Sample Question #135 (econometrics)

What is heteroskedasticity? How do you test for the presence of heteroskedasticity?

(Comment: as far as I know, heteroskedasticity, alternatively spelled as heteroscedasticity, is only discussed in econometrics, not in general statistics; I wonder why)

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ANSWER

Heteroskedasticity means the error term in a regression model has varying variances instead of a constant variance, violating one of the assumptions behind the OLS model. (Bonus question: what does this do to the OLS estimator?)[Bonus answer: it does not change the unbiasedness or consistency of the OLS estimator, but gives the wrong estimate for the OLS estimator’s standard deviation, thus leading the researcher to the wrong conclusion about the statistical significance of the OLS estimator.]

Some of the tests are the White Test, the Breusch-Pagan Test and the Goldfeld-Quandt Test. (Bonus question: how does each of these tests work? What assumptions about the form of the heteroskedasticity are behind each test procedure?)

BTW, each of the test, if detecting the presence of heteroskedasticity, also suggests a specific way to "fix" the incorrect stats on the linear estimator. In general, we can use a weighted least squares (WLS) estimator.