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FRM Part I · FRM Exam Part I · Regression Diagnostics

In a linear regression estimated by OLS, the error variance is found to increase with the size of an explanatory variable, while the errors remain uncorrelated and the model is otherwise correctly specified. Which statement about the OLS estimators is correct?

Under heteroskedasticity, OLS coefficient estimates stay unbiased and consistent because the errors still have zero conditional mean. The conventional standard errors, however, are computed assuming constant variance and are therefore unreliable, which invalidates the usual t-tests and confidence intervals unless robust standard errors are used.

  1. ACoefficient estimates remain unbiased, but the usual standard errors are unreliableCorrect
  2. BCoefficient estimates become biased, but the usual standard errors remain reliable
  3. CBoth coefficient estimates and usual standard errors remain reliable
  4. DCoefficient estimates become inconsistent and the R-squared is undefined

Explanation

Heteroskedasticity does not violate the zero conditional mean assumption, so OLS slope estimates remain unbiased and consistent. However, the conventional variance formula assumes constant error variance, so the standard errors, t-statistics and confidence intervals are unreliable. The option claiming bias confuses heteroskedasticity with omitted variable problems.

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