The Empirical Content of Binary Choice Models

14 Pages Posted: 28 Apr 2017 Last revised: 24 Sep 2018

Date Written: August 1, 2018


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 preference-heterogeneity, a pair of simple Slutsky-like shape-restrictions on choice-probability functions is equivalent to rationalizability. These restrictions differ from Slutsky-inequalities for continuous goods. Unlike McFadden-Richter's stochastic revealed-preference conditions, our shape-restrictions are (a) global, i.e., do not depend on which budget-sets are observed in-sample, (b) closed-form, and hence easy to impose on parametric and semi/non-parametric models in practical applications, and (c) provide computationally simple, theory-consistent bounds on demand and welfare predictions on counterfactual budget-sets.

Keywords: Binary choice, general heterogeneity, income effect, utility maximization, integrability/rationalizability, Slutsky inequality, shape-restrictions

JEL Classification: C14, C25, D12.

Suggested Citation

Bhattacharya, Debopam, The Empirical Content of Binary Choice Models (August 1, 2018). Available at SSRN: or

Debopam Bhattacharya (Contact Author)

University of Cambridge ( email )

Sidgwick Site
Austin Robinson Building
Cambridge, CB3 9DD
United Kingdom

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