# The Empirical Content of Binary Choice Models

## TL;DR

This paper establishes nonparametric shape-restrictions for binary choice models based on economic rationality, enabling credible demand and welfare predictions without arbitrary assumptions.

## Contribution

It introduces global, closed-form shape-restrictions for binary choice probabilities derived from utility maximization, applicable across various models and data sets.

## Key findings

- Shape-restrictions are equivalent to Slutsky-like conditions under heterogeneity.
- Restrictions are global, not dependent on observed budget-sets.
- Provide simple bounds for demand and welfare predictions.

## Abstract

An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy-interventions. Such predictions are more credible when made without arbitrary functional-form/distributional assumptions, and instead based solely on economic rationality, i.e. that choice is consistent with utility maximization by a heterogeneous population. This paper investigates nonparametric economic rationality in the empirically important context of binary choice. We show that under general unobserved heterogeneity, economic rationality 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.