True/False: Heteroskedasticity causes OLS coefficient estimates to be biased.

Answer:
False. OLS standard errors are biased, but not OLS coefficient estimates. These are still unbiased (although OLS is no longer BLUE, meaning it no longer is the best linear unbiased estimator. In other words, if errors are heteroskedastic, there exist other linear unbiased estimators that have lower variance than OLS. Consider generalized least squares)

True/False: With an omitted variable, OLS is no longer unbiased, but it is still consistent.

Answer:
False. OLS is inconsistent with an omitted (relevant) variable.