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Are you risk averse over other people's money?

1. Introduction

Decisions with uncertain outcomes are often made by one party in settings where another party bears the consequences. Whenever an individual is delegated to make decisions that affect others, such as in the typical corporate structure, does the individual make decisions that reflect the risk preferences of the party bearing the consequences? If these two parties do not have the same risk attitude, efficiency loss could result unless the affected party has access to sufficiently flexible contracts and knowledge of the risk attitude of the individual making the decisions (e.g., Grossman and Hart 1983; Kreps 1990, pp. 582-3). We examine risk attitudes of individuals making decisions on behalf of others in simple settings using controlled laboratory experiments. This is an exploratory exercise in the spirit of those that examine preferences involving risk to oneself or those that examine preferences that have a social dimension. Thus, we propose nothing beyond evaluating the possibility that subjective preferences involving outcomes to self and outcomes to others may not be the same. One set of experiments involves choices over lotteries: another involves sealed-bid auctions. We find a remarkable result: individuals lend to be significantly less risk averse when the r make decisions over another person's money compared to decisions that they make over their own money. Decisions for self reflect a certain level of risk aversion, comparable to those reported elsewhere, and vary across individuals as one would expect. However, when people are asked to make decisions for others, they tend to make decisions closer to risk-neutral preferences. This occurs despite the fact that beliefs regarding the other person's preferences appear to be unbiased. We examine behavior in two unrelated experiments and find that the effect is present in both, indicating some degree of robustness of the phenomena with respect to differences in institutions and procedures.

This result has significant implications for the analysis of behavior of principals and agents. If the principal and agent do not have the same risk preferences, in the sense that the agent does not exhibit the same risk preferences as the principal when acting on his/her behalf, there is an expected efficiency loss if they do not use elaborate contracts. Since elaborate contracts of this kind do not appear to be common, our results suggest that there could be some other advantage to using agents that compensates for such efficiency losses (e.g., Milgrom and Roberts 1992, chapter 2). Alternatively, we expect to find settings in which principals tend not to use agents whenever these other advantages do not outweigh the expected efficiency loss. Our objective is simply to note that analyses of the use and motivation of agents should allow for the fact that the agent should not be expected to behave as if they were using the principal's risk preferences, quite apart from the importance of allowing for his/her own risk preferences over his/her own earnings. (1)

In section 2 we explain the two experiments and their respective procedures. Both were developed with the goal of identifying differences in the risk preferences of principals and agents. In section 3 we examine the results. We draw conclusions in section 4.

2. Experimental Design

Lottery Choice

Measures of risk aversion can be elicited using a lottery choice task known as a multiple price list (MPL), which has been used previously by Holt and Laury (2002, 2005) and Harrison et al. (2005). Each subject is presented with a choice between two lotteries, which we call A or B. Table 1 illustrates the basic payoff matrix presented to subjects. The first row shows that lottery A offers a 10% chance of receiving 400 Indian Rupees (Rs) and a 90% chance of receiving Rs 500, since these experiments were conducted in India. The expected value of lottery A, [EV.sup.A], is shown in the third-to-last column as Rs 490, although the EV columns were not presented to subjects. Similarly, lottery B in the first row has chances of payoffs of Rs 960 and Rs 25, for an expected value, [EV.sup.B], of Rs 118. Thus, the two lotteries have a relatively large difference in expected values in this case, Rs 372. As one proceeds down the matrix, the expected value of both lotteries increases, but the expected value of lottery B becomes greater relative to the expected value of lottery A.

The subject chooses A or B in each row, and one row is later selected at random for payout for that subject. The logic behind this test for risk aversion is that only risk-loving subjects would choose lottery B in the first row, and only risk-averse subjects would choose lottery A in the second-to-last row. Assuming local non-satiation, the last row is simply a test that the subject understood the instructions. Most subjects would be expected to switch from A to B on some row in the table, and this switching point can then be used to infer their risk attitude. A risk-neutral subject should switch from choosing A to B when the EV of each is about the same, so a risk-neutral subject would choose A for the first four rows and B thereafter.

The first set of experiments was conducted in India. The payoff values were in Indian Rupees. At the time of the experiment, the official exchange rate was 1 U.S. dollar = Rs 44.8, implying prizes worth $8.90 and $11.12 in the "safe lottery" A and prizes worth $21.41 and $0.56 in the "risky lottery" B. These are approximately 5.5 times the baselines prizes offered in the experiments of Holt and Laury (2002). However, India's official exchange rate does not properly reflect the purchasing power of the Rupee in India, in terms of goods and services. Using purchasing power data for 2000 from the Penn World Tables of Heston, Summers, and Aten (2002), our payoffs can instead be calculated as $65, $52, $125 and $3.25, respectively, for a scaling of 32.5 times the baseline prizes of Holt and Laury (2002). (2) In general, the payments were significant compared to the subjects" earning power. (3) The conversion to U.S. dollars at official exchange rates or purchasing power rates does not affect inferences about risk attitudes from observed choices. All subjects were paid in cash at the end of the session. In addition to earnings, each subject received Rs 25 for turning up as agreed.

The subjects were 74 students from classes at the Indian Institute of Management (IIM) in Ahmedabad, the premier business school in India. (4) Subjects were generally representative of the student population at IIM in Ahmedabad in terms of family income levels (moderate to high, by average Indian standards), sex (predominantly male), ethnicity (predominantly Hindu), and undergraduate major (engineering and computer sciences).

All subjects came to one room initially, where they were seated and received a randomly distributed instruction packet colored red or yellow. The instruction packet was initially sealed without revealing the color, so that subjects picked their color at random. They were presented with some general instructions, including an explanation of the role of a monitor who would ensure that all instructions and information were actually applied. The monitor was chosen at random from the subjects. Half of the subjects (those with red instruction packets) were then taken to another room, and a separate experimenter conducted the instructions in each room. The substantive task instructions were handed out sequentially: When performing the first task, subjects had no information about the nature of the subsequent tasks.

In the first room, subjects were asked to make choices about the lotteries, and in the other room, the subjects were told that they had no choices to make but that they would receive the consequences of some choices made in the other room. In the first room, where the choices were made, subjects proceeded in one of two orders. Either they made decisions over their own money first, and then over another person's money, or vice versa. Thus, we controlled for order effects while obtaining in-sample responses. The subjects in the first room were told that they had been paired with one other person in the second room, but that they would never know each other's identity. The monitor verified the information provided in the instructions in each room. All random draws were resolved using a physical device, a simple 10-sided die. (5)

In addition, and after the lottery choices had been made, each subject in the first room was asked to state the number of choices of lottery A that they believed the rest of the people in the room would make. They were asked to state their belief for each of the treatments, where beliefs and actual averages were rounded to the nearest integer. This belief was elicited under simple incentives. (6) The purpose of this additional task was to find out the risk attitudes that each subject thought other people, drawn at random from the same population, would have. If the subject thought that everyone else was less risk averse than they were, they might choose a less risk averse outcome for the other person in the belief that they were selecting as they would. The data provide some checks on hypotheses of this kind.

Bidding in a First-Price Sealed-Bid Auction

The MPL task is a popular instrument that provides a direct elicitation of risk attitudes. An alternative mechanism can be found in a variant of the first-price sealed-bid auction, using independent and private values. The task is simplified by reducing the number of bidders to 2 and computer-simulating the other bidder with a risk-neutral bidding strategy. (7) The subject was told the strategy that the computerized bidder would use, although it was not described as being consistent with risk-neutral bidding behavior. This task simplification reduces the decision to one of individual choice with no strategic consideration.

The subjects were 32 students recruited from the University of Texas at Dallas. They were each seated in front of a computer terminal and separated from other subjects by dividers. The instructions were provided in written form and were then read aloud by the experimenter. The computer interface of the experiment was implemented using Z-tree, a software package developed by Fischbacher (2007).

Each participant played 25 rounds in the role of agent and 25 rounds in the role of self, for a total of 50 rounds. Half the participants played agent for 25 rounds, followed by 25 rounds of playing for themselves; the other half started playing for themselves for 25 rounds and then played as agent for another 25 rounds. A cohort in a session consisted of four participants, and players remained in the same cohort for the full 50 rounds. Throughout the 50 rounds, each participant was matched with two other participants, one of whom was his client during 25 rounds and the other his agent during the other 25 rounds. The exact order in which each participant played each role is shown in Table 2.

When bidding as agent, it was explained that all earnings from one's bidding activity would go to a different participant in the room designated as one's client. Hence, the payoff of each participant consisted of his earnings from his own bidding choices in 25 rounds in the role of self and the earnings from 25 rounds of bidding of an anonymous other participant in the group designated as his "adviser." The roles were displayed prominently at the top of the screen. Participants were assured that the person playing their agent was different from the person assigned as their client. Participants were not told the identities or matches.

Valuations were drawn uniformly from 1 to 100 tokens. (8) It was explained to subjects that to win each auction, their bid would have to be higher than the computer bidder's bid. Their payoff in each auction they won would be their own valuation minus their bid. Subjects were told that the computer would bid a number between 1 and 50, and each bid between 1 and 50 was equally likely. This is, in fact, the risk-neutral bid distribution of a bidder with the same valuation distribution as the participant. Ties would be broken arbitrarily.

The optimal bid for a risk-neutral subject in this setting is to bid half of one's valuation. This generates a win probability equal to the bid divided by 50. To help subjects with their bidding decisions, a calculator was made available to them on the computer screen showing the probability of winning and the expected payoff for each bid. The idea with this display was to make the tradeoff between one's bid and the probability of winning salient and not to test the mathematical or cognitive acumen of subjects.

After each round, whether as an agent or bidding for their own money, a subject saw his/ her own bid, the computer's bid, the winning bid, and his/her profit in that auction round. In addition, subjects saw a table with their own earnings from all previous rounds. (9) A subject did not see his/her payoff from being a client of someone else until the very end of the experiment. Thus, the agent's actions, and the outcomes of the agent's actions, did not enter the client's feedback and had no impact on the client's behavior in the experiment.

[FIGURE 1 OMITTED]

3. Results

Risk Attitudes Revealed by Lottery Choice

Figure 1 displays the main results from the MPL experiment. On the bottom axis we list each problem, corresponding to the rows in Table 1. The vertical axis shows the fraction of choices of the safe lottery, option A. The dashed line displays what a risk-neutral subject would do: pick the safe lottery A until the EV of the risky lottery B is greater than the EV of lottery A and then pick lottery B. The other lines show the observed responses, pooled over the task order, which we control for in a formal statistical analysis below. Subjects that pick the safe option more than the risk-neutral prediction are risk averse, as discussed earlier. We will refer to the treatment where subjects make decisions about their own money as "Self" and to the treatment where subjects make decisions about other people's money as "Agent." So Figure 1 provides some evidence that subjects are risk averse in "Self" but are less risk averse in "'Agent" exercises. Of course, these lines only reflect averages, and there is typically more noise around the "middle" of these pictures, so this conclusion must await a more formal statistical analysis. However, the average number of safe choices was 6.35 and 5.03 in the "Self" and "Agent" treatments, respectively. This difference is statistically significant using a two-sided t-test (p-value < 0.001) or a Wilcoxon signed-rank test (p-value < 0.001). The variance of the number of safe choice was 2.72 in "Self" versus 3.20 in "'Agent." The F test statistic for comparing variances indicates no significant difference in the variances (F[36,36] = 0.85, p = 0.69).

We next examine the data using a structural maximum likelihood estimation of the expected utility difference between the choice of the riskier and the safer lottery. Each row in the MPL provides an observation on the binary choice between lottery A and B. We evaluate each lottery using a constant relative risk aversion (CRRA) characterization. Specifically, we assume that utility is defined as U(y) = ([y.sup.I - r])/(1 - r), where r is the CRRA coefficient, and r 1. With this parameterization, r = 0 denotes risk-neutral behavior, r > 0 denotes risk aversion, and r < 0 denotes risk loving. The dependent variable is the binary choice between lottery A and B. A standard probit function links the difference in expected utility (conditional on a candidate value of r) to the observed binary choices; see Harrison and Rutstrom (2008, p. 69ff) for details of the econometric specification. We include a Fechner error term (10) to capture behavioral errors as a function of "Self" and "Agent." Since each subject provided multiple observations, there are corrections for the possible correlation of statistical errors associated with a given subject. (11)

Table 3 displays the maximum likelihood estimates of this structural model. The dependent variable is the discrete choice (lottery A or lottery B). The CRRA coefficient r is estimated as a linear function of the covariates listed. The covariates include a dummy variable for Agent (l = Agent, 0 = Self) and a dummy variable for order of decision tasks. Other covariates are demographic variables deemed to be differentiating for the Indian student sample used for this study. Parental income and education are important in Indian society. Smoking is a prevalent and risky behavior and might be indicative of a risk preference. An age dummy was meant to separate college age students from older participants. Demographic variables were primarily included to control for possible sampling effects and reflect those included in other studies (Andersen et al. 2008).

The most important result is the estimate for the binary dummy (agent) picking out the risk-aversion responses over other people's money. It shows that CRRA is 0.44 lower when making decisions about other people's money and that this effect is statistically significant (p-value < 0.001). There does not appear to be a significant effect from task order, sex, or age. However, the educational levels of parents do matter, as do income levels. Controlling for any other differences, we estimate CRRA to be 0.69 when making decisions about the participant's own money and 0.25 when making decisions about other people's money. We also find that decisions over other people's money are associated with a larger Fechner error and that this is a statistically significant effect, implying that there is less sensitivity to differences in expected utility when acting for others than when acting for self.

How do we know that this shift is not an attempt to pick risk attitudes that match those of the people to whom they will be applied? This is the role of our additional task, where we elicited beliefs about the average responses of others in the room. The results indicate that risk attitudes about one's own money and beliefs about the own risk aversion of others are virtually the same. The average number of safe choices observed was 6.35 and 5.95, respectively, for "self" and "beliefs about others own attitudes," which is not significantly different using a two-sided t-test (p-value = 0.13) or a Wilcoxon signed-rank test (p-value = 0.26). Thus, the differences observed in Figure 1 and Table 3 are not due to subjects having beliefs that their risk attitudes were unrepresentative on average, but they appear to reflect a genuine preference difference. (12)

Finally, we can exploit the in-sample nature of our responses and construct a measure of the change in risk attitudes for each subject. We can define a variable for each individual that is equal to +1 if the subject makes more choices toward the safe lottery when we compare those choices for others compared to choices for oneself,--1 if the individual makes more choices toward the risky lottery, and 0 if there is no change for that subject. (13) Thus, each subject is classified, by this measure, as -1, 0, or +1. Controlling for the task itself (a dummy variable for Agent) and allowing for the effect of task order (a dummy variable for order), but no other explanatory variables, we then estimate an ordered logit model on these summary measures. The results allow us to predict the following probabilities: The probability that a subject would be less risk averse when making choices for others is 0.57, the probability that a subject would exhibit the same degree of risk aversion is 0.38, and the probability that a subject would be more risk averse when making choices for others is only 0.05. This confirms our between-subjects conclusions.

[FIGURE 2 OMITTED]

Risk Attitudes Revealed by Bidding Behavior

Optimal bids in the first-price auction depend on risk attitudes. Using the same CRRA utility function that we used to evaluate the risk attitudes implied by the lottery task, we can infer the risk attitudes that the subjects used in the auction task by assuming that they were bidding optimally conditional on those risk attitudes (e.g., Harrison 1990). This assumption may be more tenuous in the auction task than in the lottery task for reasons that have been much debated in the older literature (e.g., Harrison 1989, 1992), but this is why we simplified the auction task to make it a relatively simple, nonstrategic decision. Moreover, the purpose of our auction task was precisely to see if the qualitative results from the direct lottery task carried over into a more natural task, such as bidding behavior, so to some extent this added structure is necessary no matter what alternative task we choose.

Optimal bids for the auction task imply that the CRRA coefficient is equal to r = 1 (valuation --bid)/bid. Figure 2 displays the density of values for each treatment. The risk attitudes revealed by bidders acting on behalf of another person imply less risk aversion than the bids entered for themselves and a marked tendency for some subjects to actually act in a risk-loving manner with the other person's expected profit. Figure 2 also shows that there are two modes when individuals bid on their own behalf: One is risk averse (r > 0), and the other is approximately risk neutral (r [approximatley equal to] 0). This conclusion from Figure 2 is reinforced by a random effects regression, reported in Table 4, of implied risk attitudes on a binary indicator of the treatment. Relative risk aversion is lower by 0.132 when bidding for others, and this estimate has a standard error of 0.040 (p-value = 0.001, 95% confidence interval between -0.21 and -0.05). (14) We find that the residual variance of risk attitudes is not significantly greater when bidding for others. (15)

4. Conclusions

We explored the relationship among risk-averse behavior, making decisions on behalf of others, and beliefs regarding others" risk attitudes. We find that, consistent with extant research, individuals are generally risk averse for the domain of income represented in our experiments. However, individuals appear less risk averse when making decisions over other people's money, and some are actually risk loving. This general pattern is statistically significant. The difference does not appear to be driven by an attempt to pick risk attitudes that reflect the risk attitudes of others.

There are other possible explanations. We want to draw attention to some possibilities that have received attention in the literature, although we leave it to future research to evaluate their validity.

One possibility arises from the observation in the literature that when risky decisions are hypothetical, lower risk aversion is observed. There is extensive evidence (Holt and Laury 2002, 2005; Harrison 2006) showing that measures of risk aversion in hypothetical choices indicate significantly lower risk aversion than choices that entail real consequences. Indeed, the qualitative pattern matches ours: Subjects are moderately risk averse over their own money and less risk averse when the decisions have no monetary consequences for them. The similarity between the results suggests that the underlying explanation might be similar. However, this is not just indifference over the outcomes to others. Even though we see an increase in the behavioral error term that is significant, if we control for this effect, the risk-aversion coefficient is reduced but still significantly different from risk neutrality.

Another possibility, consistent with the evidence of a systematic choice pattern for others, builds on the social dimension of the decision over other people's money and involves subjects exhibiting some form of "social preference" in their decisions. We know from our follow-up questions about the choices of others that this is not because they believed that others were less risk averse than they were. However, it is entirely possible that they were viewing this as a social risk decision and employing different preferences over social risk than they do over individual risk. Direct tests of this hypothesis in group tasks, and using a wide range of social choice mechanisms, are reported by Baker, Laury, and Williams (2008), Colombier et al. (2009), Harrison et al. (2010), Rockenbach, Sadrieh, and Mathauschek (2007), and Shupp and Williams (2008). (16) The evidence from these studies is mixed, but that could be due to the diverse social choice procedures employed across the different studies. The main difference between those settings and ours is that in the present study, the individual is completely removed from the consequences of his or her decision.

Whatever the explanation for the behavior found here, there is a need for a better understanding of the motivations for agents acting on behalf of others. It would also be of great interest to identify the factors that motivate individuals to hire agents (brokers, financial advisors, insurance agents, doctors) to make risky decisions on their behalf. It may very well be that some level of detachment is beneficial and even desired by the impacted party.

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(1) The role of the risk preferences of the agent over his/her own earnings has been extensively studied in the design of principal-agent contracting arrangements. See Milgrom and Roberts (1992, chapter 7) for an excellent textbook exposition of the basic ideas, and Laffont and Martimort (2002) for a superb formal account (especially sections 2.11 and 6.5 on risk averse principals). The different risk preferences of principals and agents also enter prominently in a growing literature on the delegation of risk management to financial institutions (Hakenes 2004) and portfolio managers (Baptista 2008).

(2) The official exchange rate in 2000 was very close to the rate prevailing in mid-2005, when the experiments were conducted.

(3) Teaching assistants at the IIM in Ahmedabad received average annual salaries in 2005 of Rs 96,000 ($2143), which converts to roughly Rs 50 per hour. The average starting salary for graduates in 2003 (2004) was Rs 588,000 (700, 100) per year. This converts to roughly $13,125 ($15,5481 at official exchange rates.

(4) The Web site of the Indian Institute of Management (http://www.iimahd.ernet.in/) provides more information.

(5) The complete instructions are available in an Appendix, available on request from the authors.

(6) If the estimate was exactly correct in one of the two treatments, they would receive Rs 25; if the estimates were exactly correct in both treatments, they would receive Rs 50; if it was one oft', on either side, they would receive Rs 10 for that column; if it was one off in both treatments, they would receive Rs 10 for each treatment; and if it was more than one off in both treatments, they would not receive anything from this task. This incentive system effectively elicits the modal belief of the subjective distribution if one assumes that the subject is risk neutral for the purposes of the belief-elicitation task.

(7) Computer simulation of N-l bidders in first-price sealed-bid auctions was introduced by Harrison (1989) to remove strategic considerations from the task facing the subjects.

(8) Tokens were exchanged for money at the rate of 40 tokens per dollar. Each subject also received a $5 attendance fee.

(9) Subjects did not see a total until the very end, although they could easily compute it given the information provided. This was done on purpose to allow them to learn from feedback but to minimize wealth effects.

(10) See, for example, Hey and Orme (1994).

(11) The use of clustering to allow for "panel effects" from unobserved individual effects is common in the statistical survey literature. The clustering procedures allow heteroskedasticity between and within clusters, as well as autocorrelation within clusters. Wooldridge (2003) reviews some issues in the use of clustering for panel effects, in particular noting that significant inferential problems may arise with small numbers of panels.

(12) We further find that the beliefs about the decisions of others making choices as "agents" are not significantly different from the decisions that others actually make (p = 0.28), while the difference between the two sets of beliefs is (weakly) significantly different (p = 0.06) and in the same direction as the choice differences. Thus, the observed difference in risk attitudes is also reflected in the difference in the stated beliefs of subjects.

(13) In fact, only one subject had offsetting gross changes such that the net effect was no change.

(14) Virtually the same estimates are obtained with a fixed-effects model. We also obtain the same qualitative results if we exclude some extreme risk-loving responses (e.g., one subject bid I when his principal bad a valuation of 95. and one subject bid 10 when his principal had a valuation of 95). Dropping such responses leads to an estimated reduction in the difference in risk aversion of 0.08, with a 95% confidence interval between -0.14 and -0.03. We hesitate to drop such responses, however, because it is precisely this sort of change in behavior that one might expect when individuals take actions for others instead of themselves, and uncovering that possible behavior is the whole point of the design.

(15) This finding employs a multiplicative heteroskedusticity regression model with clustering for individuals. We verity that all coefficients of interest for the baseline regression here, with no multiplicative heteroskedasticity, are virtually identical to those reported m Table 4. The effect of giving advice over other's money is to increase the residual variance, but the effect is not statistically significant (p-value = 0.17).

(16) A related experimental body of literature examines the role of advice in learning environments and the possible influence of social learning on individual decision making (e.g., Ballinger, Palumbo, and Wilcox 2003: Schoner and Sopher 2003; Kuang, Weber, and Dana 2007). A key difference between our environment and theirs is that our agents make choices for the principals, rather than just giving them advice and letting them make the final choice. These differences are worthy of careful study, since each environment has important field counterparts.

Sujoy Chakravarty, Centre for Economic Studies and Planning, School of Social Sciences, Jawaharlal Nehru University, New Mehrauli Road, New Delhi, India 110067; E-mail sujoy@mail.jnu.ac.in.

Glenn W. Harrison, Department of Risk Management & Insurance and Center for the Economic Analysis of Risk, Robinson College of Business, Georgia State University, P.O. Box 4036, Atlanta, GA 30302-4036, USA; E-mail gharrison@gsu.edu.

Ernan E. Haruvy, Department of Marketing, School of Management, University of Texas at Dallas SM 42, 800 West Campbell Road, Richardson, TX 75080-3021, USA; E-mail eharuvy@utdallas.edu; corresponding author.

E. Elisabet Rutstrom, Robinson College of Business and Department of Economics, Andrew Young School of Policy Studies, Georgia State University, Atlanta GA 30302, USA; E-mail erutstrom@gsu.edu.

Chakravarty thanks the Indian Institute of Management for research support under Seed Money Grant 1105481. Harrison and Rutstrom thank the U.S. National Science Foundation for research support under grants NSF/HSD 0527675 and NSF/SES 0616746.

Received May 2009; accepted February 2010.
Table 1. Payoff Table for Risk-Aversion Experiments

Lottery A

Chance  Payoff   Chance   Payoff   Chance
0.1     400       0.9      500     0.1
0.2     400       0.8      500     0.2
0.3     400       0.7      500     0.3
0.4     400       0.6      500     0.4
0.5     400       0.5      500     0.5
0.6     400       0.4      500     0.6
0.7     400       0.3      500     0.7
0.8     400       0.2      500     0.8
0.9     400       0.1      500     0.9
1       400       0        500     1

                   Lottery B

Chance  Pay off   Chance  Pay off   EVA   EV(a)   Difference
0.1       960      0.9       25     490   118.5     372
0.2       960      0.8       25     480   212       268
0.3       960      0.7       25     470   305.5     164.5
0.4       960      0.6       25     460   399       61
0.5       960      0.5       25     450   492.5     -42.5
0.6       960      0.4       25     440   586       -146
0.7       960      0.3       25     430   679.5     -249.5
0.8       960      0.2       25     420   773       -353
0.9       960      0.1       25     410   866.5     -456.5
1         960      0         25     400   960       -560

The last three columns in this table, showing the expected values of
the lotteries, were not shown to subjects. All currency units are
Indian Rupees (Rs). At the time of the experiment 1 U.S. dollar =
44.8 Rs using the official exchange rate.

Table 2. Matching Scheme for First-Price Sealed-Bid Auction Experiment

Rounds        Subject 1             Subject 2

1-25     Self                  Agent for subject 1
26-50    Agent for subject 4   Self

Rounds        Subject 3             Subject 4

1-25     Self                  Agent for subject 3
26-50    Agent for subject 2   Self

Table 3. Statistical Model of Risk-Aversion Responses in Lottery
Choices

Variable               Description       Estimate     Standard Error

CRRA coefficient r
  Constant                                 0.689          0.243
  Agent              Responses as         -0.441          0.117
                       agent
  Order              Agent comes           0.053          0.118
                       first
  Male               Male                  0.074          0.162
  Over22             Age over 22          -0.001          0.036
  ParentsEd          Some                 -0.296          0.121
                       postgrad
                       education
                       of parents
  IncMed             Parents               0.353          0.162
                       earned
                       [greater than
                       or equal to]
                       2.5 and
                       [less than
                       or equal to]
                       7.5 lakhs
  IncHigh            Parents               0.254          0.205
                       earned
                       >7.5 lakhs
  Smoker             Current              -0.141          0.152
                       smoker
Fechner error
  Constant                                 0.701          0.075
  Agent              Effect on             0.621          0.276
                       error term
                       from being
                       agent

                                                      Lower 95%
                                                      Confidence
Variable               Description       p-value       Interval

CRRA coefficient r
  Constant                                0.005          0.213
  Agent              Responses as         0.000         -0.670
                       agent
  Order              Agent comes          0.655         -0.178
                       first
  Male               Male                 0.644         -0.242
  Over22             Age over 22          0.980         -0.071
  ParentsEd          Some                 0.140         -0.532
                       postgrad
                       education
                       of parents
  IncMed             Parents              0.030          0.035
                       earned
                       [greater than
                       or equal to]
                       2.5 and
                       [less than
                       or equal to]
                       7.5 lakhs
  IncHigh            Parents              0.216         -0.149
                       earned
                       >7.5 lakhs
  Smoker             Current              0.355         -0.439
                       smoker
Fechner error
  Constant                                0.000          0.554
  Agent              Effect on            0.024          0.080
                       error term
                       from being
                       agent

                                        Upper 95%
                                        Confidence
Variable               Description       Interval

CRRA coefficient r
  Constant                                 1.165
  Agent              Responses as         -0.212
                       agent
  Order              Agent comes           0.283
                       first
  Male               Male                  0.392
  Over22             Age over 22           0.069
  ParentsEd          Some                 -0.059
                       postgrad
                       education
                       of parents
  IncMed             Parents               0.671
                       earned
                       [greater than
                       or equal to]
                       2.5 and
                       [less than
                       or equal to]
                       7.5 lakhs
  IncHigh            Parents               0.656
                       earned
                       >7.5 lakhs
  Smoker             Current               0.158
                       smoker
Fechner error
  Constant                                 0.848
  Agent              Effect on             1.162
                       error term
                       from being
                       agent

Structural maximum-likelihood estimate of CRRA utility function. N =
740 binary choices by 37 subjects. Estimates are corrected for
clustering on the individual. Wald test for the null hypothesis that
all coefficients are zero has a [[chi square].sub.14] value of 30.8,
implying p-value = 0.0002. We include controls for several observable
demographic characteristics not shown in this table, including sex,
age, parent education, income level, and smoking status.

Table 4. Statistical Model of Implied Risk Aversion in Auction Bids

Variable   Description         Estimate     Standard Error

Constant                         0.062           0.300
Agent      Responses as         -0.132           0.040
             agent
Order      Agent comes          -0.109           0.131
             second
Male       Male                  0.003           0.142
Age        Age over 18          -0.023           0.019
             in years
Asian      Asian                -0.212           0.202
             ethnicity
Hispanic   Hispanic             -0.031           0.152
             ethnicity
Business   Business             -0.100           0.122
             major
Graduate   Graduate              0.487           0.178
             student
Aid        Receives              0.279           0.130
             student aid
Citizen    U.S. citizen          0.035           0.193
Married    Ever married          0.171           0.195
GPAhi      GPA [greater         -0.166           0.172
             than or equal
             to] 3.75
Work       Part-time or          0.018           0.123
             full-time
             work
Session    Experimental          0.041           0.121
             session

                                            Lower 95%      Upper 95%
                                            Confidence     Confidence
Variable   Description         p-value       Interval       Interval

Constant                        0.835         -0.525          0.650
Agent      Responses as         0.001         -0.212         -0.053
             agent
Order      Agent comes          0.402         -0.365          0.147
             second
Male       Male                 0.985         -0.276          0.281
Age        Age over 18          0.244         -0.062          0.016
             in years
Asian      Asian                0.293         -0.608          0.183
             ethnicity
Hispanic   Hispanic             0.838         -0.328          0.266
             ethnicity
Business   Business             0.412         -0.340          0.139
             major
Graduate   Graduate             0.006          0.137          0.838
             student
Aid        Receives             0.033          0.023          0.534
             student aid
Citizen    U.S. citizen         0.857         -0.344          0.414
Married    Ever married         0.380         -0.210          0.551
GPAhi      GPA [greater         0.332         -0.503          0.170
             than or equal
             to] 3.75
Work       Part-time or         0.886         -0.223          0.259
             full-time
             work
Session    Experimental         0.730         -0.195          0.278
             session

Maximum-likelihood "random effects" estimates of CRRA utility
function. N = 1593 bids by 32 subjects. Wald  test for the null
hypothesis that all coefficients are zero has a [[chi square].sub.14]
value of 31.9. implying p-value = 0.0041.
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Article Details
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Comment:Are you risk averse over other people's money?
Author:Chakravarty, Sujoy; Harrison, Glenn W.; Haruvy, Ernan E.; Rutstrom, E. Elisabet
Publication:Southern Economic Journal
Geographic Code:1USA
Date:Apr 1, 2011
Words:6814
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