Moment Inequalities for Multinomial Choice with Fixed Effects

We propose a new approach to the semiparametric analysis of multinomial choice models with fixed effects and a group (or panel) structure. A traditional random utility framework is employed, and the key assumption is a group homogeneity condition on the disturbances. This assumption places no restrictions on either the joint distribution of the disturbances across choices or their within group (or across time) correlations. This work follows a substantial nonlinear panel literature (Manski 1987, Honore 1992, Abrevaya 1999, 2000) with the distinction that multiple covariate index functions now determine the outcome. A novel within-group comparison leads to a set of conditional moment inequalities that provide partial identifying information about the parameters of the observed covariate index functions, while avoiding the incidental parameter problem. We extend our framework to allow for: certain types of endogenous regressors (including lagged dependent variables and conditional heteroskedasticity), set-valued covariates, and parametric distributional information on disturbances.