Parallel Inverse Aggregate Demand Curves in Discrete Choice Models (WP-20-33)
Kory Kroft, René Leal Vizcaíno, Matthew Notowidigdo, and Ting Wang
This paper highlights a previously unnoticed property of commonly used discrete choice models, which is that they feature parallel demand curves. Specifically, the authors show that in random utility models, inverse aggregate demand curves shift in parallel with respect to variety if and only if the random utility shocks follow the Gumbel distribution. Using results from Extreme Value Theory, the authors provide conditions for other distributions to generate parallel demands asymptotically, as the number of varieties increase. They establish these results in the benchmark case of symmetric products, illustrate them using numerical simulations and show that they hold in extended versions of the model with correlated tastes and asymmetric products. Lastly, they provide a “proof of concept” of parallel demands as an economic tool by showing how to use parallel demands to identify the change in consumer surplus from an exogenous change in product variety.