by Analytical strategies in mediation analysis Case 3: Does cognitive skill (M) mediate the relation between college attendance (Z) and earnings (Y)? Case 3 involves one causal variable — college attendance — and two outcomes — one proximal (cognitive skill) and the other distal (earnings). College attendance is causal because a person may or may not go to college. Cognitive skill is not causal because one cannot be assigned or choose to have high skill; it is instead a “surrogate marker” for earnings. If prior research indicates that cognitive skill (which can be measured early) is a good predictor of later earnings, we may infer the impact of college attendance on earnings even before participants are old enough to work. Case 3 poses a tough inferential
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Analytical strategies in mediation analysis
Case 3: Does cognitive skill (M) mediate the relation between college attendance (Z) and earnings (Y)? Case 3 involves one causal variable — college attendance — and two outcomes — one proximal (cognitive skill) and the other distal (earnings). College attendance is causal because a person may or may not go to college. Cognitive skill is not causal because one cannot be assigned or choose to have high skill; it is instead a “surrogate marker” for earnings. If prior research indicates that cognitive skill (which can be measured early) is a good predictor of later earnings, we may infer the impact of college attendance on earnings even before participants are old enough to work.
Case 3 poses a tough inferential problem even though it entails only one causal variable. To say that cognitive skill accounts for the impact of college attendance on earnings is to dismiss the possibility that college attendance can have a large effect on earnings even for people whose cognitive skill is unaffected by college attendance.
This idea cannot be tested via regression but can be tested through principal stratification … We might classify participants into three principal strata — one for those whose cognitive skill would increase a great deal if they attend college, a second for those whose skill would not increase much even as a result of attending college, and a third for those whose skill would increase even without attending college. If we find that college attendance strongly increases the earnings of persons in the second and third strata, that evidence will falsify the claim that college attendance improves earnings solely by increasing cognitive skill.
But unless we have a crystal ball, we can’t know a priori which stratum to put a person in. Nevertheless, by collecting pretreatment variables that predict college attendance and cognitive skill, we may be able to identify causal effects within each stratum … This approach does not constitute a full mediation analysis, but it does put some strong claims of mediation to an important test.