A Framework for the Estimation of Demand for Differentiated Products with Simultaneous Consumer Search

We propose a tractable method for estimation of a simultaneous search model for differentiated products that allows for observed and unobserved heterogeneity in both preferences and search costs. We show that for type I extreme value distributed search costs, expressions for search and purchase probabilities can be obtained in closed form. We show that our search model belongs to the generalized extreme value (GEV) class, which implies that it has a full information discrete-choice equivalent, and hence search data are necessary to distinguish between the search model and the equivalent full information model. We allow for price endogeneity when estimating the model and show how to obtain parameter estimates using a combination of aggregate market share data and individual level data on search and purchases. To deal with the dimensionality problem that typically arises in search models due to a large number of consideration sets we propose a novel Monte Carlo estimator for the search and purchase probabilities. Monte Carlo experiments highlight the importance of allowing for sufficient consumer heterogeneity when doing policy counterfactuals and show that our Monte Carlo estimator is accurate and computationally fast. Finally, a behavioral assumption on how consumers search provides a micro-foundation for consideration probabilities widely used in the literature.