In this paper, I introduce a random attention span model (RAS) which uses stopping time to identify decision-makers' behavior under limited attention. Unlike many limited attention models, the RAS identifies preferences using time variation without any need for menu variation. In addition, the RAS allows the consideration set to be correlated with the preference. I also use the revealed preference theory that provides testable implications for observable choice probabilities. Then, I test the model and estimate the preference distribution using data from M-Turk experiments on choice behaviors that involve lotteries; there is general alignment with the distribution results from logit attention model.
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