The non-optimality of deductible contracts against fraudulent claims: an empirical evidence in automobile insurance

Insurance fraud is now recognized as a significant resource allocation problem in many markets. One explanation is the non-optimality of traditional insurance contracts. The object of this study is to verify how straight deductible contracts may affect the falsification behavior of an insured. This type of contract is observed in many markets, even if it is not optimal under costly state falsification. Consequently, a higher deductible may create incentives to fraud or cheat, particularly when the insured anticipates that the claim has a small probability of being audited or when the probability of detecting fraud during an audit is small. To verify this proposition, we estimate a loss equation for which one of the determinants is the amount of the deductible, using a data set of claims filed for damages following an automobile accident with 20 insurance companies in Quebec in 1992. Since we only have access to reported losses, a higher deductible also implies a lower probability of reporting small losses. In order to isolate the fraud effect related to the presence of a deductible in the contract, we jointly estimate a loss equation and a threshold equation. The threshold is the amount over which an insured decides to report a given loss. It can be interpreted as a personal deductible and it is not observable. Therefore, we use the method of censored dependent variable developed by Nelson (1977) and extended to the truncation case by Maddala (1983). Our results indicate, among other things, that with an appropriate correction for selectivity, the amount of the deductible is a significant determinant of the reported loss, at least when no other vehicle is involved in the accident; in other words, when the presence of witnesses is less likely.