Estimating Preferences and Substitution Patterns from Second-Choice Data Alone
Paper joint with Christopher Conlon and Paul Sarkis
Abstract:
We consider identification and estimation of a model of consumer choice where the main source of variation is in the set of products made available to consumers. Instead of relying on variation in the choice environment (prices, product characteristics) we require first-choice probabilities and a subset of (conditional) second-choice probabilities. We develop a semi-parametric low-rank approximation to the matrix of second-choice probabilities that is consistent with mixed logit models of demand but is defined in “product space” and does not require that product characteristics explain substitution patterns. In Monte Carlo experiments we show that our model can replicate a nested logit or random coefficients logit model. We apply our model to a single year of automobile data from Grieco et al. (2021) and show that we can fit substitution patterns with higher accuracy.