Simulated Maximum Likelihood Estimation of the Sequential Search Model

The authors propose a new approach to simulate the likelihood of the sequential search model. By allowing search costs to be heterogeneous across consumers and products, the authors directly compute the joint probability of the search and purchase decision 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 in order to compute the joint probabilities of consumers' search and purchase decisions. In an extensive simulation study, the proposed method is compared with existing likelihood simulators that have recently been used to estimate the sequential search model. In addition, the proposed method recovers the consumers’ relative preferences even if the utility function and/or the search cost distribution is mis-specified. The proposed method is then applied to online search data from Expedia for field-data validation. The more precise estimation of the model parameters and the improved prediction accuracy of the proposed approach stem from attributing researcher uncertainty in the search order to the consumer-product-level distribution of search costs and the randomness in the choice decision to the distribution of match values across consumers and products. From a substantive perspective, the authors find that search costs and "position" effects affect products in the lower part of the product listing page that are searched; more than they do those in the upper part of the page