Latent Variable Justifies the Stronger IV Bounds
Talkat Quantum Physics and Statistical Causal Models (Simons Institute workshop, 2022) · 2022-04-27..04-29
summary
Shows that the Balke–Pearl “sharp” IV bounds follow from the existence of a latent confounder plus stochastic exclusion, not cross-world individal exclusion; derives a set of CHSH-type inequalities from a SWIG and uses a linear program projection to prove the stronger bounds are attainable. The procedure returns exactly Balke–Pearl’s eight-and-eight linear terms, produces a polytope with 28 half-spaces (16 involving the ATE), and removing CHSH collapses to Robins–Manski.
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chapters (10)
- 0:00Introduction to study
- 1:04Model assumptions and bounds
- 5:40Weakened model assumptions
- 9:55Comparing identification bounds
- 12:21Latent variable formulations
- 16:52Connecting CHSH to causality
- 21:04Proving the bridge
- 26:05Linear programming application
- 32:52Statistical inference strategy
- 35:26Discussion and conclusion