Estimation of Semiparametric Models in the Presence of Endogeneity and Sample Selection

We analyze a semiparametric model for data that suffer from the problems of incidental truncation, where some of the data are observed for only part of the sample with a probability that depends on a selection equation, and of endogeneity, where a covariate is correlated with the disturbance term. The introduction of nonparametric functions in the model permits significant flexibility in the way covariates affect response variables. We present an efficient Bayesian method for the analysis of such models that allows us to consider general systems of outcome variables and endogenous regressors that are continuous, binary, censored, or ordered. Estimation is computationally inexpensive as it does not require data augmentation for the missing outcomes, thus reducing computational demands and enhancing the mixing of the Markov chain Monte Carlo simulation algorithm. The methods are applied in a model of women's labor force participation and log-wage determination that accounts for endogeneity, incidental truncation, and non-linear covariate effects.