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. Although objects of interest may mostly depend on a few prices, many prices should be included to control for omitted variables bias. This paper uses Lasso to mitigate the curse of dimensionality in estimating the aver-age expenditure share from cross-section data. We estimate bounds on consumer surplus (BCS) using a novel double/debiased Lasso method. These bounds allow for general, multidimensional, nonseparable heterogeneity and solve the "zeros problem" of demand by including zeros in the estimation. We also use panel data to allow for prices paid to be correlated with preferences. We average ridge regression individual slope estimators and bias correct for the ridge regularization. We ?nd that panel estimates of price elasticities are much smaller than cross section elasticities in the scanner data we consider. Thus, it is very important to allow correlation of prices and preferences to correctly estimate elasticities. We ?nd less sensitivity of consumer surplus bounds to this correlation.