Omitted budget constraint bias in discrete-choice demand models

A large body of discrete-choice demand studies estimate a demand model in which the consumer’s budget constraint is not taken into account. We illustrate how incorrectly specifying the consideration set, when in fact the budget constraint binds for some products, may bias the demand estimates. We illustrate and quantify the nature of the bias in three ways: (i) in analytical examples; (ii) in field data commonly used in the literature and (iii) in a Monte Carlo study. We find that the price sensitivity can be substantially lower when correctly imposing the budget constraint, and own-price elasticities are typically overestimated although the direction of the own-price elasticity bias is in general ambiguous and depends on the income distribution.