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

This note deals with a class of covariates that tends to amplify confounding bias in the analysis of causal effects. This class, recently discovered by Wooldridge (2009), includes instrumental variables and variables that have greater influence on treatment selection than on the outcome. We extend the results of Wooldridge by considering non-linear models and 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 selectioninduced bias.