Instrumental Variable Analysis Without Structural Equations
Zikai Shen, Dimitri Meunier, Houssam Zenati, Arthur Gretton, Nathan Kallus + 1 more
TLDR
This paper proposes a debiased inference method for instrumental variable analysis that does not require exact structural equations to exist.
Key contributions
- Proposes debiased inference for least-squares solutions to inverse problems.
- Eliminates the need to assume exact solutions exist, a common and strong assumption.
- Enables valid inference on a quantity defined regardless of solution existence.
- Applies to instrumental variables, making analysis robust to inexact structural models.
Why it matters
Current instrumental variable methods often assume exact structural models, which can lead to invalid inference. This paper offers a debiased inference approach that remains valid even when these strong assumptions don't hold, improving the robustness and reliability of IV analysis.
Original 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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