Search with Dirichlet Priors: Estimation and Implications for Consumer Demand

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In this paper, we revisit the problem of search with learning about the price distribution, as introduced by Rothschild (1974). For searchers with Dirichlet priors, we develop a novel characterization of the optimal search behavior. The advantage of our solution relative to the characterization based on reservation values is that it delivers closed form, easily computable formulas for the ex-ante purchase probabilities. Our result opens a possibility of introducing search with learning into the estimation discrete choice models of demand, when market shares data is available. We estimate a model of search with learning about the price distribution, on a dataset of prices and market shares of S&P 500 mutual funds. The same dataset was used by Hortacsu and Syverson (2004) to estimate a model of search from known distribution. Comparing the predicted demand curves from models of search with and without learning about the price distribution, we find that learning mostly affects the demand for the market leaders -- products with the lowest prices. Their market shares are now smaller, as they experience higher competition from the higher priced goods. At the same time, their own price elasticity is also smaller. According to our estimates, the magnitude of both effects is economically significant. We conduct a simulation study to explain how learning affects the price reaction of consumers with different search costs.