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Theory and Decision

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12-07-2017

Lottery- and survey-based risk attitudes linked through a multichoice elicitation task

Authors: Giuseppe Attanasi, Nikolaos Georgantzís, Valentina Rotondi, Daria Vigani

Published in: Theory and Decision | Issue 3/2018

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Abstract

We analyze the results from three different risk attitude elicitation methods. First, the broadly used test by Holt and Laury (2002), HL, second, the lottery-panel task by Sabater-Grande and Georgantzis (2002), SG, and third, responses to a survey question on self-assessment of general attitude towards risk (Dohmen et al. 2011). The first and the second task are implemented with real monetary incentives, while the third concerns all domains in life in general. Like in previous studies, the correlation of decisions across tasks is low and usually statistically non-significant. However, when we consider only subjects whose behavior across the panels of the SG task is compatible with constant relative risk aversion (CRRA), the correlation between HL and self-assessed risk attitude becomes significant. Furthermore, the correlation between HL and SG also increases for CRRA-compatible subjects, although it remains statistically non-significant.

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Weber et al. (2002) developed a psychometric scale that assesses risk taking in five different domains: financial decisions (separately for investing vs. gambling) and health/safety, recreational, ethical, and social decisions. Nevertheless, their elicitation method is unidimensional and is the same across domains, except that the framing of the question used to elicit self-assessed risk attitude is different for each specific domain.

For a recent example of five elicitation methods and reference to such results, see Crosetto and Filippin (2016). As in previous experimental studies on the topic, they also find that the estimated risk aversion parameters vary greatly across tasks.

For example, regression to the mean has been found to affect repeated choices in the same task by García-Gallego et al. (2011). Moreover, Lévy-Garboua et al. (2012) found a significantly higher elicited risk aversion in sequential than in simultaneous treatment, in decreasing and random than in increasing treatment, in high than in low-payoff condition. Their findings suggest that subjects use available information that has no value for normative theories. Cox et al. (2014) have rationalized some of these findings by showing the role of the payment mechanism in these distortions. Indeed, they find that random-lottery incentive mechanisms—as those usually employed in risk-elicitation tasks—may decrease the proportion of risky choices in the population, compared to a one-task design. This could explain why significantly more risk aversion emerges under multiple-task than under one-task elicitation methods.

See Butler and Loomes (2007) and Cubitt et al. (2015).

See Harrison et al. (2005) and Holt and Laury (2005): the former demonstrated and the latter confirmed the possibility of order effects in HL’s original design. Indeed, the order effect (participating in a low-payment choice before making a high-payment choice) magnifies the scale effect (scaling up real payments by 10 or 20 times).

A number of studies have shown that this assumption is questionable [see Wakker (2010) for a review], although other models (e.g., prospect theory) do not seem to have significantly higher explanatory power than the expected utility (Harrison and Rutström 2009).

Notice that this problem would emerge also in the absence of enforced monotonicity. In fact, in Holt and Laury (2002) a subject who switches from one lottery to the other more than once, as the probability of the best outcome increases, is still considered as if he/she has made just one switch. This is done by assigning as switch line from one lottery to the other the one corresponding to the number of safe choices the subject has made.

See Sect. 5.3 of Attanasi et al. (2014) for a discussion on the participants’ higher trust in physical rather than computerized instruments when facing random processes in laboratory experiments. Indeed, when implementing random processes in our experiment, we mainly relied on physical rather than computerized instruments. However, the subject’s relevant choice for the final payment was selected among all those made in the task (i.e., 1 over the 19 lines of the battery of lotteries) through a computerized random draw. This was made to limit the length of the experiment and to allow sufficient heterogeneity in subjects’ final payment, especially to avoid “collective winner effects” due to emotions documented in Zeelenberg and Pieters (2004). The same motivations hold for the computerized random draw of the relevant panel of lotteries in task 2 (SG).

In Sabater-Grande and Georgantzis (2002), the payoffs are expressed in pesetas, since the experimental sessions were run in Spain before the introduction of the euro as official currency in the European Union. In the cited follow-up studies, still run in Spain, the payoffs are equivalently expressed in euros.

In contrast to the claims of Diecidue and Ven (2008), while prior works have shown that typical reference points are individuals’ own current wealth or endowment (Kahneman and Tversky 1979), recent research has included aspiration levels in the literature on risky choice as reference points (Brown et al. 2012; Hoffmann et al. 2013).

Diecidue et al. (2015) report results from two experiments without finding support for an aspiration level at zero outcome, neither for simple lotteries nor for complex lotteries.

A numerical example is available upon request.

Principal component analysis uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. This transformation is defined in such a way that the first principal component has the largest possible variance (i.e., it accounts for as much of the variability in the data as possible) and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components. The resulting vectors are an uncorrelated orthogonal basis set.

To account for the ordered nature of our dependent variable, we have also estimated an ordered logit model: the results are qualitatively unchanged and available upon request.

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Title: Lottery- and survey-based risk attitudes linked through a multichoice elicitation task
Authors: Giuseppe Attanasi
Nikolaos Georgantzís
Valentina Rotondi
Daria Vigani
Publication date: 12-07-2017
Publisher: Springer US
Published in: Theory and Decision / Issue 3/2018
Print ISSN: 0040-5833
Electronic ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-017-9613-0

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