A regression finds that companies with more employee training hours have higher productivity, with a statistically significant, precisely estimated coefficient. If a third factor — say, overall management quality — independently drives both training investment and productivity, and management quality isn't included in the model, the training coefficient is biased: it's capturing part of management quality's effect, mistakenly attributed to training itself. This is endogeneity, specifically omitted variable bias, and it's one of the more consequential and easy-to-overlook problems in applied regression analysis.
What endogeneity technically describes
A regression's independent variable is endogenous when it's correlated with the model's error term — the part of the outcome not explained by the included variables — which violates a core assumption required for the estimated coefficient to represent the variable's true causal effect. Omitted variable bias is the most common practical source: when a variable that genuinely affects the outcome is left out of the model, and that omitted variable happens to be correlated with an included variable, the included variable's estimated coefficient absorbs some of the omitted variable's real effect, in a specific, mathematically predictable direction.
Why the direction and size of the bias are actually predictable
The bias's direction depends on the sign of the omitted variable's relationship with both the included variable and the outcome — if the omitted variable positively affects both, the included variable's coefficient will typically be biased upward, overstating its true effect; if the relationships run in opposite directions, the bias runs the other way. This predictability is useful diagnostically: a researcher aware of a plausible omitted confounder can often reason about which direction their reported coefficient is likely biased in, even without being able to fully correct for it.
Why more data doesn't solve this problem
A larger sample size reduces random sampling error, producing a more precisely estimated coefficient — it does nothing to correct systematic bias from an omitted variable, since the bias comes from the model's structure, not from insufficient data. A regression run on ten million observations, omitting a genuine confounder, will produce an extremely precise, tightly estimated, and still systematically biased coefficient — arguably a worse outcome than a noisier estimate, since the false precision can create unwarranted confidence in a fundamentally biased result.
What actually addresses endogeneity
Including plausible confounding variables directly in the model, where they can be measured, is the most direct fix, though it requires the researcher to actually identify and have data for the relevant confounders, which isn't always feasible. Instrumental variables methods, natural experiments, and other quasi-experimental designs are specifically built to address situations where a key confounder can't be directly measured or included, by finding some other source of variation in the independent variable that isn't itself correlated with the omitted confounder.
What this means for interpreting regression results
- Ask explicitly what plausible confounding variables might influence both the independent variable and the outcome, and whether they're included in the model
- Treat a highly precise but potentially confounded coefficient with real skepticism — precision and lack of bias are separate properties
- Consider the likely direction of omitted variable bias explicitly when a known but unmeasured confounder is plausible
- Look for a genuine identification strategy (instrumental variables, natural experiments, or similar) when causal interpretation matters and full confounder measurement isn't feasible
A regression coefficient's statistical significance and precision say nothing about whether the underlying model is free of confounding — endogeneity is a structural property of the model's specification, and no amount of additional data can substitute for actually addressing it.