Semiparametric Identification and Estimation of Substitution Patterns

Abstract

This paper studies semiparametric identification of substitution patterns between two goods using a panel multinomial choice model with bundles. My model allows the two goods to be either substitutes or complements and admits heterogeneous complementarity through observed characteristics. I characterize the sharp identified set for the model parameters and provide sufficient conditions for point identification. My identification analysis accommodates endogenous covariates through flexible dependence structures between observed characteristics and fixed effects while placing no distributional assumptions on unobserved preference shocks. I propose a two-step consistent estimator of the identified set, which through Monte Carlo simulations is shown to perform more robustly than a parametric estimator. As an empirical illustration, I apply my method to estimate substitution patterns between cigarettes and e-cigarettes using the Nielsen data.