Measuring Substitution Patterns with a Flexible Demand Model

Many empirical studies require estimating how consumers substitute across differentiated products. Examples can be found in a wide range of fields of economics, including environmental economics, health care economics, industrial organization, and international trade. In this paper, I propose a computationally simple, easy-to-implement, flexible approach to estimate substitution patterns determined by how close products are in product characteristic space. To this end, I rely on an inverse market share model that (i) is consistent with utility maximization; (ii) does not use any specific assumptions about how substitution patterns depend on product characteristics; and (iii) is agnostic about individual consumer behavior. I find that my approach only requires solving a convex quadratic program with a small number of linear inequality constraints. I further find that it can outperform the state-of-the-art BLP approach pioneered by Berry, Levinsohn, and Pakes (1995), which accommodates flexible substitution patterns by using the random coefficient logit model. In particular, this occurs when (i) there is complementarity in demand; (ii) BLP is misspecified about its random coefficients; and (iii) consumers choose baskets of products. Lastly, I apply my approach to a well-known dataset for breakfast cereals and compare it to BLP. I find that it provides a better fit to the data than BLP. I further find that it yields similar median own-price elasticities, and higher median cross-price elasticities, markups, and merger price effects