Causal inference from indirect experiments

An indirect experiment is a study in which randomized control is replaced by randomized encouragement, that is, subjects are encouraged, rather than forced, to receive a given treatment program. The purpose of this paper 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 of the encouraging instrument, data from indirect experimentation can yield significant and sometimes accurate information on the impact of a program on the population as a whole, as well as on the particular individuals who participated in the program.