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 a 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. 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.