Causal Inference from Indirect Experiments Judea Pearl

Standard experimental studies in the biological, med-ical, and behavioral sciences invariably invoke the instru-ment of randomized control, that is, subjects are assigned at random to various groups (Mso called "treatments " or "programs") and the mean differences between partici-pants in different groups are taken as measures of the ef-ficacies of the associated programs. Indirect experiments are studies in which randomized control is either infea-sible or undesirable, and randomized encouragement is instituted instead, that is, subject are still assigned at random to various groups, but members of each group are encouraged, rather than forced to receive the program associated with the group, leaving final selection among programs to individual choice. The purpose of this note is to bring to the atten-tion of experimental researchers simple mathematical re-sults that enable us to assess, from indirect experiments, the strength with which causal influences operate among variables of interest. The results reveal that despite the laxity in the encouraging instrument, indirect experimen-tation can yield significant and sometimes accurate infor-mation on the impact of a treatment on the population as a whole, as well as on the treated subjects in particular.