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?
- \(b_2\) is unbiased.
- \(b_2\) is consistent.
- \(b_2\) is efficient.
- \(SE(b_2)\) is consistent
- \(b_2/SE\left( b_2 \right)\) is approximately normal under \(H_0:β_2=0\) if \(n\) is large.
Solution
- True, (exogeneity)
- True, (exogeneity)
- False, the OLS estimator is not efficient if we have heteroscedasticity
- True, robust SE are consistent
- True, we can do inference with robust SE