A Random Attention Model

Abstract

This paper illustrates how one can deduce preference from observed choices when attention is not only limited but also random. In contrast to earlier approaches, we introduce a Random Attention Model (RAM) where we abstain from any particular attention formation, and instead consider a large class of nonparametric random attention rules. Our model imposes one intuitive condition, termed Monotonic Attention, which captures the idea that each consideration set competes for the decision-maker's attention. We then develop revealed preference theory within RAM and obtain precise testable implications for observable choice probabilities. Based on these theoretical findings, we propose econometric methods for identification, estimation, and inference of the decision maker's preferences. To illustrate the applicability of our results and their concrete empirical content in specific settings, we also develop revealed preference theory and accompanying econometric methods under additional nonparametric assumptions on the consideration set for binary choice problems. Finally, we provide general purpose software implementation of our estimation and inference results, and showcase their performance using simulations. tions that are inconsistent with observed choice behavior. Aware of this fact, a few scholars have improved deterministic limited attention models by allowing for stochastic attention Horan, 2018), which permits the decision maker to pay attention to different subsets with some non-zero probability given the same set of alternatives to choose from. All available results in this literature proceed by first parameterizing the attention rule (i.e., committing to a particular parametric attention rule), and then studying the revealed preference implications of these parametric models.In contrast to earlier approaches, we introduce a Random Attention Model (RAM) where we abstain from any specific parametric (stochastic) attention rule, and instead consider a large class of nonparametric random attention rules. Our model imposes one intuitive condition, termedMonotonic Attention, which is satisfied by many stochastic attention rules. Given that consideration sets are unobservable, this feature is crucial for applicability of our revealed preference results, as our findings and empirical implications are valid under many different, particular attention rules that could be operating in the background. In other words, our revealed preference results are derived from nonparametric restrictions on the attention rule and hence are more robust to misspecification biases.RAM is best suited for eliciting information about the preference ordering of a single decisionmaking unit when her choices are observed repeatedly. 1 For example, scanner data keeps track of the same single consumer's purchases across repeated visits, where the grocery store adjusts product varieties and arrangements regularly. Another example is web advertising on digital platforms, such as search engines or shopping sites, where not only abundant records f...

Econometrics with Partial Identification

“…The monotonicity of attention rules in (3.14) can be viewed as regularity of the process that chooses a consideration set from the subsets of the choice set. Cattaneo, Ma, Masatlioglu, and Suleymanov (2017) show that it is implied by various models of limited attention. While the violation required in (3.16) is weak in that it needs only to occur for some G, it sheds a different light on the severity of the identification problem described at the beginning of this section.…”

“…Key Insight 3.5: Cattaneo, Ma, Masatlioglu, and Suleymanov (2017) show that learning features of preference orderings in Identification Problem 3.5 requires the existence in the data of choice problems where the choice probabilities satisfy (3.16). The latter is a violation of the principle of "regularity" (Luce and Suppes, 1965) according to which the probability of choosing an alternative from any set is at least as large as the probability of choosing it from any of its supersets.…”

Gradual Pairwise Comparison and Stochastic Choice

“…5Ĩ P is well defined since P is a partition of a strict rational preference P . 6 If the decision-maker could complete all comparisons, her choice would coincide with deterministic rational choice. Her (possible) inability to do so is captured by a function π :…”

“…|B| denotes the number of elements in the set B 6. For any i < I, by definition, |M P i (A)| ≥ |M P i+1 (A)|.…”

Judgments of Length in the Economics Laboratory: Are There Brains in Choice?

“…For instance, seeMasatlioglu, Nakajima, and Ozbay (2012),Manzini and Mariotti (2014), Aguiar, Boccardi, and Dean (2016),Cattaneo, Ma, Masatlioglu, and Suleymanov (2017).6 Also seeWeibull, Mattsson, and Voorneveld (2007).…”