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FRM Part I · FRM Exam Part I · Regression Diagnostics

In a linear regression estimated by OLS, the error variance rises with the size of an explanatory variable, but the model is otherwise correctly specified and the errors are uncorrelated with the regressors. Which statement about the OLS estimators is correct?

OLS coefficients remain unbiased and consistent under heteroskedasticity because the errors are still uncorrelated with the regressors. What fails is the conventional standard error formula, which assumes constant variance, so hypothesis tests and confidence intervals become unreliable unless robust standard errors are used.

  1. AThe coefficient estimates are biased, and the standard errors are too small
  2. BThe coefficient estimates remain unbiased and consistent, but the usual standard errors are unreliableCorrect
  3. CThe coefficient estimates are biased but the usual standard errors remain valid
  4. DThe coefficient estimates are inconsistent, and R-squared must equal zero

Explanation

Heteroskedasticity does not violate the exogeneity condition, so OLS slope estimates stay unbiased and consistent. However, the conventional standard error formula assumes constant variance, so t-tests and confidence intervals become unreliable. Options claiming bias confuse heteroskedasticity with omitted variables or endogeneity.

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