Conditional Independence in Sample Selection Models

Econometric sample selection models typically use a linear latent-index with constant coefficients to model the selection prodcess and the conditional mean of the regression error in the selected sample. A feature common to most of these models is that the conditional mean function for regression errors is an invertible function of the selection propensity score, i.e., the probability of selection conditional on covariates. Consequently, conditioning on the selection propensity score controls selection bias, a fact which underlies much of the recent literature on non-parametric and semi-parametric selection models. This literature has not addressed the question of whether the propensity-score conditioning property is necessarily a feature of sample selection models. In this paper, I describe the conditional independence properties that make it possible to use the selection propensity score to control selection bias in a general sample selection model. The resulting characterization does not rely on a latent index selection mechanism and imposes no structure other than an assumption of independence between the regression error term and the regressors in random samples. This approach leads to a simple rule that can be used to determine if conditioning on the selection propensity score is sufficient to control selection bias