Embeddings and Distance-based Demand for Differentiated Products

We propose a simple method to estimate demand in markets for differentiated products. The method augments price and quantity data with triplets data (of the form "product A is closer to B than it is to C'') obtained from an online survey. Using a machine learning algorithm, the triplets data are used to estimate an embedding---i.e., a low-dimensional representation of the latent product space. Distances between pairs of products, computed from the embedding, discipline substitution patterns in a simple log-linear demand model. This approach solves the dimensionality problem of product-space demand models (too many cross-price elasticity parameters to estimate). We illustrate the performance of the method by estimating demand for ready-to-eat cereals and comparing our estimates to those obtained from the standard method of (BLP). We find that our elasticity estimates imply credible substitution patterns and compare favorably to the BLP estimates. Beyond our current implementation of the method, the embedding data can be incorporated in either characteristic-space demand approaches, or in more complex product-space models.

Full paper available at https://papers.ssrn.com/ sol3/papers.cfm?abstract_id=4113399.