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

We derive several properties of commonly used discrete choice models that are potentially undesirable if these models are to be used as structural models of demand. Specifically, we show that as the number of goods in the market becomes large in these models, i) no product has a perfect substitute, ii) Bertrand-Nash markups do not converge to zero, iii) the fraction of utility derived from the observed product characteristics tends toward zero, iv) if an outside good is present, then the deterministic portion of utility from the inside goods must tend to negative infinity and v) there is always some consumer that is willing to pay an arbitrarily large sum for each good in the market. These results support further research on alternative demand models such as those of Berry and Pakes (2001), Ackerberg and Rysman (2001), or Bajari and Benkard (2003). ∗We thank Daniel Ackerberg, Steven Berry, Richard Blundell, Jonathon Levin, Peter Reiss, and Ed Vytlacil for many helpful comments on an earlier draft of this paper, as well as seminar participants at Carnegie Mellon, Northwestern, Stanford, UBC, UCL, UCLA, Wash. Univ. in St. Louis, Wisconsin, and Yale. We gratefully acknowledge financial support of NSF grant #SES-0112106. Any remaining errors are our own. †Dept. of Economics, Stanford University, Stanford, CA 94305, [email protected] ‡Graduate School of Business, Stanford University, Stanford, CA 94305-5015, [email protected]