Skewed background risks and higher-order risk preferences: prudent versus temperate behavior

ABSTRACT

In recent economic experiments, lotteries with left-skewed background risks elicit more prudent choices than lotteries with right-skewed background risks. In this letter, we use an expected utility framework to show that a skewed zero-mean background risk may induce not only prudent but also temperate behaviour. We suggest that the experimental findings could also be due to temperance, rather than merely to prudence.

KEYWORDS:

• Decision making under risk
• background risk
• prudence
• temperance
• skewness seeking
• kurtosis aversion

JEL CLASSIFICATION:

• D8

Acknowledgements

This work benefited from comments by Stefan Felder and Miriam Krieger.

Disclosure statement

There are no financial or personal conflicts of interest.

Notes

¹ Kimball (1990) coined the term prudence for third-order risk aversion and Kimball (1992) introduced the term temperance for fourth-order risk aversion.

² Left-skewness (right-skewness) of a zero-mean risk implies that the bad outcome has a lower (higher) probability but a larger (smaller) magnitude than the good outcome.

³ Note that while the second derivative is negative, it is increasing in w since the third derivative is positive.

⁴ To avoid redundancy we will only discuss the impact of prudence and temperance given a skewed background risk but not of imprudence or intemperance.

⁵ Coebergh et al. (1999) studied 34,000 Dutch cancer patients between 1993 and 1996 and found co-morbid conditions to increase in age from a presence in 12% of patients under 45 to 63% in patients over 75. While this result underlines the importance of considering comorbidity (risk) per se, it also shows that comorbidity risk can be distributed in several ways (here: left-skewed for younger and right-skewed for older cohorts).