This paper presents a methodology for estimating a sequential model of online consumer search. The literature on such structural econometric models typically assumes that, for each alternative, there is only one stage of optimal information acquisition. For many e-commerce websites, however, there are two stages: obtaining information from (1) the search results page and (2) clicking on an alternative. We develop a methodology for estimating a model with two stages, in which the consumer makes optimal decisions in each stage. The search problem is viewed as a variant of a multi-armed bandit problem. We estimate this model using a dataset of clicks and purchases on the website expedia.com. In contrast to models with one stage of optimal information acquisition, our model can be used to analyse not only the clicking and purchasing behaviour of consumers but also the extent to which they browse alternatives on the search results page