Heteroskedasticity-Consistent Standard Errors

Heteroskedasticity-Consistent Standard Errors -...

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Heteroskedasticity-Consistent Standard Errors Review Questions For the scalar regression in deviation-from-means form y t = t + u t write the variance for the OLSE of for each of the follow- ing cases 1. V ar ( u t j X ) = ± 2 for t 6 = s Cov ( u t ;u s j X ) = 0 2. V ar ( u t j X ) = ± 2 t for t 6 = s Cov ( u t ;u s j X ) = 0 3. V ar ( u t j X ) = ± 2 t for t 6 = s Cov ( u t ;u s j X ) = ± 2 j t s j
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Goal Given y t = x 0 t + u t accurately estimate V ar ^ j X ± : X x t x 0 t ± 1 X u 2 t x t x 0 t X x t x 0 t ± 1 = 1 n ² 1 n X x t x 0 t ³ 1 1 n X u 2 t x t x 0 t ² 1 n X x t x 0 t ³ 1 ± 1 n S 1 xx S S 1 xx
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Eicker-White Estimator Need to estimate S = 1 n X u 2 t x t x 0 t Eicker-White estimator ^ S = 1 n X ^ u 2 t x t x 0 t ^ u t = y t x 0 t ^ ^ consistent for (e.g. OLSE) Heteroskedasticity-consistent standard errors c se = s 1 n S 1 xx ^ S S 1 xx
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Finite-Sample Accuracy Test H 0 : k = 0 Statistic ^ k c se Size Pr ( reject H 0 j H 0 true ) in practice: over-rejection problem
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Heteroskedasticity-Consistent Standard Errors -...

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