endogeneity

Endogeneity occurs when an explanatory variable is correlated with the error term in a statistical model, causing ordinary least squares estimates to be biased and inconsistent. This undermines causal interpretation and internal validity, making it difficult to draw reliable conclusions about the effect of the regressor on the outcome.

Common sources include omitted variable bias (unobserved factors affecting both regressor and outcome), measurement error in the regressor, simultaneity or reverse causation (the outcome influencing the regressor), and sample selection bias or dynamic panel biases. Endogeneity can arise in cross-sectional, time-series, and panel data across fields.

Consequences include biased estimated coefficients, inconsistent standard errors, and flawed policy or theory implications. Endogeneity is a central challenge in econometrics and causal inference, limiting the ability to infer causality from observational data.

Remedies typically involve using instrumental variables that are correlated with the endogenous regressor but uncorrelated with the error term, combined with methods such as two-stage least squares or generalized method of moments. Other approaches include fixed effects, difference-in-differences, control function approaches, or regression discontinuity designs when applicable. Instrument validity hinges on relevance (the instrument is correlated with the endogenous regressor) and the exclusion restriction (the instrument affects the outcome only through the regressor); weak instruments can worsen bias. Tests include the Durbin–Wu–Hausman test for endogeneity and Sargan or Hansen overidentification tests for instrument validity.

Examples: Education and earnings can be endogenous due to unobserved ability; instruments include proximity to colleges or policy changes that shift educational attainment. In microeconomics, simultaneity in supply and demand creates endogeneity for price and quantity.