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FRM Part I · FRM Exam Part I · Regression Diagnostics

In a cross-sectional regression of household food spending on household income, the dispersion of the residuals grows steadily as income rises, although the relationship remains linear. Which statement best describes the consequence for the OLS estimators?

OLS coefficients stay unbiased and consistent under heteroskedasticity because exogeneity still holds, but the conventional standard errors rely on constant error variance and so become unreliable, invalidating t-tests and confidence intervals unless robust standard errors are used.

  1. ACoefficient estimates are biased and inconsistent, and standard errors are correct
  2. BCoefficient estimates remain unbiased, but the usual standard errors are unreliableCorrect
  3. CCoefficient estimates remain unbiased and the usual standard errors remain valid
  4. DCoefficient estimates are biased, but the usual standard errors are valid

Explanation

Heteroskedasticity in the error variance does not violate the exogeneity condition, so OLS coefficients remain unbiased and consistent. However the conventional variance formula assumes constant variance, so the standard errors and t-tests are unreliable. The first option wrongly attributes bias to the coefficients.

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