Using Observational Vs Randomized Controlled Trial Data to Learn about Treatment Effects

Randomized controlled trials (RCTs) are routinely used in medicine and are becoming more popular in economics. Data from RCTs are used to learn about treatment effects of interest. This paper studies what one can learn about the average treatment response (ATR) and average treatment effect (ATE) from RCT data under various assumptions and compares that to using observational data. We find that data from an RCT need not point identify the ATR or ATE because of selection into an RCT, as subjects are not randomly assigned from the population of interest to participate in the RCT. This problem relating to external validity is the primary problem we study. So, assuming internal validity of the RCT, we study the identified features of these treatment effects under a variety of weak assumptions such as: mean independence of response from participation, an instrumental variable assumption, or that there is a linear effect of participation on response. In particular we provide assumptions sufficient to point identify the ATR or the ATE from RCT data and also shed light on when the sign of the ATE can be identified. We then characterize assumptions under which RCT data provide more information than observational data.