Identification and estimation in a correlated random coefficients binary response model

We study a linear index binary response model with random coefficients B allowed to be correlated with regressors X. We identify the mean of the distribution of B and show how the mean can be interpreted as a vector of expected relative effects. We use instruments and a control vector V to make X independent of B given V. This leads to a localize-then-average approach to both identification and estimation. We develop a -consistent and asymptotically normal estimator of a trimmed mean of the distribution of B, explore its small sample performance through simulations, and present an application.