Lec16.pdf

# Lec16.pdf - ECO441K Introduction to Econometrics Chapter...

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ECO441K Introduction to Econometrics Chapter 8/9: Multiple Linear Regression - Issues Stephen Donald Stephen Donald () Chapter 8/9: Issues 1 / 19

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Lecture 16 - Outline What is heteroskedasticity? Why is heteroskedasticity a problem? How do we tell if we have heteroskedasticity? How do most people deal with this problem? Outliers °what are they and how do we deal with them? Stephen Donald () Chapter 8/9: Issues 2 / 19
Heteroskedasticity The Homoskedasticity (constant variance) assumption: Var ( u j x 1 , ..., x k ) = σ 2 played no role in showing the unbiased (or consistency) of OLS Heteroskedasticity does NOT cause bias or inconsistency! Stephen Donald () Chapter 8/9: Issues 3 / 19

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Homoskedasticity Stephen Donald () Chapter 8/9: Issues 4 / 19
Heteroskedasticity Stephen Donald () Chapter 8/9: Issues 5 / 19

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Heteroskedasticity MLRM5 was used to ±nd variances of the coe¢ cient estimates (i.e. var ( ˆ β j ) ) Violation of MLRM5 = ) standard errors are o/ since var ( ˆ β j ) is not usual form con±dence intervals, t -statistics and F -statistics will be invalid Stephen Donald () Chapter 8/9: Issues 6 / 19
Robust Inference Easy to ±x problem Use ²robust³ option in STATA These methods are known as ² heteroskedasticity- robust° procedures Works for any form of heteroskedasticity Also works (asymptotically) under MLRM5 Stephen Donald () Chapter 8/9: Issues 7 / 19

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Robust Inference Heteroskedasticity means that: Var ( u j x 1 , ..., x k ) = σ 2 i For the population regression model y = β 0 + β 1 x 1 + β 2 x 2 + ....
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