Motivated by the Basel 3 regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to evaluate forecast performance in this context. However, little intuitive or empirical guidance is currently available,...

Several recent surveys ask for a person's subjective probabilities that the in- ation rate falls into various outcome ranges. We provide a new measure of the uncertainty implicit in such probabilities. The measure has several advantages over existing methods: It is trivial to implement, requires...