual changes in monetary

wealth (i.e. bonus checks or pay-cuts), the associated implicit penalties and rewards are defined in

terms of opportunity cost.

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Standard economic theory predicts that gains or losses generate consistent changes in

utility independently from being defined in terms of opportunity cost or actual changes in monetary

wealth (Thaler [1980]). However, empirical observations of consumer behavior led to the

formalization of the endowment effect, by which opportunity costs payoffs are underweighted

compared to out-of-pocket payoffs (Kahneman et al. [1990], Thaler [1980]). On this basis, we

would predict that the effect of subjective rewards and penalties dominates the effect of implicit

ones. However, the influence of subjectivity on the reaction to gains and losses and their actual

versus opportunity cost nature has not been fully explored. It is plausible that the perception of

bias and/or procedural injustice associated with the subjective determination of tournament

outcomes might alter the relation documented insofar by the literature. We formulate the following

hypothesis in null form:

H3: The magnitude of performance effects related to explicit subjective rewards (penalties) is not significantly different from the corresponding performance effects of implicit penalties (rewards).

The next section describes the empirical settings of our study, which exhibits features that

are very favorable to empirically test the hypotheses formulated above.

III. EMPIRICAL SETTINGS

We use field data obtained from a Chinese manufacturing firm that operates a “carrot and stick”

system to incentivize performance of its 11 departments. In each month of production, the

members of the department with highest performance receive a monetary bonus (“carrot”), while

the members of the department performing the worst are penalized with deductions from their pay

(“stick”). Top executives in the firm make the reward/penalty decision based on two criteria: (1) a

monthly department ranking based on a scorecard that aggregates multiple dimensions of

performance (objective component), and (2) executives’ discretion (subjective component).

Interviews of top executives reveal that their subjective considerations generally include

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assessments of overall attitude and employee morale, and account for uncontrollable factors

impacting objective performance. However, there are no company guidelines on what these

considerations should be and the rationale behind them is not recorded or disclosed. Thus,

employees might experience the subjective component of the incentive system as a source of

uncertainty in the mapping between effort and expected outcomes. Monetary rewards and penalties

are fixed equivalent amounts, corresponding to about 12% of the monthly salary.

At the beginning of each fiscal year, top corporate executives set quantifiable monthly

targets and weights relative to every dimension of objective performance included in the scorecard

for all departments.6 Monthly goals are set for each of the 12 months and are not renegotiated until

the next annual target setting cycle. Department goals are assigned considering their different

activities, interdependencies, and contribution to the overall performance of the firm. While

monthly goals are department-specific, management believes that they are equally attainable by

each department. In other words, the goal setting process corresponds to the handicap mechanisms

invoked by Lazear and Rosen [1981], Dye [1984], and Nalebuff and Stiglitz [1983] to ensure

fairness in the tournament process. Departments receive monthly scores based on their

achievements relative to assigned goals. Departments meeting target expectations on every

performance dimension earn 100 points, however departments can score greater amounts of points

when they exceed their targets. Departments are then ranked from best to worst based on their

aggregate performance score, and the ranking is publicly disclosed within the firm.

Rewards and penalties are assigned at the end of each month of production. There is no

carry-over of performance between tournaments. That is, performance evaluations in each month

take into account exclusively the results achieved by each department in that month, with no

6 Each department is assigned multiple monthly goals relative to financial and nonfinancial aspects of performance, as well as goals related to process improvement and human resources development.

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consideration of prior performance. For the most part, department teams are fixed across

tournaments and each team continues to perform the same activities throughout our sample period.

In addition to the objective performance scores, executives can use subjective criteria to choose

departments to reward and penalize, and these choices (but not the criteria applied) are made public

as well. Employees may therefore observe misalignment between the quantitative ranking and the

ultimate reward (penalty) receivers, in cases when the subjective evaluation overrides the objective

performance ranking.

IV. RESEARCH DESIGN

Our first hypothesis, expressed in null form, predicts that subjectivity generates no

additional influence on subsequent performance compared to rewards and penalties corresponding

uniquely to objective rankings.7 In order to disentangle the effects on performance driven by the

reward (penalty) from the effects of their subjective versus objective nature, we specify the

following model:

∆𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖,𝑡𝑡 = 𝛼𝛼 + 𝛽𝛽1𝑅𝑅𝑃𝑃𝑅𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑖𝑖,(𝑡𝑡−1) + 𝛽𝛽2𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝑃𝑃𝑅𝑅𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆𝑆𝑆(𝑡𝑡−1) + 𝛽𝛽3𝑅𝑅𝑃𝑃𝑅𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑖𝑖,(𝑡𝑡−1) ∗ 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝑃𝑃𝑅𝑅𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆𝑆𝑆(𝑡𝑡−1)+ 𝛽𝛽4𝑃𝑃𝑃𝑃𝑆𝑆𝑅𝑅𝑃𝑃𝑆𝑆𝑃𝑃𝑖𝑖,(𝑡𝑡−1) + 𝛽𝛽5𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆𝑆𝑆(𝑡𝑡−1) + 𝛽𝛽6𝑃𝑃𝑃𝑃𝑆𝑆𝑅𝑅𝑃𝑃𝑆𝑆𝑃𝑃𝑖𝑖,(𝑡𝑡−1) ∗ 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆𝑆𝑆(𝑡𝑡−1)+ 𝛽𝛽7𝐵𝐵𝑆𝑆𝐵𝐵𝑃𝑃𝐵𝐵𝑃𝑃𝑆𝑆𝑆𝑆ℎ,𝑡𝑡 + 𝛽𝛽8𝑁𝑁𝑆𝑆𝑁𝑁𝑁𝑁𝑃𝑃𝑖𝑖,𝑡𝑡 + 𝛽𝛽9𝐹𝐹𝑃𝑃𝑃𝑃𝑆𝑆𝑖𝑖,𝑡𝑡 + 𝛽𝛽10𝐴𝐴𝐴𝐴𝑃𝑃𝐴𝐴𝑃𝑃𝐵𝐵𝐵𝐵30𝑖𝑖,𝑡𝑡 +𝛽𝛽11𝛥𝛥𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖,(𝑡𝑡−1) + 𝜀𝜀 (1) where Rewardi,(t-1) is an indicator variable assuming the value of 1 if department i received a reward

in month (t-1), and zero otherwise; SubjRewEvent(t-1) is an indicator variable assuming the value

of 1 if awardees of rewards in month (t-1) were determined by a subjective override of the objective

performance rankings, and zero otherwise; Penaltyi,(t-1) is an indicator variable assuming the value

of 1 if department i received a penalty in month (t-1), and zero otherwise; SubjPenEvent(t-1) is an

7 In all cases where the reward (penalty) is assigned to the top (bottom) ranked department in the objective rankings, we assume that there is no subjective override. It is of course possible that in those cases the outcomes of subjective and objective evaluations coincide. However, in these cases subjectivity would not be apparent to the workers.

17

indicator variable assuming the value of 1 if recipients of penalties in month (t-1) were determined

by a subjective override of the objective performance rankings, and zero otherwise; BusyMontht is

an indicator variable assuming the value of 1 if month t is considered to be a month of high

production, and zero otherwise;8 NEmpli,t represents the number of employees working in

department i in month t; FPcti,t is the percentage of female employees working in department i in

month t; AgeLess30i,t is the percentage of employees younger than 30 years of age working in

department i in month t. We control for possible pre-existing performance trends by including the

lagged change in performance observed in the previous month (ΔPerfScore(t-1)). Table 1 contains

a description of all variables of interest for this study.

----- Insert Table 1 about here -----

The interaction term between reward (penalty) and subjective reward (penalty) event captures the

incremental effect of subjective rewards (penalties) over objective rewards (penalties). Estimations

yielding a significant coefficient 𝛽𝛽3 and/or 𝛽𝛽6 would allow us to reject the null hypothesis

formalized with H1. Additionally, the event variables allow us to explore the main effects of

observed subjectivity on the general population of employees that were not directly awarded a

reward or penalty, and verify whether subjectivity might have a demotivating effect on general

performance due to its interpretation as bias.

Next, we test whether contestants experience implicit and subjective rewards and penalties

in similar ways (H2). Estimating the following model allows us to do so:

∆𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖,𝑡𝑡 = 𝛼𝛼 + 𝛽𝛽1𝐼𝐼𝑁𝑁𝑁𝑁𝑃𝑃𝑅𝑅𝑃𝑃𝑅𝑅𝑖𝑖,(𝑡𝑡−1) + 𝛽𝛽2𝐼𝐼𝑁𝑁𝑁𝑁𝑃𝑃𝑃𝑃𝑃𝑃𝑆𝑆𝑖𝑖,(𝑡𝑡−1) + 𝛽𝛽3𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝑃𝑃𝑅𝑅𝑖𝑖,(𝑡𝑡−1) + 𝛽𝛽4𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃𝑃𝑃𝑆𝑆𝑖𝑖,(𝑡𝑡−1) +𝛽𝛽5𝑅𝑅𝑃𝑃𝑅𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑖𝑖,(𝑡𝑡−1) + 𝛽𝛽6𝑃𝑃𝑃𝑃𝑆𝑆𝑅𝑅𝑃𝑃𝑆𝑆𝑃𝑃𝑖𝑖,(𝑡𝑡−1) + 𝛽𝛽7𝐵𝐵𝑆𝑆𝐵𝐵𝑃𝑃𝐵𝐵𝑃𝑃𝑆𝑆𝑆𝑆ℎ𝑡𝑡 + 𝛽𝛽8𝑁𝑁𝑆𝑆𝑁𝑁𝑁𝑁𝑃𝑃𝑖𝑖,𝑡𝑡 + 𝛽𝛽9𝐹𝐹𝑃𝑃𝑃𝑃𝑆𝑆𝑖𝑖,𝑡𝑡 +𝛽𝛽10𝐴𝐴𝐴𝐴𝑃𝑃𝐴𝐴𝑃𝑃𝐵𝐵𝐵𝐵30𝑖𝑖,𝑡𝑡 + 𝛽𝛽11𝛥𝛥𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖,(𝑡𝑡−1) + 𝜀𝜀 (2)

8 The factory experiences seasonal volumes of demand with peaks of orders concentrated in specific months of the year.

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where ImplPeni,(t-1) is an indicator variable assuming the value of 1 if department i in month (t-1)

was ranked at the top of the objective performance ranking, but did not receive the reward due to

subjective considerations, and zero otherwise; ImplRewi,(t-1) is an indicator variable assuming the

value of 1 if department i in month (t-1) was ranked at the bottom of the objective performance

ranking, but did not receive the penalty due to subjective considerations, and zero otherwise. All

other variables are defined as previously described.

Model (2) allows us also to test our additional hypothesis with respect to the relative

magnitude of these effects (H3), by comparing the coefficients estimated respectively for

SubjRewi,(t-1) and ImplPeni,(t-1), and those estimated for SubjPeni,(t-1) and ImplRewi,(t-1). We report

the estimation results and our inferences in the next section. Supplemental analyses are presented

in section IV.

V. RESULTS OF HYPOTHESES TESTING

Our sample includes 25 monthly observations for each of the 11 departments of the firm. Table 2

reports the descriptive statistics. Our main dependent variable is the change in performance score

(ΔPerfScorei,t), calculated as the difference in PerfScore between time t and time (t-1). Although

the total possible number of performance points assigned at the time of target setting is 100 points

for each department, departments that exceed expectations can obtain a score greater than 100.

Departments receive a reward (penalty) on average 2.182 (2.727) times out of 25 months. . On

average, we observe that rewards and penalties are assigned subjectively about half of the times in

our sample period. In 5 out of the 25 months, where we do not observe any explicit reward (either

subjective or otherwise), while penalties are observed in each month. Subjective rewards

(penalties) are assigned in 12 (13) out of 25 months. While in the vast majority of cases, one

department per month receives the reward and one receives the penalty, in four instances during

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our sample period rewards were assigned subjectively to more than one department in the same

month (that is, both the department ranked first based on objective evaluation and another

department received a reward), and in five instances subjective penalties were assigned to more

than one department in the same month (that is, both the department ranked last based on objective

evaluations and another department were inflicted a penalty).


Correlation coefficients among our variables of interest reported in Table 3 indicate a

strong likelihood of a reward (penalty) being assigned based on subjective performance evaluation

(ρ = 0.691, p< 0.01 for rewards, and ρ = 0.637, p< 0.01 for penalties). Additionally, departments

with a high percentage of female employees tend to exhibit low performance scores (ρ = -0.154,

p< 0.05) and, consistently, high likelihood of being penalized (ρ = 0.149, p< 0.05). Departments

with a high percentage of young employees (AgeLess30) are also likely to perform at a lower level

(ρ = -0.142, p< 0.05) but are also likely to receive implicit rewards by not being penalized when

they rank last (ρ = 0.157, p< 0.01), probably due to managers’ consideration of young workers

having lower expertise and being in the steeper portion of their learning curve.


To explore whether workers react to subjective and objective rewards and penalties in the

same way (H1), we estimate model (1) using OLS regression with robust standard errors, clustered

at the department level, and include department fixed effects.9 The estimated coefficients are

reported in Table 4. We control for potential pre-existing trend effects by including the lagged

change in performance scores. We first estimate the model separately for rewards and penalties.

9 Panel data analyses often raise concerns associated with incidental parameter problems, which could bias the estimation of statistical models using OLS. The incidental parameter problem is typical of panels with large n and small t (respectively, large number of subjects and small number of periods) In our case, however, t is more than double n, thus reducing the incidental parameter concern to negligible levels (Nickell [1981]).

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Table 4, column (A) shows that subjectivity applied to the determination of a reward generates a

positive incremental performance response (β3 = 28.46, p<0.05) that more than counterbalances

the negative performance reaction observed in association with objectively determined rewards

(β1 = -15.78, p<0.10). The estimation of model (1) with respect to penalties alone (Table 4, column

(B)) shows that subjective penalties drive an incremental negative response (β6 = -11.28, p<0.05)

compared to objective penalties. These results remain consistent in the full estimation of the model

(Table 4, column (C)). Wald tests comparing the magnitude of the estimated coefficients in the

full model confirm that the incremental effect of subjectivity is larger, in absolute value, than the

effect of objectively determined rewards and penalties (p<0.01 for rewards and p<0.05 for

penalties). Interestingly, in this specification, we find that workers respond to objectively

determined rewards with a decrease in subsequent performance (β1 = -15.912 p<0.10), consistent

with prior findings with respect to complacency of the winners (Berger et al. [2013], Casas-Arce

and Martinez-Jerez [2009]), but we do not observe a significant reaction to penalties corresponding

to objective rankings. Taken together, our results reject H1 and indicate that employees respond

not only to receiving a reward or a penalty, but also to the procedure by which those awards are

determined. Our results provide evidence consistent with the predictions of reciprocity theory, in

that employees respond positively to subjective favorable treatment (subjective rewards) and

negatively to unfavorable treatment (subjective penalty).

Importantly, model (1) includes variables representing the main effect of subjectivity on

overall performance (SubjRewEvent(t-1) and SubjPenEvent(t-1)). Specifically, it is possible that

simply observing subjectivity in the determination of rewards and penalties might drive subsequent

performance changes independently from being directly impacted by it. That is, in line with the

concerns expressed by Moers [2005] and Ittner et al. [2003], subjective performance evaluations

21

might drive widespread lower effort if workers perceive subjectivity to be a signal of bias. Based

on the insignificance of the coefficients relative to SubjRewEvent and SubjPenEvent, we conclude

that this is likely not the case in our settings, and that the responses documented by our statistical

tests support our interpretation of reciprocal reactions to the subjective assignment of rewards and

penalties.


Our second hypothesis explores how employees might experience implicit rewards and

penalties. Table 5 summarizes the results of our estimation of model (2). Similarly to our tests for

H1, we estimate our model using OLS with standard errors clustered by department and include

department fixed effects. Coefficients estimated in our comprehensive specification are reported

in Colum (C). We document positive (negative) reactions associated with implicit rewards

(penalties) (β1 = 10.75, p<0.05; β2 = -12.58, p<0.05). Our tests reject the null hypothesis expressed

with H2, and show that in presence of subjective overrides of objective performance rankings,

workers respond to implicit rewards (penalties) with subsequent performance changes that have

the same sign as the reactions associated with subjective rewards (penalties) documented above.

That is, in line with the theoretical predictions of referent-dependent preferences, workers

experience implicit rewards and penalties as deviations from their rational expectations based on

objective rankings, and therefore interpret such deviations as gains and losses respectively, despite

knowing that the determination of the ultimate awards involves an element of subjectivity.

We then compare the magnitude of the effects of subjective and implicit rewards and

penalties to test H3. Based on the results of Wald tests reported at the bottom of Table 5 (p>0.10),

we conclude that the effects on subsequent performance associated with an implicit penalty

(reward) offset those generated by a corresponding subjective reward (penalty), with a net effect

22

that is not distinguishable from zero. This result fails to reject the null hypotheses described in H3

and points to some interesting tradeoffs that have not previously been explored in the literature.

Managers implementing subjective performance evaluations in tournament systems need to

consider these additional effects stemming from the introduction of implicit rewards and penalties.

Interestingly, our results are in contrast with the predictions of the endowment effect, as we

document that rewards and penalties defined in terms of opportunity cost appear to be drive similar

responses as do rewards and penalties impacting the workers monetary wealth. We conjecture that

the presence of subjectivity in the determination of rewards and penalties might be a driver of this

unexpected result. Additionally, while the endowment effect is formulated at the individual level,

our unit of analysis is the department, which could introduce group dynamics that might influence

our results.


All our results are robust to the influence of outliers. We have repeated all our tests winsorizing

the dependent variables at the 1st an 99th, 5th and 95th, and at the 10th and 90th percentile in each

month and found results (untabulated) that are consistent with those reported in this manuscript.

VI. SUPPLEMENTAL ANALYSES

VI.I: Extent of subjective override

Casas-Arce and Martinez-Jerez [2009] find that contestants tend to give up when they are not in a

winning position and the gap between their level of performance and that associated with likely

winners becomes too wide. Berger et al. [2013], on the other hand, find that contestants are more

likely to give up if they fall just outside the range of performance scores that would qualify them

for a reward. These conflicting findings suggest that the distance to winning or losing positions in

tournaments might be an important driver of subsequent behavior. We therefore analyze the impact

23

of subjectivity on subsequent performance by exploring the influence of the “magnitude” of the

subjective ex-post correction (e.g. a subjective adjustment to assign a reward to a department who

is only 5 points away from the top-ranked department is smaller than the one applied to reward a

department whose score is 20 points lower).

In our settings, the firm publicly discloses the objective performance scores and rankings

of all departments, as well as the identity of the departments assigned rewards and penalties. In

addition to allowing employees to observe whether or not there was a subjective override of the

objective performance ranking, this disclosure provides information as to the difference in

performance points between the top (bottom) ranked department and the department ultimately

awarded the reward (penalty).

On the one hand, a reciprocal response to favorable or unfavorable treatment should be

amplified by the magnitude of the subjective adjustment to the objective performance ranking.

That is, rebalancing the economic exchange between workers and organization might require a

larger effort adjustment depending on the “size” of the gift or injustice. On the other hand,

however, it is possible that employees whose performance is far from the top performers might

not believe it to be possible for them to perform at the highest level, and, therefore, they might not

increase their effort in subsequent periods (Becker and Huselid [1992], Casas-Arce and Martinez-

Jerez [2009], Prendergast and Topel [1993]). Workers that are closer to the scores of top-ranking

departments might be in a better position to improve their performance, and provide an ex-post

justification for their subjective award (Berger et al. [2013]). At the other end of the continuum,

workers that are penalized despite a larger spread between their score and that of the bottom ranked

department might perceive a greater disconnect between their effort and the reward/penalty system

and limit their future investment in effort (Aryee et al. [2004]).

24

We test the effect of the magnitude of the subjective adjustment on the intensity of the

performance response to subjective rewards and penalties by estimating model (1) on two

partitions of the original sample. First we create the variable SubjDisti,t as follows:

𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝑆𝑆𝑖𝑖,𝑡𝑡 = �𝐵𝐵𝑅𝑅𝑀𝑀𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡 − 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖,𝑡𝑡 𝑆𝑆𝑃𝑃 𝑆𝑆𝑃𝑃𝑁𝑁𝑆𝑆 𝑆𝑆 𝑆𝑆𝐵𝐵 𝑅𝑅𝑅𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃𝑅𝑅 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃 𝑅𝑅𝑃𝑃𝑅𝑅𝑅𝑅𝑃𝑃𝑅𝑅 𝑆𝑆𝑆𝑆 𝑆𝑆𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖,𝑡𝑡 − 𝐵𝐵𝑆𝑆𝑆𝑆𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡 𝑆𝑆𝑃𝑃 𝑆𝑆𝑃𝑃𝑁𝑁𝑆𝑆 𝑆𝑆 𝑆𝑆𝐵𝐵 𝑅𝑅𝑅𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃𝑅𝑅 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑃𝑃 𝑃𝑃𝑃𝑃𝑆𝑆𝑅𝑅𝑃𝑃𝑆𝑆𝑃𝑃 𝑆𝑆𝑆𝑆 𝑆𝑆

Where MaxScoret and MinScoret are, respectively, the performance scores of the top and bottom

ranked departments in month t. Then we classify observations that have values of SubjDist greater

than the median as long subjective distance, and those that have values of SubjDist below the

median as short subjective distance. We then create two subsets of our original sample by

respectively dropping observations with long subjective distance (Short Subjective Distance

Sample) and dropping observations with short subjective distance (Long Subjective Distance

Sample), and maintaining the remaining observations intact, in order to have consistent control

groups. Results of our estimations are reported in Table 6.

We find that the positive reaction to subjective rewards is driven by cases in which the

subjective adjustment is smaller (β3 = 38.07, p<0.05 for the short subjective distance sample), in

line with prior literature documenting performance improvements only for workers for whom

effort increases would make a significant difference in outcomes (Berger et al. [2013]). On the

other hand, the effect of subjective penalties is consistent with pooled sample results only in the

long subjective distance sample (β6 = -16.06, p<0.05). This result further supports our inference

about reciprocity being the underlying mechanism driving the reaction to subjective penalties, as

a longer subjective distance in the awarding of subjective penalties is likely to be interpreted as

greater organizational injustice and therefore drive greater resentment, which in turns will reduce

effort for employees seeking greater redress (Matsumura and Shin [2006]).


25

IV.II: Persistence of performance effects

Berger et al. [2013] find that there are temporal differences in the emergence of post-tournament

effects. In particular, they find that complacency is observed immediately after the award of a

prize, while giving up is observed with a delay, and only after the loser attempts a change in

strategy. In similar fashion, we examine the lagged effects of subjective and implicit rewards in

repeated tournament. We explore the timing of performance effects associated with subjective and

implicit rewards and penalties, and whether performance responses associated with subjectivity

are limited to short term reactions or persist for multiple periods. We estimate model (2) including

a second lag for the variables SubjPen, SubjRew, ImplPen, and ImplRew. Results are reported in

Table 7.10

The full estimation is reported in Table 7, Column (C). We find that the effects of subjective

rewards and penalties are temporary and tend to reverse in the subsequent period. In particular, a

department receiving a subjective reward in a certain month is likely to improve performance in

the subsequent month (β1 = 15.70, p<0.01), but exhibit no further performance change in the month

after that. With respect to penalties, instead, workers receiving subjective penalties decrease

performance in the following month (β3 = -8.63, p<0.01), but then exhibit an equivalent

improvement in the month after that (β4 = 8.03, p<0.05). That is, the effects of subjective penalties

fully reverse in the second period after the infliction of the penalty, while there are no incremental

effects beyond the short term with respect to subjective rewards.

Interestingly, however, we find that the effects of implicit rewards and penalties persist beyond

the month following the experience. In fact, our estimations reported in Column C of Table 7 show

that workers experiencing an implicit reward will improve performance both in the following

10 Perusal of our data does not indicate serial correlation between receiving awards or penalties at the department level.

26

month (β5 = 9.42, p<0.05), and in the month after that (β6 = 16.23, p<0.05). Similarly, the

performance response of workers experiencing an implicit penalty persists two months after the

experience (β8 = -8.35, p<0.10). Surprisingly, in this specification we don’t find a significant

negative response to implicit penalties in the subsequent month, however we caveat our findings

with the possibility that the full specification of the model might be suffering from low statistical

power.11


VI.III: Implicit Rewards and Penalties and Rank-First/Rank-Last Effects

It is possible that the relationship between implicit rewards (penalties) and subsequent

performance reactions might be confounded by the effect of being ranked at the bottom (top) of

the objective rankings. Workers ranked at the top of objective rankings might decrease

performance in the subsequent period for reasons other than receiving a reward or experiencing an

implicit penalty. Top-ranked workers might become overconfident in their abilities and reduce

effort. Alternatively, top ranking performance might be facilitated by stochastic events that are not

likely to repeat in the next periods. Finally, maintaining high levels of performance over extended

periods of time might be difficult. At the other end of the spectrum, being ranked at the bottom

might suffice to trigger social comparison mechanisms (Fredrickson [1992]), which in turn might

lead to performance improvements to preserve reputation. Bottom ranking might also represent

meaningful information for the workers about future likelihood of receiving a penalty if their

performance does not improve. Therefore, performance improvements might be driven by being

11 The estimation of model (2) limited to subjective rewards and penalties (Column A, Table 7) and limited to implicit rewards and penalties (Column B, Table 7) shows that performance effects of subjective rewards and penalties are consistent with prior analyses with respect to the short term reactions.

27

ranked last independently from receiving a penalty or an implicit reward. To rule out these

alternative explanations, we define and test the following model:

∆𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖,𝑡𝑡 = 𝛼𝛼 + 𝛽𝛽1𝑅𝑅𝑅𝑅𝑆𝑆𝑅𝑅𝐴𝐴𝑅𝑅𝐵𝐵𝑆𝑆𝑖𝑖,(𝑡𝑡−1) + 𝛽𝛽2𝑅𝑅𝑅𝑅𝑆𝑆𝑅𝑅𝐴𝐴𝑅𝑅𝐵𝐵𝑆𝑆 ∗ 𝐼𝐼𝑁𝑁𝑁𝑁𝑃𝑃𝑅𝑅𝑃𝑃𝑅𝑅𝑖𝑖,(𝑡𝑡−1) + 𝛽𝛽3𝑅𝑅𝑅𝑅𝑆𝑆𝑅𝑅𝐹𝐹𝑆𝑆𝑃𝑃𝐵𝐵𝑆𝑆𝑖𝑖,(𝑡𝑡−1) +𝛽𝛽4𝑅𝑅𝑅𝑅𝑆𝑆𝑅𝑅𝐹𝐹𝑆𝑆𝑃𝑃𝐵𝐵𝑆𝑆 ∗ 𝐼𝐼𝑁𝑁𝑁𝑁𝑃𝑃𝑃𝑃𝑃𝑃𝑆𝑆𝑖𝑖,(𝑡𝑡−1)+𝛽𝛽5𝐵𝐵𝑆𝑆𝐵𝐵𝑃𝑃𝐵𝐵𝑃𝑃𝑆𝑆𝑆𝑆ℎ𝑡𝑡 + 𝛽𝛽6𝑁𝑁𝑆𝑆𝑁𝑁𝑁𝑁𝑃𝑃𝑖𝑖,𝑡𝑡 + 𝛽𝛽7𝐹𝐹𝑃𝑃𝑃𝑃𝑆𝑆𝑖𝑖,𝑡𝑡 +𝛽𝛽8𝐴𝐴𝐴𝐴𝑃𝑃𝐴𝐴𝑃𝑃𝐵𝐵𝐵𝐵30𝑖𝑖,𝑡𝑡 + 𝛽𝛽9𝛥𝛥𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖,(𝑡𝑡−1) + 𝜀𝜀 (3) Estimation results are reported in Table 8. When we examine the effect of implicit rewards

controlling for the rank-last effect, we continue to find a significant incremental effect on

subsequent performance (β2 = 10.43, p<0.01 – Table 8, Column (C)), which confirms our prior

conclusions about the influence of implicit rewards on workers’ choices of effort in subsequent

tournaments. However, when controlling for the effect of being ranked first, we do not find any

additional effect of implicit penalties on subsequent performance. While we cannot conclusively

rule out alternative explanations for the performance effects of implicit penalties, these results

further support our findings with respect to implicit rewards.


VII. CONCLUSIONS

This study explores the consequences of subjectivity on subsequent performance and effort

allocations in a setting where a repeated tournament incentive system involves both rewards and

penalties. Using field data from a Chinese manufacturing company, we study the performance

response to subjective ex-post adjustments of objective performance rankings for the

determination of monthly monetary rewards and penalties. We find that subjective allocations of

tournament payoffs drive different reactions compared to assignment of rewards and penalties

determined by objective performance metrics alone. Additionally, we document how the

tournament structure of the incentive system generates additional implicit effects. That is, when a

reward (penalty) is assigned to a department not ranked at the top (bottom) based on objective

28

performance, such top (bottom) ranked department experiences an implicit penalty (reward). We

distinguish between explicit subjective penalties, which correspond to actual monetary bonuses or

pay-cuts, from implicit rewards and penalties, which are defined only in terms of opportunity cost

(i.e. missing out on a reward or being spared from a penalty). We find that implicit rewards and

penalties have performance effects consistent with those associated with subjective explicit ones.

In particular, we find that the effect of subjective explicit rewards (penalties) and implicit penalties

(rewards) counterbalance each other with an aggregate net effect that is not distinguishable from

zero. Our study is the first to document the effect of implicit rewards and penalties in tournament

settings.

Our results extend prior literature on repeated and dynamic tournaments, and are in line

with the predictions of equity theory and reciprocity, whereby workers that experience a subjective

or implicit reward interpret it as favorable treatment, and in return work even harder in the

following period, while workers experiencing an unfavorable treatment due to subjective or

implicit penalties tend to reduce subsequent effort to seek redress of unfavorable treatment.

Additionally, we find that the response to subjective rewards is predominantly driven by small

subjective adjustments, while the negative response to subjective penalties is stronger if the

subjective adjustment is large. Finally, we find that the effects of subjective rewards and penalties

tend to reverse within the next month, while the reactions to implicit rewards and penalties are

more persistent.

While our field setting is ideal to explore our phenomenon of interest, our study is subject

to the limitations that are common to field studies. In particular, since our study is based on a single

manufacturing organization based in China, the generalizability of our results to different

industries and cultures is limited. Additionally, our findings, especially those relative to implicit

29

rewards and penalties, depend on contestants having sufficient information on their objective

performance to detect the application of subjectivity in the determination of tournament outcomes.

While disclosure of both objective and subjective performance evaluation results is rarely

observed, we posit that our findings apply to any situation in which workers might have at least

some information of what tournament outcomes would have been in absence of subjectivity (e.g.

number of papers published in top journals, number of projects successfully completed, results of

physical tests).

Despite these limitations, our findings contribute to the literature on subjectivity in

incentive contracting by exploring the contemporaneous effects of subjective and implicit rewards

and penalties and providing evidence of the associated trade-offs. We contribute to the practice of

incentive design by documenting offsetting effects of subjective performance evaluations that may

significantly impact the overall effectiveness of incentive systems in organizations.

30

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33

Figure 1: Rewards and Penalties

Panel A: Effects of Subjectivity as Override of Objective Performance Rankings

Panel B: Classifications of Rewards and Penalties

Notes: Figure 1 describes the definitions of rewards and penalties we utilize in this study. Panel A represents an illustration the effect of subjective overrides on the assignment of rewards and penalties, including the generation of implicit rewards and penalties, for a hypothetical group of 6 tournament contestants. Panel B describes the relationship between explicit and implicit rewards, and the classification of explicit rewards into subjective and objective. Rewards and penalties are defined as Explicit when a department is awarded a reward or inflicted a penalty, regardless of the method of determination. When explicit rewards and penalties correspond to the objective performance rankings, we define them to be Objective, while they are Subjective if the assignment of the reward or penalty is determined by a subjective override of the objective performance rankings. Rewards (penalties) are Implicit when, due to subjective evaluations, departments are not assigned a penalty (reward) despite ranking at the bottom (top) of the distribution based on objective performance measurement.

Rewards & Penalties

Explicit

Implicit

Objective

Subjective

34

Table 1: Definition of Variables Included in the Study

Variable Description PerfScorei,t Total performance score by department i in month t Rewardi,t Indicator variable assuming the value of 1 if department i receives an explicit

reward (bonus) in month t, and 0 otherwise. This variable does not distinguish between rewards corresponding to objective rankings or resulting from subjective override of objective rankings.

Penaltyi,t Indicator variable assuming the value of 1 if department i receives an explicit penalty (pay cut) in month t, and 0 otherwise. This variable does not distinguish between rewards corresponding to objective rankings or resulting from subjective override of objective rankings.

SubjRewi,t Indicator variable assuming the value of 1 if department i receives a subjective reward in month t, and 0 otherwise

SubjPeni,t Indicator variable assuming the value of 1 if department i receives a subjective penalty in month t, and 0 otherwise

SubjDisti,t Absolute value of the difference between department i performance score in month t and the top (bottom) score in the same month, if department i is awarded a reward (penalty) subjectively in that month.

ImplRewi,t Indicator variable assuming the value of 1 if department i receives an implicit reward in month t, and 0 otherwise

ImplPeni,t Indicator variable assuming the value of 1 if department i receives an implicit penalty in month t, and 0 otherwise

RankFirsti,t Indicator variable assuming the value of 1 if department i ranks at the top of the objective ranking in month t, and 0 otherwise

RankLasti,t Indicator variable assuming the value of 1 if department i ranks at the bottom of the objective ranking in month t, and 0 otherwise

BusyMontht Indicator variable assuming the value of 1 if month t is considered to be a busy month for production, and 0 otherwise

SubjRewEventt Indicator variable assuming the value of 1 if there is a subjective override to award a reward in month t, and 0 otherwise

SubjPenEventt Indicator variable assuming the value of 1 if there is a subjective override to inflict a penalty in month t and 0 otherwise

N_Rew Number of times department i receives an explicit reward in our sample period N_Pen Number of times department i receives an explicit penalty in our sample period N_Subj_Rew Number of times department i receives a subjective reward in our sample period N_Subj_Pen Number of times department i receives a subjective penalty in our sample period NEmpli,t Number of employees in department i in month t FPcti,t Percentage of female employees in department i in month t AgeLess30i,t Percentage of employees younger than 30 in department i in month t

35

Table 2: Descriptive Statistics

N mean sd min p25 p50 p75 max PerfScore 275 63.479 17.001 23.000 52.000 65.000 75.000 107.000 Reward 275 0.087 0.283 0.000 0.000 0.000 0.000 1.000 Penalty 275 0.109 0.312 0.000 0.000 0.000 0.000 1.000 SubjRew 275 0.044 0.205 0.000 0.000 0.000 0.000 1.000 SubjPen 275 0.047 0.213 0.000 0.000 0.000 0.000 1.000 SubjDist 25 14.360 8.596 1.000 9.000 14.000 20.000 29.000 ImplRew 275 0.029 0.168 0.000 0.000 0.000 0.000 1.000 ImplPen 275 0.047 0.213 0.000 0.000 0.000 0.000 1.000 BusyMonth 275 0.480 0.501 0.000 0.000 0.000 1.000 1.000 NEmpl 275 16.255 14.944 2.000 7.000 10.000 18.000 68.000 FPct 275 0.412 0.274 0.034 0.200 0.333 0.667 1.000 AgeLess30 275 0.377 0.235 0.000 0.222 0.340 0.500 1.000 N_Rew 11 2.182 2.272 0.000 0.000 2.000 3.000 8.000 N_Pen 11 2.727 2.649 0.000 1.000 2.000 5.000 9.000 N_Subj_Rew 11 1.091 0.944 0.000 0.000 1.000 2.000 3.000 N_Subj_Pen 11 1.182 0.982 0.000 0.000 1.000 2.000 3.000

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Table 3: Correlation Matrix

1 2 3 4 5 6 7 8 9 10 11 1. PerfScore 1.0000

2. Reward 0.3432*** 1.0000

3. Penalty -0.4127*** -0.1082* 1.0000

4. SubjRew 0.1392** 0.6908*** -0.0747 1.0000

5. SubjPen -0.1436** -0.0689 0.6366*** -0.0476 1.0000

6. ImplRew -0.3020*** -0.0535 -0.0606 -0.0370 -0.0386 1.0000

7. ImplPen 0.3198*** -0.0689 -0.0779 -0.0476 -0.0496 -0.0386 1.0000

8. BusyMonth 0.0303 -0.0392 0.0374 -0.0271 -0.0082 -0.0797 0.0261 1.0000

9. NEmpl -0.0306 -0.0847 -0.0560 -0.0550 0.0284 -0.0131 -0.0406 -0.0208 1.0000

10. FPct -0.1537** -0.0508 0.1485** -0.0893 0.0725 0.0776 -0.0435 -0.0131 -0.0307 1.0000

11. AgeLess30 -0.1423** -0.0020 0.0920 0.0136 0.0080 0.1569*** -0.0633 -0.0329 -0.2613*** 0.1866*** 1.0000

Notes: This table reports the Pearson correlation coefficients among all of our variables of interest for the estimation of our statistical models. Two-tail statistical significance of the correlation coefficients is indicated as follows: * = (p<0.10), ** = (p<0.05), *** = (p<0.01).

37

Table 4: Effects of Subjective Rewards and Penalties on Subsequent Performance

(A) (B) (C) ΔPerfScore ΔPerfScore ΔPerfScore

Rewardi,(t-1) b1 -15.778*

-15.912* (-2.01)

(-1.96)

SubjRewEvent(t-1) b2 0.195

0.303 (0.10)

(0.17)

Rewardi,(t-1)*SubjRewEvent(t-1) b3 28.462**

28.143** (2.69)

(2.63)

Penaltyi,(t-1) b4

1.673 1.911 (1.07) (1.20)

SubjPenEventi,(t-1) b5

0.481 -0.142 (-0.26) (-0.06)

Penaltyi,(t-1)*SubjPenEvent(t-1) b6

-11.275** -11.284** (-2.61) (-2.51)

BusyMontht

3.539 3.636 3.202 (1.41) (1.57) (1.32)

NEmpli,t

0.156 0117 0.150 (0.91) (0.62) (0.88)

FPcti,t

8.362 14.292 13.335 (0.265) (1.20) (1.17)

AgeLess30i,t

4.696 2.714 3.330 (0.74) (0.45) (0.53)

ΔPerfScorei,(t-1)

-0.305*** -0.338*** -0.319*** (-10.36) (-6.01) (10.68)

Intercept

-10.451* -10.292** -11.127** (-1.98) (-2.32) (-2.30)

Adj. R-squared 0.155 0.113 0.167 N

253 253 253

Department Fixed Effects

Yes Yes Yes Clustering Department Department Department Test if |b1|=|b3|

14.74

14.45

[0.0033]

[0.0035] Test if |b4|=|b6|

8.51 7.14

[0.0154] [0.0234] Test if |b3|=|b6|

3.92

[0.0759] Notes: Table 4 reports the coefficients estimated for equation (1) considering only rewards (A), only penalties (B) and rewards and penalties combined (C). In all cases estimations are performed using OLS with heteroscedasticity robust standard errors. For each coefficient we reported t-statistics in parentheses. The dependent variable ΔPerfScore, is calculated as PerfScore(t) – PerfScore(t-1). We include department fixed effects and we cluster our standard errors at the department level. Two-tail statistical significance indicated by: * = (p<0.10), ** = (p<0.05), *** = (p<0.01). The bottom row reports the results of Wald tests, where we analyze the statistical significance between the indicated coefficients. The null hypothesis is that the difference between the absolute value of the coefficients is not statistically different than zero. A p-value (reported in brackets) below 0.10 (0.05) [0.01] would allow us to reject the null with confidence at the 90% (95%) [99%], two-tailed.

38

Table 5: Effects of Implicit Rewards and Penalties on Subsequent Performance

(A) (B) (C) ΔPerfScore ΔPerfScore ΔPerfScore

ImplRewi,(t-1) b1 11.466** 10.846*** 10.749** (3.17) (3.39) (2.80)

ImplPeni,(t-1) b2 -12.750** -11.643** -12.578** (-3.01) (-2.64) (-2.83)

SubjRewi,(t-1) b3

15.136*** 23.665** (3.44) (2.55)

SubjPeni,(t-1) b4

-10.780*** -11.169*** (-4.55) (-4.74)

Rewardi,(t-1) b5

-9.277 (-1.49)

Penaltyi,(t-1) b6

0.325 (0.13)

BusyMontht

4.073 3.733 3.756 (1.74) (1.50) (1.53)

NEmplt

0.117 0.148 0.136 (0.57) (0.86) (0.75)

FPctt

4.157 11.967 12.237 (0.37) (1.18) (1.15)

AgeLess30i,t

3.450 3.066 3.043 (0.64) (0.53) (0.53)

ΔPerfScorei,(t-1)

-0.279*** -0.307*** -0.284*** (-4.39) (-5.31) (-5.94)

Intercept

-7.165 -10.785** -10.244** (-1.44) (-2.57) (-2.35)

Adj. R-squared 0.134 0.188 0.194 N

253 253 253

Department Fixed Effects

Yes Yes Yes Clustering Department Department Department Test if |b1|=|b4|

0.00 0.01

[0.9892] [0.9179] Test if |b2|=|b3|

0.23 1.22

[0.6410] [0.2953] Notes: Table 5 reports the coefficients estimated for equation (2). Estimations are performed using OLS with heteroscedasticity robust standard errors. For each coefficient we reported t-statistics in parentheses. The dependent variable ΔPerfScore, is calculated as PerfScore(t) – PerfScore(t-1). We include department fixed effects and we cluster our standard errors at the department level. Two-tail statistical significance indicated by: * = (p<0.10), ** = (p<0.05), *** = (p<0.01). The bottom row reports the results of Wald tests, where we analyze the statistical significance between the indicated coefficients. The null hypothesis is that the difference between the absolute value of the coefficients is not statistically different than zero. A p-value (reported in brackets) below 0.10 (0.05) [0.01] would allow us to reject the null with confidence at the 90% (95%) [99%], two-tailed.

39

Table 6: Supplemental Analysis: Effects of Subjective Rewards and Penalties on Subsequent Performance by Long and Short Subjective Distance

(A) (B) Test if Long = Short Chi2 (Prob > chi2) Long Subjective

Distance Sample Short Subjective Distance Sample

ΔPerfScore ΔPerfScore Reward(t-1) -11.622* -25.790* 4.43

(-1.37) (-1.73) [0.0352] SubjRewEvent(t-1) -2.995 2.526

(-1.69) (0.92)

Reward(t-1)*SubjRewEvent(t-1) 23.672 38.068** 18.26 (1.73) (2.54) [0.0000]

Penalty(t-1) 4.484 4.243 0.01 (1.63) (1.35) [0.9099]

SubjPenEvent(t-1) 4.333 -4.278

(1.41) (-1.06)

Penalty(t-1)*SubjPenEvent(t-1) -16.060** -3.870 6.98 (-3.01) (-0.67) [0.0082]

BusyMonth 5.189 3.891

(1.68) (1.05)

NEmpl 0.010 0.266 (0.03) (1.41)

FPct 14.605 3.483 (1.04) (0.39)

AgeLess30i,t 4.279 -3.188 (0.48) (-0.39)

ΔPerfScorei,(t-1) -0.325*** -0.289*** (-7.27) (-4.84)

Intercept -11.684 -7.999 (-1.73) (-1.32)

Adj. R-squared 0.180 0.203 N 165 143 Department Fixed Effects Yes Yes Clustering Department Department

Notes: Table 6 reports the coefficients estimated for equation (1) on subsamples constructed by eliminating the observations that had a value of SubjDist shorter than the median value (A) and by eliminating the observations that had a value of SubjDist greater than the median (B). In both cases, we maintained the same control group. Estimations are performed using OLS with heteroscedasticity robust standard errors. For each coefficient we reported t-statistics in parentheses. The dependent variable ΔPerfScore, is calculated as PerfScore(t) – PerfScore(t-1). We include department fixed effects and we cluster our standard errors at the department level. Two-tail statistical significance indicated by: * = (p<0.10), ** = (p<0.05), *** = (p<0.01). The rightmost column reports the results of Chi-Square tests, where we compare the coefficients indicated across the two estimations. The null hypothesis is that the difference between the absolute value of the coefficients is not statistically different than zero. A p-value (reported in brackets) below 0.10 (0.05) [0.01] would allow us to reject the null with confidence at the 90% (95%) [99%], two-tailed.

40

Table 7: Supplemental Analyses: Persistence of the Effects of Subjective and Implicit Rewards and Penalties on Subsequent Performance

(A) (B) (C) "Explicit" Effects of

Subjective Reward/Penalty only

"Implicit" Effects of Subjective

Reward/Penalty only

"Explicit " and "Implicit" Effects of

Subjective Reward/Penalty

ΔPerfScore ΔPerfScore ΔPerfScore SubjRewi,(t-1) 15.909***

15.698***

(3.85)

(3.36) SubjRewi,(t-2) -9.651***

-4.728

(-2.34)

(-1.10) SubjPeni,(t-1) -10.232***

-8.630***

(-4.28)

(-3.79) SubjPeni,(t-2) 8.741**

8.027**

(2.63)

(2.96) ImplRewi,(t-1)

11.135** 9.415**

(2.88) (3.05) ImplRewi,(t-2)

15.714** 16.233**

(2.30) (2.23) ImplPeni,(t-1)

-11.180** -7.515

(-2.38) (-1.18) ImplPeni,(t-2)

-9.542** -8.352* (-2.29) (-2.01)

BusyMontht 3.810 3.854 3.613 (1.55) (1.67) (1.48)

NEmpli,t 0.136 0.138 0.168 (0.80) (0.61) (0.90)

FPcti,t 9.780 2.603 5.567 (0.73) (0.25) (0.53)

AgeLess30i,t 4.941 1.452 1.964 (0.83) (0.26) (0.34)

ΔPerfScorei,(t-1) -0.305*** -0.337*** -0.338*** (-5.48) (-4.71) (-5.03)

Intercept -10.706** -6.123 -8.593* (-2.36) (-1.17) (-1.88)

Adj. R-squared 0.181 0.169 0.228 N 253 253 253 Department Fixed Effects Yes Yes Yes Clustering Department Department Department

Notes: Table 7 reports the coefficients estimated for equation (2) considering only explicit subjective rewards and penalties (A), and explicit and implicit rewards and penalties combined (B). Estimations are performed using OLS with heteroscedasticity robust standard errors. For each coefficient we reported t-statistics in parentheses. The dependent variable ΔPerfScore, is calculated as PerfScore(t) – PerfScore(t-1). We include department fixed effects and we cluster our standard errors at the department level. Two-tail statistical significance indicated by: * = (p<0.10), ** = (p<0.05), *** = (p<0.01).

41

Table 8: Supplemental Analysis: Alternative Explanations for the Effects of Implicit Rewards and Penalties (A) (B) (C)

ΔPerfScore ΔPerfScore ΔPerfScore RankLasti,(t-1) 2.116 1.084

(1.10) (0.32) RankLasti,(t-1)*ImplRewi,(t-1) 9.989*** 10.426***

(4.30) (4.59) RankFirsti,(t-1) -10.703 -10.479

(-1.54) (-1.50) RankFirsti,(t-1)*ImplPeni,(t-1) -3.203 -3.249

(-0.47) (-0.47) BusyMontht 4.133 3.988 4.085

(1.66) (1.80) (1.78) NEmpli,t 0.127 0.100 0.106

(0.72) (0.46) (0.49) FPcti,t 8.370 3.988 4.093

(0.068) (0.31) (0.33) AgeLess30i,t 3.223 4.755 3.629

(0.49) (0.95) (0.64) ΔPerfScorei,(t-1) -0.288*** -0.282*** -0.252***

(-4.78) (-6.76) (-4.53) Intercept -9.7489** -6.422 -6.586

(-2.24) (-1.13) (-1.21) Adj. R-squared 0.107 0.138 0.143 N 253 253 253 Department Fixed Effects Yes Yes Yes Clustering Department Department Department Notes: Table 8 reports the coefficients estimated for equation (3) considering only implicit rewards (A), only implicit penalties (B) and implicit rewards and penalties combined (C). In all cases estimations are performed using OLS with heteroscedasticity robust standard errors. For each coefficient we reported t-statistics in parentheses. The dependent variable ΔPerfScore, is calculated as PerfScore(t) – PerfScore(t-1). We include department fixed effects and we cluster our standard errors at the department level. Two-tail statistical significance indicated by: * = (p<0.10), ** = (p<0.05), *** = (p<0.01).

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