Ambiguous State Dynamics, Learning, and Endogenous Long-Run Risk

Abstract

This paper considers learning about unobservable state variables when their dynamics are ambiguous. The drift of the state process is perturbed and set-estimated by inverting a test. The evolution of the set estimate is explicitly characterized up to a system of differential equations extending the conditionally Gaussian filter and is embedded in recursive maxmin expected utility. Despite the fact that the agent is unconfident only about the drift of the state process, learning under ambiguity makes her behave as if she assumed excessive volatility for the state process. This helps explain why the long-run risk model elicits seemingly excessive long-run risk from returns data.

Keywords: Ambiguity, Learning, Hypothesis Testing, State-Space Models, Long-Run Risks, Asset Pricing, Continuous Time