heterskedasticity

heterskedasticity - Multiple Regression Analysis y= + 1 x1...

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1 Multiple Regression Analysis y = ± 0 + 1 x 1 + 2 x 2 + . . . k x k + u 6. Heteroskedasticity What is Heteroskedasticity Recall the assumption of homoskedasticity implied that conditional on the explanatory variables, the variance of the unobserved error, u , was constant If this is not true, that is if the variance of u is different for different values of the x ’s, then the errors are heteroskedastic Example: estimating returns to education and ability is unobservable, and think the variance in ability differs by educational attainment
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2 . x x 1 x 2 y f( y|x ) Example of Heteroskedasticity x 3 . . E( y | x ) = ± 0 + 1 x Why Worry About Heteroskedasticity? OLS is still unbiased and consistent, even if we do not assume homoskedasticity The standard errors of the estimates are biased if we have heteroskedasticity If the standard errors are biased, we can not use the usual t statistics or F statistics or LM statistics for drawing inferences
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3 Robust Standard Errors Now that we have a consistent estimate of the variance, the square root can be used as a standard error for inference Typically call these robust standard errors Sometimes the estimated variance is corrected for degrees of freedom by multiplying by n /( n – k – 1 ) As n ± ² it’s all the same, though Robust Standard Errors (cont) Important to remember that these robust standard errors only have asymptotic justification – with small sample sizes t statistics formed with robust standard errors will not have a distribution close to the
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heterskedasticity - Multiple Regression Analysis y= + 1 x1...

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