This volume covers the commonly ignored topic of heteroskedasticity (unequal error variances) in regression analyses and provides a practical guide for how to proceed in terms of testing and correction. Emphasizing how to apply diagnostic tests and corrections for heteroskedasticity in actual data analyses, the book offers three approaches for dealing with heteroskedasticity:

variance-stabilizing transformations of the dependent variable; calculating robust standard errors, or heteroskedasticity-consistent standard errors; and; generalized least squares estimation coefficients and standard errors.

The detection and correction of heteroskedasticity is illustrated with three examples that vary in terms of sample size and the types of units analyzed (individuals, households, U.S. states). Intended as a supplementary text for graduate-level courses and a primer for quantitative researchers, the book fills the gap between the limited coverage of heteroskedasticity provided in applied regression textbooks and the more theoretical statistical treatment in advanced econometrics textbooks.

(Estimated) Generalized Least Squares Regression Model for Heteroskedasticity

Background on GLS

The GLS model is a generalization of OLS regression, which relaxes the assumption that the errors are homoskedastic and uncorrelated. That is, OLS assumes that Var(ε) = σ2I, while GLS assumes that Var(ε) = σ2Ω. σ2Ω is an n × n symmetric, invertible matrix whose diagonal elements specify the error variances for each case and whose off-diagonal elements indicate the error correlations for each pair of cases. With this change in assumptions, GLS rather than OLS is the unbiased estimator of β with the minimum sampling variance among the class of linear unbiased estimators (Greene, 2008, p. 155).1 The GLS estimator and its sampling variance are defined as (Greene, 2008, pp. 154–155):

None

Note that OLS is ...

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