Advancement to Candidacy Presentation: “Forecast Errors and Forecast Sufficiency Under Ambiguity” (Paper 1) and “When Do Revealed Beliefs Exist? Axioms and Tests” (Paper 2), Leshan Xu, University of California, Santa Barbara
Speaker
Leshan Xu, University of California, Santa Barbara
Biography
Leshan Xu is a PhD student in the Economics Department at UC Santa Barbara. He received his Bachelor's degree from UC Santa Barbara in 2022. His research focuses on behavioral and experimental economics, with particular emphasis on decision-making under uncertainty and belief formation. Leshan's current work examines the axiomatic foundations of revealed preference theory and its applications to ambiguity aversion. He is advised by Professor Ignacio Esponda.
Title
“Forecast Errors and Forecast Sufficiency Under Ambiguity” (Paper 1) and “When Do Revealed Beliefs Exist? Axioms and Tests” (Paper 2), Leshan Xu
Abstract
“Forecast Errors and Forecast Sufficiency Under Ambiguity”
We propose forecast sufficiency as a principle of decision-making under uncertainty: once a person forms a probability forecast, behavior should depend only on that forecast---not on how it was formed. This principle is central to many economic models but has rarely been tested directly. We design an experiment with Risk and Ambiguity treatments and elicit subjective forecasts, enabling us to distinguish belief formation from belief use. We find that forecast sufficiency fails: individuals act differently when a probability is known (Risk) versus when it is forecasted to be the same (Ambiguity). This failure explains about half of the behavioral gap between the two treatments. However, once forecasts are corrected for base rate neglect, forecast sufficiency largely holds, so the observed behavior can be explained without invoking violations of the principle.
JEL Codes: C91, D81, D83
Title
“When Do Revealed Beliefs Exist? Axioms and Tests”
Abstract
We study when a decision maker's choices reveal a single subjective probability. In standard expected utility theory, we infer beliefs from choices—if someone prefers one act to another when both bet on an event, they act "as if" holding some probability p about that event. But does such a belief actually exist? We say a revealed belief exists when a single probability rationalizes all choices over acts contingent on an event, regardless of stakes. We show this requires a new axiom: stake-invariance, which requires that comparing an act to an objective lottery does not reverse when outcomes change. Together with standard axioms including weak order, statewise monotonicity, continuity, and lottery monotonicity, we prove that stake-invariance is necessary and sufficient for revealed beliefs to exist. We use our framework to classify ambiguity models. Maxmin expected utility, Choquet expected utility, and source theory satisfy our axioms and admit revealed beliefs. In contrast, smooth ambiguity preferences and variational preferences violate stake-invariance. Our results clarify which behavioral assumptions are embedded in different ambiguity theories and have implications for belief elicitation and welfare analysis.
JEL Codes: D81, D83
Event Details
Leshan will be presenting two papers for this Advancement to Candidacy, “Forecast Errors and Forecast Sufficiency Under Ambiguity” (Paper 1) and “When Do Revealed Beliefs Exist? Axioms and Tests” (Paper 2). To access the Advancement papers, you must have an active UCSB NetID and password.
Please do not circulate, preliminary work
