Bad control

In statistics, bad controls are variables that introduce an unintended discrepancy between regression coefficients and the effects that said coefficients are supposed to measure.

These are contrasted with confounders which are "good controls" and need to be included to remove omitted variable bias.

[1][2][3] This issue arises when a bad control is an outcome variable (or similar to) in a causal model and thus adjusting for it would eliminate part of the desired causal path.

In other words, bad controls might as well be dependent variables in the model under consideration.

[3] Angrist and Pischke (2008) additionally differentiate two types of bad controls: a simple bad-control scenario and proxy-control scenario where the included variable partially controls for omitted factors but is partially affected by the variable of interest.

[4] A simplified example studies effect of education on wages

When considering the causal effect of education on wages of an individual, it might be tempting to control for the work-type

(thought of as for example IQ at pre-school age) is a variable influencing wages

Instead they choose before-work IQ test scores

Unfortunately, late ability (in this thought experiment) is causally determined by education and innate ability and, by controlling for it, researchers introduced collider bias into their model by opening a back-door path

causal diagram of education, work type and wages variables
Causal diagram showing a type of bad control. If we control for work type when performing regression from education to wages we have disrupted a causal path and such a regression coefficient does not have a causal interpretation.
causal diagram of education, innate ability, late ability and wages
Causal diagram showing bad proxy-control. If we control for late ability when performing regression from education to wages we have introduced a new non-causal path and thus a collider bias.