ROC and PRC approaches to evaluate recession forecasts

We have studied the relationship between Receiver Operating Characteristics (ROC) and Precision-Recall Curve (PRC) both analytically and using a real-life empirical example of yield spread as a predictor of recessions. We show that false alarm rate in ROC and inverted precision in PRC are analogous concepts, and their difference is determined by the interaction of sample imbalance and forecast bias. We found that in cases of severe class imbalance, the forecasts need to be adequately biased to mitigate the effect of imbalancedness. The mix of values of precision and recall over six sub-samples show that the predictive power of the spread has not deteriorated in recent decades, provided the optimum values of threshold are used. Using PRC, we quantify the extent to which ROC could be exaggerating the true predictive value of the yield curve in predicting recessions.