Searching for optimal insurance

I design an experiment to elicit individuals' preferred indemnity functions under different risk conditions. In particular, I vary insurance decisions along three dimensions: initial wealth, insurance loading, and loss distribution. Subjects can choose any coverage level for a given loss, provided that the indemnity principle and limited liability constraints are satisfied. The premium function is linear in the expected indemnity. Under expected utility (EU) or non-EU preferences that satisfy second-order stochastic dominance, the theoretical predictions are clear: full insurance is optimal when insurance loading is zero, whereas straight deductible contracts are optimal when insurance loading is positive. My experiment therefore put these predictions directly to the test.

2026-06-20

2026-06-28

Coverage choices

In the experiment, payoffs are denominated in points rather than dollars, with 20 points equivalent to $1. Upon entering the experiment, participants are presented with the experimental instructions and are then required to complete a set of comprehension questions. Only after answering these questions correctly do participants proceed to the main task, which consists of eight independent decision scenarios. These scenarios are based on a within-subject 2 × 2 × 2 factorial design. Specifically, we vary the initial wealth, the loss distribution, and the insurance loading across scenarios. The order of these scenarios, including the attention-check scenario, are randomized at the subject level. Only one scenario is randomly selected to determine their payment at the end of the experiment. In each decision scenario, subjects are endowed with an initial wealth that is exposed to a risk of loss. For any potential loss before an event occurs, subjects can choose how much to insure, that is, the level of coverage. If an event occurs, subjects receive the chosen coverage as indemnity.

After completing the decision tasks, subjects are invited to complete a survey that collects demographic information, including age, gender, education, and income. Subjects who successfully complete the experiment receive a fixed payment of $3 in addition to their experimental earnings. The experiment is expected to take 15 minutes. The average total earning is about $7.5.

Randomization done by a computer.

We adopt a within-subject 2 × 2 × 2 factorial design. Specifically, we vary the initial wealth, the loss distribution, and the insurance loading across eight scenarios. The order of these scenarios, including the attention-check scenario, are randomized at the subject level.

No

150 participants

8400 observations

150 participants for a within subject design.

We perform an ex ante power analysis for an OLS regression with five covariates (age, gender, education, income, and willingness to take risks (WTR)). Assuming a significance level of alpha = 0.05 and a target power of 0.80, we considered the detection of small-to-moderate effect sizes in the range f-square [0.05, 0.10] for the joint explanatory power of the regressors. Using standard power calculations based on the noncentral F-distribution in multiple regression, the required sample size depends on the number of predictors through the corresponding degrees of freedom and noncentrality parameter. For five covariates, these calculations imply a required sample size of approximately 130-180 observations. Accordingly, we recruit 150 participants.