EFIM20036: Heteroskedasticity
Spring 2024
Relevant Readings: Wooldridge; “Introduction to Econometrics, A modern Approach”
Main content: Chapter 13-14.
Exercise 1 (Sample Final: Heteroskedasticity). Consider the usual regression model:
yi = β0 + x1iβ1 + x2iβ2 + ϵi
where (yi
, xi) are i.i.d, E[ϵ4i] < ∞ and we believe that
E[ϵ|X] = 0
a) Give a condition for γ1 and γ2 such that the model has conditionally homoskedastic errors for ϵ.
b) Construct a White test for heteroskedasticity for this model based on an auxiliary re-gression. Write down the auxiliary regression. Provide the test statistic and its asymptotic distribution under the null of homoskedasticity.
c) Suppose that we know that γ1 = 2, γ2 = 3. Construct a Weighted Least Squares estimator that has smaller variance than the OLS estimator.
d) Suppose now γ1 and γ2 are unknown. Propose a two step procedure based on an auxiliary regression to construct a Feasible WLS estimator.
e) Now suppose that V is completely unknown. Propose an estimator for the variance of βˆOLS that is robust to any form. of heteroskedasticity.