We study identification and estimation in a binary response model with random coefficients B allowed to be correlated with regressors X. Our objective is to identify the mean of the distribution of B and estimate a trimmed mean of this distribution. Like Imbens and Newey (2009), we use instruments Z and a control vector V to make X independent of B given V . A consequent conditional median restriction identifies the mean of B given V . Averaging over V identifies the mean of B. This leads to an analogous localize-then-average approach to estimation. We estimate conditional means with localized smooth maximum score estimators and average to obtain a Ín-consistent and asymptotically normal estimator of a trimmed mean of the distribution of B. The method can be adapted to models with nonrandom coefficients to produce Ín-consistent and asymptotically normal estimators under the conditional median restrictions. We explore small sample performance through simulations, and present an application.
Heterogeneity Correlated Random Coefficients Endogeneity Binary Response Model Instrumental Variables Control Variables Conditional Median Restrictions