This paper studies identification and estimation of a class of dynamic models in which the decision maker (DM) is uncertain about the data-generating process. The DM surrounds a benchmark model that he or she fears is misspecified by a set of models. Decisions are evaluated under a worst-case model delivering the lowest utility among all models in this set. The DMs benchmark model and preference parameters are jointly underidentified. With the benchmark model held fixed, primitive conditions are established for identification of the DMs worst-case model and preference parameters. The key step in the identification analysis is to establish existence and uniqueness of the DMs continuation value function allowing for unbounded statespace and unbounded utilities. To do so, fixed-point results are derived for monotone, convex operators that act on a Banach space of thin-tailed functions arising naturally from the structure of the continuation value recursion. The fixed-point results are quite general; applications to models with learning and Rust-type dynamic discrete choice models are also discussed. For estimation, a perturbation result is derived which provides a necessary and sufficient condition for consistent estimation of continuation values and the worst-case model. The result also allows convergence rates of estimators to be characterized. An empirical application studies an endowment economy where the DMs benchmark model may be interpreted as an aggregate of experts forecasting models. The application reveals time-variation in the way the DM pessimistically distorts benchmark probabilities. Consequences for asset pricing are explored and connections are drawn with the literature on macroeconomic uncertainty.
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