White Test for Heteroskedasticity
Also known as: White's general heteroskedasticity test, White değişen varyans testi
The White test, introduced by Halbert White in 1980, is a general test for heteroskedasticity that makes no assumption about its functional form. It regresses the squared OLS residuals on the regressors, their squares, and their cross-products, so it can detect heteroskedasticity related to any of these terms. The same 1980 paper introduced the heteroskedasticity-consistent ('White') standard errors that are the standard remedy when the test rejects.
Key highlights
- Makes no assumption about the functional form of the heteroskedasticity, detecting a broad class of departures.
- Requires no prior knowledge of which variables drive the variance.
- Comes paired with the heteroskedasticity-consistent standard errors that remedy a rejection.
- A standard, widely implemented general specification check.
Intuition
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How it works
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When to use it
Use the White test when you want a general check for heteroskedasticity without committing to a particular form, especially when you have no prior idea which variables drive the variance. Its breadth is also its cost: with many regressors the auxiliary regression consumes many degrees of freedom, reducing power, so for a small number of suspected variance drivers the more focused Breusch-Pagan test can be more powerful. Because the White test can also pick up general misspecification (its terms overlap with a functional-form check), a rejection should be interpreted alongside other diagnostics. When heteroskedasticity is confirmed, report White (heteroskedasticity-consistent) standard errors or estimate by weighted least squares.
Strengths & limitations
- Makes no assumption about the functional form of the heteroskedasticity, detecting a broad class of departures.
- Requires no prior knowledge of which variables drive the variance.
- Comes paired with the heteroskedasticity-consistent standard errors that remedy a rejection.
- A standard, widely implemented general specification check.
- Consumes many degrees of freedom when there are many regressors, lowering power.
- Less powerful than Breusch-Pagan against a specific, known form of heteroskedasticity.
- A rejection can reflect general misspecification rather than heteroskedasticity alone.
- Detects the problem but does not reveal the variance function or how to weight.
Common pitfalls
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Applications
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Frequently asked
How is the White test different from Breusch-Pagan?
Breusch-Pagan tests for heteroskedasticity tied to a chosen set of variables (often the regressors entered linearly), giving it focus and power against that form. The White test adds the squares and cross-products of the regressors, making it agnostic about the form but spreading its power thinner and consuming more degrees of freedom.
What do I do when the White test rejects?
Heteroskedasticity leaves OLS coefficients unbiased but their standard errors invalid. The standard remedy — introduced in the same White (1980) paper — is to report heteroskedasticity-consistent (robust) standard errors; weighted least squares is an alternative if you can model the variance.
Why might the White test have low power?
Because it includes many auxiliary terms (levels, squares, cross-products), its chi-square degrees of freedom grow quickly with the number of regressors. Spreading the test across many directions reduces its power against any single form, which is why a focused Breusch-Pagan test can do better when you know what drives the variance.
Sources
- 1.White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48(4), 817–838.
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ScholarGate. (2026, June 2). White Test. ScholarGate. https://scholargate.app/econometrics/white-test