On a Class of Bias-Amplifying Variables that Endanger Effect Estimates
This work addresses a critical issue in causal inference for researchers and practitioners, highlighting risks in using instrumental variables, though it is incremental as it builds on prior discoveries.
The paper identifies a class of variables, including instrumental variables, that amplify confounding bias when conditioned on in causal effect estimation, and extends this analysis to non-linear models, showing that bias amplification persists but with limitations and potential new biases.
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: 1. the bias-amplifying potential of instrumental variables extends over to non-linear models, though not as sweepingly as in linear models; 2. in non-linear models, conditioning on instrumental variables may introduce new bias where none existed before; 3. in both linear and non-linear models, instrumental variables have no effect on selection-induced bias.