Instrumental Variable Analysis Without Structural Equations
Zikai Shen, Dimitri Meunier, Houssam Zenati, Arthur Gretton, Nathan Kallus, Aurélien Bibaut
Abstract
We consider debiased inference on least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not innocuous and their failure may well imperil inference when we impose them on the statistical model. Our approach instead allows us to conduct inference on a quantity that is defined regardless of solutions existing and coincides with the usual estimands when they do. For the case of instrumental variables, this means we can motivate the analysis with structural models but these do not need to hold exactly for the inferential procedure to remain valid.
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Classified with taxonomy v2 on Wed, 2 Sept 2026.