FRM Part I · FRM Exam Part I · Regression Diagnostics
An analyst regresses a bond spread on three variables. The true model includes a fourth variable, volatility, that is positively correlated with the included variable X1 and has a positive true coefficient. The analyst omits volatility. What is the effect on the estimated coefficient of X1?
The coefficient on X1 is biased upward. Because the omitted variable is positively correlated with X1 and has a positive true effect, OLS attributes part of that effect to X1. The sign of the bias is the product of the two positive relationships.
- AIt is biased upward, since the omitted variable's effect is partly attributed to X1Correct
- BIt is biased downward, since the omitted variable has a positive coefficient
- CIt is unbiased but inefficient
- DIt is unbiased and its standard error is unchanged
Explanation
Omitted variable bias equals the omitted coefficient times the correlation-driven slope of the omitted variable on X1. Both are positive, so the bias is positive and X1 is overstated. Unbiasedness only holds if the omitted variable is uncorrelated with X1.
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