The authors propose the sharp identifiable bounds of the potential outcome distributions using panel data. They allow for the possibility that statistical randomization of treatment assignments is not achieved until unobserved heterogeneity is properly controlled for. They use certain stationarity assumptions to obtain the sharp bounds. Their approach allows for dynamic treatment decisions, where the current treatment decisions may depend on the past treatments or the past observed outcomes.

As an empirical illustration, the authors study the effect of smoking during pregnancy on infant birthweight. They find that for the group of switchers the infant birthweight of a smoking mother is first-order stochastically dominated by that of a nonsmoking mother.