What would be the consequences for the OLS estimator if heteroscedasticity is present in a regression model but ignored? Assume that all the other classical assumptions are valid.
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1 mark, −0.333EconometricsClassical assumptions and their violationsHeteroscedasticityModerateabout 2 min
GATE 2021 Question 9: Classical assumptions and their violations
Answer and worked solution
Answer: (C)
OLS unbiasedness relies on the assumption (zero conditional mean of the error), which has nothing to do with the error's variance being constant. So OLS remains unbiased even under heteroscedasticity, as long as all other classical assumptions (including zero conditional mean) hold.
However, the Gauss-Markov theorem — which establishes that OLS is BLUE (Best Linear Unbiased Estimator, i.e., has the minimum variance among linear unbiased estimators) — specifically requires homoscedasticity as one of its conditions. Under heteroscedasticity, OLS is still unbiased but is no longer the most efficient (minimum-variance) linear unbiased estimator — a Generalized Least Squares (GLS)/Weighted Least Squares estimator that accounts for the heteroscedasticity would achieve lower variance.
OLS also remains consistent under heteroscedasticity (ruling out B and D), since consistency, like unbiasedness, doesn't depend on the error variance being constant.
Therefore the answer is (C): unbiased but inefficient.
The trap: (A) It will be biased
Students sometimes conflate heteroscedasticity's consequences with those of omitted variable bias or endogeneity (which DO cause bias), when heteroscedasticity specifically affects only efficiency and the validity of standard errors/inference — not the unbiasedness or consistency of the point estimates themselves.
Classical assumptions and their violations has come up 26 times in 7 exams since 2011.
What this question tests
This question is on Heteroscedasticity, part of Classical assumptions and their violations in Econometrics.
Unequal error variance: causes, consequences for OLS, tests and remedies.
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