Econometrics 3: Heteroscedasticity

Question 1

Does heteroscedasticity affect the unbiasedness of OLS Does autocorrelation?

Answer 1

No.

Question 2

What is the conditional variance of OLS under heteroscedasticity?

Answer 2

(X’X)^{-1}X’ΩΧ(X’X)^{-1}

Question 3

Is OLS BLUE under heteroscedasticity? Why or why not?

Answer 3

No. OLS does not take the heteroscedasticity into account, and so is less efficient than GLS.

Question 4

How can we test for heteroscedasticity?

Answer 4

White’s test.
- Estimate the model by OLS
- Regress the residuals on all regressors, squares and cross products.
- Test that all coefficients equal zero.

Question 5

In White’s test for heteroscedasticity, what distribution does nR^2 follow, under the null of homoscedasticity?

Answer 5

χ^2_{p-1}

Question 6

What should we do if we find that our errors are indeed heteroscedastic?

Answer 6

Don’t use standard inference - either use White standard errors or model the heteroscedasticity with GLS.