Probabilistic Classification in Business Cycles Identification Based on Generalized ROC

ABSTRACT The area under the receiver operating characteristic (AUROC) curve is a widely used tool for assessing and ranking global classifier performance. However, because AUROC ignores the scale of predicted probabilities, it can sometimes provide a misleading performance evaluation. To address this limitation, we build on the area under the Kuipers score curve (AUKSC), and reinterpret this metric by extending the traditional ROC curve into a three‐dimensional framework that incorporates thresholds, leading to the area of the generalized ROC (AGROC) curve, thus providing a unified measure of classification performance. Through extensive Monte Carlo simulations, we demonstrate that AGROC effectively addresses the limitations of traditional AUROC metrics, offering a more robust tool for ranking probabilistic classifiers by balancing accuracy and probabilistic differentiation. In an empirical application, we show that AGROC accurately identifies recession probabilities derived from various Markov‐switching models applied to US GDP growth data, aligning closely with NBER‐defined business cycle phases.