Estimating Sequential Search Models Based on a Partial Ranking Representation

Abstract: The rapid growth of online shopping has made consumer search data increasingly available, opening up new possibilities for empirical research. Sequential search models offer a structured approach for analyzing such data, but their estimation remains difficult. This is because consumers make optimal decisions based on private information revealed in search, which is not observed in typical data. As a result, the model's likelihood function involves high-dimensional integrals that require intensive simulation. This paper introduces a new representation that shows a consumer's optimal search decision-making can be recast as a partial ranking over all actions available throughout the consumer's search process. This reformulation yields the same choice probabilities as the original model but leads to a simpler likelihood function that relies less on simulation. Based on this insight, we provide identification arguments and propose a modified GHK-style simulator that improves both estimation performances and ease of implementation. The proposed approach also generalizes to a wide range of model variants, including those with incomplete search data and structural extensions such as search with product discovery. It enables a tractable and unified estimation strategy across different settings in sequential search models, offering both a new perspective on understanding sequential search and a practical tool for its application.