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.
Key highlights
- 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
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
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
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
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
- 1.Goldfeld, S. M., & Quandt, R. E. (1965). Some tests for homoscedasticity. Journal of the American Statistical Association, 60(310), 539–547.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 2). Goldfeld-Quandt Test. ScholarGate. https://scholargate.app/econometrics/goldfeld-quandt-test