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FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables

Which statement about the OLS estimators in a multiple regression is correct when the classical assumptions hold except that the error variance is not constant across observations?

With heteroskedastic errors, OLS slope estimates remain unbiased and consistent, but the usual standard errors are unreliable, so hypothesis tests are invalid unless heteroskedasticity-robust standard errors are used. OLS also loses its BLUE efficiency property.

  1. ASlope estimates remain unbiased, but the usual standard errors are unreliableCorrect
  2. BSlope estimates become biased and inconsistent
  3. CThe R-squared can no longer be computed
  4. DThe estimators are still BLUE under the Gauss-Markov theorem

Explanation

Heteroskedasticity does not violate the zero conditional mean assumption, so OLS slopes stay unbiased and consistent. However, conventional standard errors are incorrect, invalidating t- and F-tests unless robust errors are used. Gauss-Markov efficiency requires homoskedasticity, so OLS is not BLUE here.

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