Discrete Choice Models as Structural Models of Demand: Some Economic Implications of Common Approaches

We derive some theoretical economic properties of standard discrete choice econo-metric models that we believe are undesirable if the models are to be used as structural models of demand. We show that many standard models have the following properties: as the number of products increases, the compensating variation for removing all of the inside goods tends to infinity, all firms in a Bertrand?Nash pricing game have markups that are bounded away from zero, and for each good there is always some consumer that is willing to pay an arbitrarily large sum for the good. These undesirable properties may lead to incorrect conclusions about many policies of interest, including calculation of price indexes, the benefits of new goods, and the welfare loss due to mergers. We demonstrate that these undesirable properties hold not only in the logit model, but also in all random utility models with the following three general properties: 1) the model includes an additive error term whose conditional support is unbounded, 2) the deterministic part of the utility function satisfies standard continuity and monotonicity conditions, and 3) the hazard rate of the error distribution is bounded above. One approach to avoiding these undesirable properties is to weaken these three restrictions. However, we also show that random utility models are not in general non?parametrically identified from market shares or individual level choice data. Our findings support the use of alternative structural approaches that have better economic properties, such as those of Bajari and Benkard (2001) and Berry and Pakes (2000).