Exploiting Independent Instruments: Identification and Distribution
Generalization
- URL: http://arxiv.org/abs/2202.01864v1
- Date: Thu, 3 Feb 2022 21:49:04 GMT
- Title: Exploiting Independent Instruments: Identification and Distribution
Generalization
- Authors: Sorawit Saengkyongam, Leonard Henckel, Niklas Pfister, and Jonas
Peters
- Abstract summary: We exploit the independence for distribution generalization by taking into account higher moments.
We prove that the proposed estimator is invariant to distributional shifts on the instruments.
These results hold even in the under-identified case where the instruments are not sufficiently rich to identify the causal function.
- Score: 3.701112941066256
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Instrumental variable models allow us to identify a causal function between
covariates X and a response Y, even in the presence of unobserved confounding.
Most of the existing estimators assume that the error term in the response Y
and the hidden confounders are uncorrelated with the instruments Z. This is
often motivated by a graphical separation, an argument that also justifies
independence. Posing an independence condition, however, leads to strictly
stronger identifiability results. We connect to existing literature in
econometrics and provide a practical method for exploiting independence that
can be combined with any gradient-based learning procedure. We see that even in
identifiable settings, taking into account higher moments may yield better
finite sample results. Furthermore, we exploit the independence for
distribution generalization. We prove that the proposed estimator is invariant
to distributional shifts on the instruments and worst-case optimal whenever
these shifts are sufficiently strong. These results hold even in the
under-identified case where the instruments are not sufficiently rich to
identify the causal function.
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