Generalized Instrumental Inequalities: Complexity, Sharpness, Robustness

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Generalized instrumental inequalities extend Pearl’s IV tests to binary treatment with unrestricted (including continuous) outcome and instruments and claim a full class of observable constraints; derivations use Bayes decompositions, Fréchet (Frechet) bounds, and linear programming / inflation ideas. A sharpness proof appears for binary Y with continuous Z by constructing compatible latent models via optimal transport techniques; no proof yet for fully continuous Y. Simulations show using only some inequalities yields misleading nonempty bounds, so a minimal-relaxation procedure produces robust bounds that never become empty.

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" chapters (9)

1. 0:00Introduction and background
2. 1:05Instrumental variable model
3. 3:56Research objectives
4. 6:41Potential outcome framework
5. 12:39Deriving joint inequalities
6. 21:14Continuous vs discrete data
7. 26:03Model misspecification risks
8. 31:44Relaxing model assumptions
9. 38:57Discussion and Q&A