EFIM20036: Heteroskedasticity Spring 2024

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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.