Nonparametric Estimation of Price Elasticities: A Heterogeneous Treatment Effect Approach

Abstract

We revisit the classical problem of price elasticity estimation from a causal perspective. When the price is perceived as a continuous but endogenous treatment, the flexible estimation of price elasticity can be turned into the estimation of heterogeneous treatment effects. To this end, we develop a control function approach to deal with treatment endogeneity when estimating heterogeneous treatment effects. This strategy works by breaking the estimation of price elasticity into several intermediate problems of point-wise expectation estimation, where modern machine learning methods, such as deep neural networks and random forests, can be used for prediction. In addition, we prove that if we use the bagged nearest neighbors for point-wise prediction, the standard bootstrap procedure can be directly employed to derive inference for the price elasticity estimates. Finally, we apply our method to the IRI academic dataset on two national brands of yogurt. It is found that the competitor's yogurt in a similar size is more a substitute compared to the own brand's yogurt in a different size.