Causal Inference from Indirect Experiments

J. Pearl

Standard experimental studies in the biological, medical, and behavioral sciences invariably invoke the instrument of randomized control, that is, subjects are assigned at random to various groups (Mso called "treatments" or "programs") and the mean differences between participants in different groups are taken as measures of the efficacies of the associated programs. Indirect experiments are studies in which randomized control is either infeasible 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 attention of experimental researchers simple mathematical results 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 experimentation can yield significant and sometimes accurate information on the impact of a treatment on the population as a whole, as well as on the treated subjects in particular.

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