Parametric and semiparametric estimation of ordered response models with sample selection and individual-specific thresholds

This paper provides a set of new Stata commands for parametric and semiparametric estimation of an extended version of ordered response models that accounts for both sample selection problems and heterogeneity in the thresholds for the latent variable. The standard estimator of ordered response models is therefore generalized along three directions. First, we account for the presence of endogenous selectivity effects that may lead to inconsistent estimates of the model parameters. Second, we control for both observed and unobserved heterogeneity in response scales by allowing the thresholds to depend on a set of covariates and a random individual effect. Finally, we consider two alternative specifications of the model, one parametric and one semiparametric. In the former, the error terms are assumed to follow a multivariate Gaussian distribution and the model parameters are estimated via maximum likelihood. In the latter, the distribution function of the error terms is instead approximated by following Gallant and Nychka (1997), and the model parameters are estimated via pseudo–maximum likelihood. After discussing identification and estimation issues, we present an empirical application using the second wave of the Survey on Health, Ageing and Retirement in Europe (SHARE). Specifically, we estimate an ordered response model for self-reported health on different domains by accounting for both sample selection bias due to survey nonresponse and reporting bias in the self-assessments of health.