Conditional Independance in Sample Selection Models

In this note, 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 independance 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.