Smooth Ambiguity, Wealth Dynamics and Asset Prices with Heterogeneous Beliefs

We study a class of endowment economies with long-run risks in which agents have generalized recursive smooth ambiguity preferences and heterogeneous beliefs. The expected growth rate of aggregate consumption consists of a persistent component. Agents cannot observe the component but learn about it via Bayes' rule. Meanwhile, agents hold different beliefs about persistence of the long-run component. By examining a two-agent model, we find that: 1) the consumption share of the agent with the correct belief dominates in the long run, even when both agents have recursive preferences without smooth ambiguity, 2) smooth ambiguity, in conjunction with state uncertainty, generates uncertainty sharing motive that leads to long-run survival of both agents, 3) the time-varying weights of agents and posterior beliefs help explain the time variation of price-dividend ratios in the data, and 4) in a model with an ambiguity-averse agent and an ambiguity-loving agent, both agents survive in the long run if they hold different beliefs