Estimation of ordered response models with sample selection

We introduce two new Stata commands for the estimation of an ordered response model with sample selection. The opsel command uses a standard maximum likelihood (ML) approach to fit a parametric specification of the model where errors are assumed to follow a bivariate Gaussian distribution. The snpopsel command uses the semi-nonparametric (SNP) approach of Gallant and Nychka (1987) to fit a semiparametric specification of the model where the bivariate density function of the errors is approximated by a Hermite polynomial expansion. The snpopsel command extends the set of Stata routines for SNP estimation of discrete response models. Compared to the other SNP estimators, our routine is relatively faster because it is programmed in MATA. In addition, we provide new post-estimation routines to compute linear predictions, predicted probabilities and marginal effects. These improvements are also extended to the set of SNP Stata commands originally written by Stewart (2004) and De Luca (2008). An illustration of the new opsel and snpopsel commands is provided through an empirical application on self-reported health with selectivity due to sample attrition.