This paper considers (partial) identification of a variety of parameters, including counterfactual choice probabilities, in a general class of binary response models with possibly endogenous regressors. Importantly, our framework allows for nonseparable index functions with multi-dimensional latent variables, and does not require parametric distributional assumptions. We  demonstrate how various functional form, independence, and monotonicity assumptions can be imposed as constraints in our optimization procedure to tighten the identified set, and we show how these assumptions have meaningful interpretations in terms of restrictions on latent types. In the special case when the index function is linear in the latent variables, we leverage results in computational geometry to provide a tractable means of constructing the sharp set of constraints for our optimization problems . Finally, we apply our method to study the effects of health insurance on the decision to seek medical treatment.
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, and we show how these assumptions can be assigned meaningful interpretations in terms of restrictions on latent response types . Finally, we apply our method to study the effects of health insurance on the decision to seek medical treatment.
R
parameters, including counterfactual choice probabilities, in a general class of
counterfactual parameters in
R
Importantly, our
Our
A
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
R
have
can be assigned
R
types. In the special case when the index function is linear in the latent variables, we leverage results in computational geometry to provide a tractable means of constructing the sharp set of constraints for our optimization problems
response types