Robust identification of investor beliefs

Abstract

This paper develops a method informed by data and models to recover information about investor beliefs. Our approach uses information embedded in forward-looking asset prices in conjunction with asset pricing models. We step back from presuming rational expectations and entertain potential belief distortions bounded by a statistical measure of discrepancy. Additionally, our method allows for the direct use of sparse survey evidence to make these bounds more informative. Within our framework, market-implied beliefs may differ from those implied by rational expectations due to behavioral/psychological biases of investors, ambiguity aversion, or omitted permanent components to valuation. Formally, we represent evidence about investor beliefs using a nonlinear expectation function deduced using model-implied moment conditions and bounds on statistical divergence. We illustrate our method with a prototypical example from macrofinance using asset market data to infer belief restrictions for macroeconomic growth rates.

Statistical Model of College Students’ Mental Health Based on the Law of Large Numbers

“…A differences in genes and the environment of growth in the individual's psychological expectation model, the form of the stable emotional state within each person is also different [5]. The model can reach any condition at any point in time.…”

“…The probability of occurrence of each emotion in the emotion space is the same, . This will maximize emotional entropy (5) represents the emotional maximum of the organisms investigated in this paper.…”