The Empirical Content of Binary Choice Models

Empirical demand models used for counterfactual predictions and welfare analysis must be rationalizable, i.e. theoretically consistent with utility maximization by heterogeneous consumers. We show that for binary choice under general unobserved heterogeneity, rationalizability is equivalent to a pair of Slutsky-like shape-restrictions on choice-probability functions. The forms of these restrictions differ from Slutsky-inequalities for continuous goods. Unlike McFadden-Richter's stochastic revealed preference, our shape-restrictions (a) are global, i.e. their forms do not depend on which and how many budget-sets are observed, (b) are closed-form, hence easy to impose on parametric/semi/non-parametric models in practical applications, and (c) provide computationally simple, theory-consistent bounds on demand and welfare predictions on counterfactual budget-sets.