Goldfeld-Quandt Test for Heteroskedasticity
Also known as: GQ Test, Goldfeld-Quandt Heteroskedasticity Test, Split-Sample Variance Ratio Test, Goldfeld-Quandt Homojenlik Testi
The Goldfeld-Quandt test, introduced by Stephen Goldfeld and Richard Quandt in 1965, is a classical diagnostic procedure for detecting heteroskedasticity in OLS regression. It operates by sorting observations according to a variable suspected of driving variance, omitting a central block, fitting separate regressions on the two tail sub-samples, and comparing their residual variances via an F-ratio. The test is particularly well-suited to situations where the error variance is believed to increase or decrease monotonically with an observed regressor.
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When to use it
The Goldfeld-Quandt test is most appropriate when a researcher suspects that error variance changes monotonically with a single identifiable variable, such as firm size, income, or time. It requires the analyst to pre-specify the ordering variable and the omitted fraction before examining the data; post-hoc choice of these parameters inflates the actual rejection rate. The test assumes that OLS residuals from each sub-sample are independently and normally distributed under the null. With very small samples, degrees of freedom in each sub-regression may be insufficient for reliable inference. When heteroskedasticity depends on multiple variables or takes a non-monotone form, the Breusch-Pagan or White test is preferable.
Strengths & limitations
- Simple to implement using standard OLS routines available in any statistical package
- F-distribution critical values are exact in finite samples under normality, unlike asymptotic chi-squared tests
- Highly interpretable: the analyst compares two residual variances in a transparent, step-by-step manner
- Power is well-concentrated against monotone heteroskedasticity, making it efficient when the ordering variable is correctly chosen
- Requires the analyst to specify the ordering variable in advance, introducing subjectivity and potential specification error
- Sensitive to the choice of the omitted central fraction; different fractions can yield different conclusions
- Has low power against non-monotone or complex forms of heteroskedasticity not linked to a single ordered variable
- Assumes normally distributed errors within each sub-sample; departures from normality can distort the F-ratio
Frequently asked
How should I choose the fraction of observations to omit from the center?
Goldfeld and Quandt originally suggested omitting roughly one-third of the sample. Subsequent simulation work has confirmed that omitting between one-quarter and one-third typically balances power and precision well. The omitted fraction should be decided before inspecting residuals to preserve the validity of the F-distribution critical values.
Can the Goldfeld-Quandt test detect heteroskedasticity that is not monotone in any single variable?
No. The test is designed specifically for monotone heteroskedasticity linked to a pre-chosen ordering variable. Non-monotone patterns, heteroskedasticity driven by multiple variables, or complex error structures are better diagnosed with the White test or the Breusch-Pagan test, which do not require a single ordering variable.
What corrective action should follow a significant Goldfeld-Quandt result?
A significant result indicates heteroskedastic errors, which inflates standard error estimates from conventional OLS. Common remedies include weighted least squares using inverse-variance weights, heteroskedasticity-consistent (HC) standard errors due to White (1980), or a variance-stabilizing transformation of the dependent variable if the functional form of heteroskedasticity is known.
Sources
- Goldfeld, S. M., & Quandt, R. E. (1965). Some tests for homoscedasticity. Journal of the American Statistical Association, 60(310), 539–547. DOI: 10.1080/01621459.1965.10480811 ↗
How to cite this page
ScholarGate. (2026, June 2). Goldfeld-Quandt Test for Heteroskedasticity. ScholarGate. https://scholargate.app/en/econometrics/goldfeld-quandt-test
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Breusch-Pagan TestEconometrics↔ compare
- Weighted Least SquaresStatistics↔ compare
- White TestEconometrics↔ compare