Question

Which of the following is not one of the least squares assumptions used in Stock and Watson to show that the OLS estimators are unbiased and consistent and have approximately a normal distribution in large samples?

1) large outliers are unlikely

2) the error term is homoskedastic, i.e., Var(ui ∣ X=x) does not depend on x

3) the sample (Xi,Yi),i=1,…,n constitutes an i.i.d. random sample from the population joint distribution of X and Y

4) the conditional mean of the error term, E(ui ∣ Xi) , is equal to 0

Answer 1

We know that,

Least squares assumptions used in Stock and Watson to show that the OLS estimators are unbiased and consistent are:-

• E (ui|Xi) = 0
• (Xi, Yi) are i.i.d
• Large outliers are unlikely.

Hence,

"The error term is homoskedastic, i.e., Var(ui ∣ X=x) does not depend on x" is not a assumption.

i.e., option 2) is correct answer.

Thank you.