Relative Piece-rate, Tournament and Piece-rate schemes: an Experimental study

Transcription

1 Relative Piece-rate, Tournament and Piece-rate schemes: an Experimental study Marina Agranov and Chloe Tergiman May 7, 007 Abstract Rank-order tournaments are known for their property of filtering out common shocks. However, the realized payoffs of the agents are discontinuous in the level of exerted effort. This feature produces complicated behavioral effects that have been studied empirically and in laboratory experiments. Independent piece-rate wage schemes eliminate the discontinuity issue, but do not filter out the common shock, and this is costly to the principal. Even when tournaments theoretically outperform individual piece-rate contracts, they are informationally quite wasteful if performance levels of agents can be measured cardinally, (Holmstrom, 8). The schemes that incorporate the relative performance of agents in wage contracts are referred to as relative evaluation schemes. Such contracts incorporate the advantages of the piece-rate and tournament wage schemes: they eliminate the common shock and do not exhibit the discontinuity problem. In particular, we focus on a Relative Piece-Rate scheme (RPR). We compare it with a tournament and an individual piece-rate, both theoretically and experimentally for a given environment with additive shock structure for output. We study the performance of the three wage schemes as well as their relative ranking, in terms of the principal s profits and the efforts of the subjects. In theory, RPR always obtains higher expected profits for the principal, and this is also associated with higher effort levels. Overall, the experimental results are consistent with the theory: RPR produces higher profits for the principal. In terms of effort, results are mixed. 1 Introduction This paper is about incentive schemes in a moral hazard context. Following the seminal work of Lazear and Rosen (1981), much of the theoretical litera- 1

2 ture has looked at the relative performance of rank-order tournaments versus individual piece-rate schemes. These predictions have been studied both empirically and experimentally. 1 However, if output is a linear combination of effort and shocks and if the exact outputs of the agents are observed at low monitoring costs, neither of these two schemes is optimal. As noted by Holmstrom (198) the optimal contract in principal-agent problems should have pay dependent upon any signal that carries information on the agent s actions. If the performance of risk-averse agents are correlated (because of a common random component), then using relative performance information will improve the trade-off between incentives and risk-sharing. Rank-order tournaments make partial use of this principle. Paying agents based on the rank of observed performance filters out any common shock that affects the performance of both agents equally. When the common shock is an important part of uncertainty, rank-order tournaments guarantee the principal a higher expected profit when compared with independent contracts, in which agents are paid based solely on their absolute performance. However, rank-order tournaments [are] informationally quite wasteful if performance levels of agents can be measured cardinally rather than ordinally (Holmstrom, 198). Indeed, if the exact outputs of agents are observable at low monitoring costs, there is a better way of using this information in contract design. Contracts that make use of absolute as well as peer performance information are called relative performance evaluation (RPE) contracts and have been studied theoretically as well as empirically. Empirically, RPE contracts are often discussed in the context of constructing optimal compensation schemes for CEO s, where common industry shocks (changes in industry demand or other exogenous market specific shocks) affect the performance of managers. Empirical research on the presence and efficacy of relative evaluation schemes has produced mixed results. The existence of unobservable characteristics and the difficulty associated with their control or inference may explain the varying results obtained in empirical studies. This alone justifies testing relative evaluation schemes in a controlled laboratory setting where the experimenter is free to choose the parameters that drive the performance of these contracts. Furthermore, a controlled laboratory experiment also per- 1 Other theoretical work on rank-order tournaments and individual piece-rate schemes include Green and Stokey (1983) and Nalebuff and Stiglitz (1983). See the next section for a literature review of empirical and experimental studies on these contracts. See the next section for a more detailed discussion of the related literature.

3 mits the exogenous variation of the parameters. Thus the experimenter can measure the effects of the incentives created by the different wage schemes and he may also rigorously compare wage scheme designs. In this work, we focus on a Relative Piece-Rate scheme (RPR). Following the theoretical and empirical literature we concentrate our attention on relative piece-rate (RPR) contracts that are linear in both agents performance 3 We choose to compare it with two other wage schemes: a tournament and an individual piece-rate scheme. The reason for this is two-fold. The first is that they are not only the subject of theoretical work but are actually often used in practice. 4 It seems natural then to wonder how the theoretically optimal wage scheme would fare against them. The second reason is that to our knowledge, all past experimental papers that compared tournaments and the piece-rate schemes did so in a partial equilibrium setting, without fixing the environment that the agents face, making the comparison between wage schemes impossible in terms of principal s profits. The question that they addressed was solely how well each wage scheme elicited the predicted effort level. To discuss the question of the wage schemes comparative performance, one needs to look at the principal as well. It was thus necessary to bring all three contracts to the lab. Although rank-order tournaments entirely filter out the common shock, there are well-documented drawbacks to a tournament payment scheme. One of the most consistent results in the experimental literature is the high variance in effort levels chosen by the subjects. This feature reduces the ability to predict what happens in a particular tournament. 5 One cause for this drawback is the fact that the marginal unit of effort increases the expected payment of an agent by increasing the probability to win, but does not necessarily generate higher payment; in other words, the actual payment of an agent is discontinuous in his exerted effort. Piece rate schemes have the advantage that an agent will receive extra payment for each unit of additional effort he provides. However, its disadvantage is that the common shock is an integral part of the agents pay, and therefore of the cost to the princi- 3 For a justification see Holmstrom and Milgrom (1987,1991), Meyer and Vickers (1987), Levitt (1995), Fershtman, Hvide and Weiss (00). 4 Standard examples of rank-order tournaments include promotion tournaments for managers, bonuses for salespeople at the end of the year, a tournament for limited number of tenure positions that assistant professors compete for etc. The independent piece-rates are often used in such industries as fruit picking or in cases people are paid on commission. 5 See Bull, Schotter and Weigelt (1987), Harbring and Irlenbusch (003) and van Dijk, Sonnemans, and van Winden (001). 3

4 pal. RPR schemes combine the advantages of tournaments and piece-rate schemes while lowering their disadvantages. Two different questions are studied in this paper. We start by assessing whether subjects in the lab experiment exhibit the effort levels predicted by the different contracts. Once this question is answered, we can ask under what conditions the RPR scheme dominates other types of contracts, or, what would be the preferred contract for a principal? Theoretically, we show that for any given environment with additive shock structure and risk-averse agents, the RPR contract outperforms both the tournament and the piecerate contract in terms of the effort level exerted by the agents and in terms of the profits of the principal. We aim to investigate whether this is indeed the case in the lab experiment. To summarize our results, we find that as the theory predicts, the RPR scheme generates higher profits for the principal than the other two wage schemes do. In terms of targeting the effort levels, the relative evaluation schemes (the RPR and the tournament) do not always target the effort predicted by theory (the independent piece-rate does). However, our data shows that the RPR scheme does elicit higher effort levels than both the tournament and piece-rate contracts, independently of the environment. In addition, we find that even when the tournament should outperform the independent piece-rate contract (the common shock is the main source of uncertainty), it fails to do so in practice. The rest of the paper is organized as follows. In Section II, we state the theoretical results. In section III we present our experimental design. In section IV we state the hypotheses that will be tested in the experiment. We describe the data we obtained in section V. Our experimental results are presented and discussed in Section VI. Finally, we conclude in Section VII. 1.1 Related literature The theoretical literature on RPE schemes started with the work of Holmstrom (198) and Mookherjee (1984) who studied the conditions under which RPE contracts perform better than independent contracts. Extending those two pioneer papers, the theoretical literature on agency theory continues to investigates RPE contracts in other circumstances. Meyer and Vickers (1987) studied their performance in a dynamic setting, in which contrary to the static setting, the use of comparative performance information is ambiguous 4

5 and depends on the information structure. 6 Holmstrom and Milgrom (1991) applied the idea of RPE contracts to multi-tasking problems. Levitt (1995) showed that asymmetric RPE contracts (where one of the ex-ante identical agents is randomly chosen to be favored) can be optimal if the principal cares only about the best of the agents output. Despite the compelling theoretical argument in favor of RPE schemes, not only is the use of RPR schemes rare, but when they are used, their effectiveness has been hard to assess. Jensen and Murphy (1990) and Aggrawal and Samwick (1999) find that relative performance evaluation is not an important source of manager s contracts. Barro and Barro (1990), Joh (1999) and Janakiraman, et al (199) find that CEO s compensation increases with industry performance, and Jenter and Kanaan (006) document that firmspecific performance affects CEO dismissals most strongly when the peer group is not doing well. This is contrary to what a RPR scheme would recommend. Others have found empirical evidence of the presence of RPE contract and support of the theory: Antle and Smith (1986) as well as Gibbons and Murphy (1990) show that holding the rate of return on firm s common stock constant, higher-value weighted industry rates of return lowers growth of CEO pay. More generally, the lack of empirical evidence of the negative relationship between CEO compensation and market or industry performance is referred in the literature as the RPE puzzle. 7 Our study contributes to the growing experimental literature that test the behavioral performance of various incentive schemes (see, for example, Bull, Schotter and Weigelt (1987), Harbring and Irlenbusch (003), van Dijk, Sonnemans, and van Winden (001) and Wu, Roe and Sporleder (006)). A consistent result in this literature is that piece-rate schemes do well at eliciting the theoretically predicted level of effort, whereas tournament contracts have varied results. Bull, Schotter and Weigelt (1987), for example, report that subjects respond on target to the different piece-rate schemes, but for some tournaments their effort choices are off. 8 Wu, Roe and Sporleder (006) find that for a fixed 6 This is due to the fact that in the dynamic model there are explicit as well as the implicit incentives; the later can either reinforce or oppose the insurance effect that lead to welfare improvement in the static environment. 7 For theoretical explanations of the RPE puzzle see Celentani and Loveira (006) and Fershtman, Hvide and Weiss (00). 8 Harbring and Irelenbusch (003) focus on the effect of tournament design on effort levels. They do not make point predictions but study how well subjects understand in 5

6 total uncertainty, varying the relative importance of the common shock has a non-negligible effect on whether the observed effort targets the predicted ones. There is also a growing field experiment literature that looks at how workers output differs across different wage schemes. Lazear (000), Shearer (004) and Shi (007) have used personnel data from firms to see how worker productivity responds to fixed payment wage schemes versus piece-rates. The latter increases productivity as the theory predicts. 9 Bandiera, Barankay and Rasul (005) conducted a field experiment in a fruit picking plant and compared three wage schemes: an individual piece-rate, a relative compensation scheme where individual pay and group performance are negatively correlated, and a relative compensation scheme where individual pay and group performance are positively correlated (group incentives). They obtain that effort is higher under the individual pay schemes. One important design difference of our experiment is the fact that we can compare both how well effort levels chosen by subjects target the theoretically predicted ones and actual profits gained by the principal under all three schemes. To our knowledge, all experimental papers that study the performance of different wage schemes choose as the only criterion how well subjects target a predicted effort level, which leaves the question of which contract makes the principal better off open. 10 Theory In this section we present the solution for the optimal parameters of all three wage schemes as well as the optimal behavior of workers employed under each of those schemes. We also characterize the relative performance of the three schemes in different environments. We use a standard moral-hazard setting. A risk-neutral principal hires agents to produce output. The principal s profit consists of the total output produced by workers minus the cost of hiring them. The output of an agent has an additive structure: y = e + ɛ + η, where e is the effort level chosen by the agent, ɛ is a private production shock and η is a common prowhich direction their effort should go to maximize their payoff when faced with a different tournament structure. 9 Chiappori and Salante (000) surveys the empirical work on contracts. 10 See Section III for more details on our desing. 6

7 duction shock that affects all workers equally. Agents are risk-averse with u(x) = e rx (r is the coefficient of absolute risk aversion). Effort is costly and the cost function associated with effort e i is given by (e i) c. The effort levels of agents are not observable and therefore not contractable; the principal observes only the output produced by each agent. The private shocks are independently drawn from U[ A, A] and the common shock is drawn from U[ B, B]. There are three possible wage schemes that the principal can employ: The Tournament Scheme: The agent that obtains the highest output wins a big prize W 1, the other agent gets a small prize W. The Piece-rate Scheme: Agent i gets wage i = α + β y i The Relative piece-rate (RPR) Scheme Agent i gets wage i = α i + β i y i + γ i y j The principal chooses parameters for each of the schemes to maximize his expected profits: E [ i=1 (y i wage i ) ], taking as given the coefficient of absolute risk aversion of his agents, the distributions of the two shocks, the structure of the cost function of effort, and the outside option of the agents which we will denote by v. The agents choose their effort levels simultaneously after learning which wage scheme is used and what the exact parameters of that scheme are. Shocks are then realized and payments are distributed. The payment of agent i is wage i e i c..1 The Tournament Solution We will concentrate on the symmetric equilibrium of agents effort level, in which e 1 = e. To solve for the optimal effort, we use the approximation of expected CARA utility in terms of certainty equivalent (see Appendix A for the full solution). 11 Optimal effort is determined by e 1 = e = c(w 1 W ) 4A (1) 11 E [u( x)] u(ce( x)) = u(e x r var( x)), where x is the risky alternative and CE( x) is the certainty equivalent of x. 7

8 The principal chooses a prize pair (W 1, W ) to maximize his expected payoff given the Incentive Compatibility (IC) and Individual Rationality (IR) constraints: [ ] max E (W 1,W ) i=1 (y i W i ) { e i = c(w 1 W ) 4A IC i W (e i ) c 1r(W 8 1 W ) = v IR i Therefore, the optimal prize structure is W 1 = c + 4Ac 4(c + A r) + v and W = c 4Ac + v () 4(c + A r) To summarize, given the prize structure described above, each agent exerts an effort of e c =, and receives in expected terms u ( v), whereas the (c+a r) principal s expected payoff is: c v (3) (c + A r) Note that for a fixed structure or prizes, the optimal effort level exerted by the agents does not depend on the degree of their risk-aversion. The intuition behind this result is that in the symmetric equilibrium, each agent is equally likely to win both prizes no matter what the symmetric level of effort is. Therefore, the variance of the agents payment achieves its maximum whenever both agents choose the same effort level (this variance does not depend on the coefficient of risk aversion). As we saw above, the expected utility of a worker can be written in terms of it s certainty equivalent (CE), which consists of parts: expected payment and variance of payment scaled by r. Let s start with the case of a risk-neutral agent: he chooses an effort level which maximizes his expected payment, because he does not care about the uncertainty of the payment (since r = 0 the second term of the CE disappears). Now consider the risk-averse agent that has r > 0. He will choose exactly the same level of effort as the risk-neutral agent because the variance of payment is at its maximum in the symmetric equilibrium and the risk-neutral agent already picked the effort that maximizes the expected payment. The expected utility of a risk-averse agent will be lower than that of a risk-neutral one, but they are both going to choose the same effort level. 8

9 . The Piece-Rate Scheme Solution In equilibrium, workers will choose effort level: e 1 = e = β c (4) The principal chooses a pair of parameters (α, β) to maximize his expected payoff given the IC and IR constraints: [ ] max E (α,β) i=1 (y i α βy i ) { e i = βc IC i α + βe i (e i ) c r β ( σ ɛ + σ η) = v IRi Therefore, the optimal parameters of a linear wage scheme are β = c r ( σ ɛ + σ η ) and α = v β c + c 4 + r ( ) β ση + σɛ (5) To summarize, given these parameters, each agent exerts an effort of e = βc, and receives in expected terms u ( v), whereas the principal s expected payoff is:.3 The RPR Scheme Solution c c + 4r ( ) v (6) σɛ + ση We ve restricted our attention to the linear RPR schemes; however, we allow the principal to set different parameters for each agent if it is an optimal thing to do. So, the principal chooses parameters of the wage scheme (α i, β i, γ i ) for each agent i = 1, in order to maximize his expected profits. Agents choose their optimal effort levels given the parameters of the wage scheme determined by the principal. The certainty equivalent of agent i s expected utility is α i + β i e i + γ i e j r [( ) ( ) β i + γi σ η + σɛ + βi γ i ση] (e i ) c 9

10 Therefore, agent i will choose effort level of e i = β ic The maximization problem of the principal is: max (α i,β i,γ i ) i=1 { e i = β ic [ ] E (y i α i β i y i γ i y j ) i=1 IC i α i + β i e i + γ i e j (e i ) c r [ (β i + γi ) ( ) ] σɛ + ση + βi γ i ση = v IRi Therefore, the optimal parameters of RPR scheme are α = v + r (β + γ ) ( ) ση + σɛ + βγrσ η β c βγc 4 c β = c+r(1 ρ )(ση +σ ɛ) γ = ρβ (7) where ρ = σ η σ ɛ +σ η. It turns out that the optimal RPR scheme has identical parameters for both agents. This is contrary to the environment in which the principal cares about the best output produced by employed agents as opposed to their total output as in our model. 1 Moreover, notice that as we mentioned before an RPR scheme filters out common shocks, which happens through the negative γ coefficient. High output produced by one agent is compensated less if the other agent produced high rather than low output, and that is often the case due to the high positive common shock that affects both outputs. To summarize, given the described parameters of the wage scheme, each agent exert effort of e = βc, and receives in expectation u ( v), whereas the principal s expected payoff is c c + 4rσ ɛ σ ɛ +σ η σ ɛ +σ η v (8).4 Theoretical comparison of the three wage schemes Proposition 1: 1 See Levitt(1995), which studies what happens when a principal cares only about the best output produced by his agents. In such environment, asymmetric RPR schemes sometimes do better than the symmetric ones, although agents are ex-ante identical. 10

11 Expected payoff of the principal is always higher under the RPR scheme as compared to the piece-rate scheme and the tournament. A tournament does better than a piece-rate scheme when the common uncertainty is relatively high, that is, σ η > σ ɛ A piece-rate scheme does better than a tournament when the common uncertainty is small relatively to idiosyncratic one, that is, σ η < σ ɛ In the simple theoretical framework presented above the principal is assumed to be risk-neutral, and therefore, does not care about the variance of profits. However, in a real life situations the principal might also care about both expected profits and it s variance. The proposition below summarizes the variance of the principal s profit if agents behave according to the theory. Proposition : The variance of the principal s payoff is smallest under the piece-rate scheme, whereas it is greatest if the tournament scheme is employed: proof Piece-rate scheme: var principal = (1 β) [ σɛ + 4ση RPR scheme: var principal = (1 β + γ) [ ] σɛ + 4ση Tournament: var principal = [ ] σɛ + 4ση The Proposition is true because: β Piece-rate > β RPR + γ RPR > 0, q.e.d. ] 3 The Experimental Design Each recruited subject participated in only one session. All subjects were informed of an experiment taking place via announcement, and were recruited via the CESS software. This resulted in a diverse group of undergraduate NYU students whose departments ranged from Music, to Physics. All sessions were conducted through computer terminals, and the software was written in Z-Tree. In each experimental session subjects experienced only one of three studied wage schemes (Piece-rate, Tournament or RPR scheme). Each session 11

12 was organized according to a within subject block design: each subject went through twenty rounds of the High variance treatment, followed by 0 rounds of the Low variance treatment, and then again 0 rounds of High and twenty rounds of Low (HLHL). 13 For each wage scheme we also conducted a LHLH session to test for order effect and found none. 14 The outside option of the subject was kept constant across all schemes and sessions. In other words, in expectation, our subjects should receive the same payment from each session. To our knowledge, we are the first to use a within subject block design for the environment for this type of experiment. This allows us to study whether the subjects individually respond to an exogenous change in environment they face and adjust their behavior accordingly. We induced CARA utility with risk aversion coefficient of 0.1 using the method of Berg, Daley, Dickhaut, and OBrien (1986) and Roth and Malouf (1979). 15 The general procedure is the following: subjects play for tokens, and those tokens are converted into a probability of winning a big prize. The conversion procedure puts weights on the tokens to reflect the preferences that the experimenter would like to induce. For example, if the experimenter wants to induce risk neutrality, he/she would make the conversion linear. For risk-aversion, the conversion would be concave thus making earlier tokens more valuable. 16 Since we induce a specific risk-aversion, we were able to use the optimal coefficients in each of the wage schemes that a principal with these risk-averse workers would want to use. Note that even if this procedure did not work in practice, and left the agents with a different risk aversion parameter, this would theoretically not influence the effort choices of the subjects (see Section III to see that the effort choices are independent of the coefficient of risk aversion). In other words, a principal who believes that his agents have a risk-aversion parameter of 0.1 will choose the optimal 13 High variance treatment means that the variance of the private shock was relatively high, whereas Low variance treatment means that variance of the private shock was relatively low. 14 Using a non-parametric rank-sum test we tested whether there is a statistically significant difference between effort levels exerted by subjects in each block in each treatment in HLHL versus LHLH sessions. For all three wage schemes the answer is no. We also looked at the average per period effort level across subjects as a function of periods. This is just a descriptive way of comparing data across HLHL and LHLH sessions. Again, no order effect was detected in all three wage schemes. 15 Estimations of CARA coefficients have generally been between and see Saha, Shumway and Talpaz (1994) that summarize studies on Risk Aversion Estimations (page 175). 16 For experimental evidence on the success of inducing risk-aversion see paper by Vesna Prasnikar (00). 1

13 parameters within each wage scheme, as we derived in the theory section. In the high variance treatment, the private shock was drawn from a uniform distribution with bounds -4 and +4. In the low variance treatment, the bounds of the private shock were -14 and +14. The variance of the common shock was kept constant in both treatments and was drawn from a uniform distribution with bounds -7 and +7. Tables below present the parameters that were used in the experiments: Table 1: High Variance Treatment Tournament Piece-Rate RPR Wage(i) W 1 = *output i *output i W = *output j Effort Level Profit Table : Low Variance Treatment Tournament Piece-Rate RPR Wage(i) W 1 = *output i *output i W = *output j Effort Level Profit During each round the subjects went through the following stages: at the beginning of a round, subjects were reminded of the payment structure (Piecerate, or Tournament, or RPR) as well as the environment that they were facing (high or low private shock variance). They were randomly and anonymously matched into pairs. Subjects then had to choose an effort level. 17 After everyone made their choice, the subjects were shown their output, as well as the output of the person they were paired with, and finally the number of tokens they earned for that round. The subjects were then randomly and anonymously re-matched with another participant and moved on to the next round. At the end of the session, one round for each block was randomly chosen (so four rounds total), and the tokens the students earned for that round were then converted into a probability of winning the big prize. 17 We restricted the effort level to be between 0 and 55 as inducing risk-aversion requires that the support of the wage be bounded. 13

14 In our case, the big prize was 4 dollars and the small prize 0 dollars. So subjects could win up to 16 dollars if they won at all four blocks, or could win 0 dollars if they did not win any of the big prizes. In addition, subjects received a participation fee of 5 dollars. Sessions lasted about one hour each, and at the end subjects filled out a questionnaire in which we asked them questions about themselves, their understanding of the game and how they made their choices during the experiment. In summary, the experimental design described above has four important properties: We are fixing the environment, defined by the variance of the private and common shocks, the risk aversion parameter of the agents and their outside option, and test the three wage schemes with optimal parameters. We induce risk aversion, which is essential for comparing the three wage schemes. The common shock is the part of the designed experiment. This is crucial since it plays an important role in determining the optimal parameters within each scheme and, therefore, in comparing the performance of the tournament, piece-rate and RPR schemes. 18 Our design allows to test for both effort level of agents as well as profits of principal, which is necessary in order to establish which scheme is the preferred choice for the principal that faces a fixed environment. 4 Hypothesis The theoretical analysis described in the previous section implies several predictions that we test in the experiment. We start with checking the point predictions for the effort levels for each treatment in each game. Hypothesis 1A (B,C): In each treatment, the effort levels chosen by the subjects in the tournament (piece-rate, RPR) scheme are not statistically different from the predicted level. 18 Wu and Roe (005) and Wu, Roe and Sporleder (006) are the only papers that include the common shock in tournament experiments. 14

15 Hypothesis A (B,C): In each wage scheme, the effort levels chosen in the High variance treatment are lower than the ones chosen in the Low variance treatment. Aside from the point predictions, the theory also implies an ordinal ranking of effort levels. RPR should always elicit higher effort levels than the tournament and the piece-rate. In the Low variance treatment, the tournament elicits higher effort than piece-rate scheme, and the reverse holds for the High variance treatment. Hypothesis 3A: When the variance of the private shock is relatively low, the effort levels observed in the RPR scheme are higher than the ones in the tournament, which are in turn higher than in the piece-rate. Hypothesis 3B: When the variance of the private shock is relatively high, the effort levels observed in the RPR scheme are higher than the ones in the piece-rate, which are in turn higher than in the tournament. Our experimental design allows us to directly compare the profits of the principal across the three wage schemes. The next hypothesis addresses the following question: which wage scheme should the principal (who is faced with a fixed environment) use in order to maximize his expected profits? The last hypothesis predicts that within each wage scheme, the principal makes higher profits when private shocks are relatively low (low variance treatment). Hypothesis 4A (B): When the variance of private shock is relatively High (Low), the principal s profits in the RPR scheme are higher than in the Piecerate (Tournament) scheme, which are in turn higher than in the tournament (piece-rate) scheme. Also, in each wage scheme, the profits of the principal in the High variance treatment are lower than the ones in the Low variance treatment. 5 Description of the data We conducted a total of 10 experimental sessions. 19 For each wage scheme, the order of blocks was HLHL, except for the last session where we reversed 19 One session of the tournament scheme is excluded from the analysis because of technical problems that occurred during the experiment. 15

16 the order of the blocks to LHLH to check for the presence of order effects. Using regression analysis, we tested for the differences between session with different order of blocks. No order effect was found. 0 Using the technique suggested by Frechette (005), we tested for session effects and found none. We therefore pool the data from all session together in our analysis. In the experimental literature, it is a common observation that subjects take time to get used to the game and understand its mechanism. It was also the case for our subjects. For that reason, we restrict our analysis to the last 0 rounds of each treatment for each wage scheme. Table 3 presents the descriptive statistics of the data we collected. We report the average effort as well as averaged profits for each session by wage scheme. Table 3: Descriptive Statistics High variance Low variance Scheme Subjects Effort Profit Effort Profit Session 1 Tournament Piece-Rate RPR Session Tournament Piece-Rate RPR Session 3 Tournament Piece-Rate RPR Session 4 Tournament Graphs 1 and present the first overview of the data. We plot effort averaged per period across all subjects versus time (period). We also indicate by a horizontal dashed line the theoretical prediction for each wage scheme. Graph 1 represents the High variance treatment and Graph the Low variance treatment. In the first few rounds of the experiment the average effort per period is similar in all three wage schemes. However, as more periods are played, subjects learn the game and the average effort per period levels become distinct across schemes. In the High variance treatment, in each wage scheme, it converges 0 The regressions are available from the authors upon request. 16

17 Figure 1: High Variance Treatment High variance treatment: Effort level averaged per period across all subjects in each wage scheme Piece-rate Tournament RPR Piece-rate - theory Tournament - theory RPR - theory period RPR Piece-rate Tournament 17

18 Figure : Low Variance Treatment Low variance treatment: 55 Effort level averaged per period across all subjects in each wage scheme Piece-rate Tournament RPR Piece-rate - theory Tournament - theory RPR - theory period RPR Piece-rate Tournament 18

19 exactly to the theoretically predicted level. In the Low variance treatment, the average per period effort level in the RPR scheme beats both the tournament one and the piece-rate one, although it is below the predicted level. Moreover, the effort levels chosen by the subjects in the tournament and the piece-rate schemes are not in the order predicted by the theory: effort in the tournament not only substantially undershoots the theoretical level, but it is also even lower than the piece-rate prediction. Here we report the dispersion of the effort levels under each wage scheme. We averaged the effort level chosen by each subject across all rounds of the same treatment, and report the variance of this variable in Table 4. Table 4: Variance of effort High variance treatment Low variance treatment Tournament Piece-rate RPR Tournament Piece-rate RPR Session Session Session Session Consistent with other experimental studies, the effort levels in the tournament are more disperse than in the piece-rate scheme. 1 The smallest variance of effort is achieved under the piece-rate scheme. The piece-rate scheme is the only one in which subjects are not involved in any strategic interaction with each other. In the other two schemes, subjects play a strategic game with each other, which results in more noise and makes it more difficult to establish the effect of their effort choice on their performance. Finally, we looked at how many subjects in each session dropped out completely, that is, exerted zero effort level in last 0 rounds of both treatments. The drop-out rates (by session) in the tournament scheme are: 11%, 0%, 6% and 9%. In the other two wage schemes there are no drop-outs at all. This drop-out behavior in tournaments been noted in other experimental studies on asymmetric tournaments, where some subjects are handicapped. We observe a non-negligible percentage of drop-outs even in a completely symmetric tournament, which hasn t been found in other studies. One possible explanation is the fact that we impose risk-aversion. Playing zero effort in 1 see Bull et al (1987), van Dijk et al (001). See Schotter and Weigelt (199). 19

20 our tournament guarantees a known specific amount of tokens (no cost of effort), and because of the conversion procedure from tokens to a monetary amount, this ensures an 80% chance of winning the 4 dollars. This comes back to the discontinuity issue of the tournament mentioned above. An additional unit of effort increases the probability of wining the big prize, but the actual payment does not necessarily increase. On the contrary, in the RPR and piece-rate schemes, an additional unit of effort necessarily the final payment, making dropping out more obviously sub-optimal. 6 Experimental Results We organize this section into four subsections, each corresponding to the hypotheses stated in section Hypothesis 1 The results are summarized in the table below. We present the results from non-parametric tests only. 3 Table 5: Effort Level Point Predictions Wage Scheme Theory Sign rank test (10%) Tournament - HIGH 6.87 Statistically not different Tournament - LOW Statistically different (smaller than theory) Piece-rate - HIGH 30.8 Statistically not different Piece-rate - LOW 35. Statistically not different RPR - HIGH Statistically not different RPR - LOW 45.1 Statistically different (smaller than theory) - the measure of effort level we used is constructed as follows: for each wage scheme, for each treatment, for each subject we average the effort decisions over all periods. Experimentally, individual piece-rate contracts have typically been successful at eliciting the predicted effort levels (see Bull, Schotter and Weigelt (1987), Harbring and Irlenbusch (003) and van Dirk, Sonnemans and van Winden (001)). Those studies also found that the average effort in the Tournament 3 The results using parametric tests are not significantly different and available from the authors upon request. 0

21 does not always target the predicted one. We obtain similar results, though the magnitude of the mistake seems bigger than what other studies have found. 4 One essential difference in our experiment compared with those previously done is the common shock component that is introduced along with the private shock. To see whether the low level of effort exerted in the tournament (especially in the Low variance treatment) is the result of this complication, we ran one session of the tournament scheme, in which we emphasized that the common shock has no effect at all on the relative ranking of agent s output, and therefore should not change their behavior relative to the situation in which there would just be a private shock. 5 There are no significant differences in this session compared with the other sessions. 6 It is worth noting that the result of undershooting effort in tournaments is found in different designs. Figure 3 shows the percentage of subjects who responded to incentives in the right direction. To shed more light on why the two relative evaluation schemes do so poorly at targeting the predicted effort levels in the low variance treatment, we conducted the above test on the sub-sample of subjects who understood the incentives properly. For that sub-sample, the predicted effort level was targeted perfectly for all wage schemes for both treatments (High variance and Low variance), with the exception of the tournament in the low variance treatment. These results as well as the sub-sample summary statistics are reported in the table below. This seems to indicate that the reason RPR doesn t always target the predicted effort level is entirely due to the few subjects who did not understand the incentives as the theory states them. Two hypotheses to explain why tournaments do not do as well as predicted by the theory (as opposed to individual piece-rate contracts) are first that in a tournament there is a discontinuity issue, and second that the agents are put in a competitive environment. Our results suggest that pure competition 4 Running the same test after removing the effort choices of drop-outs does not fix the problem in the tournament. 5 This is why compared to the number of sessions for the RPR and piece-rate schemes there is one extra session of the tournament scheme. The instructions for this session included an additional example in which possible values of the common shock are considered (all else remaining equal). The example showed that the relative ranking of the agents, and therefore who gets the larger prize does not depend on the value of the common shock. 6 A rank-sum test showed no significant difference in the distribution of effort choices in each treatment compared with other sessions. 1

22 Table 6: Effort Level Point Predictions for the Sub-Sample of people who responded to the incentives in the direction predicted by theory Wage Scheme Theory Observed Sign rank test (10%) Tournament - HIGH Not different Tournament - LOW Different (smaller) Piece-rate - HIGH Not different - Piece-rate - LOW Not different RPR - HIGH Not different RPR - LOW Not different the measure of effort level we used is constructed as follows: for each wage scheme, for each treatment, for each subject who responded to the incentives in the right direction, we average the effort decisions over all periods. may not be the main source of the behavioral anomalies that have been observed in tournament wage schemes. Indeed, the RPR scheme is also a relative scheme, but payoffs of agents are continuous in exerted effort. The discontinuity issue is the crucial difference between the tournament and the RPR scheme, and seems to be what handicaps the tournament. Conclusion 1: In the High variance treatment, effort levels of subjects target precisely the ones predicted by the theory in each wage scheme. However, this is not the case in the Low variance treatment: it happens only in the piece-rate scheme, whereas in the Tournament and RPR schemes, the observed effort level is significantly below the predicted levels. 6. Hypothesis To see whether subjects respond correctly to the change in incentives within each scheme, we test for the overall statistical difference in effort levels between the High and Low variance treatments. We use a sign sign-rank test to test whether the distribution of the average effort of subjects in each treatment is the same. For the piece-rate scheme, the effort levels of the Low variance treatment are significantly higher than the ones in High variance treatment, as the theory predicts. For the tournament and RPR schemes, the results are not significant, but the direction of the change is correct. Graph 3 below shows the fraction of subjects whose effort was higher in the low variance treatment, as the theory predicts. According to the theory, the effort level in High variance treatment should be lower than in the Low variance treatment in each wage scheme. The

23 Figure 3: Distribution of correct and incorrect number of individual switches between High and Low variance treatment 70% 60% 50% RPR Tournament Piece-rate 40% 30% 0% 10% 0% RPR Tournament Piece-rate RPR Tournament Piece-rate RPR Tournament Piece-rate right direction wrong direction no switch 3

24 empirical results shows that more than half the subjects responded to the incentives in the correct direction in each scheme (50% in RPR, 55% in Piecerate and 70% in Tournament). However, we still have between 30% and 40% of subjects responding in the opposite direction. Reading the answers to the questionnaire that we ran at the end of the experiment, we learned that when the private shock was low it seems as if many of those puzzling subjects wrongly concluded that since most of the noise was common, they didn t have to exert effort to make up for the private shock instead of realizing that when total uncertainty is low, they have more power to influence the output they produce. Conclusion : More than half of the subjects in each wage scheme respond to the incentives correctly. However, the strategic interaction between players that arise when relative evaluation schemes are used, produces fewer correct individual responses to the incentives when compared with the independent wage scheme. 6.3 Hypothesis 3 To see whether the observed efforts across wage schemes are different and preserve the order predicted by the theory, we run a rank-sum test that compares the distributions of efforts in the different wage schemes. This comparison is of special importance, since it allows us to see which of the three contracts elicits the higher effort levels from agents. Hypothesis 3A is strongly supported by the data (significant at 5%). 7 That is, in the High variance treatment, the effort level in the RPR scheme is significantly higher than the one in the piece-rate scheme, which is in turn significantly higher than the one in tournament contract. Hypothesis 3B is only partially supported by the data. The RPR scheme indeed elicits higher effort levels than the piece-rate and the tournament, but the ranking of the effort levels elicited by the tournament and the piece-rate schemes are not in the predicted order. This result is not surprising in view of the point prediction results that we described above but confirms that not only are the tournament effort levels far below the expected level, but they are so low that they are even smaller than the effort levels of the piece-rate. This is still the case when we look at the sub-sample of subjects that switched 7 The rank-sum test performed when looking at the average effort level among all subject in each stage gives us the same result. 4

25 in the correct direction. These results are confirmed using regression analysis. We regress every effort decision on two dummy variables (a piece-rate indicator and an RPR indicator). 8 Another way of interpreting hypothesis 3 is to see it as a measure of dispersion of effort levels across schemes. From Conclusion 1 we know how well each wage scheme targets predicted effort levels. In answering hypothesis 3 we also show that effort across schemes are statistically significantly distinct. Conclusion 3: The RPR scheme always elicits higher effort choices than the piece-rate and tournament contracts, as predicted by the theory. In the High variance treatment the piece-rate ellicits higher effort choies than the tournament, as predicted by the theory. In the low variance treatment there are major behavioral reactions to the tournament and the piece-rate still ellicits higher effort choices than the tournament when the theory predicts the reverse. 6.4 Hypothesis 4 Hypothesis tested whether subjects respond correctly to a change in incentives. Their effort decisions obviously influence the final profits principal receives under each wage scheme, but it is not obvious what the comparaison between the profits in each wage schemes will be. Regression results show that a principal who employs the RPR scheme obtains significantly higher profits than one who would employ the piece-rate or tournament schemes, and this in both treatments. 9 In the High variance treatment, the rank of the wage schemes in terms of profits is according to the theory. However, in the Low variance treatment, the piece-rate continues to beat the tournament. These results are also confirmed when we perform a rank-sum test on the the average profits of the principal across all periods of the same treatment. Given that the subjects drastically undershoot effort predictions in the tournament, this result is not surprising. It does however highlight the risk a principal faces when employing that wage scheme: the 8 See Appendix C for the results of the regression. 9 The averaged profit for the principal is regressed on dummies for the piece-rate and RPR scheme, leaving the tournament as the base game. See appendix C for the regression results. 5

26 cost to the principal (high prize plus the low prize) is independent of the output produced by the agents. In the case where workers produce an effort below the predicted one, the principal ends up having to pay out a lot of money without being compensated for it by a high output. We also performed checks on whether the profits of the principal are higher in the Low variance treatment than in the High variance treatment within each wage scheme. This is indeed the case in the piece-rate scheme. In the RPR scheme the direction of change is correct (as predicted by theory), but the difference is not statistically significant. Finally, in the Low variance treatment of the tournament scheme, the profits of the principal are significantly lower than the ones in the higher variance treatment contrary to the theory. Again, it is not surprising given the fact that subjects significantly undershoot in their effort levels in Low variance treatment. 30 The use of tournaments is often justified based on its better performance in environments with high common uncertainty in spite of well-documented behavioral effects. Both the RPR and tournament schemes possess the property of filtering out the common shock. That is, in the Low variance treatment, under both the tournament and the RPR scheme, the principal should earn higher profits than under the piece-rate scheme. However, our results suggest that in practice only RPR does better. Conclusion 4: In both treatments, the RPR scheme yields significantly higher profits for the principal than the piece-rate and tournament schemes. When the theory predicts that the tournament should do better than the piece-rate (Low variance treatment) this is not the case. 7 Conclusions Our data clearly suggests that a principal using a Relative Piece Rate scheme would receive higher profits than if he used a piece-rate or a tournament schemes. This study may shed light on what is the preferred wage scheme for a principal faced with a fixed environment. To our knowledge our design is the only one that allows for direct comparison of the performance of all three schemes (optimal within the class), for a fixed environment. To be able to conclude on the relative performance of three wage schemes it is necessary to test them in the same environment. 30 See appendix C for the regressions. 6