Test of Choice Set Misspecification for Discrete Models of Consumer Choice

We develop and evaluate a test of choice set misspecification for a multinomial logit choice model. This test determines whether the choice set designated by the researcher mistakenly assigns relevant substitutes to the numeraire good. We develop this test by generalizing the traditional McFadden-type conditional logit model to evaluate whether the traditional model is conditioned on an overly restrictive set of substitution possibilities. The test has a convenient feature: while it requires information on potentially relevant, but omitted, substitute goods, it does not require the researcher to observe consumers choices among these omitted potential substitutes if they select the numeraire good (which contains these omitted substitutes). A comparison of the traditional multinomial logit choice model and our more general model suggests that choice set misspecification may produce biased parameters that distort welfare estimates to a consequential extent.