Risk aversion and preferences for redistribution: a laboratory experiment

Transcription

1 Risk aversion and preferences for redistribution: a laboratory experiment Matteo ASSANDRI (University of Torino Department ESOMAS) Anna MAFFIOLETTI (University of Torino Department ESOMAS) Massimiliano PIACENZA (University of Torino Department ESOMAS) Gilberto TURATI (University of Torino Department ESOMAS) Preliminary draft Abstract Preferences for redistribution have been widely studied by the economic literature, but their relationship with risk preferences received only marginal attention. The aim of this work is to test the results obtained by the scarce literature on the issue with additional robustness checks. According to our results, it is possible to conclude that the more people are risk averse, the more they are likely to be favourable to high redistribution across members of a society that allows social mobility i.e. when there is uncertainty about the final position in the income distribution. JEL Codes: C91, D81, H24, H30. Keywords: preferences for redistribution, individual effort, social mobility, risk preferences.

2 1 Introduction The economic literature has widely studied the topic of redistributive preferences by means of field studies and laboratory experiments. Many determinants have been analysed, from fairness concerns to the role of culture, from political institutions to race as pointed out by Alesina and Giuliano (2011). However, the role of risk and time preferences has received little attention. The Prospect Of Upward Mobility (POUM) hypothesis, proposed by Benabou and Ok (2001), tries to model the fact that in almost every democracy a relatively poor majority holds the political power, but there is no large scale expropriation of riches wealth by means of heavy redistribution. The argument is that people may rationally consider, that they, or their children, may better their position in the income distribution over time and thus they may be hurt by large redistributive policies in the future. However, the argument relies on assumptions about risk aversion and intertemporal preferences, since no one can be completely sure of his future position in the income distribution. Hence, risk attitudes may shape redistributive preferences. On the other hand, the outcomes of redistributive policies and social mobility need time to take place, hence time preferences may matter as well. The first references to risk attitudes in the context of interest are probably due to Rawls (1971) s veil of ignorance and the following experimental tests proposed by Beck (1994), but his design is now no more considered state-of-the-art, especially as far as elicitation of risk preferences is concerned. In more recent years, only Durante et al. (2014) refer to the issue in a context where effort is costly and risk attitudes are properly measured. The role of the effort is crucial as far as the possibility of extending the results from laboratories to the real world is concerned, since income distributions that arise in real life are certainly not random and at least partially determined by people s decisions about effort e.g. amount of hours worked or educational attainments. The argument developed by Durante et al. (2014) is that people are likely to use taxation as a form of insurance against the unknown, with the uncertainty deriving from the final position in the income distribution. Decisions were made in a context with rules determining the income ladder varying from completely random to effort-based. The authors were then able to conclude that the riskier the income determination rule, the higher the preferred redistribution displayed by subjects. Since there is few research on the topic, this work will try to verify Durante et al. (2014) s conclusions under a pure between subject design, that will also allow to test whether subjects perceived the different income determination rules as one 2

3 riskier than the other or as one more morally acceptable than the other. Moreover, we will also try to explain the lack of significance of the risk aversion coefficient in the regression analysis. The final income distribution subjects faced in Durante et al. (2014) was also completely predetermined. However, in the real world people do not always know the exact shape of the income distribution they are in, as shown by Cruces et al. (2013), and this may have an impact on effort and redistributive preferences. A more flexible income distribution, arising completely or partially from participants choices in the proposed effort tasks may be an interesting extension of their approach, because it imposes less structure on the laboratory framework. As mentioned earlier, there may be a role for time preferences as well in the context of preferences for redistribution following Benabou and Ok (2001) s social mobility hypothesis, but in this case the literature is even smaller than the one about risk. As pointed out by Beraldo et al. (2014) in a laboratory setting, the less impatient the subject, the lower the preferred tax rate. Given that the fruits of their effort can be enjoyed only in the future, those subjects are not willing to receive redistribution today if that harms their effort-based income tomorrow. On the other hand, impatient participants are willing to support redistribution of their future efforts in order to have more disposable income today. This result may provide interesting insights about poor s preferences for low tax rates, since they may hope to be better off in the future as in Benabou and Ok (2001) s hypothesis, but they may have the same preferences because of low time discount factors, or, as it is likely to be, both mechanisms are at play. However, in any attempt of analysing the relationships among time, risk and redistributive preferences it is crucial to consider what Andreoni and Sprenger (2012b) pointed out: risk and time preferences are intrinsically connected since the future can be seen as uncertain by definition. Hence, in order to deal with the estimation of a discount factor, a risk parameter has to be considered as well and the literature is trying to find ways of jointly estimating the two preferences. Andersen et al. (2008) pointed out that when that path is followed, lower discount rates arise with respect to a separate elicitation, essentially because all previous estimates had always relied on the assumption of risk neutrality. The authors were able to exploited Multiple Price Lists to elicit risk attitudes, by means of a Holt and Laury (2002) test, and an analogous method in order to obtain the data for time preferences. A joint analysis is then performed in order to take into account the interactions. Andreoni and Sprenger (2012b) propose an alternative method for the joint estimation that does not rely on two Multiple Price Lists joined econometrically, but on 3

4 a single experimental task that can elicit both parameters. The procedure, called the Convex Time Budget method (CTB) is described into detail in Andreoni and Sprenger (2012a) and allows for point estimates instead of the intervals that can be obtained with Andersen et al. (2008) approach. Even if the Convex Time Budget approach is shown to be slightly better than the rival in Andreoni et al. (2015), Holt and Laury (2002) s risk aversion measures are found to be substantially uncorrelated with the estimated utility function curvature i.e. risk aversion elicited by mean of Andreoni and Sprenger (2012b) s joint procedure. As pointed out by the authors, the more likely reason for the issue is that the choices subjects made during the experimental session were all about certain events, hence exploiting risk preferences to identify the curvature of a utility function in riskless settings may be problematic. Andreoni and Sprenger (2012a) and Andersen et al. (2008) s results showed that the joint estimation of risk and time preferences significantly bettered the precision of the latter and it is possible that in the future these techniques may become the standard approach for enquiring preferences, but up to now the separate elicitation is still the main tool adopted when risk and time preferences themselves are not the main focus of the work. Since risk and time attitudes are likely to be interrelated and since both may have a role in shaping preferences for redistribution in accordance with the Prospect Of Upward Mobility hypothesis, time can be a confounding factor if we are interested in the role of risk and vice versa if parameters are estimated separately. Fortunately, the experimental approach allows to control for that factor: mobility along the income distribution, that in real life may take years if not generations to happen, is immediate and all the monetary rewards are paid at the end of the session, eliminating any sort of late reward bias when we are interested in the effect of risk attitudes. The role of time preferences in the context of redistribution is left to a future experiment. 2 Experimental design 2.1 General framework and hypothesis The design adopted in the laboratory experiment exploits a pure 2x2 between subject design where the two dimensions of treatment are defined as the equality or inequality of the initial income distribution and the high or low risk scenario in which people have to make decisions. In the between approach, each subject is required to make choices under a single set of conditions, hence four experimental 4

5 sessions were designed in order to take into account all the possible combinations of the treatment variables as shown in Table 1. The design adopted in the already mentioned work by Durante et al. (2014) was a within subject, hence this work can provide a crucial robustness check for their results under a different approach. Table 1: Treatment sessions Equal income Non equal income Low risk Session 1 Session 4 High risk Session 2 Session 3 Taking into account the nature of the design, each session was structured in order to have 20 participants, a number considered high enough to expect significant results, while low enough to be managed with a paper and pencil approach. The design places the uncertainty in the position of the income distribution where individuals will be after the fruits of an effort task are determined. As it is possible to see from Table 1, different sessions present different levels of risk, since in the ones where the product of the effort is a sure thing, the only source of uncertainty is the amount of effort exerted by fellow participants, while in the other two sessions there is additional uncertainty from the results of the own effort. The first group of sessions will be defined as low risk, while the latter as high risk. Along the other dimension, sessions will be defined symmetrically as equal income and non equal income. We expect subjects to react to the uncertainty modifying their preferred redistribution level depending on the risk aversion parameter: given the same uncertainty of being in a given position in the final income distribution, risk averse people will prefer higher taxes than risk loving ones, so that they can insure themselves against bad outcomes i.e. falling in one of the positions in the lower half of the distribution. As just pointed out, in our framework the role of the average income is pivotal: everyone above the threshold is a net taxpayer i.e. he pays more taxes than the transfer he receives, while the opposite is true for those below the threshold as the payoff determination rule presented in the next Section shows. We expect people to exhibit higher levels of preferred redistribution in the high risk sessions with respect to the corresponding low risk scenario, consistently with evidences from Durante et al. (2014). Moreover, we also expect this difference to be positively related with the risk aversion parameter, as it is the case in any form of insurance. Along the other dimension of analysis, the inequality in the initial income distribution, we aim at testing whether the impact of risk aversion coefficients depends on it and if there are evidences of inequality aversion. Such attitude, identified for the first time by Fehr and Schmidt (1999) and later confirmed empirically, pushes 5

6 net taxpayers to prefer a non-zero tax rate in order to satisfy a personal desire for equality among members of the society. However, this desire may be driven by the fear of falling below the average income and the non-zero tax rate may be again insurance against the uncertain whose amount depends on individuals risk aversion. Hence, we will look for evidences of inequality aversion controlling for risk attitudes. As it is immediately clear from the above arguments, a key element of the design is the method for eliciting risk attitudes. The test of choice was Dohmen et al. (2010) s version of Holt and Laury (2002) s Multiple Price List. The reason for the choice is the attempt to have a finer grid for risk attitudes with respect to the one used by Durante et al. (2014) that provided mainly non-significant coefficients in the regression analysis. Moreover, this test is very similar with respect to Durante et al. (2014) s one since it involves choices between safe amounts and lotteries. The test is also easy to understand and to implement in a paper and pencil context as it is possible to see in Table 2. Table 2: The risk aversion test. Row Column A Column B Choice 1 0 tokens 50% 150 tokens 50% 0 tokens A B 2 5 tokens 50% 150 tokens 50% 0 tokens A B 3 10 tokens 50% 150 tokens 50% 0 tokens A B 4 15 tokens 50% 150 tokens 50% 0 tokens A B 5 20 tokens 50% 150 tokens 50% 0 tokens A B 6 25 tokens 50% 150 tokens 50% 0 tokens A B 7 30 tokens 50% 150 tokens 50% 0 tokens A B 8 35 tokens 50% 150 tokens 50% 0 tokens A B 9 40 tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B tokens 50% 150 tokens 50% 0 tokens A B The only difference with respect to the original version is that the magnitudes have been made proportionally smaller. It is also worth to mention that the literature about risk aversion experimental elicitation methods, e.g. Crosetto and Filippin 6

7 (2013) and Holt and Laury (2002), has shown that the degree of risk aversion depends on the stakes that are in play. Hence, the tokens in table 2 are of the same order of magnitude with respect the ones that subjects will deal with during other parts of the experiment. Specifically, the expected value of the lottery in Column B was chosen equal to the average between the lowest and the highest number of tokens we expected people may have to deal with in the redistributive framework. The first column represents a sure amount of token that increases from row to row, while the second one is a lottery where with equal probability the subject can win either 150 tokens or nothing and it is the same in each row. Subjects are asked to choose between column A and column B starting from the first row. The rational choice for the fist row is column B, but at some point the subject is expected to switch to column A: a more risk loving subject will switch later than a risk averse one and this allows us to measure on a 1-20 scale participants risk attitudes. In each session, one of the rows of the above table will be randomly selected at the end of the experiment and the choice made by subjects will be paid, allowing each subject to individually play the lottery in Column B if necessary. Another key element of the design is the cost of the effort, since it is the factor that allows the income distribution to take form even in those sessions where the initial income was equally distributed among all participants. Such cost, that was interpreted in the experimental setting as a time consuming activity that requires some ability to be performed, was designed such that each subject could choose the ideal effort-redistribution combination in a way not possible outside a laboratory experiment. Moreover, making the effort costly allows people to feel the income as non-trivially earned. The effort task chosen has been proposed by Buch and Engel (2012) and has the useful feature of being easy to administer in a paper and pencil experiment, but complex enough to require people to exert real effort in order to perform it. It consists in finding how many couples of numbers add up to 10 in 4x4 tables as the one reported in Table 3. Table 3: Example of effort task Each table that was presented had at least one couple and at most four. The size of the tables was chosen in order to make the task as challenging as possible, since in Buch and Engel (2012) four was the maximum size presented to subjects. 7

8 2.2 Experimental procedures The experiment took place in the School of Management and Economics, University of Torino with 4 sessions, on October 7 th, The desired number of subjects, 88, were recruited on a first come first serve basis among the students: each session involved 20 participants, whose earnings were determined according to their performance during the experiment and 2 reserves, 1 that were rewarded with a coffee. Subjects were recruited by means of the a leaflet among students of Business and Economics, both at graduate and undergraduate level. The desired number of enrolments was reached, but only some of the students showed up for the experimental session they booked. The issue was particularly severe in Session 4, where only 11 subjects were present. In the first Session 20 participants were present and there were enough reserves in order to reach the desired number of subjects, but in Session 2 and 3 only 19 students showed up, causing a reduction of the sample size. Each session lasted roughly 2 hours. Upon their arrival in the room where the experiment was scheduled, subjects found all the material they needed on the desks, including instructions and answer sheets that can be found in the Appendix. They were informed about the general rules of the experiment and the privacy-related laws that had to be applied in dealing with their personal data. Participants were also informed that during the whole experiment an ad-hoc currency named token had to be used and the conversion rate for the actual payment was set at 1 token = 0.01 e for the risk aversion test and 1 token = 0.03 e for the redistribution game in order to stress the role of the latter and to have higher monetary incentive on the social choice. Instructions for each part were read out loud and the participants were asked to fill in the choices. The first part was the same in each of the four sessions, since it the risk aversion test. A complete timeline, detailing the different parts of the design in chronological order can be found in the Appendix Subjects had then the possibility to practice on the effort task, so that they could familiarize with it so that they would make more pondered choices during the next parts. Such practice lasted 10 minutes and subjects faced 10 tables. At the end of that period solutions were shown so that participants could self-asses their performance. The following part of the experiment aimed at eliciting individual preferences for income redistribution. Subjects were informed about their initial income i.e. the number of tokens they owned to begin with and the income distribution among 1 Among the students of each session, the last two students to fill in the registration form were considered as reserves. 8

9 participants. In the two Sessions where the income was the same for each participant, 100 tokens were provided, while in the two where the initial income was unequally distributed, a graphical representation of the distribution was shown. Figure 1: Income distribution in the unequal income sessions. represented by a column. Each subject is Following Durante et al. (2014), the income distribution in the non equal treatments has been selected as a real world one, with the difference that in this experiment it is a starting point, while in their work it is the final one. The distribution subjects faced is displayed in Figure 1 and it is a normalized version of the 2013 Italian income distribution provided by the Ministry of Economy and Finance where the maximum income was set to 100 tokens. The lowest value is the 1 st percentile and the highest one is the 95 th one so that there is one income level for each of the 20 participants. 2 The top 5% of the income distribution was considered as an outlier, since it would have made the normalized version of the distribution not fit for our purposes, but it is reasonable to assume the probability of social mobility toward a such high level to be very low if not negligible, hence this decision is not likely to affect the results. Each subject was then asked to commit to solve a number between 0 and 25 of exercises as the ones presented in Table 3 that they had just practised on, knowing that each one of them would increase the income by 2 tokens. It is important to notice that, in order to make the task even more challenging, the commitment was for the number of correctly solved exercises, n e, hence the subjects were not allowed to leave the room until they correctly solved the number they had chosen 2 In sessions with less than 20 participants some income levels were randomly eliminated, but subjects were not informed about which ones. 9

10 in first place. In the two risky effort sessions, the link between the effort and the gains became uncertain, since 2 tokens per exercise became the maximum possible attainment: once the commitment had been made and the tables solved, a random number between 50% and 100% with increments of 10%, p, was drawn by each subject. The actual number of tokens produced by the effort was calculated according to the following formula: n e 2 p The number of token that could be earned with the effort choice was selected so that participants had the opportunity to move along the income distribution: theoretically even the poorest subject in the pre-effort distribution could end up above both the mean and the median once the effort is realized. A possible downside of our initial distribution is that there is a low probability of upward mobility for the second richest subject, but, in our opinion, the issue is offset by the advantages of exploiting a real world distribution. While committing to the desired level of effort, participants had also to choose the desired level of the tax rate that they would have liked to apply if they were a dictator under the rule that the whole amount of fiscal revenues had to be equally divided among participants. The value of the tax rate used to determine the actual payoffs was randomly drawn among participants choices, with the so called random dictator rule. Hence, the final payoff P of each subject i was determined according to the following formula, where n is the number of participants in the session, t is the tax rate extracted with the random dictator rule, y is the initial number of tokens, y e is the additional tokens obtained with the effort task. P i = (y i + y e i ) (y i + y e i ) t + 1 n n (y i + yi e ) t It is immediate to notice that the sum of the last two terms of the formula, the ones that are related to the redistribution scheme, will be positive for each subject that has a final income below the average i.e. he will receive a transfer, while it is negative for those above i.e. they will have to pay a tax. Each subject s payoff will be converted into Euro and paid at the end of the experiment, together with the outcome of the row of the risk aversion test that was randomly selected. The last part of the experiment was an exit survey that contained demographic questions and collected informations about several other variables that have shown some predictive power as far as laboratory experiments on preferences for redistri- i=1 10

11 bution are concerned. After the end of the experiment, random draws determined the random parameters that were needed in order to define payoffs. The methods were an extractions from an urn in order to determine the tax rate defined by the random dictator rule and the paid row of the risk aversion test. The toss of a dice was used to determine the outcome of the lottery and the percentage of additional tokens from the effort if the session needed it. The survey about the effort task provided comforting informations about the choice, since it was perceived as hard but not too hard by subjects: on a 1-5 scale where 1 is extremely easy and 5 extremely difficult the average response was 2.4 and no subject chose 5. The training part of the design, that allowed subject to familiarize with the task was also valued as useful, since only 10% of the students reported to have overestimated the number of exercises he was ready to solve. To be fair, roughly 50% of the subject declared that they had underestimated the number. However, increasing the training time beyond 10 minutes would have probably made the experimental session too long and the task too easy. Payments were made in cash at the end of each session. The average payment was 3.52 e, with a maximum of 5.69 e and a minimum of 0.85 e. According to data from the exit survey, 90% of the participants found the experiment interesting and 85% of them had no difficulty at all in understanding the instructions. 3 Results 3.1 Preliminary results As previously pointed out, in order to analyse the relationship between preferences for redistribution and risk attitudes, a precise measure of the latter is needed. A critical measure in order to assess the validity of the experimentally measured risk aversion coefficients is the degree to which subjects were able to understand the task. Given the structure of Multiple Price Lists, any rational individual who understood the instructions would switch column only once: multiple switches denotes lack of comprehension. In Holt and Laury (2002) s session that resemble the most the stakes into play in our test i.e. very low and hypothetical, roughly 10% of subjects did not understand the task and submitted contradicting answers. A comparable share was found in our data. It is also worth to mention that some subjects in the original Multiple Price Lists switched in the first or in the last row, exhibiting quite extreme levels 11

12 of risk aversion and love: those subjects were considered among those who did not understand the instructions, but in our data this pattern of choices was not present. A possible explanation of the difference, other than random chance, can be the selection of participants among students of Business and Economics. Another possible argument that can be developed can be that the absence of extreme choices was a consequence of the decision of using Dohmen et al. (2010) s version of the test, that aims at enhancing understandability. It is also worth to mention that the majority of subjects who switched more than once in our task displayed a clear pattern of choices, where it was possible to define a narrow switching area instead of a precise switching point. As far as those students were concerned, it was possible to estimate their degree of risk aversion as the average of the switching area. Other subjects made inconsistent choices only for extreme values, hence their level of risk aversion was clear i.e. they displayed a semi-consistent behaviour. The results obtained in the analysis are the same no matter if we consider the whole sample or if we discard observation where risk aversion was inferred rather than observed, as it will be possible to see in the following paragraphs. Only two subjects had a pattern of choices that did not allow to infer their risk aversion parameter and those observations had to be dropped. As far as the values of risk attitudes that were recoded during the experiment, all the subjects displayed risk aversion or risk neutrality, while no one could be classified as risk loving. Risk loving subjects are rare to find in experiments, but in Holt and Laury (2002) one third of subject was classified in that way and in Dohmen et al. (2010) that number was one fourth of the total. However, the difference may be due to the fact that students of Business and Economics may be less prone to value a lottery more than its expected value with respect to a generic sample. When we consider the values of risk aversion broken down by demographic categories, it is possible to notice that those subjects who were enrolled in degrees offered by the Esomas department, i.e. students of economics, displayed lower average risk aversion with respect to Business and Management students. The statistical significance of the difference across means has been tested with a nonparametric Mann-Whitney test (p = 0.06). One of the possible explanation for the difference may be found in the fact that economics students had experience in the theory of choices under uncertainty and they may be more prone to evaluate the expected value of lotteries they face and act consequently with respect to management students, who may be more naive in the approach to the test. Moreover, given that there are no risk loving subjects in the sample, the difference in the degree of risk aversion across field of studies may be amplified. 12

13 When we point our attention to gender differences in risk attitudes, the literature seem to agree that females are more risk averse than males and our results support the hypothesis (p = 0.03). However, some recent research by Crosetto and Filippin (2013) pointed out that women may seem more risk averse then men because they are more loss averse and the majority of the existing tests are not able to disentangle the two forces. The original Holt and Laury (2002) s Multiple Price Lists approach is unlikely to be affected by loss aversion and the results about gender differences are contradicting when the test is used. However, this work exploits Dohmen et al. (2010) s version, that is likely to provide reference points and hence to trigger an implicit loss aversion. As a consequence, our results seem to support Crosetto and Filippin (2013) s hypothesis. As it is possible to notice in Table 4, all demographic variables present roughly the same means across sessions. The average subject was 22 years old and the large standard error in Session 3 was mainly due to a single outlier that was 48 years old. 56% of the sample was constituted by women and subjects had attended an average of four courses in economics. 70% of students were enrolled in an undergraduate degree and 70% of participants was a Business student, while 90% was born in Italy. All values can be considered stable across sessions and consistent with the values of the whole School of Management and Economics of the University of Torino. The only value that does not seem constant across sessions is the share of Esomas students, but it seems not to affect the results, as it will be argued later on. Table 4: Demographic variables of participants by session Session Age Female # Econ courses Esomas Undergraduate Italian (1.60) 55% 3.65 (2.81) 40% 70% 90% (2.54) 55% 4.55 (2.57) 33% 61% 100% (6.31) 58% 4.39 (2.02) 26% 78% 89% (2.06) 54% 2.77 (2.45) 18% 63% 100% Total 21.9 (3.72) 56% 3.95 (2.5) 30% 69% 94% Mean values with standard errors in parenthesis. Interesting results can be obtained when we compare participants choices in the redistributive framework with their political ideology. Self-reported attitudes towards redistribution provided by subjects in the survey questions followed the standard political pattern i.e. left wing high redistribution vs right wing low redistribution, but the answers may have been given in order to fit a stereotype, since there is no difference in actual redistributive choices among self-proclaimed left or right wing voters. The statement has also been tested statistically: even if we do not considered people who declared to vote for centre parties, the average tax rate 13

14 chosen by left and right wing voter is the same (p = 0.89). A possible explanation for the result may be that in Italy political debate and ideological differences across political fields are more focused on other topics. Before presenting further results, some remarks about the outcome of the Session 4 have to be considered. In the combination of treatment non equal income and low risk, only 11 subjects showed up despite the desired number of enrolments was reached. In addition to the small sample size, ten out of eleven participants chose a tax rate equal to zero. It is not possible to measure the extent to which such extreme choices were driven by the fact that the self-selection of participants in sessions led to a sample of people that severely opposed redistribution from the possibility that some coordination took place. However, it is important to notice that the previous session lasted longer than expected and subjects exiting the room had the opportunity to meet and possibly interact with the participants involved in the problematic session, something that did not happen in other cases. Moreover, redistributional choices were much less disperse than in other sessions as displayed in Figure 2, hence the most plausible argument that can be used in order to explain the results from Session 4 is that some form of coordination among subjects happened. As a consequence, the power of the experiment in analysing the role of inequality aversion controlling for risk attitudes is reduced. Data from that session will be used in order to provide robustness checks to other results and not to enquire our relationship of interest. Average tax rate by session.4 Average tax rate (%) Session 1 Session 2 Session 3 Session 4 ± s.e. Figure 2: Average ideal tax rate proposed by subjects in each session. Session 1 and Session 2 are equal income treatments; Session 2 an Session 3 are high risk treatments. The average redistributive tax rate that was considered as ideal by subjects across all Sessions was 21%, that rises to 25% if we do not consider Session 4. The value 14

15 is considerably lower than the ones previously found in the literature, since the value in Durante et al. (2014) and Beraldo et al. (2014) s comparable treatments was around 39%. The distance from consolidated results in the literature may be attributed to the sample we considered, entirely constituted by students of Business and Economics. Moreover, the sample size is not very large, hence outliers are able to affect the results and the standard deviations sizeable. 3.2 Treatment effects According to our hypothesis, subjects should react to changes in the design selecting different tax rates i.e. asking for more or less redistribution depending on the probability of social mobility they are facing i.e. the uncertainty in the position in the final income distribution that will be used to compute their payoffs. The idea is that redistributive taxation can be seen as a form of insurance, and consequently the higher subject s risk aversion the higher its desired level. As it is possible to see in Figure 2 exploiting the between subjects nature of the design, the average tax rate chosen by individuals across Sessions seem to confirm the results obtained by Durante et al. (2014), since as the risk increases i.e. from Session 1 to Session 2 and from Session 4 to Session 3, the average tax rate increases, as if people exploited redistribution as an insurance against negative outcomes in the final income distribution. However, even if it seems that the increase is present, it is not statistically significant as proven by a Mann-Whitney test (p = 0.30). On the other hand, a perfectly similar argument can be developed for the comparison between the values of Session 3 and Session 4. In this case the test confirms that the two averages are statistically different (p = 0.00), but considering the already mentioned problems with data from Session 4 it would not be safe to attribute the decrease in the tax rate to the decrease in perceived risk from one session to the following. A possible explanation for the lack of significance in the difference is that there is not enough risk in the design for participants to react modifying their ideal tax rate. In order to test this hypothesis, the same analysis developed for the whole sample for the first two sessions can be performed on a reduced sample of highly risk averse individuals, since they are those who are expected to change their behaviour the most across different treatments. All those individuals that displayed a higher risk aversion than the average of the whole sample of subjects were considered to meet the criteria for the subsample. Considering only the subsample of interest, the average across the two Sessions is statistically different (p = 0.05) and the sign of the variation is again the expected 15

16 Average tax rate in equal income sessions for very risk averse subjects.8 Average tax rate (%) Low Risk High Risk ± s.e. Figure 3: Average tax rate proposed by highly risk averse subjects in equal income Sessions one. It is possible to notice that the average tax rate is almost double in the high risk treatment with respect to the low risk, even if standard deviation are quite high. Since the result is valid only when we consider highly risk averse individuals, it is possible that in the design of the experiment few risk was introduced, but it is nearly impossible to translate a real measure of perceived probability of social mobility in an experimental context under the form of risk. As a consequence, it is really difficult to state if the risk faced by subjects in the experiment was somehow comparable to the one faced in the real world. Our results, that are consistent with Durante et al. (2014) s ones, prove that their conclusions were not driven by the type of design, since they are robust with respect to a different approach. Moreover, they asked subjects to state desired redistribution levels depending on different rules for the distribution of the income: those rules could be ordered in terms of risk, but the same order would arise in case the criterion of choice was a moral worthiness one. As a consequence risky distributional rules could have led to higher redistribution because they were seen as rewarding unworthy people, hence subjects may have adopted moral criteria in choosing the tax rates instead of the insurance one. Our result has no possible worthiness confounding factor, since in the between subjects design only one distributional rule is presented to subjects, that know nothing about other sessions. It would have been interesting to analyse if the same pattern of insurance by means of redistribution was present also in a more realistic framework, where the initial income was unequally distributed among participants, but Session 4 does not allow 16

17 a meaningful comparison with the previous one. Other than very risk averse subjects, another group was found to be particularly sensible to the increase in risk from Session 1 to Session 2: those who believed to have worse economic opportunities with respect to their father i.e. people with negative attitudes toward social mobility. Those subjects fear of social mobility may have lead them to ask higher tax rates in the risky scenario (p = 0.03). However, the result is not robust with respect to a regression analysis, as it is possible to see in Table Regression analysis In order to strengthen the aforementioned conclusions a multivariate regression analysis has also been performed. Following Durante et al. (2014), the results that can be seen in Table 5 are from a Tobit regression. Marginal effects of the variables of interest are reported with their respective robust standard errors. Model (1) is the Baseline model and includes as regressors a measure of risk attitude, the amount of effort exerted during the experiment, the number of economics courses attended and dummy variables for sex, session, perspectives on social mobility and country of birth. Model (2) is Full and enlarges the set of demographic controls with informations about age, the degree subjects are enrolled in, further measures of attitudes with respect to social mobility and the income provided at the beginning of the session to the participant. However, the inclusion of additional regressors does not change results. Our main coefficient of interest is the measure of risk aversion, that has the expected sign and is significant. It is worth to notice that the measure of risk has been coded as the number of times the subject chose the lottery over the certain amount in the risk aversion test: the more risk averse the participant the lower the number of rows the subject needed in order to stop choosing the lottery. As a consequence, the lower the value of the variable, the higher the degree of risk aversion. Hence, given the definition, a negative sign is what we expected: the higher the risk aversion, the higher the amount of redistribution the individual will ask in order to insure against uncertainty in the final income distribution. This result is again in line with Durante et al. (2014) s ones, but in their work risk aversion was measured on a 1-5 scale and the coefficient was often not significant in the Tobit regressions. Given the results presented in Table 5, the lack of significance was probably due to a loose measure of the risk aversion parameter rather than to a weakness of the relationship of interest. When we focus on the magnitude of the coefficients, we can see that a one point 17

18 Table 5: Tobit marginal effects. Dependent variable: Tax rate (1) (2) (3) (4) (5) (6) Risk 0.027* 0.033** 0.028* 0.034* 0.041** 0.057** (0.016) (0.016) (0.017) (0.017) (0.019) (0.024) Female 0.272** 0.230* 0.243** ** 0.394** (0.110) (0.133) (0.117) (0.138) (0.111) (0.144) Italian 0.548** 0.584** 0.537** 0.554** 0.666** 0.598*** (0.221) (0.222) (0.228) (0.219) (0.250) (0.192) Economics courses 0.064*** 0.081*** 0.057** 0.077*** 0.073*** 0.099*** (0.020) (0.020) (0.022) (0.023) (0.022) (0.029) Effort (0.006) (0.006) (0.006) (0.006) (0.007) (0.010) Session * (0.115) (0.106) (0.117) (0.108) (0.127) (0.133) Session * * ** (0.116) (0.235) (0.117) (0.269) (0.140) Session *** 0.521** 0.571*** (0.159) (0.223) (0.167) Better than father (0.088) (0.097) (0.088) (0.097) (0.112) (0.171) Initial income (0.003) (0.004) Age 0.019*** 0.018*** (0.006) (0.006) Undergraduate (0.106) (0.110) Esomas (0.118) (0.122) Luck (0.057) (0.064) Poverty trap (0.048) (0.050) Income wrt average (0.003) Constant (0.247) (0.519) (0.254) (0.543) (0.270) (0.259) Observations Pseudo R Prob > χ p < 0.10, p < 0.05, p < Robust standard errors in parentheses. Session 1 is the baseline for comparisons across sessions Sessions 1 and 2 are equal income; sessions 2 and 3 are high risk Model (1) is the baseline model; Model (2) includes demographic controls; Model (3) and (4) are the equivalent of the first two, but without data from Session 4; Model (5) is equivalent to Model(1), but without subjects for which risk aversion was inferred; Model (6) is as Model(5), but only data from Session 1 and 2 are considered 18

19 increase in risk parameter, i.e. a decrease in subject s risk aversion, will lower the ideal tax rate by 2.7% in the Baseline model. It is worth to mention that the definition of the one point increase in the risk parameter is quite vague and probably a marginal effect defined in terms of the classical parameter r of a Constant Relative Risk Aversion utility function would have been easier to understand. Nevertheless, this would have implied making assumptions about the shape of the utility function. We decided to leave the scale of the risk parameter unchanged, focusing more on the sign of the effect with respect to to its magnitude. Another interesting result is that Italian born subjects ask for more redistribution than foreign born ones. A possible explanation for this pattern is that the latter are immigrants, hence they, or their parents, left the country of origin in order to better their position. As a consequence they may prefer low redistribution because of the Prospect Of Upward Mobility hypothesis i.e. they expect to better their position and to be harmed by redistribution. Another possible argument that can be used in order to interpret the result is that in their country of origin inequalities are more severe than in Italy, hence they may consider already egalitarian a society that Italian born people may consider unequal. When we consider the impact of the field of studies on preferences for redistribution, we can notice that dummies marking subjects who are enrolled in a degree offered by the Esomas department is never significant, while the higher the number of economics courses taken by the subject, the more he will be prone to redistribution. As in Durante et al. (2014) the variable has a positive coefficient, possibly because Economics studies underlines redistributive issues better than Business ones. The result about gender differences is persistent across specifications and suggests that women prefer lower levels of redistribution with respect to men. However, the majority of the literature supports the opposite conclusion and the results by Durante et al. (2014) point towards that direction as well. Nevertheless, several other recent results e.g. those by Checchi and Filippin (2004) and Beraldo et al. (2014) are consistent with our findings. One of the possible explanations for the discrepancies may be that American and European women have different attitudes toward redistribution, but further research is needed in order to understand the heterogeneity of the results across studies. As additional robustness checks, other specifications are tested. Specifically, Model (5) is equivalent to the Baseline model, but only those subjects who had a single switching point in the risk aversion test were considered i.e. participants whose parameter was estimated as average of the switching area are not included in the regression. Since the results are not influenced by the reduction of the sample, it is possible to conclude that the results were not affected by the way risk aversion 19

20 was inferred for those subjects that did not act in a perfectly rational way. Model (6) is estimated on an even smaller sample, that is the same of Model (5), but only subjects in the first two sessions are considered. The rationale for the specification is to highlight that, taking into account risk aversion and other relevant parameters, tax rates proposed by subjects in Session 2 were higher than those proposed in Session 1. The result shows that what has been found significant with comparison of descriptive statistics is still relevant in a Tobit analysis. The opposite holds for subjects beliefs about economic perspectives with respect to their father s: the result loses significance in all specifications the regression. The role of political ideology of the subjects is not relevant, as shown in the previous paragraph, hence they are not included in Table 5. If they are included in the model, the coefficients are not significant and the results are not altered. Other variables that are always not significant are the dummy that marks subjects enrolled in an undergraduate degree, and further proxies for attitudes toward social mobility obtained in the survey. It is worth to notice that the initial income and the difference with respect to the initial average income are always not significant, mainly because more than half of the observations are from equal income sessions and only Session 3 provided reliable data where those two variables had different values across subjects. On the other hand, the younger the subjects, the higher the preferred level of redistribution as in Beraldo et al. (2014) Given that data about the ideal tax rate were collected allowing subjects to choose between values that ranged from 0% to 100% with 10% increase, the dependent variable can also be seen as categorical and another possible regression approach could be the Ordered Probit. The results for this model are not different from the Tobit values presented in Table 5 as far as significance levels are concerned. The effects have a slightly different magnitude, but the results are in general widely similar. A Table with the Ordered Probit results can be found in the Appendix. 3.4 External validity Once a result is obtained in the laboratory, it is natural to ask whether it can be extended to the population of interest. Anonymity was ensured for each subject with respect to its peers, so that they would not fear moral judgements induced by the experimental setting. However, anonymity with respect to experimenter was not possible because of the paper and pencil nature of the experiment. The stakes into play in the experiment are obviously smaller than the ones agents 20

21 face in real life by obvious reasons, hence Alm and Jacobson (2007) s Reward Dominance criterion was adopted: even if small, rewards were considered large enough to be able to offset subjective costs that subjects place on the participation in the experiment. Students are likely to have quite low opportunity costs, as it is shown by the fact that 80% percent of students was already planning to visit the building where the experiment took place during the day of the experiment for attending lectures. Moreover, the whole experiment was framed in terms of tokens so that subjects would have to deal with higher numbers they are more likely to be familiar with. Subjects in laboratory experiments are usually students, but an additional issue about our specific sample may be related to the pool where it was recruited, since students of business and especially economics are probably somehow more skilled in the required tasks and decisions with respect to a standard group. Durante et al. (2014) report that roughly 85% of their sample had attended fewer than two courses in economics, while among our subjects that value was 21% and this factor has been highlighted in the data analysis. 4 Conclusions The between subjects laboratory experiment allowed to confirm the existence of a relationship between risk aversion and preferences for redistribution. When subjects faced uncertainty about the position in the income distribution, the higher the degree of risk aversion, the higher the preferred redistributive tax rate. Such conclusion is supported both by the comparison of results across different treatment sessions with high and low level of risk, both by a multivariate regression analysis, that has shown to be robust to changes in the specification. The results provide further evidence to support the only recent contribution to the literature about our relationship of interest, Durante et al. (2014), showing that their conclusions were not driven by the choice of a within subject approach, nor by differences in the moral worthiness of the income distribution methods. Moreover, a possible explanation for their lack of significance of the risk aversion coefficient in the regression analysis can be found in the loose measure of risk attitude they adopted, since that issue does not arise when the same value is measured with a more precise scale. However, some remarks about the results have to be made. First of all, one of the experimental sessions provided unreliable data, hence no conclusion could be drawn about the presence or absence of inequality aversion among the subjects. Another 21