BLP-2LASSO for aggregate discrete choice models with rich covariates

We introduce the BLP-2LASSO 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 using the 'double-LASSO' procedure proposed by Belloni, Chernozhukov, and Hansen (2013). Economists often study consumers’ aggregate behaviour across markets choosing from a menu of differentiated products. In this analysis, local demographic 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 propose a data-driven approach to estimate these models, applying penalized estimation algorithms from the recent literature in high-dimensional econometrics. Our application explores the effect of campaign spending on vote shares in data from Mexican elections