Bias Amplification: The Case of Fixed-Effects

• Activity Number: 691
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Joel Middleton* and Marc Scott and Jennifer Hill and Ronli A. Diakow
• Companies: UC Berkeley and New York University and New York University and New York University
• Keywords: bias amplification ; fixed effects ; omitted variables bias ; omitted confounder bias

Abstract

In non-experimental studies, conditioning on observable covariates is one way to try to reduce unobserved confounder bias. However, a developing literature has shown that there exist covariates which, when conditioned on, amplify bias due to unobservables. A special case of bias amplification, for example, occurs when conditioning on instruments. We describe this phenomenon in the context of a linear model. We then identify a new special case of bias amplification, in particular, when so-called fixed effects (indicators for groups) amplify bias. Bias can be amplified even when the fixed effects do not act as instruments and they absorb heterogeneity in (and are causally related to) the outcome. A method of visualizing the conditions under which fixed effects are bias amplifying is proposed and an expression for the bias is derived. Nonetheless, results suggest that researchers must bring substantive knowledge to bear when determining which covariates to include in a causal analysis. These results also suggest that advice that adding fixed effects ``might help but should not hurt" could be dangerous.