Distribution-Free Estimation of Heteroskedastic Binary Response Models in Stata

This talk demonstrates how to implement two recent semiparametric estimators for binary response models in Stata. These estimators do not require parametric assumptions on the distribution of the error term, as do the logit and probit models, and they allow for general forms of heteroskedasticity. We begin with a short introduction to binary response models and the various known identifying assumptions, including the weak conditional median independence assumption that the two estimators of interest are based on. Then we focus on two recently proposed semiparametric estimators: a sieve nonlinear least squares estimator and a local nonlinear least squares estimator. We demonstrate how both estimators can be easily implemented in Stata via simple modifications to the standard probit objective function and give several applied examples and Monte Carlo results. Finally, we introduce the dfbr package by Blevins and Khan (2013, Stata Journal, st0310) for distribution-free estimation of binary response models. Although the estimators can be implemented by hand using standard Stata commands, this package provides a standard Stata interface for the user, automates constructing the modified probit objective functions, and calculates bootstrap standard errors.