Keith J Crocker* and Sharon Tennyson**
*University of Michigan Business School
**Department of Policy Analysis and Management, Cornell University
This paper develops a model of optimal third-party settlements between a risk-neutral insurer and a risk-averse claimant. We consider an environment in which the claimant has suffered an insured loss, the magnitude of which is private information. The insurer can observe only the size of the claim, which may be larger than the actual loss if the claimant chooses to expend resources in inflating the claim. Faced with the prospects of fraudulent claiming the insurer must select a settlement strategy, which in this environment consists of an indemnification profile. An optimal settlement strategy reflects a tension between the insurer's attempts to mitigate the claimant's incentives to exaggerate the claim, and the insurer's desire to avoid costs associated with systematic claims underpayment. The primary implication of the theoretical model is that an optimal settlement strategy entails systematic underpayment of claims and the degree of underpayment will be larger for classes of claims which are most easily exaggerated. The theoretical predictions are tested empirically using a large data set of liability insurance claims for bodily injuries experienced in automobile accidents. The empirical findings are consistent with the theoretical predictions and are robust to alternative interpretations.
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