Taking Ambiguity to Reality: Robust Agents Cannot Trust the Data Too Much

Ambiguity aversion in dynamic models is motivated by the presence of unknown time-varying features, which agents do not understand and cannot theorize about. We analyze the consequences of this assumption for economic agents and model builders, who typically need to estimate a model, e.g., to implement optimal robust decision rules or to quantify the equilibrium price of ambiguity. We show that in such contexts robust estimation methods are essential for (i) limiting the sensitivity of robust policies to abnormal time-varying features and (ii) drawing coherent inference on equilibrium variables. We propose a general robust estimation methodology, applicable to many economic settings of ambiguity. In the robust portfolio problem, unknown time-varying features in expected returns or rare events generate large utility losses, which are successfully bounded by our robust approach. Time-varying features can also produce large biases in estimated equilibrium risk or ambiguity premia, while in incomplete derivative markets they tend to systematically produce overestimated bid-ask spreads. We show that a good fraction of these biases can be eliminated, using our robust estimation approach. Finally, in a real-data application with ambiguous predictability our robust approach consistently produces both portfolio weights largely insensitive to abnormal data constellations and larger out-of-sample utilities.