For the model in Exercise 1, suppose that is normally distributed, with mean zero and variance 2 1 ( x)2 Show that 2 and 2 can be consistently estimated by a regression of the least squares residuals on a constant and x2 Is this estimator efficient ...

The residuals from the least squares regression are y y a The expected value of the squared residual ...

For the model in Exercise 1, suppose that is normally distributed, with mean zero and variance

Question:

For the model in Exercise 1, suppose that ε is normally distributed, with mean zero and variance σ2 [1 + (γ x)2]. Show that σ2 and γ2 can be consistently estimated by a regression of the least squares residuals on a constant and x2. Is this estimator efficient?