Weighted least squares, properties
Problem
In the model \(y_i=β_1+β_2x_i+ε_i\) GM holds. However, you believe, incorrectly, that \(Var\left( ε_i|x_i \right)=x_iσ^2\) and you run
\[ \frac{y_i}{\sqrt{x_i}}= \frac{β_1}{\sqrt{x_i}}+β_2\sqrt{x_i}+error term\]
- Is the WLS estimator unbiased?
- Is the WLS estimator consistent?
- Is the WLS estimator efficient?
- Are the standard errors correct?
Solution
Your transformed model will now be heteroscedastic. Exogeneity will still hold so a,b are true while c,d are false.