A Random Attention Model
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We introduce a Random Attention Model (RAM) allowing for a large class of stochastic consideration maps in the context of an otherwise canonical limited attention model for decision theory. The model relies on a new restriction on the unobserved, possibly stochastic consideration map, termed Monotonic Attention, which is intuitive and nests many recent contributions in the literature on limited attention. We develop revealed preference theory within RAM and obtain precise testable implications for observable choice probabilities. Using these results, we show that a set (possibly a singleton) of strict preference orderings compatible with RAM is identifiable from the decision maker's choice probabilities, and establish a representation of this identified set of unobserved preferences as a collection of inequality constrains on her choice probabilities. Given this nonparametric identification result, we develop uniformly valid inference methods for the (partially) identifiable preferences. We showcase the performance of our proposed econometric methods using simulations, and provide general-purpose software implementation of our estimation and inference results in the R software package ramchoice. Our proposed econometric methods are computationally very fast to implement.
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