14 Heteroskedasticity-Consistent Standard Errors

14 Heteroskedasticity-Consistent Standard Errors -...

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Heteroskedasticity-Consistent Standard Errors Hayashi 2.5 Goal: Accurate standard error estimates with conditional heteroskedasticity V ar ^ ± = E ² ^ ± 2 ³ Scalar model ^ ± 2 = ( P x t u t ) 2 P x 2 t ± 2 General model ^ ± 2 = X x t x 0 t ± 1 X u 2 t x t x 0 t X x t x 0 t ± 1
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Asymptotic Variance p n ^ ± ±! N & 0 ; 1 xx S 1 xx ± 1 n P x t x 0 t P ! xx ² E ² x t x 0 t ³ 1 n P u 2 t x t x 0 t P ! S ³ form of S depends on assumptions martingale di/erence sequence assumption (no correlation) S = E h ( x t u t ) 2 i serial correlation yields S = J X j =0 E h u t u t j x t x 0 t j i
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Scalar to General Model Scalar V ar ^ = 1 P x 2 t X x 2 t u 2 t 1 P x 2 t General V ar ^ = 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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Need to estimate S = 1 n X u 2 t x t x 0 t Eicker-White estimator ^ S = 1 n X ^ u
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This note was uploaded on 12/26/2011 for the course ECON 241b taught by Professor Staff during the Fall '08 term at UCSB.

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14 Heteroskedasticity-Consistent Standard Errors -...

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