Inequity Aversion Differences: Experimental Evidence Among Prospective Teachers and Lawyers

Transcription

1 Inequity Aversion Differences: Experimental Evidence Among Prospective Teachers and Lawyers Maria Perez School of Education, Stanford University Draft version: Feb 11, Abstract Merit pay for teachers in one of the most contentious issues in the K-12 education policy arena. Proponents of merit pay suggest that rewarding teachers for student gains will improve the quality of the teacher workforce. The literature has focused largely on how merit pay affects teacher motivation, and has not investigated the mechanism through which merit pay would change the composition of the teaching force. Presumably, merit pay systems result in highly effective teachers receiving higher pay than ineffective teachers, encouraging the desired pattern of retention and turnover. In addition, it is argued that tying pay to performance will attract new individuals to enter the profession who would not have otherwise done so under the uniform salary scheme, generating a larger pool of teachers from which to hire. These theoretical predictions rest on the basic assumption that highly effective teachers are neutral when it comes to their preferences for uncertain and competitive pay schemes, and are not averse to unequal outcomes among their peers. In this study, I conduct a controlled behavioral experiment to investigate how risk aversion, inequity aversion and preferences toward competition differed among highly effective prospective teachers and lawyers. I find that prospective female teachers and lawyers do not differ in their level of risk aversion. However, female teachers had a much stronger aversion to inequity and were less likely to generate a competitive environment than female lawyers that were planning a career in private practice. Interestingly, there were no statistical differences between prospective female teachers and lawyers who planned careers in public practice. Stanford School of Education, Center for Education Policy and Practice (CEPA), 520 Galvez Mall, 5th Floor, Stanford, CA ( cuky@stanford.edu). I am indebted to my advisor Susanna Loeb for her support and encouragement throughout this project. Special thanks to Muriel Niederle for her inspiring discussions; and Miguel Socias for his creative suggestions. I thank Alicia Grunow and Stanford seminar participants for their extremely helpful feedback. I would further like to thank Mari Muraki for providing excellent research assistance in the Lab. Special thanks to Ruth Ann Costanzo, Evan Epstein, Catherine Glaze, Nancy Lobell, and Rachel Lotan for facilitating the recruitment process; and to both the Stanford Teaching Education Program and Stanford Law School participants. I gratefully acknowledge the financial support provided by the Stanford School of Education Support Grant. All errors are mine. 1

2 1 Introduction More than 99 percent of the public school teachers in the United States work in districts that use uniform salary schedules. Under such contracts, a teacher s salary does not depend on performance, and is determined exclusively by education level and years of experience. Many critics of the salary schedule (e.g., Hanushek, 1981; Bradley, 1998; Mohrman, Mohrman and Odden, 1996; Ballou and Podgursky, 2001) argue that uniform salary schedules have several limitations and that an effective way to improve the quality of the teaching workforce would be to change the approach to compensation. The U.S. Department of Education, through the Teaching Incentive Fund, has taken a leading role awarding $330 million to states and districts to implement compensation systems that tie teacher pay to student performance. However, this idea continues to be controversial. Opponents of such pay systems argue that they would increase negative competition, neglect low-performing students, and adversely affect the school environment. The accumulation of these disadvantages could result in poor instruction and declining student achievement. The theory of merit pay claims that rewarding teachers on the basis of their students outcomes will both motivate teachers to work harder, as well as change the composition of the teaching force (Lazear, 2003). Most of the research to date has been focused on the motivational effects of merit pay. However, it has been argued that in the context of education, the most important effect of performance-based pay is the change it would create in the composition of the teacher workforce. In order for merit pay to increase teaching effectiveness through this compositional mechanism, merit pay systems would need to successfully attract and retain teachers who are good at increasing student outcomes. This theory rest on some assumptions about how highly effective teachers would react to this type of incentive scheme, and in particular, how their preferences towards risk, competition, and inequality, influence their career choices. In this paper I use a behavioral economic experiment to shed light on how the preferences of highly effective prospective teachers differ from non-teachers who could potentially be attracted into the teaching profession. 2

3 The empirical basis of merit pay is extremely limited and has been mostly focused on the effectiveness of merit pay to motivate teachers to increase student outcomes. Early empirical studies have shown no effect or a small positive association between teacher participation in merit pay and student outcomes (Ladd, 1999; Cooper and Cohn, 1997; Figlio and Kenny, 2003). Studies that have used a rigorous quasi-experimental methodology have found that teacher incentives help increase student outcomes (Dee and Keys, 2004; Lavy, 2002; Lavy, 2008). However, rigorous field experiments fail to provide conclusive evidence on the effectiveness of merit pay on increasing student outcomes. The two randomized field experiments conducted abroad indicate that incentives help increase school outcomes, although sometimes via teaching to the test (Glewwe, Ilias, & Kremer, 2003; Muralidharan & Sundararaman, 2008). In contrast, the two randomized experiments carried-out in the U.S. showed no significant results in student outcomes (Springer, Hamilton, and McCaffrey, 2010; Goodman and Turner, 2009). Despite the empirical attention on the motivational effects of merit pay, arguably the more significant differences in the overall quality of teaching would come from these pay systems ability to change who enters and remains into the teaching profession. The current research on merit pay has not examined compositional effects. In order to understand how merit pay would change the teaching workforce, it is useful to understand whom the theory predicts to attract and retain under this type of pay system. Pay for performance should result in low pay for the low-performing teachers and high pay for the more effective ones, encouraging the desired pattern of retention and turnover if pay differences are considerable. Under this logic, the most effective teachers would earn the largest bonuses and have the incentive to remain in the profession if merit pay were implemented. Less effective teachers would be more likely to leave due to lack of additional compensation and recognition, opening new positions to be filled. Further, these incentives would attract new individuals who expect to perform well under a merit pay program, generating a larger pool of teachers from which to hire. This process culminates in a systematic change of the teacher workforce, where less effective teachers are replaced by more effective ones. 3

4 These theoretical predictions rest on several important assumptions that have not been rigorously explored in the literature. For example, merit pay introduces uncertainty into teachers salaries since part of their compensation would depends on how well their students perform on achievement tests. If teachers are risk averse, this type of compensation would reduce the appeal of the teaching profession. In addition, pay for performance could be designed in such a way that induces competition between teachers from the same school, district, or state. Therefore, this kind of compensation could affect the attractiveness of the teaching profession for those who dislike competitive work environments. And last, the introduction of performance pay increases the distribution of wages, making salaries more unequal among teachers. As a result, this type of compensation scheme would decrease the appeal for those who value an equal distribution of resources among a group of reference. Therefore, if highly effective teachers have preferences against risk, competition, and unequal distribution of outcomes, merit pay could fail to retain and attract them if designers of incentive schemes do not take these preferences into account. Unfortunately, we know little about teachers preferences and no study has been able to rigorously show if highly effective teachers have values or preferences that could influence or clash with the implementation of incentives. The current literature about teachers preferences suggests that the teaching profession as a whole may be characterized by preferences against risky and uncertain outcomes, competition, and unequal distributions of compensation among teachers. For example, Davis (1994) and Wagner (2001) state that teachers have a risk averse temperament. This observation comes from interviews of teachers and the fact that the teaching profession promises high security and stability. Sears, Kennedy, and Kaye (1997) conducted personality tests on a sample of 51 highly effective teachers and found that they value harmony, are very sensitive to interpersonal relationships, and avoid conflict. These personality traits may clash with a competitive working environment for teachers. Lortie (1975), in his analysis of the teaching profession, identified an egalitarian structure among teachers that contends that all teachers 4

5 are equal and deserve the same recognition. This suggests that teachers may have preferences towards a more equal distribution of outcomes. It has also been argued that teachers have a preference towards cooperation and collegiality (Milanowski and Gallagher, 2000). While a number of studies have explored teachers preferences, they have all had a number of methodological limitations. First, they rest on self-reported information of teachers. Second, they are based on stated preferences of teachers that have already entered into the profession. Thus, their preferences could have been influenced by the views and opinions of the teaching force and not represent their individual preferences. And last, these studies do not contrast teacher preferences with those of other professionals. Therefore, it is hard to predict if and how teacher preferences should be taken into account when designing incentive schemes to attract prospective teacher candidates, and it is also unclear whether teachers are distinct in comparison to other professionals in the way they could react to incentives. Behavioral economics experiments provide a unique and rigorous approach to study revealed preferences. This methodology, which has witnessed exponential growth in the past decades, draw from psychological principles, field and laboratory observation. The strength of behavioral economics lies in its ability to examine decisions people make (rather than selfreported) in a controlled setting and its ability to isolate the channels that could be driving their decisions. 1 The ideal real world situation to examine the revealed preferences of teachers towards risk, competition and distribution of outcomes would be to observe how highly effective teachers choose among different kind of payment schemes, and contrast those decisions with what highly effective non-teachers would do under the same environment. Also, we would like to see how teachers and non-teachers would perform and react under different types of incentives. To test for their preferences towards unequal distribution of outcomes, 1 For example, they have been used to study the gender gap in the propensity to enter competitive environments (Niederle and Vesterlund, 2007). To analyze if men are more effective under competition (Gneezy, Niederle and Rustichini, 2003); to study if we are more willing to compete as a team member rather than individually (Dargnies, 2009; Bornstein, Gneezy, and Nagel, 1999; Fehr and Gintis, 2007); and to explore how the institutional environment helps explain gender differences in seeking challenges (Niederle and Yestrumskas, 2008). Dohmen and Falk (2006) have also used this methodology to study the impact incentives have on workers self-selection and performance. 5

6 we would like to observe a situation in which their choices influence the distribution of outcomes of others. And last, we would also like to observe individual preferences that are not influenced by the socialization of the profession they are part of. It would be hard to create this ideal situation in a natural setting, however, we can replicate most of these conditions in a laboratory, which could allow us to get an accurate picture of the revealed preferences of teachers and non-teachers with regard to different types of incentive schemes. In this study, I conducted a controlled behavioral experiment that approximates this ideal situation. This experiment allowed me to investigate how highly effective prospective teachers and non-teachers reacted to incentives, and how they differed in terms of risk aversion, preferences towards competition, and inequity aversion. The group of non-teachers were represented by first year Stanford Law Students, a selective program that attracts high performing students. Some of these prospective lawyers have also expressed interest in following a career in public service. These students can be arguably seen as a potential pool of applicants that could be attracted to teaching if the compensation scheme were changed. My results indicate that prospective female teachers and lawyers did not differ in their risk aversion; they were equally likely to select a competitive payment scheme when choosing the incentive scheme to apply to their own performance. However, female teachers aversion to inequity greatly outweighed the aversion shown by female prospective lawyers that were planning a law career in private practice. Interestingly, there were no statistical differences in inequity aversion between prospective female teachers and prospective female lawyers who planned careers in public practice. These results suggest that when we consider the potential compositional effects merit pay systems could have, we should take into account that teacher s responses (and of other workers with public service interests) are more complex than just maximizing their individual payoffs. Inequity aversion preferences are likely to affect who decides to enter (and remain in) teaching. The results do not imply that merit pay should not be implemented, but we need to look carefully at their design. This paper is the first study to employ a rigorous methodology to provide evidence 6

7 regarding prospective teacher preferences that could impact the effectiveness of incentive plans. I start presenting the experimental design in the following section. Sections III presents the main results. The last section concludes. 2 Experimental Design In this experiment, I established an environment where I could measure the effects different incentive schemes have on performance, and observed how teachers and non-teachers differed in their propensity to select a competitive pay plan when choosing for themselves and/or the whole group of participants in the room. Experimental sessions were conducted in separate single-sex environments of approximately12 participants from the same program. Each laboratory session was assigned into one of two treatments. The experiment was designed as follows. First, participants performed under two non-competitive schemes (piece-rate and fixed-pay) and then under a competitive tournament scheme (below I explain in more detail each experimental procedure). 2 Teaching students and lawyers were also asked to guess their relative performance after completing the first task. Participants assigned to the first treatment then selected between piece-rate or tournament to apply to their own next performance. Participants assigned to the second treatment selected the payment scheme they wanted to apply to their own performance, as well as the performance of everybody in the room. Participants in both treatments performed under the same compensation schemes before making their selection. No participant was informed of her relative performance during the session, and were told their choices would be completely anonymous. This environment allowed me to determine if participants of equal performance and similar beliefs about their relative performance chose the same type of payment when selecting for themselves or for the group. 2 Piece-rate is a fixed payment per action performed. It could be seen as a form of performance-based pay that is certain and does not involve competition. Fixed-pay is a certain amount regardless of performance. And tournament is a competitive payment where only a certain number of players get compensated based on highest performance. 7

8 So how should participants decide between the different payment schemes? First, piecerate and tournament differ in three important ways: payment under tournament is uncertain, it depends on the performance of others, and its a competitive game where only some obtain a positive payment while others get nothing. Therefore, the factors that should influence a participant s anonymous choice are preferences towards competition, risk aversion, and expected payoff. Second, when participants are selecting the payment scheme for themselves, they are revealing their level of risk aversion and preferences to compete. And third, participants of the same performance level and beliefs about their performance that do not care about the distribution of payoffs of the other participants, should exhibit similar choices when deciding for themselves or for the group. Now, if a participant exhibits inequity aversion, for example, she will be less likely to select a tournament payment scheme when selecting for the group, given that she will be influencing other participant s payoffs, generating a more unequal distribution of payoffs than under a piece-rate scheme. When I contrasted the choices that participants made when selecting the payment plan for themselves and for the group, I could identify the level of inequity aversion exhibited by the participants. Perhaps the most fundamental question when this methodology is used is whether the findings from the lab are likely to provide reliable inferences to the real world. Levitt and List (2007) provide a useful framework to asses the merits of the lab. They predict that a group of laboratory results could be applicable to the field if they meet a particular set of characteristics. In this experiment, I took into account most of them. For example, the subject pool used in this study is the exact same population of interest (i.e., teachers). This is not a case of an experiment that uses undergraduate students to draw inferences about the preferences and tastes of another population. 3 Furthermore, the computational demands in the experiment are small, experience is not important, and moral concerns and self-selection into the experiment are likely affecting both groups from which comparisons are being made. 3 Harrison and List (2004) would classify this study as an artefactual field experiment because it uses real subjects. 8

9 2.1 The Task During this experiment participants solved paper mazes under different payment schemes. 4 The advantage of paper mazes is that they are easy to understand, fast, and allow measuring differences in effort as a response to incentives. There are five segments called tasks in which participants had 10 minutes to solve as many mazes as possible. 5 If participants made a mistake when solving a maze, they could simply cross out the incorrect portion (an example of how to do it was shown before the start). Participants were also permitted to skip up to three mazes (which they crossed out with an X) during each 10-minute task. Once participants were done solving the mazes, they counted how many mazes they solved correctly and entered the total into a computer. 2.2 The Subjects The primary goal of this experiment is to inform our understanding of the effects of incentives on the composition of the teaching workforce by analyzing the reaction of highly effective teachers. Since we care about the preferences that lead these individuals to choose a profession, we would want to understand the preferences they bring to the profession which may be different than those that they hold after being socialized in their work environment. For that reason, I invited students that had decided to become teachers but had not yet entered the job market. This poses a challenge of how to select highly effective teachers in the absence of observations of their performance. Given this, potential highly effective teachers needed to be selected based on personal characteristics, and the teaching program they are enrolled in that could be correlated with teaching effectiveness. The Stanford Teaching Education Program (STEP) is a highly selective teaching graduate program that attracts students with high SAT scores and that have the potential to become highly effective 4 This task has been previously used by Gneezy, Niederle and Rustichini (2003), Freeman and Gelber (2009), Niederle and Yestrumskas (2008), among others. 5 In each task, participants received 35 mazes of intermediate difficulty. 9

10 teachers. 6 Students enrolled in this program were invited to participate in this study and represent the group of teachers. While STEP students are likely to be the type of people proponents of merit pay hope to attract and retain, there are others who have not yet expressed any interest in teaching who may very well make great teachers. In order to tap into the extent to which merit pay would be appealing to high performing individuals outside of education, I decided to look at first year Stanford Law Students (SLS). This is also a highly-selective program that attracts students with high SAT scores (1,400). 7 In addition, some of these students have expressed interest in public service, so they serve as an interesting contrast, representing the potential teachers that could be attracted into the profession if merit pay were implemented. The experimental sessions were conducted separately for teaching and law students, during July and September 2010, respectively. In addition, since the literature has shown that women and men differ in their effectiveness when participating in mixed-sex settings (Gneezy, Niederle, and Rustichini, 2003), as well as in their willingness to participate in mixed-sex tournaments (Niderle and Vesterlund, 2007), sessions were conducted in single-sex environments. Teaching and law students were invited to participate to a one-hour experiment about how people make decisions during their first weeks on campus. 8 Students were told they would be paid $10 for showing-up, and between $12 - $87 depending on their performance. A total of 127 students participated in the experiment. Teaching students were recruited during their second week of classes through an announcement made during an orientation class. 9 Students interested in participating could sign-up during that same day. A total of 56 females (out of 76) and 10 males (out of 20) signed-up to participate in the study High verbal SAT scores have been shown to be correlated with high value-added measures, e.g., Hanushek (1992). 7 Notice that there are no statistically significant differences between STEP and SLS students on their SAT scores. 8 Students were invited early on to avoid having a very cohesive and friendly group of participants that could behave differently in the lab because they knew each other very well. 9 Secondary and elementary students were recruited separately in their respective orientation classes. 10 A total of 10 females and 1 male did not show-up to the study. 10

11 Similarly, first year law students were recruited during their orientation day, which happened the first day they arrived to campus. A total of 13 males and 10 females signed for the study that day. To recruit additional students, an was sent to their list, and students that signed up during the orientation day were offered $10 extra for every referred student. A total of 34 females (out of 91) and 38 males (out of 98) signed up to participate in the study. 11 Of those, only 11 were participants that said they had been referred by a friend. Given the low number of male teaching students, I only present results based on female participants. 2.3 Experimental Procedures This experiment had two phases. The first phase, which lasted about 45 minutes, consisted of a series of tasks where participants had to solve mazes. The second phase consisted of a 10 minutes online survey. Below I provide a description of the general experimental procedures. Task 1 (or Piece Rate). Participants solved mazes for 10 minutes and received $0.80 per correctly solved maze. At the end of this task, participants counted how many mazes they solved correctly, and entered that number into the computer. Task 2. Participants guessed their relative performance. They choose among quartiles of performance if they chose correctly they earned $1. This provides a measure of their beliefs about their relative performance. Participants did not know if they had guessed correctly until the end of the experiment, when they were paid in private. Task 3 (or Fixed Pay). Participants solved mazes for 10 minutes and received a fixed payment of $8, regardless of how many mazes they solved. At the end of this task, participants counted how many mazes they solved correctly and entered that number into the 11 One reason that could explain the small number of law students that signed-up during their orientation day is that it was too early for them to make a commitment to participate in a study the following week. At that point, they had not received their class schedule yet (even though they were told the study session was after class) and did not have a good sense of the level of workload of the program. In addition, students were not in a room altogether (as was the case with STEP students), but rather, they walked by the recruiting table, making it hard to reach and invite a high number of students. 11

12 computer. Task 4 (or Tournament). Participants solved mazes for 10 minutes and this time their payment depended on each participant s performance relative to three other randomly chosen participants. The participant that solved more mazes than the other three received $32. Otherwise, she received nothing. In case of a tie, the winners shared the payment equally. At the end of this task participants counted how many mazes they solved correctly and entered that number into the computer. Participants did not know if they won the tournament until the end of the experiment, when they were paid in private. Using these first four tasks I could analyze how prospective highly effective teachers and non-teachers differed in their responses to different pay systems, as measured by task performance. I could also compare how the two groups differed in their beliefs about their own performance (Task 2). Task 5 is the only task that differed across treatments. Treatment 1 participants chose the payment scheme they wanted to apply to their own performance. They could either choose piece rate ($80 cents per solved maze) or tournament ($32 for the winner of the tournament). If they chose tournament, winners were determined based on the comparison relative to other three participants previous task performance, not their performance during Task 5. Essentially, participants were competing against other participants who had already performed. This is important in order to ensure that a participant s choice does not affect the outcome of any other participant, and that their choice is based on competing against a random group of participants (not only the self-selected group that chose tournament). Once participants assigned to Treatment 1 finished with Task 5, I could compare teachers and non-teachers level of risk aversion and willingness to compete. That is, by contrasting the likelihood of tournament selection across professions I could obtain information regarding their risk aversion. In Task 5 for participants assigned to Treatment 2, participants chose the payment scheme for all the participants in the room, not just for themselves. In other words, their 12

13 choice affected the outcome of other participants. After every participant made her/his selection (between piece rate or tournament), one participant was randomly selected as the decider of the payment scheme for the group. All choices were completely anonymous. Nobody knew what others had chosen nor who was selected as the decider. In both treatments, after participants made their selection, they were able to see in the computer which was the payment scheme that would be applied to their performance. Then, they solved mazes for 10 minutes. Once they were done, they counted how many mazes they solved correctly and entered that number into the computer. The results of Task 5 across both treatments provide evidence of inequity aversion among participants. 12 I can compare what participants chose under Treatment 1 (choosing for themselves) with participants decisions under Treatment 2 (choose for the group). The major difference between Treatment 1 and Treatment 2 is that under the latter one, participants decisions affected the payoffs of the other participants in the room. Therefore, if we believe that economic self-interest is what drives participants decisions, we should not observe differences in the choices made across treatments. However, if participants do care for the material payoffs allocated to a reference group (positively or negatively), their choices across treatments could differ. During the second phase, participants answered an online survey with questions about their preferences with respect to income and inequity aversion, risk aversion, preferences towards different types of incentive schemes, their future career plans, and basic demographic characteristics (e.g., age, marital status, latest SAT, parental education). 13 The experiment lasted about 1 hour, and participants earned on average $ It is also possible that participants are not selecting tournament under Treatment 2 in order to not feel responsible of generating a competitive environment among participants. In other words, inequity aversion as well as aversion to a competitive culture could be what is driving differences in selection across treatments. 13 The question that asks about preferences towards different types of incentive schemes was also sent to all teachers in the Miami-Dade County School District to be correlated with their value-added measures. 14 The minimum payment was $23 and the maximum was $97. 13

14 3 Findings The goal of this study is threefold. First, to measure whether there are differences in performance across female teachers and lawyers when performing under different incentive plans. Second, to examine whether teachers and lawyers differ in their level of risk aversion. And last, to explore whether there is evidence of inequity aversion among teachers, and to contrast that finding with what is possible to observe among lawyers. 3.1 Effect of Different Pay Schemes on Task Performance The objective of the first four tasks in this experiment is to provide evidence about differences in performance and confidence across female teachers and lawyers. Table 1 shows the number of mazes participants solved under Task 1, Task 3 and Task 4. As a benchmark measure of differences in performance across professions, I used the results obtained under Task 1 (piece-rate). Female teachers solved on average mazes (with a standard deviation of 2.98), while female lawyers solved mazes (s.d. of 2.45). There was no significant profession difference in performance; a two sided Mann-Whitney test comparing the performance distributions of the 46 female teachers to the 34 female lawyers yields p = This is a positive result since I would like to compare how teachers and lawyers make choices for themselves and for the group in an environment where their choices are not being driven by differences in baseline performance. During Task 3 (fixed pay), participants received $8, irrespective of the number of mazes solved during the 10 minutes. Here, the rational choice (if solving mazes is costly) would be to solve zero mazes during those 10 minutes. The results of this task not only provide evidence of differences in performance under a non-competitive fixed payment scheme. They also provide information about differences across teachers and lawyers in their desire to do the right thing. As proposed by Levitt & List (2007), utility maximization could be driven not only by payoff maximization, but potentially also by an individual s desire to make the 14

15 moral choice. The weight that an individual gives to do the right thing may increase when they are being watched (as in a lab setting). Self-selection of participants that are more willing to choose for the moral choice could be a problem if, for example, teachers that decided to participate are the ones that are more willing to do the right thing. However, as can be seen, female teachers solved on average 9.41 (s.d. of 3.89) and female lawyers solved on average (s.d. of 3.26). The decrease in the number of mazes solved during fixed pay, and the level of performance during Task 3 are not statistically different across teachers and lawyers. Another possible explanation for why participants decided to solve mazes at all, could be that they wanted to practice how to solve mazes in case they needed to solve more of them in subsequent tasks. 15 During Task 4, participants solved mazes during 10 minutes under a tournament scheme. These results allowed me to see if competition affects differently lawyers and teachers. It is possible that female teachers and lawyers differed in their skills (and beliefs) when performing under competition. The results suggest that both groups increased their performance under competition (tournament), which could be due to learning or the incentive given by a competitive tournament. Table 1 also shows that female teachers solved on average mazes (s.d. of 3.3) and female lawyers solved (s.d. of 4.46) under a tournament. A two-sided Mann-Whitney test comparing the performance distributions of both groups yields a p-value of This observed difference in effectiveness under a competitive payment scheme (i.e., the difference in performance level) is driven by the performance under competition of female lawyers with private practice interests. They solved on average mazes (s.d. of 4.93). In contrast, female lawyers with public practice interest solved 13.7 mazes (s.d. of 3.53), an amount that it is not statistically different from what teachers solved. Additionally, I would also like to investigate whether female lawyers and teachers differed 15 Participants did not know which tasks where coming, they only found out what activity was coming after they finished a task. However, they knew the experiment lasted 1 hour and that payment could vary by performance, so they could have assumed that they would need to solve more mazes. 16 If we perform a Bonferroni correction to correct for the multiple test problem, differences would not be statistically significant (critical p-value would be ). 15

16 Table 1: Number of Mazes Solved Under Different Pay Schemes Teachers Lawyers Difference All Public Practice Private Practice (1) (2) (3) (4) (1)-(2) (1)-(3) (1)-(4) Task 1 (piece-rate) Task 3 (fixed-pay) Task 4 (tournament) ** ** in their performance increase when going from a non-competitive payment plan (piece-rate) to a competitive one (tournament). As shown in Table 2, the increase in performance varied somewhat across participants, however, the difference is not statistically significant (difference of mazes with p = 0.11). Female teachers solved 2.63 (s.d. of 3.36) more mazes when going from Task 1 (piece-rate) to Task 4 (tournament). Female lawyers increased in 3.97 (s.d. of 3.73). However, when I compared the increase in performance between female teachers and female lawyers with interests in private practice I could observe a significant difference (difference (1)-(4)). Lawyers with interests in private practice increased the number of mazes when going from Task 1 to Task 4 in 5.47 (s.d. of 3.97). A test comparing the performance with teachers yields a difference of mazes and a p-value of Table 2: Increase in Performance under Competition Teachers Lawyers Difference All Public Practice Private Practice (1) (2) (3) (4) (1)-(2) (1)-(3) (1)-(4) Increase ** (p-value) (0.11) (0.395) (0.011) Sample size Another interesting analysis is to compare the probability of winning the tournament, conditioning on performance, across teachers and lawyers. These results would give us information about the proportion of female teachers and female lawyers that should have selected 16

17 tournament when deciding the payment scheme for themselves if they were risk-neutral. The unconditional probability of winning the tournament was 26% for female teachers and 27% for female lawyers. Table 3 shows the probability of winning the tournament, conditioning on the number of mazes solved. This estimation was done following Niederle and Vesterlund (2005), where for a given performance level, say 10 mazes for a female teacher, I drew 1,000 groups consisting of 3 other participants using the sample of female teachers (with replacement) and compared that performance level with the formed group and estimated the probability of winning. This was repeated 100 times. The following table reports the average of these win frequencies. These results suggest that female teachers that solved more than 12 mazes had a higher expected payoff from tournament than from piece-rate. In the case of lawyers, if they solved more than 15 mazes they had a higher expected earning from tournament. 17 This indicates that lawyers needed to solve on average 2 more mazes to be able to win the tournament. Therefore, we should expect to observe a lower percentage of female lawyers choosing a tournament payment scheme when selecting between piece-rate and tournament for themselves. This analysis will be shown in the following section. Table 3: Probability of Winning Task 4 Conditional on Performance Teachers Lawyers My results suggest that there were no significant differences across teachers and lawyers in their baseline level of performance. There were, however, differences in effectiveness under tournament when I compared female teachers with female lawyers that would like to work in the private sector. In addition, on average, lawyers needed to solve slightly more mazes than teachers to win the tournament, this implies that lawyers should be less likely to enter into a tournament when compared to teachers. 17 This also means that a risk neutral teacher that solved 12 mazes should be indifferent between piece-rate and tournament. In the case of lawyers, this indifferent point is found at 15 mazes. 17

18 3.2 Female Teachers and Lawyers Do Not Differ in Risk Aversion Participants during Task 5 under Treatment 1 had to choose the payment scheme they wanted to have for themselves. They could choose between piece-rate or tournament. If a participant chose tournament, she won if she solved more mazes than what three other randomly chosen participants solved in the previous task (Task 4). That is, this competitive incentive scheme was designed in a way that it reduced the participant s decision to an individual decision making problem. Namely, the participant s tournament entry decision did not affect the payoff of other participants, nor did it depend on what other participants chose. The payment under piece-rate was $0.8 per correctly solved maze, and $32 when winning the tournament. Participants did not know their relative performance, so what could have influenced their choices? A tournament involves uncertainty in their future payoff, therefore, risk attitudes play a significant role when deciding to choose tournament or piece-rate (which is certain). If female teachers are more risk-averse than female lawyers, for example, then teachers and lawyers of the same performance level and with similar beliefs about their relative performance should differ in their likelihood to select tournament. Namely, female teachers should be less likely to choose a competitive payment scheme (tournament). Based on the estimations of the conditional probability of winning a tournament (see Table 3), a female teacher with a performance higher than 12 mazes had a higher expected payoff from the tournament than from piece-rate. If I look at the distribution of performance under Task 4, 48% of the female teachers solved more than 12 mazes (based on the baseline distribution of performance, 21% of female teachers solved more than 12 mazes). In the case of female lawyers, those with a performance higher than 15 had a higher expected earning from the tournament, corresponding to 52% of female lawyers under the distribution of Task 4 performance. Now, the observed proportion of participants that decided to apply a tournament pay scheme when choosing for themselves was 58% in the case of female teachers, and 52% in 18

19 the case of female lawyers. These proportions are not statistically significantly different from each other. This result suggests that female teachers do not exhibit a higher level of risk aversion neither a dislike for competition that is higher than female lawyers. In the following section I investigate if what predicts tournament selection differs across professions What Predicts Tournament Entry Decision? A participant won the tournament and received $32 if the number of mazes she solved under Task 5 was higher than what three other randomly chosen participants solved under the previous tournament competition (Task 4). When deciding whether to apply a piecerate scheme or a tournament, participants should be taking into account how many mazes they were able to solve in the previous tasks, and also their beliefs about their own relative performance. For example, if a risk-neutral participant believed she ranked among the top quartile of performance, her expected payoff from tournament is higher than the one from piece-rate. Note that given that participants were competing against past performance of other group members, they should not be concerned about the decisions of the other participants. In this section I explore what predicts tournament entry for female teachers and lawyers, and analyze if there were differences in the way teachers and lawyers made their selection. I start by exploring if a participant s baseline level of performance (i.e., Task 1) predicts tournament entry decisions. I then analyze if the increase in performance when going from a non-competitive scheme to tournament helps predict their tournament entry choice. I also explore the possibility that participants anticipated their performance during Task 5, and that played a role in their selection. For example, a participant could have anticipated she was not going to perform well in the last task due to tiredness, therefore, she could have decided not to select tournament. Table 4 shows the result of a probit regression of tournament choice on participants performance. The observation that female teachers were slightly more likely to select a tour- 19

20 nament than female lawyers is confirmed by the first set of results. However, this difference is not statistically significant, neither overall nor when we condition on baseline level of performance (column (2)). The improvement in performance has the expected positive coefficient (0.019 in column (3)), however is small and statistically insignificant. The results from column (1) to (3) suggest that the decision to enter into a tournament for female teachers and lawyers was not related to their past performance. Column (4) controls for the observed performance during Task 5 (i.e., this represents future performance when participants were making their selection). As mentioned, participants could have anticipated how good they thought they were going to perform in Task 5, and that could have influenced their decision. However, future performance does not significantly predict the tournament entry decision nor does controlling for it change the other relationships in the model. Table 4: Probit of Tournament Choice on Performance Treatment 1 (1) (2) (3) (4) Profession (=1 if teacher) (0.16)) (0.17) (0.17) (0.17) Baseline Performance (0.029) (0.029) (0.037) Increase (0.022) (0.027) Future Performance (0.023) Number of Observations Notes to table: Dependent variable: Task 5 choice under Tournament 1 (=1 if tournament). Baseline performance refers to the number of mazes solved under Task 1 (piece-rate). Increase refers to the change in performance between Task 1 and Task 4 (tournament). Future performance is the number of mazes solved after participants had made the choice between piece-rate or tournament (i.e., in Task 5). The table presents marginal effects on the probability of selecting the tournament evaluated at a teacher solving at the average level of performance. Standard errors are in parenthesis. We have seen that performance does not predict participants compensation choice under Treatment 1. This may be due to the fact that tournament entry depended on participants relative performance rather than absolute. Participants, however, were not aware of their 20

21 relative performance but expressed their beliefs about how good they thought they were when solving mazes under piece-rate (Task 1). After participants had completed Task 1 (piece-rate), they had to guess how their performance ranked against the other members of their session. Participants had to choose their quartile level of performance. They received $1 if their guess was correct, however, they did not find out the outcome of their guess until the end of the experiment when they received their payment in private. In Table 5 I contrast female teachers and lawyers beliefs about their relative performance during Task 1. As can be observed, the majority of teachers and lawyers (23 and 18, respectively) believed their performance ranked among the second top quartile of performance. In addition, about 37% of female teachers (17 out of 36) and 38% of female lawyers (13 out of 34) believed they ranked among the top quartile of performance. That is, about 87% and 91% of female teachers and lawyers, respectively, believed they ranked among the top half of the distribution. This suggests that both female teachers and lawyers are overconfident with respect to their relative performance. There are no statistically significant differences across professions. These results also suggest that among the low performing participants, teachers are slightly better at guessing their relative rank. Table 5: Distribution of Guessed Baseline Performance Rank Teachers Lawyers Guessed Rank Correct Guess Guessed Rank Correct Guess 1: Top Quartile : Bottom Quartile Total To determine how beliefs relate to observed performance and whether teachers and lawyers of the same performance formed different beliefs, I estimated an ordered probit to estimate the guessed rank as a function of baseline performance as well as tournament performance. Baseline level of performance is a good predictor of their formed guess, however, there were no significant differences across female lawyers and teachers, conditioning 21

22 on performance. 18 The following set of results show how own beliefs (guessed performance) about baseline performance help predict participants choice on tournament entry (Table 6). The first column shows the probability of selecting tournament unconditional on observed baseline performance. The results show that a female teacher that believed she ranked among the top quartile of performance had a 40% more likelihood to select tournament rather than piece-rate. Conditioning on observed performance, the probability increases slightly to 43%. Table 6: Probit of Tournament Choice on Beliefs Treatment 1 (1) (2) Profession (=1 if teacher) (0.17) (0.17) Guessed Rank 0.40** 0.43** (0.14) (0.14) Baseline Performance (0.03) Number of Observations Notes to table: Dependent variable: Task 5 choice under Treatment 1 (=1 if tournament). Guessed rank takes value one if a participant thinks she ranks among the top 25% of the performance distribution. Baseline performance refers to the number of mazes solved under Task 1 (piece-rate). The table presents marginal effects on the probability of selecting the tournament evaluated at a teacher guessing she is among the top performers and solves the average number of mazes under the baseline task. Standard errors are in parenthesis. In summary, in this section we observed that female teachers were not more risk-averse than female lawyers they were equally likely to select a tournament payment plan when selecting for themselves. Furthermore, what predicts tournament entry decisions are participants beliefs about their relative performance, rather than their observed past or future performance level. 18 These results are available upon request. 22