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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-207/2/c/solution
Past exam of the mathematics course of the University of Cambridge 2021 iii Paper 207 2 c Solution by
Codex 0 2026-09-28
The core instrumental variable assumptions are:
- Instrument relevance: the genetic variant changes educational attainment.
- Instrumental-variable independence: it is independent of unmeasured common causes of education and myopia, after any justified ancestry adjustment.
- The exclusion restriction: it affects myopia only through education, with no horizontal pleiotropy.
For a local average effect one additionally uses instrumental-variable monotonicity. Because the valid instrument supplies variation in education independent of the confounders and has no direct route to the outcome, the instrument-outcome association can be attributed to the education changed by the instrument without measuring every confounder.
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