Deception and Incentives How Dishonesty Undermines Effort Provision Part 1

Deception and Incentives How Dishonesty Undermines E¤ort Provision Abstract In this paper we show that subtle forms of deceit undermine the e¤ectiveness of incentives. We design an experiment in which the principal has an interest in underreporting the true performance di¤erence between the agents in a dynamic tournament. According to the standard approach, rational agents should completely disregard the performance feedback of self-interested principals and choose their e¤ort level as if they had not been given any information. However, despite substantial underreporting many principals seem to exhibit lying aversion which renders their feedback informative. Therefore, the agents respond to the feedback but discount it strongly by reducing their e¤ort relative to fully truthful performance feedback. Moreover, previous experiences of being deceived exacerbate the problem and eventually reduce average e¤ort even below the level that prevails in the absence of any feedback. Thus, both no feedback and truthful feedback are better for incentives than biased feedback. 1 Introduction Incentive design intends to shape and enhance workers’performance and rests on some sort of performance appraisal. As the above quote from the famous performance appraisal textbook by Murphy and Cleveland (1995) indicates, superiors often face the temptation to manipulate and bias performance appraisals. In fact, these authors strongly endorse biased performance appraisals and there is evidence that managers indeed provide untruthful performance feedback.1 In this paper we document that biased performance appraisals may thoroughly undermine incentives. We show that even quite subtle forms of deceit can be detrimental for incentives. It is obvious that incentives break down if promised payments are not delivered although the agent performed well. However, here we show that deceitful principals undermine incentives even if they cannot manipulate the payments to the agents, that is, even if the agents are correctly paid according to their output performance. In order to study the impact of deception on incentives we examine behavior in a dynamic tournament. Tournaments are ubiquitious in economic organizations because performance is often rewarded by promoting high-performing employees. Such tournaments are inherently dynamic as during the contest the principal often observes some interim performance measures that she can use to provide feedback to the agents. In these settings the principals often face strong incentives to provide wrong or misleading feedback. Based on a simple two-stage model of a dynamic tournament with two competing agents we show that the agents provide higher e¤ort in the second stage of the tournament if the absolute output di¤erence between the agents after the …rst stage is smaller. Therefore, if the performance di¤erence is not directly observable to the agents a self-interested principal has an incentive to report smaller than actual output 1 Longenecker, Sims and Gioia (1987), for example, interviewed 60 upper-level executive and found evidence of deliberate manipulation of formal performance appraisal ratings by executives. Executives adjusted or manipulated employee ratings in order to accomplish their own goals or agendas, most often in an attempt to increase performance by employees. 2 di¤erences to the agents.2 We examined the prediction that agents’e¤ort after feedback is decreasing in the absolute output di¤erence by conducting a laboratory experiment with truthful information feedback (the Truthful Feedback condition, TF), that is, the agents knew that they received correct feedback information after the …rst stage of the tournament. The actual e¤ort behavior in this treatment is remarkably close to the prediction of the above model. Thus, based on this result, we know that if principals are free to provide false feedback they face an incentive to underreport the actual output di¤erences because this increases the e¤ort of gullible agents. However, rational agents will anticipate the principals’incentive to underreport and, therefore, treat the principals’feedback information as completely uninformative.3 Thus, if agents are rational and the principals’messages are indeed completely uninformative we have a stark prediction: in a condition in which the principals provide feedback, the agents’ e¤ort is identical to a condition in which the agents receive no feedback at all. In other words, the principals’messages are without any consequences on e¤ort. In order to test this prediction we conducted two further treatments: a treatment in which the principals were free to choose the feedback information (the Principal Feedback treatment, PF) and a treatment without any information feedback after the …rst stage (the No Feedback treatment, NF).4 We deliberately chose the parameters of the experiment in such a way that the equilibrium e¤ort in the second stage of the NF treatment is higher than the average e¤ort after feedback in the equilibrium of the TF treatment. This means that if the cheap talk hypothesis holds, the agents in the PF condition should provide a higher average e¤ort after feedback than in the TF condition. In sharp contrast to the cheap talk hypothesis, the feedback by the principals was informative and had a sizeable negative e¤ect on the agents’e¤ort choices. However, as the principals also frequently sent false feedback the agents strongly discounted the principals’messages: when a 2 As employees’performance is often di¢ cult to assess, representing a combination of many “soft”factors such as communication and team leadership performance, innovativeness, initiative and originality, the principal’s assessment of these factors will …nally decide the outcome of the tournament. It is therefore often the case that the principals are better informed about performance and, in particular, performance di¤erences among employees than the employees themselves. In addition, employees may su¤er from self-serving biases in their performance assessment which renders balanced assessments of employee performance by human resource departments even more important. 3 We call this in the following the “cheap talk hypothesis”because in our setting the fact that “talk is cheap” implies that all communication among self-interested players is uninformative. 4 In many organizations with institutionalized performance appraisal systems, e.g. management consulting …rms and investment banks, superiors are required to give subjective and private performance feedback to their workers at regular intervals. While this forces principals to provide some form of performance appraisal, it leaves plenty of discretion for dishonest reporting. We therefore prohibited principals in the PF treatment from not giving any feedback. This feature further allows direct comparison with previous contributions to the experimental strategic communication literature which also require senders to send a message. 3 principal reported an absolute output di¤erence of the agents behaved as if the true output di¤erence was k rather than where k > 1. Therefore, for any given output di¤erence reported by a principal in the PF treatment, the agents provided much less e¤ort compared to the e¤ort level they chose in response to truthfully reported output di¤erences in the TF treatment. This e¤ort response to principals’messages also had implications for average e¤ort levels after feedback. Despite the fact that the agents in the PF treatment face a much higher frequency of small reported output di¤erences their average e¤ort after feedback is eventually even lower than in the TF and the NF treatment because the agents discount the principals’ information quite strongly. One driving force behind these e¤ort patterns is the fact that principals’ messages were not merely cheap talk, that is, they were partially informative. Some principals provided feedback that was close to the truth while others reported consistently much smaller output di¤erences than the actual ones. On average, an increase in the reported output di¤erence by one unit was associated with a true increase in the output di¤erence by two units. Therefore, it was rational for the agents to respond to variations in the reported output di¤erences in the PF condition even more strongly than to variations in truthful output di¤erences in the TF condition. Interestingly, this is exactly what we observe in these conditions. The negative e¤ect of deceitful messages on e¤ort was not limited to the post-feedback stage. Over time the agents’average e¤ort in the PF condition even declines in the pre-feedback stage, indicating a pervasive negative e¤ect of principals’deceitful messages on the overall e¤ort level. This e¤ect seems to be driven by the frequency of deceitful messages that an agent has received: agents who faced a higher frequency of small reported output di¤erences in past interactions were signi…cantly more likely to choose a low e¤ort level even in the pre-feedback period of a tournament. This …nding indicates a more general undermining of incentives through deception because, as we show in the paper, a rational agent’s …rst stage e¤ort should not be a¤ected by the expectation that a principal sends false feedback about the …rst stage output di¤erence. In the …nal part of the paper we show that a model of lying aversion provides a plausible explanation for many key features in our data. This model assumes a heterogeneous population of lying-averse subjects: some subjects are assumed to have higher psychic costs of lying than others. The assumption of heterogeneous lying aversion is supported by previous contributions by Gneezy (2005), Sanchez-Pages & Vorsatz (2007) and Blanes i Vidal (2007) which provide evidence for heterogeneous preferences for truth-telling. Heterogeneity is also supported by our …nding that strongly Machiavellian subjects, that is, subjects with a high degree of sel…shness and opportunism, lie signi…cantly more compared to subjects that score low on the Machiavelli scale. Principals who exhibit some degree of lying aversion are willing to report the truth if the costs of truth-telling are not too large. In our setting the costs of truth-telling arise because 4 principals who report a lower output di¤erence to the agents will on average induce a higher second stage performance in the tournament. Empirically it turns out that if the true output di¤erence is already “small”the bene…ts of reporting an even smaller output di¤erence are small. Thus, for small true output di¤erences a model based on heterogeneous principals predicts a higher frequency of truth-telling, which is indeed the case. Furthermore, the existence of lyingaverse principals makes it rational for the agents to attribute some informative content to the principals’messages while the existence of principals with little or no lying aversion renders it rational to discount the message of a principal partially because the agent in the experiment does not know what principal he faces in a given period. Thus, the partial informativeness of the principals’ messages and the subsequent response of the agents follows directly from heterogeneity in lying aversion and the assumption that agents behave rationally. Finally, heterogeneous lying aversion can also explain why agents who experienced deceitful messages more often, provide lower second stage e¤ort than agents who experience fewer deceitful messages. A plausible reason for this fact is that agents who experience deceitful messages more often have less trust in the principals, that is, they update the probability that they face a deceitful principal. As a consequence, they discount the principals’feedback information more strongly and provide a lower e¤ort for a given reported output di¤erence. We believe that this feature in our data captures an important e¤ect that is also likely to be relevant in real organizations. It is ironic that the negative impact of the PF treatment on e¤ort is based on the fact that some principals also send messages that are correct or close to the truth. If the principals’ messages had been completely unreliable it would have made no sense for the agents to take the principals’messages seriously –not even in a discounted way. In this case it would have been rational to completely disregard principals’ messages and choose the same high second stage e¤ort as in the NF treatment. Thus, we observe here an interesting non-monotonous e¤ect of feedback information on tournament incentives: no information or completely uninformative feedback and fully truthful information is better than partially informative feedback. This …nding may explain a stylized fact from the organizational behavior literature, namely, that performance feedback is often quite uninformative (Meyer, Kay & French (1965), Beer (1987), Gibbs (1991)). In view of the di¢ culty of forcing managers to provide truthful performance feedback to the employees it might be better to provide no or merely uninformative feedback. Our paper is related to the theoretical and experimental literature on the e¢ ciency and e¤ectiveness of dynamic tournament incentives (Lazear & Rosen (1981), Lizzeri, Meyer & Persico (1999), Aoyagi (2004), Ederer (2005), Bull, Schotter & Weigelt (1987), Schotter & Weigelt (1992), Harbring, Irlenbusch, Kräkel & Selten (forthcoming)). However, none of these papers provides an empirical examination of the impact of principals’lying incentives on e¤ort provision in a dynamic tournament. Our paper is also related to the theoretical work of Crawford 5 & Sobel (1982), Crawford (2003), Kartik, Ottaviani & Squintani (2007) and Kartik (2008) on strategic information transmission and experimental work on sender-receiver games where the interests of the sender and the receiver of a message are in con‡ict (e.g., Dickhaut, McCabe & Mukherji (1995), Blume, DeJong, Kim & Sprinkle (1998)). Central aspects of Crawford & Sobel’s theory of information transmission have found strong support in papers such as Cai & Wang (2006), Wang, Spezio & Camerer (2006) and Sanchez-Pages & Vorsatz (2007). One intriguing empirical …nding in these papers concerns overcommunication by the senders, i.e., the fact that the senders’messages are too informative about the true state of the world relative to the equilibrium with rational and self-interested players. Moreover, the work of Sanchez-Pages & Vorsatz (2007) suggests that this overcommunication is at least partly driven by preferences for truth-telling. None of the above papers examines the impact of strategic information transmission on the e¤ectiveness of performance incentives. We are also not aware of any other work that compares agents’e¤ort behavior in situations where they receive no information about the “state of the world”, fully truthful information and information that can be biased because it comes from an interested principal. It is the comparison between these three situations which enables us to identify the extent to which deceitful messages undermine incentives for e¤ort provision. The impact of deception on e¤ort provision is so pervasive that it does not only change the agents’direct e¤ort response to the performance feedback at the second stage of the tournament but it also causes a large decline in …rst stage e¤ort levels, supporting the conclusion that no performance feedback as well as truthful performance feedback is superior to an arrangement where the principal is not constrained to tell the truth. In view of the profound e¤ects of heterogenous preferences for honesty in our setting we believe that contract theory and, more generally, economics could bene…t from taking these preferences into account. There is a large class of economic problems that are characterized by lying incentives and as our results suggest heterogenous preferences for honesty may a¤ect behavior in these situations in important ways.5 5 For example, a used car salesman has an incentive to lie about the quality of the car he is attempting to sell (Akerlof 1970) or a regulated …rm has an incentive to claim high costs in order to receive higher transfer payments (La¤ont & Tirole 1993). In the absence of reputation incentives …nancial brokers will be tempted to recommend stocks or funds that further their own interests but not necessarily the clients’interests (Davis 2004) and tax payers have an incentive to underreport their income. (Allingham & Sandmo 1972). Similarly, in the insurance market the insured parties have incentives to overstate the value of claims to insurance companies. In all these cases, economic models typically assumed that a player lies whenever it is in his or her economic interest to do so. However, the existence of heterogeneous lying aversion may, for example, change the optimal insurance contract because insurance companies may want to induce self-selection of liers and honest people into di¤erent contracts. Likewise, employers may want to screen people for special jobs on the basis of the strength of an employee’s lying aversion. 6 The remainder of the paper is organized as follows. Section 2 proposes a model of the e¤ect of interim information and communication in dynamic tournaments. Section 3 describes the experiment and Section 4 presents the experimental results which we interpret in Section 5. Section 6 concludes. Appendix A contains additional proofs and Appendix B proposes a simple model of lying aversion. Appendix C shows that alternative social preference theories cannot explain the experimental results. 2 A Simple Model of Dynamic Tournaments In this section we present a model of dynamic tournaments when there is no feedback (NF), when feedback is truthful (TF) and when principals have the opportunity to provide wrong feedback (PF). For additional technical details and less restrictive modeling assumptions the reader is referred to Ederer (2005). Consider a tournament for a …xed prize between two risk-neutral agents i = A; B which takes place over 2 stages, t = 1; 2. The payo¤ of winning the contest is P and the payo¤ of losing is p. Agent i’s output in stage t is given by xit = eit + "it where eit is the privately chosen (non-negative) e¤ort level and "it is an error term. At the end of stage 2, the principal aggregates the scores from both stages to determine the winner of the contest. Agent A wins A B B the contest if his accumulated output is greater than that of agent B, i.e. if xA 1 + x2 > x 1 + x2 agent A wins and agent B wins if the reverse inequality holds. Each agent’s e¤ort eit is his private information and is not observed by the other contestant. We assume that the noise di¤erence "A "B t t is independently normally distributed for each t with cumulative density function F ( ) and density f ( ). Let G( ) and g( ) denote the distribution A and density functions of the sum of the noise di¤erences "A "B "B 1 1 + "2 2 . Note that the noise di¤erence in each stage and thus the sum of noise di¤erences in both stages are normally distributed, i.e., "A 1 "A t "B t N (0; A "B 1 + "2 "B 2 N (0; 2 2 ): 2 ) When exerting e¤ort in stage t agent i incurs a cost c(eit ). The payo¤ to agent i is given by U i = p + (P p) Pr(xi1 + xi2 > xj1 + xj2 ) c(ei1 ) c(ei2 ): (1) We intend to contrast the following three settings: no feedback, truthful feedback and feedback by self-interested principals. In the no feedback scenario, neither of the agents knows the …rst stage output di¤erence when choosing second stage e¤ort. The …rst stage output di¤erence is de…ned in the following way: xA 1 A A xB 1 = e1 + "1 7 eB 1 "B 1: In the truthful feedback scenario, the …rst stage output di¤erence is truthfully revealed to the two contestants. Hence, each agent learns the …rst stage outcome before choosing second stage e¤orts. Finally, in the last scenario feedback is given to the agents by self-interested principals who do not face any truth-telling restrictions. This third case falls between the two polar opposites of no feedback and truthful feedback. When the feedback the agents receive from principals is completely uninformative then rational agents will behave as in the no feedback setting, whereas when it is fully informative they will choose e¤orts as in the truthful feedback scenario. As we shall see, the predictions for e¤ort choice when agents do not receive any feedback are identical to those when feedback is given by self-interested principals since feedback is completely uninformative in the latter setting. We denote equilibrium e¤ort by eN F , eT F and eP F when agents receive no feedback, truthful feedback and feedback from principals, respectively. 2.1 Dynamic Tournaments without Feedback The probability of winning the contest for a given level of e¤ort choices is G( ). Therefore the maximization of equation (1) is tantamount to the maximization of p + (P p)G(ei1 + ei2 ej1 ej2 ) c(ei1 ) c(ei2 ): The resulting …rst order condition with respect to eit for an interior solution for both stages is given by c0 (eit ) = (P p)g(ei1 + ei2 ej1 ej2 ): In the unique symmetric Nash equilibrium of the game this condition simpli…es to c0 (eN F ) = (P (2) p)g(0): Since the sum of the noise di¤erences is normally distributed according to N (0; 2 2 ), the e¤ort in both stages of the NF condition is given by c0 (eN F ) = 2.2 2.2.1 P p p : 2 (3) Dynamic Tournaments with Truthful Feedback Second Stage At the beginning of the second stage agent i knows the …rst stage output di¤erence his overall payo¤ can be written as U i = p + (P p)F (ei2 8 ej2 + ) c(ei2 ) so that where F (ei2 ej2 + ) is the probability of winning the contest for given second stage e¤ort levels and a given output di¤erence . In the unique symmetric equilibrium of the second stage each i agent i chooses ei2 such that @U = 0 which yields the following …rst order condition @ei 2 c0 (eT2 F ) = (P (4) p)f ( ): Since the second stage error di¤erence is normally distributed the e¤ort in the second stage of the TF condition is given by " # 2 P p 1 0 TF c (e2 ) = p exp : (5) 2 2 Equation (5) implies that the second stage equilibrium e¤ort is decreasing in the absolute magnitude of the …rst stage output di¤erence . When the di¤erence between the two agents is large, the intensity of competition is low and thus the e¤ort of both agents is low while e¤ort is high when agents’outputs in the …rst stage are close to each other. 2.2.2 First Stage Having determined the equilibrium e¤ort choice of the second stage we can solve for the agents’ e¤ort choice in the …rst stage. Agent i chooses ei1 to maximize h i T F;i j T F;j T F;i i i i U = p + (P p)G(e1 + e2 e1 e2 ) c(e1 ) E c(e2 ) where the second stage e¤ort levels eT2 F;i and eT2 F;j depend on . Note that the …rst stage e¤ort ei1 a¤ects the agent’s payo¤ U i in three ways. First, there is a direct e¤ect of ei1 on U i because a higher ei1 increases the probability of winning and increases the …rst stage cost of e¤ort. Second, a higher ei1 changes which in turn changes the second stage equilibrium e¤ort eT2 F;i according to equation (5). Finally, a higher ei1 also a¤ects the opponent’s e¤ort choice eT2 F;j because j also responds to the change in with a change in eT2 F;j . Thus, agent i’s …rst order condition can be written as dU i @U i @U i deT2 F;i @U i deT2 F;j = + T F;i + T F;j : (6) dei1 @ei1 dei1 dei1 @e2 @e2 The second term in equation (6) is zero because for any given output di¤erence agent i T F;i @U i so that @eT F;i = 0. It turns out that because chooses the payo¤ maximizing level of e2 2 of the symmetry of the normal distribution and the symmetry of the equilibrium the third term in equation (6) is also zero. Since the proof of this assertion involves some cumbersome manipulations we relegate it to Appendix A (see also Ederer (2005)). Thus, as the second and the third term in equation (6) are zero we are left with @U i = (P @ei1 p)g(ei1 + eT2 F;i 9 ej1 eT2 F;j ) c0 (ei1 ) which simpli…es in the symmetric equilibrium to c0 (eT1 F ) = (P 2.2.3 p)g(0): (7) Comparison From the …rst order conditions (2) and (7) it follows that …rst stage e¤orts under the NF and the TF condition are equal, i.e., eN F = eT1 F . Due to the symmetric e¤ort choice of the two agents in the …rst stage of the TF condition, equation (5) for second stage e¤ort in the TF condition reduces to # " A B 2 " " P p 1 1 1 : (8) c0 (eT2 F ) = p exp 2 2 Equation (8) shows that second stage e¤ort under truthful feedback, contrary to all other "B previous e¤ort choices, is random. When = "A 1 1 = 0, the exponent of the right-hand side TF of (8) is zero and thus second stage e¤ort e2 is highest at this point. Furthermore, at = 0 second stage e¤ort eT2 F is higher than eN F as can be seen from comparing the right-hand sides of equations (8) and (3). In Appendix A we further show that expected second stage e¤ort under the TF condition is equal to e¤ort in the NF condition, E eT2 F = eN F , if the cost of e¤ort is quadratic (and marginal cost is linear), E eT2 F > eN F if marginal cost is concave and E eT2 F < eN F if marginal cost is convex. Intuitively, the convexity of marginal costs implies that due to the variability of output di¤erences the expected marginal costs for second stage e¤ort would be higher in the TF condition compared to the NF condition if the agent chose …rst and second stage e¤ort levels that are equal in expectation. However, in equilibrium marginal costs of …rst and second stage e¤ort are equalized and therefore E eT2 F is below eN F . This result is important for our purposes because in our experiments we implemented convex marginal cost of e¤ort, which implies that the average second stage e¤ort under truthful feedback, E eT2 F is predicted to be lower than the second stage e¤ort under no feedback eN F . Our analysis above shows that the …rst stage e¤ort under no feedback (NF) and under truthful feedback (TF) are identical, i.e., the fact that agents receive information about the …rst stage output di¤erence does not a¤ect …rst stage e¤orts. Aoyagi (2004) shows that this result holds more generally, in particular, for the case where feedback information about is only partially informative. That is, the equality of …rst stage e¤orts does not only hold for the two extreme cases of full information and no information feedback, but also for all intermediate cases of information release. 10 2.3 2.3.1 Dynamic Tournaments with Feedback by Self-interested Principals Preferences of Principal Consider the introduction of a risk-neutral self-interested principal. The principal’s role is to transmit information about the output di¤erence between the two contestants after the …rst stage. Her period payo¤s are a linear function of the two contestants’outputs in both stages minus the wage costs for the two agents, that is, her payo¤ is given by UP = B A B xA 1 + x1 + x2 + x2 P p; where is a positive constant and it is commonly known that > 0. The principal observes the …rst stage output di¤erence of the two contestants and must then send a private message ^ i to each agent i about the output di¤erence. We assume that the principal’s message is non-veri…able and the principal is not obliged to report truthfully to either of the agents. Since the principal’s message does not a¤ect her utility function the message is cheap talk (Crawford & Sobel 1982). For the principal feedback scenario we denote equilibrium e¤ort by eP F and reports to agent i of the output di¤erence by ^ i . 2.3.2 Communication and E¤ort Equilibrium In the above setting for all > 0 the unique Perfect Bayesian Equilibrium is a babbling equilibrium in which all messages sent to the agents by the principal are uninformative. To see this, consider the case where agents (naively) believe the principal’s message. In this case, the optimal message is ^ i = 0 because according to equation (5) this maximizes the agent’s e¤ort. More generally, for any given belief the agents hold about the principal’s message the principal will want to send the message that leads the agent to believe that the absolute value of the output di¤erence is as low as possible as this will maximize the agent’s e¤ort. As a result, for any given …rst stage output di¤erence the reported output di¤erence is independent of the actual output di¤erence. Hence, all communication is uninformative and no information is transmitted in equilibrium. Note that the present model does not make clear predictions as to what messages will actually be sent in equilibrium. As communication is completely uninformative all messages will be ignored by agents. That is, regardless which messages principals send they will not in‡uence agents’e¤ort choices and so the messages sent by principals are indeterminate. Furthermore, since the communication by principals is completely uninformative, agents ignore the messages. As a result, with regards to e¤ort choice the model reduces to the no feedback setting analyzed in Section 2.1. 11 3 An Experimental Approach for the Study of Dishonesty and Incentives The ideal data set for studying the e¤ects of dishonesty on incentives and e¤ort choices is based on a truly exogenous ceteris paribus variation in the degree of credibility of information. The exogenous variation allows the researcher to make causal inferences on the impact of di¤erent degrees of information credibility. Such a data set permits, for instance, the examination of how the possibility of dishonest reporting behavior a¤ects communication behavior of principals and the e¤ort choices of contestants. The problem is, however, that it seems almost impossible to …nd or generate …eld data to approximate this ideal data set. In real life situations, there are few completely truthful or untruthful signals and one rarely knows how credible a given piece of information is. Thus, it is particularly di¢ cult to measure and analyze the e¤ects of deception on incentives and e¤ort provision. However, experiments allow for causal inferences because one can implement exogenous ceteris paribus variations in the extent of information manipulation. Thus they overcome some of the measurement and endogeneity problems present in the …eld data. In particular, the following experiment allows us to study behavior in the three settings where agents do not receive any feedback, where they receive completely truthful feedback and where the feedback they receive can be manipulated by principals. 3.1 Experiment Design We implemented the following three treatment conditions in order to examine how dishonesty a¤ects communication and e¤ort choices. In the …rst condition, which we call the no feedback condition (NF condition), there was no principal and contestants were given no information about …rst stage outcomes before the second stage. In the second condition, which we call the truthful feedback condition (TF condition), there was no principal and the experimenter exogenously enforced truthful feedback about the …rst stage to the contestants and the subjects were informed about this. In the third condition, which we call the principal feedback condition (PF condition), feedback about the …rst stage was given by principals to the contestants; principals observed outcomes in the …rst stage and had to send non-veri…able messages about the …rst stage output levels and the output di¤erence separately and privately to each agent. The principals were free to report any output level and output di¤erence irrespective of the actual outcomes and the agents knew this. Thus the design of the experiment was chosen in such a way as to analyze di¤erences in behavior resulting from di¤erences in information transmission. By comparing e¤ort choices across the NF and TF conditions the e¤ect of credible in12 formation on e¤ort choices can be examined. Furthermore, these two conditions provide the benchmarks against which the outcomes of PF condition can be measured. Our major research questions are addressed by analyzing communication behavior in the PF condition and by comparing e¤ort choices across the PF, TF and NF conditions. There were 15 periods in each of the three conditions. In all conditions the subjects were anonymously and randomly matched at the beginning of each period.6 Each period had two stages. In stage 1, workers chose their …rst stage e¤orts ei1 . After choosing e¤ort ei1 , a normally distributed random variable "i1 was added to each agent’s e¤ort choice. An agent’s …rst stage output xi1 was the sum of his e¤ort choice ei1 and the realization of his random variable "i1 . After the end of the …rst stage, in the PF condition principals received information about the …rst stage output levels and the output di¤erence between the agents. The principals privately sent information about the …rst stage output levels and the output di¤erence to each of the two agents they were paired with. Before the beginning of the second stage of the TF and the PF condition, each contestant received information about his own …rst stage output xi1 , the …rst stage output of his opponent xj1 and the associated output di¤erence . In the TF condition this information was relayed to each agent directly and truthfully through the computer, whereas it was sent by a principal in the PF condition. The agents in the PF condition knew that the principal could only determine the feedback they received about …rst stage outcomes and that she could neither determine the overall outcome of the tournament nor in‡uence the allocation of prizes. This allocation was objectively determined by a comparison of the agents’ actual total output in the two stages in all three conditions. Contestants in the NF condition did not receive any feedback about the …rst stage. In stage 2, contestants in all conditions had to choose their second stage e¤ort levels ei2 to which another random variable "i2 was added to produce the agent’s second stage output xi2 . At the end of the second stage each agent received truthful feedback from the computer about the sum of his own …rst and second stage output level and the output sum of the other contestant. In addition, each agent was informed about who received the higher prize P . This allowed 6 Anonymous and random matching rules out reputation building by principals. We deliberately ruled out reputation formation opportunities in order to identify the principal’s preferences for truth-telling and the resulting e¤ects on agents’ behavior. There are situations in which reputational incentives for truth-telling are likely to be rather small. For example, in large management consulting …rms there is signi…cant turnover and rotation in personnel assignment to projects. Therefore, there is only a small probability that a partner who previously provided private performance feedback to an associate is paired again together with the same associate on another project. There are, of course, also situations in which the principals are - for reputational reasons - more honest than in the one-shot situation. However, in order to understand the more complicated situation it is necessary to …rst understand the motivational forces present in the simpler, one-shot, situation. The examination of the impact of reputation formation opportunities on principals’behavior, and the resulting e¤ects on agents’e¤ort, is undoubtedly an important task for future research. 13 the agents to verify the validity and fairness of the prize allocation process. Since the agents received information about the sum of outputs rather than about the separate outputs in each stage they could only imperfectly infer the truthfulness of the principal’s previous report about stage 1 outputs in the PF condition. Each principal received information about the agents’ output levels in both stages and her own pro…t at the end of the second stage. 3.2 Parameters, Procedures, and Subject Pool The material payo¤ of a contestant i was given by ( P c(ei1 ) c(ei2 ) if xi1 + xi2 > xj1 + xj2 i U = p c(ei1 ) c(ei2 ) if xi1 + xi2 < xj1 + xj2 : The material payo¤ of a principal was given by U P = (xi1 + xi2 + xj1 + xj2 ) P p: The set of feasible e¤ort levels was given by e 2 f1; 2; : : : ; 100g. The exact parameter values and theoretical predictions are shown in Table 1. The parameter values were chosen so that the equilibrium e¤ort choice did not constitute an immediate focal point such as 50 or the socially e¢ cient e¤ort level 52.38. According to the design parameters the equilibrium e¤ort in the NF condition, eN F , equals 37 in both stages. The same equilibrium e¤ort prevails in the …rst stage of the TF condition. Furthermore, as we implemented convex marginal costs, the expected equilibrium e¤ort in the second stage of the TF condition, E[eT2 F ], is lower than the equilibrium e¤ort in stage 2 of the NF and PF condition. Insert Table 1 here. The agents’ payo¤ function, the number of contestants and principals, the exact parameterization and the fact that there were 15 periods were common knowledge. However, in order to avoid vertical fairness comparisons between the principals and the agents, the agents only had qualitative information about the principals’payo¤ function, i.e., they did not know the value of . Agents only knew that the principals’payo¤ was increasing in the e¤ort exerted by them, but they did not know how much the principal earned. We implemented this procedure because we were not interested in the potential impact of vertical fairness (payo¤) comparisons; instead we wanted to study the impact of di¤erent information transmission mechanisms on the agents’behavior. The experiments were programmed and conducted with the software z-Tree (Fischbacher 2007). A total of 192 subjects participated in our experiments. We conducted a total of 16 14 sessions with 12 subjects each giving us 16 distinct matching groups which constituted the independent units of observation. There were 8 sessions where subjects participated in both the NF and TF treatments and 8 sessions where subjects were placed in the PF treatment.7 A session lasted, on average, 75 minutes. Subjects were science students from the University of Zurich and the Federal Institute of Technology in Zurich. During the experiment experimental currency units (ECU) were used to keep track of monetary earnings. The exchange rate was set at 100 ECU = 1 CHF. On average, a subject earned CHF 43.40 ( $36) in an experimental session. 3.3 Predictions Our experiment allows us to test the empirical predictions of the model presented in Section 2; we can test, in particular, the e¤ort predictions implied by the model. These predictions follow from the optimizing behavior of self-interested agents and principals and are discussed below. The …rst hypothesis concerns second stage e¤ort which should respond to feedback about the …rst stage output di¤erence. Feedback Hypothesis: In the second stage of the TF condition e¤ort is decreasing in the absolute magnitude of the …rst stage output di¤erence . The predictions of the feedback hypothesis are similar to the predictions of a tournament in which one contestant has an absolute output advantage over his opponent. Since the density of the noise di¤erence is highest at 0 (see the right-hand side of equation (5)), the greater is the advantage of one contestant the weaker are the incentives for e¤ort, and hence the lower should be the equilibrium e¤ort choices of both contestants. Note that if agents behave similar to this prediction in the PF condition, principals should have a strong incentive to misreport, as higher e¤ort can be elicited by reporting an output di¤erence that is small in absolute value. Based on the lying incentive for principals, we can now predict and analyze behavior in the PF condition where interim information is given by principals. Cheap Talk Hypothesis: In the PF condition communication by the principals does not in‡uence the agents’e¤ort choice, i.e., the agents behave in the same way as in the NF condition. It is crucial for the cheap talk hypothesis that agents know that principals are rational and sel…sh. When this is the case, the contestants in the PF condition realize that the …rst stage output di¤erences that principals report, only serve to elicit higher e¤ort levels from contestants 7 As is standard practice, throughout our analysis we use clustering on matching groups to compute standard errors because within each session observations are not independent. 15 regardless of the actual …rst stage output di¤erences. As a result, rational agents understand that messages are completely uninformative and therefore they should behave as in the NF condition. Finally, based on the model in Section 2 and for the given experimental parameters (see Table 1) we can stipulate the following hypothesis. Average E¤ort Hypothesis: The average e¤orts in both stages of the NF condition and in the …rst stage of the TF condition are equal. Furthermore, the average e¤ort in the second stage of the TF condition is lower than in the second stage of the NF condition. The equality of e¤ort in both stages of the NF and the …rst stage of the TF condition follows from the identical …rst order conditions given in equations (2) and (7). Expected second stage e¤ort in the TF condition, however, is lower than e¤ort in both stages of the NF condition since we implemented convex marginal costs. 4 Results We now present the key results obtained in our experiments. For all the tests and regressions that follow, we use clustering on matching groups because the matching groups constitute our independent units of observation. 4.1 Feedback Hypothesis We …rst focus on the behavior of contestants in the second stage of the TF condition. As shown in Section 2, the theoretical model predicts that equilibrium e¤ort is decreasing in the absolute value of the output di¤erence arising at the …rst stage. Our …rst results show that this prediction is con…rmed by the data. Result 1 (information feedback): If the information about the agents’ output di¤erences after stage 1 is truthful, the agents’average response to the feedback information closely tracks the theoretical prediction. The second stage e¤ort is decreasing in the absolute value of the output di¤erence. Figure 1 shows the results of a bivariate Epanechnikov kernel regression together with the model’s theoretical prediction. Average e¤ort is remarkably close to the theoretical predictions of the model. The …gure neatly indicates the strong e¤ort response to the information feedback for larger absolute values of the output di¤erence. Note that the experimental results are particularly close to the theoretical predictions when an agent is at a disadvantage at the 16 beginning of the second stage. The …t is worse for the case when the contestant is ahead, in particular when a contestant is very far ahead. However this oversupply of e¤ort for very large positive values of the output di¤erence is only based on a very small number of observations. It is therefore much more sensitive to statistical outliers and mistakes which are more likely to result in an oversupply e¤ort since e¤ort choice is constrained to be non-negative. Table 2 summarizes the regression results. In accordance with the theoretical predictions column (1) reports a highly signi…cant negative coe¢ cient on the absolute value of the …rst stage output di¤erence. In column (2) we further decompose this e¤ect by estimating separate coe¢ cients for …rst stage winners and losers, both of which are highly signi…cant and of the correct sign. Column (2) indicates that the discouraging e¤ect on e¤ort of the …rst stage output di¤erence seems to be weaker for winners. Columns (3) and (4) show that these results are robust to additional controls for round and an interaction e¤ect between round and the output di¤erences. Insert Table 2 here. Taken together, Result 1 shows that agents’ response to truthful feedback is remarkably close to the theoretical predictions of our model. It also powerfully demonstrates that there are strong incentives to manipulate feedback: when the output di¤erence j j falls by one unit, the average second stage e¤ort increases by 0.30 to 0.53 units. Hence, self-interested principals have strong incentives for lying if they have the opportunity to provide and manipulate the feedback information. 4.2 Cheap Talk Hypothesis So far, we have focused on a setting in which feedback is always truthful. We are interested in what happens when information is relayed to the contestants through a self-interested principal who maximizes total e¤ort and therefore has objectives that con‡ict with truth-telling behavior. We therefore turn to the analysis of the PF condition. The previous results highlight the experimental support for the standard theoretical model when there is completely credible feedback. In contrast, we will see that the theory does not perform similarly well in the present setting where there are incentives for dishonesty and information manipulation. The theory makes a particularly stark prediction with regards to the e¤orts chosen by the agents when self-interested principals relay information. It predicts that all communication should be uninformative and so the e¤ort choice of the contestants should be the same as in the case where no feedback is given to them. 17 Result 2 (cheap talk e¤ort response): (a) The cheap talk hypothesis is unambiguously refuted because the agents’ second stage e¤ort choices respond strongly to the information provided by interested principals. (b) However, for a given reported output di¤erence the agents provide considerably less second stage e¤ort in the PF condition compared to the TF condition suggesting that agents partially discount the information provided by the principals. Empirical support for Result 2a comes from Figure 2 which plots the predicted e¤ort response in stage 2 in the PF condition (which is completely ‡at), the actual average e¤ort response to output di¤erences in the TF condition (using the same Epanechnikov Kernel regression as in Figure 1) and the actual average e¤ort response in the PF condition.8 The …gure transparently shows the refutation of the cheap talk hypothesis since there is a very strong e¤ort response to the reported output di¤erence. Average e¤ort choices in the PF condition vary considerably with the reports sent by the principals. Further support for Result 2a comes from Table 3 which reports the e¤ects of principals’messages on the second stage e¤ort choices of agents in the PF condition. In column (1) in Table 3 we see that the coe¢ cient on the reported absolute output di¤erence is negative and of similar magnitude as in the setting where feedback was fully credible. The discouraging e¤ect of the reported …rst stage output di¤erence is even larger when we winsorize the sample to eliminate extreme outliers (24 reported output di¤erences that fall outside the range between -30 and 30) as shown in column (2) of Table 3. In column (3) we separately estimate the behavioral e¤ects on second stage e¤orts for interim winners and losers. The e¤ect is particularly pronounced for interim losers and in particular for the winsorized sample as shown in column (4). Since agents respond to the information given by principals in the way described above, it is perhaps not surprising that principals who lie more also earn more. Reporting a lower than actual output di¤erence elicits higher e¤ort and thus a higher payo¤ for the principal. On average, an incremental lie about the …rst stage output di¤erence of one unit gives the principal an additional payo¤ of 2.5 ECU’s. Insert Table 3 here. Figure 2 also provides …rst evidence for Result 2b. For a given reported output di¤erence average e¤ort choices in the PF condition are lower than in the TF condition. This suggests that when contestants receive information from a principal they realize, on average, that principals 8 Note that the range for which the Kernel regression for the PF condition can be drawn is much smaller than the range for the TF condition since in the former more than 95% of all the reported …rst stage output di¤erences fall in the range between -25 and 25. 18 have an incentive to report output di¤erences that are lower in absolute value than the actual output di¤erence. For this reason agents may therefore adjust their e¤ort response accordingly. We therefore investigate in detail whether the second stage e¤ort response to information given in the PF condition is signi…cantly di¤erent from that observed in the TF condition. Table 4 reports second stage e¤ort regressions with pooled data from both of these conditions. Once again, we eliminate the same extreme outliers in the speci…cations reported in columns (2) and (4). Here, PRINCIPAL is a binary variable which is equal to one for all observations in the PF condition and zero otherwise. On average, contestants exert signi…cantly less e¤ort for any given level of the …rst stage output di¤erence when the information is given to them by a self-interested principal as shown by the large negative coe¢ cient on the PRINCIPAL variable which is statistically signi…cant in all the speci…cations reported in Table 4. In addition, we are also interested in di¤erences in the slope of the average e¤ort response function. The coe¢ cient on the interaction term j ^ j*PRINCIPAL is insigni…cant in columns (1) and (2), but larger in magnitude in the winsorized sample shown in column (2). The point estimate in column (2) shows that for a one point increase in the absolute value of the reported output di¤erence in the PF condition contestants reduce their e¤ort by 0.66 units whereas they only reduce it by 0.41 in the TF condition. This stronger e¤ort response by agents in the PF condition further compensates for the “underreporting” behavior by principals which we document in later results. As the e¤ort response is potentially asymmetric for interim winners and losers, we estimate separate slopes and interaction terms in columns (3) and (4). Again, the interactions with PRINCIPAL are not signi…cant as shown in column (3). Only in the winsorized sample the slope of the e¤ort response to information about the …rst stage output di¤erence for interim losers is signi…cantly larger in the PF condition than in the TF condition whereas the e¤ect is insigni…cant for the winners as shown in column (4). Insert Table 4 here. Faced with this evidence we conclude that information feedback does indeed a¤ect contestants’behavior even when the information can be manipulated by a self-interested principal. In particular, contestants shift their e¤ort response downward suggesting that when choosing their e¤ort levels they anticipate the misreporting behavior of principals. When compared to the TF condition, the feedback given by the principals clearly elicits lower e¤ort at all reported output di¤erences. 4.3 Average E¤ort Hypothesis Although the agents’ e¤ort response to reported output di¤erences is signi…cantly lower in the PF condition it need not be the case that average e¤ort is also lower. This is because in 19 the PF condition the principals control the information feedback. If the principals compress the reported output di¤erences relative to the true output di¤erences, the agents in the PF condition may face a very di¤erent distribution of information feedback compared to the TF condition and, therefore, it is not clear whether average e¤ort rises or falls in the PF condition relative to the other two conditions. Our next result addresses this question Result 3 (average e¤ort across treatments): a) In the PF condition the average e¤ort in the …rst and the second stage decreases over time. Therefore, towards the …nal period average e¤ort in the PF condition is signi…cantly lower than in the NF and the TF condition. (b) In contrast, in the NF and the TF condition average e¤ort is constant over time and, as predicted by theory, e¤ort levels in both of the NF and the …rst stage of the TF condition are statistically indistinguishable. Moreover, in line with theory, the average second stage e¤ort in the TF condition is smaller than the second stage e¤ort in the NF condition. A …rst indication for Result 3 is provided by Figures 3 and 4. In Figure 3 we show how average e¤ort in the …rst stage evolves over time across conditions. The …gure shows that in the NF and the TF condition average e¤ort is fairly stable over time while in the PF condition it strongly decreases over time. In fact, towards the …nal periods, average e¤ort in the PF condition is almost 25% lower than in the other two conditions. The impression conveyed by Figure 3 is also supported by more formal statistical tests. In the NF and the TF condition the average e¤ort in the …rst three rounds is not signi…cantly di¤erent from the respective e¤ort levels in the …nal three rounds (t-test; p-value 0.259 for the NF condition; p-value 0.622 for the TF condition). In contrast, the same test con…rms a signi…cant di¤erence between the …rst three and the last three rounds in the PF condition (t-test, p-value 0.042), so that the average e¤ort in the PF condition is also signi…cantly below the level in the other two conditions (t-test, p-value 0.005 for the NF condition; p-value 0.013 for the TF condition). All these results are also robust if we compare just the …rst and the last round or the …rst 5 and the last …ve rounds within each treatment or across the treatments. Finally, as predicted by the model in Section 2, the …rst stage average e¤ort in the NF and the TF condition are not signi…cantly di¤erent from each other (t-test, p-value 0.109). A similar picture emerges when we examine how second stage e¤ort evolves over time although the downwards trend in the PF condition starts a bit later than in the case of …rst stage e¤ort. Figure 4 shows that the second stage e¤ort in the NF and the TF condition is rather stable over time. If we compare average e¤ort in the …rst three and the last three periods we …nd no di¤erence (t-test; p-value 0.736 for the NF condition; p-value 0.642 for the TF condition) while if we perform the same comparison in the PF treatment we observe a signi…cantly lower average e¤ort during the …nal three periods (t-test, p-value 0.023). The decline in average e¤ort in the PF condition also implies that towards the end (in the …nal three periods) average e¤ort 20 in the PF condition is signi…cantly lower than in the NF and the TF condition (t-test; p-value 0.001 for the comparison with the NF condition; p-value 0.007 for the comparison with the TF condition). Figure 4 also neatly shows that the average second stage e¤ort in the NF condition is higher than in the TF condition, a result that is also signi…cant (t-test, p-value 0.005). Taken together, Result 3 indicates that the model presented in Section 2 organizes the data very well in those conditions in which there is no feedback or fully truthful feedback. However, if the agents receive feedback from the principals their e¤ort is not only smaller for any given reported output di¤erence (Result 2) but average e¤ort eventually declines and is, …nally, signi…cantly below the e¤ort in the other two treatment conditions (Result 3). Apparently, the opportunity for the principals to deceive the agents is detrimental for e¤ort provision and seems to undermine the agents’willingness to compete in the tournament. It is also interesting that the e¤ort decline is already present in the …rst stage of the tournament. In fact, as Figure 3 and 4 reveal, the decline is even more pronounced in the …rst stage. Recall, that according to the theory presented in Section 2, the …rst stage e¤ort should not be a¤ected by the informativeness of the feedback that is given to the agents. Thus, the fact that the principals can lie in the PF treatment should not a¤ect the agents’e¤ort choices regardless of whether the principals’ feedback is informative or not. 4.4 Principals’Communication Behavior Result 2 and 3 unambiguously show that the agents’ behavior in the PF condition di¤ers substantially from the theoretical predictions. We next ask what drives these departures from the theory. One potential explanation for agents’ second stage e¤ort response documented in Result 2 is that feedback is informative. We therefore investigate the reporting behavior of principals in the PF condition. In this setting, the theory makes the particularly stark prediction that communication by the principals should be completely uninformative since the preferred message of the principal does not vary with the output di¤erence between the two agents. A sel…sh principal unconstrained by honesty norms only intends to maximize her payo¤ and therefore, regardless of the actual output di¤erence, she will report the output di¤erence that for a given belief of the agent maximizes the agent’s second stage e¤ort response. For example, if the beliefs held by the agent are such that he exerts higher e¤ort when the reported output di¤erence is smaller in absolute value, then a pro…t-maximizing principal should report an output di¤erence close to zero. As shown in Result 4 the experimental evidence is at odds with the theoretical prediction that the information provided by the principals is completely uninformative. Result 4 (feedback informativeness): The principals’ messages are partly informative for the agents because higher reported output di¤erences are associated with higher actual output 21 di¤erences. Figure 5 shows a scatter plot of actual versus reported …rst stage output di¤erences in the interval [ 30; 30] for both variables as well as an OLS regression line within this range of actual output di¤erences. The shallow slope of the regression line is a result of the compression of reported output di¤erences relative to actual output di¤erences. Although there is a large amount of untruthful reporting there is also a substantial number of observations where principals report truthfully. In particular, for small output di¤erences in the interval [ 10; 10] many observations are on the truthtelling line.9 Since agents do not know what kind of principal they face the appropriate level for the analysis of the informativeness of the principals’ feedback information is the aggregate data. When agents observe a message of ^ i they do not know whether the message comes from a truthful or a lying principal. We therefore performed OLS regressions (not reported) of on 2 3 ^ i , ^ i and ^ i . The results of these regressions provide qualitative insight into the extent to which the principals’ messages reveal information about actual output di¤erences. In particular, they address the question what prediction an agent would make about after observing ^ i if he had all the data of the experiment at his disposal. In these regressions the coe¢ cient on the reported output di¤erence ^ i is positive and significant at the 1% level throughout, indicating that there is clear link between actual realization and the content of messages sent. Moreover, the R2 of the regressions shows that almost a quarter (23%) of the variance in the actual output di¤erence is explained by the reported output di¤erence suggesting that communication is at least partially informative for the agents. In particular, if a contestant would have all the information that the experimenter has at his disposal he would estimate that a reported output di¤erence of ^ i = y would on average correspond to an actual output di¤erence of about 2y. In other words, on average the actual output di¤erence is about twice as large as the reported output di¤erence. If agents believe that there is a positive relationship between reported and actual output di¤erences, which indeed there is as documented in Result 4, then to e¤ect an increase in their own payo¤ principals should report an output di¤erence that is generally lower in absolute value than the actual output di¤erence. This aggregate underreporting behavior documented in Result 4 suggests that principals clearly seem to understand that if their message is believed and acted upon accordingly by the agents, reporting a lower output di¤erence will lead to higher second stage e¤ort choices and hence higher payo¤s. The informativeness of feedback also goes some way of explaining the e¤ort response of 9 There are also a few observations where principals “overreport” the absolute value of the actual output di¤erence. However, these observations almost exclusively occur in the …rst three rounds until principals realize that “underreporting” is more pro…table. 22 agents in the PF condition. Having established that the messages sent by principals are at least partially informative in the aggregate data, we now turn to a closer analysis of the reporting behavior of principals at the individual level. In particular, we ask what factors drive the principals’reporting behavior. Result 5 (principals’communication behavior): Reporting behavior is driven by the potential gains from lying. Principals are more likely to report the truth when the potential gains from lying are small. Furthermore, the partial informativeness of messages is due to the heterogeneity among the principals: some principals always lie maximally about the …rst stage output di¤erence, but a signi…cant share of the principals reports close to the truth if the potential gains from lying are relatively small. This heterogeneity is further supported by the fact that Machiavellian personality traits predict lying behavior. Figure 5 provides a …rst indication that principals do not lie maximally by always reporting an output di¤erence that is equal to 0, but sometimes choose to report larger output di¤erences. To empirically test the prediction that principals are more likely to lie when the potential gains to lying are larger we ran several regressions of the absolute divergence of the report from the truth j ^ i j on the maximum potential gain G from untruthful reporting. Denote the maximum possible theoretical gain G of an untruthful report, if followed naively by an agent, by h i G eT2 F;i ( ^ i = 0) eT2 F;i ( ^ i = ) : Table 5 reports the results of OLS regressions which yield highly signi…cant positive coe¢ cient for the gain G regardless of whether we control for round e¤ects and interaction e¤ects between rounds and G. On average an increase in G by one unit increases the extent of untruthful reporting by 0.4 units. Similar results hold for probit estimates (not reported) with the probability of reporting untruthfully as the dependent variable. Insert Table 5 here. We also investigated the principals’reports about agents’absolute output in addition to their reporting behavior with regard to the output di¤erence discussed above. In this case, principals almost always report the truth, since 90% of all reports are truthful. That is, the agent typically receives truthful information about his own output while the information about the output di¤erence, and, hence, the opponent’s output is biased. This provides additional evidence consistent with our conjecture that lying behavior is essentially driven by the potential gains from untruthful reporting because agents’behavior is driven by reported output di¤erences and not by their absolute output levels. 23 In order to investigate heterogeneity in principals’communication behavior in more detail, we performed the analysis displayed in Figure 5 for each of the 32 principals in our experimental data. These individual level regressions reveal heterogeneity with respect to the principals’ willingness to report the truth. Figure 6 shows the results for two principals (subjects #24 and #43). Whereas the …rst principal (subject #24) consistently reports output di¤erences that are close to zero regardless of the actual output di¤erence, the second principal (subject #43) truthfully reports for small absolute values of the …rst stage output di¤erence. The data contained in Figure 5 and, in particular, Figure 6 hint at the di¤erences in reporting behavior across principals. Given that such di¤erences exist, we are interested in analyzing reporting behavior using subject-speci…c characteristics. Table 6 reports the results of OLS regressions with the reported output di¤erence ^ i as the dependent variable. If all principals lie maximally all the time, then the coe¢ cient on should be equal to 0. As can be seen from Table 6, throughout all speci…cations this coe¢ cient is signi…cantly di¤erent from 0. This means that the actual output di¤erence in‡uences reporting behavior. However, aggregate data is not ideally suited to our analysis since there is substantial heterogeneity with respect to reporting behavior. To control for heterogeneity in reporting behavior we use the Machiavelli score. We measured subjects’Machiavellism –a combination of sel…shness and opportunism – with the Machiavelli questionnaire (Christie and Geis 1970). In this questionnaire the subjects indicate their degree of agreement with statements such as “It’s hard to get ahead without cutting corners here and there” and “The best way to deal with people is to tell them what they want to hear”. Based on their scores on this questionnaire we classi…ed principals in 3 di¤erent groups: low Machiavelli (lowest 10%), medium Machiavelli (middle 80%) and high Machiavelli (highest 10%).10 For subjects with low and high Machiavelli scores we create the binary variables LOWMACH and HIGHMACH. As can be seen from Table 6 in speci…cations (3) and (4), the interaction e¤ect *LOWMACH is positive and statistically signi…cant, showing that principals with lower Machiavelli scores on the questionnaire also lied signi…cantly less during the actual experiment. We can observe the opposite e¤ect for highly Machiavellian individuals since the interaction e¤ect *HIGHMACH is negative. However, even for these highly Machiavellian individuals the combined coe¢ cient on and *HIGHMACH is signi…cantly di¤erent from 0 (p-value 0.0005) so that we can reject the null-hypothesis that for subjects with strong Machiavellian personality traits the actual output di¤erence does not in‡uence the output di¤erence they report. Speci…cations (2) and (4) show that our analysis is robust to round e¤ects.11 10 As a robustness check we also used other speci…cations for this personality variable using the full sample and the median split. The results are qualitatively similar but statistical signi…cance is somewhat lower. 11 Note also that we included the ROUND and Machiavelli score variables separately in the regressions reported in Table 6. These non-interaction terms are not signi…cant and therefore omitted in the presentation of Table 24