Semiparametric Estimation of a CES Demand System with Observed and Unobserved Product Characteristics

We develop a characteristics based demand estimation framework for the Marshallian demand system obtained by solving a budget-constrained constant elasticity of substitution (CES) utility maximization problem. From our Marshallian CES demand system, we derive the same market share equation of Berry (1994); Berry, Levinsohn, and Pakes (1995)'s characteristics based logit demand system. Our CES demand estimation framework can accommodate zero predicted and observed market shares by conceptually separating the whether-to-buy decision and how-much-to-buy decision. Furthermore, the estimator we suggest allows a tractable semiparametric estimation strategy that is flexible regarding the distribution of unobservable product characteristics. We apply our framework to scanner data on cola sales, where we show estimated demand curves can be upward sloping if zero market shares are not accommodated properly.