Heteroskedasticity

- Hill et al Chapter 11

Predicting food expenditure

- Are we likely to be better at predicting food

expenditure at - low incomes
- high incomes?

The nature of heteroskedasticity

Violation of assumption MR. 3

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.

Whites estimator of the standard error in the

presence of hetero.

Proportional Hetero.

Transforming the model to make it homoskedastic

Comparing the estimates from OLS and GLS

GLS

OLS and White

Detecting Hetero.

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

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

Example of GQ test

A sample with a heteroskedastic partition

Quantity f (Price, Technology, Weather)

Testing the Variance Assumption

GLS through transformation

Implementation of GLS

Estimate ?2 for each sub-sample by OLS