A Fundamentally Sensible Question

Awesomely attentive reader Deepti Goel writes:
I am enjoying your book ‘Mostly Harmless Econometrics’. Thanks for writing it.

I have a question pertaining to the FUQ you define in Chapter 1. I think I understand the problem. But may be I am missing something and you can help.

So we randomly select a group of kids to start later and we compare average test scores in grade 1 for both groups (the one that started at age 6 and the other at age 7). The problem as you state is that maturation effects are confounded with start age effects (M+S)

Now what if you supplemented this study by using a new group of children none of whom go to school. Administer the same exam to one half of them at age 6 and to the other half at age 7. The difference in average performance for this group will give maturation effect (M).

Subtract M from M+S to get S.
Does this make sense? I would appreciate your help in sorting this out.

Makes sense indeed, Deepti.

As long as kids are in school there is a linear dependence between current age, years of schooling, and starting age. So for kids in school there can only be two independent effects; hence no way to answer three causal questions.

As you suggest, however, adding kids not in school solves this problem (at least hypothetically).
Kids not in school isolate a pure age effect that you could then subtract from the combined starting age and age effects for the kids in school.  The FUQ’d nature of the question arises in studies that use data on kids still enrolled.

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