Properties of robust standard errors

Problem

In the model \(y_i=β_1+β_2x_i+ε_i \) the error terms are heteroscedastic (exogeneity applies). You estimate \(b_1,b_2,SE\left( b_1 \right),SE(b_2)\) using robust standard errors (White-corrected standard errors). What is true?

  1. \(b_2\) is unbiased.
  2. \(b_2\) is consistent.
  3. \(b_2\) is efficient.
  4. \(SE(b_2)\) is consistent
  5. \(b_2/SE\left( b_2 \right)\) is approximately normal under \(H_0:β_2=0\) if \(n\) is large.

Solution

  1. True, (exogeneity)
  2. True, (exogeneity)
  3. False, the OLS estimator is not efficient if we have heteroscedasticity
  4. True, robust SE are consistent
  5. True, we can do inference with robust SE