Other-Regarding Higher Order Risk Preferences

Subjects will make choices between pairs of lotteries: 9 choices for risk aversion, 9 choices for prudence and 9 choices for temperance. Lottery pairs are scaled down versions of Deck et al. (2023). Subjects first make 3x9 choices for themselves and then make 3x9 choices for others with the understanding that one out of 54 choices will paid out at the end of the experiment. The order of the tasks (self->other vs. other->self will be randomly assigned).

We vary between subjects social distance for lottery choice decision for others. In one treatment the decision is consequential for another person in the room, unknown to the decision maker, while in another treatment the decision is consequential for a close friend.

2024-09-15

2025-03-31

Switch choice on each task: risk aversion, prudence, temperance
Intensity measures of risk aversion, prudence, temperance

Intensity measures will be constructed similar to Deck et al. (2023)

Subjects will make choices between pairs of lotteries: 9 choices for risk aversion, 9 choices for prudence and 9 choices for temperance. Lottery pairs are scaled down versions of Deck et al. (2023). Subjects first make 3x9 choices for themselves and then make 3x9 choices for others with the understanding that one out of 54 choices will paid out at the end of the experiment. The order of the tasks (self->other vs. other->self will be randomly assigned).

We vary between subjects social distance for lottery choice decision for others. In one treatment the decision is consequential for another person in the room, unknown to the decision maker, while in another treatment the decision is consequential for a close friend.

Not available

All randomizations are done by the computer.

individual

No

0

54 observations per subject (3 tasks x 9 choices x 2 decision modes) At least 200 subjects (200 x 54 = 10,800 observations)

At least 100 subjects per treatment arm.

The minimum detectable difference, d, that can be detected for a given sample size is given by Diggle et al. (2002), pp. 30; Liu and Wu (2005); Kupper and Hafner (1989): d = sigma * (z_{1-alpha/2}+z_{1-beta}) * sqrt( 2 * (1+(M - 1) * rho) / (M * n)) where d = (mu0-mu1), mu0 and mu1 are the means for each treatment group, sigma is their common standard deviation, alpha=0.05 (Type I error), beta=0.20 (Type II error), therefore z_{1-alpha/2} = 1.96, z_{1-beta} = 0.84, M the number of repeated measurements (M = 2 in our case, since subjects undertake each task twice, once for self and once for others), rho is the interclass correlation coefficient between measurements, and n is the per group sample size. Assuming values for rho = {0, 0.3, 0.6, 0.9}, a target sample size of N = 100 per group can detect differences between the treatment groups in terms of switching point as follows: For risk aversion: 0.34-0.57 For prudence: 0.43-0.73 For temperance: 0.48-0.8 Diggle, P. J., P. Heagerty, K.-Y. Liang, and S. L. Zeger (2002). Analysis of Longitudinal Data (2nd ed.). New York, USA: Oxford University Press Inc Liu, H. and T. Wu (2005). Sample size calculation and power analysis of time-averaged difference. Journal of Modern Applied Statistical Methods 4 (2), 434–445. Kupper, L. L. and K. B. Hafner (1989). How appropriate are popular sample size formulas? The American Statistician 43 (2), 101–105.