Abstract
This paper experimentally examines the impact of contract design on insurance fraud. We test how fraud behavior varies for insurance contracts with full coverage, a straight deductible or claim-dependent premiums (bonus-malus contracts), in a setup where rational and selfish individuals have an incentive to always claim the maximum possible indemnity. We find a substantial impact of contractual arrangements: Deductible contracts lead to a greater extent to claim build-up than full coverage contracts. In contrast, bonus-malus contracts that entail the same net gains from fraud as deductible contracts do not increase claim build-up. Thus, our results indicate that bonus-malus contracts may be superior to deductible contracts for behavioral reasons.
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Notes
Dionne et al. (2009), for instance, have analyzed optimal auditing procedures for an auto insurer. Given 500,000 claims (average claim 1284 €) and an optimal audit probability of 9.23%, together with average costs of an audit of 280 €, the overall costs appear in the order of 12.9 million €. In addition, they estimate that a third of all fraudulent claims remain undetected, resulting in total costs of 17 million €. So even if companies adopt optimal fraud fighting strategies, high costs of fraud will remain.
Gabaldón et al. (2014) conducted another experiment on insurance fraud with a very different setup and scope.
See Sect. 4 for a robustness check with group sizes of 24 participants.
The mutual form is common for insurance companies as for instance in life insurance. Here policyholders are at the same time the residual claimant of the insurance company. For example, in 1993 mutuals generated as much US-premium income as stock insurance companies (Mayers and Smith 2000). In the US property-liability industry the number of mutual and stock insurers were almost equal in the period of 1981–1990. However, stock firms on average are larger than mutuals in terms of costs, input and output quantities, and invested assets (Cummins et al. 1999).
Abbink and Hennig-Schmidt (2006) find that a context-free experiment framing does not have a significant impact on a bribery game. In contrast, Schoemaker and Kunreuther (1979) find a significant impact of insurance framing on participants’ behavior in their survey. We also conducted a context-free treatment (n = 72 as in the Base Treatment) and did not find any structural differences with respect to the insurance-specific wording in our Base Treatment. Average fraud probabilities for claim build-up were 39% with insurance specific framing and 33% with context-free framing. For fictitious claims, the corresponding fraud probabilities were 51 and 46%, respectively. Taking individual means over all periods as observations, the differences are not statistically significant (two-sided Mann–Whitney U tests, p = 0.270 for claim build-up and p = 0.453 for fictitious claims). These results are also confirmed using a random effects logit regression (results available from the authors on request).
This approach goes back to Selten (1967). Participants must state contingent responses for each information set, but only one response will result in an effective action and determine the responder’s and other players’ payoffs. For a survey of the differences between the strategy method and the direct response method see Brandts and Charness (2000). Of the 29 existing studies, 16 find no difference, 4 do find differences, and 9 comparisons find mixed evidence. None of these studies finds that a treatment effect that is present with the strategy method is not observed with the direct-response method.
For large groups with 24 participants, as discussed in Sect. 4, the expense ratio is 16.7%. Transaction costs in real-world insurance markets are usually measured by the expense ratio (total expenses divided by total premiums written). From 1990 to 2000 the mean expense ratio in the U.S. property-liability insurance was 0.515 (Leverty and Grace 2010). As reported by Leng and Meier (2006), in 1995 average expense ratios in the Swiss, German and Japanese property-liability market were 0.34, 0.27 and 0.46, respectively.
Recall that the net gain from claim build-up in the Base and Deduct Treatment is given by 5·0.65 = 3.25.
If psychological costs depend on the amount defrauded, this reasoning may no longer hold.
The regressions are available from the authors upon request.
Of course, this simultaneous change of two experimental components is not ideal, but it was due to financial limitations. Given that the aim of the robustness check was to strongly increase the attractiveness of committing fraud and not to disentangle the influence of group size and transaction costs, respectively, we believe this twofold change can offer valuable insights.
Of all participants, 8% very strongly prefer the bonus-malus contract (highest preference compared to deductible as lowest preference), 26% strongly prefer bonus-malus (another alternative is rated lower than bonus-malus but higher than deductible), 45% just prefer bonus-malus, 17% just prefer deductible and 4% strongly prefer the deductible.
For the SVO categorization: Pearson’s Chi square test (\(\chi^{2} = 2.590\), \(p = 0.274\)). For the fairness of the given contract: Mann–Whitney U test (p = 0.782). For the no/low/high indemnity expectations: Mann–Whitney U tests (p = 0.238; p = 0.147; p = 0.682, respectively). All tests are two-sided.
The regressions are available from the authors upon request.
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Acknowledgements
Financial support from the German Insurance Science Foundation (Deutscher Verein für Versicherungswissenschaft e.V.) is gratefully acknowledged, von Bieberstein also thanks the Volkswagen Foundation for the support (Grant No. 85 487). We thank Sebastian Ebert, Ole von Häfen, Achim Wambach, and two anonymous referees for their very valuable comments and especially the MELESSA team at the Ludwig-Maximilians-Universität Munich for their support with the experiments.
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Appendix
Appendix
1.1 General instructions (all instructions translated from German)
Welcome to the experiment. Please read through the instructions carefully. They are identical for all participants. In this experiment, you and the other participants will have to make decisions. At the end of the experiment, you will receive a payment depending on your own decisions and the decisions of the other participants. In addition, you will receive a fixed show-up fee of 4 Euro.
During the entire experiment, you may not talk to other participants, use your mobile phone, or start any programs on the computer. Should you break this rule, we will have to exclude you from the experiment and from receiving any payment. Whenever you have a question, please raise your hand. The experimenter will come to your seat to answer your question. If the question is relevant to all participants, the experimenter will repeat the question and answer it aloud.
During the experiment, we calculate payments in points instead of Euros. At the end of the experiment, the total number of points will be converted into Euros at the rate of 10 points = 1 Euro. Before we start the experiment, you will have to answer six written questions regarding the experiment to make sure that you have correctly understood the instructions.
The experiment is confidential; no other participant will receive any information regarding your answers, decisions, or final payment.
The experiment consists of two parts: In the first part, you will have to make decisions that will determine your success in the experiment and, consequently, your final payment. In the second part, you will have to answer several questions that have no influence on your success in the experiment. Your answers to these questions will be treated as strictly confidential.
1.2 Specific instructions [D: Deduct Treatment; B: Bonus-Malus Treatment]
The experiment consists of five periods. Before period 1, you will be randomly and anonymously allocated into fixed groups of four. The group composition will remain unchanged during the entire experiment.
At the beginning of each period, each participant will receive an endowment of 25 [Deduct: 27] points, thus totaling 125 [D: 135] points over the five periods. In each period, each participant runs the risk of losing a part of his or her endowment. The following losses can occur with the following probabilities in each period:
Loss | Probability (%) |
|---|---|
0 points (no loss) | 70 |
10 [D: 15] points (low loss) | 20 |
15 [D: 20] points (high loss) | 10 |
In each period, given the above probabilities, a computer randomly determines for each participant independently if any of the above losses occur. The amounts of the potential losses and the probabilities remain constant over all periods. Your decisions or losses in earlier periods, therefore, have no influence on the probability or the amount of future losses.
In order to compensate for potential losses, the four group members together build a mutual insurance group. This setup ensures that each group member automatically pays an insurance premium of 5 points [BoMa: no points mentioned here] on a joint group account (“insurance account”) at the beginning of each period.
In order to receive payment from the insurance account, group members can retrieve indemnities from the insurance account. [D: There is a deductible of 5 points.] Each group member only has the possibility to retrieve 0 points, 10 points or 15 points from the insurance account. If a group member retrieves an indemnity, he or she receives the corresponding amount from the insurance account. The other group members have no influence on this payment; it will be made automatically.
[BoMa: The insurance premium of each participant is 5 points in the first period. The insurance premium in periods 2–5 is dependent on whether indemnities have been retrieved in earlier periods. If, in a given period, an indemnity is retrieved from the insurance account, then the insurance premium in the next period increases by 2 points. If no indemnity is retrieved, the insurance premium in the next period decreases by 1 point. The following table summarizes this relation for the first three periods:
Period 1 | Period 2 | Period 3 | – | |||
|---|---|---|---|---|---|---|
Premium | Indemnity | Premium | Indemnity | Premium | – | – |
5 points | Yes | 7 points | Yes | 9 points | – | – |
No | 6 points | – | – | |||
No | 4 points | Yes | 6 points | – | – | |
No | 3 points | – | – | |||
end of insertion for BoMa]
Any indemnity payment from the insurance account results in additional transaction costs of 40 percent. Therefore, if a group member retrieves an indemnity of 10 points, the insurance account will be debited with 4 additional points (14 points overall). If 15 points are retrieved, the insurance account will be debited with 6 additional points. The following table summarizes this relation:
Retrieved indemnity | Transaction costs | Total debit to the insurance account |
|---|---|---|
0 points | 0 points | 0 points |
10 points | 4 points | 14 points |
15 points | 6 points | 21 points |
Potential credit and debit balances of the insurance account are summed up over all five periods. During the experiment, you will receive no information regarding the balance of the insurance account. After the last period, the insurance account is automatically and equally balanced by all group members. If the insurance account has a negative balance, each group member has to pay one-fourth of the balance from his or her winnings up to that point. On the other hand, if the insurance account has a positive balance, each group member receives one-fourth of the balance in addition to his or her winnings up to this point.
The timing of your decisions in each period is as follows:
- Step 1:
-
At the beginning of each period, you receive your period endowment of 25 [D: 27] points.
- Step 2:
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You must acknowledge the payment of the insurance premium of 5 points [B: no points mentioned] to the insurance account.
- Step 3:
-
You will make three decisions in each period: For each potential loss situation, you must decide how many points you will retrieve from the insurance account. Thus, for a situation in which you have not incurred a loss, you have to decide whether you want to retrieve 0 points, 10 points, or 15 points from the insurance account. You must make the same decision twice more for the situations in which you have incurred a low loss or a high loss, respectively.
- Step 4:
-
Only after you have made all three decisions will you find out whether you have indeed incurred a loss in this period. If you have incurred a loss, you will also learn whether it was a low or a high loss. You will then automatically receive the indemnity from the insurance account that you requested in step 3 for this particular situation. [B: If an indemnity is retrieved from the insurance account in this period, then the insurance premium in the next period increases by 2 points. If no indemnity is retrieved, the insurance premium in the next period decreases by 1 point.]
After the last period, the second part of the experiment will start, and you will have to answer several questions. After you have filled in the questionnaire on the computer, you will receive detailed information regarding the balance of the insurance account, your earned points, and your payment in Euros.
Please pack up your personal belongings after the experiment and sit quietly in your seat. We will call you in a random order to collect your payment outside the lab room. Thank you for your participation.
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von Bieberstein, F., Schiller, J. Contract design and insurance fraud: an experimental investigation. Rev Manag Sci 12, 711–736 (2018). https://doi.org/10.1007/s11846-017-0228-1
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DOI: https://doi.org/10.1007/s11846-017-0228-1