Estimating search with learning

In this paper we estimate a structural model of search for differentiated products, using a unique dataset of individual search histories for hotels online. We propose and implement an identification strategy that allows to separately estimate consumer's beliefs, search costs and preferences. Learning plays an essential role in this strategy: it creates variation of posterior beliefs across consumers that's orthogonal to variation in search costs. We obtain two kinds of results. First, we estimate consumer's demand from the search model and compare it to results from the static model. We find that ignoring the endogeneity of choice sets leads to biased estimates: in particular, the aggregate price elasticity is over-estimated by about 80%. Second, we attempt to evaluate an empirical performance of a model of rational search. The mean search cost is estimated to be around 40 dollars, and median is 30 dollars; however, there is also a significant variation of search costs among population. A test between models of search from known (Stigler 1967) and from unknown (Rothschild 1974) distribution favors the second one: we find a statistically significant amount of Bayesian learning, even though it doesn't seem to affect demand estimates in an economically meaningful way.