Recent research in contract theory on the effects of behavioral biases implicitly assumes that they are stable, in the sense of not being affected by the contracts themselves. In this paper, we provide evidence that this is not necessarily the case. We show that in an insurance context, being insured against losses that may be incurred in a real-effort task changes subjects' self-confidence. Our novel experimental design allows us to disentangle selection into insurance from the effects of being insured by randomly assigning coverage after subjects revealed whether they want to be insured or not. We find that uninsured subjects are underconfident while those that obtain insurance have well-calibrated beliefs. Our results suggest that there might be another mechanism through which insurance affects behavior than just moral hazard.