How does omitted variable bias distort regression results?

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AcadiFi · Accepted Answer

Omitted variable bias (OVB) arises when a relevant explanatory variable is left out of a regression and that variable is correlated with included regressors. The estimated coefficients become biased because the omitted variable's effect gets 'absorbed' into the included ones. Formula: bias on β1 = β2_true × (correlation of X2 with X1 / variance ratio). Example: Harbor Quant regresses US equity excess returns on market beta alone and finds a flat or negative slope — seeming to contradict CAPM. But they've omitted size and value factors. Small-cap value stocks tend to have HIGH returns and LOW betas; large-cap growth stocks have moderate returns and HIGH betas. So when you regress returns on beta without controlling for size/value, high-beta growth underperforms and low-beta value outperforms — creating an apparent 'anomaly' that's partly OVB. Adding SMB and HML changes beta's coefficient sign and magnitude. Practical CFA takeaway: if two economically meaningful variables are correlated, omitting one can reverse the sign of the other. This is why researchers run 'kitchen sink' robustness regressions and why R² increases matter less than coefficient stability.

How does omitted variable bias distort regression results?

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