On a Class of Bias-Amplifying Variables that Endanger Effect Estimates

Judea Pearl
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:424-431, 2010.

Abstract

This note deals with a class of variables that, if conditioned on, tends to amplify confounding bias in the analysis of causal effects. This class, independently discovered by Bhattacharya and Vogt (2007) and Wooldridge (2009), includes instrumental variables and variables that have greater influence on treatment selection than on the outcome. We offer a simple derivation and an intuitive explanation of this phenomenon and then extend the analysis to non linear models. We show that:

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-pearl10b, title = {On a Class of Bias-Amplifying Variables that Endanger Effect Estimates}, author = {Pearl, Judea}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {424--431}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/pearl10b/pearl10b.pdf}, url = {https://proceedings.mlr.press/r8/pearl10b.html}, abstract = {This note deals with a class of variables that, if conditioned on, tends to amplify confounding bias in the analysis of causal effects. This class, independently discovered by Bhattacharya and Vogt (2007) and Wooldridge (2009), includes instrumental variables and variables that have greater influence on treatment selection than on the outcome. We offer a simple derivation and an intuitive explanation of this phenomenon and then extend the analysis to non linear models. We show that:}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T On a Class of Bias-Amplifying Variables that Endanger Effect Estimates %A Judea Pearl %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-pearl10b %I PMLR %P 424--431 %U https://proceedings.mlr.press/r8/pearl10b.html %V R8 %X This note deals with a class of variables that, if conditioned on, tends to amplify confounding bias in the analysis of causal effects. This class, independently discovered by Bhattacharya and Vogt (2007) and Wooldridge (2009), includes instrumental variables and variables that have greater influence on treatment selection than on the outcome. We offer a simple derivation and an intuitive explanation of this phenomenon and then extend the analysis to non linear models. We show that: %Z Reissued by PMLR on 04 October 2026.
APA
Pearl, J.. (2010). On a Class of Bias-Amplifying Variables that Endanger Effect Estimates. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:424-431 Available from https://proceedings.mlr.press/r8/pearl10b.html. Reissued by PMLR on 04 October 2026.

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