CHAPTER 11.
HETEROSCEDASTICITY:
What happens if the error variance is nonconstant?
Steps in Heteroscedasticity
 What is the nature of heteroscedasticity?
 What are its consequences?
 How does one detect it?
 What are the remedial measures?
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E ui2   2 i  1,2,....,n
 
E ui2   i2
Reasons Behind Heteroscedasticity
 Error-Learning models; i.e. Errors of behavior become smaller over
time.
 As incomes grow, people have more discretionary income and hence
more scope for choice about the disposition of their income. Hence 2i
is likely to increase with income.
 As data collection techniques improve, 2i is likely to decrease.
 Heteroscedasticity can also arise as a result of the presence of outliers.
An outlier is an observation that is much different than the other
observations in the sample.
Outlier
Reasons to be Continued
 Another source of heteroscedasticity arises from violating Assumption 9
of CLRM, namely, that the regression model is not correctly specified.
 Another source of heteroscedasticity is skewness in the distribution of
one or more regressors in the model. i.e. It is well known that the
distribution of income and wealth in most societies is uneven.
 Incorrect data transformation
 Incorrect functional form of regression analysis
 Heteroscedasticity is more likely to happen in cross sectional data than
time series data.
OLS Estimation Allowing for Heteroscedasticity
 Larger confidence intervals for F and t values
 Inaccurate results for F and t tests
Detection of Heteroscedasticity
Informal Methods
Linear Relation
Formal Methods in Detecting Heteroscedasticity
There are multiple econometric tests to detect
the problem of heteroscedasticity such as:
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Park Test
Glejser Test
Spearman’s Rank Correlation Test
Goldfeld-Quandt Test
Breusch-Pagan-Godfrey Test
White’s General Heteroscedasticity Test
White’s test in More Details
Yi  1   2 X 2i   3i  ui
and then
û i  1   2 X 2i   3 X 3i   4 X 22i   5 X 32i   6 X 2i X 3i  vi
Null hypothesis:
H0: There is no Heteroscedasticity (where (n) times R2 follows chi-square
distribution
Where
2=3=4=5=6= 0 is to represent Heteroscedasticity