Semiparametric Discrete Choice Models For Bundles PDF Download

This paper develops a new computational method that generates all the conditional moment inequalities that characterize the identified set of the parametric components of several semi- parametric panel data models of discrete choice. I consider very flexible models that only impose weak distributional restrictions on the joint distribution of the covariates, fixed effects and shocks. By exploiting the discreteness and convexity of the problem, I show that the identified set of the parametric component of the model can be characterized from the extreme points of a polytope which I describe explicitly. A direct implication of this observation is that finding all the inequalities that characterize the sharp identified set can be viewed as a purely computational problem, and any algorithm that can retrieve all the extreme points of our polytopes recovers all the inequality restrictions that characterize the identified set. The determination of all the extreme points of a polytope is a computational difficult task, and I exploit the particular structure the polytopes that occur in discrete choice models to propose an algorithm that works well for problems of moderate size. The algorithm is used to re-derive many known results: The algorithm can, for instance, recover all the conditional moment inequalities that were found in Manski 1987, Pakes and Porter 2021 and Khan, Ponomareva, and Tamer 2021. I also use the algorithm to generate some new conditional moment inequalities under alternative distributional assumptions, as well to generate new inequalities in some cases that were left open in Pakes and Porter 2021 and Khan, Ponomareva, and Tamer 2021.