Ulric B. and Evelyn L. Bray Social Sciences Seminar

Abstract: From its inception, demand estimation has faced the problem of "many prices." While some aggregation across goods is always necessary, the problem of many prices remains even after aggregation. Economic theory shows that often the policy question of interest depends on only one, or a very few, price effects. For example, estimation of consumer surplus typically depends only on the own price effect since all other prices are held constant. Another common feature of data is that cross-price effects tend to be small. This paper uses Lasso to mitigate the curse of dimensionality in estimating the average expenditure share when cross-price effects are small. We estimate bounds on consumer surplus (BCS) using a novel double/debiased Lasso method. These bounds allow for multidimensional, nonseparable heterogeneity and thus solve the "zeros problem" of demand by including zeros in the estimation. We use a control function to correct for endogeneity of total expenditure. As an additional contribution we use panel data to control for endogeneity of prices as well as expenditure. We average regularized individual slope estimators and bias correct for the regularization. We compare these methods in estimating the welfare effects of a tax on soda using scanner data.