Accident prevention and loss inflation in insurance: Theory and experiment

2023-08-16

2023-12-31

We test how the frequency of inflated reports in stage 2 depends on (i) whether the decision about precaution investment has been taken by the subjects or by a random computer draw, (ii) whether investment took place, and (iii) whether the instructions are framed neutrally or in an insurance context. The data that is included for the different Chi2-tests for the comparisons of inflated and honest reports with and without investment is shown in Table 1 as attached in the Analysis plan section. We test the robustness of the results with regression analysis. We also analyze if, and if so how, the investment frequency differs for neutral and insurance framing.

All tests shown in Table 1 are considered primary outcomes, but our main question of interest is the impact of investment on inflated reports, separated by own investment and investment by a computer draw.

Our analysis is based on a behavioral game theoretical model. This model, however, only allows structuring the trade-offs we are interested in, but shows that the impact of investment on inflated reports is generally ambiguous, both for own investment and investment by a computer draw. Our pilot suggests that those who invest are more likely to inflate their report (46% compared to 31%). The number of observations is calculated such that this result would be significant at the 5%-level if the distribution of the data is the same as in the pilot.

We analyze the impacts of the control variables (demographics and attitudes) on the decisions to invest and to inflate the loss, depending on the treatments. We hence perform regression analyses to all the Chi2-tests for primary outcomes. We thereby also check the robustness of the results for the Chi2-tests.

We inform participants that there are two parts and a survey, and that one of the parts will be chosen for determining the bonus (each with 50% probability). We also explain to them that we will provide the instructions for part 2 only after they have finished part 1.

In the first part, each subject is assigned to the active role of a policy holder (she). The insurer is a passive player, whose payoff depends on chance and the policy holder's behavior. The policy holder is asked for (a maximum of) two decisions: In the precaution stage 1, she decides on whether to invest part of her endowment to reduce the accident risk from 90% to 50%. Our design ensures that the policy holders' expected payoff is higher without investment, whereas the joint payoff of the policy holder and the insurer is higher with investment. It hence depends on the policy holder's other-regarding preferences if she invests or not. In case of no loss, the experiment ends. With loss, we proceed to the reporting stage 2. Policy holders can report their loss to the insurer honestly, or build it up in order to receive a higher compensation. They know that there is neither a risk of detection nor of punishment.

In part 2, each subject plays the role of the insurance company (passive player), and hence there is no decision to make. Subjects are randomly paired up and a random draw then decides which player’s decision as active player is relevant for both players’ payoffs. If subject A is chosen for part 1, then subject A gets the payoff depending on their decision in part 1, and subject B gets the payoff for the passive player, also depending on the decisions of player A in part 1 (and vice versa if subject B’s active role in part 1 is chosen for the payoffs).

We apply a 2x2 design with two variables: The first variable is whether the policy holder or a random computer draw decides on precaution in stage 1. We add the treatments with a random computer draw to remove self-selection into the treatments with and without moral accounting. Comparing the frequencies of inflated reports in stage 2 between the cases with and without investment hence allows us to isolate the entitlement effect of investment (though only for the case with random draws). The second variable in our 2x2 design is whether the instructions are framed in an insurance context or neutrally. In the neutral framing, we mention only amounts and probabilities, and avoid any reference to insurance. This allows us to analyze if the reference to insurance influences decisions, in particular by reducing moral concerns.

In part 1, we assign subjects to one of the four treatments (according to their time of arrival). If the number of 240 observations required for a treatment is reached, then the randomization refers only to the remaining treatments. In part 2, each subject plays the role of the passive player, and hence no decision is to be made. To determine the bonus, subjects are randomly paired up, and a random computer draw decides which of the two decisions in the role of active player is chosen to determine the bonus of both players.

Individual level randomization.

No

No clustering.

We will have four treatments: (1) neutral treatment with investment decision, (2) neutral treatment with computer choice, (3) insurance treatment with investment decision and (4) insurance treatment with computer choice. All treatments consist of an active player (the decision maker) and a passive player whose payoff depends solely on the active player’s decisions and computer choice(s). In the neutral treatment N, instructions are neutrally framed, i.e. there is no reference to insurance. All decisions and random moves are only described with respect to probabilities and payoffs. Conversely, in the insurance treatment I, the game is framed as an insurance contract, that is, the active player (the decision maker) is referred to as policy holder and the passive player as insurer. Our power analysis shows that, for the comparison of the report of subjects who invested or didn’t invest, we need 145 subjects each who can inflate their reports with and without investment, respectively. Given that 60.8% of our subjects in the pilot invested, and that the accident probability after investment is 50%, we need about 480 subjects for getting 145 subjects who can inflate their reports after investment. We divide these 480 subjects equally between neutral and insurance framing, which yields 240 subjects for each treatment with own investment. As we want to collect the same number of observations for the treatments where a random choice decides upon investment, we will overall collect 960 observations.

As above-mentioned, we will have 4 treatments, 240 subjects per treatment, so we will collect a total of 960 observations.