Testing and Identifying Substitution and Complementarity Patterns

Abstract: This paper studies semiparametric identification of substitution and complementarity patterns between two goods using a panel multinomial choice model with bundles. The model allows the two goods to be either substitutes or complements and admits heterogeneous complementarity through observed characteristics. I first provide testable implications for the complementarity relationship between goods. I then characterize the sharp identified set for the model parameters and provide sufficient conditions for point identification. The identification analysis accommodates endogenous covariates through flexible dependence structures between observed characteristics and fixed effects while placing no distributional assumptions on unobserved preference shocks. My method is shown to perform more robustly than the parametric method through Monte Carlo simulations. As an extension, I allow for unobserved heterogeneity in the complementarity, investigate scenarios involving more than two goods, and study a class of nonseparable utility functions.