Index insurance is an alternative to crop insurance that bases payouts on a variable that is highly correlated with income but beyond the control of individual households, such as rainfall, temperature, or area-yields (i.e., output per hectare in a large area). Index insurance offers risk protection while avoiding the incentive problems that plague traditional crop insurance, and as a result is seen by many as a promising antipoverty tool. However, participation in index insurance to this point has generally been in low. In this paper, we explore one factor that might potentially depress demand for index insurance: mistaken beliefs among farmers with respect to the distribution of the insured risk. Our experiences from an area-yield insurance pilot project for cotton farmers in the Pisco valley of Peru suggest that such errors are common. Lower demand means that not only are the benefits of index insurance not realized by households, but econometric measurement of the these benefits is more difficult due to low precision. One way to counteract these effects is a “randomized encouragement design,” i.e., the random assignment of positive economic incentives for the purchase of area-yield insurance, such as discount coupons. We examine the implications of a randomized encouragement design for econometric evaluation.