Indirect experiments are studies in which randomized control is replaced by randomized encouragement, that is, subjects are encouraged, rather than forced to receive treatment programs. 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, 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. Keywords: Causal reasoning, treatment evaluation, noncompliance, graphical models 1 Introduction 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 va...

Introduction It is common in the literature on instrumental variables to remark upon the difficulty of knowing or demonstrating that a potential instrument is exogenous, in the sense of being uncorrelated with the disturbances [Bartels, 1991, Johnston, 1972]. It is also widely recognized that exogeneity is an assumption embedded in the model specification [Engle, et al, 1984], hence, it rests on subjective judgment and, like other structural assumptions of causation and "zero-restrictions", it cannot be tested in purely observational studies. The purpose of this note is to show that despite its elusive nature, exogeneity can nevertheless be given some empirical test. The test is not guaranteed to detect all violations of exogeneity but it can, in certain circumstances, screen away real bad choices of would-be instruments. 2 An Instrumental Inequality Definition 2.1 (exogeneity) A variable z is said to be exogenous relative to an ordered