Joint Identification of Beliefs and Preferences from Point and Density Forecasts

<title>Abstract</title> <p> Point forecasts and density forecasts are widely collected in surveys of expectations, yet they are typically analyzed separately. This paper studies what can be learned from their joint observation. We develop a framework that distinguishes between beliefs, preferences, and forecast reports and characterizes the identification problem that arises when both point forecasts and density forecasts are observed simultaneously. Density forecasts reveal subjective probability assessments but do not identify preferences. Point forecasts generally reflect both beliefs and preferences and therefore do not identify either object in isolation. When the two forecast types are observed jointly, additional identifying restrictions become available, although separate identification requires assumptions regarding preferences and reporting behavior. We examine these issues within a rank-dependent utility framework in which density forecasts determine subjective probability assessments and point forecasts are interpreted as certainty equivalents. The framework highlights the distinction between identification and rationalizability and provides conditions under which observed forecast pairs can or cannot be reconciled with a maintained decision-theoretic model. An empirical illustration using Survey of Professional Forecasters data show that some forecast pairs are broadly consistent with the model, whereas others imply parameter values that violate standard admissibility conditions. The results demonstrate that forecast surveys contain richer information about expectation formation than is typically recognized. <bold>JEL Codes</bold> D81; C14; D84 </p>