Abstract
Gender differences in risk attitudes have recently been shown to be context-dependent rather than ubiquitous. We manipulate three widely used risk elicitation tasks to test whether the presence of a safe option among the set of alternatives can explain the heterogeneity of the findings. We find that the availability of a safe option induces significant effects in two out of three tasks. Despite the well-known instability of elicited risk preferences, we show with a structural model that the effect on risk attitudes is rather stable across tasks, but not sufficiently strong to reach traditional significance levels.
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Notes
Studies involving apes are used to address the origins of human behavior. Several contributions show that risk attitudes are indeed shaped by evolution, although without providing evidence along a gender perspective. These studies find for instance that bonobos are more risk averse than chimpanzees (Rosati & Hare, 2013; Heilbronner et al., 2008). The two species derive from a common ancestor but evolved differently, with chimpanzees developing a riskier foraging strategy. Differences in risk taking between the two species are nowadays observed within captive populations, i.e. among subjects that are fed and do not need to undertake any foraging strategy.
The careful reader may have noticed that the Allais paradox is per se a test of the role of a riskless alternative. The experimental literature using the Allais paradox, however, is not informative towards our research goal because usually results are not displayed by gender. The few exceptions are Petit et al. (2011) who find that women are more prone to the paradox and choose more often the safe alternative (N = 938, of which 611 women), and Da Silva et al. (2013) who do find on the contrary that men are more prone to the paradox (N = 120).
Building an ad-hoc task would possibly allow us to test the effect of a safe option in a cleaner manner, but the heterogeneity of results in this literature would prevent any generalization. Therefore, we believe that the first test needs to be done with the same tasks that have been used to build the current consensus.
Crosetto and Filippin (2013) show that a roller-coaster behavior is observed even when repeating the same task several times. Menkhoff and Sakha (2017) report that if the subjects fail to properly reduce the compound lottery generated by within-subjects designs, instability and inconsistencies are to be expected. Pedroni et al. (2017) show large within-subjects inconsistencies on a large sample across seven risk elicitation tasks.
The data of the baseline BRET are the same as in Crosetto and Filippin (2013). Part of the baseline HL and EGsafe data are the same as in Crosetto and Filippin (2016). However, given the focus on gender of this study, we needed to increase the overall sample size to support a gender comparisons. We hence planned three additional HL and EGsafe sessions. The treatment conditions are entirely original data.
The custom experimental software for each task, written in Python, is available upon request. The full dataset and the scripts used to generate all results of this paper are available online at https://github.com/paolocrosetto/Safe_options_risk_attitudes_gender_data_and_analysis.
A trial run of the task was provided for the BRET and BRETsafe tasks. The presence of such a trial does not affect the results, see Crosetto and Filippin (2013).
Other methods used to compute an amount row by row as similar as possible to the corresponding lottery in Treatment 1 would deliver virtually identical results. For instance, using the expected value of the lottery would deliver slightly different amounts in only two out of ten rows. In contrast, using the same amount in all the ten lotteries would change the underlying incentives across conditions.
The fraction of inconsistent subjects in our data (\(15.6\%\)) is in line with the literature, as reported by Filippin and Crosetto (2016).
Cohen’s d is a measure of the size of an effect that is independent of the sample size. It is computed as:
$$\begin{aligned} d = \dfrac{\bar{X}_f-\bar{X}_m}{\sigma }, \end{aligned}$$where \(\bar{X}_m\) and \(\bar{X}_f\) are the average group choices and \(\sigma\) is the pooled standard deviation. Cohen (1988) indicates thresholds for interpreting his d: referring to aggregate differences, 0.2 should be considered a small effect, 0.5 a medium effect, and from 0.8 on a large effect.
Assuming a CRRA utility function only the subjects characterized by \(\rho \ge .658\) should opt for the safe option.
Results are robust to the inclusion of these two subjects, that we wish nonetheless to exclude since they submitted clearly dominated choices.
The intuition is pretty similar to the Give vs. Take manipulation in Dictator Games. Bardsley (2008) and List (2007) show that the possibility of taking affects not only those whose choice was truncated by the lower bound of zero in the Give framework. In contrast, the whole distribution, including the counterparts of those who give a positive amount, shifts towards more selfish decisions once taking is a practicable alternative.
The EG task has later been proposed in a version including a \(6^{th}\) option, with the same expected value as the \(5^{th}\) but with a larger variance, designed to identify risk seeking subjects. The two versions do not significantly differ for the purpose of our study.
The reason why gender differences in the certainty effect are significant here but not in the BRETsafe may be due to the different salience of the safe option. In the EGsafe task the safe option is one out of only five alternatives, and moving from lottery 1 to lottery 2 makes a clear difference in terms of risk incurred. In contrast, in the BRET the salience of the riskless alternative is likely diluted by the fact that the risk of the bad outcome increases at a very low rate (\(1.33\%\) per additional box.)
Note that here statistical significance cannot be computed as we have just one observation per condition.
Using cumulative weights would instead be an uninformative exercise. The distortion of probabilities would imply a sort of optimism or pessimism (i.e. the better outcome perceived not as likely as the worse one), which cannot be disentangled from risk aversion when dealing with binary lotteries (l’Haridon and Vieider, 2016).
Apesteguia and Ballester (2018) criticize the widely used random utility model (see for instance Harrison, 2008) on the ground that it shows non-monotonicity problems of the predicted choice in the degree of risk aversion of a subject. The debate on the point is ongoing, see for instance Conte and Hey (2018). We choose a random parameter model for our exercise in light of the considerations of Apesteguia and Ballester (2018), but a random utility Fecher-error model yields the same qualitative results.
One could argue that including the SOEP question in the model is not a good idea because it conceptually coincides with what we aim to estimate, i.e. risk aversion. While this variable has been shown to correlate with risk preferences elicited in an incentivized manner, the variance explained is indeed very low (Dohmen et al., 2011). Hence, there is no risk of over-controlling. The effect of including the SEOP control is that of measuring the effect of the safe-option manipulation net of the subjects’ self-representation of their risk tolerance.
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Acknowledgements
We gratefully acknowledge the financial support of the Max Planck Institute of Economics, of the Grenoble Applied Economics laboratory, and of the Small Grants program of the Einaudi Institute for Economics and Finance (EIEF). We thank Eicke Hauck, Ivan Soraperra, Iolanda Viceconte, and Claudia Zellmann for their help in running the experiments. We also thank Maria De Paola, Frank Heinemann, Doron Sonsino, and participants to seminars at the University of Göttingen, Université Paris 1 Sorbonne and University of Economics in Prague, as well as to participants to the 2013 CESifo workshop in Venice, the \(8^{th}\) Nordic Conference in Behavioral and Experimental Economics in Stockholm, the 2013 EUI Alumni Conference in Florence, and the 2014 IMEBESS conference in Oxford for useful suggestions. All remaining errors are ours.
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Appendix. Experimental instructions
Appendix. Experimental instructions
1.1 HL and HLsafe
You will be asked to make 10 choices. Each decision is a paired choice between “Option A” and “Option B”. For each decision row you will have to choose between Option A and Option B. You may choose A for some decision rows and B for other rows, and you may change your decisions and make them in any order.
Even though you will make ten decisions, only one of these will end up affecting your earnings. You will not know in advance which decision will be used. Each decision has an equal chance of being relevant for your payoffs.
Now, please look at Decision 1 at the top. Option A pays {HL: 4 euro if the throw of the ten sided die is 1, and it pays 3.2 euro if the throw is 2-10; HLsafe: 3.3 euro in any case}. Option B yields 7.7 euro if the throw of the die is 1, and it pays 0.2 euro if the throw is 2-10.
The other Decisions are similar, except that as you move down the table, the chances of the higher payoff for each option increase. In fact, for Decision 10 in the bottom row, the die will not be needed since each option pays the highest payoff for sure, so your choice here is between 4 or 7.7 euro.
To determine payoffs we will use a ten-sided die, whose faces are numbered from 1 to 10. After you have made all of your choices, we will throw this die twice, once to select one of the ten decisions to be used, and a second time to determine what your payoff is for the option you chose, A or B, for the particular decision selected.
1.2 BRET and BRETsafe
On a sheet of paper on your desk you see a square composed of 100 numbered boxes. Behind one of these boxes hides a mine; all the other 99 boxes are free from mines. You do not know where this mine lies. You only know that the mine can be in any place between {BRET: 1; BRETsafe: 26} and 100 with equal probability.
You earn 10 eurocents for every box that is collected. After you ‘Start’ in the corresponding square on your screen, every second a box is collected, starting from the top-left corner. Once collected, the box disappears from the screen and your earnings are updated accordingly. At any moment you can see the amount earned up to that point.
Such earnings are only potential, however, because behind one of these boxes hides the time bomb that destroys your earnings in case it is collected. You do not know where this time bomb lies. You only know that the time bomb {BRET: can be in any place between 1 and 100 with equal probability; BRETsafe: is not in the boxes from number 1 to 25, while it can be in any place between 26 and 100 with equal probability}. Moreover, even if you collect the time bomb, you will not know it until the end of the experiment.
Your task is to choose when to stop the collecting process. You do so by hitting ’Stop’ at any time. At the end of the experiment we will randomly determine the number of the box containing the time bomb by means of a bag containing {BRET: 100 tokens numbered from 1 to 100 ; BRETsafe: 75 tokens numbered from 26 to 100 }.
If you happen to have harvested the box where the mine is located - i.e. if your chosen number is greater than or equal to the drawn number - you will earn zero. If the mine is located in a box that you did not harvest - i.e. if your chosen number is smaller than the drawn number - you will earn in euro an amount equivalent to the number you have chosen divided by ten.
We will start with a practice round. After that, the paying experiment starts.
1.3 EG and EGnosafe
You will be asked to select from among five different gambles the one gamble you would like to play. The five different gambles will appear on your screen. You must select one and only one of these gambles. Each gamble has two possible outcomes (Event A or Event B), each happening with \(50\%\) probability.
Your earnings will be determined by: 1) which of the five gambles you select; and 2) which of the two possible events occur.
At the end of the experiment, we will roll a six-sided die to determine which event will occur. If a 1, 2, or 3 is rolled, then Event A will occur. If 4, 5, or 6 are rolled, then Event B will occur.
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Crosetto, P., Filippin, A. Safe options and gender differences in risk attitudes. J Risk Uncertain 66, 19–46 (2023). https://doi.org/10.1007/s11166-022-09400-0
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DOI: https://doi.org/10.1007/s11166-022-09400-0