SNP and SML estimation of univariate and bivariate binary–choice models

Abstract

We discuss the semi-nonparametric approach of Gallant and Nychka (1987, Econometrica 55: 363–390), the semiparametric maximum likelihood approach of Klein and Spady (1993, Econometrica 61: 387–421), and a set of new Stata commands for semiparametric estimation of three binary-choice models. The first is a univariate model, while the second and the third are bivariate models without and with sample selection, respectively. The proposed estimators are root-n consistent and asymptotically normal for the model parameters of interest under weak assumptions on the distribution of the underlying error terms. Our Monte Carlo simulations suggest that the efficiency losses of the semi-nonparametric and the semiparametric maximum likelihood estimators relative to a maximum likelihood correctly specified estimator of a parametric probit are rather small. On the other hand, a comparison of these estimators in non-Gaussian designs suggests that semi-nonparametric and semiparametric maximum likelihood estimators substantially dominate the parametric probit maximum likelihood estimator.