Nonparametric estimation of the costs of non-sequential search

We study a consumer non-sequential search oligopoly model with search cost heterogeneity. We first prove that an equilibrium in mixed strategies always exists. We then examine the nonparametric identification and estimation of the costs of search. We find that the sequence of points on the support of the search cost distribution that can be identified is convergent to zero as the number of firms increases. As a result, when the econometrician has price data from only one market, the search cost distribution cannot be identified accurately at quantiles other than the lowest. To solve this pitfall, we propose to consider a richer framework where the researcher has price data from many markets with the same underlying search cost distribution. We provide conditions under which pooling the data allows for the identification of the search cost distribution at all the points of its support. We estimate the search cost density function directly by a semi-nonparametric density estimator whose parameters are chosen to maximize the joint likelihood corresponding to all the markets. A Monte Carlo study shows the advantages of the new approach and an application using a data set of online prices for memory chips is presented.