Identification of treatment effects with selective participation in a randomized trial

Randomized trials (RTs) are used to learn about treatment effects. This paper studies identification of average treatment response (ATR) and average treatment effect (ATE) from RT data under various assumptions. The focus is the problem of external validity of the RT. RT data need not point identify the ATR or ATE because of selective participation in the RT. The paper reports partial-identification and point-identification results for the ATR and ATE based on RT data under a variety of assumptions. The results include assumptions sufficient to point identify the ATR or ATE from RT data. Under weaker assumptions, the ATR or ATE is partially identified. Further, attention is given to identification of the sign of the ATE and identification of whether participation in the RT is selective. Finally, identification from RT data is compared to identification from observational data.