We characterize the optimal loss functions for predicted click-through rates in auctions for online advertising. Whereas standard loss functions such as mean squared error or log likelihood severely penalize large mispredictions while imposing little penalty on smaller mistakes, a loss function reflecting the true economic loss from mispredictions imposes significant penalties for small mispredictions and only slightly larger penalties on large mispredictions. We illustrate that when the model is misspecified using such a loss function can improve economic efficiency, but the efficiency gain is likely to be small.
