Case analysis: a 100% recession call

Read 13.9.1. (a) Score the Bloomberg model's 12-month forecast (100%) and the economists' survey (60%) on the Brier and log scores, given the outcome recorded in the notes. (b) Suppose a model maps an index $z$ of indicators to $\Pr(\text{recession}) = 1/(1+e^{-z})$ and reports probabilities rounded to the nearest percent. What is the smallest $z$ that is reported as 100%? If the largest $z$ seen in the model's estimation sample was 3, what probability did the model ever have a chance to be validated at? (c) Propose two changes to the forecasting process that would have prevented a 100% output, and say what each costs.