  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.
