Identification and estimation of a search model with heterogeneous consumers and firms

We propose a model of nonsequential consumer search where consumers and firms differ in search and production costs respectively. We characterize the equilibrium of the game. We first show the distribution of search cost can be identified by market shares and prices. Subsequently, we identify the production cost distribution using a similar strategy to Guerre, Perrigne and Vuong (2000) as the firms’ decision problems resemble bidders’ problems in a particular procurement auction. We prove the firm’s cost density can be estimated at the same convergence rate as the optimal rate in Guerre et al. uniformly over any fixed subset on the interior of the support. The uniform convergence rate over any expanding support is slower due to a pole in the price pdf that is a feature of the equilibrium. Our simulation study confirms the theoretical features of the model. Our identification and convergence rate results also apply to two generalizations of the baseline search model that allow for: (i) vertically differentiated products; (ii) an intermediary. We apply the latter model to study loan search using UK mortgage data.