Breusch-Pagan Test for Heteroskedasticity
Also known as: BP test, Breusch-Pagan-Godfrey test, Lagrange multiplier test for heteroskedasticity, Breusch-Pagan değişen varyans testi
The Breusch-Pagan test, introduced by Trevor Breusch and Adrian Pagan in 1979, is a Lagrange-multiplier test for heteroskedasticity — the condition where the variance of a regression's errors changes with the explanatory variables. It works by regressing the squared OLS residuals on candidate variables and checking whether they explain any of the residual variation, signalling that the constant-variance assumption is violated.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Apply the Breusch-Pagan test after fitting a linear regression to check the homoskedasticity assumption before trusting the reported standard errors and significance tests. It is most natural when you suspect the variance is related to the model's own regressors, and the Koenker studentized form should be preferred because it does not assume normal errors. If you suspect a more general, unknown form of heteroskedasticity — including dependence on squares and cross-products of regressors — the White test is the broader alternative. When heteroskedasticity is detected, the usual responses are to report heteroskedasticity-consistent (robust) standard errors or to estimate by weighted least squares.
Strengths & limitations
- Simple to compute as an auxiliary regression with a chi-square statistic.
- Directly targets variance that depends on the model's regressors, the most common form of heteroskedasticity.
- The Koenker studentized version is robust to non-normal errors.
- Widely implemented and routinely reported as a standard regression diagnostic.
- Tests only the specific forms of heteroskedasticity captured by the chosen auxiliary variables.
- The original (non-studentized) version assumes normally distributed errors and is sensitive to that assumption.
- Detects heteroskedasticity but does not tell you its functional form or how to correct it.
- Can have low power if the variance depends on variables not included in the auxiliary regression.
Frequently asked
What does a significant Breusch-Pagan result mean?
It means the error variance is not constant — it depends on the variables in the auxiliary regression. Your OLS coefficient estimates remain unbiased, but their standard errors are wrong, so significance tests are unreliable. The usual fix is heteroskedasticity-robust standard errors or weighted least squares.
How does Breusch-Pagan differ from the White test?
Breusch-Pagan tests for heteroskedasticity related to a chosen set of variables (typically the regressors entered linearly). The White test is more general: it includes the regressors, their squares, and their cross-products, so it detects a broader class of heteroskedasticity at the cost of more degrees of freedom and less power against any specific form.
Should I use the studentized (Koenker) version?
Yes, in general. The original test assumes normal errors and can over- or under-reject when that fails. Koenker's studentized version is robust to non-normality and is the default in most statistical software.
Sources
- Breusch, T. S., & Pagan, A. R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica, 47(5), 1287–1294. DOI: 10.2307/1911963 ↗
- Koenker, R. (1981). A note on studentizing a test for heteroscedasticity. Journal of Econometrics, 17(1), 107–112. DOI: 10.1016/0304-4076(81)90062-2 ↗
How to cite this page
ScholarGate. (2026, June 2). Breusch-Pagan Test for Heteroskedasticity. ScholarGate. https://scholargate.app/en/econometrics/breusch-pagan-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.
- OLS RegressionEconometrics↔ compare
- Weighted Least SquaresStatistics↔ compare
- White TestEconometrics↔ compare