Heteroskedasticity

1
Heteroskedasticity

• Hill et al Chapter 11

2
Predicting food expenditure

• Are we likely to be better at predicting food
  expenditure at
• low incomes
• high incomes?

3
The nature of heteroskedasticity
4
Violation of assumption MR. 3
5
Consequences of Heteroskedasticity

• The least squares estimator is still a linear and
  unbiased estimator, but it is no longer best. It
  is no longer B.L.U.E.
• The standard errors usually computed for the
  least squares estimator are incorrect. Confidence
  intervals and hypothesis tests that use these
  standard errors may be misleading.

6
Whites estimator of the standard error in the
presence of hetero.
7
Proportional Hetero.
8
Transforming the model to make it homoskedastic
9
Comparing the estimates from OLS and GLS
GLS
OLS and White
10
Detecting Hetero.

• Residual plots.
• Simple regression
• Multiple regression, plot against
• each explanatory variable
• time
• fitted values
• Goldfield and Quandt test

11
The Goldfield and Quandt Test

• Split the sample in two (according to expected
  pattern of hetero.)
• Compute variances for both samples.
• Compute GQ stat
• Reject null of equal variances if

12
Example of GQ test



13
A sample with a heteroskedastic partition
Quantity f (Price, Technology, Weather)
14
Testing the Variance Assumption


15
GLS through transformation
16
Implementation of GLS
Estimate ?2 for each sub-sample by OLS