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 maximizes his or her continuation value under a worst-case model which lies within a nonparametric neighborhood of a benchmark model  . The DM's benchmark model and preference parameters are jointly underidentified. With the DM's benchmark model fixed, primitive conditions are established for nonparametric identification of the worst-case model and local identification of the DM's  preference parameters. The key step in the identification analysis is to establish existence and uniqueness of the DM's continuation value function allowing for unbounded statespace and unbounded utilities, both of which are important in applications. To do so, we derive new fixed-point results which use monotonicity and convexity of the value function recursion and which are embedded within a Banach space of " thin-tailed " functions that arises naturally from the structure of  recursion. The fixed-point results are quite general and are also applied to models where the DM learns about a hidden state and Rust-type dynamic discrete choice models . A perturbation result is derived which provides a necessary and sufficient condition for consistent estimation of continuation values and the worst-case model. A robust consumption-investment problem is studied as an empirical application and some connections are drawn with the literature on macroeconomic uncertainty.
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 that delivers the lowest utility among all models in this set . The DM's benchmark model and preference parameters are jointly underidentified. With the benchmark model held fixed, primitive conditions are established for identification of the DM's worst-case model and preference parameters. The key step in the identification analysis is to establish existence and uniqueness of the DM's continuation value function allowing for unbounded statespace and unbounded utilities, both of which are important in applications. To do so, new 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 DM's 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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maximizes his or her continuation value under a worst-case model which lies within a nonparametric neighborhood of a
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that he or she fears is misspecified by a set of models. Decisions are evaluated under a "worst-case" model that delivers the lowest utility among all models in this set
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DM's benchmark model
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nonparametric
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worst-case model and local identification of the
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we derive
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which use monotonicity and convexity of the value function recursion and which are embedded within
are derived for monotone, convex operators that act on
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the continuation value
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and are also applied to models where the DM learns about a hidden state
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are also discussed. For estimation, a
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A robust consumption-investment problem is studied as an empirical application and some
The result also allows convergence rates of estimators to be characterized. An empirical application studies an endowment economy where the DM's 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