Learning Models from Prices

We study a dynamic financial economy with complete markets in which agents hold heterogeneous beliefs about dividends. Beliefs combine an exogenous agent-specific model, possibly misspecified, and an endogenous market-based model derived from state prices. We show that using prices to learn improves prediction and offers a hedge against model misspecification. With Bayesian learning, agents update model weights and survive on all paths. Market beliefs converge almost surely to the most accurate exogenous model, despite heterogeneity and misspecification, and so do individual beliefs of any agent who assigns positive prior weight to it. With non-Bayesian learning, where the weight on the market model is fixed, survival is not guaranteed. Yet market accuracy weakly improves, and can exceed that of any individual model when beliefs are diverse. In such cases, relying on prices helps approximate the truth, while ignoring the market leads to vanishing. Our results characterize how endogenous use of prices shapes learning, survival, and the predictive power of markets.