Disentangling preferences and limited attention: Random-utility models with consideration sets

This paper presents a model of choice with limited attention. The decision-maker forms a consideration set, from which she chooses her most preferred alternative. Both preferences and consideration sets are stochastic. While we present axiomatisations for this model, our focus is on the following identification question: to what extent can an observer retrieve probabilities of preferences and consideration sets from observed choices? Our first conclusion is a negative one: if the observed data are choice probabilities, then probabilities of preferences and consideration sets cannot be retrieved from choice probabilities. We solve the identification problem by assuming that an “enriched” dataset is observed, which includes choice probabilities under two frames. Given this dataset, the model is “fully identified”, in the sense that we can recover from observed choices (i) the probabilities of preferences (to the same extent as in models with full attention) and (ii) the probabilities of consideration sets. While a number of recent papers have developed models of limited attention that are, in a similar sense, “fully identified”, they obtain this result not by using an enriched dataset but rather by making a restrictive assumption about the default option, which our paper avoids.