Abstract: Because of population heterogeneity, causal inference with
observational data in social science may suffer from two possible sources of
bias: (1) bias in unobserved pretreatment factors affecting the outcome even
without treatment; and (2)bias due to heterogeneity in treatment effects. Even
when we control for observed covariates, these two biases may occur if the
classic ignorability assumption is untrue. In cases where the ignorability
assumption is true, "composition bias" can occur if treatment propensity is
systematically associated with heterogeneous treatment effects.