A specification test for discrete choice models

• We propose a simple nonparametric specification test of discrete choice models.
• This test compares market shares as choice sets vary.
• We use multiple testing to explore reasons for rejection.

In standard discrete choice models, adding options cannot increase the choice probability of an existing alternative. We use this observation to construct a simple nonparametric specification test by exploiting variation in the choice sets individuals face. We use a multiple testing procedure to determine the particular kind of choice sets that produce violations. We apply these tests to the 1896 US House of Representatives election and reject commonly used discrete choice voting models.