Summary Omitted Variable Bias (OVB) Explained - Complete Mini-Guide

⚠ OMITTED VARIABLE BIAS (OVB) EXPLAINED

ECON2061 Econometrics | Complete Mini-Guide


1. What is Omitted Variable Bias?
OVB occurs when you leave out a relevant variable from your regression, causing your coefficient estimates to be biased and inconsistent.



True Model: Y = β₀ + β₁X₁ + β₂X₂ + u


Estimated Model: Y = β₀ + β₁X₁ + u* (X₂ omitted)


Result: β̂₁ is BIASED if X₂ is correlated with X₁



2. Two Conditions for OVB
BOTH conditions must be met for OVB to exist:


CONDITION 1: The omitted variable affects Y
β₂ ≠ 0 (X₂ belongs in the regression)



CONDITION 2: The omitted variable is correlated with X₁
Corr(X₁, X₂) ≠ 0




Key Rule: If either condition is NOT met, there is NO OVB.
• If X₂ doesn't affect Y → No OVB
• If X₂ is uncorrelated with X₁ → No OVB




3. The OVB Formula


OVB Formula:


β̂₁ →ᵖ β₁ + β₂ × [Cov(X₁, X₂) / Var(X₁)]


Bias = β₂ × δ
(where δ = coefficient from regressing X₂ on X₁)



4. Determining Bias Direction

The direction of bias depends on TWO things:



BIAS DIRECTION = Sign(Correlation) × Sign(Effect)




Corr(X₁, X₂) Effect of X₂ on Y (β₂) Bias Direction


+ + UPWARD ↑


+ − DOWNWARD ↓


− + DOWNWARD ↓


− − UPWARD ↑



Memory Trick:
• Same signs (++ or −−) → UPWARD bias (coefficient too high)