Regressions can be weighted by propensity scores in order to reduce bias. However, weighting is likely to increase random error in the estimates, and to bias the estimated standard errors downward, even when selection mechanisms are well understood. Moreover, in some cases, weighting will increase the bias in estimated causal parameters. If…

D. B. Rubin's model for causal inference in experiments and observational studies is enlarged to analyze the problem of "causes causing causes" and is compared to path analysis and recursive structural equations models. A special quasiexperimental design, the encouragement design, is used to give concreteness to the discussion by…