Cooperation or Competition? A Field Experiment on Non-monetary Learning Incentives

3.1 Test Format and Procedure

Each test was computerized and consisted of five multiple-choice questions to be answered in 50 minutes and covered all topics taught in the course right up to the last lecture before the test. The five tests were designed so as to keep the degree of difficulty constant. We ran them in the computer laboratory at the School of Economics at the University of Bologna.^[5] Desks were laid out in order to prevent students from talking during the tests (see Figure 3 in the Appendix). Given the high number of students and the capacity of the lab, two consecutive sessions took place for each test on the same day, and the questions were identical across sessions. To ensure that students of the first session could not communicate with those participating in the subsequent one, we asked the students assigned to the second session to gather at the entrance of the lab 10 minutes before the start of their session. Then students of the first session exited the lab from another door placed at the other end of the room. Moreover, we did not allow students to leave the lab in case they completed their test before the end of the 50 minutes assigned.

3.2 Treatments

The mark in each test consisted of an individual component, based on the number of correct answers in the test, and a number of extra points related to the experimental condition.

Our study included a baseline condition and two treatment conditions characterized, respectively, by a competitive and by a cooperative incentive scheme. The structure of the three experimental conditions is as follows. Under all conditions, in tests 1 and 5 students worked individually. In the two treatment conditions (cooperative and competitive) students were randomly matched in pairs at the beginning of tests 2–4^[6] and had the opportunity to exchange messages with their partner via a controlled chatroom, running on their computer. In the baseline condition students always worked individually. In all conditions, part of the incentive depended on individual effort. This was the only determinant of the whole score in all tests under the baseline, while under the competitive and cooperative treatments the total score in tests 2, 3 and 4 depended also on the partner’s performance.^[7]Table 1 summarizes the main characteristics of the experimental conditions, which are described in detail below.

Students were assigned to experimental conditions after test 1, before test 2.^[8] At the beginning of each of tests 2, 3 and 4 students assigned to the two treatment conditions were asked whether they wanted to use the chatroom to communicate with the assigned partner. This decision was taken simultaneously and paired up students could use the chatroom only if both declared to be willing to communicate. If two students chose to communicate, for each question in the test they could send one “signal” to indicate their preferred answer and/or one short text message of up to 180 characters. Interactions were anonymous, as students were not informed of the identity of their partner. In the baseline treatment no interaction between students was allowed.^[9]

In each test, the value pq of correct answer to each question q ranged between 0.3 and 1.2 points according to the question’s relative difficulty. The overall difficulty of the five tests was kept constant,^[10] while the topics changed across tests. Across all treatments, the number of points vi,k a student could get by correctly answering the questions of test k was:

In each test, the maximum number of points vˉ was equal to 3. This was the individual part of the mark in the test, i.e., the component which was common to all treatments.

In the competitive treatment, student i’s mark in a test was increased by 2 extra points if her score resulted to be strictly higher than her partner’s. The kth test mark vˆi,k for student i under this incentive scheme is described in eq. [1]:

This provides an incentive for both paired up students to compete.

Conversely, in the cooperative treatment, student i’s score in a test was increased by 1 extra point if the partner’s net score was sufficiently good, i.e., at least equal to a fixed threshold (1.5 points). The kth test mark vˆi,k for student i under this incentive scheme is presented in eq. [2]:

Finally, students in the baseline treatment received 1 extra point in tests 2, 3 and 4. This was done so that the maximum number of bonus points per pair is constant across treatments.^[11] This element of the design was thoroughly explained to students in class. We clarified that no treatment by design systematically granted fewer bonus points. In fact, for the design to be correctly balanced, incentives in the cooperative and competitive treatment should have the same size in expectation, i.e., holding ability constant.^[12]

Notice that in our design, communication is possible only in the cooperative and competitive treatments, but not in the baseline. Hence, the treatment effects we can possibly observe are determined as the outcome of the interplay between communication and the incentive scheme. Because communication is essential in the cooperative and competitive treatments, the only alternative would have been to allow for communication in the baseline. However, the baseline aims at measuring the performance of students in isolation, which would not be possible, had we allowed for communication.

3.3 Timeline of the Experiment

The experiment started in February 2010 and ended in July of the same year. In the first lecture of the course, on February 25th, the full set of instructions was distributed to students and each of them had two days to decide whether to take the tests or not. At that stage, students were not explicitly informed that they were taking part in an experiment;^[13] only at the very end of the course participating students were asked to sign a consent form authorizing the treatment of the data collected during the tests.^[14] In this sense, our study is a “field experiment” under the terminology defined by Harrison and List (2004).

On March 1st, during a standard class, students were asked to fill out a questionnaire collecting data on some personal characteristics (age, gender, familiarity with computers, frequency of use of e-mail and chatrooms, mother and father’s level of education). We use questionnaire answers in the econometric analysis to control for individual-specific characteristics.^[15]

On March 22nd students took the first test. Note that at this stage students had not yet been assigned to treatments, therefore the grade they obtained in the first test can be used as a measure of their effort level before being exposed to the treatment. Students were informed of the treatment to which they had been assigned only three days later, on March 25th.^[16] Right after the end of the test, students were informed about their own result in the first test and about the distribution of the first test score among participants. In this way we tried to convey common knowledge of the distribution of competences and ability within the population. Section 4 shows how this is relevant from a theoretical point of view.

The remaining four tests were taken approximately every 2 weeks, in April and May 2010, with the exception of the fifth which was administered 1 week after the fourth. Questions in this last test covered the whole spectrum of the topics of the course. These two design features should ensure that the students’ performance in the fifth test mostly depends on the level of effort exerted during the whole duration of the course, and not just in the previous few days. After the tests, students did not receive any feedback on the performance of the other students but were only informed of their own score. Students could benefit of the bonus points gained in the tests only if they took the final exam in June or July 2010. Before the experiment started, students were informed that the bonus points would expire after the summer exam term (no bonus would be granted in late retakes).

4.1 General Features

We assume that students’ abilities are in the interval θ∈[0,1 and are distributed according to a non-degenerate density function f(⋅). Students choose a level of effort ei∈[0,1, which determines their score in the tests. The dis-utility of effort is c(e) where c(⋅) is the same across the population.^[17] We further assume that c(⋅) is such that c′(⋅)>0 and c′′(⋅)>0.

The expected score in test k is increasing in ability and effort^[18] and is given by the following expression:

Thus, we assume that the productivity of effort is higher for higher-ability students and that only students with θ=1 can get the maximum score (vˉ) if they exert the maximum level of effort (ei=1).

We assume that students choose their level of effort twice: the first time when the course starts, before test 1, hence before being assigned to the treatments; the second time when the assignment to treatments takes place, i.e., after test 1. We denote the former by ei,1 and the latter by ei=ei,k,k=2,…,5.

When students choose ei, after test 1, their expected utility Ui(Bi,ci) depends on two components: (i) the cost of effort ci=c(ei) and (ii) the bonus points to be obtained in the four remaining tests

Note that the bonus points in the two treatment conditions are partly determined by the interaction with the partner.

4.2 Baseline Treatment

A student assigned to the baseline treatment does not interact with any other student. Remember that to get the bonus points from the tests, the student needs to get a sufficiently high score. If si,k=<1.5, student i obtains zero points for test k. This implies that in principle there are two possibilities: either eiBL(θi)>0 and vi,k>0,k=2,3,4,5 Z, or eiBL(θi)=0 and vi,k=0,k=2,3,4,5. The latter result emerges when the student’s ability is so low that the cost of the effort required for him to reach the threshold is higher than the marginal utility he would get from the additional points. Albeit theoretically possible, the latter case is practically implausible, hence we assume it away. Under this assumption, the expected number of bonus points he gets from tests 2 to 5 is

As a consequence, his expected utility only depends on his own type and on the chosen level of effort, and it is not affected by the distribution of efforts and types among other students. Let us assume that the expected utility function is continuous and twice differentiable, it is separable in the bonus points and effort and has a single maximum in the interval [0,1. Let us denote by eiBL(θi) the optimal level of effort in the baseline treatment, for a student with ability θi.

4.3 Competitive Treatment

In order to model students’ behavior under the two treatments and to derive predictions, we look for the equilibrium in the Bayesian-Nash games where students have private information about their own ability and a common knowledge of the distribution of ability in the population.

Under the competitive scheme, students get bonus points if their score is higher than their partner’s. Equation [5] describes the expected number of bonus points in this case:

Under regularity assumption on the distribution of ability in the population, it can be shown that:

where Φj is the mapping from the effort to the individual ability.^[19] Now, given that Φ(e)′=1/e(θ)′, we can rewrite eq. [6] as

Since we assumed that eiBL>0, then it follows that ∂Ui∂BiBL∂BiBL∂ei|eiBL(θi)=c′(eiBL(θi)). As a consequence, ∂Ui∂Bicomp∂Bicomp∂ei|eiBL(θi)>c′(eiBL(θi)), which implies that the optimal level of effort in the competitive treatment must be higher than in the baseline.

4.4 Cooperative Treatment

Under this scheme, each student has a clear incentive to share information (in tests 2, 3 and 4) because the mark depends also on their partner’s effort. Notice that by exerting an effort equal to eiBL(θi) in the cooperative treatment student i can be sure to get the bonus, if he shares his knowledge with the student he is paired with. Hence, in the neighborhood of eiBL(θi) the expected number of bonus points from tests 2–5 becomes:

The first term in eq. [7] represents the points obtained in test 5, where no interaction between students was allowed, while the second term represents the bonus obtained in tests 2, 3 and 4. The assumption that information is shared by the students is crucial and it implies that the probability of answering a question correctly is given by the probability that either one of the two students knows the solution. It follows that, since eiBL(θi)>0:

The second term on the right-hand side of eq. [8] is always non-positive and its absolute value increases with θi. It follows that ∂Ui∂Bicoop∂Bicoop∂ei|eiBL(θi)>c′(eiBL(θi)), which implies that – information being shared – each team member has an incentive to exploit the effort of the other thereby lowering his/her own effort below eiBL(θi).

To conclude, under the cooperative treatment, team members have an incentive to shrink their effort, and this detrimental effect of cooperation on effort is stronger for students with higher ability.

4.5 Testable Predictions

Our theoretical model predicts that, given the ability θi, the effort exerted by student i in the three treatments is such that:

i.e., we expect that on average students randomized into the cooperative treatment exert lower effort than students randomized into the baseline treatment, whereas students randomized into the competitive treatment should exert more effort.^[20] Conversely, in test 1, all students face the same incentives and the optimal effort depends only on their ability level, i.e., ei,1coop=ei,1BL=ei,1comp=ei,1. Moreover, the model predicts that the detrimental effect of the cooperative scheme is stronger for high-ability individuals. Note that our main testable predictions involve the differential changes in effort across treatments and ability levels. Our design allows to measure those changes, as discussed in more detail in Section 5.1.

We also expect that students assigned to the cooperative treatment will use the chatroom more frequently and will use it to exchange information. Conversely, students assigned to the competitive treatment should use the chatroom less frequently and could potentially use it for acts of sabotage, i.e., to suggest the wrong answers. Note that in our setup, even though sabotage during the experiment is possible, it should not be credible, hence it should not be part of an equilibrium strategy. We collected data to verify this claim, which is discussed in Section 5.3.

5.1 Measuring Effort

Our theoretical model predicts that for a given level of ability there is an ordering in the effort exerted by each student i, namely eicoop<eiBL<eicomp. Thus, we expect that, on average, students randomized into the cooperative treatment exert lower or equal effort than students randomized into the baseline treatment, whereas students randomized into the competitive treatment should exert more effort.

Equation [3] in our model describes the relationship between expected student’s score in each test and effort, namely si=θieivˉ, where si is the net score of individual i, θi is a measure of individual ability, ei is the effort exerted and vˉ is the maximum score.^[21] Taking logs and allowing for noise in the way in which effort generates the score, we get:

where yi≡log(si) is the log of the net score of individual i, ζi≡log(ei) is the log of the effort exerted, while ηi=log(θi)+εi and E[ηi]=log(θi), i.e., we assume that only the idiosyncratic component ε averages to 0 for any i, while the error ηi has a possibly non-zero mean equal to an individual-specific constant.

Given the mapping between performance in the test and effort as described in eq. [9], our experimental design provides a way to measure the change in effort under reasonable assumptions. As pointed out in Section 3, we observe students’ performance in test 1 – before the assignment to the treatments – and in test 5 – after exposure to the treatments. Both these tests are taken individually under all treatments, they cover similar topics, share the same structure, have the same number of multiple choice questions and are designed to keep the difficulty constant. However, by construction, the score in the first test and the effort exerted to pass it cannot be affected by the treatments because both performance and effort are pre-determined with respect to the assignment to the different incentive schemes. Conversely, the score in the last test should reflect changes in effort induced by the treatment. This is because, as explained in Section 3, the fifth test was administered 1 week after the fourth and the questions in this last test covered the entire spectrum of the topics of the course. This should ensure that the students’ performance in the fifth test mostly depends on the level of effort exerted during the whole duration of the course, hence reflecting the effect of the treatments in tests 2–4. Indeed, moving from eq. [9] and comparing the performance in test 5 and 1, we have yi,5−yi,1=ζi,5−ζi,1+εi,5−εi,1. It follows that E[yi,5−yi,1]=E[ζi,5−ζi,1, i.e., by looking at the change in the logarithm of score between the first and last test, we measure the change in the logarithm of effort net of the direct effect of any fixed individual-specific factor, such as ability.^[22]

It is important to remember that all our experimental conditions have a common individual incentive to increase effort, but they differ in the incentives to compete or cooperate. Following the theoretical predictions of our simple model, we expect an increase in effort in all treatments compared to a setup where no individual incentives are granted. Our experiment is not designed to estimate this common effect: in fact, all of our treatments have individual incentives. Instead, it is devised so as to measure the differences in the treatment effects. Our model predicts that the level of effort induced by the cooperative incentive scheme is no lower than the one induced by the baseline, while the opposite holds for the competitive incentive scheme. This ordering holds also if we consider log(e), because the logarithm is a monotonic transformation.

To test the theoretical predictions we first contrast the distribution of the change in effort under the three schemes and check for differential treatment effects over the effort distribution. We then assess the effect on the average change in log(e) by running the following regression

where β0 represents the average change in log(e) under the baseline, β1 is the average differential change in log(e) under the cooperative scheme compared to the baseline and β2 is the average differential change in log(e) under the competitive scheme compared to the baseline. The theory predicts β1<0 and β2>0.

There is also the additional prediction that β0=0, i.e., no change in effort under the baseline treatment. Indeed, our model does not consider the possibility that students’ performance may increase across tests simply thanks to the fact that they are becoming more accustomed to the type of tests and the way these are performed in the laboratory. Such an effect, however, would be common across treatments and would not affect our theoretical predictions. If it occurs, in practice the estimate of the intercept β0 will be positive. More generally the intercept captures every factor that influences performance and is constant across treatments.

5.2 Data and Descriptive Statistics

Among the 145 students attending the course, 131 applied for participation in the experiment. Our elaborations are based only on the records of the stayers, i.e., 114 students who participated in all 5 tests. We exclude from the elaborations the records of 17 students who missed at least one test, of these, 10 students assigned to the baseline treatment, 2 students assigned to the cooperative treatment and 5 students assigned to the competitive treatment (see Table 7 in the Appendix).^[23]

The samples of stayers are balanced across treatments with respect to observed pre-determined characteristics: we do not detect differences in the distribution of the score of the first test (score 1) and the average mark in previous exams (GPA) between any two treatments (baseline, cooperative, competitive) at any conventional level of confidence (see Table 2). Figures 4 and 5 in the Appendix report the empirical probability distribution of the pre-treatment variables (the score in the first test and the average mark in previous exams).

Table 1 also reports the mean value of several other individual characteristics – obtained from the subjects’ answers to the questionnaire – and p-values of tests aimed at detecting differences in these characteristics across treatments.^[24]

In general, the overall sample is well balanced across treatments. There are some exceptions: the frequency of use of e-mail is significantly higher in the baseline treatment than in the competitive and in the cooperative treatments. Significant differences emerge also in terms of the educational level achieved by the students’ fathers (but not the mothers).

To detect the role of interaction effects between treatments and students’ ability, we consider the GPA: students participating in the experiment are third-year students taking exams in the last quarter of the third year; therefore, their academic history can be a reliable proxy of their academic skills. In line with the most recent empirical evidence from Italy (AlmaLaurea 2009), in our sample females tend to perform significantly better than males in terms of GPA (Females=25.3, Males=24.3, Wilcoxon test=p-value 0.0097). We classify subjects as “high ability” if their GPA score is above the median GPA score in the sample.^[25]

5.3 Communication and Treatments

Students under both treatment schemes had two ways of communicating: they could send text messages and hints.^[26] Messages and hints were limited in two ways. First, students could not send any useful information to identify themselves (under penalty of exclusion from the test); second, for each of the five questions asked in a test, a student could send and receive only one message of each type.

Table 10 in the Appendix reports descriptive statistics on the use of the chatroom and the giving out of hints by subjects who participated in all tests (the stayers) and were paired up in each test with a student who did the same.^[27] The figures in Table 10 suggest that almost everybody under the cooperative treatment accepted to use the chatroom in tests 2, 3 and 4, resulting in a large fraction of students with an active chatroom during each test (79% in test 2, 95% in test 3, 90% in test 4). For those stayers who were always paired up with a stayer, the chatroom was active at least once in 97% of the cases and always in 74% of the cases.^[28] These proportions are reduced by between 25% and 70% when we look at the behavior of students under the competitive treatment, and generally both the acceptance rate and the fraction of subjects whose chatroom was active during each test are significantly different across treatments at 5% level.

Similar differences between treatments emerge if we look at the average number of messages sent by students and their length and if we look at the number of hints sent. Under both schemes, students used the chatroom more frequently than the hint but the number of messages and hints sent under the competitive scheme was significantly lower than under the cooperative scheme, where it was closer to the maximum number that could be exchanged (five messages and five hints per test).

We considered the data on the pairs in each test and compared the answers of the members: Table 3 shows that members of the pairs under the cooperative scheme tend to give the same answer much more frequently than the students under the competitive scheme. The difference is of about 25 percentage points in all tests. We also check whether there is a significant correlation between the activation of the chatroom and total pair performance (the sum of the test score of the pair’s members). We use the data of all pairs in test 2, test 3 and test 4 and present results in Table 4: we detect significant differences between the competitive and cooperative treatment in how using the communication tools affects pairs’ performance, but we cannot detect significant differences in the role of the average GPA of the members of each pair. The use of the chatroom is positively correlated with performance only in the cooperative treatment: here, the predicted total score of the pair increases from 3.769 to 5.135 points when the chatroom is active, while in the competitive treatment the variation is negligible. While these estimates do not have a causal interpretation, due to potential self-selection into information sharing, the observed pattern of information exchange across treatments can be interpreted as a positive response to the incentives: students understood the different mechanisms underlying the two different schemes and behaved accordingly as far as exchange of information was concerned.

Additional evidence in support of our finding that communication was used very differently in the competitive and in the cooperative treatments comes from the comparison between the hints sent and the answers given by the subjects. If we restrict our attention to the pairs where both members participated in all tests, we observe that under the cooperative treatment, the hint sent coincides with the answer given by the sender in 295 out of 323 cases (91.3%), while in the competitive in 14 out of 33 cases (42.4%). This confirms that subjects sent much fewer hints in the competitive treatment, and when they did so, they often had a deceptive intent.

We interpret the observed pattern of information exchange across treatments as a positive response to the incentives: students understood the different mechanisms underlying the two different schemes and behaved accordingly as far as exchange of information was concerned.

5.4 Treatment Effects

Figure 1 depicts the empirical distribution of the change in effort – that we measured as log(net score 5) – log(net score 1) (see Section 5.1 for more details) – across treatments.^[29] The vertical blue line represents the median of the distribution, the left hinge of the box indicates the 25th percentile, and the right hinge of the box indicates the 75th percentile. Visual inspection suggests that under the cooperative treatment, subjects perform more poorly than in the baseline treatment, while no sizeable differences emerge between the competitive and the baseline treatments.

Figure 1:

Box-plot showing the distribution of the change in effort, i.e., log(net score 5) – log(net score 1) (see Section 5.1 for more details), across treatments.

Wilcoxon tests do not reject the hypothesis that the distribution of the change in effort is the same across treatments. These tests, however, are not appropriate if we want to establish an ordering across all three treatments. Thus, we also performed a Jonckheere–Terpstra test, a non-parametric test designed to detect alternatives of ordered class differences.^[30]

This test does reject the hypothesis that the change in effort is constant across treatments versus the alternative hypothesis that it is ordered across treatments according to our main theoretical prediction (eicoop<eiBL<eicomp) at 10%. p-Values of these tests are reported in Table 5, together with the mean level of the change in effort in each treatment condition.

Results from previous experiments suggest that males and females may react differently to competitive incentives (see Section 2). Consistently with previous works, we find that the picture indeed changes when we split the sample by gender. Figure 2 reveals that the treatment effect is substantially different for male and female subjects. The detrimental effect of the cooperative treatment on the change in effort compared to the competitive treatment only emerges for males, whereas for females no clear treatment effect arises.

One-sided Wilcoxon tests confirm that males’ change in effort is significantly lower in the cooperative treatment than in the competitive treatment at the 10% level. No significant differences emerge instead when we compared the cooperative treatment with the baseline. In contrast, the same test does not reject the hypothesis of equal distribution of the change in effort between any two treatments in the female sample. To test whether the change in effort is ordered across treatments, we ran a Jonckheere–Terpstra test on the subsamples of males and females: for males, the test rejects at 5% the null hypothesis that the change in effort is not ordered across treatments, against the alternative hypothesis that the change in effort is ordered according to what is predicted by the theory; no effect is detected for females. p-Values of these tests are reported in Table 5.

Figure 2:

Box-plot showing the distribution of the change effort, i.e., log(net score 5) – log(net score 1) (see Section 5.1 for more details), across treatments, by gender.

A second noticeable difference between males and females emerges from Figure 2. For males, the variance in the change in effort is higher in the competitive treatment, as compared to the baseline treatment, while for females the opposite holds true.^[31]

The result for males is in line with the findings of several previous papers see Bull et al. 1987; Eriksson et al. 2009), but it is also in sharp contrast with what we observe for females. Previous results from the experimental literature suggest that females tend to be more risk averse than males (Croson and Gneezy 2009), and that the heterogeneity in terms of risk preferences seems to be one of the factors that explains why competitive environments tend to induce a higher variability of effort as compared to situations in which incentives are provided on a piece-rate basis (Eriksson et al. 2009). Competitive incentives boost effort for individuals who are less risk averse but decrease it for those with a stronger aversion to risk. In the presence of substantial heterogeneity in risk aversion competition may thus increase effort variance.

We checked if these arguments can explain the gender difference that we observe in our sample. Our survey measure of risk aversion (see Table 8 in the Appendix) reveals that females are (weakly) more risk averse than males and less heterogeneous than their male counterpart, however, none of these differences is statistically significant at any conventional confidence level.^[32] Taken together these figures suggest that the introduction of competitive incentives may have had an effect that is at the same time both smaller in magnitude and more uniform among females than among males, and this would be consistent with the reduction in the variance of the change in effort for females and the increase in the variance of the change in effort for males. Having only a survey measure of risk aversion, we prefer not to draw strong conclusions on this issue, which calls for further investigation.

Our theoretical model predicts heterogeneity in the effect of the incentives schemes on effort with respect to students’ ability, at least for the competitive treatment. We used linear regression models to control in a parsimonious way for individual ability and for other individual characteristics, while assessing the effects of the treatments scheme on average change in effort. We ran the analysis separately for males and females as Figure 2 suggests that they react differently to incentives.

Table 6 presents the regression results. The dependent variable in each regression is the change in effort defined at the at the beginning of this Section (and discussed in detail in Section 5.1). All regressions include controls for parental education, risk aversion and trust.^[33]

The table has four columns and two panels. The top panel reports estimates of regression coefficients while the bottom panel reports p-values of both two-sided and one-sided tests. The theory predicts the direction in which the null hypothesis of no effect is violated (eicoop<eiBL<eicomp): by exploiting this information, we increase the power of the t-test to detect significant deviations.

Each column of Table 6 corresponds to a different regression. Columns (1) and (2) correspond to regression models that do not allow for heterogeneity in the treatment effects with respect to students’ ability: column (1) reports results for males, column (2) for females. In columns (3) and (4), for males and females respectively, we run regressions that include interactions between treatments and the ability indicator based on the average mark (GPA) in previous exams.

High parental education is a binary indicator that takes the value 1 if the highest qualification of at least one of the parents of the individual is above high school and 0 otherwise. Standard errors in brackets. Three stars, two stars and one star for significant effect at the 1%, 5% and 10% levels, respectively. The sample size relevant for the regressions is 104 instead of 114, because we included control variates and 9 students did not answer the questionnaire. Besides, we had to exclude one additional record because one female student scored 0 in test 1, hence we could not compute the log of the test score 1 for her.

Results in Table 6 confirm previous results on the differential effects across treatments: there is evidence of a significant increase in the change in effort under the competitive compared with the baseline treatment for males but not for females. The effect for males is about 0.368 (see column (1)); it is statistically significant at 10% (see two sided p-value for the competitive treatment in column (1)) and non-negative at 5% (see one sided p-value for the competitive treatment in column (1)). When we control for ability, we find that: (i) the positive incentive for males is higher (0.509, column (3)) for low-ability individuals (statistically significant at 10% and non-negative at 5%) and decreases substantially for high-ability individuals (see the coefficient of the interaction term between competitive and ability in column (3) in Table 6); (ii) there is a negative but not significant detrimental effect of the cooperative treatment for high-ability individuals only (see the p-value for the one-sided test of significance of “cooperative for high ability,” reported in column (3) of Table 6). However, the difference in the effects of incentives between ability groups is not significant in our sample neither for the competitive case nor for the cooperative case (see coefficients estimates of interaction terms between treatment and ability indicator in column (3) and (4) of Table 6).^[34] In sum, the magnitude of the effect ranges between 0.368 and 0.509, i.e., between 60% and 88% of a standard deviation of the change in the logarithm effort.^[35] This represents a substantial increase, comparable in size to the one observed by Blimpo (2014), who uses monetary incentives based on the achievement of a specified score target.^[36] According to the estimates in the first column of Table 6, the change in effort in the baseline treatment is 31% of the effort exerted to prepare the first test, whereas the change in effort in the competitive treatment is 89% of the effort exerted to prepare the first test, meaning a 58 percentage points difference between the two treatments.

For females, no statistically significant treatment effect is found, but we acknowledge that the power we have to detect differences is much lower than the power of the same test for males.^[37] Allowing for heterogeneity in the effects by ability does not change this qualitative findings: no significant treatment effect can be detected for females.^[38]

Notice also that the regression results evidence no significant change in effort under the baseline treatment, hence we infer that subjects’ performance did not increase across tests because they become more accustomed to the type of tests and the way these were performed in the laboratory (see the estimates of the coefficient associated to the constant in columns (1)–(4)).

Students’ ability does not play any role in determining the increase in the change in effort in the baseline. Few regressors are relevant: risk aversion and parental background attract significant coefficients in some specifications, suggesting that individuals who are risk averse tend on average to experience larger changes in effort, while males with higher socio-economic background (here proxied by highly educated parents) tend to experience smaller changes in effort, other things equal.

Previous experiments have shown that relevant gender differences emerge in terms of risk aversion, trust and trustworthiness (see Buchan et al. 2008; Eckel and Grossman 2008; see also Croson and Gneezy 2009 for an extensive review). These factors could interact with the incentives in different ways for males and females: unfortunately, we do not have enough statistical power to detect these gender-specific differential effects in our sample.