Coarse categories in a complex world

Most news stories contain both granular quantitative information and coarse categorizations. For instance, company earnings are reported as a dollar figure alongside categorizations, such as whether earnings beat or missed market expectations. We formalize and study the hypothesis that when a decision is harder, people rely more on easier-to-integrate signals: people still discriminate between coarse categories but distinguish less granularly within them, creating higher sensitivity around category thresholds but lower sensitivity elsewhere. Using stock market reactions to earnings announcements, we document that hard-to-value stocks are associated with a more pronounced S-shaped response pattern around category thresholds. Experiments that exogenously manipulate the problem difficulty provide supporting causal evidence in individual investor behavior. We then exploit variation in investor familiarity with earnings surprises of different sizes to show that returns exhibit greater sensitivity in regions withmore historical density. Our findings speak to the ongoing debate about why economic agents display insufficient sensitivity in some instances and excessive sensitivity in others, even within the same empirical setting.