Estimating cumulative prospect theory parameters from an international survey

These survey results have also been used to shed light on the selection between culture and general risk attitudes in gains and losses (Rieger et al. 2015) and on loss aversion (Wang et al. 2016). An earlier version of the data has also been used to study the prediction quality of various CPT variants (Rieger and Bui 2011).

For more detailed description of the survey, we refer to Rieger et al. (2015).

We tried different specifications of \(w_\pm \) and v and also alternative PT models, but we do not focus on this in the current article, see Rieger and Bui (2011) for details.

To guarantee a monotone probability weighting function, the value of \(\gamma \) has to be larger than 0.279, see Rieger and Wang (2006), Ingersoll (2008) and Giorgi and Legg (2012).

There is vast empirical evidence for this behavior in gains and at least for small losses Bosch-Doménech and Silvestre (2006).

The lowest measured value was 0.30 which is still in the parameter range where the probability weighting function is monotone (Ingersoll 2008; Giorgi and Legg 2012).

The first and fourth lotteries (the lotteries with two positive outcomes and large stakes, respectively) were omitted, since it has been found that such lotteries are difficult to estimate in the standard form of CPT (Rieger and Bui 2011). Moreover, we found that the first lottery question suffered from a relatively large amount of answers that violated first-order stochastic dominance (20%), pointing to mistakes when filling in the questionnaire. In contrast to that, answers to the other lotteries violated first-order stochastic dominance on average only in less than 2% of the cases.

In the last subsection, we have noticed the lack of robustness for these two countries, Portugal and Romania.

A model-independent definition of loss aversion has already been suggested by Schmidt and Zank (2005) and an in-depth analysis of loss aversion in CPT has been given by Zank (2010).

In this study, the subjects were asked two questions related to risk attitudes. The first one was “Suppose you are the only income earner in the family, and you have a good job guaranteed to give you and your current family income every year for life. Now, you are given an opportunity to take a new and equally good job. The new job has a 50/50 chance to increase by 50% your standard of living each year during your lifetime. However, the new job also has a 50/50 chance to reduce by X percent your standard of living each year during your lifetime. Circle the maximum X percent reduction in standard of living that you are willing to accept.” The second question was similarly stated, but it was in terms of a portfolio decision rather than an income decision.

We notice that \(\alpha \) and \(\beta \) are positively correlated (\(r=0.64\), \(p<0.01\)), implying that stronger risk aversion in gains is correlated with stronger risk seeking in losses. This can probably be explained by between-person differences in sensitivity to the relative wealth change: when a person is more sensitive to wealth changes with respect to a reference point, then his value function tends to be more concave in gains and more convex in losses, thus leading to lower \(\alpha \) and \(\beta \) values.

This “linear” loss aversion \(\theta \) has been introduced by Tversky and Kahneman (1992) and has been shown for the INTRA data to depend on cultural differences between countries (Wang et al. 2016).

We used the classical four dimensions: PDI (power distance index), IDV (individualism), MAS (masculinity), and UAI (uncertainty avoidance index), but omitted the newer and less common dimensions.

Without normalization, the size of the standard deviation depends on the size of the lottery values.

We excluded the five countries with non-robust CPT measurements as defined in Table 5 from this analysis.

Age effects cannot be studied from our data, since our sample was inherently biased towards a young age group.