## Abstract

Overconfidence is a well-established bias in which someone’s subjective confidence in their own judgment is systematically greater than their objective accuracy. There is abundant anecdotal evidence that overconfident people increase their exposure to risk. In this paper, we test whether overconfident backcountry skiers underestimate the probability of incurring a snow avalanche accident. An avalanche accident is a typical “black swan” event as defined by Taleb (The black swan: the impact of the highly improbable, Random House, New York, 2007) because it has a very low probability of occurring but with potentially dramatic consequences. To consider black swan events when studying overconfidence is particularly important, in light of previous findings on the role of overconfidence when feedbacks on tasks previously performed are inconclusive and infrequent. We run our test by measuring individual overconfidence using standard tools from the literature and then use a random effect logit model to measure its effect on the probability to take the ski route. We show that (1) overconfidence is widespread in our sample; (2) practitioners who are more prone to overestimate their knowledge are also more likely to take risks associated with a ski trip under the threat of avalanche danger, a result robust to a set of specification tests we perform. This suggests that overconfident people are more exposed to black swan events, by taking a risky decision that can bring about fatal consequences.

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## Notes

- 1.
The Weather&Avalanche reports are released on a regular basis by local agencies and describe the conditions of the weather and of the snowpack in a specific area. They also provide a forecast for the coming days.

- 2.
Authors calculations based on Istituto Nazionale di Statistica (ISTAT) statistics, which can be found at the following link: http://www.istat.it/it/archivio/137546.

- 3.
Terminology about heuristics and biases is generally borrowed from the psychology literature and can acquire different meanings. This is the case for the term overconfidence, which has frequently been stretched beyond its original definition. In some research fields, in fact, it has been used to refer to the “better-than-average” effect (Svenson 1981), unrealistic optimism (Weinstein 1980) and illusion of control (Langer and Roth 1975).

- 4.
Since the recruitment procedure fully preserves the anonymity of the respondents, there was no way of obtaining their written consent. The protocol has been approved by the

*Comitato Etico per la sperimentazione con l'essere umano*(Ethics Committee) of the University of Trento. - 5.
The European Avalanche Danger Scale ranges from 1 (low) to 5 (very high). The Blachère scale for the level of the route ranges from MSA to OSA.

- 6.
Some respondents contribute less than 9 answers since we excluded from the analysis answers referring to routes that the respondent reported to not know.

- 7.
Geographical area, gender, years of experience, age at which started practicing, alpine guide/alpine club instructor, already knows the tour, number of tours per season, level of experience of the usual partners, self-assessed level of ability, knowledge of WA report keywords.

- 8.
Results hold using alternative specifications of the regression, considering both a probit and a linear probability model (in both cases clustering the observations at the respondent level). Results are available upon request.

- 9.
Accessed in April 2018.

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## Acknowledgements

The authors thank *Accademia della Montagna del Trentino* for financial support; Ulrike Malmendier, Derek Stemple and William J. Weber for critical reading of the manuscript; Andrea Ichino for suggesting the robustness checks on our results; seminar participants at IZA, in particular Arnaud Chevalier, for their helpful comments. The usual disclaimer applies.

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## Appendix A

### Appendix A

Here, we consider the case in which the explanatory variable affected by measurement errors—the overconfidence score in our case—is included in the regression together with other explanatory variables. The regression coefficient \( \beta_{a} \) in Eq. (4) is the marginal effect of a unit variation of the true overconfidence level \( a_{i} \) on \( \alpha_{i} \), the largest level of risk the *i*th respondent is available to take (and, by that way, the probability of undertaking the route) holding the other explanatory variables constant. By holding the other explanatory variables constant, the variance of the overconfidence score relevant to Eq. (10) falls to \( \sigma_{a}^{2} \left( {1 - R_{a}^{2} } \right) \), where \( R_{a}^{2} \) is the proportion of the variance of the *true* overconfidence score explained by the regression on the other explanatory variables included in Eq. (4).

Clearly, \( R_{a}^{2} \) cannot be directly measured since the regression of the true overconfidence on the other explanatory variable is not feasible. The feasible regression is the one of \( z_{i.} \)—the observable overconfidence score—on the other explanatory variables. Let \( R_{z}^{2} \) be the fraction of the variance of \( z_{i.} \) explained by this regression. Then, the following identity holds:

from which we recover:

This way we recover the multiplicative attenuation bias as:

In the case of the regression of the observable overconfidence score \( z_{i.} \) on the other explanatory variables, results are those in Table 5. The \( R^{2} \) of this regression is as large as 0.086, definitely a very low value. But this is driven by the large variance of the measurement error on the overconfidence score. By taking it into account as in \( \left( {A2} \right) \), the \( R^{2} \) of the regression of the true overconfidence on the other explanatory variables turns out as large as:

Finally, the attenuation bias resulting from \( \left( {A3} \right) \) turns out as large as:

just marginally lower than the one previously found (0.51 in (16)). As a result, the bias-corrected estimate for the effect of one standard variation of the true overconfidence is 0.1516, just slightly higher than 0.1308, the estimate in Sect. 3.

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Bonini, N., Pighin, S., Rettore, E. *et al.* Overconfident people are more exposed to “black swan” events: a case study of avalanche risk.
*Empir Econ* **57, **1443–1467 (2019). https://doi.org/10.1007/s00181-018-1489-5

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### Keywords

- Cognitive bias
- Risky decision
- Backcountry skiing
- Measurement errors
- Logit model

### JEL Classification

- D12
- D83
- I12