Moment inequalities for multinomial choice with fixed effects

This paper proposes a new approach to identification of the semiparametric multinomial choice model with fixed effects. The framework employed is the semiparametric version of the traditional multinomial logit with the fixed-effects model (Chamberlain (1980)). This semiparametric multinomial choice model places no restrictions on either the joint distribution of the random utility disturbances across choices or their within group (or across time) correlations. We show that a novel within-group comparison leads to a set of conditional moment inequalities. Our main finding shows that the derived conditional moment inequalities yield the sharp identified set for the random utility covariate index, while avoiding the incidental parameter problem. Specializing this result to the binary choice case shows that Manski (1987)'s conditional moment inequalities still lead to sharp bounds without restrictions on covariates.