Can Agents Add and Subtract when Forming Beliefs? Evidence from the Lab and Field

Abstract

We study an intrinsic property of Bayesian information processing which does not rely on individuals having rational absolute beliefs: two equally-diagnostic signals of opposite direction should cancel out. Using evidence from both the lab and field, we show that individuals not always follow this counting-based principle. Systematic violations occur whenever a sequence of identical evidence is interrupted by a signal of opposite direction, which produces strong and robust overreactions. Conversely, individuals correctly follow this counting-based principle whenever signals alternate while they underreact to sequences of same-directed evidence. Next, we empirically analyze announcement and post-announcement stock return reactions in financial markets. Consistent with our experimental evidence, we find that initial stock reactions are significantly stronger and subsequent price drifts weaker for opposite-directed earnings surprises than for same-directed earnings surprises. Our results provide novel insights to the paradoxical co-existence of over- and underreaction to new information at the individual and market level.

Keywords: Belief Formation, Bayes' Theorem, Information Processing, Overreaction

JEL Classification: D81, D83, D84, G41