Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors

TL;DR

This paper develops a nonparametric method for partially identifying counterfactual parameters in binary response models with endogenous regressors, using computational geometry techniques to compute the identified set.

Contribution

It introduces a framework that handles nonseparable index functions with multi-dimensional latent variables without relying on parametric assumptions.

Findings

Provides a tractable computational approach for identified sets.

Shows how to incorporate assumptions to tighten identification.

Applies method to health insurance and medical treatment decision data.

Abstract

This paper considers (partial) identification of a variety of counterfactual parameters in binary response models with possibly endogenous regressors. Our framework allows for nonseparable index functions with multi-dimensional latent variables, and does not require parametric distributional assumptions. We leverage results on hyperplane arrangements and cell enumeration from the literature on computational geometry in order to provide a tractable means of computing the identified set. We demonstrate how various functional form, independence, and monotonicity assumptions can be imposed as constraints in our optimization procedure to tighten the identified set. Finally, we apply our method to study the effects of health insurance on the decision to seek medical treatment.