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Heteroskedasticity

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.

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Heteroskedasticity

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  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. White’s 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

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