Heteroskedasticity

ECON 103, Lecture 16: Heteroskedasticity
(continued)
Maria Casanova

March 05 (version 1)

Maria Casanova

Lecture 16

1. Introduction

Recall the definition of heteroskedasticity we saw last week:
When the variance of Y depends on the value of X , we say that there is heteroskedasticity, or that the error term u is heteroskedastic:
Var (Yi |Xi ) = Var (ui |Xi ) = f (Xi ) = σi2
The next slide shows an example of heteroskedasticity where the variance of Y is higher for low values of X .

Maria Casanova

Lecture 16

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1. Introduction

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Percentage still learning English
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Maria Casanova

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Lecture 16

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1. Introduction
Recall also the consequences of heteroskedasticity for the OLS estimator:
Under heteroskedasticity, the OLS estimator does not have the minimum variance among all the linear, unbiased estimators of β
(i.e., it is not BLUE)
(Remember that the Gauss-Markov theorem states that homoskedasticity is a necessary condition for OLS to be BLUE)
In particular, if the error term is heteroskedastic our estimates of the
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variance of β will be biased.
This means that our usual hypothesis testing routines are unreliable in the presence of heteroskedasticity.

Maria Casanova

Lecture 16

1. Introduction

Outline for today’s talk:
Detecting heteroskedasticity
Residual plots
White test

Tackling heteroskedasticity:
Weighted Least Squares
Heteroskedasticity-robust standard errors

Maria Casanova

Lecture 16

2. Detection of heteroskedasticity
One way of detecting the presence of heteroskedasticy in the data is to graphically examine the residuals.
In particular, we can plot ui or ui2 against Xi to see if there is a pattern
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(see the next 3 slides for an example).
When there is more than 1 X, we can: plot ui or ui2 against each explanatory variable.
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plot ui or ui2 against Yi .
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If the