Simulated maximum likelihood estimation of the sequential search model

Abstract

We propose a new approach to simulate the likelihood of the sequential search model. By allowing search costs to be heterogeneous across consumers and products, we directly compute the joint probability of the search and purchase decisions when consumers are searching for the idiosyncratic preference shocks in their utility functions. Under the assumptions of Weitzman’s sequential search algorithm, the proposed procedure recursively makes random draws for each quantity that requires numerical integration while enforcing the conditions stipulated by the algorithm. In an extensive simulation study, we compare the proposed method with existing likelihood simulators that have recently been used to estimate the sequential search model. The proposed method attributes the uncertainty in the search order to the consumer-product-level distribution of search costs and the uncertainty in the purchase decision to the distribution of match values across consumers and products. This results in more precise estimation and an improvement in prediction accuracy. We also show that the proposed method allows for different assumptions on the search cost distribution and that it recovers consumers’ relative preferences even if the utility function and/or the search cost distribution is mis-specified. We then apply our approach to online search data from Expedia for field-data validation. From a substantive perspective, we find that search costs and “position” effects affect products in the lower part of the product listing page more than they do those in the upper part of the page.