We study an automobile insurance market where the quantity of insurance purchased has a large impact on the resulting frequency and severity of claims. Policyholders who purchase insurance against increases in future premiums because of at-fault claims experience a roughly 40 percent increase in reported claims. Although consistent with differences in accident rates due to adverse selection or exante moral hazard, the evidence suggests that changes in claim reporting behavior can account for nearly all of the increase in claims. After controlling for differences in observable characteristics, we show that the increase in claim frequency is concentrated in relatively small claims and claims where the policyholder is at-fault, suggesting that consumers without premium protection strategically choose not to report such claims to the insurance company. The frequency of large claims and claims where the policyholder is not at fault are nearly identical across the two groups. Using this reduced form evidence to reject the endogeneity of premium protection with underlying accident rates, we estimate a structural model with latent accidents and claim reporting thresholds to explain the observed pattern of claim frequencies and severities. The estimated differences in underlying accident rates are quite small and suggest at most a minor role for adverse selection or ex-ante moral hazard. However, the estimated differences in reporting thresholds, identified by differences in the shapes of the claim severity distributions, are large and lead to significant differences in reported claims. This result highlights a novel source of information asymmetries in automobile insurance and illustrates the importance of accounting for differences in claim reporting behavior when studying insurance markets.