BLP-LASSO for Aggregate Discrete Choice Models with Rich Covariates

We introduce the BLP-LASSO model, which augments the classic BLP (Berry, Levinsohn, and Pakes, 1995) random-coefficients logit model to allow for data-driven selection among a high- dimensional set of control variables. Economists often study consumers’ aggregate behavior across markets choosing from a menu of differentiated products. In this analysis, local demo- graphic characteristics can serve as controls for market-specific preference heterogeneity. Given rich demographic data, implementing these models requires specifying which variables to include in the analysis, an ad hoc process typically guided primarily by a researcher’s intuition. We pro- pose a data-driven approach to estimate these models applying penalized estimation algorithms imported from the machine learning literature that are known to be valid for uniform inferences with respect to variable selection. Our application explores the effect of campaign spending on vote shares in data from Mexican elections.