Endogeneity

Endogeneity is a violation of the OLS assumptions in which an explanatory variable is correlated with the regression's error term, often through an omitted variable or reverse causality, biasing the estimated coefficients.

ByHoang TruongUpdated July 5, 2026

See it move

Loading infographic...

Training's true effect on productivity is 3, but ability, an omitted variable with a true effect of 5, is correlated with training at a slope of 0.4. A regression of productivity on training alone is expected to produce a coefficient of 3 + 5 × 0.4 = 5, overstating training's real effect by 2 full units.

Where it fits

SubjectData Analysis & StatisticsAdvancedTopicRegression Diagnostics & ProblemsAdvanced

The formula

LaTeX

E[\hat\beta_1] = \beta_1 + \beta_2 \delta_1

Variables

$\hat{β}_{1}$: Estimated coefficient on the included variable, subject to bias
$β_{1}$: True coefficient on the included variable
$β_{2}$: True coefficient on the omitted variable
$δ_{1}$: Slope from regressing the omitted variable on the included variable

Shows that an omitted variable biases the estimated coefficient whenever it affects the outcome (β2 ≠ 0) and is correlated with the included regressor (δ1 ≠ 0).