Semiparametric Identification and Estimation of Multinomial Discrete Choice Models using Error Symmetry

We provide a new method to point identify and estimate cross-sectional multinomial choice models, using conditional error symmetry. Our model nests common random coefficient specifications (without having to specify which regressors have random coefficients), and more generally allows for arbitrary heteroskedasticity on most regressors, unknown error distribution, and does not require a "large support" "(such as identification at infinity) assumption. We propose an estimator that minimizes the squared di§erences of the estimated error density at pairs of symmetric points about the origin. Our estimator is root N consistent and asymptotically normal, making statistical inference straightforward.