An instrumental-variables design relies on the idea of as-if random in yet another way. Consider the challenge of inferring the impact of a given independent variable on a particular dependent variable—where this inference is made more difficult, given the strong possibility that reciprocal causation or confounding may pose a problem for causal inference. The solution offered by the instrumental-variables design is to find an additional variable—an instrument—that is correlated with the independent variable but could not be influenced by the dependent variable or correlated with its other causes. Thus, units are assigned at random or as-if at random, not to the key independent variable of interest, but rather to this instrumental variable.

Recall, for instance, Angrist’s (1990 a) study of military conscription discussed in the Introduction. Eligibility for the Vietnam draft was randomly assigned to young men, via numbers from 1 to 366 that were matched to each potential draftee’s birth date; men with lottery numbers above a particular cutoff value were not subject to the draft. Comparing men with lottery numbers above and below the cutoff estimates the effect of draft eligibility. This is “intention-to-treat” analysis, as described in Box 4.1: males are compared according their draft eligibility status, regardless of whether they actually served in the military. Intention to treat is a key principle of natural-experimental analysis, and intention-to-treat analysis should usually be reported in write-ups of research results.