Technical Notes—297
Huber/White (QML) Standard Errors
The Huber/White options for robust standard errors computes the quasi-maximum likelihood (or pseudo-ML) standard errors:
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varQML(b) |
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Note that these standard errors are not robust to heteroskedasticity in binary dependent variable models. They are robust to certain misspecifications of the underlying distribution of y .
GLM Standard Errors
Many of the discrete and limited dependent variable models described in this chapter belong to a class of models known as generalized linear models (GLM). The assumption of GLM is that the distribution of the dependent variable yi belongs to the exponential family and that the conditional mean of yi is a (smooth) nonlinear transformation of the linear part xi¢b :
E(yi |
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xi, b) = h(xi¢b). |
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Even though the QML covariance is robust to general misspecification of the conditional distribution of yi , it does not possess any efficiency properties. An alternative consistent estimate of the covariance is obtained if we impose the GLM condition that the (true) variance of yi is proportional to the variance of the distribution used to specify the log likelihood:
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xi, b) = j2varML(yi |
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xi, b). |
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In other words, the ratio of the (conditional) variance to the mean is some constant j2 that is independent of x . The most empirically relevant case is j2 > 1 , which is known as overdispersion. If this proportional variance condition holds, a consistent estimate of the GLM covariance is given by:
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where |
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If you select GLM standard errors, the estimated proportionality term jˆ 2 is reported as the variance factor estimate in EViews.
For more discussion on GLM and the phenomenon of overdispersion, see McCullaugh and Nelder (1989).
References—299
Agresti, Alan (1996). An Introduction to Categorical Data Analysis, New York: John Wiley & Sons.
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