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

We discuss the semi-nonparametric approach of Gallant and Nychka(1987, Econometrica 55: 363–390), the semiparametric maximum likelihood approachof Klein and Spady (1993, Econometrica 61: 387–421), and a set of newStata commands for semiparametric estimation of three binary-choice models. Thefirst is a univariate model, while the second and the third are bivariate modelswithout and with sample selection, respectively. The proposed estimators are root-nconsistent and asymptotically normal for the model parameters of interest underweak assumptions on the distribution of the underlying error terms. Our MonteCarlo simulations suggest that the efficiency losses of the semi-nonparametric andthe semiparametric maximum likelihood estimators relative to a maximum likelihoodcorrectly specified estimator of a parametric probit are rather small. Onthe other hand, a comparison of these estimators in non-Gaussian designs suggeststhat semi-nonparametric and semiparametric maximum likelihood estimators substantiallydominate the parametric probit maximum likelihood estimator.