FRM Part I · FRM Exam Part I · Linear Regression
Which of the following is an assumption required for the OLS estimator of the slope in a simple linear regression to be unbiased?
The key assumption for unbiased OLS is that the error term has zero conditional mean given X. Normality of errors matters only for exact finite-sample inference, and homoskedasticity affects standard errors and efficiency, not bias.
- AThe error term has zero conditional mean given XCorrect
- BThe error term is normally distributed
- CThe dependent variable has constant variance across time
- DThe explanatory variable is normally distributed
Explanation
Unbiasedness requires E(e|X) = 0 (plus variation in X and a linear model). Normality of errors is needed only for exact small-sample inference, not for unbiasedness. Normality of X is never required, and constant variance affects efficiency and standard errors, not bias.
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