Online Appendix for “Optimal Expectations and Limited Medical Testing”

In this appendix we develop a version of the optimal expectations model with continuous action choices. We focus on the case of quadratic loss, and assume symmetry (Ω = Φ). That is, we assume that the loss to moving away from the correct action is the same regardless of the true state. Given that a central argument in favor of this model is that it works with this symmetry assumption, it seems reasonable to develop the continuous action case with this assumption. It is worth noting that an extreme form of asymmetry in which the loss to taking the wrong action if the true state is “sick” is much larger than the loss to taking the wrong action when the true state is “healthy” could cause this to break down. But this is the case in the binary model as well. The goal in this appendix is simply to demonstrate that the assumption that action a is binary is not necessary to derive our results.