Inference on Semiparametric Multinomial Response Models

We explore inference on regression coefficients in semiparametric multinomial response models. We consider cross-sectional, and both static and dynamic panel settings where we focus throughout on inference under sufficient conditions for point identification. The approach to identification uses a matching insight throughout all three models and then relies on variation in regressors: with cross-section data, we match across individuals while with panel data, we match within individuals over time. Across models, IIA is not assumed as the unobserved errors across choices are allowed to be arbitrarily correlated. For the cross-sectional model, estimation is based on a localized rank objective function, analogous to that used in Abrevaya, Hausman, and Khan (2010), and presents a generalization of existing approaches. In panel data settings, rates of convergence are shown to exhibit a curse of dimensionality in the number of alternatives. The results for the dynamic panel data model generalizes the work of Honoré and Kyriazidou (2000) to cover the multinomial case. A simulation study establishes adequate finite sample properties of our new procedures. We apply our estimators to a scanner panel data set.